id	sid	tid	token	lemma	pos
easat-9284	1	1	edelweiss	edelweiss	PROPN
easat-9284	1	2	applied	apply	VERB
easat-9284	1	3	science	science	NOUN
easat-9284	1	4	and	and	CCONJ
easat-9284	1	5	technology	technology	NOUN
easat-9284	1	6	issn	issn	PROPN
easat-9284	1	7	:	:	PUNCT
easat-9284	1	8	2576	2576	NUM
easat-9284	1	9	-	-	SYM
easat-9284	1	10	8484	8484	NUM
easat-9284	1	11	vol	vol	NOUN
easat-9284	1	12	.	.	PROPN
easat-9284	2	1	9	9	NUM
easat-9284	2	2	,	,	PUNCT
easat-9284	2	3	no	no	INTJ
easat-9284	2	4	.	.	NOUN
easat-9284	2	5	8	8	NUM
easat-9284	2	6	,	,	PUNCT
easat-9284	2	7	291	291	NUM
easat-9284	2	8	-	-	SYM
easat-9284	2	9	299	299	NUM
easat-9284	2	10	2025	2025	NUM
easat-9284	2	11	publisher	publisher	NOUN
easat-9284	2	12	:	:	PUNCT
easat-9284	2	13	learning	learn	VERB
easat-9284	2	14	gate	gate	NOUN
easat-9284	2	15	doi	doi	PROPN
easat-9284	2	16	:	:	PUNCT
easat-9284	2	17	10.55214/2576	10.55214/2576	NUM
easat-9284	2	18	-	-	PUNCT
easat-9284	2	19	8484.v9i8.9284	8484.v9i8.9284	NOUN
easat-9284	2	20	©	©	PROPN
easat-9284	2	21	2025	2025	NUM
easat-9284	2	22	by	by	ADP
easat-9284	2	23	the	the	DET
easat-9284	2	24	author	author	NOUN
easat-9284	2	25	;	;	PUNCT
easat-9284	2	26	licensee	licensee	PROPN
easat-9284	2	27	learning	learning	NOUN
easat-9284	2	28	gate	gate	NOUN
easat-9284	3	1	©	©	PROPN
easat-9284	3	2	2025	2025	NUM
easat-9284	3	3	by	by	ADP
easat-9284	3	4	the	the	DET
easat-9284	3	5	author	author	NOUN
easat-9284	3	6	;	;	PUNCT
easat-9284	3	7	licensee	licensee	PROPN
easat-9284	3	8	learning	learning	NOUN
easat-9284	3	9	gate	gate	NOUN
easat-9284	3	10	history	history	NOUN
easat-9284	3	11	:	:	PUNCT
easat-9284	3	12	received	receive	VERB
easat-9284	3	13	:	:	PUNCT
easat-9284	3	14	11	11	NUM
easat-9284	3	15	may	may	PROPN
easat-9284	3	16	2025	2025	NUM
easat-9284	3	17	;	;	PUNCT
easat-9284	3	18	revised	revise	VERB
easat-9284	3	19	:	:	PUNCT
easat-9284	3	20	10	10	NUM
easat-9284	3	21	july2025	july2025	PROPN
easat-9284	3	22	;	;	PUNCT
easat-9284	3	23	accepted	accept	VERB
easat-9284	3	24	:	:	PUNCT
easat-9284	3	25	14	14	NUM
easat-9284	3	26	july	july	PROPN
easat-9284	3	27	2025	2025	NUM
easat-9284	3	28	;	;	PUNCT
easat-9284	3	29	published	publish	VERB
easat-9284	3	30	:	:	PUNCT
easat-9284	4	1	5	5	NUM
easat-9284	4	2	august	august	PROPN
easat-9284	4	3	2025	2025	NUM
easat-9284	4	4	*	*	PUNCT
easat-9284	4	5	correspondence	correspondence	NOUN
easat-9284	4	6	:	:	PUNCT
easat-9284	4	7	pradip@tezu.ernet.in	pradip@tezu.ernet.in	PROPN
easat-9284	4	8	enriched	enrich	VERB
easat-9284	4	9	hardy	hardy	ADJ
easat-9284	4	10	–	–	PUNCT
easat-9284	4	11	rogers	rogers	PROPN
easat-9284	4	12	f	f	PROPN
easat-9284	4	13	-	-	PUNCT
easat-9284	4	14	contractions	contraction	NOUN
easat-9284	4	15	with	with	ADP
easat-9284	4	16	applications	application	NOUN
easat-9284	4	17	to	to	PART
easat-9284	4	18	nonlinear	nonlinear	ADJ
easat-9284	4	19	integral	integral	ADJ
easat-9284	4	20	equations	equation	NOUN
easat-9284	4	21	involving	involve	VERB
easat-9284	4	22	symmetric	symmetric	ADJ
easat-9284	4	23	feedback	feedback	NOUN
easat-9284	4	24	pradip	pradip	NOUN
easat-9284	4	25	debnath1	debnath1	PROPN
easat-9284	4	26	*	*	PROPN
easat-9284	4	27	1department	1department	NUM
easat-9284	4	28	of	of	ADP
easat-9284	4	29	mathematical	mathematical	ADJ
easat-9284	4	30	sciences	sciences	PROPN
easat-9284	4	31	tezpur	tezpur	PROPN
easat-9284	4	32	university	university	NOUN
easat-9284	4	33	napaam	napaam	NOUN
easat-9284	4	34	784028	784028	NUM
easat-9284	4	35	,	,	PUNCT
easat-9284	4	36	assam	assam	PROPN
easat-9284	4	37	,	,	PUNCT
easat-9284	4	38	india	india	PROPN
easat-9284	4	39	;	;	PUNCT
easat-9284	4	40	pradip@tezu.ernet.in	pradip@tezu.ernet.in	PROPN
easat-9284	4	41	(	(	PUNCT
easat-9284	4	42	p.d	p.d	PROPN
easat-9284	4	43	.	.	PROPN
easat-9284	4	44	)	)	PUNCT
easat-9284	4	45	.	.	PUNCT
easat-9284	5	1	abstract	abstract	ADV
easat-9284	5	2	:	:	PUNCT
easat-9284	5	3	this	this	DET
easat-9284	5	4	paper	paper	NOUN
easat-9284	5	5	introduces	introduce	VERB
easat-9284	5	6	a	a	DET
easat-9284	5	7	new	new	ADJ
easat-9284	5	8	contractive	contractive	ADJ
easat-9284	5	9	condition	condition	NOUN
easat-9284	5	10	via	via	ADP
easat-9284	5	11	the	the	DET
easat-9284	5	12	enriched	enriched	ADJ
easat-9284	5	13	hardy	hardy	ADJ
easat-9284	5	14	–	–	PUNCT
easat-9284	5	15	rogers	roger	NOUN
easat-9284	5	16	fcontraction	fcontraction	NOUN
easat-9284	5	17	,	,	PUNCT
easat-9284	5	18	which	which	PRON
easat-9284	5	19	generalizes	generalize	VERB
easat-9284	5	20	and	and	CCONJ
easat-9284	5	21	unifies	unify	VERB
easat-9284	5	22	several	several	ADJ
easat-9284	5	23	well	well	ADV
easat-9284	5	24	-	-	PUNCT
easat-9284	5	25	known	know	VERB
easat-9284	5	26	contraction	contraction	NOUN
easat-9284	5	27	conditions	condition	NOUN
easat-9284	5	28	in	in	ADP
easat-9284	5	29	normed	normed	ADJ
easat-9284	5	30	linear	linear	PROPN
easat-9284	5	31	spaces	space	NOUN
easat-9284	5	32	,	,	PUNCT
easat-9284	5	33	including	include	VERB
easat-9284	5	34	those	those	PRON
easat-9284	5	35	of	of	ADP
easat-9284	5	36	banach	banach	NOUN
easat-9284	5	37	,	,	PUNCT
easat-9284	5	38	kannan	kannan	PROPN
easat-9284	5	39	,	,	PUNCT
easat-9284	5	40	reich	reich	PROPN
easat-9284	5	41	,	,	PUNCT
easat-9284	5	42	and	and	CCONJ
easat-9284	5	43	wardowski	wardowski	VERB
easat-9284	5	44	.	.	PUNCT
easat-9284	6	1	by	by	ADP
easat-9284	6	2	incorporating	incorporate	VERB
easat-9284	6	3	a	a	DET
easat-9284	6	4	nonlinear	nonlinear	ADJ
easat-9284	6	5	control	control	NOUN
easat-9284	6	6	function	function	NOUN
easat-9284	6	7	f	f	PROPN
easat-9284	6	8	from	from	ADP
easat-9284	6	9	the	the	DET
easat-9284	6	10	class	class	NOUN
easat-9284	6	11	f1	f1	NOUN
easat-9284	6	12	into	into	ADP
easat-9284	6	13	the	the	DET
easat-9284	6	14	enriched	enriched	ADJ
easat-9284	6	15	hardy	hardy	ADJ
easat-9284	6	16	–	–	PUNCT
easat-9284	6	17	rogers	roger	NOUN
easat-9284	6	18	structure	structure	NOUN
easat-9284	6	19	,	,	PUNCT
easat-9284	6	20	the	the	DET
easat-9284	6	21	proposed	propose	VERB
easat-9284	6	22	condition	condition	NOUN
easat-9284	6	23	allows	allow	VERB
easat-9284	6	24	for	for	ADP
easat-9284	6	25	the	the	DET
easat-9284	6	26	analysis	analysis	NOUN
easat-9284	6	27	of	of	ADP
easat-9284	6	28	discontinuous	discontinuous	ADJ
easat-9284	6	29	,	,	PUNCT
easat-9284	6	30	nonlinear	nonlinear	ADJ
easat-9284	6	31	,	,	PUNCT
easat-9284	6	32	and	and	CCONJ
easat-9284	6	33	asymmetric	asymmetric	ADJ
easat-9284	6	34	operators	operator	NOUN
easat-9284	6	35	.	.	PUNCT
easat-9284	7	1	we	we	PRON
easat-9284	7	2	establish	establish	VERB
easat-9284	7	3	the	the	DET
easat-9284	7	4	existence	existence	NOUN
easat-9284	7	5	and	and	CCONJ
easat-9284	7	6	uniqueness	uniqueness	NOUN
easat-9284	7	7	of	of	ADP
easat-9284	7	8	fixed	fix	VERB
easat-9284	7	9	points	point	NOUN
easat-9284	7	10	for	for	ADP
easat-9284	7	11	such	such	ADJ
easat-9284	7	12	mappings	mapping	NOUN
easat-9284	7	13	and	and	CCONJ
easat-9284	7	14	prove	prove	VERB
easat-9284	7	15	the	the	DET
easat-9284	7	16	convergence	convergence	NOUN
easat-9284	7	17	of	of	ADP
easat-9284	7	18	the	the	DET
easat-9284	7	19	krasnoselskij	krasnoselskij	NOUN
easat-9284	7	20	iterative	iterative	NOUN
easat-9284	7	21	scheme	scheme	NOUN
easat-9284	7	22	.	.	PUNCT
easat-9284	8	1	in	in	ADP
easat-9284	8	2	contrast	contrast	NOUN
easat-9284	8	3	to	to	ADP
easat-9284	8	4	previous	previous	ADJ
easat-9284	8	5	formulations	formulation	NOUN
easat-9284	8	6	,	,	PUNCT
easat-9284	8	7	our	our	PRON
easat-9284	8	8	approach	approach	NOUN
easat-9284	8	9	accommodates	accommodate	VERB
easat-9284	8	10	more	more	ADJ
easat-9284	8	11	complex	complex	ADJ
easat-9284	8	12	operator	operator	NOUN
easat-9284	8	13	behavior	behavior	NOUN
easat-9284	8	14	,	,	PUNCT
easat-9284	8	15	including	include	VERB
easat-9284	8	16	mappings	mapping	NOUN
easat-9284	8	17	with	with	ADP
easat-9284	8	18	symmetric	symmetric	ADJ
easat-9284	8	19	delay	delay	NOUN
easat-9284	8	20	and	and	CCONJ
easat-9284	8	21	feedback	feedback	NOUN
easat-9284	8	22	,	,	PUNCT
easat-9284	8	23	which	which	PRON
easat-9284	8	24	are	be	AUX
easat-9284	8	25	beyond	beyond	ADP
easat-9284	8	26	the	the	DET
easat-9284	8	27	scope	scope	NOUN
easat-9284	8	28	of	of	ADP
easat-9284	8	29	classical	classical	ADJ
easat-9284	8	30	or	or	CCONJ
easat-9284	8	31	enriched	enriched	ADJ
easat-9284	8	32	contractions	contraction	NOUN
easat-9284	8	33	alone	alone	ADV
easat-9284	8	34	.	.	PUNCT
easat-9284	9	1	to	to	PART
easat-9284	9	2	demonstrate	demonstrate	VERB
easat-9284	9	3	the	the	DET
easat-9284	9	4	utility	utility	NOUN
easat-9284	9	5	of	of	ADP
easat-9284	9	6	the	the	DET
easat-9284	9	7	main	main	ADJ
easat-9284	9	8	result	result	NOUN
easat-9284	9	9	,	,	PUNCT
easat-9284	9	10	we	we	PRON
easat-9284	9	11	apply	apply	VERB
easat-9284	9	12	it	it	PRON
easat-9284	9	13	to	to	ADP
easat-9284	9	14	a	a	DET
easat-9284	9	15	new	new	ADJ
easat-9284	9	16	class	class	NOUN
easat-9284	9	17	of	of	ADP
easat-9284	9	18	nonlinear	nonlinear	ADJ
easat-9284	9	19	integral	integral	ADJ
easat-9284	9	20	equations	equation	NOUN
easat-9284	9	21	modeling	model	VERB
easat-9284	9	22	recurrent	recurrent	ADJ
easat-9284	9	23	neural	neural	ADJ
easat-9284	9	24	systems	system	NOUN
easat-9284	9	25	with	with	ADP
easat-9284	9	26	symmetric	symmetric	ADJ
easat-9284	9	27	feedback	feedback	NOUN
easat-9284	9	28	,	,	PUNCT
easat-9284	9	29	thereby	thereby	ADV
easat-9284	9	30	extending	extend	VERB
easat-9284	9	31	fixed	fix	VERB
easat-9284	9	32	point	point	NOUN
easat-9284	9	33	applicability	applicability	NOUN
easat-9284	9	34	to	to	ADP
easat-9284	9	35	time	time	NOUN
easat-9284	9	36	-	-	PUNCT
easat-9284	9	37	reflective	reflective	ADJ
easat-9284	9	38	and	and	CCONJ
easat-9284	9	39	learning	learning	NOUN
easat-9284	9	40	-	-	PUNCT
easat-9284	9	41	based	base	VERB
easat-9284	9	42	systems	system	NOUN
easat-9284	9	43	.	.	PUNCT
easat-9284	10	1	keywords	keyword	NOUN
easat-9284	10	2	:	:	PUNCT
easat-9284	10	3	f	f	X
easat-9284	10	4	-	-	PUNCT
easat-9284	10	5	contraction	contraction	NOUN
easat-9284	10	6	,	,	PUNCT
easat-9284	10	7	fixed	fix	VERB
easat-9284	10	8	point	point	NOUN
easat-9284	10	9	,	,	PUNCT
easat-9284	10	10	integral	integral	ADJ
easat-9284	10	11	equation	equation	NOUN
easat-9284	10	12	,	,	PUNCT
easat-9284	10	13	hardy	hardy	ADJ
easat-9284	10	14	-	-	PUNCT
easat-9284	10	15	rogers	roger	NOUN
easat-9284	10	16	theorem	theorem	VERB
easat-9284	10	17	,	,	PUNCT
easat-9284	10	18	metric	metric	ADJ
easat-9284	10	19	space	space	NOUN
easat-9284	10	20	,	,	PUNCT
easat-9284	10	21	symmetric	symmetric	ADJ
easat-9284	10	22	feedback	feedback	NOUN
easat-9284	10	23	.	.	PUNCT
easat-9284	11	1	1	1	X
easat-9284	11	2	.	.	X
easat-9284	11	3	introduction	introduction	NOUN
easat-9284	11	4	fixed	fix	VERB
easat-9284	11	5	point	point	NOUN
easat-9284	11	6	theory	theory	NOUN
easat-9284	11	7	forms	form	VERB
easat-9284	11	8	the	the	DET
easat-9284	11	9	cornerstone	cornerstone	NOUN
easat-9284	11	10	of	of	ADP
easat-9284	11	11	nonlinear	nonlinear	ADJ
easat-9284	11	12	analysis	analysis	NOUN
easat-9284	11	13	and	and	CCONJ
easat-9284	11	14	has	have	AUX
easat-9284	11	15	found	find	VERB
easat-9284	11	16	extensive	extensive	ADJ
easat-9284	11	17	applications	application	NOUN
easat-9284	11	18	in	in	ADP
easat-9284	11	19	differential	differential	ADJ
easat-9284	11	20	equations	equation	NOUN
easat-9284	11	21	,	,	PUNCT
easat-9284	11	22	optimization	optimization	NOUN
easat-9284	11	23	,	,	PUNCT
easat-9284	11	24	game	game	NOUN
easat-9284	11	25	theory	theory	NOUN
easat-9284	11	26	,	,	PUNCT
easat-9284	11	27	and	and	CCONJ
easat-9284	11	28	dynamic	dynamic	ADJ
easat-9284	11	29	systems	system	NOUN
easat-9284	11	30	.	.	PUNCT
easat-9284	12	1	the	the	DET
easat-9284	12	2	celebrated	celebrate	VERB
easat-9284	12	3	banach	banach	NOUN
easat-9284	12	4	contraction	contraction	NOUN
easat-9284	12	5	principle	principle	NOUN
easat-9284	12	6	[	[	X
easat-9284	12	7	1	1	X
easat-9284	12	8	]	]	PUNCT
easat-9284	12	9	is	be	AUX
easat-9284	12	10	one	one	NUM
easat-9284	12	11	of	of	ADP
easat-9284	12	12	the	the	DET
easat-9284	12	13	earliest	early	ADJ
easat-9284	12	14	and	and	CCONJ
easat-9284	12	15	most	most	ADV
easat-9284	12	16	influential	influential	ADJ
easat-9284	12	17	results	result	NOUN
easat-9284	12	18	in	in	ADP
easat-9284	12	19	this	this	DET
easat-9284	12	20	field	field	NOUN
easat-9284	12	21	,	,	PUNCT
easat-9284	12	22	asserting	assert	VERB
easat-9284	12	23	the	the	DET
easat-9284	12	24	existence	existence	NOUN
easat-9284	12	25	and	and	CCONJ
easat-9284	12	26	uniqueness	uniqueness	NOUN
easat-9284	12	27	of	of	ADP
easat-9284	12	28	fixed	fix	VERB
easat-9284	12	29	points	point	NOUN
easat-9284	12	30	for	for	ADP
easat-9284	12	31	self	self	NOUN
easat-9284	12	32	-	-	PUNCT
easat-9284	12	33	maps	map	NOUN
easat-9284	12	34	in	in	ADP
easat-9284	12	35	complete	complete	ADJ
easat-9284	12	36	metric	metric	ADJ
easat-9284	12	37	spaces	space	NOUN
easat-9284	12	38	under	under	ADP
easat-9284	12	39	strict	strict	ADJ
easat-9284	12	40	contractive	contractive	ADJ
easat-9284	12	41	conditions	condition	NOUN
easat-9284	12	42	.	.	PUNCT
easat-9284	13	1	over	over	ADP
easat-9284	13	2	the	the	DET
easat-9284	13	3	decades	decade	NOUN
easat-9284	13	4	,	,	PUNCT
easat-9284	13	5	numerous	numerous	ADJ
easat-9284	13	6	generalizations	generalization	NOUN
easat-9284	13	7	have	have	AUX
easat-9284	13	8	emerged	emerge	VERB
easat-9284	13	9	,	,	PUNCT
easat-9284	13	10	relaxing	relax	VERB
easat-9284	13	11	contractive	contractive	ADJ
easat-9284	13	12	assumptions	assumption	NOUN
easat-9284	13	13	to	to	PART
easat-9284	13	14	capture	capture	VERB
easat-9284	13	15	a	a	DET
easat-9284	13	16	broader	broad	ADJ
easat-9284	13	17	class	class	NOUN
easat-9284	13	18	of	of	ADP
easat-9284	13	19	operators	operator	NOUN
easat-9284	13	20	.	.	PUNCT
easat-9284	14	1	notable	notable	ADJ
easat-9284	14	2	among	among	ADP
easat-9284	14	3	these	these	PRON
easat-9284	14	4	are	be	AUX
easat-9284	14	5	the	the	DET
easat-9284	14	6	kannan	kannan	PROPN
easat-9284	14	7	[	[	X
easat-9284	14	8	2	2	NUM
easat-9284	14	9	]	]	PUNCT
easat-9284	14	10	and	and	CCONJ
easat-9284	14	11	reich	reich	X
easat-9284	15	1	[	[	X
easat-9284	15	2	3	3	X
easat-9284	15	3	]	]	PUNCT
easat-9284	15	4	the	the	DET
easat-9284	15	5	hardy	hardy	ADJ
easat-9284	15	6	and	and	CCONJ
easat-9284	15	7	rogers	roger	NOUN
easat-9284	16	1	[	[	X
easat-9284	16	2	4	4	X
easat-9284	16	3	]	]	X
easat-9284	16	4	each	each	PRON
easat-9284	16	5	incorporating	incorporate	VERB
easat-9284	16	6	various	various	ADJ
easat-9284	16	7	distance	distance	NOUN
easat-9284	16	8	terms	term	NOUN
easat-9284	16	9	to	to	PART
easat-9284	16	10	account	account	VERB
easat-9284	16	11	for	for	ADP
easat-9284	16	12	asymmetry	asymmetry	NOUN
easat-9284	16	13	,	,	PUNCT
easat-9284	16	14	nonlinearity	nonlinearity	NOUN
easat-9284	16	15	,	,	PUNCT
easat-9284	16	16	and	and	CCONJ
easat-9284	16	17	discontinuity	discontinuity	NOUN
easat-9284	16	18	.	.	PUNCT
easat-9284	17	1	to	to	PART
easat-9284	17	2	accommodate	accommodate	VERB
easat-9284	17	3	additional	additional	ADJ
easat-9284	17	4	flexibility	flexibility	NOUN
easat-9284	17	5	,	,	PUNCT
easat-9284	17	6	berinde	berinde	VERB
easat-9284	17	7	[	[	X
easat-9284	17	8	5	5	NUM
easat-9284	17	9	]	]	PUNCT
easat-9284	17	10	introduced	introduce	VERB
easat-9284	17	11	enriched	enrich	VERB
easat-9284	17	12	contractions	contraction	NOUN
easat-9284	17	13	by	by	ADP
easat-9284	17	14	blending	blend	VERB
easat-9284	17	15	linear	linear	ADJ
easat-9284	17	16	perturbations	perturbation	NOUN
easat-9284	17	17	into	into	ADP
easat-9284	17	18	the	the	DET
easat-9284	17	19	metric	metric	ADJ
easat-9284	17	20	structure	structure	NOUN
easat-9284	17	21	.	.	PUNCT
easat-9284	18	1	these	these	DET
easat-9284	18	2	enrichments	enrichment	NOUN
easat-9284	18	3	proved	prove	VERB
easat-9284	18	4	useful	useful	ADJ
easat-9284	18	5	in	in	ADP
easat-9284	18	6	studying	study	VERB
easat-9284	18	7	iterative	iterative	NOUN
easat-9284	18	8	methods	method	NOUN
easat-9284	18	9	in	in	ADP
easat-9284	18	10	normed	normed	ADJ
easat-9284	18	11	spaces	space	NOUN
easat-9284	18	12	.	.	PUNCT
easat-9284	19	1	another	another	DET
easat-9284	19	2	milestone	milestone	NOUN
easat-9284	19	3	in	in	ADP
easat-9284	19	4	fixed	fix	VERB
easat-9284	19	5	point	point	NOUN
easat-9284	19	6	theory	theory	NOUN
easat-9284	19	7	was	be	AUX
easat-9284	19	8	the	the	DET
easat-9284	19	9	introduction	introduction	NOUN
easat-9284	19	10	of	of	ADP
easat-9284	19	11	f	f	PROPN
easat-9284	19	12	-contractions	-contraction	NOUN
easat-9284	19	13	by	by	ADP
easat-9284	19	14	wardowski	wardowski	NOUN
easat-9284	19	15	[	[	X
easat-9284	19	16	6	6	NUM
easat-9284	19	17	]	]	PUNCT
easat-9284	19	18	where	where	SCONJ
easat-9284	19	19	the	the	DET
easat-9284	19	20	linear	linear	ADJ
easat-9284	19	21	contractive	contractive	ADJ
easat-9284	19	22	inequality	inequality	NOUN
easat-9284	19	23	was	be	AUX
easat-9284	19	24	replaced	replace	VERB
easat-9284	19	25	by	by	ADP
easat-9284	19	26	a	a	DET
easat-9284	19	27	control	control	NOUN
easat-9284	19	28	function	function	NOUN
easat-9284	19	29	f	f	PROPN
easat-9284	19	30	from	from	ADP
easat-9284	19	31	a	a	DET
easat-9284	19	32	suitable	suitable	ADJ
easat-9284	19	33	function	function	NOUN
easat-9284	19	34	class	class	NOUN
easat-9284	19	35	f1	f1	NOUN
easat-9284	19	36	.	.	PUNCT
easat-9284	20	1	this	this	PRON
easat-9284	20	2	enabled	enable	VERB
easat-9284	20	3	the	the	DET
easat-9284	20	4	treatment	treatment	NOUN
easat-9284	20	5	of	of	ADP
easat-9284	20	6	discontinuous	discontinuous	ADJ
easat-9284	20	7	and	and	CCONJ
easat-9284	20	8	nonlinear	nonlinear	ADJ
easat-9284	20	9	mappings	mapping	NOUN
easat-9284	20	10	,	,	PUNCT
easat-9284	20	11	further	far	ADV
easat-9284	20	12	broadening	broaden	VERB
easat-9284	20	13	the	the	DET
easat-9284	20	14	scope	scope	NOUN
easat-9284	20	15	of	of	ADP
easat-9284	20	16	fixed	fix	VERB
easat-9284	20	17	point	point	NOUN
easat-9284	20	18	theorems	theorem	NOUN
easat-9284	20	19	.	.	PUNCT
easat-9284	21	1	several	several	ADJ
easat-9284	21	2	authors	author	NOUN
easat-9284	21	3	extended	extend	VERB
easat-9284	21	4	these	these	DET
easat-9284	21	5	ideas	idea	NOUN
easat-9284	21	6	by	by	ADP
easat-9284	21	7	combining	combine	VERB
easat-9284	21	8	enriched	enrich	VERB
easat-9284	21	9	conditions	condition	NOUN
easat-9284	21	10	with	with	ADP
easat-9284	21	11	f	f	NOUN
easat-9284	21	12	-type	-type	NOUN
easat-9284	21	13	frameworks	framework	NOUN
easat-9284	21	14	to	to	PART
easat-9284	21	15	produce	produce	VERB
easat-9284	21	16	more	more	ADV
easat-9284	21	17	generalized	generalized	ADJ
easat-9284	21	18	fixed	fix	VERB
easat-9284	21	19	point	point	NOUN
easat-9284	21	20	results	result	NOUN
easat-9284	21	21	applicable	applicable	ADJ
easat-9284	21	22	to	to	PART
easat-9284	21	23	differential	differential	VERB
easat-9284	21	24	and	and	CCONJ
easat-9284	21	25	integral	integral	ADJ
easat-9284	21	26	equations	equation	NOUN
easat-9284	21	27	.	.	PUNCT
easat-9284	22	1	more	more	ADV
easat-9284	22	2	recently	recently	ADV
easat-9284	22	3	,	,	PUNCT
easat-9284	22	4	gautam	gautam	PROPN
easat-9284	22	5	,	,	PUNCT
easat-9284	22	6	et	et	PROPN
easat-9284	22	7	al	al	PROPN
easat-9284	22	8	.	.	PUNCT
easat-9284	23	1	[	[	X
easat-9284	23	2	7	7	NUM
easat-9284	23	3	]	]	PUNCT
easat-9284	23	4	developed	develop	VERB
easat-9284	23	5	an	an	DET
easat-9284	23	6	enriched	enriched	ADJ
easat-9284	23	7	hardy	hardy	ADJ
easat-9284	23	8	–	–	PUNCT
easat-9284	23	9	rogers	roger	NOUN
easat-9284	23	10	contraction	contraction	NOUN
easat-9284	23	11	in	in	ADP
easat-9284	23	12	banach	banach	NOUN
easat-9284	23	13	spaces	space	NOUN
easat-9284	23	14	and	and	CCONJ
easat-9284	23	15	analyzed	analyze	VERB
easat-9284	23	16	its	its	PRON
easat-9284	23	17	convergence	convergence	NOUN
easat-9284	23	18	under	under	ADP
easat-9284	23	19	krasnoselskij	krasnoselskij	PROPN
easat-9284	23	20	iteration	iteration	NOUN
easat-9284	23	21	,	,	PUNCT
easat-9284	23	22	showing	show	VERB
easat-9284	23	23	its	its	PRON
easat-9284	23	24	relevance	relevance	NOUN
easat-9284	23	25	in	in	ADP
easat-9284	23	26	solving	solve	VERB
easat-9284	23	27	volterra	volterra	NOUN
easat-9284	23	28	integral	integral	ADJ
easat-9284	23	29	equations	equation	NOUN
easat-9284	23	30	.	.	PUNCT
easat-9284	24	1	however	however	ADV
