id	sid	tid	token	lemma	pos
iajs-2923	1	1	ihjpas	ihjpas	PROPN
iajs-2923	1	2	.	.	PUNCT
iajs-2923	2	1	36(1)2023	36(1)2023	NUM
iajs-2923	2	2	292	292	NUM
iajs-2923	2	3	this	this	DET
iajs-2923	2	4	work	work	NOUN
iajs-2923	2	5	is	be	AUX
iajs-2923	2	6	licensed	license	VERB
iajs-2923	2	7	under	under	ADP
iajs-2923	2	8	a	a	DET
iajs-2923	2	9	creative	creative	ADJ
iajs-2923	2	10	commons	common	NOUN
iajs-2923	2	11	attribution	attribution	NOUN
iajs-2923	2	12	4.0	4.0	NUM
iajs-2923	2	13	international	international	ADJ
iajs-2923	2	14	license	license	NOUN
iajs-2923	2	15	on	on	ADP
iajs-2923	2	16	the	the	DET
iajs-2923	2	17	stability	stability	NOUN
iajs-2923	2	18	and	and	CCONJ
iajs-2923	2	19	acceleration	acceleration	NOUN
iajs-2923	2	20	of	of	ADP
iajs-2923	2	21	projection	projection	NOUN
iajs-2923	2	22	algorithms	algorithm	NOUN
iajs-2923	2	23	abstract	abstract	VERB
iajs-2923	2	24	the	the	DET
iajs-2923	2	25	focus	focus	NOUN
iajs-2923	2	26	of	of	ADP
iajs-2923	2	27	this	this	DET
iajs-2923	2	28	paper	paper	NOUN
iajs-2923	2	29	is	be	AUX
iajs-2923	2	30	the	the	DET
iajs-2923	2	31	presentation	presentation	NOUN
iajs-2923	2	32	of	of	ADP
iajs-2923	2	33	a	a	DET
iajs-2923	2	34	new	new	ADJ
iajs-2923	2	35	type	type	NOUN
iajs-2923	2	36	of	of	ADP
iajs-2923	2	37	mapping	mapping	NOUN
iajs-2923	2	38	called	call	VERB
iajs-2923	2	39	projection	projection	NOUN
iajs-2923	2	40	jungck	jungck	PROPN
iajs-2923	2	41	znsuzuki	znsuzuki	PROPN
iajs-2923	2	42	generalized	generalize	VERB
iajs-2923	2	43	and	and	CCONJ
iajs-2923	2	44	also	also	ADV
iajs-2923	2	45	defining	define	VERB
iajs-2923	2	46	new	new	ADJ
iajs-2923	2	47	algorithms	algorithm	NOUN
iajs-2923	2	48	of	of	ADP
iajs-2923	2	49	various	various	ADJ
iajs-2923	2	50	types	type	NOUN
iajs-2923	2	51	(	(	PUNCT
iajs-2923	2	52	one	one	NUM
iajs-2923	2	53	-	-	PUNCT
iajs-2923	2	54	step	step	NOUN
iajs-2923	2	55	and	and	CCONJ
iajs-2923	2	56	two	two	NUM
iajs-2923	2	57	-	-	PUNCT
iajs-2923	2	58	step	step	NOUN
iajs-2923	2	59	algorithms	algorithm	NOUN
iajs-2923	2	60	)	)	PUNCT
iajs-2923	2	61	(	(	PUNCT
iajs-2923	2	62	projection	projection	NOUN
iajs-2923	2	63	jungck	jungck	NOUN
iajs-2923	2	64	-	-	PUNCT
iajs-2923	2	65	normal	normal	ADJ
iajs-2923	2	66	𝒩	𝒩	PROPN
iajs-2923	2	67	algorithm	algorithm	NOUN
iajs-2923	2	68	,	,	PUNCT
iajs-2923	2	69	projection	projection	NOUN
iajs-2923	2	70	jungck	jungck	NOUN
iajs-2923	2	71	-	-	PUNCT
iajs-2923	2	72	picard	picard	NOUN
iajs-2923	2	73	algorithm	algorithm	NOUN
iajs-2923	2	74	,	,	PUNCT
iajs-2923	2	75	projection	projection	NOUN
iajs-2923	2	76	jungck	jungck	PROPN
iajs-2923	2	77	-	-	PUNCT
iajs-2923	2	78	krasnoselskii	krasnoselskii	PROPN
iajs-2923	2	79	algorithm	algorithm	NOUN
iajs-2923	2	80	,	,	PUNCT
iajs-2923	2	81	and	and	CCONJ
iajs-2923	2	82	projection	projection	PROPN
iajs-2923	2	83	jungck	jungck	PROPN
iajs-2923	2	84	-	-	PUNCT
iajs-2923	2	85	thianwan	thianwan	PROPN
iajs-2923	2	86	algorithm	algorithm	PROPN
iajs-2923	2	87	)	)	PUNCT
iajs-2923	2	88	.	.	PUNCT
iajs-2923	3	1	the	the	DET
iajs-2923	3	2	convergence	convergence	NOUN
iajs-2923	3	3	of	of	ADP
iajs-2923	3	4	these	these	DET
iajs-2923	3	5	algorithms	algorithm	NOUN
iajs-2923	3	6	has	have	AUX
iajs-2923	3	7	been	be	AUX
iajs-2923	3	8	studied	study	VERB
iajs-2923	3	9	,	,	PUNCT
iajs-2923	3	10	and	and	CCONJ
iajs-2923	3	11	it	it	PRON
iajs-2923	3	12	was	be	AUX
iajs-2923	3	13	discovered	discover	VERB
iajs-2923	3	14	that	that	SCONJ
iajs-2923	3	15	they	they	PRON
iajs-2923	3	16	all	all	PRON
iajs-2923	3	17	converge	converge	VERB
iajs-2923	3	18	to	to	ADP
iajs-2923	3	19	a	a	DET
iajs-2923	3	20	fixed	fix	VERB
iajs-2923	3	21	point	point	NOUN
iajs-2923	3	22	.	.	PUNCT
iajs-2923	4	1	furthermore	furthermore	ADV
iajs-2923	4	2	,	,	PUNCT
iajs-2923	4	3	using	use	VERB
iajs-2923	4	4	the	the	DET
iajs-2923	4	5	previous	previous	ADJ
iajs-2923	4	6	three	three	NUM
iajs-2923	4	7	conditions	condition	NOUN
iajs-2923	4	8	for	for	ADP
iajs-2923	4	9	the	the	DET
iajs-2923	4	10	lemma	lemma	PROPN
iajs-2923	4	11	,	,	PUNCT
iajs-2923	4	12	we	we	PRON
iajs-2923	4	13	demonstrated	demonstrate	VERB
iajs-2923	4	14	that	that	SCONJ
iajs-2923	4	15	the	the	DET
iajs-2923	4	16	difference	difference	NOUN
iajs-2923	4	17	between	between	ADP
iajs-2923	4	18	any	any	DET
iajs-2923	4	19	two	two	NUM
iajs-2923	4	20	sequences	sequence	NOUN
iajs-2923	4	21	is	be	AUX
iajs-2923	4	22	zero	zero	NUM
iajs-2923	4	23	.	.	PUNCT
iajs-2923	5	1	these	these	DET
iajs-2923	5	2	algorithms	algorithm	NOUN
iajs-2923	5	3	'	'	PART
iajs-2923	5	4	stability	stability	NOUN
iajs-2923	5	5	was	be	AUX
iajs-2923	5	6	demonstrated	demonstrate	VERB
iajs-2923	5	7	using	use	VERB
iajs-2923	5	8	projection	projection	NOUN
iajs-2923	5	9	jungck	jungck	PROPN
iajs-2923	5	10	suzuki	suzuki	PROPN
iajs-2923	5	11	generalized	generalize	VERB
iajs-2923	5	12	mapping	mapping	NOUN
iajs-2923	5	13	.	.	PUNCT
iajs-2923	6	1	in	in	ADP
iajs-2923	6	2	contrast	contrast	NOUN
iajs-2923	6	3	,	,	PUNCT
iajs-2923	6	4	the	the	DET
iajs-2923	6	5	rate	rate	NOUN
iajs-2923	6	6	of	of	ADP
iajs-2923	6	7	convergence	convergence	NOUN
iajs-2923	6	8	of	of	ADP
iajs-2923	6	9	these	these	DET
iajs-2923	6	10	algorithms	algorithm	NOUN
iajs-2923	6	11	was	be	AUX
iajs-2923	6	12	demonstrated	demonstrate	VERB
iajs-2923	6	13	by	by	ADP
iajs-2923	6	14	contrasting	contrast	VERB
iajs-2923	6	15	the	the	DET
iajs-2923	6	16	rates	rate	NOUN
iajs-2923	6	17	of	of	ADP
iajs-2923	6	18	convergence	convergence	NOUN
iajs-2923	6	19	of	of	ADP
iajs-2923	6	20	the	the	DET
iajs-2923	6	21	various	various	ADJ
iajs-2923	6	22	algorithms	algorithm	NOUN
iajs-2923	6	23	,	,	PUNCT
iajs-2923	6	24	leading	lead	VERB
iajs-2923	6	25	us	we	PRON
iajs-2923	6	26	to	to	PART
iajs-2923	6	27	conclude	conclude	VERB
iajs-2923	6	28	that	that	SCONJ
iajs-2923	6	29	the	the	DET
iajs-2923	6	30	projection	projection	NOUN
iajs-2923	6	31	jungck	jungck	NOUN
iajs-2923	6	32	-	-	PUNCT
iajs-2923	6	33	normal	normal	ADJ
iajs-2923	6	34	𝒩	𝒩	PROPN
iajs-2923	6	35	algorithm	algorithm	NOUN
iajs-2923	6	36	is	be	AUX
iajs-2923	6	37	the	the	DET
iajs-2923	6	38	fastest	fast	ADJ
iajs-2923	6	39	of	of	ADP
iajs-2923	6	40	all	all	DET
iajs-2923	6	41	the	the	DET
iajs-2923	6	42	algorithms	algorithm	NOUN
iajs-2923	6	43	mentioned	mention	VERB
iajs-2923	6	44	above	above	ADV
iajs-2923	6	45	.	.	PUNCT
iajs-2923	7	1	keywords	keyword	NOUN
iajs-2923	7	2	:	:	PUNCT
iajs-2923	7	3	metric	metric	ADJ
iajs-2923	7	4	projection	projection	NOUN
iajs-2923	7	5	,	,	PUNCT
iajs-2923	7	6	jungck	jungck	NOUN
iajs-2923	7	7	-	-	PUNCT
iajs-2923	7	8	picard	picard	NOUN
iajs-2923	7	9	algorithm	algorithm	NOUN
iajs-2923	7	10	,	,	PUNCT
iajs-2923	7	11	jungck	jungck	NOUN
iajs-2923	7	12	-	-	PUNCT
iajs-2923	7	13	normal	normal	ADJ
iajs-2923	7	14	𝒩	𝒩	PROPN
iajs-2923	7	15	algorithm	algorithm	NOUN
iajs-2923	7	16	,	,	PUNCT
iajs-2923	7	17	jungckthianwan	jungckthianwan	PROPN
iajs-2923	7	18	algorithm	algorithm	NOUN
iajs-2923	7	19	,	,	PUNCT
iajs-2923	7	20	jungck	jungck	NOUN
iajs-2923	7	21	-	-	PUNCT
iajs-2923	7	22	krasnoselskii	krasnoselskii	PROPN
iajs-2923	7	23	algorithm	algorithm	NOUN
iajs-2923	7	24	,	,	PUNCT
iajs-2923	7	25	fixed	fix	VERB
iajs-2923	7	26	point	point	NOUN
iajs-2923	7	27	.	.	PUNCT
iajs-2923	8	1	1.introduction	1.introduction	NUM
iajs-2923	8	2	and	and	CCONJ
iajs-2923	8	3	preliminary	preliminary	ADJ
iajs-2923	8	4	there	there	PRON
iajs-2923	8	5	are	be	VERB
iajs-2923	8	6	a	a	DET
iajs-2923	8	7	lot	lot	NOUN
iajs-2923	8	8	of	of	ADP
iajs-2923	8	9	published	publish	VERB
iajs-2923	8	10	studies	study	NOUN
iajs-2923	8	11	that	that	PRON
iajs-2923	8	12	included	include	VERB
iajs-2923	8	13	new	new	ADJ
iajs-2923	8	14	algorithms	algorithm	NOUN
iajs-2923	8	15	and	and	CCONJ
iajs-2923	8	16	studied	study	VERB
iajs-2923	8	17	their	their	PRON
iajs-2923	8	18	strong	strong	ADJ
iajs-2923	8	19	convergence	convergence	NOUN
iajs-2923	8	20	and	and	CCONJ
iajs-2923	8	21	stability	stability	NOUN
iajs-2923	8	22	.	.	PUNCT
iajs-2923	9	1	in	in	ADP
iajs-2923	9	2	addition	addition	NOUN
iajs-2923	9	3	,	,	PUNCT
iajs-2923	9	4	they	they	PRON
iajs-2923	9	5	proved	prove	VERB
iajs-2923	9	6	the	the	DET
iajs-2923	9	7	rate	rate	NOUN
iajs-2923	9	8	of	of	ADP
iajs-2923	9	9	convergence	convergence	NOUN
iajs-2923	9	10	of	of	ADP
iajs-2923	9	11	these	these	DET
iajs-2923	9	12	algorithms	algorithm	NOUN
iajs-2923	9	13	,	,	PUNCT
iajs-2923	9	14	see	see	VERB
iajs-2923	9	15	[	[	X
iajs-2923	9	16	1	1	NUM
iajs-2923	9	17	-	-	SYM
iajs-2923	9	18	9	9	NUM
iajs-2923	9	19	]	]	PUNCT
iajs-2923	9	20	.	.	PUNCT
iajs-2923	10	1	these	these	DET
iajs-2923	10	2	algorithms	algorithm	NOUN
iajs-2923	10	3	are	be	AUX
iajs-2923	10	4	valuable	valuable	ADJ
iajs-2923	10	5	tools	tool	NOUN
iajs-2923	10	6	used	use	VERB
iajs-2923	10	7	to	to	PART
iajs-2923	10	8	find	find	VERB
iajs-2923	10	9	the	the	DET
iajs-2923	10	10	value	value	NOUN
iajs-2923	10	11	of	of	ADP
iajs-2923	10	12	the	the	DET
iajs-2923	10	13	fixed	fix	VERB
iajs-2923	10	14	point	point	NOUN
iajs-2923	10	15	and	and	CCONJ
iajs-2923	10	16	to	to	PART
iajs-2923	10	17	resolve	resolve	VERB
iajs-2923	10	18	some	some	DET
iajs-2923	10	19	problems	problem	NOUN
iajs-2923	10	20	.	.	PUNCT
iajs-2923	11	1	for	for	ADP
iajs-2923	11	2	example	example	NOUN
iajs-2923	11	3	,	,	PUNCT
iajs-2923	11	4	they	they	PRON
iajs-2923	11	5	were	be	AUX
iajs-2923	11	6	used	use	VERB
iajs-2923	11	7	in	in	ADP
iajs-2923	11	8	solving	solve	VERB
iajs-2923	11	9	nonlinear	nonlinear	ADJ
iajs-2923	11	10	differential	differential	ADJ
iajs-2923	11	11	equations	equation	NOUN
iajs-2923	11	12	,	,	PUNCT
iajs-2923	11	13	integration	integration	NOUN
iajs-2923	11	14	problems	problem	NOUN
iajs-2923	11	15	,	,	PUNCT
iajs-2923	11	16	etc	etc	X
iajs-2923	11	17	.	.	X
iajs-2923	12	1	the	the	DET
iajs-2923	12	2	algorithms	algorithm	NOUN
iajs-2923	12	3	presented	present	VERB
iajs-2923	12	4	by	by	ADP
iajs-2923	12	5	the	the	DET
iajs-2923	12	6	authors	author	NOUN
iajs-2923	12	7	are	be	AUX
iajs-2923	12	8	varied	varied	ADJ
iajs-2923	12	9	(	(	PUNCT
iajs-2923	12	10	one	one	NUM
iajs-2923	12	11	-	-	PUNCT
iajs-2923	12	12	step	step	NOUN
iajs-2923	12	13	,	,	PUNCT
iajs-2923	12	14	two	two	NUM
iajs-2923	12	15	-	-	PUNCT
iajs-2923	12	16	step	step	NOUN
iajs-2923	12	17	,	,	PUNCT
iajs-2923	12	18	etc	etc	X
iajs-2923	12	19	.	.	X
iajs-2923	12	20	)	)	PUNCT
iajs-2923	12	21	.	.	PUNCT
iajs-2923	13	1	in	in	ADP
iajs-2923	13	2	1967[10	1967[10	NUM
iajs-2923	13	3	]	]	PUNCT
iajs-2923	13	4	,	,	PUNCT
iajs-2923	13	5	scientist	scientist	NOUN
iajs-2923	13	6	jungck	jungck	PROPN
iajs-2923	13	7	introduced	introduce	VERB
iajs-2923	13	8	a	a	DET
iajs-2923	13	9	new	new	ADJ
iajs-2923	13	10	algorithm	algorithm	NOUN
iajs-2923	13	11	called	call	VERB
iajs-2923	13	12	jungck	jungck	PROPN
iajs-2923	13	13	picard	picard	PROPN
iajs-2923	13	14	algorithm	algorithm	PROPN
iajs-2923	13	15	,	,	PUNCT
iajs-2923	13	16	but	but	CCONJ
iajs-2923	13	17	sometimes	sometimes	ADV
iajs-2923	13	18	it	it	PRON
iajs-2923	13	19	is	be	AUX
iajs-2923	13	20	called	call	VERB
iajs-2923	13	21	jungck	jungck	NOUN
iajs-2923	13	22	algorithm	algorithm	NOUN
iajs-2923	13	23	,	,	PUNCT
iajs-2923	13	24	as	as	SCONJ
iajs-2923	13	25	it	it	PRON
iajs-2923	13	26	consists	consist	VERB
iajs-2923	13	27	of	of	ADP
iajs-2923	13	28	one	one	NUM
iajs-2923	13	29	step	step	NOUN
iajs-2923	13	30	doi	doi	NOUN
iajs-2923	13	31	,	,	PUNCT
iajs-2923	13	32	org/10.30526/36.1.2923	org/10.30526/36.1.2923	NOUN
iajs-2923	13	33	article	article	NOUN
iajs-2923	13	34	history	history	NOUN
iajs-2923	13	35	:	:	PUNCT
iajs-2923	13	36	received	receive	VERB
iajs-2923	13	37	29	29	NUM
iajs-2923	13	38	june	june	PROPN
iajs-2923	13	39	2022	2022	NUM
iajs-2923	13	40	,	,	PUNCT
iajs-2923	13	41	accepted	accept	VERB
iajs-2923	13	42	21	21	NUM
iajs-2923	13	43	augest	augest	NOUN
iajs-2923	13	44	2022	2022	NUM
iajs-2923	13	45	,	,	PUNCT
iajs-2923	13	46	published	publish	VERB
iajs-2923	13	47	in	in	ADP
iajs-2923	13	48	january	january	PROPN
iajs-2923	13	49	2023	2023	NUM
iajs-2923	13	50	.	.	PUNCT
iajs-2923	14	1	ibn	ibn	PROPN
iajs-2923	14	2	al	al	PROPN
iajs-2923	14	3	-	-	PUNCT
iajs-2923	14	4	haitham	haitham	PROPN
iajs-2923	14	5	journal	journal	PROPN
iajs-2923	14	6	for	for	ADP
iajs-2923	14	7	pure	pure	ADJ
iajs-2923	14	8	and	and	CCONJ
iajs-2923	14	9	applied	applied	ADJ
iajs-2923	14	10	sciences	sciences	PROPN
iajs-2923	14	11	journal	journal	PROPN
iajs-2923	14	12	homepage	homepage	NOUN
iajs-2923	14	13	:	:	PUNCT
iajs-2923	14	14	jih.uobaghdad.edu.iq	jih.uobaghdad.edu.iq	NOUN
iajs-2923	14	15	zena	zena	PROPN
iajs-2923	14	16	hussein	hussein	PROPN
iajs-2923	14	17	maibed	maibed	PROPN
iajs-2923	14	18	department	department	PROPN
iajs-2923	14	19	of	of	ADP
iajs-2923	14	20	mathematics	mathematics	PROPN
iajs-2923	14	21	,	,	PUNCT
iajs-2923	14	22	college	college	NOUN
iajs-2923	14	23	of	of	ADP
iajs-2923	14	24	education	education	NOUN
iajs-2923	14	25	for	for	ADP
iajs-2923	14	26	pure	pure	ADJ
iajs-2923	14	27	sciences	science	NOUN
iajs-2923	14	28	,	,	PUNCT
iajs-2923	14	29	ibn	ibn	PROPN
iajs-2923	14	30	al	al	PROPN
iajs-2923	14	31	–	–	PUNCT
iajs-2923	14	32	haitham/	haitham/	NUM
iajs-2923	14	33	university	university	NOUN
iajs-2923	14	34	of	of	ADP
iajs-2923	14	35	baghdadiraq	baghdadiraq	PROPN
iajs-2923	14	36	.	.	PUNCT
iajs-2923	15	1	mrs	mrs	PROPN
iajs-2923	15	2	_	_	PROPN
iajs-2923	15	3	zena.hussein@yahoo.com	zena.hussein@yahoo.com	X
iajs-2923	15	4	noor	noor	PROPN
iajs-2923	15	5	nabil	nabil	PROPN
iajs-2923	15	6	salem	salem	PROPN
iajs-2923	15	7	department	department	PROPN
iajs-2923	15	8	of	of	ADP
iajs-2923	15	9	mathematics	mathematics	PROPN
iajs-2923	15	10	,	,	PUNCT
iajs-2923	15	11	college	college	NOUN
iajs-2923	15	12	of	of	ADP
iajs-2923	15	13	education	education	NOUN
iajs-2923	15	14	for	for	ADP
iajs-2923	15	15	pure	pure	ADJ
iajs-2923	15	16	sciences	science	NOUN
iajs-2923	15	17	,	,	PUNCT
iajs-2923	15	18	ibn	ibn	PROPN
iajs-2923	15	19	al	al	PROPN
iajs-2923	15	20	–	–	PUNCT
iajs-2923	15	21	haitham/	haitham/	NUM
iajs-2923	15	22	university	university	NOUN
iajs-2923	15	23	of	of	ADP
iajs-2923	15	24	baghdadiraq	baghdadiraq	PROPN
iajs-2923	15	25	.	.	PUNCT
iajs-2923	16	1	nour.nabeel1203a@ihcoedu.uobaghdad.edu.iq	nour.nabeel1203a@ihcoedu.uobaghdad.edu.iq	PROPN
iajs-2923	16	2	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-2923	17	1	about	about	ADP
iajs-2923	17	2	:	:	PUNCT
iajs-2923	17	3	blank	blank	ADJ
iajs-2923	17	4	mailto:nour.nabeel1203a@ihcoedu.uobaghdad.edu.iq	mailto:nour.nabeel1203a@ihcoedu.uobaghdad.edu.iq	NOUN
iajs-2923	17	5	ihjpas	ihjpas	PROPN
iajs-2923	17	6	.	.	PUNCT
iajs-2923	18	1	36(1)2023	36(1)2023	NUM
iajs-2923	18	2	293	293	NUM
iajs-2923	18	3	ψ𝑘𝑛+1	ψ𝑘𝑛+1	PROPN
iajs-2923	18	4	=	=	SYM
iajs-2923	18	5	𝑇𝑘𝑛	𝑇𝑘𝑛	PROPN
iajs-2923	18	6	,	,	PUNCT
iajs-2923	18	7	where	where	SCONJ
iajs-2923	18	8	𝑘0	𝑘0	PROPN
iajs-2923	18	9	∈	∈	PROPN
iajs-2923	18	10	c	c	NOUN
iajs-2923	18	11	,	,	PUNCT
iajs-2923	18	12	𝑛	𝑛	DET
iajs-2923	18	13	∈	∈	PROPN
iajs-2923	18	14	ℕ.	ℕ.	PROPN
iajs-2923	18	15	in	in	ADP
iajs-2923	18	16	2011[11	2011[11	NUM
iajs-2923	18	17	]	]	PUNCT
iajs-2923	18	18	,	,	PUNCT
iajs-2923	18	19	the	the	DET
iajs-2923	18	20	author	author	NOUN
iajs-2923	18	21	alfred	alfred	PROPN
iajs-2923	18	22	olufemi	olufemi	PROPN
iajs-2923	18	23	bosede	bosede	PROPN
iajs-2923	18	24	presented	present	VERB
iajs-2923	18	25	an	an	DET
iajs-2923	18	26	algorithm	algorithm	NOUN
iajs-2923	18	27	called	call	VERB
iajs-2923	18	28	jungck	jungck	PROPN
iajs-2923	18	29	-	-	PUNCT
iajs-2923	18	30	krasnoselskii	krasnoselskii	PROPN
iajs-2923	18	31	.	.	PUNCT
iajs-2923	19	1	this	this	DET
iajs-2923	19	2	algorithm	algorithm	NOUN
iajs-2923	19	3	is	be	AUX
iajs-2923	19	4	a	a	DET
iajs-2923	19	5	special	special	ADJ
iajs-2923	19	6	case	case	NOUN
iajs-2923	19	7	of	of	ADP
iajs-2923	19	8	jungck	jungck	NOUN
iajs-2923	19	9	-	-	PUNCT
iajs-2923	19	10	mann	mann	PROPN
iajs-2923	19	11	.	.	PUNCT
iajs-2923	20	1	the	the	DET
iajs-2923	20	2	jungck	jungck	PROPN
iajs-2923	20	3	-	-	PUNCT
iajs-2923	20	4	krasnoselskii	krasnoselskii	PROPN
