id	sid	tid	token	lemma	pos
cana-5900	1	1	communications	communication	NOUN
cana-5900	1	2	on	on	ADP
cana-5900	1	3	applied	apply	VERB
cana-5900	1	4	nonlinear	nonlinear	ADJ
cana-5900	1	5	analysis	analysis	NOUN
cana-5900	1	6	issn	issn	NOUN
cana-5900	1	7	:	:	PUNCT
cana-5900	1	8	1074	1074	NUM
cana-5900	1	9	-	-	PUNCT
cana-5900	1	10	133x	133x	NUM
cana-5900	1	11	vol	vol	NOUN
cana-5900	1	12	31	31	NUM
cana-5900	1	13	no	no	NOUN
cana-5900	1	14	.	.	PUNCT
cana-5900	2	1	8s	8s	PROPN
cana-5900	2	2	(	(	PUNCT
cana-5900	2	3	2024	2024	NUM
cana-5900	2	4	)	)	PUNCT
cana-5900	2	5	1095	1095	NUM
cana-5900	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5900	2	7	computational	computational	ADJ
cana-5900	2	8	approaches	approach	NOUN
cana-5900	2	9	to	to	ADP
cana-5900	2	10	fixed	fix	VERB
cana-5900	2	11	-	-	PUNCT
cana-5900	2	12	point	point	NOUN
cana-5900	2	13	problems	problem	NOUN
cana-5900	2	14	in	in	ADP
cana-5900	2	15	convex	convex	PROPN
cana-5900	2	16	metric	metric	ADJ
cana-5900	2	17	spaces	space	NOUN
cana-5900	2	18	:	:	PUNCT
cana-5900	2	19	a	a	DET
cana-5900	2	20	generalization	generalization	NOUN
cana-5900	2	21	of	of	ADP
cana-5900	2	22	the	the	DET
cana-5900	2	23	contraction	contraction	NOUN
cana-5900	2	24	principle	principle	NOUN
cana-5900	2	25	bhawna	bhawna	VERB
cana-5900	2	26	malviya1	malviya1	NOUN
cana-5900	2	27	*	*	NOUN
cana-5900	2	28	,	,	PUNCT
cana-5900	2	29	dr	dr	PROPN
cana-5900	2	30	.	.	PROPN
cana-5900	2	31	sanjay	sanjay	PROPN
cana-5900	2	32	choudhary2	choudhary2	PROPN
cana-5900	2	33	1research	1research	NUM
cana-5900	2	34	scholar	scholar	NOUN
cana-5900	2	35	,	,	PUNCT
cana-5900	2	36	barkatullah	barkatullah	PROPN
cana-5900	2	37	university	university	PROPN
cana-5900	2	38	,	,	PUNCT
cana-5900	2	39	bhopal	bhopal	PROPN
cana-5900	2	40	,	,	PUNCT
cana-5900	2	41	mp	mp	PROPN
cana-5900	2	42	,	,	PUNCT
cana-5900	2	43	india	india	PROPN
cana-5900	2	44	.	.	PUNCT
cana-5900	2	45	email	email	NOUN
cana-5900	2	46	:	:	PUNCT
cana-5900	2	47	bhawana1105@gmail.com	bhawana1105@gmail.com	X
cana-5900	3	1	2professor	2professor	NUM
cana-5900	3	2	,	,	PUNCT
cana-5900	3	3	head	head	NOUN
cana-5900	3	4	of	of	ADP
cana-5900	3	5	mathematics	mathematics	PROPN
cana-5900	3	6	department	department	PROPN
cana-5900	3	7	,	,	PUNCT
cana-5900	3	8	govt	govt	PROPN
cana-5900	3	9	.	.	PUNCT
cana-5900	4	1	narmada	narmada	PROPN
cana-5900	4	2	college	college	PROPN
cana-5900	4	3	,	,	PUNCT
cana-5900	4	4	narmadapuram	narmadapuram	PROPN
cana-5900	4	5	,	,	PUNCT
cana-5900	4	6	mp	mp	PROPN
cana-5900	4	7	,	,	PUNCT
cana-5900	4	8	india	india	PROPN
cana-5900	4	9	.	.	PUNCT
cana-5900	4	10	email	email	NOUN
cana-5900	4	11	:	:	PUNCT
cana-5900	4	12	drsanjay0702@gmail.com	drsanjay0702@gmail.com	X
cana-5900	5	1	*	*	PUNCT
cana-5900	5	2	corresponding	correspond	VERB
cana-5900	5	3	author	author	NOUN
cana-5900	5	4	:	:	PUNCT
cana-5900	5	5	bhawana1105@gmail.com	bhawana1105@gmail.com	X
cana-5900	5	6	article	article	NOUN
cana-5900	5	7	history	history	NOUN
cana-5900	5	8	:	:	PUNCT
cana-5900	5	9	received	receive	VERB
cana-5900	5	10	:	:	PUNCT
cana-5900	5	11	02	02	NUM
cana-5900	5	12	-	-	SYM
cana-5900	5	13	10	10	NUM
cana-5900	5	14	-	-	PUNCT
cana-5900	5	15	2024	2024	NUM
cana-5900	5	16	revised	revise	VERB
cana-5900	5	17	:	:	PUNCT
cana-5900	5	18	25	25	NUM
cana-5900	5	19	-	-	SYM
cana-5900	5	20	11	11	NUM
cana-5900	5	21	-	-	PUNCT
cana-5900	5	22	2024	2024	NUM
cana-5900	5	23	accepted	accept	VERB
cana-5900	5	24	:	:	PUNCT
cana-5900	5	25	20	20	NUM
cana-5900	5	26	-	-	SYM
cana-5900	5	27	12	12	NUM
cana-5900	5	28	-	-	PUNCT
cana-5900	5	29	2024	2024	NUM
cana-5900	5	30	abstract	abstract	NOUN
cana-5900	5	31	:	:	PUNCT
cana-5900	5	32	the	the	DET
cana-5900	5	33	concept	concept	NOUN
cana-5900	5	34	of	of	ADP
cana-5900	5	35	a	a	DET
cana-5900	5	36	fixed	fix	VERB
cana-5900	5	37	point	point	NOUN
cana-5900	5	38	,	,	PUNCT
cana-5900	5	39	a	a	DET
cana-5900	5	40	point	point	NOUN
cana-5900	5	41	that	that	PRON
cana-5900	5	42	remains	remain	VERB
cana-5900	5	43	unchanged	unchanged	ADJ
cana-5900	5	44	under	under	ADP
cana-5900	5	45	a	a	DET
cana-5900	5	46	given	give	VERB
cana-5900	5	47	transformation	transformation	NOUN
cana-5900	5	48	,	,	PUNCT
cana-5900	5	49	lies	lie	VERB
cana-5900	5	50	at	at	ADP
cana-5900	5	51	the	the	DET
cana-5900	5	52	heart	heart	NOUN
cana-5900	5	53	of	of	ADP
cana-5900	5	54	numerous	numerous	ADJ
cana-5900	5	55	mathematical	mathematical	ADJ
cana-5900	5	56	disciplines	discipline	NOUN
cana-5900	5	57	,	,	PUNCT
cana-5900	5	58	from	from	ADP
cana-5900	5	59	topology	topology	NOUN
cana-5900	5	60	and	and	CCONJ
cana-5900	5	61	analysis	analysis	NOUN
cana-5900	5	62	to	to	ADP
cana-5900	5	63	economics	economic	NOUN
cana-5900	5	64	and	and	CCONJ
cana-5900	5	65	engineering	engineering	NOUN
cana-5900	5	66	.	.	PUNCT
cana-5900	6	1	the	the	DET
cana-5900	6	2	renowned	renowned	ADJ
cana-5900	6	3	banach	banach	NOUN
cana-5900	6	4	contraction	contraction	NOUN
cana-5900	6	5	principle	principle	NOUN
cana-5900	6	6	provides	provide	VERB
cana-5900	6	7	an	an	DET
cana-5900	6	8	elegant	elegant	ADJ
cana-5900	6	9	and	and	CCONJ
cana-5900	6	10	powerful	powerful	ADJ
cana-5900	6	11	tool	tool	NOUN
cana-5900	6	12	for	for	ADP
cana-5900	6	13	guaranteeing	guarantee	VERB
cana-5900	6	14	the	the	DET
cana-5900	6	15	existence	existence	NOUN
cana-5900	6	16	and	and	CCONJ
cana-5900	6	17	uniqueness	uniqueness	NOUN
cana-5900	6	18	of	of	ADP
cana-5900	6	19	fixed	fix	VERB
cana-5900	6	20	points	point	NOUN
cana-5900	6	21	for	for	ADP
cana-5900	6	22	contraction	contraction	NOUN
cana-5900	6	23	mappings	mapping	NOUN
cana-5900	6	24	in	in	ADP
cana-5900	6	25	complete	complete	ADJ
cana-5900	6	26	metric	metric	ADJ
cana-5900	6	27	spaces	space	NOUN
cana-5900	6	28	.	.	PUNCT
cana-5900	7	1	however	however	ADV
cana-5900	7	2	,	,	PUNCT
cana-5900	7	3	the	the	DET
cana-5900	7	4	strict	strict	ADJ
cana-5900	7	5	contractive	contractive	ADJ
cana-5900	7	6	condition	condition	NOUN
cana-5900	7	7	often	often	ADV
cana-5900	7	8	limits	limit	VERB
cana-5900	7	9	its	its	PRON
cana-5900	7	10	applicability	applicability	NOUN
cana-5900	7	11	in	in	ADP
cana-5900	7	12	real	real	ADJ
cana-5900	7	13	-	-	PUNCT
cana-5900	7	14	world	world	NOUN
cana-5900	7	15	scenarios	scenario	NOUN
cana-5900	7	16	.	.	PUNCT
cana-5900	8	1	this	this	PRON
cana-5900	8	2	has	have	AUX
cana-5900	8	3	driven	drive	VERB
cana-5900	8	4	extensive	extensive	ADJ
cana-5900	8	5	research	research	NOUN
cana-5900	8	6	into	into	ADP
cana-5900	8	7	generalizing	generalize	VERB
cana-5900	8	8	the	the	DET
cana-5900	8	9	contraction	contraction	NOUN
cana-5900	8	10	principle	principle	NOUN
cana-5900	8	11	to	to	ADP
cana-5900	8	12	broader	broad	ADJ
cana-5900	8	13	classes	class	NOUN
cana-5900	8	14	of	of	ADP
cana-5900	8	15	mappings	mapping	NOUN
cana-5900	8	16	and	and	CCONJ
cana-5900	8	17	more	more	ADJ
cana-5900	8	18	complex	complex	ADJ
cana-5900	8	19	spaces	space	NOUN
cana-5900	8	20	,	,	PUNCT
cana-5900	8	21	particularly	particularly	ADV
cana-5900	8	22	convex	convex	VERB
cana-5900	8	23	metric	metric	ADJ
cana-5900	8	24	spaces	space	NOUN
cana-5900	8	25	.	.	PUNCT
cana-5900	9	1	the	the	DET
cana-5900	9	2	computational	computational	ADJ
cana-5900	9	3	approaches	approach	NOUN
cana-5900	9	4	to	to	ADP
cana-5900	9	5	solving	solve	VERB
cana-5900	9	6	these	these	DET
cana-5900	9	7	generalized	generalize	VERB
cana-5900	9	8	fixed	fix	VERB
cana-5900	9	9	-	-	PUNCT
cana-5900	9	10	point	point	NOUN
cana-5900	9	11	problems	problem	NOUN
cana-5900	9	12	in	in	ADP
cana-5900	9	13	such	such	ADJ
cana-5900	9	14	spaces	space	NOUN
cana-5900	9	15	represent	represent	VERB
cana-5900	9	16	a	a	DET
cana-5900	9	17	vibrant	vibrant	ADJ
cana-5900	9	18	and	and	CCONJ
cana-5900	9	19	crucial	crucial	ADJ
cana-5900	9	20	area	area	NOUN
cana-5900	9	21	of	of	ADP
cana-5900	9	22	modern	modern	ADJ
cana-5900	9	23	mathematics	mathematic	NOUN
cana-5900	9	24	,	,	PUNCT
cana-5900	9	25	offering	offer	VERB
cana-5900	9	26	robust	robust	ADJ
cana-5900	9	27	frameworks	framework	NOUN
cana-5900	9	28	for	for	ADP
cana-5900	9	29	addressing	address	VERB
cana-5900	9	30	diverse	diverse	ADJ
cana-5900	9	31	practical	practical	ADJ
cana-5900	9	32	challenges	challenge	NOUN
cana-5900	9	33	.	.	PUNCT
cana-5900	10	1	convex	convex	VERB
cana-5900	10	2	metric	metric	ADJ
cana-5900	10	3	spaces	space	NOUN
cana-5900	10	4	,	,	PUNCT
cana-5900	10	5	which	which	PRON
cana-5900	10	6	include	include	VERB
cana-5900	10	7	normed	norme	VERB
cana-5900	10	8	linear	linear	PROPN
cana-5900	10	9	spaces	space	NOUN
cana-5900	10	10	and	and	CCONJ
cana-5900	10	11	cat(0	cat(0	ADJ
cana-5900	10	12	)	)	PUNCT
cana-5900	10	13	spaces	space	NOUN
cana-5900	10	14	as	as	ADP
cana-5900	10	15	special	special	ADJ
cana-5900	10	16	cases	case	NOUN
cana-5900	10	17	,	,	PUNCT
cana-5900	10	18	provide	provide	VERB
cana-5900	10	19	a	a	DET
cana-5900	10	20	richer	rich	ADJ
cana-5900	10	21	geometric	geometric	ADJ
cana-5900	10	22	structure	structure	NOUN
cana-5900	10	23	than	than	ADP
cana-5900	10	24	general	general	ADJ
cana-5900	10	25	metric	metric	ADJ
cana-5900	10	26	spaces	space	NOUN
cana-5900	10	27	.	.	PUNCT
cana-5900	11	1	this	this	DET
cana-5900	11	2	convexity	convexity	NOUN
cana-5900	11	3	allows	allow	VERB
cana-5900	11	4	for	for	ADP
cana-5900	11	5	the	the	DET
cana-5900	11	6	development	development	NOUN
cana-5900	11	7	of	of	ADP
cana-5900	11	8	more	more	ADV
cana-5900	11	9	sophisticated	sophisticated	ADJ
cana-5900	11	10	iterative	iterative	ADJ
cana-5900	11	11	algorithms	algorithm	NOUN
cana-5900	11	12	that	that	PRON
cana-5900	11	13	leverage	leverage	VERB
cana-5900	11	14	the	the	DET
cana-5900	11	15	"	"	PUNCT
cana-5900	11	16	averaging	averaging	NOUN
cana-5900	11	17	"	"	PUNCT
cana-5900	11	18	or	or	CCONJ
cana-5900	11	19	"	"	PUNCT
cana-5900	11	20	midpoint	midpoint	NOUN
cana-5900	11	21	"	"	PUNCT
cana-5900	11	22	properties	property	NOUN
cana-5900	11	23	of	of	ADP
cana-5900	11	24	the	the	DET
cana-5900	11	25	space	space	NOUN
cana-5900	11	26	.	.	PUNCT
cana-5900	12	1	one	one	NUM
cana-5900	12	2	of	of	ADP
cana-5900	12	3	the	the	DET
cana-5900	12	4	most	most	ADV
cana-5900	12	5	significant	significant	ADJ
cana-5900	12	6	generalizations	generalization	NOUN
cana-5900	12	7	of	of	ADP
cana-5900	12	8	the	the	DET
cana-5900	12	9	contraction	contraction	NOUN
cana-5900	12	10	principle	principle	NOUN
cana-5900	12	11	in	in	ADP
cana-5900	12	12	this	this	DET
cana-5900	12	13	context	context	NOUN
cana-5900	12	14	involves	involve	VERB
cana-5900	12	15	extending	extend	VERB
cana-5900	12	16	the	the	DET
cana-5900	12	17	notion	notion	NOUN
cana-5900	12	18	of	of	ADP
cana-5900	12	19	contraction	contraction	NOUN
cana-5900	12	20	to	to	ADP
cana-5900	12	21	various	various	ADJ
cana-5900	12	22	non	non	ADJ
cana-5900	12	23	-	-	ADJ
cana-5900	12	24	expansive	expansive	ADJ
cana-5900	12	25	or	or	CCONJ
cana-5900	12	26	quasi	quasi	ADJ
cana-5900	12	27	-	-	ADJ
cana-5900	12	28	nonexpansive	nonexpansive	ADJ
cana-5900	12	29	mappings	mapping	NOUN
cana-5900	12	30	.	.	PUNCT
cana-5900	13	1	while	while	SCONJ
cana-5900	13	2	these	these	DET
cana-5900	13	3	mappings	mapping	NOUN
cana-5900	13	4	do	do	AUX
cana-5900	13	5	not	not	PART
cana-5900	13	6	necessarily	necessarily	ADV