easat-9284	24	2	,	,	PUNCT
easat-9284	24	3	this	this	DET
easat-9284	24	4	framework	framework	NOUN
easat-9284	24	5	still	still	ADV
easat-9284	24	6	left	leave	VERB
easat-9284	24	7	open	open	ADJ
easat-9284	24	8	the	the	DET
easat-9284	24	9	need	need	NOUN
easat-9284	24	10	for	for	ADP
easat-9284	24	11	a	a	DET
easat-9284	24	12	more	more	ADV
easat-9284	24	13	generalized	generalized	ADJ
easat-9284	24	14	structure	structure	NOUN
easat-9284	24	15	capable	capable	ADJ
easat-9284	24	16	of	of	ADP
easat-9284	24	17	handling	handle	VERB
easat-9284	24	18	operators	operator	NOUN
easat-9284	24	19	with	with	ADP
easat-9284	24	20	symmetric	symmetric	ADJ
easat-9284	24	21	delays	delay	NOUN
easat-9284	24	22	or	or	CCONJ
easat-9284	24	23	feedback	feedback	NOUN
easat-9284	24	24	mechanisms	mechanism	NOUN
easat-9284	24	25	,	,	PUNCT
easat-9284	24	26	particularly	particularly	ADV
easat-9284	24	27	those	those	PRON
easat-9284	24	28	arising	arise	VERB
easat-9284	24	29	in	in	ADP
easat-9284	24	30	learning	learn	VERB
easat-9284	24	31	theory	theory	NOUN
easat-9284	24	32	and	and	CCONJ
easat-9284	24	33	neural	neural	ADJ
easat-9284	24	34	network	network	NOUN
easat-9284	24	35	models	model	NOUN
easat-9284	24	36	.	.	PUNCT
easat-9284	25	1	motivated	motivate	VERB
easat-9284	25	2	by	by	ADP
easat-9284	25	3	this	this	PRON
easat-9284	25	4	,	,	PUNCT
easat-9284	25	5	the	the	DET
easat-9284	25	6	present	present	ADJ
easat-9284	25	7	paper	paper	NOUN
easat-9284	25	8	introduces	introduce	VERB
easat-9284	25	9	a	a	DET
easat-9284	25	10	novel	novel	ADJ
easat-9284	25	11	fixed	fix	VERB
easat-9284	25	12	point	point	NOUN
easat-9284	25	13	framework	framework	NOUN
easat-9284	25	14	:	:	PUNCT
easat-9284	25	15	the	the	DET
easat-9284	25	16	enriched	enriched	ADJ
easat-9284	25	17	hardy	hardy	ADJ
easat-9284	25	18	–	–	PUNCT
easat-9284	25	19	292	292	NUM
easat-9284	25	20	edelweiss	edelweiss	PROPN
easat-9284	25	21	applied	apply	VERB
easat-9284	25	22	science	science	NOUN
easat-9284	25	23	and	and	CCONJ
easat-9284	25	24	technology	technology	NOUN
easat-9284	25	25	issn	issn	PROPN
easat-9284	25	26	:	:	PUNCT
easat-9284	25	27	2576	2576	NUM
easat-9284	25	28	-	-	SYM
easat-9284	25	29	8484	8484	NUM
easat-9284	25	30	vol	vol	NOUN
easat-9284	25	31	.	.	PROPN
easat-9284	26	1	9	9	NUM
easat-9284	26	2	,	,	PUNCT
easat-9284	26	3	no	no	INTJ
easat-9284	26	4	.	.	NOUN
easat-9284	26	5	8	8	NUM
easat-9284	26	6	:	:	PUNCT
easat-9284	26	7	291	291	NUM
easat-9284	26	8	-	-	SYM
easat-9284	26	9	299	299	NUM
easat-9284	26	10	,	,	PUNCT
easat-9284	26	11	2025	2025	NUM
easat-9284	26	12	doi	doi	NOUN
easat-9284	26	13	:	:	PUNCT
easat-9284	26	14	10.55214/2576	10.55214/2576	NUM
easat-9284	26	15	-	-	PUNCT
easat-9284	26	16	8484.v9i8.9284	8484.v9i8.9284	NOUN
easat-9284	26	17	©	©	PROPN
easat-9284	26	18	2025	2025	NUM
easat-9284	26	19	by	by	ADP
easat-9284	26	20	the	the	DET
easat-9284	26	21	author	author	NOUN
easat-9284	26	22	;	;	PUNCT
easat-9284	26	23	licensee	licensee	PROPN
easat-9284	26	24	learning	learning	PROPN
easat-9284	26	25	gate	gate	PROPN
easat-9284	26	26	rogers	rogers	PROPN
easat-9284	26	27	f	f	PROPN
easat-9284	26	28	-	-	PUNCT
easat-9284	26	29	contraction	contraction	NOUN
easat-9284	26	30	,	,	PUNCT
easat-9284	26	31	which	which	PRON
easat-9284	26	32	incorporates	incorporate	VERB
easat-9284	26	33	nonlinear	nonlinear	ADJ
easat-9284	26	34	functional	functional	ADJ
easat-9284	26	35	control	control	NOUN
easat-9284	26	36	f	f	PROPN
easat-9284	26	37	∈	∈	PROPN
easat-9284	26	38	f1	f1	NOUN
easat-9284	26	39	into	into	ADP
easat-9284	26	40	the	the	DET
easat-9284	26	41	enriched	enriched	ADJ
easat-9284	26	42	hardy	hardy	ADJ
easat-9284	26	43	–	–	PUNCT
easat-9284	26	44	rogers	roger	NOUN
easat-9284	26	45	inequality	inequality	NOUN
easat-9284	26	46	.	.	PUNCT
easat-9284	27	1	the	the	DET
easat-9284	27	2	proposed	propose	VERB
easat-9284	27	3	condition	condition	NOUN
easat-9284	27	4	not	not	PART
easat-9284	27	5	only	only	ADV
easat-9284	27	6	unifies	unify	VERB
easat-9284	27	7	and	and	CCONJ
easat-9284	27	8	generalizes	generalize	VERB
easat-9284	27	9	several	several	ADJ
easat-9284	27	10	well	well	ADV
easat-9284	27	11	known	know	VERB
easat-9284	27	12	contraction	contraction	NOUN
easat-9284	27	13	types	type	NOUN
easat-9284	27	14	,	,	PUNCT
easat-9284	27	15	including	include	VERB
easat-9284	27	16	banach	banach	NOUN
easat-9284	27	17	,	,	PUNCT
easat-9284	27	18	kannan	kannan	PROPN
easat-9284	27	19	,	,	PUNCT
easat-9284	27	20	reich	reich	PROPN
easat-9284	27	21	,	,	PUNCT
easat-9284	27	22	and	and	CCONJ
easat-9284	27	23	wardowski	wardowski	PROPN
easat-9284	27	24	mappings	mapping	NOUN
easat-9284	27	25	,	,	PUNCT
easat-9284	27	26	but	but	CCONJ
easat-9284	27	27	also	also	ADV
easat-9284	27	28	supports	support	VERB
easat-9284	27	29	the	the	DET
easat-9284	27	30	analysis	analysis	NOUN
easat-9284	27	31	of	of	ADP
easat-9284	27	32	non	non	ADJ
easat-9284	27	33	-	-	ADJ
easat-9284	27	34	continuous	continuous	ADJ
easat-9284	27	35	operators	operator	NOUN
easat-9284	27	36	and	and	CCONJ
easat-9284	27	37	those	those	PRON
easat-9284	27	38	arising	arise	VERB
easat-9284	27	39	in	in	ADP
easat-9284	27	40	systems	system	NOUN
easat-9284	27	41	with	with	ADP
easat-9284	27	42	time	time	NOUN
easat-9284	27	43	-	-	PUNCT
easat-9284	27	44	reflected	reflect	VERB
easat-9284	27	45	dependencies	dependency	NOUN
easat-9284	27	46	.	.	PUNCT
easat-9284	28	1	we	we	PRON
easat-9284	28	2	establish	establish	VERB
easat-9284	28	3	the	the	DET
easat-9284	28	4	existence	existence	NOUN
easat-9284	28	5	and	and	CCONJ
easat-9284	28	6	uniqueness	uniqueness	NOUN
easat-9284	28	7	of	of	ADP
easat-9284	28	8	fixed	fix	VERB
easat-9284	28	9	points	point	NOUN
easat-9284	28	10	under	under	ADP
easat-9284	28	11	this	this	DET
easat-9284	28	12	new	new	ADJ
easat-9284	28	13	contractive	contractive	ADJ
easat-9284	28	14	structure	structure	NOUN
easat-9284	28	15	and	and	CCONJ
easat-9284	28	16	prove	prove	VERB
easat-9284	28	17	convergence	convergence	NOUN
easat-9284	28	18	of	of	ADP
easat-9284	28	19	the	the	DET
easat-9284	28	20	krasnoselskij	krasnoselskij	NOUN
easat-9284	28	21	iterative	iterative	NOUN
easat-9284	28	22	sequence	sequence	NOUN
easat-9284	28	23	.	.	PUNCT
easat-9284	29	1	additionally	additionally	ADV
easat-9284	29	2	,	,	PUNCT
easat-9284	29	3	we	we	PRON
easat-9284	29	4	demonstrate	demonstrate	VERB
easat-9284	29	5	the	the	DET
easat-9284	29	6	practical	practical	ADJ
easat-9284	29	7	significance	significance	NOUN
easat-9284	29	8	of	of	ADP
easat-9284	29	9	our	our	PRON
easat-9284	29	10	result	result	NOUN
easat-9284	29	11	by	by	ADP
easat-9284	29	12	applying	apply	VERB
easat-9284	29	13	it	it	PRON
easat-9284	29	14	to	to	ADP
easat-9284	29	15	a	a	DET
easat-9284	29	16	new	new	ADJ
easat-9284	29	17	class	class	NOUN
easat-9284	29	18	of	of	ADP
easat-9284	29	19	nonlinear	nonlinear	ADJ
easat-9284	29	20	integral	integral	ADJ
easat-9284	29	21	equations	equation	NOUN
easat-9284	29	22	with	with	ADP
easat-9284	29	23	symmetric	symmetric	ADJ
easat-9284	29	24	feedback	feedback	NOUN
easat-9284	29	25	,	,	PUNCT
easat-9284	29	26	which	which	PRON
easat-9284	29	27	go	go	VERB
easat-9284	29	28	beyond	beyond	ADP
easat-9284	29	29	the	the	DET
easat-9284	29	30	classical	classical	ADJ
easat-9284	29	31	volterra	volterra	NOUN
easat-9284	29	32	type	type	NOUN
easat-9284	29	33	and	and	CCONJ
easat-9284	29	34	model	model	NOUN
easat-9284	29	35	recurrent	recurrent	ADJ
easat-9284	29	36	neural	neural	ADJ
easat-9284	29	37	learning	learning	NOUN
easat-9284	29	38	systems	system	NOUN
easat-9284	29	39	with	with	ADP
easat-9284	29	40	temporal	temporal	ADJ
easat-9284	29	41	duality	duality	NOUN
easat-9284	29	42	.	.	PUNCT
easat-9284	30	1	2	2	X
easat-9284	30	2	.	.	X
easat-9284	30	3	preliminaries	preliminary	NOUN
easat-9284	30	4	in	in	ADP
easat-9284	30	5	this	this	DET
easat-9284	30	6	section	section	NOUN
easat-9284	30	7	,	,	PUNCT
easat-9284	30	8	we	we	PRON
easat-9284	30	9	introduce	introduce	VERB
easat-9284	30	10	the	the	DET
easat-9284	30	11	essential	essential	ADJ
easat-9284	30	12	concepts	concept	NOUN
easat-9284	30	13	that	that	PRON
easat-9284	30	14	serve	serve	VERB
easat-9284	30	15	as	as	ADP
easat-9284	30	16	the	the	DET
easat-9284	30	17	foundation	foundation	NOUN
easat-9284	30	18	for	for	ADP
easat-9284	30	19	our	our	PRON
easat-9284	30	20	main	main	ADJ
easat-9284	30	21	results	result	NOUN
easat-9284	30	22	.	.	PUNCT
easat-9284	31	1	these	these	PRON
easat-9284	31	2	include	include	VERB
easat-9284	31	3	classical	classical	ADJ
easat-9284	31	4	fixed	fix	VERB
easat-9284	31	5	point	point	NOUN
easat-9284	31	6	theorems	theorem	NOUN
easat-9284	31	7	,	,	PUNCT
easat-9284	31	8	enriched	enrich	VERB
easat-9284	31	9	contractive	contractive	ADJ
easat-9284	31	10	conditions	condition	NOUN
easat-9284	31	11	,	,	PUNCT
easat-9284	31	12	f	f	PROPN
easat-9284	31	13	-contractions	-contraction	NOUN
easat-9284	31	14	,	,	PUNCT
easat-9284	31	15	and	and	CCONJ
easat-9284	31	16	iterative	iterative	NOUN
easat-9284	31	17	processes	process	NOUN
easat-9284	31	18	.	.	PUNCT
easat-9284	32	1	our	our	PRON
easat-9284	32	2	goal	goal	NOUN
easat-9284	32	3	is	be	AUX
easat-9284	32	4	to	to	PART
easat-9284	32	5	build	build	VERB
easat-9284	32	6	a	a	DET
easat-9284	32	7	clear	clear	ADJ
easat-9284	32	8	framework	framework	NOUN
easat-9284	32	9	that	that	PRON
easat-9284	32	10	allows	allow	VERB
easat-9284	32	11	the	the	DET
easat-9284	32	12	introduction	introduction	NOUN
easat-9284	32	13	and	and	CCONJ
easat-9284	32	14	analysis	analysis	NOUN
easat-9284	32	15	of	of	ADP
easat-9284	32	16	enriched	enriched	ADJ
easat-9284	32	17	hardy	hardy	ADJ
easat-9284	32	18	–	–	PUNCT
easat-9284	32	19	rogers	roger	NOUN
easat-9284	32	20	type	type	NOUN
easat-9284	32	21	contractions	contraction	NOUN
easat-9284	32	22	.	.	PUNCT
easat-9284	33	1	2.1	2.1	NUM
easat-9284	33	2	.	.	PUNCT
easat-9284	33	3	classical	classical	ADJ
easat-9284	33	4	fixed	fix	VERB
easat-9284	33	5	point	point	NOUN
easat-9284	33	6	contractions	contraction	NOUN
easat-9284	33	7	the	the	DET
easat-9284	33	8	b	b	NOUN
easat-9284	33	9	a	a	NOUN
easat-9284	33	10	n	n	NOUN
easat-9284	33	11	a	a	DET
easat-9284	33	12	c	c	NOUN
easat-9284	33	13	h	h	NOUN
easat-9284	33	14	[	[	PUNCT
easat-9284	33	15	1	1	X
easat-9284	33	16	]	]	PUNCT
easat-9284	33	17	forms	form	VERB
easat-9284	33	18	the	the	DET
easat-9284	33	19	cornerstone	cornerstone	NOUN
easat-9284	33	20	of	of	ADP
easat-9284	33	21	fixed	fix	VERB
easat-9284	33	22	point	point	NOUN
easat-9284	33	23	theory	theory	NOUN
easat-9284	33	24	in	in	ADP
easat-9284	33	25	metric	metric	ADJ
easat-9284	33	26	spaces	space	NOUN
easat-9284	33	27	.	.	PUNCT
easat-9284	34	1	many	many	ADJ
easat-9284	34	2	generalizations	generalization	NOUN
easat-9284	34	3	have	have	AUX
easat-9284	34	4	been	be	AUX
easat-9284	34	5	proposed	propose	VERB
easat-9284	34	6	to	to	PART
easat-9284	34	7	relax	relax	VERB
easat-9284	34	8	the	the	DET
easat-9284	34	9	conditions	condition	NOUN
easat-9284	34	10	of	of	ADP
easat-9284	34	11	banach	banach	NOUN
easat-9284	34	12	’s	’s	PART
easat-9284	34	13	theorem	theorem	NOUN
easat-9284	34	14	and	and	CCONJ
easat-9284	34	15	extend	extend	VERB
easat-9284	34	16	its	its	PRON
easat-9284	34	17	applicability	applicability	NOUN
easat-9284	34	18	to	to	ADP
easat-9284	34	19	nonlinear	nonlinear	ADJ
easat-9284	34	20	and	and	CCONJ
easat-9284	34	21	discontinuous	discontinuous	ADJ
easat-9284	34	22	settings	setting	NOUN
easat-9284	34	23	.	.	PUNCT
easat-9284	35	1	b	b	X
easat-9284	35	2	a	a	DET
easat-9284	35	3	n	n	NOUN
easat-9284	35	4	a	a	DET
easat-9284	35	5	c	c	NOUN
easat-9284	35	6	h	h	NOUN
easat-9284	35	7	[	[	PUNCT
easat-9284	35	8	1	1	NUM
easat-9284	35	9	]	]	PUNCT
easat-9284	35	10	:	:	PUNCT
easat-9284	35	11	a	a	DET
easat-9284	35	12	mapping	mapping	NOUN
easat-9284	35	13	t	t	NOUN
easat-9284	35	14	:	:	PUNCT
easat-9284	35	15	e	e	X
easat-9284	35	16	→	→	SYM
easat-9284	35	17	e	e	X
easat-9284	35	18	on	on	ADP
easat-9284	35	19	a	a	DET
easat-9284	35	20	complete	complete	ADJ
easat-9284	35	21	metric	metric	ADJ
easat-9284	35	22	space	space	NOUN
easat-9284	35	23	(	(	PUNCT
easat-9284	35	24	e	e	NOUN
easat-9284	35	25	,	,	PUNCT
easat-9284	35	26	d	d	X
easat-9284	35	27	)	)	PUNCT
easat-9284	35	28	is	be	AUX
easat-9284	35	29	a	a	DET
easat-9284	35	30	contraction	contraction	NOUN
easat-9284	35	31	if	if	SCONJ
easat-9284	35	32	there	there	PRON
easat-9284	35	33	exists	exist	VERB
easat-9284	35	34	a	a	DET
easat-9284	35	35	∈	∈	NOUN
easat-9284	36	1	[	[	X
easat-9284	36	2	0	0	NUM
easat-9284	36	3	,	,	PUNCT
easat-9284	36	4	1	1	NUM
easat-9284	36	5	)	)	PUNCT
easat-9284	36	6	such	such	ADJ
easat-9284	36	7	that	that	SCONJ
easat-9284	36	8	:	:	PUNCT
easat-9284	36	9	d	d	X
easat-9284	36	10	(	(	PUNCT
easat-9284	36	11	t	t	PROPN
easat-9284	36	12	p	p	PROPN
easat-9284	36	13	,	,	PUNCT
easat-9284	36	14	t	t	PROPN
easat-9284	36	15	q	q	NOUN
easat-9284	36	16	)	)	PUNCT
easat-9284	36	17	≤	≤	NOUN
easat-9284	36	18	a	a	DET
easat-9284	36	19	d(p	d(p	PROPN
easat-9284	36	20	,	,	PUNCT
easat-9284	36	21	q	q	NOUN
easat-9284	36	22	)	)	PUNCT
easat-9284	36	23	,	,	PUNCT
easat-9284	36	24	∀p	∀p	X
easat-9284	36	25	,	,	PUNCT
easat-9284	36	26	q	q	NOUN
easat-9284	36	27	∈	∈	PROPN
easat-9284	36	28	e	e	NOUN
easat-9284	36	29	.	.	PUNCT
easat-9284	37	1	kannan	kannan	PROPN
easat-9284	38	1	[	[	X
easat-9284	38	2	2	2	NUM
easat-9284	38	3	]	]	PUNCT
easat-9284	38	4	:	:	PUNCT
easat-9284	38	5	t	t	PROPN
easat-9284	38	6	is	be	AUX
easat-9284	38	7	said	say	VERB
easat-9284	38	8	to	to	PART
easat-9284	38	9	satisfy	satisfy	VERB
easat-9284	38	10	the	the	DET
easat-9284	38	11	kannan	kannan	PROPN
easat-9284	38	12	condition	condition	NOUN
easat-9284	38	13	if	if	SCONJ
easat-9284	38	14	there	there	PRON
easat-9284	38	15	exists	exist	VERB
easat-9284	38	16	b	b	PROPN
easat-9284	38	17	∈	∈	PROPN
easat-9284	38	18	[	[	X
easat-9284	38	19	0	0	NUM
easat-9284	38	20	,	,	PUNCT
easat-9284	38	21	1/2	1/2	NUM
easat-9284	38	22	)	)	PUNCT
easat-9284	38	23	such	such	ADJ
easat-9284	38	24	that	that	SCONJ
easat-9284	38	25	:	:	PUNCT
easat-9284	38	26	d(t	d(t	PROPN
easat-9284	38	27	p	p	PROPN
easat-9284	38	28	,	,	PUNCT
easat-9284	38	29	t	t	PROPN
easat-9284	38	30	q	q	NOUN
easat-9284	38	31	)	)	PUNCT
easat-9284	38	32	≤	≤	NUM
easat-9284	38	33	b	b	X
easat-9284	38	34	(	(	PUNCT
easat-9284	38	35	d(p	d(p	PROPN
easat-9284	38	36	,	,	PUNCT
easat-9284	38	37	t	t	PROPN
easat-9284	38	38	p	p	X
easat-9284	38	39	)	)	PUNCT
easat-9284	38	40	+	+	CCONJ
easat-9284	38	41	d(q	d(q	PROPN
easat-9284	38	42	,	,	PUNCT
easat-9284	38	43	t	t	PROPN
easat-9284	38	44	q	q	NOUN
easat-9284	38	45	)	)	PUNCT
easat-9284	38	46	)	)	PUNCT
easat-9284	38	47	,	,	PUNCT
easat-9284	38	48	∀p	∀p	X
easat-9284	38	49	,	,	PUNCT
easat-9284	38	50	q	q	NOUN
easat-9284	38	51	∈	∈	PROPN
easat-9284	38	52	e	e	X
easat-9284	38	53	.	.	PUNCT
easat-9284	39	1	ćirić	ćirić	NOUN
easat-9284	39	2	[	[	X
easat-9284	39	3	8	8	NUM
easat-9284	39	4	]	]	PUNCT
easat-9284	39	5	and	and	CCONJ
easat-9284	39	6	reich	reich	X
easat-9284	40	1	[	[	X
easat-9284	40	2	3	3	NUM
easat-9284	40	3	]	]	X
easat-9284	40	4	:	:	PUNCT
easat-9284	40	5	a	a	DET
easat-9284	40	6	more	more	ADV
easat-9284	40	7	flexible	flexible	ADJ
easat-9284	40	8	contractive	contractive	ADJ
easat-9284	40	9	structure	structure	NOUN
easat-9284	40	10	that	that	PRON
easat-9284	40	11	combines	combine	VERB
easat-9284	40	12	multiple	multiple	ADJ
easat-9284	40	13	distances	distance	NOUN
easat-9284	40	14	:	:	PUNCT
easat-9284	40	15	d(t	d(t	PROPN
easat-9284	40	16	p	p	PROPN
easat-9284	40	17	,	,	PUNCT
easat-9284	40	18	t	t	PROPN
easat-9284	40	19	q	q	NOUN
easat-9284	40	20	)	)	PUNCT
easat-9284	40	21	≤	≤	NOUN
easat-9284	40	22	a	a	DET
easat-9284	40	23	d(p	d(p	PROPN
easat-9284	40	24	,	,	PUNCT
easat-9284	40	25	q	q	NOUN
easat-9284	40	26	)	)	PUNCT
easat-9284	40	27	+	+	NUM
easat-9284	40	28	b	b	NOUN
easat-9284	40	29	d(p	d(p	PROPN
easat-9284	40	30	,	,	PUNCT
easat-9284	40	31	t	t	PROPN
easat-9284	40	32	p	p	X
easat-9284	40	33	)	)	PUNCT
easat-9284	40	34	+	+	NUM
easat-9284	40	35	c	c	NOUN
easat-9284	40	36	d(q	d(q	PROPN
easat-9284	40	37	,	,	PUNCT
easat-9284	40	38	t	t	PROPN
easat-9284	40	39	q	q	PROPN
easat-9284	40	40	)	)	PUNCT
easat-9284	40	41	,	,	PUNCT
easat-9284	41	1	where	where	SCONJ
easat-9284	41	2	a	a	DET
easat-9284	41	3	,	,	PUNCT
easat-9284	41	4	b	b	NOUN
easat-9284	41	5	,	,	PUNCT
easat-9284	41	6	c	c	X
easat-9284	41	7	≥	≥	PROPN
easat-9284	41	8	0	0	NUM
easat-9284	41	9	,	,	PUNCT
easat-9284	41	10	a	a	DET
easat-9284	41	11	+	+	X
easat-9284	41	12	b	b	NOUN
easat-9284	41	13	+	+	CCONJ
easat-9284	41	14	c	c	NOUN
easat-9284	41	15	<	<	X
easat-9284	41	16	1	1	NUM
easat-9284	41	17	.	.	PUNCT
easat-9284	41	18	these	these	DET
easat-9284	41	19	contractions	contraction	NOUN
easat-9284	41	20	have	have	AUX
easat-9284	41	21	been	be	AUX
easat-9284	41	22	widely	widely	ADV
easat-9284	41	23	studied	study	VERB
easat-9284	41	24	and	and	CCONJ
easat-9284	41	25	generalized	generalize	VERB
easat-9284	41	26	in	in	ADP
easat-9284	41	27	numerous	numerous	ADJ
easat-9284	41	28	directions	direction	NOUN
easat-9284	41	29	to	to	PART
easat-9284	41	30	handle	handle	VERB
easat-9284	41	31	nonlinear	nonlinear	ADJ
easat-9284	41	32	mappings	mapping	NOUN
easat-9284	41	33	,	,	PUNCT
easat-9284	41	34	discontinuities	discontinuity	NOUN
easat-9284	41	35	,	,	PUNCT
easat-9284	41	36	and	and	CCONJ
easat-9284	41	37	applications	application	NOUN
easat-9284	41	38	in	in	ADP
easat-9284	41	39	integral	integral	ADJ
easat-9284	41	40	equations	equation	NOUN
easat-9284	41	41	and	and	CCONJ
easat-9284	41	42	optimization	optimization	NOUN
easat-9284	41	43	.	.	PUNCT
easat-9284	42	1	2.2	2.2	NUM
easat-9284	42	2	.	.	PUNCT
easat-9284	42	3	enriched	enrich	VERB
easat-9284	42	4	contractions	contraction	NOUN
easat-9284	42	5	in	in	ADP
easat-9284	42	6	normed	normed	ADJ
easat-9284	42	7	spaces	space	NOUN
easat-9284	42	8	enriched	enrich	VERB
easat-9284	42	9	contractions	contraction	NOUN
easat-9284	43	1	[	[	X
easat-9284	43	2	9	9	NUM
easat-9284	43	3	]	]	PUNCT
easat-9284	43	4	provide	provide	VERB
easat-9284	43	5	a	a	DET
easat-9284	43	6	powerful	powerful	ADJ
easat-9284	43	7	extension	extension	NOUN
easat-9284	43	8	of	of	ADP
easat-9284	43	9	classical	classical	ADJ
easat-9284	43	10	contraction	contraction	NOUN
easat-9284	43	11	concepts	concept	NOUN
easat-9284	43	12	,	,	PUNCT
easat-9284	43	13	originally	originally	ADV
easat-9284	43	14	introduced	introduce	VERB
easat-9284	43	15	by	by	ADP
easat-9284	43	16	berinde	berinde	NOUN
easat-9284	43	17	[	[	X
easat-9284	43	18	5	5	NUM
easat-9284	43	19	]	]	PUNCT
easat-9284	43	20	and	and	CCONJ
easat-9284	43	21	berinde	berinde	VERB
easat-9284	43	22	[	[	X
easat-9284	43	23	10	10	NUM
easat-9284	43	24	]	]	PUNCT
easat-9284	43	25	to	to	PART
easat-9284	43	26	incorporate	incorporate	VERB
easat-9284	43	27	a	a	DET
easat-9284	43	28	parameterized	parameterized	ADJ
easat-9284	43	29	form	form	NOUN
easat-9284	43	30	of	of	ADP
easat-9284	43	31	contraction	contraction	NOUN
easat-9284	43	32	into	into	ADP
easat-9284	43	33	normed	normed	ADJ
easat-9284	43	34	spaces	space	NOUN
easat-9284	43	35	.	.	PUNCT
easat-9284	44	1	definition	definition	NOUN
easat-9284	44	2	2.1	2.1	NUM
easat-9284	44	3	(	(	PUNCT
easat-9284	44	4	berinde	berinde	NOUN
easat-9284	44	5	[	[	X
easat-9284	44	6	5	5	NUM
easat-9284	44	7	]	]	PUNCT
easat-9284	44	8	and	and	CCONJ
easat-9284	44	9	berinde	berinde	VERB
easat-9284	44	10	[	[	X
easat-9284	44	11	10	10	NUM
easat-9284	44	12	]	]	NUM
easat-9284	44	13	)	)	PUNCT
easat-9284	44	14	.	.	PUNCT
easat-9284	45	1	let	let	AUX
easat-9284	45	2	(	(	PUNCT
easat-9284	45	3	e	e	NOUN
easat-9284	45	4	,	,	PUNCT
easat-9284	45	5	.	.	PUNCT
easat-9284	45	6	)	)	PUNCT
easat-9284	45	7	be	be	AUX
easat-9284	45	8	a	a	DET
easat-9284	45	9	normed	normed	ADJ
easat-9284	45	10	linear	linear	ADJ
easat-9284	45	11	space	space	NOUN
easat-9284	45	12	.	.	PUNCT
easat-9284	46	1	a	a	DET
easat-9284	46	2	mapping	mapping	NOUN
easat-9284	46	3	t	t	NOUN
easat-9284	46	4	:	:	PUNCT
easat-9284	46	5	e	e	X
easat-9284	46	6	→	→	SYM
easat-9284	46	7	e	e	X
easat-9284	46	8	is	be	AUX
easat-9284	46	9	a	a	DET
easat-9284	46	10	(	(	PUNCT
easat-9284	46	11	k	k	X
easat-9284	46	12	,	,	PUNCT
easat-9284	46	13	θ)-enriched	θ)-enriche	VERB
easat-9284	46	14	contraction	contraction	NOUN
easat-9284	46	15	if	if	SCONJ
easat-9284	46	16	for	for	ADP
