id	sid	tid	token	lemma	pos
ejpam-5744	1	1	european	european	PROPN
ejpam-5744	1	2	journal	journal	PROPN
ejpam-5744	1	3	of	of	ADP
ejpam-5744	1	4	pure	pure	ADJ
ejpam-5744	1	5	and	and	CCONJ
ejpam-5744	1	6	applied	applied	ADJ
ejpam-5744	1	7	mathematics	mathematic	NOUN
ejpam-5744	1	8	2025	2025	NUM
ejpam-5744	1	9	,	,	PUNCT
ejpam-5744	1	10	vol	vol	NOUN
ejpam-5744	1	11	.	.	PROPN
ejpam-5744	1	12	18	18	NUM
ejpam-5744	1	13	,	,	PUNCT
ejpam-5744	1	14	issue	issue	NOUN
ejpam-5744	1	15	1	1	NUM
ejpam-5744	1	16	,	,	PUNCT
ejpam-5744	1	17	article	article	NOUN
ejpam-5744	1	18	number	number	NOUN
ejpam-5744	1	19	5744	5744	NUM
ejpam-5744	1	20	issn	issn	PROPN
ejpam-5744	1	21	1307	1307	NUM
ejpam-5744	1	22	-	-	SYM
ejpam-5744	1	23	5543	5543	NUM
ejpam-5744	1	24	–	–	PUNCT
ejpam-5744	1	25	ejpam.com	ejpam.com	X
ejpam-5744	1	26	published	publish	VERB
ejpam-5744	1	27	by	by	ADP
ejpam-5744	1	28	new	new	PROPN
ejpam-5744	1	29	york	york	PROPN
ejpam-5744	1	30	business	business	PROPN
ejpam-5744	1	31	global	global	PROPN
ejpam-5744	1	32	a	a	DET
ejpam-5744	1	33	four	four	NUM
ejpam-5744	1	34	-	-	PUNCT
ejpam-5744	1	35	step	step	NOUN
ejpam-5744	1	36	semi	semi	ADJ
ejpam-5744	1	37	-	-	ADJ
ejpam-5744	1	38	implicit	implicit	ADJ
ejpam-5744	1	39	midpoint	midpoint	NOUN
ejpam-5744	1	40	approximation	approximation	NOUN
ejpam-5744	1	41	scheme	scheme	NOUN
ejpam-5744	1	42	for	for	ADP
ejpam-5744	1	43	fixed	fix	VERB
ejpam-5744	1	44	point	point	NOUN
ejpam-5744	1	45	with	with	ADP
ejpam-5744	1	46	applications	application	NOUN
ejpam-5744	1	47	mohammad	mohammad	PROPN
ejpam-5744	1	48	akram	akram	PROPN
ejpam-5744	1	49	department	department	PROPN
ejpam-5744	1	50	of	of	ADP
ejpam-5744	1	51	mathematics	mathematic	NOUN
ejpam-5744	1	52	,	,	PUNCT
ejpam-5744	1	53	faculty	faculty	NOUN
ejpam-5744	1	54	of	of	ADP
ejpam-5744	1	55	science	science	NOUN
ejpam-5744	1	56	,	,	PUNCT
ejpam-5744	1	57	islamic	islamic	PROPN
ejpam-5744	1	58	university	university	PROPN
ejpam-5744	1	59	of	of	ADP
ejpam-5744	1	60	madinah	madinah	PROPN
ejpam-5744	1	61	,	,	PUNCT
ejpam-5744	1	62	madinah	madinah	PROPN
ejpam-5744	1	63	42351	42351	NUM
ejpam-5744	1	64	saudi	saudi	PROPN
ejpam-5744	1	65	arabia	arabia	PROPN
ejpam-5744	1	66	abstract	abstract	NOUN
ejpam-5744	1	67	.	.	PUNCT
ejpam-5744	2	1	this	this	DET
ejpam-5744	2	2	paper	paper	NOUN
ejpam-5744	2	3	aims	aim	VERB
ejpam-5744	2	4	to	to	PART
ejpam-5744	2	5	put	put	VERB
ejpam-5744	2	6	forward	forward	ADV
ejpam-5744	2	7	and	and	CCONJ
ejpam-5744	2	8	design	design	VERB
ejpam-5744	2	9	a	a	DET
ejpam-5744	2	10	four	four	NUM
ejpam-5744	2	11	-	-	PUNCT
ejpam-5744	2	12	step	step	NOUN
ejpam-5744	2	13	semi	semi	ADJ
ejpam-5744	2	14	-	-	ADJ
ejpam-5744	2	15	implicit	implicit	ADJ
ejpam-5744	2	16	approximation	approximation	NOUN
ejpam-5744	2	17	scheme	scheme	NOUN
ejpam-5744	2	18	to	to	PART
ejpam-5744	2	19	work	work	VERB
ejpam-5744	2	20	out	out	ADP
ejpam-5744	2	21	the	the	DET
ejpam-5744	2	22	fixed	fix	VERB
ejpam-5744	2	23	point	point	NOUN
ejpam-5744	2	24	of	of	ADP
ejpam-5744	2	25	a	a	DET
ejpam-5744	2	26	contractive	contractive	ADJ
ejpam-5744	2	27	mapping	mapping	NOUN
ejpam-5744	2	28	.	.	PUNCT
ejpam-5744	3	1	convergence	convergence	NOUN
ejpam-5744	3	2	analysis	analysis	NOUN
ejpam-5744	3	3	and	and	CCONJ
ejpam-5744	3	4	stability	stability	NOUN
ejpam-5744	3	5	of	of	ADP
ejpam-5744	3	6	the	the	DET
ejpam-5744	3	7	proposed	propose	VERB
ejpam-5744	3	8	scheme	scheme	NOUN
ejpam-5744	3	9	is	be	AUX
ejpam-5744	3	10	incorporated	incorporate	VERB
ejpam-5744	3	11	under	under	ADP
ejpam-5744	3	12	some	some	DET
ejpam-5744	3	13	mild	mild	ADJ
ejpam-5744	3	14	assumptions	assumption	NOUN
ejpam-5744	3	15	.	.	PUNCT
ejpam-5744	4	1	finally	finally	ADV
ejpam-5744	4	2	,	,	PUNCT
ejpam-5744	4	3	the	the	DET
ejpam-5744	4	4	significance	significance	NOUN
ejpam-5744	4	5	and	and	CCONJ
ejpam-5744	4	6	applications	application	NOUN
ejpam-5744	4	7	of	of	ADP
ejpam-5744	4	8	the	the	DET
ejpam-5744	4	9	proposed	propose	VERB
ejpam-5744	4	10	scheme	scheme	NOUN
ejpam-5744	4	11	and	and	CCONJ
ejpam-5744	4	12	theoretical	theoretical	ADJ
ejpam-5744	4	13	findings	finding	NOUN
ejpam-5744	4	14	are	be	AUX
ejpam-5744	4	15	proven	prove	VERB
ejpam-5744	4	16	by	by	ADP
ejpam-5744	4	17	exploring	explore	VERB
ejpam-5744	4	18	a	a	DET
ejpam-5744	4	19	general	general	ADJ
ejpam-5744	4	20	quasi	quasi	ADJ
ejpam-5744	4	21	-	-	ADJ
ejpam-5744	4	22	variational	variational	ADJ
ejpam-5744	4	23	inequality	inequality	NOUN
ejpam-5744	4	24	and	and	CCONJ
ejpam-5744	4	25	a	a	DET
ejpam-5744	4	26	nonlinear	nonlinear	ADJ
ejpam-5744	4	27	fractional	fractional	ADJ
ejpam-5744	4	28	differential	differential	NOUN
ejpam-5744	4	29	equation	equation	NOUN
ejpam-5744	4	30	.	.	PUNCT
ejpam-5744	5	1	2020	2020	NUM
ejpam-5744	5	2	mathematics	mathematic	NOUN
ejpam-5744	5	3	subject	subject	NOUN
ejpam-5744	5	4	classifications	classification	NOUN
ejpam-5744	5	5	:	:	PUNCT
ejpam-5744	5	6	47h09	47h09	NUM
ejpam-5744	5	7	,	,	PUNCT
ejpam-5744	5	8	47h10	47h10	NUM
ejpam-5744	5	9	,	,	PUNCT
ejpam-5744	5	10	47h22	47h22	NUM
ejpam-5744	5	11	,	,	PUNCT
ejpam-5744	5	12	47h25	47h25	NUM
ejpam-5744	5	13	,	,	PUNCT
ejpam-5744	5	14	49j40	49j40	NUM
ejpam-5744	5	15	key	key	ADJ
ejpam-5744	5	16	words	word	NOUN
ejpam-5744	5	17	and	and	CCONJ
ejpam-5744	5	18	phrases	phrase	NOUN
ejpam-5744	5	19	:	:	PUNCT
ejpam-5744	5	20	semi	semi	ADJ
ejpam-5744	5	21	-	-	ADJ
ejpam-5744	5	22	implicit	implicit	ADJ
ejpam-5744	5	23	midpoint	midpoint	NOUN
ejpam-5744	5	24	approximation	approximation	NOUN
ejpam-5744	5	25	,	,	PUNCT
ejpam-5744	5	26	fixed	fix	VERB
ejpam-5744	5	27	point	point	NOUN
ejpam-5744	5	28	,	,	PUNCT
ejpam-5744	5	29	convergence	convergence	NOUN
ejpam-5744	5	30	and	and	CCONJ
ejpam-5744	5	31	stability	stability	NOUN
ejpam-5744	5	32	,	,	PUNCT
ejpam-5744	5	33	quasi	quasi	ADJ
ejpam-5744	5	34	-	-	ADJ
ejpam-5744	5	35	variational	variational	ADJ
ejpam-5744	5	36	inequality	inequality	NOUN
ejpam-5744	5	37	,	,	PUNCT
ejpam-5744	5	38	nonlinear	nonlinear	ADJ
ejpam-5744	5	39	fractional	fractional	ADJ
ejpam-5744	5	40	differential	differential	ADJ
ejpam-5744	5	41	equation	equation	NOUN
ejpam-5744	5	42	1	1	NUM
ejpam-5744	5	43	.	.	PUNCT
ejpam-5744	5	44	introduction	introduction	NOUN
ejpam-5744	5	45	throughout	throughout	ADP
ejpam-5744	5	46	this	this	DET
ejpam-5744	5	47	paper	paper	NOUN
ejpam-5744	5	48	,	,	PUNCT
ejpam-5744	5	49	we	we	PRON
ejpam-5744	5	50	presume	presume	VERB
ejpam-5744	5	51	that	that	SCONJ
ejpam-5744	5	52	ω	ω	NOUN
ejpam-5744	5	53	̸=	̸=	PROPN
ejpam-5744	5	54	ϕ	ϕ	NOUN
ejpam-5744	5	55	is	be	AUX
ejpam-5744	5	56	a	a	DET
ejpam-5744	5	57	subset	subset	NOUN
ejpam-5744	5	58	of	of	ADP
ejpam-5744	5	59	a	a	DET
ejpam-5744	5	60	banach	banach	NOUN
ejpam-5744	5	61	space	space	NOUN
ejpam-5744	5	62	x	x	NOUN
ejpam-5744	5	63	,	,	PUNCT
ejpam-5744	5	64	r	r	NOUN
ejpam-5744	5	65	signifies	signify	VERB
ejpam-5744	5	66	the	the	DET
ejpam-5744	5	67	set	set	NOUN
ejpam-5744	5	68	of	of	ADP
ejpam-5744	5	69	real	real	ADJ
ejpam-5744	5	70	numbers	number	NOUN
ejpam-5744	5	71	and	and	CCONJ
ejpam-5744	5	72	ξ(ψ	ξ(ψ	NUM
ejpam-5744	5	73	)	)	PUNCT
ejpam-5744	5	74	=	=	PRON
ejpam-5744	5	75	{	{	PUNCT
ejpam-5744	5	76	ϱ	ϱ	PROPN
ejpam-5744	5	77	∈	∈	PROPN
ejpam-5744	5	78	ω	ω	NOUN
ejpam-5744	5	79	:	:	PUNCT
ejpam-5744	5	80	ψϱ	ψϱ	ADP
ejpam-5744	5	81	=	=	SYM
ejpam-5744	5	82	ϱ	ϱ	VERB
ejpam-5744	5	83	}	}	PUNCT
ejpam-5744	5	84	,	,	PUNCT
ejpam-5744	5	85	the	the	DET
ejpam-5744	5	86	set	set	NOUN
ejpam-5744	5	87	of	of	ADP
ejpam-5744	5	88	fixed	fix	VERB
ejpam-5744	5	89	points	point	NOUN
ejpam-5744	5	90	of	of	ADP
ejpam-5744	5	91	the	the	DET
ejpam-5744	5	92	mapping	mapping	NOUN
ejpam-5744	5	93	ψ	ψ	NOUN
ejpam-5744	5	94	.	.	PUNCT
ejpam-5744	6	1	a	a	DET
ejpam-5744	6	2	mapping	mapping	NOUN
ejpam-5744	6	3	ψ	ψ	X
ejpam-5744	6	4	:	:	PUNCT
ejpam-5744	6	5	ω	ω	PROPN
ejpam-5744	6	6	→	→	SYM
ejpam-5744	6	7	ω	ω	PROPN
ejpam-5744	6	8	is	be	AUX
ejpam-5744	6	9	referred	refer	VERB
ejpam-5744	6	10	to	to	ADP
ejpam-5744	6	11	as	as	ADP
ejpam-5744	6	12	contraction	contraction	NOUN
ejpam-5744	6	13	if	if	SCONJ
ejpam-5744	6	14	∃κ	∃κ	PROPN
ejpam-5744	6	15	∈	∈	PROPN
ejpam-5744	7	1	[	[	X
ejpam-5744	7	2	0	0	NUM
ejpam-5744	7	3	,	,	PUNCT
ejpam-5744	7	4	1	1	NUM
ejpam-5744	7	5	)	)	PUNCT
ejpam-5744	7	6	such	such	ADJ
ejpam-5744	7	7	that	that	SCONJ
ejpam-5744	7	8	∥ψϱ	∥ψϱ	VERB
ejpam-5744	7	9	−	−	PROPN
ejpam-5744	7	10	ψς∥	ψς∥	PROPN
ejpam-5744	7	11	≤	≤	PROPN
ejpam-5744	7	12	κ∥ϱ	κ∥ϱ	VERB
ejpam-5744	7	13	−	−	NOUN
ejpam-5744	7	14	ς∥,∀ϱ	ς∥,∀ϱ	NUM
ejpam-5744	7	15	,	,	PUNCT
ejpam-5744	7	16	ς	ς	PROPN
ejpam-5744	7	17	∈	∈	PROPN
ejpam-5744	7	18	ω	ω	PROPN
ejpam-5744	7	19	and	and	CCONJ
ejpam-5744	7	20	non	non	ADJ
ejpam-5744	7	21	-	-	ADJ
ejpam-5744	7	22	expansive	expansive	ADJ
ejpam-5744	7	23	for	for	ADP
ejpam-5744	7	24	κ	κ	NOUN
ejpam-5744	7	25	=	=	SYM
ejpam-5744	7	26	1	1	X
ejpam-5744	7	27	.	.	PUNCT
ejpam-5744	8	1	non	non	ADJ
ejpam-5744	8	2	-	-	ADJ
ejpam-5744	8	3	expansive	expansive	ADJ
ejpam-5744	8	4	mappings	mapping	NOUN
ejpam-5744	8	5	are	be	AUX
ejpam-5744	8	6	crucial	crucial	ADJ
ejpam-5744	8	7	generalized	generalized	ADJ
ejpam-5744	8	8	notion	notion	NOUN
ejpam-5744	8	9	of	of	ADP
ejpam-5744	8	10	contraction	contraction	NOUN
ejpam-5744	8	11	mappings	mapping	NOUN
ejpam-5744	8	12	and	and	CCONJ
ejpam-5744	8	13	fundamental	fundamental	ADJ
ejpam-5744	8	14	tools	tool	NOUN
ejpam-5744	8	15	in	in	ADP
ejpam-5744	8	16	the	the	DET
ejpam-5744	8	17	theory	theory	NOUN
ejpam-5744	8	18	of	of	ADP
ejpam-5744	8	19	fixed	fix	VERB
ejpam-5744	8	20	points	point	NOUN
ejpam-5744	8	21	,	,	PUNCT
ejpam-5744	8	22	see	see	VERB
ejpam-5744	8	23	,	,	PUNCT
ejpam-5744	8	24	[	[	X
ejpam-5744	8	25	48	48	NUM
ejpam-5744	8	26	]	]	PUNCT
ejpam-5744	8	27	.	.	PUNCT
ejpam-5744	9	1	clearly	clearly	ADV
ejpam-5744	9	2	,	,	PUNCT
ejpam-5744	9	3	ξ(ψ	ξ(ψ	PROPN
ejpam-5744	9	4	)	)	PUNCT
ejpam-5744	9	5	for	for	ADP
ejpam-5744	9	6	a	a	DET
ejpam-5744	9	7	non	non	ADJ
ejpam-5744	9	8	-	-	ADJ
ejpam-5744	9	9	expansive	expansive	ADJ
ejpam-5744	9	10	self	self	NOUN
ejpam-5744	9	11	mapping	mapping	NOUN
ejpam-5744	9	12	ψ	ψ	NOUN
ejpam-5744	9	13	on	on	ADP
ejpam-5744	9	14	a	a	DET
ejpam-5744	9	15	bounded	bound	VERB
ejpam-5744	9	16	,	,	PUNCT
ejpam-5744	9	17	closed	closed	ADJ
ejpam-5744	9	18	and	and	CCONJ
ejpam-5744	9	19	convex	convex	PROPN
ejpam-5744	9	20	subset	subset	NOUN
ejpam-5744	9	21	ω	ω	PROPN
ejpam-5744	9	22	is	be	AUX
ejpam-5744	9	23	non	non	ADJ
ejpam-5744	9	24	-	-	ADJ
ejpam-5744	9	25	empty	empty	ADJ
ejpam-5744	9	26	,	,	PUNCT
ejpam-5744	9	27	see	see	VERB
ejpam-5744	9	28	,	,	PUNCT
ejpam-5744	9	29	[	[	X
ejpam-5744	9	30	10	10	NUM
ejpam-5744	9	31	]	]	PUNCT
ejpam-5744	9	32	.	.	PUNCT
ejpam-5744	10	1	detailed	detailed	ADJ
ejpam-5744	10	2	information	information	NOUN
ejpam-5744	10	3	on	on	ADP
ejpam-5744	10	4	non	non	ADJ
ejpam-5744	10	5	-	-	ADJ
ejpam-5744	10	6	expansive	expansive	ADJ
ejpam-5744	10	7	mappings	mapping	NOUN
ejpam-5744	10	8	and	and	CCONJ
ejpam-5744	10	9	related	relate	VERB
ejpam-5744	10	10	results	result	NOUN
ejpam-5744	10	11	can	can	AUX
ejpam-5744	10	12	be	be	AUX
ejpam-5744	10	13	found	find	VERB
ejpam-5744	10	14	in	in	ADP
ejpam-5744	10	15	[	[	X
ejpam-5744	10	16	16	16	NUM
ejpam-5744	10	17	,	,	PUNCT
ejpam-5744	10	18	38	38	NUM
ejpam-5744	10	19	]	]	PUNCT
ejpam-5744	10	20	.	.	PUNCT
ejpam-5744	11	1	non	non	ADJ
ejpam-5744	11	2	-	-	ADJ
ejpam-5744	11	3	expansive	expansive	ADJ
ejpam-5744	11	4	mappings	mapping	NOUN
ejpam-5744	11	5	play	play	VERB
ejpam-5744	11	6	vital	vital	ADJ
ejpam-5744	11	7	role	role	NOUN
ejpam-5744	11	8	in	in	ADP
ejpam-5744	11	9	the	the	DET
ejpam-5744	11	10	journey	journey	NOUN
ejpam-5744	11	11	of	of	ADP
ejpam-5744	11	12	nonlinear	nonlinear	ADJ
ejpam-5744	11	13	analysis	analysis	NOUN
ejpam-5744	11	14	and	and	CCONJ
ejpam-5744	11	15	have	have	AUX
ejpam-5744	11	16	been	be	AUX
ejpam-5744	11	17	employed	employ	VERB
ejpam-5744	11	18	to	to	PART
ejpam-5744	11	19	deal	deal	VERB
ejpam-5744	11	20	various	various	ADJ
ejpam-5744	11	21	problems	problem	NOUN
ejpam-5744	11	22	of	of	ADP
ejpam-5744	11	23	nonlinear	nonlinear	ADJ
ejpam-5744	11	24	analysis	analysis	NOUN
ejpam-5744	11	25	such	such	ADJ
ejpam-5744	11	26	as	as	ADP
ejpam-5744	11	27	variational	variational	ADJ
ejpam-5744	11	28	inequality	inequality	NOUN
ejpam-5744	11	29	,	,	PUNCT
ejpam-5744	11	30	optimization	optimization	NOUN
ejpam-5744	11	31	,	,	PUNCT
ejpam-5744	11	32	equilibrium	equilibrium	NOUN
ejpam-5744	11	33	and	and	CCONJ
ejpam-5744	11	34	initial	initial	ADJ
ejpam-5744	11	35	value	value	NOUN
ejpam-5744	11	36	problems	problem	NOUN
ejpam-5744	11	37	.	.	PUNCT
ejpam-5744	12	1	in	in	ADP
ejpam-5744	12	2	fact	fact	NOUN
ejpam-5744	12	3	,	,	PUNCT
ejpam-5744	12	4	a	a	DET
ejpam-5744	12	5	non	non	ADJ
ejpam-5744	12	6	-	-	ADJ
ejpam-5744	12	7	expansive	expansive	ADJ
ejpam-5744	12	8	self	self	NOUN
ejpam-5744	12	9	-	-	PUNCT
ejpam-5744	12	10	mapping	mapping	NOUN
ejpam-5744	12	11	on	on	ADP
ejpam-5744	12	12	a	a	DET
ejpam-5744	12	13	complete	complete	ADJ
ejpam-5744	12	14	metric	metric	ADJ
ejpam-5744	12	15	space	space	NOUN
ejpam-5744	12	16	not	not	PART
ejpam-5744	12	17	necessarily	necessarily	ADV
ejpam-5744	12	18	owns	own	VERB
ejpam-5744	12	19	a	a	DET
ejpam-5744	12	20	fixed	fix	VERB
ejpam-5744	12	21	point	point	NOUN
ejpam-5744	12	22	.	.	PUNCT
ejpam-5744	12	23	example	example	NOUN
ejpam-5744	13	1	1	1	NUM
ejpam-5744	13	2	.	.	PUNCT
ejpam-5744	14	1	[	[	X
ejpam-5744	14	2	37	37	NUM
ejpam-5744	14	3	]	]	PUNCT
ejpam-5744	14	4	consider	consider	VERB
ejpam-5744	14	5	a	a	DET
ejpam-5744	14	6	closed	closed	ADJ
ejpam-5744	14	7	and	and	CCONJ
ejpam-5744	14	8	bounded	bound	VERB
ejpam-5744	14	9	subset	subset	PROPN
ejpam-5744	14	10	ω	ω	PROPN
ejpam-5744	14	11	=	=	X
ejpam-5744	14	12	{	{	PUNCT
ejpam-5744	14	13	ϱ	ϱ	PROPN
ejpam-5744	14	14	=	=	PUNCT
ejpam-5744	14	15	(	(	PUNCT
ejpam-5744	14	16	ϱ1	ϱ1	PROPN
ejpam-5744	14	17	,	,	PUNCT
ejpam-5744	14	18	ϱ2	ϱ2	NOUN
ejpam-5744	14	19	,	,	PUNCT
ejpam-5744	14	20	·	·	PUNCT
ejpam-5744	14	21	·	·	PUNCT
ejpam-5744	14	22	·	·	PUNCT
ejpam-5744	14	23	)	)	PUNCT
ejpam-5744	14	24	:	:	PUNCT
ejpam-5744	14	25	ϱk	ϱk	ADP
ejpam-5744	14	26	≥	≥	NOUN
ejpam-5744	14	27	0	0	NUM
ejpam-5744	14	28	,	,	PUNCT
ejpam-5744	14	29	∀k	∀k	NOUN
ejpam-5744	14	30	,	,	PUNCT
ejpam-5744	14	31	∞∑	∞∑	ADJ
ejpam-5744	14	32	k=1	k=1	X
ejpam-5744	14	33	ϱk	ϱk	NOUN
ejpam-5744	14	34	=	=	NOUN
ejpam-5744	14	35	1	1	NUM
ejpam-5744	14	36	}	}	PUNCT
ejpam-5744	14	37	of	of	ADP
ejpam-5744	14	38	a	a	DET
ejpam-5744	14	39	banach	banach	NOUN
ejpam-5744	14	40	space	space	NOUN
ejpam-5744	14	41	x	x	PUNCT
ejpam-5744	14	42	of	of	ADP
ejpam-5744	14	43	all	all	DET
ejpam-5744	14	44	real	real	ADJ
ejpam-5744	14	45	absolutely	absolutely	ADV
ejpam-5744	14	46	summable	summable	ADJ
ejpam-5744	14	47	sequences	sequence	NOUN
ejpam-5744	14	48	(	(	PUNCT
ejpam-5744	14	49	l1	l1	PROPN
ejpam-5744	14	50	,	,	PUNCT
ejpam-5744	14	51	∥	∥	X
ejpam-5744	14	52	·	·	SYM
ejpam-5744	14	53	∥1	∥1	NUM
ejpam-5744	14	54	)	)	PUNCT
ejpam-5744	14	55	.	.	PUNCT
ejpam-5744	15	1	then	then	ADV
ejpam-5744	15	2	the	the	DET
ejpam-5744	15	3	non	non	ADJ
ejpam-5744	15	4	-	-	ADJ
ejpam-5744	15	5	expansive	expansive	ADJ
ejpam-5744	15	6	mapping	mapping	NOUN
ejpam-5744	15	7	ψ	ψ	X
ejpam-5744	15	8	:	:	PUNCT
ejpam-5744	15	9	ω	ω	PROPN
ejpam-5744	15	10	→	→	PROPN
ejpam-5744	15	11	ω	ω	PROPN
ejpam-5744	15	12	described	describe	VERB
ejpam-5744	15	13	by	by	ADP
ejpam-5744	15	14	ψ(ϱ	ψ(ϱ	NOUN
ejpam-5744	15	15	)	)	PUNCT
ejpam-5744	15	16	=	=	SYM
ejpam-5744	15	17	(	(	PUNCT
ejpam-5744	15	18	0	0	NUM
ejpam-5744	15	19	,	,	PUNCT
ejpam-5744	15	20	ϱ1	ϱ1	NOUN
ejpam-5744	15	21	,	,	PUNCT
ejpam-5744	15	22	ϱ2	ϱ2	NOUN
ejpam-5744	15	23	,	,	PUNCT
ejpam-5744	15	24	·	·	PUNCT
ejpam-5744	15	25	)	)	PUNCT
ejpam-5744	15	26	does	do	AUX
ejpam-5744	15	27	not	not	PART
ejpam-5744	15	28	admit	admit	VERB
ejpam-5744	15	29	a	a	DET
ejpam-5744	15	30	fixed	fix	VERB
ejpam-5744	15	31	point	point	NOUN
ejpam-5744	15	32	.	.	PUNCT
ejpam-5744	16	1	doi	doi	NOUN
ejpam-5744	16	2	:	:	PUNCT
ejpam-5744	16	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5744	https://doi.org/10.29020/nybg.ejpam.v18i1.5744	PRON
ejpam-5744	16	4	email	email	NOUN
ejpam-5744	16	5	address	address	NOUN
ejpam-5744	16	6	:	:	PUNCT
ejpam-5744	16	7	akramkhan	akramkhan	PROPN
ejpam-5744	16	8	20@rediffmail.com	20@rediffmail.com	PROPN
ejpam-5744	16	9	(	(	PUNCT
ejpam-5744	16	10	m.	m.	NOUN
ejpam-5744	16	11	akram	akram	PROPN
ejpam-5744	16	12	)	)	PUNCT
ejpam-5744	16	13	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5744	17	1	1	1	NUM
ejpam-5744	17	2	copyright	copyright	NOUN
ejpam-5744	17	3	:	:	PUNCT
ejpam-5744	17	4	©	©	PROPN
ejpam-5744	17	5	2025	2025	NUM
ejpam-5744	17	6	the	the	DET
ejpam-5744	17	7	author(s	author(s	NOUN
ejpam-5744	17	8	)	)	PUNCT
ejpam-5744	17	9	.	.	PUNCT
ejpam-5744	18	1	(	(	PUNCT
ejpam-5744	18	2	cc	cc	NOUN
ejpam-5744	18	3	by	by	ADP
ejpam-5744	18	4	-	-	PUNCT
ejpam-5744	18	5	nc	nc	PROPN
ejpam-5744	18	6	4.0	4.0	NUM
ejpam-5744	18	7	)	)	PUNCT
ejpam-5744	18	8	m.	m.	NOUN
ejpam-5744	18	9	akram	akram	PROPN
ejpam-5744	18	10	/	/	PUNCT
ejpam-5744	18	11	eur	eur	PROPN
ejpam-5744	18	12	.	.	PUNCT
ejpam-5744	19	1	j.	j.	PROPN
ejpam-5744	19	2	pure	pure	PROPN
ejpam-5744	19	3	appl	appl	PROPN
ejpam-5744	19	4	.	.	PROPN
ejpam-5744	19	5	math	math	PROPN
ejpam-5744	19	6	,	,	PUNCT
ejpam-5744	19	7	18	18	NUM
ejpam-5744	19	8	(	(	PUNCT
ejpam-5744	19	9	1	1	NUM
ejpam-5744	19	10	)	)	PUNCT
ejpam-5744	19	11	(	(	PUNCT
ejpam-5744	19	12	2025	2025	NUM
ejpam-5744	19	13	)	)	PUNCT
ejpam-5744	19	14	,	,	PUNCT
ejpam-5744	19	15	5744	5744	NUM
ejpam-5744	19	16	2	2	NUM
ejpam-5744	19	17	of	of	ADP
ejpam-5744	19	18	19	19	NUM
ejpam-5744	19	19	also	also	ADV
ejpam-5744	19	20	,	,	PUNCT
ejpam-5744	19	21	unlike	unlike	ADP
ejpam-5744	19	22	the	the	DET
ejpam-5744	19	23	contraction	contraction	NOUN
ejpam-5744	19	24	mappings	mapping	NOUN
ejpam-5744	19	25	,	,	PUNCT
ejpam-5744	19	26	the	the	DET
ejpam-5744	19	27	picard	picard	NOUN
ejpam-5744	19	28	sequence	sequence	NOUN
ejpam-5744	19	29	may	may	AUX
ejpam-5744	19	30	not	not	PART
ejpam-5744	19	31	converge	converge	VERB
ejpam-5744	19	32	to	to	ADP
ejpam-5744	19	33	a	a	DET
ejpam-5744	19	34	fixed	fix	VERB
ejpam-5744	19	35	point	point	NOUN
ejpam-5744	19	36	of	of	ADP
ejpam-5744	19	37	a	a	DET
ejpam-5744	19	38	non	non	ADJ
ejpam-5744	19	39	-	-	ADJ
ejpam-5744	19	40	expansive	expansive	ADJ
ejpam-5744	19	41	mapping	mapping	NOUN
ejpam-5744	19	42	.	.	PUNCT
ejpam-5744	20	1	these	these	DET
ejpam-5744	20	2	facts	fact	NOUN
ejpam-5744	20	3	motivated	motivate	VERB
ejpam-5744	20	4	the	the	DET
ejpam-5744	20	5	researchers	researcher	NOUN
ejpam-5744	20	6	to	to	PART
ejpam-5744	20	7	explore	explore	VERB
ejpam-5744	20	8	the	the	DET
ejpam-5744	20	9	mappings	mapping	NOUN
ejpam-5744	20	10	which	which	PRON
ejpam-5744	20	11	own	own	VERB
ejpam-5744	20	12	fixed	fix	VERB
ejpam-5744	20	13	points	point	NOUN
ejpam-5744	20	14	over	over	ADP
ejpam-5744	20	15	such	such	ADJ
ejpam-5744	20	16	spaces	space	NOUN
ejpam-5744	20	17	.	.	PUNCT
ejpam-5744	21	1	a	a	DET
ejpam-5744	21	2	class	class	NOUN
ejpam-5744	21	3	of	of	ADP
ejpam-5744	21	4	weak	weak	ADJ
ejpam-5744	21	5	contractions	contraction	NOUN
ejpam-5744	21	6	also	also	ADV
ejpam-5744	21	7	known	know	VERB
ejpam-5744	21	8	as	as	ADP
ejpam-5744	21	9	almost	almost	ADV
ejpam-5744	21	10	contraction	contraction	NOUN
ejpam-5744	21	11	mappings	mapping	NOUN
ejpam-5744	21	12	(	(	PUNCT
ejpam-5744	21	13	acm	acm	PROPN
ejpam-5744	21	14	)	)	PUNCT
ejpam-5744	21	15	was	be	AUX
ejpam-5744	21	16	brought	bring	VERB
ejpam-5744	21	17	into	into	ADP
ejpam-5744	21	18	existence	existence	NOUN
ejpam-5744	21	19	by	by	ADP
ejpam-5744	21	20	berinde	berinde	NOUN
ejpam-5744	21	21	[	[	X
ejpam-5744	21	22	8	8	NUM
ejpam-5744	21	23	]	]	PUNCT
ejpam-5744	21	24	which	which	PRON
ejpam-5744	21	25	is	be	AUX
ejpam-5744	21	26	defined	define	VERB
ejpam-5744	21	27	below	below	ADP
ejpam-5744	21	28	:	:	PUNCT
ejpam-5744	21	29	definition	definition	NOUN
ejpam-5744	21	30	1	1	NUM
ejpam-5744	21	31	.	.	PUNCT
ejpam-5744	22	1	a	a	DET
ejpam-5744	22	2	mapping	mapping	NOUN
ejpam-5744	22	3	ψ	ψ	X
ejpam-5744	22	4	:	:	PUNCT
ejpam-5744	22	5	ω	ω	PROPN
ejpam-5744	22	6	→	→	SYM
ejpam-5744	22	7	ω	ω	PROPN
ejpam-5744	22	8	is	be	AUX
ejpam-5744	22	9	called	call	VERB
ejpam-5744	22	10	acm	acm	PROPN
ejpam-5744	22	11	if	if	SCONJ
ejpam-5744	22	12	for	for	ADP
ejpam-5744	22	13	some	some	DET
ejpam-5744	22	14	κ	κ	PRON
ejpam-5744	23	1	≥	≥	NOUN
ejpam-5744	23	2	0,∃τ	0,∃τ	NOUN
ejpam-5744	23	3	∈	∈	PROPN
ejpam-5744	23	4	(	(	PUNCT
ejpam-5744	23	5	0	0	NUM
ejpam-5744	23	6	,	,	PUNCT
ejpam-5744	23	7	1	1	NUM
ejpam-5744	23	8	)	)	PUNCT
ejpam-5744	23	9	so	so	SCONJ
ejpam-5744	23	10	that	that	SCONJ
ejpam-5744	23	11	∥ψ(ϱ)−ψ(ς)∥	∥ψ(ϱ)−ψ(ς)∥	VERB
ejpam-5744	23	12	≤	≤	NUM
ejpam-5744	23	13	τ∥ϱ−	τ∥ϱ−	NOUN
ejpam-5744	23	14	ς∥+	ς∥+	PROPN
ejpam-5744	23	15	κ∥ϱ−ψ(ϱ)∥,∀ϱ	κ∥ϱ−ψ(ϱ)∥,∀ϱ	NOUN
ejpam-5744	23	16	,	,	PUNCT
ejpam-5744	23	17	ς	ς	PROPN
ejpam-5744	23	18	∈	∈	PROPN
ejpam-5744	23	19	ω	ω	PROPN
ejpam-5744	23	20	.	.	PUNCT
ejpam-5744	24	1	(	(	PUNCT
ejpam-5744	24	2	1	1	X
ejpam-5744	24	3	)	)	PUNCT
ejpam-5744	25	1	osilike	osilike	ADP
ejpam-5744	25	2	obtained	obtain	VERB
ejpam-5744	25	3	contractive	contractive	ADJ
ejpam-5744	25	4	condition	condition	NOUN
ejpam-5744	25	5	(	(	PUNCT
ejpam-5744	25	6	1	1	NUM
ejpam-5744	25	7	)	)	PUNCT
ejpam-5744	25	8	by	by	ADP
ejpam-5744	25	9	extending	extend	VERB
ejpam-5744	25	10	the	the	DET
ejpam-5744	25	11	work	work	NOUN
ejpam-5744	25	12	of	of	ADP
ejpam-5744	25	13	rhoades	rhoade	NOUN
ejpam-5744	25	14	[	[	X
ejpam-5744	25	15	39	39	NUM
ejpam-5744	25	16	]	]	PUNCT
ejpam-5744	25	17	and	and	CCONJ
ejpam-5744	25	18	the	the	DET
ejpam-5744	25	19	author	author	NOUN
ejpam-5744	25	20	proved	prove	VERB
ejpam-5744	25	21	numerous	numerous	ADJ
ejpam-5744	25	22	stability	stability	NOUN
ejpam-5744	25	23	results	result	NOUN
ejpam-5744	25	24	for	for	ADP
ejpam-5744	25	25	(	(	PUNCT
ejpam-5744	25	26	1	1	NUM
ejpam-5744	25	27	)	)	PUNCT
ejpam-5744	25	28	.	.	PUNCT
ejpam-5744	26	1	if	if	SCONJ
ejpam-5744	26	2	κ	κ	NOUN
ejpam-5744	26	3	=	=	SYM
ejpam-5744	26	4	2δ	2δ	NOUN
ejpam-5744	26	5	,	,	PUNCT
ejpam-5744	26	6	τ	τ	PROPN
ejpam-5744	26	7	=	=	SYM
ejpam-5744	26	8	δ	δ	PROPN
ejpam-5744	26	9	,	,	PUNCT
ejpam-5744	26	10	then	then	ADV
ejpam-5744	26	11	acm	acm	PROPN
ejpam-5744	26	12	coincides	coincide	VERB
ejpam-5744	26	13	with	with	ADP
ejpam-5744	26	14	zamfirescu	zamfirescu	PROPN
ejpam-5744	26	15	contraction	contraction	PROPN
ejpam-5744	27	1	[	[	X
ejpam-5744	27	2	7	7	NUM
ejpam-5744	27	3	,	,	PUNCT
ejpam-5744	27	4	19	19	NUM
ejpam-5744	27	5	]	]	PUNCT
ejpam-5744	27	6	,	,	PUNCT
ejpam-5744	27	7	where	where	SCONJ
ejpam-5744	27	8	δ	δ	PROPN
ejpam-5744	27	9	=	=	PROPN
ejpam-5744	27	10	max	max	PROPN
ejpam-5744	27	11	{	{	PUNCT
ejpam-5744	27	12	α	α	NOUN
ejpam-5744	27	13	,	,	PUNCT
ejpam-5744	27	14	β	β	X
ejpam-5744	27	15	1−	1−	NUM
ejpam-5744	27	16	β	β	X
ejpam-5744	27	17	,	,	PUNCT
ejpam-5744	27	18	γ	γ	X
ejpam-5744	27	19	1−	1−	NUM
ejpam-5744	27	20	γ	γ	PROPN
ejpam-5744	27	21	}	}	PUNCT
ejpam-5744	27	22	,	,	PUNCT
ejpam-5744	27	23	α	α	PROPN
ejpam-5744	27	24	∈	∈	PROPN
ejpam-5744	28	1	[	[	X
ejpam-5744	28	2	0	0	NUM
ejpam-5744	28	3	,	,	PUNCT
ejpam-5744	28	4	1	1	NUM
ejpam-5744	28	5	)	)	PUNCT
ejpam-5744	28	6	,	,	PUNCT
ejpam-5744	28	7	β	β	X
ejpam-5744	28	8	,	,	PUNCT
ejpam-5744	28	9	γ	γ	PROPN
ejpam-5744	28	10	∈	∈	PROPN
ejpam-5744	29	1	[	[	X
ejpam-5744	29	2	0	0	NUM
ejpam-5744	29	3	,	,	PUNCT
ejpam-5744	29	4	0.5	0.5	NUM
ejpam-5744	29	5	]	]	PUNCT
ejpam-5744	29	6	.	.	PUNCT
ejpam-5744	30	1	further	far	ADV
ejpam-5744	30	2	,	,	PUNCT
ejpam-5744	30	3	imoru	imoru	NOUN
ejpam-5744	30	4	and	and	CCONJ
ejpam-5744	30	5	olantiwo	olantiwo	NOUN
ejpam-5744	31	1	[	[	X
ejpam-5744	31	2	22	22	NUM
ejpam-5744	31	3	]	]	PUNCT
ejpam-5744	31	4	generalized	generalize	VERB
ejpam-5744	31	5	the	the	DET
ejpam-5744	31	6	mapping	mapping	NOUN
ejpam-5744	31	7	defined	define	VERB
ejpam-5744	31	8	in	in	ADP
ejpam-5744	31	9	(	(	PUNCT
ejpam-5744	31	10	1	1	NUM
ejpam-5744	31	11	)	)	PUNCT
ejpam-5744	31	12	by	by	ADP
ejpam-5744	31	13	involving	involve	VERB
ejpam-5744	31	14	monotonic	monotonic	ADJ
ejpam-5744	31	15	increasing	increase	VERB
ejpam-5744	31	16	function	function	NOUN
ejpam-5744	31	17	and	and	CCONJ
ejpam-5744	31	18	defined	define	VERB
ejpam-5744	31	19	as	as	ADP
ejpam-5744	31	20	under	under	ADJ
ejpam-5744	31	21	:	:	PUNCT
ejpam-5744	31	22	definition	definition	NOUN
ejpam-5744	31	23	2	2	NUM
ejpam-5744	31	24	.	.	PUNCT
ejpam-5744	32	1	a	a	DET
ejpam-5744	32	2	mapping	mapping	NOUN
ejpam-5744	32	3	ψ	ψ	X
ejpam-5744	32	4	:	:	PUNCT
ejpam-5744	32	5	ω	ω	PROPN
ejpam-5744	32	6	→	→	SYM
ejpam-5744	32	7	ω	ω	PROPN
ejpam-5744	32	8	is	be	AUX
ejpam-5744	32	9	referred	refer	VERB
ejpam-5744	32	10	to	to	ADP
ejpam-5744	32	11	as	as	ADP
ejpam-5744	32	12	contractive	contractive	ADJ
ejpam-5744	32	13	-	-	ADJ
ejpam-5744	32	14	like	like	ADJ
ejpam-5744	32	15	if	if	SCONJ
ejpam-5744	32	16	there	there	PRON
ejpam-5744	32	17	exists	exist	VERB
ejpam-5744	32	18	a	a	DET
ejpam-5744	32	19	strictly	strictly	ADV
ejpam-5744	32	20	increasing	increase	VERB
ejpam-5744	32	21	continuous	continuous	ADJ
ejpam-5744	32	22	function	function	NOUN
ejpam-5744	32	23	g	g	NOUN
ejpam-5744	32	24	:	:	PUNCT
ejpam-5744	33	1	[	[	X
ejpam-5744	33	2	0,∞	0,∞	NOUN
ejpam-5744	33	3	)	)	PUNCT
ejpam-5744	33	4	→	→	PUNCT
ejpam-5744	34	1	[	[	X
ejpam-5744	34	2	0,∞	0,∞	NOUN
ejpam-5744	34	3	)	)	PUNCT
ejpam-5744	34	4	with	with	ADP
ejpam-5744	34	5	g(0	g(0	NOUN
ejpam-5744	34	6	)	)	PUNCT
ejpam-5744	34	7	=	=	SYM
ejpam-5744	34	8	0	0	NUM
ejpam-5744	35	1	and	and	CCONJ
ejpam-5744	35	2	τ	τ	PROPN
ejpam-5744	35	3	∈	∈	PROPN
ejpam-5744	36	1	[	[	X
ejpam-5744	36	2	0	0	NUM
ejpam-5744	36	3	,	,	PUNCT
ejpam-5744	36	4	1	1	NUM
ejpam-5744	36	5	)	)	PUNCT
ejpam-5744	36	6	so	so	SCONJ
ejpam-5744	36	7	that	that	SCONJ
ejpam-5744	36	8	∥ψ(ϱ)−ψ(ς)∥	∥ψ(ϱ)−ψ(ς)∥	VERB
ejpam-5744	36	9	≤	≤	NUM
ejpam-5744	36	10	g(∥ϱ−ψ(ϱ)∥	g(∥ϱ−ψ(ϱ)∥	NOUN
ejpam-5744	36	11	)	)	PUNCT
ejpam-5744	37	1	+	+	CCONJ
ejpam-5744	37	2	τ∥ϱ−	τ∥ϱ−	NOUN
ejpam-5744	37	3	ς∥,∀ϱ	ς∥,∀ϱ	NUM
ejpam-5744	37	4	,	,	PUNCT
ejpam-5744	37	5	ς	ς	PROPN
ejpam-5744	37	6	∈	∈	PROPN
ejpam-5744	37	7	ω	ω	PROPN
ejpam-5744	37	8	.	.	PUNCT
ejpam-5744	38	1	(	(	PUNCT
ejpam-5744	38	2	2	2	X
ejpam-5744	38	3	)	)	PUNCT
ejpam-5744	38	4	the	the	DET
ejpam-5744	38	5	contractive	contractive	ADJ
ejpam-5744	38	6	condition	condition	NOUN
ejpam-5744	38	7	in	in	ADP
ejpam-5744	38	8	(	(	PUNCT
ejpam-5744	38	9	2	2	NUM
ejpam-5744	38	10	)	)	PUNCT
ejpam-5744	38	11	is	be	AUX
ejpam-5744	38	12	much	much	ADV
ejpam-5744	38	13	broader	broad	ADJ
ejpam-5744	38	14	which	which	PRON
ejpam-5744	38	15	include	include	VERB
ejpam-5744	38	16	several	several	ADJ
ejpam-5744	38	17	contractive	contractive	ADJ
ejpam-5744	38	18	conditions	condition	NOUN
ejpam-5744	38	19	,	,	PUNCT
ejpam-5744	38	20	see	see	VERB
ejpam-5744	38	21	,	,	PUNCT
ejpam-5744	38	22	[	[	X
ejpam-5744	38	23	7	7	NUM
ejpam-5744	38	24	,	,	PUNCT
ejpam-5744	38	25	19	19	NUM
ejpam-5744	38	26	,	,	PUNCT
ejpam-5744	38	27	35	35	NUM
ejpam-5744	38	28	,	,	PUNCT
ejpam-5744	38	29	39	39	NUM
ejpam-5744	38	30	,	,	PUNCT
ejpam-5744	38	31	40	40	NUM
ejpam-5744	38	32	]	]	PUNCT
ejpam-5744	38	33	.	.	PUNCT
ejpam-5744	39	1	if	if	SCONJ
ejpam-5744	39	2	gu	gu	NOUN
ejpam-5744	39	3	=	=	PUNCT
ejpam-5744	39	4	κu	κu	NOUN
ejpam-5744	39	5	,	,	PUNCT
ejpam-5744	39	6	where	where	SCONJ
ejpam-5744	39	7	κ	κ	PROPN
ejpam-5744	39	8	≥	≥	X
ejpam-5744	39	9	0	0	PUNCT
ejpam-5744	40	1	then	then	ADV
ejpam-5744	40	2	(	(	PUNCT
ejpam-5744	40	3	2	2	X
ejpam-5744	40	4	)	)	PUNCT
ejpam-5744	40	5	coincides	coincide	VERB
ejpam-5744	40	6	with	with	ADP
ejpam-5744	40	7	(	(	PUNCT
ejpam-5744	40	8	1	1	NUM
ejpam-5744	40	9	)	)	PUNCT
ejpam-5744	40	10	.	.	PUNCT
ejpam-5744	41	1	further	far	ADV
ejpam-5744	41	2	,	,	PUNCT
ejpam-5744	41	3	for	for	ADP
ejpam-5744	41	4	κ	κ	NOUN
ejpam-5744	41	5	=	=	SYM
ejpam-5744	41	6	mτ	mτ	NOUN
ejpam-5744	41	7	,	,	PUNCT
ejpam-5744	41	8	m	m	VERB
ejpam-5744	41	9	=	=	PUNCT
ejpam-5744	41	10	(	(	PUNCT
ejpam-5744	41	11	1	1	NUM
ejpam-5744	41	12	−	−	NOUN
ejpam-5744	41	13	τ)−1	τ)−1	NOUN
ejpam-5744	41	14	,	,	PUNCT
ejpam-5744	41	15	0	0	NUM
ejpam-5744	41	16	≤	≤	NUM
ejpam-5744	41	17	τ	τ	X
ejpam-5744	41	18	<	<	X
ejpam-5744	41	19	1	1	NUM
ejpam-5744	41	20	,	,	PUNCT
ejpam-5744	41	21	we	we	PRON
ejpam-5744	41	22	acquire	acquire	VERB
ejpam-5744	41	23	the	the	DET
ejpam-5744	41	24	contractive	contractive	ADJ
ejpam-5744	41	25	condition	condition	NOUN
ejpam-5744	41	26	due	due	ADP
ejpam-5744	41	27	to	to	ADP
ejpam-5744	41	28	rhoades	rhoade	NOUN
ejpam-5744	41	29	[	[	X
ejpam-5744	41	30	40	40	NUM
ejpam-5744	41	31	]	]	PUNCT
ejpam-5744	41	32	.	.	PUNCT
ejpam-5744	42	1	further	far	ADV
ejpam-5744	42	2	,	,	PUNCT
ejpam-5744	42	3	if	if	SCONJ
ejpam-5744	42	4	κu	κu	ADP
ejpam-5744	42	5	=	=	SYM
ejpam-5744	42	6	0	0	PROPN
ejpam-5744	42	7	,	,	PUNCT
ejpam-5744	42	8	then	then	ADV
ejpam-5744	42	9	(	(	PUNCT
ejpam-5744	42	10	2	2	X
ejpam-5744	42	11	)	)	PUNCT
ejpam-5744	42	12	becomes	become	VERB
ejpam-5744	42	13	∥ψ(ϱ)−ψ(ς)∥	∥ψ(ϱ)−ψ(ς)∥	VERB
ejpam-5744	42	14	≤	≤	ADJ
ejpam-5744	42	15	τ∥ϱ−	τ∥ϱ−	NOUN
ejpam-5744	42	16	ς∥	ς∥	NUM
ejpam-5744	42	17	,	,	PUNCT
ejpam-5744	42	18	τ	τ	PROPN
ejpam-5744	42	19	∈	∈	PROPN
ejpam-5744	43	1	[	[	X
ejpam-5744	43	2	0	0	NUM
ejpam-5744	43	3	,	,	PUNCT
ejpam-5744	43	4	1),∀ϱ	1),∀ϱ	NUM
ejpam-5744	43	5	,	,	PUNCT
ejpam-5744	43	6	ς	ς	PROPN
ejpam-5744	43	7	∈	∈	PROPN
ejpam-5744	43	8	ω	ω	PROPN
ejpam-5744	43	9	,	,	PUNCT
ejpam-5744	43	10	(	(	PUNCT
ejpam-5744	43	11	3	3	X
ejpam-5744	43	12	)	)	PUNCT
ejpam-5744	43	13	which	which	PRON
ejpam-5744	43	14	is	be	AUX
ejpam-5744	43	15	considered	consider	VERB
ejpam-5744	43	16	by	by	ADP
ejpam-5744	43	17	berinde	berinde	NOUN
ejpam-5744	43	18	[	[	X
ejpam-5744	43	19	7	7	NUM
ejpam-5744	43	20	]	]	PUNCT
ejpam-5744	43	21	,	,	PUNCT
ejpam-5744	43	22	and	and	CCONJ
ejpam-5744	43	23	harder	hard	ADV
ejpam-5744	43	24	and	and	CCONJ
ejpam-5744	43	25	hicks	hick	VERB
ejpam-5744	44	1	[	[	X
ejpam-5744	44	2	19	19	NUM
ejpam-5744	44	3	]	]	PUNCT
ejpam-5744	44	4	.	.	PUNCT
ejpam-5744	45	1	in	in	ADP
ejpam-5744	45	2	past	past	ADJ
ejpam-5744	45	3	few	few	ADJ
ejpam-5744	45	4	years	year	NOUN
ejpam-5744	45	5	,	,	PUNCT
ejpam-5744	45	6	a	a	DET
ejpam-5744	45	7	tremendous	tremendous	ADJ
ejpam-5744	45	8	interest	interest	NOUN
ejpam-5744	45	9	has	have	AUX
ejpam-5744	45	10	been	be	AUX
ejpam-5744	45	11	shown	show	VERB
ejpam-5744	45	12	to	to	ADP
ejpam-5744	45	13	the	the	DET
ejpam-5744	45	14	fixed	fix	VERB
ejpam-5744	45	15	point	point	NOUN
ejpam-5744	45	16	theory	theory	NOUN
ejpam-5744	45	17	which	which	PRON
ejpam-5744	45	18	has	have	AUX
ejpam-5744	45	19	become	become	VERB
ejpam-5744	45	20	most	most	ADV
ejpam-5744	45	21	versatile	versatile	ADJ
ejpam-5744	45	22	and	and	CCONJ
ejpam-5744	45	23	applicable	applicable	ADJ
ejpam-5744	45	24	area	area	NOUN
ejpam-5744	45	25	of	of	ADP
ejpam-5744	45	26	research	research	NOUN
ejpam-5744	45	27	.	.	PUNCT
ejpam-5744	46	1	several	several	ADJ
ejpam-5744	46	2	problems	problem	NOUN
ejpam-5744	46	3	which	which	PRON
ejpam-5744	46	4	we	we	PRON
ejpam-5744	46	5	encounter	encounter	VERB
ejpam-5744	46	6	in	in	ADP
ejpam-5744	46	7	real	real	ADJ
ejpam-5744	46	8	-	-	PUNCT
ejpam-5744	46	9	world	world	NOUN
ejpam-5744	46	10	including	include	VERB
ejpam-5744	46	11	zeros	zero	NOUN
ejpam-5744	46	12	of	of	ADP
ejpam-5744	46	13	monotone	monotone	ADJ
ejpam-5744	46	14	operators	operator	NOUN
ejpam-5744	46	15	,	,	PUNCT
ejpam-5744	46	16	odes	ode	NOUN
ejpam-5744	46	17	,	,	PUNCT
ejpam-5744	46	18	pdes	pde	NOUN
ejpam-5744	46	19	,	,	PUNCT
ejpam-5744	46	20	integral	integral	ADJ
ejpam-5744	46	21	equations	equation	NOUN
ejpam-5744	46	22	,	,	PUNCT
ejpam-5744	46	23	vis	vis	X
ejpam-5744	46	24	,	,	PUNCT
ejpam-5744	46	25	etc	etc	X
ejpam-5744	46	26	.	.	X
ejpam-5744	46	27	,	,	PUNCT
ejpam-5744	46	28	can	can	AUX
ejpam-5744	46	29	be	be	AUX
ejpam-5744	46	30	reformulated	reformulate	VERB
ejpam-5744	46	31	as	as	ADP
ejpam-5744	46	32	a	a	DET
ejpam-5744	46	33	fixed	fix	VERB
ejpam-5744	46	34	point	point	NOUN
ejpam-5744	46	35	problem	problem	NOUN
ejpam-5744	46	36	.	.	PUNCT
ejpam-5744	47	1	owing	owe	VERB
ejpam-5744	47	2	to	to	ADP
ejpam-5744	47	3	the	the	DET
ejpam-5744	47	4	significance	significance	NOUN
ejpam-5744	47	5	of	of	ADP
ejpam-5744	47	6	fixed	fix	VERB
ejpam-5744	47	7	point	point	NOUN
ejpam-5744	47	8	theory	theory	NOUN
ejpam-5744	47	9	,	,	PUNCT
ejpam-5744	47	10	numerous	numerous	ADJ
ejpam-5744	47	11	approaches	approach	NOUN
ejpam-5744	47	12	have	have	AUX
ejpam-5744	47	13	been	be	AUX
ejpam-5744	47	14	carried	carry	VERB
ejpam-5744	47	15	out	out	ADP
ejpam-5744	47	16	to	to	PART
ejpam-5744	47	17	deal	deal	VERB
ejpam-5744	47	18	with	with	ADP
ejpam-5744	47	19	fixed	fix	VERB
ejpam-5744	47	20	point	point	NOUN
ejpam-5744	47	21	problems	problem	NOUN
ejpam-5744	47	22	.	.	PUNCT
ejpam-5744	48	1	among	among	ADP
ejpam-5744	48	2	these	these	DET
ejpam-5744	48	3	approaches	approach	NOUN
ejpam-5744	48	4	,	,	PUNCT
ejpam-5744	48	5	iterative	iterative	NOUN
ejpam-5744	48	6	approximation	approximation	NOUN
ejpam-5744	48	7	is	be	AUX
ejpam-5744	48	8	one	one	NUM
ejpam-5744	48	9	of	of	ADP
ejpam-5744	48	10	the	the	DET
ejpam-5744	48	11	most	most	ADV
ejpam-5744	48	12	handy	handy	ADJ
ejpam-5744	48	13	and	and	CCONJ
ejpam-5744	48	14	applicable	applicable	ADJ
ejpam-5744	48	15	tools	tool	NOUN
ejpam-5744	48	16	for	for	ADP
ejpam-5744	48	17	exploring	explore	VERB
ejpam-5744	48	18	nonlinear	nonlinear	ADJ
ejpam-5744	48	19	problems	problem	NOUN
ejpam-5744	48	20	.	.	PUNCT
ejpam-5744	49	1	in	in	ADP
ejpam-5744	49	2	recent	recent	ADJ
ejpam-5744	49	3	time	time	NOUN
ejpam-5744	49	4	,	,	PUNCT
ejpam-5744	49	5	several	several	ADJ
ejpam-5744	49	6	new	new	ADJ
ejpam-5744	49	7	iterative	iterative	NOUN
ejpam-5744	49	8	schemes	scheme	NOUN
ejpam-5744	49	9	have	have	AUX
ejpam-5744	49	10	been	be	AUX
ejpam-5744	49	11	designed	design	VERB
ejpam-5744	49	12	and	and	CCONJ
ejpam-5744	49	13	employed	employ	VERB
ejpam-5744	49	14	.	.	PUNCT
ejpam-5744	50	1	one	one	NUM
ejpam-5744	50	2	of	of	ADP
ejpam-5744	50	3	the	the	DET
ejpam-5744	50	4	most	most	ADV
ejpam-5744	50	5	common	common	ADJ
ejpam-5744	50	6	schemes	scheme	NOUN
ejpam-5744	50	7	for	for	ADP
ejpam-5744	50	8	investigating	investigate	VERB
ejpam-5744	50	9	fixed	fix	VERB
ejpam-5744	50	10	points	point	NOUN
ejpam-5744	50	11	is	be	AUX
ejpam-5744	50	12	named	name	VERB
ejpam-5744	50	13	as	as	ADP
ejpam-5744	50	14	mann	mann	PROPN
ejpam-5744	50	15	iterative	iterative	NOUN
ejpam-5744	50	16	scheme	scheme	NOUN
ejpam-5744	50	17	[	[	X
ejpam-5744	50	18	28	28	NUM
ejpam-5744	50	19	]	]	X
ejpam-5744	50	20	:	:	PUNCT
ejpam-5744	50	21	{	{	PUNCT
ejpam-5744	50	22	ϱ0	ϱ0	NOUN
ejpam-5744	50	23	∈	∈	PROPN
ejpam-5744	50	24	ω	ω	NOUN
ejpam-5744	50	25	,	,	PUNCT
ejpam-5744	50	26	ϱk+1	ϱk+1	X
ejpam-5744	50	27	=	=	SYM
ejpam-5744	50	28	(	(	PUNCT
ejpam-5744	50	29	1−	1−	NUM
ejpam-5744	50	30	αk)ϱk	αk)ϱk	X
ejpam-5744	50	31	+	+	CCONJ
ejpam-5744	50	32	αkψ(ϱk	αkψ(ϱk	NUM
ejpam-5744	50	33	)	)	PUNCT
ejpam-5744	50	34	,	,	PUNCT
ejpam-5744	50	35	k	k	PROPN
ejpam-5744	50	36	∈	∈	PROPN
ejpam-5744	50	37	n	n	CCONJ
ejpam-5744	50	38	,	,	PUNCT
ejpam-5744	50	39	(	(	PUNCT
ejpam-5744	50	40	4	4	X
ejpam-5744	50	41	)	)	PUNCT
ejpam-5744	50	42	m.	m.	NOUN
ejpam-5744	50	43	akram	akram	PROPN
ejpam-5744	50	44	/	/	PUNCT
ejpam-5744	50	45	eur	eur	PROPN
ejpam-5744	50	46	.	.	PUNCT
ejpam-5744	51	1	j.	j.	PROPN
ejpam-5744	51	2	pure	pure	PROPN
ejpam-5744	51	3	appl	appl	PROPN
ejpam-5744	51	4	.	.	PROPN
ejpam-5744	51	5	math	math	PROPN
ejpam-5744	51	6	,	,	PUNCT
ejpam-5744	51	7	18	18	NUM
ejpam-5744	51	8	(	(	PUNCT
ejpam-5744	51	9	1	1	NUM
ejpam-5744	51	10	)	)	PUNCT
ejpam-5744	51	11	(	(	PUNCT
ejpam-5744	51	12	2025	2025	NUM
ejpam-5744	51	13	)	)	PUNCT
ejpam-5744	51	14	,	,	PUNCT
ejpam-5744	51	15	5744	5744	NUM
ejpam-5744	51	16	3	3	NUM
ejpam-5744	51	17	of	of	ADP
ejpam-5744	51	18	19	19	NUM
ejpam-5744	51	19	where	where	SCONJ
ejpam-5744	51	20	{	{	PUNCT
ejpam-5744	51	21	αk	αk	NOUN
ejpam-5744	51	22	}	}	PUNCT
ejpam-5744	51	23	∈	∈	NOUN
ejpam-5744	52	1	[	[	X
ejpam-5744	52	2	0	0	NUM
ejpam-5744	52	3	,	,	PUNCT
ejpam-5744	52	4	1	1	NUM
ejpam-5744	52	5	]	]	PUNCT
ejpam-5744	52	6	and	and	CCONJ
ejpam-5744	52	7	ψ	ψ	X
ejpam-5744	52	8	:	:	PUNCT
ejpam-5744	52	9	ω	ω	PROPN
ejpam-5744	52	10	→	→	SYM
ejpam-5744	52	11	ω	ω	PROPN
ejpam-5744	52	12	is	be	AUX
ejpam-5744	52	13	a	a	DET
ejpam-5744	52	14	non	non	ADJ
ejpam-5744	52	15	-	-	ADJ
ejpam-5744	52	16	expansive	expansive	ADJ
ejpam-5744	52	17	mapping	mapping	NOUN
ejpam-5744	52	18	.	.	PUNCT
ejpam-5744	53	1	in	in	ADP
ejpam-5744	53	2	1974	1974	NUM
ejpam-5744	53	3	,	,	PUNCT
ejpam-5744	53	4	ishikawa	ishikawa	PROPN
ejpam-5744	53	5	[	[	X
ejpam-5744	53	6	23	23	NUM
ejpam-5744	53	7	]	]	PUNCT
ejpam-5744	53	8	approximated	approximate	VERB
ejpam-5744	53	9	the	the	DET
ejpam-5744	53	10	fixed	fix	VERB
ejpam-5744	53	11	points	point	NOUN
ejpam-5744	53	12	by	by	ADP
ejpam-5744	53	13	designing	design	VERB
ejpam-5744	53	14	the	the	DET
ejpam-5744	53	15	scheme	scheme	NOUN
ejpam-5744	53	16	as	as	ADP
ejpam-5744	53	17	under:	under:	PROPN
ejpam-5744	53	18	ϱ0	ϱ0	PROPN
ejpam-5744	53	19	∈	∈	PROPN
ejpam-5744	53	20	ω	ω	PROPN
ejpam-5744	53	21	,	,	PUNCT
ejpam-5744	53	22	σk	σk	X
ejpam-5744	53	23	=	=	SYM
ejpam-5744	53	24	(	(	PUNCT
ejpam-5744	53	25	1−	1−	NUM
ejpam-5744	53	26	βk)ϱk	βk)ϱk	SYM
ejpam-5744	53	27	+	+	CCONJ
ejpam-5744	53	28	βkψ(ϱk	βkψ(ϱk	NOUN
ejpam-5744	53	29	)	)	PUNCT
ejpam-5744	53	30	,	,	PUNCT
ejpam-5744	53	31	ϱk+1	ϱk+1	VERB
ejpam-5744	53	32	=	=	SYM
ejpam-5744	53	33	(	(	PUNCT
ejpam-5744	53	34	1−	1−	NUM
ejpam-5744	53	35	αk)ϱk	αk)ϱk	X
ejpam-5744	53	36	+	+	CCONJ
ejpam-5744	53	37	αkψ(σk	αkψ(σk	NUM
ejpam-5744	53	38	)	)	PUNCT
ejpam-5744	53	39	,	,	PUNCT
ejpam-5744	53	40	k	k	PROPN
ejpam-5744	53	41	∈	∈	PROPN
ejpam-5744	53	42	n	n	CCONJ
ejpam-5744	53	43	,	,	PUNCT
ejpam-5744	53	44	(	(	PUNCT
ejpam-5744	53	45	5	5	NUM
ejpam-5744	53	46	)	)	PUNCT
ejpam-5744	53	47	where	where	SCONJ
ejpam-5744	53	48	{	{	PUNCT
ejpam-5744	53	49	αk	αk	NOUN
ejpam-5744	53	50	}	}	PUNCT
ejpam-5744	53	51	,	,	PUNCT
ejpam-5744	53	52	{	{	PUNCT
ejpam-5744	53	53	βk	βk	NOUN
ejpam-5744	53	54	}	}	PUNCT
ejpam-5744	53	55	∈	∈	PROPN
ejpam-5744	54	1	[	[	X
ejpam-5744	54	2	0	0	NUM
ejpam-5744	54	3	,	,	PUNCT
ejpam-5744	54	4	1	1	NUM
ejpam-5744	54	5	]	]	PUNCT
ejpam-5744	54	6	.	.	PUNCT
ejpam-5744	55	1	further	far	ADV
ejpam-5744	55	2	,	,	PUNCT
ejpam-5744	55	3	noor[33	noor[33	PROPN
ejpam-5744	55	4	]	]	PUNCT
ejpam-5744	55	5	posed	pose	VERB
ejpam-5744	55	6	a	a	DET
ejpam-5744	55	7	three	three	NUM
ejpam-5744	55	8	-	-	PUNCT
ejpam-5744	55	9	step	step	NOUN
ejpam-5744	55	10	scheme	scheme	NOUN
ejpam-5744	55	11	which	which	PRON
ejpam-5744	55	12	comprises	comprise	VERB
ejpam-5744	55	13	mann	mann	PROPN
ejpam-5744	55	14	[	[	X
ejpam-5744	55	15	28	28	NUM
ejpam-5744	55	16	]	]	PUNCT
ejpam-5744	55	17	and	and	CCONJ
ejpam-5744	55	18	ishikawa	ishikawa	PROPN
ejpam-5744	55	19	[	[	X
ejpam-5744	55	20	23	23	NUM
ejpam-5744	55	21	]	]	PUNCT
ejpam-5744	55	22	schemes	scheme	NOUN
ejpam-5744	55	23	and	and	CCONJ
ejpam-5744	55	24	expressed	express	VERB
ejpam-5744	55	25	as	as	ADP
ejpam-5744	55	26	under:	under:	PROPN
ejpam-5744	55	27	ϱ0	ϱ0	NOUN
ejpam-5744	55	28	∈	∈	PROPN
ejpam-5744	55	29	ω	ω	NOUN
ejpam-5744	55	30	,	,	PUNCT
ejpam-5744	55	31	ρk	ρk	ADP
ejpam-5744	55	32	=	=	SYM
ejpam-5744	55	33	(	(	PUNCT
ejpam-5744	55	34	1−	1−	NUM
ejpam-5744	55	35	γk)ϱk	γk)ϱk	PUNCT
ejpam-5744	55	36	+	+	NUM
ejpam-5744	55	37	γkψ(ϱk	γkψ(ϱk	NOUN
ejpam-5744	55	38	)	)	PUNCT
ejpam-5744	55	39	,	,	PUNCT
ejpam-5744	55	40	σk	σk	ADV
ejpam-5744	55	41	=	=	SYM
ejpam-5744	55	42	(	(	PUNCT
ejpam-5744	55	43	1−	1−	NUM
ejpam-5744	55	44	βk)ϱk	βk)ϱk	PUNCT
ejpam-5744	55	45	+	+	CCONJ
ejpam-5744	55	46	βkψ(ρk	βkψ(ρk	NUM
ejpam-5744	55	47	)	)	PUNCT
ejpam-5744	55	48	,	,	PUNCT
ejpam-5744	55	49	ϱk+1	ϱk+1	VERB
ejpam-5744	55	50	=	=	SYM
ejpam-5744	55	51	(	(	PUNCT
ejpam-5744	55	52	1−	1−	NUM
ejpam-5744	55	53	αk)ϱk	αk)ϱk	X
ejpam-5744	55	54	+	+	CCONJ
ejpam-5744	55	55	αkψ(σk	αkψ(σk	NUM
ejpam-5744	55	56	)	)	PUNCT
ejpam-5744	55	57	,	,	PUNCT