cana-5900	13	7	shrink	shrink	VERB
cana-5900	13	8	distances	distance	NOUN
cana-5900	13	9	between	between	ADP
cana-5900	13	10	all	all	DET
cana-5900	13	11	points	point	NOUN
cana-5900	13	12	,	,	PUNCT
cana-5900	13	13	they	they	PRON
cana-5900	13	14	possess	possess	VERB
cana-5900	13	15	properties	property	NOUN
cana-5900	13	16	that	that	PRON
cana-5900	13	17	still	still	ADV
cana-5900	13	18	allow	allow	VERB
cana-5900	13	19	for	for	ADP
cana-5900	13	20	the	the	DET
cana-5900	13	21	convergence	convergence	NOUN
cana-5900	13	22	of	of	ADP
cana-5900	13	23	iterative	iterative	ADJ
cana-5900	13	24	sequences	sequence	NOUN
cana-5900	13	25	to	to	ADP
cana-5900	13	26	a	a	DET
cana-5900	13	27	fixed	fix	VERB
cana-5900	13	28	point	point	NOUN
cana-5900	13	29	.	.	PUNCT
cana-5900	14	1	examples	example	NOUN
cana-5900	14	2	include	include	VERB
cana-5900	14	3	firmly	firmly	ADV
cana-5900	14	4	nonexpansive	nonexpansive	ADJ
cana-5900	14	5	mappings	mapping	NOUN
cana-5900	14	6	,	,	PUNCT
cana-5900	14	7	suzuki	suzuki	PROPN
cana-5900	14	8	generalized	generalize	VERB
cana-5900	14	9	non	non	ADJ
cana-5900	14	10	-	-	ADJ
cana-5900	14	11	expansive	expansive	ADJ
cana-5900	14	12	mappings	mapping	NOUN
cana-5900	14	13	,	,	PUNCT
cana-5900	14	14	and	and	CCONJ
cana-5900	14	15	mappings	mapping	NOUN
cana-5900	14	16	satisfying	satisfy	VERB
cana-5900	14	17	more	more	ADJ
cana-5900	14	18	abstract	abstract	ADJ
cana-5900	14	19	contractive	contractive	ADJ
cana-5900	14	20	conditions	condition	NOUN
cana-5900	14	21	,	,	PUNCT
cana-5900	14	22	all	all	PRON
cana-5900	14	23	of	of	ADP
cana-5900	14	24	which	which	PRON
cana-5900	14	25	are	be	AUX
cana-5900	14	26	instrumental	instrumental	ADJ
cana-5900	14	27	in	in	ADP
cana-5900	14	28	modeling	model	VERB
cana-5900	14	29	phenomena	phenomenon	NOUN
cana-5900	14	30	where	where	SCONJ
cana-5900	14	31	strict	strict	ADJ
cana-5900	14	32	contraction	contraction	NOUN
cana-5900	14	33	might	might	AUX
cana-5900	14	34	not	not	PART
cana-5900	14	35	hold	hold	VERB
cana-5900	14	36	.	.	PUNCT
cana-5900	15	1	we	we	PRON
cana-5900	15	2	used	use	VERB
cana-5900	15	3	the	the	DET
cana-5900	15	4	python	python	NOUN
cana-5900	15	5	language	language	NOUN
cana-5900	15	6	.	.	PUNCT
cana-5900	16	1	picard	picard	NOUN
cana-5900	16	2	iteration	iteration	NOUN
cana-5900	16	3	was	be	AUX
cana-5900	16	4	used	use	VERB
cana-5900	16	5	to	to	PART
cana-5900	16	6	find	find	VERB
cana-5900	16	7	a	a	DET
cana-5900	16	8	fixed	fix	VERB
cana-5900	16	9	point	point	NOUN
cana-5900	16	10	of	of	ADP
cana-5900	16	11	a	a	DET
cana-5900	16	12	mapping	mapping	NOUN
cana-5900	16	13	.	.	PUNCT
cana-5900	17	1	mann	mann	PROPN
cana-5900	17	2	iteration	iteration	PROPN
cana-5900	17	3	was	be	AUX
cana-5900	17	4	used	use	VERB
cana-5900	17	5	in	in	ADP
cana-5900	17	6	convex	convex	ADJ
cana-5900	17	7	space	space	NOUN
cana-5900	17	8	.	.	PUNCT
cana-5900	18	1	keywords	keyword	NOUN
cana-5900	18	2	:	:	PUNCT
cana-5900	18	3	computational	computational	ADJ
cana-5900	18	4	,	,	PUNCT
cana-5900	18	5	fixed	fix	VERB
cana-5900	18	6	-	-	PUNCT
cana-5900	18	7	point	point	NOUN
cana-5900	18	8	,	,	PUNCT
cana-5900	18	9	convex	convex	NOUN
cana-5900	18	10	,	,	PUNCT
cana-5900	18	11	metric	metric	ADJ
cana-5900	18	12	,	,	PUNCT
cana-5900	18	13	spaces	space	NOUN
cana-5900	18	14	introduction	introduction	NOUN
cana-5900	18	15	the	the	DET
cana-5900	18	16	computational	computational	ADJ
cana-5900	18	17	backbone	backbone	NOUN
cana-5900	18	18	of	of	ADP
cana-5900	18	19	solving	solve	VERB
cana-5900	18	20	these	these	DET
cana-5900	18	21	generalized	generalize	VERB
cana-5900	18	22	fixed	fix	VERB
cana-5900	18	23	-	-	PUNCT
cana-5900	18	24	point	point	NOUN
cana-5900	18	25	problems	problem	NOUN
cana-5900	18	26	lies	lie	VERB
cana-5900	18	27	in	in	ADP
cana-5900	18	28	the	the	DET
cana-5900	18	29	design	design	NOUN
cana-5900	18	30	and	and	CCONJ
cana-5900	18	31	analysis	analysis	NOUN
cana-5900	18	32	of	of	ADP
cana-5900	18	33	iterative	iterative	ADJ
cana-5900	18	34	algorithms	algorithm	NOUN
cana-5900	18	35	.	.	PUNCT
cana-5900	19	1	the	the	DET
cana-5900	19	2	classical	classical	ADJ
cana-5900	19	3	picard	picard	NOUN
cana-5900	19	4	iteration	iteration	NOUN
cana-5900	19	5	,	,	PUNCT
cana-5900	19	6	while	while	SCONJ
cana-5900	19	7	effective	effective	ADJ
cana-5900	19	8	for	for	ADP
cana-5900	19	9	strict	strict	ADJ
cana-5900	19	10	contractions	contraction	NOUN
cana-5900	19	11	,	,	PUNCT
cana-5900	19	12	often	often	ADV
cana-5900	19	13	fails	fail	VERB
cana-5900	19	14	for	for	ADP
cana-5900	19	15	non	non	ADJ
cana-5900	19	16	-	-	ADJ
cana-5900	19	17	expansive	expansive	ADJ
cana-5900	19	18	mappings	mapping	NOUN
cana-5900	19	19	.	.	PUNCT
cana-5900	20	1	this	this	PRON
cana-5900	20	2	necessitates	necessitate	VERB
cana-5900	20	3	the	the	DET
cana-5900	20	4	development	development	NOUN
cana-5900	20	5	of	of	ADP
cana-5900	20	6	more	more	ADV
cana-5900	20	7	advanced	advanced	ADJ
cana-5900	20	8	techniques	technique	NOUN
cana-5900	20	9	.	.	PUNCT
cana-5900	21	1	prominent	prominent	ADJ
cana-5900	21	2	among	among	ADP
cana-5900	21	3	these	these	PRON
cana-5900	21	4	are	be	AUX
cana-5900	21	5	mann	mann	PROPN
cana-5900	21	6	iteration	iteration	NOUN
cana-5900	21	7	,	,	PUNCT
cana-5900	21	8	ishikawa	ishikawa	PROPN
cana-5900	21	9	iteration	iteration	NOUN
cana-5900	21	10	,	,	PUNCT
cana-5900	21	11	and	and	CCONJ
cana-5900	21	12	their	their	PRON
cana-5900	21	13	mailto:bhawana1105@gmail.com	mailto:bhawana1105@gmail.com	PROPN
cana-5900	21	14	communications	communication	NOUN
cana-5900	21	15	on	on	ADP
cana-5900	21	16	applied	apply	VERB
cana-5900	21	17	nonlinear	nonlinear	ADJ
cana-5900	21	18	analysis	analysis	NOUN
cana-5900	21	19	issn	issn	NOUN
cana-5900	21	20	:	:	PUNCT
cana-5900	21	21	1074	1074	NUM
cana-5900	21	22	-	-	PUNCT
cana-5900	21	23	133x	133x	NUM
cana-5900	21	24	vol	vol	NOUN
cana-5900	21	25	31	31	NUM
cana-5900	21	26	no	no	NOUN
cana-5900	21	27	.	.	PUNCT
cana-5900	22	1	8s	8s	PROPN
cana-5900	22	2	(	(	PUNCT
cana-5900	22	3	2024	2024	NUM
cana-5900	22	4	)	)	PUNCT
cana-5900	22	5	1096	1096	NUM
cana-5900	22	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5900	22	7	numerous	numerous	ADJ
cana-5900	22	8	variants	variant	NOUN
cana-5900	22	9	.	.	PUNCT
cana-5900	23	1	these	these	DET
cana-5900	23	2	methods	method	NOUN
cana-5900	23	3	introduce	introduce	VERB
cana-5900	23	4	averaging	average	VERB
cana-5900	23	5	parameters	parameter	NOUN
cana-5900	23	6	or	or	CCONJ
cana-5900	23	7	multi	multi	ADJ
cana-5900	23	8	-	-	ADJ
cana-5900	23	9	step	step	ADJ
cana-5900	23	10	processes	process	NOUN
cana-5900	23	11	to	to	PART
cana-5900	23	12	enhance	enhance	VERB
cana-5900	23	13	convergence	convergence	NOUN
cana-5900	23	14	properties	property	NOUN
cana-5900	23	15	and	and	CCONJ
cana-5900	23	16	stabilize	stabilize	VERB
cana-5900	23	17	the	the	DET
cana-5900	23	18	iterative	iterative	NOUN
cana-5900	23	19	sequence	sequence	NOUN
cana-5900	23	20	.	.	PUNCT
cana-5900	24	1	the	the	DET
cana-5900	24	2	judicious	judicious	ADJ
cana-5900	24	3	selection	selection	NOUN
cana-5900	24	4	of	of	ADP
cana-5900	24	5	these	these	DET
cana-5900	24	6	parameters	parameter	NOUN
cana-5900	24	7	,	,	PUNCT
cana-5900	24	8	often	often	ADV
cana-5900	24	9	guided	guide	VERB
cana-5900	24	10	by	by	ADP
cana-5900	24	11	theoretical	theoretical	ADJ
cana-5900	24	12	convergence	convergence	NOUN
cana-5900	24	13	analyses	analysis	NOUN
cana-5900	24	14	,	,	PUNCT
cana-5900	24	15	plays	play	VERB
cana-5900	24	16	a	a	DET
cana-5900	24	17	critical	critical	ADJ
cana-5900	24	18	role	role	NOUN
cana-5900	24	19	in	in	ADP
cana-5900	24	20	the	the	DET
cana-5900	24	21	efficiency	efficiency	NOUN
cana-5900	24	22	and	and	CCONJ
cana-5900	24	23	stability	stability	NOUN
cana-5900	24	24	of	of	ADP
cana-5900	24	25	the	the	DET
cana-5900	24	26	algorithms	algorithm	NOUN
cana-5900	24	27	.	.	PUNCT
cana-5900	25	1	(	(	PUNCT
cana-5900	25	2	ding	ding	NOUN
cana-5900	25	3	,	,	PUNCT
cana-5900	25	4	2024	2024	NUM
cana-5900	25	5	)	)	PUNCT
cana-5900	25	6	the	the	DET
cana-5900	25	7	practical	practical	ADJ
cana-5900	25	8	implications	implication	NOUN
cana-5900	25	9	of	of	ADP
cana-5900	25	10	these	these	DET
cana-5900	25	11	computational	computational	ADJ
cana-5900	25	12	approaches	approach	NOUN
cana-5900	25	13	are	be	AUX
cana-5900	25	14	far	far	ADV
cana-5900	25	15	-	-	PUNCT
cana-5900	25	16	reaching	reach	VERB
cana-5900	25	17	.	.	PUNCT
cana-5900	26	1	in	in	ADP
cana-5900	26	2	optimization	optimization	NOUN
cana-5900	26	3	theory	theory	NOUN
cana-5900	26	4	,	,	PUNCT
cana-5900	26	5	many	many	ADJ
cana-5900	26	6	convex	convex	ADJ
cana-5900	26	7	optimization	optimization	NOUN
cana-5900	26	8	problems	problem	NOUN
cana-5900	26	9	can	can	AUX
cana-5900	26	10	be	be	AUX
cana-5900	26	11	reformulated	reformulate	VERB
cana-5900	26	12	as	as	ADP
cana-5900	26	13	fixed	fix	VERB
cana-5900	26	14	-	-	PUNCT
cana-5900	26	15	point	point	NOUN
cana-5900	26	16	problems	problem	NOUN
cana-5900	26	17	for	for	ADP
cana-5900	26	18	suitable	suitable	ADJ
cana-5900	26	19	operators	operator	NOUN
cana-5900	26	20	.	.	PUNCT
cana-5900	27	1	for	for	ADP
cana-5900	27	2	example	example	NOUN
cana-5900	27	3	,	,	PUNCT
cana-5900	27	4	the	the	DET
cana-5900	27	5	resolvent	resolvent	NOUN
cana-5900	27	6	of	of	ADP
cana-5900	27	7	a	a	DET
cana-5900	27	8	maximal	maximal	ADJ
cana-5900	27	9	monotone	monotone	NOUN
cana-5900	27	10	operator	operator	NOUN
cana-5900	27	11	is	be	AUX
cana-5900	27	12	firmly	firmly	ADV
cana-5900	27	13	nonexpansive	nonexpansive	ADJ
cana-5900	27	14	,	,	PUNCT
cana-5900	27	15	allowing	allow	VERB
cana-5900	27	16	for	for	ADP
cana-5900	27	17	the	the	DET
cana-5900	27	18	application	application	NOUN
cana-5900	27	19	of	of	ADP
cana-5900	27	20	fixed	fix	VERB
cana-5900	27	21	-	-	PUNCT
cana-5900	27	22	point	point	NOUN
cana-5900	27	23	algorithms	algorithm	NOUN
cana-5900	27	24	to	to	PART
cana-5900	27	25	solve	solve	VERB
cana-5900	27	26	variational	variational	ADJ
cana-5900	27	27	inequalities	inequality	NOUN
cana-5900	27	28	,	,	PUNCT
cana-5900	27	29	equilibrium	equilibrium	NOUN
cana-5900	27	30	problems	problem	NOUN
cana-5900	27	31	,	,	PUNCT
cana-5900	27	32	and	and	CCONJ
cana-5900	27	33	image	image	NOUN
cana-5900	27	34	reconstruction	reconstruction	NOUN
cana-5900	27	35	tasks	task	NOUN
cana-5900	27	36	.	.	PUNCT
cana-5900	28	1	in	in	ADP
cana-5900	28	2	signal	signal	ADJ
cana-5900	28	3	processing	processing	NOUN
cana-5900	28	4	,	,	PUNCT
cana-5900	28	5	iterative	iterative	NOUN
cana-5900	28	6	algorithms	algorithm	NOUN
cana-5900	28	7	based	base	VERB
cana-5900	28	8	on	on	ADP
cana-5900	28	9	fixed	fix	VERB
cana-5900	28	10	-	-	PUNCT
cana-5900	28	11	point	point	NOUN
cana-5900	28	12	theory	theory	NOUN
cana-5900	28	13	are	be	AUX
cana-5900	28	14	used	use	VERB
cana-5900	28	15	for	for	ADP
cana-5900	28	16	denoising	denoising	NOUN
cana-5900	28	17	,	,	PUNCT
cana-5900	28	18	deblurring	deblurring	NOUN
cana-5900	28	19	,	,	PUNCT
cana-5900	28	20	and	and	CCONJ
cana-5900	28	21	compressed	compressed	ADJ
cana-5900	28	22	sensing	sensing	NOUN
cana-5900	28	23	.	.	PUNCT
cana-5900	29	1	furthermore	furthermore	ADV
cana-5900	29	2	,	,	PUNCT
cana-5900	29	3	in	in	ADP
cana-5900	29	4	areas	area	NOUN