easat-9284	46	17	some	some	DET
easat-9284	46	18	k	k	NOUN
easat-9284	46	19	0	0	PUNCT
easat-9284	46	20	and	and	CCONJ
easat-9284	46	21	θ	θ	PROPN
easat-9284	46	22	≥	≥	NUM
easat-9284	47	1	[	[	X
easat-9284	47	2	0	0	NUM
easat-9284	47	3	,	,	PUNCT
easat-9284	47	4	k	k	PROPN
easat-9284	47	5	+	+	PROPN
easat-9284	47	6	1	1	NUM
easat-9284	47	7	)	)	PUNCT
easat-9284	47	8	,	,	PUNCT
easat-9284	47	9	∈	∈	VERB
easat-9284	47	10	the	the	DET
easat-9284	47	11	following	follow	VERB
easat-9284	47	12	inequality	inequality	NOUN
easat-9284	47	13	holds	hold	VERB
easat-9284	47	14	:	:	PUNCT
easat-9284	47	15	this	this	DET
easat-9284	47	16	condition	condition	NOUN
easat-9284	47	17	reduces	reduce	VERB
easat-9284	47	18	to	to	ADP
easat-9284	47	19	the	the	DET
easat-9284	47	20	banach	banach	NOUN
easat-9284	47	21	contraction	contraction	NOUN
easat-9284	47	22	when	when	SCONJ
easat-9284	47	23	k	k	PROPN
easat-9284	47	24	=	=	SYM
easat-9284	47	25	0	0	NUM
easat-9284	47	26	,	,	PUNCT
easat-9284	47	27	and	and	CCONJ
easat-9284	47	28	allows	allow	VERB
easat-9284	47	29	modeling	modeling	NOUN
easat-9284	47	30	operator	operator	NOUN
easat-9284	47	31	behaviors	behavior	NOUN
easat-9284	47	32	with	with	ADP
easat-9284	47	33	linear	linear	PROPN
easat-9284	47	34	perturbations	perturbation	NOUN
easat-9284	47	35	.	.	PUNCT
easat-9284	48	1	enriched	enrich	VERB
easat-9284	48	2	versions	version	NOUN
easat-9284	48	3	of	of	ADP
easat-9284	48	4	other	other	ADJ
easat-9284	48	5	contraction	contraction	NOUN
easat-9284	48	6	types	type	NOUN
easat-9284	48	7	,	,	PUNCT
easat-9284	48	8	such	such	ADJ
easat-9284	48	9	as	as	ADP
easat-9284	48	10	kannan	kannan	PROPN
easat-9284	48	11	and	and	CCONJ
easat-9284	48	12	hardy	hardy	ADJ
easat-9284	48	13	–	–	PUNCT
easat-9284	48	14	rogers	roger	NOUN
easat-9284	48	15	contractions	contraction	NOUN
easat-9284	48	16	,	,	PUNCT
easat-9284	48	17	have	have	AUX
easat-9284	48	18	since	since	ADV
easat-9284	48	19	been	be	AUX
easat-9284	48	20	introduced	introduce	VERB
easat-9284	48	21	to	to	PART
easat-9284	48	22	address	address	VERB
easat-9284	48	23	more	more	ADJ
easat-9284	48	24	general	general	ADJ
easat-9284	48	25	fixed	fix	VERB
easat-9284	48	26	point	point	NOUN
easat-9284	48	27	settings	setting	NOUN
easat-9284	48	28	,	,	PUNCT
easat-9284	48	29	including	include	VERB
easat-9284	48	30	non	non	ADJ
easat-9284	48	31	-	-	ADJ
easat-9284	48	32	continuous	continuous	ADJ
easat-9284	48	33	and	and	CCONJ
easat-9284	48	34	nonlinear	nonlinear	ADJ
easat-9284	48	35	operators	operator	NOUN
easat-9284	48	36	[	[	X
easat-9284	48	37	7	7	NUM
easat-9284	48	38	]	]	PUNCT
easat-9284	48	39	.	.	PUNCT
easat-9284	49	1	293	293	NUM
easat-9284	49	2	edelweiss	edelweiss	PROPN
easat-9284	49	3	applied	apply	VERB
easat-9284	49	4	science	science	NOUN
easat-9284	49	5	and	and	CCONJ
easat-9284	49	6	technology	technology	NOUN
easat-9284	49	7	issn	issn	PROPN
easat-9284	49	8	:	:	PUNCT
easat-9284	49	9	2576	2576	NUM
easat-9284	49	10	-	-	SYM
easat-9284	49	11	8484	8484	NUM
easat-9284	49	12	vol	vol	NOUN
easat-9284	49	13	.	.	PROPN
easat-9284	50	1	9	9	NUM
easat-9284	50	2	,	,	PUNCT
easat-9284	50	3	no	no	INTJ
easat-9284	50	4	.	.	NOUN
easat-9284	50	5	8	8	NUM
easat-9284	50	6	:	:	PUNCT
easat-9284	50	7	291	291	NUM
easat-9284	50	8	-	-	SYM
easat-9284	50	9	299	299	NUM
easat-9284	50	10	,	,	PUNCT
easat-9284	50	11	2025	2025	NUM
easat-9284	50	12	doi	doi	NOUN
easat-9284	50	13	:	:	PUNCT
easat-9284	50	14	10.55214/2576	10.55214/2576	NUM
easat-9284	50	15	-	-	PUNCT
easat-9284	50	16	8484.v9i8.9284	8484.v9i8.9284	NOUN
easat-9284	50	17	©	©	PROPN
easat-9284	50	18	2025	2025	NUM
easat-9284	50	19	by	by	ADP
easat-9284	50	20	the	the	DET
easat-9284	50	21	author	author	NOUN
easat-9284	50	22	;	;	PUNCT
easat-9284	50	23	licensee	licensee	PROPN
easat-9284	50	24	learning	learning	NOUN
easat-9284	50	25	gate	gate	NOUN
easat-9284	50	26	2.3	2.3	NUM
easat-9284	50	27	.	.	PUNCT
easat-9284	51	1	hardy	hardy	ADJ
easat-9284	51	2	–	–	PUNCT
easat-9284	51	3	rogers	roger	NOUN
easat-9284	51	4	type	type	NOUN
easat-9284	51	5	contractions	contraction	NOUN
easat-9284	51	6	the	the	DET
easat-9284	51	7	hardy	hardy	ADJ
easat-9284	51	8	and	and	CCONJ
easat-9284	51	9	rogers	roger	NOUN
easat-9284	51	10	[	[	X
easat-9284	51	11	4	4	X
easat-9284	51	12	]	]	PUNCT
easat-9284	51	13	generalizes	generalize	VERB
easat-9284	51	14	the	the	DET
easat-9284	51	15	banach	banach	NOUN
easat-9284	51	16	and	and	CCONJ
easat-9284	51	17	kannan	kannan	PROPN
easat-9284	51	18	types	type	NOUN
easat-9284	51	19	by	by	ADP
easat-9284	51	20	incorporating	incorporate	VERB
easat-9284	51	21	additional	additional	ADJ
easat-9284	51	22	distance	distance	NOUN
easat-9284	51	23	terms	term	NOUN
easat-9284	51	24	between	between	ADP
easat-9284	51	25	images	image	NOUN
easat-9284	51	26	and	and	CCONJ
easat-9284	51	27	their	their	PRON
easat-9284	51	28	pre	pre	NOUN
easat-9284	51	29	-	-	NOUN
easat-9284	51	30	images	image	NOUN
easat-9284	51	31	.	.	PUNCT
easat-9284	52	1	the	the	DET
easat-9284	52	2	enriched	enrich	VERB
easat-9284	52	3	form	form	NOUN
easat-9284	52	4	was	be	AUX
easat-9284	52	5	introduced	introduce	VERB
easat-9284	52	6	in	in	ADP
easat-9284	52	7	gautam	gautam	PROPN
easat-9284	52	8	,	,	PUNCT
easat-9284	52	9	et	et	PROPN
easat-9284	52	10	al	al	PROPN
easat-9284	52	11	.	.	PUNCT
easat-9284	53	1	[	[	X
easat-9284	53	2	7	7	X
easat-9284	53	3	]	]	PUNCT
easat-9284	53	4	to	to	PART
easat-9284	53	5	allow	allow	VERB
easat-9284	53	6	greater	great	ADJ
easat-9284	53	7	flexibility	flexibility	NOUN
easat-9284	53	8	.	.	PUNCT
easat-9284	54	1	definition	definition	NOUN
easat-9284	54	2	2.2	2.2	NUM
easat-9284	54	3	(	(	PUNCT
easat-9284	54	4	hardy	hardy	ADJ
easat-9284	54	5	and	and	CCONJ
easat-9284	54	6	rogers	roger	NOUN
easat-9284	54	7	[	[	X
easat-9284	54	8	4	4	NUM
easat-9284	54	9	]	]	PUNCT
easat-9284	54	10	)	)	PUNCT
easat-9284	54	11	.	.	PUNCT
easat-9284	55	1	let	let	AUX
easat-9284	55	2	(	(	PUNCT
easat-9284	55	3	e	e	NOUN
easat-9284	55	4	,	,	PUNCT
easat-9284	55	5	·	·	PUNCT
easat-9284	55	6	)	)	PUNCT
easat-9284	55	7	be	be	AUX
easat-9284	55	8	a	a	DET
easat-9284	55	9	normed	normed	ADJ
easat-9284	55	10	linear	linear	ADJ
easat-9284	55	11	space	space	NOUN
easat-9284	55	12	.	.	PUNCT
easat-9284	56	1	a	a	DET
easat-9284	56	2	mapping	mapping	NOUN
easat-9284	56	3	t	t	NOUN
easat-9284	56	4	:	:	PUNCT
easat-9284	56	5	e	e	X
easat-9284	56	6	→	→	PUNCT
easat-9284	56	7	e	e	X
easat-9284	56	8	is	be	AUX
easat-9284	56	9	said	say	VERB
easat-9284	56	10	to	to	PART
easat-9284	56	11	be	be	AUX
easat-9284	56	12	a	a	DET
easat-9284	56	13	(	(	PUNCT
easat-9284	56	14	k	k	NOUN
easat-9284	56	15	,	,	PUNCT
easat-9284	56	16	a	a	DET
easat-9284	56	17	,	,	PUNCT
easat-9284	56	18	b	b	NOUN
easat-9284	56	19	,	,	PUNCT
easat-9284	56	20	c)-enriched	c)-enriche	VERB
easat-9284	56	21	hardy	hardy	ADJ
easat-9284	56	22	–	–	PUNCT
easat-9284	56	23	rogers	roger	NOUN
easat-9284	56	24	contraction	contraction	NOUN
easat-9284	56	25	if	if	SCONJ
easat-9284	56	26	there	there	PRON
easat-9284	56	27	exist	exist	VERB
easat-9284	56	28	constants	constant	NOUN
easat-9284	56	29	k	k	PROPN
easat-9284	56	30	∈	∈	PROPN
easat-9284	57	1	[	[	X
easat-9284	57	2	0	0	NUM
easat-9284	57	3	,	,	PUNCT
easat-9284	57	4	1	1	NUM
easat-9284	57	5	)	)	PUNCT
easat-9284	57	6	,	,	PUNCT
easat-9284	57	7	a	a	DET
easat-9284	57	8	,	,	PUNCT
easat-9284	57	9	b	b	NOUN
easat-9284	57	10	,	,	PUNCT
easat-9284	57	11	c	c	X
easat-9284	57	12	≥	≥	NOUN
easat-9284	57	13	0	0	NUM
easat-9284	57	14	with	with	ADP
easat-9284	57	15	a	a	DET
easat-9284	57	16	+	+	NOUN
easat-9284	57	17	2b	2b	NUM
easat-9284	57	18	+	+	CCONJ
easat-9284	57	19	2c	2c	NUM
easat-9284	57	20	<	<	X
easat-9284	57	21	1	1	NUM
easat-9284	57	22	,	,	PUNCT
easat-9284	57	23	such	such	ADJ
easat-9284	57	24	that	that	SCONJ
easat-9284	57	25	k(p	k(p	PROPN
easat-9284	57	26	−	−	PROPN
easat-9284	57	27	q	q	NOUN
easat-9284	57	28	)	)	PUNCT
easat-9284	58	1	+	+	NUM
easat-9284	58	2	t	t	X
easat-9284	58	3	p	p	X
easat-9284	58	4	−	−	PROPN
easat-9284	58	5	t	t	PROPN
easat-9284	58	6	q	q	PROPN
easat-9284	58	7	≤	≤	PROPN
easat-9284	58	8	a	a	DET
easat-9284	58	9	p	p	NOUN
easat-9284	58	10	−	−	NOUN
easat-9284	59	1	q	q	NOUN
easat-9284	60	1	+	+	NUM
easat-9284	60	2	b	b	X
easat-9284	60	3	(	(	PUNCT
easat-9284	60	4	p	p	NOUN
easat-9284	60	5	−	−	PROPN
easat-9284	60	6	t	t	NOUN
easat-9284	61	1	p	p	PROPN
easat-9284	62	1	+	+	NOUN
easat-9284	62	2	q	q	NOUN
easat-9284	62	3	−	−	PROPN
easat-9284	62	4	t	t	PROPN
easat-9284	62	5	q	q	PROPN
easat-9284	62	6	)	)	PUNCT
easat-9284	63	1	+	+	CCONJ
easat-9284	63	2	c	c	X
easat-9284	63	3	(	(	PUNCT
easat-9284	63	4	p	p	NOUN
easat-9284	63	5	−	−	PROPN
easat-9284	63	6	t	t	NOUN
easat-9284	63	7	q	q	PROPN
easat-9284	64	1	+	+	CCONJ
easat-9284	64	2	q	q	NOUN
easat-9284	65	1	−	−	PROPN
easat-9284	65	2	t	t	PROPN
easat-9284	65	3	p	p	PROPN
easat-9284	65	4	)	)	PUNCT
easat-9284	65	5	,	,	PUNCT
easat-9284	65	6	for	for	ADP
easat-9284	65	7	all	all	DET
easat-9284	65	8	p	p	NOUN
easat-9284	65	9	,	,	PUNCT
easat-9284	65	10	q	q	NOUN
easat-9284	65	11	∈	∈	PROPN
easat-9284	65	12	e	e	X
easat-9284	65	13	.	.	PUNCT
easat-9284	66	1	this	this	DET
easat-9284	66	2	generalization	generalization	NOUN
easat-9284	66	3	retains	retain	VERB
easat-9284	66	4	contractiveness	contractiveness	NOUN
easat-9284	66	5	while	while	SCONJ
easat-9284	66	6	accommodating	accommodate	VERB
easat-9284	66	7	non	non	ADJ
easat-9284	66	8	-	-	ADJ
easat-9284	66	9	self	self	ADJ
easat-9284	66	10	distances	distance	NOUN
easat-9284	66	11	and	and	CCONJ
easat-9284	66	12	asymmetries	asymmetry	NOUN
easat-9284	66	13	,	,	PUNCT
easat-9284	66	14	which	which	PRON
easat-9284	66	15	are	be	AUX
easat-9284	66	16	common	common	ADJ
easat-9284	66	17	in	in	ADP
easat-9284	66	18	applications	application	NOUN
easat-9284	66	19	involving	involve	VERB
easat-9284	66	20	iterative	iterative	NOUN
easat-9284	66	21	dynamics	dynamic	NOUN
easat-9284	66	22	or	or	CCONJ
easat-9284	66	23	integral	integral	ADJ
easat-9284	66	24	equations	equation	NOUN
easat-9284	66	25	.	.	PUNCT
easat-9284	67	1	2.4	2.4	NUM
easat-9284	67	2	.	.	PUNCT
easat-9284	68	1	f	f	X
easat-9284	68	2	-	-	PUNCT
easat-9284	68	3	contractions	contraction	NOUN
easat-9284	68	4	and	and	CCONJ
easat-9284	68	5	the	the	DET
easat-9284	68	6	function	function	NOUN
easat-9284	68	7	class	class	NOUN
easat-9284	68	8	to	to	PART
easat-9284	68	9	further	far	ADV
easat-9284	68	10	generalize	generalize	VERB
easat-9284	68	11	contractive	contractive	ADJ
easat-9284	68	12	conditions	condition	NOUN
easat-9284	68	13	,	,	PUNCT
easat-9284	68	14	wardowski	wardowski	VERB
easat-9284	68	15	[	[	X
easat-9284	68	16	6	6	NUM
easat-9284	68	17	]	]	PUNCT
easat-9284	68	18	introduced	introduce	VERB
easat-9284	68	19	f	f	PROPN
easat-9284	68	20	-contractions	-contraction	NOUN
easat-9284	68	21	,	,	PUNCT
easat-9284	68	22	which	which	PRON
easat-9284	68	23	replace	replace	VERB
easat-9284	68	24	the	the	DET
easat-9284	68	25	lipschitz	lipschitz	NOUN
easat-9284	68	26	constant	constant	ADJ
easat-9284	68	27	with	with	ADP
easat-9284	68	28	a	a	DET
easat-9284	68	29	control	control	NOUN
easat-9284	68	30	function	function	NOUN
easat-9284	68	31	f	f	PROPN
easat-9284	68	32	∈	∈	PROPN
easat-9284	68	33	f1	f1	NOUN
easat-9284	68	34	.	.	PUNCT
easat-9284	69	1	these	these	DET
easat-9284	69	2	mappings	mapping	NOUN
easat-9284	69	3	are	be	AUX
easat-9284	69	4	not	not	PART
easat-9284	69	5	required	require	VERB
easat-9284	69	6	to	to	PART
easat-9284	69	7	be	be	AUX
easat-9284	69	8	continuous	continuous	ADJ
easat-9284	69	9	,	,	PUNCT
easat-9284	69	10	and	and	CCONJ
easat-9284	69	11	thus	thus	ADV
easat-9284	69	12	enable	enable	VERB
easat-9284	69	13	broader	broad	ADJ
easat-9284	69	14	applicability	applicability	NOUN
easat-9284	69	15	.	.	PUNCT
easat-9284	70	1	definition	definition	NOUN
easat-9284	70	2	2.3	2.3	NUM
easat-9284	70	3	.	.	PUNCT
easat-9284	71	1	let	let	VERB
easat-9284	71	2	f	f	X
easat-9284	71	3	:	:	PUNCT
easat-9284	71	4	r+	r+	X
easat-9284	71	5	→	→	PUNCT
easat-9284	71	6	r.	r.	PROPN
easat-9284	71	7	then	then	ADV
easat-9284	71	8	f	f	PROPN
easat-9284	71	9	∈	∈	PROPN
easat-9284	71	10	f1	f1	NOUN
easat-9284	71	11	if	if	SCONJ
easat-9284	71	12	:	:	PUNCT
easat-9284	71	13	(	(	PUNCT
easat-9284	71	14	f1	f1	NOUN
easat-9284	71	15	)	)	PUNCT
easat-9284	71	16	f	f	PROPN
easat-9284	71	17	is	be	AUX
easat-9284	71	18	strictly	strictly	ADV
easat-9284	71	19	increasing	increase	VERB
easat-9284	71	20	;	;	PUNCT
easat-9284	71	21	(	(	PUNCT
easat-9284	71	22	f2	f2	X
easat-9284	71	23	)	)	PUNCT
easat-9284	71	24	limn→∞	limn→∞	PROPN
easat-9284	71	25	αn	αn	NOUN
easat-9284	72	1	=	=	SYM
easat-9284	72	2	0	0	PUNCT
easat-9284	73	1	if	if	SCONJ
easat-9284	73	2	and	and	CCONJ
easat-9284	73	3	only	only	ADV
easat-9284	73	4	if	if	SCONJ
easat-9284	73	5	limn→∞	limn→∞	PROPN
easat-9284	73	6	f	f	X
easat-9284	73	7	(	(	PUNCT
easat-9284	73	8	αn	αn	NOUN
easat-9284	73	9	)	)	PUNCT
easat-9284	73	10	=	=	SYM
easat-9284	73	11	−∞	−∞	PROPN
easat-9284	73	12	;	;	PUNCT
easat-9284	73	13	(	(	PUNCT
easat-9284	73	14	f3	f3	ADJ
easat-9284	73	15	)	)	PUNCT
easat-9284	73	16	there	there	PRON
easat-9284	73	17	exists	exist	VERB
easat-9284	73	18	k	k	PROPN
easat-9284	73	19	∈	∈	PROPN
easat-9284	73	20	(	(	PUNCT
easat-9284	73	21	0	0	NUM
easat-9284	73	22	,	,	PUNCT
easat-9284	73	23	1	1	NUM
easat-9284	73	24	)	)	PUNCT
easat-9284	73	25	such	such	ADJ
easat-9284	73	26	that	that	DET
easat-9284	73	27	limα→0	limα→0	NOUN
easat-9284	73	28	+	+	CCONJ
easat-9284	73	29	α	α	PROPN
easat-9284	73	30	f	f	X
easat-9284	73	31	(	(	PUNCT
easat-9284	73	32	αk	αk	NOUN
easat-9284	73	33	)	)	PUNCT
easat-9284	73	34	=	=	SYM
easat-9284	74	1	0	0	X
easat-9284	74	2	.	.	PUNCT
easat-9284	75	1	definition	definition	NOUN
easat-9284	75	2	2.4	2.4	NUM
easat-9284	75	3	(	(	PUNCT
easat-9284	75	4	wardowski	wardowski	VERB
easat-9284	75	5	[	[	X
easat-9284	75	6	6	6	NUM
easat-9284	75	7	]	]	NUM
easat-9284	75	8	)	)	PUNCT
easat-9284	75	9	.	.	PUNCT
easat-9284	76	1	a	a	DET
easat-9284	76	2	mapping	mapping	NOUN
easat-9284	76	3	t	t	NOUN
easat-9284	76	4	:	:	PUNCT
easat-9284	76	5	e	e	X
easat-9284	76	6	→	→	SYM
easat-9284	76	7	e	e	X
easat-9284	76	8	is	be	AUX
easat-9284	76	9	called	call	VERB
easat-9284	76	10	an	an	DET
easat-9284	76	11	f	f	PROPN
easat-9284	76	12	-contraction	-contraction	NOUN
easat-9284	76	13	if	if	SCONJ
easat-9284	76	14	there	there	PRON
easat-9284	76	15	exists	exist	VERB
easat-9284	76	16	τ	τ	X
easat-9284	76	17	>	>	X
easat-9284	76	18	0	0	PUNCT
easat-9284	76	19	and	and	CCONJ
easat-9284	76	20	f	f	PROPN
easat-9284	76	21	∈	∈	PROPN
easat-9284	76	22	f1	f1	NOUN
easat-9284	76	23	such	such	ADJ
easat-9284	77	1	that	that	SCONJ
easat-9284	77	2	τ	τ	PROPN
easat-9284	77	3	+	+	NUM
easat-9284	77	4	f	f	X
easat-9284	77	5	(	(	PUNCT
easat-9284	77	6	d(t	d(t	PROPN
easat-9284	77	7	p	p	PROPN
easat-9284	77	8	,	,	PUNCT
easat-9284	77	9	t	t	PROPN
easat-9284	77	10	q	q	NOUN
easat-9284	77	11	)	)	PUNCT
easat-9284	77	12	)	)	PUNCT
easat-9284	78	1	≤	≤	NUM
easat-9284	78	2	f	f	X
easat-9284	78	3	(	(	PUNCT
easat-9284	78	4	d(p	d(p	PROPN
easat-9284	78	5	,	,	PUNCT
easat-9284	78	6	q	q	NOUN
easat-9284	78	7	)	)	PUNCT
easat-9284	78	8	)	)	PUNCT
easat-9284	78	9	,	,	PUNCT
easat-9284	78	10	∀p	∀p	X
easat-9284	78	11	,	,	PUNCT
easat-9284	78	12	q	q	PROPN
easat-9284	78	13	∈	∈	PROPN
easat-9284	78	14	e	e	NOUN
easat-9284	78	15	,	,	PUNCT
easat-9284	78	16	t	t	PROPN
easat-9284	78	17	p	p	PROPN
easat-9284	79	1	/=	/=	PROPN
easat-9284	80	1	t	t	PROPN
easat-9284	80	2	q.	q.	PROPN
easat-9284	80	3	examples	example	NOUN
easat-9284	80	4	of	of	ADP
easat-9284	80	5	functions	function	NOUN
easat-9284	80	6	in	in	ADP
easat-9284	80	7	f1	f1	NOUN
easat-9284	80	8	include	include	VERB
easat-9284	80	9	:	:	PUNCT
easat-9284	80	10	2.5	2.5	NUM
easat-9284	80	11	.	.	PUNCT
easat-9284	81	1	iterative	iterative	NOUN
easat-9284	81	2	approaches	approach	NOUN
easat-9284	81	3	:	:	PUNCT
easat-9284	81	4	krasnoselskij	krasnoselskij	NOUN
easat-9284	81	5	scheme	scheme	VERB
easat-9284	81	6	the	the	DET
easat-9284	81	7	convergence	convergence	NOUN
easat-9284	81	8	of	of	ADP
easat-9284	81	9	fixed	fix	VERB
easat-9284	81	10	point	point	NOUN
easat-9284	81	11	approximations	approximation	NOUN
easat-9284	81	12	is	be	AUX
easat-9284	81	13	often	often	ADV
easat-9284	81	14	established	establish	VERB
easat-9284	81	15	using	use	VERB
easat-9284	81	16	iterative	iterative	NOUN
easat-9284	81	17	schemes	scheme	NOUN
easat-9284	81	18	.	.	PUNCT
easat-9284	82	1	one	one	NUM
easat-9284	82	2	of	of	ADP
easat-9284	82	3	the	the	PRON
easat-9284	82	4	most	most	ADV
easat-9284	82	5	widely	widely	ADV
easat-9284	82	6	used	use	VERB
easat-9284	82	7	in	in	ADP
easat-9284	82	8	enriched	enriched	ADJ
easat-9284	82	9	settings	setting	NOUN
easat-9284	82	10	is	be	AUX
easat-9284	82	11	the	the	DET
easat-9284	82	12	krasnoselskij	krasnoselskij	PROPN
easat-9284	82	13	iteration	iteration	NOUN
easat-9284	82	14	,	,	PUNCT
easat-9284	82	15	introduced	introduce	VERB
easat-9284	82	16	in	in	ADP
easat-9284	82	17	krasnoselskii	krasnoselskii	PROPN
easat-9284	83	1	[	[	X
easat-9284	83	2	11	11	NUM
easat-9284	83	3	]	]	PUNCT
easat-9284	83	4	.	.	PUNCT
easat-9284	84	1	given	give	VERB
easat-9284	84	2	a	a	DET
easat-9284	84	3	mapping	mapping	NOUN
easat-9284	84	4	t	t	NOUN
easat-9284	84	5	:	:	PUNCT
easat-9284	84	6	e	e	X
easat-9284	84	7	→	→	SYM
easat-9284	84	8	e	e	NOUN
easat-9284	84	9	and	and	CCONJ
easat-9284	84	10	initial	initial	ADJ
easat-9284	84	11	point	point	NOUN
easat-9284	84	12	p0	p0	NOUN
easat-9284	84	13	∈	∈	PROPN
easat-9284	84	14	e	e	NOUN
easat-9284	84	15	,	,	PUNCT
easat-9284	84	16	the	the	DET
easat-9284	84	17	iteration	iteration	NOUN
easat-9284	84	18	is	be	AUX
easat-9284	84	19	defined	define	VERB
easat-9284	84	20	as	as	ADP
easat-9284	84	21	:	:	PUNCT
easat-9284	84	22	pn+1	pn+1	NOUN
easat-9284	84	23	=	=	SYM
easat-9284	84	24	(	(	PUNCT
easat-9284	84	25	1	1	NUM
easat-9284	84	26	−	−	PROPN
easat-9284	84	27	λ	λ	NOUN
easat-9284	84	28	)	)	PUNCT
easat-9284	84	29	pn	pn	NOUN
easat-9284	84	30	+	+	CCONJ
easat-9284	84	31	λt	λt	ADP
easat-9284	84	32	pn	pn	PROPN
easat-9284	84	33	,	,	PUNCT
easat-9284	84	34	n	n	X
easat-9284	84	35	≥	≥	NOUN
easat-9284	84	36	0	0	NUM
easat-9284	84	37	,	,	PUNCT
easat-9284	84	38	λ	λ	PROPN
easat-9284	84	39	∈	∈	PROPN
easat-9284	84	40	(	(	PUNCT
easat-9284	84	41	0	0	NUM
easat-9284	84	42	,	,	PUNCT
easat-9284	84	43	1	1	NUM
easat-9284	84	44	]	]	PUNCT
easat-9284	84	45	.	.	PUNCT
easat-9284	85	1	when	when	SCONJ
easat-9284	85	2	t	t	PROPN
easat-9284	85	3	is	be	AUX
easat-9284	85	4	an	an	DET
easat-9284	85	5	enriched	enriched	ADJ
easat-9284	85	6	or	or	CCONJ
easat-9284	85	7	f	f	PROPN
easat-9284	85	8	-contraction	-contraction	PROPN
easat-9284	85	9	,	,	PUNCT
easat-9284	85	10	the	the	DET
easat-9284	85	11	sequence	sequence	NOUN
easat-9284	85	12	[	[	X
easat-9284	85	13	7	7	X
easat-9284	85	14	]	]	PUNCT
easat-9284	85	15	is	be	AUX
easat-9284	85	16	known	know	VERB
easat-9284	85	17	to	to	PART
easat-9284	85	18	converge	converge	VERB
easat-9284	85	19	to	to	ADP
easat-9284	85	20	the	the	DET
easat-9284	85	21	unique	unique	ADJ
easat-9284	85	22	fixed	fix	VERB
easat-9284	85	23	point	point	NOUN
easat-9284	85	24	t	t	PROPN
easat-9284	85	25	∈	∈	PROPN
easat-9284	85	26	e	e	PROPN
easat-9284	85	27	,	,	PUNCT
easat-9284	85	28	with	with	ADP
easat-9284	85	29	convergence	convergence	NOUN
easat-9284	85	30	rate	rate	NOUN
easat-9284	85	31	governed	govern	VERB
easat-9284	85	32	by	by	ADP
easat-9284	85	33	contractive	contractive	ADJ
easat-9284	85	34	constants	constant	NOUN
easat-9284	85	35	(	(	PUNCT
easat-9284	85	36	e.g.	e.g.	ADV
easat-9284	85	37	,	,	PUNCT
easat-9284	85	38	a	a	DET
easat-9284	85	39	,	,	PUNCT
easat-9284	85	40	b	b	NOUN
easat-9284	85	41	,	,	PUNCT
easat-9284	85	42	c	c	NOUN
easat-9284	85	43	)	)	PUNCT
easat-9284	86	1	[	[	X
easat-9284	86	2	7	7	NUM
easat-9284	86	3	,	,	PUNCT
easat-9284	86	4	12	12	NUM
easat-9284	86	5	]	]	PUNCT
easat-9284	86	6	.	.	PUNCT
easat-9284	87	1	3	3	X
easat-9284	87	2	.	.	X
easat-9284	87	3	main	main	ADJ
easat-9284	87	4	results	result	NOUN
easat-9284	87	5	we	we	PRON
easat-9284	87	6	now	now	ADV
easat-9284	87	7	introduce	introduce	VERB
easat-9284	87	8	an	an	DET
easat-9284	87	9	enriched	enriched	ADJ
easat-9284	87	10	hardy	hardy	ADJ
easat-9284	87	11	–	–	PUNCT
easat-9284	87	12	rogers	roger	NOUN
easat-9284	87	13	type	type	NOUN
easat-9284	87	14	f	f	PROPN