iajs-2923	20	5	algorithm	algorithm	NOUN
iajs-2923	20	6	is	be	AUX
iajs-2923	20	7	defined	define	VERB
iajs-2923	20	8	as	as	SCONJ
iajs-2923	20	9	follows	follow	VERB
iajs-2923	20	10	:	:	PUNCT
iajs-2923	21	1	ψ𝑛𝑛+1	ψ𝑛𝑛+1	NUM
iajs-2923	21	2	=	=	SYM
iajs-2923	21	3	(	(	PUNCT
iajs-2923	21	4	1	1	NUM
iajs-2923	21	5	−	−	PROPN
iajs-2923	21	6	𝛿)ψ𝑛𝑛	𝛿)ψ𝑛𝑛	NOUN
iajs-2923	21	7	+	+	CCONJ
iajs-2923	21	8	𝛿	𝛿	DET
iajs-2923	21	9	𝑇𝑛𝑛	𝑇𝑛𝑛	NOUN
iajs-2923	21	10	,	,	PUNCT
iajs-2923	21	11	where	where	SCONJ
iajs-2923	21	12	𝑛0	𝑛0	VERB
iajs-2923	21	13	∈	∈	PROPN
iajs-2923	21	14	c	c	NOUN
iajs-2923	21	15	,	,	PUNCT
iajs-2923	21	16	𝑛	𝑛	PROPN
iajs-2923	21	17	∈	∈	PROPN
iajs-2923	21	18	ℕ	ℕ	PROPN
iajs-2923	21	19	,	,	PUNCT
iajs-2923	21	20	and	and	CCONJ
iajs-2923	21	21	𝛿	𝛿	PRON
iajs-2923	21	22	∈	∈	PROPN
iajs-2923	21	23	(	(	PUNCT
iajs-2923	21	24	0,1).he	0,1).he	ADV
iajs-2923	21	25	also	also	ADV
iajs-2923	21	26	proved	prove	VERB
iajs-2923	21	27	the	the	DET
iajs-2923	21	28	stability	stability	NOUN
iajs-2923	21	29	of	of	ADP
iajs-2923	21	30	jungck	jungck	PROPN
iajs-2923	21	31	-	-	PUNCT
iajs-2923	21	32	mann	mann	PROPN
iajs-2923	21	33	and	and	CCONJ
iajs-2923	21	34	jungck	jungck	NOUN
iajs-2923	21	35	-	-	PUNCT
iajs-2923	21	36	krasnoselskii	krasnoselskii	PROPN
iajs-2923	21	37	algorithms	algorithm	NOUN
iajs-2923	21	38	.	.	PUNCT
iajs-2923	22	1	on	on	ADP
iajs-2923	22	2	the	the	DET
iajs-2923	22	3	other	other	ADJ
iajs-2923	22	4	hand	hand	NOUN
iajs-2923	22	5	,	,	PUNCT
iajs-2923	22	6	v.	v.	ADP
iajs-2923	22	7	brined	brine	VERB
iajs-2923	22	8	proved	prove	VERB
iajs-2923	22	9	in	in	ADP
iajs-2923	22	10	2004[12	2004[12	NUM
iajs-2923	22	11	]	]	PUNCT
iajs-2923	22	12	that	that	SCONJ
iajs-2923	22	13	the	the	DET
iajs-2923	22	14	picard	picard	PROPN
iajs-2923	22	15	algorithm	algorithm	NOUN
iajs-2923	22	16	converges	converge	VERB
iajs-2923	22	17	faster	fast	ADV
iajs-2923	22	18	than	than	ADP
iajs-2923	22	19	the	the	DET
iajs-2923	22	20	mann	mann	PROPN
iajs-2923	22	21	algorithm	algorithm	NOUN
iajs-2923	22	22	.	.	PUNCT
iajs-2923	23	1	in	in	ADP
iajs-2923	23	2	2008	2008	NUM
iajs-2923	23	3	,	,	PUNCT
iajs-2923	23	4	[	[	X
iajs-2923	23	5	13	13	NUM
iajs-2923	23	6	]	]	PUNCT
iajs-2923	23	7	presented	present	VERB
iajs-2923	23	8	a	a	DET
iajs-2923	23	9	new	new	ADJ
iajs-2923	23	10	two	two	NUM
iajs-2923	23	11	-	-	PUNCT
iajs-2923	23	12	step	step	NOUN
iajs-2923	23	13	algorithm	algorithm	NOUN
iajs-2923	23	14	named	name	VERB
iajs-2923	23	15	after	after	ADP
iajs-2923	23	16	him	he	PRON
iajs-2923	23	17	.	.	PUNCT
iajs-2923	24	1	the	the	DET
iajs-2923	24	2	thianwan	thianwan	PROPN
iajs-2923	24	3	algorithm	algorithm	PROPN
iajs-2923	24	4	is	be	AUX
iajs-2923	24	5	defined	define	VERB
iajs-2923	24	6	as	as	SCONJ
iajs-2923	24	7	follows	follow	VERB
iajs-2923	24	8	:	:	PUNCT
iajs-2923	24	9	𝓏𝑛+1	𝓏𝑛+1	PROPN
iajs-2923	24	10	=	=	PUNCT
iajs-2923	24	11	(	(	PUNCT
iajs-2923	24	12	1	1	NUM
iajs-2923	24	13	−	−	NOUN
iajs-2923	24	14	𝑎𝑛)𝓇𝑛	𝑎𝑛)𝓇𝑛	NOUN
iajs-2923	24	15	+	+	CCONJ
iajs-2923	24	16	𝑎𝑛	𝑎𝑛	PROPN
iajs-2923	24	17	𝑇𝓇𝑛	𝑇𝓇𝑛	PROPN
iajs-2923	24	18	𝓇𝑛	𝓇𝑛	NOUN
iajs-2923	24	19	=	=	PUNCT
iajs-2923	24	20	(	(	PUNCT
iajs-2923	24	21	1	1	NUM
iajs-2923	24	22	−	−	NOUN
iajs-2923	24	23	𝛽𝑛)𝓏𝑛	𝛽𝑛)𝓏𝑛	PUNCT
iajs-2923	25	1	+	+	NUM
iajs-2923	25	2	𝛽𝑛	𝛽𝑛	PROPN
iajs-2923	25	3	𝑇𝓏𝑛	𝑇𝓏𝑛	PROPN
iajs-2923	25	4	,	,	PUNCT
iajs-2923	25	5	where	where	SCONJ
iajs-2923	25	6	𝓏0	𝓏0	ADJ
iajs-2923	25	7	∈	∈	PROPN
iajs-2923	25	8	c	c	NOUN
iajs-2923	25	9	,	,	PUNCT
iajs-2923	25	10	𝑛	𝑛	PROPN
iajs-2923	25	11	∈	∈	PROPN
iajs-2923	25	12	ℕ	ℕ	PROPN
iajs-2923	25	13	,	,	PUNCT
iajs-2923	25	14	and	and	CCONJ
iajs-2923	25	15	{	{	PUNCT
iajs-2923	25	16	𝛼𝑛}𝑛=0	𝛼𝑛}𝑛=0	NOUN
iajs-2923	25	17	∞	∞	PROPN
iajs-2923	25	18	and	and	CCONJ
iajs-2923	25	19	{	{	PUNCT
iajs-2923	25	20	𝛽𝑛}𝑛=0	𝛽𝑛}𝑛=0	NOUN
iajs-2923	25	21	∞	∞	PROPN
iajs-2923	25	22	are	be	AUX
iajs-2923	25	23	the	the	DET
iajs-2923	25	24	real	real	ADJ
iajs-2923	25	25	sequence	sequence	NOUN
iajs-2923	25	26	in	in	ADP
iajs-2923	25	27	[	[	X
iajs-2923	25	28	0,1	0,1	NUM
iajs-2923	25	29	]	]	PUNCT
iajs-2923	25	30	.	.	PUNCT
iajs-2923	26	1	in	in	ADP
iajs-2923	26	2	addition	addition	NOUN
iajs-2923	26	3	,	,	PUNCT
iajs-2923	26	4	it	it	PRON
iajs-2923	26	5	has	have	AUX
iajs-2923	26	6	been	be	AUX
iajs-2923	26	7	proven	prove	VERB
iajs-2923	26	8	the	the	DET
iajs-2923	26	9	strong	strong	ADJ
iajs-2923	26	10	and	and	CCONJ
iajs-2923	26	11	weak	weak	ADJ
iajs-2923	26	12	convergence	convergence	NOUN
iajs-2923	26	13	of	of	ADP
iajs-2923	26	14	this	this	DET
iajs-2923	26	15	algorithm	algorithm	NOUN
iajs-2923	26	16	in	in	ADP
iajs-2923	26	17	the	the	DET
iajs-2923	26	18	uniformly	uniformly	ADJ
iajs-2923	26	19	convex	convex	NOUN
iajs-2923	26	20	banach	banach	NOUN
iajs-2923	26	21	space	space	NOUN
iajs-2923	26	22	.	.	PUNCT
iajs-2923	27	1	now	now	ADV
iajs-2923	27	2	,	,	PUNCT
iajs-2923	27	3	we	we	PRON
iajs-2923	27	4	will	will	AUX
iajs-2923	27	5	mention	mention	VERB
iajs-2923	27	6	some	some	PRON
iajs-2923	27	7	of	of	ADP
iajs-2923	27	8	the	the	DET
iajs-2923	27	9	priorities	priority	NOUN
iajs-2923	27	10	we	we	PRON
iajs-2923	27	11	need	need	VERB
iajs-2923	27	12	:	:	PUNCT
iajs-2923	27	13	definition	definition	NOUN
iajs-2923	27	14	(	(	PUNCT
iajs-2923	27	15	1.1):[12	1.1):[12	NUM
iajs-2923	27	16	]	]	X
iajs-2923	27	17	let	let	VERB
iajs-2923	27	18	{	{	PUNCT
iajs-2923	27	19	𝓂𝑛}𝑛=0	𝓂𝑛}𝑛=0	PROPN
iajs-2923	27	20	∞	∞	PROPN
iajs-2923	27	21	,	,	PUNCT
iajs-2923	27	22	{	{	PUNCT
iajs-2923	27	23	𝓃𝑛}𝑛=0	𝓃𝑛}𝑛=0	NOUN
iajs-2923	27	24	∞	∞	NUM
iajs-2923	27	25	are	be	AUX
iajs-2923	27	26	two	two	NUM
iajs-2923	27	27	sequence	sequence	NOUN
iajs-2923	27	28	lies	lie	VERB
iajs-2923	27	29	in	in	ADP
iajs-2923	27	30	r	r	NOUN
iajs-2923	27	31	such	such	ADJ
iajs-2923	27	32	that	that	SCONJ
iajs-2923	27	33	{	{	PUNCT
iajs-2923	27	34	𝓂𝑛}𝑛=0	𝓂𝑛}𝑛=0	PROPN
iajs-2923	27	35	∞	∞	NUM
iajs-2923	27	36	converge	converge	VERB
iajs-2923	27	37	to	to	ADP
iajs-2923	27	38	𝓂	𝓂	NOUN
iajs-2923	27	39	,	,	PUNCT
iajs-2923	27	40	{	{	PUNCT
iajs-2923	27	41	𝓃𝑛}𝑛=0	𝓃𝑛}𝑛=0	NOUN
iajs-2923	27	42	∞	∞	NUM
iajs-2923	27	43	converge	converge	NOUN
iajs-2923	27	44	to	to	ADP
iajs-2923	27	45	𝓃	𝓃	NOUN
iajs-2923	27	46	,	,	PUNCT
iajs-2923	27	47	and	and	CCONJ
iajs-2923	27	48	𝒲	𝒲	PROPN
iajs-2923	27	49	=	=	SYM
iajs-2923	27	50	lim	lim	NOUN
iajs-2923	27	51	𝑛→∞	𝑛→∞	NUM
iajs-2923	27	52	|𝓂𝑛−𝓂|	|𝓂𝑛−𝓂|	NUM
iajs-2923	27	53	|𝓃𝑛−𝓃|	|𝓃𝑛−𝓃|	NUM
iajs-2923	27	54	1	1	NUM
iajs-2923	27	55	.	.	PUNCT
iajs-2923	28	1	if	if	SCONJ
iajs-2923	28	2	𝒲	𝒲	PROPN
iajs-2923	28	3	=	=	SYM
iajs-2923	28	4	0	0	NUM
iajs-2923	28	5	⟶	⟶	NOUN
iajs-2923	28	6	the	the	DET
iajs-2923	28	7	sequence	sequence	NOUN
iajs-2923	28	8	{	{	PUNCT
iajs-2923	28	9	𝓂𝑛}𝑛=0	𝓂𝑛}𝑛=0	PROPN
iajs-2923	28	10	∞	∞	PROPN
iajs-2923	28	11	is	be	AUX
iajs-2923	28	12	converge	converge	ADJ
iajs-2923	28	13	to	to	ADP
iajs-2923	28	14	𝓂	𝓂	NOUN
iajs-2923	28	15	faster	fast	ADV
iajs-2923	28	16	then	then	ADV
iajs-2923	28	17	{	{	PUNCT
iajs-2923	28	18	𝓃𝑛}𝑛=0	𝓃𝑛}𝑛=0	NOUN
iajs-2923	28	19	∞	∞	NUM
iajs-2923	28	20	converge	converge	NOUN
iajs-2923	28	21	to	to	ADP
iajs-2923	28	22	𝓃.	𝓃.	NOUN
iajs-2923	28	23	2	2	NUM
iajs-2923	28	24	.	.	PUNCT
iajs-2923	29	1	if	if	SCONJ
iajs-2923	29	2	0	0	NUM
iajs-2923	29	3	<	<	X
iajs-2923	29	4	𝒲	𝒲	PROPN
iajs-2923	29	5	<	<	X
iajs-2923	29	6	∞	∞	NUM
iajs-2923	29	7	→	→	SYM
iajs-2923	29	8	{	{	PUNCT
iajs-2923	29	9	𝓂𝑛}𝑛=0	𝓂𝑛}𝑛=0	PROPN
iajs-2923	29	10	∞	∞	PROPN
iajs-2923	29	11	and	and	CCONJ
iajs-2923	29	12	{	{	PUNCT
iajs-2923	29	13	𝓃𝑛}𝑛=0	𝓃𝑛}𝑛=0	NOUN
iajs-2923	29	14	∞	∞	NUM
iajs-2923	29	15	have	have	VERB
iajs-2923	29	16	the	the	DET
iajs-2923	29	17	same	same	ADJ
iajs-2923	29	18	rate	rate	NOUN
iajs-2923	29	19	of	of	ADP
iajs-2923	29	20	convergence	convergence	NOUN
iajs-2923	29	21	.	.	PUNCT
iajs-2923	30	1	lemma	lemma	PROPN
iajs-2923	30	2	(	(	PUNCT
iajs-2923	30	3	1.2):[14	1.2):[14	PROPN
iajs-2923	30	4	]	]	X
iajs-2923	30	5	let	let	VERB
iajs-2923	30	6	𝒰	𝒰	PROPN
iajs-2923	30	7	be	be	AUX
iajs-2923	30	8	a	a	DET
iajs-2923	30	9	uniformly	uniformly	ADV
iajs-2923	30	10	convex	convex	NOUN
iajs-2923	30	11	banach	banach	NOUN
iajs-2923	30	12	space	space	NOUN
iajs-2923	30	13	and	and	CCONJ
iajs-2923	30	14	{	{	PUNCT
iajs-2923	30	15	𝓂𝑛}𝑛=0	𝓂𝑛}𝑛=0	PROPN
iajs-2923	30	16	∞	∞	PROPN
iajs-2923	30	17	be	be	VERB
iajs-2923	30	18	any	any	DET
iajs-2923	30	19	sequence	sequence	NOUN
iajs-2923	30	20	such	such	ADJ
iajs-2923	30	21	that	that	SCONJ
iajs-2923	30	22	0	0	NUM
iajs-2923	30	23	<	<	X
iajs-2923	30	24	𝔭	𝔭	VERB
iajs-2923	30	25	≤	≤	NUM
iajs-2923	31	1	𝛼𝑛	𝛼𝑛	NOUN
iajs-2923	31	2	≤	≤	NUM
iajs-2923	31	3	𝔮	𝔮	X
iajs-2923	31	4	<	<	X
iajs-2923	31	5	1	1	NUM
iajs-2923	31	6	,	,	PUNCT
iajs-2923	31	7	for	for	ADP
iajs-2923	31	8	some	some	DET
iajs-2923	31	9	𝔭,𝔮	𝔭,𝔮	NOUN
iajs-2923	31	10	∈	∈	NOUN
iajs-2923	31	11	ℝ+	ℝ+	PUNCT
iajs-2923	31	12	and	and	CCONJ
iajs-2923	31	13	for	for	ADP
iajs-2923	31	14	all	all	DET
iajs-2923	31	15	𝑛	𝑛	DET
iajs-2923	31	16	≥	≥	NOUN
iajs-2923	31	17	1	1	NUM
iajs-2923	31	18	.	.	PUNCT
iajs-2923	32	1	let	let	VERB
iajs-2923	32	2	{	{	PUNCT
iajs-2923	32	3	𝓂𝑛}𝑛=0	𝓂𝑛}𝑛=0	PROPN
iajs-2923	32	4	∞	∞	PROPN
iajs-2923	32	5	and	and	CCONJ
iajs-2923	32	6	{	{	PUNCT
iajs-2923	32	7	𝓃𝑛}𝑛=0	𝓃𝑛}𝑛=0	NOUN
iajs-2923	32	8	∞	∞	NUM
iajs-2923	32	9	are	be	AUX
iajs-2923	32	10	two	two	NUM
iajs-2923	32	11	sequences	sequence	NOUN
iajs-2923	32	12	of	of	ADP
iajs-2923	32	13	𝒰	𝒰	PROPN
iajs-2923	33	1	such	such	ADJ
iajs-2923	33	2	that	that	PRON
iajs-2923	33	3	:	:	PUNCT
iajs-2923	33	4	lim	lim	PROPN
iajs-2923	33	5	𝑛→∞	𝑛→∞	NUM
iajs-2923	33	6	sup‖𝓂𝑛‖	sup‖𝓂𝑛‖	NOUN
iajs-2923	33	7	≤	≤	NUM
iajs-2923	33	8	𝑐	𝑐	PROPN
iajs-2923	33	9	,	,	PUNCT
iajs-2923	33	10	lim	lim	PROPN
iajs-2923	33	11	𝑛→∞	𝑛→∞	NUM
iajs-2923	33	12	sup‖𝓃𝑛‖	sup‖𝓃𝑛‖	NOUN
iajs-2923	33	13	≤	≤	PROPN
iajs-2923	33	14	𝑐	𝑐	PROPN
iajs-2923	33	15	and	and	CCONJ
iajs-2923	33	16	lim	lim	PROPN
iajs-2923	33	17	𝑛→∞	𝑛→∞	NUM
iajs-2923	33	18	sup‖𝛼𝑛𝓂𝑛	sup‖𝛼𝑛𝓂𝑛	NOUN
iajs-2923	33	19	+	+	CCONJ
iajs-2923	33	20	(	(	PUNCT
iajs-2923	33	21	1	1	NUM
iajs-2923	33	22	−	−	NOUN
iajs-2923	33	23	𝛼𝑛)𝓃𝑛‖	𝛼𝑛)𝓃𝑛‖	NOUN
iajs-2923	33	24	=	=	SYM
iajs-2923	33	25	𝑐	𝑐	PROPN
iajs-2923	33	26	for	for	ADP
iajs-2923	33	27	some	some	DET
iajs-2923	33	28	𝑐	𝑐	PROPN
iajs-2923	33	29	≥	≥	NOUN
iajs-2923	33	30	0	0	NUM
iajs-2923	34	1	then	then	ADV
iajs-2923	34	2	lim	lim	PROPN
iajs-2923	34	3	𝑛→∞	𝑛→∞	NUM
iajs-2923	34	4	‖𝓂𝑛	‖𝓂𝑛	NUM
iajs-2923	34	5	−	−	NOUN
iajs-2923	34	6	𝓃𝑛‖	𝓃𝑛‖	NOUN
iajs-2923	34	7	=	=	SYM
iajs-2923	34	8	0	0	NUM
iajs-2923	34	9	definition	definition	NOUN
iajs-2923	34	10	(	(	PUNCT
iajs-2923	34	11	1.3	1.3	NUM
iajs-2923	34	12	):	):	PUNCT
iajs-2923	34	13	[	[	X
iajs-2923	34	14	15	15	NUM
iajs-2923	34	15	]	]	X
iajs-2923	34	16	let	let	VERB
iajs-2923	34	17	ψ	ψ	NOUN
iajs-2923	34	18	,	,	PUNCT
iajs-2923	34	19	𝑇	𝑇	PROPN
iajs-2923	34	20	∶	∶	PROPN
iajs-2923	34	21	𝐶	𝐶	PROPN
iajs-2923	34	22	→	→	SYM
iajs-2923	34	23	𝐶	𝐶	PROPN
iajs-2923	34	24	such	such	ADJ
iajs-2923	34	25	that	that	DET
iajs-2923	34	26	𝑇(𝐶	𝑇(𝐶	NOUN
iajs-2923	34	27	)	)	PUNCT
iajs-2923	34	28			PROPN
iajs-2923	34	29	ψ(𝐶	ψ(𝐶	PRON
iajs-2923	34	30	)	)	PUNCT
iajs-2923	34	31	and	and	CCONJ
iajs-2923	34	32	𝑝	𝑝	ADP
iajs-2923	34	33	a	a	DET
iajs-2923	34	34	coincidence	coincidence	NOUN
iajs-2923	34	35	point	point	NOUN
iajs-2923	34	36	of	of	ADP
iajs-2923	34	37	ψ	ψ	PROPN
iajs-2923	34	38	and	and	CCONJ
iajs-2923	34	39	𝑇	𝑇	PROPN
iajs-2923	34	40	,	,	PUNCT
iajs-2923	34	41	that	that	ADV
iajs-2923	34	42	is	is	ADV
iajs-2923	34	43	,	,	PUNCT
iajs-2923	34	44	ψ𝑝	ψ𝑝	VERB
iajs-2923	34	45	=	=	SYM
iajs-2923	34	46	𝑇𝑝	𝑇𝑝	PROPN
iajs-2923	34	47	=	=	SYM
iajs-2923	34	48	𝑝.	𝑝.	NOUN
iajs-2923	34	49	for	for	ADP
iajs-2923	34	50	𝑎𝑛𝑦	𝑎𝑛𝑦	PROPN
iajs-2923	34	51	𝒸0	𝒸0	PROPN
iajs-2923	34	52	𝐶	𝐶	PROPN
iajs-2923	34	53	,	,	PUNCT
iajs-2923	34	54	let	let	VERB
iajs-2923	34	55	the	the	DET
iajs-2923	34	56	sequence	sequence	NOUN
iajs-2923	34	57	{	{	PUNCT
iajs-2923	34	58	ψ𝓂𝑛}𝑛=0	ψ𝓂𝑛}𝑛=0	X
iajs-2923	34	59	∞	∞	PRON
iajs-2923	34	60	generated	generate	VERB
iajs-2923	34	61	by	by	ADP
iajs-2923	34	62	the	the	DET
iajs-2923	34	63	algorithm	algorithm	NOUN
iajs-2923	34	64	procedure	procedure	NOUN
iajs-2923	34	65	ψ𝓂𝑛	ψ𝓂𝑛	NOUN
iajs-2923	34	66	=	=	SYM
iajs-2923	34	67	𝑓(𝑇	𝑓(𝑇	ADJ
iajs-2923	34	68	,	,	PUNCT
iajs-2923	34	69	𝓂𝑛	𝓂𝑛	NOUN
iajs-2923	34	70	)	)	PUNCT
iajs-2923	34	71	𝑛	𝑛	PRON
iajs-2923	34	72	≥	≥	NUM
iajs-2923	34	73	0	0	NUM
iajs-2923	34	74	converge	converge	VERB
iajs-2923	34	75	to	to	PART
iajs-2923	34	76	𝑝.	𝑝.	VERB
iajs-2923	34	77	let	let	VERB
iajs-2923	34	78	{	{	PUNCT
iajs-2923	34	79	ψ𝓎𝑛}𝑛=0	ψ𝓎𝑛}𝑛=0	PUNCT
iajs-2923	34	80	∞	∞	PROPN
iajs-2923	34	81	⊂	⊂	PROPN
iajs-2923	34	82	𝐶	𝐶	PROPN
iajs-2923	34	83	be	be	AUX
iajs-2923	34	84	an	an	DET
iajs-2923	34	85	arbitrary	arbitrary	ADJ
iajs-2923	34	86	sequence	sequence	NOUN
iajs-2923	34	87	and	and	CCONJ
iajs-2923	34	88	set	set	VERB
iajs-2923	34	89	휀𝑛	휀𝑛	ADP
iajs-2923	34	90	=	=	SYM
iajs-2923	34	91	𝑑(ψ𝓎𝑛+1	𝑑(ψ𝓎𝑛+1	PROPN
iajs-2923	34	92	,	,	PUNCT
iajs-2923	34	93	𝑓(𝑇	𝑓(𝑇	PRON
iajs-2923	34	94	,	,	PUNCT
iajs-2923	34	95	𝓎𝑛	𝓎𝑛	NOUN
iajs-2923	34	96	)	)	PUNCT
iajs-2923	34	97	)	)	PUNCT
iajs-2923	34	98	,	,	PUNCT
iajs-2923	34	99	𝑛	𝑛	PROPN
iajs-2923	34	100	=	=	SYM
iajs-2923	34	101	0	0	NUM
iajs-2923	34	102	,	,	PUNCT
iajs-2923	34	103	1	1	NUM
iajs-2923	34	104	,	,	PUNCT
iajs-2923	34	105	·	·	PUNCT
iajs-2923	34	106	·	·	PUNCT
iajs-2923	34	107	·	·	PUNCT
iajs-2923	34	108	.	.	PUNCT
iajs-2923	35	1	then	then	ADV
iajs-2923	35	2	,	,	PUNCT
iajs-2923	35	3	the	the	DET
iajs-2923	35	4	algorithm	algorithm	NOUN
iajs-2923	35	5	ψ𝒸𝑛	ψ𝒸𝑛	NOUN
iajs-2923	35	6	will	will	AUX
iajs-2923	35	7	be	be	AUX
iajs-2923	35	8	called	call	VERB
iajs-2923	35	9	(	(	PUNCT
iajs-2923	35	10	ψ	ψ	X
iajs-2923	35	11	,	,	PUNCT
iajs-2923	35	12	𝑇	𝑇	PROPN
iajs-2923	35	13	)	)	PUNCT
iajs-2923	35	14	−	−	PROPN
iajs-2923	35	15	𝑠𝑡𝑎𝑏𝑙𝑒	𝑠𝑡𝑎𝑏𝑙𝑒	ADJ
iajs-2923	36	1	if	if	SCONJ
iajs-2923	36	2	and	and	CCONJ
iajs-2923	36	3	only	only	ADV
iajs-2923	36	4	if	if	SCONJ
iajs-2923	36	5	lim	lim	PROPN
iajs-2923	36	6	𝑛→∞	𝑛→∞	NUM
iajs-2923	36	7	𝜖𝑛	𝜖𝑛	PROPN
iajs-2923	36	8	=	=	SYM
iajs-2923	36	9	0	0	PROPN
iajs-2923	36	10	implies	imply	VERB
iajs-2923	36	11	that	that	SCONJ
iajs-2923	36	12	lim	lim	PROPN
iajs-2923	36	13	𝑛→∞	𝑛→∞	NUM
iajs-2923	36	14	ψ𝓎𝑛	ψ𝓎𝑛	X
iajs-2923	36	15	=	=	SYM
iajs-2923	36	16	𝑝.	𝑝.	PROPN
iajs-2923	36	17	lemma	lemma	PROPN
iajs-2923	36	18	(	(	PUNCT
iajs-2923	36	19	1.4	1.4	NUM
iajs-2923	36	20	):	):	PUNCT
iajs-2923	36	21	[	[	X
iajs-2923	36	22	12	12	NUM
iajs-2923	36	23	]	]	X
iajs-2923	36	24	if	if	SCONJ
iajs-2923	36	25	𝜂	𝜂	NOUN
iajs-2923	36	26	is	be	AUX
iajs-2923	36	27	a	a	DET
iajs-2923	36	28	real	real	ADJ
iajs-2923	36	29	number	number	NOUN
iajs-2923	36	30	such	such	ADJ
iajs-2923	36	31	that	that	SCONJ
iajs-2923	36	32	0	0	NUM
iajs-2923	36	33	<	<	X
iajs-2923	36	34	𝜂	𝜂	X
iajs-2923	36	35	<	<	X
iajs-2923	36	36	1	1	NUM
iajs-2923	36	37	and	and	CCONJ
iajs-2923	36	38	{	{	PUNCT
iajs-2923	36	39	𝜖𝑛}𝑛=0	𝜖𝑛}𝑛=0	NOUN
iajs-2923	36	40	∞	∞	PROPN
iajs-2923	36	41	is	be	AUX
iajs-2923	36	42	a	a	DET
iajs-2923	36	43	sequence	sequence	NOUN
iajs-2923	36	44	of	of	ADP
iajs-2923	36	45	positive	positive	ADJ
iajs-2923	36	46	numbers	number	NOUN
iajs-2923	36	47	,	,	PUNCT
iajs-2923	36	48	such	such	ADJ
iajs-2923	36	49	that	that	SCONJ
iajs-2923	36	50	lim	lim	PROPN
iajs-2923	36	51	𝑛→∞	𝑛→∞	NUM
iajs-2923	36	52	𝜖𝑛	𝜖𝑛	PROPN
iajs-2923	36	53	=	=	NOUN
iajs-2923	36	54	0	0	PUNCT
iajs-2923	37	1	then	then	ADV
iajs-2923	37	2	,	,	PUNCT
iajs-2923	37	3	for	for	ADP
iajs-2923	37	4	any	any	DET
iajs-2923	37	5	sequence	sequence	NOUN
iajs-2923	37	6	of	of	ADP
iajs-2923	37	7	positive	positive	ADJ
iajs-2923	37	8	numbers	number	NOUN
iajs-2923	37	9	{	{	PUNCT
iajs-2923	37	10	𝓂𝑛}𝑛=0	𝓂𝑛}𝑛=0	PROPN
iajs-2923	37	11	∞	∞	PROPN
iajs-2923	37	12	satisfying	satisfy	VERB
iajs-2923	37	13	𝓂𝑛+1	𝓂𝑛+1	PRON
iajs-2923	37	14	≤	≤	NUM
iajs-2923	37	15	𝜂𝓂𝑛	𝜂𝓂𝑛	NOUN
iajs-2923	37	16	+	+	CCONJ
iajs-2923	37	17	𝜖𝑛	𝜖𝑛	ADJ
iajs-2923	37	18	definition	definition	NOUN
iajs-2923	37	19	(	(	PUNCT
iajs-2923	37	20	1.5	1.5	NUM
iajs-2923	37	21	):	):	PUNCT
iajs-2923	37	22	[	[	X
iajs-2923	37	23	16	16	NUM