ejpam-5744	55	58	k	k	PROPN
ejpam-5744	55	59	∈	∈	PROPN
ejpam-5744	55	60	n	n	CCONJ
ejpam-5744	55	61	,	,	PUNCT
ejpam-5744	55	62	(	(	PUNCT
ejpam-5744	55	63	6	6	NUM
ejpam-5744	55	64	)	)	PUNCT
ejpam-5744	55	65	where	where	SCONJ
ejpam-5744	55	66	{	{	PUNCT
ejpam-5744	55	67	αk	αk	NOUN
ejpam-5744	55	68	}	}	PUNCT
ejpam-5744	55	69	,	,	PUNCT
ejpam-5744	55	70	{	{	PUNCT
ejpam-5744	55	71	βk	βk	NOUN
ejpam-5744	55	72	}	}	PUNCT
ejpam-5744	55	73	,	,	PUNCT
ejpam-5744	55	74	{	{	PUNCT
ejpam-5744	55	75	γk	γk	NOUN
ejpam-5744	55	76	}	}	PUNCT
ejpam-5744	55	77	∈	∈	PROPN
ejpam-5744	56	1	[	[	X
ejpam-5744	56	2	0	0	NUM
ejpam-5744	56	3	,	,	PUNCT
ejpam-5744	56	4	1	1	NUM
ejpam-5744	56	5	]	]	PUNCT
ejpam-5744	56	6	.	.	PUNCT
ejpam-5744	57	1	among	among	ADP
ejpam-5744	57	2	the	the	DET
ejpam-5744	57	3	numerous	numerous	ADJ
ejpam-5744	57	4	iterative	iterative	NOUN
ejpam-5744	57	5	methods	method	NOUN
ejpam-5744	57	6	posed	pose	VERB
ejpam-5744	57	7	so	so	ADV
ejpam-5744	57	8	far	far	ADV
ejpam-5744	57	9	,	,	PUNCT
ejpam-5744	57	10	a	a	DET
ejpam-5744	57	11	few	few	ADJ
ejpam-5744	57	12	common	common	ADJ
ejpam-5744	57	13	and	and	CCONJ
ejpam-5744	57	14	intensively	intensively	ADV
ejpam-5744	57	15	used	use	VERB
ejpam-5744	57	16	schemes	scheme	NOUN
ejpam-5744	57	17	include	include	VERB
ejpam-5744	57	18	s	s	NOUN
ejpam-5744	57	19	-	-	NOUN
ejpam-5744	57	20	iteration	iteration	NOUN
ejpam-5744	57	21	[	[	X
ejpam-5744	57	22	41	41	NUM
ejpam-5744	57	23	]	]	PUNCT
ejpam-5744	57	24	,	,	PUNCT
ejpam-5744	57	25	m	m	PROPN
ejpam-5744	57	26	-iteration	-iteration	PROPN
ejpam-5744	57	27	[	[	X
ejpam-5744	57	28	49	49	NUM
ejpam-5744	57	29	]	]	PUNCT
ejpam-5744	57	30	,	,	PUNCT
ejpam-5744	57	31	normal	normal	ADJ
ejpam-5744	57	32	-	-	PUNCT
ejpam-5744	57	33	s	s	X
ejpam-5744	57	34	[	[	X
ejpam-5744	57	35	43	43	NUM
ejpam-5744	57	36	]	]	PUNCT
ejpam-5744	57	37	,	,	PUNCT
ejpam-5744	57	38	picard	picard	NOUN
ejpam-5744	57	39	-	-	PUNCT
ejpam-5744	57	40	ishikawa	ishikawa	PROPN
ejpam-5744	57	41	scheme	scheme	NOUN
ejpam-5744	58	1	[	[	X
ejpam-5744	58	2	34	34	NUM
ejpam-5744	58	3	]	]	PUNCT
ejpam-5744	58	4	,	,	PUNCT
ejpam-5744	58	5	etc	etc	X
ejpam-5744	58	6	..	..	X
ejpam-5744	58	7	recently	recently	ADV
ejpam-5744	58	8	,	,	PUNCT
ejpam-5744	58	9	okeke	okeke	VERB
ejpam-5744	58	10	et	et	PROPN
ejpam-5744	58	11	al	al	PROPN
ejpam-5744	58	12	.	.	PUNCT
ejpam-5744	59	1	[	[	X
ejpam-5744	59	2	15	15	NUM
ejpam-5744	59	3	]	]	X
ejpam-5744	59	4	contrived	contrive	VERB
ejpam-5744	59	5	an	an	DET
ejpam-5744	59	6	efficient	efficient	ADJ
ejpam-5744	59	7	four	four	NUM
ejpam-5744	59	8	step	step	NOUN
ejpam-5744	59	9	iterative	iterative	NOUN
ejpam-5744	59	10	scheme:	scheme:	PROPN
ejpam-5744	59	11	ϱ0	ϱ0	PROPN
ejpam-5744	59	12	∈	∈	PROPN
ejpam-5744	59	13	ω	ω	NOUN
ejpam-5744	59	14	,	,	PUNCT
ejpam-5744	59	15	ϱk+1	ϱk+1	VERB
ejpam-5744	59	16	=	=	SYM
ejpam-5744	59	17	ψ(ςk	ψ(ςk	PROPN
ejpam-5744	59	18	)	)	PUNCT
ejpam-5744	59	19	,	,	PUNCT
ejpam-5744	59	20	ςk	ςk	NOUN
ejpam-5744	59	21	=	=	SYM
ejpam-5744	59	22	ψ[(1−	ψ[(1−	PROPN
ejpam-5744	59	23	αk)ϑk	αk)ϑk	PROPN
ejpam-5744	59	24	+	+	NUM
ejpam-5744	59	25	αkψ(ϑk	αkψ(ϑk	NUM
ejpam-5744	59	26	)	)	PUNCT
ejpam-5744	59	27	]	]	PUNCT
ejpam-5744	59	28	,	,	PUNCT
ejpam-5744	59	29	ϑk	ϑk	PROPN
ejpam-5744	59	30	=	=	SYM
ejpam-5744	59	31	(	(	PUNCT
ejpam-5744	59	32	1−	1−	NUM
ejpam-5744	59	33	βk)ψ(ϱk	βk)ψ(ϱk	NUM
ejpam-5744	59	34	)	)	PUNCT
ejpam-5744	60	1	+	+	CCONJ
ejpam-5744	60	2	βkψ(εk	βkψ(εk	X
ejpam-5744	60	3	)	)	PUNCT
ejpam-5744	60	4	,	,	PUNCT
ejpam-5744	60	5	εk	εk	NOUN
ejpam-5744	60	6	=	=	SYM
ejpam-5744	60	7	(	(	PUNCT
ejpam-5744	60	8	1−	1−	NUM
ejpam-5744	60	9	γk)ϱk	γk)ϱk	PUNCT
ejpam-5744	60	10	+	+	NUM
ejpam-5744	60	11	γkψ(ϱk	γkψ(ϱk	NOUN
ejpam-5744	60	12	)	)	PUNCT
ejpam-5744	60	13	,	,	PUNCT
ejpam-5744	60	14	k	k	PROPN
ejpam-5744	60	15	∈	∈	PROPN
ejpam-5744	60	16	n	n	CCONJ
ejpam-5744	60	17	,	,	PUNCT
ejpam-5744	60	18	(	(	PUNCT
ejpam-5744	60	19	7	7	X
ejpam-5744	60	20	)	)	PUNCT
ejpam-5744	60	21	where	where	SCONJ
ejpam-5744	60	22	{	{	PUNCT
ejpam-5744	60	23	αk	αk	NOUN
ejpam-5744	60	24	}	}	PUNCT
ejpam-5744	60	25	,	,	PUNCT
ejpam-5744	60	26	{	{	PUNCT
ejpam-5744	60	27	βk	βk	NOUN
ejpam-5744	60	28	}	}	PUNCT
ejpam-5744	60	29	,	,	PUNCT
ejpam-5744	60	30	{	{	PUNCT
ejpam-5744	60	31	γk	γk	X
ejpam-5744	60	32	}	}	PUNCT
ejpam-5744	60	33	⊂	⊂	PROPN
ejpam-5744	61	1	[	[	X
ejpam-5744	61	2	0	0	NUM
ejpam-5744	61	3	,	,	PUNCT
ejpam-5744	61	4	1	1	NUM
ejpam-5744	61	5	]	]	PUNCT
ejpam-5744	61	6	.	.	PUNCT
ejpam-5744	62	1	the	the	DET
ejpam-5744	62	2	authors	author	NOUN
ejpam-5744	62	3	approximated	approximate	VERB
ejpam-5744	62	4	the	the	DET
ejpam-5744	62	5	fixed	fix	VERB
ejpam-5744	62	6	point	point	NOUN
ejpam-5744	62	7	of	of	ADP
ejpam-5744	62	8	a	a	DET
ejpam-5744	62	9	contraction	contraction	NOUN
ejpam-5744	62	10	mapping	mapping	NOUN
ejpam-5744	62	11	in	in	ADP
ejpam-5744	62	12	a	a	DET
ejpam-5744	62	13	uniformly	uniformly	ADJ
ejpam-5744	62	14	convex	convex	NOUN
ejpam-5744	62	15	banach	banach	NOUN
ejpam-5744	62	16	space	space	NOUN
ejpam-5744	62	17	and	and	CCONJ
ejpam-5744	62	18	proved	prove	VERB
ejpam-5744	62	19	the	the	DET
ejpam-5744	62	20	stability	stability	NOUN
ejpam-5744	62	21	of	of	ADP
ejpam-5744	62	22	the	the	DET
ejpam-5744	62	23	proposed	propose	VERB
ejpam-5744	62	24	scheme	scheme	NOUN
ejpam-5744	62	25	.	.	PUNCT
ejpam-5744	63	1	additionally	additionally	ADV
ejpam-5744	63	2	,	,	PUNCT
ejpam-5744	63	3	the	the	DET
ejpam-5744	63	4	weak	weak	ADJ
ejpam-5744	63	5	convergence	convergence	NOUN
ejpam-5744	63	6	for	for	ADP
ejpam-5744	63	7	suzuki	suzuki	PROPN
ejpam-5744	63	8	’s	’s	PART
ejpam-5744	63	9	generalized	generalize	VERB
ejpam-5744	63	10	non	non	ADJ
ejpam-5744	63	11	-	-	ADJ
ejpam-5744	63	12	expansive	expansive	ADJ
ejpam-5744	63	13	mapping	mapping	NOUN
ejpam-5744	63	14	was	be	AUX
ejpam-5744	63	15	analyzed	analyze	VERB
ejpam-5744	63	16	.	.	PUNCT
ejpam-5744	64	1	the	the	DET
ejpam-5744	64	2	efficiency	efficiency	NOUN
ejpam-5744	64	3	of	of	ADP
ejpam-5744	64	4	the	the	DET
ejpam-5744	64	5	scheme	scheme	NOUN
ejpam-5744	64	6	was	be	AUX
ejpam-5744	64	7	demonstrated	demonstrate	VERB
ejpam-5744	64	8	by	by	ADP
ejpam-5744	64	9	illustrative	illustrative	ADJ
ejpam-5744	64	10	example	example	NOUN
ejpam-5744	64	11	and	and	CCONJ
ejpam-5744	64	12	comparing	compare	VERB
ejpam-5744	64	13	some	some	DET
ejpam-5744	64	14	known	know	VERB
ejpam-5744	64	15	schemes	scheme	NOUN
ejpam-5744	64	16	.	.	PUNCT
ejpam-5744	65	1	a	a	DET
ejpam-5744	65	2	mapping	mapping	NOUN
ejpam-5744	65	3	ψ	ψ	NOUN
ejpam-5744	65	4	in	in	ADP
ejpam-5744	65	5	a	a	DET
ejpam-5744	65	6	banach	banach	NOUN
ejpam-5744	65	7	space	space	NOUN
ejpam-5744	65	8	x	x	PUNCT
ejpam-5744	65	9	with	with	ADP
ejpam-5744	65	10	domain	domain	NOUN
ejpam-5744	65	11	d(ψ	d(ψ	NOUN
ejpam-5744	65	12	)	)	PUNCT
ejpam-5744	65	13	and	and	CCONJ
ejpam-5744	65	14	range	range	NOUN
ejpam-5744	65	15	r(ψ	r(ψ	PROPN
ejpam-5744	65	16	)	)	PUNCT
ejpam-5744	65	17	is	be	AUX
ejpam-5744	65	18	referred	refer	VERB
ejpam-5744	65	19	to	to	ADP
ejpam-5744	65	20	as	as	ADV
ejpam-5744	65	21	accretive	accretive	ADJ
ejpam-5744	65	22	,	,	PUNCT
ejpam-5744	65	23	if	if	SCONJ
ejpam-5744	65	24	⟨ψϱ−ψς	⟨ψϱ−ψς	PROPN
ejpam-5744	65	25	,	,	PUNCT
ejpam-5744	65	26	j(ϱ−	j(ϱ−	PROPN
ejpam-5744	65	27	ς)⟩	ς)⟩	PROPN
ejpam-5744	65	28	≥	≥	NOUN
ejpam-5744	65	29	0	0	NUM
ejpam-5744	65	30	,	,	PUNCT
ejpam-5744	65	31	∀ϱ	∀ϱ	PROPN
ejpam-5744	65	32	,	,	PUNCT
ejpam-5744	65	33	ς	ς	PROPN
ejpam-5744	65	34	∈	∈	PROPN
ejpam-5744	65	35	d(ψ	d(ψ	PROPN
ejpam-5744	65	36	)	)	PUNCT
ejpam-5744	65	37	,	,	PUNCT
ejpam-5744	65	38	where	where	SCONJ
ejpam-5744	65	39	j	j	NOUN
ejpam-5744	65	40	:	:	PUNCT
ejpam-5744	65	41	x	x	X
ejpam-5744	65	42	→	→	SYM
ejpam-5744	65	43	x	x	NOUN
ejpam-5744	65	44	∗	∗	NOUN
ejpam-5744	65	45	is	be	AUX
ejpam-5744	65	46	the	the	DET
ejpam-5744	65	47	duality	duality	NOUN
ejpam-5744	65	48	mapping	mapping	NOUN
ejpam-5744	65	49	and	and	CCONJ
ejpam-5744	65	50	ψ	ψ	NOUN
ejpam-5744	65	51	is	be	AUX
ejpam-5744	65	52	referred	refer	VERB
ejpam-5744	65	53	to	to	ADP
ejpam-5744	65	54	as	as	ADV
ejpam-5744	65	55	monotone	monotone	ADJ
ejpam-5744	65	56	,	,	PUNCT
ejpam-5744	65	57	if	if	SCONJ
ejpam-5744	65	58	⟨ψϱ−ψς	⟨ψϱ−ψς	PROPN
ejpam-5744	65	59	,	,	PUNCT
ejpam-5744	66	1	ϱ−	ϱ−	CCONJ
ejpam-5744	66	2	ς⟩	ς⟩	NOUN
ejpam-5744	66	3	≥	≥	NUM
ejpam-5744	66	4	0,∀ϱ	0,∀ϱ	NOUN
ejpam-5744	66	5	,	,	PUNCT
ejpam-5744	66	6	ς	ς	PROPN
ejpam-5744	66	7	∈	∈	PROPN
ejpam-5744	66	8	d(ψ	d(ψ	PROPN
ejpam-5744	66	9	)	)	PUNCT
ejpam-5744	66	10	.	.	PUNCT
ejpam-5744	67	1	if	if	SCONJ
ejpam-5744	67	2	x	x	PRON
ejpam-5744	67	3	=	=	SYM
ejpam-5744	67	4	h	h	NOUN
ejpam-5744	67	5	,	,	PUNCT
ejpam-5744	67	6	a	a	DET
ejpam-5744	67	7	hilbert	hilbert	NOUN
ejpam-5744	67	8	space	space	NOUN
ejpam-5744	67	9	,	,	PUNCT
ejpam-5744	67	10	then	then	ADV
ejpam-5744	67	11	both	both	CCONJ
ejpam-5744	67	12	the	the	DET
ejpam-5744	67	13	concepts	concept	NOUN
ejpam-5744	67	14	are	be	AUX
ejpam-5744	67	15	identical	identical	ADJ
ejpam-5744	67	16	in	in	ADP
ejpam-5744	67	17	the	the	DET
ejpam-5744	67	18	sense	sense	NOUN
ejpam-5744	67	19	of	of	ADP
ejpam-5744	67	20	minty	minty	ADJ
ejpam-5744	67	21	[	[	X
ejpam-5744	67	22	30	30	NUM
ejpam-5744	67	23	]	]	PUNCT
ejpam-5744	67	24	and	and	CCONJ
ejpam-5744	67	25	browder	browder	NOUN
ejpam-5744	67	26	[	[	X
ejpam-5744	67	27	10	10	NUM
ejpam-5744	67	28	]	]	PUNCT
ejpam-5744	67	29	.	.	PUNCT
ejpam-5744	68	1	on	on	ADP
ejpam-5744	68	2	the	the	DET
ejpam-5744	68	3	contrary	contrary	NOUN
ejpam-5744	68	4	,	,	PUNCT
ejpam-5744	68	5	number	number	NOUN
ejpam-5744	68	6	of	of	ADP
ejpam-5744	68	7	real	real	ADJ
ejpam-5744	68	8	-	-	PUNCT
ejpam-5744	68	9	life	life	NOUN
ejpam-5744	68	10	problems	problem	NOUN
ejpam-5744	68	11	appearing	appear	VERB
ejpam-5744	68	12	in	in	ADP
ejpam-5744	68	13	science	science	NOUN
ejpam-5744	68	14	and	and	CCONJ
ejpam-5744	68	15	engineering	engineering	NOUN
ejpam-5744	68	16	can	can	AUX
ejpam-5744	68	17	be	be	AUX
ejpam-5744	68	18	studied	study	VERB
ejpam-5744	68	19	by	by	ADP
ejpam-5744	68	20	formulating	formulate	VERB
ejpam-5744	68	21	as	as	ADP
ejpam-5744	68	22	a	a	DET
ejpam-5744	68	23	model	model	NOUN
ejpam-5744	68	24	of	of	ADP
ejpam-5744	68	25	the	the	DET
ejpam-5744	68	26	following	follow	VERB
ejpam-5744	68	27	initial	initial	ADJ
ejpam-5744	68	28	-	-	PUNCT
ejpam-5744	68	29	value	value	NOUN
ejpam-5744	68	30	problem	problem	NOUN
ejpam-5744	68	31	(	(	PUNCT
ejpam-5744	68	32	ivp	ivp	NOUN
ejpam-5744	68	33	):	):	PUNCT
ejpam-5744	68	34	dϱ	dϱ	NOUN
ejpam-5744	68	35	dt	dt	NOUN
ejpam-5744	68	36	=	=	SYM
ejpam-5744	68	37	ψ(ϱ	ψ(ϱ	NOUN
ejpam-5744	68	38	)	)	PUNCT
ejpam-5744	68	39	;	;	PUNCT
ejpam-5744	69	1	ϱ(0	ϱ(0	NOUN
ejpam-5744	69	2	)	)	PUNCT
ejpam-5744	69	3	=	=	SYM
ejpam-5744	69	4	ϱ0	ϱ0	NOUN
ejpam-5744	69	5	.	.	PUNCT
ejpam-5744	70	1	(	(	PUNCT
ejpam-5744	70	2	8)	8)	NUM
ejpam-5744	70	3	m.	m.	NOUN
ejpam-5744	70	4	akram	akram	PROPN
ejpam-5744	70	5	/	/	PUNCT
ejpam-5744	70	6	eur	eur	PROPN
ejpam-5744	70	7	.	.	PUNCT
ejpam-5744	71	1	j.	j.	PROPN
ejpam-5744	71	2	pure	pure	PROPN
ejpam-5744	71	3	appl	appl	PROPN
ejpam-5744	71	4	.	.	PROPN
ejpam-5744	71	5	math	math	PROPN
ejpam-5744	71	6	,	,	PUNCT
ejpam-5744	71	7	18	18	NUM
ejpam-5744	71	8	(	(	PUNCT
ejpam-5744	71	9	1	1	NUM
ejpam-5744	71	10	)	)	PUNCT
ejpam-5744	71	11	(	(	PUNCT
ejpam-5744	71	12	2025	2025	NUM
ejpam-5744	71	13	)	)	PUNCT
ejpam-5744	71	14	,	,	PUNCT
ejpam-5744	71	15	5744	5744	NUM
ejpam-5744	71	16	4	4	NUM
ejpam-5744	71	17	of	of	ADP
ejpam-5744	71	18	19	19	NUM
ejpam-5744	71	19	since	since	SCONJ
ejpam-5744	71	20	the	the	DET
ejpam-5744	71	21	accretive	accretive	ADJ
ejpam-5744	71	22	and	and	CCONJ
ejpam-5744	71	23	monotone	monotone	ADJ
ejpam-5744	71	24	mappings	mapping	NOUN
ejpam-5744	71	25	are	be	AUX
ejpam-5744	71	26	connected	connect	VERB
ejpam-5744	71	27	to	to	ADP
ejpam-5744	71	28	the	the	DET
ejpam-5744	71	29	evolution	evolution	NOUN
ejpam-5744	71	30	model	model	NOUN
ejpam-5744	71	31	(	(	PUNCT
ejpam-5744	71	32	8)	8)	NUM
ejpam-5744	71	33	and	and	CCONJ
ejpam-5744	71	34	this	this	DET
ejpam-5744	71	35	relation	relation	NOUN
ejpam-5744	71	36	makes	make	VERB
ejpam-5744	71	37	these	these	DET
ejpam-5744	71	38	mappings	mapping	NOUN
ejpam-5744	71	39	quite	quite	ADV
ejpam-5744	71	40	fruitful	fruitful	ADJ
ejpam-5744	71	41	and	and	CCONJ
ejpam-5744	71	42	applicable	applicable	ADJ
ejpam-5744	71	43	.	.	PUNCT
ejpam-5744	72	1	a	a	DET
ejpam-5744	72	2	fundamental	fundamental	ADJ
ejpam-5744	72	3	result	result	NOUN
ejpam-5744	72	4	documented	document	VERB
ejpam-5744	72	5	by	by	ADP
ejpam-5744	72	6	[	[	PUNCT
ejpam-5744	72	7	10	10	NUM
ejpam-5744	72	8	]	]	PUNCT
ejpam-5744	72	9	affirms	affirm	VERB
ejpam-5744	72	10	that	that	SCONJ
ejpam-5744	72	11	(	(	PUNCT
ejpam-5744	72	12	8)	8)	NUM
ejpam-5744	72	13	admits	admit	VERB
ejpam-5744	72	14	a	a	DET
ejpam-5744	72	15	solution	solution	NOUN
ejpam-5744	72	16	when	when	SCONJ
ejpam-5744	72	17	ψ	ψ	NOUN
ejpam-5744	72	18	is	be	AUX
ejpam-5744	72	19	locally	locally	ADV
ejpam-5744	72	20	lipshitzian	lipshitzian	ADJ
ejpam-5744	72	21	and	and	CCONJ
ejpam-5744	72	22	accretive	accretive	VERB
ejpam-5744	72	23	on	on	ADP
ejpam-5744	72	24	x	x	X
ejpam-5744	72	25	.	.	PUNCT
ejpam-5744	73	1	additionally	additionally	ADV
ejpam-5744	73	2	,	,	PUNCT
ejpam-5744	73	3	estimating	estimate	VERB
ejpam-5744	73	4	a	a	DET
ejpam-5744	73	5	zero	zero	NUM
ejpam-5744	73	6	of	of	ADP
ejpam-5744	73	7	nonlinear	nonlinear	ADJ
ejpam-5744	73	8	mapping	mapping	NOUN
ejpam-5744	73	9	ψ	ψ	NOUN
ejpam-5744	73	10	,	,	PUNCT
ejpam-5744	73	11	i.e.	i.e.	X
ejpam-5744	73	12	,	,	PUNCT
ejpam-5744	73	13	0	0	X
ejpam-5744	73	14	∈	∈	NOUN
ejpam-5744	73	15	ψϱ	ψϱ	NOUN
ejpam-5744	73	16	is	be	AUX
ejpam-5744	73	17	a	a	DET
ejpam-5744	73	18	significant	significant	ADJ
ejpam-5744	73	19	and	and	CCONJ
ejpam-5744	73	20	powerful	powerful	ADJ
ejpam-5744	73	21	tool	tool	NOUN
ejpam-5744	73	22	in	in	ADP
ejpam-5744	73	23	approximation	approximation	NOUN
ejpam-5744	73	24	theory	theory	NOUN
ejpam-5744	73	25	because	because	SCONJ
ejpam-5744	73	26	solutions	solution	NOUN
ejpam-5744	73	27	of	of	ADP
ejpam-5744	73	28	elliptic	elliptic	ADJ
ejpam-5744	73	29	differential	differential	ADJ
ejpam-5744	73	30	equations	equation	NOUN
ejpam-5744	73	31	,	,	PUNCT
ejpam-5744	73	32	optimization	optimization	NOUN
ejpam-5744	73	33	problems	problem	NOUN
ejpam-5744	73	34	,	,	PUNCT
ejpam-5744	73	35	inclusion	inclusion	NOUN
ejpam-5744	73	36	problems	problem	NOUN
ejpam-5744	73	37	,	,	PUNCT
ejpam-5744	73	38	fixed	fix	VERB
ejpam-5744	73	39	point	point	NOUN
ejpam-5744	73	40	problems	problem	NOUN
ejpam-5744	73	41	can	can	AUX
ejpam-5744	73	42	be	be	AUX
ejpam-5744	73	43	obtained	obtain	VERB
ejpam-5744	73	44	as	as	ADP
ejpam-5744	73	45	a	a	DET
ejpam-5744	73	46	model	model	NOUN
ejpam-5744	73	47	of	of	ADP
ejpam-5744	73	48	inclusion	inclusion	NOUN
ejpam-5744	73	49	problem	problem	NOUN
ejpam-5744	74	1	0	0	NUM
ejpam-5744	74	2	∈	∈	PROPN
ejpam-5744	74	3	ψϱ	ψϱ	ADP
ejpam-5744	74	4	which	which	PRON
ejpam-5744	74	5	is	be	AUX
ejpam-5744	74	6	identical	identical	ADJ
ejpam-5744	74	7	to	to	ADP
ejpam-5744	74	8	the	the	DET
ejpam-5744	74	9	equilibrium	equilibrium	NOUN
ejpam-5744	74	10	state	state	NOUN
ejpam-5744	74	11	:	:	PUNCT
ejpam-5744	74	12	dϱ	dϱ	NOUN
ejpam-5744	74	13	dt	dt	X
ejpam-5744	74	14	=	=	SYM
ejpam-5744	74	15	0,ψ(ϱ	0,ψ(ϱ	PROPN
ejpam-5744	74	16	)	)	PUNCT
ejpam-5744	74	17	=	=	SYM
ejpam-5744	74	18	0	0	NUM
ejpam-5744	74	19	,	,	PUNCT
ejpam-5744	74	20	see	see	VERB
ejpam-5744	74	21	,	,	PUNCT
ejpam-5744	74	22	[	[	X
ejpam-5744	74	23	10	10	NUM
ejpam-5744	74	24	,	,	PUNCT
ejpam-5744	74	25	11	11	NUM
ejpam-5744	74	26	]	]	PUNCT
ejpam-5744	74	27	.	.	PUNCT
ejpam-5744	75	1	to	to	PART
ejpam-5744	75	2	obtain	obtain	VERB
ejpam-5744	75	3	a	a	DET
ejpam-5744	75	4	numerical	numerical	ADJ
ejpam-5744	75	5	solution	solution	NOUN
ejpam-5744	75	6	is	be	AUX
ejpam-5744	75	7	challenging	challenge	VERB
ejpam-5744	75	8	task	task	NOUN
ejpam-5744	75	9	when	when	SCONJ
ejpam-5744	75	10	the	the	DET
ejpam-5744	75	11	involved	involved	ADJ
ejpam-5744	75	12	mapping	mapping	NOUN
ejpam-5744	75	13	ψ	ψ	NOUN
ejpam-5744	75	14	is	be	AUX
ejpam-5744	75	15	not	not	PART
ejpam-5744	75	16	continuous	continuous	ADJ
ejpam-5744	75	17	.	.	PUNCT
ejpam-5744	76	1	several	several	ADJ
ejpam-5744	76	2	researchers	researcher	NOUN
ejpam-5744	76	3	obtained	obtain	VERB
ejpam-5744	76	4	numerical	numerical	ADJ
ejpam-5744	76	5	solutions	solution	NOUN
ejpam-5744	76	6	of	of	ADP
ejpam-5744	76	7	(	(	PUNCT
ejpam-5744	76	8	8)	8)	NUM
ejpam-5744	76	9	by	by	ADP
ejpam-5744	76	10	approximation	approximation	NOUN
ejpam-5744	76	11	approaches	approach	NOUN
ejpam-5744	76	12	,	,	PUNCT
ejpam-5744	76	13	see	see	VERB
ejpam-5744	76	14	,	,	PUNCT
ejpam-5744	76	15	mustafa	mustafa	PROPN
ejpam-5744	77	1	[	[	X
ejpam-5744	77	2	47	47	NUM
ejpam-5744	77	3	]	]	PUNCT
ejpam-5744	77	4	,	,	PUNCT
ejpam-5744	77	5	duffull	duffull	ADJ
ejpam-5744	77	6	and	and	CCONJ
ejpam-5744	77	7	hegarty	hegarty	NOUN
ejpam-5744	78	1	[	[	X
ejpam-5744	78	2	13	13	NUM
ejpam-5744	78	3	]	]	PUNCT
ejpam-5744	78	4	,	,	PUNCT
ejpam-5744	78	5	khorasani	khorasani	PROPN
ejpam-5744	78	6	and	and	CCONJ
ejpam-5744	78	7	adibi	adibi	NOUN
ejpam-5744	78	8	[	[	X
ejpam-5744	78	9	25	25	NUM
ejpam-5744	78	10	]	]	PUNCT
ejpam-5744	78	11	.	.	PUNCT
ejpam-5744	79	1	one	one	NUM
ejpam-5744	79	2	of	of	ADP
ejpam-5744	79	3	the	the	DET
ejpam-5744	79	4	fundamental	fundamental	ADJ
ejpam-5744	79	5	and	and	CCONJ
ejpam-5744	79	6	impressive	impressive	ADJ
ejpam-5744	79	7	techniques	technique	NOUN
ejpam-5744	79	8	is	be	AUX
ejpam-5744	79	9	implicit	implicit	ADJ
ejpam-5744	79	10	midpoint	midpoint	NOUN
ejpam-5744	79	11	rule	rule	NOUN
ejpam-5744	79	12	(	(	PUNCT
ejpam-5744	79	13	imr	imr	NOUN
ejpam-5744	79	14	):	):	PUNCT
ejpam-5744	79	15	1	1	NUM
ejpam-5744	79	16	µ	µ	NOUN
ejpam-5744	79	17	(	(	PUNCT
ejpam-5744	79	18	ϱk+1	ϱk+1	NUM
ejpam-5744	79	19	−	−	PROPN
ejpam-5744	79	20	ϱk	ϱk	NOUN
ejpam-5744	79	21	)	)	PUNCT
ejpam-5744	79	22	=	=	SYM
ejpam-5744	79	23	ψ	ψ	X
ejpam-5744	79	24	(	(	PUNCT
ejpam-5744	79	25	ϱk+1	ϱk+1	NUM
ejpam-5744	79	26	+	+	CCONJ
ejpam-5744	79	27	ϱk	ϱk	ADP
ejpam-5744	79	28	2	2	NUM
ejpam-5744	79	29	)	)	PUNCT
ejpam-5744	79	30	,	,	PUNCT
ejpam-5744	79	31	(	(	PUNCT
ejpam-5744	79	32	9	9	X
ejpam-5744	79	33	)	)	PUNCT
ejpam-5744	79	34	where	where	SCONJ
ejpam-5744	79	35	µ	µ	X
ejpam-5744	79	36	>	>	X
ejpam-5744	79	37	0	0	NUM
ejpam-5744	79	38	is	be	AUX
ejpam-5744	79	39	a	a	DET
ejpam-5744	79	40	step	step	NOUN
ejpam-5744	79	41	-	-	PUNCT
ejpam-5744	79	42	size	size	NOUN
ejpam-5744	79	43	.	.	PUNCT
ejpam-5744	80	1	the	the	DET
ejpam-5744	80	2	sequence	sequence	NOUN
ejpam-5744	80	3	{	{	PUNCT
ejpam-5744	80	4	ϱk	ϱk	NOUN
ejpam-5744	80	5	}	}	PUNCT
ejpam-5744	80	6	induced	induce	VERB
ejpam-5744	80	7	by	by	ADP
ejpam-5744	80	8	(	(	PUNCT
ejpam-5744	80	9	9	9	X
ejpam-5744	80	10	)	)	PUNCT
ejpam-5744	80	11	converges	converge	NOUN
ejpam-5744	80	12	to	to	ADP
ejpam-5744	80	13	the	the	DET
ejpam-5744	80	14	exact	exact	ADJ
ejpam-5744	80	15	solution	solution	NOUN
ejpam-5744	80	16	of	of	ADP
ejpam-5744	80	17	(	(	PUNCT
ejpam-5744	80	18	8)	8)	NUM
ejpam-5744	80	19	under	under	ADP
ejpam-5744	80	20	modest	modest	ADJ
ejpam-5744	80	21	assumptions	assumption	NOUN
ejpam-5744	80	22	,	,	PUNCT
ejpam-5744	80	23	see	see	VERB
ejpam-5744	80	24	,	,	PUNCT
ejpam-5744	80	25	[	[	X
ejpam-5744	80	26	3	3	NUM
ejpam-5744	80	27	,	,	PUNCT
ejpam-5744	80	28	5	5	NUM
ejpam-5744	80	29	]	]	PUNCT
ejpam-5744	80	30	.	.	PUNCT
ejpam-5744	81	1	if	if	SCONJ
ejpam-5744	81	2	ψ	ψ	NOUN
ejpam-5744	81	3	is	be	AUX
ejpam-5744	81	4	expressed	express	VERB
ejpam-5744	81	5	as	as	ADP
ejpam-5744	81	6	ψ(ϱ	ψ(ϱ	NOUN
ejpam-5744	81	7	)	)	PUNCT
ejpam-5744	81	8	:	:	PUNCT
ejpam-5744	81	9	=	=	SYM
ejpam-5744	81	10	γ(ϱ)−ϱ	γ(ϱ)−ϱ	PRON
ejpam-5744	81	11	,	,	PUNCT
ejpam-5744	81	12	then	then	ADV
ejpam-5744	81	13	the	the	DET
ejpam-5744	81	14	ivp	ivp	X
ejpam-5744	81	15	(	(	PUNCT
ejpam-5744	81	16	8)	8)	NUM
ejpam-5744	81	17	transformed	transform	VERB
ejpam-5744	81	18	into	into	ADP
ejpam-5744	81	19	ϱ	ϱ	PROPN
ejpam-5744	81	20	′	′	NUM
ejpam-5744	81	21	=	=	SYM
ejpam-5744	81	22	ϱ−	ϱ−	PROPN
ejpam-5744	81	23	γ(ϱ	γ(ϱ	NOUN
ejpam-5744	81	24	)	)	PUNCT
ejpam-5744	81	25	,	,	PUNCT
ejpam-5744	81	26	ϱ(0	ϱ(0	NOUN
ejpam-5744	81	27	)	)	PUNCT
ejpam-5744	81	28	=	=	SYM
ejpam-5744	81	29	ϱ0	ϱ0	NOUN
ejpam-5744	81	30	(	(	PUNCT
ejpam-5744	81	31	10	10	NUM
ejpam-5744	81	32	)	)	PUNCT
ejpam-5744	81	33	and	and	CCONJ
ejpam-5744	81	34	the	the	DET
ejpam-5744	81	35	imr	imr	NOUN
ejpam-5744	81	36	(	(	PUNCT
ejpam-5744	81	37	9	9	NUM
ejpam-5744	81	38	)	)	PUNCT
ejpam-5744	81	39	becomes	become	VERB
ejpam-5744	81	40	:	:	PUNCT
ejpam-5744	81	41	1	1	NUM
ejpam-5744	81	42	µ	µ	X
ejpam-5744	81	43	(	(	PUNCT
ejpam-5744	81	44	ϱk+1	ϱk+1	NUM
ejpam-5744	81	45	−	−	PROPN
ejpam-5744	81	46	ϱk	ϱk	NOUN
ejpam-5744	81	47	)	)	PUNCT
ejpam-5744	81	48	=	=	PUNCT
ejpam-5744	82	1	[	[	X
ejpam-5744	82	2	ϱk+1	ϱk+1	NUM
ejpam-5744	82	3	+	+	SYM
ejpam-5744	82	4	ϱk	ϱk	ADP
ejpam-5744	82	5	2	2	NUM
ejpam-5744	82	6	−	−	NOUN
ejpam-5744	82	7	γ	γ	NOUN
ejpam-5744	82	8	(	(	PUNCT
ejpam-5744	82	9	ϱk+1	ϱk+1	NUM
ejpam-5744	82	10	+	+	CCONJ
ejpam-5744	82	11	ϱk	ϱk	ADP
ejpam-5744	82	12	2	2	NUM
ejpam-5744	82	13	)	)	PUNCT
ejpam-5744	82	14	]	]	PUNCT
ejpam-5744	82	15	,	,	PUNCT
ejpam-5744	82	16	(	(	PUNCT
ejpam-5744	82	17	11	11	NUM
ejpam-5744	82	18	)	)	PUNCT
ejpam-5744	82	19	in	in	ADP
ejpam-5744	82	20	[	[	X
ejpam-5744	82	21	26	26	NUM
ejpam-5744	82	22	]	]	PUNCT
ejpam-5744	82	23	,	,	PUNCT
ejpam-5744	82	24	the	the	DET
ejpam-5744	82	25	authors	author	NOUN
ejpam-5744	82	26	deployed	deploy	VERB
ejpam-5744	82	27	the	the	DET
ejpam-5744	82	28	fact	fact	NOUN
ejpam-5744	82	29	that	that	SCONJ
ejpam-5744	82	30	equilibrium	equilibrium	NOUN
ejpam-5744	82	31	associated	associate	VERB
ejpam-5744	82	32	to	to	ADP
ejpam-5744	82	33	(	(	PUNCT
ejpam-5744	82	34	10	10	NUM
ejpam-5744	82	35	)	)	PUNCT
ejpam-5744	82	36	is	be	AUX
ejpam-5744	82	37	identical	identical	ADJ
ejpam-5744	82	38	to	to	ADP
ejpam-5744	82	39	the	the	DET
ejpam-5744	82	40	fixed	fixed	ADJ
ejpam-5744	82	41	point	point	NOUN
ejpam-5744	82	42	ϱ	ϱ	ADP
ejpam-5744	82	43	=	=	SYM
ejpam-5744	82	44	γ(ϱ	γ(ϱ	NOUN
ejpam-5744	82	45	)	)	PUNCT
ejpam-5744	82	46	,	,	PUNCT
ejpam-5744	82	47	which	which	PRON
ejpam-5744	82	48	compelled	compel	VERB
ejpam-5744	82	49	the	the	DET
ejpam-5744	82	50	authors	author	NOUN
ejpam-5744	82	51	to	to	PART
ejpam-5744	82	52	design	design	VERB
ejpam-5744	82	53	the	the	DET
ejpam-5744	82	54	following	following	ADJ
ejpam-5744	82	55	fixed	fix	VERB
ejpam-5744	82	56	point	point	NOUN
ejpam-5744	82	57	implicit	implicit	ADJ
ejpam-5744	82	58	iterative	iterative	NOUN
ejpam-5744	82	59	scheme	scheme	NOUN
ejpam-5744	82	60	:	:	PUNCT
ejpam-5744	82	61	ϱk+1	ϱk+1	NUM
ejpam-5744	82	62	=	=	SYM
ejpam-5744	82	63	(	(	PUNCT
ejpam-5744	82	64	1−	1−	NUM
ejpam-5744	82	65	αk)ϱk	αk)ϱk	X
ejpam-5744	82	66	+	+	NUM
ejpam-5744	82	67	αkγ	αkγ	NOUN
ejpam-5744	82	68	(	(	PUNCT
ejpam-5744	82	69	ϱk+1	ϱk+1	NUM
ejpam-5744	82	70	+	+	CCONJ
ejpam-5744	82	71	ϱk	ϱk	ADP
ejpam-5744	82	72	2	2	NUM
ejpam-5744	82	73	)	)	PUNCT
ejpam-5744	82	74	,	,	PUNCT
ejpam-5744	82	75	(	(	PUNCT
ejpam-5744	82	76	12	12	NUM
ejpam-5744	82	77	)	)	PUNCT
ejpam-5744	82	78	where	where	SCONJ
ejpam-5744	82	79	{	{	PUNCT
ejpam-5744	82	80	αk	αk	NOUN
ejpam-5744	82	81	}	}	PUNCT
ejpam-5744	82	82	⊂	⊂	PROPN
ejpam-5744	82	83	(	(	PUNCT
ejpam-5744	82	84	0	0	NUM
ejpam-5744	82	85	,	,	PUNCT
ejpam-5744	82	86	1	1	NUM
ejpam-5744	82	87	)	)	PUNCT
ejpam-5744	82	88	and	and	CCONJ
ejpam-5744	82	89	γ	γ	X
ejpam-5744	82	90	:	:	PUNCT
ejpam-5744	82	91	h	h	PROPN
ejpam-5744	82	92	→	→	SYM
ejpam-5744	82	93	h	h	NOUN
ejpam-5744	82	94	is	be	AUX
ejpam-5744	82	95	nonexpansive	nonexpansive	ADJ
ejpam-5744	82	96	.	.	PUNCT
ejpam-5744	83	1	the	the	DET
ejpam-5744	83	2	authors	author	NOUN
ejpam-5744	83	3	carried	carry	VERB
ejpam-5744	83	4	out	out	ADP
ejpam-5744	83	5	weak	weak	ADJ
ejpam-5744	83	6	convergence	convergence	NOUN
ejpam-5744	83	7	results	result	NOUN
ejpam-5744	83	8	by	by	ADP
ejpam-5744	83	9	taking	take	VERB
ejpam-5744	83	10	some	some	DET
ejpam-5744	83	11	modest	modest	ADJ
ejpam-5744	83	12	assumptions	assumption	NOUN
ejpam-5744	83	13	into	into	ADP
ejpam-5744	83	14	consideration	consideration	NOUN
ejpam-5744	83	15	.	.	PUNCT
ejpam-5744	84	1	same	same	ADJ
ejpam-5744	84	2	fact	fact	NOUN
ejpam-5744	84	3	motivated	motivate	VERB
ejpam-5744	84	4	,	,	PUNCT
ejpam-5744	84	5	xu	xu	PROPN
ejpam-5744	84	6	et	et	PROPN
ejpam-5744	84	7	al	al	PROPN
ejpam-5744	84	8	.	.	PUNCT
ejpam-5744	85	1	[	[	X
ejpam-5744	85	2	20	20	NUM
ejpam-5744	85	3	]	]	PUNCT
ejpam-5744	85	4	to	to	PART
ejpam-5744	85	5	design	design	VERB
ejpam-5744	85	6	the	the	DET
ejpam-5744	85	7	following	follow	VERB
ejpam-5744	85	8	implicit	implicit	ADJ
ejpam-5744	85	9	midpoint	midpoint	NOUN
ejpam-5744	85	10	method	method	NOUN
ejpam-5744	85	11	using	use	VERB
ejpam-5744	85	12	viscosity	viscosity	NOUN
ejpam-5744	85	13	technique	technique	NOUN
ejpam-5744	85	14	for	for	ADP
ejpam-5744	85	15	non	non	ADJ
ejpam-5744	85	16	-	-	ADJ
ejpam-5744	85	17	expansive	expansive	ADJ
ejpam-5744	85	18	mapping	mapping	NOUN
ejpam-5744	85	19	:	:	PUNCT
ejpam-5744	85	20	ϱk+1	ϱk+1	NUM
ejpam-5744	85	21	=	=	SYM
ejpam-5744	85	22	αkψ(ϱk	αkψ(ϱk	X
ejpam-5744	85	23	)	)	PUNCT
ejpam-5744	86	1	+	+	CCONJ
ejpam-5744	86	2	(	(	PUNCT
ejpam-5744	86	3	1−	1−	NUM
ejpam-5744	86	4	αk)γ	αk)γ	NUM
ejpam-5744	86	5	(	(	PUNCT
ejpam-5744	86	6	ϱk+1	ϱk+1	VERB
ejpam-5744	86	7	+	+	CCONJ
ejpam-5744	86	8	ϱk	ϱk	ADP
ejpam-5744	86	9	2	2	NUM
ejpam-5744	86	10	)	)	PUNCT
ejpam-5744	86	11	,	,	PUNCT
ejpam-5744	86	12	(	(	PUNCT
ejpam-5744	86	13	13	13	NUM
ejpam-5744	86	14	)	)	PUNCT
ejpam-5744	86	15	where	where	SCONJ
ejpam-5744	86	16	,	,	PUNCT
ejpam-5744	86	17	γ	γ	PROPN
ejpam-5744	86	18	is	be	AUX
ejpam-5744	86	19	non	non	ADJ
ejpam-5744	86	20	-	-	ADJ
ejpam-5744	86	21	expansive	expansive	ADJ
ejpam-5744	86	22	and	and	CCONJ
ejpam-5744	86	23	ψ	ψ	NOUN
ejpam-5744	86	24	is	be	AUX
ejpam-5744	86	25	contraction	contraction	NOUN
ejpam-5744	86	26	mapping	mapping	NOUN
ejpam-5744	86	27	.	.	PUNCT
ejpam-5744	87	1	more	more	ADV
ejpam-5744	87	2	precisely	precisely	ADV
ejpam-5744	87	3	,	,	PUNCT
ejpam-5744	87	4	following	follow	VERB
ejpam-5744	87	5	result	result	NOUN
ejpam-5744	87	6	was	be	AUX
ejpam-5744	87	7	proved	prove	VERB
ejpam-5744	87	8	.	.	PUNCT
ejpam-5744	88	1	theorem	theorem	NOUN
ejpam-5744	88	2	1	1	X
ejpam-5744	88	3	.	.	PUNCT
ejpam-5744	89	1	let	let	VERB
ejpam-5744	89	2	ω	ω	NUM
ejpam-5744	89	3	̸=	̸=	PROPN
ejpam-5744	89	4	∅	∅	NOUN
ejpam-5744	89	5	be	be	AUX
ejpam-5744	89	6	a	a	DET
ejpam-5744	89	7	closed	closed	ADJ
ejpam-5744	89	8	convex	convex	NOUN
ejpam-5744	89	9	set	set	VERB
ejpam-5744	89	10	in	in	ADP
ejpam-5744	89	11	a	a	DET
ejpam-5744	89	12	hilbert	hilbert	NOUN
ejpam-5744	89	13	space	space	NOUN
ejpam-5744	89	14	h	h	NOUN
ejpam-5744	89	15	.	.	PUNCT
ejpam-5744	90	1	suppose	suppose	VERB
ejpam-5744	90	2	that	that	SCONJ
ejpam-5744	90	3	γ	γ	X
ejpam-5744	90	4	:	:	PUNCT
ejpam-5744	90	5	ω	ω	PROPN
ejpam-5744	90	6	→	→	SYM
ejpam-5744	90	7	ω	ω	PROPN
ejpam-5744	90	8	is	be	AUX
ejpam-5744	90	9	a	a	DET
ejpam-5744	90	10	non	non	ADJ
ejpam-5744	90	11	-	-	ADJ
ejpam-5744	90	12	expansive	expansive	ADJ
ejpam-5744	90	13	and	and	CCONJ
ejpam-5744	90	14	ψ	ψ	NOUN
ejpam-5744	90	15	:	:	PUNCT
ejpam-5744	90	16	ω	ω	PROPN
ejpam-5744	90	17	→	→	SYM
ejpam-5744	90	18	ω	ω	PROPN
ejpam-5744	90	19	is	be	AUX
ejpam-5744	90	20	a	a	DET
ejpam-5744	90	21	contraction	contraction	NOUN
ejpam-5744	90	22	mapping	mapping	NOUN
ejpam-5744	90	23	.	.	PUNCT
ejpam-5744	91	1	if	if	SCONJ
ejpam-5744	91	2	{	{	PUNCT
ejpam-5744	91	3	αk	αk	NOUN
ejpam-5744	91	4	}	}	PUNCT
ejpam-5744	91	5	complies	complie	NOUN
ejpam-5744	91	6	with	with	ADP
ejpam-5744	91	7	the	the	DET
ejpam-5744	91	8	following	follow	VERB
ejpam-5744	91	9	preassumptions	preassumption	NOUN
ejpam-5744	91	10	:	:	PUNCT
ejpam-5744	91	11	m.	m.	NOUN
ejpam-5744	91	12	akram	akram	PROPN
ejpam-5744	91	13	/	/	PUNCT
ejpam-5744	91	14	eur	eur	PROPN
ejpam-5744	91	15	.	.	PUNCT
ejpam-5744	92	1	j.	j.	PROPN
ejpam-5744	92	2	pure	pure	PROPN
ejpam-5744	92	3	appl	appl	PROPN
ejpam-5744	92	4	.	.	PROPN
ejpam-5744	92	5	math	math	PROPN
ejpam-5744	92	6	,	,	PUNCT
ejpam-5744	92	7	18	18	NUM
ejpam-5744	92	8	(	(	PUNCT
ejpam-5744	92	9	1	1	NUM
ejpam-5744	92	10	)	)	PUNCT
ejpam-5744	92	11	(	(	PUNCT
ejpam-5744	92	12	2025	2025	NUM
ejpam-5744	92	13	)	)	PUNCT
ejpam-5744	92	14	,	,	PUNCT
ejpam-5744	92	15	5744	5744	NUM
ejpam-5744	92	16	5	5	NUM
ejpam-5744	92	17	of	of	ADP
ejpam-5744	92	18	19	19	NUM
ejpam-5744	92	19	(	(	PUNCT
ejpam-5744	92	20	p1	p1	PROPN
ejpam-5744	92	21	)	)	PUNCT
ejpam-5744	92	22	lim	lim	PROPN
ejpam-5744	92	23	k→∞	k→∞	NOUN
ejpam-5744	92	24	αk	αk	NOUN
ejpam-5744	92	25	=	=	NOUN
ejpam-5744	92	26	0	0	NUM
ejpam-5744	92	27	;	;	PUNCT
ejpam-5744	92	28	(	(	PUNCT
ejpam-5744	92	29	p2	p2	NOUN
ejpam-5744	92	30	)	)	PUNCT
ejpam-5744	92	31	∞∑	∞∑	NUM
ejpam-5744	92	32	k=0	k=0	PUNCT
ejpam-5744	92	33	αk	αk	ADP
ejpam-5744	92	34	=	=	SYM
ejpam-5744	92	35	∞	∞	PROPN
ejpam-5744	92	36	;	;	PUNCT
ejpam-5744	92	37	(	(	PUNCT
ejpam-5744	92	38	p3	p3	NOUN
ejpam-5744	92	39	)	)	PUNCT
ejpam-5744	93	1	∞∑	∞∑	DET
ejpam-5744	93	2	k=0	k=0	PROPN
ejpam-5744	93	3	|αk+1	|αk+1	VERB
ejpam-5744	93	4	−	−	PROPN
ejpam-5744	93	5	αk|	αk|	NOUN
ejpam-5744	93	6	<	<	X
ejpam-5744	93	7	∞.	∞.	PROPN
ejpam-5744	93	8	then	then	ADV
ejpam-5744	93	9	{	{	PUNCT
ejpam-5744	93	10	ϱk}∞k=1	ϱk}∞k=1	PUNCT
ejpam-5744	93	11	produced	produce	VERB
ejpam-5744	93	12	by	by	ADP
ejpam-5744	93	13	(	(	PUNCT
ejpam-5744	93	14	13	13	NUM
ejpam-5744	93	15	)	)	PUNCT
ejpam-5744	93	16	converges	converge	VERB
ejpam-5744	93	17	to	to	ADP
ejpam-5744	93	18	ϱ	ϱ	PROPN
ejpam-5744	93	19	∈	∈	PROPN
ejpam-5744	93	20	fix(γ	fix(γ	PROPN
ejpam-5744	93	21	)	)	PUNCT
ejpam-5744	93	22	and	and	CCONJ
ejpam-5744	93	23	ϱ	ϱ	ADP
ejpam-5744	93	24	solves	solve	NOUN
ejpam-5744	93	25	the	the	DET
ejpam-5744	93	26	following	follow	VERB
ejpam-5744	93	27	variational	variational	ADJ
ejpam-5744	93	28	inequality	inequality	NOUN
ejpam-5744	93	29	:	:	PUNCT
ejpam-5744	93	30	⟨(i	⟨(i	PROPN
ejpam-5744	93	31	−	−	PROPN
ejpam-5744	93	32	τ)ψ	τ)ψ	NOUN
ejpam-5744	93	33	,	,	PUNCT
ejpam-5744	93	34	ϱ−	ϱ−	CCONJ
ejpam-5744	93	35	τ⟩	τ⟩	PUNCT
ejpam-5744	93	36	≥	≥	NOUN
ejpam-5744	93	37	0	0	NUM
ejpam-5744	93	38	,	,	PUNCT
ejpam-5744	93	39	∀ϱ	∀ϱ	PROPN
ejpam-5744	93	40	∈	∈	PROPN
ejpam-5744	93	41	fix(γ	fix(γ	PROPN
ejpam-5744	93	42	)	)	PUNCT
ejpam-5744	93	43	.	.	PUNCT
ejpam-5744	94	1	luo	luo	PROPN
ejpam-5744	94	2	et	et	PROPN
ejpam-5744	94	3	al	al	PROPN
ejpam-5744	94	4	.	.	PUNCT
ejpam-5744	95	1	[	[	X
ejpam-5744	95	2	36	36	NUM
ejpam-5744	95	3	]	]	PUNCT
ejpam-5744	95	4	obtained	obtain	VERB
ejpam-5744	95	5	the	the	DET
ejpam-5744	95	6	results	result	NOUN
ejpam-5744	95	7	of	of	ADP
ejpam-5744	95	8	xu	xu	PROPN
ejpam-5744	95	9	et	et	PROPN
ejpam-5744	95	10	al	al	PROPN
ejpam-5744	95	11	.	.	PUNCT
ejpam-5744	96	1	[	[	X
ejpam-5744	96	2	20	20	NUM
ejpam-5744	96	3	]	]	PUNCT
ejpam-5744	96	4	in	in	ADP
ejpam-5744	96	5	uniformly	uniformly	ADV
ejpam-5744	96	6	smooth	smooth	ADJ
ejpam-5744	96	7	banach	banach	NOUN
ejpam-5744	96	8	space	space	NOUN
ejpam-5744	96	9	.	.	PUNCT
ejpam-5744	97	1	for	for	ADP
ejpam-5744	97	2	more	more	ADJ
ejpam-5744	97	3	details	detail	NOUN
ejpam-5744	97	4	on	on	ADP
ejpam-5744	97	5	implicit	implicit	ADJ
ejpam-5744	97	6	schemes	scheme	NOUN
ejpam-5744	97	7	,	,	PUNCT
ejpam-5744	97	8	we	we	PRON
ejpam-5744	97	9	refer	refer	VERB
ejpam-5744	97	10	,	,	PUNCT
ejpam-5744	97	11	[	[	X
ejpam-5744	97	12	12	12	NUM
ejpam-5744	97	13	,	,	PUNCT
ejpam-5744	97	14	21	21	NUM
ejpam-5744	97	15	,	,	PUNCT
ejpam-5744	97	16	31	31	NUM
ejpam-5744	97	17	,	,	PUNCT
ejpam-5744	97	18	51	51	NUM
ejpam-5744	97	19	]	]	PUNCT
ejpam-5744	97	20	.	.	PUNCT
ejpam-5744	98	1	motivated	motivated	ADJ
ejpam-5744	98	2	and	and	CCONJ
ejpam-5744	98	3	encouraged	encourage	VERB
ejpam-5744	98	4	by	by	ADP
ejpam-5744	98	5	the	the	DET
ejpam-5744	98	6	earlier	early	ADJ
ejpam-5744	98	7	revealed	reveal	VERB
ejpam-5744	98	8	results	result	NOUN
ejpam-5744	98	9	and	and	CCONJ
ejpam-5744	98	10	iterative	iterative	NOUN
ejpam-5744	98	11	process	process	NOUN
ejpam-5744	98	12	(	(	PUNCT
ejpam-5744	98	13	7	7	NUM
ejpam-5744	98	14	)	)	PUNCT
ejpam-5744	98	15	,	,	PUNCT
ejpam-5744	98	16	we	we	PRON
ejpam-5744	98	17	propose	propose	VERB
ejpam-5744	98	18	and	and	CCONJ
ejpam-5744	98	19	design	design	VERB
ejpam-5744	98	20	a	a	DET
ejpam-5744	98	21	four	four	NUM
ejpam-5744	98	22	-	-	PUNCT
ejpam-5744	98	23	step	step	NOUN
ejpam-5744	98	24	semi	semi	ADJ
ejpam-5744	98	25	-	-	ADJ
ejpam-5744	98	26	implicit	implicit	ADJ
ejpam-5744	98	27	approximation	approximation	NOUN
ejpam-5744	98	28	scheme	scheme	NOUN
ejpam-5744	98	29	(	(	PUNCT
ejpam-5744	98	30	14	14	NUM
ejpam-5744	98	31	)	)	PUNCT
ejpam-5744	98	32	to	to	PART
ejpam-5744	98	33	work	work	VERB
ejpam-5744	98	34	out	out	ADP
ejpam-5744	98	35	the	the	DET
ejpam-5744	98	36	fixed	fix	VERB
ejpam-5744	98	37	point	point	NOUN
ejpam-5744	98	38	of	of	ADP
ejpam-5744	98	39	a	a	DET
ejpam-5744	98	40	contractive	contractive	ADJ
ejpam-5744	98	41	mapping	mapping	NOUN
ejpam-5744	98	42	.	.	PUNCT
ejpam-5744	99	1	the	the	DET
ejpam-5744	99	2	accomplishment	accomplishment	NOUN
ejpam-5744	99	3	of	of	ADP
ejpam-5744	99	4	the	the	DET
ejpam-5744	99	5	task	task	NOUN
ejpam-5744	99	6	is	be	AUX
ejpam-5744	99	7	performed	perform	VERB
ejpam-5744	99	8	as	as	ADP
ejpam-5744	99	9	mentioned	mention	VERB
ejpam-5744	99	10	herein	herein	NOUN
ejpam-5744	99	11	:	:	PUNCT
ejpam-5744	99	12	second	second	ADJ
ejpam-5744	99	13	section	section	NOUN
ejpam-5744	99	14	begins	begin	VERB
ejpam-5744	99	15	with	with	ADP
ejpam-5744	99	16	the	the	DET
ejpam-5744	99	17	designing	designing	NOUN
ejpam-5744	99	18	of	of	ADP
ejpam-5744	99	19	a	a	DET
ejpam-5744	99	20	semi	semi	ADJ
ejpam-5744	99	21	-	-	ADJ
ejpam-5744	99	22	implicit	implicit	ADJ
ejpam-5744	99	23	mid	mid	ADJ
ejpam-5744	99	24	point	point	NOUN
ejpam-5744	99	25	scheme	scheme	NOUN
ejpam-5744	99	26	followed	follow	VERB
ejpam-5744	99	27	by	by	ADP
ejpam-5744	99	28	some	some	DET
ejpam-5744	99	29	basic	basic	ADJ
ejpam-5744	99	30	results	result	NOUN
ejpam-5744	99	31	.	.	PUNCT
ejpam-5744	100	1	convergence	convergence	NOUN
ejpam-5744	100	2	of	of	ADP
ejpam-5744	100	3	the	the	DET
ejpam-5744	100	4	planned	plan	VERB
ejpam-5744	100	5	is	be	AUX
ejpam-5744	100	6	analyzed	analyze	VERB
ejpam-5744	100	7	to	to	PART
ejpam-5744	100	8	explore	explore	VERB
ejpam-5744	100	9	a	a	DET
ejpam-5744	100	10	fixed	fix	VERB
ejpam-5744	100	11	point	point	NOUN
ejpam-5744	100	12	of	of	ADP
ejpam-5744	100	13	a	a	DET
ejpam-5744	100	14	contractive	contractive	ADJ
ejpam-5744	100	15	mapping	mapping	NOUN
ejpam-5744	100	16	and	and	CCONJ
ejpam-5744	100	17	the	the	DET
ejpam-5744	100	18	uniqueness	uniqueness	NOUN
ejpam-5744	100	19	of	of	ADP
ejpam-5744	100	20	the	the	DET
ejpam-5744	100	21	solution	solution	NOUN
ejpam-5744	100	22	is	be	AUX
ejpam-5744	100	23	established	establish	VERB
ejpam-5744	100	24	.	.	PUNCT
ejpam-5744	101	1	further	far	ADV
ejpam-5744	101	2	,	,	PUNCT
ejpam-5744	101	3	the	the	DET
ejpam-5744	101	4	stability	stability	NOUN
ejpam-5744	101	5	of	of	ADP
ejpam-5744	101	6	the	the	DET
ejpam-5744	101	7	designed	design	VERB
ejpam-5744	101	8	scheme	scheme	NOUN
ejpam-5744	101	9	is	be	AUX
ejpam-5744	101	10	discussed	discuss	VERB
ejpam-5744	101	11	.	.	PUNCT
ejpam-5744	102	1	in	in	ADP
ejpam-5744	102	2	the	the	DET
ejpam-5744	102	3	third	third	ADJ
ejpam-5744	102	4	section	section	NOUN
ejpam-5744	102	5	,	,	PUNCT
ejpam-5744	102	6	we	we	PRON
ejpam-5744	102	7	discuss	discuss	VERB
ejpam-5744	102	8	the	the	DET
ejpam-5744	102	9	significance	significance	NOUN
ejpam-5744	102	10	and	and	CCONJ
ejpam-5744	102	11	applicability	applicability	NOUN
ejpam-5744	102	12	of	of	ADP
ejpam-5744	102	13	our	our	PRON
ejpam-5744	102	14	designed	design	VERB
ejpam-5744	102	15	scheme	scheme	NOUN
ejpam-5744	102	16	.	.	PUNCT
ejpam-5744	103	1	a	a	DET
ejpam-5744	103	2	general	general	ADJ
ejpam-5744	103	3	quasi	quasi	ADJ
ejpam-5744	103	4	-	-	ADJ
ejpam-5744	103	5	variational	variational	ADJ
ejpam-5744	103	6	inequality	inequality	NOUN
ejpam-5744	103	7	and	and	CCONJ
ejpam-5744	103	8	a	a	DET
ejpam-5744	103	9	fractional	fractional	ADJ
ejpam-5744	103	10	differential	differential	NOUN
ejpam-5744	103	11	equation	equation	NOUN
ejpam-5744	103	12	are	be	AUX
ejpam-5744	103	13	investigated	investigate	VERB
ejpam-5744	103	14	by	by	ADP
ejpam-5744	103	15	employing	employ	VERB
ejpam-5744	103	16	our	our	PRON
ejpam-5744	103	17	designed	design	VERB
ejpam-5744	103	18	scheme	scheme	NOUN
ejpam-5744	103	19	.	.	PUNCT
ejpam-5744	104	1	the	the	DET
ejpam-5744	104	2	concluding	conclude	VERB
ejpam-5744	104	3	comments	comment	NOUN
ejpam-5744	104	4	and	and	CCONJ
ejpam-5744	104	5	expected	expect	VERB
ejpam-5744	104	6	future	future	ADJ
ejpam-5744	104	7	research	research	NOUN
ejpam-5744	104	8	plans	plan	NOUN
ejpam-5744	104	9	are	be	AUX
ejpam-5744	104	10	outlined	outline	VERB
ejpam-5744	104	11	in	in	ADP
ejpam-5744	104	12	the	the	DET
ejpam-5744	104	13	last	last	ADJ
ejpam-5744	104	14	section	section	NOUN
ejpam-5744	104	15	.	.	PUNCT
ejpam-5744	105	1	2	2	X
ejpam-5744	105	2	.	.	NOUN
ejpam-5744	105	3	iterative	iterative	NOUN
ejpam-5744	105	4	scheme	scheme	NOUN
ejpam-5744	105	5	and	and	CCONJ
ejpam-5744	105	6	convergence	convergence	NOUN
ejpam-5744	105	7	let	let	VERB
ejpam-5744	105	8	∅	∅	NOUN
ejpam-5744	105	9	̸=	̸=	PROPN
ejpam-5744	105	10	ω	ω	NUM
ejpam-5744	105	11	be	be	AUX
ejpam-5744	105	12	a	a	DET
ejpam-5744	105	13	closed	closed	ADJ
ejpam-5744	105	14	convex	convex	NOUN
ejpam-5744	105	15	subset	subset	NOUN
ejpam-5744	105	16	of	of	ADP
ejpam-5744	105	17	a	a	DET
ejpam-5744	105	18	banach	banach	NOUN
ejpam-5744	105	19	space	space	NOUN
ejpam-5744	105	20	x	x	PUNCT
ejpam-5744	105	21	equipped	equip	VERB
ejpam-5744	105	22	with	with	ADP
ejpam-5744	105	23	norm	norm	NOUN
ejpam-5744	105	24	∥	∥	X
ejpam-5744	105	25	·	·	PUNCT
ejpam-5744	105	26	∥.	∥.	PRON
ejpam-5744	105	27	suppose	suppose	VERB
ejpam-5744	105	28	the	the	DET
ejpam-5744	105	29	mapping	mapping	NOUN
ejpam-5744	105	30	ψ	ψ	X
ejpam-5744	105	31	:	:	PUNCT
ejpam-5744	105	32	ω	ω	PROPN
ejpam-5744	105	33	→	→	SYM
ejpam-5744	105	34	ω	ω	NUM
ejpam-5744	105	35	satisfies	satisfie	NOUN
ejpam-5744	105	36	contractive	contractive	ADJ
ejpam-5744	105	37	condition	condition	NOUN
ejpam-5744	105	38	(	(	PUNCT
ejpam-5744	105	39	2	2	NUM
ejpam-5744	105	40	)	)	PUNCT
ejpam-5744	105	41	.	.	PUNCT
ejpam-5744	106	1	based	base	VERB
ejpam-5744	106	2	on	on	ADP
ejpam-5744	106	3	the	the	DET
ejpam-5744	106	4	iterative	iterative	NOUN
ejpam-5744	106	5	scheme	scheme	NOUN
ejpam-5744	106	6	(	(	PUNCT
ejpam-5744	106	7	7	7	NUM
ejpam-5744	106	8	)	)	PUNCT
ejpam-5744	106	9	,	,	PUNCT
ejpam-5744	106	10	we	we	PRON
ejpam-5744	106	11	are	be	AUX
ejpam-5744	106	12	interested	interested	ADJ
ejpam-5744	106	13	to	to	PART
ejpam-5744	106	14	suggest	suggest	VERB
ejpam-5744	106	15	and	and	CCONJ
ejpam-5744	106	16	analyze	analyze	VERB
ejpam-5744	106	17	the	the	DET
ejpam-5744	106	18	following	follow	VERB
ejpam-5744	106	19	semi	semi	ADJ
ejpam-5744	106	20	-	-	ADJ
ejpam-5744	106	21	implicit	implicit	ADJ
ejpam-5744	106	22	midpoint	midpoint	NOUN
ejpam-5744	106	23	scheme	scheme	NOUN
ejpam-5744	106	24	(	(	PUNCT
ejpam-5744	106	25	simps	simp	NOUN
ejpam-5744	106	26	)	)	PUNCT
ejpam-5744	106	27	as	as	ADP
ejpam-5744	106	28	under:	under:	X
ejpam-5744	106	29	ϱk+1	ϱk+1	NUM
ejpam-5744	106	30	=	=	PUNCT
ejpam-5744	106	31	ψ(σk	ψ(σk	PROPN
ejpam-5744	106	32	)	)	PUNCT
ejpam-5744	106	33	,	,	PUNCT
ejpam-5744	106	34	σk	σk	PROPN
ejpam-5744	106	35	=	=	SYM
ejpam-5744	106	36	ψ	ψ	X
ejpam-5744	106	37	[	[	PUNCT
ejpam-5744	106	38	(	(	PUNCT
ejpam-5744	106	39	1−	1−	NUM
ejpam-5744	106	40	αk	αk	NOUN
ejpam-5744	106	41	)	)	PUNCT
ejpam-5744	106	42	(	(	PUNCT
ejpam-5744	106	43	σk	σk	CCONJ
ejpam-5744	106	44	+	+	NUM
ejpam-5744	106	45	ϑk	ϑk	PROPN
ejpam-5744	106	46	2	2	NUM
ejpam-5744	106	47	)	)	PUNCT
ejpam-5744	107	1	+	+	CCONJ
ejpam-5744	107	2	αkψ	αkψ	NOUN
ejpam-5744	107	3	(	(	PUNCT
ejpam-5744	107	4	σk	σk	PROPN