cana-5900	29	5	like	like	ADP
cana-5900	29	6	game	game	NOUN
cana-5900	29	7	theory	theory	NOUN
cana-5900	29	8	and	and	CCONJ
cana-5900	29	9	economic	economic	ADJ
cana-5900	29	10	modeling	modeling	NOUN
cana-5900	29	11	,	,	PUNCT
cana-5900	29	12	the	the	DET
cana-5900	29	13	existence	existence	NOUN
cana-5900	29	14	and	and	CCONJ
cana-5900	29	15	computation	computation	NOUN
cana-5900	29	16	of	of	ADP
cana-5900	29	17	equilibrium	equilibrium	NOUN
cana-5900	29	18	points	point	NOUN
cana-5900	29	19	often	often	ADV
cana-5900	29	20	reduce	reduce	VERB
cana-5900	29	21	to	to	ADP
cana-5900	29	22	finding	find	VERB
cana-5900	29	23	fixed	fix	VERB
cana-5900	29	24	points	point	NOUN
cana-5900	29	25	of	of	ADP
cana-5900	29	26	certain	certain	ADJ
cana-5900	29	27	mappings	mapping	NOUN
cana-5900	29	28	,	,	PUNCT
cana-5900	29	29	and	and	CCONJ
cana-5900	29	30	the	the	DET
cana-5900	29	31	generalized	generalized	ADJ
cana-5900	29	32	contraction	contraction	NOUN
cana-5900	29	33	principles	principle	NOUN
cana-5900	29	34	provide	provide	VERB
cana-5900	29	35	the	the	DET
cana-5900	29	36	theoretical	theoretical	ADJ
cana-5900	29	37	underpinning	underpinning	NOUN
cana-5900	29	38	for	for	ADP
cana-5900	29	39	developing	develop	VERB
cana-5900	29	40	effective	effective	ADJ
cana-5900	29	41	solution	solution	NOUN
cana-5900	29	42	strategies	strategy	NOUN
cana-5900	29	43	.	.	PUNCT
cana-5900	30	1	furthermore	furthermore	ADV
cana-5900	30	2	,	,	PUNCT
cana-5900	30	3	the	the	DET
cana-5900	30	4	concept	concept	NOUN
cana-5900	30	5	of	of	ADP
cana-5900	30	6	a	a	DET
cana-5900	30	7	metric	metric	NOUN
cana-5900	30	8	has	have	AUX
cana-5900	30	9	been	be	AUX
cana-5900	30	10	generalized	generalize	VERB
cana-5900	30	11	to	to	ADP
cana-5900	30	12	generalized	generalize	VERB
cana-5900	30	13	metric	metric	ADJ
cana-5900	30	14	spaces	space	NOUN
cana-5900	30	15	(	(	PUNCT
cana-5900	30	16	where	where	SCONJ
cana-5900	30	17	the	the	DET
cana-5900	30	18	metric	metric	NOUN
cana-5900	30	19	can	can	AUX
cana-5900	30	20	take	take	VERB
cana-5900	30	21	values	value	NOUN
cana-5900	30	22	in	in	ADP
cana-5900	30	23	a	a	DET
cana-5900	30	24	banach	banach	NOUN
cana-5900	30	25	space	space	NOUN
cana-5900	30	26	or	or	CCONJ
cana-5900	30	27	a	a	DET
cana-5900	30	28	cone	cone	NOUN
cana-5900	30	29	)	)	PUNCT
cana-5900	30	30	,	,	PUNCT
cana-5900	30	31	b	b	X
cana-5900	30	32	-	-	PUNCT
cana-5900	30	33	metric	metric	ADJ
cana-5900	30	34	spaces	space	NOUN
cana-5900	30	35	(	(	PUNCT
cana-5900	30	36	where	where	SCONJ
cana-5900	30	37	the	the	DET
cana-5900	30	38	triangle	triangle	NOUN
cana-5900	30	39	inequality	inequality	NOUN
cana-5900	30	40	is	be	AUX
cana-5900	30	41	relaxed	relaxed	ADJ
cana-5900	30	42	)	)	PUNCT
cana-5900	30	43	,	,	PUNCT
cana-5900	30	44	and	and	CCONJ
cana-5900	30	45	fuzzy	fuzzy	ADJ
cana-5900	30	46	metric	metric	ADJ
cana-5900	30	47	spaces	space	NOUN
cana-5900	30	48	(	(	PUNCT
cana-5900	30	49	where	where	SCONJ
cana-5900	30	50	the	the	DET
cana-5900	30	51	distance	distance	NOUN
cana-5900	30	52	is	be	AUX
cana-5900	30	53	a	a	DET
cana-5900	30	54	fuzzy	fuzzy	ADJ
cana-5900	30	55	set	set	NOUN
cana-5900	30	56	)	)	PUNCT
cana-5900	30	57	.	.	PUNCT
cana-5900	31	1	these	these	DET
cana-5900	31	2	generalizations	generalization	NOUN
cana-5900	31	3	open	open	VERB
cana-5900	31	4	doors	door	NOUN
cana-5900	31	5	for	for	ADP
cana-5900	31	6	applying	apply	VERB
cana-5900	31	7	fixed	fix	VERB
cana-5900	31	8	-	-	PUNCT
cana-5900	31	9	point	point	NOUN
cana-5900	31	10	theory	theory	NOUN
cana-5900	31	11	to	to	ADP
cana-5900	31	12	a	a	DET
cana-5900	31	13	broader	broad	ADJ
cana-5900	31	14	spectrum	spectrum	NOUN
cana-5900	31	15	of	of	ADP
cana-5900	31	16	abstract	abstract	ADJ
cana-5900	31	17	spaces	space	NOUN
cana-5900	31	18	.	.	PUNCT
cana-5900	32	1	beyond	beyond	ADP
cana-5900	32	2	weakening	weaken	VERB
cana-5900	32	3	the	the	DET
cana-5900	32	4	contractive	contractive	ADJ
cana-5900	32	5	condition	condition	NOUN
cana-5900	32	6	and	and	CCONJ
cana-5900	32	7	generalizing	generalize	VERB
cana-5900	32	8	the	the	DET
cana-5900	32	9	space	space	NOUN
cana-5900	32	10	,	,	PUNCT
cana-5900	32	11	other	other	ADJ
cana-5900	32	12	significant	significant	ADJ
cana-5900	32	13	generalizations	generalization	NOUN
cana-5900	32	14	include	include	VERB
cana-5900	32	15	:	:	PUNCT
cana-5900	32	16	*	*	PUNCT
cana-5900	32	17	multi	multi	ADJ
cana-5900	32	18	-	-	ADJ
cana-5900	32	19	valued	value	VERB
cana-5900	32	20	contractions	contraction	NOUN
cana-5900	32	21	:	:	PUNCT
cana-5900	32	22	these	these	PRON
cana-5900	32	23	deal	deal	VERB
cana-5900	32	24	with	with	ADP
cana-5900	32	25	mappings	mapping	NOUN
cana-5900	32	26	that	that	PRON
cana-5900	32	27	send	send	VERB
cana-5900	32	28	a	a	DET
cana-5900	32	29	point	point	NOUN
cana-5900	32	30	to	to	ADP
cana-5900	32	31	a	a	DET
cana-5900	32	32	set	set	NOUN
cana-5900	32	33	of	of	ADP
cana-5900	32	34	points	point	NOUN
cana-5900	32	35	,	,	PUNCT
cana-5900	32	36	rather	rather	ADV
cana-5900	32	37	than	than	ADP
cana-5900	32	38	a	a	DET
cana-5900	32	39	single	single	ADJ
cana-5900	32	40	point	point	NOUN
cana-5900	32	41	.	.	PUNCT
cana-5900	33	1	such	such	ADJ
cana-5900	33	2	mappings	mapping	NOUN
cana-5900	33	3	are	be	AUX
cana-5900	33	4	common	common	ADJ
cana-5900	33	5	in	in	ADP
cana-5900	33	6	optimization	optimization	NOUN
cana-5900	33	7	problems	problem	NOUN
cana-5900	33	8	and	and	CCONJ
cana-5900	33	9	control	control	NOUN
cana-5900	33	10	theory	theory	NOUN
cana-5900	33	11	.	.	PUNCT
cana-5900	34	1	fixed	fix	VERB
cana-5900	34	2	-	-	PUNCT
cana-5900	34	3	point	point	NOUN
cana-5900	34	4	theorems	theorem	NOUN
cana-5900	34	5	for	for	ADP
cana-5900	34	6	multi	multi	ADJ
cana-5900	34	7	-	-	ADJ
cana-5900	34	8	valued	value	VERB
cana-5900	34	9	contractions	contraction	NOUN
cana-5900	34	10	often	often	ADV
cana-5900	34	11	involve	involve	VERB
cana-5900	34	12	concepts	concept	NOUN
cana-5900	34	13	like	like	ADP
cana-5900	34	14	hausdorff	hausdorff	NOUN
cana-5900	34	15	distance	distance	NOUN
cana-5900	34	16	.	.	PUNCT
cana-5900	35	1	*	*	PUNCT
cana-5900	35	2	contractions	contraction	NOUN
cana-5900	35	3	in	in	ADP
cana-5900	35	4	product	product	NOUN
cana-5900	35	5	spaces	space	VERB
cana-5900	35	6	:	:	PUNCT
cana-5900	35	7	when	when	SCONJ
cana-5900	35	8	dealing	deal	VERB
cana-5900	35	9	with	with	ADP
cana-5900	35	10	systems	system	NOUN
cana-5900	35	11	of	of	ADP
cana-5900	35	12	equations	equation	NOUN
cana-5900	35	13	or	or	CCONJ
cana-5900	35	14	coupled	couple	VERB
cana-5900	35	15	problems	problem	NOUN
cana-5900	35	16	,	,	PUNCT
cana-5900	35	17	it	it	PRON
cana-5900	35	18	is	be	AUX
cana-5900	35	19	often	often	ADV
cana-5900	35	20	useful	useful	ADJ
cana-5900	35	21	to	to	PART
cana-5900	35	22	consider	consider	VERB
cana-5900	35	23	mappings	mapping	NOUN
cana-5900	35	24	defined	define	VERB
cana-5900	35	25	on	on	ADP
cana-5900	35	26	product	product	NOUN
cana-5900	35	27	spaces	space	NOUN
cana-5900	35	28	.	.	PUNCT
cana-5900	36	1	generalizations	generalization	NOUN
cana-5900	36	2	of	of	ADP
cana-5900	36	3	the	the	DET
cana-5900	36	4	contraction	contraction	NOUN
cana-5900	36	5	principle	principle	NOUN
cana-5900	36	6	to	to	ADP
cana-5900	36	7	these	these	DET
cana-5900	36	8	settings	setting	NOUN
cana-5900	36	9	provide	provide	VERB
cana-5900	36	10	tools	tool	NOUN
cana-5900	36	11	for	for	ADP
cana-5900	36	12	analyzing	analyze	VERB
cana-5900	36	13	the	the	DET
cana-5900	36	14	existence	existence	NOUN
cana-5900	36	15	and	and	CCONJ
cana-5900	36	16	uniqueness	uniqueness	NOUN
cana-5900	36	17	of	of	ADP
cana-5900	36	18	solutions	solution	NOUN
cana-5900	36	19	to	to	ADP
cana-5900	36	20	such	such	ADJ
cana-5900	36	21	systems	system	NOUN
cana-5900	36	22	.	.	PUNCT
cana-5900	37	1	*	*	PUNCT
cana-5900	37	2	iterated	iterate	VERB
cana-5900	37	3	function	function	NOUN
cana-5900	37	4	systems	system	NOUN
cana-5900	37	5	(	(	PUNCT
cana-5900	37	6	ifs	ifs	PROPN
cana-5900	37	7	):	):	PUNCT
cana-5900	37	8	the	the	DET
cana-5900	37	9	contraction	contraction	NOUN
cana-5900	37	10	principle	principle	NOUN
cana-5900	37	11	forms	form	VERB
cana-5900	37	12	the	the	DET
cana-5900	37	13	theoretical	theoretical	ADJ
cana-5900	37	14	basis	basis	NOUN
cana-5900	37	15	for	for	ADP
cana-5900	37	16	ifs	ifs	PROPN
cana-5900	37	17	,	,	PUNCT
cana-5900	37	18	which	which	PRON
cana-5900	37	19	are	be	AUX
cana-5900	37	20	used	use	VERB
cana-5900	37	21	to	to	PART
cana-5900	37	22	generate	generate	VERB
cana-5900	37	23	fractals	fractal	NOUN
cana-5900	37	24	.	.	PUNCT
cana-5900	38	1	generalizations	generalization	NOUN
cana-5900	38	2	in	in	ADP
cana-5900	38	3	this	this	DET
cana-5900	38	4	context	context	NOUN
cana-5900	38	5	involve	involve	VERB
cana-5900	38	6	studying	study	VERB
cana-5900	38	7	the	the	DET
cana-5900	38	8	convergence	convergence	NOUN
cana-5900	38	9	of	of	ADP
cana-5900	38	10	sequences	sequence	NOUN
cana-5900	38	11	generated	generate	VERB
cana-5900	38	12	by	by	ADP
cana-5900	38	13	multiple	multiple	ADJ
cana-5900	38	14	contraction	contraction	NOUN
cana-5900	38	15	mappings	mapping	NOUN
cana-5900	38	16	.	.	PUNCT
cana-5900	39	1	*	*	PUNCT
cana-5900	39	2	approximation	approximation	NOUN
cana-5900	39	3	fixed	fix	VERB
cana-5900	39	4	-	-	PUNCT
cana-5900	39	5	point	point	NOUN
cana-5900	39	6	theorems	theorem	NOUN
cana-5900	39	7	:	:	PUNCT
cana-5900	39	8	in	in	ADP
cana-5900	39	9	cases	case	NOUN
cana-5900	39	10	where	where	SCONJ
cana-5900	39	11	a	a	DET
cana-5900	39	12	strict	strict	ADJ
cana-5900	39	13	fixed	fix	VERB
cana-5900	39	14	point	point	NOUN
cana-5900	39	15	may	may	AUX
cana-5900	39	16	not	not	PART
cana-5900	39	17	exist	exist	VERB
cana-5900	39	18	,	,	PUNCT
cana-5900	39	19	approximation	approximation	NOUN
cana-5900	39	20	fixed	fix	VERB
cana-5900	39	21	-	-	PUNCT
cana-5900	39	22	point	point	NOUN
cana-5900	39	23	theorems	theorem	NOUN
cana-5900	39	24	provide	provide	VERB
cana-5900	39	25	conditions	condition	NOUN
cana-5900	39	26	under	under	ADP
cana-5900	39	27	which	which	PRON
cana-5900	39	28	a	a	DET
cana-5900	39	29	point	point	NOUN
cana-5900	39	30	is	be	AUX
cana-5900	39	31	“	"	PUNCT
cana-5900	39	32	almost	almost	ADV
cana-5900	39	33	”	"	PUNCT
cana-5900	39	34	a	a	DET
cana-5900	39	35	fixed	fix	VERB
cana-5900	39	36	point	point	NOUN
cana-5900	39	37	.	.	PUNCT
cana-5900	40	1	these	these	PRON
cana-5900	40	2	are	be	AUX
cana-5900	40	3	crucial	crucial	ADJ
cana-5900	40	4	in	in	ADP
cana-5900	40	5	numerical	numerical	ADJ
cana-5900	40	6	methods	method	NOUN
cana-5900	40	7	and	and	CCONJ
cana-5900	40	8	optimization	optimization	NOUN
cana-5900	40	9	.	.	PUNCT
cana-5900	41	1	communications	communication	NOUN
cana-5900	41	2	on	on	ADP
cana-5900	41	3	applied	apply	VERB
cana-5900	41	4	nonlinear	nonlinear	ADJ
cana-5900	41	5	analysis	analysis	NOUN
cana-5900	41	6	issn	issn	NOUN
cana-5900	41	7	:	:	PUNCT
cana-5900	41	8	1074	1074	NUM
cana-5900	41	9	-	-	PUNCT
cana-5900	41	10	133x	133x	NUM
cana-5900	41	11	vol	vol	NOUN
cana-5900	41	12	31	31	NUM
cana-5900	41	13	no	no	NOUN
cana-5900	41	14	.	.	PUNCT
cana-5900	42	1	8s	8s	PROPN
cana-5900	42	2	(	(	PUNCT
cana-5900	42	3	2024	2024	NUM
cana-5900	42	4	)	)	PUNCT
cana-5900	42	5	1097	1097	NUM
cana-5900	42	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5900	42	7	the	the	DET