iajs-2923	37	24	]	]	PUNCT
iajs-2923	37	25	the	the	DET
iajs-2923	37	26	mapping	mapping	NOUN
iajs-2923	37	27	𝑇	𝑇	PROPN
iajs-2923	37	28	:	:	PUNCT
iajs-2923	37	29	𝐶	𝐶	PROPN
iajs-2923	37	30	→	→	SYM
iajs-2923	37	31	𝐶	𝐶	PROPN
iajs-2923	37	32	is	be	AUX
iajs-2923	37	33	said	say	VERB
iajs-2923	37	34	suzuki	suzuki	PROPN
iajs-2923	37	35	if	if	SCONJ
iajs-2923	37	36	satisfying	satisfy	VERB
iajs-2923	37	37	the	the	DET
iajs-2923	37	38	following	follow	VERB
iajs-2923	37	39	condition	condition	NOUN
iajs-2923	37	40	:	:	PUNCT
iajs-2923	37	41	1	1	NUM
iajs-2923	37	42	2	2	NUM
iajs-2923	37	43	‖𝓂	‖𝓂	NOUN
iajs-2923	37	44	−	−	NOUN
iajs-2923	37	45	𝑇(𝓂)‖	𝑇(𝓂)‖	NOUN
iajs-2923	37	46	≤	≤	NUM
iajs-2923	37	47	‖𝓂	‖𝓂	NOUN
iajs-2923	38	1	−	−	PROPN
iajs-2923	39	1	𝓃‖	𝓃‖	PROPN
iajs-2923	39	2	⟹	⟹	X
iajs-2923	39	3	‖𝑇(𝓂	‖𝑇(𝓂	ADJ
iajs-2923	39	4	)	)	PUNCT
iajs-2923	39	5	−	−	PROPN
iajs-2923	39	6	𝑇(𝓃)‖	𝑇(𝓃)‖	PROPN
iajs-2923	39	7	≤	≤	NUM
iajs-2923	39	8	‖𝓂	‖𝓂	NOUN
iajs-2923	39	9	−	−	NOUN
iajs-2923	39	10	𝓃‖	𝓃‖	ADJ
iajs-2923	39	11	,	,	PUNCT
iajs-2923	39	12	∀𝓂	∀𝓂	PROPN
iajs-2923	39	13	,	,	PUNCT
iajs-2923	39	14	𝓃	𝓃	PROPN
iajs-2923	39	15	∈	∈	PROPN
iajs-2923	39	16	𝐶	𝐶	PROPN
iajs-2923	39	17	2	2	NUM
iajs-2923	39	18	.main	.main	PUNCT
iajs-2923	39	19	results	result	NOUN
iajs-2923	39	20	we	we	PRON
iajs-2923	39	21	introduce	introduce	VERB
iajs-2923	39	22	a	a	DET
iajs-2923	39	23	new	new	ADJ
iajs-2923	39	24	type	type	NOUN
iajs-2923	39	25	of	of	ADP
iajs-2923	39	26	mapping	mapping	NOUN
iajs-2923	39	27	called	call	VERB
iajs-2923	39	28	projection	projection	NOUN
iajs-2923	39	29	jungck	jungck	PROPN
iajs-2923	39	30	zn	zn	PROPN
iajs-2923	39	31	-	-	PUNCT
iajs-2923	39	32	suzuki	suzuki	NOUN
iajs-2923	39	33	generalized	generalize	VERB
iajs-2923	39	34	and	and	CCONJ
iajs-2923	39	35	by	by	ADP
iajs-2923	39	36	using	use	VERB
iajs-2923	39	37	this	this	DET
iajs-2923	39	38	type	type	NOUN
iajs-2923	39	39	of	of	ADP
iajs-2923	39	40	mapping	mapping	NOUN
iajs-2923	39	41	,	,	PUNCT
iajs-2923	39	42	we	we	PRON
iajs-2923	39	43	will	will	AUX
iajs-2923	39	44	propose	propose	VERB
iajs-2923	39	45	new	new	ADJ
iajs-2923	39	46	algorithms	algorithm	NOUN
iajs-2923	39	47	and	and	CCONJ
iajs-2923	39	48	analyse	analyse	VERB
iajs-2923	39	49	their	their	PRON
iajs-2923	39	50	convergence	convergence	NOUN
iajs-2923	39	51	and	and	CCONJ
iajs-2923	39	52	rate	rate	NOUN
iajs-2923	39	53	of	of	ADP
iajs-2923	39	54	convergence	convergence	NOUN
iajs-2923	39	55	.	.	PUNCT
iajs-2923	40	1	definition	definition	NOUN
iajs-2923	40	2	(	(	PUNCT
iajs-2923	40	3	2.1	2.1	NUM
iajs-2923	40	4	):	):	PUNCT
iajs-2923	40	5	let	let	VERB
iajs-2923	40	6	𝒳	𝒳	PRON
iajs-2923	40	7	be	be	AUX
iajs-2923	40	8	a	a	DET
iajs-2923	40	9	normed	normed	ADJ
iajs-2923	40	10	space	space	NOUN
iajs-2923	40	11	,	,	PUNCT
iajs-2923	40	12	𝐶	𝐶	PROPN
iajs-2923	40	13	be	be	AUX
iajs-2923	40	14	a	a	DET
iajs-2923	40	15	nonempty	nonempty	ADV
iajs-2923	40	16	closed	close	VERB
iajs-2923	40	17	convex	convex	NOUN
iajs-2923	40	18	subset	subset	NOUN
iajs-2923	40	19	of	of	ADP
iajs-2923	40	20	𝒳.	𝒳.	PROPN
iajs-2923	40	21	a	a	DET
iajs-2923	40	22	mapping	mapping	NOUN
iajs-2923	40	23	𝑇	𝑇	PROPN
iajs-2923	40	24	,	,	PUNCT
iajs-2923	40	25	ψ	ψ	ADP
iajs-2923	40	26	:	:	PUNCT
iajs-2923	40	27	𝐶	𝐶	PROPN
iajs-2923	40	28	→	→	SYM
iajs-2923	40	29	𝐶	𝐶	PROPN
iajs-2923	40	30	and	and	CCONJ
iajs-2923	40	31	𝒫𝒸	𝒫𝒸	PROPN
iajs-2923	40	32	are	be	AUX
iajs-2923	40	33	called	call	VERB
iajs-2923	40	34	projection	projection	NOUN
iajs-2923	40	35	jungck	jungck	PROPN
iajs-2923	40	36	zn	zn	PROPN
iajs-2923	40	37	-	-	PUNCT
iajs-2923	40	38	suzuki	suzuki	NOUN
iajs-2923	40	39	generalized	generalize	VERB
iajs-2923	40	40	mapping	mapping	NOUN
iajs-2923	40	41	if	if	SCONJ
iajs-2923	40	42	1	1	NUM
iajs-2923	40	43	2	2	NUM
iajs-2923	40	44	‖𝑥	‖𝑥	NOUN
iajs-2923	40	45	−	−	NOUN
iajs-2923	40	46	𝑇(𝑥)‖	𝑇(𝑥)‖	SCONJ
iajs-2923	40	47	≤	≤	NOUN
iajs-2923	41	1	‖ψ𝑥	‖ψ𝑥	PUNCT
iajs-2923	41	2	−	−	NOUN
iajs-2923	41	3	ψ𝑦‖	ψ𝑦‖	ADJ
iajs-2923	41	4	implies	imply	VERB
iajs-2923	41	5	that	that	SCONJ
iajs-2923	41	6	‖𝑇(𝑥	‖𝑇(𝑥	PROPN
iajs-2923	41	7	)	)	PUNCT
iajs-2923	41	8	−	−	PROPN
iajs-2923	42	1	𝑇(𝑦)‖	𝑇(𝑦)‖	VERB
iajs-2923	42	2	≤	≤	ADJ
iajs-2923	42	3	𝐿‖ψ𝑥	𝐿‖ψ𝑥	PROPN
iajs-2923	42	4	−	−	PROPN
iajs-2923	42	5	ψ𝑦‖	ψ𝑦‖	PROPN
iajs-2923	42	6	+	+	CCONJ
iajs-2923	42	7	𝜙(‖𝑥−𝒫𝒸(𝑥)‖+‖𝑥−ψ𝑥‖	𝜙(‖𝑥−𝒫𝒸(𝑥)‖+‖𝑥−ψ𝑥‖	NUM
iajs-2923	42	8	)	)	PUNCT
iajs-2923	42	9	1+𝑚𝑎𝑥	1+𝑚𝑎𝑥	NOUN
iajs-2923	42	10	{	{	PUNCT
iajs-2923	42	11	‖𝒫𝒸(𝑥)−𝒫𝒸(𝑦)‖,‖ψ𝑥−ψ𝑦‖	‖𝒫𝒸(𝑥)−𝒫𝒸(𝑦)‖,‖ψ𝑥−ψ𝑦‖	PROPN
iajs-2923	42	12	}	}	PUNCT
iajs-2923	42	13	𝜙	𝜙	NOUN
iajs-2923	42	14	:	:	PUNCT
iajs-2923	42	15	ℛ+	ℛ+	NOUN
iajs-2923	42	16	→	→	SYM
iajs-2923	42	17	ℛ+	ℛ+	NUM
iajs-2923	42	18	is	be	AUX
iajs-2923	42	19	a	a	DET
iajs-2923	42	20	monotone	monotone	ADJ
iajs-2923	42	21	increasing	increase	VERB
iajs-2923	42	22	function	function	NOUN
iajs-2923	42	23	such	such	ADJ
iajs-2923	42	24	that	that	SCONJ
iajs-2923	42	25	𝜙(0	𝜙(0	NOUN
iajs-2923	42	26	)	)	PUNCT
iajs-2923	43	1	=	=	SYM
iajs-2923	43	2	0	0	NUM
iajs-2923	43	3	and	and	CCONJ
iajs-2923	43	4	𝐿	𝐿	PROPN
iajs-2923	43	5	≤	≤	PROPN
iajs-2923	43	6	1	1	NUM
iajs-2923	43	7	.	.	PUNCT
iajs-2923	43	8	ihjpas	ihjpas	PROPN
iajs-2923	43	9	.	.	PUNCT
iajs-2923	44	1	36(1)2023	36(1)2023	NUM
iajs-2923	44	2	294	294	NUM
iajs-2923	44	3	definition	definition	NOUN
iajs-2923	44	4	(	(	PUNCT
iajs-2923	44	5	2.2	2.2	NUM
iajs-2923	44	6	):	):	PUNCT
iajs-2923	44	7	the	the	DET
iajs-2923	44	8	projection	projection	NOUN
iajs-2923	44	9	jungck	jungck	NOUN
iajs-2923	44	10	-	-	PUNCT
iajs-2923	44	11	picard	picard	NOUN
iajs-2923	44	12	algorithm	algorithm	NOUN
iajs-2923	44	13	is	be	AUX
iajs-2923	44	14	defined	define	VERB
iajs-2923	44	15	as	as	SCONJ
iajs-2923	44	16	follows	follow	VERB
iajs-2923	44	17	:	:	PUNCT
iajs-2923	44	18	ψ𝑘𝑛+1	ψ𝑘𝑛+1	PROPN
iajs-2923	44	19	=	=	SYM
iajs-2923	44	20	𝒫𝒸𝑇𝑘𝑛	𝒫𝒸𝑇𝑘𝑛	PROPN
iajs-2923	44	21	,	,	PUNCT
iajs-2923	44	22	𝑘0	𝑘0	PROPN
iajs-2923	44	23	∈	∈	PROPN
iajs-2923	44	24	c.	c.	NOUN
iajs-2923	44	25	definition	definition	NOUN
iajs-2923	44	26	(	(	PUNCT
iajs-2923	44	27	2.3	2.3	NUM
iajs-2923	44	28	):	):	PUNCT
iajs-2923	44	29	the	the	DET
iajs-2923	44	30	projection	projection	NOUN
iajs-2923	44	31	jungck	jungck	PROPN
iajs-2923	44	32	-	-	PUNCT
iajs-2923	44	33	krasnoselskii	krasnoselskii	PROPN
iajs-2923	44	34	is	be	AUX
iajs-2923	44	35	defined	define	VERB
iajs-2923	44	36	as	as	SCONJ
iajs-2923	44	37	follows	follow	VERB
iajs-2923	44	38	:	:	PUNCT
iajs-2923	44	39	ψ𝑛𝑛+1	ψ𝑛𝑛+1	NUM
iajs-2923	44	40	=	=	SYM
iajs-2923	44	41	(	(	PUNCT
iajs-2923	44	42	1	1	NUM
iajs-2923	44	43	−	−	PROPN
iajs-2923	44	44	𝛿)ψ𝒫𝒸(𝑛𝑛	𝛿)ψ𝒫𝒸(𝑛𝑛	NOUN
iajs-2923	44	45	)	)	PUNCT
iajs-2923	45	1	+	+	CCONJ
iajs-2923	45	2	𝛿𝒫𝒸𝑇𝑛𝑛	𝛿𝒫𝒸𝑇𝑛𝑛	PROPN
iajs-2923	45	3	,	,	PUNCT
iajs-2923	45	4	𝑛0	𝑛0	VERB
iajs-2923	45	5	∈	∈	PROPN
iajs-2923	45	6	c	c	NOUN
iajs-2923	45	7	where	where	SCONJ
iajs-2923	45	8	𝒫𝒸	𝒫𝒸	PROPN
iajs-2923	45	9	is	be	AUX
iajs-2923	45	10	metric	metric	ADJ
iajs-2923	45	11	projection	projection	NOUN
iajs-2923	45	12	and	and	CCONJ
iajs-2923	45	13	𝛿	𝛿	PRON
iajs-2923	45	14	∈	∈	PROPN
iajs-2923	45	15	(	(	PUNCT
iajs-2923	45	16	0,1	0,1	NUM
iajs-2923	45	17	)	)	PUNCT
iajs-2923	45	18	.	.	PUNCT
iajs-2923	46	1	definition	definition	NOUN
iajs-2923	46	2	(	(	PUNCT
iajs-2923	46	3	2.4	2.4	NUM
iajs-2923	46	4	):	):	PUNCT
iajs-2923	46	5	the	the	DET
iajs-2923	46	6	projection	projection	NOUN
iajs-2923	46	7	jungck	jungck	NOUN
iajs-2923	46	8	-	-	PUNCT
iajs-2923	46	9	normal	normal	ADJ
iajs-2923	46	10	𝒩	𝒩	PROPN
iajs-2923	46	11	algorithm	algorithm	NOUN
iajs-2923	46	12	is	be	AUX
iajs-2923	46	13	defined	define	VERB
iajs-2923	46	14	as	as	SCONJ
iajs-2923	46	15	follows	follow	VERB
iajs-2923	46	16	:	:	PUNCT
iajs-2923	46	17	ψ𝑢𝑛+1	ψ𝑢𝑛+1	NOUN
iajs-2923	46	18	=	=	SYM
iajs-2923	46	19	𝒫𝒸𝑇((1	𝒫𝒸𝑇((1	PROPN
iajs-2923	46	20	−	−	PROPN
iajs-2923	46	21	𝛼𝑛)ψ𝑢𝑛	𝛼𝑛)ψ𝑢𝑛	PROPN
iajs-2923	46	22	+	+	CCONJ
iajs-2923	46	23	𝛼𝑛𝒫𝒸(𝑢𝑛	𝛼𝑛𝒫𝒸(𝑢𝑛	NUM
iajs-2923	46	24	)	)	PUNCT
iajs-2923	46	25	)	)	PUNCT
iajs-2923	46	26	,	,	PUNCT
iajs-2923	47	1	𝓊0	𝓊0	PROPN
iajs-2923	47	2	∈	∈	PROPN
iajs-2923	48	1	c	c	X
iajs-2923	48	2	where	where	SCONJ
iajs-2923	48	3	𝛼𝑛	𝛼𝑛	PROPN
iajs-2923	48	4	∈	∈	PROPN
iajs-2923	49	1	[	[	X
iajs-2923	49	2	0,1	0,1	NUM
iajs-2923	49	3	]	]	PUNCT
iajs-2923	49	4	and	and	CCONJ
iajs-2923	49	5	ψ	ψ	NOUN
iajs-2923	49	6	has	have	VERB
iajs-2923	49	7	property	property	NOUN
iajs-2923	49	8	𝒩	𝒩	PROPN
iajs-2923	49	9	,	,	PUNCT
iajs-2923	49	10	i.e.	i.e.	X
iajs-2923	49	11	,	,	PUNCT
iajs-2923	49	12	ψψ(𝑥	ψψ(𝑥	NOUN
iajs-2923	49	13	)	)	PUNCT
iajs-2923	49	14	≤	≤	NUM
iajs-2923	49	15	ψ(𝑥	ψ(𝑥	NOUN
iajs-2923	49	16	)	)	PUNCT
iajs-2923	49	17	,	,	PUNCT
iajs-2923	49	18	𝑥	𝑥	PROPN
iajs-2923	49	19	∈	∈	PROPN
iajs-2923	49	20	𝐶	𝐶	PROPN
iajs-2923	49	21	&	&	CCONJ
iajs-2923	49	22	ψ	ψ	PROPN
iajs-2923	49	23	is	be	AUX
iajs-2923	49	24	a	a	DET
iajs-2923	49	25	linear	linear	ADJ
iajs-2923	49	26	map	map	NOUN
iajs-2923	49	27	definition	definition	NOUN
iajs-2923	49	28	(	(	PUNCT
iajs-2923	49	29	2.5	2.5	NUM
iajs-2923	49	30	):	):	PUNCT
iajs-2923	49	31	the	the	DET
iajs-2923	49	32	projection	projection	NOUN
iajs-2923	49	33	jungck	jungck	PROPN
iajs-2923	49	34	-	-	PUNCT
iajs-2923	49	35	thianwan	thianwan	PROPN
iajs-2923	49	36	algorithm	algorithm	PROPN
iajs-2923	49	37	is	be	AUX
iajs-2923	49	38	defined	define	VERB
iajs-2923	49	39	as	as	SCONJ
iajs-2923	49	40	follows	follow	VERB
iajs-2923	49	41	:	:	PUNCT
iajs-2923	49	42	ψ𝓏𝑛+1	ψ𝓏𝑛+1	PROPN
iajs-2923	49	43	=	=	SYM
iajs-2923	49	44	(	(	PUNCT
iajs-2923	49	45	1	1	NUM
iajs-2923	49	46	−	−	PROPN
iajs-2923	49	47	𝛼𝑛)ψ𝒫𝒸(𝓇𝑛	𝛼𝑛)ψ𝒫𝒸(𝓇𝑛	PROPN
iajs-2923	49	48	)	)	PUNCT
iajs-2923	50	1	+	+	CCONJ
iajs-2923	50	2	𝛼𝑛𝒫𝒸𝑇𝓇𝑛	𝛼𝑛𝒫𝒸𝑇𝓇𝑛	ADV
iajs-2923	50	3	ψ𝓇𝑛	ψ𝓇𝑛	NOUN
iajs-2923	50	4	=	=	X
iajs-2923	50	5	(	(	PUNCT
iajs-2923	50	6	1	1	NUM
iajs-2923	50	7	−	−	NOUN
iajs-2923	50	8	𝛽𝑛)ψ𝒫𝒸(𝓏𝑛	𝛽𝑛)ψ𝒫𝒸(𝓏𝑛	NOUN
iajs-2923	50	9	)	)	PUNCT
iajs-2923	51	1	+	+	CCONJ
iajs-2923	51	2	𝛽𝑛𝒫𝒸𝑇𝓏𝑛	𝛽𝑛𝒫𝒸𝑇𝓏𝑛	NOUN
iajs-2923	51	3	,	,	PUNCT
iajs-2923	51	4	𝓏0	𝓏0	PROPN
iajs-2923	51	5	∈	∈	PROPN
iajs-2923	51	6	𝐶.	𝐶.	PROPN
iajs-2923	51	7	and	and	CCONJ
iajs-2923	51	8	this	this	DET
iajs-2923	51	9	mapping	mapping	NOUN
iajs-2923	51	10	is	be	AUX
iajs-2923	51	11	commute	commute	NOUN
iajs-2923	51	12	if	if	SCONJ
iajs-2923	51	13	ψ𝒫𝒸(𝓍𝑛	ψ𝒫𝒸(𝓍𝑛	NOUN
iajs-2923	51	14	)	)	PUNCT
iajs-2923	51	15	=	=	SYM
iajs-2923	51	16	𝒫𝒸ψ(𝓍𝑛	𝒫𝒸ψ(𝓍𝑛	PROPN
iajs-2923	51	17	)	)	PUNCT
iajs-2923	51	18	.	.	PUNCT
iajs-2923	52	1	now	now	ADV
iajs-2923	52	2	,	,	PUNCT
iajs-2923	52	3	we	we	PRON
iajs-2923	52	4	talk	talk	VERB
iajs-2923	52	5	about	about	ADP
iajs-2923	52	6	convergence	convergence	NOUN
iajs-2923	52	7	,	,	PUNCT
iajs-2923	52	8	stability	stability	NOUN
iajs-2923	52	9	and	and	CCONJ
iajs-2923	52	10	rate	rate	NOUN
iajs-2923	52	11	of	of	ADP
iajs-2923	52	12	convergence	convergence	NOUN
iajs-2923	52	13	.	.	PUNCT
iajs-2923	53	1	lemma	lemma	PROPN
iajs-2923	53	2	(	(	PUNCT
iajs-2923	53	3	2.6	2.6	NUM
iajs-2923	53	4	):	):	PUNCT
iajs-2923	53	5	let	let	VERB
iajs-2923	53	6	𝐶	𝐶	PROPN
iajs-2923	53	7	be	be	AUX
iajs-2923	53	8	a	a	DET
iajs-2923	53	9	non	non	ADJ
iajs-2923	53	10	-	-	ADJ
iajs-2923	53	11	empty	empty	ADJ
iajs-2923	53	12	closed	closed	ADJ
iajs-2923	53	13	convex	convex	NOUN
iajs-2923	53	14	subset	subset	NOUN
iajs-2923	53	15	of	of	ADP
iajs-2923	53	16	a	a	DET
iajs-2923	53	17	uniformly	uniformly	ADJ
iajs-2923	53	18	convex	convex	NOUN
iajs-2923	53	19	banach	banach	NOUN
iajs-2923	53	20	space	space	NOUN
iajs-2923	53	21	𝒰.	𝒰.	NOUN
iajs-2923	53	22	the	the	DET
iajs-2923	53	23	mappings	mapping	NOUN
iajs-2923	53	24	𝑇	𝑇	PROPN
iajs-2923	53	25	,	,	PUNCT
iajs-2923	53	26	ψ	ψ	ADP
iajs-2923	53	27	:	:	PUNCT
iajs-2923	53	28	𝐶	𝐶	PROPN
iajs-2923	53	29	→	→	SYM
iajs-2923	53	30	𝐶	𝐶	PROPN
iajs-2923	53	31	are	be	AUX
iajs-2923	53	32	a	a	DET
iajs-2923	53	33	projection	projection	NOUN
iajs-2923	53	34	jungck	jungck	NOUN
iajs-2923	53	35	zn	zn	PROPN
iajs-2923	53	36	-	-	PUNCT
iajs-2923	53	37	suzuki	suzuki	PROPN
iajs-2923	53	38	generalized	generalize	VERB
iajs-2923	53	39	if	if	SCONJ
iajs-2923	53	40	{	{	PUNCT
iajs-2923	53	41	ψ𝑢𝑛	ψ𝑢𝑛	NOUN
iajs-2923	53	42	}	}	PUNCT
iajs-2923	53	43	generated	generate	VERB
iajs-2923	53	44	by	by	ADP
iajs-2923	53	45	projection	projection	NOUN
iajs-2923	53	46	jungck	jungck	PROPN
iajs-2923	53	47	-	-	PUNCT
iajs-2923	53	48	normal	normal	ADJ
iajs-2923	53	49	𝒩	𝒩	PROPN
iajs-2923	53	50	algorithm	algorithm	NOUN
iajs-2923	53	51	,	,	PUNCT
iajs-2923	53	52	such	such	ADJ
iajs-2923	53	53	that	that	SCONJ
iajs-2923	53	54	1	1	NUM
iajs-2923	53	55	.	.	PUNCT
iajs-2923	54	1	lim	lim	NOUN
iajs-2923	54	2	𝑛→∞	𝑛→∞	NUM
iajs-2923	54	3	‖ψ𝑢𝑛	‖ψ𝑢𝑛	PROPN
iajs-2923	54	4	−	−	PROPN
iajs-2923	54	5	𝑝‖	𝑝‖	ADP
iajs-2923	54	6	exists	exist	VERB
iajs-2923	54	7	for	for	ADP
iajs-2923	54	8	all	all	DET
iajs-2923	54	9	𝑝	𝑝	PROPN
iajs-2923	54	10	∈	∈	PROPN
iajs-2923	54	11	𝒞ℱ(𝒫𝒸	𝒞ℱ(𝒫𝒸	PROPN
iajs-2923	54	12	,	,	PUNCT
iajs-2923	54	13	𝑇	𝑇	PROPN
iajs-2923	54	14	,	,	PUNCT
iajs-2923	54	15	ψ	ψ	NOUN
iajs-2923	54	16	)	)	PUNCT
iajs-2923	54	17	,	,	PUNCT
iajs-2923	54	18	where	where	SCONJ
iajs-2923	54	19	𝒞ℱ(𝒫𝒸	𝒞ℱ(𝒫𝒸	PROPN
iajs-2923	54	20	,	,	PUNCT
iajs-2923	54	21	𝑇	𝑇	PROPN
iajs-2923	54	22	,	,	PUNCT
iajs-2923	54	23	ψ	ψ	NOUN
iajs-2923	54	24	)	)	PUNCT
iajs-2923	54	25	is	be	AUX
iajs-2923	54	26	the	the	DET
iajs-2923	54	27	family	family	NOUN
iajs-2923	54	28	of	of	ADP
iajs-2923	54	29	a	a	DET
iajs-2923	54	30	common	common	ADJ
iajs-2923	54	31	fixed	fix	VERB
iajs-2923	54	32	point	point	NOUN
iajs-2923	54	33	.	.	PUNCT
iajs-2923	55	1	2	2	X
iajs-2923	55	2	.	.	X
iajs-2923	55	3	lim	lim	NOUN
iajs-2923	55	4	𝑛→∞	𝑛→∞	NUM
iajs-2923	55	5	‖ψψ𝑢𝑛	‖ψψ𝑢𝑛	NOUN
iajs-2923	55	6	−	−	NOUN
iajs-2923	55	7	ψ𝒫𝒸(𝑢𝑛)‖	ψ𝒫𝒸(𝑢𝑛)‖	X
iajs-2923	55	8	=	=	SYM
iajs-2923	55	9	0	0	NUM
iajs-2923	56	1	proof	proof	NOUN
iajs-2923	56	2	:	:	PUNCT
iajs-2923	56	3	let	let	VERB
iajs-2923	56	4	𝑝	𝑝	PROPN
iajs-2923	56	5	∈	∈	PROPN
iajs-2923	56	6	𝒞ℱ(𝒫𝒸	𝒞ℱ(𝒫𝒸	PROPN
iajs-2923	56	7	,	,	PUNCT
iajs-2923	56	8	𝑇	𝑇	PROPN
iajs-2923	56	9	,	,	PUNCT
iajs-2923	56	10	ψ	ψ	NOUN
iajs-2923	56	11	)	)	PUNCT
iajs-2923	56	12	,	,	PUNCT
iajs-2923	56	13	‖ψ𝑢𝑛+1	‖ψ𝑢𝑛+1	ADP
iajs-2923	56	14	−	−	X
iajs-2923	56	15	𝑝‖	𝑝‖	NOUN
iajs-2923	56	16	=	=	SYM
iajs-2923	56	17	‖𝒫𝒸𝑇((1	‖𝒫𝒸𝑇((1	PROPN
iajs-2923	56	18	−	−	PROPN
iajs-2923	56	19	𝛼𝑛)ψ𝑢𝑛	𝛼𝑛)ψ𝑢𝑛	PROPN
iajs-2923	56	20	+	+	CCONJ
iajs-2923	56	21	𝛼𝑛𝒫𝒸(𝑢𝑛	𝛼𝑛𝒫𝒸(𝑢𝑛	NUM
iajs-2923	56	22	)	)	PUNCT
iajs-2923	56	23	)	)	PUNCT
iajs-2923	57	1	−	−	PROPN
iajs-2923	57	2	𝑝‖	𝑝‖	PROPN
iajs-2923	57	3	≤	≤	PROPN
iajs-2923	57	4	‖𝑇((1	‖𝑇((1	VERB
iajs-2923	57	5	−	−	PROPN
iajs-2923	57	6	𝛼𝑛)ψ𝑢𝑛	𝛼𝑛)ψ𝑢𝑛	PROPN
iajs-2923	57	7	+	+	CCONJ
iajs-2923	57	8	𝛼𝑛𝒫𝒸(𝑢𝑛	𝛼𝑛𝒫𝒸(𝑢𝑛	NUM
iajs-2923	57	9	)	)	PUNCT
iajs-2923	57	10	)	)	PUNCT
iajs-2923	58	1	−	−	PROPN
iajs-2923	58	2	𝑝‖	𝑝‖	PROPN
iajs-2923	58	3	≤	≤	PROPN
iajs-2923	58	4	𝐿‖ψ((1	𝐿‖ψ((1	VERB
iajs-2923	58	5	−	−	PROPN
iajs-2923	58	6	𝛼𝑛)ψ𝑢𝑛	𝛼𝑛)ψ𝑢𝑛	PROPN
iajs-2923	58	7	+	+	CCONJ
iajs-2923	58	8	𝛼𝑛𝒫𝒸(𝑢𝑛	𝛼𝑛𝒫𝒸(𝑢𝑛	NUM
iajs-2923	58	9	)	)	PUNCT
iajs-2923	58	10	)	)	PUNCT
iajs-2923	59	1	−	−	PROPN
iajs-2923	59	2	𝑝‖	𝑝‖	NOUN
iajs-2923	59	3	+	+	SYM
iajs-2923	59	4	𝜙(‖𝑝−𝒫𝒸(𝑝)‖+‖𝑝−ψ𝑝‖	𝜙(‖𝑝−𝒫𝒸(𝑝)‖+‖𝑝−ψ𝑝‖	NOUN
iajs-2923	59	5	)	)	PUNCT
iajs-2923	59	6	1+max{‖𝒫𝒸(𝑝)−𝒫𝒸((1−𝛼𝑛)ψ𝑢𝑛+𝛼𝑛𝒫𝒸(𝑢𝑛))‖,‖ψ𝑝−ψ((1−𝛼𝑛)ψ𝑢𝑛+𝛼𝑛𝒫𝒸(𝑢𝑛))‖	1+max{‖𝒫𝒸(𝑝)−𝒫𝒸((1−𝛼𝑛)ψ𝑢𝑛+𝛼𝑛𝒫𝒸(𝑢𝑛))‖,‖ψ𝑝−ψ((1−𝛼𝑛)ψ𝑢𝑛+𝛼𝑛𝒫𝒸(𝑢𝑛))‖	NUM
iajs-2923	59	7	}	}	PUNCT
iajs-2923	59	8	≤	≤	NOUN
iajs-2923	60	1	[	[	X
iajs-2923	60	2	(	(	PUNCT
iajs-2923	60	3	1	1	NUM
iajs-2923	60	4	−	−	PROPN
iajs-2923	60	5	𝛼𝑛)‖ψψ𝑢𝑛	𝛼𝑛)‖ψψ𝑢𝑛	PROPN
iajs-2923	60	6	−	−	PUNCT
iajs-2923	60	7	𝑝‖	𝑝‖	NOUN
iajs-2923	60	8	+	+	SYM
iajs-2923	60	9	𝛼𝑛‖ψ𝒫𝒸(𝑢𝑛	𝛼𝑛‖ψ𝒫𝒸(𝑢𝑛	NOUN
iajs-2923	60	10	)	)	PUNCT
iajs-2923	60	11	−	−	ADP
iajs-2923	61	1	𝑝‖	𝑝‖	PROPN
iajs-2923	61	2	]	]	PUNCT
iajs-2923	61	3	≤	≤	NUM
iajs-2923	62	1	[	[	X
iajs-2923	62	2	(	(	PUNCT
iajs-2923	62	3	1	1	NUM
iajs-2923	62	4	−	−	PROPN
iajs-2923	62	5	𝛼𝑛)‖ψ𝑢𝑛	𝛼𝑛)‖ψ𝑢𝑛	NUM
iajs-2923	62	6	−	−	PROPN
iajs-2923	62	7	𝑝‖	𝑝‖	PROPN
iajs-2923	62	8	+	+	SYM
iajs-2923	62	9	𝛼𝑛‖𝒫𝒸ψ(𝑢𝑛	𝛼𝑛‖𝒫𝒸ψ(𝑢𝑛	PROPN
iajs-2923	62	10	)	)	PUNCT
iajs-2923	62	11	−	−	ADP
iajs-2923	62	12	𝑝‖	𝑝‖	PROPN
iajs-2923	62	13	]	]	PUNCT