ejpam-5744	107	5	+	+	NUM
ejpam-5744	107	6	ϑk	ϑk	PROPN
ejpam-5744	107	7	2	2	NUM
ejpam-5744	107	8	)	)	PUNCT
ejpam-5744	107	9	]	]	PUNCT
ejpam-5744	107	10	,	,	PUNCT
ejpam-5744	107	11	ϑk	ϑk	PROPN
ejpam-5744	107	12	=	=	PRON
ejpam-5744	107	13	(	(	PUNCT
ejpam-5744	107	14	1−	1−	NUM
ejpam-5744	107	15	βk)ψ	βk)ψ	NUM
ejpam-5744	107	16	(	(	PUNCT
ejpam-5744	107	17	ϑk	ϑk	PROPN
ejpam-5744	107	18	+	+	CCONJ
ejpam-5744	107	19	ϱk	ϱk	NOUN
ejpam-5744	107	20	2	2	NUM
ejpam-5744	107	21	)	)	PUNCT
ejpam-5744	107	22	+	+	CCONJ
ejpam-5744	107	23	βkψ	βkψ	X
ejpam-5744	107	24	(	(	PUNCT
ejpam-5744	107	25	ϑk	ϑk	PROPN
ejpam-5744	107	26	+	+	NUM
ejpam-5744	107	27	θk	θk	PROPN
ejpam-5744	107	28	2	2	NUM
ejpam-5744	107	29	)	)	PUNCT
ejpam-5744	107	30	,	,	PUNCT
ejpam-5744	107	31	θk	θk	NOUN
ejpam-5744	107	32	=	=	SYM
ejpam-5744	107	33	(	(	PUNCT
ejpam-5744	107	34	1−	1−	NUM
ejpam-5744	107	35	γk	γk	NOUN
ejpam-5744	107	36	)	)	PUNCT
ejpam-5744	107	37	(	(	PUNCT
ejpam-5744	107	38	ϱk	ϱk	NOUN
ejpam-5744	107	39	+	+	NUM
ejpam-5744	107	40	θk	θk	NOUN
ejpam-5744	107	41	2	2	NUM
ejpam-5744	107	42	)	)	PUNCT
ejpam-5744	107	43	+	+	CCONJ
ejpam-5744	107	44	γkψ	γkψ	NOUN
ejpam-5744	107	45	(	(	PUNCT
ejpam-5744	107	46	ϱk	ϱk	NOUN
ejpam-5744	107	47	+	+	NUM
ejpam-5744	107	48	θk	θk	NOUN
ejpam-5744	107	49	2	2	NUM
ejpam-5744	107	50	)	)	PUNCT
ejpam-5744	107	51	]	]	PUNCT
ejpam-5744	107	52	,	,	PUNCT
ejpam-5744	107	53	(	(	PUNCT
ejpam-5744	107	54	14	14	NUM
ejpam-5744	107	55	)	)	PUNCT
ejpam-5744	107	56	where	where	SCONJ
ejpam-5744	107	57	{	{	PUNCT
ejpam-5744	107	58	αk	αk	NOUN
ejpam-5744	107	59	}	}	PUNCT
ejpam-5744	107	60	,	,	PUNCT
ejpam-5744	107	61	{	{	PUNCT
ejpam-5744	107	62	βk	βk	NOUN
ejpam-5744	107	63	}	}	PUNCT
ejpam-5744	107	64	,	,	PUNCT
ejpam-5744	107	65	{	{	PUNCT
ejpam-5744	107	66	γk	γk	NOUN
ejpam-5744	107	67	}	}	PUNCT
ejpam-5744	107	68	⊆	⊆	NUM
ejpam-5744	107	69	(	(	PUNCT
ejpam-5744	107	70	0	0	NUM
ejpam-5744	107	71	,	,	PUNCT
ejpam-5744	107	72	1	1	NUM
ejpam-5744	107	73	)	)	PUNCT
ejpam-5744	107	74	.	.	PUNCT
ejpam-5744	108	1	definition	definition	NOUN
ejpam-5744	108	2	3	3	NUM
ejpam-5744	108	3	.	.	PUNCT
ejpam-5744	109	1	[	[	X
ejpam-5744	109	2	9	9	NUM
ejpam-5744	109	3	]	]	X
ejpam-5744	109	4	let	let	AUX
ejpam-5744	109	5	{	{	PUNCT
ejpam-5744	109	6	φk	φk	ADP
ejpam-5744	109	7	}	}	PUNCT
ejpam-5744	109	8	⊂	⊂	PROPN
ejpam-5744	109	9	ω	ω	NOUN
ejpam-5744	109	10	be	be	AUX
ejpam-5744	109	11	an	an	DET
ejpam-5744	109	12	arbitrary	arbitrary	ADJ
ejpam-5744	109	13	sequence	sequence	NOUN
ejpam-5744	109	14	.	.	PUNCT
ejpam-5744	110	1	an	an	DET
ejpam-5744	110	2	iterative	iterative	NOUN
ejpam-5744	110	3	scheme	scheme	NOUN
ejpam-5744	110	4	ϱk+1	ϱk+1	NUM
ejpam-5744	110	5	=	=	PUNCT
ejpam-5744	110	6	λ(ψ	λ(ψ	PROPN
ejpam-5744	110	7	,	,	PUNCT
ejpam-5744	110	8	ϱk	ϱk	NOUN
ejpam-5744	110	9	)	)	PUNCT
ejpam-5744	110	10	so	so	ADV
ejpam-5744	110	11	as	as	ADP
ejpam-5744	110	12	{	{	PUNCT
ejpam-5744	110	13	ϱk	ϱk	NOUN
ejpam-5744	110	14	}	}	PUNCT
ejpam-5744	110	15	→	→	SYM
ejpam-5744	110	16	ϱ	ϱ	PROPN
ejpam-5744	110	17	∈	∈	PROPN
ejpam-5744	110	18	ξ(ψ	ξ(ψ	NOUN
ejpam-5744	110	19	)	)	PUNCT
ejpam-5744	110	20	is	be	AUX
ejpam-5744	110	21	said	say	VERB
ejpam-5744	110	22	to	to	PART
ejpam-5744	110	23	be	be	AUX
ejpam-5744	110	24	ψ	ψ	NOUN
ejpam-5744	110	25	-	-	ADJ
ejpam-5744	110	26	stable	stable	ADJ
ejpam-5744	110	27	.	.	PUNCT
ejpam-5744	111	1	if	if	SCONJ
ejpam-5744	111	2	for	for	ADP
ejpam-5744	111	3	µk	µk	NOUN
ejpam-5744	111	4	=	=	NOUN
ejpam-5744	111	5	∥φk+1	∥φk+1	ADP
ejpam-5744	111	6	−	−	PROPN
ejpam-5744	111	7	λ(ψ	λ(ψ	PROPN
ejpam-5744	111	8	,	,	PUNCT
ejpam-5744	111	9	φk)∥	φk)∥	NOUN
ejpam-5744	111	10	,	,	PUNCT
ejpam-5744	111	11	lim	lim	PROPN
ejpam-5744	111	12	k→∞	k→∞	NOUN
ejpam-5744	111	13	µk	µk	NOUN
ejpam-5744	111	14	=	=	NOUN
ejpam-5744	111	15	0	0	PUNCT
ejpam-5744	112	1	if	if	SCONJ
ejpam-5744	112	2	and	and	CCONJ
ejpam-5744	112	3	only	only	ADV
ejpam-5744	112	4	if	if	SCONJ
ejpam-5744	112	5	lim	lim	PROPN
ejpam-5744	112	6	k→∞	k→∞	NOUN
ejpam-5744	112	7	φk	φk	ADP
ejpam-5744	112	8	=	=	PROPN
ejpam-5744	112	9	ϱ.	ϱ.	PROPN
ejpam-5744	112	10	lemma	lemma	PROPN
ejpam-5744	112	11	1	1	NUM
ejpam-5744	112	12	.	.	PUNCT
ejpam-5744	113	1	[	[	X
ejpam-5744	113	2	50	50	NUM
ejpam-5744	113	3	]	]	PUNCT
ejpam-5744	113	4	suppose	suppose	VERB
ejpam-5744	113	5	the	the	DET
ejpam-5744	113	6	nonnegative	nonnegative	ADJ
ejpam-5744	113	7	real	real	ADJ
ejpam-5744	113	8	sequences	sequence	NOUN
ejpam-5744	113	9	{	{	PUNCT
ejpam-5744	113	10	ϱk}∞k=1	ϱk}∞k=1	PUNCT
ejpam-5744	113	11	and	and	CCONJ
ejpam-5744	113	12	{	{	PUNCT
ejpam-5744	113	13	ςk}∞k=1	ςk}∞k=1	PRON
ejpam-5744	113	14	satisfy	satisfy	VERB
ejpam-5744	113	15	ϱk+1	ϱk+1	NUM
ejpam-5744	113	16	≤	≤	NUM
ejpam-5744	113	17	(	(	PUNCT
ejpam-5744	113	18	1−	1−	NUM
ejpam-5744	113	19	pk)ϱk	pk)ϱk	X
ejpam-5744	113	20	+	+	CCONJ
ejpam-5744	113	21	ςk	ςk	NUM
ejpam-5744	113	22	,	,	PUNCT
ejpam-5744	113	23	where	where	SCONJ
ejpam-5744	113	24	pk	pk	NOUN
ejpam-5744	113	25	∈	∈	PROPN
ejpam-5744	113	26	(	(	PUNCT
ejpam-5744	113	27	0	0	NUM
ejpam-5744	113	28	,	,	PUNCT
ejpam-5744	113	29	1	1	NUM
ejpam-5744	113	30	)	)	PUNCT
ejpam-5744	113	31	,	,	PUNCT
ejpam-5744	113	32	∞∑	∞∑	NUM
ejpam-5744	113	33	k=1	k=1	X
ejpam-5744	113	34	pk	pk	NOUN
ejpam-5744	113	35	=	=	SYM
ejpam-5744	113	36	∞	∞	PROPN
ejpam-5744	113	37	and	and	CCONJ
ejpam-5744	113	38	lim	lim	PROPN
ejpam-5744	113	39	k→∞	k→∞	PROPN
ejpam-5744	113	40	ςk	ςk	PROPN
ejpam-5744	113	41	pk	pk	PROPN
ejpam-5744	113	42	=	=	NOUN
ejpam-5744	113	43	0	0	PROPN
ejpam-5744	113	44	.	.	PUNCT
ejpam-5744	114	1	then	then	ADV
ejpam-5744	114	2	lim	lim	PROPN
ejpam-5744	114	3	k→∞	k→∞	PROPN
ejpam-5744	114	4	ϱk	ϱk	PROPN
ejpam-5744	114	5	=	=	SYM
ejpam-5744	114	6	0	0	PROPN
ejpam-5744	114	7	.	.	PUNCT
ejpam-5744	114	8	m.	m.	PROPN
ejpam-5744	114	9	akram	akram	PROPN
ejpam-5744	114	10	/	/	PUNCT
ejpam-5744	114	11	eur	eur	PROPN
ejpam-5744	114	12	.	.	PUNCT
ejpam-5744	115	1	j.	j.	PROPN
ejpam-5744	115	2	pure	pure	PROPN
ejpam-5744	115	3	appl	appl	PROPN
ejpam-5744	115	4	.	.	PROPN
ejpam-5744	115	5	math	math	PROPN
ejpam-5744	115	6	,	,	PUNCT
ejpam-5744	115	7	18	18	NUM
ejpam-5744	115	8	(	(	PUNCT
ejpam-5744	115	9	1	1	NUM
ejpam-5744	115	10	)	)	PUNCT
ejpam-5744	115	11	(	(	PUNCT
ejpam-5744	115	12	2025	2025	NUM
ejpam-5744	115	13	)	)	PUNCT
ejpam-5744	115	14	,	,	PUNCT
ejpam-5744	115	15	5744	5744	NUM
ejpam-5744	115	16	6	6	NUM
ejpam-5744	115	17	of	of	ADP
ejpam-5744	115	18	19	19	NUM
ejpam-5744	115	19	theorem	theorem	NOUN
ejpam-5744	115	20	2	2	NUM
ejpam-5744	115	21	.	.	PUNCT
ejpam-5744	116	1	let	let	VERB
ejpam-5744	116	2	∅	∅	NOUN
ejpam-5744	116	3	=	=	NOUN
ejpam-5744	116	4	̸	̸	NUM
ejpam-5744	116	5	ω	ω	NOUN
ejpam-5744	116	6	⊆	⊆	NUM
ejpam-5744	116	7	x	x	PUNCT
ejpam-5744	116	8	be	be	AUX
ejpam-5744	116	9	a	a	DET
ejpam-5744	116	10	closed	closed	ADJ
ejpam-5744	116	11	convex	convex	NOUN
ejpam-5744	116	12	bounded	bound	VERB
ejpam-5744	116	13	set	set	NOUN
ejpam-5744	116	14	and	and	CCONJ
ejpam-5744	116	15	ψ	ψ	NOUN
ejpam-5744	116	16	:	:	PUNCT
ejpam-5744	116	17	ω	ω	PROPN
ejpam-5744	116	18	→	→	SYM
ejpam-5744	116	19	ω	ω	NUM
ejpam-5744	116	20	satisfies	satisfie	NOUN
ejpam-5744	116	21	(	(	PUNCT
ejpam-5744	116	22	2	2	NUM
ejpam-5744	116	23	)	)	PUNCT
ejpam-5744	116	24	.	.	PUNCT
ejpam-5744	117	1	if	if	SCONJ
ejpam-5744	117	2	ξ(ψ	ξ(ψ	NUM
ejpam-5744	117	3	)	)	PUNCT
ejpam-5744	117	4	̸=	̸=	PROPN
ejpam-5744	117	5	∅	∅	NOUN
ejpam-5744	117	6	,	,	PUNCT
ejpam-5744	117	7	then	then	ADV
ejpam-5744	117	8	{	{	PUNCT
ejpam-5744	117	9	ϱk}∞k=1	ϱk}∞k=1	PUNCT
ejpam-5744	117	10	initiated	initiate	VERB
ejpam-5744	117	11	by	by	ADP
ejpam-5744	117	12	simps	simp	NOUN
ejpam-5744	117	13	(	(	PUNCT
ejpam-5744	117	14	14	14	NUM
ejpam-5744	117	15	)	)	PUNCT
ejpam-5744	117	16	converges	converge	VERB
ejpam-5744	117	17	strongly	strongly	ADV
ejpam-5744	117	18	to	to	ADP
ejpam-5744	117	19	ϱ	ϱ	PROPN
ejpam-5744	117	20	∈	∈	PROPN
ejpam-5744	117	21	ξ(ψ	ξ(ψ	NUM
ejpam-5744	117	22	)	)	PUNCT
ejpam-5744	117	23	.	.	PUNCT
ejpam-5744	118	1	proof	proof	NOUN
ejpam-5744	118	2	.	.	PUNCT
ejpam-5744	119	1	suppose	suppose	VERB
ejpam-5744	119	2	that	that	SCONJ
ejpam-5744	119	3	ϱ	ϱ	ADP
ejpam-5744	119	4	∈	∈	PROPN
ejpam-5744	119	5	ξ(ψ	ξ(ψ	NUM
ejpam-5744	119	6	)	)	PUNCT
ejpam-5744	119	7	.	.	PUNCT
ejpam-5744	120	1	then	then	ADV
ejpam-5744	120	2	,	,	PUNCT
ejpam-5744	120	3	it	it	PRON
ejpam-5744	120	4	results	result	VERB
ejpam-5744	120	5	from	from	ADP
ejpam-5744	120	6	the	the	DET
ejpam-5744	120	7	last	last	ADJ
ejpam-5744	120	8	formulation	formulation	NOUN
ejpam-5744	120	9	of	of	ADP
ejpam-5744	120	10	(	(	PUNCT
ejpam-5744	120	11	14	14	NUM
ejpam-5744	120	12	)	)	PUNCT
ejpam-5744	120	13	that	that	PRON
ejpam-5744	120	14	∥θk	∥θk	PROPN
ejpam-5744	120	15	−	−	PROPN
ejpam-5744	120	16	ϱ∥	ϱ∥	NOUN
ejpam-5744	120	17	=	=	SYM
ejpam-5744	120	18	∥∥∥(1−	∥∥∥(1−	PROPN
ejpam-5744	120	19	γk	γk	NOUN
ejpam-5744	120	20	)	)	PUNCT
ejpam-5744	120	21	(	(	PUNCT
ejpam-5744	120	22	ϱk	ϱk	NOUN
ejpam-5744	120	23	+	+	NUM
ejpam-5744	120	24	θk	θk	NOUN
ejpam-5744	120	25	2	2	NUM
ejpam-5744	120	26	)	)	PUNCT
ejpam-5744	120	27	+	+	CCONJ
ejpam-5744	120	28	γkψ	γkψ	NOUN
ejpam-5744	120	29	(	(	PUNCT
ejpam-5744	120	30	ϱk	ϱk	NOUN
ejpam-5744	120	31	+	+	NUM
ejpam-5744	120	32	θk	θk	NOUN
ejpam-5744	120	33	2	2	NUM
ejpam-5744	120	34	)	)	PUNCT
ejpam-5744	120	35	]	]	PUNCT
ejpam-5744	121	1	−	−	ADP
ejpam-5744	121	2	ϱ	ϱ	ADP
ejpam-5744	121	3	∥∥∥	∥∥∥	PROPN
ejpam-5744	121	4	≤	≤	NUM
ejpam-5744	121	5	(	(	PUNCT
ejpam-5744	121	6	1−	1−	NUM
ejpam-5744	121	7	γk	γk	NOUN
ejpam-5744	121	8	)	)	PUNCT
ejpam-5744	122	1	∥∥∥ϱk	∥∥∥ϱk	NOUN
ejpam-5744	122	2	+	+	CCONJ
ejpam-5744	122	3	θk	θk	NOUN
ejpam-5744	122	4	2	2	NUM
ejpam-5744	122	5	−	−	NOUN
ejpam-5744	122	6	ϱ	ϱ	ADP
ejpam-5744	122	7	∥∥∥+	∥∥∥+	PROPN
ejpam-5744	122	8	γk	γk	PROPN
ejpam-5744	122	9	∥∥∥ψ(ϱk	∥∥∥ψ(ϱk	PUNCT
ejpam-5744	123	1	+	+	CCONJ
ejpam-5744	123	2	θk	θk	NOUN
ejpam-5744	123	3	2	2	NUM
ejpam-5744	123	4	)	)	PUNCT
ejpam-5744	123	5	−	−	ADP
ejpam-5744	123	6	ϱ	ϱ	ADP
ejpam-5744	123	7	∥∥∥	∥∥∥	PROPN
ejpam-5744	123	8	=	=	SYM
ejpam-5744	123	9	(	(	PUNCT
ejpam-5744	123	10	1−	1−	NUM
ejpam-5744	123	11	γk	γk	NOUN
ejpam-5744	123	12	)	)	PUNCT
ejpam-5744	124	1	∥∥∥ϱk	∥∥∥ϱk	NOUN
ejpam-5744	124	2	+	+	CCONJ
ejpam-5744	124	3	θk	θk	NOUN
ejpam-5744	124	4	2	2	NUM
ejpam-5744	124	5	−	−	NOUN
ejpam-5744	124	6	ϱ	ϱ	ADP
ejpam-5744	124	7	∥∥∥+	∥∥∥+	PROPN
ejpam-5744	124	8	γk	γk	PROPN
ejpam-5744	124	9	∥∥∥ψ(ϱ)−ψ	∥∥∥ψ(ϱ)−ψ	NOUN
ejpam-5744	124	10	(	(	PUNCT
ejpam-5744	124	11	ϱk	ϱk	NOUN
ejpam-5744	124	12	+	+	CCONJ
ejpam-5744	124	13	θk	θk	NOUN
ejpam-5744	124	14	2	2	NUM
ejpam-5744	124	15	)	)	PUNCT
ejpam-5744	124	16	∥∥∥	∥∥∥	NOUN
ejpam-5744	124	17	≤	≤	NUM
ejpam-5744	124	18	(	(	PUNCT
ejpam-5744	124	19	1−	1−	NUM
ejpam-5744	124	20	γk	γk	NOUN
ejpam-5744	124	21	)	)	PUNCT
ejpam-5744	125	1	∥∥∥ϱk	∥∥∥ϱk	NOUN
ejpam-5744	125	2	+	+	CCONJ
ejpam-5744	125	3	θk	θk	NOUN
ejpam-5744	125	4	2	2	NUM
ejpam-5744	125	5	−	−	NOUN
ejpam-5744	125	6	ϱ	ϱ	ADP
ejpam-5744	125	7	∥∥∥+	∥∥∥+	PROPN
ejpam-5744	125	8	γk	γk	X
ejpam-5744	125	9	[	[	PUNCT
ejpam-5744	125	10	g(∥ϱ−ψ(ϱ)∥	g(∥ϱ−ψ(ϱ)∥	NOUN
ejpam-5744	125	11	)	)	PUNCT
ejpam-5744	126	1	+	+	CCONJ
ejpam-5744	126	2	τ	τ	X
ejpam-5744	126	3	∥∥∥(ϱk	∥∥∥(ϱk	X
ejpam-5744	126	4	+	+	NUM
ejpam-5744	126	5	θk	θk	NOUN
ejpam-5744	126	6	2	2	NUM
ejpam-5744	126	7	)	)	PUNCT
ejpam-5744	126	8	−	−	ADP
ejpam-5744	126	9	ϱ	ϱ	ADP
ejpam-5744	126	10	∥∥∥	∥∥∥	PROPN
ejpam-5744	126	11	]	]	PUNCT
ejpam-5744	126	12	≤	≤	NUM
ejpam-5744	126	13	εk	εk	X
ejpam-5744	126	14	2	2	NUM
ejpam-5744	126	15	(	(	PUNCT
ejpam-5744	126	16	∥ϱk	∥ϱk	NOUN
ejpam-5744	126	17	−	−	NOUN
ejpam-5744	126	18	ϱ∥+	ϱ∥+	NOUN
ejpam-5744	126	19	∥θk	∥θk	NOUN
ejpam-5744	126	20	−	−	NOUN
ejpam-5744	126	21	ϱ∥	ϱ∥	NOUN
ejpam-5744	126	22	)	)	PUNCT
ejpam-5744	126	23	,	,	PUNCT
ejpam-5744	126	24	where	where	SCONJ
ejpam-5744	126	25	εk	εk	NOUN
ejpam-5744	126	26	=	=	SYM
ejpam-5744	126	27	(	(	PUNCT
ejpam-5744	126	28	1−	1−	NUM
ejpam-5744	126	29	γk	γk	NOUN
ejpam-5744	126	30	+	+	CCONJ
ejpam-5744	126	31	τγk	τγk	PROPN
ejpam-5744	126	32	)	)	PUNCT
ejpam-5744	126	33	,	,	PUNCT
ejpam-5744	126	34	which	which	PRON
ejpam-5744	126	35	turns	turn	VERB
ejpam-5744	126	36	after	after	ADP
ejpam-5744	126	37	simplification	simplification	NOUN
ejpam-5744	126	38	into	into	ADP
ejpam-5744	126	39	∥θk	∥θk	PROPN
ejpam-5744	126	40	−	−	PROPN
ejpam-5744	126	41	ϱ∥	ϱ∥	NOUN
ejpam-5744	126	42	≤	≤	NUM
ejpam-5744	126	43	εk	εk	X
ejpam-5744	126	44	(	(	PUNCT
ejpam-5744	126	45	2−	2−	NUM
ejpam-5744	126	46	εk	εk	NOUN
ejpam-5744	126	47	)	)	PUNCT
ejpam-5744	126	48	∥ϱk	∥ϱk	NOUN
ejpam-5744	126	49	−	−	PROPN
ejpam-5744	126	50	ϱ∥.	ϱ∥.	PROPN
ejpam-5744	126	51	(	(	PUNCT
ejpam-5744	126	52	15	15	NUM
ejpam-5744	126	53	)	)	PUNCT
ejpam-5744	126	54	again	again	ADV
ejpam-5744	126	55	it	it	PRON
ejpam-5744	126	56	yields	yield	VERB
ejpam-5744	126	57	from	from	ADP
ejpam-5744	126	58	scheme	scheme	NOUN
ejpam-5744	126	59	(	(	PUNCT
ejpam-5744	126	60	14	14	NUM
ejpam-5744	126	61	)	)	PUNCT
ejpam-5744	127	1	that	that	SCONJ
ejpam-5744	127	2	∥ϑk	∥ϑk	NOUN
ejpam-5744	128	1	−	−	NOUN
ejpam-5744	129	1	ϱ∥	ϱ∥	NOUN
ejpam-5744	129	2	=	=	SYM
ejpam-5744	129	3	∥∥∥(1−	∥∥∥(1−	PROPN
ejpam-5744	129	4	βk)ψ	βk)ψ	PROPN
ejpam-5744	129	5	(	(	PUNCT
ejpam-5744	129	6	ϑk	ϑk	PROPN
ejpam-5744	129	7	+	+	CCONJ
ejpam-5744	129	8	ϱk	ϱk	NOUN
ejpam-5744	129	9	2	2	NUM
ejpam-5744	129	10	)	)	PUNCT
ejpam-5744	129	11	+	+	CCONJ
ejpam-5744	129	12	βkψ	βkψ	X
ejpam-5744	129	13	(	(	PUNCT
ejpam-5744	129	14	ϑk	ϑk	PROPN
ejpam-5744	129	15	+	+	NUM
ejpam-5744	129	16	θk	θk	PROPN
ejpam-5744	129	17	2	2	NUM
ejpam-5744	129	18	)	)	PUNCT
ejpam-5744	129	19	−	−	ADP
ejpam-5744	129	20	ϱ	ϱ	ADP
ejpam-5744	129	21	∥∥∥	∥∥∥	PROPN
ejpam-5744	129	22	≤	≤	NUM
ejpam-5744	129	23	(	(	PUNCT
ejpam-5744	129	24	1−	1−	NUM
ejpam-5744	129	25	βk	βk	NOUN
ejpam-5744	129	26	)	)	PUNCT
ejpam-5744	129	27	∥∥∥ψ(ϑk	∥∥∥ψ(ϑk	NOUN
ejpam-5744	130	1	+	+	CCONJ
ejpam-5744	130	2	ϱk	ϱk	ADP
ejpam-5744	130	3	2	2	NUM
ejpam-5744	130	4	)	)	PUNCT
ejpam-5744	130	5	−	−	ADP
ejpam-5744	130	6	ϱ	ϱ	ADP
ejpam-5744	130	7	∥∥∥+	∥∥∥+	NOUN
ejpam-5744	130	8	βk	βk	ADP
ejpam-5744	130	9	∥∥∥ψ(ϑk	∥∥∥ψ(ϑk	NOUN
ejpam-5744	130	10	+	+	CCONJ
ejpam-5744	130	11	θk	θk	NOUN
ejpam-5744	130	12	2	2	NUM
ejpam-5744	130	13	)	)	PUNCT
ejpam-5744	130	14	−	−	ADP
ejpam-5744	130	15	ϱ	ϱ	ADP
ejpam-5744	130	16	∥∥∥	∥∥∥	PROPN
ejpam-5744	130	17	≤	≤	NUM
ejpam-5744	130	18	(	(	PUNCT
ejpam-5744	130	19	1−	1−	NUM
ejpam-5744	130	20	βk	βk	NOUN
ejpam-5744	130	21	)	)	PUNCT
ejpam-5744	130	22	∥∥∥ψ(ϱ)−ψ	∥∥∥ψ(ϱ)−ψ	NOUN
ejpam-5744	130	23	(	(	PUNCT
ejpam-5744	130	24	ϑk	ϑk	PROPN
ejpam-5744	130	25	+	+	CCONJ
ejpam-5744	130	26	ϱk	ϱk	ADP
ejpam-5744	130	27	2	2	NUM
ejpam-5744	130	28	)	)	PUNCT
ejpam-5744	130	29	∥∥∥+	∥∥∥+	VERB
ejpam-5744	130	30	βk	βk	NOUN
ejpam-5744	130	31	∥∥∥ψ(ϱ)−ψ	∥∥∥ψ(ϱ)−ψ	NOUN
ejpam-5744	131	1	(	(	PUNCT
ejpam-5744	131	2	ϑk	ϑk	PROPN
ejpam-5744	131	3	+	+	NUM
ejpam-5744	131	4	θk	θk	PROPN
ejpam-5744	131	5	2	2	NUM
ejpam-5744	131	6	)	)	PUNCT
ejpam-5744	131	7	∥∥∥	∥∥∥	NOUN
ejpam-5744	131	8	≤	≤	NUM
ejpam-5744	131	9	(	(	PUNCT
ejpam-5744	131	10	1−	1−	NUM
ejpam-5744	131	11	βk	βk	NOUN
ejpam-5744	131	12	)	)	PUNCT
ejpam-5744	131	13	[	[	PUNCT
ejpam-5744	131	14	g(∥ϱ−ψ(ϱ)∥	g(∥ϱ−ψ(ϱ)∥	NOUN
ejpam-5744	131	15	)	)	PUNCT
ejpam-5744	132	1	+	+	CCONJ
ejpam-5744	132	2	τ	τ	PROPN
ejpam-5744	132	3	∥∥∥(ϑk	∥∥∥(ϑk	PROPN
ejpam-5744	132	4	+	+	CCONJ
ejpam-5744	132	5	ϱk	ϱk	ADP
ejpam-5744	132	6	2	2	NUM
ejpam-5744	132	7	)	)	PUNCT
ejpam-5744	132	8	−	−	ADP
ejpam-5744	132	9	ϱ	ϱ	ADP
ejpam-5744	132	10	∥∥∥	∥∥∥	PROPN
ejpam-5744	132	11	]	]	PUNCT
ejpam-5744	133	1	+	+	CCONJ
ejpam-5744	133	2	βk	βk	ADJ
ejpam-5744	133	3	[	[	PUNCT
ejpam-5744	133	4	g(∥ϱ−ψ(ϱ)∥	g(∥ϱ−ψ(ϱ)∥	NOUN
ejpam-5744	133	5	)	)	PUNCT
ejpam-5744	134	1	+	+	CCONJ
ejpam-5744	134	2	τ	τ	PROPN
ejpam-5744	134	3	∥∥∥(ϑk	∥∥∥(ϑk	X
ejpam-5744	134	4	+	+	CCONJ
ejpam-5744	134	5	θk	θk	PROPN
ejpam-5744	134	6	2	2	NUM
ejpam-5744	134	7	)	)	PUNCT
ejpam-5744	134	8	−	−	ADP
ejpam-5744	134	9	ϱ	ϱ	ADP
ejpam-5744	134	10	∥∥∥	∥∥∥	PROPN
ejpam-5744	134	11	]	]	X
ejpam-5744	134	12	≤	≤	NUM
ejpam-5744	134	13	(	(	PUNCT
ejpam-5744	134	14	1−	1−	NUM
ejpam-5744	134	15	βk)τ	βk)τ	PROPN
ejpam-5744	134	16	∥∥∥(ϑk	∥∥∥(ϑk	PROPN
ejpam-5744	134	17	+	+	NUM
ejpam-5744	134	18	ϱk	ϱk	ADP
ejpam-5744	134	19	2	2	NUM
ejpam-5744	134	20	)	)	PUNCT
ejpam-5744	134	21	−	−	ADP
ejpam-5744	135	1	ϱ	ϱ	ADP
ejpam-5744	135	2	∥∥∥+	∥∥∥+	PROPN
ejpam-5744	135	3	βkτ	βkτ	ADJ
ejpam-5744	135	4	∥∥∥(ϑk	∥∥∥(ϑk	NOUN
ejpam-5744	135	5	+	+	CCONJ
ejpam-5744	135	6	θk	θk	NOUN
ejpam-5744	135	7	2	2	NUM
ejpam-5744	135	8	)	)	PUNCT
ejpam-5744	135	9	−	−	ADP
ejpam-5744	135	10	ϱ	ϱ	ADP
ejpam-5744	135	11	∥∥∥	∥∥∥	PROPN
ejpam-5744	135	12	≤	≤	NUM
ejpam-5744	135	13	τ	τ	PROPN
ejpam-5744	135	14	2	2	NUM
ejpam-5744	135	15	∥ϑk	∥ϑk	NOUN
ejpam-5744	135	16	−	−	NOUN
ejpam-5744	135	17	ϱ∥+	ϱ∥+	NOUN
ejpam-5744	135	18	τ	τ	X
ejpam-5744	135	19	2	2	NUM
ejpam-5744	135	20	[	[	X
ejpam-5744	135	21	(	(	PUNCT
ejpam-5744	135	22	1−	1−	NUM
ejpam-5744	135	23	βk)∥ϱk	βk)∥ϱk	NUM
ejpam-5744	135	24	−	−	NOUN
ejpam-5744	135	25	ϱ∥+	ϱ∥+	NOUN
ejpam-5744	135	26	βk∥θk	βk∥θk	PROPN
ejpam-5744	135	27	−	−	PROPN
ejpam-5744	135	28	ϱ∥	ϱ∥	NOUN
ejpam-5744	135	29	]	]	X
ejpam-5744	135	30	,	,	PUNCT
ejpam-5744	135	31	which	which	PRON
ejpam-5744	135	32	yields	yield	VERB
ejpam-5744	135	33	into	into	ADP
ejpam-5744	135	34	∥ϑk	∥ϑk	NOUN
ejpam-5744	135	35	−	−	NOUN
ejpam-5744	136	1	ϱ∥	ϱ∥	NOUN
ejpam-5744	136	2	≤	≤	NUM
ejpam-5744	136	3	τ	τ	X
ejpam-5744	136	4	(	(	PUNCT
ejpam-5744	136	5	2−	2−	NUM
ejpam-5744	136	6	τ	τ	X
ejpam-5744	136	7	)	)	PUNCT
ejpam-5744	137	1	[	[	X
ejpam-5744	137	2	(	(	PUNCT
ejpam-5744	137	3	1−	1−	NUM
ejpam-5744	137	4	βk)∥ϱk	βk)∥ϱk	NUM
ejpam-5744	137	5	−	−	NOUN
ejpam-5744	137	6	ϱ∥+	ϱ∥+	NOUN
ejpam-5744	137	7	βk∥θk	βk∥θk	PROPN
ejpam-5744	137	8	−	−	PROPN
ejpam-5744	137	9	ϱ∥	ϱ∥	NOUN
ejpam-5744	137	10	]	]	X
ejpam-5744	137	11	.	.	PUNCT
ejpam-5744	138	1	(	(	PUNCT
ejpam-5744	138	2	16	16	X
ejpam-5744	138	3	)	)	PUNCT
ejpam-5744	138	4	combining	combine	VERB
ejpam-5744	138	5	(	(	PUNCT
ejpam-5744	138	6	15	15	NUM
ejpam-5744	138	7	)	)	PUNCT
ejpam-5744	138	8	and	and	CCONJ
ejpam-5744	138	9	(	(	PUNCT
ejpam-5744	138	10	16	16	NUM
ejpam-5744	138	11	)	)	PUNCT
ejpam-5744	138	12	,	,	PUNCT
ejpam-5744	138	13	one	one	PRON
ejpam-5744	138	14	gets	get	VERB
ejpam-5744	138	15	∥ϑk	∥ϑk	NOUN
ejpam-5744	139	1	−	−	NOUN
ejpam-5744	139	2	ϱ∥	ϱ∥	NOUN
ejpam-5744	139	3	≤	≤	NUM
ejpam-5744	139	4	τ	τ	X
ejpam-5744	140	1	(	(	PUNCT
ejpam-5744	140	2	2−	2−	NUM
ejpam-5744	140	3	τ	τ	X
ejpam-5744	140	4	)	)	PUNCT
ejpam-5744	141	1	[	[	PUNCT
ejpam-5744	141	2	1−	1−	NUM
ejpam-5744	141	3	βk	βk	ADP
ejpam-5744	141	4	(	(	PUNCT
ejpam-5744	141	5	1−	1−	NUM
ejpam-5744	141	6	εk	εk	PROPN
ejpam-5744	141	7	(	(	PUNCT
ejpam-5744	141	8	2−	2−	NUM
ejpam-5744	141	9	εk	εk	NOUN
ejpam-5744	141	10	)	)	PUNCT
ejpam-5744	141	11	)	)	PUNCT
ejpam-5744	141	12	]	]	PUNCT
ejpam-5744	141	13	∥ϱk	∥ϱk	VERB
ejpam-5744	141	14	−	−	PROPN
ejpam-5744	141	15	ϱ∥.	ϱ∥.	PROPN
ejpam-5744	141	16	(	(	PUNCT
ejpam-5744	141	17	17	17	NUM
ejpam-5744	141	18	)	)	PUNCT
ejpam-5744	141	19	m.	m.	NOUN
ejpam-5744	141	20	akram	akram	PROPN
ejpam-5744	141	21	/	/	PUNCT
ejpam-5744	141	22	eur	eur	PROPN
ejpam-5744	141	23	.	.	PUNCT
ejpam-5744	142	1	j.	j.	PROPN
ejpam-5744	142	2	pure	pure	PROPN
ejpam-5744	142	3	appl	appl	PROPN
ejpam-5744	142	4	.	.	PROPN
ejpam-5744	142	5	math	math	PROPN
ejpam-5744	142	6	,	,	PUNCT
ejpam-5744	142	7	18	18	NUM
ejpam-5744	142	8	(	(	PUNCT
ejpam-5744	142	9	1	1	NUM
ejpam-5744	142	10	)	)	PUNCT
ejpam-5744	142	11	(	(	PUNCT
ejpam-5744	142	12	2025	2025	NUM
ejpam-5744	142	13	)	)	PUNCT
ejpam-5744	142	14	,	,	PUNCT
ejpam-5744	142	15	5744	5744	NUM
ejpam-5744	142	16	7	7	NUM
ejpam-5744	142	17	of	of	ADP
ejpam-5744	142	18	19	19	NUM
ejpam-5744	142	19	further	far	ADV
ejpam-5744	142	20	,	,	PUNCT
ejpam-5744	142	21	the	the	DET
ejpam-5744	142	22	second	second	ADJ
ejpam-5744	142	23	formulation	formulation	NOUN
ejpam-5744	142	24	of	of	ADP
ejpam-5744	142	25	simps	simp	NOUN
ejpam-5744	142	26	(	(	PUNCT
ejpam-5744	142	27	14	14	NUM
ejpam-5744	142	28	)	)	PUNCT
ejpam-5744	142	29	yields	yield	NOUN
ejpam-5744	142	30	∥σk	∥σk	PART
ejpam-5744	142	31	−	−	NOUN
ejpam-5744	142	32	ϱ∥	ϱ∥	NOUN
ejpam-5744	142	33	=	=	PUNCT
ejpam-5744	142	34	∥∥∥ψ	∥∥∥ψ	NOUN
ejpam-5744	142	35	[	[	PUNCT
ejpam-5744	142	36	(	(	PUNCT
ejpam-5744	142	37	1−	1−	NUM
ejpam-5744	142	38	αk	αk	NOUN
ejpam-5744	142	39	)	)	PUNCT
ejpam-5744	142	40	(	(	PUNCT
ejpam-5744	142	41	σk	σk	CCONJ
ejpam-5744	142	42	+	+	NUM
ejpam-5744	142	43	ϑk	ϑk	PROPN
ejpam-5744	142	44	2	2	NUM
ejpam-5744	142	45	)	)	PUNCT
ejpam-5744	143	1	+	+	CCONJ
ejpam-5744	143	2	αkψ	αkψ	NOUN
ejpam-5744	143	3	(	(	PUNCT
ejpam-5744	143	4	σk	σk	PROPN
ejpam-5744	143	5	+	+	NUM
ejpam-5744	143	6	ϑk	ϑk	PROPN
ejpam-5744	143	7	2	2	NUM
ejpam-5744	143	8	)	)	PUNCT
ejpam-5744	143	9	]	]	PUNCT
ejpam-5744	144	1	−	−	PUNCT
ejpam-5744	144	2	ϱ	ϱ	ADP
ejpam-5744	144	3	∥∥∥	∥∥∥	PROPN
ejpam-5744	144	4	=	=	SYM
ejpam-5744	144	5	∥∥∥ψ(ϱ)−ψ	∥∥∥ψ(ϱ)−ψ	NOUN
ejpam-5744	144	6	[	[	PUNCT
ejpam-5744	144	7	(	(	PUNCT
ejpam-5744	144	8	1−	1−	NUM
ejpam-5744	144	9	αk	αk	NOUN
ejpam-5744	144	10	)	)	PUNCT
ejpam-5744	144	11	(	(	PUNCT
ejpam-5744	144	12	σk	σk	CCONJ
ejpam-5744	144	13	+	+	NUM
ejpam-5744	144	14	ϑk	ϑk	PROPN
ejpam-5744	144	15	2	2	NUM
ejpam-5744	144	16	)	)	PUNCT
ejpam-5744	144	17	+	+	CCONJ
ejpam-5744	144	18	αkψ	αkψ	NOUN
ejpam-5744	144	19	(	(	PUNCT
ejpam-5744	144	20	σk	σk	PROPN
ejpam-5744	144	21	+	+	NUM
ejpam-5744	144	22	ϑk	ϑk	PROPN
ejpam-5744	144	23	2	2	NUM
ejpam-5744	144	24	)	)	PUNCT
ejpam-5744	144	25	]	]	PUNCT
ejpam-5744	144	26	∥∥∥	∥∥∥	X
ejpam-5744	144	27	≤	≤	NUM
ejpam-5744	144	28	g(∥ϱ−ψ(ϱ)∥	g(∥ϱ−ψ(ϱ)∥	NOUN
ejpam-5744	144	29	)	)	PUNCT
ejpam-5744	145	1	+	+	CCONJ
ejpam-5744	145	2	τ	τ	X
ejpam-5744	145	3	∥∥∥[(1−	∥∥∥[(1−	PROPN
ejpam-5744	145	4	αk	αk	NOUN
ejpam-5744	145	5	)	)	PUNCT
ejpam-5744	145	6	(	(	PUNCT
ejpam-5744	145	7	σk	σk	CCONJ
ejpam-5744	145	8	+	+	NUM
ejpam-5744	145	9	ϑk	ϑk	PROPN
ejpam-5744	145	10	2	2	NUM
ejpam-5744	145	11	)	)	PUNCT
ejpam-5744	146	1	+	+	CCONJ
ejpam-5744	146	2	αkψ	αkψ	NOUN
ejpam-5744	146	3	(	(	PUNCT
ejpam-5744	146	4	σk	σk	PROPN
ejpam-5744	146	5	+	+	NUM
ejpam-5744	146	6	ϑk	ϑk	PROPN
ejpam-5744	146	7	2	2	NUM
ejpam-5744	146	8	)	)	PUNCT
ejpam-5744	146	9	]	]	PUNCT
ejpam-5744	147	1	−	−	PUNCT
ejpam-5744	147	2	ϱ	ϱ	ADP
ejpam-5744	147	3	∥∥∥	∥∥∥	PROPN
ejpam-5744	147	4	≤	≤	NOUN
ejpam-5744	147	5	τ(1−	τ(1−	ADP
ejpam-5744	147	6	αk	αk	NOUN
ejpam-5744	147	7	)	)	PUNCT
ejpam-5744	147	8	∥∥∥(σk	∥∥∥(σk	PROPN
ejpam-5744	147	9	+	+	CCONJ
ejpam-5744	147	10	ϑk	ϑk	PROPN
ejpam-5744	147	11	2	2	NUM
ejpam-5744	147	12	)	)	PUNCT
ejpam-5744	147	13	−	−	ADP
ejpam-5744	147	14	ϱ	ϱ	ADP
ejpam-5744	147	15	∥∥∥+	∥∥∥+	PROPN
ejpam-5744	147	16	ταk	ταk	NOUN
ejpam-5744	147	17	∥∥∥ψ(ϱ)−ψ	∥∥∥ψ(ϱ)−ψ	NOUN
ejpam-5744	147	18	(	(	PUNCT
ejpam-5744	147	19	σk	σk	PROPN
ejpam-5744	147	20	+	+	NUM
ejpam-5744	147	21	ϑk	ϑk	PROPN
ejpam-5744	147	22	2	2	NUM
ejpam-5744	147	23	)	)	PUNCT
ejpam-5744	147	24	∥∥∥	∥∥∥	PROPN
ejpam-5744	147	25	≤	≤	PUNCT
ejpam-5744	148	1	τ	τ	PUNCT
ejpam-5744	149	1	[	[	X
ejpam-5744	149	2	1−	1−	NUM
ejpam-5744	149	3	αk(1−	αk(1−	PROPN
ejpam-5744	149	4	τ	τ	PROPN
ejpam-5744	149	5	)	)	PUNCT
ejpam-5744	149	6	]	]	PUNCT
ejpam-5744	150	1	∥∥∥(σk	∥∥∥(σk	PROPN
ejpam-5744	150	2	+	+	CCONJ
ejpam-5744	150	3	ϑk	ϑk	PROPN
ejpam-5744	150	4	2	2	NUM
ejpam-5744	150	5	)	)	PUNCT
ejpam-5744	150	6	−	−	ADP
ejpam-5744	150	7	ϱ	ϱ	ADP
ejpam-5744	150	8	∥∥∥	∥∥∥	PROPN
ejpam-5744	150	9	=	=	PUNCT
ejpam-5744	150	10	πk	πk	ADP
ejpam-5744	150	11	2	2	NUM
ejpam-5744	151	1	[	[	X
ejpam-5744	151	2	∥σk	∥σk	NOUN
ejpam-5744	151	3	−	−	NOUN
ejpam-5744	151	4	ϱ∥+	ϱ∥+	NOUN
ejpam-5744	151	5	∥ϑk	∥ϑk	NOUN
ejpam-5744	151	6	−	−	NOUN
ejpam-5744	151	7	ϱ∥	ϱ∥	NOUN
ejpam-5744	151	8	]	]	PUNCT
ejpam-5744	151	9	.	.	PUNCT
ejpam-5744	152	1	thus	thus	ADV
ejpam-5744	152	2	,	,	PUNCT
ejpam-5744	152	3	we	we	PRON
ejpam-5744	152	4	acquire	acquire	VERB
ejpam-5744	152	5	∥σk	∥σk	NOUN
ejpam-5744	152	6	−	−	PROPN
ejpam-5744	152	7	ϱ∥	ϱ∥	NOUN
ejpam-5744	152	8	≤	≤	NUM
ejpam-5744	152	9	πk	πk	ADP
ejpam-5744	152	10	(	(	PUNCT
ejpam-5744	152	11	2−	2−	NUM
ejpam-5744	152	12	πk	πk	NOUN
ejpam-5744	152	13	)	)	PUNCT
ejpam-5744	152	14	∥ϑk	∥ϑk	NOUN
ejpam-5744	152	15	−	−	NOUN
ejpam-5744	152	16	ϱ∥	ϱ∥	NOUN
ejpam-5744	152	17	,	,	PUNCT
ejpam-5744	152	18	(	(	PUNCT
ejpam-5744	152	19	18	18	NUM
ejpam-5744	152	20	)	)	PUNCT
ejpam-5744	152	21	where	where	SCONJ
ejpam-5744	152	22	πk	πk	VERB
ejpam-5744	152	23	=	=	SYM
ejpam-5744	152	24	τ	τ	PROPN
ejpam-5744	153	1	[	[	X
ejpam-5744	153	2	1−αk(1−	1−αk(1−	NUM
ejpam-5744	153	3	τ	τ	X
ejpam-5744	153	4	)	)	PUNCT
ejpam-5744	153	5	]	]	PUNCT
ejpam-5744	153	6	.	.	PUNCT
ejpam-5744	154	1	the	the	DET
ejpam-5744	154	2	straightforward	straightforward	ADJ
ejpam-5744	154	3	calculation	calculation	NOUN
ejpam-5744	154	4	after	after	ADP
ejpam-5744	154	5	taking	take	VERB
ejpam-5744	154	6	the	the	DET
ejpam-5744	154	7	assumptions	assumption	NOUN
ejpam-5744	154	8	{	{	PUNCT
ejpam-5744	154	9	αk}∞k=1	αk}∞k=1	NUM
ejpam-5744	154	10	∈	∈	PROPN
ejpam-5744	154	11	(	(	PUNCT
ejpam-5744	154	12	0	0	NUM
ejpam-5744	154	13	,	,	PUNCT
ejpam-5744	154	14	1	1	NUM
ejpam-5744	154	15	)	)	PUNCT
ejpam-5744	154	16	,	,	PUNCT
ejpam-5744	154	17	τ	τ	PROPN
ejpam-5744	154	18	∈	∈	PROPN
ejpam-5744	155	1	[	[	X
ejpam-5744	155	2	0	0	NUM
ejpam-5744	155	3	,	,	PUNCT
ejpam-5744	155	4	1	1	NUM
ejpam-5744	155	5	)	)	PUNCT
ejpam-5744	155	6	and	and	CCONJ
ejpam-5744	155	7	(	(	PUNCT
ejpam-5744	155	8	17	17	NUM
ejpam-5744	155	9	)	)	PUNCT
ejpam-5744	155	10	into	into	ADP
ejpam-5744	155	11	play	play	NOUN
ejpam-5744	155	12	leads	lead	VERB
ejpam-5744	155	13	εk	εk	PROPN
ejpam-5744	155	14	∈	∈	PROPN
ejpam-5744	156	1	[	[	X
ejpam-5744	156	2	0	0	NUM
ejpam-5744	156	3	,	,	PUNCT
ejpam-5744	156	4	1	1	NUM
ejpam-5744	156	5	)	)	PUNCT
ejpam-5744	156	6	.	.	PUNCT
ejpam-5744	157	1	thus	thus	ADV
ejpam-5744	157	2	,	,	PUNCT
ejpam-5744	157	3	we	we	PRON
ejpam-5744	157	4	acquire	acquire	VERB
ejpam-5744	157	5	1	1	NUM
ejpam-5744	157	6	−	−	NOUN
ejpam-5744	157	7	βk	βk	ADP
ejpam-5744	157	8	(	(	PUNCT
ejpam-5744	157	9	1−	1−	NUM
ejpam-5744	157	10	εk	εk	PROPN
ejpam-5744	157	11	2−	2−	NUM
ejpam-5744	157	12	εk	εk	NOUN
ejpam-5744	157	13	)	)	PUNCT
ejpam-5744	157	14	≤	≤	NUM
ejpam-5744	157	15	1	1	NUM
ejpam-5744	157	16	and	and	CCONJ
ejpam-5744	157	17	hence	hence	ADV
ejpam-5744	157	18	,	,	PUNCT
ejpam-5744	157	19	∥σk	∥σk	NOUN
ejpam-5744	157	20	−	−	NOUN
ejpam-5744	157	21	ϱ∥	ϱ∥	NOUN
ejpam-5744	157	22	≤	≤	NUM
ejpam-5744	157	23	πk	πk	ADP
ejpam-5744	157	24	(	(	PUNCT
ejpam-5744	157	25	2−	2−	NUM
ejpam-5744	157	26	πk	πk	NOUN
ejpam-5744	157	27	)	)	PUNCT
ejpam-5744	157	28	τ	τ	PROPN
ejpam-5744	157	29	(	(	PUNCT
ejpam-5744	157	30	2−	2−	NUM
ejpam-5744	157	31	τ	τ	NOUN
ejpam-5744	157	32	)	)	PUNCT
ejpam-5744	157	33	∥ϱk	∥ϱk	PROPN
ejpam-5744	157	34	−	−	PROPN
ejpam-5744	157	35	ϱ∥.	ϱ∥.	PROPN
ejpam-5744	157	36	(	(	PUNCT
ejpam-5744	157	37	19	19	NUM
ejpam-5744	157	38	)	)	PUNCT
ejpam-5744	157	39	finally	finally	ADV
ejpam-5744	157	40	,	,	PUNCT
ejpam-5744	157	41	the	the	DET
ejpam-5744	157	42	first	first	ADJ
ejpam-5744	157	43	formulation	formulation	NOUN
ejpam-5744	157	44	of	of	ADP
ejpam-5744	157	45	simps	simp	NOUN
ejpam-5744	157	46	(	(	PUNCT
ejpam-5744	157	47	14	14	NUM
ejpam-5744	157	48	)	)	PUNCT
ejpam-5744	157	49	along	along	ADP
ejpam-5744	157	50	with	with	ADP
ejpam-5744	157	51	(	(	PUNCT
ejpam-5744	157	52	19	19	NUM
ejpam-5744	157	53	)	)	PUNCT
ejpam-5744	157	54	turns	turn	VERB
ejpam-5744	157	55	into	into	ADP
ejpam-5744	157	56	∥ϱk+1	∥ϱk+1	PRON
ejpam-5744	157	57	−	−	PROPN
ejpam-5744	157	58	ϱ∥	ϱ∥	NOUN
ejpam-5744	157	59	=	=	SYM
ejpam-5744	157	60	∥ψ(σk)−	∥ψ(σk)−	PROPN
ejpam-5744	157	61	ϱ∥	ϱ∥	NOUN
ejpam-5744	157	62	=	=	SYM
ejpam-5744	157	63	∥ψ(ϱ)−ψ(σk)∥	∥ψ(ϱ)−ψ(σk)∥	VERB
ejpam-5744	157	64	≤	≤	NUM
ejpam-5744	157	65	g(∥ϱ−ψ(ϱ)∥	g(∥ϱ−ψ(ϱ)∥	NOUN
ejpam-5744	157	66	)	)	PUNCT
ejpam-5744	157	67	+	+	CCONJ
ejpam-5744	158	1	τ∥σk	τ∥σk	NOUN
ejpam-5744	158	2	−	−	NOUN
ejpam-5744	158	3	ϱ∥	ϱ∥	NOUN
ejpam-5744	158	4	≤	≤	NUM
ejpam-5744	158	5	(	(	PUNCT
ejpam-5744	158	6	1−	1−	NUM
ejpam-5744	158	7	ℓ̂k)∥ϱk	ℓ̂k)∥ϱk	PROPN
ejpam-5744	158	8	−	−	PROPN
ejpam-5744	158	9	ϱ∥	ϱ∥	NOUN
ejpam-5744	158	10	,	,	PUNCT
ejpam-5744	158	11	(	(	PUNCT
ejpam-5744	158	12	20	20	NUM
ejpam-5744	158	13	)	)	PUNCT
ejpam-5744	158	14	where	where	SCONJ
ejpam-5744	158	15	,	,	PUNCT
ejpam-5744	158	16	ℓ̂k	ℓ̂k	PROPN
ejpam-5744	158	17	=	=	SYM
ejpam-5744	158	18	(	(	PUNCT
ejpam-5744	158	19	2−	2−	NUM
ejpam-5744	158	20	τ)(2−	τ)(2−	NOUN
ejpam-5744	158	21	πk)−	πk)−	NOUN
ejpam-5744	158	22	τ2πk	τ2πk	PUNCT
ejpam-5744	158	23	(	(	PUNCT
ejpam-5744	158	24	2−	2−	NUM
ejpam-5744	158	25	τ)(2−	τ)(2−	NOUN
ejpam-5744	158	26	πk	πk	PROPN
ejpam-5744	158	27	)	)	PUNCT
ejpam-5744	158	28	.	.	PUNCT
ejpam-5744	159	1	(	(	PUNCT
ejpam-5744	159	2	21	21	NUM
ejpam-5744	159	3	)	)	PUNCT
ejpam-5744	159	4	since	since	SCONJ
ejpam-5744	159	5	πk	πk	PROPN
ejpam-5744	159	6	=	=	SYM
ejpam-5744	159	7	τ(1−αk+	τ(1−αk+	PROPN
ejpam-5744	159	8	ταk	ταk	PROPN
ejpam-5744	159	9	)	)	PUNCT
ejpam-5744	159	10	,	,	PUNCT
ejpam-5744	159	11	τ	τ	PROPN
ejpam-5744	159	12	∈	∈	PROPN
ejpam-5744	160	1	[	[	X
ejpam-5744	160	2	0	0	NUM
ejpam-5744	160	3	,	,	PUNCT
ejpam-5744	160	4	1	1	NUM
ejpam-5744	160	5	)	)	PUNCT
ejpam-5744	160	6	and	and	CCONJ
ejpam-5744	160	7	{	{	PUNCT
ejpam-5744	160	8	αk}∞k=1	αk}∞k=1	NUM
ejpam-5744	160	9	⊆	⊆	NUM
ejpam-5744	160	10	(	(	PUNCT
ejpam-5744	160	11	0	0	NUM
ejpam-5744	160	12	,	,	PUNCT
ejpam-5744	160	13	1	1	X
ejpam-5744	160	14	)	)	PUNCT
ejpam-5744	160	15	yields	yield	NOUN
ejpam-5744	160	16	πk	πk	ADP
ejpam-5744	160	17	≤	≤	NUM
ejpam-5744	160	18	τ	τ	X
ejpam-5744	160	19	.	.	PUNCT
ejpam-5744	161	1	thus	thus	ADV
ejpam-5744	161	2	,	,	PUNCT
ejpam-5744	161	3	we	we	PRON
ejpam-5744	161	4	obtain	obtain	VERB
ejpam-5744	161	5	ℓ̂k	ℓ̂k	NUM
ejpam-5744	161	6	≥	≥	NOUN
ejpam-5744	161	7	1	1	NUM
ejpam-5744	161	8	4	4	NUM
ejpam-5744	161	9	[	[	X
ejpam-5744	161	10	(	(	PUNCT
ejpam-5744	161	11	2−	2−	NUM
ejpam-5744	161	12	τ)(2−	τ)(2−	NOUN
ejpam-5744	161	13	πk)−	πk)−	NOUN
ejpam-5744	161	14	τ2πk	τ2πk	NUM
ejpam-5744	161	15	]	]	PUNCT
ejpam-5744	161	16	≥	≥	NOUN
ejpam-5744	161	17	1	1	NUM
ejpam-5744	161	18	4	4	NUM
ejpam-5744	161	19	[	[	SYM
ejpam-5744	161	20	1	1	NUM
ejpam-5744	161	21	+	+	CCONJ
ejpam-5744	161	22	(	(	PUNCT
ejpam-5744	161	23	1−	1−	NUM
ejpam-5744	161	24	τ)][1	τ)][1	NOUN
ejpam-5744	161	25	+	+	CCONJ
ejpam-5744	161	26	(	(	PUNCT
ejpam-5744	161	27	1−	1−	NUM
ejpam-5744	161	28	τ)]−	τ)]−	NOUN
ejpam-5744	161	29	τ3	τ3	NOUN
ejpam-5744	161	30	>	>	X
ejpam-5744	161	31	0	0	X
ejpam-5744	161	32	.	.	PUNCT
ejpam-5744	162	1	further	far	ADV
ejpam-5744	162	2	,	,	PUNCT
ejpam-5744	162	3	1	1	NUM
ejpam-5744	162	4	−	−	NUM
ejpam-5744	162	5	ℓ̂k	ℓ̂k	NUM
ejpam-5744	162	6	=	=	SYM
ejpam-5744	162	7	τ2πk	τ2πk	PUNCT
ejpam-5744	162	8	(	(	PUNCT
ejpam-5744	162	9	2−	2−	NUM
ejpam-5744	162	10	τ)(2−	τ)(2−	PROPN
ejpam-5744	162	11	πk	πk	PROPN
ejpam-5744	162	12	)	)	PUNCT
ejpam-5744	162	13	≥	≥	NOUN
ejpam-5744	162	14	0	0	NUM
ejpam-5744	162	15	and	and	CCONJ
ejpam-5744	162	16	∞∑	∞∑	PRON
ejpam-5744	162	17	k=0	k=0	PROPN
ejpam-5744	162	18	ℓ̂k	ℓ̂k	PROPN
ejpam-5744	163	1	=	=	SYM
ejpam-5744	163	2	∞.	∞.	PROPN
ejpam-5744	163	3	utilizing	utilize	VERB
ejpam-5744	163	4	lemma	lemma	PROPN
ejpam-5744	163	5	1	1	NUM
ejpam-5744	163	6	,	,	PUNCT
ejpam-5744	163	7	it	it	PRON
ejpam-5744	163	8	follows	follow	VERB
ejpam-5744	163	9	from	from	ADP
ejpam-5744	163	10	(	(	PUNCT
ejpam-5744	163	11	20	20	NUM
ejpam-5744	163	12	)	)	PUNCT
ejpam-5744	163	13	that	that	PRON
ejpam-5744	163	14	lim	lim	PROPN
ejpam-5744	163	15	k→∞	k→∞	PROPN
ejpam-5744	163	16	∥ϱk	∥ϱk	PROPN
ejpam-5744	164	1	−	−	PROPN
ejpam-5744	164	2	ϱ∥	ϱ∥	NOUN
ejpam-5744	164	3	=	=	NOUN
ejpam-5744	164	4	0	0	X
ejpam-5744	164	5	.	.	PUNCT
ejpam-5744	165	1	next	next	ADV
ejpam-5744	165	2	,	,	PUNCT
ejpam-5744	165	3	we	we	PRON
ejpam-5744	165	4	manifest	manifest	VERB
ejpam-5744	165	5	the	the	DET
ejpam-5744	165	6	uniqueness	uniqueness	NOUN
ejpam-5744	165	7	of	of	ADP
ejpam-5744	165	8	ϱ	ϱ	NOUN
ejpam-5744	165	9	,	,	PUNCT
ejpam-5744	165	10	suppose	suppose	VERB
ejpam-5744	165	11	that	that	SCONJ
ejpam-5744	165	12	m.	m.	PROPN
ejpam-5744	165	13	akram	akram	PROPN
ejpam-5744	165	14	/	/	PUNCT
ejpam-5744	165	15	eur	eur	PROPN
ejpam-5744	165	16	.	.	PUNCT
ejpam-5744	166	1	j.	j.	PROPN
ejpam-5744	166	2	pure	pure	PROPN
ejpam-5744	166	3	appl	appl	PROPN
ejpam-5744	166	4	.	.	PROPN
ejpam-5744	166	5	math	math	PROPN
ejpam-5744	166	6	,	,	PUNCT
ejpam-5744	166	7	18	18	NUM
ejpam-5744	166	8	(	(	PUNCT
ejpam-5744	166	9	1	1	NUM
ejpam-5744	166	10	)	)	PUNCT
ejpam-5744	166	11	(	(	PUNCT
ejpam-5744	166	12	2025	2025	NUM
ejpam-5744	166	13	)	)	PUNCT
ejpam-5744	166	14	,	,	PUNCT
ejpam-5744	166	15	5744	5744	NUM
ejpam-5744	166	16	8	8	NUM
ejpam-5744	166	17	of	of	ADP
ejpam-5744	166	18	19	19	NUM
ejpam-5744	166	19	ϱ1	ϱ1	NOUN
ejpam-5744	166	20	,	,	PUNCT
ejpam-5744	166	21	ϱ2	ϱ2	NOUN
ejpam-5744	166	22	∈	∈	PROPN
ejpam-5744	167	1	ω	ω	NUM
ejpam-5744	168	1	so	so	SCONJ
ejpam-5744	168	2	that	that	SCONJ
ejpam-5744	168	3	ϱ1	ϱ1	PROPN
ejpam-5744	168	4	̸=	̸=	PROPN
ejpam-5744	168	5	ϱ2	ϱ2	NOUN
ejpam-5744	168	6	and	and	CCONJ
ejpam-5744	168	7	ϱ1	ϱ1	NOUN
ejpam-5744	168	8	,	,	PUNCT
ejpam-5744	168	9	ϱ2	ϱ2	NOUN
ejpam-5744	168	10	∈	∈	PROPN
ejpam-5744	168	11	ξ(ψ	ξ(ψ	PROPN
ejpam-5744	168	12	)	)	PUNCT
ejpam-5744	168	13	.	.	PUNCT
ejpam-5744	169	1	then	then	ADV
ejpam-5744	169	2	∥ϱ1	∥ϱ1	VERB
ejpam-5744	169	3	−	−	PROPN
ejpam-5744	169	4	ϱ2∥	ϱ2∥	PROPN
ejpam-5744	169	5	=	=	PUNCT
ejpam-5744	169	6	∥ψ(ϱ1)−ψ(ϱ2)∥	∥ψ(ϱ1)−ψ(ϱ2)∥	PROPN
ejpam-5744	169	7	≤	≤	NUM
ejpam-5744	169	8	g(∥ϱ1	g(∥ϱ1	NOUN
ejpam-5744	169	9	−ψ(ϱ1)∥	−ψ(ϱ1)∥	PROPN
ejpam-5744	169	10	)	)	PUNCT
ejpam-5744	169	11	+	+	CCONJ
ejpam-5744	169	12	τ∥ϱ1	τ∥ϱ1	PUNCT
ejpam-5744	170	1	−	−	PROPN
ejpam-5744	170	2	ϱ2∥	ϱ2∥	NOUN
ejpam-5744	170	3	=	=	PUNCT
ejpam-5744	170	4	τ∥ϱ1	τ∥ϱ1	PUNCT
ejpam-5744	170	5	−	−	NUM
ejpam-5744	170	6	ϱ2∥.	ϱ2∥.	NOUN
ejpam-5744	170	7	(	(	PUNCT
ejpam-5744	170	8	22	22	NUM
ejpam-5744	170	9	)	)	PUNCT
ejpam-5744	170	10	since	since	SCONJ
ejpam-5744	170	11	τ	τ	X
ejpam-5744	170	12	∈	∈	PROPN
ejpam-5744	171	1	[	[	X
ejpam-5744	171	2	0	0	NUM
ejpam-5744	171	3	,	,	PUNCT
ejpam-5744	171	4	1	1	NUM
ejpam-5744	171	5	)	)	PUNCT
ejpam-5744	171	6	,	,	PUNCT
ejpam-5744	171	7	then	then	ADV
ejpam-5744	171	8	(	(	PUNCT
ejpam-5744	171	9	22	22	NUM
ejpam-5744	171	10	)	)	PUNCT
ejpam-5744	171	11	gives	give	VERB
ejpam-5744	171	12	∥ϱ1	∥ϱ1	NOUN
ejpam-5744	171	13	−	−	PROPN
ejpam-5744	171	14	ϱ2∥	ϱ2∥	NOUN
ejpam-5744	171	15	=	=	PUNCT
ejpam-5744	171	16	0	0	NUM
ejpam-5744	171	17	and	and	CCONJ
ejpam-5744	171	18	consequently	consequently	ADV
ejpam-5744	171	19	ϱ1	ϱ1	PROPN
ejpam-5744	171	20	=	=	SYM
ejpam-5744	171	21	ϱ2	ϱ2	NOUN
ejpam-5744	171	22	.	.	PUNCT
ejpam-5744	172	1	theorem	theorem	NOUN
ejpam-5744	172	2	3	3	X
ejpam-5744	172	3	.	.	PUNCT
ejpam-5744	172	4	suppose	suppose	VERB
ejpam-5744	172	5	that	that	SCONJ
ejpam-5744	172	6	∅	∅	NOUN
ejpam-5744	172	7	=	=	NOUN
ejpam-5744	172	8	̸	̸	NUM
ejpam-5744	172	9	ω	ω	NOUN
ejpam-5744	172	10	⊆	⊆	NUM
ejpam-5744	172	11	x	x	X
ejpam-5744	172	12	is	be	AUX
ejpam-5744	172	13	a	a	DET
ejpam-5744	172	14	closed	closed	ADJ
ejpam-5744	172	15	convex	convex	NOUN
ejpam-5744	172	16	bounded	bound	VERB
ejpam-5744	172	17	set	set	NOUN
ejpam-5744	172	18	and	and	CCONJ
ejpam-5744	172	19	the	the	DET
ejpam-5744	172	20	mapping	mapping	NOUN
ejpam-5744	172	21	ψ	ψ	X
ejpam-5744	172	22	:	:	PUNCT
ejpam-5744	172	23	ω	ω	PROPN
ejpam-5744	172	24	→	→	SYM
ejpam-5744	172	25	ω	ω	NUM
ejpam-5744	172	26	satisfies	satisfie	NOUN
ejpam-5744	172	27	(	(	PUNCT
ejpam-5744	172	28	2	2	NUM
ejpam-5744	172	29	)	)	PUNCT
ejpam-5744	172	30	.	.	PUNCT
ejpam-5744	173	1	if	if	SCONJ
ejpam-5744	173	2	ϱ	ϱ	PROPN
ejpam-5744	173	3	∈	∈	PROPN
ejpam-5744	173	4	ξ(ψ	ξ(ψ	PROPN
ejpam-5744	173	5	)	)	PUNCT
ejpam-5744	173	6	,	,	PUNCT
ejpam-5744	173	7	then	then	ADV
ejpam-5744	173	8	{	{	PUNCT
ejpam-5744	173	9	ϱk}∞k=1	ϱk}∞k=1	PUNCT
ejpam-5744	173	10	initiated	initiate	VERB
ejpam-5744	173	11	by	by	ADP
ejpam-5744	173	12	simps	simp	NOUN
ejpam-5744	173	13	(	(	PUNCT
ejpam-5744	173	14	14	14	NUM
ejpam-5744	173	15	)	)	PUNCT
ejpam-5744	173	16	is	be	AUX
ejpam-5744	173	17	ψ	ψ	VERB
ejpam-5744	173	18	-	-	ADJ
ejpam-5744	173	19	stable	stable	ADJ
ejpam-5744	173	20	.	.	PUNCT
ejpam-5744	174	1	proof	proof	NOUN
ejpam-5744	174	2	.	.	PUNCT
ejpam-5744	175	1	let	let	AUX
ejpam-5744	175	2	{	{	PUNCT
ejpam-5744	175	3	φk	φk	ADP
ejpam-5744	175	4	}	}	PUNCT
ejpam-5744	175	5	⊂	⊂	PROPN
ejpam-5744	175	6	ω	ω	NOUN
ejpam-5744	175	7	be	be	AUX
ejpam-5744	175	8	an	an	DET
ejpam-5744	175	9	arbitrary	arbitrary	ADJ
ejpam-5744	175	10	sequence	sequence	NOUN
ejpam-5744	175	11	and	and	CCONJ
ejpam-5744	175	12	{	{	PUNCT
ejpam-5744	175	13	ϱk}∞k=1	ϱk}∞k=1	X
ejpam-5744	175	14	initiated	initiate	VERB
ejpam-5744	175	15	by	by	ADP
ejpam-5744	175	16	simps	simp	NOUN
ejpam-5744	175	17	(	(	PUNCT
ejpam-5744	175	18	14	14	NUM
ejpam-5744	175	19	)	)	PUNCT
ejpam-5744	175	20	is	be	AUX
ejpam-5744	175	21	ϱk+1	ϱk+1	VERB
ejpam-5744	175	22	=	=	PUNCT
ejpam-5744	175	23	λ(ψ	λ(ψ	PROPN
ejpam-5744	175	24	,	,	PUNCT
ejpam-5744	175	25	ϱk	ϱk	NOUN
ejpam-5744	175	26	)	)	PUNCT
ejpam-5744	175	27	such	such	ADJ
ejpam-5744	175	28	as	as	ADP
ejpam-5744	175	29	{	{	PUNCT
ejpam-5744	175	30	ϱk	ϱk	NOUN
ejpam-5744	175	31	}	}	PUNCT
ejpam-5744	175	32	→	→	SYM
ejpam-5744	175	33	ϱ	ϱ	PROPN
ejpam-5744	175	34	∈	∈	PROPN
ejpam-5744	175	35	ξ(ψ	ξ(ψ	NUM
ejpam-5744	175	36	)	)	PUNCT
ejpam-5744	175	37	.	.	PUNCT
ejpam-5744	176	1	suppose	suppose	VERB
ejpam-5744	176	2	that	that	SCONJ
ejpam-5744	176	3	µk	µk	PRON
ejpam-5744	176	4	=	=	NOUN
ejpam-5744	176	5	∥φk+1	∥φk+1	ADP
ejpam-5744	176	6	−	−	PROPN
ejpam-5744	176	7	λ(ψ	λ(ψ	PROPN
ejpam-5744	176	8	,	,	PUNCT
ejpam-5744	176	9	φk)∥	φk)∥	NOUN
ejpam-5744	176	10	,	,	PUNCT
ejpam-5744	176	11	where	where	SCONJ
ejpam-5744	176	12	{	{	PUNCT
ejpam-5744	176	13	φk	φk	ADP
ejpam-5744	176	14	}	}	PUNCT
ejpam-5744	176	15	is	be	AUX
ejpam-5744	176	16	initiated	initiate	VERB
ejpam-5744	176	17	as	as	ADP
ejpam-5744	176	18	under:	under:	PROPN
ejpam-5744	176	19	φk+1	φk+1	NOUN
ejpam-5744	176	20	=	=	SYM
ejpam-5744	176	21	ψ(ζk	ψ(ζk	PROPN
ejpam-5744	176	22	)	)	PUNCT
ejpam-5744	176	23	,	,	PUNCT
ejpam-5744	176	24	ζk	ζk	PROPN
ejpam-5744	176	25	=	=	SYM
ejpam-5744	176	26	ψ	ψ	X
ejpam-5744	176	27	[	[	PUNCT
ejpam-5744	176	28	(	(	PUNCT
ejpam-5744	176	29	1−	1−	NUM
ejpam-5744	176	30	αk	αk	NOUN
ejpam-5744	176	31	)	)	PUNCT
ejpam-5744	176	32	(	(	PUNCT
ejpam-5744	176	33	ζk	ζk	X
ejpam-5744	176	34	+	+	X
ejpam-5744	176	35	ξk	ξk	ADP
ejpam-5744	176	36	2	2	NUM
ejpam-5744	176	37	)	)	PUNCT
ejpam-5744	177	1	+	+	CCONJ
ejpam-5744	177	2	αkψ	αkψ	INTJ
ejpam-5744	177	3	(	(	PUNCT
ejpam-5744	177	4	ζk	ζk	PROPN
ejpam-5744	177	5	+	+	X
ejpam-5744	177	6	ξk	ξk	ADP
ejpam-5744	177	7	2	2	NUM
ejpam-5744	177	8	)	)	PUNCT
ejpam-5744	177	9	]	]	PUNCT
ejpam-5744	177	10	,	,	PUNCT
ejpam-5744	177	11	ξk	ξk	ADV
ejpam-5744	177	12	=	=	SYM
ejpam-5744	177	13	(	(	PUNCT
ejpam-5744	177	14	1−	1−	NUM
ejpam-5744	177	15	βk)ψ	βk)ψ	NUM
ejpam-5744	177	16	(	(	PUNCT
ejpam-5744	177	17	ξk	ξk	ADP
ejpam-5744	177	18	+	+	CCONJ
ejpam-5744	177	19	φk	φk	ADP
ejpam-5744	177	20	2	2	NUM
ejpam-5744	177	21	)	)	PUNCT
ejpam-5744	178	1	+	+	CCONJ
ejpam-5744	178	2	βkψ	βkψ	X
ejpam-5744	178	3	(	(	PUNCT
ejpam-5744	178	4	ξk	ξk	ADP
ejpam-5744	178	5	+	+	CCONJ
ejpam-5744	178	6	ωk	ωk	ADP
ejpam-5744	178	7	2	2	NUM
ejpam-5744	178	8	)	)	PUNCT
ejpam-5744	178	9	,	,	PUNCT
ejpam-5744	178	10	ωk	ωk	ADP
ejpam-5744	178	11	=	=	SYM
ejpam-5744	178	12	(	(	PUNCT
ejpam-5744	178	13	1−	1−	NUM
ejpam-5744	178	14	γk	γk	NOUN
ejpam-5744	178	15	)	)	PUNCT
ejpam-5744	178	16	(	(	PUNCT
ejpam-5744	178	17	φk	φk	ADP
ejpam-5744	178	18	+	+	X
ejpam-5744	178	19	ωk	ωk	ADP
ejpam-5744	178	20	2	2	NUM
ejpam-5744	178	21	)	)	PUNCT
ejpam-5744	178	22	+	+	CCONJ
ejpam-5744	178	23	γkψ	γkψ	NOUN
ejpam-5744	178	24	(	(	PUNCT
ejpam-5744	178	25	φk	φk	ADP
ejpam-5744	178	26	+	+	X
ejpam-5744	178	27	ωk	ωk	ADP
ejpam-5744	178	28	2	2	NUM
ejpam-5744	178	29	)	)	PUNCT
ejpam-5744	178	30	]	]	PUNCT
ejpam-5744	178	31	.	.	PUNCT
ejpam-5744	179	1	(	(	PUNCT
ejpam-5744	179	2	23	23	NUM
ejpam-5744	179	3	)	)	PUNCT
ejpam-5744	179	4	to	to	PART