cana-5900	42	8	importance	importance	NOUN
cana-5900	42	9	of	of	ADP
cana-5900	42	10	these	these	DET
cana-5900	42	11	generalizations	generalization	NOUN
cana-5900	42	12	lies	lie	VERB
cana-5900	42	13	in	in	ADP
cana-5900	42	14	their	their	PRON
cana-5900	42	15	ability	ability	NOUN
cana-5900	42	16	to	to	PART
cana-5900	42	17	expand	expand	VERB
cana-5900	42	18	the	the	DET
cana-5900	42	19	reach	reach	NOUN
cana-5900	42	20	of	of	ADP
cana-5900	42	21	fixed	fix	VERB
cana-5900	42	22	-	-	PUNCT
cana-5900	42	23	point	point	NOUN
cana-5900	42	24	theory	theory	NOUN
cana-5900	42	25	to	to	ADP
cana-5900	42	26	a	a	DET
cana-5900	42	27	wider	wide	ADJ
cana-5900	42	28	array	array	NOUN
cana-5900	42	29	of	of	ADP
cana-5900	42	30	mathematical	mathematical	ADJ
cana-5900	42	31	problems	problem	NOUN
cana-5900	42	32	.	.	PUNCT
cana-5900	43	1	for	for	ADP
cana-5900	43	2	instance	instance	NOUN
cana-5900	43	3	,	,	PUNCT
cana-5900	43	4	the	the	DET
cana-5900	43	5	study	study	NOUN
cana-5900	43	6	of	of	ADP
cana-5900	43	7	integral	integral	ADJ
cana-5900	43	8	equations	equation	NOUN
cana-5900	43	9	,	,	PUNCT
cana-5900	43	10	which	which	PRON
cana-5900	43	11	often	often	ADV
cana-5900	43	12	do	do	AUX
cana-5900	43	13	not	not	PART
cana-5900	43	14	satisfy	satisfy	VERB
cana-5900	43	15	the	the	DET
cana-5900	43	16	strict	strict	ADJ
cana-5900	43	17	contraction	contraction	NOUN
cana-5900	43	18	property	property	NOUN
cana-5900	43	19	globally	globally	ADV
cana-5900	43	20	,	,	PUNCT
cana-5900	43	21	greatly	greatly	ADV
cana-5900	43	22	benefits	benefit	NOUN
cana-5900	43	23	from	from	ADP
cana-5900	43	24	weak	weak	ADJ
cana-5900	43	25	contraction	contraction	NOUN
cana-5900	43	26	principles	principle	NOUN
cana-5900	43	27	.	.	PUNCT
cana-5900	44	1	similarly	similarly	ADV
cana-5900	44	2	,	,	PUNCT
cana-5900	44	3	in	in	ADP
cana-5900	44	4	game	game	NOUN
cana-5900	44	5	theory	theory	NOUN
cana-5900	44	6	,	,	PUNCT
cana-5900	44	7	where	where	SCONJ
cana-5900	44	8	equilibrium	equilibrium	NOUN
cana-5900	44	9	points	point	NOUN
cana-5900	44	10	are	be	AUX
cana-5900	44	11	sought	seek	VERB
cana-5900	44	12	,	,	PUNCT
cana-5900	44	13	generalized	generalized	ADJ
cana-5900	44	14	contraction	contraction	NOUN
cana-5900	44	15	principles	principle	NOUN
cana-5900	44	16	can	can	AUX
cana-5900	44	17	be	be	AUX
cana-5900	44	18	applied	apply	VERB
cana-5900	44	19	to	to	PART
cana-5900	44	20	prove	prove	VERB
cana-5900	44	21	the	the	DET
cana-5900	44	22	existence	existence	NOUN
cana-5900	44	23	of	of	ADP
cana-5900	44	24	nash	nash	PROPN
cana-5900	44	25	equilibria	equilibria	PROPN
cana-5900	44	26	.	.	PUNCT
cana-5900	45	1	in	in	ADP
cana-5900	45	2	computer	computer	NOUN
cana-5900	45	3	science	science	NOUN
cana-5900	45	4	,	,	PUNCT
cana-5900	45	5	fixed	fix	VERB
cana-5900	45	6	-	-	PUNCT
cana-5900	45	7	point	point	NOUN
cana-5900	45	8	theory	theory	NOUN
cana-5900	45	9	underpins	underpin	VERB
cana-5900	45	10	the	the	DET
cana-5900	45	11	semantics	semantic	NOUN
cana-5900	45	12	of	of	ADP
cana-5900	45	13	programming	programming	NOUN
cana-5900	45	14	languages	language	NOUN
cana-5900	45	15	and	and	CCONJ
cana-5900	45	16	the	the	DET
cana-5900	45	17	analysis	analysis	NOUN
cana-5900	45	18	of	of	ADP
cana-5900	45	19	recursive	recursive	ADJ
cana-5900	45	20	algorithms	algorithm	NOUN
cana-5900	45	21	.	.	PUNCT
cana-5900	46	1	(	(	PUNCT
cana-5900	46	2	matthews	matthews	NOUN
cana-5900	46	3	,	,	PUNCT
cana-5900	46	4	2021	2021	NUM
cana-5900	46	5	)	)	PUNCT
cana-5900	46	6	literature	literature	NOUN
cana-5900	46	7	review	review	NOUN
cana-5900	46	8	takahashi	takahashi	PROPN
cana-5900	46	9	et	et	PROPN
cana-5900	46	10	al	al	PROPN
cana-5900	46	11	.	.	PROPN
cana-5900	47	1	(	(	PUNCT
cana-5900	47	2	2024	2024	NUM
cana-5900	47	3	):	):	PUNCT
cana-5900	47	4	the	the	DET
cana-5900	47	5	contraction	contraction	NOUN
cana-5900	47	6	principle	principle	NOUN
cana-5900	47	7	,	,	PUNCT
cana-5900	47	8	while	while	SCONJ
cana-5900	47	9	fundamental	fundamental	ADJ
cana-5900	47	10	,	,	PUNCT
cana-5900	47	11	serves	serve	VERB
cana-5900	47	12	as	as	ADP
cana-5900	47	13	a	a	DET
cana-5900	47	14	starting	starting	NOUN
cana-5900	47	15	point	point	NOUN
cana-5900	47	16	for	for	ADP
cana-5900	47	17	a	a	DET
cana-5900	47	18	vast	vast	ADJ
cana-5900	47	19	and	and	CCONJ
cana-5900	47	20	rich	rich	ADJ
cana-5900	47	21	area	area	NOUN
cana-5900	47	22	of	of	ADP
cana-5900	47	23	mathematical	mathematical	ADJ
cana-5900	47	24	research	research	NOUN
cana-5900	47	25	.	.	PUNCT
cana-5900	48	1	the	the	DET
cana-5900	48	2	continuous	continuous	ADJ
cana-5900	48	3	effort	effort	NOUN
cana-5900	48	4	to	to	PART
cana-5900	48	5	generalize	generalize	VERB
cana-5900	48	6	this	this	DET
cana-5900	48	7	principle	principle	NOUN
cana-5900	48	8	,	,	PUNCT
cana-5900	48	9	by	by	ADP
cana-5900	48	10	relaxing	relax	VERB
cana-5900	48	11	its	its	PRON
cana-5900	48	12	conditions	condition	NOUN
cana-5900	48	13	on	on	ADP
cana-5900	48	14	the	the	DET
cana-5900	48	15	mapping	mapping	NOUN
cana-5900	48	16	,	,	PUNCT
cana-5900	48	17	the	the	DET
cana-5900	48	18	space	space	NOUN
cana-5900	48	19	,	,	PUNCT
cana-5900	48	20	or	or	CCONJ
cana-5900	48	21	the	the	DET
cana-5900	48	22	nature	nature	NOUN
cana-5900	48	23	of	of	ADP
cana-5900	48	24	the	the	DET
cana-5900	48	25	fixed	fixed	ADJ
cana-5900	48	26	point	point	NOUN
cana-5900	48	27	itself	itself	PRON
cana-5900	48	28	,	,	PUNCT
cana-5900	48	29	underscores	underscore	VERB
cana-5900	48	30	its	its	PRON
cana-5900	48	31	enduring	endure	VERB
cana-5900	48	32	significance	significance	NOUN
cana-5900	48	33	.	.	PUNCT
cana-5900	49	1	samet	samet	PROPN
cana-5900	49	2	et	et	PROPN
cana-5900	49	3	al	al	PROPN
cana-5900	49	4	.	.	PROPN
cana-5900	50	1	(	(	PUNCT
cana-5900	50	2	2023	2023	NUM
cana-5900	50	3	):	):	PUNCT
cana-5900	50	4	generalizations	generalization	NOUN
cana-5900	50	5	not	not	PART
cana-5900	50	6	only	only	ADV
cana-5900	50	7	broaden	broaden	VERB
cana-5900	50	8	the	the	DET
cana-5900	50	9	theoretical	theoretical	ADJ
cana-5900	50	10	landscape	landscape	NOUN
cana-5900	50	11	of	of	ADP
cana-5900	50	12	functional	functional	ADJ
cana-5900	50	13	analysis	analysis	NOUN
cana-5900	50	14	but	but	CCONJ
cana-5900	50	15	also	also	ADV
cana-5900	50	16	provide	provide	VERB
cana-5900	50	17	indispensable	indispensable	ADJ
cana-5900	50	18	tools	tool	NOUN
cana-5900	50	19	for	for	ADP
cana-5900	50	20	tackling	tackle	VERB
cana-5900	50	21	complex	complex	ADJ
cana-5900	50	22	problems	problem	NOUN
cana-5900	50	23	across	across	ADP
cana-5900	50	24	diverse	diverse	ADJ
cana-5900	50	25	scientific	scientific	ADJ
cana-5900	50	26	and	and	CCONJ
cana-5900	50	27	engineering	engineering	NOUN
cana-5900	50	28	disciplines	discipline	NOUN
cana-5900	50	29	,	,	PUNCT
cana-5900	50	30	reaffirming	reaffirm	VERB
cana-5900	50	31	the	the	DET
cana-5900	50	32	principle	principle	NOUN
cana-5900	50	33	’s	’s	PART
cana-5900	50	34	role	role	NOUN
cana-5900	50	35	as	as	ADP
cana-5900	50	36	a	a	DET
cana-5900	50	37	cornerstone	cornerstone	NOUN
cana-5900	50	38	of	of	ADP
cana-5900	50	39	modern	modern	ADJ
cana-5900	50	40	mathematics	mathematic	NOUN
cana-5900	50	41	.	.	PUNCT
cana-5900	51	1	kaur	kaur	PROPN
cana-5900	51	2	et	et	PROPN
cana-5900	51	3	al	al	PROPN
cana-5900	51	4	.	.	PROPN
cana-5900	52	1	(	(	PUNCT
cana-5900	52	2	2023	2023	NUM
cana-5900	52	3	):	):	PUNCT
cana-5900	52	4	the	the	DET
cana-5900	52	5	ongoing	ongoing	ADJ
cana-5900	52	6	research	research	NOUN
cana-5900	52	7	in	in	ADP
cana-5900	52	8	this	this	DET
cana-5900	52	9	field	field	NOUN
cana-5900	52	10	focuses	focus	VERB
cana-5900	52	11	on	on	ADP
cana-5900	52	12	several	several	ADJ
cana-5900	52	13	key	key	ADJ
cana-5900	52	14	areas	area	NOUN
cana-5900	52	15	.	.	PUNCT
cana-5900	53	1	firstly	firstly	ADV
cana-5900	53	2	,	,	PUNCT
cana-5900	53	3	there	there	PRON
cana-5900	53	4	is	be	VERB
cana-5900	53	5	a	a	DET
cana-5900	53	6	continuous	continuous	ADJ
cana-5900	53	7	effort	effort	NOUN
cana-5900	53	8	to	to	PART
cana-5900	53	9	develop	develop	VERB
cana-5900	53	10	faster	fast	ADJ
cana-5900	53	11	and	and	CCONJ
cana-5900	53	12	more	more	ADV
cana-5900	53	13	robust	robust	ADJ
cana-5900	53	14	algorithms	algorithm	NOUN
cana-5900	53	15	,	,	PUNCT
cana-5900	53	16	particularly	particularly	ADV
cana-5900	53	17	for	for	ADP
cana-5900	53	18	large	large	ADJ
cana-5900	53	19	-	-	PUNCT
cana-5900	53	20	scale	scale	NOUN
cana-5900	53	21	problems	problem	NOUN
cana-5900	53	22	where	where	SCONJ
cana-5900	53	23	computational	computational	ADJ
cana-5900	53	24	efficiency	efficiency	NOUN
cana-5900	53	25	is	be	AUX
cana-5900	53	26	paramount	paramount	ADJ
cana-5900	53	27	.	.	PUNCT
cana-5900	54	1	this	this	PRON
cana-5900	54	2	often	often	ADV
cana-5900	54	3	involves	involve	VERB
cana-5900	54	4	combining	combine	VERB
cana-5900	54	5	fixed	fix	VERB
cana-5900	54	6	-	-	PUNCT
cana-5900	54	7	point	point	NOUN
cana-5900	54	8	iterations	iteration	NOUN
cana-5900	54	9	with	with	ADP
cana-5900	54	10	inertial	inertial	ADJ
cana-5900	54	11	terms	term	NOUN
cana-5900	54	12	or	or	CCONJ
cana-5900	54	13	gradient	gradient	NOUN
cana-5900	54	14	-	-	PUNCT
cana-5900	54	15	based	base	VERB
cana-5900	54	16	methods	method	NOUN
cana-5900	54	17	.	.	PUNCT
cana-5900	55	1	mustafa	mustafa	PROPN
cana-5900	55	2	et	et	PROPN
cana-5900	55	3	al	al	PROPN
cana-5900	55	4	.	.	PROPN
cana-5900	56	1	(	(	PUNCT
cana-5900	56	2	2021	2021	NUM
cana-5900	56	3	):	):	PUNCT
cana-5900	56	4	the	the	DET
cana-5900	56	5	study	study	NOUN
cana-5900	56	6	of	of	ADP
cana-5900	56	7	fixed	fix	VERB
cana-5900	56	8	-	-	PUNCT
cana-5900	56	9	point	point	NOUN
cana-5900	56	10	problems	problem	NOUN
cana-5900	56	11	in	in	ADP
cana-5900	56	12	more	more	ADV
cana-5900	56	13	abstract	abstract	ADJ
cana-5900	56	14	and	and	CCONJ
cana-5900	56	15	complex	complex	ADJ
cana-5900	56	16	convex	convex	NOUN
cana-5900	56	17	structures	structure	NOUN
cana-5900	56	18	,	,	PUNCT
cana-5900	56	19	such	such	ADJ
cana-5900	56	20	as	as	ADP
cana-5900	56	21	modular	modular	ADJ
cana-5900	56	22	spaces	space	NOUN
cana-5900	56	23	and	and	CCONJ
cana-5900	56	24	cones	cone	NOUN
cana-5900	56	25	,	,	PUNCT
cana-5900	56	26	continues	continue	VERB
cana-5900	56	27	to	to	PART
cana-5900	56	28	expand	expand	VERB
cana-5900	56	29	the	the	DET
cana-5900	56	30	theoretical	theoretical	ADJ
cana-5900	56	31	boundaries	boundary	NOUN
cana-5900	56	32	.	.	PUNCT
cana-5900	57	1	thirdly	thirdly	ADV
cana-5900	57	2	,	,	PUNCT
cana-5900	57	3	the	the	DET
cana-5900	57	4	robustness	robustness	NOUN
cana-5900	57	5	of	of	ADP
cana-5900	57	6	these	these	DET
cana-5900	57	7	algorithms	algorithm	NOUN
cana-5900	57	8	to	to	ADP
cana-5900	57	9	various	various	ADJ
cana-5900	57	10	forms	form	NOUN
cana-5900	57	11	of	of	ADP
cana-5900	57	12	noise	noise	NOUN
cana-5900	57	13	and	and	CCONJ
cana-5900	57	14	uncertainties	uncertainty	NOUN
cana-5900	57	15	,	,	PUNCT
cana-5900	57	16	a	a	DET
cana-5900	57	17	critical	critical	ADJ
cana-5900	57	18	aspect	aspect	NOUN
cana-5900	57	19	for	for	ADP
cana-5900	57	20	real	real	ADJ
cana-5900	57	21	-	-	PUNCT
cana-5900	57	22	world	world	NOUN
cana-5900	57	23	applications	application	NOUN
cana-5900	57	24	,	,	PUNCT
cana-5900	57	25	is	be	AUX