iajs-2923	62	14	≤	≤	NUM
iajs-2923	62	15	‖ψ𝑢𝑛	‖ψ𝑢𝑛	PROPN
iajs-2923	62	16	−	−	NOUN
iajs-2923	62	17	𝑝‖	𝑝‖	PROPN
iajs-2923	63	1	so	so	ADV
iajs-2923	63	2	,	,	PUNCT
iajs-2923	63	3	we	we	PRON
iajs-2923	63	4	have	have	VERB
iajs-2923	63	5	‖ψ𝑢𝑛+1	‖ψ𝑢𝑛+1	ADP
iajs-2923	63	6	−	−	VERB
iajs-2923	63	7	𝑝‖	𝑝‖	NOUN
iajs-2923	63	8	≤	≤	NUM
iajs-2923	63	9	‖ψ𝑢𝑛	‖ψ𝑢𝑛	PROPN
iajs-2923	63	10	−	−	PROPN
iajs-2923	63	11	𝑝‖	𝑝‖	NOUN
iajs-2923	63	12	(	(	PUNCT
iajs-2923	63	13	2.1	2.1	NUM
iajs-2923	63	14	)	)	PUNCT
iajs-2923	63	15	≤	≤	NOUN
iajs-2923	63	16	‖ψ𝑢𝑛−1	‖ψ𝑢𝑛−1	NOUN
iajs-2923	63	17	−	−	PROPN
iajs-2923	63	18	𝑝‖	𝑝‖	NOUN
iajs-2923	63	19	:	:	PUNCT
iajs-2923	63	20	≤	≤	NUM
iajs-2923	63	21	‖ψ𝑢0	‖ψ𝑢0	NOUN
iajs-2923	63	22	−	−	ADP
iajs-2923	63	23	𝑝‖	𝑝‖	NOUN
iajs-2923	63	24	(	(	PUNCT
iajs-2923	63	25	2.2	2.2	NUM
iajs-2923	63	26	)	)	PUNCT
iajs-2923	63	27	from	from	ADP
iajs-2923	63	28	(	(	PUNCT
iajs-2923	63	29	2.1	2.1	NUM
iajs-2923	63	30	)	)	PUNCT
iajs-2923	63	31	and	and	CCONJ
iajs-2923	63	32	(	(	PUNCT
iajs-2923	63	33	2.2	2.2	NUM
iajs-2923	63	34	)	)	PUNCT
iajs-2923	63	35	lim	lim	NOUN
iajs-2923	63	36	𝑛→∞	𝑛→∞	NUM
iajs-2923	63	37	‖ψ𝑢𝑛	‖ψ𝑢𝑛	PROPN
iajs-2923	63	38	−	−	PROPN
iajs-2923	63	39	𝑝‖	𝑝‖	PRON
iajs-2923	63	40	is	be	AUX
iajs-2923	63	41	exist	exist	VERB
iajs-2923	63	42	now	now	ADV
iajs-2923	63	43	to	to	PART
iajs-2923	63	44	prove	prove	VERB
iajs-2923	63	45	lim	lim	NOUN
iajs-2923	63	46	𝑛→∞	𝑛→∞	NUM
iajs-2923	63	47	‖ψψ𝑢𝑛	‖ψψ𝑢𝑛	NOUN
iajs-2923	63	48	−	−	NOUN
iajs-2923	63	49	ψ𝒫𝒸(𝑢𝑛)‖	ψ𝒫𝒸(𝑢𝑛)‖	PUNCT
iajs-2923	63	50	=	=	SYM
iajs-2923	63	51	0	0	PUNCT
iajs-2923	63	52	since	since	SCONJ
iajs-2923	63	53	,	,	PUNCT
iajs-2923	63	54	lim	lim	PROPN
iajs-2923	63	55	𝑛→∞	𝑛→∞	NUM
iajs-2923	63	56	‖ψ𝑢𝑛	‖ψ𝑢𝑛	PROPN
iajs-2923	63	57	−	−	NOUN
iajs-2923	63	58	𝑝‖	𝑝‖	NOUN
iajs-2923	63	59	=	=	SYM
iajs-2923	63	60	𝑐	𝑐	PROPN
iajs-2923	63	61	ihjpas	ihjpa	VERB
iajs-2923	63	62	.	.	PUNCT
iajs-2923	64	1	36(1)2023	36(1)2023	NUM
iajs-2923	64	2	295	295	NUM
iajs-2923	64	3	⟹	⟹	NUM
iajs-2923	64	4	lim	lim	PROPN
iajs-2923	64	5	𝑛→∞	𝑛→∞	NUM
iajs-2923	64	6	𝑠𝑢𝑝‖ψ𝑢𝑛	𝑠𝑢𝑝‖ψ𝑢𝑛	PROPN
iajs-2923	64	7	−	−	PROPN
iajs-2923	64	8	𝑝‖	𝑝‖	NOUN
iajs-2923	64	9	=	=	SYM
iajs-2923	64	10	𝑐	𝑐	PROPN
iajs-2923	64	11	now	now	ADV
iajs-2923	64	12	,	,	PUNCT
iajs-2923	64	13	lim	lim	PROPN
iajs-2923	64	14	𝑛→∞	𝑛→∞	NUM
iajs-2923	64	15	𝑠𝑢𝑝	𝑠𝑢𝑝	VERB
iajs-2923	64	16	‖ψψ𝑢𝑛	‖ψψ𝑢𝑛	NUM
iajs-2923	64	17	−	−	PROPN
iajs-2923	64	18	𝑝‖	𝑝‖	NOUN
iajs-2923	64	19	≤	≤	PROPN
iajs-2923	64	20	lim	lim	PROPN
iajs-2923	64	21	𝑛→∞	𝑛→∞	NUM
iajs-2923	64	22	𝑠𝑢𝑝	𝑠𝑢𝑝	NOUN
iajs-2923	64	23	‖ψ𝑢𝑛	‖ψ𝑢𝑛	PROPN
iajs-2923	64	24	−	−	NOUN
iajs-2923	64	25	𝑝‖	𝑝‖	NOUN
iajs-2923	64	26	=	=	SYM
iajs-2923	64	27	𝑐	𝑐	PROPN
iajs-2923	65	1	so	so	ADV
iajs-2923	65	2	,	,	PUNCT
iajs-2923	65	3	lim	lim	PROPN
iajs-2923	65	4	𝑛→∞	𝑛→∞	NUM
iajs-2923	65	5	𝑠𝑢𝑝	𝑠𝑢𝑝	VERB
iajs-2923	65	6	‖ψψ𝑢𝑛	‖ψψ𝑢𝑛	NUM
iajs-2923	65	7	−	−	PROPN
iajs-2923	65	8	𝑝‖	𝑝‖	NOUN
iajs-2923	65	9	≤	≤	PROPN
iajs-2923	65	10	𝑐	𝑐	PROPN
iajs-2923	65	11	(	(	PUNCT
iajs-2923	65	12	2.3	2.3	NUM
iajs-2923	65	13	)	)	PUNCT
iajs-2923	65	14	to	to	ADP
iajs-2923	65	15	proof	proof	NOUN
iajs-2923	65	16	lim	lim	PROPN
iajs-2923	65	17	𝑛→∞	𝑛→∞	NUM
iajs-2923	65	18	𝑠𝑢𝑝	𝑠𝑢𝑝	NOUN
iajs-2923	65	19	‖ψ𝒫𝒸(𝑢𝑛	‖ψ𝒫𝒸(𝑢𝑛	NUM
iajs-2923	65	20	)	)	PUNCT
iajs-2923	65	21	−	−	PROPN
iajs-2923	65	22	𝑝‖	𝑝‖	NOUN
iajs-2923	65	23	≤	≤	PROPN
iajs-2923	65	24	𝑐	𝑐	PROPN
iajs-2923	65	25	lim	lim	PROPN
iajs-2923	65	26	𝑛→∞	𝑛→∞	NUM
iajs-2923	65	27	𝑠𝑢𝑝	𝑠𝑢𝑝	NOUN
iajs-2923	65	28	‖ψ𝒫𝒸(𝑢𝑛	‖ψ𝒫𝒸(𝑢𝑛	NUM
iajs-2923	65	29	)	)	PUNCT
iajs-2923	65	30	−	−	PROPN
iajs-2923	65	31	𝑝‖	𝑝‖	NOUN
iajs-2923	65	32	≤	≤	NUM
iajs-2923	65	33	lim	lim	PROPN
iajs-2923	65	34	𝑛→∞	𝑛→∞	NUM
iajs-2923	65	35	𝑠𝑢𝑝	𝑠𝑢𝑝	NOUN
iajs-2923	65	36	‖𝒫𝒸ψ(𝑢𝑛	‖𝒫𝒸ψ(𝑢𝑛	NUM
iajs-2923	65	37	)	)	PUNCT
iajs-2923	65	38	−	−	PROPN
iajs-2923	65	39	𝑝‖	𝑝‖	PROPN
iajs-2923	65	40	≤	≤	NUM
iajs-2923	65	41	lim	lim	PROPN
iajs-2923	65	42	𝑛→∞	𝑛→∞	NUM
iajs-2923	65	43	𝑠𝑢𝑝‖ψ𝑢𝑛	𝑠𝑢𝑝‖ψ𝑢𝑛	PROPN
iajs-2923	65	44	−	−	PROPN
iajs-2923	65	45	𝑝‖	𝑝‖	NOUN
iajs-2923	65	46	=	=	SYM
iajs-2923	65	47	𝑐	𝑐	PROPN
iajs-2923	65	48	so	so	ADV
iajs-2923	65	49	,	,	PUNCT
iajs-2923	65	50	lim	lim	PROPN
iajs-2923	65	51	𝑛→∞	𝑛→∞	NUM
iajs-2923	65	52	𝑠𝑢𝑝	𝑠𝑢𝑝	NOUN
iajs-2923	65	53	‖ψ𝒫𝒸(𝑢𝑛	‖ψ𝒫𝒸(𝑢𝑛	NUM
iajs-2923	65	54	)	)	PUNCT
iajs-2923	65	55	−	−	PROPN
iajs-2923	65	56	𝑝‖	𝑝‖	NOUN
iajs-2923	65	57	≤	≤	PROPN
iajs-2923	65	58	𝑐	𝑐	PROPN
iajs-2923	65	59	(	(	PUNCT
iajs-2923	65	60	2.4	2.4	NUM
iajs-2923	65	61	)	)	PUNCT
iajs-2923	65	62	since	since	SCONJ
iajs-2923	65	63	𝑐	𝑐	PROPN
iajs-2923	65	64	=	=	SYM
iajs-2923	65	65	lim	lim	PROPN
iajs-2923	65	66	𝑛→∞	𝑛→∞	NUM
iajs-2923	65	67	𝑠𝑢𝑝‖ψ𝑢𝑛+1	𝑠𝑢𝑝‖ψ𝑢𝑛+1	NOUN
iajs-2923	65	68	−	−	PROPN
iajs-2923	65	69	𝑝‖	𝑝‖	PROPN
iajs-2923	65	70	=	=	SYM
iajs-2923	65	71	lim	lim	PROPN
iajs-2923	65	72	𝑛→∞	𝑛→∞	NUM
iajs-2923	65	73	𝑠𝑢𝑝‖𝒫𝒸𝑇((1	𝑠𝑢𝑝‖𝒫𝒸𝑇((1	PROPN
iajs-2923	65	74	−	−	PROPN
iajs-2923	65	75	𝛼𝑛)ψ𝑢𝑛	𝛼𝑛)ψ𝑢𝑛	PROPN
iajs-2923	65	76	+	+	CCONJ
iajs-2923	65	77	𝛼𝑛𝒫𝒸(𝑢𝑛	𝛼𝑛𝒫𝒸(𝑢𝑛	NUM
iajs-2923	65	78	)	)	PUNCT
iajs-2923	65	79	)	)	PUNCT
iajs-2923	65	80	−	−	PROPN
iajs-2923	65	81	𝑝‖	𝑝‖	PROPN
iajs-2923	65	82	≤	≤	NUM
iajs-2923	65	83	lim	lim	PROPN
iajs-2923	65	84	𝑛→∞	𝑛→∞	NUM
iajs-2923	65	85	𝑠𝑢𝑝‖𝑇((1	𝑠𝑢𝑝‖𝑇((1	PROPN
iajs-2923	65	86	−	−	PROPN
iajs-2923	65	87	𝛼𝑛)ψ𝑢𝑛	𝛼𝑛)ψ𝑢𝑛	PROPN
iajs-2923	65	88	+	+	CCONJ
iajs-2923	65	89	𝛼𝑛𝒫𝒸(𝑢𝑛	𝛼𝑛𝒫𝒸(𝑢𝑛	NUM
iajs-2923	65	90	)	)	PUNCT
iajs-2923	65	91	)	)	PUNCT
iajs-2923	66	1	−	−	PROPN
iajs-2923	66	2	𝑝‖	𝑝‖	PROPN
iajs-2923	66	3	≤	≤	NUM
iajs-2923	66	4	lim	lim	PROPN
iajs-2923	66	5	𝑛→∞	𝑛→∞	NUM
iajs-2923	66	6	𝑠𝑢𝑝‖(1	𝑠𝑢𝑝‖(1	NOUN
iajs-2923	66	7	−	−	PROPN
iajs-2923	66	8	𝛼𝑛)(ψψ𝑢𝑛	𝛼𝑛)(ψψ𝑢𝑛	PROPN
iajs-2923	66	9	−	−	PROPN
iajs-2923	66	10	𝑝	𝑝	PROPN
iajs-2923	66	11	)	)	PUNCT
iajs-2923	66	12	+	+	NUM
iajs-2923	66	13	𝛼𝑛(ψ𝒫𝒸(𝑢𝑛	𝛼𝑛(ψ𝒫𝒸(𝑢𝑛	NUM
iajs-2923	66	14	)	)	PUNCT
iajs-2923	66	15	−	−	NOUN
iajs-2923	66	16	𝑝)‖	𝑝)‖	NOUN
iajs-2923	66	17	(	(	PUNCT
iajs-2923	66	18	2.5	2.5	NUM
iajs-2923	66	19	)	)	PUNCT
iajs-2923	66	20	≤	≤	NOUN
iajs-2923	66	21	lim	lim	PROPN
iajs-2923	66	22	𝑛→∞	𝑛→∞	NUM
iajs-2923	66	23	𝑠𝑢𝑝[(1	𝑠𝑢𝑝[(1	PROPN
iajs-2923	66	24	−	−	PROPN
iajs-2923	66	25	𝛼𝑛)‖ψ𝑢𝑛	𝛼𝑛)‖ψ𝑢𝑛	PROPN
iajs-2923	66	26	−	−	PROPN
iajs-2923	66	27	𝑝‖	𝑝‖	PROPN
iajs-2923	66	28	+	+	SYM
iajs-2923	66	29	𝛼𝑛‖𝒫𝒸ψ(𝑢𝑛	𝛼𝑛‖𝒫𝒸ψ(𝑢𝑛	PROPN
iajs-2923	66	30	)	)	PUNCT
iajs-2923	66	31	−	−	ADP
iajs-2923	67	1	𝑝‖	𝑝‖	PROPN
iajs-2923	67	2	]	]	PUNCT
iajs-2923	67	3	≤	≤	NUM
iajs-2923	67	4	lim	lim	PROPN
iajs-2923	67	5	𝑛→∞	𝑛→∞	NUM
iajs-2923	67	6	𝑠𝑢𝑝[(1	𝑠𝑢𝑝[(1	PROPN
iajs-2923	67	7	−	−	PROPN
iajs-2923	67	8	𝛼𝑛)‖ψ𝑢𝑛	𝛼𝑛)‖ψ𝑢𝑛	PROPN
iajs-2923	67	9	−	−	PROPN
iajs-2923	67	10	𝑝‖	𝑝‖	PROPN
iajs-2923	67	11	+	+	CCONJ
iajs-2923	67	12	𝛼𝑛‖ψ𝑢𝑛	𝛼𝑛‖ψ𝑢𝑛	X
iajs-2923	67	13	−	−	PROPN
iajs-2923	67	14	𝑝‖	𝑝‖	AUX
iajs-2923	67	15	]	]	X
iajs-2923	67	16	=	=	SYM
iajs-2923	67	17	lim	lim	PROPN
iajs-2923	67	18	𝑛→∞	𝑛→∞	NUM
iajs-2923	67	19	𝑠𝑢𝑝‖ψ𝑢𝑛	𝑠𝑢𝑝‖ψ𝑢𝑛	PROPN
iajs-2923	67	20	−	−	PROPN
iajs-2923	67	21	𝑝‖	𝑝‖	NOUN
iajs-2923	67	22	=	=	SYM
iajs-2923	67	23	𝑐	𝑐	PROPN
iajs-2923	67	24	so	so	ADV
iajs-2923	67	25	,	,	PUNCT
iajs-2923	67	26	lim	lim	PROPN
iajs-2923	67	27	𝑛→∞	𝑛→∞	NUM
iajs-2923	67	28	𝑠𝑢𝑝‖(1	𝑠𝑢𝑝‖(1	NOUN
iajs-2923	67	29	−	−	PROPN
iajs-2923	67	30	𝛼𝑛)(ψψ𝑢𝑛	𝛼𝑛)(ψψ𝑢𝑛	PROPN
iajs-2923	67	31	−	−	PROPN
iajs-2923	67	32	𝑝	𝑝	PROPN
iajs-2923	67	33	)	)	PUNCT
iajs-2923	67	34	+	+	NUM
iajs-2923	67	35	𝛼𝑛(ψ𝒫𝒸(𝑢𝑛	𝛼𝑛(ψ𝒫𝒸(𝑢𝑛	NUM
iajs-2923	67	36	)	)	PUNCT
iajs-2923	68	1	−	−	ADP
iajs-2923	68	2	𝑝)‖	𝑝)‖	NOUN
iajs-2923	68	3	=	=	SYM
iajs-2923	68	4	𝑐	𝑐	NOUN
iajs-2923	68	5	from	from	ADP
iajs-2923	68	6	(	(	PUNCT
iajs-2923	68	7	2.3	2.3	NUM
iajs-2923	68	8	)	)	PUNCT
iajs-2923	68	9	,	,	PUNCT
iajs-2923	68	10	(	(	PUNCT
iajs-2923	68	11	2.4	2.4	NUM
iajs-2923	68	12	)	)	PUNCT
iajs-2923	68	13	,	,	PUNCT
iajs-2923	68	14	(	(	PUNCT
iajs-2923	68	15	2.5	2.5	NUM
iajs-2923	68	16	)	)	PUNCT
iajs-2923	68	17	and	and	CCONJ
iajs-2923	68	18	by	by	ADP
iajs-2923	68	19	using	use	VERB
iajs-2923	68	20	lemma	lemma	PROPN
iajs-2923	68	21	(	(	PUNCT
iajs-2923	68	22	1.2	1.2	NUM
iajs-2923	68	23	)	)	PUNCT
iajs-2923	68	24	we	we	PRON
iajs-2923	68	25	get	get	VERB
iajs-2923	68	26	lim	lim	NOUN
iajs-2923	68	27	𝑛→∞	𝑛→∞	NUM
iajs-2923	68	28	‖ψψ𝑢𝑛	‖ψψ𝑢𝑛	NOUN
iajs-2923	68	29	−	−	NOUN
iajs-2923	68	30	ψ𝒫𝒸(𝑢𝑛)‖	ψ𝒫𝒸(𝑢𝑛)‖	X
iajs-2923	69	1	=	=	SYM
iajs-2923	69	2	0	0	X
iajs-2923	69	3	.	.	PUNCT
iajs-2923	70	1	lemma	lemma	PROPN
iajs-2923	70	2	(	(	PUNCT
iajs-2923	70	3	2.7	2.7	NUM
iajs-2923	70	4	):	):	PUNCT
iajs-2923	70	5	let	let	VERB
iajs-2923	70	6	𝑇	𝑇	PROPN
iajs-2923	70	7	,	,	PUNCT
iajs-2923	70	8	ψ	ψ	ADP
iajs-2923	70	9	:	:	PUNCT
iajs-2923	70	10	𝐶	𝐶	PROPN
iajs-2923	70	11	→	→	SYM
iajs-2923	70	12	𝐶	𝐶	PROPN
iajs-2923	70	13	are	be	AUX
iajs-2923	70	14	a	a	DET
iajs-2923	70	15	projection	projection	NOUN
iajs-2923	70	16	jungck	jungck	NOUN
iajs-2923	70	17	zn	zn	PROPN
iajs-2923	70	18	-	-	PUNCT
iajs-2923	70	19	suzuki	suzuki	PROPN
iajs-2923	70	20	generalized	generalize	VERB
iajs-2923	70	21	if	if	SCONJ
iajs-2923	70	22	{	{	PUNCT
iajs-2923	70	23	ψ𝑘𝑛	ψ𝑘𝑛	NOUN
iajs-2923	70	24	}	}	PUNCT
iajs-2923	70	25	generated	generate	VERB
iajs-2923	70	26	by	by	ADP
iajs-2923	70	27	the	the	DET
iajs-2923	70	28	projection	projection	NOUN
iajs-2923	70	29	jungck	jungck	PROPN
iajs-2923	70	30	-	-	PUNCT
iajs-2923	70	31	picard	picard	NOUN
iajs-2923	70	32	algorithm	algorithm	NOUN
iajs-2923	70	33	,	,	PUNCT
iajs-2923	70	34	such	such	ADJ
iajs-2923	70	35	that	that	SCONJ
iajs-2923	70	36	lim	lim	PROPN
iajs-2923	70	37	𝑛→∞	𝑛→∞	NUM
iajs-2923	70	38	‖ψ𝑘𝑛	‖ψ𝑘𝑛	PROPN
iajs-2923	70	39	−	−	PROPN
iajs-2923	70	40	𝑝‖	𝑝‖	NOUN
iajs-2923	70	41	exists	exist	VERB
iajs-2923	70	42	for	for	ADP
iajs-2923	70	43	all	all	DET
iajs-2923	70	44	𝑝	𝑝	PROPN
iajs-2923	70	45	∈	∈	PROPN
iajs-2923	70	46	𝒞ℱ(𝒫𝒸	𝒞ℱ(𝒫𝒸	PROPN
iajs-2923	70	47	,	,	PUNCT
iajs-2923	70	48	𝑇	𝑇	PROPN
iajs-2923	70	49	,	,	PUNCT
iajs-2923	70	50	ψ	ψ	NOUN
iajs-2923	70	51	)	)	PUNCT
iajs-2923	70	52	proof	proof	NOUN
iajs-2923	70	53	:	:	PUNCT
iajs-2923	70	54	let	let	VERB
iajs-2923	70	55	,	,	PUNCT
iajs-2923	70	56	𝑝	𝑝	PROPN
iajs-2923	70	57	∈	∈	PROPN
iajs-2923	70	58	𝒞ℱ(𝒫𝒸	𝒞ℱ(𝒫𝒸	PROPN
iajs-2923	70	59	,	,	PUNCT
iajs-2923	70	60	𝑇	𝑇	PROPN
iajs-2923	70	61	,	,	PUNCT
iajs-2923	70	62	ψ	ψ	NOUN
iajs-2923	70	63	)	)	PUNCT
iajs-2923	70	64	‖ψ𝑘𝑛+1	‖ψ𝑘𝑛+1	PUNCT
iajs-2923	71	1	−	−	X
iajs-2923	71	2	𝑝‖	𝑝‖	PROPN
iajs-2923	71	3	=	=	SYM
iajs-2923	71	4	‖𝒫𝒸𝑇𝑘𝑛	‖𝒫𝒸𝑇𝑘𝑛	PROPN
iajs-2923	71	5	−	−	PROPN
iajs-2923	71	6	𝑝‖	𝑝‖	PROPN
iajs-2923	71	7	≤	≤	PROPN
iajs-2923	71	8	‖𝑇𝑘𝑛	‖𝑇𝑘𝑛	PROPN
iajs-2923	71	9	−	−	NOUN
iajs-2923	71	10	𝑝‖	𝑝‖	NOUN
iajs-2923	71	11	≤	≤	NUM
iajs-2923	71	12	𝐿‖ψ𝑘𝑛	𝐿‖ψ𝑘𝑛	PROPN
iajs-2923	71	13	−	−	PROPN
iajs-2923	71	14	𝑝‖	𝑝‖	PROPN
iajs-2923	71	15	+	+	CCONJ
iajs-2923	71	16	𝜙(‖𝑝−𝒫𝒸(𝑝)‖+‖𝑝−ψ𝑝‖	𝜙(‖𝑝−𝒫𝒸(𝑝)‖+‖𝑝−ψ𝑝‖	NOUN
iajs-2923	71	17	)	)	PUNCT
iajs-2923	71	18	1+𝑚𝑎𝑥{‖𝒫𝒸(𝑝)−𝒫𝒸(𝑘𝑛)‖,‖ψ𝑝−ψ𝑘𝑛‖	1+𝑚𝑎𝑥{‖𝒫𝒸(𝑝)−𝒫𝒸(𝑘𝑛)‖,‖ψ𝑝−ψ𝑘𝑛‖	ADJ
iajs-2923	71	19	}	}	PUNCT
iajs-2923	71	20	≤	≤	NUM
iajs-2923	71	21	‖ψ𝑘𝑛	‖ψ𝑘𝑛	NOUN
iajs-2923	71	22	−	−	NOUN
iajs-2923	71	23	𝑝‖	𝑝‖	NOUN
iajs-2923	71	24	so	so	ADV
iajs-2923	71	25	,	,	PUNCT
iajs-2923	71	26	we	we	PRON
iajs-2923	71	27	have	have	VERB
iajs-2923	71	28	‖ψ𝑘𝑛+1	‖ψ𝑘𝑛+1	CCONJ
iajs-2923	71	29	−	−	X
iajs-2923	71	30	𝑝‖	𝑝‖	PROPN
iajs-2923	71	31	≤	≤	NUM
iajs-2923	71	32	‖ψ𝑘𝑛	‖ψ𝑘𝑛	PROPN
iajs-2923	71	33	−	−	PROPN
iajs-2923	71	34	𝑝‖	𝑝‖	PROPN
iajs-2923	71	35	⟹	⟹	PUNCT
iajs-2923	71	36	{	{	PUNCT
iajs-2923	71	37	ψ𝑘𝑛	ψ𝑘𝑛	NOUN
iajs-2923	71	38	}	}	PUNCT
iajs-2923	71	39	is	be	AUX
iajs-2923	71	40	non	non	ADJ
iajs-2923	71	41	-	-	ADJ
iajs-2923	71	42	increasing	increase	VERB
iajs-2923	71	43	sequence	sequence	NOUN
iajs-2923	71	44	(	(	PUNCT
iajs-2923	71	45	2.6	2.6	NUM
iajs-2923	71	46	)	)	PUNCT
iajs-2923	71	47	≤	≤	NUM
iajs-2923	71	48	‖ψ𝑘𝑛−1	‖ψ𝑘𝑛−1	NOUN
iajs-2923	71	49	−	−	PROPN
iajs-2923	71	50	𝑝‖	𝑝‖	PROPN
iajs-2923	71	51	:	:	PUNCT
iajs-2923	71	52	≤	≤	NUM
iajs-2923	71	53	‖ψ𝑘0	‖ψ𝑘0	PROPN
iajs-2923	71	54	−	−	PROPN
iajs-2923	71	55	𝑝‖	𝑝‖	PROPN
iajs-2923	71	56	⟹	⟹	PUNCT
iajs-2923	71	57	{	{	PUNCT
iajs-2923	71	58	ψ𝑘𝑛	ψ𝑘𝑛	NOUN
iajs-2923	71	59	}	}	PUNCT
iajs-2923	71	60	is	be	AUX
iajs-2923	71	61	bounded	bound	VERB
iajs-2923	71	62	sequence	sequence	NOUN
iajs-2923	71	63	(	(	PUNCT
iajs-2923	71	64	2.7	2.7	NUM
iajs-2923	71	65	)	)	PUNCT
iajs-2923	71	66	from	from	ADP
iajs-2923	71	67	(	(	PUNCT
iajs-2923	71	68	2.6	2.6	NUM
iajs-2923	71	69	)	)	PUNCT
iajs-2923	71	70	and	and	CCONJ
iajs-2923	71	71	(	(	PUNCT
iajs-2923	71	72	2.7	2.7	NUM
iajs-2923	71	73	)	)	PUNCT
iajs-2923	71	74	the	the	DET
iajs-2923	71	75	lim	lim	PROPN
iajs-2923	71	76	𝑛→∞	𝑛→∞	NUM
iajs-2923	71	77	‖ψ𝑘𝑛	‖ψ𝑘𝑛	PROPN
iajs-2923	71	78	−	−	PROPN
iajs-2923	71	79	𝑝‖	𝑝‖	NOUN
iajs-2923	71	80	is	be	AUX
iajs-2923	71	81	exist	exist	VERB
iajs-2923	71	82	.	.	PUNCT
iajs-2923	72	1	lemma	lemma	PROPN
iajs-2923	72	2	(	(	PUNCT
iajs-2923	72	3	2.8	2.8	NUM
iajs-2923	72	4	):	):	PUNCT
iajs-2923	72	5	let	let	VERB
iajs-2923	72	6	𝑇	𝑇	PROPN
iajs-2923	72	7	,	,	PUNCT
iajs-2923	72	8	ψ	ψ	ADP
iajs-2923	72	9	:	:	PUNCT
iajs-2923	72	10	𝐶	𝐶	PROPN
iajs-2923	72	11	→	→	SYM
iajs-2923	72	12	𝐶	𝐶	PROPN
iajs-2923	72	13	be	be	AUX
iajs-2923	72	14	a	a	DET
iajs-2923	72	15	projection	projection	NOUN
iajs-2923	72	16	jungck	jungck	NOUN
iajs-2923	72	17	zn	zn	PROPN
iajs-2923	72	18	-	-	PUNCT
iajs-2923	72	19	suzuki	suzuki	NOUN
iajs-2923	72	20	generalized	generalize	VERB
iajs-2923	72	21	mapping	mapping	NOUN
iajs-2923	72	22	if	if	SCONJ
iajs-2923	72	23	{	{	PUNCT
iajs-2923	72	24	ψ𝑛𝑛	ψ𝑛𝑛	NOUN
iajs-2923	72	25	}	}	PUNCT
iajs-2923	72	26	is	be	AUX
iajs-2923	72	27	generated	generate	VERB
iajs-2923	72	28	by	by	ADP
iajs-2923	72	29	the	the	DET
iajs-2923	72	30	projection	projection	PROPN
iajs-2923	72	31	jungck	jungck	PROPN
iajs-2923	72	32	-	-	PUNCT
iajs-2923	72	33	krasnoselskii	krasnoselskii	PROPN
iajs-2923	72	34	algorithm	algorithm	NOUN
iajs-2923	72	35	,	,	PUNCT
iajs-2923	72	36	such	such	ADJ
iajs-2923	72	37	that	that	SCONJ
iajs-2923	72	38	ihjpas	ihjpa	NOUN
iajs-2923	72	39	.	.	PUNCT
iajs-2923	73	1	36(1)2023	36(1)2023	NUM
iajs-2923	73	2	296	296	NUM
iajs-2923	73	3	1	1	NUM
iajs-2923	73	4	.	.	PUNCT
iajs-2923	74	1	lim	lim	NOUN
iajs-2923	74	2	𝑛→∞	𝑛→∞	NUM
iajs-2923	74	3	‖ψ𝑛𝑛	‖ψ𝑛𝑛	NOUN
iajs-2923	74	4	−	−	NOUN
iajs-2923	74	5	𝑝‖	𝑝‖	NOUN
iajs-2923	74	6	exists	exist	VERB
iajs-2923	74	7	for	for	ADP
iajs-2923	74	8	all	all	DET
iajs-2923	74	9	𝑝	𝑝	PROPN
iajs-2923	74	10	∈	∈	PROPN
iajs-2923	74	11	𝒞ℱ(𝒫𝒸	𝒞ℱ(𝒫𝒸	PROPN
iajs-2923	74	12	,	,	PUNCT
iajs-2923	74	13	𝑇	𝑇	PROPN
iajs-2923	74	14	,	,	PUNCT
iajs-2923	74	15	ψ	ψ	NOUN
iajs-2923	74	16	)	)	PUNCT
iajs-2923	74	17	2	2	NUM
iajs-2923	74	18	.	.	X
iajs-2923	75	1	lim	lim	PROPN
iajs-2923	75	2	𝑛→∞	𝑛→∞	NUM
iajs-2923	75	3	‖ψ𝒫𝒸(𝑛𝑛	‖ψ𝒫𝒸(𝑛𝑛	PROPN
iajs-2923	75	4	)	)	PUNCT
iajs-2923	75	5	−	−	NOUN
iajs-2923	76	1	𝒫𝒸𝑇𝑛𝑛‖	𝒫𝒸𝑇𝑛𝑛‖	PROPN
iajs-2923	76	2	=	=	SYM
iajs-2923	76	3	0	0	NUM
iajs-2923	76	4	proof	proof	NOUN
iajs-2923	76	5	:	:	PUNCT
iajs-2923	76	6	by	by	ADP
iajs-2923	76	7	following	follow	VERB
iajs-2923	76	8	the	the	DET
iajs-2923	76	9	same	same	ADJ
iajs-2923	76	10	steps	step	NOUN
iajs-2923	76	11	for	for	ADP
iajs-2923	76	12	the	the	DET
iajs-2923	76	13	proof	proof	NOUN
iajs-2923	76	14	of	of	ADP
iajs-2923	76	15	theorem	theorem	NOUN
iajs-2923	76	16	(	(	PUNCT
iajs-2923	76	17	2.6	2.6	NUM
iajs-2923	76	18	)	)	PUNCT
iajs-2923	76	19	,	,	PUNCT
iajs-2923	76	20	we	we	PRON
iajs-2923	76	21	get	get	VERB
iajs-2923	76	22	the	the	DET
iajs-2923	76	23	wanted	wanted	ADJ
iajs-2923	76	24	results	result	NOUN
iajs-2923	76	25	.	.	PUNCT
iajs-2923	77	1	lemma	lemma	PROPN
iajs-2923	77	2	(	(	PUNCT
iajs-2923	77	3	2.9	2.9	NUM
iajs-2923	77	4	):	):	PUNCT
iajs-2923	77	5	let	let	VERB
iajs-2923	77	6	𝑇	𝑇	PROPN
iajs-2923	77	7	,	,	PUNCT
iajs-2923	77	8	ψ	ψ	ADP
iajs-2923	77	9	:	:	PUNCT
iajs-2923	77	10	𝐶	𝐶	PROPN
iajs-2923	77	11	→	→	SYM
iajs-2923	77	12	𝐶	𝐶	PROPN
iajs-2923	77	13	are	be	AUX
iajs-2923	77	14	a	a	DET
iajs-2923	77	15	projection	projection	NOUN
iajs-2923	77	16	jungck	jungck	NOUN
iajs-2923	77	17	zn	zn	PROPN
iajs-2923	77	18	-	-	PUNCT
iajs-2923	77	19	suzuki	suzuki	NOUN
iajs-2923	77	20	generalized	generalize	VERB
iajs-2923	77	21	mapping	mapping	NOUN
iajs-2923	77	22	if	if	SCONJ
iajs-2923	77	23	{	{	PUNCT
iajs-2923	77	24	ψ𝓏𝑛	ψ𝓏𝑛	NOUN