ejpam-5744	179	5	establish	establish	VERB
ejpam-5744	179	6	the	the	DET
ejpam-5744	179	7	ψ	ψ	NOUN
ejpam-5744	179	8	-	-	NOUN
ejpam-5744	179	9	stability	stability	NOUN
ejpam-5744	179	10	of	of	ADP
ejpam-5744	179	11	the	the	DET
ejpam-5744	179	12	scheme	scheme	NOUN
ejpam-5744	179	13	(	(	PUNCT
ejpam-5744	179	14	14	14	NUM
ejpam-5744	179	15	)	)	PUNCT
ejpam-5744	179	16	,	,	PUNCT
ejpam-5744	179	17	we	we	PRON
ejpam-5744	179	18	corroborate	corroborate	VERB
ejpam-5744	179	19	lim	lim	PROPN
ejpam-5744	179	20	k→∞	k→∞	NOUN
ejpam-5744	179	21	µk	µk	NOUN
ejpam-5744	180	1	=	=	NOUN
ejpam-5744	180	2	0	0	PUNCT
ejpam-5744	181	1	if	if	SCONJ
ejpam-5744	181	2	and	and	CCONJ
ejpam-5744	181	3	only	only	ADV
ejpam-5744	181	4	if	if	SCONJ
ejpam-5744	181	5	lim	lim	PROPN
ejpam-5744	181	6	k→∞	k→∞	NOUN
ejpam-5744	181	7	φk	φk	ADP
ejpam-5744	181	8	=	=	ADJ
ejpam-5744	181	9	ϱ.	ϱ.	NOUN
ejpam-5744	181	10	assume	assume	VERB
ejpam-5744	181	11	that	that	SCONJ
ejpam-5744	181	12	lim	lim	PROPN
ejpam-5744	181	13	k→∞	k→∞	NOUN
ejpam-5744	181	14	µk	µk	NOUN
ejpam-5744	181	15	=	=	NOUN
ejpam-5744	181	16	0	0	NUM
ejpam-5744	181	17	.	.	PUNCT
ejpam-5744	181	18	by	by	ADP
ejpam-5744	181	19	utilizing	utilize	VERB
ejpam-5744	181	20	the	the	DET
ejpam-5744	181	21	triangle	triangle	NOUN
ejpam-5744	181	22	inequality	inequality	NOUN
ejpam-5744	181	23	,	,	PUNCT
ejpam-5744	181	24	we	we	PRON
ejpam-5744	181	25	acquire	acquire	VERB
ejpam-5744	181	26	∥φk+1	∥φk+1	ADP
ejpam-5744	181	27	−	−	PROPN
ejpam-5744	181	28	ϱ∥	ϱ∥	NOUN
ejpam-5744	181	29	=	=	PRON
ejpam-5744	181	30	∥φk+1	∥φk+1	ADP
ejpam-5744	181	31	−	−	PROPN
ejpam-5744	181	32	λ(ψ	λ(ψ	PROPN
ejpam-5744	181	33	,	,	PUNCT
ejpam-5744	181	34	φk	φk	ADP
ejpam-5744	181	35	)	)	PUNCT
ejpam-5744	182	1	+	+	CCONJ
ejpam-5744	182	2	λ(ψ	λ(ψ	PROPN
ejpam-5744	182	3	,	,	PUNCT
ejpam-5744	182	4	φk)−	φk)−	NOUN
ejpam-5744	182	5	ϱ∥	ϱ∥	NOUN
ejpam-5744	182	6	≤	≤	NUM
ejpam-5744	182	7	∥φk+1	∥φk+1	ADP
ejpam-5744	182	8	−	−	PROPN
ejpam-5744	182	9	λ(ψ	λ(ψ	PROPN
ejpam-5744	182	10	,	,	PUNCT
ejpam-5744	182	11	φk)∥+	φk)∥+	ADJ
ejpam-5744	182	12	∥λ(ψ	∥λ(ψ	PROPN
ejpam-5744	182	13	,	,	PUNCT
ejpam-5744	182	14	φk)−	φk)−	NOUN
ejpam-5744	182	15	ϱ∥	ϱ∥	NOUN
ejpam-5744	182	16	≤	≤	NUM
ejpam-5744	182	17	µk	µk	NOUN
ejpam-5744	182	18	+	+	CCONJ
ejpam-5744	182	19	∥φk+1	∥φk+1	ADP
ejpam-5744	182	20	−	−	PROPN
ejpam-5744	182	21	ϱ∥	ϱ∥	NOUN
ejpam-5744	182	22	=	=	NOUN
ejpam-5744	182	23	µk	µk	NOUN
ejpam-5744	183	1	+	+	CCONJ
ejpam-5744	184	1	∥ψ(ζk)−	∥ψ(ζk)−	PROPN
ejpam-5744	184	2	ϱ∥	ϱ∥	VERB
ejpam-5744	184	3	≤	≤	NUM
ejpam-5744	184	4	µk	µk	ADP
ejpam-5744	184	5	+	+	CCONJ
ejpam-5744	184	6	g(∥ϱ−ψ(ϱ)∥	g(∥ϱ−ψ(ϱ)∥	NOUN
ejpam-5744	184	7	)	)	PUNCT
ejpam-5744	184	8	+	+	CCONJ
ejpam-5744	185	1	τ∥ζk	τ∥ζk	PRON
ejpam-5744	185	2	−	−	NOUN
ejpam-5744	185	3	ϱ∥	ϱ∥	NOUN
ejpam-5744	185	4	=	=	NOUN
ejpam-5744	185	5	µk	µk	NOUN
ejpam-5744	185	6	+	+	NOUN
ejpam-5744	185	7	τ∥ζk	τ∥ζk	PROPN
ejpam-5744	185	8	−	−	PROPN
ejpam-5744	185	9	ϱ∥.	ϱ∥.	PROPN
ejpam-5744	185	10	(	(	PUNCT
ejpam-5744	185	11	24	24	NUM
ejpam-5744	185	12	)	)	PUNCT
ejpam-5744	185	13	m.	m.	NOUN
ejpam-5744	185	14	akram	akram	PROPN
ejpam-5744	185	15	/	/	PUNCT
ejpam-5744	185	16	eur	eur	PROPN
ejpam-5744	185	17	.	.	PUNCT
ejpam-5744	186	1	j.	j.	PROPN
ejpam-5744	186	2	pure	pure	PROPN
ejpam-5744	186	3	appl	appl	PROPN
ejpam-5744	186	4	.	.	PROPN
ejpam-5744	186	5	math	math	PROPN
ejpam-5744	186	6	,	,	PUNCT
ejpam-5744	186	7	18	18	NUM
ejpam-5744	186	8	(	(	PUNCT
ejpam-5744	186	9	1	1	NUM
ejpam-5744	186	10	)	)	PUNCT
ejpam-5744	186	11	(	(	PUNCT
ejpam-5744	186	12	2025	2025	NUM
ejpam-5744	186	13	)	)	PUNCT
ejpam-5744	186	14	,	,	PUNCT
ejpam-5744	186	15	5744	5744	NUM
ejpam-5744	186	16	9	9	NUM
ejpam-5744	186	17	of	of	ADP
ejpam-5744	186	18	19	19	NUM
ejpam-5744	186	19	again	again	ADV
ejpam-5744	186	20	,	,	PUNCT
ejpam-5744	186	21	from	from	ADP
ejpam-5744	186	22	second	second	ADJ
ejpam-5744	186	23	equation	equation	NOUN
ejpam-5744	186	24	of	of	ADP
ejpam-5744	186	25	(	(	PUNCT
ejpam-5744	186	26	23	23	NUM
ejpam-5744	186	27	)	)	PUNCT
ejpam-5744	187	1	,	,	PUNCT
ejpam-5744	187	2	we	we	PRON
ejpam-5744	187	3	estimate	estimate	VERB
ejpam-5744	187	4	∥ζk	∥ζk	NOUN
ejpam-5744	187	5	−	−	NOUN
ejpam-5744	187	6	ϱ∥	ϱ∥	NOUN
ejpam-5744	187	7	=	=	PUNCT
ejpam-5744	187	8	∥∥∥ψ	∥∥∥ψ	NOUN
ejpam-5744	187	9	[	[	PUNCT
ejpam-5744	187	10	(	(	PUNCT
ejpam-5744	187	11	1−	1−	NUM
ejpam-5744	187	12	αk	αk	NOUN
ejpam-5744	187	13	)	)	PUNCT
ejpam-5744	187	14	(	(	PUNCT
ejpam-5744	187	15	ζk	ζk	X
ejpam-5744	187	16	+	+	X
ejpam-5744	187	17	ξk	ξk	ADP
ejpam-5744	187	18	2	2	NUM
ejpam-5744	187	19	)	)	PUNCT
ejpam-5744	187	20	+	+	CCONJ
ejpam-5744	187	21	αkψ	αkψ	INTJ
ejpam-5744	187	22	(	(	PUNCT
ejpam-5744	187	23	ζk	ζk	PROPN
ejpam-5744	187	24	+	+	X
ejpam-5744	187	25	ξk	ξk	ADP
ejpam-5744	187	26	2	2	NUM
ejpam-5744	187	27	)	)	PUNCT
ejpam-5744	187	28	]	]	PUNCT
ejpam-5744	188	1	−	−	PUNCT
ejpam-5744	188	2	ϱ	ϱ	ADP
ejpam-5744	188	3	∥∥∥	∥∥∥	PROPN
ejpam-5744	188	4	=	=	SYM
ejpam-5744	188	5	∥∥∥φ(ϱ)−ψ	∥∥∥φ(ϱ)−ψ	NOUN
ejpam-5744	188	6	[	[	PUNCT
ejpam-5744	188	7	(	(	PUNCT
ejpam-5744	188	8	1−	1−	NUM
ejpam-5744	188	9	αk	αk	NOUN
ejpam-5744	188	10	)	)	PUNCT
ejpam-5744	188	11	(	(	PUNCT
ejpam-5744	188	12	ζk	ζk	X
ejpam-5744	188	13	+	+	X
ejpam-5744	188	14	ξk	ξk	ADP
ejpam-5744	188	15	2	2	NUM
ejpam-5744	188	16	)	)	PUNCT
ejpam-5744	188	17	+	+	CCONJ
ejpam-5744	188	18	αkψ	αkψ	INTJ
ejpam-5744	188	19	(	(	PUNCT
ejpam-5744	188	20	ζk	ζk	PROPN
ejpam-5744	188	21	+	+	X
ejpam-5744	188	22	ξk	ξk	ADP
ejpam-5744	188	23	2	2	NUM
ejpam-5744	188	24	)	)	PUNCT
ejpam-5744	188	25	]	]	PUNCT
ejpam-5744	188	26	∥∥∥	∥∥∥	X
ejpam-5744	188	27	≤	≤	NUM
ejpam-5744	188	28	g(∥ϱ−ψ(ϱ)∥	g(∥ϱ−ψ(ϱ)∥	NOUN
ejpam-5744	188	29	)	)	PUNCT
ejpam-5744	189	1	+	+	CCONJ
ejpam-5744	189	2	τ	τ	PROPN
ejpam-5744	189	3	∥∥∥(1−	∥∥∥(1−	PROPN
ejpam-5744	189	4	αk	αk	NOUN
ejpam-5744	189	5	)	)	PUNCT
ejpam-5744	189	6	(	(	PUNCT
ejpam-5744	189	7	ζk	ζk	X
ejpam-5744	189	8	+	+	X
ejpam-5744	189	9	ξk	ξk	ADP
ejpam-5744	189	10	2	2	NUM
ejpam-5744	189	11	)	)	PUNCT
ejpam-5744	190	1	+	+	CCONJ
ejpam-5744	190	2	αkψ	αkψ	INTJ
ejpam-5744	190	3	(	(	PUNCT
ejpam-5744	190	4	ζk	ζk	PROPN
ejpam-5744	190	5	+	+	X
ejpam-5744	190	6	ξk	ξk	ADP
ejpam-5744	190	7	2	2	NUM
ejpam-5744	190	8	)	)	PUNCT
ejpam-5744	190	9	−	−	ADP
ejpam-5744	190	10	ϱ	ϱ	ADP
ejpam-5744	190	11	∥∥∥	∥∥∥	PROPN
ejpam-5744	190	12	≤	≤	NOUN
ejpam-5744	190	13	τ(1−	τ(1−	ADP
ejpam-5744	190	14	αk	αk	NOUN
ejpam-5744	190	15	)	)	PUNCT
ejpam-5744	190	16	∥∥∥(ζk	∥∥∥(ζk	PROPN
ejpam-5744	191	1	+	+	CCONJ
ejpam-5744	191	2	ξk	ξk	ADP
ejpam-5744	191	3	2	2	NUM
ejpam-5744	191	4	)	)	PUNCT
ejpam-5744	191	5	−	−	ADP
ejpam-5744	191	6	ϱ	ϱ	ADP
ejpam-5744	191	7	∥∥∥+	∥∥∥+	PROPN
ejpam-5744	191	8	ταk	ταk	NOUN
ejpam-5744	191	9	∥∥∥ψ(ζk	∥∥∥ψ(ζk	PUNCT
ejpam-5744	192	1	+	+	CCONJ
ejpam-5744	192	2	ξk	ξk	ADP
ejpam-5744	192	3	2	2	NUM
ejpam-5744	192	4	)	)	PUNCT
ejpam-5744	192	5	−	−	ADP
ejpam-5744	192	6	ϱ	ϱ	ADP
ejpam-5744	192	7	∥∥∥	∥∥∥	PROPN
ejpam-5744	192	8	≤	≤	NOUN
ejpam-5744	192	9	τ(1−	τ(1−	ADP
ejpam-5744	192	10	αk	αk	NOUN
ejpam-5744	192	11	)	)	PUNCT
ejpam-5744	192	12	∥∥∥(ζk	∥∥∥(ζk	PROPN
ejpam-5744	192	13	+	+	CCONJ
ejpam-5744	192	14	ξk	ξk	ADP
ejpam-5744	192	15	2	2	NUM
ejpam-5744	192	16	)	)	PUNCT
ejpam-5744	192	17	−	−	ADP
ejpam-5744	192	18	ϱ	ϱ	ADP
ejpam-5744	192	19	∥∥∥+	∥∥∥+	PROPN
ejpam-5744	192	20	ταk	ταk	X
ejpam-5744	192	21	[	[	PUNCT
ejpam-5744	192	22	g(∥ϱ−ψ(ϱ)∥	g(∥ϱ−ψ(ϱ)∥	NOUN
ejpam-5744	192	23	)	)	PUNCT
ejpam-5744	193	1	+	+	CCONJ
ejpam-5744	193	2	τ	τ	PROPN
ejpam-5744	193	3	∥∥∥(ζk	∥∥∥(ζk	PROPN
ejpam-5744	193	4	+	+	CCONJ
ejpam-5744	193	5	ξk	ξk	ADP
ejpam-5744	193	6	2	2	NUM
ejpam-5744	193	7	)	)	PUNCT
ejpam-5744	193	8	−	−	ADP
ejpam-5744	193	9	ϱ	ϱ	ADP
ejpam-5744	193	10	∥∥∥	∥∥∥	PROPN
ejpam-5744	193	11	]	]	PUNCT
ejpam-5744	193	12	≤	≤	NUM
ejpam-5744	193	13	τ	τ	X
ejpam-5744	193	14	2	2	NUM
ejpam-5744	194	1	[	[	X
ejpam-5744	194	2	1−	1−	NUM
ejpam-5744	194	3	αk(1−	αk(1−	NOUN
ejpam-5744	194	4	τ)][∥ζk	τ)][∥ζk	PROPN
ejpam-5744	194	5	−	−	NOUN
ejpam-5744	194	6	ϱ∥+	ϱ∥+	NOUN
ejpam-5744	194	7	∥ξk	∥ξk	NOUN
ejpam-5744	194	8	−	−	NOUN
ejpam-5744	194	9	ϱ∥	ϱ∥	NOUN
ejpam-5744	194	10	]	]	X
ejpam-5744	194	11	=	=	PUNCT
ejpam-5744	194	12	πk	πk	ADP
ejpam-5744	194	13	2	2	NUM
ejpam-5744	195	1	[	[	X
ejpam-5744	195	2	∥ζk	∥ζk	NOUN
ejpam-5744	195	3	−	−	NOUN
ejpam-5744	195	4	ϱ∥+	ϱ∥+	NOUN
ejpam-5744	195	5	∥ξk	∥ξk	NOUN
ejpam-5744	195	6	−	−	NOUN
ejpam-5744	195	7	ϱ∥	ϱ∥	NOUN
ejpam-5744	195	8	]	]	PUNCT
ejpam-5744	195	9	which	which	PRON
ejpam-5744	195	10	turns	turn	VERB
ejpam-5744	195	11	into	into	ADP
ejpam-5744	195	12	∥ζk	∥ζk	NOUN
ejpam-5744	196	1	−	−	PROPN
ejpam-5744	196	2	ϱ∥	ϱ∥	NOUN
ejpam-5744	196	3	≤	≤	NUM
ejpam-5744	196	4	πk	πk	ADP
ejpam-5744	196	5	(	(	PUNCT
ejpam-5744	196	6	2−	2−	NUM
ejpam-5744	196	7	πk	πk	NOUN
ejpam-5744	196	8	)	)	PUNCT
ejpam-5744	196	9	∥ξk	∥ξk	PROPN
ejpam-5744	197	1	−	−	PROPN
ejpam-5744	197	2	ϱ∥.	ϱ∥.	PROPN
ejpam-5744	197	3	(	(	PUNCT
ejpam-5744	197	4	25	25	NUM
ejpam-5744	197	5	)	)	PUNCT
ejpam-5744	197	6	∥ξk	∥ξk	NOUN
ejpam-5744	198	1	−	−	NOUN
ejpam-5744	199	1	ϱ∥	ϱ∥	NOUN
ejpam-5744	199	2	=	=	SYM
ejpam-5744	199	3	∥∥∥(1−	∥∥∥(1−	PROPN
ejpam-5744	199	4	βk)ψ	βk)ψ	PROPN
ejpam-5744	200	1	(	(	PUNCT
ejpam-5744	200	2	ξk	ξk	ADP
ejpam-5744	200	3	+	+	CCONJ
ejpam-5744	200	4	φk	φk	ADP
ejpam-5744	200	5	2	2	NUM
ejpam-5744	200	6	)	)	PUNCT
ejpam-5744	201	1	+	+	CCONJ
ejpam-5744	201	2	βkψ	βkψ	X
ejpam-5744	201	3	(	(	PUNCT
ejpam-5744	201	4	ξk	ξk	ADP
ejpam-5744	201	5	+	+	CCONJ
ejpam-5744	201	6	ωk	ωk	ADP
ejpam-5744	201	7	2	2	NUM
ejpam-5744	201	8	)	)	PUNCT
ejpam-5744	201	9	−	−	ADP
ejpam-5744	201	10	ϱ	ϱ	ADP
ejpam-5744	201	11	∥∥∥	∥∥∥	PROPN
ejpam-5744	201	12	≤	≤	NUM
ejpam-5744	201	13	(	(	PUNCT
ejpam-5744	201	14	1−	1−	NUM
ejpam-5744	201	15	βk	βk	NOUN
ejpam-5744	201	16	)	)	PUNCT
ejpam-5744	201	17	∥∥∥ψ(ξk	∥∥∥ψ(ξk	PROPN
ejpam-5744	202	1	+	+	CCONJ
ejpam-5744	202	2	φk	φk	ADP
ejpam-5744	202	3	2	2	NUM
ejpam-5744	202	4	)	)	PUNCT
ejpam-5744	202	5	−	−	ADP
ejpam-5744	202	6	ϱ	ϱ	ADP
ejpam-5744	202	7	∥∥∥+	∥∥∥+	PROPN
ejpam-5744	202	8	βk	βk	ADP
ejpam-5744	202	9	∥∥∥ψ(ξk	∥∥∥ψ(ξk	PROPN
ejpam-5744	202	10	+	+	X
ejpam-5744	202	11	ωk	ωk	ADP
ejpam-5744	202	12	2	2	NUM
ejpam-5744	202	13	)	)	PUNCT
ejpam-5744	202	14	−	−	ADP
ejpam-5744	202	15	ϱ	ϱ	ADP
ejpam-5744	202	16	∥∥∥	∥∥∥	PROPN
ejpam-5744	202	17	≤	≤	NUM
ejpam-5744	202	18	(	(	PUNCT
ejpam-5744	202	19	1−	1−	NUM
ejpam-5744	202	20	βk	βk	NOUN
ejpam-5744	202	21	)	)	PUNCT
ejpam-5744	202	22	[	[	PUNCT
ejpam-5744	202	23	g(∥ϱ−ψ(ϱ)∥	g(∥ϱ−ψ(ϱ)∥	NOUN
ejpam-5744	202	24	)	)	PUNCT
ejpam-5744	203	1	+	+	CCONJ
ejpam-5744	204	1	τ	τ	X
ejpam-5744	205	1	∥∥∥(ξk	∥∥∥(ξk	PROPN
ejpam-5744	205	2	+	+	CCONJ
ejpam-5744	205	3	φk	φk	ADP
ejpam-5744	205	4	2	2	NUM
ejpam-5744	205	5	)	)	PUNCT
ejpam-5744	205	6	−	−	ADP
ejpam-5744	205	7	ϱ	ϱ	ADP
ejpam-5744	205	8	∥∥∥	∥∥∥	PROPN
ejpam-5744	205	9	]	]	PUNCT
ejpam-5744	206	1	+	+	CCONJ
ejpam-5744	206	2	βk	βk	ADJ
ejpam-5744	206	3	[	[	PUNCT
ejpam-5744	206	4	g(∥ϱ−ψ(ϱ)∥	g(∥ϱ−ψ(ϱ)∥	NOUN
ejpam-5744	206	5	)	)	PUNCT
ejpam-5744	207	1	+	+	CCONJ
ejpam-5744	207	2	τ	τ	PUNCT
ejpam-5744	208	1	∥∥∥(ξk	∥∥∥(ξk	PROPN
ejpam-5744	208	2	+	+	CCONJ
ejpam-5744	208	3	ωk	ωk	ADP
ejpam-5744	208	4	2	2	NUM
ejpam-5744	208	5	)	)	PUNCT
ejpam-5744	208	6	−	−	ADP
ejpam-5744	208	7	ϱ	ϱ	ADP
ejpam-5744	208	8	∥∥∥	∥∥∥	PROPN
ejpam-5744	208	9	]	]	PUNCT
ejpam-5744	208	10	≤	≤	NUM
ejpam-5744	208	11	τ	τ	X
ejpam-5744	208	12	2	2	NUM
ejpam-5744	208	13	∥ξk	∥ξk	NOUN
ejpam-5744	208	14	−	−	NOUN
ejpam-5744	208	15	ρ∥+	ρ∥+	PROPN
ejpam-5744	208	16	τ	τ	X
ejpam-5744	208	17	2	2	NUM
ejpam-5744	208	18	[	[	X
ejpam-5744	208	19	(	(	PUNCT
ejpam-5744	208	20	1−	1−	NUM
ejpam-5744	208	21	βk)∥φk	βk)∥φk	NUM
ejpam-5744	208	22	−	−	NOUN
ejpam-5744	208	23	ϱ∥+	ϱ∥+	NOUN
ejpam-5744	208	24	βk∥ωk	βk∥ωk	NOUN
ejpam-5744	208	25	−	−	PROPN
ejpam-5744	208	26	ϱ∥	ϱ∥	NOUN
ejpam-5744	208	27	]	]	PUNCT
ejpam-5744	208	28	which	which	PRON
ejpam-5744	208	29	turns	turn	VERB
ejpam-5744	208	30	into	into	ADP
ejpam-5744	208	31	∥ξk	∥ξk	PROPN
ejpam-5744	208	32	−	−	NOUN
ejpam-5744	208	33	ϱ∥	ϱ∥	NOUN
ejpam-5744	208	34	≤	≤	NUM
ejpam-5744	208	35	τ	τ	X
ejpam-5744	208	36	(	(	PUNCT
ejpam-5744	208	37	2−	2−	NUM
ejpam-5744	208	38	τ	τ	X
ejpam-5744	208	39	)	)	PUNCT
ejpam-5744	209	1	[	[	X
ejpam-5744	209	2	(	(	PUNCT
ejpam-5744	209	3	1−	1−	NUM
ejpam-5744	209	4	βk)∥φk	βk)∥φk	NUM
ejpam-5744	209	5	−	−	NOUN
ejpam-5744	209	6	ϱ∥+	ϱ∥+	NOUN
ejpam-5744	209	7	βk∥ωk	βk∥ωk	NOUN
ejpam-5744	209	8	−	−	PROPN
ejpam-5744	209	9	ϱ∥	ϱ∥	NOUN
ejpam-5744	209	10	]	]	PUNCT
ejpam-5744	209	11	,	,	PUNCT
ejpam-5744	209	12	(	(	PUNCT
ejpam-5744	209	13	26	26	NUM
ejpam-5744	209	14	)	)	PUNCT
ejpam-5744	209	15	and	and	CCONJ
ejpam-5744	209	16	∥ωk	∥ωk	NOUN
ejpam-5744	209	17	−	−	PROPN
ejpam-5744	209	18	ϱ∥	ϱ∥	NOUN
ejpam-5744	209	19	=	=	SYM
ejpam-5744	209	20	∥∥∥(1−	∥∥∥(1−	PROPN
ejpam-5744	209	21	γk	γk	NOUN
ejpam-5744	209	22	)	)	PUNCT
ejpam-5744	209	23	(	(	PUNCT
ejpam-5744	209	24	φk	φk	ADP
ejpam-5744	209	25	+	+	X
ejpam-5744	209	26	ωk	ωk	ADP
ejpam-5744	209	27	2	2	NUM
ejpam-5744	209	28	)	)	PUNCT
ejpam-5744	210	1	+	+	CCONJ
ejpam-5744	210	2	γkψ	γkψ	NOUN
ejpam-5744	210	3	(	(	PUNCT
ejpam-5744	210	4	φk	φk	ADP
ejpam-5744	210	5	+	+	X
ejpam-5744	210	6	ωk	ωk	ADP
ejpam-5744	210	7	2	2	NUM
ejpam-5744	210	8	)	)	PUNCT
ejpam-5744	210	9	−	−	ADP
ejpam-5744	210	10	ϱ	ϱ	ADP
ejpam-5744	210	11	∥∥∥	∥∥∥	PROPN
ejpam-5744	210	12	≤	≤	NUM
ejpam-5744	210	13	(	(	PUNCT
ejpam-5744	210	14	1−	1−	NUM
ejpam-5744	210	15	γk	γk	NOUN
ejpam-5744	210	16	)	)	PUNCT
ejpam-5744	210	17	∥∥∥(φk	∥∥∥(φk	PROPN
ejpam-5744	210	18	+	+	CCONJ
ejpam-5744	210	19	ωk	ωk	ADP
ejpam-5744	210	20	2	2	NUM
ejpam-5744	210	21	)	)	PUNCT
ejpam-5744	210	22	−	−	ADP
ejpam-5744	210	23	ϱ	ϱ	ADP
ejpam-5744	210	24	∥∥∥+	∥∥∥+	PROPN
ejpam-5744	210	25	γk	γk	PROPN
ejpam-5744	210	26	∥∥∥ψ(φk	∥∥∥ψ(φk	PROPN
ejpam-5744	210	27	+	+	CCONJ
ejpam-5744	210	28	ωk	ωk	ADP
ejpam-5744	210	29	2	2	NUM
ejpam-5744	210	30	)	)	PUNCT
ejpam-5744	210	31	−	−	ADP
ejpam-5744	210	32	ϱ	ϱ	ADP
ejpam-5744	210	33	∥∥∥	∥∥∥	PROPN
ejpam-5744	210	34	≤	≤	NUM
ejpam-5744	210	35	(	(	PUNCT
ejpam-5744	210	36	1−	1−	NUM
ejpam-5744	210	37	γk	γk	NOUN
ejpam-5744	210	38	)	)	PUNCT
ejpam-5744	210	39	∥∥∥(φk	∥∥∥(φk	PROPN
ejpam-5744	210	40	+	+	CCONJ
ejpam-5744	210	41	ωk	ωk	ADP
ejpam-5744	210	42	2	2	NUM
ejpam-5744	210	43	)	)	PUNCT
ejpam-5744	210	44	−	−	ADP
ejpam-5744	210	45	ϱ	ϱ	ADP
ejpam-5744	210	46	∥∥∥+	∥∥∥+	PROPN
ejpam-5744	210	47	γk	γk	X
ejpam-5744	210	48	[	[	PUNCT
ejpam-5744	210	49	g(∥ϱ−ψ(ϱ)∥	g(∥ϱ−ψ(ϱ)∥	NOUN
ejpam-5744	210	50	)	)	PUNCT
ejpam-5744	210	51	+	+	CCONJ
ejpam-5744	210	52	τ	τ	X
ejpam-5744	210	53	∥∥∥(φk	∥∥∥(φk	PROPN
ejpam-5744	210	54	+	+	CCONJ
ejpam-5744	210	55	ωk	ωk	ADP
ejpam-5744	210	56	2	2	NUM
ejpam-5744	210	57	)	)	PUNCT
ejpam-5744	210	58	−	−	ADP
ejpam-5744	210	59	ϱ	ϱ	ADP
ejpam-5744	210	60	∥∥∥	∥∥∥	PROPN
ejpam-5744	210	61	]	]	PUNCT
ejpam-5744	210	62	≤	≤	NUM
ejpam-5744	210	63	εk	εk	NOUN
ejpam-5744	210	64	2	2	NUM
ejpam-5744	211	1	[	[	NOUN
ejpam-5744	211	2	∥φk	∥φk	NUM
ejpam-5744	211	3	−	−	NUM
ejpam-5744	211	4	ϱ∥+	ϱ∥+	NOUN
ejpam-5744	211	5	∥ωk	∥ωk	NOUN
ejpam-5744	211	6	−	−	NOUN
ejpam-5744	211	7	ϱ∥	ϱ∥	NOUN
ejpam-5744	211	8	]	]	PUNCT
ejpam-5744	211	9	which	which	PRON
ejpam-5744	211	10	turns	turn	VERB
ejpam-5744	211	11	into	into	ADP
ejpam-5744	211	12	∥ωk	∥ωk	NOUN
ejpam-5744	211	13	−	−	PROPN
ejpam-5744	211	14	ϱ∥	ϱ∥	NOUN
ejpam-5744	211	15	≤	≤	NUM
ejpam-5744	211	16	εk	εk	X
ejpam-5744	211	17	(	(	PUNCT
ejpam-5744	211	18	2−	2−	NUM
ejpam-5744	211	19	εk	εk	NOUN
ejpam-5744	211	20	)	)	PUNCT
ejpam-5744	211	21	∥φk	∥φk	PART
ejpam-5744	211	22	−	−	PROPN
ejpam-5744	211	23	ϱ∥	ϱ∥	NOUN
ejpam-5744	211	24	,	,	PUNCT
ejpam-5744	211	25	(	(	PUNCT
ejpam-5744	211	26	27	27	NUM
ejpam-5744	211	27	)	)	PUNCT
ejpam-5744	211	28	m.	m.	NOUN
ejpam-5744	211	29	akram	akram	PROPN
ejpam-5744	211	30	/	/	PUNCT
ejpam-5744	211	31	eur	eur	PROPN
ejpam-5744	211	32	.	.	PUNCT
ejpam-5744	212	1	j.	j.	PROPN
ejpam-5744	212	2	pure	pure	PROPN
ejpam-5744	212	3	appl	appl	PROPN
ejpam-5744	212	4	.	.	PROPN
ejpam-5744	212	5	math	math	PROPN
ejpam-5744	212	6	,	,	PUNCT
ejpam-5744	212	7	18	18	NUM
ejpam-5744	212	8	(	(	PUNCT
ejpam-5744	212	9	1	1	NUM
ejpam-5744	212	10	)	)	PUNCT
ejpam-5744	212	11	(	(	PUNCT
ejpam-5744	212	12	2025	2025	NUM
ejpam-5744	212	13	)	)	PUNCT
ejpam-5744	212	14	,	,	PUNCT
ejpam-5744	212	15	5744	5744	NUM
ejpam-5744	212	16	10	10	NUM
ejpam-5744	212	17	of	of	ADP
ejpam-5744	212	18	19	19	NUM
ejpam-5744	212	19	where	where	SCONJ
ejpam-5744	212	20	εk	εk	NOUN
ejpam-5744	212	21	=	=	SYM
ejpam-5744	212	22	(	(	PUNCT
ejpam-5744	212	23	1−γk+τγk	1−γk+τγk	NUM
ejpam-5744	212	24	)	)	PUNCT
ejpam-5744	212	25	.	.	PUNCT
ejpam-5744	213	1	by	by	ADP
ejpam-5744	213	2	implementing	implement	VERB
ejpam-5744	213	3	back	back	ADP
ejpam-5744	213	4	substitution	substitution	NOUN
ejpam-5744	213	5	from	from	ADP
ejpam-5744	213	6	(	(	PUNCT
ejpam-5744	213	7	25)-(27	25)-(27	NUM
ejpam-5744	213	8	)	)	PUNCT
ejpam-5744	213	9	,	,	PUNCT
ejpam-5744	213	10	(	(	PUNCT
ejpam-5744	213	11	24	24	NUM
ejpam-5744	213	12	)	)	PUNCT
ejpam-5744	213	13	becomes	become	VERB
ejpam-5744	213	14	∥φk+1	∥φk+1	ADP
ejpam-5744	213	15	−	−	PROPN
ejpam-5744	213	16	ϱ∥	ϱ∥	NOUN
ejpam-5744	213	17	≤	≤	NUM
ejpam-5744	213	18	µk	µk	NOUN
ejpam-5744	213	19	+	+	X
ejpam-5744	213	20	(	(	PUNCT
ejpam-5744	213	21	1−	1−	NUM
ejpam-5744	213	22	ℓ̂k)∥φk	ℓ̂k)∥φk	NOUN
ejpam-5744	214	1	−	−	ADP
ejpam-5744	214	2	ϱ∥	ϱ∥	NOUN
ejpam-5744	214	3	,	,	PUNCT
ejpam-5744	214	4	(	(	PUNCT
ejpam-5744	214	5	28	28	NUM
ejpam-5744	214	6	)	)	PUNCT
ejpam-5744	214	7	where	where	SCONJ
ejpam-5744	214	8	ℓ̂k	ℓ̂k	PROPN
ejpam-5744	214	9	is	be	AUX
ejpam-5744	214	10	identical	identical	ADJ
ejpam-5744	214	11	as	as	SCONJ
ejpam-5744	214	12	given	give	VERB
ejpam-5744	214	13	in	in	ADP
ejpam-5744	214	14	(	(	PUNCT
ejpam-5744	214	15	21	21	NUM
ejpam-5744	214	16	)	)	PUNCT
ejpam-5744	214	17	.	.	PUNCT
ejpam-5744	215	1	by	by	ADP
ejpam-5744	215	2	availing	avail	VERB
ejpam-5744	215	3	the	the	DET
ejpam-5744	215	4	assumption	assumption	NOUN
ejpam-5744	215	5	lim	lim	PROPN
ejpam-5744	215	6	k→∞	k→∞	NOUN
ejpam-5744	215	7	µk	µk	PROPN
ejpam-5744	215	8	=	=	SYM
ejpam-5744	215	9	0	0	NUM
ejpam-5744	215	10	,	,	PUNCT
ejpam-5744	215	11	lemma	lemma	PROPN
ejpam-5744	215	12	1	1	NUM
ejpam-5744	215	13	yeilds	yeild	NOUN
ejpam-5744	215	14	∥φk	∥φk	PROPN
ejpam-5744	215	15	−	−	PROPN
ejpam-5744	215	16	ϱ∥	ϱ∥	NOUN
ejpam-5744	215	17	→	→	SYM
ejpam-5744	215	18	0	0	PUNCT
ejpam-5744	216	1	as	as	ADP
ejpam-5744	216	2	k	k	PROPN
ejpam-5744	216	3	→	→	SYM
ejpam-5744	216	4	∞	∞	PROPN
ejpam-5744	216	5	,	,	PUNCT
ejpam-5744	216	6	i.e.	i.e.	X
ejpam-5744	216	7	,	,	PUNCT
ejpam-5744	216	8	lim	lim	PROPN
ejpam-5744	216	9	k→∞	k→∞	NOUN
ejpam-5744	216	10	φk	φk	ADP
ejpam-5744	216	11	=	=	PUNCT
ejpam-5744	216	12	ϱ.	ϱ.	NOUN
ejpam-5744	216	13	conversely	conversely	ADV
ejpam-5744	216	14	,	,	PUNCT
ejpam-5744	216	15	assume	assume	VERB
ejpam-5744	216	16	that	that	SCONJ
ejpam-5744	216	17	lim	lim	PROPN
ejpam-5744	216	18	k→∞	k→∞	NOUN
ejpam-5744	216	19	φk	φk	ADP
ejpam-5744	216	20	=	=	SYM
ejpam-5744	216	21	ϱ	ϱ	VERB
ejpam-5744	216	22	,	,	PUNCT
ejpam-5744	216	23	and	and	CCONJ
ejpam-5744	216	24	following	follow	VERB
ejpam-5744	216	25	the	the	DET
ejpam-5744	216	26	same	same	ADJ
ejpam-5744	216	27	procedure	procedure	NOUN
ejpam-5744	216	28	,	,	PUNCT
ejpam-5744	216	29	we	we	PRON
ejpam-5744	216	30	achieve	achieve	VERB
ejpam-5744	216	31	µk	µk	NOUN
ejpam-5744	216	32	=	=	NOUN
ejpam-5744	216	33	∥φk+1	∥φk+1	ADP
ejpam-5744	216	34	−	−	PROPN
ejpam-5744	216	35	λ(ψ	λ(ψ	PROPN
ejpam-5744	216	36	,	,	PUNCT
ejpam-5744	216	37	φk)∥	φk)∥	NOUN
ejpam-5744	217	1	=	=	SYM
ejpam-5744	217	2	∥φk+1	∥φk+1	ADP
ejpam-5744	217	3	−	−	NOUN
ejpam-5744	217	4	ϱ+	ϱ+	PUNCT
ejpam-5744	217	5	ϱ−	ϱ−	ADP
ejpam-5744	217	6	λ(ψ	λ(ψ	PROPN
ejpam-5744	217	7	,	,	PUNCT
ejpam-5744	217	8	φk)∥	φk)∥	NOUN
ejpam-5744	217	9	≤	≤	NUM
ejpam-5744	217	10	∥φk+1	∥φk+1	ADP
ejpam-5744	217	11	−	−	NOUN
ejpam-5744	217	12	ϱ∥+	ϱ∥+	NOUN
ejpam-5744	217	13	∥λ(ψ	∥λ(ψ	NOUN
ejpam-5744	217	14	,	,	PUNCT
ejpam-5744	217	15	φk)−	φk)−	NOUN
ejpam-5744	217	16	ϱ∥	ϱ∥	NOUN
ejpam-5744	217	17	≤	≤	NUM
ejpam-5744	217	18	∥φk+1	∥φk+1	ADP
ejpam-5744	217	19	−	−	NOUN
ejpam-5744	217	20	ϱ∥+	ϱ∥+	NOUN
ejpam-5744	217	21	(	(	PUNCT
ejpam-5744	217	22	1−	1−	NUM
ejpam-5744	217	23	ℓ̂k)∥φk	ℓ̂k)∥φk	NOUN
ejpam-5744	217	24	−	−	PROPN
ejpam-5744	217	25	ϱ∥.	ϱ∥.	NOUN
ejpam-5744	217	26	appealing	appeal	VERB
ejpam-5744	217	27	to	to	ADP
ejpam-5744	217	28	the	the	DET
ejpam-5744	217	29	assumption	assumption	NOUN
ejpam-5744	217	30	lim	lim	PROPN
ejpam-5744	217	31	k→∞	k→∞	PROPN
ejpam-5744	217	32	φk	φk	ADP
ejpam-5744	217	33	=	=	SYM
ejpam-5744	217	34	ϱ	ϱ	PROPN
ejpam-5744	217	35	,	,	PUNCT
ejpam-5744	217	36	it	it	PRON
ejpam-5744	217	37	follows	follow	VERB
ejpam-5744	217	38	that	that	SCONJ
ejpam-5744	217	39	lim	lim	PROPN
ejpam-5744	217	40	k→∞	k→∞	NOUN
ejpam-5744	217	41	µk	µk	NOUN
ejpam-5744	217	42	=	=	NOUN
ejpam-5744	217	43	0	0	NUM
ejpam-5744	217	44	.	.	PUNCT
ejpam-5744	218	1	hence	hence	ADV
ejpam-5744	218	2	,	,	PUNCT
ejpam-5744	218	3	simps	simp	NOUN
ejpam-5744	218	4	(	(	PUNCT
ejpam-5744	218	5	14	14	NUM
ejpam-5744	218	6	)	)	PUNCT
ejpam-5744	218	7	is	be	AUX
ejpam-5744	218	8	ψ	ψ	VERB
ejpam-5744	218	9	-	-	ADJ
ejpam-5744	218	10	stable	stable	ADJ
ejpam-5744	218	11	.	.	PUNCT
ejpam-5744	219	1	3	3	X
ejpam-5744	219	2	.	.	X
ejpam-5744	219	3	applications	application	NOUN
ejpam-5744	219	4	in	in	ADP
ejpam-5744	219	5	this	this	DET
ejpam-5744	219	6	section	section	NOUN
ejpam-5744	219	7	,	,	PUNCT
ejpam-5744	219	8	we	we	PRON
ejpam-5744	219	9	shall	shall	AUX
ejpam-5744	219	10	explore	explore	VERB
ejpam-5744	219	11	and	and	CCONJ
ejpam-5744	219	12	examine	examine	VERB
ejpam-5744	219	13	a	a	DET
ejpam-5744	219	14	general	general	ADJ
ejpam-5744	219	15	quasi	quasi	ADJ
ejpam-5744	219	16	-	-	ADJ
ejpam-5744	219	17	variational	variational	ADJ
ejpam-5744	219	18	inequality	inequality	NOUN
ejpam-5744	219	19	and	and	CCONJ
ejpam-5744	219	20	a	a	DET
ejpam-5744	219	21	nonlinear	nonlinear	ADJ
ejpam-5744	219	22	fractional	fractional	ADJ
ejpam-5744	219	23	differential	differential	NOUN
ejpam-5744	219	24	equation	equation	NOUN
ejpam-5744	219	25	by	by	ADP
ejpam-5744	219	26	employing	employ	VERB
ejpam-5744	219	27	our	our	PRON
ejpam-5744	219	28	outlined	outline	VERB
ejpam-5744	219	29	semi	semi	ADJ
ejpam-5744	219	30	-	-	ADJ
ejpam-5744	219	31	implicit	implicit	ADJ
ejpam-5744	219	32	midpoint	midpoint	NOUN
ejpam-5744	219	33	scheme	scheme	NOUN
ejpam-5744	219	34	.	.	PUNCT
ejpam-5744	220	1	3.1	3.1	NUM
ejpam-5744	220	2	.	.	PUNCT
ejpam-5744	220	3	general	general	ADJ
ejpam-5744	220	4	quasi	quasi	ADJ
ejpam-5744	220	5	-	-	ADJ
ejpam-5744	220	6	variational	variational	ADJ
ejpam-5744	220	7	inequality	inequality	NOUN
ejpam-5744	220	8	let	let	VERB
ejpam-5744	220	9	h	h	NOUN
ejpam-5744	220	10	be	be	AUX
ejpam-5744	220	11	a	a	DET
ejpam-5744	220	12	hilbert	hilbert	NOUN
ejpam-5744	220	13	space	space	NOUN
ejpam-5744	220	14	over	over	ADP
ejpam-5744	220	15	r	r	NOUN
ejpam-5744	220	16	and	and	CCONJ
ejpam-5744	220	17	c(h	c(h	PROPN
ejpam-5744	220	18	)	)	PUNCT
ejpam-5744	220	19	,	,	PUNCT
ejpam-5744	220	20	the	the	DET
ejpam-5744	220	21	collection	collection	NOUN
ejpam-5744	220	22	of	of	ADP
ejpam-5744	220	23	non	non	ADJ
ejpam-5744	220	24	empty	empty	ADJ
ejpam-5744	220	25	closed	closed	ADJ
ejpam-5744	220	26	convex	convex	ADJ
ejpam-5744	220	27	subsets	subset	NOUN
ejpam-5744	220	28	of	of	ADP
ejpam-5744	220	29	h	h	NOUN
ejpam-5744	220	30	.	.	PUNCT
ejpam-5744	221	1	we	we	PRON
ejpam-5744	221	2	contemplate	contemplate	VERB
ejpam-5744	221	3	the	the	DET
ejpam-5744	221	4	problem	problem	NOUN
ejpam-5744	221	5	to	to	PART
ejpam-5744	221	6	observe	observe	VERB
ejpam-5744	221	7	an	an	DET
ejpam-5744	221	8	element	element	NOUN
ejpam-5744	221	9	ϱ	ϱ	ADP
ejpam-5744	221	10	∈	∈	PROPN
ejpam-5744	221	11	h	h	NOUN
ejpam-5744	221	12	:	:	PUNCT
ejpam-5744	221	13	ψ(ϱ	ψ(ϱ	X
ejpam-5744	221	14	)	)	PUNCT
ejpam-5744	221	15	∈	∈	PROPN
ejpam-5744	221	16	c(ϱ	c(ϱ	PROPN
ejpam-5744	221	17	)	)	PUNCT
ejpam-5744	221	18	so	so	SCONJ
ejpam-5744	221	19	that	that	SCONJ
ejpam-5744	221	20	⟨ψ(ϱ	⟨ψ(ϱ	ADJ
ejpam-5744	221	21	)	)	PUNCT
ejpam-5744	221	22	,	,	PUNCT
ejpam-5744	221	23	ψ(ς)−	ψ(ς)−	NOUN
ejpam-5744	221	24	ψ(ϱ)⟩	ψ(ϱ)⟩	PROPN
ejpam-5744	221	25	≥	≥	NOUN
ejpam-5744	221	26	0,∀ς	0,∀ς	NUM
ejpam-5744	222	1	∈	∈	PROPN
ejpam-5744	222	2	h	h	NOUN
ejpam-5744	222	3	,	,	PUNCT
ejpam-5744	222	4	ψ(ς	ψ(ς	PROPN
ejpam-5744	222	5	)	)	PUNCT
ejpam-5744	222	6	∈	∈	PROPN
ejpam-5744	222	7	c(ϱ	c(ϱ	PROPN
ejpam-5744	222	8	)	)	PUNCT
ejpam-5744	222	9	,	,	PUNCT
ejpam-5744	222	10	(	(	PUNCT
ejpam-5744	222	11	29	29	NUM
ejpam-5744	222	12	)	)	PUNCT
ejpam-5744	222	13	where	where	SCONJ
ejpam-5744	222	14	ψ	ψ	X
ejpam-5744	222	15	,	,	PUNCT
ejpam-5744	222	16	ψ	ψ	X
ejpam-5744	222	17	:	:	PUNCT
ejpam-5744	222	18	h	h	NOUN
ejpam-5744	222	19	→	→	SYM
ejpam-5744	222	20	h	h	NOUN
ejpam-5744	222	21	be	be	AUX
ejpam-5744	222	22	(	(	PUNCT
ejpam-5744	222	23	not	not	PART
ejpam-5744	222	24	necessarily	necessarily	ADV
ejpam-5744	222	25	)	)	PUNCT
ejpam-5744	222	26	linear	linear	ADJ
ejpam-5744	222	27	mappings	mapping	NOUN
ejpam-5744	222	28	,	,	PUNCT
ejpam-5744	222	29	and	and	CCONJ
ejpam-5744	222	30	the	the	DET
ejpam-5744	222	31	set	set	NOUN
ejpam-5744	222	32	-	-	PUNCT
ejpam-5744	222	33	valued	value	VERB
ejpam-5744	222	34	mapping	mapping	NOUN
ejpam-5744	222	35	c	c	NOUN
ejpam-5744	222	36	:	:	PUNCT
ejpam-5744	222	37	h	h	NOUN
ejpam-5744	222	38	→	→	SYM
ejpam-5744	222	39	2h	2h	NUM
ejpam-5744	222	40	assigns	assign	NOUN
ejpam-5744	222	41	each	each	DET
ejpam-5744	222	42	element	element	NOUN
ejpam-5744	222	43	ϱ	ϱ	ADP
ejpam-5744	222	44	∈	∈	PROPN
ejpam-5744	222	45	h	h	NOUN
ejpam-5744	222	46	,	,	PUNCT
ejpam-5744	222	47	a	a	DET
ejpam-5744	222	48	closed	closed	ADJ
ejpam-5744	222	49	convex	convex	NOUN
ejpam-5744	222	50	subset	subset	VERB
ejpam-5744	222	51	c(ϱ	c(ϱ	NOUN
ejpam-5744	222	52	)	)	PUNCT
ejpam-5744	222	53	of	of	ADP
ejpam-5744	222	54	h	h	NOUN
ejpam-5744	222	55	.	.	PUNCT
ejpam-5744	223	1	the	the	DET
ejpam-5744	223	2	inequality	inequality	NOUN
ejpam-5744	223	3	(	(	PUNCT
ejpam-5744	223	4	29	29	NUM
ejpam-5744	223	5	)	)	PUNCT
ejpam-5744	223	6	is	be	AUX
ejpam-5744	223	7	called	call	VERB
ejpam-5744	223	8	the	the	DET
ejpam-5744	223	9	generalized	generalize	VERB
ejpam-5744	223	10	quasi	quasi	ADJ
ejpam-5744	223	11	variational	variational	ADJ
ejpam-5744	223	12	inequality	inequality	NOUN
ejpam-5744	223	13	(	(	PUNCT
ejpam-5744	223	14	gqv	gqv	NOUN
ejpam-5744	223	15	i	i	PROPN
ejpam-5744	223	16	)	)	PUNCT
ejpam-5744	223	17	and	and	CCONJ
ejpam-5744	223	18	we	we	PRON
ejpam-5744	223	19	signify	signify	VERB
ejpam-5744	223	20	its	its	PRON
ejpam-5744	223	21	solution	solution	NOUN
ejpam-5744	223	22	set	set	VERB
ejpam-5744	223	23	by	by	ADP
ejpam-5744	223	24	✠	✠	PROPN
ejpam-5744	223	25	(	(	PUNCT
ejpam-5744	223	26	c(ϱ),ψ	c(ϱ),ψ	PROPN
ejpam-5744	223	27	,	,	PUNCT
ejpam-5744	223	28	ψ	ψ	NOUN
ejpam-5744	223	29	)	)	PUNCT
ejpam-5744	223	30	.	.	PUNCT
ejpam-5744	224	1	in	in	ADP
ejpam-5744	224	2	fact	fact	NOUN
ejpam-5744	224	3	,	,	PUNCT
ejpam-5744	224	4	a	a	DET
ejpam-5744	224	5	quasi	quasi	ADJ
ejpam-5744	224	6	-	-	ADJ
ejpam-5744	224	7	variational	variational	ADJ
ejpam-5744	224	8	inequality	inequality	NOUN
ejpam-5744	224	9	(	(	PUNCT
ejpam-5744	224	10	qv	qv	INTJ
ejpam-5744	224	11	i	i	PROPN
ejpam-5744	224	12	)	)	PUNCT
ejpam-5744	224	13	is	be	AUX
ejpam-5744	224	14	a	a	DET
ejpam-5744	224	15	kind	kind	NOUN
ejpam-5744	224	16	of	of	ADP
ejpam-5744	224	17	modified	modify	VERB
ejpam-5744	224	18	variational	variational	ADJ
ejpam-5744	224	19	inequality	inequality	NOUN
ejpam-5744	224	20	in	in	ADP
ejpam-5744	224	21	which	which	PRON
ejpam-5744	224	22	the	the	DET
ejpam-5744	224	23	constraint	constraint	NOUN
ejpam-5744	224	24	set	set	VERB
ejpam-5744	224	25	varies	vary	VERB
ejpam-5744	224	26	with	with	ADP
ejpam-5744	224	27	the	the	DET
ejpam-5744	224	28	variable	variable	NOUN
ejpam-5744	224	29	.	.	PUNCT
ejpam-5744	225	1	numerous	numerous	ADJ
ejpam-5744	225	2	economic	economic	ADJ
ejpam-5744	225	3	and	and	CCONJ
ejpam-5744	225	4	engineering	engineering	NOUN
ejpam-5744	225	5	problems	problem	NOUN
ejpam-5744	225	6	,	,	PUNCT
ejpam-5744	225	7	such	such	ADJ
ejpam-5744	225	8	as	as	ADP
ejpam-5744	225	9	nash	nash	PROPN
ejpam-5744	225	10	equilibrium	equilibrium	NOUN
ejpam-5744	225	11	problems	problem	NOUN
ejpam-5744	225	12	,	,	PUNCT
ejpam-5744	225	13	control	control	NOUN
ejpam-5744	225	14	and	and	CCONJ
ejpam-5744	225	15	optimization	optimization	NOUN
ejpam-5744	225	16	,	,	PUNCT
ejpam-5744	225	17	operations	operation	NOUN
ejpam-5744	225	18	research	research	NOUN
ejpam-5744	225	19	,	,	PUNCT
ejpam-5744	225	20	etc	etc	X
ejpam-5744	225	21	.	.	X
ejpam-5744	225	22	,	,	PUNCT
ejpam-5744	225	23	are	be	AUX
ejpam-5744	225	24	recognized	recognize	VERB
ejpam-5744	225	25	to	to	PART
ejpam-5744	225	26	be	be	AUX
ejpam-5744	225	27	well	well	ADV
ejpam-5744	225	28	suited	suited	ADJ
ejpam-5744	225	29	for	for	ADP
ejpam-5744	225	30	modeling	modeling	NOUN
ejpam-5744	225	31	and	and	CCONJ
ejpam-5744	225	32	analysis	analysis	NOUN
ejpam-5744	225	33	using	use	VERB
ejpam-5744	225	34	qv	qv	NOUN
ejpam-5744	225	35	is	be	AUX
ejpam-5744	225	36	.	.	PUNCT
ejpam-5744	226	1	gqv	gqv	PROPN
ejpam-5744	226	2	i	i	PRON
ejpam-5744	226	3	(	(	PUNCT
ejpam-5744	226	4	29	29	NUM
ejpam-5744	226	5	)	)	PUNCT
ejpam-5744	226	6	can	can	AUX
ejpam-5744	226	7	be	be	AUX
ejpam-5744	226	8	seen	see	VERB
ejpam-5744	226	9	as	as	ADP
ejpam-5744	226	10	a	a	DET
ejpam-5744	226	11	unified	unified	ADJ
ejpam-5744	226	12	problem	problem	NOUN
ejpam-5744	226	13	and	and	CCONJ
ejpam-5744	226	14	consists	consist	VERB
ejpam-5744	226	15	several	several	ADJ
ejpam-5744	226	16	considerably	considerably	ADV
ejpam-5744	226	17	significant	significant	ADJ
ejpam-5744	226	18	problems	problem	NOUN
ejpam-5744	226	19	as	as	ADP
ejpam-5744	226	20	special	special	ADJ
ejpam-5744	226	21	cases	case	NOUN
ejpam-5744	226	22	which	which	PRON
ejpam-5744	226	23	are	be	AUX
ejpam-5744	226	24	listed	list	VERB
ejpam-5744	226	25	as	as	ADP
ejpam-5744	226	26	under	under	ADV
ejpam-5744	226	27	.	.	PUNCT
ejpam-5744	227	1	(	(	PUNCT
ejpam-5744	227	2	i	i	NOUN
ejpam-5744	227	3	)	)	PUNCT
ejpam-5744	227	4	for	for	ADP
ejpam-5744	227	5	c(ϱ	c(ϱ	NOUN
ejpam-5744	227	6	)	)	PUNCT
ejpam-5744	228	1	=	=	SYM
ejpam-5744	229	1	c	c	X
ejpam-5744	229	2	,	,	PUNCT
ejpam-5744	229	3	gqv	gqv	X
ejpam-5744	229	4	i	i	X
ejpam-5744	229	5	(	(	PUNCT
ejpam-5744	229	6	29	29	NUM
ejpam-5744	229	7	)	)	PUNCT
ejpam-5744	229	8	is	be	AUX
ejpam-5744	229	9	identical	identical	ADJ
ejpam-5744	229	10	to	to	ADP
ejpam-5744	229	11	the	the	DET
ejpam-5744	229	12	following	follow	VERB
ejpam-5744	229	13	general	general	ADJ
ejpam-5744	229	14	variational	variational	ADJ
ejpam-5744	229	15	inequality	inequality	NOUN
ejpam-5744	229	16	which	which	PRON
ejpam-5744	229	17	was	be	AUX
ejpam-5744	229	18	set	set	VERB
ejpam-5744	229	19	forth	forth	ADV
ejpam-5744	229	20	by	by	ADP
ejpam-5744	229	21	noor	noor	PROPN
ejpam-5744	229	22	[	[	X
ejpam-5744	229	23	32	32	NUM
ejpam-5744	229	24	]	]	PUNCT
ejpam-5744	229	25	.	.	PUNCT
ejpam-5744	230	1	⟨ψ(ϱ	⟨ψ(ϱ	ADJ
ejpam-5744	230	2	)	)	PUNCT
ejpam-5744	230	3	,	,	PUNCT
ejpam-5744	230	4	ψ(ς)−	ψ(ς)−	NOUN
ejpam-5744	230	5	ψ(ϱ)⟩	ψ(ϱ)⟩	PROPN
ejpam-5744	230	6	≥	≥	NOUN
ejpam-5744	230	7	0,∀ς	0,∀ς	NUM
ejpam-5744	231	1	∈	∈	PROPN
ejpam-5744	231	2	h	h	NOUN
ejpam-5744	231	3	,	,	PUNCT
ejpam-5744	231	4	ψ(ς	ψ(ς	PROPN
ejpam-5744	231	5	)	)	PUNCT
ejpam-5744	231	6	∈	∈	PROPN
ejpam-5744	231	7	c.	c.	NOUN
ejpam-5744	231	8	(	(	PUNCT
ejpam-5744	231	9	30	30	NUM
ejpam-5744	231	10	)	)	PUNCT
ejpam-5744	231	11	m.	m.	NOUN
ejpam-5744	231	12	akram	akram	PROPN
ejpam-5744	231	13	/	/	PUNCT
ejpam-5744	231	14	eur	eur	PROPN
ejpam-5744	231	15	.	.	PUNCT
ejpam-5744	232	1	j.	j.	PROPN
ejpam-5744	232	2	pure	pure	PROPN
ejpam-5744	232	3	appl	appl	PROPN
ejpam-5744	232	4	.	.	PROPN
ejpam-5744	232	5	math	math	PROPN
ejpam-5744	232	6	,	,	PUNCT
ejpam-5744	232	7	18	18	NUM
ejpam-5744	232	8	(	(	PUNCT
ejpam-5744	232	9	1	1	NUM
ejpam-5744	232	10	)	)	PUNCT
ejpam-5744	232	11	(	(	PUNCT
ejpam-5744	232	12	2025	2025	NUM
ejpam-5744	232	13	)	)	PUNCT
ejpam-5744	232	14	,	,	PUNCT
ejpam-5744	232	15	5744	5744	NUM
ejpam-5744	232	16	11	11	NUM
ejpam-5744	232	17	of	of	ADP
ejpam-5744	232	18	19	19	NUM
ejpam-5744	232	19	(	(	PUNCT
ejpam-5744	232	20	ii	ii	NOUN
ejpam-5744	232	21	)	)	PUNCT
ejpam-5744	232	22	further	far	ADV
ejpam-5744	232	23	for	for	ADP
ejpam-5744	232	24	ψ	ψ	X
ejpam-5744	232	25	=	=	SYM
ejpam-5744	232	26	i	i	PROPN
ejpam-5744	232	27	,	,	PUNCT
ejpam-5744	232	28	problem	problem	NOUN
ejpam-5744	232	29	(	(	PUNCT
ejpam-5744	232	30	30	30	NUM
ejpam-5744	232	31	)	)	PUNCT
ejpam-5744	232	32	becomes	become	VERB
ejpam-5744	232	33	the	the	DET
ejpam-5744	232	34	classical	classical	ADJ
ejpam-5744	232	35	variational	variational	ADJ
ejpam-5744	232	36	inequality	inequality	NOUN
ejpam-5744	232	37	introduced	introduce	VERB
ejpam-5744	232	38	by	by	ADP
ejpam-5744	232	39	stampacchia[45	stampacchia[45	NOUN
ejpam-5744	232	40	]	]	PUNCT
ejpam-5744	232	41	.	.	PUNCT
ejpam-5744	233	1	(	(	PUNCT
ejpam-5744	233	2	iii	iii	X
ejpam-5744	233	3	)	)	PUNCT
ejpam-5744	233	4	if	if	SCONJ
ejpam-5744	233	5	ψ	ψ	X
ejpam-5744	233	6	=	=	SYM
ejpam-5744	233	7	i	i	PROPN
ejpam-5744	233	8	,	,	PUNCT
ejpam-5744	233	9	gqvi	gqvi	NOUN
ejpam-5744	233	10	(	(	PUNCT
ejpam-5744	233	11	29	29	NUM
ejpam-5744	233	12	)	)	PUNCT
ejpam-5744	233	13	turns	turn	VERB
ejpam-5744	233	14	into	into	ADP
ejpam-5744	233	15	the	the	DET
ejpam-5744	233	16	following	follow	VERB
ejpam-5744	233	17	classical	classical	ADJ
ejpam-5744	233	18	quasi	quasi	ADJ
ejpam-5744	233	19	-	-	ADJ
ejpam-5744	233	20	variational	variational	ADJ
ejpam-5744	233	21	inequality	inequality	NOUN
ejpam-5744	233	22	introduced	introduce	VERB
ejpam-5744	233	23	in	in	ADP
ejpam-5744	233	24	[	[	X
ejpam-5744	233	25	6	6	NUM
ejpam-5744	233	26	]	]	PUNCT
ejpam-5744	233	27	:	:	PUNCT
ejpam-5744	233	28	⟨ψ(ϱ	⟨ψ(ϱ	ADJ
ejpam-5744	233	29	)	)	PUNCT
ejpam-5744	233	30	,	,	PUNCT
ejpam-5744	233	31	ς	ς	PROPN
ejpam-5744	233	32	−	−	PROPN
ejpam-5744	233	33	ϱ⟩	ϱ⟩	VERB
ejpam-5744	233	34	≥	≥	NOUN
ejpam-5744	233	35	0	0	NUM
ejpam-5744	233	36	,	,	PUNCT
ejpam-5744	233	37	∀ς	∀ς	PROPN
ejpam-5744	233	38	∈	∈	PROPN
ejpam-5744	233	39	c(ϱ	c(ϱ	PROPN
ejpam-5744	233	40	)	)	PUNCT
ejpam-5744	233	41	.	.	PUNCT
ejpam-5744	234	1	(	(	PUNCT
ejpam-5744	234	2	31	31	NUM
ejpam-5744	234	3	)	)	PUNCT
ejpam-5744	234	4	(	(	PUNCT
ejpam-5744	234	5	iv	iv	X
ejpam-5744	234	6	)	)	PUNCT
ejpam-5744	234	7	for	for	ADP
ejpam-5744	234	8	ϱ0	ϱ0	NOUN
ejpam-5744	234	9	∈	∈	PROPN
ejpam-5744	234	10	h	h	NOUN
ejpam-5744	234	11	,	,	PUNCT
ejpam-5744	234	12	the	the	DET
ejpam-5744	234	13	dual	dual	ADJ
ejpam-5744	234	14	cone	cone	NOUN
ejpam-5744	234	15	of	of	ADP
ejpam-5744	234	16	c(ϱ0	c(ϱ0	NOUN
ejpam-5744	234	17	)	)	PUNCT
ejpam-5744	235	1	⊂	⊂	PROPN
ejpam-5744	235	2	h	h	PROPN
ejpam-5744	235	3	is	be	AUX
ejpam-5744	235	4	described	describe	VERB
ejpam-5744	235	5	by	by	ADP
ejpam-5744	235	6	c̄(ϱ0	c̄(ϱ0	PROPN
ejpam-5744	235	7	)	)	PUNCT
ejpam-5744	236	1	=	=	PRON
ejpam-5744	236	2	{	{	PUNCT
ejpam-5744	236	3	ϱ	ϱ	PROPN
ejpam-5744	236	4	∈	∈	PROPN
ejpam-5744	236	5	h	h	NOUN
ejpam-5744	236	6	:	:	PUNCT
ejpam-5744	236	7	⟨ϱ	⟨ϱ	PROPN
ejpam-5744	236	8	,	,	PUNCT
ejpam-5744	236	9	ς⟩	ς⟩	X
ejpam-5744	236	10	≥	≥	NOUN
ejpam-5744	236	11	0	0	NUM
ejpam-5744	236	12	,	,	PUNCT
ejpam-5744	236	13	∀ς	∀ς	PROPN
ejpam-5744	236	14	∈	∈	PROPN
ejpam-5744	236	15	c(ϱ0	c(ϱ0	NOUN
ejpam-5744	236	16	)	)	PUNCT
ejpam-5744	236	17	}	}	PUNCT
ejpam-5744	236	18	.	.	PUNCT
ejpam-5744	237	1	then	then	ADV
ejpam-5744	237	2	problem	problem	NOUN
ejpam-5744	237	3	(	(	PUNCT
ejpam-5744	237	4	30	30	NUM
ejpam-5744	237	5	)	)	PUNCT
ejpam-5744	237	6	turns	turn	VERB
ejpam-5744	237	7	into	into	ADP
ejpam-5744	237	8	a	a	DET
ejpam-5744	237	9	general	general	ADJ
ejpam-5744	237	10	complementarity	complementarity	NOUN
ejpam-5744	237	11	problem	problem	NOUN
ejpam-5744	237	12	of	of	ADP
ejpam-5744	237	13	discerning	discern	VERB
ejpam-5744	237	14	an	an	DET
ejpam-5744	237	15	element	element	NOUN
ejpam-5744	237	16	ϱ	ϱ	ADP
ejpam-5744	237	17	∈	∈	NOUN
ejpam-5744	237	18	h	h	NOUN
ejpam-5744	237	19	so	so	SCONJ
ejpam-5744	237	20	that	that	SCONJ
ejpam-5744	237	21	⟨ψ(ϱ	⟨ψ(ϱ	ADJ
ejpam-5744	237	22	)	)	PUNCT
ejpam-5744	237	23	,	,	PUNCT
ejpam-5744	237	24	ψ(ϱ)⟩	ψ(ϱ)⟩	VERB
ejpam-5744	237	25	≥	≥	NOUN
ejpam-5744	237	26	0	0	NUM
ejpam-5744	237	27	,	,	PUNCT
ejpam-5744	237	28	ψ(ϱ	ψ(ϱ	PRON
ejpam-5744	237	29	)	)	PUNCT
ejpam-5744	237	30	∈	∈	PROPN
ejpam-5744	237	31	c(ϱ	c(ϱ	PROPN
ejpam-5744	237	32	)	)	PUNCT
ejpam-5744	237	33	and	and	CCONJ
ejpam-5744	237	34	ψ(ϱ	ψ(ϱ	NOUN
ejpam-5744	237	35	)	)	PUNCT
ejpam-5744	237	36	∈	∈	NOUN
ejpam-5744	237	37	c̄(ϱ	c̄(ϱ	PROPN
ejpam-5744	237	38	)	)	PUNCT
ejpam-5744	237	39	.	.	PUNCT
ejpam-5744	238	1	(	(	PUNCT
ejpam-5744	238	2	32	32	NUM
ejpam-5744	238	3	)	)	PUNCT
ejpam-5744	238	4	now	now	ADV
ejpam-5744	238	5	,	,	PUNCT
ejpam-5744	238	6	to	to	PART
ejpam-5744	238	7	bring	bring	VERB
ejpam-5744	238	8	off	off	ADP
ejpam-5744	238	9	the	the	DET
ejpam-5744	238	10	required	require	VERB
ejpam-5744	238	11	goal	goal	NOUN
ejpam-5744	238	12	,	,	PUNCT
ejpam-5744	238	13	we	we	PRON
ejpam-5744	238	14	accumulate	accumulate	VERB
ejpam-5744	238	15	a	a	DET
ejpam-5744	238	16	few	few	ADJ
ejpam-5744	238	17	supplementary	supplementary	ADJ
ejpam-5744	238	18	results	result	NOUN
ejpam-5744	238	19	and	and	CCONJ
ejpam-5744	238	20	definitions	definition	NOUN
ejpam-5744	238	21	below	below	ADV
ejpam-5744	238	22	.	.	PUNCT
ejpam-5744	239	1	lemma	lemma	PROPN
ejpam-5744	239	2	2	2	NUM
ejpam-5744	239	3	.	.	PUNCT
ejpam-5744	240	1	[	[	X
ejpam-5744	240	2	4	4	X
ejpam-5744	240	3	]	]	X
ejpam-5744	240	4	if	if	SCONJ
ejpam-5744	240	5	for	for	ADP
ejpam-5744	240	6	any	any	DET
ejpam-5744	240	7	ς	ς	PROPN
ejpam-5744	240	8	∈	∈	PROPN
ejpam-5744	240	9	h	h	NOUN
ejpam-5744	240	10	,	,	PUNCT
ejpam-5744	240	11	ϱ	ϱ	PROPN
ejpam-5744	240	12	∈	∈	PROPN
ejpam-5744	240	13	c(ϱ	c(ϱ	PROPN
ejpam-5744	240	14	)	)	PUNCT
ejpam-5744	240	15	,	,	PUNCT
ejpam-5744	240	16	the	the	DET
ejpam-5744	240	17	implicit	implicit	ADJ
ejpam-5744	240	18	projection	projection	NOUN
ejpam-5744	240	19	pc(ϱ	pc(ϱ	NOUN
ejpam-5744	240	20	)	)	PUNCT
ejpam-5744	240	21	:	:	PUNCT
ejpam-5744	241	1	h	h	NOUN
ejpam-5744	241	2	→	→	SYM
ejpam-5744	241	3	c(ϱ	c(ϱ	PROPN
ejpam-5744	241	4	)	)	PUNCT
ejpam-5744	242	1	⊂	⊂	PROPN
ejpam-5744	242	2	h	h	PROPN
ejpam-5744	242	3	obeys	obey	VERB
ejpam-5744	242	4	the	the	DET
ejpam-5744	242	5	inequality	inequality	NOUN
ejpam-5744	242	6	⟨κ−	⟨κ−	NUM
ejpam-5744	242	7	ω,ϖ	ω,ϖ	PRON
ejpam-5744	242	8	−	−	PROPN
ejpam-5744	242	9	κ⟩	κ⟩	NOUN
ejpam-5744	242	10	≥	≥	NOUN
ejpam-5744	242	11	0	0	PUNCT
ejpam-5744	243	1	if	if	SCONJ
ejpam-5744	243	2	and	and	CCONJ
ejpam-5744	243	3	only	only	ADV
ejpam-5744	243	4	if	if	SCONJ
ejpam-5744	243	5	pc(ϱ)(ω	pc(ϱ)(ω	ADJ
ejpam-5744	243	6	)	)	PUNCT
ejpam-5744	244	1	=	=	PUNCT
ejpam-5744	245	1	κ,∀ϖ	κ,∀ϖ	PRON
ejpam-5744	245	2	∈	∈	PROPN
ejpam-5744	245	3	c(ϱ	c(ϱ	PROPN
ejpam-5744	245	4	)	)	PUNCT
ejpam-5744	245	5	.	.	PUNCT
ejpam-5744	246	1	next	next	ADV
ejpam-5744	246	2	,	,	PUNCT
ejpam-5744	246	3	we	we	PRON
ejpam-5744	246	4	shall	shall	AUX
ejpam-5744	246	5	design	design	VERB
ejpam-5744	246	6	the	the	DET
ejpam-5744	246	7	following	following	ADJ
ejpam-5744	246	8	fixed	fix	VERB
ejpam-5744	246	9	point	point	NOUN
ejpam-5744	246	10	problem	problem	NOUN
ejpam-5744	246	11	associated	associate	VERB
ejpam-5744	246	12	to	to	ADP
ejpam-5744	246	13	gqv	gqv	PROPN
ejpam-5744	246	14	i	i	PROPN
ejpam-5744	246	15	(	(	PUNCT
ejpam-5744	246	16	29	29	NUM
ejpam-5744	246	17	)	)	PUNCT
ejpam-5744	246	18	by	by	ADP
ejpam-5744	246	19	imposing	impose	VERB
ejpam-5744	246	20	the	the	DET
ejpam-5744	246	21	lemma	lemma	PROPN
ejpam-5744	246	22	2	2	NUM
ejpam-5744	246	23	.	.	PUNCT
ejpam-5744	247	1	lemma	lemma	PROPN
ejpam-5744	247	2	3	3	NUM
ejpam-5744	247	3	.	.	PUNCT
ejpam-5744	248	1	an	an	DET
ejpam-5744	248	2	element	element	NOUN
ejpam-5744	248	3	ϱ	ϱ	ADP
ejpam-5744	248	4	∈	∈	PROPN
ejpam-5744	248	5	h	h	NOUN
ejpam-5744	248	6	:	:	PUNCT
ejpam-5744	248	7	ψ(ϱ	ψ(ϱ	X
ejpam-5744	248	8	)	)	PUNCT