cana-5900	57	26	a	a	DET
cana-5900	57	27	subject	subject	NOUN
cana-5900	57	28	of	of	ADP
cana-5900	57	29	active	active	ADJ
cana-5900	57	30	investigation	investigation	NOUN
cana-5900	57	31	.	.	PUNCT
cana-5900	58	1	bakhtin	bakhtin	NOUN
cana-5900	58	2	et	et	PROPN
cana-5900	58	3	al	al	PROPN
cana-5900	58	4	.	.	PROPN
cana-5900	58	5	(	(	PUNCT
cana-5900	58	6	2020	2020	NUM
cana-5900	58	7	):	):	PUNCT
cana-5900	58	8	in	in	ADP
cana-5900	58	9	the	the	DET
cana-5900	58	10	realm	realm	NOUN
cana-5900	58	11	of	of	ADP
cana-5900	58	12	mathematics	mathematic	NOUN
cana-5900	58	13	,	,	PUNCT
cana-5900	58	14	particularly	particularly	ADV
cana-5900	58	15	in	in	ADP
cana-5900	58	16	topology	topology	NOUN
cana-5900	58	17	and	and	CCONJ
cana-5900	58	18	functional	functional	ADJ
cana-5900	58	19	analysis	analysis	NOUN
cana-5900	58	20	,	,	PUNCT
cana-5900	58	21	the	the	DET
cana-5900	58	22	concept	concept	NOUN
cana-5900	58	23	of	of	ADP
cana-5900	58	24	a	a	DET
cana-5900	58	25	metric	metric	ADJ
cana-5900	58	26	space	space	NOUN
cana-5900	58	27	provides	provide	VERB
cana-5900	58	28	a	a	DET
cana-5900	58	29	fundamental	fundamental	ADJ
cana-5900	58	30	framework	framework	NOUN
cana-5900	58	31	for	for	ADP
cana-5900	58	32	defining	define	VERB
cana-5900	58	33	notions	notion	NOUN
cana-5900	58	34	of	of	ADP
cana-5900	58	35	distance	distance	NOUN
cana-5900	58	36	,	,	PUNCT
cana-5900	58	37	convergence	convergence	NOUN
cana-5900	58	38	,	,	PUNCT
cana-5900	58	39	and	and	CCONJ
cana-5900	58	40	continuity	continuity	NOUN
cana-5900	58	41	.	.	PUNCT
cana-5900	59	1	alqahtani	alqahtani	PROPN
cana-5900	59	2	et	et	PROPN
cana-5900	59	3	al	al	PROPN
cana-5900	59	4	.	.	PROPN
cana-5900	60	1	(	(	PUNCT
cana-5900	60	2	2020	2020	NUM
cana-5900	60	3	):	):	PUNCT
cana-5900	60	4	a	a	DET
cana-5900	60	5	metric	metric	ADJ
cana-5900	60	6	space	space	NOUN
cana-5900	60	7	(	(	PUNCT
cana-5900	60	8	x	x	X
cana-5900	60	9	,	,	PUNCT
cana-5900	60	10	d	d	NOUN
cana-5900	60	11	)	)	PUNCT
cana-5900	60	12	consists	consist	VERB
cana-5900	60	13	of	of	ADP
cana-5900	60	14	a	a	DET
cana-5900	60	15	set	set	NOUN
cana-5900	60	16	x	x	PUNCT
cana-5900	60	17	and	and	CCONJ
cana-5900	60	18	a	a	DET
cana-5900	60	19	metric	metric	ADJ
cana-5900	60	20	d	d	NOUN
cana-5900	60	21	:	:	PUNCT
cana-5900	60	22	x	x	PUNCT
cana-5900	60	23	\times	\times	ADP
cana-5900	60	24	x	x	PROPN
cana-5900	60	25	\to	\to	PROPN
cana-5900	60	26	\mathbb{r	\mathbb{r	PROPN
cana-5900	60	27	}	}	PUNCT
cana-5900	60	28	that	that	PRON
cana-5900	60	29	satisfies	satisfy	VERB
cana-5900	60	30	certain	certain	ADJ
cana-5900	60	31	properties	property	NOUN
cana-5900	60	32	,	,	PUNCT
cana-5900	60	33	namely	namely	ADV
cana-5900	60	34	non	non	ADJ
cana-5900	60	35	-	-	ADJ
cana-5900	60	36	negativity	negativity	ADJ
cana-5900	60	37	,	,	PUNCT
cana-5900	60	38	identity	identity	NOUN
cana-5900	60	39	of	of	ADP
cana-5900	60	40	indiscernibles	indiscernible	NOUN
cana-5900	60	41	,	,	PUNCT
cana-5900	60	42	symmetry	symmetry	NOUN
cana-5900	60	43	,	,	PUNCT
cana-5900	60	44	and	and	CCONJ
cana-5900	60	45	the	the	DET
cana-5900	60	46	triangle	triangle	NOUN
cana-5900	60	47	inequality	inequality	NOUN
cana-5900	60	48	.	.	PUNCT
cana-5900	61	1	building	build	VERB
cana-5900	61	2	upon	upon	SCONJ
cana-5900	61	3	this	this	DET
cana-5900	61	4	foundational	foundational	ADJ
cana-5900	61	5	idea	idea	NOUN
cana-5900	61	6	,	,	PUNCT
cana-5900	61	7	the	the	DET
cana-5900	61	8	notion	notion	NOUN
cana-5900	61	9	of	of	ADP
cana-5900	61	10	a	a	DET
cana-5900	61	11	convex	convex	ADJ
cana-5900	61	12	metric	metric	ADJ
cana-5900	61	13	space	space	NOUN
cana-5900	61	14	introduces	introduce	NOUN
cana-5900	61	15	an	an	DET
cana-5900	61	16	additional	additional	ADJ
cana-5900	61	17	structural	structural	ADJ
cana-5900	61	18	property	property	NOUN
cana-5900	61	19	related	relate	VERB
cana-5900	61	20	to	to	ADP
cana-5900	61	21	the	the	DET
cana-5900	61	22	“	"	PUNCT
cana-5900	61	23	straightness	straightness	NOUN
cana-5900	61	24	”	"	PUNCT
cana-5900	61	25	or	or	CCONJ
cana-5900	61	26	“	"	PUNCT
cana-5900	61	27	geodesic	geodesic	ADJ
cana-5900	61	28	”	"	PUNCT
cana-5900	61	29	properties	property	NOUN
cana-5900	61	30	within	within	ADP
cana-5900	61	31	the	the	DET
cana-5900	61	32	space	space	NOUN
cana-5900	61	33	.	.	PUNCT
cana-5900	62	1	communications	communication	NOUN
cana-5900	62	2	on	on	ADP
cana-5900	62	3	applied	apply	VERB
cana-5900	62	4	nonlinear	nonlinear	ADJ
cana-5900	62	5	analysis	analysis	NOUN
cana-5900	62	6	issn	issn	NOUN
cana-5900	62	7	:	:	PUNCT
cana-5900	62	8	1074	1074	NUM
cana-5900	62	9	-	-	PUNCT
cana-5900	62	10	133x	133x	NUM
cana-5900	62	11	vol	vol	NOUN
cana-5900	62	12	31	31	NUM
cana-5900	62	13	no	no	NOUN
cana-5900	62	14	.	.	PUNCT
cana-5900	63	1	8s	8s	PROPN
cana-5900	63	2	(	(	PUNCT
cana-5900	63	3	2024	2024	NUM
cana-5900	63	4	)	)	PUNCT
cana-5900	63	5	1098	1098	NUM
cana-5900	63	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5900	64	1	kannan	kannan	PROPN
cana-5900	64	2	et	et	PROPN
cana-5900	64	3	al	al	PROPN
cana-5900	64	4	.	.	PROPN
cana-5900	64	5	(	(	PUNCT
cana-5900	64	6	2021	2021	NUM
cana-5900	64	7	):	):	PUNCT
cana-5900	64	8	intuitively	intuitively	ADV
cana-5900	64	9	,	,	PUNCT
cana-5900	64	10	a	a	DET
cana-5900	64	11	convex	convex	ADJ
cana-5900	64	12	metric	metric	ADJ
cana-5900	64	13	space	space	NOUN
cana-5900	64	14	is	be	AUX
cana-5900	64	15	one	one	NUM
cana-5900	64	16	where	where	SCONJ
cana-5900	64	17	for	for	ADP
cana-5900	64	18	any	any	DET
cana-5900	64	19	two	two	NUM
cana-5900	64	20	points	point	NOUN
cana-5900	64	21	,	,	PUNCT
cana-5900	64	22	there	there	PRON
cana-5900	64	23	exists	exist	VERB
cana-5900	64	24	a	a	DET
cana-5900	64	25	“	"	PUNCT
cana-5900	64	26	middle	middle	ADJ
cana-5900	64	27	point	point	NOUN
cana-5900	64	28	”	"	PUNCT
cana-5900	64	29	or	or	CCONJ
cana-5900	64	30	a	a	DET
cana-5900	64	31	continuous	continuous	ADJ
cana-5900	64	32	“	"	PUNCT
cana-5900	64	33	path	path	NOUN
cana-5900	64	34	”	"	PUNCT
cana-5900	64	35	between	between	ADP
cana-5900	64	36	them	they	PRON
cana-5900	64	37	that	that	PRON
cana-5900	64	38	can	can	AUX
cana-5900	64	39	be	be	AUX
cana-5900	64	40	characterized	characterize	VERB
cana-5900	64	41	in	in	ADP
cana-5900	64	42	a	a	DET
cana-5900	64	43	specific	specific	ADJ
cana-5900	64	44	way	way	NOUN
cana-5900	64	45	related	relate	VERB
cana-5900	64	46	to	to	ADP
cana-5900	64	47	the	the	DET
cana-5900	64	48	distance	distance	NOUN
cana-5900	64	49	.	.	PUNCT
cana-5900	65	1	more	more	ADV
cana-5900	65	2	formally	formally	ADV
cana-5900	65	3	,	,	PUNCT
cana-5900	65	4	there	there	PRON
cana-5900	65	5	are	be	VERB
cana-5900	65	6	several	several	ADJ
cana-5900	65	7	equivalent	equivalent	ADJ
cana-5900	65	8	definitions	definition	NOUN
cana-5900	65	9	of	of	ADP
cana-5900	65	10	convexity	convexity	NOUN
cana-5900	65	11	in	in	ADP
cana-5900	65	12	metric	metric	ADJ
cana-5900	65	13	spaces	space	NOUN
cana-5900	65	14	,	,	PUNCT
cana-5900	65	15	each	each	PRON
cana-5900	65	16	highlighting	highlight	VERB
cana-5900	65	17	different	different	ADJ
cana-5900	65	18	aspects	aspect	NOUN
cana-5900	65	19	of	of	ADP
cana-5900	65	20	this	this	DET
cana-5900	65	21	property	property	NOUN
cana-5900	65	22	.	.	PUNCT
cana-5900	66	1	results	result	VERB
cana-5900	66	2	the	the	DET
cana-5900	66	3	classical	classical	ADJ
cana-5900	66	4	contraction	contraction	NOUN
cana-5900	66	5	principle	principle	NOUN
cana-5900	66	6	often	often	ADV
cana-5900	66	7	proves	prove	VERB
cana-5900	66	8	too	too	ADV
cana-5900	66	9	restrictive	restrictive	ADJ
cana-5900	66	10	for	for	ADP
cana-5900	66	11	many	many	ADJ
cana-5900	66	12	real	real	ADJ
cana-5900	66	13	-	-	PUNCT
cana-5900	66	14	world	world	NOUN
cana-5900	66	15	scenarios	scenario	NOUN
cana-5900	66	16	,	,	PUNCT
cana-5900	66	17	necessitating	necessitate	VERB
cana-5900	66	18	the	the	DET
cana-5900	66	19	development	development	NOUN
cana-5900	66	20	of	of	ADP
cana-5900	66	21	numerous	numerous	ADJ
cana-5900	66	22	generalizations	generalization	NOUN
cana-5900	66	23	.	.	PUNCT
cana-5900	67	1	these	these	DET
cana-5900	67	2	extensions	extension	NOUN
cana-5900	67	3	aim	aim	VERB
cana-5900	67	4	to	to	PART
cana-5900	67	5	broaden	broaden	VERB
cana-5900	67	6	the	the	DET
cana-5900	67	7	applicability	applicability	NOUN
cana-5900	67	8	of	of	ADP
cana-5900	67	9	the	the	DET
cana-5900	67	10	principle	principle	NOUN
cana-5900	67	11	by	by	ADP
cana-5900	67	12	relaxing	relax	VERB
cana-5900	67	13	some	some	PRON
cana-5900	67	14	of	of	ADP
cana-5900	67	15	its	its	PRON
cana-5900	67	16	stringent	stringent	ADJ
cana-5900	67	17	conditions	condition	NOUN
cana-5900	67	18	,	,	PUNCT
cana-5900	67	19	thereby	thereby	ADV
cana-5900	67	20	allowing	allow	VERB
cana-5900	67	21	for	for	ADP
cana-5900	67	22	the	the	DET
cana-5900	67	23	analysis	analysis	NOUN
cana-5900	67	24	of	of	ADP
cana-5900	67	25	more	more	ADV
cana-5900	67	26	complex	complex	ADJ
cana-5900	67	27	and	and	CCONJ
cana-5900	67	28	diverse	diverse	ADJ
cana-5900	67	29	mathematical	mathematical	ADJ
cana-5900	67	30	structures	structure	NOUN
cana-5900	67	31	.	.	PUNCT
cana-5900	68	1	the	the	DET
cana-5900	68	2	contraction	contraction	NOUN
cana-5900	68	3	principle	principle	NOUN
cana-5900	68	4	states	state	VERB
cana-5900	68	5	that	that	SCONJ
cana-5900	68	6	if	if	SCONJ
cana-5900	68	7	(	(	PUNCT
cana-5900	68	8	x	x	NOUN
cana-5900	68	9	,	,	PUNCT
cana-5900	68	10	d	d	NOUN
cana-5900	68	11	)	)	PUNCT
cana-5900	68	12	is	be	AUX
cana-5900	68	13	a	a	DET
cana-5900	68	14	complete	complete	ADJ
cana-5900	68	15	metric	metric	ADJ
cana-5900	68	16	space	space	NOUN
cana-5900	68	17	and	and	CCONJ
cana-5900	68	18	t	t	PROPN
cana-5900	68	19	:	:	PUNCT
cana-5900	68	20	x	x	X
cana-5900	68	21	\to	\to	NOUN
cana-5900	68	22	x	x	PUNCT
cana-5900	68	23	is	be	AUX
cana-5900	68	24	a	a	DET
cana-5900	68	25	contraction	contraction	NOUN
cana-5900	68	26	mapping	mapping	NOUN
cana-5900	68	27	(	(	PUNCT
cana-5900	68	28	i.e.	i.e.	X
cana-5900	68	29	,	,	PUNCT
cana-5900	68	30	d(tx	d(tx	PROPN
cana-5900	68	31	,	,	PUNCT
cana-5900	68	32	ty	ty	NOUN
cana-5900	68	33	)	)	PUNCT
cana-5900	68	34	\le	\le	PROPN
cana-5900	68	35	k	k	NOUN
cana-5900	68	36	d(x	d(x	PROPN
cana-5900	68	37	,	,	PUNCT
cana-5900	68	38	y	y	NOUN
cana-5900	68	39	)	)	PUNCT
cana-5900	68	40	for	for	ADP
cana-5900	68	41	some	some	PRON
cana-5900	68	42	0	0	NUM
cana-5900	68	43	\le	\le	PROPN
cana-5900	68	44	k	k	NOUN
cana-5900	68	45	<	<	X
cana-5900	68	46	1	1	NUM
cana-5900	68	47	and	and	CCONJ
cana-5900	68	48	all	all	DET
cana-5900	68	49	x	x	NOUN
cana-5900	68	50	,	,	PUNCT
cana-5900	68	51	y	y	PROPN
cana-5900	68	52	\in	\in	PROPN
cana-5900	68	53	x	x	PROPN
cana-5900	68	54	)	)	PUNCT
cana-5900	68	55	,	,	PUNCT
cana-5900	68	56	then	then	ADV
cana-5900	68	57	t	t	PROPN
cana-5900	68	58	has	have	VERB
cana-5900	68	59	a	a	DET
cana-5900	68	60	unique	unique	ADJ
cana-5900	68	61	fixed	fix	VERB
cana-5900	68	62	point	point	NOUN
cana-5900	68	63	.	.	PUNCT
cana-5900	69	1	the	the	DET
cana-5900	69	2	key	key	ADJ
cana-5900	69	3	elements	element	NOUN
cana-5900	69	4	here	here	ADV
cana-5900	69	5	are	be	AUX
cana-5900	69	6	completeness	completeness	NOUN
cana-5900	69	7	of	of	ADP
cana-5900	69	8	the	the	DET
cana-5900	69	9	space	space	NOUN
cana-5900	69	10	and	and	CCONJ