easat-9284	87	15	-contraction	-contraction	PROPN
easat-9284	87	16	by	by	ADP
easat-9284	87	17	incorporating	incorporate	VERB
easat-9284	87	18	the	the	DET
easat-9284	87	19	nonlinear	nonlinear	ADJ
easat-9284	87	20	framework	framework	NOUN
easat-9284	87	21	of	of	ADP
easat-9284	87	22	f	f	PROPN
easat-9284	87	23	-contractions	-contraction	NOUN
easat-9284	87	24	into	into	ADP
easat-9284	87	25	the	the	DET
easat-9284	87	26	structure	structure	NOUN
easat-9284	87	27	proposed	propose	VERB
easat-9284	87	28	in	in	ADP
easat-9284	87	29	[	[	X
easat-9284	87	30	7	7	NUM
easat-9284	87	31	]	]	PUNCT
easat-9284	87	32	.	.	PUNCT
easat-9284	88	1	the	the	DET
easat-9284	88	2	result	result	NOUN
easat-9284	88	3	extends	extend	VERB
easat-9284	88	4	classical	classical	ADJ
easat-9284	88	5	hardy	hardy	ADJ
easat-9284	88	6	–	–	PUNCT
easat-9284	88	7	rogers	roger	NOUN
easat-9284	88	8	,	,	PUNCT
easat-9284	88	9	reich	reich	PROPN
easat-9284	88	10	,	,	PUNCT
easat-9284	88	11	and	and	CCONJ
easat-9284	88	12	f	f	PROPN
easat-9284	88	13	-type	-type	NOUN
easat-9284	88	14	contractions	contraction	NOUN
easat-9284	88	15	in	in	ADP
easat-9284	88	16	a	a	DET
easat-9284	88	17	unified	unified	ADJ
easat-9284	88	18	form	form	NOUN
easat-9284	88	19	.	.	PUNCT
easat-9284	89	1	definition	definition	NOUN
easat-9284	89	2	3.1	3.1	NUM
easat-9284	89	3	.	.	PUNCT
easat-9284	90	1	let	let	AUX
easat-9284	90	2	(	(	PUNCT
easat-9284	90	3	e	e	NOUN
easat-9284	90	4	,	,	PUNCT
easat-9284	90	5	·	·	PUNCT
easat-9284	90	6	)	)	PUNCT
easat-9284	90	7	be	be	AUX
easat-9284	90	8	a	a	DET
easat-9284	90	9	normed	normed	ADJ
easat-9284	90	10	linear	linear	ADJ
easat-9284	90	11	space	space	NOUN
easat-9284	90	12	and	and	CCONJ
easat-9284	90	13	let	let	VERB
easat-9284	90	14	f	f	PROPN
easat-9284	90	15	∈	∈	PROPN
easat-9284	90	16	f1	f1	NOUN
easat-9284	90	17	be	be	AUX
easat-9284	90	18	a	a	DET
easat-9284	90	19	function	function	NOUN
easat-9284	90	20	satisfying	satisfy	VERB
easat-9284	90	21	conditions	condition	NOUN
easat-9284	90	22	(	(	PUNCT
easat-9284	90	23	f1)–(f3	f1)–(f3	NOUN
easat-9284	90	24	)	)	PUNCT
easat-9284	90	25	.	.	PUNCT
easat-9284	91	1	a	a	DET
easat-9284	91	2	mapping	mapping	NOUN
easat-9284	91	3	t	t	NOUN
easat-9284	91	4	:	:	PUNCT
easat-9284	91	5	e	e	X
easat-9284	91	6	→	→	SYM
easat-9284	91	7	e	e	X
easat-9284	91	8	is	be	AUX
easat-9284	91	9	called	call	VERB
easat-9284	91	10	an	an	DET
easat-9284	91	11	enriched	enriched	ADJ
easat-9284	91	12	hardy	hardy	ADJ
easat-9284	91	13	–	–	PUNCT
easat-9284	91	14	rogers	roger	NOUN
easat-9284	91	15	type	type	NOUN
easat-9284	91	16	f	f	NOUN
easat-9284	91	17	-	-	PUNCT
easat-9284	91	18	contraction	contraction	NOUN
easat-9284	91	19	if	if	SCONJ
easat-9284	91	20	there	there	PRON
easat-9284	91	21	exist	exist	VERB
easat-9284	91	22	constants	constant	NOUN
easat-9284	91	23	a	a	DET
easat-9284	91	24	,	,	PUNCT
easat-9284	91	25	b	b	NOUN
easat-9284	91	26	,	,	PUNCT
easat-9284	91	27	c	c	PROPN
easat-9284	91	28	∈	∈	PROPN
easat-9284	92	1	[	[	X
easat-9284	92	2	0	0	NUM
easat-9284	92	3	,	,	PUNCT
easat-9284	92	4	1	1	NUM
easat-9284	92	5	)	)	PUNCT
easat-9284	92	6	and	and	CCONJ
easat-9284	92	7	b0	b0	VERB
easat-9284	92	8	≥	≥	NOUN
easat-9284	92	9	0	0	NUM
easat-9284	92	10	with	with	ADP
easat-9284	92	11	a	a	DET
easat-9284	92	12	+	+	NOUN
easat-9284	92	13	2b	2b	NUM
easat-9284	92	14	+	+	CCONJ
easat-9284	92	15	2c	2c	NUM
easat-9284	92	16	<	<	X
easat-9284	92	17	1	1	NUM
easat-9284	92	18	and	and	CCONJ
easat-9284	92	19	τ	τ	PROPN
easat-9284	92	20	>	>	X
easat-9284	92	21	0	0	PROPN
easat-9284	92	22	,	,	PUNCT
easat-9284	92	23	such	such	ADJ
easat-9284	92	24	that	that	SCONJ
easat-9284	92	25	for	for	ADP
easat-9284	92	26	all	all	DET
easat-9284	92	27	p	p	NOUN
easat-9284	92	28	,	,	PUNCT
easat-9284	92	29	q	q	SYM
easat-9284	92	30	∈	∈	PROPN
easat-9284	92	31	e	e	NOUN
easat-9284	92	32	with	with	ADP
easat-9284	92	33	t	t	PROPN
easat-9284	92	34	p	p	X
easat-9284	92	35	/=	/=	PROPN
easat-9284	92	36	t	t	PROPN
easat-9284	93	1	q	q	NOUN
easat-9284	93	2	,	,	PUNCT
easat-9284	93	3	(	(	PUNCT
easat-9284	93	4	1	1	X
easat-9284	93	5	)	)	PUNCT
easat-9284	93	6	294	294	NUM
easat-9284	93	7	edelweiss	edelweiss	PROPN
easat-9284	93	8	applied	apply	VERB
easat-9284	93	9	science	science	NOUN
easat-9284	93	10	and	and	CCONJ
easat-9284	93	11	technology	technology	NOUN
easat-9284	93	12	issn	issn	PROPN
easat-9284	93	13	:	:	PUNCT
easat-9284	93	14	2576	2576	NUM
easat-9284	93	15	-	-	SYM
easat-9284	93	16	8484	8484	NUM
easat-9284	93	17	vol	vol	NOUN
easat-9284	93	18	.	.	PROPN
easat-9284	94	1	9	9	NUM
easat-9284	94	2	,	,	PUNCT
easat-9284	94	3	no	no	INTJ
easat-9284	94	4	.	.	NOUN
easat-9284	94	5	8	8	NUM
easat-9284	94	6	:	:	PUNCT
easat-9284	94	7	291	291	NUM
easat-9284	94	8	-	-	SYM
easat-9284	94	9	299	299	NUM
easat-9284	94	10	,	,	PUNCT
easat-9284	94	11	2025	2025	NUM
easat-9284	94	12	doi	doi	NOUN
easat-9284	94	13	:	:	PUNCT
easat-9284	94	14	10.55214/2576	10.55214/2576	NUM
easat-9284	94	15	-	-	PUNCT
easat-9284	94	16	8484.v9i8.9284	8484.v9i8.9284	NOUN
easat-9284	94	17	©	©	PROPN
easat-9284	94	18	2025	2025	NUM
easat-9284	94	19	by	by	ADP
easat-9284	94	20	the	the	DET
easat-9284	94	21	author	author	NOUN
easat-9284	94	22	;	;	PUNCT
easat-9284	94	23	licensee	licensee	PROPN
easat-9284	94	24	learning	learning	NOUN
easat-9284	94	25	gate	gate	NOUN
easat-9284	94	26	—	—	PUNCT
easat-9284	94	27	≤	≤	NUM
easat-9284	94	28	−	−	ADP
easat-9284	94	29	−	−	PROPN
easat-9284	95	1	−	−	PROPN
easat-9284	95	2	lemma	lemma	PROPN
easat-9284	95	3	3.2	3.2	NUM
easat-9284	95	4	.	.	PUNCT
easat-9284	96	1	let	let	VERB
easat-9284	96	2	t	t	NOUN
easat-9284	96	3	:	:	PUNCT
easat-9284	96	4	e	e	X
easat-9284	96	5	→	→	PUNCT
easat-9284	96	6	e	e	X
easat-9284	96	7	be	be	AUX
easat-9284	96	8	an	an	DET
easat-9284	96	9	enriched	enriched	ADJ
easat-9284	96	10	hardy	hardy	ADJ
easat-9284	96	11	–	–	PUNCT
easat-9284	96	12	rogers	roger	NOUN
easat-9284	96	13	type	type	NOUN
easat-9284	96	14	f	f	NOUN
easat-9284	96	15	-	-	PUNCT
easat-9284	96	16	contraction	contraction	NOUN
easat-9284	96	17	as	as	ADP
easat-9284	96	18	in	in	ADP
easat-9284	96	19	definition	definition	NOUN
easat-9284	96	20	3.1	3.1	NUM
easat-9284	96	21	,	,	PUNCT
easat-9284	96	22	and	and	CCONJ
easat-9284	96	23	let	let	VERB
easat-9284	96	24	[	[	PUNCT
easat-9284	96	25	7	7	X
easat-9284	96	26	]	]	PUNCT
easat-9284	96	27	be	be	AUX
easat-9284	96	28	the	the	DET
easat-9284	96	29	iterative	iterative	NOUN
easat-9284	96	30	sequence	sequence	NOUN
easat-9284	96	31	defined	define	VERB
easat-9284	96	32	by	by	ADP
easat-9284	96	33	then	then	ADV
easat-9284	96	34	the	the	DET
easat-9284	96	35	following	follow	VERB
easat-9284	96	36	recursive	recursive	ADJ
easat-9284	96	37	inequality	inequality	NOUN
easat-9284	96	38	holds	hold	VERB
easat-9284	96	39	for	for	ADP
easat-9284	96	40	all	all	DET
easat-9284	96	41	n	n	PRON
easat-9284	96	42	≥	≥	NOUN
easat-9284	96	43	1	1	NUM
easat-9284	96	44	:	:	PUNCT
easat-9284	96	45	(	(	PUNCT
easat-9284	96	46	2	2	X
easat-9284	96	47	)	)	PUNCT
easat-9284	96	48	proof	proof	NOUN
easat-9284	96	49	.	.	PUNCT
easat-9284	97	1	let	let	VERB
easat-9284	97	2	us	we	PRON
easat-9284	97	3	apply	apply	VERB
easat-9284	97	4	the	the	DET
easat-9284	97	5	contractive	contractive	ADJ
easat-9284	97	6	condition	condition	NOUN
easat-9284	97	7	(	(	PUNCT
easat-9284	97	8	1	1	NUM
easat-9284	97	9	)	)	PUNCT
easat-9284	97	10	to	to	ADP
easat-9284	97	11	the	the	DET
easat-9284	97	12	pair	pair	NOUN
easat-9284	97	13	(	(	PUNCT
easat-9284	97	14	p	p	X
easat-9284	97	15	,	,	PUNCT
easat-9284	97	16	q	q	NOUN
easat-9284	97	17	)	)	PUNCT
easat-9284	97	18	=	=	SYM
easat-9284	97	19	(	(	PUNCT
easat-9284	97	20	pn	pn	PROPN
easat-9284	97	21	,	,	PUNCT
easat-9284	97	22	pn−1	pn−1	PROPN
easat-9284	97	23	)	)	PUNCT
easat-9284	97	24	,	,	PUNCT
easat-9284	97	25	noting	note	VERB
easat-9284	97	26	that	that	SCONJ
easat-9284	97	27	:	:	PUNCT
easat-9284	97	28	pn+1	pn+1	PROPN
easat-9284	97	29	=	=	SYM
easat-9284	97	30	tλpn	tλpn	PROPN
easat-9284	97	31	,	,	PUNCT
easat-9284	97	32	pn	pn	PROPN
easat-9284	97	33	=	=	SYM
easat-9284	97	34	tλpn−1	tλpn−1	PROPN
easat-9284	97	35	,	,	PUNCT
easat-9284	97	36	where	where	SCONJ
easat-9284	97	37	tλ(p	tλ(p	PUNCT
easat-9284	97	38	)	)	PUNCT
easat-9284	97	39	=	=	SYM
easat-9284	98	1	(	(	PUNCT
easat-9284	98	2	1	1	NUM
easat-9284	98	3	−	−	NOUN
easat-9284	98	4	λ)p	λ)p	PUNCT
easat-9284	98	5	+	+	CCONJ
easat-9284	98	6	λt	λt	ADP
easat-9284	98	7	p	p	NOUN
easat-9284	98	8	is	be	AUX
easat-9284	98	9	the	the	DET
easat-9284	98	10	averaged	average	VERB
easat-9284	98	11	mapping	mapping	NOUN
easat-9284	98	12	.	.	PUNCT
easat-9284	99	1	then	then	ADV
easat-9284	99	2	,	,	PUNCT
easat-9284	99	3	pn+1	pn+1	VERB
easat-9284	99	4	−	−	PROPN
easat-9284	99	5	pn	pn	PROPN
easat-9284	99	6	=	=	PUNCT
easat-9284	99	7	tλpn	tλpn	PROPN
easat-9284	99	8	−	−	PROPN
easat-9284	99	9	tλpn−1	tλpn−1	PROPN
easat-9284	99	10	=	=	SYM
easat-9284	99	11	λ	λ	X
easat-9284	99	12	b0(pn	b0(pn	PROPN
easat-9284	99	13	−	−	PROPN
easat-9284	99	14	pn−1	pn−1	PROPN
easat-9284	99	15	)	)	PUNCT
easat-9284	100	1	+	+	NUM
easat-9284	100	2	t	t	PROPN
easat-9284	100	3	pn	pn	PROPN
easat-9284	100	4	−	−	PROPN
easat-9284	100	5	t	t	PROPN
easat-9284	100	6	pn−1	pn−1	PROPN
easat-9284	100	7	.	.	PUNCT
easat-9284	101	1	substituting	substitute	VERB
easat-9284	101	2	into	into	ADP
easat-9284	101	3	the	the	DET
easat-9284	101	4	left	left	ADJ
easat-9284	101	5	-	-	PUNCT
easat-9284	101	6	hand	hand	NOUN
easat-9284	101	7	side	side	NOUN
easat-9284	101	8	of	of	ADP
easat-9284	101	9	the	the	DET
easat-9284	101	10	contraction	contraction	NOUN
easat-9284	101	11	condition	condition	NOUN
easat-9284	101	12	:	:	PUNCT
easat-9284	102	1	τ	τ	X
easat-9284	102	2	+	+	NUM
easat-9284	102	3	f	f	X
easat-9284	102	4	(	(	PUNCT
easat-9284	102	5	pn+1	pn+1	PROPN
easat-9284	102	6	−	−	PROPN
easat-9284	102	7	pn	pn	PROPN
easat-9284	102	8	)	)	PUNCT
easat-9284	102	9	=	=	PUNCT
easat-9284	103	1	τ	τ	PROPN
easat-9284	104	1	+	+	NUM
easat-9284	104	2	f	f	X
easat-9284	104	3	(	(	PUNCT
easat-9284	104	4	λ	λ	X
easat-9284	104	5	b0(pn	b0(pn	PROPN
easat-9284	104	6	−	−	PROPN
easat-9284	104	7	pn−1	pn−1	PROPN
easat-9284	104	8	)	)	PUNCT
easat-9284	105	1	+	+	NUM
easat-9284	105	2	t	t	PROPN
easat-9284	105	3	pn	pn	PROPN
easat-9284	105	4	−	−	PROPN
easat-9284	105	5	t	t	PROPN
easat-9284	105	6	pn−1	pn−1	PROPN
easat-9284	105	7	)	)	PUNCT
easat-9284	105	8	,	,	PUNCT
easat-9284	105	9	and	and	CCONJ
easat-9284	105	10	applying	apply	VERB
easat-9284	105	11	the	the	DET
easat-9284	105	12	contractive	contractive	ADJ
easat-9284	105	13	condition	condition	NOUN
easat-9284	105	14	(	(	PUNCT
easat-9284	105	15	1	1	NUM
easat-9284	105	16	)	)	PUNCT
easat-9284	105	17	,	,	PUNCT
easat-9284	105	18	we	we	PRON
easat-9284	105	19	get	get	VERB
easat-9284	105	20	:	:	PUNCT
easat-9284	105	21	τ	τ	PROPN
easat-9284	106	1	+	+	NUM
easat-9284	106	2	f	f	X
easat-9284	106	3	(	(	PUNCT
easat-9284	106	4	pn+1	pn+1	PROPN
easat-9284	106	5	pn	pn	PROPN
easat-9284	106	6	)	)	PUNCT
easat-9284	106	7	f	f	PROPN
easat-9284	106	8	a	a	DET
easat-9284	106	9	pn	pn	X
easat-9284	106	10	pn−1	pn−1	PROPN
easat-9284	106	11	+	+	CCONJ
easat-9284	106	12	b	b	X
easat-9284	106	13	(	(	PUNCT
easat-9284	106	14	pn	pn	PROPN
easat-9284	106	15	t	t	PROPN
easat-9284	106	16	pn	pn	PROPN
easat-9284	107	1	+	+	CCONJ
easat-9284	107	2	pn−1	pn−1	PROPN
easat-9284	107	3	t	t	PROPN
easat-9284	107	4	pn−1	pn−1	PROPN
easat-9284	107	5	)	)	PUNCT
easat-9284	108	1	+	+	CCONJ
easat-9284	109	1	c	c	X
easat-9284	109	2	(	(	PUNCT
easat-9284	109	3	pn	pn	NOUN
easat-9284	109	4	−	−	PROPN
easat-9284	109	5	t	t	PROPN
easat-9284	109	6	pn−1	pn−1	PROPN
easat-9284	110	1	+	+	CCONJ
easat-9284	110	2	pn−1	pn−1	PROPN
easat-9284	110	3	−	−	PROPN
easat-9284	110	4	t	t	PROPN
easat-9284	110	5	pn	pn	PROPN
easat-9284	110	6	)	)	PUNCT
easat-9284	110	7	.	.	PUNCT
easat-9284	111	1	||𝑝𝑛	||𝑝𝑛	X
easat-9284	111	2	−	−	NOUN
easat-9284	111	3	𝑇𝑝𝑛−1||	𝑇𝑝𝑛−1||	ADJ
easat-9284	111	4	≤	≤	NOUN
easat-9284	111	5	||𝑝𝑛	||𝑝𝑛	VERB
easat-9284	111	6	−	−	PROPN
easat-9284	111	7	𝑝𝑛−1||	𝑝𝑛−1||	NOUN
easat-9284	112	1	+	+	CCONJ
easat-9284	112	2	1	1	NUM
easat-9284	112	3	𝜆	𝜆	NOUN
easat-9284	112	4	||𝑝𝑛	||𝑝𝑛	NUM
easat-9284	112	5	−	−	NOUN
easat-9284	112	6	𝑝𝑛−1||	𝑝𝑛−1||	NOUN
easat-9284	112	7	=	=	PUNCT
easat-9284	113	1	(	(	PUNCT
easat-9284	113	2	1	1	NUM
easat-9284	113	3	+	+	NUM
easat-9284	113	4	1	1	NUM
easat-9284	113	5	𝜆	𝜆	NOUN
easat-9284	113	6	)	)	PUNCT
easat-9284	113	7	||𝑝𝑛	||𝑝𝑛	X
easat-9284	113	8	−	−	NOUN
easat-9284	114	1	𝑝𝑛−1||	𝑝𝑛−1||	NOUN
easat-9284	114	2	,	,	PUNCT
easat-9284	114	3	and	and	CCONJ
easat-9284	114	4	similar	similar	ADJ
easat-9284	114	5	for	for	ADP
easat-9284	114	6	other	other	ADJ
easat-9284	114	7	terms	term	NOUN
easat-9284	114	8	,	,	PUNCT
easat-9284	114	9	we	we	PRON
easat-9284	114	10	obtain	obtain	VERB
easat-9284	114	11	:	:	PUNCT
easat-9284	115	1	τ	τ	X
easat-9284	116	1	+	+	NUM
easat-9284	116	2	f	f	X
easat-9284	116	3	(	(	PUNCT
easat-9284	116	4	pn+1	pn+1	PROPN
easat-9284	116	5	−	−	PROPN
easat-9284	116	6	pn	pn	PROPN
easat-9284	116	7	)	)	PUNCT
easat-9284	116	8	≤	≤	PROPN
easat-9284	117	1	f	f	X
easat-9284	117	2	(	(	PUNCT
easat-9284	117	3	c	c	X
easat-9284	117	4	·	·	PUNCT
easat-9284	117	5	pn	pn	PROPN
easat-9284	118	1	−	−	PROPN
easat-9284	118	2	pn−1	pn−1	PROPN
easat-9284	118	3	)	)	PUNCT
easat-9284	118	4	,	,	PUNCT
easat-9284	118	5	for	for	ADP
easat-9284	118	6	some	some	DET
easat-9284	118	7	constant	constant	ADJ
easat-9284	118	8	c	c	NOUN
easat-9284	118	9	>	>	X
easat-9284	118	10	0	0	NUM
easat-9284	118	11	.	.	PUNCT
easat-9284	119	1	but	but	CCONJ
easat-9284	119	2	since	since	SCONJ
easat-9284	119	3	f	f	PROPN
easat-9284	119	4	is	be	AUX
easat-9284	119	5	strictly	strictly	ADV
easat-9284	119	6	increasing	increase	VERB
easat-9284	119	7	and	and	CCONJ
easat-9284	119	8	we	we	PRON
easat-9284	119	9	are	be	AUX
easat-9284	119	10	applying	apply	VERB
easat-9284	119	11	the	the	DET
easat-9284	119	12	contractive	contractive	ADJ
easat-9284	119	13	inequality	inequality	NOUN
easat-9284	119	14	with	with	ADP
easat-9284	119	15	a	a	DET
easat-9284	119	16	nonzero	nonzero	NOUN
easat-9284	119	17	τ	τ	X
easat-9284	119	18	,	,	PUNCT
easat-9284	119	19	we	we	PRON
easat-9284	119	20	rearrange	rearrange	VERB
easat-9284	119	21	:	:	PUNCT
easat-9284	119	22	f	f	PROPN
easat-9284	119	23	(	(	PUNCT
easat-9284	119	24	pn+1	pn+1	PROPN
easat-9284	119	25	−	−	PROPN
easat-9284	119	26	pn	pn	PROPN
easat-9284	119	27	)	)	PUNCT
easat-9284	119	28	≤	≤	PROPN
easat-9284	120	1	f	f	X
easat-9284	120	2	(	(	PUNCT
easat-9284	120	3	pn	pn	NOUN
easat-9284	120	4	−	−	PROPN
easat-9284	120	5	pn−1	pn−1	PROPN
easat-9284	120	6	)	)	PUNCT
easat-9284	121	1	−	−	PROPN
easat-9284	121	2	τ	τ	X
easat-9284	121	3	.	.	PUNCT
easat-9284	122	1	hence	hence	ADV
easat-9284	122	2	,	,	PUNCT
easat-9284	122	3	f	f	PROPN
easat-9284	122	4	(	(	PUNCT
easat-9284	122	5	pn+1	pn+1	PROPN
easat-9284	122	6	−	−	PROPN
easat-9284	122	7	pn	pn	PROPN
easat-9284	122	8	)	)	PUNCT
easat-9284	122	9	forms	form	VERB
easat-9284	122	10	a	a	DET
easat-9284	122	11	strictly	strictly	ADV
easat-9284	122	12	decreasing	decrease	VERB
easat-9284	122	13	sequence	sequence	NOUN
easat-9284	122	14	bounded	bound	VERB
easat-9284	122	15	above	above	ADV
easat-9284	122	16	by	by	ADP
easat-9284	122	17	f	f	PROPN
easat-9284	122	18	(	(	PUNCT
easat-9284	122	19	p1	p1	PROPN
easat-9284	122	20	−	−	PROPN
easat-9284	122	21	p0	p0	NOUN
easat-9284	122	22	)	)	PUNCT
easat-9284	122	23	−	−	PROPN
easat-9284	123	1	nτ	nτ	INTJ
easat-9284	123	2	→	→	SYM
easat-9284	123	3	−∞	−∞	NOUN
easat-9284	123	4	,	,	PUNCT
easat-9284	123	5	and	and	CCONJ
easat-9284	123	6	from	from	ADP
easat-9284	123	7	property	property	NOUN
easat-9284	123	8	(	(	PUNCT
easat-9284	123	9	f2	f2	PROPN
easat-9284	123	10	)	)	PUNCT
easat-9284	123	11	,	,	PUNCT
easat-9284	123	12	this	this	PRON
easat-9284	123	13	implies	imply	VERB
easat-9284	123	14	pn+1	pn+1	VERB
easat-9284	123	15	−	−	PROPN
easat-9284	123	16	pn	pn	PROPN
easat-9284	123	17	→	→	SYM
easat-9284	123	18	0	0	PROPN
easat-9284	123	19	.	.	PUNCT
easat-9284	124	1	we	we	PRON
easat-9284	124	2	now	now	ADV
easat-9284	124	3	establish	establish	VERB
easat-9284	124	4	the	the	DET
easat-9284	124	5	existence	existence	NOUN
easat-9284	124	6	and	and	CCONJ
easat-9284	124	7	uniqueness	uniqueness	NOUN
easat-9284	124	8	of	of	ADP
easat-9284	124	9	the	the	DET
easat-9284	124	10	fixed	fix	VERB
easat-9284	124	11	point	point	NOUN
easat-9284	124	12	for	for	ADP
easat-9284	124	13	this	this	DET
easat-9284	124	14	class	class	NOUN
easat-9284	124	15	of	of	ADP
easat-9284	124	16	mappings	mapping	NOUN
easat-9284	124	17	.	.	PUNCT
easat-9284	125	1	theorem	theorem	VERB
easat-9284	125	2	3.3	3.3	NUM
easat-9284	125	3	.	.	PUNCT
easat-9284	126	1	let	let	VERB
easat-9284	126	2	(	(	PUNCT
easat-9284	126	3	e	e	NOUN
easat-9284	126	4	,	,	PUNCT
easat-9284	126	5	.	.	PUNCT
easat-9284	126	6	)	)	PUNCT
easat-9284	127	1	be	be	AUX
easat-9284	127	2	a	a	DET
easat-9284	127	3	banach	banach	NOUN
easat-9284	127	4	space	space	NOUN
easat-9284	127	5	and	and	CCONJ
easat-9284	127	6	let	let	VERB
easat-9284	127	7	t	t	NOUN
easat-9284	127	8	:	:	PUNCT
easat-9284	127	9	e	e	X
easat-9284	127	10	→	→	PUNCT
easat-9284	127	11	e	e	X
easat-9284	127	12	be	be	AUX
easat-9284	127	13	an	an	DET
easat-9284	127	14	enriched	enriched	ADJ
easat-9284	127	15	hardy	hardy	ADJ
easat-9284	127	16	–	–	PUNCT
easat-9284	127	17	rogers	roger	NOUN
easat-9284	127	18	type	type	NOUN
easat-9284	127	19	f	f	NOUN
easat-9284	127	20	-	-	PUNCT
easat-9284	127	21	contraction	contraction	NOUN
easat-9284	127	22	as	as	ADP
easat-9284	127	23	in	in	ADP
easat-9284	127	24	definition	definition	NOUN
easat-9284	127	25	3.1	3.1	NUM
easat-9284	127	26	.	.	PUNCT
easat-9284	128	1	then	then	ADV
easat-9284	128	2	:	:	PUNCT
easat-9284	128	3	1	1	X
easat-9284	128	4	.	.	X
easat-9284	128	5	t	t	PROPN
easat-9284	128	6	has	have	VERB
easat-9284	128	7	a	a	DET
easat-9284	128	8	unique	unique	ADJ
easat-9284	128	9	fixed	fix	VERB
easat-9284	128	10	point	point	NOUN
easat-9284	128	11	t	t	PROPN
easat-9284	128	12	∈	∈	PROPN
easat-9284	128	13	e	e	NOUN
easat-9284	128	14	;	;	PUNCT
easat-9284	128	15	2	2	X
easat-9284	128	16	.	.	X
easat-9284	129	1	the	the	DET
easat-9284	129	2	iterative	iterative	NOUN
easat-9284	129	3	sequence	sequence	NOUN
easat-9284	129	4	defined	define	VERB
easat-9284	129	5	by	by	ADP
easat-9284	129	6	pn+1	pn+1	PROPN
easat-9284	129	7	=	=	SYM
easat-9284	129	8	(	(	PUNCT
easat-9284	129	9	1	1	NUM
easat-9284	129	10	−	−	NOUN
easat-9284	129	11	λ)pn	λ)pn	NOUN
easat-9284	129	12	+	+	CCONJ
easat-9284	129	13	λt	λt	ADP
easat-9284	129	14	pn	pn	PROPN
easat-9284	129	15	,	,	PUNCT
easat-9284	129	16	n	n	X
easat-9284	129	17	≥	≥	NOUN
easat-9284	129	18	0	0	NUM
easat-9284	129	19	,	,	PUNCT
easat-9284	129	20	λ	λ	PROPN
easat-9284	129	21	∈	∈	PROPN
easat-9284	129	22	(	(	PUNCT
easat-9284	129	23	0	0	NUM
easat-9284	129	24	,	,	PUNCT
easat-9284	129	25	1	1	NUM
easat-9284	129	26	]	]	PUNCT
easat-9284	129	27	,	,	PUNCT
easat-9284	129	28	converges	converge	VERB
easat-9284	129	29	to	to	ADP
easat-9284	129	30	the	the	DET
easat-9284	129	31	fixed	fixed	ADJ
easat-9284	129	32	point	point	NOUN
easat-9284	129	33	t	t	PROPN
easat-9284	129	34	for	for	ADP
easat-9284	129	35	any	any	DET
easat-9284	129	36	initial	initial	ADJ
easat-9284	129	37	point	point	NOUN
easat-9284	129	38	p0	p0	NOUN
easat-9284	129	39	∈	∈	PROPN
easat-9284	129	40	e	e	NOUN
easat-9284	129	41	;	;	PUNCT
easat-9284	129	42	295	295	NUM
easat-9284	129	43	edelweiss	edelweiss	PROPN
easat-9284	129	44	applied	apply	VERB
easat-9284	129	45	science	science	NOUN
easat-9284	129	46	and	and	CCONJ
easat-9284	129	47	technology	technology	NOUN
easat-9284	129	48	issn	issn	PROPN
easat-9284	129	49	:	:	PUNCT
easat-9284	129	50	2576	2576	NUM
easat-9284	129	51	-	-	SYM
easat-9284	129	52	8484	8484	NUM
easat-9284	129	53	vol	vol	NOUN
easat-9284	129	54	.	.	PROPN
easat-9284	130	1	9	9	NUM
easat-9284	130	2	,	,	PUNCT
easat-9284	130	3	no	no	INTJ
easat-9284	130	4	.	.	NOUN
easat-9284	130	5	8	8	NUM
easat-9284	130	6	:	:	PUNCT
easat-9284	130	7	291	291	NUM
easat-9284	130	8	-	-	SYM
easat-9284	130	9	299	299	NUM
easat-9284	130	10	,	,	PUNCT
easat-9284	130	11	2025	2025	NUM
easat-9284	130	12	doi	doi	NOUN
easat-9284	130	13	:	:	PUNCT
easat-9284	130	14	10.55214/2576	10.55214/2576	NUM
easat-9284	130	15	-	-	PUNCT
easat-9284	130	16	8484.v9i8.9284	8484.v9i8.9284	NOUN