ejpam-5744	248	9	∈	∈	PROPN
ejpam-5744	248	10	c(ϱ	c(ϱ	PROPN
ejpam-5744	248	11	)	)	PUNCT
ejpam-5744	248	12	solves	solve	VERB
ejpam-5744	248	13	gqvi	gqvi	NOUN
ejpam-5744	248	14	(	(	PUNCT
ejpam-5744	248	15	29	29	NUM
ejpam-5744	248	16	)	)	PUNCT
ejpam-5744	249	1	if	if	SCONJ
ejpam-5744	250	1	and	and	CCONJ
ejpam-5744	250	2	only	only	ADV
ejpam-5744	250	3	if	if	SCONJ
ejpam-5744	250	4	ϱ	ϱ	PROPN
ejpam-5744	250	5	∈	∈	PROPN
ejpam-5744	250	6	ξ(π	ξ(π	NOUN
ejpam-5744	250	7	)	)	PUNCT
ejpam-5744	250	8	,	,	PUNCT
ejpam-5744	250	9	where	where	SCONJ
ejpam-5744	250	10	π(ϱ	π(ϱ	ADJ
ejpam-5744	250	11	)	)	PUNCT
ejpam-5744	250	12	=	=	SYM
ejpam-5744	250	13	ϱ−	ϱ−	NOUN
ejpam-5744	251	1	ψ(ϱ	ψ(ϱ	PROPN
ejpam-5744	251	2	)	)	PUNCT
ejpam-5744	252	1	+	+	NUM
ejpam-5744	252	2	pc(ϱ)[ψ(ϱ)−	pc(ϱ)[ψ(ϱ)−	NOUN
ejpam-5744	252	3	λψ(ϱ	λψ(ϱ	NUM
ejpam-5744	252	4	)	)	PUNCT
ejpam-5744	252	5	]	]	PUNCT
ejpam-5744	252	6	and	and	CCONJ
ejpam-5744	252	7	λ	λ	X
ejpam-5744	252	8	>	>	X
ejpam-5744	252	9	0	0	PUNCT
ejpam-5744	252	10	is	be	AUX
ejpam-5744	252	11	a	a	DET
ejpam-5744	252	12	constant	constant	ADJ
ejpam-5744	252	13	.	.	PUNCT
ejpam-5744	253	1	proof	proof	NOUN
ejpam-5744	253	2	.	.	PUNCT
ejpam-5744	254	1	assume	assume	VERB
ejpam-5744	254	2	that	that	SCONJ
ejpam-5744	254	3	ϱ	ϱ	ADP
ejpam-5744	254	4	∈	∈	PROPN
ejpam-5744	254	5	✠	✠	PROPN
ejpam-5744	254	6	(	(	PUNCT
ejpam-5744	254	7	c(ϱ),ψ	c(ϱ),ψ	PROPN
ejpam-5744	254	8	,	,	PUNCT
ejpam-5744	254	9	ψ	ψ	NOUN
ejpam-5744	254	10	)	)	PUNCT
ejpam-5744	254	11	then	then	ADV
ejpam-5744	254	12	⟨ψ(ϱ	⟨ψ(ϱ	NOUN
ejpam-5744	254	13	)	)	PUNCT
ejpam-5744	254	14	,	,	PUNCT
ejpam-5744	254	15	ψ(ς	ψ(ς	PROPN
ejpam-5744	254	16	)	)	PUNCT
ejpam-5744	254	17	−	−	PROPN
ejpam-5744	254	18	ψ(ϱ)⟩	ψ(ϱ)⟩	VERB
ejpam-5744	254	19	≥	≥	NOUN
ejpam-5744	254	20	0	0	NUM
ejpam-5744	254	21	,	,	PUNCT
ejpam-5744	254	22	∀ς	∀ς	PROPN
ejpam-5744	254	23	∈	∈	PROPN
ejpam-5744	254	24	h	h	NOUN
ejpam-5744	254	25	:	:	PUNCT
ejpam-5744	254	26	ψ(ς	ψ(ς	X
ejpam-5744	254	27	)	)	PUNCT
ejpam-5744	254	28	∈	∈	PROPN
ejpam-5744	254	29	c(ϱ	c(ϱ	PROPN
ejpam-5744	254	30	)	)	PUNCT
ejpam-5744	254	31	.	.	PUNCT
ejpam-5744	255	1	by	by	ADP
ejpam-5744	255	2	making	make	VERB
ejpam-5744	255	3	use	use	NOUN
ejpam-5744	255	4	of	of	ADP
ejpam-5744	255	5	lemma	lemma	PROPN
ejpam-5744	255	6	2	2	NUM
ejpam-5744	255	7	,	,	PUNCT
ejpam-5744	255	8	we	we	PRON
ejpam-5744	255	9	acquire	acquire	VERB
ejpam-5744	255	10	πc(ϱ)[ψ(ϱ)−	πc(ϱ)[ψ(ϱ)−	PRON
ejpam-5744	255	11	λψ(ϱ	λψ(ϱ	NOUN
ejpam-5744	255	12	)	)	PUNCT
ejpam-5744	255	13	]	]	PUNCT
ejpam-5744	256	1	=	=	PUNCT
ejpam-5744	256	2	ψ(ϱ	ψ(ϱ	NOUN
ejpam-5744	256	3	)	)	PUNCT
ejpam-5744	256	4	.	.	PUNCT
ejpam-5744	257	1	so	so	ADV
ejpam-5744	257	2	,	,	PUNCT
ejpam-5744	257	3	ϱ	ϱ	PROPN
ejpam-5744	257	4	∈	∈	NOUN
ejpam-5744	257	5	ξ(π	ξ(π	NOUN
ejpam-5744	257	6	)	)	PUNCT
ejpam-5744	257	7	.	.	PUNCT
ejpam-5744	258	1	on	on	ADP
ejpam-5744	258	2	the	the	DET
ejpam-5744	258	3	other	other	ADJ
ejpam-5744	258	4	side	side	NOUN
ejpam-5744	258	5	,	,	PUNCT
ejpam-5744	258	6	assume	assume	VERB
ejpam-5744	258	7	that	that	SCONJ
ejpam-5744	258	8	ϱ	ϱ	PROPN
ejpam-5744	258	9	∈	∈	PROPN
ejpam-5744	258	10	ξ(π	ξ(π	NOUN
ejpam-5744	258	11	)	)	PUNCT
ejpam-5744	258	12	then	then	ADV
ejpam-5744	258	13	for	for	ADP
ejpam-5744	258	14	all	all	PRON
ejpam-5744	258	15	ϱ	ϱ	ADP
ejpam-5744	258	16	∈	∈	PROPN
ejpam-5744	258	17	h	h	NOUN
ejpam-5744	258	18	:	:	PUNCT
ejpam-5744	258	19	ψ(ϱ	ψ(ϱ	X
ejpam-5744	258	20	)	)	PUNCT
ejpam-5744	258	21	∈	∈	PROPN
ejpam-5744	258	22	c(ϱ	c(ϱ	PROPN
ejpam-5744	258	23	)	)	PUNCT
ejpam-5744	258	24	,	,	PUNCT
ejpam-5744	258	25	we	we	PRON
ejpam-5744	258	26	obtain	obtain	VERB
ejpam-5744	258	27	π(ϱ	π(ϱ	NOUN
ejpam-5744	258	28	)	)	PUNCT
ejpam-5744	258	29	=	=	SYM
ejpam-5744	258	30	ϱ	ϱ	PROPN
ejpam-5744	258	31	,	,	PUNCT
ejpam-5744	258	32	thus	thus	ADV
ejpam-5744	258	33	,	,	PUNCT
ejpam-5744	258	34	one	one	PRON
ejpam-5744	258	35	can	can	AUX
ejpam-5744	258	36	write	write	VERB
ejpam-5744	258	37	ψ(ϱ	ψ(ϱ	NOUN
ejpam-5744	258	38	)	)	PUNCT
ejpam-5744	258	39	=	=	SYM
ejpam-5744	258	40	πc(ϱ)[ψ(ϱ)−λψ(ϱ	πc(ϱ)[ψ(ϱ)−λψ(ϱ	NOUN
ejpam-5744	258	41	)	)	PUNCT
ejpam-5744	258	42	]	]	PUNCT
ejpam-5744	258	43	.	.	PUNCT
ejpam-5744	259	1	again	again	ADV
ejpam-5744	259	2	,	,	PUNCT
ejpam-5744	259	3	by	by	ADP
ejpam-5744	259	4	the	the	DET
ejpam-5744	259	5	virtue	virtue	NOUN
ejpam-5744	259	6	of	of	ADP
ejpam-5744	259	7	lemma	lemma	PROPN
ejpam-5744	259	8	2	2	NUM
ejpam-5744	259	9	,	,	PUNCT
ejpam-5744	259	10	we	we	PRON
ejpam-5744	259	11	get	get	VERB
ejpam-5744	259	12	⟨ψ(ϱ	⟨ψ(ϱ	ADV
ejpam-5744	259	13	)	)	PUNCT
ejpam-5744	259	14	,	,	PUNCT
ejpam-5744	259	15	ψ(ς)−	ψ(ς)−	NOUN
ejpam-5744	259	16	ψ(ϱ)⟩	ψ(ϱ)⟩	PROPN
ejpam-5744	259	17	≥	≥	NOUN
ejpam-5744	259	18	0	0	NUM
ejpam-5744	259	19	,	,	PUNCT
ejpam-5744	259	20	∀ς	∀ς	PROPN
ejpam-5744	259	21	∈	∈	PROPN
ejpam-5744	259	22	h	h	NOUN
ejpam-5744	259	23	:	:	PUNCT
ejpam-5744	259	24	ψ(ς	ψ(ς	X
ejpam-5744	259	25	)	)	PUNCT
ejpam-5744	259	26	∈	∈	PROPN
ejpam-5744	259	27	c(ϱ	c(ϱ	PROPN
ejpam-5744	259	28	)	)	PUNCT
ejpam-5744	259	29	,	,	PUNCT
ejpam-5744	259	30	i.e.	i.e.	X
ejpam-5744	259	31	,	,	PUNCT
ejpam-5744	259	32	ϱ	ϱ	PROPN
ejpam-5744	259	33	∈	∈	PROPN
ejpam-5744	259	34	✠	✠	PROPN
ejpam-5744	259	35	(	(	PUNCT
ejpam-5744	259	36	c(ϱ),ψ	c(ϱ),ψ	PROPN
ejpam-5744	259	37	,	,	PUNCT
ejpam-5744	259	38	ψ	ψ	NOUN
ejpam-5744	259	39	)	)	PUNCT
ejpam-5744	259	40	.	.	PUNCT
ejpam-5744	260	1	now	now	ADV
ejpam-5744	260	2	,	,	PUNCT
ejpam-5744	260	3	we	we	PRON
ejpam-5744	260	4	take	take	VERB
ejpam-5744	260	5	the	the	DET
ejpam-5744	260	6	following	following	ADJ
ejpam-5744	260	7	assumption	assumption	NOUN
ejpam-5744	260	8	into	into	ADP
ejpam-5744	260	9	account	account	NOUN
ejpam-5744	260	10	to	to	PART
ejpam-5744	260	11	accomplish	accomplish	VERB
ejpam-5744	260	12	the	the	DET
ejpam-5744	260	13	required	require	VERB
ejpam-5744	260	14	goal	goal	NOUN
ejpam-5744	260	15	.	.	PUNCT
ejpam-5744	261	1	assumption	assumption	NOUN
ejpam-5744	261	2	a	a	PRON
ejpam-5744	261	3	:	:	PUNCT
ejpam-5744	261	4	for	for	ADP
ejpam-5744	261	5	given	give	VERB
ejpam-5744	261	6	elements	element	NOUN
ejpam-5744	261	7	ϱ	ϱ	ADP
ejpam-5744	261	8	,	,	PUNCT
ejpam-5744	261	9	τ	τ	PROPN
ejpam-5744	261	10	,	,	PUNCT
ejpam-5744	261	11	ς	ς	PROPN
ejpam-5744	261	12	∈	∈	PROPN
ejpam-5744	261	13	h	h	NOUN
ejpam-5744	261	14	and	and	CCONJ
ejpam-5744	261	15	κ	κ	X
ejpam-5744	261	16	>	>	X
ejpam-5744	261	17	0	0	NUM
ejpam-5744	261	18	,	,	PUNCT
ejpam-5744	261	19	pc	pc	NOUN
ejpam-5744	261	20	obeys	obey	VERB
ejpam-5744	261	21	the	the	DET
ejpam-5744	261	22	following	follow	VERB
ejpam-5744	261	23	inequality	inequality	NOUN
ejpam-5744	261	24	∥pc(τ)(ς)−	∥pc(τ)(ς)−	PUNCT
ejpam-5744	261	25	pc(ϱ)(ς)∥	pc(ϱ)(ς)∥	PROPN
ejpam-5744	261	26	≤	≤	PROPN
ejpam-5744	261	27	κ∥τ	κ∥τ	NOUN
ejpam-5744	261	28	−	−	PROPN
ejpam-5744	262	1	ϱ∥.	ϱ∥.	PROPN
ejpam-5744	262	2	definition	definition	NOUN
ejpam-5744	262	3	4	4	NUM
ejpam-5744	262	4	.	.	PUNCT
ejpam-5744	263	1	a	a	DET
ejpam-5744	263	2	mapping	mapping	NOUN
ejpam-5744	263	3	ψ	ψ	X
ejpam-5744	263	4	:	:	PUNCT
ejpam-5744	263	5	h	h	NOUN
ejpam-5744	263	6	→	→	SYM
ejpam-5744	263	7	h	h	NOUN
ejpam-5744	263	8	is	be	AUX
ejpam-5744	263	9	called	call	VERB
ejpam-5744	263	10	•	•	NUM
ejpam-5744	263	11	ρ1	ρ1	NOUN
ejpam-5744	263	12	-	-	PUNCT
ejpam-5744	263	13	strongly	strongly	ADV
ejpam-5744	263	14	monotone	monotone	ADJ
ejpam-5744	263	15	if	if	SCONJ
ejpam-5744	263	16	∃ρ1	∃ρ1	NOUN
ejpam-5744	263	17	>	>	X
ejpam-5744	263	18	0	0	PUNCT
ejpam-5744	264	1	so	so	SCONJ
ejpam-5744	264	2	that	that	PRON
ejpam-5744	264	3	⟨ψ(ϱ)−ψ(ς	⟨ψ(ϱ)−ψ(ς	NOUN
ejpam-5744	264	4	)	)	PUNCT
ejpam-5744	264	5	,	,	PUNCT
ejpam-5744	265	1	ϱ−	ϱ−	CCONJ
ejpam-5744	265	2	ς⟩	ς⟩	NOUN
ejpam-5744	265	3	≥	≥	NUM
ejpam-5744	265	4	ρ1∥ϱ−	ρ1∥ϱ−	NOUN
ejpam-5744	265	5	ς∥2,∀ϱ	ς∥2,∀ϱ	NOUN
ejpam-5744	265	6	,	,	PUNCT
ejpam-5744	265	7	ς	ς	PROPN
ejpam-5744	265	8	∈	∈	PROPN
ejpam-5744	265	9	h	h	NOUN
ejpam-5744	265	10	;	;	PUNCT
ejpam-5744	265	11	•	•	ADP
ejpam-5744	265	12	relaxed	relaxed	ADJ
ejpam-5744	265	13	(	(	PUNCT
ejpam-5744	265	14	u	u	NOUN
ejpam-5744	265	15	,	,	PUNCT
ejpam-5744	265	16	v)-cocoercive	v)-cocoercive	ADJ
ejpam-5744	265	17	,	,	PUNCT
ejpam-5744	265	18	if	if	SCONJ
ejpam-5744	265	19	∃u	∃u	NOUN
ejpam-5744	265	20	,	,	PUNCT
ejpam-5744	265	21	v	v	ADP
ejpam-5744	265	22	>	>	X
ejpam-5744	265	23	0	0	PUNCT
ejpam-5744	266	1	so	so	SCONJ
ejpam-5744	266	2	that	that	PRON
ejpam-5744	266	3	⟨ψ(ϱ)−ψ(ς	⟨ψ(ϱ)−ψ(ς	NOUN
ejpam-5744	266	4	)	)	PUNCT
ejpam-5744	266	5	,	,	PUNCT
ejpam-5744	266	6	ϱ−	ϱ−	CCONJ
ejpam-5744	266	7	ς⟩	ς⟩	NOUN
ejpam-5744	266	8	≥	≥	NUM
ejpam-5744	266	9	(	(	PUNCT
ejpam-5744	266	10	−u)∥ψ(ϱ)−ψ(ς)∥2	−u)∥ψ(ϱ)−ψ(ς)∥2	NOUN
ejpam-5744	266	11	+	+	CCONJ
ejpam-5744	266	12	v∥ϱ−	v∥ϱ−	NOUN
ejpam-5744	266	13	ς∥2	ς∥2	NOUN
ejpam-5744	266	14	,	,	PUNCT
ejpam-5744	266	15	∀ϱ	∀ϱ	PROPN
ejpam-5744	266	16	,	,	PUNCT
ejpam-5744	266	17	ς	ς	PROPN
ejpam-5744	266	18	∈	∈	PROPN
ejpam-5744	266	19	h	h	NOUN
ejpam-5744	266	20	;	;	PUNCT
ejpam-5744	266	21	•	•	NUM
ejpam-5744	266	22	ρ2	ρ2	NOUN
ejpam-5744	266	23	-	-	PUNCT
ejpam-5744	266	24	lipschitz	lipschitz	NOUN
ejpam-5744	266	25	continuous	continuous	ADJ
ejpam-5744	266	26	,	,	PUNCT
ejpam-5744	266	27	if	if	SCONJ
ejpam-5744	266	28	∃ρ2	∃ρ2	PROPN
ejpam-5744	266	29	>	>	X
ejpam-5744	266	30	0	0	PUNCT
ejpam-5744	267	1	so	so	SCONJ
ejpam-5744	267	2	that	that	SCONJ
ejpam-5744	267	3	∥ψ(ϱ)−ψ(ς)∥	∥ψ(ϱ)−ψ(ς)∥	VERB
ejpam-5744	267	4	≤	≤	ADJ
ejpam-5744	267	5	ρ2∥ϱ−	ρ2∥ϱ−	PROPN
ejpam-5744	267	6	ς∥,∀ϱ	ς∥,∀ϱ	NUM
ejpam-5744	267	7	,	,	PUNCT
ejpam-5744	267	8	ς	ς	PROPN
ejpam-5744	267	9	∈	∈	PROPN
ejpam-5744	267	10	h	h	NOUN
ejpam-5744	267	11	.	.	PUNCT
ejpam-5744	268	1	m.	m.	PROPN
ejpam-5744	268	2	akram	akram	PROPN
ejpam-5744	268	3	/	/	PUNCT
ejpam-5744	268	4	eur	eur	PROPN
ejpam-5744	268	5	.	.	PUNCT
ejpam-5744	269	1	j.	j.	PROPN
ejpam-5744	269	2	pure	pure	PROPN
ejpam-5744	269	3	appl	appl	PROPN
ejpam-5744	269	4	.	.	PROPN
ejpam-5744	269	5	math	math	PROPN
ejpam-5744	269	6	,	,	PUNCT
ejpam-5744	269	7	18	18	NUM
ejpam-5744	269	8	(	(	PUNCT
ejpam-5744	269	9	1	1	NUM
ejpam-5744	269	10	)	)	PUNCT
ejpam-5744	269	11	(	(	PUNCT
ejpam-5744	269	12	2025	2025	NUM
ejpam-5744	269	13	)	)	PUNCT
ejpam-5744	269	14	,	,	PUNCT
ejpam-5744	269	15	5744	5744	NUM
ejpam-5744	269	16	12	12	NUM
ejpam-5744	269	17	of	of	ADP
ejpam-5744	269	18	19	19	NUM
ejpam-5744	269	19	now	now	ADV
ejpam-5744	269	20	,	,	PUNCT
ejpam-5744	269	21	as	as	ADP
ejpam-5744	269	22	an	an	DET
ejpam-5744	269	23	application	application	NOUN
ejpam-5744	269	24	of	of	ADP
ejpam-5744	269	25	simps	simp	NOUN
ejpam-5744	269	26	(	(	PUNCT
ejpam-5744	269	27	14	14	NUM
ejpam-5744	269	28	)	)	PUNCT
ejpam-5744	269	29	,	,	PUNCT
ejpam-5744	269	30	we	we	PRON
ejpam-5744	269	31	shall	shall	AUX
ejpam-5744	269	32	re	re	VERB
ejpam-5744	269	33	-	-	VERB
ejpam-5744	269	34	structure	structure	VERB
ejpam-5744	269	35	the	the	DET
ejpam-5744	269	36	following	follow	VERB
ejpam-5744	269	37	semiimplicit	semiimplicit	ADJ
ejpam-5744	269	38	midpoint	midpoint	NOUN
ejpam-5744	269	39	scheme	scheme	NOUN
ejpam-5744	269	40	to	to	PART
ejpam-5744	269	41	find	find	VERB
ejpam-5744	269	42	the	the	DET
ejpam-5744	269	43	common	common	ADJ
ejpam-5744	269	44	solution	solution	NOUN
ejpam-5744	269	45	of	of	ADP
ejpam-5744	269	46	gqv	gqv	NOUN
ejpam-5744	269	47	i	i	X
ejpam-5744	269	48	(	(	PUNCT
ejpam-5744	269	49	29	29	NUM
ejpam-5744	269	50	)	)	PUNCT
ejpam-5744	269	51	and	and	CCONJ
ejpam-5744	269	52	fixed	fix	VERB
ejpam-5744	269	53	point	point	NOUN
ejpam-5744	269	54	of	of	ADP
ejpam-5744	269	55	the	the	DET
ejpam-5744	269	56	mapping	mapping	NOUN
ejpam-5744	269	57	defined	define	VERB
ejpam-5744	269	58	in	in	ADP
ejpam-5744	269	59	(	(	PUNCT
ejpam-5744	269	60	2	2	NUM
ejpam-5744	269	61	)	)	PUNCT
ejpam-5744	269	62	.	.	PUNCT
ejpam-5744	270	1	algorithm	algorithm	PROPN
ejpam-5744	270	2	1	1	NUM
ejpam-5744	270	3	.	.	PUNCT
ejpam-5744	271	1	for	for	ADP
ejpam-5744	271	2	given	give	VERB
ejpam-5744	271	3	initial	initial	ADJ
ejpam-5744	271	4	point	point	NOUN
ejpam-5744	271	5	ϱ0	ϱ0	NOUN
ejpam-5744	271	6	,	,	PUNCT
ejpam-5744	271	7	estimate	estimate	VERB
ejpam-5744	271	8	the	the	DET
ejpam-5744	271	9	sequence	sequence	NOUN
ejpam-5744	271	10	{	{	PUNCT
ejpam-5744	271	11	ϱk}∞k=1	ϱk}∞k=1	X
ejpam-5744	271	12	by	by	ADP
ejpam-5744	271	13	the	the	DET
ejpam-5744	271	14	following	following	ADJ
ejpam-5744	271	15	implicit	implicit	ADJ
ejpam-5744	271	16	iterative	iterative	NOUN
ejpam-5744	271	17	scheme:	scheme:	NOUN
ejpam-5744	271	18	ϱk+1	ϱk+1	NUM
ejpam-5744	271	19	=	=	SYM
ejpam-5744	271	20	ψ[σk	ψ[σk	ADJ
ejpam-5744	271	21	−	−	NOUN
ejpam-5744	271	22	ψ(σk	ψ(σk	PROPN
ejpam-5744	271	23	)	)	PUNCT
ejpam-5744	271	24	+	+	CCONJ
ejpam-5744	271	25	pc(σk)[ψ(σk)−	pc(σk)[ψ(σk)−	PROPN
ejpam-5744	271	26	λψ(σk	λψ(σk	PROPN
ejpam-5744	271	27	)	)	PUNCT
ejpam-5744	271	28	]	]	PUNCT
ejpam-5744	272	1	]	]	PUNCT
ejpam-5744	272	2	,	,	PUNCT
ejpam-5744	272	3	σk	σk	PROPN
ejpam-5744	272	4	=	=	SYM
ejpam-5744	272	5	ψ	ψ	X
ejpam-5744	272	6	[	[	PUNCT
ejpam-5744	272	7	(	(	PUNCT
ejpam-5744	272	8	1−	1−	NUM
ejpam-5744	272	9	αk	αk	NOUN
ejpam-5744	272	10	)	)	PUNCT
ejpam-5744	272	11	(	(	PUNCT
ejpam-5744	272	12	σk	σk	CCONJ
ejpam-5744	272	13	+	+	NUM
ejpam-5744	272	14	ϑk	ϑk	PROPN
ejpam-5744	272	15	2	2	NUM
ejpam-5744	272	16	)	)	PUNCT
ejpam-5744	272	17	+	+	CCONJ
ejpam-5744	272	18	αkψ	αkψ	NOUN
ejpam-5744	272	19	(	(	PUNCT
ejpam-5744	272	20	σk	σk	PROPN
ejpam-5744	272	21	+	+	NUM
ejpam-5744	272	22	ϑk	ϑk	PROPN
ejpam-5744	272	23	2	2	NUM
ejpam-5744	272	24	)	)	PUNCT
ejpam-5744	272	25	]	]	PUNCT
ejpam-5744	272	26	,	,	PUNCT
ejpam-5744	272	27	ϑk	ϑk	PROPN
ejpam-5744	272	28	=	=	PRON
ejpam-5744	272	29	(	(	PUNCT
ejpam-5744	272	30	1−	1−	NUM
ejpam-5744	272	31	βk)ψ	βk)ψ	NUM
ejpam-5744	272	32	(	(	PUNCT
ejpam-5744	272	33	ϑk	ϑk	PROPN
ejpam-5744	272	34	+	+	CCONJ
ejpam-5744	272	35	ϱk	ϱk	NOUN
ejpam-5744	272	36	2	2	NUM
ejpam-5744	272	37	)	)	PUNCT
ejpam-5744	272	38	+	+	CCONJ
ejpam-5744	272	39	βkψ	βkψ	X
ejpam-5744	272	40	(	(	PUNCT
ejpam-5744	272	41	ϑk	ϑk	PROPN
ejpam-5744	272	42	+	+	NUM
ejpam-5744	272	43	θk	θk	PROPN
ejpam-5744	272	44	2	2	NUM
ejpam-5744	272	45	)	)	PUNCT
ejpam-5744	272	46	,	,	PUNCT
ejpam-5744	272	47	θk	θk	NOUN
ejpam-5744	272	48	=	=	SYM
ejpam-5744	272	49	(	(	PUNCT
ejpam-5744	272	50	1−	1−	NUM
ejpam-5744	272	51	γk	γk	NOUN
ejpam-5744	272	52	)	)	PUNCT
ejpam-5744	272	53	(	(	PUNCT
ejpam-5744	272	54	ϱk	ϱk	NOUN
ejpam-5744	272	55	+	+	NUM
ejpam-5744	272	56	θk	θk	NOUN
ejpam-5744	272	57	2	2	NUM
ejpam-5744	272	58	)	)	PUNCT
ejpam-5744	272	59	+	+	CCONJ
ejpam-5744	272	60	γkψ	γkψ	NOUN
ejpam-5744	272	61	(	(	PUNCT
ejpam-5744	272	62	ϱk	ϱk	NOUN
ejpam-5744	272	63	+	+	NUM
ejpam-5744	272	64	θk	θk	NOUN
ejpam-5744	272	65	2	2	NUM
ejpam-5744	272	66	)	)	PUNCT
ejpam-5744	272	67	]	]	PUNCT
ejpam-5744	272	68	,	,	PUNCT
ejpam-5744	272	69	(	(	PUNCT
ejpam-5744	272	70	33	33	NUM
ejpam-5744	272	71	)	)	PUNCT
ejpam-5744	272	72	where	where	SCONJ
ejpam-5744	272	73	{	{	PUNCT
ejpam-5744	272	74	αk	αk	NOUN
ejpam-5744	272	75	}	}	PUNCT
ejpam-5744	272	76	,	,	PUNCT
ejpam-5744	272	77	{	{	PUNCT
ejpam-5744	272	78	βk	βk	NOUN
ejpam-5744	272	79	}	}	PUNCT
ejpam-5744	272	80	,	,	PUNCT
ejpam-5744	272	81	{	{	PUNCT
ejpam-5744	272	82	γk	γk	NOUN
ejpam-5744	272	83	}	}	PUNCT
ejpam-5744	272	84	⊆	⊆	NUM
ejpam-5744	272	85	(	(	PUNCT
ejpam-5744	272	86	0	0	NUM
ejpam-5744	272	87	,	,	PUNCT
ejpam-5744	272	88	1	1	NUM
ejpam-5744	272	89	)	)	PUNCT
ejpam-5744	272	90	.	.	PUNCT
ejpam-5744	273	1	theorem	theorem	ADJ
ejpam-5744	273	2	4	4	NUM
ejpam-5744	273	3	.	.	PUNCT
ejpam-5744	273	4	let	let	VERB
ejpam-5744	273	5	pc(ϱ	pc(ϱ	PRON
ejpam-5744	273	6	)	)	PUNCT
ejpam-5744	273	7	:	:	PUNCT
ejpam-5744	274	1	h	h	NOUN
ejpam-5744	274	2	→	→	SYM
ejpam-5744	274	3	c(ϱ	c(ϱ	PROPN
ejpam-5744	274	4	)	)	PUNCT
ejpam-5744	274	5	be	be	AUX
ejpam-5744	274	6	a	a	DET
ejpam-5744	274	7	projection	projection	NOUN
ejpam-5744	274	8	mapping	mapping	NOUN
ejpam-5744	274	9	and	and	CCONJ
ejpam-5744	274	10	ψ	ψ	NOUN
ejpam-5744	274	11	,	,	PUNCT
ejpam-5744	274	12	ψ	ψ	X
ejpam-5744	274	13	:	:	PUNCT
ejpam-5744	274	14	h	h	NOUN
ejpam-5744	274	15	→	→	SYM
ejpam-5744	274	16	h	h	NOUN
ejpam-5744	274	17	be	be	AUX
ejpam-5744	274	18	non	non	ADJ
ejpam-5744	274	19	-	-	ADJ
ejpam-5744	274	20	linear	linear	ADJ
ejpam-5744	274	21	mappings	mapping	NOUN
ejpam-5744	274	22	so	so	SCONJ
ejpam-5744	274	23	that	that	SCONJ
ejpam-5744	274	24	ψ	ψ	ADP
ejpam-5744	274	25	satisfies	satisfie	NOUN
ejpam-5744	274	26	(	(	PUNCT
ejpam-5744	274	27	2	2	NUM
ejpam-5744	274	28	)	)	PUNCT
ejpam-5744	274	29	and	and	CCONJ
ejpam-5744	274	30	ξ(ψ	ξ(ψ	PROPN
ejpam-5744	274	31	)	)	PUNCT
ejpam-5744	274	32	∩	∩	PROPN
ejpam-5744	274	33	✠	✠	PROPN
ejpam-5744	274	34	(	(	PUNCT
ejpam-5744	274	35	c(ϱ),ψ	c(ϱ),ψ	PROPN
ejpam-5744	274	36	,	,	PUNCT
ejpam-5744	274	37	ψ	ψ	NOUN
ejpam-5744	274	38	)	)	PUNCT
ejpam-5744	274	39	̸=	̸=	PROPN
ejpam-5744	274	40	∅.	∅.	ADV
ejpam-5744	274	41	assume	assume	VERB
ejpam-5744	274	42	that	that	SCONJ
ejpam-5744	274	43	the	the	DET
ejpam-5744	274	44	assumption	assumption	NOUN
ejpam-5744	274	45	a	a	PRON
ejpam-5744	274	46	and	and	CCONJ
ejpam-5744	274	47	the	the	DET
ejpam-5744	274	48	following	follow	VERB
ejpam-5744	274	49	relations	relation	NOUN
ejpam-5744	274	50	hold	hold	VERB
ejpam-5744	274	51	:	:	PUNCT
ejpam-5744	274	52	(	(	PUNCT
ejpam-5744	274	53	r1	r1	PROPN
ejpam-5744	274	54	)	)	PUNCT
ejpam-5744	274	55	ψ	ψ	NOUN
ejpam-5744	274	56	is	be	AUX
ejpam-5744	274	57	l	l	ADJ
ejpam-5744	274	58	-	-	ADJ
ejpam-5744	274	59	lipschitz	lipschitz	ADJ
ejpam-5744	274	60	continuous	continuous	ADJ
ejpam-5744	274	61	and	and	CCONJ
ejpam-5744	274	62	relaxed	relaxed	ADJ
ejpam-5744	274	63	(	(	PUNCT
ejpam-5744	274	64	u	u	NOUN
ejpam-5744	274	65	,	,	PUNCT
ejpam-5744	274	66	v)-cocoercive	v)-cocoercive	PUNCT
ejpam-5744	274	67	and	and	CCONJ
ejpam-5744	274	68	ψ	ψ	NOUN
ejpam-5744	274	69	is	be	AUX
ejpam-5744	274	70	t	t	NOUN
ejpam-5744	274	71	-	-	PUNCT
ejpam-5744	274	72	lipschitz	lipschitz	NOUN
ejpam-5744	274	73	continuous	continuous	ADJ
ejpam-5744	274	74	and	and	CCONJ
ejpam-5744	274	75	r	r	NOUN
ejpam-5744	274	76	-	-	PUNCT
ejpam-5744	274	77	strongly	strongly	ADV
ejpam-5744	274	78	monotone	monotone	ADJ
ejpam-5744	274	79	.	.	PUNCT
ejpam-5744	275	1	(	(	PUNCT
ejpam-5744	275	2	r2	r2	PROPN
ejpam-5744	275	3	)	)	PUNCT
ejpam-5744	275	4	the	the	DET
ejpam-5744	275	5	constant	constant	ADJ
ejpam-5744	275	6	λ	λ	X
ejpam-5744	275	7	>	>	SYM
ejpam-5744	275	8	0	0	NUM
ejpam-5744	275	9	obeys	obey	VERB
ejpam-5744	275	10	the	the	DET
ejpam-5744	275	11	following	follow	VERB
ejpam-5744	275	12	relation	relation	NOUN
ejpam-5744	275	13	:	:	PUNCT
ejpam-5744	275	14	λl2	λl2	X
ejpam-5744	275	15	≤	≤	NUM
ejpam-5744	275	16	2λv	2λv	NOUN
ejpam-5744	276	1	+	+	ADJ
ejpam-5744	276	2	∆(∆−	∆(∆−	PROPN
ejpam-5744	276	3	2	2	NUM
ejpam-5744	276	4	)	)	PUNCT
ejpam-5744	276	5	λ+	λ+	PUNCT
ejpam-5744	276	6	2u	2u	NOUN
ejpam-5744	276	7	,	,	PUNCT
ejpam-5744	276	8	∆	∆	PROPN
ejpam-5744	276	9	=	=	SYM
ejpam-5744	276	10	2	2	NUM
ejpam-5744	276	11	√	√	NUM
ejpam-5744	276	12	1−	1−	NUM
ejpam-5744	276	13	2r	2r	NUM
ejpam-5744	276	14	+	+	CCONJ
ejpam-5744	276	15	t2	t2	NOUN
ejpam-5744	276	16	+	+	CCONJ
ejpam-5744	276	17	κ	κ	X
ejpam-5744	276	18	.	.	PUNCT
ejpam-5744	277	1	(	(	PUNCT
ejpam-5744	277	2	34	34	NUM
ejpam-5744	277	3	)	)	PUNCT
ejpam-5744	277	4	then	then	ADV
ejpam-5744	277	5	{	{	PUNCT
ejpam-5744	277	6	ϱk}∞k=1	ϱk}∞k=1	PUNCT
ejpam-5744	277	7	approximated	approximate	VERB
ejpam-5744	277	8	by	by	ADP
ejpam-5744	277	9	(	(	PUNCT
ejpam-5744	277	10	33	33	NUM
ejpam-5744	277	11	)	)	PUNCT
ejpam-5744	277	12	converges	converge	VERB
ejpam-5744	277	13	strongly	strongly	ADV
ejpam-5744	277	14	to	to	ADP
ejpam-5744	277	15	ϱ	ϱ	ADP
ejpam-5744	277	16	∈	∈	PROPN
ejpam-5744	277	17	ξ(ψ	ξ(ψ	NUM
ejpam-5744	277	18	)	)	PUNCT
ejpam-5744	277	19	∩	∩	PROPN
ejpam-5744	277	20	✠	✠	NOUN
ejpam-5744	277	21	(c(ϱ),ψ	(c(ϱ),ψ	PROPN
ejpam-5744	277	22	,	,	PUNCT
ejpam-5744	277	23	ψ	ψ	NOUN
ejpam-5744	277	24	)	)	PUNCT
ejpam-5744	277	25	.	.	PUNCT
ejpam-5744	278	1	proof	proof	NOUN
ejpam-5744	278	2	.	.	PUNCT
ejpam-5744	279	1	invoking	invoke	VERB
ejpam-5744	279	2	the	the	DET
ejpam-5744	279	3	l	l	ADJ
ejpam-5744	279	4	-	-	ADJ
ejpam-5744	279	5	lipschitz	lipschitz	ADJ
ejpam-5744	279	6	continuity	continuity	NOUN
ejpam-5744	279	7	and	and	CCONJ
ejpam-5744	279	8	relaxed	relaxed	ADJ
ejpam-5744	279	9	(	(	PUNCT
ejpam-5744	279	10	u	u	NOUN
ejpam-5744	279	11	,	,	PUNCT
ejpam-5744	279	12	v)-cocoercivity	v)-cocoercivity	NUM
ejpam-5744	279	13	of	of	ADP
ejpam-5744	279	14	ψ	ψ	NOUN
ejpam-5744	279	15	yields	yield	NOUN
ejpam-5744	279	16	∥(σk	∥(σk	PUNCT
ejpam-5744	279	17	−	−	PROPN
ejpam-5744	279	18	ϱ)−	ϱ)−	PROPN
ejpam-5744	279	19	λ[ψ(σk)−ψ(ϱ)]∥2	λ[ψ(σk)−ψ(ϱ)]∥2	PROPN
ejpam-5744	279	20	=	=	PUNCT
ejpam-5744	279	21	∥σk	∥σk	NOUN
ejpam-5744	279	22	−	−	NOUN
ejpam-5744	279	23	ϱ∥2	ϱ∥2	ADJ
ejpam-5744	279	24	−	−	PROPN
ejpam-5744	279	25	2λ⟨ψ(σk)−ψ(ϱ	2λ⟨ψ(σk)−ψ(ϱ	NUM
ejpam-5744	279	26	)	)	PUNCT
ejpam-5744	279	27	,	,	PUNCT
ejpam-5744	279	28	σk	σk	SCONJ
ejpam-5744	279	29	−	−	PROPN
ejpam-5744	279	30	ϱ⟩+	ϱ⟩+	PROPN
ejpam-5744	279	31	λ2∥ψ(σk)−ψ(ϱ)∥2	λ2∥ψ(σk)−ψ(ϱ)∥2	PROPN
ejpam-5744	279	32	≤	≤	PROPN
ejpam-5744	279	33	∥σk	∥σk	PART
ejpam-5744	279	34	−	−	NOUN
ejpam-5744	279	35	ϱ∥2	ϱ∥2	ADJ
ejpam-5744	279	36	+	+	PROPN
ejpam-5744	280	1	2λu∥ψ(σk)−ψ(ϱ)∥2	2λu∥ψ(σk)−ψ(ϱ)∥2	NUM
ejpam-5744	280	2	−	−	NOUN
ejpam-5744	280	3	2λv∥σk	2λv∥σk	NUM
ejpam-5744	281	1	−	−	NOUN
ejpam-5744	281	2	ϱ∥2	ϱ∥2	ADJ
ejpam-5744	281	3	+	+	CCONJ
ejpam-5744	281	4	λ2l2∥σk	λ2l2∥σk	PROPN
ejpam-5744	281	5	−	−	NOUN
ejpam-5744	281	6	ϱ∥2	ϱ∥2	VERB
ejpam-5744	281	7	≤	≤	NOUN
ejpam-5744	281	8	∥σk	∥σk	PART
ejpam-5744	281	9	−	−	NOUN
ejpam-5744	281	10	ϱ∥2	ϱ∥2	ADJ
ejpam-5744	281	11	+	+	CCONJ
ejpam-5744	281	12	2λul2∥σk	2λul2∥σk	NUM
ejpam-5744	281	13	−	−	NOUN
ejpam-5744	281	14	ϱ∥2	ϱ∥2	VERB
ejpam-5744	281	15	−	−	PROPN
ejpam-5744	281	16	2λv∥σk	2λv∥σk	NUM
ejpam-5744	281	17	−	−	NOUN
ejpam-5744	281	18	ϱ∥2	ϱ∥2	ADJ
ejpam-5744	281	19	+	+	CCONJ
ejpam-5744	281	20	λ2l2∥σk	λ2l2∥σk	PROPN
ejpam-5744	281	21	−	−	NOUN
ejpam-5744	281	22	ϱ∥2	ϱ∥2	ADJ
ejpam-5744	281	23	=	=	PUNCT
ejpam-5744	282	1	[	[	X
ejpam-5744	282	2	1−	1−	NUM
ejpam-5744	282	3	2λ(v	2λ(v	NUM
ejpam-5744	282	4	−	−	NOUN
ejpam-5744	282	5	ul2	ul2	VERB
ejpam-5744	282	6	)	)	PUNCT
ejpam-5744	283	1	+	+	CCONJ
ejpam-5744	283	2	λ2l2]∥σk	λ2l2]∥σk	NOUN
ejpam-5744	283	3	−	−	NOUN
ejpam-5744	283	4	ϱ∥2	ϱ∥2	ADJ
ejpam-5744	283	5	=	=	PUNCT
ejpam-5744	283	6	b2∥σk	b2∥σk	NOUN
ejpam-5744	283	7	−	−	PROPN
ejpam-5744	283	8	ϱ∥2	ϱ∥2	ADJ
ejpam-5744	283	9	.	.	PUNCT
ejpam-5744	284	1	(	(	PUNCT
ejpam-5744	284	2	35	35	NUM
ejpam-5744	284	3	)	)	PUNCT
ejpam-5744	284	4	employing	employ	VERB
ejpam-5744	284	5	the	the	DET
ejpam-5744	284	6	t	t	NOUN
ejpam-5744	284	7	-	-	PUNCT
ejpam-5744	284	8	lipschitz	lipschitz	NOUN
ejpam-5744	284	9	continuity	continuity	NOUN
ejpam-5744	284	10	and	and	CCONJ
ejpam-5744	284	11	r	r	NOUN
ejpam-5744	284	12	-	-	PUNCT
ejpam-5744	284	13	strongly	strongly	ADV
ejpam-5744	284	14	monotone	monotone	ADJ
ejpam-5744	284	15	property	property	NOUN
ejpam-5744	284	16	of	of	ADP
ejpam-5744	284	17	ψ	ψ	PRON
ejpam-5744	284	18	provide	provide	VERB
ejpam-5744	284	19	with	with	ADP
ejpam-5744	284	20	the	the	DET
ejpam-5744	284	21	relation	relation	NOUN
ejpam-5744	284	22	∥σk	∥σk	NOUN
ejpam-5744	284	23	−	−	PROPN
ejpam-5744	284	24	ϱ−	ϱ−	PROPN
ejpam-5744	285	1	[	[	X
ejpam-5744	285	2	ψ(σk)−	ψ(σk)−	X
ejpam-5744	285	3	ψ(ϱ)]∥2	ψ(ϱ)]∥2	ADJ
ejpam-5744	285	4	=	=	PUNCT
ejpam-5744	285	5	∥σk	∥σk	NOUN
ejpam-5744	285	6	−	−	NOUN
ejpam-5744	285	7	ϱ∥2	ϱ∥2	ADJ
ejpam-5744	285	8	−	−	PROPN
ejpam-5744	285	9	2⟨ψ(σk)−	2⟨ψ(σk)−	NUM
ejpam-5744	285	10	ψ(ϱ	ψ(ϱ	NOUN
ejpam-5744	285	11	)	)	PUNCT
ejpam-5744	285	12	,	,	PUNCT
ejpam-5744	285	13	σk	σk	ADP
ejpam-5744	285	14	−	−	PROPN
ejpam-5744	285	15	ϱ⟩+	ϱ⟩+	PROPN
ejpam-5744	285	16	∥ψ(σk)−	∥ψ(σk)−	PROPN
ejpam-5744	285	17	ψ(ϱ)∥2	ψ(ϱ)∥2	NOUN
ejpam-5744	285	18	≤	≤	NOUN
ejpam-5744	285	19	∥σk	∥σk	PART
ejpam-5744	285	20	−	−	NOUN
ejpam-5744	285	21	ϱ∥2	ϱ∥2	ADJ
ejpam-5744	285	22	−	−	PROPN
ejpam-5744	285	23	2r∥σk	2r∥σk	NUM
ejpam-5744	285	24	−	−	NOUN
ejpam-5744	285	25	ϱ∥2	ϱ∥2	ADJ
ejpam-5744	285	26	+	+	CCONJ
ejpam-5744	285	27	t2∥σk	t2∥σk	NOUN
ejpam-5744	285	28	−	−	NOUN
ejpam-5744	285	29	ϱ∥2	ϱ∥2	ADJ
ejpam-5744	285	30	=	=	SYM
ejpam-5744	285	31	(	(	PUNCT
ejpam-5744	285	32	1−	1−	NUM
ejpam-5744	285	33	2r	2r	NUM
ejpam-5744	285	34	+	+	CCONJ
ejpam-5744	285	35	t2)∥σk	t2)∥σk	ADP
ejpam-5744	285	36	−	−	ADV
ejpam-5744	285	37	ϱ∥2	ϱ∥2	ADJ
ejpam-5744	285	38	=	=	SYM
ejpam-5744	285	39	a2∥σk	a2∥σk	NOUN
ejpam-5744	285	40	−	−	PROPN
ejpam-5744	285	41	ϱ∥2	ϱ∥2	ADJ
ejpam-5744	285	42	.	.	PUNCT
ejpam-5744	286	1	(	(	PUNCT
ejpam-5744	286	2	36	36	NUM
ejpam-5744	286	3	)	)	PUNCT
ejpam-5744	286	4	m.	m.	NOUN
ejpam-5744	286	5	akram	akram	PROPN
ejpam-5744	286	6	/	/	PUNCT
ejpam-5744	286	7	eur	eur	PROPN
ejpam-5744	286	8	.	.	PUNCT
ejpam-5744	287	1	j.	j.	PROPN
ejpam-5744	287	2	pure	pure	PROPN
ejpam-5744	287	3	appl	appl	PROPN
ejpam-5744	287	4	.	.	PROPN
ejpam-5744	287	5	math	math	PROPN
ejpam-5744	287	6	,	,	PUNCT
ejpam-5744	287	7	18	18	NUM
ejpam-5744	287	8	(	(	PUNCT
ejpam-5744	287	9	1	1	NUM
ejpam-5744	287	10	)	)	PUNCT
ejpam-5744	287	11	(	(	PUNCT
ejpam-5744	287	12	2025	2025	NUM
ejpam-5744	287	13	)	)	PUNCT
ejpam-5744	287	14	,	,	PUNCT
ejpam-5744	287	15	5744	5744	NUM
ejpam-5744	287	16	13	13	NUM
ejpam-5744	287	17	of	of	ADP
ejpam-5744	287	18	19	19	NUM
ejpam-5744	287	19	∥ϱk+1	∥ϱk+1	NOUN
ejpam-5744	287	20	−	−	PROPN
ejpam-5744	287	21	ϱ∥	ϱ∥	NOUN
ejpam-5744	287	22	=	=	SYM
ejpam-5744	287	23	∥ψ[σk	∥ψ[σk	PROPN
ejpam-5744	287	24	−	−	NOUN
ejpam-5744	287	25	ψ(σk	ψ(σk	PROPN
ejpam-5744	287	26	)	)	PUNCT
ejpam-5744	288	1	+	+	CCONJ
ejpam-5744	288	2	pc(σk)[ψ(σk)−	pc(σk)[ψ(σk)−	ADJ
ejpam-5744	288	3	λψ(σk)]]−	λψ(σk)]]−	PROPN
ejpam-5744	288	4	ϱ∥	ϱ∥	NOUN
ejpam-5744	288	5	=	=	PUNCT
ejpam-5744	288	6	∥ψ(ϱ)−ψ[σk	∥ψ(ϱ)−ψ[σk	VERB
ejpam-5744	288	7	−	−	NOUN
ejpam-5744	288	8	ψ(σk	ψ(σk	NOUN
ejpam-5744	288	9	)	)	PUNCT
ejpam-5744	289	1	+	+	CCONJ
ejpam-5744	289	2	pc(σk)[ψ(σk)−	pc(σk)[ψ(σk)−	ADJ
ejpam-5744	289	3	λψ(σk)]]∥	λψ(σk)]]∥	NOUN
ejpam-5744	289	4	≤	≤	NUM
ejpam-5744	289	5	g(∥ϱ−ψ(ϱ)∥	g(∥ϱ−ψ(ϱ)∥	NOUN
ejpam-5744	289	6	)	)	PUNCT
ejpam-5744	290	1	+	+	CCONJ
ejpam-5744	290	2	τ∥σk	τ∥σk	ADJ
ejpam-5744	290	3	−	−	NOUN
ejpam-5744	290	4	ψ(σk	ψ(σk	NOUN
ejpam-5744	290	5	)	)	PUNCT
ejpam-5744	291	1	+	+	CCONJ
ejpam-5744	291	2	pc(σk)[ψ(σk)−	pc(σk)[ψ(σk)−	PROPN
ejpam-5744	291	3	λψ(σk)]−	λψ(σk)]−	PROPN
ejpam-5744	291	4	ϱ∥	ϱ∥	NOUN
ejpam-5744	291	5	=	=	SYM
ejpam-5744	291	6	τ∥σk	τ∥σk	NOUN
ejpam-5744	291	7	−	−	NOUN
ejpam-5744	291	8	ψ(σk	ψ(σk	PROPN
ejpam-5744	291	9	)	)	PUNCT
ejpam-5744	291	10	+	+	CCONJ
ejpam-5744	291	11	pc(σk)[ψ(σk)−	pc(σk)[ψ(σk)−	ADJ
ejpam-5744	291	12	λψ(σk)]−	λψ(σk)]−	PROPN
ejpam-5744	291	13	[	[	X
ejpam-5744	291	14	ϱ−	ϱ−	X
ejpam-5744	291	15	ψ(ϱ	ψ(ϱ	NOUN
ejpam-5744	291	16	)	)	PUNCT
ejpam-5744	292	1	+	+	NUM
ejpam-5744	292	2	pc(ϱ)[ψ(ϱ)−	pc(ϱ)[ψ(ϱ)−	PROPN
ejpam-5744	292	3	λψ(ϱ)]∥	λψ(ϱ)]∥	PROPN
ejpam-5744	292	4	≤	≤	NUM
ejpam-5744	292	5	τ	τ	X
ejpam-5744	292	6	(	(	PUNCT
ejpam-5744	292	7	∥σk	∥σk	NOUN
ejpam-5744	292	8	−	−	PROPN
ejpam-5744	292	9	ϱ−	ϱ−	PROPN
ejpam-5744	293	1	[	[	X
ejpam-5744	293	2	ψ(σk)−	ψ(σk)−	NOUN
ejpam-5744	293	3	ψ(ϱ)]∥+	ψ(ϱ)]∥+	X
ejpam-5744	293	4	∥ψ(σk)−	∥ψ(σk)−	PROPN
ejpam-5744	293	5	ψ(ϱ)−	ψ(ϱ)−	VERB
ejpam-5744	293	6	λ[ψ(σk)−ψ(ϱ)]∥+	λ[ψ(σk)−ψ(ϱ)]∥+	PROPN
ejpam-5744	293	7	κ∥σk	κ∥σk	ADJ
ejpam-5744	293	8	−	−	PROPN
ejpam-5744	293	9	ϱ∥	ϱ∥	NOUN
ejpam-5744	293	10	)	)	PUNCT
ejpam-5744	294	1	≤	≤	NUM
ejpam-5744	294	2	2τ∥σk	2τ∥σk	NUM
ejpam-5744	294	3	−	−	NOUN
ejpam-5744	294	4	ϱ−	ϱ−	PROPN
ejpam-5744	295	1	[	[	X
ejpam-5744	295	2	ψ(σk)−	ψ(σk)−	NOUN
ejpam-5744	295	3	ψ(ϱ)]∥+	ψ(ϱ)]∥+	X
ejpam-5744	295	4	τ∥(σk	τ∥(σk	PROPN
ejpam-5744	295	5	−	−	PROPN
ejpam-5744	296	1	ϱ)−	ϱ)−	PROPN
ejpam-5744	296	2	λ[ψ(σk)−ψ(ϱ)]∥+	λ[ψ(σk)−ψ(ϱ)]∥+	PART
ejpam-5744	296	3	τκ∥σk	τκ∥σk	NOUN
ejpam-5744	296	4	−	−	NOUN
ejpam-5744	296	5	ϱ∥	ϱ∥	NOUN
ejpam-5744	296	6	≤	≤	NUM
ejpam-5744	296	7	τ(2a+	τ(2a+	ADV
ejpam-5744	296	8	b+	b+	X
ejpam-5744	296	9	κ)∥σk	κ)∥σk	PROPN
ejpam-5744	296	10	−	−	PROPN
ejpam-5744	296	11	ϱ∥.	ϱ∥.	PROPN
ejpam-5744	296	12	(	(	PUNCT
ejpam-5744	296	13	37	37	NUM
ejpam-5744	296	14	)	)	PUNCT
ejpam-5744	296	15	replicating	replicate	VERB
ejpam-5744	296	16	the	the	DET
ejpam-5744	296	17	process	process	NOUN
ejpam-5744	296	18	as	as	ADP
ejpam-5744	296	19	from	from	ADP
ejpam-5744	296	20	(	(	PUNCT
ejpam-5744	296	21	15)-(19	15)-(19	NUM
ejpam-5744	296	22	)	)	PUNCT
ejpam-5744	296	23	and	and	CCONJ
ejpam-5744	296	24	combining	combine	VERB
ejpam-5744	296	25	with	with	ADP
ejpam-5744	296	26	(	(	PUNCT
ejpam-5744	296	27	37	37	NUM
ejpam-5744	296	28	)	)	PUNCT
ejpam-5744	296	29	yields	yield	NOUN
ejpam-5744	296	30	∥ϱk+1	∥ϱk+1	PRON
ejpam-5744	296	31	−	−	PROPN
ejpam-5744	296	32	ϱ∥	ϱ∥	NOUN
ejpam-5744	296	33	≤	≤	NUM
ejpam-5744	296	34	(	(	PUNCT
ejpam-5744	296	35	1−	1−	NUM
ejpam-5744	296	36	ℓ̂n)(2a+	ℓ̂n)(2a+	NUM
ejpam-5744	296	37	b+	b+	X
ejpam-5744	296	38	κ)∥ϱk	κ)∥ϱk	PROPN
ejpam-5744	296	39	−	−	PROPN
ejpam-5744	296	40	ϱ∥	ϱ∥	NOUN
ejpam-5744	296	41	,	,	PUNCT
ejpam-5744	296	42	(	(	PUNCT
ejpam-5744	296	43	38	38	NUM
ejpam-5744	296	44	)	)	PUNCT
ejpam-5744	296	45	where	where	SCONJ
ejpam-5744	296	46	ℓ̂k	ℓ̂k	PROPN
ejpam-5744	296	47	is	be	AUX
ejpam-5744	296	48	described	describe	VERB
ejpam-5744	296	49	in	in	ADP
ejpam-5744	296	50	(	(	PUNCT
ejpam-5744	296	51	21	21	NUM
ejpam-5744	296	52	)	)	PUNCT
ejpam-5744	296	53	.	.	PUNCT
ejpam-5744	297	1	evidently	evidently	ADV
ejpam-5744	297	2	,	,	PUNCT
ejpam-5744	297	3	(	(	PUNCT
ejpam-5744	297	4	2a	2a	NUM
ejpam-5744	297	5	+	+	CCONJ
ejpam-5744	297	6	b	b	NOUN
ejpam-5744	297	7	+	+	NUM
ejpam-5744	297	8	κ	κ	NOUN
ejpam-5744	297	9	)	)	PUNCT
ejpam-5744	297	10	<	<	X
ejpam-5744	297	11	1	1	NUM
ejpam-5744	297	12	from	from	ADP
ejpam-5744	297	13	the	the	DET
ejpam-5744	297	14	assumption	assumption	NOUN
ejpam-5744	297	15	(	(	PUNCT
ejpam-5744	297	16	r2	r2	PROPN
ejpam-5744	297	17	)	)	PUNCT
ejpam-5744	297	18	.	.	PUNCT
ejpam-5744	298	1	then	then	ADV
ejpam-5744	298	2	(	(	PUNCT
ejpam-5744	298	3	38	38	NUM
ejpam-5744	298	4	)	)	PUNCT
ejpam-5744	298	5	turns	turn	VERB
ejpam-5744	298	6	into	into	ADP
ejpam-5744	298	7	∥ϱk+1	∥ϱk+1	PRON
ejpam-5744	298	8	−	−	PROPN
ejpam-5744	298	9	ϱ∥	ϱ∥	NOUN
ejpam-5744	298	10	≤	≤	NUM
ejpam-5744	298	11	(	(	PUNCT
ejpam-5744	298	12	1−	1−	NUM
ejpam-5744	298	13	ℓ̂n)∥ϱk	ℓ̂n)∥ϱk	NUM
ejpam-5744	298	14	−	−	PROPN
ejpam-5744	298	15	ϱ∥.	ϱ∥.	PROPN
ejpam-5744	298	16	(	(	PUNCT
ejpam-5744	298	17	39	39	NUM
ejpam-5744	298	18	)	)	PUNCT
ejpam-5744	298	19	thus	thus	ADV
ejpam-5744	298	20	,	,	PUNCT
ejpam-5744	298	21	from	from	ADP
ejpam-5744	298	22	(	(	PUNCT
ejpam-5744	298	23	39	39	NUM
ejpam-5744	298	24	)	)	PUNCT
ejpam-5744	298	25	and	and	CCONJ
ejpam-5744	298	26	implementing	implement	VERB
ejpam-5744	298	27	lemma	lemma	PROPN
ejpam-5744	298	28	1	1	NUM
ejpam-5744	298	29	,	,	PUNCT
ejpam-5744	298	30	we	we	PRON
ejpam-5744	298	31	acquire	acquire	VERB
ejpam-5744	298	32	lim	lim	PROPN
ejpam-5744	298	33	k→∞	k→∞	PROPN
ejpam-5744	298	34	∥ϱk	∥ϱk	PROPN
ejpam-5744	299	1	−	−	PROPN
ejpam-5744	299	2	ϱ∥	ϱ∥	NOUN
ejpam-5744	299	3	=	=	NOUN
ejpam-5744	299	4	0	0	X
ejpam-5744	299	5	.	.	PUNCT
ejpam-5744	299	6	by	by	ADP
ejpam-5744	299	7	taking	take	VERB
ejpam-5744	299	8	c(ϱ	c(ϱ	NOUN
ejpam-5744	299	9	)	)	PUNCT
ejpam-5744	300	1	=	=	PRON
ejpam-5744	300	2	:	:	PUNCT
ejpam-5744	300	3	c	c	X
ejpam-5744	300	4	,	,	PUNCT
ejpam-5744	300	5	we	we	PRON
ejpam-5744	300	6	deduce	deduce	VERB
ejpam-5744	300	7	the	the	DET
ejpam-5744	300	8	following	follow	VERB
ejpam-5744	300	9	corollary	corollary	NOUN
ejpam-5744	300	10	to	to	PART
ejpam-5744	300	11	estimate	estimate	VERB
ejpam-5744	300	12	the	the	DET
ejpam-5744	300	13	common	common	ADJ
ejpam-5744	300	14	solution	solution	NOUN
ejpam-5744	300	15	of	of	ADP
ejpam-5744	300	16	the	the	DET
ejpam-5744	300	17	gv	gv	PROPN
ejpam-5744	300	18	i	i	PRON
ejpam-5744	300	19	(	(	PUNCT
ejpam-5744	300	20	30	30	NUM
ejpam-5744	300	21	)	)	PUNCT
ejpam-5744	300	22	and	and	CCONJ
ejpam-5744	300	23	the	the	DET
ejpam-5744	300	24	contractive	contractive	ADJ
ejpam-5744	300	25	mapping	mapping	NOUN
ejpam-5744	300	26	(	(	PUNCT
ejpam-5744	300	27	2	2	NUM
ejpam-5744	300	28	)	)	PUNCT
ejpam-5744	300	29	.	.	PUNCT
ejpam-5744	301	1	corollary	corollary	ADJ
ejpam-5744	301	2	1	1	NUM
ejpam-5744	301	3	.	.	PUNCT
ejpam-5744	302	1	let	let	VERB
ejpam-5744	302	2	pc	pc	NOUN
ejpam-5744	302	3	:	:	PUNCT
ejpam-5744	302	4	h	h	NOUN
ejpam-5744	302	5	→	→	PUNCT
ejpam-5744	302	6	c	c	AUX
ejpam-5744	302	7	be	be	AUX
ejpam-5744	302	8	a	a	DET
ejpam-5744	302	9	projection	projection	NOUN
ejpam-5744	302	10	mapping	mapping	NOUN
ejpam-5744	302	11	and	and	CCONJ
ejpam-5744	302	12	ψ	ψ	NOUN
ejpam-5744	302	13	,	,	PUNCT
ejpam-5744	302	14	ψ	ψ	X
ejpam-5744	302	15	:	:	PUNCT
ejpam-5744	302	16	h	h	NOUN
ejpam-5744	302	17	→	→	SYM
ejpam-5744	302	18	h	h	NOUN
ejpam-5744	302	19	be	be	AUX
ejpam-5744	302	20	non	non	ADJ
ejpam-5744	302	21	-	-	ADJ
ejpam-5744	302	22	linear	linear	ADJ
ejpam-5744	302	23	mappings	mapping	NOUN
ejpam-5744	302	24	so	so	SCONJ
ejpam-5744	302	25	that	that	SCONJ
ejpam-5744	302	26	ψ	ψ	ADP
ejpam-5744	302	27	satisfies	satisfie	NOUN
ejpam-5744	302	28	(	(	PUNCT
ejpam-5744	302	29	2	2	NUM
ejpam-5744	302	30	)	)	PUNCT
ejpam-5744	302	31	and	and	CCONJ
ejpam-5744	302	32	ξ(ψ)∩	ξ(ψ)∩	PROPN
ejpam-5744	302	33	✠	✠	PROPN
ejpam-5744	302	34	(c	(c	PROPN
ejpam-5744	302	35	,	,	PUNCT
ejpam-5744	302	36	ψ	ψ	PROPN
ejpam-5744	302	37	,	,	PUNCT
ejpam-5744	302	38	ψ	ψ	NOUN
ejpam-5744	302	39	)	)	PUNCT
ejpam-5744	302	40	̸=	̸=	NOUN
ejpam-5744	302	41	∅	∅	NOUN
ejpam-5744	302	42	,	,	PUNCT
ejpam-5744	302	43	where	where	SCONJ
ejpam-5744	302	44	✠	✠	PROPN
ejpam-5744	302	45	(	(	PUNCT
ejpam-5744	302	46	c	c	PROPN
ejpam-5744	302	47	,	,	PUNCT
ejpam-5744	302	48	ψ	ψ	X
ejpam-5744	302	49	,	,	PUNCT
ejpam-5744	302	50	ψ	ψ	NOUN
ejpam-5744	302	51	)	)	PUNCT
ejpam-5744	302	52	signifies	signify	VERB
ejpam-5744	302	53	the	the	DET
ejpam-5744	302	54	solution	solution	NOUN
ejpam-5744	302	55	set	set	VERB
ejpam-5744	302	56	of	of	ADP
ejpam-5744	302	57	the	the	DET
ejpam-5744	302	58	gv	gv	PROPN
ejpam-5744	302	59	i	i	PRON
ejpam-5744	302	60	(	(	PUNCT
ejpam-5744	302	61	30	30	NUM
ejpam-5744	302	62	)	)	PUNCT
ejpam-5744	302	63	.	.	PUNCT
ejpam-5744	303	1	assume	assume	VERB
ejpam-5744	303	2	that	that	SCONJ
ejpam-5744	303	3	the	the	DET
ejpam-5744	303	4	following	follow	VERB
ejpam-5744	303	5	relations	relation	NOUN
ejpam-5744	303	6	hold	hold	VERB
ejpam-5744	303	7	:	:	PUNCT
ejpam-5744	303	8	(	(	PUNCT
ejpam-5744	303	9	v1	v1	NOUN
ejpam-5744	303	10	)	)	PUNCT
ejpam-5744	303	11	ψ	ψ	NOUN
ejpam-5744	303	12	is	be	AUX
ejpam-5744	303	13	l	l	ADJ
ejpam-5744	303	14	-	-	ADJ
ejpam-5744	303	15	lipschitz	lipschitz	ADJ
ejpam-5744	303	16	continuous	continuous	ADJ
ejpam-5744	303	17	and	and	CCONJ
ejpam-5744	303	18	relaxed	relaxed	ADJ
ejpam-5744	303	19	(	(	PUNCT
ejpam-5744	303	20	u	u	NOUN
ejpam-5744	303	21	,	,	PUNCT
ejpam-5744	303	22	v)-cocoercive	v)-cocoercive	PUNCT
ejpam-5744	303	23	and	and	CCONJ
ejpam-5744	303	24	ψ	ψ	NOUN
ejpam-5744	303	25	is	be	AUX
ejpam-5744	303	26	t	t	NOUN
ejpam-5744	303	27	-	-	PUNCT
ejpam-5744	303	28	lipschitz	lipschitz	NOUN
ejpam-5744	303	29	continuous	continuous	ADJ
ejpam-5744	303	30	and	and	CCONJ
ejpam-5744	303	31	r	r	NOUN
ejpam-5744	303	32	-	-	PUNCT
ejpam-5744	303	33	strongly	strongly	ADV
ejpam-5744	303	34	monotone	monotone	ADJ
ejpam-5744	303	35	.	.	PUNCT
ejpam-5744	304	1	(	(	PUNCT
ejpam-5744	304	2	v2	v2	NOUN
ejpam-5744	304	3	)	)	PUNCT
ejpam-5744	304	4	the	the	DET
ejpam-5744	304	5	constant	constant	ADJ
ejpam-5744	304	6	λ	λ	X
ejpam-5744	304	7	>	>	SYM
ejpam-5744	304	8	0	0	NUM
ejpam-5744	304	9	obeys	obey	VERB
ejpam-5744	304	10	the	the	DET
ejpam-5744	304	11	following	follow	VERB
ejpam-5744	304	12	relation	relation	NOUN
ejpam-5744	304	13	:	:	PUNCT
ejpam-5744	304	14	λl2	λl2	X
ejpam-5744	304	15	≤	≤	NUM
ejpam-5744	304	16	2λv	2λv	NOUN
ejpam-5744	305	1	+	+	ADJ
ejpam-5744	305	2	∆(∆−	∆(∆−	PROPN
ejpam-5744	305	3	2	2	NUM
ejpam-5744	305	4	)	)	PUNCT
ejpam-5744	305	5	λ+	λ+	PUNCT
ejpam-5744	305	6	2u	2u	NOUN
ejpam-5744	305	7	,	,	PUNCT
ejpam-5744	305	8	∆	∆	PROPN
ejpam-5744	305	9	=	=	SYM
ejpam-5744	305	10	2	2	NUM
ejpam-5744	305	11	√	√	NUM
ejpam-5744	305	12	1−	1−	NUM
ejpam-5744	305	13	2r	2r	NUM
ejpam-5744	305	14	+	+	CCONJ
ejpam-5744	305	15	t2	t2	NOUN
ejpam-5744	305	16	.	.	PUNCT
ejpam-5744	306	1	(	(	PUNCT
ejpam-5744	306	2	40	40	NUM
ejpam-5744	306	3	)	)	PUNCT
ejpam-5744	306	4	then	then	ADV
ejpam-5744	306	5	{	{	PUNCT
ejpam-5744	306	6	ϱk}∞k=1	ϱk}∞k=1	PUNCT
ejpam-5744	306	7	approximated	approximate	VERB
ejpam-5744	306	8	by	by	ADP
ejpam-5744	306	9	(	(	PUNCT
ejpam-5744	306	10	33	33	NUM
ejpam-5744	306	11	)	)	PUNCT
ejpam-5744	306	12	converges	converge	VERB
ejpam-5744	306	13	strongly	strongly	ADV
ejpam-5744	306	14	to	to	ADP
ejpam-5744	306	15	ϱ	ϱ	ADP
ejpam-5744	306	16	∈	∈	PROPN
ejpam-5744	306	17	ξ(ψ	ξ(ψ	NUM
ejpam-5744	306	18	)	)	PUNCT
ejpam-5744	306	19	∩	∩	PROPN
ejpam-5744	306	20	✠	✠	PROPN
ejpam-5744	306	21	(c	(c	PROPN
ejpam-5744	306	22	,	,	PUNCT
ejpam-5744	306	23	ψ	ψ	X
ejpam-5744	306	24	,	,	PUNCT
ejpam-5744	306	25	ψ	ψ	NOUN
ejpam-5744	306	26	)	)	PUNCT
ejpam-5744	306	27	.	.	PUNCT
ejpam-5744	307	1	example	example	NOUN
ejpam-5744	308	1	2	2	NUM
ejpam-5744	308	2	.	.	X
ejpam-5744	308	3	let	let	VERB
ejpam-5744	308	4	l2	l2	NOUN
ejpam-5744	308	5	=	=	SYM
ejpam-5744	308	6	{	{	PUNCT
ejpam-5744	308	7	ϱ	ϱ	PROPN
ejpam-5744	308	8	=	=	PUNCT
ejpam-5744	308	9	(	(	PUNCT
ejpam-5744	308	10	ϱ0	ϱ0	NOUN
ejpam-5744	308	11	,	,	PUNCT
ejpam-5744	308	12	ϱ1	ϱ1	NOUN
ejpam-5744	308	13	,	,	PUNCT
ejpam-5744	308	14	ϱ2	ϱ2	NOUN
ejpam-5744	308	15	,	,	PUNCT
ejpam-5744	308	16	·	·	PUNCT
ejpam-5744	308	17	·	·	PUNCT
ejpam-5744	308	18	·	·	PUNCT
ejpam-5744	308	19	)	)	PUNCT
ejpam-5744	308	20	:	:	PUNCT
ejpam-5744	308	21	∑∞	∑∞	NOUN
ejpam-5744	308	22	k=0	k=0	PROPN
ejpam-5744	308	23	|ϱ2k|	|ϱ2k|	VERB
ejpam-5744	308	24	<	<	X
ejpam-5744	308	25	∞	∞	PROPN
ejpam-5744	308	26	,	,	PUNCT
ejpam-5744	308	27	ϱk	ϱk	ADP
ejpam-5744	308	28	∈	∈	PROPN
ejpam-5744	308	29	r	r	NOUN
ejpam-5744	308	30	,	,	PUNCT
ejpam-5744	308	31	∀n	∀n	NUM
ejpam-5744	308	32	=	=	SYM
ejpam-5744	308	33	0	0	NUM
ejpam-5744	308	34	,	,	PUNCT
ejpam-5744	308	35	1	1	NUM
ejpam-5744	308	36	,	,	PUNCT
ejpam-5744	308	37	2	2	NUM
ejpam-5744	308	38	,	,	PUNCT
ejpam-5744	308	39	·	·	PUNCT
ejpam-5744	308	40	·	·	PUNCT
ejpam-5744	308	41	·	·	PUNCT
ejpam-5744	308	42	}	}	PUNCT
ejpam-5744	308	43	be	be	AUX
ejpam-5744	308	44	a	a	DET
ejpam-5744	308	45	hilbert	hilbert	NOUN
ejpam-5744	308	46	space	space	NOUN
ejpam-5744	308	47	with	with	ADP
ejpam-5744	308	48	norm	norm	NOUN
ejpam-5744	308	49	∥ϱ∥2	∥ϱ∥2	VERB
ejpam-5744	308	50	=	=	SYM
ejpam-5744	308	51	√∑∞	√∑∞	PROPN
ejpam-5744	308	52	k=0	k=0	PUNCT
ejpam-5744	308	53	|ϱ2k|	|ϱ2k|	PROPN
ejpam-5744	308	54	.	.	PUNCT
ejpam-5744	309	1	define	define	VERB
ejpam-5744	309	2	ψ	ψ	NOUN
ejpam-5744	309	3	,	,	PUNCT
ejpam-5744	309	4	ψ	ψ	X
ejpam-5744	309	5	:	:	PUNCT
ejpam-5744	309	6	l2	l2	NOUN
ejpam-5744	309	7	→	→	SYM
ejpam-5744	309	8	l2	l2	NOUN
ejpam-5744	309	9	by	by	ADP
ejpam-5744	309	10	ψ(ϱ	ψ(ϱ	NOUN
ejpam-5744	309	11	)	)	PUNCT
ejpam-5744	310	1	=	=	SYM
ejpam-5744	310	2	(	(	PUNCT
ejpam-5744	310	3	ϱ0	ϱ0	NOUN
ejpam-5744	310	4	3	3	NUM
ejpam-5744	310	5	,	,	PUNCT
ejpam-5744	310	6	0	0	NUM
ejpam-5744	310	7	,	,	PUNCT
ejpam-5744	310	8	0	0	NUM
ejpam-5744	310	9	,	,	PUNCT
ejpam-5744	310	10	·	·	PUNCT
ejpam-5744	310	11	·	·	PUNCT
ejpam-5744	310	12	·	·	PUNCT
ejpam-5744	310	13	)	)	PUNCT
ejpam-5744	310	14	,	,	PUNCT
ejpam-5744	310	15	and	and	CCONJ
ejpam-5744	310	16	ψ(ϱ	ψ(ϱ	NOUN
ejpam-5744	310	17	)	)	PUNCT
ejpam-5744	310	18	=	=	SYM
ejpam-5744	310	19	(	(	PUNCT
ejpam-5744	310	20	3ϱ0	3ϱ0	NUM
ejpam-5744	310	21	4	4	NUM
ejpam-5744	310	22	,	,	PUNCT
ejpam-5744	310	23	0	0	NUM
ejpam-5744	310	24	,	,	PUNCT
ejpam-5744	310	25	0	0	NUM
ejpam-5744	310	26	,	,	PUNCT
ejpam-5744	310	27	·	·	PUNCT
ejpam-5744	310	28	·	·	PUNCT
ejpam-5744	310	29	·	·	PUNCT
ejpam-5744	310	30	)	)	PUNCT
ejpam-5744	310	31	,	,	PUNCT
ejpam-5744	310	32	∀ϱ	∀ϱ	NOUN
ejpam-5744	310	33	∈	∈	NOUN
ejpam-5744	310	34	l2	l2	NOUN
ejpam-5744	310	35	.	.	PUNCT
ejpam-5744	311	1	then	then	ADV