cana-5900	69	11	the	the	DET
cana-5900	69	12	strict	strict	ADJ
cana-5900	69	13	contraction	contraction	NOUN
cana-5900	69	14	property	property	NOUN
cana-5900	69	15	of	of	ADP
cana-5900	69	16	the	the	DET
cana-5900	69	17	mapping	mapping	NOUN
cana-5900	69	18	.	.	PUNCT
cana-5900	70	1	generalizations	generalization	NOUN
cana-5900	70	2	often	often	ADV
cana-5900	70	3	focus	focus	VERB
cana-5900	70	4	on	on	ADP
cana-5900	70	5	relaxing	relax	VERB
cana-5900	70	6	one	one	NUM
cana-5900	70	7	or	or	CCONJ
cana-5900	70	8	both	both	PRON
cana-5900	70	9	of	of	ADP
cana-5900	70	10	these	these	DET
cana-5900	70	11	conditions	condition	NOUN
cana-5900	70	12	.	.	PUNCT
cana-5900	71	1	one	one	NUM
cana-5900	71	2	significant	significant	ADJ
cana-5900	71	3	direction	direction	NOUN
cana-5900	71	4	of	of	ADP
cana-5900	71	5	generalization	generalization	NOUN
cana-5900	71	6	involves	involve	VERB
cana-5900	71	7	weakening	weaken	VERB
cana-5900	71	8	the	the	DET
cana-5900	71	9	contractive	contractive	ADJ
cana-5900	71	10	condition	condition	NOUN
cana-5900	71	11	.	.	PUNCT
cana-5900	72	1	instead	instead	ADV
cana-5900	72	2	of	of	ADP
cana-5900	72	3	a	a	DET
cana-5900	72	4	strict	strict	ADJ
cana-5900	72	5	contraction	contraction	NOUN
cana-5900	72	6	,	,	PUNCT
cana-5900	72	7	researchers	researcher	NOUN
cana-5900	72	8	have	have	AUX
cana-5900	72	9	explored	explore	VERB
cana-5900	72	10	various	various	ADJ
cana-5900	72	11	types	type	NOUN
cana-5900	72	12	of	of	ADP
cana-5900	72	13	mappings	mapping	NOUN
cana-5900	72	14	that	that	PRON
cana-5900	72	15	are	be	AUX
cana-5900	72	16	“	"	PUNCT
cana-5900	72	17	contractive	contractive	ADJ
cana-5900	72	18	in	in	ADP
cana-5900	72	19	some	some	DET
cana-5900	72	20	sense	sense	NOUN
cana-5900	72	21	.	.	PUNCT
cana-5900	72	22	”	"	PUNCT
cana-5900	73	1	for	for	ADP
cana-5900	73	2	instance	instance	NOUN
cana-5900	73	3	,	,	PUNCT
cana-5900	73	4	weak	weak	ADJ
cana-5900	73	5	contractions	contraction	NOUN
cana-5900	73	6	(	(	PUNCT
cana-5900	73	7	also	also	ADV
cana-5900	73	8	known	know	VERB
cana-5900	73	9	as	as	ADP
cana-5900	73	10	kannan	kannan	PROPN
cana-5900	73	11	mappings	mapping	NOUN
cana-5900	73	12	or	or	CCONJ
cana-5900	73	13	\phicontractions	\phicontractions	PROPN
cana-5900	73	14	)	)	PUNCT
cana-5900	73	15	replace	replace	VERB
cana-5900	73	16	the	the	DET
cana-5900	73	17	constant	constant	ADJ
cana-5900	73	18	k	k	NOUN
cana-5900	73	19	with	with	ADP
cana-5900	73	20	a	a	DET
cana-5900	73	21	function	function	NOUN
cana-5900	73	22	\phi	\phi	NOUN
cana-5900	73	23	:	:	PUNCT
cana-5900	73	24	[	[	X
cana-5900	73	25	0	0	NUM
cana-5900	73	26	,	,	PUNCT
cana-5900	73	27	\infty	\infty	PROPN
cana-5900	73	28	)	)	PUNCT
cana-5900	73	29	\to	\to	PROPN
cana-5900	74	1	[	[	X
cana-5900	74	2	0	0	NUM
cana-5900	74	3	,	,	PUNCT
cana-5900	74	4	\infty	\infty	PROPN
cana-5900	74	5	)	)	PUNCT
cana-5900	74	6	such	such	ADJ
cana-5900	74	7	that	that	SCONJ
cana-5900	74	8	\phi(t	\phi(t	NOUN
cana-5900	74	9	)	)	PUNCT
cana-5900	74	10	<	<	X
cana-5900	74	11	t	t	PROPN
cana-5900	74	12	for	for	ADP
cana-5900	74	13	t	t	PROPN
cana-5900	74	14	>	>	X
cana-5900	74	15	0	0	PROPN
cana-5900	74	16	.	.	PUNCT
cana-5900	75	1	this	this	PRON
cana-5900	75	2	allows	allow	VERB
cana-5900	75	3	for	for	ADP
cana-5900	75	4	a	a	DET
cana-5900	75	5	more	more	ADV
cana-5900	75	6	flexible	flexible	ADJ
cana-5900	75	7	contraction	contraction	NOUN
cana-5900	75	8	rate	rate	NOUN
cana-5900	75	9	,	,	PUNCT
cana-5900	75	10	potentially	potentially	ADV
cana-5900	75	11	varying	vary	VERB
cana-5900	75	12	with	with	ADP
cana-5900	75	13	the	the	DET
cana-5900	75	14	distance	distance	NOUN
cana-5900	75	15	between	between	ADP
cana-5900	75	16	points	point	NOUN
cana-5900	75	17	.	.	PUNCT
cana-5900	76	1	similarly	similarly	ADV
cana-5900	76	2	,	,	PUNCT
cana-5900	76	3	chatterjea	chatterjea	ADJ
cana-5900	76	4	contractions	contraction	NOUN
cana-5900	76	5	,	,	PUNCT
cana-5900	76	6	ćirić	ćirić	NOUN
cana-5900	76	7	contractions	contraction	NOUN
cana-5900	76	8	,	,	PUNCT
cana-5900	76	9	and	and	CCONJ
cana-5900	76	10	reich	reich	PROPN
cana-5900	76	11	contractions	contraction	NOUN
cana-5900	76	12	introduce	introduce	VERB
cana-5900	76	13	different	different	ADJ
cana-5900	76	14	inequalities	inequality	NOUN
cana-5900	76	15	that	that	PRON
cana-5900	76	16	still	still	ADV
cana-5900	76	17	guarantee	guarantee	VERB
cana-5900	76	18	the	the	DET
cana-5900	76	19	existence	existence	NOUN
cana-5900	76	20	of	of	ADP
cana-5900	76	21	a	a	DET
cana-5900	76	22	fixed	fix	VERB
cana-5900	76	23	point	point	NOUN
cana-5900	76	24	.	.	PUNCT
cana-5900	77	1	these	these	DET
cana-5900	77	2	generalizations	generalization	NOUN
cana-5900	77	3	are	be	AUX
cana-5900	77	4	particularly	particularly	ADV
cana-5900	77	5	useful	useful	ADJ
cana-5900	77	6	when	when	SCONJ
cana-5900	77	7	dealing	deal	VERB
cana-5900	77	8	with	with	ADP
cana-5900	77	9	mappings	mapping	NOUN
cana-5900	77	10	that	that	PRON
cana-5900	77	11	do	do	AUX
cana-5900	77	12	not	not	PART
cana-5900	77	13	exhibit	exhibit	VERB
cana-5900	77	14	a	a	DET
cana-5900	77	15	uniform	uniform	ADJ
cana-5900	77	16	contraction	contraction	NOUN
cana-5900	77	17	over	over	ADP
cana-5900	77	18	the	the	DET
cana-5900	77	19	entire	entire	ADJ
cana-5900	77	20	space	space	NOUN
cana-5900	77	21	.	.	PUNCT
cana-5900	78	1	the	the	DET
cana-5900	78	2	most	most	ADV
cana-5900	78	3	common	common	ADJ
cana-5900	78	4	numerical	numerical	ADJ
cana-5900	78	5	approach	approach	NOUN
cana-5900	78	6	to	to	ADP
cana-5900	78	7	finding	find	VERB
cana-5900	78	8	fixed	fix	VERB
cana-5900	78	9	points	point	NOUN
cana-5900	78	10	is	be	AUX
cana-5900	78	11	picard	picard	NOUN
cana-5900	78	12	iteration	iteration	NOUN
cana-5900	78	13	(	(	PUNCT
cana-5900	78	14	also	also	ADV
cana-5900	78	15	known	know	VERB
cana-5900	78	16	as	as	ADP
cana-5900	78	17	fixed	fix	VERB
cana-5900	78	18	-	-	PUNCT
cana-5900	78	19	point	point	NOUN
cana-5900	78	20	iteration	iteration	NOUN
cana-5900	78	21	)	)	PUNCT
cana-5900	78	22	.	.	PUNCT
cana-5900	79	1	if	if	SCONJ
cana-5900	79	2	t	t	PROPN
cana-5900	79	3	is	be	AUX
cana-5900	79	4	a	a	DET
cana-5900	79	5	contraction	contraction	NOUN
cana-5900	79	6	,	,	PUNCT
cana-5900	79	7	this	this	DET
cana-5900	79	8	iteration	iteration	NOUN
cana-5900	79	9	will	will	AUX
cana-5900	79	10	converge	converge	VERB
cana-5900	79	11	to	to	ADP
cana-5900	79	12	the	the	DET
cana-5900	79	13	unique	unique	ADJ
cana-5900	79	14	fixed	fix	VERB
cana-5900	79	15	point	point	NOUN
cana-5900	79	16	.	.	PUNCT
cana-5900	80	1	def	def	ADJ
cana-5900	80	2	find_fixed_point_picard_iteration(mapping	find_fixed_point_picard_iteration(mapping	NOUN
cana-5900	80	3	,	,	PUNCT
cana-5900	80	4	initial_guess	initial_guess	PROPN
cana-5900	80	5	,	,	PUNCT
cana-5900	80	6	distance_metric	distance_metric	NUM
cana-5900	80	7	,	,	PUNCT
cana-5900	80	8	tolerance=1e-6	tolerance=1e-6	NUM
cana-5900	80	9	,	,	PUNCT
cana-5900	80	10	max_iterations=1000	max_iterations=1000	NUM
cana-5900	80	11	):	):	PUNCT
cana-5900	80	12	"	"	PUNCT
cana-5900	80	13	"	"	PUNCT
cana-5900	80	14	"	"	PUNCT
cana-5900	80	15	finds	find	VERB
cana-5900	80	16	a	a	DET
cana-5900	80	17	fixed	fixed	ADJ
cana-5900	80	18	point	point	NOUN
cana-5900	80	19	of	of	ADP
cana-5900	80	20	a	a	DET
cana-5900	80	21	mapping	mapping	NOUN
cana-5900	80	22	using	use	VERB
cana-5900	80	23	picard	picard	NOUN
cana-5900	80	24	iteration	iteration	NOUN
cana-5900	80	25	.	.	PUNCT
cana-5900	81	1	args	args	ADJ
cana-5900	81	2	:	:	PUNCT
cana-5900	82	1	mapping	mapping	NOUN
cana-5900	82	2	:	:	PUNCT
cana-5900	82	3	the	the	DET
cana-5900	82	4	function	function	NOUN
cana-5900	82	5	t	t	PROPN
cana-5900	82	6	:	:	PUNCT
cana-5900	82	7	x	x	X
cana-5900	82	8	-	-	PUNCT
cana-5900	82	9	>	>	X
cana-5900	82	10	x.	x.	NOUN
cana-5900	82	11	communications	communication	NOUN
cana-5900	82	12	on	on	ADP
cana-5900	82	13	applied	apply	VERB
cana-5900	82	14	nonlinear	nonlinear	ADJ
cana-5900	82	15	analysis	analysis	NOUN
cana-5900	82	16	issn	issn	NOUN
cana-5900	82	17	:	:	PUNCT
cana-5900	82	18	1074	1074	NUM
cana-5900	82	19	-	-	PUNCT
cana-5900	82	20	133x	133x	NUM
cana-5900	82	21	vol	vol	NOUN
cana-5900	82	22	31	31	NUM
cana-5900	82	23	no	no	NOUN
cana-5900	82	24	.	.	PUNCT
cana-5900	83	1	8s	8s	PROPN
cana-5900	83	2	(	(	PUNCT
cana-5900	83	3	2024	2024	NUM
cana-5900	83	4	)	)	PUNCT
cana-5900	83	5	1099	1099	NUM
cana-5900	83	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5900	84	1	initial_guess	initial_guess	NUM
cana-5900	84	2	:	:	PUNCT
cana-5900	84	3	an	an	DET
cana-5900	84	4	initial	initial	ADJ
cana-5900	84	5	point	point	NOUN
cana-5900	84	6	in	in	ADP
cana-5900	84	7	x.	x.	PROPN
cana-5900	84	8	distance_metric	distance_metric	PROPN
cana-5900	84	9	:	:	PUNCT
cana-5900	84	10	the	the	DET
cana-5900	84	11	distance	distance	NOUN
cana-5900	84	12	function	function	NOUN
cana-5900	84	13	d(p1	d(p1	NOUN
cana-5900	84	14	,	,	PUNCT
cana-5900	84	15	p2	p2	PROPN
cana-5900	84	16	)	)	PUNCT
cana-5900	84	17	.	.	PUNCT
cana-5900	85	1	tolerance	tolerance	NOUN
cana-5900	85	2	:	:	PUNCT
cana-5900	85	3	the	the	DET
cana-5900	85	4	maximum	maximum	ADJ
cana-5900	85	5	allowed	allow	VERB
cana-5900	85	6	distance	distance	NOUN
cana-5900	85	7	between	between	ADP
cana-5900	85	8	consecutive	consecutive	ADJ
cana-5900	85	9	iterations	iteration	NOUN
cana-5900	85	10	.	.	PUNCT
cana-5900	86	1	max_iterations	max_iteration	NOUN
cana-5900	86	2	:	:	PUNCT
cana-5900	86	3	maximum	maximum	ADJ
cana-5900	86	4	number	number	NOUN
cana-5900	86	5	of	of	ADP
cana-5900	86	6	iterations	iteration	NOUN
cana-5900	86	7	to	to	PART
cana-5900	86	8	perform	perform	VERB
cana-5900	86	9	.	.	PUNCT
cana-5900	87	1	returns	return	NOUN
cana-5900	87	2	:	:	PUNCT
cana-5900	87	3	the	the	DET
cana-5900	87	4	approximate	approximate	ADJ
cana-5900	87	5	fixed	fix	VERB
cana-5900	87	6	point	point	NOUN
cana-5900	87	7	,	,	PUNCT
cana-5900	87	8	or	or	CCONJ
cana-5900	87	9	none	none	NOUN
cana-5900	87	10	if	if	SCONJ
cana-5900	87	11	not	not	PART
cana-5900	87	12	converged	converge	VERB
cana-5900	87	13	.	.	PUNCT
cana-5900	88	1	"	"	PUNCT
cana-5900	88	2	"	"	PUNCT
cana-5900	88	3	"	"	PUNCT
cana-5900	88	4	current_point	current_point	NOUN
cana-5900	88	5	=	=	SYM
cana-5900	88	6	initial_guess	initial_guess	PROPN
cana-5900	88	7	for	for	ADP
cana-5900	88	8	i	i	PRON
cana-5900	88	9	in	in	ADP
cana-5900	88	10	range(max_iterations	range(max_iteration	NOUN
cana-5900	88	11	):	):	PUNCT
cana-5900	88	12	next_point	next_point	NOUN
cana-5900	88	13	=	=	SYM
cana-5900	88	14	mapping(current_point	mapping(current_point	NOUN
cana-5900	88	15	)	)	PUNCT
cana-5900	88	16	if	if	SCONJ
cana-5900	88	17	distance_metric(current_point	distance_metric(current_point	NOUN
cana-5900	88	18	,	,	PUNCT
cana-5900	88	19	next_point	next_point	NOUN
cana-5900	88	20	)	)	PUNCT
cana-5900	88	21	<	<	X
cana-5900	88	22	tolerance	tolerance	NOUN
cana-5900	88	23	:	:	PUNCT
cana-5900	88	24	print(f"converged	print(f"converge	VERB
cana-5900	88	25	in	in	ADP
cana-5900	88	26	{	{	PUNCT
cana-5900	88	27	i+1	i+1	NOUN
cana-5900	88	28	}	}	PUNCT
cana-5900	88	29	iterations	iteration	NOUN
cana-5900	88	30	.	.	PUNCT
cana-5900	88	31	"	"	PUNCT
cana-5900	88	32	)	)	PUNCT
cana-5900	88	33	return	return	VERB
cana-5900	88	34	next_point	next_point	NOUN