iajs-2923	77	25	}	}	PUNCT
iajs-2923	77	26	is	be	AUX
iajs-2923	77	27	generated	generate	VERB
iajs-2923	77	28	by	by	ADP
iajs-2923	77	29	the	the	DET
iajs-2923	77	30	projection	projection	PROPN
iajs-2923	77	31	jungck	jungck	PROPN
iajs-2923	77	32	-	-	PUNCT
iajs-2923	77	33	thianwan	thianwan	PROPN
iajs-2923	77	34	algorithm	algorithm	PROPN
iajs-2923	77	35	,	,	PUNCT
iajs-2923	77	36	such	such	ADJ
iajs-2923	77	37	that	that	SCONJ
iajs-2923	77	38	:	:	PUNCT
iajs-2923	77	39	1	1	X
iajs-2923	77	40	.	.	X
iajs-2923	78	1	lim	lim	NOUN
iajs-2923	78	2	𝑛→∞	𝑛→∞	NUM
iajs-2923	78	3	‖ψ𝓏𝑛	‖ψ𝓏𝑛	PROPN
iajs-2923	78	4	−	−	PROPN
iajs-2923	78	5	𝑝‖	𝑝‖	NOUN
iajs-2923	78	6	exists	exist	VERB
iajs-2923	78	7	for	for	ADP
iajs-2923	78	8	all	all	DET
iajs-2923	78	9	𝑝	𝑝	PROPN
iajs-2923	78	10	∈	∈	PROPN
iajs-2923	78	11	𝒞ℱ(𝒫𝒸	𝒞ℱ(𝒫𝒸	PROPN
iajs-2923	78	12	,	,	PUNCT
iajs-2923	78	13	𝑇	𝑇	PROPN
iajs-2923	78	14	,	,	PUNCT
iajs-2923	78	15	ψ	ψ	NOUN
iajs-2923	78	16	)	)	PUNCT
iajs-2923	78	17	2	2	NUM
iajs-2923	78	18	.	.	PUNCT
iajs-2923	79	1	lim	lim	PROPN
iajs-2923	79	2	𝑛→∞	𝑛→∞	NUM
iajs-2923	79	3	‖ψ𝒫𝒸(𝓇𝑛	‖ψ𝒫𝒸(𝓇𝑛	PROPN
iajs-2923	79	4	)	)	PUNCT
iajs-2923	79	5	−	−	PROPN
iajs-2923	79	6	𝒫𝒸𝑇(𝓇𝑛)‖	𝒫𝒸𝑇(𝓇𝑛)‖	PROPN
iajs-2923	79	7	=	=	SYM
iajs-2923	79	8	0	0	NUM
iajs-2923	79	9	proof	proof	NOUN
iajs-2923	79	10	:	:	PUNCT
iajs-2923	79	11	proof	proof	NOUN
iajs-2923	79	12	in	in	ADP
iajs-2923	79	13	the	the	DET
iajs-2923	79	14	same	same	ADJ
iajs-2923	79	15	way	way	NOUN
iajs-2923	79	16	as	as	SCONJ
iajs-2923	79	17	lemma	lemma	PROPN
iajs-2923	79	18	proof	proof	NOUN
iajs-2923	79	19	(	(	PUNCT
iajs-2923	79	20	2.6	2.6	NUM
iajs-2923	79	21	)	)	PUNCT
iajs-2923	79	22	theorem	theorem	NOUN
iajs-2923	79	23	(	(	PUNCT
iajs-2923	79	24	2.10	2.10	NUM
iajs-2923	79	25	):	):	PUNCT
iajs-2923	79	26	let	let	VERB
iajs-2923	79	27	𝑇	𝑇	PROPN
iajs-2923	79	28	,	,	PUNCT
iajs-2923	79	29	ψ	ψ	ADP
iajs-2923	79	30	:	:	PUNCT
iajs-2923	79	31	𝐶	𝐶	PROPN
iajs-2923	79	32	→	→	SYM
iajs-2923	79	33	𝐶	𝐶	PROPN
iajs-2923	79	34	are	be	AUX
iajs-2923	79	35	a	a	DET
iajs-2923	79	36	projection	projection	NOUN
iajs-2923	79	37	jungck	jungck	NOUN
iajs-2923	79	38	zn	zn	PROPN
iajs-2923	79	39	-	-	PUNCT
iajs-2923	79	40	suzuki	suzuki	PROPN
iajs-2923	79	41	generalized	generalize	VERB
iajs-2923	79	42	mapping	mapping	NOUN
iajs-2923	79	43	with	with	ADP
iajs-2923	79	44	𝐿	𝐿	PROPN
iajs-2923	79	45	∈	∈	PROPN
iajs-2923	79	46	(	(	PUNCT
iajs-2923	79	47	0,1	0,1	NUM
iajs-2923	79	48	)	)	PUNCT
iajs-2923	79	49	.	.	PUNCT
iajs-2923	80	1	let	let	VERB
iajs-2923	80	2	{	{	PUNCT
iajs-2923	80	3	ψ𝑛𝑛	ψ𝑛𝑛	AUX
iajs-2923	80	4	}	}	PUNCT
iajs-2923	80	5	be	be	AUX
iajs-2923	80	6	projection	projection	NOUN
iajs-2923	80	7	jungck	jungck	NOUN
iajs-2923	80	8	-	-	PUNCT
iajs-2923	80	9	krasnoselskii	krasnoselskii	PROPN
iajs-2923	80	10	algorithm	algorithm	NOUN
iajs-2923	80	11	converging	converge	VERB
iajs-2923	80	12	to	to	ADP
iajs-2923	80	13	𝑝	𝑝	NOUN
iajs-2923	80	14	where	where	SCONJ
iajs-2923	80	15	𝛿	𝛿	DET
iajs-2923	80	16	∈	∈	PROPN
iajs-2923	80	17	(	(	PUNCT
iajs-2923	80	18	0,1	0,1	NUM
iajs-2923	80	19	)	)	PUNCT
iajs-2923	80	20	.	.	PUNCT
iajs-2923	81	1	then	then	ADV
iajs-2923	81	2	,	,	PUNCT
iajs-2923	81	3	the	the	DET
iajs-2923	81	4	projection	projection	NOUN
iajs-2923	81	5	jungck	jungck	PROPN
iajs-2923	81	6	-	-	PUNCT
iajs-2923	81	7	krasnoselskii	krasnoselskii	PROPN
iajs-2923	81	8	algorithm	algorithm	NOUN
iajs-2923	81	9	is	be	AUX
iajs-2923	81	10	(	(	PUNCT
iajs-2923	81	11	ψ	ψ	X
iajs-2923	81	12	,	,	PUNCT
iajs-2923	81	13	𝑇	𝑇	PROPN
iajs-2923	81	14	,	,	PUNCT
iajs-2923	81	15	𝒫𝒸)-stable	𝒫𝒸)-stable	PROPN
iajs-2923	81	16	.	.	PUNCT
iajs-2923	82	1	proof	proof	NOUN
iajs-2923	82	2	:	:	PUNCT
iajs-2923	82	3	let	let	VERB
iajs-2923	82	4	{	{	PUNCT
iajs-2923	82	5	𝓎𝑛	𝓎𝑛	PROPN
iajs-2923	82	6	}	}	PUNCT
iajs-2923	82	7	⊂	⊂	PROPN
iajs-2923	82	8	𝐶	𝐶	PROPN
iajs-2923	82	9	and	and	CCONJ
iajs-2923	82	10	휀𝑛	휀𝑛	NOUN
iajs-2923	82	11	=	=	SYM
iajs-2923	82	12	‖ψ𝓎𝑛+1	‖ψ𝓎𝑛+1	NOUN
iajs-2923	82	13	−	−	NOUN
iajs-2923	82	14	𝑓(𝑇	𝑓(𝑇	SYM
iajs-2923	82	15	,	,	PUNCT
iajs-2923	82	16	𝓎𝑛)‖	𝓎𝑛)‖	PROPN
iajs-2923	82	17	=	=	SYM
iajs-2923	82	18	‖ψ𝓎𝑛+1	‖ψ𝓎𝑛+1	PROPN
iajs-2923	82	19	−	−	PROPN
iajs-2923	82	20	(	(	PUNCT
iajs-2923	82	21	1	1	NUM
iajs-2923	82	22	−	−	PROPN
iajs-2923	82	23	𝛿)ψ𝒫𝒸(𝓎𝑛	𝛿)ψ𝒫𝒸(𝓎𝑛	PROPN
iajs-2923	82	24	)	)	PUNCT
iajs-2923	83	1	+	+	CCONJ
iajs-2923	83	2	𝛿𝒫𝒸𝑇𝓎𝑛‖	𝛿𝒫𝒸𝑇𝓎𝑛‖	PROPN
iajs-2923	83	3	so	so	ADV
iajs-2923	83	4	,	,	PUNCT
iajs-2923	83	5	휀𝑛	휀𝑛	PROPN
iajs-2923	83	6	=	=	SYM
iajs-2923	83	7	‖ψ𝓎𝑛+1	‖ψ𝓎𝑛+1	NUM
iajs-2923	83	8	−	−	NOUN
iajs-2923	83	9	(	(	PUNCT
iajs-2923	83	10	1	1	NUM
iajs-2923	83	11	−	−	PROPN
iajs-2923	83	12	𝛿)ψ𝒫𝒸(𝓎𝑛	𝛿)ψ𝒫𝒸(𝓎𝑛	PROPN
iajs-2923	83	13	)	)	PUNCT
iajs-2923	84	1	+	+	CCONJ
iajs-2923	84	2	𝛿𝒫𝒸𝑇𝓎𝑛‖	𝛿𝒫𝒸𝑇𝓎𝑛‖	PROPN
iajs-2923	84	3	if	if	SCONJ
iajs-2923	84	4	lim	lim	PROPN
iajs-2923	84	5	𝑛→∞	𝑛→∞	NUM
iajs-2923	84	6	휀𝑛	휀𝑛	VERB
iajs-2923	84	7	=	=	NOUN
iajs-2923	84	8	0	0	NUM
iajs-2923	84	9	,	,	PUNCT
iajs-2923	84	10	we	we	PRON
iajs-2923	84	11	get	get	VERB
iajs-2923	84	12	lim	lim	PROPN
iajs-2923	84	13	𝑛→∞	𝑛→∞	NUM
iajs-2923	84	14	ψ𝓎𝑛+1	ψ𝓎𝑛+1	ADJ
iajs-2923	84	15	=	=	SYM
iajs-2923	84	16	𝑝	𝑝	NOUN
iajs-2923	84	17	then	then	ADV
iajs-2923	84	18	,	,	PUNCT
iajs-2923	84	19	the	the	DET
iajs-2923	84	20	projection	projection	NOUN
iajs-2923	84	21	jungck	jungck	PROPN
iajs-2923	84	22	-	-	PUNCT
iajs-2923	84	23	krasnoselskii	krasnoselskii	PROPN
iajs-2923	84	24	algorithm	algorithm	NOUN
iajs-2923	84	25	is	be	AUX
iajs-2923	84	26	(	(	PUNCT
iajs-2923	84	27	ψ	ψ	X
iajs-2923	84	28	,	,	PUNCT
iajs-2923	84	29	𝑇	𝑇	PROPN
iajs-2923	84	30	,	,	PUNCT
iajs-2923	84	31	𝒫𝒸)-stable	𝒫𝒸)-stable	PROPN
iajs-2923	84	32	.	.	PUNCT
iajs-2923	85	1	theorem	theorem	NOUN
iajs-2923	85	2	(	(	PUNCT
iajs-2923	85	3	2.11	2.11	NUM
iajs-2923	85	4	):	):	PUNCT
iajs-2923	85	5	let	let	VERB
iajs-2923	85	6	𝑇	𝑇	PROPN
iajs-2923	85	7	,	,	PUNCT
iajs-2923	85	8	ψ	ψ	ADP
iajs-2923	85	9	:	:	PUNCT
iajs-2923	85	10	𝐶	𝐶	PROPN
iajs-2923	85	11	→	→	SYM
iajs-2923	85	12	𝐶	𝐶	PROPN
iajs-2923	85	13	are	be	AUX
iajs-2923	85	14	a	a	DET
iajs-2923	85	15	projection	projection	NOUN
iajs-2923	85	16	jungck	jungck	NOUN
iajs-2923	85	17	zn	zn	PROPN
iajs-2923	85	18	-	-	PUNCT
iajs-2923	85	19	suzuki	suzuki	PROPN
iajs-2923	85	20	generalized	generalize	VERB
iajs-2923	85	21	mapping	mapping	NOUN
iajs-2923	85	22	with	with	ADP
iajs-2923	85	23	𝐿	𝐿	PROPN
iajs-2923	85	24	∈	∈	PROPN
iajs-2923	85	25	(	(	PUNCT
iajs-2923	85	26	0,1	0,1	NUM
iajs-2923	85	27	)	)	PUNCT
iajs-2923	85	28	.	.	PUNCT
iajs-2923	86	1	let	let	VERB
iajs-2923	86	2	{	{	PUNCT
iajs-2923	86	3	ψ𝑢𝑛	ψ𝑢𝑛	NOUN
iajs-2923	86	4	}	}	PUNCT
iajs-2923	86	5	be	be	AUX
iajs-2923	86	6	a	a	DET
iajs-2923	86	7	projection	projection	NOUN
iajs-2923	86	8	jungck	jungck	NOUN
iajs-2923	86	9	-	-	PUNCT
iajs-2923	86	10	normal	normal	ADJ
iajs-2923	86	11	𝒩	𝒩	PROPN
iajs-2923	86	12	algorithm	algorithm	NOUN
iajs-2923	86	13	converging	converge	VERB
iajs-2923	86	14	to	to	ADP
iajs-2923	86	15	𝑝	𝑝	NOUN
iajs-2923	86	16	,	,	PUNCT
iajs-2923	86	17	where	where	SCONJ
iajs-2923	86	18	{	{	PUNCT
iajs-2923	86	19	𝛼𝑛	𝛼𝑛	NOUN
iajs-2923	86	20	}	}	PUNCT
iajs-2923	86	21	are	be	AUX
iajs-2923	86	22	sequences	sequence	NOUN
iajs-2923	86	23	in	in	ADP
iajs-2923	86	24	[	[	X
iajs-2923	86	25	0,1	0,1	NUM
iajs-2923	86	26	]	]	PUNCT
iajs-2923	86	27	,	,	PUNCT
iajs-2923	86	28	such	such	ADJ
iajs-2923	86	29	that	that	SCONJ
iajs-2923	86	30	0	0	NUM
iajs-2923	86	31	<	<	X
iajs-2923	86	32	𝛼	𝛼	PROPN
iajs-2923	86	33	≤	≤	PROPN
iajs-2923	86	34	𝛼𝑛.	𝛼𝑛.	PROPN
iajs-2923	86	35	then	then	ADV
iajs-2923	86	36	,	,	PUNCT
iajs-2923	86	37	the	the	DET
iajs-2923	86	38	projection	projection	NOUN
iajs-2923	86	39	jungck	jungck	NOUN
iajs-2923	86	40	-	-	PUNCT
iajs-2923	86	41	normal	normal	ADJ
iajs-2923	86	42	𝒩	𝒩	PROPN
iajs-2923	86	43	algorithm	algorithm	NOUN
iajs-2923	86	44	is	be	AUX
iajs-2923	86	45	(	(	PUNCT
iajs-2923	86	46	ψ	ψ	X
iajs-2923	86	47	,	,	PUNCT
iajs-2923	86	48	𝑇	𝑇	PROPN
iajs-2923	86	49	,	,	PUNCT
iajs-2923	86	50	𝒫𝒸)-stable	𝒫𝒸)-stable	PROPN
iajs-2923	86	51	.	.	PUNCT
iajs-2923	87	1	proof	proof	NOUN
iajs-2923	87	2	:	:	PUNCT
iajs-2923	87	3	let	let	VERB
iajs-2923	87	4	{	{	PUNCT
iajs-2923	87	5	𝓎𝑛	𝓎𝑛	PROPN
iajs-2923	87	6	}	}	PUNCT
iajs-2923	87	7	⊂	⊂	PROPN
iajs-2923	87	8	𝐶	𝐶	PROPN
iajs-2923	87	9	and	and	CCONJ
iajs-2923	87	10	휀𝑛	휀𝑛	NOUN
iajs-2923	87	11	=	=	SYM
iajs-2923	87	12	‖ψ𝓎𝑛+1	‖ψ𝓎𝑛+1	NOUN
iajs-2923	87	13	−	−	NOUN
iajs-2923	87	14	𝑓(𝑇	𝑓(𝑇	SYM
iajs-2923	87	15	,	,	PUNCT
iajs-2923	87	16	𝓎𝑛)‖	𝓎𝑛)‖	PROPN
iajs-2923	87	17	=	=	SYM
iajs-2923	87	18	‖ψ𝓎𝑛+1	‖ψ𝓎𝑛+1	PROPN
iajs-2923	87	19	−	−	PROPN
iajs-2923	87	20	𝒫𝒸𝑇((1	𝒫𝒸𝑇((1	PROPN
iajs-2923	87	21	−	−	PROPN
iajs-2923	87	22	𝛼𝑛)ψ𝓎𝑛	𝛼𝑛)ψ𝓎𝑛	PROPN
iajs-2923	87	23	+	+	CCONJ
iajs-2923	87	24	𝛼𝑛𝒫𝒸(𝓎𝑛))‖	𝛼𝑛𝒫𝒸(𝓎𝑛))‖	NOUN
iajs-2923	87	25	so	so	ADV
iajs-2923	87	26	,	,	PUNCT
iajs-2923	87	27	휀𝑛	휀𝑛	PROPN
iajs-2923	87	28	=	=	SYM
iajs-2923	87	29	‖ψ𝓎𝑛+1	‖ψ𝓎𝑛+1	PROPN
iajs-2923	87	30	−	−	PROPN
iajs-2923	87	31	𝒫𝒸𝑇((1	𝒫𝒸𝑇((1	PROPN
iajs-2923	87	32	−	−	PROPN
iajs-2923	87	33	𝛼𝑛)ψ𝓎𝑛	𝛼𝑛)ψ𝓎𝑛	PROPN
iajs-2923	87	34	+	+	CCONJ
iajs-2923	87	35	𝛼𝑛𝒫𝒸(𝓎𝑛))‖	𝛼𝑛𝒫𝒸(𝓎𝑛))‖	NUM
iajs-2923	87	36	if	if	SCONJ
iajs-2923	87	37	lim	lim	PROPN
iajs-2923	87	38	𝑛→∞	𝑛→∞	NUM
iajs-2923	87	39	휀𝑛	휀𝑛	VERB
iajs-2923	87	40	=	=	SYM
iajs-2923	87	41	0	0	NUM
iajs-2923	87	42	,	,	PUNCT
iajs-2923	87	43	we	we	PRON
iajs-2923	87	44	get	get	VERB
iajs-2923	87	45	lim	lim	PROPN
iajs-2923	87	46	𝑛→∞	𝑛→∞	NUM
iajs-2923	87	47	ψ𝓎𝑛+1	ψ𝓎𝑛+1	ADJ
iajs-2923	87	48	=	=	SYM
iajs-2923	87	49	𝑝	𝑝	NOUN
iajs-2923	87	50	then	then	ADV
iajs-2923	87	51	,	,	PUNCT
iajs-2923	87	52	the	the	DET
iajs-2923	87	53	projection	projection	NOUN
iajs-2923	87	54	jungck	jungck	NOUN
iajs-2923	87	55	-	-	PUNCT
iajs-2923	87	56	normal	normal	ADJ
iajs-2923	87	57	𝒩	𝒩	PROPN
iajs-2923	87	58	algorithm	algorithm	NOUN
iajs-2923	87	59	is	be	AUX
iajs-2923	87	60	(	(	PUNCT
iajs-2923	87	61	ψ	ψ	X
iajs-2923	87	62	,	,	PUNCT
iajs-2923	87	63	𝑇	𝑇	PROPN
iajs-2923	87	64	,	,	PUNCT
iajs-2923	87	65	𝒫𝒸)-stable	𝒫𝒸)-stable	PROPN
iajs-2923	87	66	.	.	PUNCT
iajs-2923	88	1	theorem	theorem	NOUN
iajs-2923	88	2	(	(	PUNCT
iajs-2923	88	3	2.12	2.12	NUM
iajs-2923	88	4	):	):	PUNCT
iajs-2923	88	5	let	let	VERB
iajs-2923	88	6	𝑇	𝑇	PROPN
iajs-2923	88	7	,	,	PUNCT
iajs-2923	88	8	ψ	ψ	ADP
iajs-2923	88	9	:	:	PUNCT
iajs-2923	88	10	𝐶	𝐶	PROPN
iajs-2923	88	11	→	→	SYM
iajs-2923	88	12	𝐶	𝐶	PROPN
iajs-2923	88	13	are	be	AUX
iajs-2923	88	14	projection	projection	ADJ
iajs-2923	88	15	jungck	jungck	NOUN
iajs-2923	88	16	zn	zn	PROPN
iajs-2923	88	17	-	-	PUNCT
iajs-2923	88	18	suzuki	suzuki	PROPN
iajs-2923	88	19	generalized	generalize	VERB
iajs-2923	88	20	mapping	mapping	NOUN
iajs-2923	88	21	with	with	ADP
iajs-2923	88	22	𝐿	𝐿	PROPN
iajs-2923	88	23	∈	∈	PROPN
iajs-2923	88	24	(	(	PUNCT
iajs-2923	88	25	0,1	0,1	NUM
iajs-2923	88	26	)	)	PUNCT
iajs-2923	88	27	.	.	PUNCT
iajs-2923	89	1	let	let	VERB
iajs-2923	89	2	{	{	PUNCT
iajs-2923	89	3	ψ𝑘𝑛	ψ𝑘𝑛	NOUN
iajs-2923	89	4	}	}	PUNCT
iajs-2923	89	5	be	be	AUX
iajs-2923	89	6	a	a	DET
iajs-2923	89	7	projection	projection	NOUN
iajs-2923	89	8	jungck	jungck	NOUN
iajs-2923	89	9	-	-	PUNCT
iajs-2923	89	10	picard	picard	NOUN
iajs-2923	89	11	algorithm	algorithm	NOUN
iajs-2923	89	12	converging	converge	VERB
iajs-2923	89	13	to	to	ADP
iajs-2923	89	14	𝑝	𝑝	NOUN
iajs-2923	89	15	,	,	PUNCT
iajs-2923	89	16	where	where	SCONJ
iajs-2923	89	17	{	{	PUNCT
iajs-2923	89	18	𝛼𝑛	𝛼𝑛	NOUN
iajs-2923	89	19	}	}	PUNCT
iajs-2923	89	20	are	be	AUX
iajs-2923	89	21	sequences	sequence	NOUN
iajs-2923	89	22	in	in	ADP
iajs-2923	89	23	[	[	X
iajs-2923	89	24	0,1	0,1	NUM
iajs-2923	89	25	]	]	PUNCT
iajs-2923	89	26	.	.	PUNCT
iajs-2923	90	1	then	then	ADV
iajs-2923	90	2	,	,	PUNCT
iajs-2923	90	3	the	the	DET
iajs-2923	90	4	projection	projection	NOUN
iajs-2923	90	5	jungck	jungck	NOUN
iajs-2923	90	6	-	-	PUNCT
iajs-2923	90	7	picard	picard	NOUN
iajs-2923	90	8	algorithm	algorithm	NOUN
iajs-2923	90	9	is	be	AUX
iajs-2923	90	10	(	(	PUNCT
iajs-2923	90	11	ψ	ψ	X
iajs-2923	90	12	,	,	PUNCT
iajs-2923	90	13	𝑇	𝑇	PROPN
iajs-2923	90	14	,	,	PUNCT
iajs-2923	90	15	𝒫𝒸)-stable	𝒫𝒸)-stable	PROPN
iajs-2923	90	16	.	.	PUNCT
iajs-2923	91	1	theorem	theorem	NOUN
iajs-2923	91	2	(	(	PUNCT
iajs-2923	91	3	2.13	2.13	NUM
iajs-2923	91	4	):	):	PUNCT
iajs-2923	91	5	let	let	VERB
iajs-2923	91	6	𝑇	𝑇	PROPN
iajs-2923	91	7	,	,	PUNCT
iajs-2923	91	8	ψ	ψ	ADP
iajs-2923	91	9	:	:	PUNCT
iajs-2923	91	10	𝐶	𝐶	PROPN
iajs-2923	91	11	→	→	SYM
iajs-2923	91	12	𝐶	𝐶	PROPN
iajs-2923	91	13	are	be	AUX
iajs-2923	91	14	projection	projection	ADJ
iajs-2923	91	15	jungck	jungck	NOUN
iajs-2923	91	16	zn	zn	PROPN
iajs-2923	91	17	-	-	PUNCT
iajs-2923	91	18	suzuki	suzuki	PROPN
iajs-2923	91	19	generalized	generalize	VERB
iajs-2923	91	20	mapping	mapping	NOUN
iajs-2923	91	21	with	with	ADP
iajs-2923	91	22	𝐿	𝐿	PROPN
iajs-2923	91	23	∈	∈	PROPN
iajs-2923	91	24	(	(	PUNCT
iajs-2923	91	25	0,1	0,1	NUM
iajs-2923	91	26	)	)	PUNCT
iajs-2923	91	27	.	.	PUNCT
iajs-2923	92	1	let	let	VERB
iajs-2923	92	2	{	{	PUNCT
iajs-2923	92	3	ψ𝓏𝑛	ψ𝓏𝑛	AUX
iajs-2923	92	4	}	}	PUNCT
iajs-2923	92	5	be	be	AUX
iajs-2923	92	6	a	a	DET
iajs-2923	92	7	projection	projection	ADJ
iajs-2923	92	8	jungckthianwan	jungckthianwan	NOUN
iajs-2923	92	9	algorithm	algorithm	NOUN
iajs-2923	92	10	converging	converge	VERB
iajs-2923	92	11	to	to	ADP
iajs-2923	92	12	𝑝	𝑝	NOUN
iajs-2923	92	13	,	,	PUNCT
iajs-2923	93	1	where	where	SCONJ
iajs-2923	93	2	{	{	PUNCT
iajs-2923	93	3	𝛼𝑛	𝛼𝑛	NOUN
iajs-2923	93	4	}	}	PUNCT
iajs-2923	93	5	and	and	CCONJ
iajs-2923	93	6	{	{	PUNCT
iajs-2923	93	7	𝛽𝑛	𝛽𝑛	NOUN
iajs-2923	93	8	}	}	PUNCT
iajs-2923	93	9	are	be	AUX
iajs-2923	93	10	sequences	sequence	NOUN
iajs-2923	93	11	in	in	ADP
iajs-2923	93	12	[	[	X
iajs-2923	93	13	0,1	0,1	NUM
iajs-2923	93	14	]	]	PUNCT
iajs-2923	93	15	such	such	ADJ
iajs-2923	93	16	that	that	SCONJ
iajs-2923	93	17	0	0	NUM
iajs-2923	93	18	<	<	X
iajs-2923	93	19	𝛼	𝛼	X
iajs-2923	93	20	≤	≤	NUM
iajs-2923	93	21	𝛼𝑛	𝛼𝑛	PROPN
iajs-2923	93	22	and	and	CCONJ
iajs-2923	93	23	,	,	PUNCT
iajs-2923	93	24	0	0	NUM
iajs-2923	93	25	<	<	X
iajs-2923	93	26	𝛽	𝛽	X
iajs-2923	93	27	≤	≤	PUNCT
iajs-2923	93	28	𝛽𝑛	𝛽𝑛	PUNCT
iajs-2923	93	29	then	then	ADV
iajs-2923	93	30	,	,	PUNCT
iajs-2923	93	31	the	the	DET
iajs-2923	93	32	projection	projection	NOUN
iajs-2923	93	33	jungckthianwan	jungckthianwan	PROPN
iajs-2923	93	34	algorithm	algorithm	NOUN
iajs-2923	93	35	is	be	AUX
iajs-2923	93	36	(	(	PUNCT
iajs-2923	93	37	ψ	ψ	X
iajs-2923	93	38	,	,	PUNCT
iajs-2923	93	39	𝑇	𝑇	PROPN
iajs-2923	93	40	,	,	PUNCT
iajs-2923	93	41	𝒫𝒸)-stable	𝒫𝒸)-stable	PROPN
iajs-2923	93	42	.	.	PUNCT
iajs-2923	94	1	proof	proof	NOUN
iajs-2923	94	2	:	:	PUNCT
iajs-2923	94	3	by	by	ADP
iajs-2923	94	4	following	follow	VERB
iajs-2923	94	5	the	the	DET
iajs-2923	94	6	same	same	ADJ
iajs-2923	94	7	steps	step	NOUN
iajs-2923	94	8	of	of	ADP
iajs-2923	94	9	the	the	DET
iajs-2923	94	10	proof	proof	NOUN
iajs-2923	94	11	of	of	ADP
iajs-2923	94	12	theorem	theorem	NOUN
iajs-2923	94	13	(	(	PUNCT
iajs-2923	94	14	2.9	2.9	NUM
iajs-2923	94	15	)	)	PUNCT
iajs-2923	94	16	,	,	PUNCT
iajs-2923	94	17	we	we	PRON
iajs-2923	94	18	get	get	VERB
iajs-2923	94	19	the	the	DET
iajs-2923	94	20	wanted	wanted	ADJ
iajs-2923	94	21	results	result	NOUN
iajs-2923	94	22	.	.	PUNCT
iajs-2923	95	1	ihjpas	ihjpas	PROPN
iajs-2923	95	2	.	.	PUNCT
iajs-2923	96	1	36(1)2023	36(1)2023	NUM
iajs-2923	96	2	297	297	NUM
iajs-2923	96	3	theorem	theorem	NOUN
iajs-2923	96	4	(	(	PUNCT
iajs-2923	96	5	2.14	2.14	NUM
iajs-2923	96	6	):	):	PUNCT
iajs-2923	96	7	let	let	VERB
iajs-2923	96	8	𝑇	𝑇	PROPN
iajs-2923	96	9	,	,	PUNCT
iajs-2923	96	10	ψ	ψ	X
iajs-2923	96	11	are	be	AUX
iajs-2923	96	12	projection	projection	ADJ
iajs-2923	96	13	jungck	jungck	PROPN
iajs-2923	96	14	zn	zn	PROPN
iajs-2923	96	15	-	-	PUNCT
iajs-2923	96	16	suzuki	suzuki	NOUN
iajs-2923	96	17	generalized	generalize	VERB
iajs-2923	96	18	mapping	mapping	NOUN
iajs-2923	96	19	and	and	CCONJ
iajs-2923	96	20	𝒞ℱ(𝒫𝒸	𝒞ℱ(𝒫𝒸	PROPN
iajs-2923	96	21	,	,	PUNCT
iajs-2923	96	22	𝑇	𝑇	PROPN
iajs-2923	96	23	,	,	PUNCT
iajs-2923	96	24	ψ	ψ	NOUN
iajs-2923	96	25	)	)	PUNCT
iajs-2923	96	26	≠	≠	PROPN
iajs-2923	96	27	𝜙.	𝜙.	NOUN