ejpam-5744	311	2	,	,	PUNCT
ejpam-5744	311	3	for	for	ADP
ejpam-5744	311	4	all	all	DET
ejpam-5744	311	5	ϱ	ϱ	PROPN
ejpam-5744	311	6	,	,	PUNCT
ejpam-5744	311	7	ω	ω	PROPN
ejpam-5744	311	8	∈	∈	PROPN
ejpam-5744	311	9	l2	l2	NOUN
ejpam-5744	311	10	,	,	PUNCT
ejpam-5744	311	11	we	we	PRON
ejpam-5744	311	12	calculate	calculate	VERB
ejpam-5744	311	13	⟨ψ(ϱ)−ψ(ω	⟨ψ(ϱ)−ψ(ω	PROPN
ejpam-5744	311	14	)	)	PUNCT
ejpam-5744	311	15	,	,	PUNCT
ejpam-5744	312	1	ϱ−	ϱ−	CCONJ
ejpam-5744	312	2	ω⟩	ω⟩	NOUN
ejpam-5744	312	3	=	=	SYM
ejpam-5744	312	4	〈	〈	PROPN
ejpam-5744	312	5	(	(	PUNCT
ejpam-5744	312	6	ϱ0	ϱ0	NOUN
ejpam-5744	312	7	3	3	NUM
ejpam-5744	312	8	−	−	NOUN
ejpam-5744	312	9	ω0	ω0	ADP
ejpam-5744	312	10	3	3	NUM
ejpam-5744	312	11	,	,	PUNCT
ejpam-5744	312	12	0	0	NUM
ejpam-5744	312	13	,	,	PUNCT
ejpam-5744	312	14	0	0	NUM
ejpam-5744	312	15	,	,	PUNCT
ejpam-5744	312	16	·	·	PUNCT
ejpam-5744	312	17	·	·	PUNCT
ejpam-5744	312	18	·	·	PUNCT
ejpam-5744	312	19	)	)	PUNCT
ejpam-5744	312	20	,	,	PUNCT
ejpam-5744	312	21	(	(	PUNCT
ejpam-5744	312	22	ϱ0	ϱ0	NOUN
ejpam-5744	312	23	−	−	PROPN
ejpam-5744	312	24	ω0	ω0	NOUN
ejpam-5744	312	25	,	,	PUNCT
ejpam-5744	312	26	ϱ1	ϱ1	PROPN
ejpam-5744	312	27	−	−	PROPN
ejpam-5744	312	28	ω1	ω1	PROPN
ejpam-5744	312	29	,	,	PUNCT
ejpam-5744	312	30	ϱ2	ϱ2	NOUN
ejpam-5744	312	31	−	−	PROPN
ejpam-5744	312	32	ω2	ω2	ADJ
ejpam-5744	312	33	,	,	PUNCT
ejpam-5744	312	34	·	·	PUNCT
ejpam-5744	312	35	·	·	PUNCT
ejpam-5744	312	36	·	·	PUNCT
ejpam-5744	312	37	)	)	PUNCT
ejpam-5744	312	38	〉	〉	NOUN
ejpam-5744	312	39	≥	≥	NUM
ejpam-5744	312	40	−1	−1	NOUN
ejpam-5744	312	41	3	3	NUM
ejpam-5744	312	42	∥ψ(ϱ)−ψ(ω)∥22	∥ψ(ϱ)−ψ(ω)∥22	NOUN
ejpam-5744	312	43	+	+	CCONJ
ejpam-5744	312	44	1	1	NUM
ejpam-5744	312	45	3	3	NUM
ejpam-5744	312	46	∥ϱ−	∥ϱ−	PROPN
ejpam-5744	312	47	ω∥22	ω∥22	NUM
ejpam-5744	312	48	,	,	PUNCT
ejpam-5744	312	49	∥ψ(ϱ)−ψ(ω)∥2	∥ψ(ϱ)−ψ(ω)∥2	PROPN
ejpam-5744	312	50	=	=	PUNCT
ejpam-5744	312	51	∥∥∥ϱ	∥∥∥ϱ	NOUN
ejpam-5744	312	52	3	3	NUM
ejpam-5744	312	53	−	−	PROPN
ejpam-5744	312	54	ω	ω	NUM
ejpam-5744	312	55	3	3	NUM
ejpam-5744	312	56	∥∥∥	∥∥∥	PROPN
ejpam-5744	312	57	2	2	NUM
ejpam-5744	312	58	=	=	SYM
ejpam-5744	312	59	1	1	NUM
ejpam-5744	312	60	3	3	NUM
ejpam-5744	312	61	∥ϱ−	∥ϱ−	PROPN
ejpam-5744	312	62	ω∥2	ω∥2	NOUN
ejpam-5744	312	63	,	,	PUNCT
ejpam-5744	312	64	m.	m.	NOUN
ejpam-5744	312	65	akram	akram	PROPN
ejpam-5744	312	66	/	/	PUNCT
ejpam-5744	312	67	eur	eur	PROPN
ejpam-5744	312	68	.	.	PUNCT
ejpam-5744	313	1	j.	j.	PROPN
ejpam-5744	313	2	pure	pure	PROPN
ejpam-5744	313	3	appl	appl	PROPN
ejpam-5744	313	4	.	.	PROPN
ejpam-5744	313	5	math	math	PROPN
ejpam-5744	313	6	,	,	PUNCT
ejpam-5744	313	7	18	18	NUM
ejpam-5744	313	8	(	(	PUNCT
ejpam-5744	313	9	1	1	NUM
ejpam-5744	313	10	)	)	PUNCT
ejpam-5744	313	11	(	(	PUNCT
ejpam-5744	313	12	2025	2025	NUM
ejpam-5744	313	13	)	)	PUNCT
ejpam-5744	313	14	,	,	PUNCT
ejpam-5744	313	15	5744	5744	NUM
ejpam-5744	313	16	14	14	NUM
ejpam-5744	313	17	of	of	ADP
ejpam-5744	313	18	19	19	NUM
ejpam-5744	313	19	i.e.	i.e.	X
ejpam-5744	313	20	,	,	PUNCT
ejpam-5744	313	21	ψ	ψ	X
ejpam-5744	313	22	is	be	AUX
ejpam-5744	313	23	relaxed	relax	VERB
ejpam-5744	313	24	(	(	PUNCT
ejpam-5744	313	25	13	13	NUM
ejpam-5744	313	26	,	,	PUNCT
ejpam-5744	313	27	1	1	NUM
ejpam-5744	313	28	3)-cocoercive	3)-cocoercive	NUM
ejpam-5744	313	29	and	and	CCONJ
ejpam-5744	313	30	1	1	NUM
ejpam-5744	313	31	3	3	NUM
ejpam-5744	313	32	-lipschitz	-lipschitz	NOUN
ejpam-5744	313	33	continuous	continuous	ADJ
ejpam-5744	313	34	and	and	CCONJ
ejpam-5744	313	35	⟨ψ(ϱ)−	⟨ψ(ϱ)−	NOUN
ejpam-5744	313	36	ψ(ω	ψ(ω	PROPN
ejpam-5744	313	37	)	)	PUNCT
ejpam-5744	313	38	,	,	PUNCT
ejpam-5744	314	1	ϱ−	ϱ−	CCONJ
ejpam-5744	314	2	ω⟩	ω⟩	NOUN
ejpam-5744	314	3	=	=	SYM
ejpam-5744	314	4	〈	〈	PROPN
ejpam-5744	314	5	(	(	PUNCT
ejpam-5744	314	6	3ϱ0	3ϱ0	NUM
ejpam-5744	314	7	4	4	NUM
ejpam-5744	314	8	−	−	NOUN
ejpam-5744	314	9	3ω0	3ω0	NUM
ejpam-5744	314	10	4	4	NUM
ejpam-5744	314	11	,	,	PUNCT
ejpam-5744	314	12	0	0	NUM
ejpam-5744	314	13	,	,	PUNCT
ejpam-5744	314	14	0	0	NUM
ejpam-5744	314	15	,	,	PUNCT
ejpam-5744	314	16	·	·	PUNCT
ejpam-5744	314	17	·	·	PUNCT
ejpam-5744	314	18	·	·	PUNCT
ejpam-5744	314	19	)	)	PUNCT
ejpam-5744	314	20	,	,	PUNCT
ejpam-5744	314	21	(	(	PUNCT
ejpam-5744	314	22	ϱ0	ϱ0	NOUN
ejpam-5744	314	23	−	−	PROPN
ejpam-5744	314	24	ω0	ω0	NOUN
ejpam-5744	314	25	,	,	PUNCT
ejpam-5744	314	26	ϱ1	ϱ1	PROPN
ejpam-5744	314	27	−	−	PROPN
ejpam-5744	314	28	ω1	ω1	PROPN
ejpam-5744	314	29	,	,	PUNCT
ejpam-5744	314	30	ϱ2	ϱ2	NOUN
ejpam-5744	314	31	−	−	PROPN
ejpam-5744	314	32	ω2	ω2	ADJ
ejpam-5744	314	33	,	,	PUNCT
ejpam-5744	314	34	·	·	PUNCT
ejpam-5744	314	35	·	·	PUNCT
ejpam-5744	314	36	·	·	PUNCT
ejpam-5744	314	37	)	)	PUNCT
ejpam-5744	314	38	〉	〉	NOUN
ejpam-5744	314	39	=	=	SYM
ejpam-5744	315	1	3	3	NUM
ejpam-5744	315	2	4	4	NUM
ejpam-5744	315	3	∥ϱ−	∥ϱ−	PROPN
ejpam-5744	315	4	ω∥22	ω∥22	NUM
ejpam-5744	315	5	,	,	PUNCT
ejpam-5744	315	6	∥ψ(ϱ)−	∥ψ(ϱ)−	VERB
ejpam-5744	315	7	ψ(ω)∥2	ψ(ω)∥2	NOUN
ejpam-5744	315	8	=	=	PUNCT
ejpam-5744	315	9	∥∥∥3ϱ	∥∥∥3ϱ	ADP
ejpam-5744	315	10	4	4	NUM
ejpam-5744	315	11	−	−	NOUN
ejpam-5744	315	12	3ω	3ω	NOUN
ejpam-5744	315	13	4	4	NUM
ejpam-5744	315	14	∥∥∥	∥∥∥	NUM
ejpam-5744	315	15	2	2	NUM
ejpam-5744	315	16	=	=	SYM
ejpam-5744	315	17	3	3	NUM
ejpam-5744	315	18	4	4	NUM
ejpam-5744	315	19	∥ϱ−	∥ϱ−	PROPN
ejpam-5744	315	20	ω∥2	ω∥2	NOUN
ejpam-5744	315	21	.	.	PUNCT
ejpam-5744	316	1	thus	thus	ADV
ejpam-5744	316	2	,	,	PUNCT
ejpam-5744	316	3	ψ	ψ	X
ejpam-5744	316	4	is	be	AUX
ejpam-5744	316	5	3	3	NUM
ejpam-5744	316	6	4	4	NUM
ejpam-5744	316	7	-strongly	-strongly	ADV
ejpam-5744	316	8	monotone	monotone	ADJ
ejpam-5744	316	9	and	and	CCONJ
ejpam-5744	316	10	3	3	NUM
ejpam-5744	316	11	4	4	NUM
ejpam-5744	316	12	-lipschitz	-lipschitz	NOUN
ejpam-5744	316	13	continuous	continuous	ADJ
ejpam-5744	316	14	.	.	PUNCT
ejpam-5744	317	1	also	also	ADV
ejpam-5744	317	2	,	,	PUNCT
ejpam-5744	317	3	for	for	ADP
ejpam-5744	317	4	τ	τ	PROPN
ejpam-5744	317	5	=	=	SYM
ejpam-5744	317	6	1	1	NUM
ejpam-5744	317	7	3	3	NUM
ejpam-5744	317	8	and	and	CCONJ
ejpam-5744	317	9	strictly	strictly	ADV
ejpam-5744	317	10	continuous	continuous	ADJ
ejpam-5744	317	11	function	function	NOUN
ejpam-5744	317	12	g	g	NOUN
ejpam-5744	317	13	:	:	PUNCT
ejpam-5744	317	14	[	[	X
ejpam-5744	317	15	0,∞	0,∞	NOUN
ejpam-5744	317	16	)	)	PUNCT
ejpam-5744	317	17	→	→	PUNCT
ejpam-5744	318	1	[	[	X
ejpam-5744	318	2	0,∞	0,∞	NOUN
ejpam-5744	318	3	)	)	PUNCT
ejpam-5744	318	4	with	with	ADP
ejpam-5744	318	5	g(0	g(0	NOUN
ejpam-5744	318	6	)	)	PUNCT
ejpam-5744	318	7	=	=	SYM
ejpam-5744	318	8	0	0	NUM
ejpam-5744	318	9	,	,	PUNCT
ejpam-5744	318	10	we	we	PRON
ejpam-5744	318	11	have	have	VERB
ejpam-5744	318	12	∥ψ(ϱ)−ψ(ω)∥	∥ψ(ϱ)−ψ(ω)∥	ADP
ejpam-5744	318	13	−	−	NOUN
ejpam-5744	318	14	τ∥ϱ−	τ∥ϱ−	NOUN
ejpam-5744	318	15	ω∥	ω∥	ADP
ejpam-5744	318	16	−	−	NOUN
ejpam-5744	318	17	g(∥ϱ−ψ(ϱ)∥	g(∥ϱ−ψ(ϱ)∥	NOUN
ejpam-5744	318	18	)	)	PUNCT
ejpam-5744	318	19	=	=	SYM
ejpam-5744	318	20	1	1	NUM
ejpam-5744	318	21	3	3	NUM
ejpam-5744	318	22	|ϱ−	|ϱ−	NOUN
ejpam-5744	318	23	ω|	ω|	NOUN
ejpam-5744	318	24	−	−	NOUN
ejpam-5744	318	25	1	1	NUM
ejpam-5744	318	26	3	3	NUM
ejpam-5744	318	27	|ϱ−	|ϱ−	NOUN
ejpam-5744	318	28	ω|	ω|	NOUN
ejpam-5744	318	29	−	−	PUNCT
ejpam-5744	318	30	g(|ϱ−	g(|ϱ−	PROPN
ejpam-5744	318	31	ϱ	ϱ	ADP
ejpam-5744	318	32	3	3	NUM
ejpam-5744	318	33	|	|	NOUN
ejpam-5744	318	34	)	)	PUNCT
ejpam-5744	319	1	=	=	SYM
ejpam-5744	319	2	−g	−g	NOUN
ejpam-5744	319	3	(	(	PUNCT
ejpam-5744	319	4	2ϱ	2ϱ	NOUN
ejpam-5744	319	5	3	3	NUM
ejpam-5744	319	6	)	)	PUNCT
ejpam-5744	319	7	≤	≤	NOUN
ejpam-5744	319	8	0	0	NUM
ejpam-5744	319	9	,	,	PUNCT
ejpam-5744	319	10	i.e.	i.e.	X
ejpam-5744	319	11	,	,	PUNCT
ejpam-5744	319	12	∥ψ(ϱ	∥ψ(ϱ	ADJ
ejpam-5744	319	13	)	)	PUNCT
ejpam-5744	319	14	−	−	NOUN
ejpam-5744	319	15	ψ(ω)∥	ψ(ω)∥	NOUN
ejpam-5744	319	16	≤	≤	NOUN
ejpam-5744	319	17	τ∥ϱ	τ∥ϱ	PUNCT
ejpam-5744	320	1	−	−	NUM
ejpam-5744	320	2	ω∥	ω∥	NUM
ejpam-5744	320	3	+	+	NUM
ejpam-5744	320	4	g(∥ϱ	g(∥ϱ	NOUN
ejpam-5744	320	5	−	−	NOUN
ejpam-5744	320	6	ψ(ϱ)∥	ψ(ϱ)∥	NOUN
ejpam-5744	320	7	)	)	PUNCT
ejpam-5744	320	8	.	.	PUNCT
ejpam-5744	321	1	thus	thus	ADV
ejpam-5744	321	2	,	,	PUNCT
ejpam-5744	321	3	ψ	ψ	ADP
ejpam-5744	321	4	satisfies	satisfie	NOUN
ejpam-5744	321	5	(	(	PUNCT
ejpam-5744	321	6	2	2	NUM
ejpam-5744	321	7	)	)	PUNCT
ejpam-5744	321	8	and	and	CCONJ
ejpam-5744	321	9	also	also	ADV
ejpam-5744	321	10	ϱ∗	ϱ∗	VERB
ejpam-5744	321	11	=	=	SYM
ejpam-5744	321	12	(	(	PUNCT
ejpam-5744	321	13	0	0	NUM
ejpam-5744	321	14	,	,	PUNCT
ejpam-5744	321	15	0	0	NUM
ejpam-5744	321	16	,	,	PUNCT
ejpam-5744	321	17	0	0	NUM
ejpam-5744	321	18	,	,	PUNCT
ejpam-5744	321	19	·	·	PUNCT
ejpam-5744	321	20	·	·	PUNCT
ejpam-5744	321	21	·	·	PUNCT
ejpam-5744	321	22	)	)	PUNCT
ejpam-5744	321	23	∈	∈	PROPN
ejpam-5744	321	24	ξ(ψ	ξ(ψ	PROPN
ejpam-5744	321	25	)	)	PUNCT
ejpam-5744	321	26	.	.	PUNCT
ejpam-5744	322	1	now	now	ADV
ejpam-5744	322	2	,	,	PUNCT
ejpam-5744	322	3	define	define	VERB
ejpam-5744	322	4	c	c	NOUN
ejpam-5744	322	5	:	:	PUNCT
ejpam-5744	322	6	h	h	NOUN
ejpam-5744	322	7	→	→	SYM
ejpam-5744	322	8	h	h	NOUN
ejpam-5744	322	9	by	by	ADP
ejpam-5744	322	10	c(ϱ	c(ϱ	PROPN
ejpam-5744	322	11	)	)	PUNCT
ejpam-5744	322	12	=	=	SYM
ejpam-5744	322	13	c({ϱn	c({ϱn	NOUN
ejpam-5744	322	14	}	}	PUNCT
ejpam-5744	322	15	)	)	PUNCT
ejpam-5744	323	1	=	=	PRON
ejpam-5744	323	2	{	{	PUNCT
ejpam-5744	323	3	a	a	X
ejpam-5744	323	4	=	=	X
ejpam-5744	323	5	{	{	PUNCT
ejpam-5744	323	6	ak	ak	PROPN
ejpam-5744	323	7	}	}	PUNCT
ejpam-5744	323	8	:	:	PUNCT
ejpam-5744	323	9	a0	a0	NOUN
ejpam-5744	323	10	≥	≥	NOUN
ejpam-5744	323	11	9	9	NUM
ejpam-5744	323	12	16ϱ0	16ϱ0	NUM
ejpam-5744	323	13	,	,	PUNCT
ejpam-5744	323	14	ak	ak	PROPN
ejpam-5744	323	15	=	=	PUNCT
ejpam-5744	323	16	0,∀n	0,∀n	PROPN
ejpam-5744	324	1	=	=	SYM
ejpam-5744	324	2	1	1	NUM
ejpam-5744	324	3	,	,	PUNCT
ejpam-5744	324	4	2	2	NUM
ejpam-5744	324	5	,	,	PUNCT
ejpam-5744	324	6	·	·	PUNCT
ejpam-5744	324	7	·	·	PUNCT
ejpam-5744	324	8	·	·	PUNCT
ejpam-5744	324	9	}	}	PUNCT
ejpam-5744	324	10	.	.	PUNCT
ejpam-5744	325	1	now	now	ADV
ejpam-5744	325	2	,	,	PUNCT
ejpam-5744	325	3	for	for	ADP
ejpam-5744	325	4	any	any	DET
ejpam-5744	325	5	α	α	NOUN
ejpam-5744	325	6	∈	∈	PROPN
ejpam-5744	326	1	[	[	X
ejpam-5744	326	2	0	0	NUM
ejpam-5744	326	3	,	,	PUNCT
ejpam-5744	326	4	1	1	NUM
ejpam-5744	326	5	]	]	PUNCT
ejpam-5744	326	6	and	and	CCONJ
ejpam-5744	326	7	a0	a0	PROPN
ejpam-5744	326	8	,	,	PUNCT
ejpam-5744	326	9	b0	b0	PROPN
ejpam-5744	326	10	∈	∈	PROPN
ejpam-5744	326	11	c(ϱ	c(ϱ	NOUN
ejpam-5744	326	12	)	)	PUNCT
ejpam-5744	326	13	gives	give	VERB
ejpam-5744	326	14	αa0	αa0	PRON
ejpam-5744	326	15	+	+	PUNCT
ejpam-5744	326	16	(	(	PUNCT
ejpam-5744	326	17	1	1	NUM
ejpam-5744	326	18	−	−	PROPN
ejpam-5744	326	19	α)b0	α)b0	X
ejpam-5744	326	20	≥	≥	NOUN
ejpam-5744	326	21	9	9	NUM
ejpam-5744	326	22	16ϱ0	16ϱ0	NUM
ejpam-5744	326	23	,	,	PUNCT
ejpam-5744	326	24	thus	thus	ADV
ejpam-5744	326	25	,	,	PUNCT
ejpam-5744	326	26	c(ϱ	c(ϱ	PROPN
ejpam-5744	326	27	)	)	PUNCT
ejpam-5744	326	28	is	be	AUX
ejpam-5744	326	29	convex	convex	NOUN
ejpam-5744	326	30	set	set	NOUN
ejpam-5744	326	31	.	.	PUNCT
ejpam-5744	327	1	now	now	ADV
ejpam-5744	327	2	,	,	PUNCT
ejpam-5744	327	3	we	we	PRON
ejpam-5744	327	4	shall	shall	AUX
ejpam-5744	327	5	verify	verify	VERB
ejpam-5744	327	6	that	that	DET
ejpam-5744	327	7	c(ϱ	c(ϱ	NOUN
ejpam-5744	327	8	)	)	PUNCT
ejpam-5744	327	9	is	be	AUX
ejpam-5744	327	10	closed	close	VERB
ejpam-5744	327	11	.	.	PUNCT
ejpam-5744	328	1	define	define	VERB
ejpam-5744	328	2	q	q	NOUN
ejpam-5744	328	3	:	:	PUNCT
ejpam-5744	328	4	[	[	PUNCT
ejpam-5744	328	5	916ϱ0,∞	916ϱ0,∞	NUM
ejpam-5744	328	6	)	)	PUNCT
ejpam-5744	328	7	→	→	SYM
ejpam-5744	328	8	c(ϱ	c(ϱ	PROPN
ejpam-5744	328	9	)	)	PUNCT
ejpam-5744	328	10	by	by	ADP
ejpam-5744	328	11	q(s	q(	VERB
ejpam-5744	328	12	)	)	PUNCT
ejpam-5744	328	13	=	=	PUNCT
ejpam-5744	328	14	(	(	PUNCT
ejpam-5744	328	15	s	s	PROPN
ejpam-5744	328	16	,	,	PUNCT
ejpam-5744	328	17	0	0	NUM
ejpam-5744	328	18	,	,	PUNCT
ejpam-5744	328	19	0	0	NUM
ejpam-5744	328	20	,	,	PUNCT
ejpam-5744	328	21	·	·	PUNCT
ejpam-5744	328	22	·	·	PUNCT
ejpam-5744	328	23	·	·	PUNCT
ejpam-5744	328	24	)	)	PUNCT
ejpam-5744	328	25	.	.	PUNCT
ejpam-5744	329	1	then	then	ADV
ejpam-5744	329	2	q	q	X
ejpam-5744	329	3	is	be	AUX
ejpam-5744	329	4	well	well	ADV
ejpam-5744	329	5	defined	define	VERB
ejpam-5744	329	6	and	and	CCONJ
ejpam-5744	329	7	for	for	ADP
ejpam-5744	329	8	distinct	distinct	ADJ
ejpam-5744	329	9	a0	a0	NOUN
ejpam-5744	329	10	,	,	PUNCT
ejpam-5744	329	11	b0	b0	NOUN
ejpam-5744	329	12	∈	∈	PROPN
ejpam-5744	329	13	[	[	PUNCT
ejpam-5744	329	14	916ϱ0,∞	916ϱ0,∞	NUM
ejpam-5744	329	15	)	)	PUNCT
ejpam-5744	329	16	,	,	PUNCT
ejpam-5744	329	17	we	we	PRON
ejpam-5744	329	18	acquire	acquire	VERB
ejpam-5744	329	19	(	(	PUNCT
ejpam-5744	329	20	a0	a0	NOUN
ejpam-5744	329	21	,	,	PUNCT
ejpam-5744	329	22	0	0	NUM
ejpam-5744	329	23	,	,	PUNCT
ejpam-5744	329	24	0	0	NUM
ejpam-5744	329	25	,	,	PUNCT
ejpam-5744	329	26	·	·	PUNCT
ejpam-5744	329	27	·	·	PUNCT
ejpam-5744	329	28	·	·	PUNCT
ejpam-5744	329	29	)	)	PUNCT
ejpam-5744	330	1	̸=	̸=	PROPN
ejpam-5744	330	2	(	(	PUNCT
ejpam-5744	330	3	b0	b0	NOUN
ejpam-5744	330	4	,	,	PUNCT
ejpam-5744	330	5	0	0	NUM
ejpam-5744	330	6	,	,	PUNCT
ejpam-5744	330	7	0	0	NUM
ejpam-5744	330	8	,	,	PUNCT
ejpam-5744	330	9	·	·	PUNCT
ejpam-5744	330	10	·	·	PUNCT
ejpam-5744	330	11	·	·	PUNCT
ejpam-5744	330	12	)	)	PUNCT
ejpam-5744	330	13	,	,	PUNCT
ejpam-5744	330	14	i.e.	i.e.	X
ejpam-5744	330	15	,	,	PUNCT
ejpam-5744	330	16	q	q	X
ejpam-5744	330	17	is	be	AUX
ejpam-5744	330	18	one	one	NUM
ejpam-5744	330	19	-	-	PUNCT
ejpam-5744	330	20	to	to	ADP
ejpam-5744	330	21	-	-	PUNCT
ejpam-5744	330	22	one	one	NUM
ejpam-5744	330	23	and	and	CCONJ
ejpam-5744	330	24	there	there	PRON
ejpam-5744	330	25	exists	exist	VERB
ejpam-5744	330	26	an	an	DET
ejpam-5744	330	27	a0	a0	PROPN
ejpam-5744	330	28	∈	∈	PROPN
ejpam-5744	330	29	[	[	PUNCT
ejpam-5744	330	30	916a0,∞	916a0,∞	NUM
ejpam-5744	330	31	)	)	PUNCT
ejpam-5744	330	32	,	,	PUNCT
ejpam-5744	330	33	such	such	ADJ
ejpam-5744	330	34	that	that	SCONJ
ejpam-5744	330	35	q(a0	q(a0	VERB
ejpam-5744	330	36	)	)	PUNCT
ejpam-5744	331	1	=	=	SYM
ejpam-5744	331	2	(	(	PUNCT
ejpam-5744	331	3	a0	a0	PROPN
ejpam-5744	331	4	,	,	PUNCT
ejpam-5744	331	5	0	0	NUM
ejpam-5744	331	6	,	,	PUNCT
ejpam-5744	331	7	0	0	NUM
ejpam-5744	331	8	,	,	PUNCT
ejpam-5744	331	9	·	·	PUNCT
ejpam-5744	331	10	·	·	PUNCT
ejpam-5744	331	11	·	·	PUNCT
ejpam-5744	331	12	)	)	PUNCT
ejpam-5744	331	13	,	,	PUNCT
ejpam-5744	331	14	∀a	∀a	X
ejpam-5744	331	15	=	=	SYM
ejpam-5744	331	16	(	(	PUNCT
ejpam-5744	331	17	a0	a0	PROPN
ejpam-5744	331	18	,	,	PUNCT
ejpam-5744	331	19	0	0	NUM
ejpam-5744	331	20	,	,	PUNCT
ejpam-5744	331	21	0	0	NUM
ejpam-5744	331	22	,	,	PUNCT
ejpam-5744	331	23	·	·	PUNCT
ejpam-5744	331	24	·	·	PUNCT
ejpam-5744	331	25	·	·	PUNCT
ejpam-5744	331	26	)	)	PUNCT
ejpam-5744	332	1	∈	∈	PROPN
ejpam-5744	332	2	c(ϱ	c(ϱ	PROPN
ejpam-5744	332	3	)	)	PUNCT
ejpam-5744	332	4	,	,	PUNCT
ejpam-5744	332	5	i.e.	i.e.	X
ejpam-5744	332	6	,	,	PUNCT
ejpam-5744	332	7	q	q	PROPN
ejpam-5744	332	8	is	be	AUX
ejpam-5744	332	9	onto	onto	ADP
ejpam-5744	332	10	.	.	PUNCT
ejpam-5744	333	1	consider	consider	VERB
ejpam-5744	333	2	the	the	DET
ejpam-5744	333	3	usual	usual	ADJ
ejpam-5744	333	4	metric	metric	ADJ
ejpam-5744	333	5	spaces	space	NOUN
ejpam-5744	333	6	(	(	PUNCT
ejpam-5744	333	7	r	r	NOUN
ejpam-5744	333	8	,	,	PUNCT
ejpam-5744	333	9	d	d	NOUN
ejpam-5744	333	10	)	)	PUNCT
ejpam-5744	333	11	and	and	CCONJ
ejpam-5744	333	12	(	(	PUNCT
ejpam-5744	333	13	l2	l2	NOUN
ejpam-5744	333	14	,	,	PUNCT
ejpam-5744	333	15	d	d	NOUN
ejpam-5744	333	16	′	′	NUM
ejpam-5744	333	17	)	)	PUNCT
ejpam-5744	333	18	,	,	PUNCT
ejpam-5744	333	19	then	then	ADV
ejpam-5744	333	20	for	for	ADP
ejpam-5744	333	21	all	all	DET
ejpam-5744	333	22	a	a	DET
ejpam-5744	333	23	,	,	PUNCT
ejpam-5744	333	24	b	b	X
ejpam-5744	333	25	∈	∈	PROPN
ejpam-5744	333	26	[	[	PUNCT
ejpam-5744	333	27	916a0,∞	916a0,∞	NUM
ejpam-5744	333	28	)	)	PUNCT
ejpam-5744	333	29	,	,	PUNCT
ejpam-5744	333	30	we	we	PRON
ejpam-5744	333	31	acquire	acquire	VERB
ejpam-5744	333	32	d	d	PROPN
ejpam-5744	333	33	′	′	NUM
ejpam-5744	333	34	(	(	PUNCT
ejpam-5744	333	35	q(a	q(a	NOUN
ejpam-5744	333	36	)	)	PUNCT
ejpam-5744	333	37	,	,	PUNCT
ejpam-5744	333	38	q(b	q(b	ADJ
ejpam-5744	333	39	)	)	PUNCT
ejpam-5744	333	40	)	)	PUNCT
ejpam-5744	334	1	=	=	PUNCT
ejpam-5744	335	1	d	d	NOUN
ejpam-5744	335	2	′	′	NUM
ejpam-5744	335	3	(	(	PUNCT
ejpam-5744	335	4	(	(	PUNCT
ejpam-5744	335	5	a0	a0	NOUN
ejpam-5744	335	6	,	,	PUNCT
ejpam-5744	335	7	0	0	NUM
ejpam-5744	335	8	,	,	PUNCT
ejpam-5744	335	9	0	0	NUM
ejpam-5744	335	10	,	,	PUNCT
ejpam-5744	335	11	·	·	PUNCT
ejpam-5744	335	12	·	·	PUNCT
ejpam-5744	335	13	·	·	PUNCT
ejpam-5744	335	14	)	)	PUNCT
ejpam-5744	335	15	,	,	PUNCT
ejpam-5744	335	16	(	(	PUNCT
ejpam-5744	335	17	b0	b0	NOUN
ejpam-5744	335	18	,	,	PUNCT
ejpam-5744	335	19	0	0	NUM
ejpam-5744	335	20	,	,	PUNCT
ejpam-5744	335	21	0	0	NUM
ejpam-5744	335	22	,	,	PUNCT
ejpam-5744	335	23	·	·	PUNCT
ejpam-5744	335	24	·	·	PUNCT
ejpam-5744	335	25	·	·	PUNCT
ejpam-5744	335	26	)	)	PUNCT
ejpam-5744	335	27	)	)	PUNCT
ejpam-5744	336	1	=	=	NOUN
ejpam-5744	336	2	|a−	|a−	NOUN
ejpam-5744	336	3	b|	b|	PROPN
ejpam-5744	336	4	=	=	SYM
ejpam-5744	336	5	d(a	d(a	PROPN
ejpam-5744	336	6	,	,	PUNCT
ejpam-5744	336	7	b	b	NOUN
ejpam-5744	336	8	)	)	PUNCT
ejpam-5744	336	9	.	.	PUNCT
ejpam-5744	337	1	thus	thus	ADV
ejpam-5744	337	2	,	,	PUNCT
ejpam-5744	337	3	q	q	PROPN
ejpam-5744	337	4	is	be	AUX
ejpam-5744	337	5	continuous	continuous	ADJ
ejpam-5744	337	6	.	.	PUNCT
ejpam-5744	338	1	q−1	q−1	PROPN
ejpam-5744	338	2	is	be	AUX
ejpam-5744	338	3	also	also	ADV
ejpam-5744	338	4	continuous	continuous	ADJ
ejpam-5744	338	5	and	and	CCONJ
ejpam-5744	338	6	one	one	NUM
ejpam-5744	338	7	-	-	PUNCT
ejpam-5744	338	8	to	to	ADP
ejpam-5744	338	9	-	-	PUNCT
ejpam-5744	338	10	one	one	NUM
ejpam-5744	338	11	and	and	CCONJ
ejpam-5744	338	12	onto	onto	ADP
ejpam-5744	338	13	,	,	PUNCT
ejpam-5744	338	14	so	so	ADV
ejpam-5744	338	15	q	q	PROPN
ejpam-5744	338	16	is	be	AUX
ejpam-5744	338	17	homeomorphism	homeomorphism	X
ejpam-5744	338	18	.	.	PUNCT
ejpam-5744	339	1	since	since	SCONJ
ejpam-5744	339	2	c(ϱ	c(ϱ	PROPN
ejpam-5744	339	3	)	)	PUNCT
ejpam-5744	339	4	is	be	AUX
ejpam-5744	339	5	the	the	DET
ejpam-5744	339	6	homeomorphic	homeomorphic	ADJ
ejpam-5744	339	7	image	image	NOUN
ejpam-5744	339	8	of	of	ADP
ejpam-5744	339	9	a	a	DET
ejpam-5744	339	10	closed	closed	ADJ
ejpam-5744	339	11	set	set	NOUN
ejpam-5744	339	12	[	[	PUNCT
ejpam-5744	339	13	916a0,∞	916a0,∞	NUM
ejpam-5744	339	14	)	)	PUNCT
ejpam-5744	339	15	,	,	PUNCT
ejpam-5744	339	16	and	and	CCONJ
ejpam-5744	339	17	hence	hence	ADV
ejpam-5744	339	18	closed	close	VERB
ejpam-5744	339	19	.	.	PUNCT
ejpam-5744	340	1	define	define	VERB
ejpam-5744	340	2	pc(ϱ	pc(ϱ	NOUN
ejpam-5744	340	3	)	)	PUNCT
ejpam-5744	340	4	:	:	PUNCT
ejpam-5744	341	1	h	h	NOUN
ejpam-5744	341	2	→	→	SYM
ejpam-5744	341	3	c(ϱ	c(ϱ	PROPN
ejpam-5744	341	4	)	)	PUNCT
ejpam-5744	341	5	as	as	ADP
ejpam-5744	341	6	under	under	ADV
ejpam-5744	341	7	:	:	PUNCT
ejpam-5744	341	8	pc(ϱ)(l0	pc(ϱ)(l0	NOUN
ejpam-5744	341	9	,	,	PUNCT
ejpam-5744	341	10	l1	l1	PROPN
ejpam-5744	341	11	,	,	PUNCT
ejpam-5744	341	12	l2	l2	NOUN
ejpam-5744	341	13	,	,	PUNCT
ejpam-5744	341	14	·	·	PUNCT
ejpam-5744	341	15	·	·	PUNCT
ejpam-5744	341	16	·	·	PUNCT
ejpam-5744	341	17	)	)	PUNCT
ejpam-5744	342	1	=	=	PUNCT
ejpam-5744	342	2			PROPN
ejpam-5744	342	3	(	(	PUNCT
ejpam-5744	342	4	l0	l0	PROPN
ejpam-5744	342	5	,	,	PUNCT
ejpam-5744	342	6	l1	l1	PROPN
ejpam-5744	342	7	,	,	PUNCT
ejpam-5744	342	8	l2	l2	NOUN
ejpam-5744	342	9	,	,	PUNCT
ejpam-5744	342	10	·	·	PUNCT
ejpam-5744	342	11	·	·	PUNCT
ejpam-5744	342	12	·	·	PUNCT
ejpam-5744	342	13	)	)	PUNCT
ejpam-5744	342	14	,	,	PUNCT
ejpam-5744	342	15	if	if	SCONJ
ejpam-5744	342	16	(	(	PUNCT
ejpam-5744	342	17	l0	l0	PROPN
ejpam-5744	342	18	,	,	PUNCT
ejpam-5744	342	19	l1	l1	PROPN
ejpam-5744	342	20	,	,	PUNCT
ejpam-5744	342	21	l2	l2	NOUN
ejpam-5744	342	22	,	,	PUNCT
ejpam-5744	342	23	·	·	PUNCT
ejpam-5744	342	24	·	·	PUNCT
ejpam-5744	342	25	·	·	PUNCT
ejpam-5744	342	26	)	)	PUNCT
ejpam-5744	343	1	∈	∈	PROPN
ejpam-5744	343	2	c(ϱ	c(ϱ	PROPN
ejpam-5744	343	3	)	)	PUNCT
ejpam-5744	343	4	(	(	PUNCT
ejpam-5744	343	5	9	9	NUM
ejpam-5744	343	6	16ϱ0	16ϱ0	NUM
ejpam-5744	343	7	,	,	PUNCT
ejpam-5744	343	8	0	0	NUM
ejpam-5744	343	9	,	,	PUNCT
ejpam-5744	343	10	0	0	NUM
ejpam-5744	343	11	,	,	PUNCT
ejpam-5744	343	12	·	·	PUNCT
ejpam-5744	343	13	·	·	PUNCT
ejpam-5744	343	14	·	·	PUNCT
ejpam-5744	343	15	)	)	PUNCT
ejpam-5744	343	16	,	,	PUNCT
ejpam-5744	343	17	if	if	SCONJ
ejpam-5744	343	18	(	(	PUNCT
ejpam-5744	343	19	l0	l0	PROPN
ejpam-5744	343	20	,	,	PUNCT
ejpam-5744	343	21	l1	l1	PROPN
ejpam-5744	343	22	,	,	PUNCT
ejpam-5744	343	23	l2	l2	NOUN
ejpam-5744	343	24	,	,	PUNCT
ejpam-5744	343	25	·	·	PUNCT
ejpam-5744	343	26	·	·	PUNCT
ejpam-5744	343	27	·	·	PUNCT
ejpam-5744	343	28	)	)	PUNCT
ejpam-5744	343	29	/∈	/∈	PUNCT
ejpam-5744	344	1	c(ϱ	c(ϱ	NOUN
ejpam-5744	344	2	)	)	PUNCT
ejpam-5744	344	3	,	,	PUNCT
ejpam-5744	345	1	l0	l0	PROPN
ejpam-5744	345	2	<	<	X
ejpam-5744	345	3	9	9	NUM
ejpam-5744	345	4	16ϱ0	16ϱ0	NUM
ejpam-5744	345	5	(	(	PUNCT
ejpam-5744	345	6	l0	l0	PROPN
ejpam-5744	345	7	,	,	PUNCT
ejpam-5744	345	8	0	0	NUM
ejpam-5744	345	9	,	,	PUNCT
ejpam-5744	345	10	0	0	NUM
ejpam-5744	345	11	,	,	PUNCT
ejpam-5744	345	12	·	·	PUNCT
ejpam-5744	345	13	·	·	PUNCT
ejpam-5744	345	14	·	·	PUNCT
ejpam-5744	345	15	)	)	PUNCT
ejpam-5744	345	16	,	,	PUNCT
ejpam-5744	345	17	if(l0	if(l0	NOUN
ejpam-5744	345	18	,	,	PUNCT
ejpam-5744	345	19	l1	l1	PROPN
ejpam-5744	345	20	,	,	PUNCT
ejpam-5744	345	21	l2	l2	NOUN
ejpam-5744	345	22	,	,	PUNCT
ejpam-5744	345	23	·	·	PUNCT
ejpam-5744	345	24	·	·	PUNCT
ejpam-5744	345	25	·	·	PUNCT
ejpam-5744	345	26	)	)	PUNCT
ejpam-5744	345	27	/∈	/∈	PUNCT
ejpam-5744	346	1	c(ϱ	c(ϱ	NOUN
ejpam-5744	346	2	)	)	PUNCT
ejpam-5744	346	3	,	,	PUNCT
ejpam-5744	347	1	l0	l0	PROPN
ejpam-5744	347	2	≥	≥	NUM
ejpam-5744	347	3	9	9	NUM
ejpam-5744	347	4	16ϱ0	16ϱ0	NUM
ejpam-5744	347	5	.	.	PUNCT
ejpam-5744	348	1	then	then	ADV
ejpam-5744	348	2	∥pc(a)(l	∥pc(a)(l	NOUN
ejpam-5744	348	3	)	)	PUNCT
ejpam-5744	348	4	−	−	PROPN
ejpam-5744	348	5	pc(b)(l)∥	pc(b)(l)∥	NOUN
ejpam-5744	348	6	≤	≤	NUM
ejpam-5744	348	7	9	9	NUM
ejpam-5744	348	8	16∥a	16∥a	NUM
ejpam-5744	348	9	−	−	NOUN
ejpam-5744	348	10	b∥	b∥	NOUN
ejpam-5744	348	11	,	,	PUNCT
ejpam-5744	348	12	i.e.	i.e.	X
ejpam-5744	348	13	,	,	PUNCT
ejpam-5744	348	14	pc	pc	NOUN
ejpam-5744	348	15	fulfills	fulfill	VERB
ejpam-5744	348	16	assumption	assumption	NOUN
ejpam-5744	348	17	a.	a.	NOUN
ejpam-5744	348	18	next	next	ADV
ejpam-5744	348	19	,	,	PUNCT
ejpam-5744	348	20	we	we	PRON
ejpam-5744	348	21	shall	shall	AUX
ejpam-5744	348	22	explore	explore	VERB
ejpam-5744	348	23	an	an	DET
ejpam-5744	348	24	element	element	NOUN
ejpam-5744	348	25	ϱ∗	ϱ∗	NOUN
ejpam-5744	348	26	such	such	ADJ
ejpam-5744	348	27	that	that	DET
ejpam-5744	348	28	ϱ∗	ϱ∗	PROPN
ejpam-5744	348	29	∈	∈	PROPN
ejpam-5744	348	30	ξ(ψ	ξ(ψ	NUM
ejpam-5744	348	31	)	)	PUNCT
ejpam-5744	348	32	∩	∩	NOUN
ejpam-5744	348	33	ξ(π	ξ(π	NOUN
ejpam-5744	348	34	)	)	PUNCT
ejpam-5744	348	35	.	.	PUNCT
ejpam-5744	349	1	consider	consider	VERB
ejpam-5744	349	2	ϱ∗	ϱ∗	NOUN
ejpam-5744	349	3	=	=	SYM
ejpam-5744	349	4	(	(	PUNCT
ejpam-5744	349	5	ϱ∗0	ϱ∗0	PROPN
ejpam-5744	349	6	,	,	PUNCT
ejpam-5744	349	7	0	0	NUM
ejpam-5744	349	8	,	,	PUNCT
ejpam-5744	349	9	0	0	NUM
ejpam-5744	349	10	,	,	PUNCT
ejpam-5744	349	11	·	·	PUNCT
ejpam-5744	349	12	·	·	PUNCT
ejpam-5744	349	13	·	·	PUNCT
ejpam-5744	349	14	)	)	PUNCT
ejpam-5744	349	15	:	:	PUNCT
ejpam-5744	350	1	ϱ∗0	ϱ∗0	PROPN
ejpam-5744	350	2	≥	≥	NOUN
ejpam-5744	350	3	0	0	NUM
ejpam-5744	350	4	.	.	PUNCT
ejpam-5744	351	1	if	if	SCONJ
ejpam-5744	351	2	ϱ∗	ϱ∗	PROPN
ejpam-5744	351	3	>	>	X
ejpam-5744	351	4	0	0	NUM
ejpam-5744	351	5	,	,	PUNCT
ejpam-5744	351	6	then	then	ADV
ejpam-5744	351	7	⟨ψ(ϱ∗	⟨ψ(ϱ∗	PROPN
ejpam-5744	351	8	)	)	PUNCT
ejpam-5744	351	9	,	,	PUNCT
ejpam-5744	351	10	ψ(ω∗)−	ψ(ω∗)−	PROPN
ejpam-5744	351	11	ψ(ϱ∗)⟩	ψ(ϱ∗)⟩	PUNCT
ejpam-5744	352	1	=	=	PUNCT
ejpam-5744	352	2	〈	〈	PROPN
ejpam-5744	352	3	ϱ∗	ϱ∗	NOUN
ejpam-5744	352	4	3	3	NUM
ejpam-5744	352	5	,	,	PUNCT
ejpam-5744	352	6	3ω∗	3ω∗	NUM
ejpam-5744	352	7	4	4	NUM
ejpam-5744	352	8	−	−	NOUN
ejpam-5744	352	9	3ϱ∗	3ϱ∗	NUM
ejpam-5744	352	10	4	4	NUM
ejpam-5744	352	11	〉	〉	NOUN
ejpam-5744	352	12	=	=	SYM
ejpam-5744	352	13	1	1	NUM
ejpam-5744	352	14	4	4	NUM
ejpam-5744	352	15	⟨(ϱ∗0	⟨(ϱ∗0	NOUN
ejpam-5744	352	16	,	,	PUNCT
ejpam-5744	352	17	0	0	NUM
ejpam-5744	352	18	,	,	PUNCT
ejpam-5744	352	19	0	0	NUM
ejpam-5744	352	20	,	,	PUNCT
ejpam-5744	352	21	·	·	PUNCT
ejpam-5744	352	22	·	·	PUNCT
ejpam-5744	352	23	·	·	PUNCT
ejpam-5744	352	24	)	)	PUNCT
ejpam-5744	352	25	,	,	PUNCT
ejpam-5744	352	26	(	(	PUNCT
ejpam-5744	352	27	ω∗	ω∗	NOUN
ejpam-5744	352	28	0	0	NUM
ejpam-5744	352	29	−	−	PROPN
ejpam-5744	352	30	ϱ∗0	ϱ∗0	PROPN
ejpam-5744	352	31	,	,	PUNCT
ejpam-5744	352	32	0	0	NUM
ejpam-5744	352	33	,	,	PUNCT
ejpam-5744	352	34	0	0	NUM
ejpam-5744	352	35	,	,	PUNCT
ejpam-5744	352	36	·	·	PUNCT
ejpam-5744	352	37	·	·	PUNCT
ejpam-5744	352	38	·	·	PUNCT
ejpam-5744	352	39	)	)	PUNCT
ejpam-5744	352	40	⟩	⟩	NOUN
ejpam-5744	352	41	<	<	X
ejpam-5744	352	42	0	0	NUM
ejpam-5744	352	43	,	,	PUNCT
ejpam-5744	352	44	∀ω∗	∀ω∗	NOUN
ejpam-5744	352	45	=	=	SYM
ejpam-5744	352	46	(	(	PUNCT
ejpam-5744	352	47	ω∗	ω∗	NOUN
ejpam-5744	352	48	0	0	NUM
ejpam-5744	352	49	,	,	PUNCT
ejpam-5744	352	50	0	0	NUM
ejpam-5744	352	51	,	,	PUNCT
ejpam-5744	352	52	0	0	NUM
ejpam-5744	352	53	,	,	PUNCT
ejpam-5744	352	54	·	·	PUNCT
ejpam-5744	352	55	·	·	PUNCT
ejpam-5744	352	56	·	·	PUNCT
ejpam-5744	352	57	)	)	PUNCT
ejpam-5744	352	58	∈	∈	PROPN
ejpam-5744	352	59	c(ϱ∗	c(ϱ∗	NOUN
ejpam-5744	352	60	)	)	PUNCT
ejpam-5744	352	61	.	.	PUNCT
ejpam-5744	353	1	m.	m.	PROPN
ejpam-5744	353	2	akram	akram	PROPN
ejpam-5744	353	3	/	/	PUNCT
ejpam-5744	353	4	eur	eur	PROPN
ejpam-5744	353	5	.	.	PUNCT
ejpam-5744	354	1	j.	j.	PROPN
ejpam-5744	354	2	pure	pure	PROPN
ejpam-5744	354	3	appl	appl	PROPN
ejpam-5744	354	4	.	.	PROPN
ejpam-5744	354	5	math	math	PROPN
ejpam-5744	354	6	,	,	PUNCT
ejpam-5744	354	7	18	18	NUM
ejpam-5744	354	8	(	(	PUNCT
ejpam-5744	354	9	1	1	NUM
ejpam-5744	354	10	)	)	PUNCT
ejpam-5744	354	11	(	(	PUNCT
ejpam-5744	354	12	2025	2025	NUM
ejpam-5744	354	13	)	)	PUNCT
ejpam-5744	354	14	,	,	PUNCT
ejpam-5744	354	15	5744	5744	NUM
ejpam-5744	354	16	15	15	NUM
ejpam-5744	354	17	of	of	ADP
ejpam-5744	354	18	19	19	NUM
ejpam-5744	354	19	on	on	ADP
ejpam-5744	354	20	the	the	DET
ejpam-5744	354	21	other	other	ADJ
ejpam-5744	354	22	hand	hand	NOUN
ejpam-5744	354	23	,	,	PUNCT
ejpam-5744	354	24	for	for	ADP
ejpam-5744	354	25	ϱ∗	ϱ∗	NOUN
ejpam-5744	354	26	=	=	SYM
ejpam-5744	354	27	(	(	PUNCT
ejpam-5744	354	28	0	0	NUM
ejpam-5744	354	29	,	,	PUNCT
ejpam-5744	354	30	0	0	NUM
ejpam-5744	354	31	,	,	PUNCT
ejpam-5744	354	32	0	0	NUM
ejpam-5744	354	33	,	,	PUNCT
ejpam-5744	354	34	·	·	PUNCT
ejpam-5744	354	35	·	·	PUNCT
ejpam-5744	354	36	·	·	PUNCT
ejpam-5744	354	37	)	)	PUNCT
ejpam-5744	355	1	,	,	PUNCT
ejpam-5744	355	2	we	we	PRON
ejpam-5744	355	3	acquire	acquire	VERB
ejpam-5744	355	4	⟨ψ(ϱ∗	⟨ψ(ϱ∗	PROPN
ejpam-5744	355	5	)	)	PUNCT
ejpam-5744	355	6	,	,	PUNCT
ejpam-5744	355	7	ψ(ω∗)−ψ(ϱ∗)⟩	ψ(ω∗)−ψ(ϱ∗)⟩	X
ejpam-5744	355	8	=	=	PUNCT
ejpam-5744	355	9	⟨(0	⟨(0	PROPN
ejpam-5744	355	10	,	,	PUNCT
ejpam-5744	355	11	0	0	NUM
ejpam-5744	355	12	,	,	PUNCT
ejpam-5744	355	13	0	0	NUM
ejpam-5744	355	14	,	,	PUNCT
ejpam-5744	355	15	·	·	PUNCT
ejpam-5744	355	16	·	·	PUNCT
ejpam-5744	355	17	·	·	PUNCT
ejpam-5744	355	18	)	)	PUNCT
ejpam-5744	355	19	,	,	PUNCT
ejpam-5744	355	20	(	(	PUNCT
ejpam-5744	355	21	ω∗	ω∗	PROPN
ejpam-5744	355	22	0−ϱ∗0	0−ϱ∗0	PROPN
ejpam-5744	355	23	,	,	PUNCT
ejpam-5744	355	24	0	0	NUM
ejpam-5744	355	25	,	,	PUNCT
ejpam-5744	355	26	0	0	NUM
ejpam-5744	355	27	,	,	PUNCT
ejpam-5744	355	28	·	·	PUNCT
ejpam-5744	355	29	·	·	PUNCT
ejpam-5744	355	30	·	·	PUNCT
ejpam-5744	355	31	)	)	PUNCT
ejpam-5744	356	1	⟩	⟩	NOUN
ejpam-5744	356	2	=	=	SYM
ejpam-5744	356	3	0	0	NUM
ejpam-5744	356	4	,	,	PUNCT
ejpam-5744	356	5	∀ω∗	∀ω∗	NOUN
ejpam-5744	356	6	=	=	SYM
ejpam-5744	356	7	(	(	PUNCT
ejpam-5744	356	8	ω∗	ω∗	NOUN
ejpam-5744	356	9	0	0	NUM
ejpam-5744	356	10	,	,	PUNCT
ejpam-5744	356	11	0	0	NUM
ejpam-5744	356	12	,	,	PUNCT
ejpam-5744	356	13	0	0	NUM
ejpam-5744	356	14	,	,	PUNCT
ejpam-5744	356	15	·	·	PUNCT
ejpam-5744	356	16	·	·	PUNCT
ejpam-5744	356	17	·	·	PUNCT
ejpam-5744	356	18	)	)	PUNCT
ejpam-5744	356	19	∈	∈	PROPN
ejpam-5744	356	20	c(ϱ∗	c(ϱ∗	NOUN
ejpam-5744	356	21	)	)	PUNCT
ejpam-5744	356	22	.	.	PUNCT
ejpam-5744	357	1	thus	thus	ADV
ejpam-5744	357	2	,	,	PUNCT
ejpam-5744	357	3	for	for	ADP
ejpam-5744	357	4	ϱ∗	ϱ∗	NOUN
ejpam-5744	357	5	=	=	SYM
ejpam-5744	357	6	(	(	PUNCT
ejpam-5744	357	7	0	0	NUM
ejpam-5744	357	8	,	,	PUNCT
ejpam-5744	357	9	0	0	NUM
ejpam-5744	357	10	,	,	PUNCT
ejpam-5744	357	11	0	0	NUM
ejpam-5744	357	12	,	,	PUNCT
ejpam-5744	357	13	·	·	PUNCT
ejpam-5744	357	14	·	·	PUNCT
ejpam-5744	357	15	·	·	PUNCT
ejpam-5744	357	16	)	)	PUNCT
ejpam-5744	357	17	∈	∈	PROPN
ejpam-5744	357	18	ξ(ψ	ξ(ψ	PROPN
ejpam-5744	357	19	)	)	PUNCT
ejpam-5744	357	20	∩	∩	NOUN
ejpam-5744	357	21	ξ(π	ξ(π	NOUN
ejpam-5744	357	22	)	)	PUNCT
ejpam-5744	357	23	.	.	PUNCT
ejpam-5744	358	1	3.2	3.2	NUM
ejpam-5744	358	2	.	.	PUNCT
ejpam-5744	358	3	fractional	fractional	ADJ
ejpam-5744	358	4	differential	differential	ADJ
ejpam-5744	358	5	equation	equation	NOUN
ejpam-5744	358	6	the	the	DET
ejpam-5744	358	7	history	history	NOUN
ejpam-5744	358	8	of	of	ADP
ejpam-5744	358	9	fractional	fractional	ADJ
ejpam-5744	358	10	calculus	calculus	NOUN
ejpam-5744	358	11	can	can	AUX
ejpam-5744	358	12	be	be	AUX
ejpam-5744	358	13	traced	trace	VERB
ejpam-5744	358	14	back	back	ADV
ejpam-5744	358	15	to	to	ADP
ejpam-5744	358	16	the	the	DET
ejpam-5744	358	17	middle	middle	NOUN
ejpam-5744	358	18	of	of	ADP
ejpam-5744	358	19	the	the	DET
ejpam-5744	358	20	19th	19th	ADJ
ejpam-5744	358	21	century	century	NOUN
ejpam-5744	358	22	from	from	ADP
ejpam-5744	358	23	the	the	DET
ejpam-5744	358	24	pure	pure	ADJ
ejpam-5744	358	25	mathematics	mathematic	NOUN
ejpam-5744	358	26	.	.	PUNCT
ejpam-5744	359	1	but	but	CCONJ
ejpam-5744	359	2	a	a	DET
ejpam-5744	359	3	century	century	NOUN
ejpam-5744	359	4	later	later	ADV
ejpam-5744	359	5	,	,	PUNCT
ejpam-5744	359	6	its	its	PRON
ejpam-5744	359	7	substantial	substantial	ADJ
ejpam-5744	359	8	and	and	CCONJ
ejpam-5744	359	9	significant	significant	ADJ
ejpam-5744	359	10	applications	application	NOUN
ejpam-5744	359	11	have	have	AUX
ejpam-5744	359	12	been	be	AUX
ejpam-5744	359	13	drawn	draw	VERB
ejpam-5744	359	14	by	by	ADP
ejpam-5744	359	15	engineers	engineer	NOUN
ejpam-5744	359	16	and	and	CCONJ
ejpam-5744	359	17	physicists	physicist	NOUN
ejpam-5744	359	18	in	in	ADP
ejpam-5744	359	19	their	their	PRON
ejpam-5744	359	20	respective	respective	ADJ
ejpam-5744	359	21	fields	field	NOUN
ejpam-5744	359	22	.	.	PUNCT
ejpam-5744	360	1	fractional	fractional	ADJ
ejpam-5744	360	2	derivatives	derivative	NOUN
ejpam-5744	360	3	are	be	AUX
ejpam-5744	360	4	generalization	generalization	NOUN
ejpam-5744	360	5	of	of	ADP
ejpam-5744	360	6	ordinary	ordinary	ADJ
ejpam-5744	360	7	derivatives	derivative	NOUN
ejpam-5744	360	8	which	which	PRON
ejpam-5744	360	9	simultaneously	simultaneously	ADV
ejpam-5744	360	10	set	set	VERB
ejpam-5744	360	11	out	out	ADP
ejpam-5744	360	12	the	the	DET
ejpam-5744	360	13	behavior	behavior	NOUN
ejpam-5744	360	14	of	of	ADP
ejpam-5744	360	15	several	several	ADJ
ejpam-5744	360	16	physical	physical	ADJ
ejpam-5744	360	17	phenomena	phenomenon	NOUN
ejpam-5744	360	18	.	.	PUNCT
ejpam-5744	361	1	a	a	DET
ejpam-5744	361	2	very	very	ADV
ejpam-5744	361	3	much	much	ADJ
ejpam-5744	361	4	attention	attention	NOUN
ejpam-5744	361	5	have	have	AUX
ejpam-5744	361	6	been	be	AUX
ejpam-5744	361	7	paid	pay	VERB
ejpam-5744	361	8	to	to	ADP
ejpam-5744	361	9	fractional	fractional	ADJ
ejpam-5744	361	10	differential	differential	ADJ
ejpam-5744	361	11	equations	equation	NOUN
ejpam-5744	361	12	(	(	PUNCT
ejpam-5744	361	13	fdes	fde	NOUN
ejpam-5744	361	14	)	)	PUNCT
ejpam-5744	361	15	due	due	ADP
ejpam-5744	361	16	to	to	ADP
ejpam-5744	361	17	their	their	PRON
ejpam-5744	361	18	worthy	worthy	ADJ
ejpam-5744	361	19	applications	application	NOUN
ejpam-5744	361	20	in	in	ADP
ejpam-5744	361	21	several	several	ADJ
ejpam-5744	361	22	physical	physical	ADJ
ejpam-5744	361	23	phenomena	phenomenon	NOUN
ejpam-5744	361	24	appearing	appear	VERB
ejpam-5744	361	25	in	in	ADP
ejpam-5744	361	26	engineering	engineering	NOUN
ejpam-5744	361	27	,	,	PUNCT
ejpam-5744	361	28	mechanics	mechanic	NOUN
ejpam-5744	361	29	,	,	PUNCT
ejpam-5744	361	30	economics	economic	NOUN
ejpam-5744	361	31	,	,	PUNCT
ejpam-5744	361	32	biology	biology	NOUN
ejpam-5744	361	33	,	,	PUNCT
ejpam-5744	361	34	etc	etc	X
ejpam-5744	361	35	.	.	X
ejpam-5744	361	36	,	,	PUNCT
ejpam-5744	361	37	see	see	VERB
ejpam-5744	361	38	,	,	PUNCT
ejpam-5744	361	39	[	[	X
ejpam-5744	361	40	27	27	NUM
ejpam-5744	361	41	,	,	PUNCT
ejpam-5744	361	42	29	29	NUM
ejpam-5744	361	43	,	,	PUNCT
ejpam-5744	361	44	46	46	NUM
ejpam-5744	361	45	,	,	PUNCT
ejpam-5744	361	46	52	52	NUM
ejpam-5744	361	47	,	,	PUNCT
ejpam-5744	361	48	53	53	NUM
ejpam-5744	361	49	]	]	PUNCT
ejpam-5744	361	50	and	and	CCONJ
ejpam-5744	361	51	references	reference	NOUN
ejpam-5744	361	52	therein	therein	ADV
ejpam-5744	361	53	and	and	CCONJ
ejpam-5744	361	54	so	so	ADV
ejpam-5744	361	55	these	these	DET
ejpam-5744	361	56	equations	equation	NOUN
ejpam-5744	361	57	are	be	AUX
ejpam-5744	361	58	widely	widely	ADV
ejpam-5744	361	59	used	use	VERB
ejpam-5744	361	60	in	in	ADP
ejpam-5744	361	61	many	many	ADJ
ejpam-5744	361	62	different	different	ADJ
ejpam-5744	361	63	domains	domain	NOUN
ejpam-5744	361	64	.	.	PUNCT
ejpam-5744	362	1	now	now	ADV
ejpam-5744	362	2	a	a	DET
ejpam-5744	362	3	days	day	NOUN
ejpam-5744	362	4	,	,	PUNCT
ejpam-5744	362	5	fixed	fix	VERB
ejpam-5744	362	6	point	point	NOUN
ejpam-5744	362	7	theory	theory	NOUN
ejpam-5744	362	8	has	have	AUX
ejpam-5744	362	9	become	become	VERB
ejpam-5744	362	10	a	a	DET
ejpam-5744	362	11	crucial	crucial	ADJ
ejpam-5744	362	12	tool	tool	NOUN
ejpam-5744	362	13	to	to	PART
ejpam-5744	362	14	handle	handle	VERB
ejpam-5744	362	15	nonlinear	nonlinear	ADJ
ejpam-5744	362	16	problems	problem	NOUN
ejpam-5744	362	17	arising	arise	VERB
ejpam-5744	362	18	in	in	ADP
ejpam-5744	362	19	multi	multi	ADJ
ejpam-5744	362	20	-	-	ADJ
ejpam-5744	362	21	disciplinary	disciplinary	ADJ
ejpam-5744	362	22	sciences	science	NOUN
ejpam-5744	362	23	.	.	PUNCT
ejpam-5744	363	1	its	its	PRON
ejpam-5744	363	2	capacity	capacity	NOUN
ejpam-5744	363	3	and	and	CCONJ
ejpam-5744	363	4	aptitude	aptitude	NOUN
ejpam-5744	363	5	to	to	PART
ejpam-5744	363	6	demonstrate	demonstrate	VERB
ejpam-5744	363	7	the	the	DET
ejpam-5744	363	8	existence	existence	NOUN
ejpam-5744	363	9	and	and	CCONJ
ejpam-5744	363	10	uniqueness	uniqueness	NOUN
ejpam-5744	363	11	of	of	ADP
ejpam-5744	363	12	solutions	solution	NOUN
ejpam-5744	363	13	,	,	PUNCT
ejpam-5744	363	14	provides	provide	VERB
ejpam-5744	363	15	researchers	researcher	NOUN
ejpam-5744	363	16	to	to	PART
ejpam-5744	363	17	construct	construct	VERB
ejpam-5744	363	18	fixed	fix	VERB
ejpam-5744	363	19	point	point	NOUN
ejpam-5744	363	20	iterative	iterative	NOUN
ejpam-5744	363	21	methods	method	NOUN
ejpam-5744	363	22	to	to	PART
ejpam-5744	363	23	research	research	VERB
ejpam-5744	363	24	and	and	CCONJ
ejpam-5744	363	25	examine	examine	VERB
ejpam-5744	363	26	fdes	fde	NOUN
ejpam-5744	363	27	.	.	PUNCT
ejpam-5744	364	1	in	in	ADP
ejpam-5744	364	2	recent	recent	ADJ
ejpam-5744	364	3	time	time	NOUN
ejpam-5744	364	4	,	,	PUNCT
ejpam-5744	364	5	researchers	researcher	NOUN
ejpam-5744	364	6	have	have	AUX
ejpam-5744	364	7	been	be	AUX
ejpam-5744	364	8	explored	explore	VERB
ejpam-5744	364	9	different	different	ADJ
ejpam-5744	364	10	classes	class	NOUN
ejpam-5744	364	11	of	of	ADP
ejpam-5744	364	12	fdes	fde	NOUN
ejpam-5744	364	13	by	by	ADP
ejpam-5744	364	14	implementing	implement	VERB
ejpam-5744	364	15	fundamental	fundamental	ADJ
ejpam-5744	364	16	tools	tool	NOUN
ejpam-5744	364	17	of	of	ADP
ejpam-5744	364	18	fixed	fix	VERB
ejpam-5744	364	19	point	point	NOUN
ejpam-5744	364	20	theory	theory	NOUN
ejpam-5744	364	21	,	,	PUNCT
ejpam-5744	364	22	for	for	ADP
ejpam-5744	364	23	more	more	ADJ
ejpam-5744	364	24	details	detail	NOUN
ejpam-5744	364	25	,	,	PUNCT
ejpam-5744	364	26	we	we	PRON
ejpam-5744	364	27	refer	refer	VERB
ejpam-5744	364	28	,	,	PUNCT
ejpam-5744	364	29	[	[	X
ejpam-5744	364	30	1	1	NUM
ejpam-5744	364	31	,	,	PUNCT
ejpam-5744	364	32	2	2	NUM
ejpam-5744	364	33	,	,	PUNCT
ejpam-5744	364	34	14	14	NUM
ejpam-5744	364	35	,	,	PUNCT
ejpam-5744	364	36	17	17	NUM
ejpam-5744	364	37	,	,	PUNCT
ejpam-5744	364	38	18	18	NUM
ejpam-5744	364	39	,	,	PUNCT
ejpam-5744	364	40	24	24	NUM
ejpam-5744	364	41	,	,	PUNCT
ejpam-5744	364	42	42	42	NUM
ejpam-5744	364	43	,	,	PUNCT
ejpam-5744	364	44	44	44	NUM
ejpam-5744	364	45	]	]	PUNCT
ejpam-5744	364	46	.	.	PUNCT
ejpam-5744	365	1	now	now	ADV
ejpam-5744	365	2	,	,	PUNCT
ejpam-5744	365	3	we	we	PRON
ejpam-5744	365	4	take	take	VERB
ejpam-5744	365	5	simps	simp	NOUN
ejpam-5744	365	6	(	(	PUNCT
ejpam-5744	365	7	14	14	NUM
ejpam-5744	365	8	)	)	PUNCT
ejpam-5744	365	9	into	into	ADP
ejpam-5744	365	10	account	account	NOUN
ejpam-5744	365	11	to	to	PART
ejpam-5744	365	12	examine	examine	VERB
ejpam-5744	365	13	the	the	DET
ejpam-5744	365	14	following	follow	VERB
ejpam-5744	365	15	caputo	caputo	NOUN
ejpam-5744	365	16	-	-	PUNCT
ejpam-5744	365	17	type	type	NOUN
ejpam-5744	365	18	nonlinear	nonlinear	ADJ
ejpam-5744	365	19	fractional	fractional	ADJ
ejpam-5744	365	20	differential	differential	NOUN
ejpam-5744	365	21	equation	equation	NOUN
ejpam-5744	365	22	(	(	PUNCT
ejpam-5744	365	23	c	c	NOUN
ejpam-5744	365	24	-	-	PUNCT
ejpam-5744	365	25	nfde	nfde	NOUN
ejpam-5744	365	26	):	):	PUNCT
ejpam-5744	365	27	{	{	PUNCT
ejpam-5744	365	28	γdξϱ(u	γdξϱ(u	NOUN
ejpam-5744	365	29	)	)	PUNCT
ejpam-5744	366	1	+	+	CCONJ
ejpam-5744	366	2	φ(u	φ(u	NOUN
ejpam-5744	366	3	,	,	PUNCT
ejpam-5744	366	4	ϱ(u	ϱ(u	ADP
ejpam-5744	366	5	)	)	PUNCT
ejpam-5744	366	6	)	)	PUNCT
ejpam-5744	367	1	=	=	SYM
ejpam-5744	367	2	0	0	NUM
ejpam-5744	367	3	,	,	PUNCT
ejpam-5744	367	4	ϱ(0	ϱ(0	NOUN
ejpam-5744	367	5	)	)	PUNCT
ejpam-5744	367	6	=	=	SYM
ejpam-5744	367	7	ϱ(1	ϱ(1	NOUN
ejpam-5744	367	8	)	)	PUNCT
ejpam-5744	367	9	=	=	SYM
ejpam-5744	368	1	0	0	NUM
ejpam-5744	368	2	,	,	PUNCT
ejpam-5744	368	3	1	1	NUM
ejpam-5744	368	4	<	<	X
ejpam-5744	368	5	ξ	ξ	X
ejpam-5744	368	6	<	<	X
ejpam-5744	368	7	2	2	NUM
ejpam-5744	368	8	,	,	PUNCT
ejpam-5744	368	9	u	u	NOUN
ejpam-5744	368	10	∈	∈	PROPN
ejpam-5744	369	1	[	[	X
ejpam-5744	369	2	0	0	NUM
ejpam-5744	369	3	,	,	PUNCT
ejpam-5744	369	4	1	1	NUM
ejpam-5744	369	5	]	]	PUNCT
ejpam-5744	369	6	,	,	PUNCT
ejpam-5744	369	7	(	(	PUNCT
ejpam-5744	369	8	41	41	NUM
ejpam-5744	369	9	)	)	PUNCT
ejpam-5744	369	10	here	here	ADV
ejpam-5744	369	11	,	,	PUNCT
ejpam-5744	369	12	γdξ	γdξ	VERB
ejpam-5744	369	13	signifies	signify	VERB
ejpam-5744	369	14	a	a	DET
ejpam-5744	369	15	caputo	caputo	PROPN
ejpam-5744	369	16	-	-	PUNCT
ejpam-5744	369	17	fractional	fractional	ADJ
ejpam-5744	369	18	derivative	derivative	NOUN
ejpam-5744	369	19	of	of	ADP
ejpam-5744	369	20	order	order	NOUN
ejpam-5744	369	21	ξ	ξ	PROPN
ejpam-5744	369	22	and	and	CCONJ
ejpam-5744	369	23	φ	φ	NUM
ejpam-5744	369	24	:	:	PUNCT
ejpam-5744	370	1	[	[	X
ejpam-5744	370	2	0	0	NUM
ejpam-5744	370	3	,	,	PUNCT
ejpam-5744	370	4	1	1	NUM
ejpam-5744	370	5	]	]	SYM
ejpam-5744	370	6	×	×	NOUN
ejpam-5744	370	7	r	r	NOUN
ejpam-5744	370	8	→	→	SYM
ejpam-5744	370	9	r	r	NOUN
ejpam-5744	370	10	is	be	AUX
ejpam-5744	370	11	a	a	DET
ejpam-5744	370	12	continuous	continuous	ADJ
ejpam-5744	370	13	function	function	NOUN
ejpam-5744	370	14	.	.	PUNCT
ejpam-5744	371	1	let	let	VERB
ejpam-5744	371	2	x	x	PUNCT
ejpam-5744	371	3	=	=	PRON
ejpam-5744	371	4	{	{	PUNCT
ejpam-5744	371	5	ℑ	ℑ	NOUN
ejpam-5744	371	6	:	:	PUNCT
ejpam-5744	371	7	ℑ	ℑ	NOUN
ejpam-5744	371	8	:	:	PUNCT
ejpam-5744	371	9	[	[	X