cana-5900	88	35	current_point	current_point	NOUN
cana-5900	88	36	=	=	SYM
cana-5900	88	37	next_point	next_point	NOUN
cana-5900	88	38	print(f"did	print(f"did	AUX
cana-5900	88	39	not	not	PART
cana-5900	88	40	converge	converge	VERB
cana-5900	88	41	within	within	ADP
cana-5900	88	42	{	{	PUNCT
cana-5900	88	43	max_iterations	max_iteration	NOUN
cana-5900	88	44	}	}	PUNCT
cana-5900	88	45	iterations	iteration	NOUN
cana-5900	88	46	.	.	PUNCT
cana-5900	88	47	"	"	PUNCT
cana-5900	88	48	)	)	PUNCT
cana-5900	88	49	return	return	VERB
cana-5900	88	50	none	none	NOUN
cana-5900	88	51	another	another	DET
cana-5900	88	52	crucial	crucial	ADJ
cana-5900	88	53	area	area	NOUN
cana-5900	88	54	of	of	ADP
cana-5900	88	55	generalization	generalization	NOUN
cana-5900	88	56	concerns	concern	VERB
cana-5900	88	57	the	the	DET
cana-5900	88	58	space	space	NOUN
cana-5900	88	59	itself	itself	PRON
cana-5900	88	60	.	.	PUNCT
cana-5900	89	1	while	while	SCONJ
cana-5900	89	2	the	the	DET
cana-5900	89	3	original	original	ADJ
cana-5900	89	4	principle	principle	NOUN
cana-5900	89	5	requires	require	VERB
cana-5900	89	6	a	a	DET
cana-5900	89	7	complete	complete	ADJ
cana-5900	89	8	metric	metric	ADJ
cana-5900	89	9	space	space	NOUN
cana-5900	89	10	,	,	PUNCT
cana-5900	89	11	many	many	ADJ
cana-5900	89	12	mathematical	mathematical	ADJ
cana-5900	89	13	problems	problem	NOUN
cana-5900	89	14	naturally	naturally	ADV
cana-5900	89	15	arise	arise	VERB
cana-5900	89	16	in	in	ADP
cana-5900	89	17	more	more	ADJ
cana-5900	89	18	general	general	ADJ
cana-5900	89	19	topological	topological	ADJ
cana-5900	89	20	spaces	space	NOUN
cana-5900	89	21	.	.	PUNCT
cana-5900	90	1	this	this	PRON
cana-5900	90	2	has	have	AUX
cana-5900	90	3	led	lead	VERB
cana-5900	90	4	to	to	ADP
cana-5900	90	5	the	the	DET
cana-5900	90	6	development	development	NOUN
cana-5900	90	7	of	of	ADP
cana-5900	90	8	fixed	fix	VERB
cana-5900	90	9	-	-	PUNCT
cana-5900	90	10	point	point	NOUN
cana-5900	90	11	theorems	theorem	NOUN
cana-5900	90	12	in	in	ADP
cana-5900	90	13	partially	partially	ADV
cana-5900	90	14	ordered	order	VERB
cana-5900	90	15	metric	metric	ADJ
cana-5900	90	16	spaces	space	NOUN
cana-5900	90	17	,	,	PUNCT
cana-5900	90	18	where	where	SCONJ
cana-5900	90	19	the	the	DET
cana-5900	90	20	contraction	contraction	NOUN
cana-5900	90	21	condition	condition	NOUN
cana-5900	90	22	is	be	AUX
cana-5900	90	23	only	only	ADV
cana-5900	90	24	required	require	VERB
cana-5900	90	25	for	for	ADP
cana-5900	90	26	comparable	comparable	ADJ
cana-5900	90	27	elements	element	NOUN
cana-5900	90	28	.	.	PUNCT
cana-5900	91	1	this	this	DET
cana-5900	91	2	framework	framework	NOUN
cana-5900	91	3	is	be	AUX
cana-5900	91	4	particularly	particularly	ADV
cana-5900	91	5	relevant	relevant	ADJ
cana-5900	91	6	in	in	ADP
cana-5900	91	7	areas	area	NOUN
cana-5900	91	8	like	like	ADP
cana-5900	91	9	integral	integral	ADJ
cana-5900	91	10	equations	equation	NOUN
cana-5900	91	11	and	and	CCONJ
cana-5900	91	12	dynamic	dynamic	ADJ
cana-5900	91	13	systems	system	NOUN
cana-5900	91	14	where	where	SCONJ
cana-5900	91	15	solutions	solution	NOUN
cana-5900	91	16	often	often	ADV
cana-5900	91	17	exhibit	exhibit	VERB
cana-5900	91	18	monotonicity	monotonicity	NOUN
cana-5900	91	19	.	.	PUNCT
cana-5900	92	1	this	this	DET
cana-5900	92	2	condition	condition	NOUN
cana-5900	92	3	essentially	essentially	ADV
cana-5900	92	4	implies	imply	VERB
cana-5900	92	5	that	that	SCONJ
cana-5900	92	6	for	for	ADP
cana-5900	92	7	any	any	DET
cana-5900	92	8	two	two	NUM
cana-5900	92	9	points	point	NOUN
cana-5900	92	10	,	,	PUNCT
cana-5900	92	11	there	there	PRON
cana-5900	92	12	is	be	VERB
cana-5900	92	13	an	an	DET
cana-5900	92	14	intermediate	intermediate	ADJ
cana-5900	92	15	point	point	NOUN
cana-5900	92	16	that	that	PRON
cana-5900	92	17	lies	lie	VERB
cana-5900	92	18	“	"	PUNCT
cana-5900	92	19	on	on	ADP
cana-5900	92	20	a	a	DET
cana-5900	92	21	geodesic	geodesic	ADJ
cana-5900	92	22	segment	segment	NOUN
cana-5900	92	23	”	"	PUNCT
cana-5900	92	24	connecting	connect	VERB
cana-5900	92	25	them	they	PRON
cana-5900	92	26	.	.	PUNCT
cana-5900	93	1	repeating	repeat	VERB
cana-5900	93	2	this	this	DET
cana-5900	93	3	process	process	NOUN
cana-5900	93	4	,	,	PUNCT
cana-5900	93	5	one	one	PRON
cana-5900	93	6	can	can	AUX
cana-5900	93	7	imagine	imagine	VERB
cana-5900	93	8	filling	fill	VERB
cana-5900	93	9	in	in	ADP
cana-5900	93	10	all	all	DET
cana-5900	93	11	points	point	NOUN
cana-5900	93	12	along	along	ADP
cana-5900	93	13	the	the	DET
cana-5900	93	14	“	"	PUNCT
cana-5900	93	15	straight	straight	ADJ
cana-5900	93	16	line	line	NOUN
cana-5900	93	17	”	"	PUNCT
cana-5900	93	18	between	between	ADP
cana-5900	93	19	x	x	PROPN
cana-5900	93	20	and	and	CCONJ
cana-5900	93	21	y.	y.	PROPN
cana-5900	93	22	another	another	PRON
cana-5900	93	23	,	,	PUNCT
cana-5900	93	24	perhaps	perhaps	ADV
cana-5900	93	25	more	more	ADV
cana-5900	93	26	intuitive	intuitive	ADJ
cana-5900	93	27	,	,	PUNCT
cana-5900	93	28	definition	definition	NOUN
cana-5900	93	29	relates	relate	VERB
cana-5900	93	30	to	to	ADP
cana-5900	93	31	the	the	DET
cana-5900	93	32	existence	existence	NOUN
cana-5900	93	33	of	of	ADP
cana-5900	93	34	metric	metric	ADJ
cana-5900	93	35	segments	segment	NOUN
cana-5900	93	36	.	.	PUNCT
cana-5900	94	1	this	this	DET
cana-5900	94	2	definition	definition	NOUN
cana-5900	94	3	directly	directly	ADV
cana-5900	94	4	implies	imply	VERB
cana-5900	94	5	the	the	DET
cana-5900	94	6	existence	existence	NOUN
cana-5900	94	7	of	of	ADP
cana-5900	94	8	a	a	DET
cana-5900	94	9	point	point	NOUN
cana-5900	94	10	at	at	ADP
cana-5900	94	11	any	any	DET
cana-5900	94	12	proportional	proportional	ADJ
cana-5900	94	13	distance	distance	NOUN
cana-5900	94	14	along	along	ADP
cana-5900	94	15	the	the	DET
cana-5900	94	16	“	"	PUNCT
cana-5900	94	17	straight	straight	ADJ
cana-5900	94	18	communications	communication	NOUN
cana-5900	94	19	on	on	ADP
cana-5900	94	20	applied	apply	VERB
cana-5900	94	21	nonlinear	nonlinear	ADJ
cana-5900	94	22	analysis	analysis	NOUN
cana-5900	94	23	issn	issn	NOUN
cana-5900	94	24	:	:	PUNCT
cana-5900	94	25	1074	1074	NUM
cana-5900	94	26	-	-	PUNCT
cana-5900	94	27	133x	133x	NUM
cana-5900	94	28	vol	vol	NOUN
cana-5900	94	29	31	31	NUM
cana-5900	94	30	no	no	NOUN
cana-5900	94	31	.	.	PUNCT
cana-5900	95	1	8s	8s	PROPN
cana-5900	95	2	(	(	PUNCT
cana-5900	95	3	2024	2024	NUM
cana-5900	95	4	)	)	PUNCT
cana-5900	95	5	1100	1100	NUM
cana-5900	95	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5900	95	7	line	line	NOUN
cana-5900	95	8	”	"	PUNCT
cana-5900	95	9	connecting	connect	VERB
cana-5900	95	10	x	x	PUNCT
cana-5900	95	11	and	and	CCONJ
cana-5900	95	12	y.	y.	NOUN
cana-5900	95	13	if	if	SCONJ
cana-5900	95	14	such	such	DET
cana-5900	95	15	a	a	DET
cana-5900	95	16	point	point	NOUN
cana-5900	95	17	z	z	NOUN
cana-5900	95	18	is	be	AUX
cana-5900	95	19	unique	unique	ADJ
cana-5900	95	20	for	for	ADP
cana-5900	95	21	all	all	DET
cana-5900	95	22	\alpha	\alpha	PROPN
cana-5900	95	23	,	,	PUNCT
cana-5900	95	24	the	the	DET
cana-5900	95	25	space	space	NOUN
cana-5900	95	26	is	be	AUX
cana-5900	95	27	called	call	VERB
cana-5900	95	28	a	a	DET
cana-5900	95	29	uniquely	uniquely	ADV
cana-5900	95	30	geodesic	geodesic	ADJ
cana-5900	95	31	space	space	NOUN
cana-5900	95	32	.	.	PUNCT
cana-5900	96	1	let	let	VERB
cana-5900	96	2	's	us	PRON
cana-5900	96	3	demonstrate	demonstrate	VERB
cana-5900	96	4	mann	mann	PROPN
cana-5900	96	5	iteration	iteration	NOUN
cana-5900	96	6	in	in	ADP
cana-5900	96	7	a	a	DET
cana-5900	96	8	simple	simple	ADJ
cana-5900	96	9	euclidean	euclidean	NOUN
cana-5900	96	10	setting	setting	NOUN
cana-5900	96	11	(	(	PUNCT
cana-5900	96	12	which	which	PRON
cana-5900	96	13	is	be	AUX
cana-5900	96	14	a	a	DET
cana-5900	96	15	banach	banach	NOUN
cana-5900	96	16	space	space	NOUN
cana-5900	96	17	and	and	CCONJ
cana-5900	96	18	hence	hence	ADV
cana-5900	96	19	convex	convex	ADJ
cana-5900	96	20	)	)	PUNCT
cana-5900	96	21	.	.	PUNCT
cana-5900	97	1	def	def	ADJ
cana-5900	97	2	find_fixed_point_mann_iteration(mapping	find_fixed_point_mann_iteration(mapping	PROPN
cana-5900	97	3	,	,	PUNCT
cana-5900	97	4	initial_guess	initial_guess	PROPN
cana-5900	97	5	,	,	PUNCT
cana-5900	97	6	distance_metric	distance_metric	NUM
cana-5900	97	7	,	,	PUNCT
cana-5900	97	8	tolerance=1e-6	tolerance=1e-6	NUM
cana-5900	97	9	,	,	PUNCT
cana-5900	97	10	max_iterations=1000	max_iterations=1000	X
cana-5900	97	11	,	,	PUNCT
cana-5900	97	12	alpha=0.5	alpha=0.5	NUM
cana-5900	97	13	):	):	PUNCT
cana-5900	97	14	"	"	PUNCT
cana-5900	97	15	"	"	PUNCT
cana-5900	97	16	"	"	PUNCT
cana-5900	97	17	finds	find	VERB
cana-5900	97	18	a	a	DET
cana-5900	97	19	fixed	fix	VERB
cana-5900	97	20	point	point	NOUN
cana-5900	97	21	using	use	VERB
cana-5900	97	22	mann	mann	PROPN
cana-5900	97	23	iteration	iteration	NOUN
cana-5900	97	24	.	.	PUNCT
cana-5900	98	1	applicable	applicable	ADJ
cana-5900	98	2	for	for	ADP
cana-5900	98	3	nonexpansive	nonexpansive	ADJ
cana-5900	98	4	mappings	mapping	NOUN
cana-5900	98	5	in	in	ADP
cana-5900	98	6	certain	certain	ADJ
cana-5900	98	7	convex	convex	NOUN
cana-5900	98	8	metric	metric	ADJ
cana-5900	98	9	spaces	space	NOUN
cana-5900	98	10	(	(	PUNCT
cana-5900	98	11	e.g.	e.g.	ADV
cana-5900	98	12	,	,	PUNCT
cana-5900	98	13	banach	banach	NOUN
cana-5900	98	14	spaces	space	NOUN
cana-5900	98	15	)	)	PUNCT
cana-5900	98	16	.	.	PUNCT
cana-5900	99	1	args	args	PROPN
cana-5900	99	2	:	:	PUNCT
cana-5900	100	1	mapping	mapping	NOUN
cana-5900	100	2	:	:	PUNCT
cana-5900	100	3	the	the	DET
cana-5900	100	4	function	function	NOUN
cana-5900	100	5	t	t	PROPN
cana-5900	100	6	:	:	PUNCT
cana-5900	100	7	x	x	X
cana-5900	100	8	-	-	PUNCT
cana-5900	100	9	>	>	X
cana-5900	100	10	x.	x.	PROPN
cana-5900	100	11	initial_guess	initial_guess	PROPN
cana-5900	100	12	:	:	PUNCT
cana-5900	100	13	an	an	DET
cana-5900	100	14	initial	initial	ADJ
cana-5900	100	15	point	point	NOUN
cana-5900	100	16	in	in	ADP
cana-5900	100	17	x.	x.	PROPN
cana-5900	100	18	distance_metric	distance_metric	PROPN
cana-5900	100	19	:	:	PUNCT
cana-5900	100	20	the	the	DET
cana-5900	100	21	distance	distance	NOUN
cana-5900	100	22	function	function	NOUN
cana-5900	100	23	d(p1	d(p1	NOUN
cana-5900	100	24	,	,	PUNCT
cana-5900	100	25	p2	p2	PROPN
cana-5900	100	26	)	)	PUNCT
cana-5900	100	27	.	.	PUNCT
cana-5900	101	1	tolerance	tolerance	NOUN
cana-5900	101	2	:	:	PUNCT
cana-5900	101	3	the	the	DET
cana-5900	101	4	maximum	maximum	ADJ
cana-5900	101	5	allowed	allow	VERB
cana-5900	101	6	distance	distance	NOUN
cana-5900	101	7	between	between	ADP
cana-5900	101	8	consecutive	consecutive	ADJ
cana-5900	101	9	iterations	iteration	NOUN
cana-5900	101	10	.	.	PUNCT
cana-5900	102	1	max_iterations	max_iteration	NOUN
cana-5900	102	2	:	:	PUNCT
cana-5900	102	3	maximum	maximum	ADJ
cana-5900	102	4	number	number	NOUN
cana-5900	102	5	of	of	ADP
cana-5900	102	6	iterations	iteration	NOUN
cana-5900	102	7	to	to	PART
cana-5900	102	8	perform	perform	VERB
cana-5900	102	9	.	.	PUNCT
cana-5900	103	1	alpha	alpha	NOUN
cana-5900	103	2	:	:	PUNCT
cana-5900	103	3	relaxation	relaxation	NOUN
cana-5900	103	4	parameter	parameter	NOUN
cana-5900	103	5	(	(	PUNCT
cana-5900	103	6	0	0	PUNCT
cana-5900	103	7	<	<	X