iajs-2923	96	28	then	then	ADV
iajs-2923	96	29	,	,	PUNCT
iajs-2923	96	30	the	the	DET
iajs-2923	96	31	projection	projection	NOUN
iajs-2923	96	32	jungck	jungck	NOUN
iajs-2923	96	33	-	-	PUNCT
iajs-2923	96	34	picard	picard	NOUN
iajs-2923	96	35	algorithm	algorithm	NOUN
iajs-2923	96	36	converges	converge	VERB
iajs-2923	96	37	faster	fast	ADV
iajs-2923	96	38	than	than	ADP
iajs-2923	96	39	projection	projection	NOUN
iajs-2923	96	40	jungck	jungck	PROPN
iajs-2923	96	41	-	-	PUNCT
iajs-2923	96	42	krasnoselskii	krasnoselskii	PROPN
iajs-2923	96	43	algorithm	algorithm	NOUN
iajs-2923	96	44	.	.	PUNCT
iajs-2923	97	1	proof	proof	NOUN
iajs-2923	97	2	:	:	PUNCT
iajs-2923	97	3	for	for	ADP
iajs-2923	97	4	projection	projection	NOUN
iajs-2923	97	5	jungck	jungck	NOUN
iajs-2923	97	6	-	-	PUNCT
iajs-2923	97	7	picard	picard	NOUN
iajs-2923	97	8	algorithm	algorithm	NOUN
iajs-2923	97	9	‖ψ𝑘𝑛+1	‖ψ𝑘𝑛+1	CCONJ
iajs-2923	97	10	−	−	X
iajs-2923	97	11	𝑝‖	𝑝‖	PROPN
iajs-2923	97	12	=	=	SYM
iajs-2923	97	13	‖𝒫𝒸𝑇𝑘𝑛	‖𝒫𝒸𝑇𝑘𝑛	PROPN
iajs-2923	97	14	−	−	PROPN
iajs-2923	97	15	𝑝‖	𝑝‖	PROPN
iajs-2923	97	16	≤	≤	PROPN
iajs-2923	97	17	‖𝑇𝑘𝑛	‖𝑇𝑘𝑛	PROPN
iajs-2923	97	18	−	−	NOUN
iajs-2923	97	19	𝑝‖	𝑝‖	NOUN
iajs-2923	97	20	≤	≤	NUM
iajs-2923	97	21	𝐿‖ψ𝑘𝑛	𝐿‖ψ𝑘𝑛	PROPN
iajs-2923	97	22	−	−	PROPN
iajs-2923	97	23	𝑝‖	𝑝‖	PROPN
iajs-2923	97	24	+	+	CCONJ
iajs-2923	97	25	𝜙(‖𝑝−𝒫𝒸(𝑝)‖+‖𝑝−ψ𝑝‖	𝜙(‖𝑝−𝒫𝒸(𝑝)‖+‖𝑝−ψ𝑝‖	NOUN
iajs-2923	97	26	)	)	PUNCT
iajs-2923	97	27	1+𝑚𝑎𝑥{‖𝒫𝒸(𝑝)−𝒫𝒸(𝑘𝑛)‖,‖ψ𝑝−ψ𝑘𝑛‖	1+𝑚𝑎𝑥{‖𝒫𝒸(𝑝)−𝒫𝒸(𝑘𝑛)‖,‖ψ𝑝−ψ𝑘𝑛‖	NOUN
iajs-2923	97	28	}	}	PUNCT
iajs-2923	97	29	:	:	PUNCT
iajs-2923	97	30	≤	≤	NUM
iajs-2923	97	31	𝐿𝑛‖ψ𝑘0	𝐿𝑛‖ψ𝑘0	NOUN
iajs-2923	97	32	−	−	PROPN
iajs-2923	97	33	𝑝‖	𝑝‖	PRON
iajs-2923	97	34	put	put	VERB
iajs-2923	97	35	𝒫.	𝒫.	NOUN
iajs-2923	97	36	𝒥.	𝒥.	NOUN
iajs-2923	97	37	𝑃.	𝑃.	PROPN
iajs-2923	97	38	𝒜	𝒜	NOUN
iajs-2923	97	39	=	=	NOUN
iajs-2923	97	40	𝐿𝑛‖ψ𝑘0	𝐿𝑛‖ψ𝑘0	NOUN
iajs-2923	97	41	−	−	PROPN
iajs-2923	97	42	𝑝‖	𝑝‖	PROPN
iajs-2923	97	43	for	for	ADP
iajs-2923	97	44	projection	projection	NOUN
iajs-2923	97	45	jungck	jungck	PROPN
iajs-2923	97	46	-	-	PUNCT
iajs-2923	97	47	krasnoselskii	krasnoselskii	PROPN
iajs-2923	97	48	algorithm	algorithm	NOUN
iajs-2923	97	49	.	.	PUNCT
iajs-2923	98	1	‖ψ𝑛𝑛+1	‖ψ𝑛𝑛+1	PUNCT
iajs-2923	99	1	−	−	X
iajs-2923	99	2	𝑝‖	𝑝‖	NOUN
iajs-2923	99	3	=	=	SYM
iajs-2923	99	4	‖(1	‖(1	NUM
iajs-2923	99	5	−	−	NUM
iajs-2923	99	6	𝛿)ψ𝒫𝒸(𝑛𝑛	𝛿)ψ𝒫𝒸(𝑛𝑛	NOUN
iajs-2923	99	7	)	)	PUNCT
iajs-2923	100	1	+	+	CCONJ
iajs-2923	100	2	𝛿𝒫𝒸𝑇𝑛𝑛	𝛿𝒫𝒸𝑇𝑛𝑛	PROPN
iajs-2923	100	3	−	−	PROPN
iajs-2923	100	4	𝑝‖	𝑝‖	NOUN
iajs-2923	100	5	≤	≤	NUM
iajs-2923	100	6	(	(	PUNCT
iajs-2923	100	7	1	1	NUM
iajs-2923	100	8	−	−	PROPN
iajs-2923	100	9	𝛿)‖ψ𝒫𝒸(𝑛𝑛	𝛿)‖ψ𝒫𝒸(𝑛𝑛	NOUN
iajs-2923	100	10	)	)	PUNCT
iajs-2923	100	11	−	−	PROPN
iajs-2923	100	12	𝑝‖	𝑝‖	NOUN
iajs-2923	100	13	+	+	NUM
iajs-2923	100	14	𝛿‖𝒫𝒸𝑇𝑛𝑛	𝛿‖𝒫𝒸𝑇𝑛𝑛	NOUN
iajs-2923	100	15	−	−	NOUN
iajs-2923	100	16	𝑝‖	𝑝‖	NOUN
iajs-2923	100	17	=	=	SYM
iajs-2923	100	18	(	(	PUNCT
iajs-2923	100	19	1	1	NUM
iajs-2923	100	20	−	−	PROPN
iajs-2923	100	21	𝛿)‖𝒫𝒸ψ(𝑛𝑛	𝛿)‖𝒫𝒸ψ(𝑛𝑛	NOUN
iajs-2923	100	22	)	)	PUNCT
iajs-2923	100	23	−	−	NOUN
iajs-2923	100	24	𝑝‖	𝑝‖	NOUN
iajs-2923	100	25	+	+	NUM
iajs-2923	100	26	𝛿‖𝒫𝒸𝑇𝑛𝑛	𝛿‖𝒫𝒸𝑇𝑛𝑛	NOUN
iajs-2923	100	27	−	−	ADP
iajs-2923	100	28	𝑝‖	𝑝‖	NOUN
iajs-2923	100	29	≤	≤	NUM
iajs-2923	100	30	(	(	PUNCT
iajs-2923	100	31	1	1	NUM
iajs-2923	100	32	−	−	PROPN
iajs-2923	100	33	𝛿)‖ψ𝑛𝑛	𝛿)‖ψ𝑛𝑛	NOUN
iajs-2923	100	34	−	−	PROPN
iajs-2923	100	35	𝑝‖	𝑝‖	PROPN
iajs-2923	100	36	+	+	CCONJ
iajs-2923	100	37	𝐿𝛿‖ψ𝑛𝑛	𝐿𝛿‖ψ𝑛𝑛	PROPN
iajs-2923	100	38	−	−	PROPN
iajs-2923	100	39	𝑝‖	𝑝‖	NOUN
iajs-2923	100	40	+	+	SYM
iajs-2923	100	41	𝜙(‖𝑝−𝒫𝒸(𝑝)‖+‖𝑝−ψ𝑝‖	𝜙(‖𝑝−𝒫𝒸(𝑝)‖+‖𝑝−ψ𝑝‖	NOUN
iajs-2923	100	42	)	)	PUNCT
iajs-2923	100	43	1+max{‖𝒫𝒸(𝑝)−𝒫𝒸(𝑛𝑛)‖,‖ψ𝑝−ψ𝑛𝑛‖	1+max{‖𝒫𝒸(𝑝)−𝒫𝒸(𝑛𝑛)‖,‖ψ𝑝−ψ𝑛𝑛‖	ADV
iajs-2923	100	44	}	}	PUNCT
iajs-2923	100	45	≤	≤	NOUN
iajs-2923	100	46	(	(	PUNCT
iajs-2923	100	47	1	1	NUM
iajs-2923	100	48	−	−	PROPN
iajs-2923	100	49	𝛿(1	𝛿(1	PROPN
iajs-2923	100	50	−	−	PROPN
iajs-2923	100	51	𝐿))‖ψ𝑛𝑛	𝐿))‖ψ𝑛𝑛	NOUN
iajs-2923	100	52	−	−	NOUN
iajs-2923	100	53	𝑝‖	𝑝‖	NOUN
iajs-2923	100	54	:	:	PUNCT
iajs-2923	100	55	≤	≤	NUM
iajs-2923	101	1	[	[	X
iajs-2923	101	2	1	1	NUM
iajs-2923	101	3	−	−	PROPN
iajs-2923	101	4	𝛿(1	𝛿(1	PROPN
iajs-2923	101	5	−	−	PROPN
iajs-2923	101	6	𝐿)]𝑛‖ψ𝑛0	𝐿)]𝑛‖ψ𝑛0	NOUN
iajs-2923	101	7	−	−	PROPN
iajs-2923	101	8	𝑝‖	𝑝‖	PROPN
iajs-2923	101	9	put	put	VERB
iajs-2923	101	10	:	:	PUNCT
iajs-2923	101	11	𝒫.	𝒫.	PROPN
iajs-2923	101	12	𝒥.	𝒥.	NOUN
iajs-2923	101	13	𝒦.	𝒦.	NOUN
iajs-2923	101	14	𝒜	𝒜	NOUN
iajs-2923	101	15	=	=	PUNCT
iajs-2923	102	1	[	[	X
iajs-2923	102	2	1	1	NUM
iajs-2923	102	3	−	−	PROPN
iajs-2923	102	4	𝛿(1	𝛿(1	PROPN
iajs-2923	102	5	−	−	PROPN
iajs-2923	102	6	𝐿)]𝑛‖ψ𝑛0	𝐿)]𝑛‖ψ𝑛0	NOUN
iajs-2923	102	7	−	−	PROPN
iajs-2923	102	8	𝑝‖	𝑝‖	PROPN
iajs-2923	102	9	now	now	ADV
iajs-2923	102	10	since	since	SCONJ
iajs-2923	102	11	:	:	PUNCT
iajs-2923	102	12	𝒫.𝒥.𝑃.𝒜	𝒫.𝒥.𝑃.𝒜	PROPN
iajs-2923	102	13	𝒫.𝒥.𝒦.𝒜	𝒫.𝒥.𝒦.𝒜	PROPN
iajs-2923	102	14	=	=	PUNCT
iajs-2923	102	15	𝐿𝑛‖ψ𝑘0−𝑝‖	𝐿𝑛‖ψ𝑘0−𝑝‖	VERB
iajs-2923	102	16	[	[	X
iajs-2923	102	17	1−𝛿(1−𝐿)]𝑛‖ψ𝑛0−𝑝‖	1−𝛿(1−𝐿)]𝑛‖ψ𝑛0−𝑝‖	NUM
iajs-2923	102	18	→	→	SYM
iajs-2923	102	19	0	0	NUM
iajs-2923	102	20	as	as	ADP
iajs-2923	102	21	𝑛	𝑛	PROPN
iajs-2923	102	22	→	→	SYM
iajs-2923	102	23	∞.	∞.	PROPN
iajs-2923	102	24	hence	hence	ADV
iajs-2923	102	25	,	,	PUNCT
iajs-2923	102	26	the	the	DET
iajs-2923	102	27	projection	projection	NOUN
iajs-2923	102	28	jungck	jungck	NOUN
iajs-2923	102	29	-	-	PUNCT
iajs-2923	102	30	picard	picard	NOUN
iajs-2923	102	31	algorithm	algorithm	NOUN
iajs-2923	102	32	converges	converge	VERB
iajs-2923	102	33	to	to	ADP
iajs-2923	102	34	𝑝	𝑝	NOUN
iajs-2923	102	35	faster	fast	ADV
iajs-2923	102	36	than	than	ADP
iajs-2923	102	37	the	the	DET
iajs-2923	102	38	projection	projection	NOUN
iajs-2923	102	39	jungckkrasnoselskii	jungckkrasnoselskii	PROPN
iajs-2923	102	40	algorithm	algorithm	PROPN
iajs-2923	102	41	.	.	PUNCT
iajs-2923	103	1	theorem	theorem	NOUN
iajs-2923	103	2	(	(	PUNCT
iajs-2923	103	3	2.15	2.15	NUM
iajs-2923	103	4	):	):	PUNCT
iajs-2923	103	5	let	let	VERB
iajs-2923	103	6	𝑇	𝑇	PROPN
iajs-2923	103	7	,	,	PUNCT
iajs-2923	103	8	ψ	ψ	PART
iajs-2923	103	9	be	be	AUX
iajs-2923	103	10	a	a	DET
iajs-2923	103	11	projection	projection	NOUN
iajs-2923	103	12	jungck	jungck	NOUN
iajs-2923	103	13	zn	zn	PROPN
iajs-2923	103	14	-	-	PUNCT
iajs-2923	103	15	suzuki	suzuki	NOUN
iajs-2923	103	16	generalized	generalize	VERB
iajs-2923	103	17	mapping	mapping	NOUN
iajs-2923	103	18	and	and	CCONJ
iajs-2923	103	19	𝒞ℱ(𝒫𝒸	𝒞ℱ(𝒫𝒸	PROPN
iajs-2923	103	20	,	,	PUNCT
iajs-2923	103	21	𝑇	𝑇	PROPN
iajs-2923	103	22	,	,	PUNCT
iajs-2923	103	23	ψ	ψ	NOUN
iajs-2923	103	24	)	)	PUNCT
iajs-2923	103	25	≠	≠	PROPN
iajs-2923	103	26	𝜙.	𝜙.	NOUN
iajs-2923	103	27	then	then	ADV
iajs-2923	103	28	,	,	PUNCT
iajs-2923	103	29	the	the	DET
iajs-2923	103	30	projection	projection	NOUN
iajs-2923	103	31	jungck	jungck	NOUN
iajs-2923	103	32	-	-	PUNCT
iajs-2923	103	33	normal	normal	ADJ
iajs-2923	103	34	𝒩	𝒩	PROPN
iajs-2923	103	35	algorithm	algorithm	NOUN
iajs-2923	103	36	converges	converge	VERB
iajs-2923	103	37	faster	fast	ADV
iajs-2923	103	38	than	than	ADP
iajs-2923	103	39	the	the	DET
iajs-2923	103	40	projection	projection	NOUN
iajs-2923	103	41	jungckpicard	jungckpicard	ADP
iajs-2923	103	42	algorithm	algorithm	NOUN
iajs-2923	103	43	.	.	PUNCT
iajs-2923	104	1	proof	proof	NOUN
iajs-2923	104	2	:	:	PUNCT
iajs-2923	104	3	let	let	VERB
iajs-2923	104	4	𝑝	𝑝	PROPN
iajs-2923	104	5	∈	∈	PROPN
iajs-2923	104	6	𝒞ℱ(𝒫𝒸	𝒞ℱ(𝒫𝒸	PROPN
iajs-2923	104	7	,	,	PUNCT
iajs-2923	104	8	𝑇	𝑇	PROPN
iajs-2923	104	9	,	,	PUNCT
iajs-2923	104	10	ψ	ψ	NOUN
iajs-2923	104	11	)	)	PUNCT
iajs-2923	104	12	and	and	CCONJ
iajs-2923	104	13	suppose	suppose	VERB
iajs-2923	104	14	that	that	SCONJ
iajs-2923	104	15	there	there	PRON
iajs-2923	104	16	exists	exist	VERB
iajs-2923	104	17	ʎ	ʎ	ADJ
iajs-2923	104	18	;	;	PUNCT
iajs-2923	104	19	0	0	NUM
iajs-2923	104	20	≤	≤	NUM
iajs-2923	105	1	ʎ	ʎ	PRON
iajs-2923	105	2	≤	≤	NUM
iajs-2923	105	3	𝛼𝑛	𝛼𝑛	NOUN
iajs-2923	105	4	≤	≤	NUM
iajs-2923	105	5	1	1	NUM
iajs-2923	105	6	for	for	ADP
iajs-2923	105	7	projection	projection	NOUN
iajs-2923	105	8	jungck	jungck	NOUN
iajs-2923	105	9	–	–	PUNCT
iajs-2923	105	10	picard	picard	NOUN
iajs-2923	105	11	algorithm	algorithm	NOUN
iajs-2923	105	12	we	we	PRON
iajs-2923	105	13	have	have	VERB
iajs-2923	105	14	,	,	PUNCT
iajs-2923	105	15	𝒫.	𝒫.	PROPN
iajs-2923	105	16	𝒥.	𝒥.	PROPN
iajs-2923	105	17	𝑃.	𝑃.	PROPN
iajs-2923	105	18	𝒜	𝒜	NOUN
iajs-2923	105	19	=	=	NOUN
iajs-2923	105	20	𝐿𝑛‖ψ𝑘0	𝐿𝑛‖ψ𝑘0	NOUN
iajs-2923	105	21	−	−	PROPN
iajs-2923	105	22	𝑝‖	𝑝‖	NOUN
iajs-2923	105	23	from	from	ADP
iajs-2923	105	24	projection	projection	PROPN
iajs-2923	105	25	jungck	jungck	NOUN
iajs-2923	105	26	-	-	PUNCT
iajs-2923	105	27	normal	normal	ADJ
iajs-2923	105	28	𝒩algorithm	𝒩algorithm	PROPN
iajs-2923	105	29	‖ψ𝑢𝑛+1	‖ψ𝑢𝑛+1	PUNCT
iajs-2923	105	30	−	−	X
iajs-2923	105	31	𝑝‖	𝑝‖	NOUN
iajs-2923	105	32	=	=	SYM
iajs-2923	105	33	‖𝒫𝒸𝑇((1	‖𝒫𝒸𝑇((1	PROPN
iajs-2923	105	34	−	−	PROPN
iajs-2923	105	35	𝛼𝑛)ψ𝑢𝑛	𝛼𝑛)ψ𝑢𝑛	PROPN
iajs-2923	105	36	+	+	CCONJ
iajs-2923	105	37	𝛼𝑛𝒫𝒸(𝑢𝑛	𝛼𝑛𝒫𝒸(𝑢𝑛	NUM
iajs-2923	105	38	)	)	PUNCT
iajs-2923	105	39	)	)	PUNCT
iajs-2923	106	1	−	−	PROPN
iajs-2923	106	2	𝑝‖	𝑝‖	PROPN
iajs-2923	106	3	≤	≤	PROPN
iajs-2923	106	4	‖𝑇((1	‖𝑇((1	VERB
iajs-2923	106	5	−	−	PROPN
iajs-2923	106	6	𝛼𝑛)ψ𝑢𝑛	𝛼𝑛)ψ𝑢𝑛	PROPN
iajs-2923	106	7	+	+	CCONJ
iajs-2923	106	8	𝛼𝑛𝒫𝒸(𝑢𝑛	𝛼𝑛𝒫𝒸(𝑢𝑛	NUM
iajs-2923	106	9	)	)	PUNCT
iajs-2923	106	10	)	)	PUNCT
iajs-2923	107	1	−	−	PROPN
iajs-2923	107	2	𝑝‖	𝑝‖	PROPN
iajs-2923	107	3	≤	≤	PROPN
iajs-2923	107	4	𝐿‖ψ((1	𝐿‖ψ((1	VERB
iajs-2923	107	5	−	−	PROPN
iajs-2923	107	6	𝛼𝑛)ψ𝑢𝑛	𝛼𝑛)ψ𝑢𝑛	PROPN
iajs-2923	107	7	+	+	CCONJ
iajs-2923	107	8	𝛼𝑛𝒫𝒸(𝑢𝑛	𝛼𝑛𝒫𝒸(𝑢𝑛	NUM
iajs-2923	107	9	)	)	PUNCT
iajs-2923	107	10	)	)	PUNCT
iajs-2923	108	1	−	−	PROPN
iajs-2923	108	2	𝑝‖	𝑝‖	NOUN
iajs-2923	108	3	+	+	SYM
iajs-2923	108	4	𝜙(‖𝑝−𝒫𝒸(𝑝)‖+‖𝑝−ψ𝑝‖	𝜙(‖𝑝−𝒫𝒸(𝑝)‖+‖𝑝−ψ𝑝‖	NOUN
iajs-2923	108	5	)	)	PUNCT
iajs-2923	108	6	1+𝑚𝑎𝑥{‖𝒫𝒸(𝑝)−𝒫𝒸((1−𝛼𝑛)ψ𝑢𝑛+𝛼𝑛𝒫𝒸(𝑢𝑛))‖,‖ψ𝑝−ψ((1−𝛼𝑛)ψ𝑢𝑛+𝛼𝑛𝒫𝒸(𝑢𝑛))‖	1+𝑚𝑎𝑥{‖𝒫𝒸(𝑝)−𝒫𝒸((1−𝛼𝑛)ψ𝑢𝑛+𝛼𝑛𝒫𝒸(𝑢𝑛))‖,‖ψ𝑝−ψ((1−𝛼𝑛)ψ𝑢𝑛+𝛼𝑛𝒫𝒸(𝑢𝑛))‖	NOUN
iajs-2923	108	7	}	}	PUNCT
iajs-2923	108	8	≤	≤	NUM
iajs-2923	108	9	𝐿‖ψ((1	𝐿‖ψ((1	VERB
iajs-2923	108	10	−	−	PROPN
iajs-2923	108	11	𝛼𝑛)ψ𝑢𝑛	𝛼𝑛)ψ𝑢𝑛	PROPN
iajs-2923	108	12	+	+	CCONJ
iajs-2923	108	13	𝛼𝑛𝒫𝒸(𝑢𝑛	𝛼𝑛𝒫𝒸(𝑢𝑛	NUM
iajs-2923	108	14	)	)	PUNCT
iajs-2923	108	15	)	)	PUNCT
iajs-2923	109	1	−	−	PROPN
iajs-2923	109	2	𝑝‖	𝑝‖	PROPN
iajs-2923	109	3	≤	≤	NUM
iajs-2923	109	4	𝐿‖(1	𝐿‖(1	NUM
iajs-2923	109	5	−	−	PROPN
iajs-2923	109	6	𝛼𝑛)ψψ𝑢𝑛	𝛼𝑛)ψψ𝑢𝑛	NOUN
iajs-2923	109	7	+	+	NUM
iajs-2923	109	8	𝛼𝑛ψ𝒫𝒸(𝑢𝑛	𝛼𝑛ψ𝒫𝒸(𝑢𝑛	NUM
iajs-2923	109	9	)	)	PUNCT
iajs-2923	109	10	−	−	PROPN
iajs-2923	110	1	(	(	PUNCT
iajs-2923	110	2	1	1	NUM
iajs-2923	110	3	−	−	PROPN
iajs-2923	110	4	𝛼𝑛	𝛼𝑛	NOUN
iajs-2923	110	5	+	+	NOUN
iajs-2923	110	6	𝛼𝑛)𝑝‖	𝛼𝑛)𝑝‖	NOUN
iajs-2923	110	7	≤	≤	NUM
iajs-2923	110	8	𝐿‖(1	𝐿‖(1	NUM
iajs-2923	110	9	−	−	PROPN
iajs-2923	110	10	𝛼𝑛)(ψψ𝑢𝑛	𝛼𝑛)(ψψ𝑢𝑛	PROPN
iajs-2923	110	11	−	−	PROPN
iajs-2923	110	12	𝑝	𝑝	PROPN
iajs-2923	110	13	)	)	PUNCT
iajs-2923	110	14	+	+	NUM
iajs-2923	110	15	𝛼𝑛(ψ𝒫𝒸(𝑢𝑛	𝛼𝑛(ψ𝒫𝒸(𝑢𝑛	NUM
iajs-2923	110	16	)	)	PUNCT
iajs-2923	110	17	−	−	NOUN
iajs-2923	110	18	𝑝)‖	𝑝)‖	VERB
iajs-2923	110	19	≤	≤	NUM
iajs-2923	110	20	𝐿[(1	𝐿[(1	PROPN
iajs-2923	110	21	−	−	PROPN
iajs-2923	110	22	𝛼𝑛)‖ψψ𝑢𝑛	𝛼𝑛)‖ψψ𝑢𝑛	PROPN
iajs-2923	110	23	−	−	PUNCT
iajs-2923	110	24	𝑝‖	𝑝‖	NOUN
iajs-2923	110	25	+	+	SYM
iajs-2923	110	26	𝛼𝑛‖ψ𝒫𝒸(𝑢𝑛	𝛼𝑛‖ψ𝒫𝒸(𝑢𝑛	NOUN
iajs-2923	110	27	)	)	PUNCT
iajs-2923	110	28	−	−	ADP
iajs-2923	111	1	𝑝‖	𝑝‖	PROPN
iajs-2923	111	2	]	]	PUNCT
iajs-2923	111	3	≤	≤	NUM
iajs-2923	111	4	𝐿[(1	𝐿[(1	PROPN
iajs-2923	111	5	−	−	PROPN
iajs-2923	111	6	𝛼𝑛)‖ψ𝑢𝑛	𝛼𝑛)‖ψ𝑢𝑛	NUM
iajs-2923	111	7	−	−	PROPN
iajs-2923	111	8	𝑝‖	𝑝‖	NOUN
iajs-2923	111	9	+	+	SYM
iajs-2923	111	10	𝛼𝑛‖ψ𝒫𝒸(𝑢𝑛	𝛼𝑛‖ψ𝒫𝒸(𝑢𝑛	NOUN
iajs-2923	111	11	)	)	PUNCT
iajs-2923	111	12	−	−	ADP
iajs-2923	111	13	𝑝‖	𝑝‖	NOUN
iajs-2923	111	14	]	]	X
iajs-2923	111	15	=	=	PUNCT
iajs-2923	111	16	𝐿[(1	𝐿[(1	ADJ
iajs-2923	112	1	−	−	PROPN
iajs-2923	112	2	𝛼𝑛)‖ψ𝑢𝑛	𝛼𝑛)‖ψ𝑢𝑛	NUM
iajs-2923	112	3	−	−	PROPN
iajs-2923	112	4	𝑝‖	𝑝‖	PROPN
iajs-2923	112	5	+	+	SYM
iajs-2923	112	6	𝛼𝑛‖𝒫𝒸ψ(𝑢𝑛	𝛼𝑛‖𝒫𝒸ψ(𝑢𝑛	PROPN
iajs-2923	112	7	)	)	PUNCT
iajs-2923	112	8	−	−	ADP
iajs-2923	113	1	𝑝‖	𝑝‖	PROPN
iajs-2923	113	2	]	]	PUNCT
iajs-2923	113	3	≤	≤	NUM
iajs-2923	113	4	𝐿[(1	𝐿[(1	PROPN
iajs-2923	113	5	−	−	PROPN
iajs-2923	113	6	𝛼𝑛)‖ψ𝑢𝑛	𝛼𝑛)‖ψ𝑢𝑛	NUM
iajs-2923	113	7	−	−	PROPN
iajs-2923	113	8	𝑝‖	𝑝‖	NOUN
iajs-2923	113	9	+	+	CCONJ
iajs-2923	113	10	𝛼𝑛‖ψ𝑢𝑛	𝛼𝑛‖ψ𝑢𝑛	X
iajs-2923	113	11	−	−	PROPN
iajs-2923	113	12	𝑝‖	𝑝‖	AUX
iajs-2923	113	13	]	]	PUNCT
iajs-2923	113	14	≤	≤	PROPN
iajs-2923	114	1	𝐿[1	𝐿[1	PROPN
iajs-2923	114	2	−	−	PROPN
iajs-2923	115	1	𝜆(1	𝜆(1	NOUN
iajs-2923	115	2	−	−	PUNCT
iajs-2923	115	3	𝐿)]‖ψ𝑢𝑛	𝐿)]‖ψ𝑢𝑛	PROPN
iajs-2923	115	4	−	−	PROPN
iajs-2923	115	5	𝑝‖	𝑝‖	NOUN
iajs-2923	115	6	:	:	PUNCT
iajs-2923	115	7	ihjpas	ihjpas	PROPN
iajs-2923	115	8	.	.	PUNCT
iajs-2923	116	1	36(1)2023	36(1)2023	NUM
iajs-2923	116	2	298	298	NUM
iajs-2923	116	3	≤	≤	NUM
iajs-2923	116	4	𝐿𝑛[1	𝐿𝑛[1	PROPN
iajs-2923	116	5	−	−	PROPN
iajs-2923	117	1	𝜆(1	𝜆(1	NOUN
iajs-2923	117	2	−	−	PROPN
iajs-2923	117	3	𝐿)]𝑛‖ψ𝑢0	𝐿)]𝑛‖ψ𝑢0	PROPN
iajs-2923	117	4	−	−	PROPN
iajs-2923	117	5	𝑝‖	𝑝‖	ADV
iajs-2923	117	6	let	let	VERB
iajs-2923	117	7	,	,	PUNCT
iajs-2923	117	8	𝒫.	𝒫.	PROPN
iajs-2923	117	9	𝒥.	𝒥.	PROPN
iajs-2923	117	10	𝒩.	𝒩.	PROPN
iajs-2923	117	11	𝒜	𝒜	NOUN
iajs-2923	117	12	=	=	SYM
iajs-2923	117	13	𝐿𝑛[1	𝐿𝑛[1	PROPN
iajs-2923	117	14	−	−	PROPN
iajs-2923	118	1	𝜆(1	𝜆(1	NOUN
iajs-2923	118	2	−	−	PROPN
iajs-2923	118	3	𝐿)]𝑛‖ψ𝑢0	𝐿)]𝑛‖ψ𝑢0	PROPN
iajs-2923	118	4	−	−	PROPN
iajs-2923	118	5	𝑝‖	𝑝‖	PROPN
iajs-2923	118	6	now	now	ADV
iajs-2923	118	7	,	,	PUNCT
iajs-2923	118	8	since	since	SCONJ
iajs-2923	118	9	:	:	PUNCT
iajs-2923	118	10	𝒫.𝒥.𝒩.𝒜	𝒫.𝒥.𝒩.𝒜	PROPN
iajs-2923	118	11	𝒫.𝒥.𝑃.𝒜	𝒫.𝒥.𝑃.𝒜	PROPN
iajs-2923	118	12	=	=	NOUN
iajs-2923	118	13	𝐿𝑛[1−𝛼𝑛(1−𝐿)]𝑛‖ψ𝑢0−𝑝‖	𝐿𝑛[1−𝛼𝑛(1−𝐿)]𝑛‖ψ𝑢0−𝑝‖	NOUN
iajs-2923	118	14	𝐿𝑛‖ψ𝑘0−𝑝‖	𝐿𝑛‖ψ𝑘0−𝑝‖	NOUN
iajs-2923	118	15	→	→	SYM
iajs-2923	118	16	0	0	NUM
iajs-2923	118	17	as	as	ADP
iajs-2923	118	18	𝑛	𝑛	PROPN
iajs-2923	118	19	→	→	SYM
iajs-2923	118	20	∞	∞	NUM
iajs-2923	118	21	hence	hence	ADV
iajs-2923	118	22	,	,	PUNCT
iajs-2923	118	23	the	the	DET
iajs-2923	118	24	projection	projection	NOUN
iajs-2923	118	25	jungck	jungck	NOUN
iajs-2923	118	26	-	-	PUNCT
iajs-2923	118	27	normal	normal	ADJ
iajs-2923	118	28	𝒩	𝒩	PROPN
iajs-2923	118	29	algorithm	algorithm	NOUN
iajs-2923	118	30	converges	converge	VERB
iajs-2923	118	31	to	to	ADP
iajs-2923	118	32	𝑝	𝑝	NOUN
iajs-2923	118	33	faster	fast	ADV
iajs-2923	118	34	than	than	ADP
iajs-2923	118	35	the	the	DET
iajs-2923	118	36	projection	projection	NOUN
iajs-2923	118	37	jungck	jungck	NOUN
iajs-2923	118	38	-	-	PUNCT
iajs-2923	118	39	picard	picard	NOUN
iajs-2923	118	40	algorithm	algorithm	NOUN
iajs-2923	118	41	.	.	PUNCT
iajs-2923	119	1	theorem	theorem	NOUN
iajs-2923	119	2	(	(	PUNCT
iajs-2923	119	3	2.16	2.16	NUM
iajs-2923	119	4	)	)	PUNCT
iajs-2923	119	5	let	let	VERB
iajs-2923	119	6	𝒳	𝒳	PRON
iajs-2923	119	7	be	be	AUX
iajs-2923	119	8	a	a	DET
iajs-2923	119	9	normed	normed	ADJ
iajs-2923	119	10	space	space	NOUN
iajs-2923	119	11	and	and	CCONJ
iajs-2923	119	12	c	c	PROPN
iajs-2923	119	13	be	be	AUX
iajs-2923	119	14	a	a	DET
iajs-2923	119	15	nonempty	nonempty	ADV
iajs-2923	119	16	closed	close	VERB
iajs-2923	119	17	convex	convex	NOUN
iajs-2923	119	18	subset	subset	NOUN
iajs-2923	119	19	of	of	ADP
iajs-2923	119	20	𝒳	𝒳	PRON
iajs-2923	119	21	if	if	SCONJ
iajs-2923	119	22	t	t	PROPN
iajs-2923	119	23	is	be	AUX
iajs-2923	119	24	a	a	DET
iajs-2923	119	25	projection	projection	NOUN
iajs-2923	119	26	jungck	jungck	NOUN
iajs-2923	119	27	zn	zn	PROPN
iajs-2923	119	28	-	-	PUNCT
iajs-2923	119	29	suzuki	suzuki	NOUN
iajs-2923	119	30	generalized	generalize	VERB
iajs-2923	119	31	mapping	mapping	NOUN
iajs-2923	119	32	and	and	CCONJ
iajs-2923	119	33	𝒞ℱ(𝒫𝒸	𝒞ℱ(𝒫𝒸	PROPN
iajs-2923	119	34	,	,	PUNCT
iajs-2923	119	35	𝑇	𝑇	PROPN
iajs-2923	119	36	,	,	PUNCT
iajs-2923	119	37	ψ	ψ	NOUN