ejpam-5744	371	10	0	0	NUM
ejpam-5744	371	11	,	,	PUNCT
ejpam-5744	371	12	1	1	NUM
ejpam-5744	371	13	]	]	PUNCT
ejpam-5744	371	14	→	→	SYM
ejpam-5744	371	15	r	r	X
ejpam-5744	371	16	}	}	PUNCT
ejpam-5744	371	17	is	be	AUX
ejpam-5744	371	18	a	a	DET
ejpam-5744	371	19	real	real	ADJ
ejpam-5744	371	20	continuous	continuous	ADJ
ejpam-5744	371	21	function	function	NOUN
ejpam-5744	371	22	equipped	equip	VERB
ejpam-5744	371	23	with	with	ADP
ejpam-5744	371	24	supremum	supremum	ADJ
ejpam-5744	371	25	norm	norm	NOUN
ejpam-5744	371	26	.	.	PUNCT
ejpam-5744	372	1	the	the	DET
ejpam-5744	372	2	green	green	PROPN
ejpam-5744	372	3	’s	’s	PART
ejpam-5744	372	4	function	function	NOUN
ejpam-5744	372	5	related	relate	VERB
ejpam-5744	372	6	to	to	ADP
ejpam-5744	372	7	(	(	PUNCT
ejpam-5744	372	8	41	41	NUM
ejpam-5744	372	9	)	)	PUNCT
ejpam-5744	372	10	is	be	AUX
ejpam-5744	372	11	expressed	express	VERB
ejpam-5744	372	12	as	as	ADP
ejpam-5744	372	13	under	under	ADV
ejpam-5744	372	14	:	:	PUNCT
ejpam-5744	372	15	g(u	g(u	PROPN
ejpam-5744	372	16	,	,	PUNCT
ejpam-5744	372	17	v	v	NOUN
ejpam-5744	372	18	)	)	PUNCT
ejpam-5744	372	19	=	=	NOUN
ejpam-5744	372	20	{	{	PUNCT
ejpam-5744	372	21	1	1	NUM
ejpam-5744	372	22	γ(ξ)(u(1−	γ(ξ)(u(1−	ADJ
ejpam-5744	372	23	v)(ξ−1	v)(ξ−1	NUM
ejpam-5744	372	24	)	)	PUNCT
ejpam-5744	372	25	−	−	PROPN
ejpam-5744	373	1	(	(	PUNCT
ejpam-5744	373	2	u−	u−	PROPN
ejpam-5744	373	3	v)(ξ−1	v)(ξ−1	NUM
ejpam-5744	373	4	)	)	PUNCT
ejpam-5744	373	5	)	)	PUNCT
ejpam-5744	374	1	,	,	PUNCT
ejpam-5744	374	2	if	if	SCONJ
ejpam-5744	374	3	0	0	NUM
ejpam-5744	374	4	≤	≤	NUM
ejpam-5744	374	5	v	v	NOUN
ejpam-5744	374	6	≤	≤	NUM
ejpam-5744	374	7	u	u	NOUN
ejpam-5744	374	8	≤	≤	NUM
ejpam-5744	374	9	1	1	NUM
ejpam-5744	374	10	,	,	PUNCT
ejpam-5744	374	11	u(1−v)(ξ−1	u(1−v)(ξ−1	ADJ
ejpam-5744	374	12	)	)	PUNCT
ejpam-5744	374	13	γ(ξ	γ(ξ	PROPN
ejpam-5744	374	14	)	)	PUNCT
ejpam-5744	374	15	,	,	PUNCT
ejpam-5744	374	16	if	if	SCONJ
ejpam-5744	374	17	0	0	NUM
ejpam-5744	374	18	≤	≤	NUM
ejpam-5744	374	19	u	u	NOUN
ejpam-5744	374	20	≤	≤	NOUN
ejpam-5744	374	21	v	v	ADJ
ejpam-5744	374	22	≤	≤	NUM
ejpam-5744	374	23	1	1	NUM
ejpam-5744	374	24	.	.	PUNCT
ejpam-5744	375	1	now	now	ADV
ejpam-5744	375	2	,	,	PUNCT
ejpam-5744	375	3	we	we	PRON
ejpam-5744	375	4	proceed	proceed	VERB
ejpam-5744	375	5	to	to	PART
ejpam-5744	375	6	accomplish	accomplish	VERB
ejpam-5744	375	7	the	the	DET
ejpam-5744	375	8	goal	goal	NOUN
ejpam-5744	375	9	of	of	ADP
ejpam-5744	375	10	this	this	DET
ejpam-5744	375	11	sub	sub	NOUN
ejpam-5744	375	12	-	-	NOUN
ejpam-5744	375	13	section	section	NOUN
ejpam-5744	375	14	.	.	PUNCT
ejpam-5744	376	1	theorem	theorem	NOUN
ejpam-5744	376	2	5	5	NUM
ejpam-5744	376	3	.	.	PUNCT
ejpam-5744	377	1	let	let	VERB
ejpam-5744	377	2	x	x	SYM
ejpam-5744	377	3	=	=	SYM
ejpam-5744	377	4	c[0	c[0	PROPN
ejpam-5744	377	5	,	,	PUNCT
ejpam-5744	377	6	1	1	NUM
ejpam-5744	377	7	]	]	PUNCT
ejpam-5744	377	8	and	and	CCONJ
ejpam-5744	377	9	the	the	DET
ejpam-5744	377	10	operator	operator	NOUN
ejpam-5744	377	11	ℑ	ℑ	NOUN
ejpam-5744	377	12	:	:	PUNCT
ejpam-5744	377	13	x	x	SYM
ejpam-5744	377	14	→	→	PUNCT
ejpam-5744	377	15	x	x	X
ejpam-5744	377	16	is	be	AUX
ejpam-5744	377	17	defined	define	VERB
ejpam-5744	377	18	by	by	ADP
ejpam-5744	377	19	ℑ(ϱ(u	ℑ(ϱ(u	NOUN
ejpam-5744	377	20	)	)	PUNCT
ejpam-5744	377	21	)	)	PUNCT
ejpam-5744	378	1	=	=	PUNCT
ejpam-5744	378	2	∫	∫	PROPN
ejpam-5744	379	1	1	1	NUM
ejpam-5744	379	2	0	0	NUM
ejpam-5744	379	3	g(u	g(u	PROPN
ejpam-5744	379	4	,	,	PUNCT
ejpam-5744	379	5	v)φ(v	v)φ(v	PROPN
ejpam-5744	379	6	,	,	PUNCT
ejpam-5744	379	7	h(v))dv,∀ϱ	h(v))dv,∀ϱ	NOUN
ejpam-5744	379	8	∈	∈	NOUN
ejpam-5744	379	9	x	x	X
ejpam-5744	379	10	.	.	PUNCT
ejpam-5744	380	1	if	if	SCONJ
ejpam-5744	380	2	,	,	PUNCT
ejpam-5744	380	3	|φ(v	|φ(v	PROPN
ejpam-5744	380	4	,	,	PUNCT
ejpam-5744	380	5	ϱ(v))−	ϱ(v))−	NOUN
ejpam-5744	380	6	φ(v	φ(v	ADV
ejpam-5744	380	7	,	,	PUNCT
ejpam-5744	380	8	j(v))|	j(v))|	NOUN
ejpam-5744	380	9	≤	≤	ADJ
ejpam-5744	380	10	g(ϱ−ℑ(ϱ	g(ϱ−ℑ(ϱ	NOUN
ejpam-5744	380	11	)	)	PUNCT
ejpam-5744	380	12	)	)	PUNCT
ejpam-5744	380	13	+	+	CCONJ
ejpam-5744	380	14	τ	τ	PROPN
ejpam-5744	380	15	|ϱ−	|ϱ−	NOUN
ejpam-5744	380	16	j|,∀v	j|,∀v	NOUN
ejpam-5744	380	17	∈	∈	PROPN
ejpam-5744	381	1	[	[	X
ejpam-5744	381	2	0	0	NUM
ejpam-5744	381	3	,	,	PUNCT
ejpam-5744	381	4	1	1	NUM
ejpam-5744	381	5	]	]	PUNCT
ejpam-5744	381	6	,	,	PUNCT
ejpam-5744	381	7	ϱ	ϱ	PROPN
ejpam-5744	381	8	,	,	PUNCT
ejpam-5744	381	9	j	j	PROPN
ejpam-5744	381	10	∈	∈	PROPN
ejpam-5744	381	11	x	x	X
ejpam-5744	381	12	.	.	PUNCT
ejpam-5744	381	13	(	(	PUNCT
ejpam-5744	381	14	42	42	NUM
ejpam-5744	381	15	)	)	PUNCT
ejpam-5744	381	16	then	then	ADV
ejpam-5744	381	17	the	the	DET
ejpam-5744	381	18	scheme	scheme	NOUN
ejpam-5744	381	19	(	(	PUNCT
ejpam-5744	381	20	14	14	NUM
ejpam-5744	381	21	)	)	PUNCT
ejpam-5744	381	22	associated	associate	VERB
ejpam-5744	381	23	to	to	ADP
ejpam-5744	381	24	ℑ	ℑ	PROPN
ejpam-5744	381	25	converges	converge	VERB
ejpam-5744	381	26	to	to	ADP
ejpam-5744	381	27	the	the	DET
ejpam-5744	381	28	solution	solution	NOUN
ejpam-5744	381	29	of	of	ADP
ejpam-5744	381	30	c	c	NOUN
ejpam-5744	381	31	-	-	PUNCT
ejpam-5744	381	32	nfde	nfde	NOUN
ejpam-5744	381	33	(	(	PUNCT
ejpam-5744	381	34	41	41	NUM
ejpam-5744	381	35	)	)	PUNCT
ejpam-5744	381	36	.	.	PUNCT
ejpam-5744	382	1	m.	m.	PROPN
ejpam-5744	382	2	akram	akram	PROPN
ejpam-5744	382	3	/	/	PUNCT
ejpam-5744	382	4	eur	eur	PROPN
ejpam-5744	382	5	.	.	PUNCT
ejpam-5744	383	1	j.	j.	PROPN
ejpam-5744	383	2	pure	pure	PROPN
ejpam-5744	383	3	appl	appl	PROPN
ejpam-5744	383	4	.	.	PROPN
ejpam-5744	383	5	math	math	PROPN
ejpam-5744	383	6	,	,	PUNCT
ejpam-5744	383	7	18	18	NUM
ejpam-5744	383	8	(	(	PUNCT
ejpam-5744	383	9	1	1	NUM
ejpam-5744	383	10	)	)	PUNCT
ejpam-5744	383	11	(	(	PUNCT
ejpam-5744	383	12	2025	2025	NUM
ejpam-5744	383	13	)	)	PUNCT
ejpam-5744	383	14	,	,	PUNCT
ejpam-5744	383	15	5744	5744	NUM
ejpam-5744	383	16	16	16	NUM
ejpam-5744	383	17	of	of	ADP
ejpam-5744	383	18	19	19	NUM
ejpam-5744	383	19	proof	proof	NOUN
ejpam-5744	383	20	.	.	PUNCT
ejpam-5744	384	1	evidently	evidently	ADV
ejpam-5744	384	2	,	,	PUNCT
ejpam-5744	384	3	if	if	SCONJ
ejpam-5744	384	4	ϱ	ϱ	PROPN
ejpam-5744	384	5	∈	∈	PROPN
ejpam-5744	384	6	x	x	PUNCT
ejpam-5744	384	7	solves	solve	NOUN
ejpam-5744	384	8	(	(	PUNCT
ejpam-5744	384	9	41	41	NUM
ejpam-5744	384	10	)	)	PUNCT
ejpam-5744	384	11	iff	iff	PROPN
ejpam-5744	384	12	ϱ	ϱ	PROPN
ejpam-5744	384	13	solves	solve	NOUN
ejpam-5744	384	14	:	:	PUNCT
ejpam-5744	384	15	ϱ(u	ϱ(u	ADP
ejpam-5744	384	16	)	)	PUNCT
ejpam-5744	384	17	=	=	SYM
ejpam-5744	385	1	∫	∫	PROPN
ejpam-5744	385	2	1	1	NUM
ejpam-5744	386	1	0	0	NUM
ejpam-5744	386	2	g(u	g(u	PROPN
ejpam-5744	386	3	,	,	PUNCT
ejpam-5744	386	4	v)φ(v	v)φ(v	PROPN
ejpam-5744	386	5	,	,	PUNCT
ejpam-5744	386	6	h(v))dv	h(v))dv	NOUN
ejpam-5744	386	7	.	.	PUNCT
ejpam-5744	387	1	then	then	ADV
ejpam-5744	387	2	for	for	ADP
ejpam-5744	387	3	all	all	DET
ejpam-5744	387	4	ϱ	ϱ	NOUN
ejpam-5744	387	5	,	,	PUNCT
ejpam-5744	387	6	j	j	PROPN
ejpam-5744	387	7	∈	∈	PROPN
ejpam-5744	387	8	x	x	X
ejpam-5744	387	9	and	and	CCONJ
ejpam-5744	387	10	u	u	PROPN
ejpam-5744	387	11	∈	∈	PROPN
ejpam-5744	388	1	[	[	X
ejpam-5744	388	2	0	0	NUM
ejpam-5744	388	3	,	,	PUNCT
ejpam-5744	388	4	1	1	NUM
ejpam-5744	388	5	]	]	PUNCT
ejpam-5744	388	6	,	,	PUNCT
ejpam-5744	388	7	imposing	impose	VERB
ejpam-5744	388	8	the	the	DET
ejpam-5744	388	9	assumption	assumption	NOUN
ejpam-5744	388	10	(	(	PUNCT
ejpam-5744	388	11	42	42	NUM
ejpam-5744	388	12	)	)	PUNCT
ejpam-5744	388	13	and	and	CCONJ
ejpam-5744	388	14	employing	employ	VERB
ejpam-5744	388	15	the	the	DET
ejpam-5744	388	16	definition	definition	NOUN
ejpam-5744	388	17	of	of	ADP
ejpam-5744	388	18	operator	operator	NOUN
ejpam-5744	388	19	ℑ	ℑ	PROPN
ejpam-5744	388	20	,	,	PUNCT
ejpam-5744	388	21	we	we	PRON
ejpam-5744	388	22	acquire	acquire	VERB
ejpam-5744	388	23	∥ℑ(ϱ(u))−ℑ(j(u))∥	∥ℑ(ϱ(u))−ℑ(j(u))∥	PUNCT
ejpam-5744	389	1	=	=	PUNCT
ejpam-5744	389	2	∣∣∣	∣∣∣	NOUN
ejpam-5744	389	3	∫	∫	PROPN
ejpam-5744	389	4	1	1	NUM
ejpam-5744	389	5	0	0	NUM
ejpam-5744	389	6	g(u	g(u	PROPN
ejpam-5744	389	7	,	,	PUNCT
ejpam-5744	389	8	v)φ(v	v)φ(v	PROPN
ejpam-5744	389	9	,	,	PUNCT
ejpam-5744	389	10	ϱ(v))dv	ϱ(v))dv	PROPN
ejpam-5744	389	11	−	−	NUM
ejpam-5744	389	12	∫	∫	NOUN
ejpam-5744	389	13	1	1	NUM
ejpam-5744	389	14	0	0	NUM
ejpam-5744	389	15	g(u	g(u	PROPN
ejpam-5744	389	16	,	,	PUNCT
ejpam-5744	389	17	v)φ(v	v)φ(v	PROPN
ejpam-5744	389	18	,	,	PUNCT
ejpam-5744	389	19	j(v))dv	j(v))dv	NOUN
ejpam-5744	389	20	∣∣∣	∣∣∣	NOUN
ejpam-5744	389	21	=	=	SYM
ejpam-5744	389	22	∣∣∣	∣∣∣	NOUN
ejpam-5744	389	23	∫	∫	PROPN
ejpam-5744	389	24	1	1	NUM
ejpam-5744	389	25	0	0	NUM
ejpam-5744	389	26	g(u	g(u	PROPN
ejpam-5744	389	27	,	,	PUNCT
ejpam-5744	389	28	v)[φ(v	v)[φ(v	ADV
ejpam-5744	389	29	,	,	PUNCT
ejpam-5744	389	30	ϱ(v))−	ϱ(v))−	VERB
ejpam-5744	389	31	φ(v	φ(v	ADV
ejpam-5744	389	32	,	,	PUNCT
ejpam-5744	389	33	j(v))]dv	j(v))]dv	PROPN
ejpam-5744	389	34	∣∣∣	∣∣∣	ADJ
ejpam-5744	389	35	≤	≤	NUM
ejpam-5744	389	36	∫	∫	PROPN
ejpam-5744	389	37	1	1	NUM
ejpam-5744	389	38	0	0	NUM
ejpam-5744	389	39	g(u	g(u	PROPN
ejpam-5744	389	40	,	,	PUNCT
ejpam-5744	389	41	v)|φ(v	v)|φ(v	CCONJ
ejpam-5744	389	42	,	,	PUNCT
ejpam-5744	389	43	ϱ(v))−	ϱ(v))−	NOUN
ejpam-5744	389	44	φ(v	φ(v	PROPN
ejpam-5744	389	45	,	,	PUNCT
ejpam-5744	389	46	j(v))|dv	j(v))|dv	PROPN
ejpam-5744	389	47	≤	≤	PROPN
ejpam-5744	389	48	∫	∫	PROPN
ejpam-5744	390	1	1	1	NUM
ejpam-5744	390	2	0	0	NUM
ejpam-5744	390	3	g(u	g(u	NOUN
ejpam-5744	390	4	,	,	PUNCT
ejpam-5744	390	5	v)[g(|ϱ(v)−ℑ(ϱ(v))|	v)[g(|ϱ(v)−ℑ(ϱ(v))|	PROPN
ejpam-5744	390	6	)	)	PUNCT
ejpam-5744	391	1	+	+	CCONJ
ejpam-5744	391	2	τ	τ	PROPN
ejpam-5744	391	3	|ϱ(v)−	|ϱ(v)−	NOUN
ejpam-5744	391	4	j(v)|]dv	j(v)|]dv	PROPN
ejpam-5744	391	5	≤	≤	PROPN
ejpam-5744	391	6	sup	sup	PROPN
ejpam-5744	391	7	u∈[0,1	u∈[0,1	NOUN
ejpam-5744	391	8	]	]	X
ejpam-5744	391	9	∫	∫	PROPN
ejpam-5744	391	10	1	1	NUM
ejpam-5744	391	11	0	0	NUM
ejpam-5744	391	12	g(u	g(u	NOUN
ejpam-5744	391	13	,	,	PUNCT
ejpam-5744	391	14	v)[g(|ϱ(v)−ℑ(ϱ(v))|	v)[g(|ϱ(v)−ℑ(ϱ(v))|	PROPN
ejpam-5744	391	15	)	)	PUNCT
ejpam-5744	392	1	+	+	CCONJ
ejpam-5744	392	2	τ	τ	PROPN
ejpam-5744	392	3	|ϱ(v)−	|ϱ(v)−	NOUN
ejpam-5744	392	4	j(v)|]dv	j(v)|]dv	PROPN
ejpam-5744	392	5	≤	≤	PUNCT
ejpam-5744	392	6	g(∥ϱ(v)−ℑ(ϱ(v))∥	g(∥ϱ(v)−ℑ(ϱ(v))∥	PROPN
ejpam-5744	392	7	)	)	PUNCT
ejpam-5744	392	8	+	+	CCONJ
ejpam-5744	392	9	τ∥ϱ(v)−	τ∥ϱ(v)−	PROPN
ejpam-5744	392	10	j(v)∥	j(v)∥	NOUN
ejpam-5744	392	11	,	,	PUNCT
ejpam-5744	392	12	(	(	PUNCT
ejpam-5744	392	13	43	43	NUM
ejpam-5744	392	14	)	)	PUNCT
ejpam-5744	392	15	which	which	PRON
ejpam-5744	392	16	yields	yield	VERB
ejpam-5744	392	17	∥ℑ(ϱ)−ℑ(j)∥	∥ℑ(ϱ)−ℑ(j)∥	PRON
ejpam-5744	392	18	≤	≤	ADJ
ejpam-5744	392	19	g(∥ϱ−ℑ(ϱ)∥	g(∥ϱ−ℑ(ϱ)∥	NOUN
ejpam-5744	392	20	)	)	PUNCT
ejpam-5744	392	21	+	+	CCONJ
ejpam-5744	392	22	τ∥ϱ−	τ∥ϱ−	NOUN
ejpam-5744	392	23	j∥.	j∥.	VERB
ejpam-5744	392	24	so	so	ADV
ejpam-5744	392	25	,	,	PUNCT
ejpam-5744	392	26	ℑ	ℑ	PROPN
ejpam-5744	392	27	satisfies	satisfy	VERB
ejpam-5744	392	28	(	(	PUNCT
ejpam-5744	392	29	2	2	NUM
ejpam-5744	392	30	)	)	PUNCT
ejpam-5744	392	31	and	and	CCONJ
ejpam-5744	392	32	by	by	ADP
ejpam-5744	392	33	the	the	DET
ejpam-5744	392	34	virtue	virtue	NOUN
ejpam-5744	392	35	of	of	ADP
ejpam-5744	392	36	the	the	DET
ejpam-5744	392	37	theorem	theorem	NOUN
ejpam-5744	392	38	2	2	NUM
ejpam-5744	392	39	,	,	PUNCT
ejpam-5744	392	40	the	the	DET
ejpam-5744	392	41	sequence	sequence	NOUN
ejpam-5744	392	42	initiated	initiate	VERB
ejpam-5744	392	43	by	by	ADP
ejpam-5744	392	44	simps	simp	NOUN
ejpam-5744	392	45	(	(	PUNCT
ejpam-5744	392	46	14	14	NUM
ejpam-5744	392	47	)	)	PUNCT
ejpam-5744	392	48	converges	converge	VERB
ejpam-5744	392	49	to	to	ADP
ejpam-5744	392	50	an	an	DET
ejpam-5744	392	51	element	element	NOUN
ejpam-5744	392	52	in	in	ADP
ejpam-5744	392	53	ξ(ℑ	ξ(ℑ	NOUN
ejpam-5744	392	54	)	)	PUNCT
ejpam-5744	392	55	which	which	PRON
ejpam-5744	392	56	solves	solve	VERB
ejpam-5744	392	57	c	c	NOUN
ejpam-5744	392	58	-	-	PUNCT
ejpam-5744	392	59	nfde	nfde	NOUN
ejpam-5744	392	60	(	(	PUNCT
ejpam-5744	392	61	41	41	NUM
ejpam-5744	392	62	)	)	PUNCT
ejpam-5744	392	63	.	.	PUNCT
ejpam-5744	393	1	4	4	X
ejpam-5744	393	2	.	.	X
ejpam-5744	393	3	conclusions	conclusion	NOUN
ejpam-5744	393	4	a	a	DET
ejpam-5744	393	5	four	four	NUM
ejpam-5744	393	6	-	-	PUNCT
ejpam-5744	393	7	step	step	NOUN
ejpam-5744	393	8	semi	semi	ADJ
ejpam-5744	393	9	-	-	ADJ
ejpam-5744	393	10	implicit	implicit	ADJ
ejpam-5744	393	11	midpoint	midpoint	NOUN
ejpam-5744	393	12	scheme	scheme	NOUN
ejpam-5744	393	13	is	be	AUX
ejpam-5744	393	14	designed	design	VERB
ejpam-5744	393	15	to	to	PART
ejpam-5744	393	16	investigate	investigate	VERB
ejpam-5744	393	17	the	the	DET
ejpam-5744	393	18	fixed	fix	VERB
ejpam-5744	393	19	point	point	NOUN
ejpam-5744	393	20	of	of	ADP
ejpam-5744	393	21	a	a	DET
ejpam-5744	393	22	contractive	contractive	ADJ
ejpam-5744	393	23	mapping	mapping	NOUN
ejpam-5744	393	24	under	under	ADP
ejpam-5744	393	25	some	some	DET
ejpam-5744	393	26	mild	mild	ADJ
ejpam-5744	393	27	assumptions	assumption	NOUN
ejpam-5744	393	28	.	.	PUNCT
ejpam-5744	394	1	convergence	convergence	NOUN
ejpam-5744	394	2	analysis	analysis	NOUN
ejpam-5744	394	3	and	and	CCONJ
ejpam-5744	394	4	stability	stability	NOUN
ejpam-5744	394	5	results	result	NOUN
ejpam-5744	394	6	of	of	ADP
ejpam-5744	394	7	the	the	DET
ejpam-5744	394	8	implied	imply	VERB
ejpam-5744	394	9	scheme	scheme	NOUN
ejpam-5744	394	10	are	be	AUX
ejpam-5744	394	11	exhibited	exhibit	VERB
ejpam-5744	394	12	.	.	PUNCT
ejpam-5744	395	1	furthermore	furthermore	ADV
ejpam-5744	395	2	,	,	PUNCT
ejpam-5744	395	3	we	we	PRON
ejpam-5744	395	4	applied	apply	VERB
ejpam-5744	395	5	our	our	PRON
ejpam-5744	395	6	scheme	scheme	NOUN
ejpam-5744	395	7	to	to	PART
ejpam-5744	395	8	examine	examine	VERB
ejpam-5744	395	9	a	a	DET
ejpam-5744	395	10	general	general	ADJ
ejpam-5744	395	11	quasi	quasi	ADJ
ejpam-5744	395	12	-	-	ADJ
ejpam-5744	395	13	variational	variational	ADJ
ejpam-5744	395	14	inequality	inequality	NOUN
ejpam-5744	395	15	.	.	PUNCT
ejpam-5744	396	1	by	by	ADP
ejpam-5744	396	2	redesigning	redesign	VERB
ejpam-5744	396	3	the	the	DET
ejpam-5744	396	4	proposed	propose	VERB
ejpam-5744	396	5	mid	mid	ADJ
ejpam-5744	396	6	-	-	ADJ
ejpam-5744	396	7	point	point	NOUN
ejpam-5744	396	8	rule	rule	NOUN
ejpam-5744	396	9	,	,	PUNCT
ejpam-5744	396	10	we	we	PRON
ejpam-5744	396	11	inspected	inspect	VERB
ejpam-5744	396	12	a	a	DET
ejpam-5744	396	13	common	common	ADJ
ejpam-5744	396	14	solution	solution	NOUN
ejpam-5744	396	15	of	of	ADP
ejpam-5744	396	16	a	a	DET
ejpam-5744	396	17	contractive	contractive	ADJ
ejpam-5744	396	18	mapping	mapping	NOUN
ejpam-5744	396	19	and	and	CCONJ
ejpam-5744	396	20	a	a	DET
ejpam-5744	396	21	general	general	ADJ
ejpam-5744	396	22	quasi	quasi	ADJ
ejpam-5744	396	23	-	-	ADJ
ejpam-5744	396	24	variational	variational	ADJ
ejpam-5744	396	25	inequality	inequality	NOUN
ejpam-5744	396	26	.	.	PUNCT
ejpam-5744	397	1	finally	finally	ADV
ejpam-5744	397	2	,	,	PUNCT
ejpam-5744	397	3	a	a	DET
ejpam-5744	397	4	nonlinear	nonlinear	ADJ
ejpam-5744	397	5	fractional	fractional	ADJ
ejpam-5744	397	6	differential	differential	NOUN
ejpam-5744	397	7	equation	equation	NOUN
ejpam-5744	397	8	is	be	AUX
ejpam-5744	397	9	studied	study	VERB
ejpam-5744	397	10	by	by	ADP
ejpam-5744	397	11	employing	employ	VERB
ejpam-5744	397	12	simps	simp	NOUN
ejpam-5744	397	13	(	(	PUNCT
ejpam-5744	397	14	14	14	NUM
ejpam-5744	397	15	)	)	PUNCT
ejpam-5744	397	16	.	.	PUNCT
ejpam-5744	398	1	in	in	ADP
ejpam-5744	398	2	future	future	ADJ
ejpam-5744	398	3	,	,	PUNCT
ejpam-5744	398	4	semi	semi	ADJ
ejpam-5744	398	5	-	-	ADJ
ejpam-5744	398	6	implicit	implicit	ADJ
ejpam-5744	398	7	type	type	NOUN
ejpam-5744	398	8	schemes	scheme	NOUN
ejpam-5744	398	9	could	could	AUX
ejpam-5744	398	10	be	be	AUX
ejpam-5744	398	11	implemented	implement	VERB
ejpam-5744	398	12	to	to	PART
ejpam-5744	398	13	explore	explore	VERB
ejpam-5744	398	14	fixed	fix	VERB
ejpam-5744	398	15	points	point	NOUN
ejpam-5744	398	16	of	of	ADP
ejpam-5744	398	17	some	some	DET
ejpam-5744	398	18	generalized	generalize	VERB
ejpam-5744	398	19	nonexpansive	nonexpansive	ADJ
ejpam-5744	398	20	mappings	mapping	NOUN
ejpam-5744	398	21	including	include	VERB
ejpam-5744	398	22	suzuki	suzuki	PROPN
ejpam-5744	398	23	’s	’s	PART
ejpam-5744	398	24	generalized	generalize	VERB
ejpam-5744	398	25	nonexpansive	nonexpansive	ADJ
ejpam-5744	398	26	mapping	mapping	NOUN
ejpam-5744	398	27	,	,	PUNCT
ejpam-5744	398	28	asymptotically	asymptotically	ADV
ejpam-5744	398	29	and	and	CCONJ
ejpam-5744	398	30	total	total	ADJ
ejpam-5744	398	31	asymptotically	asymptotically	ADV
ejpam-5744	398	32	non	non	ADJ
ejpam-5744	398	33	-	-	ADJ
ejpam-5744	398	34	expansive	expansive	ADJ
ejpam-5744	398	35	mappings	mapping	NOUN
ejpam-5744	398	36	.	.	PUNCT
ejpam-5744	399	1	some	some	DET
ejpam-5744	399	2	nonlinear	nonlinear	ADJ
ejpam-5744	399	3	problems	problem	NOUN
ejpam-5744	399	4	such	such	ADJ
ejpam-5744	399	5	as	as	ADP
ejpam-5744	399	6	variational	variational	ADJ
ejpam-5744	399	7	inequalities	inequality	NOUN
ejpam-5744	399	8	,	,	PUNCT
ejpam-5744	399	9	quasi	quasi	ADJ
ejpam-5744	399	10	-	-	ADJ
ejpam-5744	399	11	variational	variational	ADJ
ejpam-5744	399	12	inequalities	inequality	NOUN
ejpam-5744	399	13	and	and	CCONJ
ejpam-5744	399	14	inclusions	inclusion	NOUN
ejpam-5744	399	15	are	be	AUX
ejpam-5744	399	16	some	some	DET
ejpam-5744	399	17	worthy	worthy	ADJ
ejpam-5744	399	18	future	future	ADJ
ejpam-5744	399	19	research	research	NOUN
ejpam-5744	399	20	directions	direction	NOUN
ejpam-5744	399	21	.	.	PUNCT
ejpam-5744	400	1	acknowledgements	acknowledgement	NOUN
ejpam-5744	400	2	the	the	DET
ejpam-5744	400	3	author	author	NOUN
ejpam-5744	400	4	would	would	AUX
ejpam-5744	400	5	like	like	VERB
ejpam-5744	400	6	to	to	PART
ejpam-5744	400	7	thank	thank	VERB
ejpam-5744	400	8	the	the	DET
ejpam-5744	400	9	referees	referee	NOUN
ejpam-5744	400	10	for	for	ADP
ejpam-5744	400	11	their	their	PRON
ejpam-5744	400	12	valuable	valuable	ADJ
ejpam-5744	400	13	comments	comment	NOUN
ejpam-5744	400	14	and	and	CCONJ
ejpam-5744	400	15	dsr	dsr	PROPN
ejpam-5744	400	16	,	,	PUNCT
ejpam-5744	400	17	islamic	islamic	PROPN
ejpam-5744	400	18	university	university	PROPN
ejpam-5744	400	19	of	of	ADP
ejpam-5744	400	20	madinah	madinah	PROPN
ejpam-5744	400	21	.	.	PUNCT
ejpam-5744	401	1	m.	m.	PROPN
ejpam-5744	401	2	akram	akram	PROPN
ejpam-5744	401	3	/	/	PUNCT
ejpam-5744	401	4	eur	eur	PROPN
ejpam-5744	401	5	.	.	PUNCT
ejpam-5744	402	1	j.	j.	PROPN
ejpam-5744	402	2	pure	pure	PROPN
ejpam-5744	402	3	appl	appl	PROPN
ejpam-5744	402	4	.	.	PROPN
ejpam-5744	402	5	math	math	PROPN
ejpam-5744	402	6	,	,	PUNCT
ejpam-5744	402	7	18	18	NUM
ejpam-5744	402	8	(	(	PUNCT
ejpam-5744	402	9	1	1	NUM
ejpam-5744	402	10	)	)	PUNCT
ejpam-5744	402	11	(	(	PUNCT
ejpam-5744	402	12	2025	2025	NUM
ejpam-5744	402	13	)	)	PUNCT
ejpam-5744	402	14	,	,	PUNCT
ejpam-5744	402	15	5744	5744	NUM
ejpam-5744	402	16	17	17	NUM
ejpam-5744	402	17	of	of	ADP
ejpam-5744	402	18	19	19	NUM
ejpam-5744	402	19	references	reference	NOUN
ejpam-5744	402	20	[	[	X
ejpam-5744	402	21	1	1	NUM
ejpam-5744	402	22	]	]	PUNCT
ejpam-5744	402	23	aan	aan	PROPN
ejpam-5744	402	24	abdou	abdou	PROPN
ejpam-5744	402	25	.	.	PUNCT
ejpam-5744	403	1	fixed	fix	VERB
ejpam-5744	403	2	point	point	NOUN
ejpam-5744	403	3	theorems	theorem	VERB
ejpam-5744	403	4	:	:	PUNCT
ejpam-5744	403	5	exploring	explore	VERB
ejpam-5744	403	6	applications	application	NOUN
ejpam-5744	403	7	in	in	ADP
ejpam-5744	403	8	fractional	fractional	ADJ
ejpam-5744	403	9	differential	differential	ADJ
ejpam-5744	403	10	equations	equation	NOUN
ejpam-5744	403	11	for	for	ADP
ejpam-5744	403	12	economic	economic	ADJ
ejpam-5744	403	13	growth	growth	NOUN
ejpam-5744	403	14	.	.	PUNCT
ejpam-5744	404	1	fractal	fractal	ADJ
ejpam-5744	404	2	fract	fract	PROPN
ejpam-5744	404	3	.	.	PUNCT
ejpam-5744	404	4	,	,	PUNCT
ejpam-5744	404	5	8	8	NUM
ejpam-5744	404	6	,	,	PUNCT
ejpam-5744	404	7	2024	2024	NUM
ejpam-5744	404	8	.	.	PUNCT
ejpam-5744	405	1	[	[	X
ejpam-5744	405	2	2	2	NUM
ejpam-5744	405	3	]	]	PUNCT
ejpam-5744	405	4	a.	a.	NOUN
ejpam-5744	405	5	ahmadkhanlu	ahmadkhanlu	PROPN
ejpam-5744	405	6	.	.	PUNCT
ejpam-5744	406	1	existence	existence	NOUN
ejpam-5744	406	2	and	and	CCONJ
ejpam-5744	406	3	uniquensess	uniquensess	NOUN
ejpam-5744	406	4	for	for	ADP
ejpam-5744	406	5	a	a	DET
ejpam-5744	406	6	class	class	NOUN
ejpam-5744	406	7	of	of	ADP
ejpam-5744	406	8	fractional	fractional	ADJ
ejpam-5744	406	9	differential	differential	ADJ
ejpam-5744	406	10	equations	equation	NOUN
ejpam-5744	406	11	with	with	ADP
ejpam-5744	406	12	an	an	DET
ejpam-5744	406	13	integral	integral	ADJ
ejpam-5744	406	14	fractional	fractional	ADJ
ejpam-5744	406	15	boundary	boundary	ADJ
ejpam-5744	406	16	condition	condition	NOUN
ejpam-5744	406	17	.	.	PUNCT
ejpam-5744	407	1	filomat	filomat	NOUN
ejpam-5744	407	2	,	,	PUNCT
ejpam-5744	407	3	31(5):1241–1246	31(5):1241–1246	NUM
ejpam-5744	407	4	,	,	PUNCT
ejpam-5744	407	5	2017	2017	NUM
ejpam-5744	407	6	.	.	PUNCT
ejpam-5744	408	1	[	[	X
ejpam-5744	408	2	3	3	X
ejpam-5744	408	3	]	]	X
ejpam-5744	408	4	g.	g.	PROPN
ejpam-5744	408	5	bader	bader	PROPN
ejpam-5744	408	6	and	and	CCONJ
ejpam-5744	408	7	p.	p.	PROPN
ejpam-5744	408	8	deuflhard	deuflhard	NOUN
ejpam-5744	408	9	.	.	PUNCT
ejpam-5744	409	1	a	a	DET
ejpam-5744	409	2	semi	semi	ADJ
ejpam-5744	409	3	-	-	ADJ
ejpam-5744	409	4	implicit	implicit	ADJ
ejpam-5744	409	5	midpoint	midpoint	NOUN
ejpam-5744	409	6	rule	rule	NOUN
ejpam-5744	409	7	for	for	ADP
ejpam-5744	409	8	stiff	stiff	ADJ
ejpam-5744	409	9	systems	system	NOUN
ejpam-5744	409	10	of	of	ADP
ejpam-5744	409	11	ordinary	ordinary	ADJ
ejpam-5744	409	12	differential	differential	ADJ
ejpam-5744	409	13	equations	equation	NOUN
ejpam-5744	409	14	.	.	PUNCT
ejpam-5744	410	1	numer	numer	PROPN
ejpam-5744	410	2	.	.	PUNCT
ejpam-5744	410	3	math	math	PROPN
ejpam-5744	410	4	.	.	PUNCT
ejpam-5744	410	5	,	,	PUNCT
ejpam-5744	410	6	41:373–398	41:373–398	PROPN
ejpam-5744	410	7	,	,	PUNCT
ejpam-5744	410	8	1983	1983	NUM
ejpam-5744	410	9	.	.	PUNCT
ejpam-5744	411	1	[	[	X
ejpam-5744	411	2	4	4	NUM
ejpam-5744	411	3	]	]	X
ejpam-5744	411	4	c.	c.	PROPN
ejpam-5744	411	5	baiocchi	baiocchi	PROPN
ejpam-5744	411	6	and	and	CCONJ
ejpam-5744	411	7	a.	a.	NOUN
ejpam-5744	411	8	capelo	capelo	NOUN
ejpam-5744	411	9	.	.	PUNCT
ejpam-5744	412	1	variational	variational	ADJ
ejpam-5744	412	2	and	and	CCONJ
ejpam-5744	412	3	quasi	quasi	ADJ
ejpam-5744	412	4	variational	variational	ADJ
ejpam-5744	412	5	inequalities	inequality	NOUN
ejpam-5744	412	6	.	.	PUNCT
ejpam-5744	413	1	wiley	wiley	PROPN
ejpam-5744	413	2	,	,	PUNCT
ejpam-5744	413	3	new	new	PROPN
ejpam-5744	413	4	york	york	PROPN
ejpam-5744	413	5	,	,	PUNCT
ejpam-5744	413	6	1984	1984	NUM
ejpam-5744	413	7	.	.	PUNCT
ejpam-5744	414	1	[	[	X
ejpam-5744	414	2	5	5	NUM
ejpam-5744	414	3	]	]	PUNCT
ejpam-5744	414	4	a.	a.	NOUN
ejpam-5744	414	5	bayreuth	bayreuth	NOUN
ejpam-5744	414	6	.	.	PUNCT
ejpam-5744	415	1	the	the	DET
ejpam-5744	415	2	implicit	implicit	ADJ
ejpam-5744	415	3	midpoint	midpoint	NOUN
ejpam-5744	415	4	rule	rule	NOUN
ejpam-5744	415	5	applied	apply	VERB
ejpam-5744	415	6	to	to	ADP
ejpam-5744	415	7	discontinuous	discontinuous	ADJ
ejpam-5744	415	8	differential	differential	NOUN
ejpam-5744	415	9	equations	equation	NOUN
ejpam-5744	415	10	.	.	PUNCT
ejpam-5744	416	1	computing	compute	VERB
ejpam-5744	416	2	.	.	PUNCT
ejpam-5744	416	3	,	,	PUNCT
ejpam-5744	416	4	49:45–62	49:45–62	NUM
ejpam-5744	416	5	,	,	PUNCT
ejpam-5744	416	6	1992	1992	NUM
ejpam-5744	416	7	.	.	PUNCT
ejpam-5744	417	1	[	[	X
ejpam-5744	417	2	6	6	NUM
ejpam-5744	417	3	]	]	PUNCT
ejpam-5744	417	4	a.	a.	NOUN
ejpam-5744	417	5	bensoussan	bensoussan	PROPN
ejpam-5744	417	6	and	and	CCONJ
ejpam-5744	417	7	j.l	j.l	PROPN
ejpam-5744	417	8	.	.	PROPN
ejpam-5744	417	9	lions	lion	NOUN
ejpam-5744	417	10	.	.	PUNCT
ejpam-5744	418	1	vapplication	vapplication	PROPN
ejpam-5744	418	2	des	des	PROPN
ejpam-5744	418	3	inequalities	inequalities	PROPN
ejpam-5744	418	4	variationnelles	variationnelle	NOUN
ejpam-5744	418	5	en	en	ADP
ejpam-5744	418	6	control	control	NOUN
ejpam-5744	418	7	eten	eten	ADJ
ejpam-5744	418	8	stochastique	stochastique	NOUN
ejpam-5744	418	9	.	.	PUNCT
ejpam-5744	419	1	dunod	dunod	PROPN
ejpam-5744	419	2	,	,	PUNCT
ejpam-5744	419	3	paris	paris	PROPN
ejpam-5744	419	4	,	,	PUNCT
ejpam-5744	419	5	france	france	PROPN
ejpam-5744	419	6	,	,	PUNCT
ejpam-5744	419	7	1978	1978	NUM
ejpam-5744	419	8	.	.	PUNCT
ejpam-5744	420	1	[	[	X
ejpam-5744	420	2	7	7	X
ejpam-5744	420	3	]	]	X
ejpam-5744	420	4	v.	v.	CCONJ
ejpam-5744	420	5	berinde	berinde	NOUN
ejpam-5744	420	6	.	.	PUNCT
ejpam-5744	421	1	on	on	ADP
ejpam-5744	421	2	the	the	DET
ejpam-5744	421	3	stability	stability	NOUN
ejpam-5744	421	4	of	of	ADP
ejpam-5744	421	5	some	some	DET
ejpam-5744	421	6	fixed	fix	VERB
ejpam-5744	421	7	point	point	NOUN
ejpam-5744	421	8	procedures	procedure	NOUN
ejpam-5744	421	9	.	.	PUNCT
ejpam-5744	422	1	bul	bul	PROPN
ejpam-5744	422	2	.	.	PUNCT
ejpam-5744	423	1	ştiinţ.	ştiinţ.	PROPN
ejpam-5744	423	2	univ	univ	PROPN
ejpam-5744	423	3	.	.	PUNCT
ejpam-5744	424	1	baia	baia	PROPN
ejpam-5744	424	2	mare	mare	PROPN
ejpam-5744	424	3	,	,	PUNCT
ejpam-5744	424	4	ser	ser	PROPN
ejpam-5744	424	5	.	.	PROPN
ejpam-5744	424	6	b.	b.	PROPN
ejpam-5744	424	7	matematică	matematică	PROPN
ejpam-5744	424	8	informatică	informatică	PROPN
ejpam-5744	424	9	,	,	PUNCT
ejpam-5744	424	10	18(1):7–14	18(1):7–14	NUM
ejpam-5744	424	11	,	,	PUNCT
ejpam-5744	424	12	2002	2002	NUM
ejpam-5744	424	13	.	.	PUNCT
ejpam-5744	425	1	[	[	X
ejpam-5744	425	2	8	8	NUM
ejpam-5744	425	3	]	]	X
ejpam-5744	425	4	v.	v.	CCONJ
ejpam-5744	425	5	berinde	berinde	NOUN
ejpam-5744	425	6	.	.	PUNCT
ejpam-5744	426	1	on	on	ADP
ejpam-5744	426	2	the	the	DET
ejpam-5744	426	3	approximation	approximation	NOUN
ejpam-5744	426	4	of	of	ADP
ejpam-5744	426	5	fixed	fix	VERB
ejpam-5744	426	6	points	point	NOUN
ejpam-5744	426	7	of	of	ADP
ejpam-5744	426	8	weak	weak	ADJ
ejpam-5744	426	9	contractive	contractive	ADJ
ejpam-5744	426	10	mapping	mapping	NOUN
ejpam-5744	426	11	.	.	PUNCT
ejpam-5744	427	1	carpath	carpath	PROPN
ejpam-5744	427	2	j.	j.	PROPN
ejpam-5744	427	3	math	math	PROPN
ejpam-5744	427	4	.	.	PUNCT
ejpam-5744	427	5	,	,	PUNCT
ejpam-5744	427	6	17:7–22	17:7–22	NUM
ejpam-5744	427	7	,	,	PUNCT
ejpam-5744	427	8	2003	2003	NUM
ejpam-5744	427	9	.	.	PUNCT
ejpam-5744	428	1	[	[	X
ejpam-5744	428	2	9	9	NUM
ejpam-5744	428	3	]	]	PUNCT
ejpam-5744	428	4	v.	v.	CCONJ
ejpam-5744	428	5	berinde	berinde	NOUN
ejpam-5744	428	6	.	.	PUNCT
ejpam-5744	429	1	picard	picard	NOUN
ejpam-5744	429	2	iteration	iteration	PROPN
ejpam-5744	429	3	converges	converge	VERB
ejpam-5744	429	4	faster	fast	ADV
ejpam-5744	429	5	than	than	ADP
ejpam-5744	429	6	mann	mann	PROPN
ejpam-5744	429	7	iteration	iteration	NOUN
ejpam-5744	429	8	for	for	ADP
ejpam-5744	429	9	a	a	DET
ejpam-5744	429	10	class	class	NOUN
ejpam-5744	429	11	of	of	ADP
ejpam-5744	429	12	quasicontractive	quasicontractive	ADJ
ejpam-5744	429	13	operators	operator	NOUN
ejpam-5744	429	14	.	.	PUNCT
ejpam-5744	430	1	fixed	fix	VERB
ejpam-5744	430	2	point	point	NOUN
ejpam-5744	430	3	theory	theory	NOUN
ejpam-5744	430	4	appl	appl	PROPN
ejpam-5744	430	5	.	.	PROPN
ejpam-5744	430	6	,	,	PUNCT
ejpam-5744	430	7	2:1–9	2:1–9	PROPN
ejpam-5744	430	8	,	,	PUNCT
ejpam-5744	430	9	2004	2004	NUM
ejpam-5744	430	10	.	.	PUNCT
ejpam-5744	431	1	[	[	X
ejpam-5744	431	2	10	10	NUM
ejpam-5744	431	3	]	]	X
ejpam-5744	431	4	f.e	f.e	PROPN
ejpam-5744	431	5	.	.	PROPN
ejpam-5744	431	6	browder	browder	PROPN
ejpam-5744	431	7	.	.	PUNCT
ejpam-5744	432	1	nonlinear	nonlinear	ADJ
ejpam-5744	432	2	mappings	mapping	NOUN
ejpam-5744	432	3	of	of	ADP
ejpam-5744	432	4	nonexpansive	nonexpansive	ADJ
ejpam-5744	432	5	and	and	CCONJ
ejpam-5744	432	6	accretive	accretive	ADJ
ejpam-5744	432	7	-	-	PUNCT
ejpam-5744	432	8	type	type	NOUN
ejpam-5744	432	9	in	in	ADP
ejpam-5744	432	10	banach	banach	NOUN
ejpam-5744	432	11	spaces	space	NOUN
ejpam-5744	432	12	.	.	PUNCT
ejpam-5744	433	1	bull	bull	NOUN
ejpam-5744	433	2	.	.	PUNCT
ejpam-5744	434	1	amer	amer	PROPN
ejpam-5744	434	2	.	.	PUNCT
ejpam-5744	434	3	math	math	PROPN
ejpam-5744	434	4	.	.	PUNCT
ejpam-5744	435	1	soc	soc	PROPN
ejpam-5744	435	2	.	.	PUNCT
ejpam-5744	435	3	,	,	PUNCT
ejpam-5744	435	4	73:875–882	73:875–882	PROPN
ejpam-5744	435	5	,	,	PUNCT
ejpam-5744	435	6	1967	1967	NUM
ejpam-5744	435	7	.	.	PUNCT
ejpam-5744	436	1	[	[	X
ejpam-5744	436	2	11	11	NUM
ejpam-5744	436	3	]	]	X
ejpam-5744	436	4	c.e	c.e	PROPN
ejpam-5744	436	5	.	.	PROPN
ejpam-5744	436	6	chidume	chidume	PROPN
ejpam-5744	436	7	.	.	PUNCT
ejpam-5744	437	1	geometric	geometric	ADJ
ejpam-5744	437	2	properties	property	NOUN
ejpam-5744	437	3	of	of	ADP
ejpam-5744	437	4	banach	banach	NOUN
ejpam-5744	437	5	spaces	space	NOUN
ejpam-5744	437	6	and	and	CCONJ
ejpam-5744	437	7	nonlinear	nonlinear	ADJ
ejpam-5744	437	8	iterations	iteration	NOUN
ejpam-5744	437	9	.	.	PUNCT
ejpam-5744	437	10	,	,	PUNCT
ejpam-5744	437	11	volume	volume	NOUN
ejpam-5744	437	12	1965	1965	NUM
ejpam-5744	437	13	.	.	PUNCT
ejpam-5744	438	1	springer	springer	NOUN
ejpam-5744	438	2	,	,	PUNCT
ejpam-5744	438	3	london	london	PROPN
ejpam-5744	438	4	,	,	PUNCT
ejpam-5744	438	5	2009	2009	NUM
ejpam-5744	438	6	.	.	PUNCT
ejpam-5744	439	1	[	[	X
ejpam-5744	439	2	12	12	NUM
ejpam-5744	439	3	]	]	PUNCT
ejpam-5744	439	4	m.	m.	NOUN
ejpam-5744	439	5	dilshad	dilshad	PROPN
ejpam-5744	439	6	d.	d.	PROPN
ejpam-5744	439	7	filali	filali	PROPN
ejpam-5744	439	8	,	,	PUNCT
ejpam-5744	439	9	m.	m.	NOUN
ejpam-5744	439	10	akram	akram	PROPN
ejpam-5744	439	11	and	and	CCONJ
ejpam-5744	439	12	a.a	a.a	PROPN
ejpam-5744	439	13	.	.	PROPN
ejpam-5744	439	14	khidir	khidir	PROPN
ejpam-5744	439	15	.	.	PUNCT
ejpam-5744	440	1	general	general	ADJ
ejpam-5744	440	2	semi	semi	ADJ
ejpam-5744	440	3	-	-	ADJ
ejpam-5744	440	4	implicit	implicit	ADJ
ejpam-5744	440	5	midpoint	midpoint	NOUN
ejpam-5744	440	6	approximation	approximation	NOUN
ejpam-5744	440	7	for	for	ADP
ejpam-5744	440	8	fixed	fix	VERB
ejpam-5744	440	9	point	point	NOUN
ejpam-5744	440	10	of	of	ADP
ejpam-5744	440	11	almost	almost	ADV
ejpam-5744	440	12	contraction	contraction	NOUN
ejpam-5744	440	13	mapping	mapping	NOUN
ejpam-5744	440	14	and	and	CCONJ
ejpam-5744	440	15	applications	application	NOUN
ejpam-5744	440	16	.	.	PUNCT
ejpam-5744	441	1	applied	apply	VERB
ejpam-5744	441	2	mathematics	mathematic	NOUN
ejpam-5744	441	3	in	in	ADP
ejpam-5744	441	4	science	science	NOUN
ejpam-5744	441	5	and	and	CCONJ
ejpam-5744	441	6	engineering	engineering	NOUN
ejpam-5744	441	7	,	,	PUNCT
ejpam-5744	441	8	32(1	32(1	NUM
ejpam-5744	441	9	)	)	PUNCT
ejpam-5744	441	10	,	,	PUNCT
ejpam-5744	441	11	2024	2024	NUM
ejpam-5744	441	12	.	.	PUNCT
ejpam-5744	442	1	doi	doi	NOUN
ejpam-5744	442	2	:	:	PUNCT
ejpam-5744	442	3	10.1080/27690911.2024.2365687	10.1080/27690911.2024.2365687	NUM
ejpam-5744	442	4	.	.	PUNCT
ejpam-5744	443	1	[	[	X
ejpam-5744	443	2	13	13	NUM
ejpam-5744	443	3	]	]	SYM
ejpam-5744	443	4	s.b	s.b	PROPN
ejpam-5744	443	5	.	.	PROPN
ejpam-5744	443	6	duffull	duffull	PROPN
ejpam-5744	443	7	and	and	CCONJ
ejpam-5744	443	8	g.	g.	PROPN
ejpam-5744	443	9	hegarty	hegarty	PROPN
ejpam-5744	443	10	.	.	PUNCT
ejpam-5744	444	1	an	an	DET
ejpam-5744	444	2	inductive	inductive	ADJ
ejpam-5744	444	3	approximation	approximation	NOUN
ejpam-5744	444	4	to	to	ADP
ejpam-5744	444	5	the	the	DET
ejpam-5744	444	6	solution	solution	NOUN
ejpam-5744	444	7	of	of	ADP
ejpam-5744	444	8	systems	system	NOUN
ejpam-5744	444	9	of	of	ADP
ejpam-5744	444	10	nonlinear	nonlinear	ADJ
ejpam-5744	444	11	ordinary	ordinary	ADJ
ejpam-5744	444	12	differential	differential	ADJ
ejpam-5744	444	13	equations	equation	NOUN
ejpam-5744	444	14	in	in	ADP
ejpam-5744	444	15	pharmacokinetics	pharmacokinetic	NOUN
ejpam-5744	444	16	-	-	PUNCT
ejpam-5744	444	17	pharmacodynamics	pharmacodynamic	NOUN
ejpam-5744	444	18	.	.	PUNCT
ejpam-5744	445	1	j.	j.	PROPN
ejpam-5744	445	2	theor	theor	PROPN
ejpam-5744	445	3	.	.	PUNCT
ejpam-5744	446	1	comput	comput	PROPN
ejpam-5744	446	2	.	.	PUNCT
ejpam-5744	447	1	sci	sci	PROPN
ejpam-5744	447	2	.	.	PROPN
ejpam-5744	447	3	,	,	PUNCT
ejpam-5744	447	4	1:4(1	1:4(1	NUM
ejpam-5744	447	5	)	)	PUNCT
ejpam-5744	447	6	,	,	PUNCT
ejpam-5744	447	7	2014	2014	NUM
ejpam-5744	447	8	.	.	PUNCT
ejpam-5744	448	1	doi	doi	NOUN
ejpam-5744	448	2	:	:	PUNCT
ejpam-5744	448	3	10.4172	10.4172	NUM
ejpam-5744	448	4	/	/	SYM
ejpam-5744	448	5	jtco.1000119	jtco.1000119	PROPN
ejpam-5744	448	6	.	.	PUNCT
ejpam-5744	449	1	[	[	X
ejpam-5744	449	2	14	14	NUM
ejpam-5744	449	3	]	]	PUNCT
ejpam-5744	449	4	m.	m.	NOUN
ejpam-5744	449	5	turkyilmazoglu	turkyilmazoglu	PROPN
ejpam-5744	449	6	g.	g.	PROPN
ejpam-5744	449	7	h.	h.	PROPN
ejpam-5744	449	8	ibraheem	ibraheem	PROPN
ejpam-5744	449	9	and	and	CCONJ
ejpam-5744	449	10	m.a	m.a	PROPN
ejpam-5744	449	11	.	.	PROPN
ejpam-5744	449	12	al	al	PROPN
ejpam-5744	449	13	-	-	PUNCT
ejpam-5744	449	14	jawary	jawary	PROPN
ejpam-5744	449	15	.	.	PUNCT
ejpam-5744	450	1	novel	novel	ADJ
ejpam-5744	450	2	approximate	approximate	ADJ
ejpam-5744	450	3	solution	solution	NOUN
ejpam-5744	450	4	for	for	ADP
ejpam-5744	450	5	fractional	fractional	ADJ
ejpam-5744	450	6	differential	differential	ADJ
ejpam-5744	450	7	equations	equation	NOUN
ejpam-5744	450	8	by	by	ADP
ejpam-5744	450	9	the	the	DET
ejpam-5744	450	10	optimal	optimal	ADJ
ejpam-5744	450	11	variational	variational	ADJ
ejpam-5744	450	12	iteration	iteration	NOUN
ejpam-5744	450	13	method	method	NOUN
ejpam-5744	450	14	.	.	PUNCT
ejpam-5744	451	1	j.	j.	PROPN
ejpam-5744	451	2	comput	comput	PROPN
ejpam-5744	451	3	.	.	PUNCT
ejpam-5744	452	1	sci	sci	PROPN
ejpam-5744	452	2	.	.	PROPN
ejpam-5744	452	3	,	,	PUNCT
ejpam-5744	452	4	64	64	NUM
ejpam-5744	452	5	,	,	PUNCT
ejpam-5744	452	6	2022	2022	NUM
ejpam-5744	452	7	.	.	PUNCT
ejpam-5744	453	1	doi	doi	NOUN
ejpam-5744	453	2	:	:	PUNCT
ejpam-5744	453	3	10.1016	10.1016	NUM
ejpam-5744	453	4	/	/	SYM
ejpam-5744	453	5	j.jocs.2022.101841	j.jocs.2022.101841	NOUN
ejpam-5744	453	6	.	.	PUNCT
ejpam-5744	454	1	[	[	X
ejpam-5744	454	2	15	15	NUM
ejpam-5744	454	3	]	]	X
ejpam-5744	454	4	r.t	r.t	PROPN
ejpam-5744	454	5	.	.	PROPN
ejpam-5744	454	6	alqahtani	alqahtani	PROPN
ejpam-5744	454	7	g.a	g.a	PROPN
ejpam-5744	454	8	.	.	PROPN
ejpam-5744	454	9	okeke	okeke	PROPN
ejpam-5744	454	10	,	,	PUNCT
ejpam-5744	454	11	a.v	a.v	PROPN
ejpam-5744	454	12	.	.	PROPN
ejpam-5744	454	13	udo	udo	PROPN
ejpam-5744	454	14	and	and	CCONJ
ejpam-5744	454	15	n.h	n.h	PROPN
ejpam-5744	454	16	.	.	PROPN
ejpam-5744	454	17	alharthi	alharthi	PROPN
ejpam-5744	454	18	.	.	PUNCT
ejpam-5744	455	1	a	a	DET
ejpam-5744	455	2	faster	fast	ADJ
ejpam-5744	455	3	iterative	iterative	NOUN
ejpam-5744	455	4	scheme	scheme	NOUN
ejpam-5744	455	5	for	for	ADP
ejpam-5744	455	6	solving	solve	VERB
ejpam-5744	455	7	nonlinear	nonlinear	ADJ
ejpam-5744	455	8	fractional	fractional	ADJ
ejpam-5744	455	9	differential	differential	ADJ
ejpam-5744	455	10	equations	equation	NOUN
ejpam-5744	455	11	of	of	ADP
ejpam-5744	455	12	the	the	DET
ejpam-5744	455	13	caputo	caputo	PROPN
ejpam-5744	455	14	type	type	NOUN
ejpam-5744	455	15	.	.	PUNCT
ejpam-5744	456	1	aims	aim	VERB
ejpam-5744	456	2	mathematics	mathematic	NOUN
ejpam-5744	456	3	,	,	PUNCT
ejpam-5744	456	4	8:28488–28516	8:28488–28516	NUM
ejpam-5744	456	5	,	,	PUNCT
ejpam-5744	456	6	2023	2023	NUM
ejpam-5744	456	7	.	.	PUNCT
ejpam-5744	457	1	[	[	X
ejpam-5744	457	2	16	16	NUM
ejpam-5744	457	3	]	]	PUNCT
ejpam-5744	457	4	k.	k.	PROPN
ejpam-5744	457	5	goebel	goebel	PROPN
ejpam-5744	457	6	and	and	CCONJ
ejpam-5744	457	7	s.	s.	PROPN
ejpam-5744	457	8	reich	reich	PROPN
ejpam-5744	457	9	.	.	PROPN
ejpam-5744	458	1	uniform	uniform	PROPN
ejpam-5744	458	2	convexity	convexity	NOUN
ejpam-5744	458	3	,	,	PUNCT
ejpam-5744	458	4	hyperbolic	hyperbolic	ADJ
ejpam-5744	458	5	geometry	geometry	NOUN
ejpam-5744	458	6	,	,	PUNCT
ejpam-5744	458	7	and	and	CCONJ
ejpam-5744	458	8	non	non	ADJ
ejpam-5744	458	9	-	-	ADJ
ejpam-5744	458	10	expansive	expansive	ADJ
ejpam-5744	458	11	mappings	mapping	NOUN
ejpam-5744	458	12	.	.	PUNCT
ejpam-5744	459	1	marcel	marcel	PROPN
ejpam-5744	459	2	dekker	dekker	PROPN
ejpam-5744	459	3	,	,	PUNCT
ejpam-5744	459	4	new	new	PROPN
ejpam-5744	459	5	york	york	PROPN
ejpam-5744	459	6	and	and	CCONJ
ejpam-5744	459	7	basel	basel	PROPN
ejpam-5744	459	8	,	,	PUNCT
ejpam-5744	459	9	1984	1984	NUM
ejpam-5744	459	10	.	.	PUNCT
ejpam-5744	460	1	[	[	X
ejpam-5744	460	2	17	17	NUM
ejpam-5744	460	3	]	]	X
ejpam-5744	460	4	h.	h.	PROPN
ejpam-5744	460	5	aydi	aydi	PROPN
ejpam-5744	460	6	h.a	h.a	PROPN
ejpam-5744	460	7	.	.	PROPN
ejpam-5744	460	8	hammad	hammad	PROPN
ejpam-5744	460	9	and	and	CCONJ
ejpam-5744	460	10	d.a	d.a	PROPN
ejpam-5744	460	11	.	.	PROPN
ejpam-5744	460	12	kattan	kattan	PROPN
ejpam-5744	460	13	.	.	PUNCT
ejpam-5744	461	1	new	new	ADJ
ejpam-5744	461	2	contributions	contribution	NOUN
ejpam-5744	461	3	to	to	ADP
ejpam-5744	461	4	fixed	fix	VERB
ejpam-5744	461	5	point	point	NOUN
ejpam-5744	461	6	techniques	technique	NOUN
ejpam-5744	461	7	with	with	ADP
ejpam-5744	461	8	applications	application	NOUN
ejpam-5744	461	9	for	for	ADP
ejpam-5744	461	10	solving	solve	VERB
ejpam-5744	461	11	fractional	fractional	ADJ
ejpam-5744	461	12	and	and	CCONJ
ejpam-5744	461	13	differential	differential	ADJ
ejpam-5744	461	14	equations	equation	NOUN
ejpam-5744	461	15	.	.	PUNCT
ejpam-5744	462	1	qual	qual	X
ejpam-5744	462	2	.	.	PUNCT
ejpam-5744	462	3	theory	theory	NOUN
ejpam-5744	462	4	dyn	dyn	PROPN
ejpam-5744	462	5	.	.	PUNCT
ejpam-5744	463	1	syst	syst	PROPN
ejpam-5744	463	2	.	.	PROPN
ejpam-5744	463	3	,	,	PUNCT
ejpam-5744	463	4	23	23	NUM
ejpam-5744	463	5	,	,	PUNCT
ejpam-5744	463	6	2024	2024	NUM
ejpam-5744	463	7	.	.	PUNCT
ejpam-5744	464	1	doi	doi	NOUN
ejpam-5744	464	2	:	:	PUNCT
ejpam-5744	464	3	10.1007	10.1007	NUM
ejpam-5744	464	4	/	/	SYM
ejpam-5744	464	5	s12346	s12346	NOUN
ejpam-5744	464	6	-	-	PUNCT
ejpam-5744	464	7	023	023	NUM
ejpam-5744	464	8	-	-	PUNCT
ejpam-5744	464	9	00932	00932	NUM
ejpam-5744	464	10	-	-	PUNCT
ejpam-5744	464	11	7	7	NUM
ejpam-5744	464	12	.	.	PUNCT
ejpam-5744	464	13	m.	m.	NOUN
ejpam-5744	464	14	akram	akram	PROPN
ejpam-5744	464	15	/	/	PUNCT
ejpam-5744	464	16	eur	eur	PROPN
ejpam-5744	464	17	.	.	PUNCT
ejpam-5744	465	1	j.	j.	PROPN
ejpam-5744	465	2	pure	pure	PROPN
ejpam-5744	465	3	appl	appl	PROPN
ejpam-5744	465	4	.	.	PROPN
ejpam-5744	465	5	math	math	PROPN
ejpam-5744	465	6	,	,	PUNCT
ejpam-5744	465	7	18	18	NUM
ejpam-5744	465	8	(	(	PUNCT
ejpam-5744	465	9	1	1	NUM
ejpam-5744	465	10	)	)	PUNCT
ejpam-5744	465	11	(	(	PUNCT
ejpam-5744	465	12	2025	2025	NUM
ejpam-5744	465	13	)	)	PUNCT
ejpam-5744	465	14	,	,	PUNCT
ejpam-5744	465	15	5744	5744	NUM
ejpam-5744	465	16	18	18	NUM
ejpam-5744	465	17	of	of	ADP
ejpam-5744	465	18	19	19	NUM
ejpam-5744	465	19	[	[	SYM
ejpam-5744	465	20	18	18	NUM
ejpam-5744	465	21	]	]	X
ejpam-5744	465	22	h.a	h.a	PROPN
ejpam-5744	465	23	.	.	PROPN
ejpam-5744	465	24	hammad	hammad	PROPN
ejpam-5744	465	25	and	and	CCONJ
ejpam-5744	465	26	s.f	s.f	PROPN
ejpam-5744	465	27	.	.	PROPN
ejpam-5744	465	28	aljurbua	aljurbua	PROPN
ejpam-5744	465	29	.	.	PUNCT
ejpam-5744	466	1	solving	solve	VERB
ejpam-5744	466	2	fractional	fractional	ADJ
ejpam-5744	466	3	random	random	ADJ
ejpam-5744	466	4	differential	differential	NOUN
ejpam-5744	466	5	equations	equation	NOUN
ejpam-5744	466	6	by	by	ADP
ejpam-5744	466	7	using	use	VERB
ejpam-5744	466	8	fixed	fix	VERB
ejpam-5744	466	9	point	point	NOUN
ejpam-5744	466	10	methodologies	methodology	NOUN
ejpam-5744	466	11	under	under	ADP
ejpam-5744	466	12	mild	mild	ADJ
ejpam-5744	466	13	boundary	boundary	ADJ
ejpam-5744	466	14	conditions	condition	NOUN
ejpam-5744	466	15	.	.	PUNCT
ejpam-5744	467	1	fractal	fractal	ADJ
ejpam-5744	467	2	fract	fract	PROPN
ejpam-5744	467	3	.	.	PUNCT
ejpam-5744	467	4	,	,	PUNCT
ejpam-5744	467	5	8	8	NUM
ejpam-5744	467	6	,	,	PUNCT
ejpam-5744	467	7	2024	2024	NUM
ejpam-5744	467	8	.	.	PUNCT
ejpam-5744	468	1	doi	doi	NOUN