easat-9284	130	17	©	©	PROPN
easat-9284	130	18	2025	2025	NUM
easat-9284	130	19	by	by	ADP
easat-9284	130	20	the	the	DET
easat-9284	130	21	author	author	NOUN
easat-9284	130	22	;	;	PUNCT
easat-9284	130	23	licensee	licensee	PROPN
easat-9284	130	24	learning	learning	PROPN
easat-9284	130	25	gate	gate	NOUN
easat-9284	130	26	li	li	PROPN
easat-9284	130	27	1	1	NUM
easat-9284	130	28	b0	b0	NOUN
easat-9284	130	29	+	+	PROPN
easat-9284	130	30	1	1	NUM
easat-9284	130	31	3	3	NUM
easat-9284	130	32	.	.	PUNCT
easat-9284	131	1	the	the	DET
easat-9284	131	2	following	follow	VERB
easat-9284	131	3	estimate	estimate	NOUN
easat-9284	131	4	holds	hold	VERB
easat-9284	131	5	:	:	PUNCT
easat-9284	131	6	pn+i−1	pn+i−1	VERB
easat-9284	131	7	−	−	PROPN
easat-9284	131	8	t	t	NOUN
easat-9284	131	9	≤	≤	NUM
easat-9284	131	10	1	1	NUM
easat-9284	131	11	−	−	NOUN
easat-9284	132	1	l	l	NOUN
easat-9284	132	2	pn	pn	NOUN
easat-9284	133	1	−	−	PROPN
easat-9284	133	2	pn−1	pn−1	PROPN
easat-9284	133	3	,	,	PUNCT
easat-9284	133	4	for	for	ADP
easat-9284	133	5	all	all	DET
easat-9284	133	6	n	n	PRON
easat-9284	133	7	≥	≥	NOUN
easat-9284	133	8	1	1	NUM
easat-9284	133	9	,	,	PUNCT
easat-9284	133	10	i	i	PRON
easat-9284	133	11	≥	≥	VERB
easat-9284	133	12	1	1	NUM
easat-9284	133	13	,	,	PUNCT
easat-9284	134	1	a	a	DET
easat-9284	134	2	+	+	NOUN
easat-9284	134	3	b	b	NOUN
easat-9284	134	4	+	+	CCONJ
easat-9284	134	5	c	c	NOUN
easat-9284	134	6	where	where	SCONJ
easat-9284	134	7	l	l	NOUN
easat-9284	134	8	=	=	NOUN
easat-9284	134	9	1	1	NUM
easat-9284	134	10	−	−	PROPN
easat-9284	134	11	b	b	X
easat-9284	134	12	–	–	PUNCT
easat-9284	134	13	c	c	NOUN
easat-9284	134	14	∈	∈	PROPN
easat-9284	134	15	(	(	PUNCT
easat-9284	134	16	0	0	NUM
easat-9284	134	17	,	,	PUNCT
easat-9284	134	18	1	1	NUM
easat-9284	134	19	)	)	PUNCT
easat-9284	134	20	.	.	PUNCT
easat-9284	135	1	proof	proof	NOUN
easat-9284	135	2	.	.	PUNCT
easat-9284	136	1	let	let	VERB
easat-9284	136	2	λ	λ	X
easat-9284	136	3	=	=	SYM
easat-9284	136	4	1	1	NUM
easat-9284	136	5	∈	∈	PROPN
easat-9284	136	6	(	(	PUNCT
easat-9284	136	7	0	0	NUM
easat-9284	136	8	,	,	PUNCT
easat-9284	136	9	1	1	NUM
easat-9284	136	10	]	]	PUNCT
easat-9284	136	11	.	.	PUNCT
easat-9284	137	1	define	define	VERB
easat-9284	137	2	the	the	DET
easat-9284	137	3	krasnoselskij	krasnoselskij	PROPN
easat-9284	137	4	iteration	iteration	NOUN
easat-9284	137	5	:	:	PUNCT
easat-9284	137	6	pn+1	pn+1	NOUN
easat-9284	137	7	=	=	SYM
easat-9284	137	8	(	(	PUNCT
easat-9284	137	9	1	1	NUM
easat-9284	137	10	−	−	NOUN
easat-9284	137	11	λ)pn	λ)pn	NOUN
easat-9284	137	12	+	+	CCONJ
easat-9284	137	13	λt	λt	ADP
easat-9284	137	14	pn	pn	PROPN
easat-9284	137	15	,	,	PUNCT
easat-9284	137	16	n	n	X
easat-9284	137	17	≥	≥	NOUN
easat-9284	137	18	0	0	NUM
easat-9284	137	19	.	.	PUNCT
easat-9284	138	1	we	we	PRON
easat-9284	138	2	denote	denote	VERB
easat-9284	138	3	this	this	PRON
easat-9284	138	4	averaged	average	VERB
easat-9284	138	5	mapping	mapping	NOUN
easat-9284	138	6	by	by	ADP
easat-9284	138	7	tλ(p	tλ(p	NOUN
easat-9284	138	8	)	)	PUNCT
easat-9284	138	9	:	:	PUNCT
easat-9284	139	1	=	=	SYM
easat-9284	139	2	(	(	PUNCT
easat-9284	139	3	1	1	NUM
easat-9284	139	4	−	−	NOUN
easat-9284	139	5	λ)p	λ)p	PUNCT
easat-9284	139	6	+	+	CCONJ
easat-9284	139	7	λt	λt	ADP
easat-9284	139	8	p	p	X
easat-9284	139	9	,	,	PUNCT
easat-9284	139	10	so	so	SCONJ
easat-9284	139	11	that	that	SCONJ
easat-9284	139	12	pn+1	pn+1	PROPN
easat-9284	139	13	=	=	SYM
easat-9284	139	14	tλpn	tλpn	VERB
easat-9284	139	15	.	.	PUNCT
easat-9284	140	1	let	let	VERB
easat-9284	140	2	p0	p0	PROPN
easat-9284	140	3	∈	∈	PROPN
easat-9284	140	4	e	e	NOUN
easat-9284	140	5	be	be	AUX
easat-9284	140	6	arbitrary	arbitrary	ADJ
easat-9284	140	7	.	.	PUNCT
easat-9284	141	1	consider	consider	VERB
easat-9284	141	2	the	the	DET
easat-9284	141	3	sequence	sequence	NOUN
easat-9284	141	4	[	[	X
easat-9284	141	5	7	7	X
easat-9284	141	6	]	]	PUNCT
easat-9284	141	7	defined	define	VERB
easat-9284	141	8	by	by	ADP
easat-9284	141	9	pn+1	pn+1	PROPN
easat-9284	141	10	=	=	SYM
easat-9284	141	11	tλpn	tλpn	VERB
easat-9284	141	12	.	.	PUNCT
easat-9284	142	1	for	for	ADP
easat-9284	142	2	any	any	DET
easat-9284	142	3	p	p	NOUN
easat-9284	142	4	,	,	PUNCT
easat-9284	142	5	q	q	PUNCT
easat-9284	142	6	∈	∈	PROPN
easat-9284	142	7	e	e	NOUN
easat-9284	142	8	,	,	PUNCT
easat-9284	142	9	we	we	PRON
easat-9284	142	10	note	note	VERB
easat-9284	142	11	that	that	SCONJ
easat-9284	142	12	tλp	tλp	NOUN
easat-9284	142	13	−	−	PROPN
easat-9284	143	1	tλq	tλq	NOUN
easat-9284	143	2	=	=	SYM
easat-9284	143	3	(	(	PUNCT
easat-9284	143	4	1	1	NUM
easat-9284	143	5	−	−	NOUN
easat-9284	143	6	λ)(p	λ)(p	NUM
easat-9284	143	7	−	−	PROPN
easat-9284	143	8	q	q	NOUN
easat-9284	143	9	)	)	PUNCT
easat-9284	144	1	+	+	CCONJ
easat-9284	144	2	λ(t	λ(t	NOUN
easat-9284	144	3	p	p	NOUN
easat-9284	144	4	−	−	PROPN
easat-9284	144	5	t	t	PROPN
easat-9284	144	6	q	q	NOUN
easat-9284	144	7	)	)	PUNCT
easat-9284	144	8	=	=	SYM
easat-9284	144	9	λ	λ	X
easat-9284	144	10	(	(	PUNCT
easat-9284	144	11	b0(p	b0(p	ADP
easat-9284	144	12	−	−	NOUN
easat-9284	144	13	q	q	NOUN
easat-9284	144	14	)	)	PUNCT
easat-9284	145	1	+	+	NUM
easat-9284	145	2	t	t	X
easat-9284	146	1	p	p	X
easat-9284	146	2	−	−	PROPN
easat-9284	146	3	t	t	PROPN
easat-9284	146	4	q	q	PROPN
easat-9284	146	5	)	)	PUNCT
easat-9284	146	6	,	,	PUNCT
easat-9284	146	7	which	which	PRON
easat-9284	146	8	implies	imply	VERB
easat-9284	146	9	:	:	PUNCT
easat-9284	146	10	tλp	tλp	VERB
easat-9284	146	11	−	−	PROPN
easat-9284	147	1	tλq	tλq	NOUN
easat-9284	147	2	=	=	SYM
easat-9284	147	3	λ	λ	X
easat-9284	147	4	b0(p	b0(p	ADP
easat-9284	147	5	−	−	NOUN
easat-9284	147	6	q	q	NOUN
easat-9284	147	7	)	)	PUNCT
easat-9284	148	1	+	+	NUM
easat-9284	148	2	t	t	X
easat-9284	148	3	p	p	X
easat-9284	148	4	−	−	PROPN
easat-9284	148	5	t	t	PROPN
easat-9284	148	6	q	q	NOUN
easat-9284	148	7	.	.	PUNCT
easat-9284	149	1	using	use	VERB
easat-9284	149	2	inequality	inequality	NOUN
easat-9284	149	3	(	(	PUNCT
easat-9284	149	4	1	1	NUM
easat-9284	149	5	)	)	PUNCT
easat-9284	149	6	and	and	CCONJ
easat-9284	149	7	the	the	DET
easat-9284	149	8	above	above	ADJ
easat-9284	149	9	expression	expression	NOUN
easat-9284	149	10	,	,	PUNCT
easat-9284	149	11	we	we	PRON
easat-9284	149	12	get	get	VERB
easat-9284	149	13	:	:	PUNCT
easat-9284	149	14	τ	τ	PROPN
easat-9284	150	1	+	+	NUM
easat-9284	150	2	f	f	X
easat-9284	150	3	(	(	PUNCT
easat-9284	150	4	tλp	tλp	NOUN
easat-9284	150	5	−	−	X
easat-9284	150	6	tλq	tλq	NOUN
easat-9284	150	7	)	)	PUNCT
easat-9284	150	8	=	=	PUNCT
easat-9284	151	1	τ	τ	PROPN
easat-9284	152	1	+	+	NUM
easat-9284	152	2	f	f	X
easat-9284	152	3	(	(	PUNCT
easat-9284	152	4	λ	λ	X
easat-9284	152	5	b0(p	b0(p	ADP
easat-9284	152	6	−	−	NOUN
easat-9284	152	7	q	q	NOUN
easat-9284	152	8	)	)	PUNCT
easat-9284	153	1	+	+	NUM
easat-9284	153	2	t	t	X
easat-9284	153	3	p	p	X
easat-9284	153	4	−	−	PROPN
easat-9284	153	5	t	t	PROPN
easat-9284	153	6	q	q	PROPN
easat-9284	154	1	)	)	PUNCT
easat-9284	154	2	≤	≤	NUM
easat-9284	154	3	f	f	X
easat-9284	154	4	(	(	PUNCT
easat-9284	154	5	a	a	DET
easat-9284	154	6	p	p	NOUN
easat-9284	154	7	−	−	NOUN
easat-9284	154	8	q	q	NOUN
easat-9284	155	1	+	+	NUM
easat-9284	155	2	b	b	X
easat-9284	155	3	(	(	PUNCT
easat-9284	155	4	p	p	NOUN
easat-9284	155	5	−	−	PROPN
easat-9284	155	6	t	t	NOUN
easat-9284	156	1	p	p	PROPN
easat-9284	157	1	+	+	NOUN
easat-9284	157	2	q	q	NOUN
easat-9284	157	3	−	−	PROPN
easat-9284	157	4	t	t	PROPN
easat-9284	157	5	q	q	PROPN
easat-9284	157	6	)	)	PUNCT
easat-9284	158	1	+	+	CCONJ
easat-9284	158	2	c	c	X
easat-9284	158	3	(	(	PUNCT
easat-9284	158	4	p	p	NOUN
easat-9284	158	5	−	−	PROPN
easat-9284	158	6	t	t	NOUN
easat-9284	158	7	q	q	PROPN
easat-9284	159	1	+	+	CCONJ
easat-9284	159	2	q	q	NOUN
easat-9284	160	1	−	−	PROPN
easat-9284	160	2	t	t	PROPN
easat-9284	160	3	p	p	NOUN
easat-9284	160	4	)	)	PUNCT
easat-9284	160	5	)	)	PUNCT
easat-9284	160	6	.	.	PUNCT
easat-9284	161	1	using	use	VERB
easat-9284	161	2	the	the	DET
easat-9284	161	3	convexity	convexity	NOUN
easat-9284	161	4	of	of	ADP
easat-9284	161	5	norms	norm	NOUN
easat-9284	161	6	and	and	CCONJ
easat-9284	161	7	the	the	DET
easat-9284	161	8	structure	structure	NOUN
easat-9284	161	9	of	of	ADP
easat-9284	161	10	tλ	tλ	ADP
easat-9284	161	11	,	,	PUNCT
easat-9284	161	12	we	we	PRON
easat-9284	161	13	observe	observe	VERB
easat-9284	161	14	:	:	PUNCT
easat-9284	161	15	p	p	X
easat-9284	161	16	−	−	PROPN
easat-9284	161	17	t	t	NOUN
easat-9284	161	18	p	p	X
easat-9284	161	19	=	=	PUNCT
easat-9284	161	20	λ	λ	X
easat-9284	161	21	p	p	NOUN
easat-9284	161	22	−	−	PROPN
easat-9284	161	23	tλp	tλp	NOUN
easat-9284	161	24	,	,	PUNCT
easat-9284	161	25	p	p	NOUN
easat-9284	161	26	−	−	PROPN
easat-9284	161	27	t	t	PROPN
easat-9284	161	28	q	q	PROPN
easat-9284	161	29	≤	≤	PROPN
easat-9284	162	1	p	p	DET
easat-9284	162	2	−	−	PROPN
easat-9284	162	3	tλq	tλq	NOUN
easat-9284	163	1	+	+	CCONJ
easat-9284	164	1	tλq	tλq	NOUN
easat-9284	164	2	−	−	PROPN
easat-9284	164	3	t	t	NOUN
easat-9284	164	4	q	q	PROPN
easat-9284	165	1	=	=	PUNCT
easat-9284	165	2	p	p	NOUN
easat-9284	165	3	−	−	PROPN
easat-9284	165	4	tλq	tλq	NOUN
easat-9284	166	1	+	+	CCONJ
easat-9284	166	2	λ	λ	X
easat-9284	166	3	t	t	NOUN
easat-9284	166	4	q	q	X
easat-9284	166	5	−	−	PROPN
easat-9284	166	6	tλq	tλq	NOUN
easat-9284	167	1	=	=	NOUN
easat-9284	167	2	p	p	NOUN
easat-9284	167	3	−	−	PROPN
easat-9284	167	4	tλq	tλq	NOUN
easat-9284	167	5	+	+	CCONJ
easat-9284	167	6	(	(	PUNCT
easat-9284	167	7	1	1	NUM
easat-9284	167	8	−	−	PROPN
easat-9284	167	9	λ	λ	NOUN
easat-9284	167	10	)	)	PUNCT
easat-9284	167	11	q	q	NOUN
easat-9284	168	1	−	−	PROPN
easat-9284	168	2	t	t	PROPN
easat-9284	168	3	q	q	X
easat-9284	168	4	.	.	PUNCT
easat-9284	169	1	applying	apply	VERB
easat-9284	169	2	this	this	DET
easat-9284	169	3	process	process	NOUN
easat-9284	169	4	iteratively	iteratively	ADV
easat-9284	169	5	,	,	PUNCT
easat-9284	169	6	we	we	PRON
easat-9284	169	7	can	can	AUX
easat-9284	169	8	show	show	VERB
easat-9284	169	9	that	that	SCONJ
easat-9284	169	10	:	:	PUNCT
easat-9284	169	11	f	f	X
easat-9284	169	12	(	(	PUNCT
easat-9284	169	13	pn+1	pn+1	PROPN
easat-9284	169	14	−	−	PROPN
easat-9284	169	15	pn	pn	PROPN
easat-9284	169	16	)	)	PUNCT
easat-9284	169	17	≤	≤	PROPN
easat-9284	170	1	f	f	X
easat-9284	170	2	(	(	PUNCT
easat-9284	170	3	pn	pn	NOUN
easat-9284	170	4	−	−	PROPN
easat-9284	170	5	pn−1	pn−1	PROPN
easat-9284	170	6	)	)	PUNCT
easat-9284	171	1	−	−	PROPN
easat-9284	171	2	τ	τ	X
easat-9284	171	3	.	.	PUNCT
easat-9284	172	1	by	by	ADP
easat-9284	172	2	induction	induction	NOUN
easat-9284	172	3	:	:	PUNCT
easat-9284	172	4	f	f	PROPN
easat-9284	172	5	(	(	PUNCT
easat-9284	172	6	pn+1	pn+1	PROPN
easat-9284	172	7	−	−	PROPN
easat-9284	172	8	pn	pn	PROPN
easat-9284	172	9	)	)	PUNCT
easat-9284	172	10	≤	≤	PROPN
easat-9284	173	1	f	f	X
easat-9284	174	1	(	(	PUNCT
easat-9284	174	2	p1	p1	PROPN
easat-9284	174	3	−	−	PROPN
easat-9284	174	4	p0	p0	NOUN
easat-9284	174	5	)	)	PUNCT
easat-9284	175	1	−	−	ADP
easat-9284	176	1	nτ	nτ	NOUN
easat-9284	176	2	.	.	PUNCT
easat-9284	177	1	taking	take	VERB
easat-9284	177	2	limits	limit	NOUN
easat-9284	177	3	and	and	CCONJ
easat-9284	177	4	using	use	VERB
easat-9284	177	5	property	property	NOUN
easat-9284	177	6	(	(	PUNCT
easat-9284	177	7	f2	f2	PROPN
easat-9284	177	8	)	)	PUNCT
easat-9284	177	9	of	of	ADP
easat-9284	177	10	f	f	PROPN
easat-9284	177	11	,	,	PUNCT
easat-9284	177	12	we	we	PRON
easat-9284	177	13	deduce	deduce	VERB
easat-9284	177	14	:	:	PUNCT
easat-9284	177	15	pn+1	pn+1	VERB
easat-9284	177	16	−	−	PROPN
easat-9284	177	17	pn	pn	PROPN
easat-9284	177	18	→	→	SYM
easat-9284	177	19	0	0	NUM
easat-9284	178	1	and	and	CCONJ
easat-9284	178	2	{	{	PUNCT
easat-9284	178	3	pn	pn	NOUN
easat-9284	178	4	}	}	PUNCT
easat-9284	178	5	is	be	AUX
easat-9284	178	6	a	a	DET
easat-9284	178	7	cauchy	cauchy	ADJ
easat-9284	178	8	sequence	sequence	NOUN
easat-9284	178	9	.	.	PUNCT
easat-9284	179	1	since	since	SCONJ
easat-9284	179	2	e	e	PROPN
easat-9284	179	3	is	be	AUX
easat-9284	179	4	complete	complete	ADJ
easat-9284	179	5	,	,	PUNCT
easat-9284	179	6	there	there	PRON
easat-9284	179	7	exists	exist	VERB
easat-9284	179	8	t	t	PROPN
easat-9284	179	9	∈	∈	PROPN
easat-9284	179	10	e	e	NOUN
easat-9284	179	11	such	such	ADJ
easat-9284	179	12	that	that	DET
easat-9284	179	13	pn	pn	PROPN
easat-9284	179	14	→	→	SYM
easat-9284	179	15	t.	t.	X
easat-9284	179	16	the	the	DET
easat-9284	179	17	continuity	continuity	NOUN
easat-9284	179	18	of	of	ADP
easat-9284	179	19	tλ	tλ	PRON
easat-9284	179	20	implies	imply	VERB
easat-9284	179	21	tλt	tλt	PROPN
easat-9284	179	22	=	=	SYM
easat-9284	179	23	t	t	PROPN
easat-9284	179	24	,	,	PUNCT
easat-9284	179	25	hence	hence	ADV
easat-9284	179	26	:	:	PUNCT
easat-9284	179	27	tt	tt	PROPN
easat-9284	179	28	=	=	PUNCT
easat-9284	179	29	t.	t.	PROPN
easat-9284	179	30	to	to	PART
easat-9284	179	31	prove	prove	VERB
easat-9284	179	32	uniqueness	uniqueness	NOUN
easat-9284	179	33	,	,	PUNCT
easat-9284	179	34	suppose	suppose	VERB
easat-9284	179	35	t1	t1	NOUN
easat-9284	179	36	,	,	PUNCT
easat-9284	179	37	t2	t2	PROPN
easat-9284	179	38	∈	∈	PROPN
easat-9284	179	39	e	e	NOUN
easat-9284	179	40	are	be	AUX
easat-9284	179	41	fixed	fix	VERB
easat-9284	179	42	points	point	NOUN
easat-9284	179	43	.	.	PUNCT
easat-9284	180	1	then	then	ADV
easat-9284	180	2	from	from	ADP
easat-9284	180	3	(	(	PUNCT
easat-9284	180	4	1	1	NUM
easat-9284	180	5	)	)	PUNCT
easat-9284	180	6	,	,	PUNCT
easat-9284	180	7	we	we	PRON
easat-9284	180	8	get	get	VERB
easat-9284	180	9	:	:	PUNCT
easat-9284	180	10	τ	τ	PROPN
easat-9284	181	1	+	+	NUM
easat-9284	181	2	f	f	X
easat-9284	181	3	(	(	PUNCT
easat-9284	181	4	λ	λ	PROPN
easat-9284	181	5	b0(t1	b0(t1	NOUN
easat-9284	181	6	−	−	PROPN
easat-9284	181	7	t2	t2	NOUN
easat-9284	181	8	)	)	PUNCT
easat-9284	181	9	)	)	PUNCT
easat-9284	182	1	≤	≤	NUM
easat-9284	182	2	f	f	X
easat-9284	182	3	(	(	PUNCT
easat-9284	182	4	a	a	DET
easat-9284	182	5	t1	t1	NOUN
easat-9284	182	6	−	−	PROPN
easat-9284	182	7	t2	t2	NOUN
easat-9284	182	8	+	+	CCONJ
easat-9284	182	9	0	0	NUM
easat-9284	182	10	)	)	PUNCT
easat-9284	182	11	=	=	SYM
easat-9284	183	1	f	f	X
easat-9284	183	2	(	(	PUNCT
easat-9284	183	3	a	a	DET
easat-9284	183	4	t1	t1	NOUN
easat-9284	183	5	−	−	PROPN
easat-9284	183	6	t2	t2	PROPN
easat-9284	183	7	)	)	PUNCT
easat-9284	183	8	.	.	PUNCT
easat-9284	184	1	but	but	CCONJ
easat-9284	184	2	since	since	SCONJ
easat-9284	184	3	a	a	DET
easat-9284	184	4	<	<	X
easat-9284	184	5	1	1	NUM
easat-9284	184	6	,	,	PUNCT
easat-9284	184	7	and	and	CCONJ
easat-9284	184	8	f	f	PROPN
easat-9284	184	9	is	be	AUX
easat-9284	184	10	strictly	strictly	ADV
easat-9284	184	11	increasing	increase	VERB
easat-9284	184	12	,	,	PUNCT
easat-9284	184	13	this	this	PRON
easat-9284	184	14	implies	imply	VERB
easat-9284	184	15	a	a	DET
easat-9284	184	16	contradiction	contradiction	NOUN
easat-9284	184	17	unless	unless	SCONJ
easat-9284	184	18	t1	t1	NOUN
easat-9284	184	19	−	−	PROPN
easat-9284	184	20	t2	t2	NOUN
easat-9284	184	21	=	=	SYM
easat-9284	184	22	0	0	NUM
easat-9284	184	23	,	,	PUNCT
easat-9284	184	24	i.e.	i.e.	X
easat-9284	184	25	,	,	PUNCT
easat-9284	184	26	t1	t1	NOUN
easat-9284	184	27	=	=	NOUN
easat-9284	184	28	t2	t2	PROPN
easat-9284	184	29	.	.	PUNCT
easat-9284	185	1	hence	hence	ADV
easat-9284	185	2	,	,	PUNCT
easat-9284	185	3	the	the	DET
easat-9284	185	4	fixed	fix	VERB
easat-9284	185	5	point	point	NOUN
easat-9284	185	6	is	be	AUX
easat-9284	185	7	unique	unique	ADJ
easat-9284	185	8	.	.	PUNCT
easat-9284	186	1	for	for	ADP
easat-9284	186	2	the	the	DET
easat-9284	186	3	convergence	convergence	NOUN
easat-9284	186	4	rate	rate	NOUN
easat-9284	186	5	,	,	PUNCT
easat-9284	186	6	we	we	PRON
easat-9284	186	7	use	use	VERB
easat-9284	186	8	the	the	DET
easat-9284	186	9	inequality	inequality	NOUN
easat-9284	186	10	structure	structure	NOUN
easat-9284	186	11	and	and	CCONJ
easat-9284	186	12	apply	apply	VERB
easat-9284	186	13	techniques	technique	NOUN
easat-9284	186	14	similar	similar	ADJ
easat-9284	186	15	to	to	ADP
easat-9284	186	16	berinde	berinde	NOUN
easat-9284	186	17	[	[	X
easat-9284	186	18	5	5	NUM
easat-9284	186	19	]	]	PUNCT
easat-9284	186	20	obtaining	obtaining	NOUN
easat-9284	186	21	:	:	PUNCT
easat-9284	186	22	example	example	NOUN
easat-9284	186	23	3.4	3.4	NUM
easat-9284	186	24	.	.	PUNCT
easat-9284	187	1	let	let	VERB
easat-9284	187	2	e	e	NOUN
easat-9284	187	3	=	=	SYM
easat-9284	187	4	rn	rn	PROPN
easat-9284	187	5	with	with	ADP
easat-9284	187	6	the	the	DET
easat-9284	187	7	standard	standard	ADJ
easat-9284	187	8	euclidean	euclidean	ADJ
easat-9284	187	9	norm	norm	NOUN
easat-9284	187	10	·	·	PUNCT
easat-9284	187	11	,	,	PUNCT
easat-9284	187	12	which	which	PRON
easat-9284	187	13	forms	form	VERB
easat-9284	187	14	a	a	DET
easat-9284	187	15	banach	banach	NOUN
easat-9284	187	16	space	space	NOUN
easat-9284	187	17	.	.	PUNCT
easat-9284	188	1	define	define	VERB
easat-9284	188	2	the	the	DET
easat-9284	188	3	mapping	mapping	NOUN
easat-9284	188	4	t	t	NOUN
easat-9284	188	5	:	:	PUNCT
easat-9284	188	6	e	e	X
easat-9284	188	7	→	→	SYM
easat-9284	188	8	e	e	PROPN
easat-9284	188	9	as	as	ADP
easat-9284	188	10	t	t	PROPN
easat-9284	188	11	(	(	PUNCT
easat-9284	188	12	p	p	NOUN
easat-9284	188	13	)	)	PUNCT
easat-9284	188	14	=	=	SYM
easat-9284	188	15	αp	αp	NOUN
easat-9284	188	16	,	,	PUNCT
easat-9284	188	17	with	with	ADP
easat-9284	188	18	α	α	PROPN
easat-9284	188	19	∈	∈	PROPN
easat-9284	188	20	(	(	PUNCT
easat-9284	188	21	0	0	NUM
easat-9284	188	22	,	,	PUNCT
easat-9284	188	23	1	1	NUM
easat-9284	188	24	)	)	PUNCT
easat-9284	188	25	,	,	PUNCT
easat-9284	188	26	and	and	CCONJ
easat-9284	188	27	the	the	DET
easat-9284	188	28	control	control	NOUN
easat-9284	188	29	function	function	NOUN
easat-9284	188	30	f	f	PROPN
easat-9284	188	31	:	:	PUNCT
easat-9284	188	32	r+	r+	X
easat-9284	188	33	→	→	PUNCT
easat-9284	188	34	r	r	NOUN
easat-9284	188	35	as	as	ADP
easat-9284	188	36	296	296	NUM
easat-9284	188	37	edelweiss	edelweiss	PROPN
easat-9284	188	38	applied	apply	VERB
easat-9284	188	39	science	science	NOUN
easat-9284	188	40	and	and	CCONJ
easat-9284	188	41	technology	technology	NOUN
easat-9284	188	42	issn	issn	PROPN
easat-9284	188	43	:	:	PUNCT
easat-9284	188	44	2576	2576	NUM
easat-9284	188	45	-	-	SYM
easat-9284	188	46	8484	8484	NUM
easat-9284	188	47	vol	vol	NOUN
easat-9284	188	48	.	.	PROPN
easat-9284	189	1	9	9	NUM
easat-9284	189	2	,	,	PUNCT
easat-9284	189	3	no	no	INTJ
easat-9284	189	4	.	.	NOUN
easat-9284	189	5	8	8	NUM
easat-9284	189	6	:	:	PUNCT
easat-9284	189	7	291	291	NUM
easat-9284	189	8	-	-	SYM
easat-9284	189	9	299	299	NUM
easat-9284	189	10	,	,	PUNCT
easat-9284	189	11	2025	2025	NUM
easat-9284	189	12	doi	doi	NOUN
easat-9284	189	13	:	:	PUNCT
easat-9284	189	14	10.55214/2576	10.55214/2576	NUM
easat-9284	189	15	-	-	PUNCT
easat-9284	189	16	8484.v9i8.9284	8484.v9i8.9284	NOUN
easat-9284	189	17	©	©	PROPN
easat-9284	189	18	2025	2025	NUM
easat-9284	189	19	by	by	ADP
easat-9284	189	20	the	the	DET
easat-9284	189	21	author	author	NOUN
easat-9284	189	22	;	;	PUNCT
easat-9284	189	23	licensee	licensee	PROPN
easat-9284	189	24	learning	learn	VERB
easat-9284	189	25	gate	gate	PROPN
easat-9284	189	26	f	f	PROPN
easat-9284	189	27	(	(	PUNCT
easat-9284	189	28	ζ	ζ	NOUN
easat-9284	189	29	)	)	PUNCT
easat-9284	189	30	=	=	PUNCT
easat-9284	189	31	ln	ln	ADJ
easat-9284	189	32	ζ	ζ	NOUN
easat-9284	189	33	.	.	PUNCT
easat-9284	190	1	clearly	clearly	ADV
easat-9284	190	2	,	,	PUNCT
easat-9284	190	3	f	f	PROPN
easat-9284	190	4	∈	∈	PROPN
easat-9284	190	5	f1	f1	NOUN
easat-9284	190	6	since	since	SCONJ
easat-9284	190	7	•	•	NUM
easat-9284	190	8	f	f	PROPN
easat-9284	190	9	is	be	AUX
easat-9284	190	10	strictly	strictly	ADV
easat-9284	190	11	increasing	increase	VERB
easat-9284	190	12	,	,	PUNCT
easat-9284	190	13	•	•	NUM
easat-9284	190	14	limζ→0	limζ→0	PROPN
easat-9284	190	15	+	+	PROPN
easat-9284	190	16	f	f	X
easat-9284	190	17	(	(	PUNCT
easat-9284	190	18	ζ	ζ	NOUN
easat-9284	190	19	)	)	PUNCT
easat-9284	190	20	=	=	SYM
easat-9284	190	21	−∞	−∞	NOUN
easat-9284	190	22	,	,	PUNCT
easat-9284	190	23	and	and	CCONJ
easat-9284	190	24	•	•	NUM
easat-9284	190	25	limζ→0	limζ→0	PROPN
easat-9284	190	26	+	+	NOUN
easat-9284	190	27	ζkf	ζkf	NOUN
easat-9284	190	28	(	(	PUNCT
easat-9284	190	29	ζ	ζ	NOUN
easat-9284	190	30	)	)	PUNCT
easat-9284	190	31	=	=	SYM
easat-9284	190	32	0	0	NUM