iajs-2923	119	38	)	)	PUNCT
iajs-2923	119	39	≠	≠	PROPN
iajs-2923	119	40	ϕ.	ϕ.	NOUN
iajs-2923	119	41	then	then	ADV
iajs-2923	119	42	,	,	PUNCT
iajs-2923	119	43	the	the	DET
iajs-2923	119	44	projection	projection	NOUN
iajs-2923	119	45	jungcknormal	jungcknormal	NOUN
iajs-2923	119	46	𝒩algorithm	𝒩algorithm	PROPN
iajs-2923	119	47	converges	converge	VERB
iajs-2923	119	48	faster	fast	ADV
iajs-2923	119	49	than	than	ADP
iajs-2923	119	50	the	the	DET
iajs-2923	119	51	projection	projection	NOUN
iajs-2923	119	52	jungck	jungck	PROPN
iajs-2923	119	53	-	-	PUNCT
iajs-2923	119	54	thianwan	thianwan	PROPN
iajs-2923	119	55	algorithm	algorithm	NOUN
iajs-2923	119	56	.	.	PUNCT
iajs-2923	120	1	proof	proof	NOUN
iajs-2923	120	2	:	:	PUNCT
iajs-2923	120	3	let	let	VERB
iajs-2923	120	4	𝑝	𝑝	PROPN
iajs-2923	120	5	∈	∈	PROPN
iajs-2923	120	6	𝒞ℱ(𝒫𝒸	𝒞ℱ(𝒫𝒸	PROPN
iajs-2923	120	7	,	,	PUNCT
iajs-2923	120	8	𝑇	𝑇	PROPN
iajs-2923	120	9	,	,	PUNCT
iajs-2923	120	10	ψ)and	ψ)and	VERB
iajs-2923	120	11	suppose	suppose	VERB
iajs-2923	120	12	that	that	SCONJ
iajs-2923	120	13	there	there	PRON
iajs-2923	120	14	exists	exist	VERB
iajs-2923	120	15	ʎ	ʎ	ADJ
iajs-2923	120	16	;	;	PUNCT
iajs-2923	120	17	0	0	NUM
iajs-2923	120	18	≤	≤	NUM
iajs-2923	120	19	ʎ	ʎ	VERB
iajs-2923	120	20	≤	≤	NUM
iajs-2923	120	21	𝛽𝑛	𝛽𝑛	PROPN
iajs-2923	120	22	,	,	PUNCT
iajs-2923	120	23	𝛼𝑛	𝛼𝑛	PROPN
iajs-2923	120	24	≤	≤	NUM
iajs-2923	120	25	1	1	NUM
iajs-2923	120	26	for	for	ADP
iajs-2923	120	27	projection	projection	NOUN
iajs-2923	120	28	jungck	jungck	NOUN
iajs-2923	120	29	thianwan	thianwan	PROPN
iajs-2923	120	30	-	-	PUNCT
iajs-2923	120	31	algorithm	algorithm	PROPN
iajs-2923	120	32	‖ψ𝓏𝑛+1	‖ψ𝓏𝑛+1	PUNCT
iajs-2923	120	33	−	−	NOUN
iajs-2923	120	34	𝑝‖	𝑝‖	NOUN
iajs-2923	120	35	=	=	SYM
iajs-2923	120	36	‖(1	‖(1	NUM
iajs-2923	120	37	−	−	NOUN
iajs-2923	120	38	𝛼𝑛)ψ𝒫𝒸(𝓇𝑛	𝛼𝑛)ψ𝒫𝒸(𝓇𝑛	PROPN
iajs-2923	120	39	)	)	PUNCT
iajs-2923	121	1	+	+	CCONJ
iajs-2923	121	2	𝛼𝑛𝒫𝒸𝑇𝓇𝑛	𝛼𝑛𝒫𝒸𝑇𝓇𝑛	ADV
iajs-2923	121	3	−	−	X
iajs-2923	121	4	(	(	PUNCT
iajs-2923	121	5	1	1	NUM
iajs-2923	121	6	−	−	PROPN
iajs-2923	121	7	𝛼𝑛	𝛼𝑛	NOUN
iajs-2923	121	8	+	+	NOUN
iajs-2923	121	9	𝛼𝑛)𝑝‖	𝛼𝑛)𝑝‖	NOUN
iajs-2923	121	10	≤	≤	NUM
iajs-2923	121	11	(	(	PUNCT
iajs-2923	121	12	1	1	NUM
iajs-2923	121	13	−	−	PROPN
iajs-2923	121	14	𝛼𝑛)‖ψ𝒫𝒸(𝓇𝑛	𝛼𝑛)‖ψ𝒫𝒸(𝓇𝑛	PROPN
iajs-2923	121	15	)	)	PUNCT
iajs-2923	121	16	−	−	PROPN
iajs-2923	121	17	𝑝‖	𝑝‖	PROPN
iajs-2923	121	18	+	+	NUM
iajs-2923	121	19	𝛼𝑛‖𝒫𝒸𝑇𝓇𝑛	𝛼𝑛‖𝒫𝒸𝑇𝓇𝑛	PROPN
iajs-2923	121	20	−	−	PROPN
iajs-2923	121	21	𝑝‖	𝑝‖	NOUN
iajs-2923	121	22	=	=	SYM
iajs-2923	121	23	(	(	PUNCT
iajs-2923	121	24	1	1	NUM
iajs-2923	121	25	−	−	NUM
iajs-2923	121	26	𝛼𝑛)‖𝒫𝒸ψ(𝓇𝑛	𝛼𝑛)‖𝒫𝒸ψ(𝓇𝑛	NOUN
iajs-2923	121	27	)	)	PUNCT
iajs-2923	122	1	−	−	PROPN
iajs-2923	122	2	𝑝‖	𝑝‖	PROPN
iajs-2923	122	3	+	+	CCONJ
iajs-2923	122	4	𝛼𝑛‖𝒫𝒸𝑇𝓇𝑛	𝛼𝑛‖𝒫𝒸𝑇𝓇𝑛	PROPN
iajs-2923	122	5	−	−	PROPN
iajs-2923	122	6	𝑝‖	𝑝‖	PROPN
iajs-2923	122	7	≤	≤	NUM
iajs-2923	122	8	(	(	PUNCT
iajs-2923	122	9	1	1	NUM
iajs-2923	122	10	−	−	PROPN
iajs-2923	122	11	𝛼𝑛)‖ψ𝓇𝑛	𝛼𝑛)‖ψ𝓇𝑛	PROPN
iajs-2923	122	12	−	−	PROPN
iajs-2923	122	13	𝑝‖	𝑝‖	PROPN
iajs-2923	122	14	+	+	CCONJ
iajs-2923	122	15	𝛼𝑛‖𝑇𝓇𝑛	𝛼𝑛‖𝑇𝓇𝑛	PROPN
iajs-2923	122	16	−	−	PROPN
iajs-2923	122	17	𝑝‖	𝑝‖	PROPN
iajs-2923	122	18	≤	≤	NUM
iajs-2923	122	19	(	(	PUNCT
iajs-2923	122	20	1	1	NUM
iajs-2923	122	21	−	−	PROPN
iajs-2923	122	22	𝛼𝑛)‖ψ𝓇𝑛	𝛼𝑛)‖ψ𝓇𝑛	PROPN
iajs-2923	122	23	−	−	PROPN
iajs-2923	122	24	𝑝‖	𝑝‖	PROPN
iajs-2923	122	25	+	+	CCONJ
iajs-2923	122	26	𝐿𝛼𝑛‖ψ𝓇𝑛	𝐿𝛼𝑛‖ψ𝓇𝑛	PROPN
iajs-2923	122	27	−	−	NOUN
iajs-2923	122	28	𝑝‖	𝑝‖	NOUN
iajs-2923	122	29	+	+	SYM
iajs-2923	122	30	𝜙(‖𝑝−𝒫𝒸(𝑝)‖+‖𝑝−ψ𝑝‖	𝜙(‖𝑝−𝒫𝒸(𝑝)‖+‖𝑝−ψ𝑝‖	NOUN
iajs-2923	122	31	)	)	PUNCT
iajs-2923	122	32	1+𝑚𝑎𝑥{‖𝒫𝒸(𝑝)−𝒫𝒸(𝓇𝑛)‖,‖ψ𝑝−ψ𝓇𝑛‖	1+𝑚𝑎𝑥{‖𝒫𝒸(𝑝)−𝒫𝒸(𝓇𝑛)‖,‖ψ𝑝−ψ𝓇𝑛‖	PROPN
iajs-2923	122	33	}	}	PUNCT
iajs-2923	122	34	≤	≤	NOUN
iajs-2923	122	35	(	(	PUNCT
iajs-2923	122	36	1	1	NUM
iajs-2923	122	37	−	−	PROPN
iajs-2923	122	38	𝛼𝑛(1	𝛼𝑛(1	PROPN
iajs-2923	122	39	−	−	PROPN
iajs-2923	122	40	𝐿)‖ψ𝓇𝑛	𝐿)‖ψ𝓇𝑛	NOUN
iajs-2923	122	41	−	−	PROPN
iajs-2923	122	42	𝑝‖	𝑝‖	NOUN
iajs-2923	122	43	(	(	PUNCT
iajs-2923	122	44	2.8	2.8	NUM
iajs-2923	122	45	)	)	PUNCT
iajs-2923	122	46	now	now	ADV
iajs-2923	122	47	,	,	PUNCT
iajs-2923	122	48	‖ψ𝓇𝑛	‖ψ𝓇𝑛	PROPN
iajs-2923	122	49	−	−	NOUN
iajs-2923	122	50	𝑝‖	𝑝‖	NOUN
iajs-2923	122	51	=	=	SYM
iajs-2923	122	52	‖(1	‖(1	NUM
iajs-2923	122	53	−	−	NOUN
iajs-2923	122	54	𝛽𝑛)ψ𝒫𝒸(𝓏𝑛	𝛽𝑛)ψ𝒫𝒸(𝓏𝑛	NOUN
iajs-2923	122	55	)	)	PUNCT
iajs-2923	122	56	+	+	NUM
iajs-2923	123	1	𝛽𝑛𝒫𝒸𝑇𝓏𝑛	𝛽𝑛𝒫𝒸𝑇𝓏𝑛	PROPN
iajs-2923	123	2	−	−	PROPN
iajs-2923	123	3	(	(	PUNCT
iajs-2923	123	4	1	1	NUM
iajs-2923	123	5	−	−	PROPN
iajs-2923	123	6	𝛽𝑛	𝛽𝑛	PROPN
iajs-2923	123	7	+	+	CCONJ
iajs-2923	123	8	𝛽𝑛)𝑝‖	𝛽𝑛)𝑝‖	NOUN
iajs-2923	123	9	≤	≤	NUM
iajs-2923	123	10	(	(	PUNCT
iajs-2923	123	11	1	1	NUM
iajs-2923	123	12	−	−	PROPN
iajs-2923	123	13	𝛽𝑛)‖ψ𝒫𝒸(𝓏𝑛	𝛽𝑛)‖ψ𝒫𝒸(𝓏𝑛	PROPN
iajs-2923	123	14	)	)	PUNCT
iajs-2923	123	15	−	−	PROPN
iajs-2923	123	16	𝑝‖	𝑝‖	NOUN
iajs-2923	123	17	+	+	CCONJ
iajs-2923	123	18	𝛽𝑛‖𝒫𝒸𝑇𝓏𝑛	𝛽𝑛‖𝒫𝒸𝑇𝓏𝑛	NOUN
iajs-2923	123	19	−	−	NOUN
iajs-2923	123	20	𝑝‖	𝑝‖	NOUN
iajs-2923	123	21	=	=	SYM
iajs-2923	123	22	(	(	PUNCT
iajs-2923	123	23	1	1	NUM
iajs-2923	123	24	−	−	NOUN
iajs-2923	123	25	𝛽𝑛)‖𝒫𝒸ψ(𝓏𝑛	𝛽𝑛)‖𝒫𝒸ψ(𝓏𝑛	PROPN
iajs-2923	123	26	)	)	PUNCT
iajs-2923	123	27	−	−	PROPN
iajs-2923	123	28	𝑝‖	𝑝‖	NOUN
iajs-2923	123	29	+	+	CCONJ
iajs-2923	123	30	𝛽𝑛‖𝒫𝒸𝑇𝓏𝑛	𝛽𝑛‖𝒫𝒸𝑇𝓏𝑛	NOUN
iajs-2923	123	31	−	−	PROPN
iajs-2923	123	32	𝑝‖	𝑝‖	NOUN
iajs-2923	123	33	≤	≤	NUM
iajs-2923	123	34	(	(	PUNCT
iajs-2923	123	35	1	1	NUM
iajs-2923	123	36	−	−	NOUN
iajs-2923	123	37	𝛽𝑛)‖ψ𝓏𝑛	𝛽𝑛)‖ψ𝓏𝑛	ADP
iajs-2923	123	38	−	−	PROPN
iajs-2923	123	39	𝑝‖	𝑝‖	NOUN
iajs-2923	123	40	+	+	CCONJ
iajs-2923	123	41	𝛽𝑛‖𝑇𝓏𝑛	𝛽𝑛‖𝑇𝓏𝑛	ADJ
iajs-2923	123	42	−	−	PROPN
iajs-2923	123	43	𝑝‖	𝑝‖	NOUN
iajs-2923	123	44	≤	≤	NUM
iajs-2923	123	45	(	(	PUNCT
iajs-2923	123	46	1	1	NUM
iajs-2923	123	47	−	−	NOUN
iajs-2923	123	48	𝛽𝑛)‖ψ𝓏𝑛	𝛽𝑛)‖ψ𝓏𝑛	ADP
iajs-2923	123	49	−	−	PROPN
iajs-2923	123	50	𝑝‖	𝑝‖	NOUN
iajs-2923	123	51	+	+	CCONJ
iajs-2923	123	52	𝐿𝛽𝑛‖ψ𝓏𝑛	𝐿𝛽𝑛‖ψ𝓏𝑛	PROPN
iajs-2923	123	53	−	−	PROPN
iajs-2923	123	54	𝑝‖	𝑝‖	NOUN
iajs-2923	123	55	+	+	SYM
iajs-2923	123	56	𝜙(‖𝑝−𝒫𝒸(𝑝)‖+‖𝑝−ψ𝑝‖	𝜙(‖𝑝−𝒫𝒸(𝑝)‖+‖𝑝−ψ𝑝‖	NOUN
iajs-2923	123	57	)	)	PUNCT
iajs-2923	123	58	1+𝑚𝑎𝑥{‖𝒫𝒸(𝑝)−𝒫𝒸(𝓏𝑛)‖,‖ψ𝑝−ψ𝓏𝑛‖	1+𝑚𝑎𝑥{‖𝒫𝒸(𝑝)−𝒫𝒸(𝓏𝑛)‖,‖ψ𝑝−ψ𝓏𝑛‖	NOUN
iajs-2923	123	59	}	}	PUNCT
iajs-2923	123	60	=	=	PUNCT
iajs-2923	123	61	(	(	PUNCT
iajs-2923	123	62	1	1	NUM
iajs-2923	123	63	−	−	PROPN
iajs-2923	123	64	𝛽𝑛(1	𝛽𝑛(1	PROPN
iajs-2923	123	65	−	−	PROPN
iajs-2923	123	66	𝐿))‖ψ𝓏𝑛	𝐿))‖ψ𝓏𝑛	NOUN
iajs-2923	123	67	−	−	NOUN
iajs-2923	123	68	𝑝‖	𝑝‖	NOUN
iajs-2923	123	69	≤	≤	X
iajs-2923	123	70	(	(	PUNCT
iajs-2923	123	71	1	1	NUM
iajs-2923	123	72	−	−	NOUN
iajs-2923	123	73	𝜆(1	𝜆(1	NOUN
iajs-2923	123	74	−	−	NUM
iajs-2923	123	75	𝐿))‖ψ𝓏𝑛	𝐿))‖ψ𝓏𝑛	NOUN
iajs-2923	123	76	−	−	NOUN
iajs-2923	123	77	𝑝‖	𝑝‖	PROPN
iajs-2923	123	78	(	(	PUNCT
iajs-2923	123	79	2.9	2.9	NUM
iajs-2923	123	80	)	)	PUNCT
iajs-2923	123	81	substitute	substitute	NOUN
iajs-2923	123	82	equation	equation	NOUN
iajs-2923	123	83	(	(	PUNCT
iajs-2923	123	84	2.9	2.9	NUM
iajs-2923	123	85	)	)	PUNCT
iajs-2923	123	86	in	in	ADP
iajs-2923	123	87	to	to	ADP
iajs-2923	123	88	equation	equation	NOUN
iajs-2923	123	89	(	(	PUNCT
iajs-2923	123	90	2.8	2.8	NUM
iajs-2923	123	91	)	)	PUNCT
iajs-2923	123	92	‖ψ𝓏𝑛+1	‖ψ𝓏𝑛+1	PUNCT
iajs-2923	124	1	−	−	PROPN
iajs-2923	124	2	𝑝‖	𝑝‖	NOUN
iajs-2923	124	3	≤	≤	NUM
iajs-2923	124	4	(	(	PUNCT
iajs-2923	124	5	1	1	NUM
iajs-2923	124	6	−	−	PROPN
iajs-2923	124	7	𝛼𝑛(1	𝛼𝑛(1	PROPN
iajs-2923	124	8	−	−	PROPN
iajs-2923	124	9	𝐿)[(1	𝐿)[(1	NOUN
iajs-2923	124	10	−	−	PROPN
iajs-2923	125	1	𝜆(1	𝜆(1	NOUN
iajs-2923	126	1	−	−	NUM
iajs-2923	126	2	𝐿))‖ψ𝓏𝑛	𝐿))‖ψ𝓏𝑛	NOUN
iajs-2923	126	3	−	−	PROPN
iajs-2923	127	1	𝑝‖	𝑝‖	X
iajs-2923	127	2	]	]	PUNCT
iajs-2923	127	3	=	=	PUNCT
iajs-2923	128	1	[	[	X
iajs-2923	128	2	1	1	NUM
iajs-2923	128	3	−	−	NOUN
iajs-2923	128	4	𝜆(1	𝜆(1	NOUN
iajs-2923	128	5	−	−	PROPN
iajs-2923	128	6	𝐿	𝐿	PROPN
iajs-2923	128	7	)	)	PUNCT
iajs-2923	128	8	−	−	PROPN
iajs-2923	129	1	𝛼𝑛(1	𝛼𝑛(1	PROPN
iajs-2923	129	2	−	−	PROPN
iajs-2923	129	3	𝐿	𝐿	PROPN
iajs-2923	129	4	)	)	PUNCT
iajs-2923	130	1	+	+	NUM
iajs-2923	130	2	𝛼𝑛𝜆(1	𝛼𝑛𝜆(1	ADJ
iajs-2923	130	3	−	−	PROPN
iajs-2923	130	4	𝐿)]‖ψ𝓏𝑛	𝐿)]‖ψ𝓏𝑛	PROPN
iajs-2923	130	5	−	−	PROPN
iajs-2923	130	6	𝑝‖	𝑝‖	NOUN
iajs-2923	130	7	≤	≤	NOUN
iajs-2923	131	1	[	[	X
iajs-2923	131	2	1	1	NUM
iajs-2923	131	3	−	−	NOUN
iajs-2923	131	4	𝜆(1	𝜆(1	NOUN
iajs-2923	131	5	−	−	PROPN
iajs-2923	131	6	𝐿	𝐿	PROPN
iajs-2923	131	7	)	)	PUNCT
iajs-2923	131	8	−	−	PROPN
iajs-2923	132	1	𝜆(1	𝜆(1	NOUN
iajs-2923	132	2	−	−	PROPN
iajs-2923	132	3	𝐿	𝐿	PROPN
iajs-2923	132	4	)	)	PUNCT
iajs-2923	133	1	+	+	NUM
iajs-2923	133	2	𝜆2(1	𝜆2(1	NOUN
iajs-2923	133	3	−	−	NOUN
iajs-2923	133	4	𝐿)]‖ψ𝓏𝑛	𝐿)]‖ψ𝓏𝑛	PROPN
iajs-2923	133	5	−	−	PROPN
iajs-2923	133	6	𝑝‖	𝑝‖	NOUN
iajs-2923	133	7	≤	≤	NOUN
iajs-2923	134	1	[	[	X
iajs-2923	134	2	1	1	NUM
iajs-2923	134	3	−	−	NUM
iajs-2923	134	4	2𝜆(1	2𝜆(1	NUM
iajs-2923	135	1	−	−	PROPN
iajs-2923	135	2	𝐿	𝐿	PROPN
iajs-2923	135	3	)	)	PUNCT
iajs-2923	135	4	+	+	NUM
iajs-2923	135	5	𝜆2(1	𝜆2(1	NOUN
iajs-2923	135	6	−	−	NOUN
iajs-2923	135	7	𝐿)]‖ψ𝓏𝑛	𝐿)]‖ψ𝓏𝑛	PROPN
iajs-2923	135	8	−	−	PROPN
iajs-2923	135	9	𝑝‖	𝑝‖	NOUN
iajs-2923	135	10	≤	≤	NOUN
iajs-2923	136	1	[	[	X
iajs-2923	136	2	1	1	NUM
iajs-2923	136	3	−	−	NOUN
iajs-2923	136	4	𝜆(1	𝜆(1	NOUN
iajs-2923	136	5	−	−	PROPN
iajs-2923	137	1	𝐿)]2‖ψ𝓏𝑛	𝐿)]2‖ψ𝓏𝑛	NUM
iajs-2923	137	2	−	−	PROPN
iajs-2923	137	3	𝑝‖	𝑝‖	NOUN
iajs-2923	137	4	:	:	PUNCT
iajs-2923	137	5	≤	≤	NUM
iajs-2923	138	1	[	[	X
iajs-2923	138	2	1	1	NUM
iajs-2923	138	3	−	−	NOUN
iajs-2923	139	1	𝜆(1	𝜆(1	NOUN
iajs-2923	139	2	−	−	PROPN
iajs-2923	140	1	𝐿)]2𝑛‖ψ𝓏0	𝐿)]2𝑛‖ψ𝓏0	X
iajs-2923	140	2	−	−	PROPN
iajs-2923	140	3	𝑝‖	𝑝‖	PROPN
iajs-2923	140	4	put	put	VERB
iajs-2923	140	5	:	:	PUNCT
iajs-2923	140	6	𝒫.	𝒫.	PROPN
iajs-2923	140	7	𝒥.	𝒥.	PROPN
iajs-2923	140	8	𝒯.	𝒯.	PROPN
iajs-2923	140	9	𝒜	𝒜	NOUN
iajs-2923	140	10	=	=	PUNCT
iajs-2923	141	1	[	[	X
iajs-2923	141	2	1	1	NUM
iajs-2923	141	3	−	−	NOUN
iajs-2923	142	1	𝜆(1	𝜆(1	NOUN
iajs-2923	142	2	−	−	PROPN
iajs-2923	143	1	𝐿)]2𝑛‖ψ𝓏0	𝐿)]2𝑛‖ψ𝓏0	X
iajs-2923	143	2	−	−	PROPN
iajs-2923	143	3	𝑝‖	𝑝‖	PROPN
iajs-2923	143	4	from	from	ADP
iajs-2923	143	5	projection	projection	PROPN
iajs-2923	143	6	jungck	jungck	NOUN
iajs-2923	143	7	-	-	PUNCT
iajs-2923	143	8	normal	normal	ADJ
iajs-2923	143	9	𝒩algorithm	𝒩algorithm	PROPN
iajs-2923	143	10	𝒫.	𝒫.	PROPN
iajs-2923	143	11	𝒥.	𝒥.	PROPN
iajs-2923	143	12	𝒩.	𝒩.	PROPN
iajs-2923	143	13	𝒜	𝒜	NOUN
iajs-2923	143	14	=	=	SYM
iajs-2923	143	15	𝐿𝑛[1	𝐿𝑛[1	PROPN
iajs-2923	143	16	−	−	PROPN
iajs-2923	144	1	𝜆(1	𝜆(1	NOUN
iajs-2923	144	2	−	−	PROPN
iajs-2923	144	3	𝐿)]𝑛‖ψ𝑢0	𝐿)]𝑛‖ψ𝑢0	PROPN
iajs-2923	144	4	−	−	PROPN
iajs-2923	144	5	𝑝‖	𝑝‖	PROPN
iajs-2923	144	6	now	now	ADV
iajs-2923	144	7	since	since	SCONJ
iajs-2923	144	8	:	:	PUNCT
iajs-2923	144	9	𝒫.𝒥.𝒩.𝒜	𝒫.𝒥.𝒩.𝒜	PROPN
iajs-2923	144	10	𝒫.𝒥.𝒯.𝒜	𝒫.𝒥.𝒯.𝒜	PROPN
iajs-2923	144	11	=	=	PRON
iajs-2923	144	12	𝐿𝑛[1−𝜆(1−𝐿)]𝑛‖ψ𝑢0−𝑝‖	𝐿𝑛[1−𝜆(1−𝐿)]𝑛‖ψ𝑢0−𝑝‖	VERB
iajs-2923	145	1	[	[	X
iajs-2923	145	2	1−𝜆(1−𝐿)]2𝑛‖ψ𝓏0−𝑝‖	1−𝜆(1−𝐿)]2𝑛‖ψ𝓏0−𝑝‖	NUM
iajs-2923	145	3	as	as	ADP
iajs-2923	145	4	𝑛	𝑛	PROPN
iajs-2923	145	5	→	→	SYM
iajs-2923	145	6	∞	∞	NUM
iajs-2923	145	7	hence	hence	ADV
iajs-2923	145	8	,	,	PUNCT
iajs-2923	145	9	the	the	DET
iajs-2923	145	10	projection	projection	NOUN
iajs-2923	145	11	jungck	jungck	NOUN
iajs-2923	145	12	-	-	PUNCT
iajs-2923	145	13	normal	normal	ADJ
iajs-2923	145	14	𝒩	𝒩	PROPN
iajs-2923	145	15	algorithm	algorithm	NOUN
iajs-2923	145	16	converges	converge	VERB
iajs-2923	145	17	to	to	ADP
iajs-2923	145	18	𝑝	𝑝	PROPN
iajs-2923	145	19	is	be	AUX
iajs-2923	145	20	faster	fast	ADJ
iajs-2923	145	21	than	than	ADP
iajs-2923	145	22	the	the	DET
iajs-2923	145	23	projection	projection	NOUN
iajs-2923	145	24	jungckthianwan	jungckthianwan	PROPN
iajs-2923	145	25	algorithm	algorithm	NOUN
iajs-2923	145	26	.	.	PUNCT
iajs-2923	146	1	ihjpas	ihjpas	PROPN
iajs-2923	146	2	.	.	PUNCT
iajs-2923	147	1	36(1)2023	36(1)2023	NUM
iajs-2923	147	2	299	299	NUM
iajs-2923	147	3	3	3	NUM
iajs-2923	147	4	.	.	PUNCT
iajs-2923	147	5	conclusion	conclusion	NOUN
iajs-2923	147	6	this	this	DET
iajs-2923	147	7	paper	paper	NOUN
iajs-2923	147	8	offered	offer	VERB
iajs-2923	147	9	a	a	DET
iajs-2923	147	10	new	new	ADJ
iajs-2923	147	11	type	type	NOUN
iajs-2923	147	12	of	of	ADP
iajs-2923	147	13	mapping	mapping	NOUN
iajs-2923	147	14	as	as	ADV
iajs-2923	147	15	well	well	ADV
iajs-2923	147	16	as	as	ADP
iajs-2923	147	17	introduced	introduce	VERB
iajs-2923	147	18	new	new	ADJ
iajs-2923	147	19	algorithms	algorithm	NOUN
iajs-2923	147	20	and	and	CCONJ
iajs-2923	147	21	demonstrated	demonstrate	VERB
iajs-2923	147	22	their	their	PRON
iajs-2923	147	23	convergence	convergence	NOUN
iajs-2923	147	24	and	and	CCONJ
iajs-2923	147	25	stability	stability	NOUN
iajs-2923	147	26	.	.	PUNCT
iajs-2923	148	1	on	on	ADP
iajs-2923	148	2	the	the	DET
iajs-2923	148	3	other	other	ADJ
iajs-2923	148	4	hand	hand	NOUN
iajs-2923	148	5	,	,	PUNCT
iajs-2923	148	6	the	the	DET
iajs-2923	148	7	acceleration	acceleration	NOUN
iajs-2923	148	8	and	and	CCONJ
iajs-2923	148	9	stability	stability	NOUN
iajs-2923	148	10	were	be	AUX
iajs-2923	148	11	examined	examine	VERB
iajs-2923	148	12	.	.	PUNCT
iajs-2923	149	1	we	we	PRON
iajs-2923	149	2	discovered	discover	VERB
iajs-2923	149	3	that	that	SCONJ
iajs-2923	149	4	the	the	DET
iajs-2923	149	5	projection	projection	NOUN
iajs-2923	149	6	jungck	jungck	NOUN
iajs-2923	149	7	-	-	PUNCT
iajs-2923	149	8	normal	normal	ADJ
iajs-2923	149	9	algorithm	algorithm	NOUN
iajs-2923	149	10	is	be	AUX
iajs-2923	149	11	quicker	quick	ADJ
iajs-2923	149	12	than	than	ADP
iajs-2923	149	13	the	the	DET
iajs-2923	149	14	techniques	technique	NOUN
iajs-2923	149	15	stated	state	VERB
iajs-2923	149	16	in	in	ADP
iajs-2923	149	17	this	this	DET
iajs-2923	149	18	paper	paper	NOUN
iajs-2923	149	19	to	to	PART
iajs-2923	149	20	achieve	achieve	VERB
iajs-2923	149	21	the	the	DET
iajs-2923	149	22	fixed	fix	VERB
iajs-2923	149	23	point	point	NOUN
iajs-2923	149	24	.	.	PUNCT
iajs-2923	150	1	references	reference	NOUN
iajs-2923	150	2	1	1	NUM
iajs-2923	150	3	.	.	X
iajs-2923	150	4	rathee	rathee	PROPN
iajs-2923	150	5	,	,	PUNCT
iajs-2923	150	6	s.	s.	PROPN
iajs-2923	150	7	;	;	PUNCT
iajs-2923	150	8	swami	swami	PROPN
iajs-2923	150	9	,	,	PUNCT
iajs-2923	150	10	m.	m.	NOUN
iajs-2923	150	11	convergence	convergence	NOUN
iajs-2923	150	12	rate	rate	NOUN
iajs-2923	150	13	of	of	ADP
iajs-2923	150	14	various	various	ADJ
iajs-2923	150	15	iterations	iteration	NOUN
iajs-2923	150	16	with	with	ADP
iajs-2923	150	17	sm	sm	NOUN
iajs-2923	150	18	-	-	NOUN
iajs-2923	150	19	iteration	iteration	NOUN
iajs-2923	150	20	for	for	ADP
iajs-2923	150	21	continuous	continuous	ADJ
iajs-2923	150	22	functi	functi	PROPN
iajs-2923	150	23	savita	savita	PROPN
iajs-2923	150	24	ratheel	ratheel	PROPN
iajs-2923	150	25	.	.	PUNCT
iajs-2923	151	1	journal	journal	PROPN
iajs-2923	151	2	of	of	ADP
iajs-2923	151	3	mathematical	mathematical	ADJ
iajs-2923	151	4	and	and	CCONJ
iajs-2923	151	5	computational	computational	ADJ
iajs-2923	151	6	science	science	NOUN
iajs-2923	151	7	.	.	PUNCT
iajs-2923	152	1	2020	2020	NUM
iajs-2923	152	2	,	,	PUNCT
iajs-2923	152	3	3074	3074	NUM
iajs-2923	152	4	-	-	SYM
iajs-2923	152	5	3089	3089	NUM
iajs-2923	152	6	.	.	PUNCT
iajs-2923	153	1	2	2	X
iajs-2923	153	2	.	.	X
iajs-2923	153	3	maibed	maibed	PROPN
iajs-2923	153	4	,	,	PUNCT
iajs-2923	153	5	z.	z.	PROPN
iajs-2923	153	6	;	;	PUNCT
iajs-2923	153	7	thajil	thajil	X
iajs-2923	153	8	,	,	PUNCT
iajs-2923	153	9	a.	a.	NOUN
iajs-2923	153	10	zenali	zenali	VERB
iajs-2923	153	11	iteration	iteration	NOUN
iajs-2923	153	12	method	method	NOUN
iajs-2923	153	13	for	for	ADP
iajs-2923	153	14	approximating	approximate	VERB
iajs-2923	153	15	fixed	fix	VERB
iajs-2923	153	16	point	point	NOUN
iajs-2923	153	17	of	of	ADP
iajs-2923	153	18	za	za	PROPN
iajs-2923	153	19	quasi	quasi	PROPN
iajs-2923	153	20	contractive	contractive	ADJ
iajs-2923	153	21	mappings	mapping	NOUN
iajs-2923	153	22	.	.	PUNCT
iajs-2923	154	1	haitham	haitham	PROPN