ejpam-5744	468	2	:	:	PUNCT
ejpam-5744	468	3	10.3390	10.3390	NUM
ejpam-5744	468	4	/	/	SYM
ejpam-5744	468	5	fractalfract8070384	fractalfract8070384	PROPN
ejpam-5744	468	6	.	.	PUNCT
ejpam-5744	469	1	[	[	X
ejpam-5744	469	2	19	19	NUM
ejpam-5744	469	3	]	]	PUNCT
ejpam-5744	469	4	a.m.	a.m.	ADV
ejpam-5744	469	5	harder	hard	ADV
ejpam-5744	469	6	and	and	CCONJ
ejpam-5744	469	7	t.l	t.l	PROPN
ejpam-5744	469	8	.	.	PROPN
ejpam-5744	469	9	hicks	hicks	PROPN
ejpam-5744	469	10	.	.	PUNCT
ejpam-5744	470	1	stability	stability	NOUN
ejpam-5744	470	2	results	result	VERB
ejpam-5744	470	3	for	for	ADP
ejpam-5744	470	4	fixed	fix	VERB
ejpam-5744	470	5	point	point	NOUN
ejpam-5744	470	6	iteration	iteration	NOUN
ejpam-5744	470	7	procedures	procedure	NOUN
ejpam-5744	470	8	.	.	PUNCT
ejpam-5744	471	1	math	math	NOUN
ejpam-5744	471	2	.	.	PUNCT
ejpam-5744	472	1	japonica	japonica	PROPN
ejpam-5744	472	2	,	,	PUNCT
ejpam-5744	472	3	33:693–706	33:693–706	PROPN
ejpam-5744	472	4	,	,	PUNCT
ejpam-5744	472	5	1998	1998	NUM
ejpam-5744	472	6	.	.	PUNCT
ejpam-5744	473	1	[	[	X
ejpam-5744	473	2	20	20	NUM
ejpam-5744	473	3	]	]	X
ejpam-5744	473	4	m.a	m.a	PROPN
ejpam-5744	473	5	.	.	PROPN
ejpam-5744	473	6	alghamdi	alghamdi	PROPN
ejpam-5744	473	7	h.k	h.k	PROPN
ejpam-5744	473	8	.	.	PROPN
ejpam-5744	473	9	xu	xu	PROPN
ejpam-5744	473	10	and	and	CCONJ
ejpam-5744	473	11	n.	n.	PROPN
ejpam-5744	473	12	shahzad	shahzad	PROPN
ejpam-5744	473	13	.	.	PUNCT
ejpam-5744	474	1	the	the	DET
ejpam-5744	474	2	viscosity	viscosity	NOUN
ejpam-5744	474	3	technique	technique	NOUN
ejpam-5744	474	4	for	for	ADP
ejpam-5744	474	5	the	the	DET
ejpam-5744	474	6	implicit	implicit	ADJ
ejpam-5744	474	7	midpoint	midpoint	NOUN
ejpam-5744	474	8	rule	rule	NOUN
ejpam-5744	474	9	of	of	ADP
ejpam-5744	474	10	nonexpansive	nonexpansive	ADJ
ejpam-5744	474	11	mappings	mapping	NOUN
ejpam-5744	474	12	in	in	ADP
ejpam-5744	474	13	hilbert	hilbert	PROPN
ejpam-5744	474	14	spaces	space	NOUN
ejpam-5744	474	15	.	.	PUNCT
ejpam-5744	475	1	fixed	fix	VERB
ejpam-5744	475	2	point	point	NOUN
ejpam-5744	475	3	theory	theory	NOUN
ejpam-5744	475	4	appl	appl	PROPN
ejpam-5744	475	5	.	.	PROPN
ejpam-5744	475	6	,	,	PUNCT
ejpam-5744	475	7	2015	2015	NUM
ejpam-5744	475	8	.	.	PUNCT
ejpam-5744	476	1	doi	doi	NOUN
ejpam-5744	476	2	:	:	PUNCT
ejpam-5744	476	3	10.1186	10.1186	NUM
ejpam-5744	476	4	/	/	SYM
ejpam-5744	476	5	s13663	s13663	PROPN
ejpam-5744	476	6	-	-	PUNCT
ejpam-5744	476	7	015	015	NUM
ejpam-5744	476	8	-	-	PUNCT
ejpam-5744	476	9	0282	0282	NUM
ejpam-5744	476	10	-	-	SYM
ejpam-5744	476	11	9	9	NUM
ejpam-5744	476	12	.	.	PUNCT
ejpam-5744	477	1	[	[	X
ejpam-5744	477	2	21	21	NUM
ejpam-5744	477	3	]	]	X
ejpam-5744	477	4	h.y	h.y	PROPN
ejpam-5744	477	5	.	.	PROPN
ejpam-5744	477	6	lan	lan	PROPN
ejpam-5744	477	7	h.y	h.y	PROPN
ejpam-5744	477	8	.	.	PROPN
ejpam-5744	477	9	xu	xu	PROPN
ejpam-5744	477	10	and	and	CCONJ
ejpam-5744	477	11	f.	f.	PROPN
ejpam-5744	477	12	zhang	zhang	PROPN
ejpam-5744	477	13	.	.	PUNCT
ejpam-5744	478	1	general	general	ADJ
ejpam-5744	478	2	semi	semi	ADJ
ejpam-5744	478	3	-	-	ADJ
ejpam-5744	478	4	implicit	implicit	ADJ
ejpam-5744	478	5	approximations	approximation	NOUN
ejpam-5744	478	6	with	with	ADP
ejpam-5744	478	7	errors	error	NOUN
ejpam-5744	478	8	for	for	ADP
ejpam-5744	478	9	common	common	ADJ
ejpam-5744	478	10	fixed	fix	VERB
ejpam-5744	478	11	points	point	NOUN
ejpam-5744	478	12	of	of	ADP
ejpam-5744	478	13	nonexpansive	nonexpansive	ADJ
ejpam-5744	478	14	-	-	PUNCT
ejpam-5744	478	15	type	type	NOUN
ejpam-5744	478	16	operators	operator	NOUN
ejpam-5744	478	17	and	and	CCONJ
ejpam-5744	478	18	applications	application	NOUN
ejpam-5744	478	19	to	to	PART
ejpam-5744	478	20	stampacchia	stampacchia	VERB
ejpam-5744	478	21	variational	variational	ADJ
ejpam-5744	478	22	inequality	inequality	NOUN
ejpam-5744	478	23	.	.	PUNCT
ejpam-5744	479	1	comput	comput	NOUN
ejpam-5744	479	2	.	.	PUNCT
ejpam-5744	480	1	appl	appl	PROPN
ejpam-5744	480	2	.	.	PROPN
ejpam-5744	480	3	math	math	PROPN
ejpam-5744	480	4	.	.	PUNCT
ejpam-5744	480	5	,	,	PUNCT
ejpam-5744	480	6	31	31	NUM
ejpam-5744	480	7	,	,	PUNCT
ejpam-5744	480	8	2022	2022	NUM
ejpam-5744	480	9	.	.	PUNCT
ejpam-5744	481	1	doi	doi	NOUN
ejpam-5744	481	2	:	:	PUNCT
ejpam-5744	481	3	10.1007	10.1007	NUM
ejpam-5744	481	4	/	/	SYM
ejpam-5744	481	5	s40314	s40314	NOUN
ejpam-5744	481	6	-	-	PUNCT
ejpam-5744	481	7	02201890	02201890	NUM
ejpam-5744	481	8	-	-	PUNCT
ejpam-5744	481	9	7	7	NUM
ejpam-5744	481	10	.	.	PUNCT
ejpam-5744	482	1	[	[	X
ejpam-5744	482	2	22	22	NUM
ejpam-5744	482	3	]	]	X
ejpam-5744	482	4	c.o	c.o	PROPN
ejpam-5744	482	5	.	.	PROPN
ejpam-5744	482	6	imoru	imoru	NOUN
ejpam-5744	482	7	and	and	CCONJ
ejpam-5744	482	8	m.o	m.o	PROPN
ejpam-5744	482	9	.	.	PROPN
ejpam-5744	482	10	olatinwo	olatinwo	PROPN
ejpam-5744	482	11	.	.	PUNCT
ejpam-5744	483	1	on	on	ADP
ejpam-5744	483	2	the	the	DET
ejpam-5744	483	3	stability	stability	NOUN
ejpam-5744	483	4	of	of	ADP
ejpam-5744	483	5	picard	picard	PROPN
ejpam-5744	483	6	and	and	CCONJ
ejpam-5744	483	7	mann	mann	PROPN
ejpam-5744	483	8	iteration	iteration	NOUN
ejpam-5744	483	9	processes	process	NOUN
ejpam-5744	483	10	.	.	PUNCT
ejpam-5744	484	1	carpathian	carpathian	PROPN
ejpam-5744	484	2	j.	j.	PROPN
ejpam-5744	484	3	math	math	PROPN
ejpam-5744	484	4	.	.	PUNCT
ejpam-5744	484	5	,	,	PUNCT
ejpam-5744	484	6	19:155–160	19:155–160	NUM
ejpam-5744	484	7	,	,	PUNCT
ejpam-5744	484	8	2003	2003	NUM
ejpam-5744	484	9	.	.	PUNCT
ejpam-5744	485	1	[	[	X
ejpam-5744	485	2	23	23	NUM
ejpam-5744	485	3	]	]	X
ejpam-5744	485	4	s.	s.	PROPN
ejpam-5744	485	5	ishikawa	ishikawa	PROPN
ejpam-5744	485	6	.	.	PUNCT
ejpam-5744	485	7	fixed	fix	VERB
ejpam-5744	485	8	points	point	NOUN
ejpam-5744	485	9	by	by	ADP
ejpam-5744	485	10	a	a	DET
ejpam-5744	485	11	new	new	ADJ
ejpam-5744	485	12	iteration	iteration	NOUN
ejpam-5744	485	13	method	method	NOUN
ejpam-5744	485	14	.	.	PUNCT
ejpam-5744	486	1	proc	proc	NOUN
ejpam-5744	486	2	.	.	PUNCT
ejpam-5744	487	1	amer	amer	PROPN
ejpam-5744	487	2	.	.	PUNCT
ejpam-5744	487	3	math	math	PROPN
ejpam-5744	487	4	.	.	PUNCT
ejpam-5744	488	1	soc	soc	PROPN
ejpam-5744	488	2	.	.	PUNCT
ejpam-5744	488	3	,	,	PUNCT
ejpam-5744	488	4	44	44	NUM
ejpam-5744	488	5	:	:	SYM
ejpam-5744	488	6	147–150	147–150	NUM
ejpam-5744	488	7	,	,	PUNCT
ejpam-5744	488	8	1974	1974	NUM
ejpam-5744	488	9	.	.	PUNCT
ejpam-5744	489	1	[	[	X
ejpam-5744	489	2	24	24	NUM
ejpam-5744	489	3	]	]	X
ejpam-5744	489	4	h.a	h.a	PROPN
ejpam-5744	489	5	.	.	PROPN
ejpam-5744	489	6	hammad	hammad	PROPN
ejpam-5744	489	7	j.	j.	PROPN
ejpam-5744	489	8	ahmad	ahmad	PROPN
ejpam-5744	489	9	,	,	PUNCT
ejpam-5744	489	10	k.	k.	PROPN
ejpam-5744	489	11	ullah	ullah	PROPN
ejpam-5744	489	12	and	and	CCONJ
ejpam-5744	489	13	r.	r.	PROPN
ejpam-5744	489	14	george	george	PROPN
ejpam-5744	489	15	.	.	PUNCT
ejpam-5744	490	1	a	a	DET
ejpam-5744	490	2	solution	solution	NOUN
ejpam-5744	490	3	of	of	ADP
ejpam-5744	490	4	a	a	DET
ejpam-5744	490	5	fractional	fractional	ADJ
ejpam-5744	490	6	differential	differential	ADJ
ejpam-5744	490	7	equation	equation	NOUN
ejpam-5744	490	8	via	via	ADP
ejpam-5744	490	9	novel	novel	ADJ
ejpam-5744	490	10	fixed	fix	VERB
ejpam-5744	490	11	-	-	PUNCT
ejpam-5744	490	12	point	point	NOUN
ejpam-5744	490	13	approaches	approach	NOUN
ejpam-5744	490	14	in	in	ADP
ejpam-5744	490	15	banach	banach	NOUN
ejpam-5744	490	16	spaces	space	NOUN
ejpam-5744	490	17	.	.	PUNCT
ejpam-5744	491	1	aims	aim	VERB
ejpam-5744	491	2	mathematics	mathematic	NOUN
ejpam-5744	491	3	,	,	PUNCT
ejpam-5744	491	4	8(6):12657–12670	8(6):12657–12670	NUM
ejpam-5744	491	5	,	,	PUNCT
ejpam-5744	491	6	2023	2023	NUM
ejpam-5744	491	7	.	.	PUNCT
ejpam-5744	492	1	[	[	X
ejpam-5744	492	2	25	25	NUM
ejpam-5744	492	3	]	]	X
ejpam-5744	492	4	s.	s.	PROPN
ejpam-5744	492	5	khorasani	khorasani	PROPN
ejpam-5744	492	6	and	and	CCONJ
ejpam-5744	492	7	a.	a.	NOUN
ejpam-5744	492	8	adibi	adibi	NOUN
ejpam-5744	492	9	.	.	PUNCT
ejpam-5744	493	1	analytical	analytical	ADJ
ejpam-5744	493	2	solution	solution	NOUN
ejpam-5744	493	3	of	of	ADP
ejpam-5744	493	4	linear	linear	ADJ
ejpam-5744	493	5	ordinary	ordinary	ADJ
ejpam-5744	493	6	differential	differential	ADJ
ejpam-5744	493	7	equations	equation	NOUN
ejpam-5744	493	8	by	by	ADP
ejpam-5744	493	9	differential	differential	ADJ
ejpam-5744	493	10	transfer	transfer	NOUN
ejpam-5744	493	11	matric	matric	NOUN
ejpam-5744	493	12	method	method	NOUN
ejpam-5744	493	13	.	.	PUNCT
ejpam-5744	494	1	electron	electron	PROPN
ejpam-5744	494	2	.	.	PUNCT
ejpam-5744	495	1	j.	j.	PROPN
ejpam-5744	495	2	differ	differ	VERB
ejpam-5744	495	3	.	.	PUNCT
ejpam-5744	496	1	equ	equ	PROPN
ejpam-5744	496	2	.	.	PROPN
ejpam-5744	496	3	,	,	PUNCT
ejpam-5744	496	4	79:1–8	79:1–8	NOUN
ejpam-5744	496	5	,	,	PUNCT
ejpam-5744	496	6	2003	2003	NUM
ejpam-5744	496	7	.	.	PUNCT
ejpam-5744	497	1	[	[	X
ejpam-5744	497	2	26	26	NUM
ejpam-5744	497	3	]	]	X
ejpam-5744	497	4	n.	n.	PROPN
ejpam-5744	497	5	shahzad	shahzad	PROPN
ejpam-5744	497	6	m.a	m.a	PROPN
ejpam-5744	497	7	.	.	PROPN
ejpam-5744	497	8	alghamdi	alghamdi	PROPN
ejpam-5744	497	9	,	,	PUNCT
ejpam-5744	497	10	a.m.	a.m.	PROPN
ejpam-5744	497	11	alghamdi	alghamdi	PROPN
ejpam-5744	497	12	and	and	CCONJ
ejpam-5744	497	13	h.k	h.k	PROPN
ejpam-5744	497	14	.	.	PROPN
ejpam-5744	497	15	xu	xu	PROPN
ejpam-5744	497	16	.	.	PUNCT
ejpam-5744	498	1	the	the	DET
ejpam-5744	498	2	implicit	implicit	ADJ
ejpam-5744	498	3	midpoint	midpoint	NOUN
ejpam-5744	498	4	rule	rule	NOUN
ejpam-5744	498	5	for	for	ADP
ejpam-5744	498	6	nonexpansive	nonexpansive	ADJ
ejpam-5744	498	7	mappings	mapping	NOUN
ejpam-5744	498	8	.	.	PUNCT
ejpam-5744	499	1	fixed	fix	VERB
ejpam-5744	499	2	point	point	NOUN
ejpam-5744	499	3	theory	theory	NOUN
ejpam-5744	499	4	appl	appl	PROPN
ejpam-5744	499	5	.	.	PROPN
ejpam-5744	499	6	,	,	PUNCT
ejpam-5744	499	7	96	96	NUM
ejpam-5744	499	8	,	,	PUNCT
ejpam-5744	499	9	2014	2014	NUM
ejpam-5744	499	10	.	.	PUNCT
ejpam-5744	500	1	doi	doi	NOUN
ejpam-5744	500	2	:	:	PUNCT
ejpam-5744	500	3	10.1186/16871812	10.1186/16871812	NUM
ejpam-5744	500	4	-	-	SYM
ejpam-5744	500	5	2014	2014	NUM
ejpam-5744	500	6	-	-	SYM
ejpam-5744	500	7	96	96	NUM
ejpam-5744	500	8	.	.	PUNCT
ejpam-5744	501	1	[	[	X
ejpam-5744	501	2	27	27	NUM
ejpam-5744	501	3	]	]	X
ejpam-5744	501	4	r.l	r.l	PROPN
ejpam-5744	501	5	.	.	PROPN
ejpam-5744	501	6	magin	magin	PROPN
ejpam-5744	501	7	.	.	PUNCT
ejpam-5744	502	1	fractional	fractional	ADJ
ejpam-5744	502	2	calculus	calculus	NOUN
ejpam-5744	502	3	models	model	NOUN
ejpam-5744	502	4	of	of	ADP
ejpam-5744	502	5	complex	complex	ADJ
ejpam-5744	502	6	dynamics	dynamic	NOUN
ejpam-5744	502	7	in	in	ADP
ejpam-5744	502	8	biological	biological	ADJ
ejpam-5744	502	9	tissues	tissue	NOUN
ejpam-5744	502	10	.	.	PUNCT
ejpam-5744	503	1	comput	comput	NOUN
ejpam-5744	503	2	.	.	PUNCT
ejpam-5744	504	1	math	math	NOUN
ejpam-5744	504	2	.	.	PUNCT
ejpam-5744	505	1	appl	appl	PROPN
ejpam-5744	505	2	.	.	PROPN
ejpam-5744	505	3	,	,	PUNCT
ejpam-5744	505	4	59:1586–1593	59:1586–1593	NUM
ejpam-5744	505	5	,	,	PUNCT
ejpam-5744	505	6	2010	2010	NUM
ejpam-5744	505	7	.	.	PUNCT
ejpam-5744	506	1	[	[	X
ejpam-5744	506	2	28	28	NUM
ejpam-5744	506	3	]	]	X
ejpam-5744	506	4	w.r	w.r	PROPN
ejpam-5744	506	5	.	.	PROPN
ejpam-5744	506	6	mann	mann	PROPN
ejpam-5744	506	7	.	.	PUNCT
ejpam-5744	507	1	mean	mean	VERB
ejpam-5744	507	2	value	value	NOUN
ejpam-5744	507	3	methods	method	NOUN
ejpam-5744	507	4	in	in	ADP
ejpam-5744	507	5	iteration	iteration	NOUN
ejpam-5744	507	6	.	.	PUNCT
ejpam-5744	508	1	proc	proc	PROPN
ejpam-5744	508	2	.	.	PUNCT
ejpam-5744	509	1	amer	amer	PROPN
ejpam-5744	509	2	.	.	PUNCT
ejpam-5744	509	3	math	math	PROPN
ejpam-5744	509	4	.	.	PUNCT
ejpam-5744	510	1	soc	soc	PROPN
ejpam-5744	510	2	.	.	PUNCT
ejpam-5744	510	3	,	,	PUNCT
ejpam-5744	510	4	4:506–510	4:506–510	NUM
ejpam-5744	510	5	,	,	PUNCT
ejpam-5744	510	6	1953	1953	NUM
ejpam-5744	510	7	.	.	PUNCT
ejpam-5744	511	1	[	[	X
ejpam-5744	511	2	29	29	NUM
ejpam-5744	511	3	]	]	X
ejpam-5744	511	4	k.s	k.s	PROPN
ejpam-5744	511	5	.	.	PROPN
ejpam-5744	511	6	miller	miller	PROPN
ejpam-5744	511	7	and	and	CCONJ
ejpam-5744	511	8	b.	b.	PROPN
ejpam-5744	511	9	ross	ross	PROPN
ejpam-5744	511	10	.	.	PUNCT
ejpam-5744	512	1	an	an	DET
ejpam-5744	512	2	introduction	introduction	NOUN
ejpam-5744	512	3	to	to	ADP
ejpam-5744	512	4	fractional	fractional	ADJ
ejpam-5744	512	5	calculus	calculus	NOUN
ejpam-5744	512	6	and	and	CCONJ
ejpam-5744	512	7	fractional	fractional	ADJ
ejpam-5744	512	8	differential	differential	ADJ
ejpam-5744	512	9	equations	equation	NOUN
ejpam-5744	512	10	.	.	PUNCT
ejpam-5744	513	1	wiley	wiley	PROPN
ejpam-5744	513	2	,	,	PUNCT
ejpam-5744	513	3	new	new	PROPN
ejpam-5744	513	4	york	york	PROPN
ejpam-5744	513	5	,	,	PUNCT
ejpam-5744	513	6	1993	1993	NUM
ejpam-5744	513	7	.	.	PUNCT
ejpam-5744	514	1	[	[	X
ejpam-5744	514	2	30	30	NUM
ejpam-5744	514	3	]	]	X
ejpam-5744	514	4	g.j	g.j	PROPN
ejpam-5744	514	5	.	.	PROPN
ejpam-5744	514	6	minty	minty	PROPN
ejpam-5744	514	7	.	.	PUNCT
ejpam-5744	515	1	monotone	monotone	ADJ
ejpam-5744	515	2	(	(	PUNCT
ejpam-5744	515	3	nonlinear	nonlinear	ADJ
ejpam-5744	515	4	)	)	PUNCT
ejpam-5744	515	5	operators	operator	NOUN
ejpam-5744	515	6	in	in	ADP
ejpam-5744	515	7	hilbert	hilbert	PROPN
ejpam-5744	515	8	space	space	NOUN
ejpam-5744	515	9	.	.	PUNCT
ejpam-5744	516	1	duke	duke	PROPN
ejpam-5744	516	2	math	math	PROPN
ejpam-5744	516	3	.	.	PUNCT
ejpam-5744	517	1	j.	j.	PROPN
ejpam-5744	517	2	,	,	PUNCT
ejpam-5744	517	3	29(4	29(4	NOUN
ejpam-5744	517	4	):	):	PUNCT
ejpam-5744	517	5	341–346	341–346	NUM
ejpam-5744	517	6	,	,	PUNCT
ejpam-5744	517	7	1962	1962	NUM
ejpam-5744	517	8	.	.	PUNCT
ejpam-5744	518	1	[	[	X
ejpam-5744	518	2	31	31	NUM
ejpam-5744	518	3	]	]	X
ejpam-5744	518	4	s.c	s.c	PROPN
ejpam-5744	518	5	.	.	PROPN
ejpam-5744	518	6	thakur	thakur	PROPN
ejpam-5744	518	7	m.o	m.o	PROPN
ejpam-5744	518	8	.	.	PROPN
ejpam-5744	518	9	aibinu	aibinu	PROPN
ejpam-5744	518	10	and	and	CCONJ
ejpam-5744	518	11	s.	s.	PROPN
ejpam-5744	518	12	moyo	moyo	PROPN
ejpam-5744	518	13	.	.	PUNCT
ejpam-5744	519	1	the	the	DET
ejpam-5744	519	2	implicit	implicit	ADJ
ejpam-5744	519	3	midpoint	midpoint	NOUN
ejpam-5744	519	4	procedures	procedure	NOUN
ejpam-5744	519	5	for	for	ADP
ejpam-5744	519	6	asymptotically	asymptotically	ADV
ejpam-5744	519	7	nonexpansive	nonexpansive	ADJ
ejpam-5744	519	8	mappings	mapping	NOUN
ejpam-5744	519	9	.	.	PUNCT
ejpam-5744	520	1	journal	journal	NOUN
ejpam-5744	520	2	of	of	ADP
ejpam-5744	520	3	mathematics	mathematic	NOUN
ejpam-5744	520	4	,	,	PUNCT
ejpam-5744	520	5	2020	2020	NUM
ejpam-5744	520	6	.	.	PUNCT
ejpam-5744	521	1	[	[	X
ejpam-5744	521	2	32	32	NUM
ejpam-5744	521	3	]	]	X
ejpam-5744	521	4	m.a	m.a	PROPN
ejpam-5744	521	5	.	.	PROPN
ejpam-5744	521	6	noor	noor	PROPN
ejpam-5744	521	7	.	.	PUNCT
ejpam-5744	522	1	general	general	ADJ
ejpam-5744	522	2	variational	variational	ADJ
ejpam-5744	522	3	inequalities	inequality	NOUN
ejpam-5744	522	4	.	.	PUNCT
ejpam-5744	523	1	appl	appl	PROPN
ejpam-5744	523	2	.	.	PROPN
ejpam-5744	523	3	math	math	PROPN
ejpam-5744	523	4	.	.	PUNCT
ejpam-5744	524	1	lett	lett	PROPN
ejpam-5744	524	2	.	.	PROPN
ejpam-5744	524	3	,	,	PUNCT
ejpam-5744	524	4	1:119–122	1:119–122	NUM
ejpam-5744	524	5	,	,	PUNCT
ejpam-5744	524	6	1988	1988	NUM
ejpam-5744	524	7	.	.	PUNCT
ejpam-5744	525	1	[	[	X
ejpam-5744	525	2	33	33	NUM
ejpam-5744	525	3	]	]	X
ejpam-5744	525	4	m.a	m.a	PROPN
ejpam-5744	525	5	.	.	PROPN
ejpam-5744	525	6	noor	noor	PROPN
ejpam-5744	525	7	.	.	PUNCT
ejpam-5744	526	1	new	new	ADJ
ejpam-5744	526	2	approximation	approximation	NOUN
ejpam-5744	526	3	scheme	scheme	NOUN
ejpam-5744	526	4	for	for	ADP
ejpam-5744	526	5	general	general	ADJ
ejpam-5744	526	6	variational	variational	ADJ
ejpam-5744	526	7	inequalities	inequality	NOUN
ejpam-5744	526	8	.	.	PUNCT
ejpam-5744	527	1	j.	j.	PROPN
ejpam-5744	527	2	math	math	PROPN
ejpam-5744	527	3	.	.	PUNCT
ejpam-5744	528	1	anal	anal	PROPN
ejpam-5744	528	2	.	.	PUNCT
ejpam-5744	529	1	appl	appl	PROPN
ejpam-5744	529	2	.	.	PROPN
ejpam-5744	529	3	,	,	PUNCT
ejpam-5744	529	4	251:217–229	251:217–229	NUM
ejpam-5744	529	5	,	,	PUNCT
ejpam-5744	529	6	2000	2000	NUM
ejpam-5744	529	7	.	.	PUNCT
ejpam-5744	530	1	[	[	X
ejpam-5744	530	2	34	34	NUM
ejpam-5744	530	3	]	]	X
ejpam-5744	530	4	g.a	g.a	PROPN
ejpam-5744	530	5	.	.	PROPN
ejpam-5744	530	6	okeke	okeke	PROPN
ejpam-5744	530	7	.	.	PUNCT
ejpam-5744	531	1	convergence	convergence	NOUN
ejpam-5744	531	2	analysis	analysis	NOUN
ejpam-5744	531	3	of	of	ADP
ejpam-5744	531	4	the	the	DET
ejpam-5744	531	5	picard	picard	NOUN
ejpam-5744	531	6	-	-	PUNCT
ejpam-5744	531	7	ishikawa	ishikawa	PROPN
ejpam-5744	531	8	hybrid	hybrid	ADJ
ejpam-5744	531	9	iterative	iterative	NOUN
ejpam-5744	531	10	process	process	NOUN
ejpam-5744	531	11	with	with	ADP
ejpam-5744	531	12	applications	application	NOUN
ejpam-5744	531	13	.	.	PUNCT
ejpam-5744	532	1	afr	afr	PROPN
ejpam-5744	532	2	.	.	PUNCT
ejpam-5744	533	1	mat	mat	PROPN
ejpam-5744	533	2	.	.	PROPN
ejpam-5744	533	3	,	,	PUNCT
ejpam-5744	533	4	30:817–835	30:817–835	PROPN
ejpam-5744	533	5	,	,	PUNCT
ejpam-5744	533	6	2019	2019	NUM
ejpam-5744	533	7	.	.	PUNCT
ejpam-5744	534	1	[	[	X
ejpam-5744	534	2	35	35	NUM
ejpam-5744	534	3	]	]	X
ejpam-5744	534	4	m.o	m.o	PROPN
ejpam-5744	534	5	.	.	PROPN
ejpam-5744	534	6	osilike	osilike	PROPN
ejpam-5744	534	7	.	.	PUNCT
ejpam-5744	535	1	some	some	DET
ejpam-5744	535	2	stability	stability	NOUN
ejpam-5744	535	3	results	result	VERB
ejpam-5744	535	4	for	for	ADP
ejpam-5744	535	5	fixed	fix	VERB
ejpam-5744	535	6	point	point	NOUN
ejpam-5744	535	7	iteration	iteration	NOUN
ejpam-5744	535	8	procedures	procedure	NOUN
ejpam-5744	535	9	.	.	PUNCT
ejpam-5744	536	1	j.	j.	PROPN
ejpam-5744	536	2	nigerian	nigerian	PROPN
ejpam-5744	536	3	math	math	PROPN
ejpam-5744	536	4	.	.	PUNCT
ejpam-5744	537	1	soc	soc	PROPN
ejpam-5744	537	2	.	.	PUNCT
ejpam-5744	537	3	,	,	PUNCT
ejpam-5744	537	4	14	14	NUM
ejpam-5744	537	5	-	-	SYM
ejpam-5744	537	6	15:17–29	15:17–29	NUM
ejpam-5744	537	7	,	,	PUNCT
ejpam-5744	537	8	1995	1995	NUM
ejpam-5744	537	9	.	.	PUNCT
ejpam-5744	538	1	[	[	X
ejpam-5744	538	2	36	36	NUM
ejpam-5744	538	3	]	]	X
ejpam-5744	539	1	g.	g.	PROPN
ejpam-5744	539	2	cai	cai	PROPN
ejpam-5744	539	3	p.	p.	PROPN
ejpam-5744	539	4	luo	luo	PROPN
ejpam-5744	539	5	and	and	CCONJ
ejpam-5744	539	6	y.	y.	PROPN
ejpam-5744	539	7	shehu	shehu	PROPN
ejpam-5744	539	8	.	.	PUNCT
ejpam-5744	540	1	the	the	DET
ejpam-5744	540	2	viscosity	viscosity	NOUN
ejpam-5744	540	3	iterative	iterative	NOUN
ejpam-5744	540	4	algorithms	algorithm	NOUN
ejpam-5744	540	5	for	for	ADP
ejpam-5744	540	6	the	the	DET
ejpam-5744	540	7	implicit	implicit	ADJ
ejpam-5744	540	8	midpoint	midpoint	NOUN
ejpam-5744	540	9	rule	rule	NOUN
ejpam-5744	540	10	of	of	ADP
ejpam-5744	540	11	nonexpansive	nonexpansive	ADJ
ejpam-5744	540	12	mappings	mapping	NOUN
ejpam-5744	540	13	in	in	ADP
ejpam-5744	540	14	uniformly	uniformly	ADV
ejpam-5744	540	15	smooth	smooth	ADJ
ejpam-5744	540	16	banach	banach	NOUN
ejpam-5744	540	17	spaces	space	VERB
ejpam-5744	540	18	.	.	PUNCT
ejpam-5744	541	1	j.	j.	PROPN
ejpam-5744	541	2	m.	m.	PROPN
ejpam-5744	541	3	akram	akram	PROPN
ejpam-5744	541	4	/	/	PUNCT
ejpam-5744	541	5	eur	eur	PROPN
ejpam-5744	541	6	.	.	PUNCT
ejpam-5744	542	1	j.	j.	PROPN
ejpam-5744	542	2	pure	pure	PROPN
ejpam-5744	542	3	appl	appl	PROPN
ejpam-5744	542	4	.	.	PROPN
ejpam-5744	542	5	math	math	PROPN
ejpam-5744	542	6	,	,	PUNCT
ejpam-5744	542	7	18	18	NUM
ejpam-5744	542	8	(	(	PUNCT
ejpam-5744	542	9	1	1	NUM
ejpam-5744	542	10	)	)	PUNCT
ejpam-5744	542	11	(	(	PUNCT
ejpam-5744	542	12	2025	2025	NUM
ejpam-5744	542	13	)	)	PUNCT
ejpam-5744	542	14	,	,	PUNCT
ejpam-5744	542	15	5744	5744	NUM
ejpam-5744	542	16	19	19	NUM
ejpam-5744	542	17	of	of	ADP
ejpam-5744	542	18	19	19	NUM
ejpam-5744	542	19	inequal	inequal	ADJ
ejpam-5744	542	20	.	.	PUNCT
ejpam-5744	543	1	appl	appl	PROPN
ejpam-5744	543	2	.	.	PROPN
ejpam-5744	543	3	,	,	PUNCT
ejpam-5744	543	4	2017	2017	NUM
ejpam-5744	543	5	.	.	PUNCT
ejpam-5744	544	1	doi	doi	NOUN
ejpam-5744	544	2	:	:	PUNCT
ejpam-5744	544	3	10.1186	10.1186	NUM
ejpam-5744	544	4	/	/	SYM
ejpam-5744	544	5	s13660	s13660	NOUN
ejpam-5744	544	6	-	-	PUNCT
ejpam-5744	544	7	017	017	NUM
ejpam-5744	544	8	-	-	PUNCT
ejpam-5744	544	9	1426	1426	NUM
ejpam-5744	544	10	-	-	SYM
ejpam-5744	544	11	8	8	NUM
ejpam-5744	544	12	.	.	PUNCT
ejpam-5744	545	1	[	[	X
ejpam-5744	545	2	37	37	NUM
ejpam-5744	545	3	]	]	X
ejpam-5744	545	4	r.	r.	PROPN
ejpam-5744	545	5	pant	pant	PROPN
ejpam-5744	545	6	,	,	PUNCT
ejpam-5744	545	7	r.	r.	PROPN
ejpam-5744	545	8	shukla	shukla	PROPN
ejpam-5744	545	9	,	,	PUNCT
ejpam-5744	545	10	and	and	CCONJ
ejpam-5744	545	11	p.	p.	PROPN
ejpam-5744	545	12	patel	patel	PROPN
ejpam-5744	545	13	.	.	PUNCT
ejpam-5744	546	1	nonexpansive	nonexpansive	ADJ
ejpam-5744	546	2	mappings	mapping	NOUN
ejpam-5744	546	3	,	,	PUNCT
ejpam-5744	546	4	their	their	PRON
ejpam-5744	546	5	extensions	extension	NOUN
ejpam-5744	546	6	and	and	CCONJ
ejpam-5744	546	7	generalizations	generalization	NOUN
ejpam-5744	546	8	in	in	ADP
ejpam-5744	546	9	banach	banach	NOUN
ejpam-5744	546	10	spaces	space	NOUN
ejpam-5744	546	11	.	.	PUNCT
ejpam-5744	547	1	in	in	ADP
ejpam-5744	547	2	p.	p.	PROPN
ejpam-5744	547	3	debnath	debnath	PROPN
ejpam-5744	547	4	,	,	PUNCT
ejpam-5744	547	5	n.	n.	PROPN
ejpam-5744	547	6	konwar	konwar	PROPN
ejpam-5744	547	7	,	,	PUNCT
ejpam-5744	547	8	and	and	CCONJ
ejpam-5744	547	9	s.	s.	PROPN
ejpam-5744	547	10	radenović	radenović	VERB
ejpam-5744	547	11	,	,	PUNCT
ejpam-5744	547	12	editors	editor	NOUN
ejpam-5744	547	13	,	,	PUNCT
ejpam-5744	547	14	metric	metric	ADJ
ejpam-5744	547	15	fixed	fix	VERB
ejpam-5744	547	16	point	point	NOUN
ejpam-5744	547	17	theory	theory	NOUN
ejpam-5744	547	18	,	,	PUNCT
ejpam-5744	547	19	forum	forum	NOUN
ejpam-5744	547	20	for	for	ADP
ejpam-5744	547	21	interdisciplinary	interdisciplinary	ADJ
ejpam-5744	547	22	mathematics	mathematic	NOUN
ejpam-5744	547	23	.	.	PUNCT
ejpam-5744	548	1	springer	springer	PROPN
ejpam-5744	548	2	,	,	PUNCT
ejpam-5744	548	3	singapore	singapore	PROPN
ejpam-5744	548	4	,	,	PUNCT
ejpam-5744	548	5	2021	2021	NUM
ejpam-5744	548	6	.	.	PUNCT
ejpam-5744	549	1	[	[	X
ejpam-5744	549	2	38	38	NUM
ejpam-5744	549	3	]	]	PUNCT
ejpam-5744	549	4	s.	s.	PROPN
ejpam-5744	549	5	reich	reich	PROPN
ejpam-5744	549	6	.	.	PUNCT
ejpam-5744	550	1	some	some	DET
ejpam-5744	550	2	remarks	remark	NOUN
ejpam-5744	550	3	concerning	concern	VERB
ejpam-5744	550	4	contraction	contraction	NOUN
ejpam-5744	550	5	mappings	mapping	NOUN
ejpam-5744	550	6	.	.	PUNCT
ejpam-5744	551	1	canad	canad	PROPN
ejpam-5744	551	2	.	.	PUNCT
ejpam-5744	552	1	math	math	NOUN
ejpam-5744	552	2	.	.	PUNCT
ejpam-5744	553	1	bull	bull	PROPN
ejpam-5744	553	2	.	.	PUNCT
ejpam-5744	553	3	,	,	PUNCT
ejpam-5744	553	4	14	14	NUM
ejpam-5744	553	5	(	(	PUNCT
ejpam-5744	553	6	1):121–124	1):121–124	NUM
ejpam-5744	553	7	,	,	PUNCT
ejpam-5744	553	8	1971	1971	NUM
ejpam-5744	553	9	.	.	PUNCT
ejpam-5744	554	1	[	[	X
ejpam-5744	554	2	39	39	NUM
ejpam-5744	554	3	]	]	X
ejpam-5744	554	4	b.e	b.e	PROPN
ejpam-5744	554	5	.	.	PROPN
ejpam-5744	554	6	rhoades	rhoade	NOUN
ejpam-5744	554	7	.	.	PUNCT
ejpam-5744	555	1	some	some	DET
ejpam-5744	555	2	fixed	fix	VERB
ejpam-5744	555	3	point	point	NOUN
ejpam-5744	555	4	iteration	iteration	NOUN
ejpam-5744	555	5	procedures	procedure	NOUN
ejpam-5744	555	6	.	.	PUNCT
ejpam-5744	556	1	int	int	NOUN
ejpam-5744	556	2	.	.	PUNCT
ejpam-5744	557	1	j.	j.	PROPN
ejpam-5744	557	2	math	math	PROPN
ejpam-5744	557	3	.	.	PUNCT
ejpam-5744	558	1	math	math	NOUN
ejpam-5744	558	2	.	.	PUNCT
ejpam-5744	559	1	sci	sci	PROPN
ejpam-5744	559	2	.	.	PROPN
ejpam-5744	559	3	,	,	PUNCT
ejpam-5744	559	4	14	14	NUM
ejpam-5744	559	5	:	:	PUNCT
ejpam-5744	559	6	1–16	1–16	NOUN
ejpam-5744	559	7	,	,	PUNCT
ejpam-5744	559	8	1991	1991	NUM
ejpam-5744	559	9	.	.	PUNCT
ejpam-5744	560	1	[	[	X
ejpam-5744	560	2	40	40	NUM
ejpam-5744	560	3	]	]	X
ejpam-5744	560	4	b.e	b.e	PROPN
ejpam-5744	560	5	.	.	PROPN
ejpam-5744	560	6	rhoades	rhoades	PROPN
ejpam-5744	560	7	.	.	PUNCT
ejpam-5744	561	1	fixed	fix	VERB
ejpam-5744	561	2	point	point	NOUN
ejpam-5744	561	3	theorems	theorem	NOUN
ejpam-5744	561	4	and	and	CCONJ
ejpam-5744	561	5	stability	stability	NOUN
ejpam-5744	561	6	results	result	NOUN
ejpam-5744	561	7	for	for	ADP
ejpam-5744	561	8	fixed	fix	VERB
ejpam-5744	561	9	point	point	NOUN
ejpam-5744	561	10	iteration	iteration	NOUN
ejpam-5744	561	11	procedures	procedure	NOUN
ejpam-5744	561	12	ii	ii	PROPN
ejpam-5744	561	13	.	.	PUNCT
ejpam-5744	562	1	indian	indian	PROPN
ejpam-5744	562	2	j.	j.	PROPN
ejpam-5744	562	3	pure	pure	PROPN
ejpam-5744	562	4	appl	appl	PROPN
ejpam-5744	562	5	.	.	PUNCT
ejpam-5744	562	6	math	math	PROPN
ejpam-5744	562	7	.	.	PUNCT
ejpam-5744	562	8	,	,	PUNCT
ejpam-5744	562	9	24(11):691–703	24(11):691–703	NUM
ejpam-5744	562	10	,	,	PUNCT
ejpam-5744	562	11	1993	1993	NUM
ejpam-5744	562	12	.	.	PUNCT
ejpam-5744	563	1	[	[	X
ejpam-5744	563	2	41	41	NUM
ejpam-5744	563	3	]	]	X
ejpam-5744	563	4	d.o	d.o	PROPN
ejpam-5744	563	5	’	'	PUNCT
ejpam-5744	563	6	regan	regan	PROPN
ejpam-5744	563	7	r.p	r.p	PROPN
ejpam-5744	563	8	.	.	PROPN
ejpam-5744	563	9	agarwal	agarwal	PROPN
ejpam-5744	563	10	and	and	CCONJ
ejpam-5744	563	11	d.r.sahu	d.r.sahu	PROPN
ejpam-5744	563	12	.	.	PUNCT
ejpam-5744	564	1	iterative	iterative	NOUN
ejpam-5744	564	2	construction	construction	NOUN
ejpam-5744	564	3	of	of	ADP
ejpam-5744	564	4	fixed	fix	VERB
ejpam-5744	564	5	points	point	NOUN
ejpam-5744	564	6	of	of	ADP
ejpam-5744	564	7	nearly	nearly	ADV
ejpam-5744	564	8	asymptotically	asymptotically	ADV
ejpam-5744	564	9	nonexpansive	nonexpansive	ADJ
ejpam-5744	564	10	mappings	mapping	NOUN
ejpam-5744	564	11	.	.	PUNCT
ejpam-5744	565	1	j.	j.	PROPN
ejpam-5744	565	2	nonlinear	nonlinear	PROPN
ejpam-5744	565	3	convex	convex	PROPN
ejpam-5744	565	4	anal	anal	NOUN
ejpam-5744	565	5	.	.	PUNCT
ejpam-5744	565	6	,	,	PUNCT
ejpam-5744	565	7	8(1):61	8(1):61	NUM
ejpam-5744	565	8	–	–	PUNCT
ejpam-5744	565	9	79	79	NUM
ejpam-5744	565	10	,	,	PUNCT
ejpam-5744	565	11	2007	2007	NUM
ejpam-5744	565	12	.	.	PUNCT
ejpam-5744	566	1	[	[	X
ejpam-5744	566	2	42	42	NUM
ejpam-5744	566	3	]	]	X
ejpam-5744	566	4	i.	i.	PROPN
ejpam-5744	566	5	uddin	uddin	PROPN
ejpam-5744	566	6	s.	s.	PROPN
ejpam-5744	566	7	khatoon	khatoon	PROPN
ejpam-5744	566	8	and	and	CCONJ
ejpam-5744	566	9	d.	d.	PROPN
ejpam-5744	566	10	baleanu	baleanu	PROPN
ejpam-5744	566	11	.	.	PUNCT
ejpam-5744	567	1	approximation	approximation	NOUN
ejpam-5744	567	2	of	of	ADP
ejpam-5744	567	3	fixed	fix	VERB
ejpam-5744	567	4	point	point	NOUN
ejpam-5744	567	5	and	and	CCONJ
ejpam-5744	567	6	its	its	PRON
ejpam-5744	567	7	application	application	NOUN
ejpam-5744	567	8	to	to	ADP
ejpam-5744	567	9	fractional	fractional	ADJ
ejpam-5744	567	10	differential	differential	ADJ
ejpam-5744	567	11	equation	equation	NOUN
ejpam-5744	567	12	.	.	PUNCT
ejpam-5744	568	1	j.	j.	PROPN
ejpam-5744	568	2	appl	appl	PROPN
ejpam-5744	568	3	.	.	PROPN
ejpam-5744	568	4	math	math	PROPN
ejpam-5744	568	5	.	.	PUNCT
ejpam-5744	569	1	comput	comput	NOUN
ejpam-5744	569	2	.	.	PUNCT
ejpam-5744	569	3	,	,	PUNCT
ejpam-5744	570	1	66:507–525	66:507–525	PROPN
ejpam-5744	570	2	,	,	PUNCT
ejpam-5744	570	3	2021	2021	NUM
ejpam-5744	570	4	.	.	PUNCT
ejpam-5744	571	1	[	[	X
ejpam-5744	571	2	43	43	NUM
ejpam-5744	571	3	]	]	X
ejpam-5744	571	4	d.r	d.r	PROPN
ejpam-5744	571	5	.	.	PROPN
ejpam-5744	571	6	sahu	sahu	PROPN
ejpam-5744	571	7	and	and	CCONJ
ejpam-5744	571	8	a.	a.	NOUN
ejpam-5744	571	9	petrusel	petrusel	NOUN
ejpam-5744	571	10	.	.	PUNCT
ejpam-5744	572	1	strong	strong	ADJ
ejpam-5744	572	2	convergence	convergence	NOUN
ejpam-5744	572	3	of	of	ADP
ejpam-5744	572	4	iterative	iterative	ADJ
ejpam-5744	572	5	methods	method	NOUN
ejpam-5744	572	6	by	by	ADP
ejpam-5744	572	7	strictly	strictly	ADV
ejpam-5744	572	8	pseudocontractive	pseudocontractive	ADJ
ejpam-5744	572	9	mappings	mapping	NOUN
ejpam-5744	572	10	in	in	ADP
ejpam-5744	572	11	banach	banach	NOUN
ejpam-5744	572	12	spaces	space	NOUN
ejpam-5744	572	13	.	.	PUNCT
ejpam-5744	573	1	nonlinear	nonlinear	ADJ
ejpam-5744	573	2	anal	anal	PROPN
ejpam-5744	573	3	.	.	PUNCT
ejpam-5744	574	1	theory	theory	NOUN
ejpam-5744	574	2	methods	method	NOUN
ejpam-5744	574	3	appl	appl	PROPN
ejpam-5744	574	4	.	.	PROPN
ejpam-5744	574	5	,	,	PUNCT
ejpam-5744	574	6	74:6012–6023	74:6012–6023	NUM
ejpam-5744	574	7	,	,	PUNCT
ejpam-5744	574	8	2011	2011	NUM
ejpam-5744	574	9	.	.	PUNCT
ejpam-5744	575	1	[	[	X
ejpam-5744	575	2	44	44	NUM
ejpam-5744	575	3	]	]	X
ejpam-5744	575	4	a.o	a.o	PROPN
ejpam-5744	575	5	.	.	PROPN
ejpam-5744	575	6	nazek	nazek	PROPN
ejpam-5744	575	7	s.r	s.r	PROPN
ejpam-5744	575	8	.	.	PROPN
ejpam-5744	575	9	mahmoud	mahmoud	PROPN
ejpam-5744	575	10	and	and	CCONJ
ejpam-5744	575	11	a.	a.	PROPN
ejpam-5744	575	12	hala	hala	PROPN
ejpam-5744	575	13	.	.	PUNCT
ejpam-5744	576	1	new	new	ADJ
ejpam-5744	576	2	class	class	NOUN
ejpam-5744	576	3	of	of	ADP
ejpam-5744	576	4	nonlinear	nonlinear	ADJ
ejpam-5744	576	5	fractional	fractional	ADJ
ejpam-5744	576	6	integrodifferential	integrodifferential	ADJ
ejpam-5744	576	7	equations	equation	NOUN
ejpam-5744	576	8	with	with	ADP
ejpam-5744	576	9	theoretical	theoretical	ADJ
ejpam-5744	576	10	analysis	analysis	NOUN
ejpam-5744	576	11	via	via	ADP
ejpam-5744	576	12	fixed	fix	VERB
ejpam-5744	576	13	point	point	NOUN
ejpam-5744	576	14	approach	approach	NOUN
ejpam-5744	576	15	:	:	PUNCT
ejpam-5744	576	16	numerical	numerical	ADJ
ejpam-5744	576	17	and	and	CCONJ
ejpam-5744	576	18	exact	exact	ADJ
ejpam-5744	576	19	solutions	solution	NOUN
ejpam-5744	576	20	.	.	PUNCT
ejpam-5744	577	1	j.	j.	PROPN
ejpam-5744	577	2	appl	appl	PROPN
ejpam-5744	577	3	.	.	PROPN
ejpam-5744	578	1	anal	anal	PROPN
ejpam-5744	578	2	.	.	PUNCT
ejpam-5744	579	1	comput	comput	NOUN
ejpam-5744	579	2	.	.	PUNCT
ejpam-5744	579	3	,	,	PUNCT
ejpam-5744	579	4	13(5):2767–2787	13(5):2767–2787	NUM
ejpam-5744	579	5	,	,	PUNCT
ejpam-5744	579	6	2023	2023	NUM
ejpam-5744	579	7	.	.	PUNCT
ejpam-5744	580	1	[	[	X
ejpam-5744	580	2	45	45	NUM
ejpam-5744	580	3	]	]	X
ejpam-5744	580	4	g.	g.	PROPN
ejpam-5744	580	5	stampacchia	stampacchia	PROPN
ejpam-5744	580	6	.	.	PUNCT
ejpam-5744	581	1	formes	forme	NOUN
ejpam-5744	581	2	bilineaires	bilineaire	VERB
ejpam-5744	581	3	coercivites	coercivite	VERB
ejpam-5744	581	4	sur	sur	PROPN
ejpam-5744	581	5	les	le	NOUN
ejpam-5744	581	6	ensembles	ensemble	NOUN
ejpam-5744	581	7	convexes	convexe	NOUN
ejpam-5744	581	8	.	.	PUNCT
ejpam-5744	582	1	comptes	compte	VERB
ejpam-5744	582	2	rendus	rendus	PROPN
ejpam-5744	582	3	de	de	PROPN
ejpam-5744	582	4	l’academie	l’academie	VERB
ejpam-5744	582	5	des	des	PROPN
ejpam-5744	582	6	sciences	sciences	PROPN
ejpam-5744	582	7	,	,	PUNCT
ejpam-5744	582	8	258:4413–4416	258:4413–4416	NUM
ejpam-5744	582	9	,	,	PUNCT
ejpam-5744	582	10	1964	1964	NUM
ejpam-5744	582	11	.	.	PUNCT
ejpam-5744	583	1	[	[	X
ejpam-5744	583	2	46	46	NUM
ejpam-5744	583	3	]	]	X
ejpam-5744	583	4	x.	x.	PROPN
ejpam-5744	583	5	su	su	PROPN
ejpam-5744	583	6	.	.	PROPN
ejpam-5744	583	7	boundary	boundary	ADJ
ejpam-5744	583	8	value	value	NOUN
ejpam-5744	583	9	problem	problem	NOUN
ejpam-5744	583	10	for	for	ADP
ejpam-5744	583	11	a	a	DET
ejpam-5744	583	12	coupled	couple	VERB
ejpam-5744	583	13	system	system	NOUN
ejpam-5744	583	14	of	of	ADP
ejpam-5744	583	15	nonlinear	nonlinear	ADJ
ejpam-5744	583	16	fractional	fractional	ADJ
ejpam-5744	583	17	differential	differential	ADJ
ejpam-5744	583	18	equations	equation	NOUN
ejpam-5744	583	19	.	.	PUNCT
ejpam-5744	584	1	appl	appl	PROPN
ejpam-5744	584	2	.	.	PROPN
ejpam-5744	584	3	math	math	PROPN
ejpam-5744	584	4	.	.	PUNCT
ejpam-5744	585	1	lett	lett	PROPN
ejpam-5744	585	2	.	.	PROPN
ejpam-5744	585	3	,	,	PUNCT
ejpam-5744	585	4	22:64–69	22:64–69	NUM
ejpam-5744	585	5	,	,	PUNCT
ejpam-5744	585	6	2009	2009	NUM
ejpam-5744	585	7	.	.	PUNCT
ejpam-5744	586	1	[	[	X
ejpam-5744	586	2	47	47	NUM
ejpam-5744	586	3	]	]	PUNCT
ejpam-5744	586	4	m.	m.	NOUN
ejpam-5744	586	5	turkyilmazoglu	turkyilmazoglu	PROPN
ejpam-5744	586	6	.	.	PUNCT
ejpam-5744	587	1	approximate	approximate	ADJ
ejpam-5744	587	2	analytical	analytical	ADJ
ejpam-5744	587	3	solution	solution	NOUN
ejpam-5744	587	4	of	of	ADP
ejpam-5744	587	5	the	the	DET
ejpam-5744	587	6	nonlinear	nonlinear	ADJ
ejpam-5744	587	7	system	system	NOUN
ejpam-5744	587	8	of	of	ADP
ejpam-5744	587	9	differential	differential	ADJ
ejpam-5744	587	10	equations	equation	NOUN
ejpam-5744	587	11	having	have	VERB
ejpam-5744	587	12	asymptotically	asymptotically	ADV
ejpam-5744	587	13	stable	stable	ADJ
ejpam-5744	587	14	equilibrium	equilibrium	NOUN
ejpam-5744	587	15	.	.	PUNCT
ejpam-5744	588	1	filomat	filomat	NOUN
ejpam-5744	588	2	,	,	PUNCT
ejpam-5744	588	3	31(9):2633–2641	31(9):2633–2641	NUM
ejpam-5744	588	4	,	,	PUNCT
ejpam-5744	588	5	2017	2017	NUM
ejpam-5744	588	6	.	.	PUNCT
ejpam-5744	589	1	[	[	X
ejpam-5744	589	2	48	48	NUM
ejpam-5744	589	3	]	]	PUNCT
ejpam-5744	589	4	m.	m.	NOUN
ejpam-5744	589	5	turkyilmazoglu	turkyilmazoglu	NOUN
ejpam-5744	589	6	.	.	PUNCT
ejpam-5744	590	1	optimization	optimization	NOUN
ejpam-5744	590	2	by	by	ADP
ejpam-5744	590	3	the	the	DET
ejpam-5744	590	4	convergence	convergence	NOUN
ejpam-5744	590	5	control	control	NOUN
ejpam-5744	590	6	parameter	parameter	NOUN
ejpam-5744	590	7	in	in	ADP
ejpam-5744	590	8	iterative	iterative	ADJ
ejpam-5744	590	9	methods	method	NOUN
ejpam-5744	590	10	.	.	PUNCT
ejpam-5744	591	1	appl	appl	PROPN
ejpam-5744	591	2	.	.	PROPN
ejpam-5744	591	3	math	math	PROPN
ejpam-5744	591	4	.	.	PUNCT
ejpam-5744	592	1	lett	lett	PROPN
ejpam-5744	592	2	.	.	PROPN
ejpam-5744	592	3	,	,	PUNCT
ejpam-5744	592	4	23(2):105–116	23(2):105–116	PROPN
ejpam-5744	592	5	,	,	PUNCT
ejpam-5744	592	6	2024	2024	NUM
ejpam-5744	592	7	.	.	PUNCT
ejpam-5744	593	1	[	[	X
ejpam-5744	593	2	49	49	NUM
ejpam-5744	593	3	]	]	PUNCT
ejpam-5744	593	4	k.	k.	PROPN
ejpam-5744	593	5	ullah	ullah	PROPN
ejpam-5744	593	6	and	and	CCONJ
ejpam-5744	593	7	m.	m.	PROPN
ejpam-5744	593	8	arshad	arshad	PROPN
ejpam-5744	593	9	.	.	PROPN
ejpam-5744	594	1	numerical	numerical	PROPN
ejpam-5744	594	2	reckoning	reckon	VERB
ejpam-5744	594	3	fixed	fix	VERB
ejpam-5744	594	4	points	point	NOUN
ejpam-5744	594	5	for	for	ADP
ejpam-5744	594	6	suzuki	suzuki	PROPN
ejpam-5744	594	7	’s	’s	PART
ejpam-5744	594	8	generalized	generalize	VERB
ejpam-5744	594	9	nonexpansive	nonexpansive	ADJ
ejpam-5744	594	10	mappings	mapping	NOUN
ejpam-5744	594	11	via	via	ADP
ejpam-5744	594	12	new	new	ADJ
ejpam-5744	594	13	iteration	iteration	NOUN
ejpam-5744	594	14	process	process	NOUN
ejpam-5744	594	15	.	.	PUNCT
ejpam-5744	595	1	filomat	filomat	NOUN
ejpam-5744	595	2	,	,	PUNCT
ejpam-5744	595	3	32:187–196	32:187–196	NUM
ejpam-5744	595	4	,	,	PUNCT
ejpam-5744	595	5	2018	2018	NUM
ejpam-5744	595	6	.	.	PUNCT
ejpam-5744	596	1	[	[	X
ejpam-5744	596	2	50	50	NUM
ejpam-5744	596	3	]	]	PUNCT
ejpam-5744	596	4	x.	x.	NOUN
ejpam-5744	596	5	weng	weng	PROPN
ejpam-5744	596	6	.	.	PUNCT
ejpam-5744	597	1	fixed	fix	VERB
ejpam-5744	597	2	point	point	NOUN
ejpam-5744	597	3	iteration	iteration	NOUN
ejpam-5744	597	4	for	for	ADP
ejpam-5744	597	5	local	local	ADJ
ejpam-5744	597	6	strictly	strictly	ADV
ejpam-5744	597	7	pseudo	pseudo	ADJ
ejpam-5744	597	8	-	-	ADJ
ejpam-5744	597	9	contractive	contractive	ADJ
ejpam-5744	597	10	mappings	mapping	NOUN
ejpam-5744	597	11	.	.	PUNCT
ejpam-5744	598	1	proc	proc	NOUN
ejpam-5744	598	2	.	.	PUNCT
ejpam-5744	599	1	amer	amer	PROPN
ejpam-5744	599	2	.	.	PUNCT
ejpam-5744	599	3	math	math	PROPN
ejpam-5744	599	4	.	.	PUNCT
ejpam-5744	600	1	soc	soc	PROPN
ejpam-5744	600	2	.	.	PUNCT
ejpam-5744	600	3	,	,	PUNCT
ejpam-5744	600	4	113:727–731	113:727–731	NUM
ejpam-5744	600	5	,	,	PUNCT
ejpam-5744	600	6	1991	1991	NUM
ejpam-5744	600	7	.	.	PUNCT
ejpam-5744	601	1	[	[	X
ejpam-5744	601	2	51	51	NUM
ejpam-5744	601	3	]	]	X
ejpam-5744	601	4	n.	n.	PROPN
ejpam-5744	601	5	shahzad	shahzad	PROPN
ejpam-5744	601	6	y.	y.	PROPN
ejpam-5744	601	7	yao	yao	PROPN
ejpam-5744	601	8	and	and	CCONJ
ejpam-5744	601	9	y.c	y.c	PROPN
ejpam-5744	601	10	.	.	PROPN
ejpam-5744	601	11	liou	liou	NOUN
ejpam-5744	601	12	.	.	PUNCT
ejpam-5744	602	1	modified	modify	VERB
ejpam-5744	602	2	semi	semi	ADJ
ejpam-5744	602	3	-	-	ADJ
ejpam-5744	602	4	implicit	implicit	ADJ
ejpam-5744	602	5	midpoint	midpoint	NOUN
ejpam-5744	602	6	rule	rule	NOUN
ejpam-5744	602	7	for	for	ADP
ejpam-5744	602	8	nonexpansive	nonexpansive	ADJ
ejpam-5744	602	9	mappings	mapping	NOUN
ejpam-5744	602	10	.	.	PUNCT
ejpam-5744	603	1	fixed	fix	VERB
ejpam-5744	603	2	point	point	NOUN
ejpam-5744	603	3	theory	theory	NOUN
ejpam-5744	603	4	appl	appl	PROPN
ejpam-5744	603	5	.	.	PROPN
ejpam-5744	603	6	,	,	PUNCT
ejpam-5744	603	7	2015	2015	NUM
ejpam-5744	603	8	.	.	PUNCT
ejpam-5744	604	1	doi	doi	NOUN
ejpam-5744	604	2	:	:	PUNCT
ejpam-5744	604	3	10.1186	10.1186	NUM
ejpam-5744	604	4	/	/	SYM
ejpam-5744	604	5	s13663	s13663	PROPN
ejpam-5744	604	6	-	-	PUNCT
ejpam-5744	604	7	015	015	NUM
ejpam-5744	604	8	-	-	PUNCT
ejpam-5744	604	9	0414	0414	NUM
ejpam-5744	604	10	-	-	SYM
ejpam-5744	604	11	2	2	NUM
ejpam-5744	604	12	.	.	PUNCT
ejpam-5744	605	1	[	[	X
ejpam-5744	605	2	52	52	NUM
ejpam-5744	605	3	]	]	PUNCT
ejpam-5744	605	4	j.	j.	PROPN
ejpam-5744	605	5	yu	yu	PROPN
ejpam-5744	605	6	and	and	CCONJ
ejpam-5744	605	7	y.	y.	PROPN
ejpam-5744	605	8	feng	feng	PROPN
ejpam-5744	605	9	.	.	PUNCT
ejpam-5744	606	1	symmetry	symmetry	NOUN
ejpam-5744	606	2	analysis	analysis	NOUN
ejpam-5744	606	3	,	,	PUNCT
ejpam-5744	606	4	optimal	optimal	ADJ
ejpam-5744	606	5	system	system	NOUN
ejpam-5744	606	6	,	,	PUNCT
ejpam-5744	606	7	conservation	conservation	NOUN
ejpam-5744	606	8	laws	law	NOUN
ejpam-5744	606	9	and	and	CCONJ
ejpam-5744	606	10	exact	exact	ADJ
ejpam-5744	606	11	solutions	solution	NOUN
ejpam-5744	606	12	of	of	ADP
ejpam-5744	606	13	time	time	NOUN
ejpam-5744	606	14	fractional	fractional	ADJ
ejpam-5744	606	15	diffusion	diffusion	NOUN
ejpam-5744	606	16	-	-	PUNCT
ejpam-5744	606	17	type	type	NOUN
ejpam-5744	606	18	equation	equation	NOUN
ejpam-5744	606	19	.	.	PUNCT
ejpam-5744	607	1	int	int	NOUN
ejpam-5744	607	2	.	.	PUNCT
ejpam-5744	608	1	j.	j.	PROPN
ejpam-5744	608	2	geom	geom	PROPN
ejpam-5744	608	3	.	.	PUNCT
ejpam-5744	609	1	methods	methods	PROPN
ejpam-5744	609	2	mod	mod	PROPN
ejpam-5744	609	3	.	.	PUNCT
ejpam-5744	610	1	phys	phy	NOUN
ejpam-5744	610	2	.	.	PUNCT
ejpam-5744	610	3	,	,	PUNCT
ejpam-5744	610	4	2024	2024	NUM
ejpam-5744	610	5	.	.	PUNCT
ejpam-5744	611	1	doi	doi	NOUN
ejpam-5744	611	2	:	:	PUNCT
ejpam-5744	611	3	10.1142	10.1142	NUM
ejpam-5744	611	4	/	/	SYM
ejpam-5744	611	5	s0219887824502864	s0219887824502864	NOUN
ejpam-5744	611	6	.	.	PUNCT
ejpam-5744	612	1	[	[	X
ejpam-5744	612	2	53	53	NUM
ejpam-5744	612	3	]	]	PUNCT
ejpam-5744	612	4	j.	j.	PROPN
ejpam-5744	612	5	yu	yu	PROPN
ejpam-5744	612	6	and	and	CCONJ
ejpam-5744	612	7	y.	y.	PROPN
ejpam-5744	612	8	feng	feng	PROPN
ejpam-5744	612	9	.	.	PUNCT
ejpam-5744	613	1	on	on	ADP
ejpam-5744	613	2	the	the	DET
ejpam-5744	613	3	generalized	generalized	ADJ
ejpam-5744	613	4	time	time	NOUN
ejpam-5744	613	5	fractional	fractional	ADJ
ejpam-5744	613	6	reaction	reaction	NOUN
ejpam-5744	613	7	-	-	PUNCT
ejpam-5744	613	8	diffusion	diffusion	NOUN
ejpam-5744	613	9	equation	equation	NOUN
ejpam-5744	613	10	:	:	PUNCT
ejpam-5744	613	11	lie	lie	NOUN
ejpam-5744	613	12	symmetries	symmetry	NOUN
ejpam-5744	613	13	,	,	PUNCT
ejpam-5744	613	14	exact	exact	ADJ
ejpam-5744	613	15	solutions	solution	NOUN
ejpam-5744	613	16	and	and	CCONJ
ejpam-5744	613	17	conservation	conservation	NOUN
ejpam-5744	613	18	laws	law	NOUN
ejpam-5744	613	19	.	.	PUNCT
ejpam-5744	614	1	chaos	chaos	NOUN
ejpam-5744	614	2	solit	solit	NOUN
ejpam-5744	614	3	.	.	PUNCT
ejpam-5744	615	1	fractals	fractal	NOUN
ejpam-5744	615	2	,	,	PUNCT
ejpam-5744	615	3	182	182	NUM
ejpam-5744	615	4	,	,	PUNCT
ejpam-5744	615	5	2024	2024	NUM
ejpam-5744	615	6	.	.	PUNCT
ejpam-5744	616	1	doi	doi	NOUN
ejpam-5744	616	2	:	:	PUNCT
ejpam-5744	616	3	10.1016	10.1016	NUM
ejpam-5744	616	4	/	/	SYM
ejpam-5744	616	5	j.chaos.2024.114855	j.chaos.2024.114855	NOUN
ejpam-5744	616	6	.	.	PUNCT