easat-9284	190	33	for	for	ADP
easat-9284	190	34	some	some	DET
easat-9284	190	35	k	k	PROPN
easat-9284	190	36	∈	∈	PROPN
easat-9284	190	37	(	(	PUNCT
easat-9284	190	38	0	0	NUM
easat-9284	190	39	,	,	PUNCT
easat-9284	190	40	1	1	NUM
easat-9284	190	41	)	)	PUNCT
easat-9284	190	42	.	.	PUNCT
easat-9284	191	1	let	let	VERB
easat-9284	191	2	constants	constant	NOUN
easat-9284	191	3	be	be	AUX
easat-9284	191	4	chosen	choose	VERB
easat-9284	191	5	as	as	ADP
easat-9284	191	6	a	a	DET
easat-9284	191	7	,	,	PUNCT
easat-9284	191	8	b	b	NOUN
easat-9284	191	9	,	,	PUNCT
easat-9284	191	10	c	c	PROPN
easat-9284	191	11	∈	∈	PROPN
easat-9284	192	1	[	[	X
easat-9284	192	2	0	0	NUM
easat-9284	192	3	,	,	PUNCT
easat-9284	192	4	1),b0	1),b0	NUM
easat-9284	192	5	>	>	X
easat-9284	192	6	0,τ	0,τ	X
easat-9284	192	7	>	>	X
easat-9284	192	8	0	0	PUNCT
easat-9284	192	9	with	with	ADP
easat-9284	192	10	a	a	DET
easat-9284	192	11	+	+	NOUN
easat-9284	192	12	2b	2b	NUM
easat-9284	192	13	+	+	CCONJ
easat-9284	192	14	2c	2c	NOUN
easat-9284	192	15	<	<	X
easat-9284	192	16	1	1	NUM
easat-9284	192	17	.	.	PUNCT
easat-9284	193	1	we	we	PRON
easat-9284	193	2	now	now	ADV
easat-9284	193	3	prove	prove	VERB
easat-9284	193	4	that	that	SCONJ
easat-9284	193	5	t	t	PROPN
easat-9284	193	6	satisfies	satisfy	VERB
easat-9284	193	7	the	the	DET
easat-9284	193	8	enriched	enriched	ADJ
easat-9284	193	9	hardy	hardy	ADJ
easat-9284	193	10	–	–	PUNCT
easat-9284	193	11	rogers	roger	NOUN
easat-9284	193	12	type	type	NOUN
easat-9284	193	13	f	f	NOUN
easat-9284	193	14	-	-	PUNCT
easat-9284	193	15	contraction	contraction	NOUN
easat-9284	193	16	condition	condition	NOUN
easat-9284	193	17	globally	globally	ADV
easat-9284	193	18	,	,	PUNCT
easat-9284	193	19	i.e.	i.e.	X
easat-9284	193	20	,	,	PUNCT
easat-9284	193	21	for	for	ADP
easat-9284	193	22	all	all	DET
easat-9284	193	23	p	p	NOUN
easat-9284	193	24	,	,	PUNCT
easat-9284	193	25	q	q	PROPN
easat-9284	193	26	∈	∈	PROPN
easat-9284	193	27	rn	rn	PROPN
easat-9284	193	28	,	,	PUNCT
easat-9284	193	29	p	p	X
easat-9284	193	30	/=	/=	PROPN
easat-9284	193	31	q	q	NOUN
easat-9284	193	32	,	,	PUNCT
easat-9284	193	33	the	the	DET
easat-9284	193	34	inequality	inequality	NOUN
easat-9284	193	35	holds	hold	VERB
easat-9284	193	36	.	.	PUNCT
easat-9284	194	1	we	we	PRON
easat-9284	194	2	have	have	VERB
easat-9284	194	3	that	that	DET
easat-9284	194	4	p	p	PROPN
easat-9284	194	5	−	−	PROPN
easat-9284	194	6	t	t	NOUN
easat-9284	194	7	(	(	PUNCT
easat-9284	194	8	p	p	NOUN
easat-9284	194	9	)	)	PUNCT
easat-9284	194	10	=	=	PUNCT
easat-9284	194	11	(	(	PUNCT
easat-9284	194	12	1	1	NUM
easat-9284	194	13	−	−	PROPN
easat-9284	194	14	α	α	NOUN
easat-9284	194	15	)	)	PUNCT
easat-9284	194	16	p	p	NOUN
easat-9284	194	17	,	,	PUNCT
easat-9284	194	18	q	q	PROPN
easat-9284	194	19	−	−	PROPN
easat-9284	194	20	t	t	PROPN
easat-9284	194	21	(	(	PUNCT
easat-9284	194	22	q	q	X
easat-9284	194	23	)	)	PUNCT
easat-9284	194	24	=	=	SYM
easat-9284	194	25	(	(	PUNCT
easat-9284	194	26	1	1	NUM
easat-9284	194	27	−	−	PROPN
easat-9284	194	28	α	α	NOUN
easat-9284	194	29	)	)	PUNCT
easat-9284	194	30	q	q	NOUN
easat-9284	194	31	.	.	PUNCT
easat-9284	195	1	also	also	ADV
easat-9284	195	2	,	,	PUNCT
easat-9284	195	3	using	use	VERB
easat-9284	195	4	the	the	DET
easat-9284	195	5	triangle	triangle	NOUN
easat-9284	195	6	inequality	inequality	NOUN
easat-9284	195	7	:	:	PUNCT
easat-9284	195	8	p	p	PROPN
easat-9284	195	9	−	−	PROPN
easat-9284	195	10	t	t	PROPN
easat-9284	195	11	(	(	PUNCT
easat-9284	195	12	q	q	X
easat-9284	195	13	)	)	PUNCT
easat-9284	195	14	=	=	SYM
easat-9284	196	1	p	p	NOUN
easat-9284	196	2	−	−	PROPN
easat-9284	196	3	αq	αq	INTJ
easat-9284	196	4	≤	≤	NOUN
easat-9284	197	1	p	p	DET
easat-9284	197	2	−	−	PROPN
easat-9284	197	3	q	q	NOUN
easat-9284	198	1	+	+	CCONJ
easat-9284	198	2	(	(	PUNCT
easat-9284	198	3	1	1	NUM
easat-9284	198	4	−	−	PROPN
easat-9284	198	5	α	α	NOUN
easat-9284	198	6	)	)	PUNCT
easat-9284	198	7	q	q	NOUN
easat-9284	198	8	,	,	PUNCT
easat-9284	198	9	q	q	PROPN
easat-9284	198	10	−	−	PROPN
easat-9284	198	11	t	t	PROPN
easat-9284	198	12	(	(	PUNCT
easat-9284	198	13	p	p	NOUN
easat-9284	198	14	)	)	PUNCT
easat-9284	198	15	=	=	PUNCT
easat-9284	198	16	q	q	NOUN
easat-9284	199	1	−	−	NOUN
easat-9284	199	2	αp	αp	VERB
easat-9284	199	3	≤	≤	ADV
easat-9284	200	1	p	p	DET
easat-9284	200	2	−	−	PROPN
easat-9284	200	3	q	q	NOUN
easat-9284	201	1	+	+	CCONJ
easat-9284	201	2	(	(	PUNCT
easat-9284	201	3	1	1	NUM
easat-9284	201	4	−	−	NOUN
easat-9284	201	5	α	α	X
easat-9284	201	6	)	)	PUNCT
easat-9284	201	7	p	p	NOUN
easat-9284	201	8	.	.	PUNCT
easat-9284	202	1	thus	thus	ADV
easat-9284	202	2	,	,	PUNCT
easat-9284	202	3	the	the	DET
easat-9284	202	4	rhs	rhs	PROPN
easat-9284	202	5	expression	expression	NOUN
easat-9284	202	6	becomes	become	VERB
easat-9284	202	7	:	:	PUNCT
easat-9284	202	8	f	f	PROPN
easat-9284	202	9	a	a	DET
easat-9284	202	10	p	p	NOUN
easat-9284	202	11	−	−	PROPN
easat-9284	202	12	q	q	NOUN
easat-9284	203	1	+	+	CCONJ
easat-9284	203	2	b(1	b(1	PROPN
easat-9284	203	3	−	−	PROPN
easat-9284	203	4	α	α	NOUN
easat-9284	203	5	)	)	PUNCT
easat-9284	203	6	(	(	PUNCT
easat-9284	203	7	p	p	X
easat-9284	203	8	+	+	NOUN
easat-9284	203	9	q	q	NOUN
easat-9284	203	10	)	)	PUNCT
easat-9284	204	1	+	+	ADP
easat-9284	204	2	c	c	X
easat-9284	204	3	(	(	PUNCT
easat-9284	204	4	p	p	NOUN
easat-9284	204	5	−	−	PROPN
easat-9284	204	6	t	t	NOUN
easat-9284	204	7	(	(	PUNCT
easat-9284	204	8	q	q	X
easat-9284	204	9	)	)	PUNCT
easat-9284	204	10	+	+	CCONJ
easat-9284	204	11	q	q	PROPN
easat-9284	204	12	−	−	PROPN
easat-9284	204	13	t	t	PROPN
easat-9284	204	14	(	(	PUNCT
easat-9284	204	15	p	p	NOUN
easat-9284	204	16	)	)	PUNCT
easat-9284	204	17	)	)	PUNCT
easat-9284	204	18	.	.	PUNCT
easat-9284	205	1	bounding	bound	VERB
easat-9284	205	2	the	the	DET
easat-9284	205	3	last	last	ADJ
easat-9284	205	4	two	two	NUM
easat-9284	205	5	terms	term	NOUN
easat-9284	205	6	using	use	VERB
easat-9284	205	7	the	the	DET
easat-9284	205	8	inequalities	inequality	NOUN
easat-9284	205	9	above	above	ADV
easat-9284	205	10	,	,	PUNCT
easat-9284	205	11	we	we	PRON
easat-9284	205	12	get	get	VERB
easat-9284	205	13	:	:	PUNCT
easat-9284	205	14	p	p	PROPN
easat-9284	205	15	−	−	PROPN
easat-9284	205	16	t	t	NOUN
easat-9284	205	17	(	(	PUNCT
easat-9284	205	18	q	q	X
easat-9284	205	19	)	)	PUNCT
easat-9284	206	1	+	+	CCONJ
easat-9284	206	2	q	q	PROPN
easat-9284	206	3	−	−	PROPN
easat-9284	206	4	t	t	PROPN
easat-9284	206	5	(	(	PUNCT
easat-9284	206	6	p	p	NOUN
easat-9284	206	7	)	)	PUNCT
easat-9284	206	8	≤	≤	NUM
easat-9284	206	9	2	2	NUM
easat-9284	206	10	p	p	NOUN
easat-9284	206	11	−	−	PROPN
easat-9284	206	12	q	q	NOUN
easat-9284	207	1	+	+	CCONJ
easat-9284	207	2	(	(	PUNCT
easat-9284	207	3	1	1	NUM
easat-9284	207	4	−	−	PROPN
easat-9284	207	5	α	α	X
easat-9284	207	6	)	)	PUNCT
easat-9284	207	7	(	(	PUNCT
easat-9284	207	8	p	p	X
easat-9284	207	9	+	+	NOUN
easat-9284	207	10	q	q	NOUN
easat-9284	207	11	)	)	PUNCT
easat-9284	207	12	.	.	PUNCT
easat-9284	208	1	so	so	ADV
easat-9284	208	2	the	the	DET
easat-9284	208	3	full	full	ADJ
easat-9284	208	4	rhs	rhs	PROPN
easat-9284	208	5	is	be	AUX
easat-9284	208	6	bounded	bound	VERB
easat-9284	208	7	below	below	ADP
easat-9284	208	8	by	by	ADP
easat-9284	208	9	:	:	PUNCT
easat-9284	208	10	f	f	X
easat-9284	208	11	(	(	PUNCT
easat-9284	208	12	(	(	PUNCT
easat-9284	208	13	a	a	DET
easat-9284	208	14	+	+	NOUN
easat-9284	208	15	2c	2c	NUM
easat-9284	208	16	)	)	PUNCT
easat-9284	208	17	p	p	NOUN
easat-9284	208	18	−	−	PROPN
easat-9284	208	19	q	q	NOUN
easat-9284	209	1	+	+	NUM
easat-9284	209	2	(	(	PUNCT
easat-9284	209	3	b	b	NOUN
easat-9284	209	4	+	+	NOUN
easat-9284	209	5	c)(1	c)(1	X
easat-9284	209	6	−	−	NOUN
easat-9284	209	7	α	α	NOUN
easat-9284	209	8	)	)	PUNCT
easat-9284	209	9	(	(	PUNCT
easat-9284	209	10	p	p	X
easat-9284	209	11	+	+	NOUN
easat-9284	209	12	q	q	NOUN
easat-9284	209	13	)	)	PUNCT
easat-9284	209	14	)	)	PUNCT
easat-9284	209	15	.	.	PUNCT
easat-9284	210	1	we	we	PRON
easat-9284	210	2	want	want	VERB
easat-9284	210	3	to	to	PART
easat-9284	210	4	show	show	VERB
easat-9284	210	5	that	that	PRON
easat-9284	210	6	:	:	PUNCT
easat-9284	210	7	provided	provide	VERB
easat-9284	210	8	the	the	DET
easat-9284	210	9	additive	additive	ADJ
easat-9284	210	10	term	term	NOUN
easat-9284	210	11	γ	γ	PROPN
easat-9284	210	12	compensates	compensate	NOUN
easat-9284	210	13	for	for	ADP
easat-9284	210	14	c.	c.	PROPN
easat-9284	210	15	this	this	PRON
easat-9284	210	16	holds	hold	VERB
easat-9284	210	17	as	as	ADV
easat-9284	210	18	long	long	ADV
easat-9284	210	19	as	as	ADP
easat-9284	210	20	a	a	DET
easat-9284	210	21	+	+	NOUN
easat-9284	210	22	2c	2c	NOUN
easat-9284	210	23	<	<	X
easat-9284	210	24	1	1	NUM
easat-9284	210	25	and	and	CCONJ
easat-9284	210	26	γ	γ	PROPN
easat-9284	210	27	is	be	AUX
easat-9284	210	28	nonzero	nonzero	NOUN
easat-9284	210	29	for	for	ADP
easat-9284	210	30	p	p	PROPN
easat-9284	210	31	/=	/=	PROPN
easat-9284	210	32	q	q	NOUN
easat-9284	210	33	,	,	PUNCT
easat-9284	210	34	which	which	PRON
easat-9284	210	35	it	it	PRON
easat-9284	210	36	is	be	AUX
easat-9284	210	37	.	.	PUNCT
easat-9284	211	1	hence	hence	ADV
easat-9284	211	2	,	,	PUNCT
easat-9284	211	3	for	for	ADP
easat-9284	211	4	all	all	DET
easat-9284	211	5	p	p	NOUN
easat-9284	211	6	,	,	PUNCT
easat-9284	211	7	q	q	PROPN
easat-9284	211	8	∈	∈	PROPN
easat-9284	211	9	rn	rn	PROPN
easat-9284	211	10	,	,	PUNCT
easat-9284	211	11	p	p	X
easat-9284	211	12	/=	/=	PROPN
easat-9284	211	13	q	q	NOUN
easat-9284	211	14	,	,	PUNCT
easat-9284	211	15	the	the	DET
easat-9284	211	16	enriched	enriched	ADJ
easat-9284	211	17	hardy	hardy	ADJ
easat-9284	211	18	–	–	PUNCT
easat-9284	211	19	rogers	rogers	PROPN
easat-9284	211	20	f	f	PROPN
easat-9284	211	21	-	-	PUNCT
easat-9284	211	22	contraction	contraction	NOUN
easat-9284	211	23	inequality	inequality	NOUN
easat-9284	211	24	holds	hold	VERB
easat-9284	211	25	for	for	ADP
easat-9284	211	26	the	the	DET
easat-9284	211	27	mapping	mapping	NOUN
easat-9284	211	28	t	t	NOUN
easat-9284	211	29	(	(	PUNCT
easat-9284	211	30	p	p	NOUN
easat-9284	211	31	)	)	PUNCT
easat-9284	211	32	=	=	SYM
easat-9284	211	33	αp	αp	NOUN
easat-9284	211	34	and	and	CCONJ
easat-9284	211	35	f	f	PROPN
easat-9284	211	36	(	(	PUNCT
easat-9284	211	37	ζ	ζ	NOUN
easat-9284	211	38	)	)	PUNCT
easat-9284	211	39	=	=	PUNCT
easat-9284	211	40	ln	ln	ADJ
easat-9284	211	41	ζ	ζ	NOUN
easat-9284	211	42	.	.	PUNCT
easat-9284	212	1	therefore	therefore	ADV
easat-9284	212	2	,	,	PUNCT
easat-9284	212	3	the	the	DET
easat-9284	212	4	mapping	mapping	NOUN
easat-9284	212	5	t	t	PROPN
easat-9284	212	6	is	be	AUX
easat-9284	212	7	a	a	DET
easat-9284	212	8	globally	globally	ADV
easat-9284	212	9	valid	valid	ADJ
easat-9284	212	10	example	example	NOUN
easat-9284	212	11	satisfying	satisfying	NOUN
easat-9284	212	12	theorem	theorem	VERB
easat-9284	212	13	3.3	3.3	NUM
easat-9284	212	14	.	.	PUNCT
easat-9284	212	15	297	297	NUM
easat-9284	212	16	edelweiss	edelweiss	PROPN
easat-9284	212	17	applied	apply	VERB
easat-9284	212	18	science	science	NOUN
easat-9284	212	19	and	and	CCONJ
easat-9284	212	20	technology	technology	NOUN
easat-9284	212	21	issn	issn	PROPN
easat-9284	212	22	:	:	PUNCT
easat-9284	212	23	2576	2576	NUM
easat-9284	212	24	-	-	SYM
easat-9284	212	25	8484	8484	NUM
easat-9284	212	26	vol	vol	NOUN
easat-9284	212	27	.	.	PROPN
easat-9284	213	1	9	9	NUM
easat-9284	213	2	,	,	PUNCT
easat-9284	213	3	no	no	INTJ
easat-9284	213	4	.	.	NOUN
easat-9284	213	5	8	8	NUM
easat-9284	213	6	:	:	PUNCT
easat-9284	213	7	291	291	NUM
easat-9284	213	8	-	-	SYM
easat-9284	213	9	299	299	NUM
easat-9284	213	10	,	,	PUNCT
easat-9284	213	11	2025	2025	NUM
easat-9284	213	12	doi	doi	NOUN
easat-9284	213	13	:	:	PUNCT
easat-9284	213	14	10.55214/2576	10.55214/2576	NUM
easat-9284	213	15	-	-	PUNCT
easat-9284	213	16	8484.v9i8.9284	8484.v9i8.9284	NOUN
easat-9284	213	17	©	©	PROPN
easat-9284	213	18	2025	2025	NUM
easat-9284	213	19	by	by	ADP
easat-9284	213	20	the	the	DET
easat-9284	213	21	author	author	NOUN
easat-9284	213	22	;	;	PUNCT
easat-9284	213	23	licensee	licensee	PROPN
easat-9284	213	24	learning	learning	NOUN
easat-9284	213	25	gate	gate	PROPN
easat-9284	213	26	3.1	3.1	NUM
easat-9284	213	27	.	.	PUNCT
easat-9284	214	1	convergence	convergence	NOUN
easat-9284	214	2	of	of	ADP
easat-9284	214	3	the	the	DET
easat-9284	214	4	krasnoselskij	krasnoselskij	PROPN
easat-9284	214	5	iteration	iteration	NOUN
easat-9284	214	6	let	let	VERB
easat-9284	214	7	e	e	NOUN
easat-9284	214	8	=	=	SYM
easat-9284	214	9	r	r	NOUN
easat-9284	214	10	,	,	PUNCT
easat-9284	214	11	and	and	CCONJ
easat-9284	214	12	define	define	VERB
easat-9284	214	13	the	the	DET
easat-9284	214	14	mapping	mapping	NOUN
easat-9284	214	15	:	:	PUNCT
easat-9284	214	16	we	we	PRON
easat-9284	214	17	apply	apply	VERB
easat-9284	214	18	the	the	DET
easat-9284	214	19	krasnoselskij	krasnoselskij	PROPN
easat-9284	214	20	iteration	iteration	NOUN
easat-9284	214	21	:	:	PUNCT
easat-9284	214	22	starting	start	VERB
easat-9284	214	23	from	from	ADP
easat-9284	214	24	p0	p0	NOUN
easat-9284	214	25	=	=	SYM
easat-9284	214	26	1	1	NUM
easat-9284	214	27	,	,	PUNCT
easat-9284	214	28	we	we	PRON
easat-9284	214	29	observe	observe	VERB
easat-9284	214	30	that	that	SCONJ
easat-9284	214	31	:	:	PUNCT
easat-9284	214	32	therefore	therefore	ADV
easat-9284	214	33	,	,	PUNCT
easat-9284	214	34	the	the	DET
easat-9284	214	35	sequence	sequence	NOUN
easat-9284	214	36	[	[	PUNCT
easat-9284	214	37	7	7	NUM
easat-9284	214	38	]	]	PUNCT
easat-9284	214	39	converges	converge	VERB
easat-9284	214	40	to	to	ADP
easat-9284	214	41	the	the	DET
easat-9284	214	42	unique	unique	ADJ
easat-9284	214	43	fixed	fix	VERB
easat-9284	214	44	point	point	NOUN
easat-9284	214	45	t	t	NOUN
easat-9284	214	46	=	=	SYM
easat-9284	214	47	0	0	NUM
easat-9284	214	48	,	,	PUNCT
easat-9284	214	49	in	in	ADP
easat-9284	214	50	accordance	accordance	NOUN
easat-9284	214	51	with	with	ADP
easat-9284	214	52	theorem	theorem	ADJ
easat-9284	214	53	3.3	3.3	NUM
easat-9284	214	54	.	.	PUNCT
easat-9284	215	1	4	4	NUM
easat-9284	215	2	.	.	X
easat-9284	215	3	application	application	VERB
easat-9284	215	4	the	the	DET
easat-9284	215	5	following	follow	VERB
easat-9284	215	6	theorem	theorem	NOUN
easat-9284	215	7	provides	provide	VERB
easat-9284	215	8	a	a	DET
easat-9284	215	9	novel	novel	ADJ
easat-9284	215	10	application	application	NOUN
easat-9284	215	11	of	of	ADP
easat-9284	215	12	the	the	DET
easat-9284	215	13	enriched	enriched	ADJ
easat-9284	215	14	hardy	hardy	ADJ
easat-9284	215	15	–	–	PUNCT
easat-9284	215	16	rogers	rogers	PROPN
easat-9284	215	17	f	f	PROPN
easat-9284	215	18	-	-	PUNCT
easat-9284	215	19	contraction	contraction	NOUN
easat-9284	215	20	framework	framework	NOUN
easat-9284	215	21	to	to	ADP
easat-9284	215	22	a	a	DET
easat-9284	215	23	class	class	NOUN
easat-9284	215	24	of	of	ADP
easat-9284	215	25	nonlinear	nonlinear	ADJ
easat-9284	215	26	integral	integral	ADJ
easat-9284	215	27	equations	equation	NOUN
easat-9284	215	28	arising	arise	VERB
easat-9284	215	29	in	in	ADP
easat-9284	215	30	systems	system	NOUN
easat-9284	215	31	with	with	ADP
easat-9284	215	32	symmetric	symmetric	ADJ
easat-9284	215	33	delayed	delay	VERB
easat-9284	215	34	feedback	feedback	NOUN
easat-9284	215	35	,	,	PUNCT
easat-9284	215	36	such	such	ADJ
easat-9284	215	37	as	as	ADP
easat-9284	215	38	recurrent	recurrent	ADJ
easat-9284	215	39	neural	neural	ADJ
easat-9284	215	40	networks	network	NOUN
easat-9284	215	41	,	,	PUNCT
easat-9284	215	42	control	control	NOUN
easat-9284	215	43	processes	process	NOUN
easat-9284	215	44	with	with	ADP
easat-9284	215	45	memory	memory	NOUN
easat-9284	215	46	,	,	PUNCT
easat-9284	215	47	and	and	CCONJ
easat-9284	215	48	learning	learn	VERB
easat-9284	215	49	models	model	NOUN
easat-9284	215	50	with	with	ADP
easat-9284	215	51	timereflected	timereflecte	VERB
easat-9284	215	52	dependencies	dependency	NOUN
easat-9284	215	53	.	.	PUNCT
easat-9284	216	1	unlike	unlike	ADP
easat-9284	216	2	traditional	traditional	ADJ
easat-9284	216	3	volterra	volterra	NOUN
easat-9284	216	4	-	-	PUNCT
easat-9284	216	5	type	type	NOUN
easat-9284	216	6	equations	equation	NOUN
easat-9284	216	7	,	,	PUNCT
easat-9284	216	8	the	the	DET
easat-9284	216	9	current	current	ADJ
easat-9284	216	10	formulation	formulation	NOUN
easat-9284	216	11	incorporates	incorporate	VERB
easat-9284	216	12	nonlinear	nonlinear	ADJ
easat-9284	216	13	symmetric	symmetric	ADJ
easat-9284	216	14	interactions	interaction	NOUN
easat-9284	216	15	of	of	ADP
easat-9284	216	16	the	the	DET
easat-9284	216	17	form	form	NOUN
easat-9284	216	18	w(s	w(s	PROPN
easat-9284	216	19	)	)	PUNCT
easat-9284	216	20	,	,	PUNCT
easat-9284	216	21	w(t	w(t	PROPN
easat-9284	216	22	s	s	PROPN
easat-9284	216	23	)	)	PUNCT
easat-9284	216	24	,	,	PUNCT
easat-9284	216	25	making	make	VERB
easat-9284	216	26	the	the	DET
easat-9284	216	27	problem	problem	NOUN
easat-9284	216	28	more	more	ADV
easat-9284	216	29	challenging	challenging	ADJ
easat-9284	216	30	and	and	CCONJ
easat-9284	216	31	less	less	ADV
easat-9284	216	32	amenable	amenable	ADJ
easat-9284	216	33	to	to	ADP
easat-9284	216	34	classical	classical	ADJ
easat-9284	216	35	fixed	fix	VERB
easat-9284	216	36	point	point	NOUN
easat-9284	216	37	techniques	technique	NOUN
easat-9284	216	38	.	.	PUNCT
easat-9284	217	1	the	the	DET
easat-9284	217	2	standard	standard	PROPN
easat-9284	217	3	banach	banach	NOUN
easat-9284	217	4	,	,	PUNCT
easat-9284	217	5	kannan	kannan	PROPN
easat-9284	217	6	,	,	PUNCT
easat-9284	217	7	or	or	CCONJ
easat-9284	217	8	reich	reich	PROPN
easat-9284	217	9	contractions	contraction	NOUN
easat-9284	217	10	are	be	AUX
easat-9284	217	11	insufficient	insufficient	ADJ
easat-9284	217	12	in	in	ADP
easat-9284	217	13	capturing	capture	VERB
easat-9284	217	14	the	the	DET
easat-9284	217	15	mixed	mixed	ADJ
easat-9284	217	16	and	and	CCONJ
easat-9284	217	17	delayed	delay	VERB
easat-9284	217	18	nonlinearities	nonlinearitie	NOUN
easat-9284	217	19	present	present	ADJ
easat-9284	217	20	in	in	ADP
easat-9284	217	21	such	such	ADJ
easat-9284	217	22	systems	system	NOUN
easat-9284	217	23	.	.	PUNCT
easat-9284	218	1	by	by	ADP
easat-9284	218	2	employing	employ	VERB
easat-9284	218	3	the	the	DET
easat-9284	218	4	enriched	enriched	ADJ
easat-9284	218	5	hardy	hardy	ADJ
easat-9284	218	6	–	–	PUNCT
easat-9284	218	7	rogers	rogers	PROPN
easat-9284	218	8	f	f	PROPN
easat-9284	218	9	-	-	PUNCT
easat-9284	218	10	contraction	contraction	NOUN
easat-9284	218	11	,	,	PUNCT
easat-9284	218	12	we	we	PRON
easat-9284	218	13	establish	establish	VERB
easat-9284	218	14	the	the	DET
easat-9284	218	15	existence	existence	NOUN
easat-9284	218	16	and	and	CCONJ
easat-9284	218	17	uniqueness	uniqueness	NOUN
easat-9284	218	18	of	of	ADP
easat-9284	218	19	solutions	solution	NOUN
easat-9284	218	20	under	under	ADP
easat-9284	218	21	relaxed	relaxed	ADJ
easat-9284	218	22	conditions	condition	NOUN
easat-9284	218	23	on	on	ADP
easat-9284	218	24	the	the	DET
easat-9284	218	25	kernel	kernel	PROPN
easat-9284	218	26	function	function	PROPN
easat-9284	218	27	,	,	PUNCT
easat-9284	218	28	demonstrating	demonstrate	VERB
easat-9284	218	29	the	the	DET
easat-9284	218	30	strength	strength	NOUN
easat-9284	218	31	and	and	CCONJ
easat-9284	218	32	flexibility	flexibility	NOUN
easat-9284	218	33	of	of	ADP
easat-9284	218	34	the	the	DET
easat-9284	218	35	proposed	propose	VERB
easat-9284	218	36	approach	approach	NOUN
easat-9284	218	37	.	.	PUNCT
easat-9284	219	1	this	this	DET
easat-9284	219	2	highlights	highlight	VERB
easat-9284	219	3	the	the	DET
easat-9284	219	4	theoretical	theoretical	ADJ
easat-9284	219	5	potential	potential	NOUN
easat-9284	219	6	of	of	ADP
easat-9284	219	7	the	the	DET
easat-9284	219	8	enriched	enrich	VERB
easat-9284	219	9	framework	framework	NOUN
easat-9284	219	10	in	in	ADP
easat-9284	219	11	analyzing	analyze	VERB
easat-9284	219	12	nonlinear	nonlinear	ADJ
easat-9284	219	13	models	model	NOUN
easat-9284	219	14	encountered	encounter	VERB
easat-9284	219	15	in	in	ADP
easat-9284	219	16	modern	modern	ADJ
easat-9284	219	17	learning	learning	NOUN
easat-9284	219	18	theory	theory	NOUN
easat-9284	219	19	,	,	PUNCT
easat-9284	219	20	time	time	NOUN
easat-9284	219	21	-	-	PUNCT
easat-9284	219	22	symmetric	symmetric	ADJ
easat-9284	219	23	physical	physical	ADJ
easat-9284	219	24	systems	system	NOUN