iajs-2923	154	2	journal	journal	PROPN
iajs-2923	154	3	for	for	ADP
iajs-2923	154	4	pure	pure	ADJ
iajs-2923	154	5	and	and	CCONJ
iajs-2923	154	6	applied	applied	ADJ
iajs-2923	154	7	science	science	NOUN
iajs-2923	154	8	.	.	PUNCT
iajs-2923	155	1	2021	2021	NUM
iajs-2923	155	2	,	,	PUNCT
iajs-2923	155	3	78	78	NUM
iajs-2923	155	4	-	-	SYM
iajs-2923	155	5	91	91	NUM
iajs-2923	155	6	.	.	PUNCT
iajs-2923	156	1	3	3	X
iajs-2923	156	2	.	.	X
iajs-2923	156	3	jamil	jamil	PROPN
iajs-2923	156	4	,	,	PUNCT
iajs-2923	156	5	z.	z.	PROPN
iajs-2923	156	6	;	;	PUNCT
iajs-2923	156	7	abed	abe	VERB
iajs-2923	156	8	,	,	PUNCT
iajs-2923	156	9	b	b	NOUN
iajs-2923	156	10	,	,	PUNCT
iajs-2923	156	11	on	on	ADP
iajs-2923	156	12	a	a	DET
iajs-2923	156	13	modified	modify	VERB
iajs-2923	156	14	sp	sp	NOUN
iajs-2923	156	15	-	-	PUNCT
iajs-2923	156	16	iterative	iterative	NOUN
iajs-2923	156	17	scheme	scheme	NOUN
iajs-2923	156	18	for	for	ADP
iajs-2923	156	19	approximating	approximate	VERB
iajs-2923	156	20	fixed	fix	VERB
iajs-2923	156	21	point	point	NOUN
iajs-2923	156	22	of	of	ADP
iajs-2923	156	23	a	a	DET
iajs-2923	156	24	contraction	contraction	NOUN
iajs-2923	156	25	mapping	mapping	NOUN
iajs-2923	156	26	.	.	PUNCT
iajs-2923	157	1	iraqi	iraqi	ADJ
iajs-2923	157	2	journal	journal	PROPN
iajs-2923	157	3	of	of	ADP
iajs-2923	157	4	scienceno	scienceno	PROPN
iajs-2923	157	5	.	.	PUNCT
iajs-2923	158	1	2015	2015	NUM
iajs-2923	158	2	,	,	PUNCT
iajs-2923	158	3	56	56	NUM
iajs-2923	158	4	,	,	PUNCT
iajs-2923	158	5	3230	3230	NUM
iajs-2923	158	6	-	-	SYM
iajs-2923	158	7	3239	3239	NUM
iajs-2923	158	8	.	.	PUNCT
iajs-2923	159	1	4	4	NUM
iajs-2923	159	2	.	.	X
iajs-2923	159	3	daengsaen	daengsaen	PROPN
iajs-2923	159	4	,	,	PUNCT
iajs-2923	159	5	j.	j.	PROPN
iajs-2923	159	6	;	;	PUNCT
iajs-2923	159	7	khemphet	khemphet	PROPN
iajs-2923	159	8	,	,	PUNCT
iajs-2923	159	9	a.	a.	NOUN
iajs-2923	159	10	on	on	ADP
iajs-2923	159	11	the	the	DET
iajs-2923	159	12	rate	rate	NOUN
iajs-2923	159	13	of	of	ADP
iajs-2923	159	14	convergence	convergence	NOUN
iajs-2923	159	15	of	of	ADP
iajs-2923	159	16	p	p	NOUN
iajs-2923	159	17	-	-	PUNCT
iajs-2923	159	18	iteration	iteration	NOUN
iajs-2923	159	19	,	,	PUNCT
iajs-2923	159	20	sp	sp	NOUN
iajs-2923	159	21	-	-	PUNCT
iajs-2923	159	22	iteration	iteration	NOUN
iajs-2923	159	23	,	,	PUNCT
iajs-2923	159	24	and	and	CCONJ
iajs-2923	159	25	diteration	diteration	NOUN
iajs-2923	159	26	methods	method	NOUN
iajs-2923	159	27	for	for	ADP
iajs-2923	159	28	continuous	continuous	ADJ
iajs-2923	159	29	nondecreasing	nondecreasing	ADJ
iajs-2923	159	30	functions	function	NOUN
iajs-2923	159	31	on	on	ADP
iajs-2923	159	32	closed	closed	ADJ
iajs-2923	159	33	intervals	interval	NOUN
iajs-2923	159	34	.	.	PUNCT
iajs-2923	160	1	hindawi	hindawi	VERB
iajs-2923	160	2	abstr	abstr	PROPN
iajs-2923	160	3	.	.	PUNCT
iajs-2923	161	1	appl	appl	PROPN
iajs-2923	161	2	.	.	PUNCT
iajs-2923	162	1	anal	anal	PROPN
iajs-2923	162	2	.	.	PUNCT
iajs-2923	163	1	2018	2018	NUM
iajs-2923	163	2	,	,	PUNCT
iajs-2923	163	3	6	6	NUM
iajs-2923	163	4	.	.	NOUN
iajs-2923	163	5	5	5	NUM
iajs-2923	163	6	.	.	PUNCT
iajs-2923	164	1	ullah	ullah	PROPN
iajs-2923	164	2	,	,	PUNCT
iajs-2923	164	3	k.	k.	PROPN
iajs-2923	164	4	;	;	PUNCT
iajs-2923	164	5	muhammad	muhammad	PROPN
iajs-2923	164	6	,	,	PUNCT
iajs-2923	164	7	a.	a.	NOUN
iajs-2923	164	8	new	new	ADJ
iajs-2923	164	9	three	three	NUM
iajs-2923	164	10	-	-	PUNCT
iajs-2923	164	11	step	step	NOUN
iajs-2923	164	12	iteration	iteration	NOUN
iajs-2923	164	13	process	process	NOUN
iajs-2923	164	14	and	and	CCONJ
iajs-2923	164	15	fixed	fix	VERB
iajs-2923	164	16	point	point	NOUN
iajs-2923	164	17	approximation	approximation	NOUN
iajs-2923	164	18	in	in	ADP
iajs-2923	164	19	banach	banach	NOUN
iajs-2923	164	20	spaces	space	NOUN
iajs-2923	164	21	.	.	PUNCT
iajs-2923	165	1	linear	linear	PROPN
iajs-2923	165	2	topol	topol	PROPN
iajs-2923	165	3	.	.	PUNCT
iajs-2923	166	1	algebra	algebra	NOUN
iajs-2923	166	2	.	.	PUNCT
iajs-2923	167	1	2018,7	2018,7	NUM
iajs-2923	167	2	,	,	PUNCT
iajs-2923	167	3	87–100	87–100	PROPN
iajs-2923	167	4	.	.	PROPN
iajs-2923	167	5	6	6	NUM
iajs-2923	167	6	.	.	X
iajs-2923	168	1	maibed	maibe	VERB
iajs-2923	168	2	,	,	PUNCT
iajs-2923	168	3	z.h	z.h	PROPN
iajs-2923	168	4	.	.	PROPN
iajs-2923	168	5	;	;	PUNCT
iajs-2923	168	6	thajil	thajil	X
iajs-2923	168	7	,	,	PUNCT
iajs-2923	168	8	a.	a.	NOUN
iajs-2923	168	9	q.	q.	PROPN
iajs-2923	168	10	equivalence	equivalence	NOUN
iajs-2923	168	11	of	of	ADP
iajs-2923	168	12	some	some	DET
iajs-2923	168	13	iterations	iteration	NOUN
iajs-2923	168	14	for	for	ADP
iajs-2923	168	15	class	class	NOUN
iajs-2923	168	16	of	of	ADP
iajs-2923	168	17	quasi	quasi	NOUN
iajs-2923	168	18	contractive	contractive	ADJ
iajs-2923	168	19	mappings	mapping	NOUN
iajs-2923	168	20	.	.	PUNCT
iajs-2923	169	1	j.	j.	PROPN
iajs-2923	169	2	phys	phys	PROPN
iajs-2923	169	3	.	.	PUNCT
iajs-2923	169	4	:	:	PUNCT
iajs-2923	169	5	conf	conf	NOUN
iajs-2923	169	6	.	.	PUNCT
iajs-2923	170	1	ser.1879	ser.1879	NUM
iajs-2923	170	2	022115	022115	NUM
iajs-2923	170	3	.	.	PUNCT
iajs-2923	171	1	2021	2021	NUM
iajs-2923	171	2	,	,	PUNCT
iajs-2923	171	3	7	7	X
iajs-2923	171	4	.	.	X
iajs-2923	171	5	maldar	maldar	PROPN
iajs-2923	171	6	,	,	PUNCT
iajs-2923	171	7	s.	s.	PROPN
iajs-2923	171	8	;	;	PUNCT
iajs-2923	171	9	dogan	dogan	PROPN
iajs-2923	171	10	,	,	PUNCT
iajs-2923	171	11	k.	k.	PROPN
iajs-2923	171	12	comparison	comparison	NOUN
iajs-2923	171	13	rate	rate	NOUN
iajs-2923	171	14	of	of	ADP
iajs-2923	171	15	convergence	convergence	NOUN
iajs-2923	171	16	and	and	CCONJ
iajs-2923	171	17	data	datum	NOUN
iajs-2923	171	18	dependence	dependence	NOUN
iajs-2923	171	19	for	for	ADP
iajs-2923	171	20	a	a	DET
iajs-2923	171	21	new	new	ADJ
iajs-2923	171	22	iteration	iteration	NOUN
iajs-2923	171	23	method	method	NOUN
iajs-2923	171	24	.	.	PUNCT
iajs-2923	172	1	tbilisi	tbilisi	PROPN
iajs-2923	172	2	mathematical	mathematical	PROPN
iajs-2923	172	3	journal	journal	PROPN
iajs-2923	172	4	.	.	PUNCT
iajs-2923	173	1	2020	2020	NUM
iajs-2923	173	2	,	,	PUNCT
iajs-2923	173	3	65	65	NUM
iajs-2923	173	4	-	-	SYM
iajs-2923	173	5	79	79	NUM
iajs-2923	173	6	.	.	PUNCT
iajs-2923	174	1	8	8	NUM
iajs-2923	174	2	.	.	X
iajs-2923	175	1	maldar	maldar	PROPN
iajs-2923	175	2	,	,	PUNCT
iajs-2923	175	3	s.	s.	PROPN
iajs-2923	175	4	;	;	PUNCT
iajs-2923	175	5	karakaya	karakaya	PROPN
iajs-2923	175	6	,	,	PUNCT
iajs-2923	175	7	v.	v.	ADP
iajs-2923	175	8	convergence	convergence	NOUN
iajs-2923	175	9	of	of	ADP
iajs-2923	175	10	jungck	jungck	PROPN
iajs-2923	175	11	-	-	PUNCT
iajs-2923	175	12	kirk	kirk	PROPN
iajs-2923	175	13	type	type	PROPN
iajs-2923	175	14	iteration	iteration	NOUN
iajs-2923	175	15	method	method	NOUN
iajs-2923	175	16	with	with	ADP
iajs-2923	175	17	applications	application	NOUN
iajs-2923	175	18	.	.	PUNCT
iajs-2923	176	1	punjab	punjab	PROPN
iajs-2923	176	2	university	university	PROPN
iajs-2923	176	3	journal	journal	NOUN
iajs-2923	176	4	of	of	ADP
iajs-2923	176	5	mathematics	mathematic	NOUN
iajs-2923	176	6	.	.	PUNCT
iajs-2923	177	1	2022	2022	NUM
iajs-2923	177	2	,	,	PUNCT
iajs-2923	177	3	54	54	NUM
iajs-2923	177	4	,	,	PUNCT
iajs-2923	177	5	75	75	NUM
iajs-2923	177	6	-	-	SYM
iajs-2923	177	7	87	87	NUM
iajs-2923	177	8	.	.	PUNCT
iajs-2923	178	1	9	9	X
iajs-2923	178	2	.	.	X
iajs-2923	178	3	albaqeri	albaqeri	PROPN
iajs-2923	178	4	,	,	PUNCT
iajs-2923	178	5	d.	d.	PROPN
iajs-2923	178	6	;	;	PUNCT
iajs-2923	178	7	rashwan	rashwan	PROPN
iajs-2923	178	8	,	,	PUNCT
iajs-2923	178	9	r.	r.	VERB
iajs-2923	178	10	the	the	DET
iajs-2923	178	11	comparably	comparably	ADV
iajs-2923	178	12	almost	almost	ADV
iajs-2923	178	13	(	(	PUNCT
iajs-2923	178	14	s	s	X
iajs-2923	178	15	,	,	PUNCT
iajs-2923	178	16	t)stability	t)stability	NOUN
iajs-2923	178	17	for	for	ADP
iajs-2923	178	18	random	random	ADJ
iajs-2923	178	19	jungck	jungck	NOUN
iajs-2923	178	20	-	-	PUNCT
iajs-2923	178	21	type	type	NOUN
iajs-2923	178	22	iterative	iterative	NOUN
iajs-2923	178	23	scheme	scheme	NOUN
iajs-2923	178	24	.	.	PUNCT
iajs-2923	179	1	facta	facta	NOUN
iajs-2923	179	2	universities	university	NOUN
iajs-2923	179	3	(	(	PUNCT
iajs-2923	179	4	nisˇ	nisˇ	NOUN
iajs-2923	179	5	)	)	PUNCT
iajs-2923	179	6	.	.	PUNCT
iajs-2923	180	1	2019	2019	NUM
iajs-2923	180	2	,	,	PUNCT
iajs-2923	180	3	34	34	NUM
iajs-2923	180	4	,	,	PUNCT
iajs-2923	180	5	2	2	NUM
iajs-2923	180	6	,	,	PUNCT
iajs-2923	180	7	175	175	NUM
iajs-2923	180	8	-	-	SYM
iajs-2923	180	9	192	192	NUM
iajs-2923	180	10	.	.	PUNCT
iajs-2923	181	1	10	10	NUM
iajs-2923	181	2	.	.	PUNCT
iajs-2923	182	1	jungck	jungck	PROPN
iajs-2923	182	2	,	,	PUNCT
iajs-2923	182	3	g.	g.	PROPN
iajs-2923	182	4	commuting	commute	VERB
iajs-2923	182	5	mapping	mapping	NOUN
iajs-2923	182	6	and	and	CCONJ
iajs-2923	182	7	fixed	fix	VERB
iajs-2923	182	8	point	point	NOUN
iajs-2923	182	9	.	.	PUNCT
iajs-2923	183	1	the	the	DET
iajs-2923	183	2	american	american	PROPN
iajs-2923	183	3	mathematical	mathematical	PROPN
iajs-2923	183	4	monthly	monthly	ADV
iajs-2923	183	5	.	.	PUNCT
iajs-2923	184	1	1976	1976	NUM
iajs-2923	184	2	,	,	PUNCT
iajs-2923	184	3	83	83	NUM
iajs-2923	184	4	,	,	PUNCT
iajs-2923	184	5	4	4	NUM
iajs-2923	184	6	,	,	PUNCT
iajs-2923	184	7	261	261	NUM
iajs-2923	184	8	-	-	SYM
iajs-2923	184	9	263	263	NUM
iajs-2923	184	10	.	.	PUNCT
iajs-2923	185	1	11	11	NUM
iajs-2923	185	2	.	.	PUNCT
iajs-2923	186	1	bosede	bosede	PROPN
iajs-2923	186	2	,	,	PUNCT
iajs-2923	186	3	a.	a.	NOUN
iajs-2923	186	4	on	on	ADP
iajs-2923	186	5	the	the	DET
iajs-2923	186	6	stability	stability	NOUN
iajs-2923	186	7	of	of	ADP
iajs-2923	186	8	jungck	jungck	NOUN
iajs-2923	186	9	-	-	PUNCT
iajs-2923	186	10	mann	mann	PROPN
iajs-2923	186	11	,	,	PUNCT
iajs-2923	186	12	jungck	jungck	NOUN
iajs-2923	186	13	krasnoselskij	krasnoselskij	NOUN
iajs-2923	186	14	and	and	CCONJ
iajs-2923	186	15	jungck	jungck	PROPN
iajs-2923	186	16	iteration	iteration	NOUN
iajs-2923	186	17	process	process	NOUN
iajs-2923	186	18	in	in	ADP
iajs-2923	186	19	arbitrary	arbitrary	ADJ
iajs-2923	186	20	banach	banach	NOUN
iajs-2923	186	21	spaces	space	NOUN
iajs-2923	186	22	.	.	PUNCT
iajs-2923	187	1	acta	acta	PROPN
iajs-2923	187	2	univ	univ	PROPN
iajs-2923	187	3	.	.	PUNCT
iajs-2923	188	1	palacki	palacki	PROPN
iajs-2923	188	2	.	.	PUNCT
iajs-2923	189	1	olomuc	olomuc	PROPN
iajs-2923	189	2	.	.	PUNCT
iajs-2923	190	1	fac	fac	PROPN
iajs-2923	190	2	.	.	PUNCT
iajs-2923	190	3	rer	rer	PROPN
iajs-2923	190	4	.	.	PUNCT
iajs-2923	191	1	nat	nat	PROPN
iajs-2923	191	2	.	.	PUNCT
iajs-2923	191	3	,	,	PUNCT
iajs-2923	191	4	mathematica	mathematica	PROPN
iajs-2923	191	5	.	.	PROPN
iajs-2923	192	1	2011	2011	NUM
iajs-2923	192	2	,	,	PUNCT
iajs-2923	192	3	50	50	NUM
iajs-2923	192	4	,	,	PUNCT
iajs-2923	192	5	1	1	NUM
iajs-2923	192	6	,	,	PUNCT
iajs-2923	192	7	17	17	NUM
iajs-2923	192	8	-	-	SYM
iajs-2923	192	9	22	22	NUM
iajs-2923	192	10	.	.	PUNCT
iajs-2923	193	1	12	12	NUM
iajs-2923	193	2	.	.	PUNCT
iajs-2923	194	1	berinde	berinde	NOUN
iajs-2923	194	2	,	,	PUNCT
iajs-2923	194	3	v.	v.	ADP
iajs-2923	194	4	picard	picard	PROPN
iajs-2923	194	5	iteration	iteration	NOUN
iajs-2923	194	6	converges	converge	VERB
iajs-2923	194	7	faster	fast	ADV
iajs-2923	194	8	than	than	ADP
iajs-2923	194	9	mann	mann	PROPN
iajs-2923	194	10	iteration	iteration	NOUN
iajs-2923	194	11	for	for	ADP
iajs-2923	194	12	a	a	DET
iajs-2923	194	13	class	class	NOUN
iajs-2923	194	14	of	of	ADP
iajs-2923	194	15	quasi	quasi	NOUN
iajs-2923	194	16	contractive	contractive	ADJ
iajs-2923	194	17	operators	operator	NOUN
iajs-2923	194	18	.	.	PUNCT
iajs-2923	195	1	fixed	fix	VERB
iajs-2923	195	2	point	point	NOUN
iajs-2923	195	3	theory	theory	NOUN
iajs-2923	195	4	and	and	CCONJ
iajs-2923	195	5	appl2	appl2	NOUN
iajs-2923	195	6	.	.	PUNCT
iajs-2923	196	1	2004	2004	NUM
iajs-2923	196	2	,	,	PUNCT
iajs-2923	196	3	97	97	NUM
iajs-2923	196	4	-	-	SYM
iajs-2923	196	5	105	105	NUM
iajs-2923	196	6	.	.	PUNCT
iajs-2923	197	1	13.thianwan	13.thianwan	NUM
iajs-2923	197	2	,	,	PUNCT
iajs-2923	197	3	s.	s.	PROPN
iajs-2923	197	4	common	common	ADJ
iajs-2923	197	5	fixed	fix	VERB
iajs-2923	197	6	points	point	NOUN
iajs-2923	197	7	of	of	ADP
iajs-2923	197	8	new	new	ADJ
iajs-2923	197	9	iterations	iteration	NOUN
iajs-2923	197	10	for	for	ADP
iajs-2923	197	11	two	two	NUM
iajs-2923	197	12	asymptotically	asymptotically	ADV
iajs-2923	197	13	nonexpansive	nonexpansive	ADJ
iajs-2923	197	14	nonself	nonself	NOUN
iajs-2923	197	15	-	-	PUNCT
iajs-2923	197	16	mappings	mapping	NOUN
iajs-2923	197	17	in	in	ADP
iajs-2923	197	18	a	a	DET
iajs-2923	197	19	banach	banach	NOUN
iajs-2923	197	20	space	space	NOUN
iajs-2923	197	21	.	.	PUNCT
iajs-2923	198	1	journal	journal	NOUN
iajs-2923	198	2	of	of	ADP
iajs-2923	198	3	computational	computational	ADJ
iajs-2923	198	4	and	and	CCONJ
iajs-2923	198	5	applied	applied	ADJ
iajs-2923	198	6	mathematics	mathematic	NOUN
iajs-2923	198	7	.	.	PUNCT
iajs-2923	199	1	2009	2009	NUM
iajs-2923	199	2	,	,	PUNCT
iajs-2923	199	3	224	224	NUM
iajs-2923	199	4	,	,	PUNCT
iajs-2923	199	5	2	2	NUM
iajs-2923	199	6	,	,	PUNCT
iajs-2923	199	7	688–695	688–695	NUM
iajs-2923	199	8	.	.	PUNCT
iajs-2923	200	1	14	14	NUM
iajs-2923	200	2	.	.	PUNCT
iajs-2923	201	1	agarwal	agarwal	PROPN
iajs-2923	201	2	,	,	PUNCT
iajs-2923	201	3	r.	r.	PROPN
iajs-2923	201	4	;	;	PUNCT
iajs-2923	201	5	sahu	sahu	PROPN
iajs-2923	201	6	,	,	PUNCT
iajs-2923	201	7	d.	d.	PROPN
iajs-2923	201	8	fixed	fix	VERB
iajs-2923	201	9	point	point	NOUN
iajs-2923	201	10	theory	theory	NOUN
iajs-2923	201	11	for	for	ADP
iajs-2923	201	12	lipschitzian	lipschitzian	ADJ
iajs-2923	201	13	-	-	PUNCT
iajs-2923	201	14	type	type	NOUN
iajs-2923	201	15	mappings	mapping	NOUN
iajs-2923	201	16	with	with	ADP
iajs-2923	201	17	applications	application	NOUN
iajs-2923	201	18	;	;	PUNCT
iajs-2923	201	19	new	new	PROPN
iajs-2923	201	20	york	york	PROPN
iajs-2923	201	21	:	:	PUNCT
iajs-2923	201	22	springer	springer	NOUN
iajs-2923	201	23	,	,	PUNCT
iajs-2923	201	24	2009	2009	NUM
iajs-2923	201	25	.	.	PUNCT
iajs-2923	202	1	15	15	NUM
iajs-2923	202	2	.	.	X
iajs-2923	202	3	olatinwo	olatinwo	PROPN
iajs-2923	202	4	,	,	PUNCT
iajs-2923	202	5	m.	m.	VERB
iajs-2923	202	6	some	some	DET
iajs-2923	202	7	stability	stability	NOUN
iajs-2923	202	8	and	and	CCONJ
iajs-2923	202	9	strong	strong	ADJ
iajs-2923	202	10	convergence	convergence	NOUN
iajs-2923	202	11	results	result	NOUN
iajs-2923	202	12	for	for	ADP
iajs-2923	202	13	the	the	DET
iajs-2923	202	14	jungck	jungck	NOUN
iajs-2923	202	15	-	-	PUNCT
iajs-2923	202	16	ishikawa	ishikawa	PROPN
iajs-2923	202	17	iteration	iteration	NOUN
iajs-2923	202	18	process	process	NOUN
iajs-2923	202	19	.	.	PUNCT
iajs-2923	203	1	creative	creative	ADJ
iajs-2923	203	2	mathematics	mathematic	NOUN
iajs-2923	203	3	and	and	CCONJ
iajs-2923	203	4	informatics	informatic	NOUN
iajs-2923	203	5	.	.	PUNCT
iajs-2923	203	6	2008	2008	NUM
iajs-2923	203	7	,	,	PUNCT
iajs-2923	203	8	17	17	NUM
iajs-2923	203	9	,	,	PUNCT
iajs-2923	203	10	33–42	33–42	NUM
iajs-2923	203	11	.	.	NOUN
iajs-2923	203	12	16	16	NUM
iajs-2923	203	13	.	.	PUNCT
iajs-2923	204	1	suzuki	suzuki	PROPN
iajs-2923	204	2	,	,	PUNCT
iajs-2923	204	3	t.	t.	PROPN
iajs-2923	204	4	fixed	fix	VERB
iajs-2923	204	5	point	point	NOUN
iajs-2923	204	6	theorems	theorem	NOUN
iajs-2923	204	7	and	and	CCONJ
iajs-2923	204	8	convergence	convergence	NOUN
iajs-2923	204	9	theorems	theorem	NOUN
iajs-2923	204	10	for	for	ADP
iajs-2923	204	11	some	some	DET
iajs-2923	204	12	generalized	generalize	VERB
iajs-2923	204	13	nonexpansive	nonexpansive	ADJ
iajs-2923	204	14	mappings	mapping	NOUN
iajs-2923	204	15	.	.	PUNCT
iajs-2923	205	1	j.	j.	PROPN
iajs-2923	205	2	math	math	PROPN
iajs-2923	205	3	.	.	PUNCT
iajs-2923	206	1	anal	anal	PROPN
iajs-2923	206	2	.	.	PUNCT
iajs-2923	207	1	appl	appl	PROPN
iajs-2923	207	2	.	.	PROPN
iajs-2923	208	1	340	340	NUM
iajs-2923	208	2	.	.	NUM
iajs-2923	208	3	2008	2008	NUM
iajs-2923	208	4	,	,	PUNCT
iajs-2923	208	5	1088	1088	NUM
iajs-2923	208	6	-	-	SYM
iajs-2923	208	7	1095	1095	NUM
iajs-2923	208	8	.	.	PUNCT