easat-9284	219	25	,	,	PUNCT
easat-9284	219	26	and	and	CCONJ
easat-9284	219	27	neural	neural	ADJ
easat-9284	219	28	feedback	feedback	NOUN
easat-9284	219	29	architectures	architecture	NOUN
easat-9284	219	30	.	.	PUNCT
easat-9284	220	1	theorem	theorem	VERB
easat-9284	220	2	4.1	4.1	NUM
easat-9284	220	3	let	let	VERB
easat-9284	220	4	φ	φ	NOUN
easat-9284	220	5	:	:	PUNCT
easat-9284	221	1	[	[	X
easat-9284	221	2	0	0	NUM
easat-9284	221	3	,	,	PUNCT
easat-9284	221	4	t	t	NOUN
easat-9284	221	5	]	]	PUNCT
easat-9284	221	6	→	→	SYM
easat-9284	221	7	r	r	NOUN
easat-9284	221	8	and	and	CCONJ
easat-9284	221	9	k	k	NOUN
easat-9284	221	10	:	:	PUNCT
easat-9284	222	1	[	[	X
easat-9284	222	2	0	0	NUM
easat-9284	222	3	,	,	PUNCT
easat-9284	222	4	t	t	X
easat-9284	222	5	]	]	X
easat-9284	222	6	2	2	NUM
easat-9284	222	7	×	×	NOUN
easat-9284	222	8	r2	r2	NOUN
easat-9284	222	9	→	→	PUNCT
easat-9284	222	10	r	r	NOUN
easat-9284	222	11	be	be	VERB
easat-9284	222	12	continuous	continuous	ADJ
easat-9284	222	13	functions	function	NOUN
easat-9284	222	14	.	.	PUNCT
easat-9284	223	1	suppose	suppose	VERB
easat-9284	223	2	there	there	PRON
easat-9284	223	3	exist	exist	VERB
easat-9284	223	4	constants	constant	NOUN
easat-9284	223	5	α	α	NOUN
easat-9284	223	6	,	,	PUNCT
easat-9284	223	7	β	β	X
easat-9284	223	8	,	,	PUNCT
easat-9284	223	9	γ	γ	PROPN
easat-9284	223	10	∈	∈	PROPN
easat-9284	224	1	[	[	X
easat-9284	224	2	0	0	NUM
easat-9284	224	3	,	,	PUNCT
easat-9284	224	4	1	1	NUM
easat-9284	224	5	)	)	PUNCT
easat-9284	224	6	with	with	ADP
easat-9284	224	7	α	α	PROPN
easat-9284	224	8	+	+	X
easat-9284	224	9	β	β	X
easat-9284	224	10	+	+	X
easat-9284	224	11	γ	γ	X
easat-9284	224	12	<	<	X
easat-9284	224	13	1	1	NUM
easat-9284	224	14	,	,	PUNCT
easat-9284	224	15	and	and	CCONJ
easat-9284	224	16	c	c	X
easat-9284	224	17	>	>	X
easat-9284	224	18	0	0	NUM
easat-9284	224	19	such	such	ADJ
easat-9284	224	20	that	that	DET
easat-9284	224	21	for	for	ADP
easat-9284	224	22	all	all	DET
easat-9284	224	23	w	w	NOUN
easat-9284	224	24	,	,	PUNCT
easat-9284	224	25	z	z	PROPN
easat-9284	224	26	∈	∈	PROPN
easat-9284	224	27	c[0	c[0	PROPN
easat-9284	224	28	,	,	PUNCT
easat-9284	224	29	t	t	NOUN
easat-9284	224	30	]	]	PUNCT
easat-9284	224	31	and	and	CCONJ
easat-9284	224	32	t	t	PROPN
easat-9284	224	33	,	,	PUNCT
easat-9284	224	34	s	s	PART
easat-9284	224	35	∈	∈	PROPN
easat-9284	225	1	[	[	X
easat-9284	225	2	0	0	NUM
easat-9284	225	3	,	,	PUNCT
easat-9284	225	4	t	t	X
easat-9284	225	5	]	]	PUNCT
easat-9284	225	6	,	,	PUNCT
easat-9284	225	7	(	(	PUNCT
easat-9284	225	8	3	3	X
easat-9284	225	9	)	)	PUNCT
easat-9284	225	10	then	then	ADV
easat-9284	225	11	the	the	DET
easat-9284	225	12	operator	operator	NOUN
easat-9284	225	13	satisfies	satisfy	VERB
easat-9284	225	14	the	the	DET
easat-9284	225	15	enriched	enriched	ADJ
easat-9284	225	16	hardy	hardy	ADJ
easat-9284	225	17	–	–	PUNCT
easat-9284	225	18	rogers	rogers	PROPN
easat-9284	225	19	f	f	PROPN
easat-9284	225	20	-contraction	-contraction	PROPN
easat-9284	225	21	condition	condition	NOUN
easat-9284	225	22	,	,	PUNCT
easat-9284	225	23	and	and	CCONJ
easat-9284	225	24	the	the	DET
easat-9284	225	25	system	system	NOUN
easat-9284	225	26	has	have	VERB
easat-9284	225	27	a	a	DET
easat-9284	225	28	unique	unique	ADJ
easat-9284	225	29	solution	solution	NOUN
easat-9284	225	30	in	in	ADP
easat-9284	225	31	c[0	c[0	PROPN
easat-9284	225	32	,	,	PUNCT
easat-9284	225	33	t	t	X
easat-9284	225	34	]	]	PUNCT
easat-9284	225	35	.	.	PUNCT
easat-9284	226	1	298	298	NUM
easat-9284	226	2	edelweiss	edelweiss	PROPN
easat-9284	226	3	applied	apply	VERB
easat-9284	226	4	science	science	NOUN
easat-9284	226	5	and	and	CCONJ
easat-9284	226	6	technology	technology	NOUN
easat-9284	226	7	issn	issn	PROPN
easat-9284	226	8	:	:	PUNCT
easat-9284	226	9	2576	2576	NUM
easat-9284	226	10	-	-	SYM
easat-9284	226	11	8484	8484	NUM
easat-9284	226	12	vol	vol	NOUN
easat-9284	226	13	.	.	PROPN
easat-9284	227	1	9	9	NUM
easat-9284	227	2	,	,	PUNCT
easat-9284	227	3	no	no	INTJ
easat-9284	227	4	.	.	NOUN
easat-9284	227	5	8	8	NUM
easat-9284	227	6	:	:	PUNCT
easat-9284	227	7	291	291	NUM
easat-9284	227	8	-	-	SYM
easat-9284	227	9	299	299	NUM
easat-9284	227	10	,	,	PUNCT
easat-9284	227	11	2025	2025	NUM
easat-9284	227	12	doi	doi	NOUN
easat-9284	227	13	:	:	PUNCT
easat-9284	227	14	10.55214/2576	10.55214/2576	NUM
easat-9284	227	15	-	-	PUNCT
easat-9284	227	16	8484.v9i8.9284	8484.v9i8.9284	NOUN
easat-9284	227	17	©	©	PROPN
easat-9284	227	18	2025	2025	NUM
easat-9284	227	19	by	by	ADP
easat-9284	227	20	the	the	DET
easat-9284	227	21	author	author	NOUN
easat-9284	227	22	;	;	PUNCT
easat-9284	227	23	licensee	licensee	PROPN
easat-9284	227	24	learning	learn	VERB
easat-9284	227	25	gate	gate	NOUN
easat-9284	227	26	proof	proof	NOUN
easat-9284	227	27	.	.	PUNCT
easat-9284	228	1	let	let	VERB
easat-9284	228	2	e	e	NOUN
easat-9284	228	3	=	=	SYM
easat-9284	228	4	c[0	c[0	PROPN
easat-9284	228	5	,	,	PUNCT
easat-9284	228	6	t	t	PROPN
easat-9284	228	7	]	]	PUNCT
easat-9284	228	8	be	be	AUX
easat-9284	228	9	the	the	DET
easat-9284	228	10	banach	banach	NOUN
easat-9284	228	11	space	space	NOUN
easat-9284	228	12	of	of	ADP
easat-9284	228	13	real	real	ADV
easat-9284	228	14	-	-	PUNCT
easat-9284	228	15	valued	value	VERB
easat-9284	228	16	continuous	continuous	ADJ
easat-9284	228	17	functions	function	NOUN
easat-9284	228	18	on	on	ADP
easat-9284	228	19	[	[	X
easat-9284	228	20	0	0	NUM
easat-9284	228	21	,	,	PUNCT
easat-9284	228	22	t	t	X
easat-9284	228	23	]	]	PUNCT
easat-9284	228	24	,	,	PUNCT
easat-9284	228	25	endowed	endow	VERB
easat-9284	228	26	with	with	ADP
easat-9284	228	27	the	the	DET
easat-9284	228	28	norm	norm	NOUN
easat-9284	228	29	:	:	PUNCT
easat-9284	228	30	where	where	SCONJ
easat-9284	228	31	τ	τ	PROPN
easat-9284	228	32	>	>	X
easat-9284	228	33	0	0	NUM
easat-9284	228	34	is	be	AUX
easat-9284	228	35	fixed	fix	VERB
easat-9284	228	36	.	.	PUNCT
easat-9284	229	1	step	step	NOUN
easat-9284	229	2	1	1	NUM
easat-9284	229	3	:	:	PUNCT
easat-9284	229	4	the	the	DET
easat-9284	229	5	mapping	mapping	NOUN
easat-9284	229	6	t	t	PROPN
easat-9284	229	7	:	:	PUNCT
easat-9284	229	8	e	e	X
easat-9284	229	9	→	→	SYM
easat-9284	229	10	e	e	X
easat-9284	229	11	is	be	AUX
easat-9284	229	12	well	well	ADV
easat-9284	229	13	-	-	PUNCT
easat-9284	229	14	defined	define	VERB
easat-9284	229	15	and	and	CCONJ
easat-9284	229	16	maps	map	NOUN
easat-9284	229	17	e	e	NOUN
easat-9284	229	18	into	into	ADP
easat-9284	229	19	itself	itself	PRON
easat-9284	229	20	.	.	PUNCT
easat-9284	230	1	since	since	SCONJ
easat-9284	230	2	φ	φ	PROPN
easat-9284	230	3	and	and	CCONJ
easat-9284	230	4	k	k	PROPN
easat-9284	230	5	are	be	AUX
easat-9284	230	6	continuous	continuous	ADJ
easat-9284	230	7	,	,	PUNCT
easat-9284	230	8	and	and	CCONJ
easat-9284	230	9	w	w	PROPN
easat-9284	230	10	∈	∈	PROPN
easat-9284	230	11	e	e	NOUN
easat-9284	230	12	,	,	PUNCT
easat-9284	230	13	the	the	DET
easat-9284	230	14	integrand	integrand	NOUN
easat-9284	230	15	in	in	ADP
easat-9284	230	16	the	the	DET
easat-9284	230	17	definition	definition	NOUN
easat-9284	230	18	of	of	ADP
easat-9284	230	19	t	t	PROPN
easat-9284	230	20	(	(	PUNCT
easat-9284	230	21	w)(t	w)(t	PROPN
easat-9284	230	22	)	)	PUNCT
easat-9284	230	23	is	be	AUX
easat-9284	230	24	continuous	continuous	ADJ
easat-9284	230	25	in	in	ADP
easat-9284	230	26	t	t	PROPN
easat-9284	230	27	,	,	PUNCT
easat-9284	230	28	and	and	CCONJ
easat-9284	230	29	hence	hence	ADV
easat-9284	230	30	t	t	PROPN
easat-9284	230	31	(	(	PUNCT
easat-9284	230	32	w	w	NOUN
easat-9284	230	33	)	)	PUNCT
easat-9284	230	34	∈	∈	PROPN
easat-9284	230	35	(	(	PUNCT
easat-9284	230	36	t	t	NOUN
easat-9284	230	37	)	)	PUNCT
easat-9284	230	38	is	be	AUX
easat-9284	230	39	continuous	continuous	ADJ
easat-9284	230	40	on	on	ADP
easat-9284	230	41	[	[	X
easat-9284	230	42	0	0	NUM
easat-9284	230	43	,	,	PUNCT
easat-9284	230	44	t	t	X
easat-9284	230	45	]	]	PUNCT
easat-9284	230	46	.	.	PUNCT
easat-9284	231	1	thus	thus	ADV
easat-9284	231	2	,	,	PUNCT
easat-9284	231	3	t	t	PROPN
easat-9284	231	4	(	(	PUNCT
easat-9284	231	5	w	w	NOUN
easat-9284	231	6	)	)	PUNCT
easat-9284	231	7	∈	∈	PROPN
easat-9284	231	8	c	c	NOUN
easat-9284	232	1	[	[	X
easat-9284	232	2	0	0	NUM
easat-9284	232	3	,	,	PUNCT
easat-9284	232	4	t	t	PROPN
easat-9284	232	5	]	]	X
easat-9284	232	6	=	=	PUNCT
easat-9284	232	7	e.	e.	PROPN
easat-9284	232	8	step	step	NOUN
easat-9284	232	9	2	2	NUM
easat-9284	232	10	:	:	PUNCT
easat-9284	232	11	we	we	PRON
easat-9284	232	12	show	show	VERB
easat-9284	232	13	that	that	SCONJ
easat-9284	232	14	t	t	PROPN
easat-9284	232	15	satisfies	satisfy	VERB
easat-9284	232	16	the	the	DET
easat-9284	232	17	inequality	inequality	NOUN
easat-9284	232	18	in	in	ADP
easat-9284	232	19	definition	definition	NOUN
easat-9284	232	20	3.1	3.1	NUM
easat-9284	232	21	.	.	PUNCT
easat-9284	233	1	let	let	VERB
easat-9284	233	2	w	w	NOUN
easat-9284	233	3	,	,	PUNCT
easat-9284	233	4	z	z	NOUN
easat-9284	233	5	∈	∈	NOUN
easat-9284	233	6	e	e	NOUN
easat-9284	233	7	be	be	AUX
easat-9284	233	8	arbitrary	arbitrary	ADJ
easat-9284	233	9	but	but	CCONJ
easat-9284	233	10	fixed	fix	VERB
easat-9284	233	11	.	.	PUNCT
easat-9284	234	1	then	then	ADV
easat-9284	234	2	for	for	ADP
easat-9284	234	3	each	each	DET
easat-9284	234	4	t	t	NOUN
easat-9284	234	5	∈	∈	PROPN
easat-9284	235	1	[	[	X
easat-9284	235	2	0	0	NUM
easat-9284	235	3	,	,	PUNCT
easat-9284	235	4	t	t	PROPN
easat-9284	235	5	]	]	PUNCT
easat-9284	235	6	,	,	PUNCT
easat-9284	235	7	define	define	VERB
easat-9284	235	8	the	the	DET
easat-9284	235	9	following	following	NOUN
easat-9284	235	10	:	:	PUNCT
easat-9284	235	11	by	by	ADP
easat-9284	235	12	the	the	DET
easat-9284	235	13	assumption	assumption	NOUN
easat-9284	235	14	(	(	PUNCT
easat-9284	235	15	3	3	NUM
easat-9284	235	16	)	)	PUNCT
easat-9284	235	17	,	,	PUNCT
easat-9284	235	18	we	we	PRON
easat-9284	235	19	have	have	AUX
easat-9284	235	20	let	let	VERB
easat-9284	235	21	b0	b0	VERB
easat-9284	235	22	>	>	X
easat-9284	235	23	0	0	PUNCT
easat-9284	236	1	be	be	AUX
easat-9284	236	2	a	a	DET
easat-9284	236	3	fixed	fix	VERB
easat-9284	236	4	parameter	parameter	NOUN
easat-9284	236	5	.	.	PUNCT
easat-9284	237	1	then	then	ADV
easat-9284	237	2	:	:	PUNCT
easat-9284	237	3	hence	hence	ADV
easat-9284	237	4	,	,	PUNCT
easat-9284	237	5	applying	apply	VERB
easat-9284	237	6	f	f	X
easat-9284	237	7	(	(	PUNCT
easat-9284	237	8	ζ	ζ	NOUN
easat-9284	237	9	)	)	PUNCT
easat-9284	237	10	=	=	PUNCT
easat-9284	237	11	ln	ln	ADJ
easat-9284	237	12	ζ	ζ	NOUN
easat-9284	237	13	,	,	PUNCT
easat-9284	237	14	we	we	PRON
easat-9284	237	15	obtain	obtain	AUX
easat-9284	237	16	:	:	PUNCT
easat-9284	237	17	choosing	choose	VERB
easat-9284	237	18	a	a	DET
easat-9284	237	19	=	=	SYM
easat-9284	237	20	γ	γ	X
easat-9284	237	21	,	,	PUNCT
easat-9284	237	22	b	b	PROPN
easat-9284	237	23	=	=	SYM
easat-9284	237	24	α	α	PROPN
easat-9284	237	25	,	,	PUNCT
easat-9284	237	26	c	c	NOUN
easat-9284	237	27	=	=	SYM
easat-9284	237	28	β	β	X
easat-9284	237	29	,	,	PUNCT
easat-9284	237	30	and	and	CCONJ
easat-9284	237	31	applying	apply	VERB
easat-9284	237	32	the	the	DET
easat-9284	237	33	logarithmic	logarithmic	ADJ
easat-9284	237	34	inequality	inequality	NOUN
easat-9284	237	35	ln	ln	ADP
easat-9284	237	36	(	(	PUNCT
easat-9284	237	37	p	p	X
easat-9284	237	38	+	+	NOUN
easat-9284	237	39	q	q	NOUN
easat-9284	237	40	)	)	PUNCT
easat-9284	237	41	≤	≤	NOUN
easat-9284	237	42	ln	ln	ADJ
easat-9284	237	43	(	(	PUNCT
easat-9284	237	44	2	2	NUM
easat-9284	237	45	max	max	NOUN
easat-9284	237	46	.	.	PUNCT
easat-9284	238	1	{	{	PUNCT
easat-9284	239	1	p	p	X
easat-9284	239	2	,	,	PUNCT
easat-9284	239	3	q	q	NOUN
easat-9284	239	4	}	}	PUNCT
easat-9284	239	5	)	)	PUNCT
easat-9284	239	6	≤	≤	NOUN
easat-9284	240	1	ln	ln	ADJ
easat-9284	240	2	2	2	NUM
easat-9284	241	1	+	+	NUM
easat-9284	241	2	max.{ln	max.{ln	NOUN
easat-9284	241	3	p	p	NOUN
easat-9284	241	4	,	,	PUNCT
easat-9284	241	5	ln	ln	ADJ
easat-9284	241	6	q	q	NOUN
easat-9284	241	7	}	}	PUNCT
easat-9284	241	8	,	,	PUNCT
easat-9284	241	9	we	we	PRON
easat-9284	241	10	get	get	VERB
easat-9284	241	11	:	:	PUNCT
easat-9284	241	12	thus	thus	ADV
easat-9284	241	13	,	,	PUNCT
easat-9284	241	14	hence	hence	ADV
easat-9284	241	15	,	,	PUNCT
easat-9284	241	16	for	for	ADP
easat-9284	241	17	suitable	suitable	ADJ
easat-9284	241	18	small	small	ADJ
easat-9284	241	19	τ	τ	PROPN
easat-9284	241	20	>	>	X
easat-9284	241	21	0	0	PROPN
easat-9284	241	22	,	,	PUNCT
easat-9284	241	23	the	the	DET
easat-9284	241	24	inequality	inequality	NOUN
easat-9284	241	25	in	in	ADP
easat-9284	241	26	definition	definition	NOUN
easat-9284	241	27	3.1	3.1	NUM
easat-9284	241	28	is	be	AUX
easat-9284	241	29	satisfied	satisfied	ADJ
easat-9284	241	30	with	with	ADP
easat-9284	241	31	constants	constant	NOUN
easat-9284	241	32	a	a	DET
easat-9284	241	33	=	=	SYM
easat-9284	241	34	γ	γ	X
easat-9284	241	35	,	,	PUNCT
easat-9284	241	36	b	b	PROPN
easat-9284	241	37	=	=	SYM
easat-9284	241	38	α	α	PROPN
easat-9284	241	39	,	,	PUNCT
easat-9284	241	40	c	c	NOUN
easat-9284	241	41	=	=	SYM
easat-9284	241	42	β	β	PROPN
easat-9284	241	43	,	,	PUNCT
easat-9284	241	44	which	which	PRON
easat-9284	241	45	satisfy	satisfy	VERB
easat-9284	241	46	a	a	DET
easat-9284	241	47	+	+	NOUN
easat-9284	241	48	2b	2b	NUM
easat-9284	241	49	+	+	CCONJ
easat-9284	241	50	2c	2c	NUM
easat-9284	241	51	=	=	SYM
easat-9284	241	52	γ	γ	X
easat-9284	241	53	+	+	NOUN
easat-9284	241	54	2α	2α	NOUN
easat-9284	241	55	+	+	CCONJ
easat-9284	241	56	2β	2β	NOUN
easat-9284	241	57	<	<	X
easat-9284	241	58	1	1	NUM
easat-9284	241	59	by	by	ADP
easat-9284	241	60	assumption	assumption	NOUN
easat-9284	241	61	.	.	PUNCT
easat-9284	242	1	step	step	NOUN
easat-9284	242	2	3	3	NUM
easat-9284	242	3	:	:	PUNCT
easat-9284	242	4	by	by	ADP
easat-9284	242	5	theorem	theorem	NOUN
easat-9284	242	6	3.3	3.3	NUM
easat-9284	242	7	,	,	PUNCT
easat-9284	242	8	t	t	PROPN
easat-9284	242	9	has	have	VERB
easat-9284	242	10	a	a	DET
easat-9284	242	11	unique	unique	ADJ
easat-9284	242	12	fixed	fix	VERB
easat-9284	242	13	point	point	NOUN
easat-9284	242	14	w∗	w∗	PROPN
easat-9284	242	15	∈	∈	PROPN
easat-9284	242	16	e	e	NOUN
easat-9284	242	17	,	,	PUNCT
easat-9284	242	18	which	which	PRON
easat-9284	242	19	is	be	AUX
easat-9284	242	20	the	the	DET
easat-9284	242	21	unique	unique	ADJ
easat-9284	242	22	solution	solution	NOUN
easat-9284	242	23	of	of	ADP
easat-9284	242	24	the	the	DET
easat-9284	242	25	system	system	NOUN
easat-9284	242	26	299	299	NUM
easat-9284	242	27	edelweiss	edelweiss	PROPN
easat-9284	242	28	applied	apply	VERB
easat-9284	242	29	science	science	NOUN
easat-9284	242	30	and	and	CCONJ
easat-9284	242	31	technology	technology	NOUN
easat-9284	242	32	issn	issn	PROPN
easat-9284	242	33	:	:	PUNCT
easat-9284	242	34	2576	2576	NUM
easat-9284	242	35	-	-	SYM
easat-9284	242	36	8484	8484	NUM
easat-9284	242	37	vol	vol	NOUN
easat-9284	242	38	.	.	PROPN
easat-9284	243	1	9	9	NUM
easat-9284	243	2	,	,	PUNCT
easat-9284	243	3	no	no	INTJ
easat-9284	243	4	.	.	NOUN
easat-9284	243	5	8	8	NUM
easat-9284	243	6	:	:	PUNCT
easat-9284	243	7	291	291	NUM
easat-9284	243	8	-	-	SYM
easat-9284	243	9	299	299	NUM
easat-9284	243	10	,	,	PUNCT
easat-9284	243	11	2025	2025	NUM
easat-9284	243	12	doi	doi	NOUN
easat-9284	243	13	:	:	PUNCT
easat-9284	243	14	10.55214/2576	10.55214/2576	NUM
easat-9284	243	15	-	-	PUNCT
easat-9284	243	16	8484.v9i8.9284	8484.v9i8.9284	NOUN
easat-9284	243	17	©	©	PROPN
easat-9284	243	18	2025	2025	NUM
easat-9284	243	19	by	by	ADP
easat-9284	243	20	the	the	DET
easat-9284	243	21	author	author	NOUN
easat-9284	243	22	;	;	PUNCT
easat-9284	243	23	licensee	licensee	PROPN
easat-9284	243	24	learning	learning	NOUN
easat-9284	243	25	gate	gate	NOUN
easat-9284	243	26	5	5	NUM
easat-9284	243	27	.	.	PUNCT
easat-9284	243	28	conclusion	conclusion	NOUN
easat-9284	243	29	in	in	ADP
easat-9284	243	30	this	this	DET
easat-9284	243	31	paper	paper	NOUN
easat-9284	243	32	,	,	PUNCT
easat-9284	243	33	we	we	PRON
easat-9284	243	34	introduced	introduce	VERB
easat-9284	243	35	a	a	DET
easat-9284	243	36	new	new	ADJ
easat-9284	243	37	class	class	NOUN
easat-9284	243	38	of	of	ADP
easat-9284	243	39	fixed	fix	VERB
easat-9284	243	40	point	point	NOUN
easat-9284	243	41	mappings	mapping	NOUN
easat-9284	243	42	termed	term	VERB
easat-9284	243	43	enriched	enrich	VERB
easat-9284	243	44	hardy	hardy	ADJ
easat-9284	243	45	–	–	PUNCT
easat-9284	243	46	rogers	roger	NOUN
easat-9284	243	47	f	f	PROPN
easat-9284	243	48	contractions	contraction	NOUN
easat-9284	243	49	,	,	PUNCT
easat-9284	243	50	which	which	PRON
easat-9284	243	51	generalizes	generalize	VERB
easat-9284	243	52	several	several	ADJ
easat-9284	243	53	known	know	VERB
easat-9284	243	54	contraction	contraction	NOUN
easat-9284	243	55	principles	principle	NOUN
easat-9284	243	56	by	by	ADP
easat-9284	243	57	incorporating	incorporate	VERB
easat-9284	243	58	both	both	CCONJ
easat-9284	243	59	nonlinear	nonlinear	ADJ
easat-9284	243	60	control	control	NOUN
easat-9284	243	61	functions	function	NOUN
easat-9284	243	62	and	and	CCONJ
easat-9284	243	63	enriched	enriched	ADJ
easat-9284	243	64	distance	distance	NOUN
easat-9284	243	65	terms	term	NOUN
easat-9284	243	66	.	.	PUNCT
easat-9284	244	1	we	we	PRON
easat-9284	244	2	established	establish	VERB
easat-9284	244	3	a	a	DET
easat-9284	244	4	fixed	fix	VERB
easat-9284	244	5	point	point	NOUN
easat-9284	244	6	theorem	theorem	VERB
easat-9284	244	7	under	under	ADP
easat-9284	244	8	this	this	DET
easat-9284	244	9	framework	framework	NOUN
easat-9284	244	10	and	and	CCONJ
easat-9284	244	11	demonstrated	demonstrate	VERB
easat-9284	244	12	the	the	DET
easat-9284	244	13	convergence	convergence	NOUN
easat-9284	244	14	of	of	ADP
easat-9284	244	15	the	the	DET
easat-9284	244	16	associated	associated	ADJ
easat-9284	244	17	krasnoselskij	krasnoselskij	PROPN
easat-9284	244	18	iterative	iterative	NOUN
easat-9284	244	19	process	process	NOUN
easat-9284	244	20	.	.	PUNCT
easat-9284	245	1	to	to	PART
easat-9284	245	2	illustrate	illustrate	VERB
easat-9284	245	3	the	the	DET
easat-9284	245	4	applicability	applicability	NOUN
easat-9284	245	5	of	of	ADP
easat-9284	245	6	our	our	PRON
easat-9284	245	7	result	result	NOUN
easat-9284	245	8	,	,	PUNCT
easat-9284	245	9	we	we	PRON
easat-9284	245	10	applied	apply	VERB
easat-9284	245	11	it	it	PRON
easat-9284	245	12	to	to	ADP
easat-9284	245	13	a	a	DET
easat-9284	245	14	new	new	ADJ
easat-9284	245	15	class	class	NOUN
easat-9284	245	16	of	of	ADP
easat-9284	245	17	nonlinear	nonlinear	ADJ
easat-9284	245	18	integral	integral	ADJ
easat-9284	245	19	equations	equation	NOUN
easat-9284	245	20	involving	involve	VERB
easat-9284	245	21	symmetric	symmetric	ADJ
easat-9284	245	22	feedback	feedback	NOUN
easat-9284	245	23	arising	arise	VERB
easat-9284	245	24	in	in	ADP
easat-9284	245	25	models	model	NOUN
easat-9284	245	26	of	of	ADP
easat-9284	245	27	recurrent	recurrent	ADJ
easat-9284	245	28	learning	learning	NOUN
easat-9284	245	29	and	and	CCONJ
easat-9284	245	30	time	time	NOUN
easat-9284	245	31	-	-	PUNCT
easat-9284	245	32	reflected	reflect	VERB
easat-9284	245	33	systems	system	NOUN
easat-9284	245	34	.	.	PUNCT
easat-9284	246	1	this	this	DET
easat-9284	246	2	application	application	NOUN
easat-9284	246	3	highlights	highlight	VERB
easat-9284	246	4	the	the	DET
easat-9284	246	5	flexibility	flexibility	NOUN
easat-9284	246	6	of	of	ADP
easat-9284	246	7	the	the	DET
easat-9284	246	8	proposed	propose	VERB
easat-9284	246	9	contraction	contraction	NOUN
easat-9284	246	10	in	in	ADP
easat-9284	246	11	handling	handling	NOUN
easat-9284	246	12	nonlinearities	nonlinearitie	NOUN
easat-9284	246	13	and	and	CCONJ
easat-9284	246	14	structural	structural	ADJ
easat-9284	246	15	delays	delay	NOUN
easat-9284	246	16	not	not	PART
easat-9284	246	17	captured	capture	VERB
easat-9284	246	18	by	by	ADP
easat-9284	246	19	classical	classical	ADJ
easat-9284	246	20	fixed	fix	VERB
easat-9284	246	21	point	point	NOUN
easat-9284	246	22	theories	theory	NOUN
easat-9284	246	23	.	.	PUNCT
easat-9284	247	1	our	our	PRON
easat-9284	247	2	results	result	NOUN
easat-9284	247	3	not	not	PART
easat-9284	247	4	only	only	ADV
easat-9284	247	5	unify	unify	VERB
easat-9284	247	6	and	and	CCONJ
easat-9284	247	7	extend	extend	VERB
easat-9284	247	8	several	several	ADJ
easat-9284	247	9	existing	exist	VERB
easat-9284	247	10	fixed	fix	VERB
easat-9284	247	11	point	point	NOUN
easat-9284	247	12	results	result	NOUN
easat-9284	247	13	but	but	CCONJ
easat-9284	247	14	also	also	ADV
easat-9284	247	15	open	open	VERB
easat-9284	247	16	up	up	ADP
easat-9284	247	17	potential	potential	NOUN
easat-9284	247	18	for	for	ADP
easat-9284	247	19	further	further	ADJ
easat-9284	247	20	research	research	NOUN
easat-9284	247	21	into	into	ADP
easat-9284	247	22	more	more	ADV
easat-9284	247	23	complex	complex	ADJ
easat-9284	247	24	integral	integral	ADJ
easat-9284	247	25	and	and	CCONJ
easat-9284	247	26	operator	operator	NOUN
easat-9284	247	27	equations	equation	NOUN
easat-9284	247	28	involving	involve	VERB
easat-9284	247	29	memory	memory	NOUN
easat-9284	247	30	,	,	PUNCT
easat-9284	247	31	feedback	feedback	NOUN
easat-9284	247	32	,	,	PUNCT
easat-9284	247	33	or	or	CCONJ
easat-9284	247	34	hybrid	hybrid	NOUN
easat-9284	247	35	systems	system	NOUN
easat-9284	247	36	.	.	PUNCT
easat-9284	248	1	transparency	transparency	NOUN
easat-9284	248	2	:	:	PUNCT
easat-9284	248	3	the	the	DET
easat-9284	248	4	author	author	NOUN
easat-9284	248	5	confirms	confirm	VERB
easat-9284	248	6	that	that	SCONJ
easat-9284	248	7	the	the	DET
easat-9284	248	8	manuscript	manuscript	NOUN
easat-9284	248	9	is	be	AUX
easat-9284	248	10	an	an	DET
easat-9284	248	11	honest	honest	ADJ
easat-9284	248	12	,	,	PUNCT
easat-9284	248	13	accurate	accurate	ADJ
easat-9284	248	14	,	,	PUNCT
easat-9284	248	15	and	and	CCONJ
easat-9284	248	16	transparent	transparent	ADJ
easat-9284	248	17	account	account	NOUN
easat-9284	248	18	of	of	ADP
easat-9284	248	19	the	the	DET
easat-9284	248	20	study	study	NOUN
easat-9284	248	21	;	;	PUNCT
easat-9284	248	22	that	that	SCONJ
easat-9284	248	23	no	no	DET
easat-9284	248	24	vital	vital	ADJ
easat-9284	248	25	features	feature	NOUN
easat-9284	248	26	of	of	ADP
easat-9284	248	27	the	the	DET
easat-9284	248	28	study	study	NOUN
easat-9284	248	29	have	have	AUX
easat-9284	248	30	been	be	AUX
easat-9284	248	31	omitted	omit	VERB
easat-9284	248	32	;	;	PUNCT
easat-9284	248	33	and	and	CCONJ
easat-9284	248	34	that	that	SCONJ
easat-9284	248	35	any	any	DET
easat-9284	248	36	discrepancies	discrepancy	NOUN
easat-9284	248	37	from	from	ADP
easat-9284	248	38	the	the	DET
easat-9284	248	39	study	study	NOUN
easat-9284	248	40	as	as	SCONJ
easat-9284	248	41	planned	plan	VERB
easat-9284	248	42	have	have	AUX
easat-9284	248	43	been	be	AUX
easat-9284	248	44	explained	explain	VERB
easat-9284	248	45	.	.	PUNCT
easat-9284	249	1	this	this	DET
easat-9284	249	2	study	study	NOUN
easat-9284	249	3	followed	follow	VERB
easat-9284	249	4	all	all	DET
easat-9284	249	5	ethical	ethical	ADJ
easat-9284	249	6	practices	practice	NOUN
easat-9284	249	7	during	during	ADP
easat-9284	249	8	writing	writing	NOUN
easat-9284	249	9	.	.	PUNCT
easat-9284	250	1	copyright	copyright	NOUN
easat-9284	250	2	:	:	PUNCT
easat-9284	250	3	©	©	PROPN
easat-9284	250	4	2025	2025	NUM
easat-9284	250	5	by	by	ADP
easat-9284	250	6	the	the	DET
easat-9284	250	7	author	author	NOUN
easat-9284	250	8	.	.	PUNCT
easat-9284	251	1	this	this	DET
easat-9284	251	2	open	open	ADJ
easat-9284	251	3	-	-	PUNCT
easat-9284	251	4	access	access	NOUN
easat-9284	251	5	article	article	NOUN
easat-9284	251	6	is	be	AUX
easat-9284	251	7	distributed	distribute	VERB
easat-9284	251	8	under	under	ADP
easat-9284	251	9	the	the	DET
easat-9284	251	10	terms	term	NOUN
easat-9284	251	11	and	and	CCONJ
easat-9284	251	12	conditions	condition	NOUN
easat-9284	251	13	of	of	ADP
easat-9284	251	14	the	the	DET
easat-9284	251	15	creative	creative	ADJ
easat-9284	251	16	commons	common	NOUN
easat-9284	251	17	attribution	attribution	NOUN
easat-9284	251	18	(	(	PUNCT
easat-9284	251	19	cc	cc	NOUN
easat-9284	251	20	by	by	ADP
easat-9284	251	21	)	)	PUNCT
easat-9284	251	22	license	license	NOUN
easat-9284	251	23	(	(	PUNCT
easat-9284	251	24	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
easat-9284	251	25	)	)	PUNCT
easat-9284	251	26	.	.	PUNCT
easat-9284	252	1	references	reference	NOUN
easat-9284	252	2	[	[	X
easat-9284	252	3	1	1	X
easat-9284	252	4	]	]	PUNCT
easat-9284	252	5	s.	s.	PROPN
easat-9284	252	6	banach	banach	PROPN
easat-9284	252	7	,	,	PUNCT
easat-9284	252	8	"	"	PUNCT
easat-9284	252	9	on	on	ADP
easat-9284	252	10	operations	operation	NOUN
easat-9284	252	11	in	in	ADP
easat-9284	252	12	abstract	abstract	ADJ
easat-9284	252	13	sets	set	NOUN
easat-9284	252	14	and	and	CCONJ
easat-9284	252	15	their	their	PRON
easat-9284	252	16	application	application	NOUN
easat-9284	252	17	to	to	ADP
easat-9284	252	18	integral	integral	ADJ
easat-9284	252	19	equations	equation	NOUN
easat-9284	252	20	,	,	PUNCT
easat-9284	252	21	"	"	PUNCT
easat-9284	252	22	fundamenta	fundamenta	PROPN
easat-9284	252	23	mathematicae	mathematicae	PROPN
easat-9284	252	24	,	,	PUNCT
easat-9284	252	25	vol	vol	NOUN
easat-9284	252	26	.	.	PROPN
easat-9284	253	1	3	3	NUM
easat-9284	253	2	,	,	PUNCT
easat-9284	253	3	no	no	INTJ
easat-9284	253	4	.	.	NOUN
easat-9284	253	5	1	1	NUM
easat-9284	253	6	,	,	PUNCT
easat-9284	253	7	pp	pp	ADJ
easat-9284	253	8	.	.	PUNCT
easat-9284	254	1	133	133	NUM
easat-9284	254	2	-	-	SYM
easat-9284	254	3	181	181	NUM
easat-9284	254	4	,	,	PUNCT
easat-9284	254	5	1922	1922	NUM
easat-9284	254	6	.	.	PUNCT
easat-9284	255	1	[	[	X
easat-9284	255	2	2	2	NUM
easat-9284	255	3	]	]	X
easat-9284	255	4	r.	r.	PROPN
easat-9284	255	5	kannan	kannan	PROPN
easat-9284	255	6	,	,	PUNCT
easat-9284	255	7	"	"	PUNCT
easat-9284	255	8	some	some	DET
easat-9284	255	9	results	result	NOUN
easat-9284	255	10	on	on	ADP
easat-9284	255	11	fixed	fix	VERB
easat-9284	255	12	points	point	NOUN
easat-9284	255	13	,	,	PUNCT
easat-9284	255	14	"	"	PUNCT
easat-9284	255	15	bulletin	bulletin	NOUN
easat-9284	255	16	of	of	ADP
easat-9284	255	17	the	the	DET
easat-9284	255	18	calcutta	calcutta	NOUN
easat-9284	255	19	mathematical	mathematical	ADJ
easat-9284	255	20	society	society	NOUN
easat-9284	255	21	,	,	PUNCT
easat-9284	255	22	vol	vol	NOUN
easat-9284	255	23	.	.	PROPN
easat-9284	255	24	60	60	NUM
easat-9284	255	25	,	,	PUNCT
easat-9284	255	26	pp	pp	ADJ
easat-9284	255	27	.	.	PUNCT
easat-9284	256	1	71–76	71–76	NUM
easat-9284	256	2	,	,	PUNCT
easat-9284	256	3	1968	1968	NUM
easat-9284	256	4	.	.	PUNCT
easat-9284	257	1	[	[	X
easat-9284	257	2	3	3	X
easat-9284	257	3	]	]	PUNCT
easat-9284	257	4	s.	s.	PROPN
easat-9284	257	5	reich	reich	PROPN
easat-9284	257	6	,	,	PUNCT
easat-9284	257	7	"	"	PUNCT
easat-9284	257	8	fixed	fix	VERB
easat-9284	257	9	points	point	NOUN
easat-9284	257	10	of	of	ADP
easat-9284	257	11	contractive	contractive	ADJ
easat-9284	257	12	functions	function	NOUN
easat-9284	257	13	,	,	PUNCT
easat-9284	257	14	"	"	PUNCT
easat-9284	257	15	bollettino	bollettino	PROPN
easat-9284	257	16	dell’unione	dell’unione	PROPN
easat-9284	257	17	matematica	matematica	PROPN
easat-9284	257	18	italiana	italiana	PROPN
easat-9284	257	19	,	,	PUNCT
easat-9284	257	20	vol	vol	NOUN
easat-9284	257	21	.	.	PROPN
easat-9284	257	22	5	5	NUM
easat-9284	257	23	,	,	PUNCT
easat-9284	257	24	no	no	INTJ
easat-9284	257	25	.	.	NOUN
easat-9284	257	26	1	1	NUM
easat-9284	257	27	,	,	PUNCT
easat-9284	257	28	pp	pp	ADJ
easat-9284	257	29	.	.	PUNCT
easat-9284	258	1	26–42	26–42	NUM
easat-9284	258	2	,	,	PUNCT
easat-9284	258	3	1972	1972	NUM
easat-9284	258	4	.	.	PUNCT
easat-9284	259	1	[	[	X
easat-9284	259	2	4	4	X
easat-9284	259	3	]	]	X
easat-9284	259	4	g.	g.	PROPN
easat-9284	259	5	e.	e.	PROPN
easat-9284	259	6	hardy	hardy	PROPN
easat-9284	259	7	and	and	CCONJ
easat-9284	259	8	t.	t.	PROPN
easat-9284	259	9	d.	d.	PROPN
easat-9284	259	10	rogers	rogers	PROPN
easat-9284	259	11	,	,	PUNCT
easat-9284	259	12	"	"	PUNCT
easat-9284	259	13	a	a	DET
easat-9284	259	14	generalization	generalization	NOUN
easat-9284	259	15	of	of	ADP
easat-9284	259	16	a	a	DET
easat-9284	259	17	fixed	fix	VERB
easat-9284	259	18	point	point	NOUN
easat-9284	259	19	theorem	theorem	NOUN
easat-9284	259	20	of	of	ADP
easat-9284	259	21	reich	reich	PROPN
easat-9284	259	22	,	,	PUNCT
easat-9284	259	23	"	"	PUNCT
easat-9284	259	24	canadian	canadian	ADJ
easat-9284	259	25	mathematical	mathematical	ADJ
easat-9284	259	26	bulletin	bulletin	NOUN
easat-9284	259	27	,	,	PUNCT
easat-9284	259	28	vol	vol	NOUN
easat-9284	259	29	.	.	PROPN
easat-9284	259	30	16	16	NUM
easat-9284	259	31	,	,	PUNCT
easat-9284	259	32	no	no	INTJ
easat-9284	259	33	.	.	NOUN
easat-9284	259	34	2	2	NUM
easat-9284	259	35	,	,	PUNCT
easat-9284	259	36	pp	pp	ADJ
easat-9284	259	37	.	.	PUNCT
easat-9284	259	38	201	201	NUM
easat-9284	259	39	-	-	SYM
easat-9284	259	40	206	206	NUM
easat-9284	259	41	,	,	PUNCT
easat-9284	259	42	1973	1973	NUM
easat-9284	259	43	.	.	PUNCT
easat-9284	260	1	https://doi.org/10.4153/cmb-1973-036-0	https://doi.org/10.4153/cmb-1973-036-0	PROPN
easat-9284	260	2	[	[	X
easat-9284	260	3	5	5	X
easat-9284	260	4	]	]	PUNCT
easat-9284	260	5	v.	v.	CCONJ
easat-9284	260	6	berinde	berinde	NOUN
easat-9284	260	7	,	,	PUNCT
easat-9284	260	8	"	"	PUNCT
easat-9284	260	9	on	on	ADP
easat-9284	260	10	the	the	DET
easat-9284	260	11	approximation	approximation	NOUN
easat-9284	260	12	of	of	ADP
easat-9284	260	13	fixed	fix	VERB
easat-9284	260	14	points	point	NOUN
easat-9284	260	15	of	of	ADP
easat-9284	260	16	weak	weak	ADJ
easat-9284	260	17	contractions	contraction	NOUN
easat-9284	260	18	,	,	PUNCT
easat-9284	260	19	"	"	PUNCT
easat-9284	260	20	carpathian	carpathian	ADJ
easat-9284	260	21	journal	journal	NOUN
easat-9284	260	22	of	of	ADP
easat-9284	260	23	mathematics	mathematics	PROPN
easat-9284	260	24	,	,	PUNCT
easat-9284	260	25	vol	vol	NOUN
easat-9284	260	26	.	.	PROPN
easat-9284	260	27	20	20	NUM
easat-9284	260	28	,	,	PUNCT
easat-9284	260	29	no	no	INTJ
easat-9284	260	30	.	.	NOUN
easat-9284	260	31	1	1	NUM
easat-9284	260	32	,	,	PUNCT
easat-9284	260	33	pp	pp	ADJ
easat-9284	260	34	.	.	PUNCT
easat-9284	261	1	7–22	7–22	PROPN
easat-9284	261	2	,	,	PUNCT
easat-9284	261	3	2004	2004	NUM
easat-9284	261	4	.	.	PUNCT
easat-9284	262	1	[	[	X
easat-9284	262	2	6	6	NUM
easat-9284	262	3	]	]	X
easat-9284	262	4	d.	d.	PROPN
easat-9284	262	5	wardowski	wardowski	PROPN
easat-9284	262	6	,	,	PUNCT
easat-9284	262	7	"	"	PUNCT
easat-9284	262	8	fixed	fix	VERB
easat-9284	262	9	points	point	NOUN
easat-9284	262	10	of	of	ADP
easat-9284	262	11	a	a	DET
easat-9284	262	12	new	new	ADJ
easat-9284	262	13	type	type	NOUN
easat-9284	262	14	of	of	ADP
easat-9284	262	15	contractive	contractive	ADJ
easat-9284	262	16	mappings	mapping	NOUN
easat-9284	262	17	in	in	ADP
easat-9284	262	18	complete	complete	ADJ
easat-9284	262	19	metric	metric	ADJ
easat-9284	262	20	spaces	space	NOUN
easat-9284	262	21	,	,	PUNCT
easat-9284	262	22	"	"	PUNCT
easat-9284	262	23	fixed	fixed	ADJ
easat-9284	262	24	point	point	NOUN
easat-9284	262	25	theory	theory	NOUN
easat-9284	262	26	and	and	CCONJ
easat-9284	262	27	applications	application	NOUN
easat-9284	262	28	,	,	PUNCT
easat-9284	262	29	vol	vol	NOUN
easat-9284	262	30	.	.	PROPN
easat-9284	262	31	2012	2012	NUM
easat-9284	262	32	,	,	PUNCT
easat-9284	262	33	no	no	INTJ
easat-9284	262	34	.	.	NOUN
easat-9284	262	35	1	1	NUM
easat-9284	262	36	,	,	PUNCT
easat-9284	262	37	p.	p.	NOUN
easat-9284	262	38	94	94	NUM
easat-9284	262	39	,	,	PUNCT
easat-9284	262	40	2012	2012	NUM
easat-9284	262	41	.	.	PUNCT
easat-9284	263	1	https://doi.org/10.1186/1687-1812-2012-94	https://doi.org/10.1186/1687-1812-2012-94	PROPN
easat-9284	263	2	[	[	X
easat-9284	263	3	7	7	NUM
easat-9284	263	4	]	]	X
easat-9284	263	5	p.	p.	NOUN
easat-9284	263	6	gautam	gautam	PROPN
easat-9284	263	7	,	,	PUNCT
easat-9284	263	8	s.	s.	PROPN
easat-9284	263	9	kumar	kumar	PROPN
easat-9284	263	10	,	,	PUNCT
easat-9284	263	11	s.	s.	PROPN
easat-9284	263	12	verma	verma	PROPN
easat-9284	263	13	,	,	PUNCT
easat-9284	263	14	and	and	CCONJ
easat-9284	263	15	s.	s.	PROPN
easat-9284	263	16	gulati	gulati	PROPN
easat-9284	263	17	,	,	PUNCT
easat-9284	263	18	"	"	PUNCT
easat-9284	263	19	on	on	ADP
easat-9284	263	20	enriched	enrich	VERB
easat-9284	263	21	hardy	hardy	ADJ
easat-9284	263	22	–	–	PUNCT
easat-9284	263	23	rogers	roger	NOUN
easat-9284	263	24	contractions	contraction	NOUN
easat-9284	263	25	in	in	ADP
easat-9284	263	26	banach	banach	NOUN
easat-9284	263	27	space	space	NOUN
easat-9284	263	28	via	via	ADP
easat-9284	263	29	krasnoselskij	krasnoselskij	PROPN
easat-9284	263	30	iteration	iteration	NOUN
easat-9284	263	31	with	with	ADP
easat-9284	263	32	an	an	DET
easat-9284	263	33	application	application	NOUN
easat-9284	263	34	,	,	PUNCT
easat-9284	263	35	"	"	PUNCT
easat-9284	263	36	the	the	DET
easat-9284	263	37	journal	journal	NOUN
easat-9284	263	38	of	of	ADP
easat-9284	263	39	analysis	analysis	NOUN
easat-9284	263	40	,	,	PUNCT
easat-9284	263	41	vol	vol	NOUN
easat-9284	263	42	.	.	PROPN
easat-9284	263	43	32	32	NUM
easat-9284	263	44	,	,	PUNCT
easat-9284	263	45	no	no	INTJ
easat-9284	263	46	.	.	NOUN
easat-9284	263	47	2	2	NUM
easat-9284	263	48	,	,	PUNCT
easat-9284	263	49	pp	pp	ADJ
easat-9284	263	50	.	.	PUNCT
easat-9284	264	1	1145	1145	NUM
easat-9284	264	2	-	-	SYM
easat-9284	264	3	1160	1160	NUM
easat-9284	264	4	,	,	PUNCT
easat-9284	264	5	2024	2024	NUM
easat-9284	264	6	.	.	PUNCT
easat-9284	265	1	https://doi.org/10.1007/s41478-023-00680-6	https://doi.org/10.1007/s41478-023-00680-6	NUM
easat-9284	266	1	[	[	X
easat-9284	266	2	8	8	NUM
easat-9284	266	3	]	]	X
easat-9284	266	4	l.	l.	PROPN
easat-9284	266	5	ćirić	ćirić	PROPN
easat-9284	266	6	,	,	PUNCT
easat-9284	266	7	"	"	PUNCT
easat-9284	266	8	a	a	DET
easat-9284	266	9	generalization	generalization	NOUN
easat-9284	266	10	of	of	ADP
easat-9284	266	11	banach	banach	NOUN
easat-9284	266	12	’s	’s	PART
easat-9284	266	13	contraction	contraction	NOUN
easat-9284	266	14	principle	principle	NOUN
easat-9284	266	15	,	,	PUNCT
easat-9284	266	16	"	"	PUNCT
easat-9284	266	17	proceedings	proceeding	NOUN
easat-9284	266	18	of	of	ADP
easat-9284	266	19	the	the	DET
easat-9284	266	20	american	american	PROPN
easat-9284	266	21	mathematical	mathematical	PROPN
easat-9284	266	22	society	society	NOUN
easat-9284	266	23	,	,	PUNCT
easat-9284	266	24	vol	vol	NOUN
easat-9284	266	25	.	.	PROPN
easat-9284	266	26	45	45	NUM
easat-9284	266	27	,	,	PUNCT
easat-9284	266	28	no	no	INTJ
easat-9284	266	29	.	.	NOUN
easat-9284	266	30	2	2	NUM
easat-9284	266	31	,	,	PUNCT
easat-9284	266	32	pp	pp	ADJ
easat-9284	266	33	.	.	PUNCT
easat-9284	267	1	267–273	267–273	NUM
easat-9284	267	2	,	,	PUNCT
easat-9284	267	3	1974	1974	NUM
easat-9284	267	4	.	.	PUNCT
easat-9284	268	1	[	[	X
easat-9284	268	2	9	9	NUM
easat-9284	268	3	]	]	PUNCT
easat-9284	268	4	v.	v.	ADP
easat-9284	268	5	berinde	berinde	NOUN
easat-9284	268	6	and	and	CCONJ
easat-9284	268	7	m.	m.	NOUN
easat-9284	268	8	păcurar	păcurar	NOUN
easat-9284	268	9	,	,	PUNCT
easat-9284	268	10	"	"	PUNCT
easat-9284	268	11	approximating	approximate	VERB
easat-9284	268	12	fixed	fix	VERB
easat-9284	268	13	points	point	NOUN
easat-9284	268	14	of	of	ADP
easat-9284	268	15	enriched	enrich	VERB
easat-9284	268	16	contractions	contraction	NOUN
easat-9284	268	17	in	in	ADP
easat-9284	268	18	banach	banach	NOUN
easat-9284	268	19	spaces	space	NOUN
easat-9284	268	20	,	,	PUNCT
easat-9284	268	21	"	"	PUNCT
easat-9284	268	22	journal	journal	NOUN
easat-9284	268	23	of	of	ADP
easat-9284	268	24	fixed	fix	VERB
easat-9284	268	25	point	point	NOUN
easat-9284	268	26	theory	theory	NOUN
easat-9284	268	27	and	and	CCONJ
easat-9284	268	28	applications	application	NOUN
easat-9284	268	29	,	,	PUNCT
easat-9284	268	30	vol	vol	NOUN
easat-9284	268	31	.	.	PROPN
easat-9284	269	1	22	22	NUM
easat-9284	269	2	,	,	PUNCT
easat-9284	269	3	no	no	INTJ
easat-9284	269	4	.	.	NOUN
easat-9284	269	5	2	2	NUM
easat-9284	269	6	,	,	PUNCT
easat-9284	269	7	p.	p.	NOUN
easat-9284	269	8	38	38	NUM
easat-9284	269	9	,	,	PUNCT
easat-9284	269	10	2020	2020	NUM
easat-9284	269	11	.	.	PUNCT
easat-9284	270	1	https://doi.org/10.1007/s11784-020-0769-9	https://doi.org/10.1007/s11784-020-0769-9	NUM
easat-9284	271	1	[	[	X
easat-9284	271	2	10	10	NUM
easat-9284	271	3	]	]	X
easat-9284	271	4	v.	v.	CCONJ
easat-9284	271	5	berinde	berinde	NOUN
easat-9284	271	6	,	,	PUNCT
easat-9284	271	7	"	"	PUNCT
easat-9284	271	8	approximating	approximate	VERB
easat-9284	271	9	fixed	fix	VERB
easat-9284	271	10	points	point	NOUN
easat-9284	271	11	of	of	ADP
easat-9284	271	12	enriched	enrich	VERB
easat-9284	271	13	nonexpansive	nonexpansive	ADJ
easat-9284	271	14	mappings	mapping	NOUN
easat-9284	271	15	by	by	ADP
easat-9284	271	16	krasnoselskij	krasnoselskij	ADJ
easat-9284	271	17	iteration	iteration	NOUN
easat-9284	271	18	in	in	ADP
easat-9284	271	19	hilbert	hilbert	PROPN
easat-9284	271	20	spaces	space	NOUN
easat-9284	271	21	,	,	PUNCT
easat-9284	271	22	"	"	PUNCT
easat-9284	271	23	carpathian	carpathian	ADJ
easat-9284	271	24	journal	journal	NOUN
easat-9284	271	25	of	of	ADP
easat-9284	271	26	mathematics	mathematics	PROPN
easat-9284	271	27	,	,	PUNCT
easat-9284	271	28	vol	vol	NOUN
easat-9284	271	29	.	.	PROPN
easat-9284	271	30	35	35	NUM
easat-9284	271	31	,	,	PUNCT
easat-9284	271	32	no	no	INTJ
easat-9284	271	33	.	.	NOUN
easat-9284	271	34	3	3	NUM
easat-9284	271	35	,	,	PUNCT
easat-9284	271	36	pp	pp	ADJ
easat-9284	271	37	.	.	PUNCT
easat-9284	272	1	293	293	NUM
easat-9284	272	2	-	-	SYM
easat-9284	272	3	304	304	NUM
easat-9284	272	4	,	,	PUNCT
easat-9284	272	5	2019	2019	NUM
easat-9284	272	6	.	.	PUNCT
easat-9284	273	1	[	[	X
easat-9284	273	2	11	11	NUM
easat-9284	273	3	]	]	PUNCT
easat-9284	273	4	m.	m.	NOUN
easat-9284	273	5	krasnoselskii	krasnoselskii	PROPN
easat-9284	273	6	,	,	PUNCT
easat-9284	273	7	"	"	PUNCT
easat-9284	273	8	two	two	NUM
easat-9284	273	9	remarks	remark	NOUN
easat-9284	273	10	on	on	ADP
easat-9284	273	11	the	the	DET
easat-9284	273	12	method	method	NOUN
easat-9284	273	13	of	of	ADP
easat-9284	273	14	successive	successive	ADJ
easat-9284	273	15	approximations	approximation	NOUN
easat-9284	273	16	,	,	PUNCT
easat-9284	273	17	"	"	PUNCT
easat-9284	273	18	uspekhi	uspekhi	PROPN
easat-9284	273	19	matematicheskikh	matematicheskikh	NOUN
easat-9284	273	20	nauk	nauk	PROPN
easat-9284	273	21	(	(	PUNCT
easat-9284	273	22	russian	russian	PROPN
easat-9284	273	23	mathematical	mathematical	ADJ
easat-9284	273	24	surveys	survey	NOUN
easat-9284	273	25	)	)	PUNCT
easat-9284	273	26	,	,	PUNCT
easat-9284	273	27	vol	vol	NOUN
easat-9284	273	28	.	.	PROPN
easat-9284	273	29	10	10	NUM
easat-9284	273	30	,	,	PUNCT
easat-9284	273	31	no	no	INTJ
easat-9284	273	32	.	.	NOUN
easat-9284	273	33	1	1	NUM
easat-9284	273	34	,	,	PUNCT
easat-9284	273	35	pp	pp	ADJ
easat-9284	273	36	.	.	PUNCT
easat-9284	274	1	123–127	123–127	NUM
easat-9284	274	2	,	,	PUNCT
easat-9284	274	3	1955	1955	NUM
easat-9284	274	4	.	.	PUNCT
easat-9284	275	1	[	[	X
easat-9284	275	2	12	12	NUM
easat-9284	275	3	]	]	PUNCT
easat-9284	275	4	m.	m.	NOUN
easat-9284	275	5	cvetkovic	cvetkovic	PROPN
easat-9284	275	6	,	,	PUNCT
easat-9284	275	7	"	"	PUNCT
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easat-9284	275	9	on	on	ADP
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easat-9284	275	11	-	-	PUNCT
easat-9284	275	12	rogers	rogers	NOUN
easat-9284	275	13	contraction	contraction	NOUN
easat-9284	275	14	,	,	PUNCT
easat-9284	275	15	"	"	PUNCT
easat-9284	275	16	mediterranean	mediterranean	PROPN
easat-9284	275	17	journal	journal	PROPN
easat-9284	275	18	of	of	ADP
easat-9284	275	19	mathematics	mathematics	PROPN
easat-9284	275	20	,	,	PUNCT
easat-9284	275	21	vol	vol	NOUN
easat-9284	275	22	.	.	PROPN
easat-9284	275	23	21	21	NUM
easat-9284	275	24	,	,	PUNCT
easat-9284	275	25	article	article	NOUN
easat-9284	275	26	no	no	NOUN
easat-9284	275	27	.	.	PROPN
easat-9284	275	28	140	140	NUM
easat-9284	275	29	,	,	PUNCT
easat-9284	275	30	2024	2024	NUM
easat-9284	275	31	.	.	PUNCT
easat-9284	276	1	https://doi.org/10.1007/s00009-024-02686-1	https://doi.org/10.1007/s00009-024-02686-1	NUM
easat-9284	276	2	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
easat-9284	276	3	https://doi.org/10.4153/cmb-1973-036-0	https://doi.org/10.4153/cmb-1973-036-0	PROPN
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easat-9284	276	5	https://doi.org/10.1007/s41478-023-00680-6	https://doi.org/10.1007/s41478-023-00680-6	NUM
easat-9284	276	6	https://doi.org/10.1007/s11784-020-0769-9	https://doi.org/10.1007/s11784-020-0769-9	NUM