cana-5900	103	8	alpha	alpha	X
cana-5900	103	9	<	<	X
cana-5900	103	10	1	1	NUM
cana-5900	103	11	)	)	PUNCT
cana-5900	103	12	.	.	PUNCT
cana-5900	104	1	returns	return	NOUN
cana-5900	104	2	:	:	PUNCT
cana-5900	104	3	the	the	DET
cana-5900	104	4	approximate	approximate	ADJ
cana-5900	104	5	fixed	fix	VERB
cana-5900	104	6	point	point	NOUN
cana-5900	104	7	,	,	PUNCT
cana-5900	104	8	or	or	CCONJ
cana-5900	104	9	none	none	NOUN
cana-5900	104	10	if	if	SCONJ
cana-5900	104	11	not	not	PART
cana-5900	104	12	converged	converge	VERB
cana-5900	104	13	.	.	PUNCT
cana-5900	105	1	"	"	PUNCT
cana-5900	105	2	"	"	PUNCT
cana-5900	105	3	"	"	PUNCT
cana-5900	105	4	current_point	current_point	NOUN
cana-5900	105	5	=	=	SYM
cana-5900	105	6	np.array(initial_guess	np.array(initial_guess	NOUN
cana-5900	105	7	)	)	PUNCT
cana-5900	105	8	#	#	NOUN
cana-5900	105	9	ensure	ensure	VERB
cana-5900	105	10	it	it	PRON
cana-5900	105	11	's	be	AUX
cana-5900	105	12	a	a	DET
cana-5900	105	13	numpy	numpy	NOUN
cana-5900	105	14	array	array	NOUN
cana-5900	105	15	for	for	ADP
cana-5900	105	16	element	element	ADJ
cana-5900	105	17	-	-	ADJ
cana-5900	105	18	wise	wise	ADJ
cana-5900	105	19	ops	op	NOUN
cana-5900	105	20	for	for	ADP
cana-5900	105	21	i	i	PRON
cana-5900	105	22	in	in	ADP
cana-5900	105	23	range(max_iterations	range(max_iteration	NOUN
cana-5900	105	24	):	):	PUNCT
cana-5900	105	25	tx	tx	PROPN
cana-5900	105	26	=	=	SYM
cana-5900	105	27	np.array(mapping(current_point	np.array(mapping(current_point	NOUN
cana-5900	105	28	)	)	PUNCT
cana-5900	105	29	)	)	PUNCT
cana-5900	105	30	next_point	next_point	NOUN
cana-5900	105	31	=	=	PUNCT
cana-5900	105	32	(	(	PUNCT
cana-5900	105	33	1	1	NUM
cana-5900	105	34	alpha	alpha	NOUN
cana-5900	105	35	)	)	PUNCT
cana-5900	105	36	*	*	PUNCT
cana-5900	106	1	current_point	current_point	NOUN
cana-5900	106	2	+	+	CCONJ
cana-5900	106	3	alpha	alpha	NOUN
cana-5900	106	4	*	*	PUNCT
cana-5900	106	5	tx	tx	ADP
cana-5900	106	6	communications	communication	NOUN
cana-5900	106	7	on	on	ADP
cana-5900	106	8	applied	apply	VERB
cana-5900	106	9	nonlinear	nonlinear	ADJ
cana-5900	106	10	analysis	analysis	NOUN
cana-5900	106	11	issn	issn	NOUN
cana-5900	106	12	:	:	PUNCT
cana-5900	106	13	1074	1074	NUM
cana-5900	106	14	-	-	PUNCT
cana-5900	106	15	133x	133x	NUM
cana-5900	106	16	vol	vol	NOUN
cana-5900	106	17	31	31	NUM
cana-5900	106	18	no	no	NOUN
cana-5900	106	19	.	.	PUNCT
cana-5900	107	1	8s	8s	PROPN
cana-5900	107	2	(	(	PUNCT
cana-5900	107	3	2024	2024	NUM
cana-5900	107	4	)	)	PUNCT
cana-5900	107	5	1101	1101	NUM
cana-5900	107	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5900	107	7	if	if	SCONJ
cana-5900	107	8	distance_metric(current_point	distance_metric(current_point	NOUN
cana-5900	107	9	,	,	PUNCT
cana-5900	107	10	next_point	next_point	NOUN
cana-5900	107	11	)	)	PUNCT
cana-5900	107	12	<	<	X
cana-5900	107	13	tolerance	tolerance	NOUN
cana-5900	107	14	:	:	PUNCT
cana-5900	107	15	print(f"converged	print(f"converge	VERB
cana-5900	107	16	in	in	ADP
cana-5900	107	17	{	{	PUNCT
cana-5900	107	18	i+1	i+1	NOUN
cana-5900	107	19	}	}	PUNCT
cana-5900	107	20	iterations	iteration	NOUN
cana-5900	107	21	using	use	VERB
cana-5900	107	22	mann	mann	PROPN
cana-5900	107	23	iteration	iteration	NOUN
cana-5900	107	24	.	.	PUNCT
cana-5900	107	25	"	"	PUNCT
cana-5900	107	26	)	)	PUNCT
cana-5900	107	27	return	return	VERB
cana-5900	107	28	next_point	next_point	NOUN
cana-5900	107	29	current_point	current_point	NOUN
cana-5900	107	30	=	=	SYM
cana-5900	107	31	next_point	next_point	NOUN
cana-5900	107	32	print(f"did	print(f"did	AUX
cana-5900	107	33	not	not	PART
cana-5900	107	34	converge	converge	VERB
cana-5900	107	35	within	within	ADP
cana-5900	107	36	{	{	PUNCT
cana-5900	107	37	max_iterations	max_iteration	NOUN
cana-5900	107	38	}	}	PUNCT
cana-5900	107	39	iterations	iteration	NOUN
cana-5900	107	40	using	use	VERB
cana-5900	107	41	mann	mann	PROPN
cana-5900	107	42	iteration	iteration	NOUN
cana-5900	107	43	.	.	PUNCT
cana-5900	107	44	"	"	PUNCT
cana-5900	107	45	)	)	PUNCT
cana-5900	107	46	return	return	VERB
cana-5900	107	47	none	none	NOUN
cana-5900	107	48	#	#	NOUN
cana-5900	107	49	example	example	NOUN
cana-5900	107	50	of	of	ADP
cana-5900	107	51	a	a	DET
cana-5900	107	52	nonexpansive	nonexpansive	ADJ
cana-5900	107	53	mapping	mapping	NOUN
cana-5900	107	54	(	(	PUNCT
cana-5900	107	55	not	not	PART
cana-5900	107	56	a	a	DET
cana-5900	107	57	contraction	contraction	NOUN
cana-5900	107	58	,	,	PUNCT
cana-5900	107	59	but	but	CCONJ
cana-5900	107	60	still	still	ADV
cana-5900	107	61	has	have	VERB
cana-5900	107	62	a	a	DET
cana-5900	107	63	fixed	fix	VERB
cana-5900	107	64	point	point	NOUN
cana-5900	107	65	)	)	PUNCT
cana-5900	107	66	#	#	NOUN
cana-5900	107	67	t(x	t(x	PROPN
cana-5900	107	68	)	)	PUNCT
cana-5900	107	69	=	=	PUNCT
cana-5900	108	1	x	x	PUNCT
cana-5900	108	2	for	for	ADP
cana-5900	108	3	all	all	PRON
cana-5900	108	4	x.	x.	NOUN
cana-5900	109	1	this	this	PRON
cana-5900	109	2	is	be	AUX
cana-5900	109	3	nonexpansive	nonexpansive	ADJ
cana-5900	109	4	and	and	CCONJ
cana-5900	109	5	has	have	VERB
cana-5900	109	6	infinitely	infinitely	ADV
cana-5900	109	7	many	many	ADJ
cana-5900	109	8	fixed	fix	VERB
cana-5900	109	9	points	point	NOUN
cana-5900	109	10	.	.	PUNCT
cana-5900	110	1	#	#	NOUN
cana-5900	110	2	let	let	VERB
cana-5900	110	3	's	us	PRON
cana-5900	110	4	consider	consider	VERB
cana-5900	110	5	a	a	DET
cana-5900	110	6	mapping	mapping	NOUN
cana-5900	110	7	that	that	SCONJ
cana-5900	110	8	shifts	shift	NOUN
cana-5900	110	9	but	but	CCONJ
cana-5900	110	10	does	do	AUX
cana-5900	110	11	n't	not	PART
cana-5900	110	12	shrink	shrink	VERB
cana-5900	110	13	.	.	PUNCT
cana-5900	111	1	#	#	NOUN
cana-5900	111	2	for	for	ADP
cana-5900	111	3	example	example	NOUN
cana-5900	111	4	,	,	PUNCT
cana-5900	111	5	t(x	t(x	PROPN
cana-5900	111	6	)	)	PUNCT
cana-5900	111	7	=	=	X
cana-5900	111	8	x/2	x/2	PUNCT
cana-5900	111	9	+	+	CCONJ
cana-5900	111	10	1	1	NUM
cana-5900	111	11	if	if	SCONJ
cana-5900	111	12	x	x	PROPN
cana-5900	111	13	<	<	X
cana-5900	111	14	2	2	NUM
cana-5900	111	15	,	,	PUNCT
cana-5900	111	16	t(x	t(x	PROPN
cana-5900	111	17	)	)	PUNCT
cana-5900	112	1	=	=	PUNCT
cana-5900	113	1	x	x	X
cana-5900	113	2	if	if	SCONJ
cana-5900	113	3	x	x	X
cana-5900	113	4	>	>	X
cana-5900	113	5	=	=	SYM
cana-5900	113	6	2	2	X
cana-5900	113	7	.	.	PUNCT
cana-5900	114	1	this	this	PRON
cana-5900	114	2	is	be	AUX
cana-5900	114	3	not	not	PART
cana-5900	114	4	linear	linear	ADJ
cana-5900	114	5	.	.	PUNCT
cana-5900	115	1	#	#	NOUN
cana-5900	115	2	let	let	VERB
cana-5900	115	3	's	us	PRON
cana-5900	115	4	use	use	VERB
cana-5900	115	5	a	a	DET
cana-5900	115	6	simpler	simple	ADJ
cana-5900	115	7	linear	linear	ADJ
cana-5900	115	8	example	example	NOUN
cana-5900	115	9	in	in	ADP
cana-5900	115	10	r	r	NOUN
cana-5900	115	11	:	:	PUNCT
cana-5900	115	12	t(x	t(x	PROPN
cana-5900	115	13	)	)	PUNCT
cana-5900	116	1	=	=	PUNCT
cana-5900	117	1	x	x	PUNCT
cana-5900	117	2	for	for	ADP
cana-5900	117	3	illustration	illustration	NOUN
cana-5900	117	4	of	of	ADP
cana-5900	117	5	mann	mann	PROPN
cana-5900	117	6	.	.	PUNCT
cana-5900	118	1	#	#	NOUN
cana-5900	118	2	in	in	ADP
cana-5900	118	3	a	a	DET
cana-5900	118	4	real	real	ADJ
cana-5900	118	5	fixed	fix	VERB
cana-5900	118	6	-	-	PUNCT
cana-5900	118	7	point	point	NOUN
cana-5900	118	8	problem	problem	NOUN
cana-5900	118	9	context	context	NOUN
cana-5900	118	10	,	,	PUNCT
cana-5900	118	11	t	t	PROPN
cana-5900	118	12	would	would	AUX
cana-5900	118	13	be	be	AUX
cana-5900	118	14	a	a	DET
cana-5900	118	15	specific	specific	ADJ
cana-5900	118	16	function	function	NOUN
cana-5900	118	17	.	.	PUNCT
cana-5900	119	1	#	#	NOUN
cana-5900	119	2	let	let	VERB
cana-5900	119	3	's	us	PRON
cana-5900	119	4	consider	consider	VERB
cana-5900	119	5	t(x	t(x	PROPN
cana-5900	119	6	)	)	PUNCT
cana-5900	120	1	=	=	PUNCT
cana-5900	120	2	x	x	PUNCT
cana-5900	120	3	for	for	ADP
cana-5900	120	4	x	x	SYM
cana-5900	120	5	in	in	ADP
cana-5900	120	6	[	[	X
cana-5900	120	7	0,1	0,1	NUM
cana-5900	120	8	]	]	PUNCT
cana-5900	120	9	,	,	PUNCT
cana-5900	120	10	and	and	CCONJ
cana-5900	120	11	t(x	t(x	PROPN
cana-5900	120	12	)	)	PUNCT
cana-5900	120	13	=	=	NOUN
cana-5900	120	14	1	1	NUM
cana-5900	120	15	for	for	ADP
cana-5900	120	16	x	x	PUNCT
cana-5900	120	17	>	>	X
cana-5900	120	18	1	1	NUM
cana-5900	120	19	,	,	PUNCT
cana-5900	120	20	t(x	t(x	PROPN
cana-5900	120	21	)	)	PUNCT
cana-5900	120	22	=	=	SYM
cana-5900	120	23	0	0	NUM
cana-5900	120	24	for	for	ADP
cana-5900	120	25	x	x	PUNCT
cana-5900	120	26	<	<	X
cana-5900	120	27	0	0	NUM
cana-5900	120	28	.	.	PUNCT
cana-5900	121	1	#	#	NOUN
cana-5900	121	2	this	this	PRON
cana-5900	121	3	is	be	AUX
cana-5900	121	4	a	a	DET
cana-5900	121	5	projection	projection	NOUN
cana-5900	121	6	onto	onto	ADP
cana-5900	121	7	[	[	X
cana-5900	121	8	0,1	0,1	NUM
cana-5900	121	9	]	]	PUNCT
cana-5900	121	10	def	def	PROPN
cana-5900	121	11	projection_onto_unit_interval(x	projection_onto_unit_interval(x	PROPN
cana-5900	121	12	):	):	PUNCT
cana-5900	121	13	return	return	NOUN
cana-5900	121	14	max(0	max(0	NOUN
cana-5900	121	15	,	,	PUNCT
cana-5900	121	16	min(x	min(x	PROPN
cana-5900	121	17	,	,	PUNCT
cana-5900	121	18	1	1	NUM
cana-5900	121	19	)	)	PUNCT
cana-5900	121	20	)	)	PUNCT
cana-5900	122	1	#	#	NOUN
cana-5900	122	2	this	this	PRON
cana-5900	122	3	is	be	AUX
cana-5900	122	4	nonexpansive	nonexpansive	ADJ
cana-5900	122	5	:	:	PUNCT
cana-5900	122	6	|t(x	|t(x	PROPN
cana-5900	122	7	)	)	PUNCT
cana-5900	122	8	t(y)|	t(y)|	PROPN
cana-5900	122	9	<	<	NOUN
cana-5900	122	10	=	=	X
cana-5900	122	11	|x	|x	PROPN
cana-5900	122	12	y|	y|	NOUN
cana-5900	122	13	.	.	PUNCT
cana-5900	123	1	the	the	DET
cana-5900	123	2	significance	significance	NOUN
cana-5900	123	3	of	of	ADP
cana-5900	123	4	convex	convex	NOUN
cana-5900	123	5	metric	metric	ADJ
cana-5900	123	6	spaces	space	NOUN
cana-5900	123	7	lies	lie	VERB
cana-5900	123	8	in	in	ADP
cana-5900	123	9	their	their	PRON
cana-5900	123	10	rich	rich	ADJ
cana-5900	123	11	geometric	geometric	ADJ
cana-5900	123	12	structure	structure	NOUN
cana-5900	123	13	,	,	PUNCT
cana-5900	123	14	which	which	PRON
cana-5900	123	15	allows	allow	VERB
cana-5900	123	16	for	for	ADP
cana-5900	123	17	the	the	DET
cana-5900	123	18	generalization	generalization	NOUN
cana-5900	123	19	of	of	ADP
cana-5900	123	20	many	many	ADJ
cana-5900	123	21	results	result	NOUN
cana-5900	123	22	from	from	ADP
cana-5900	123	23	euclidean	euclidean	ADJ
cana-5900	123	24	geometry	geometry	NOUN
cana-5900	123	25	and	and	CCONJ
cana-5900	123	26	normed	normed	ADJ
cana-5900	123	27	linear	linear	ADJ
cana-5900	123	28	spaces	space	NOUN
cana-5900	123	29	.	.	PUNCT
cana-5900	124	1	for	for	ADP
cana-5900	124	2	instance	instance	NOUN
cana-5900	124	3	,	,	PUNCT
cana-5900	124	4	in	in	ADP
cana-5900	124	5	a	a	DET
cana-5900	124	6	complete	complete	ADJ
cana-5900	124	7	convex	convex	NOUN
cana-5900	124	8	metric	metric	ADJ
cana-5900	124	9	space	space	NOUN
cana-5900	124	10	,	,	PUNCT
cana-5900	124	11	concepts	concept	NOUN
cana-5900	124	12	like	like	ADP
cana-5900	124	13	geodesics	geodesic	NOUN
cana-5900	124	14	(	(	PUNCT
cana-5900	124	15	shortest	short	ADJ
cana-5900	124	16	paths	path	NOUN
cana-5900	124	17	between	between	ADP
cana-5900	124	18	two	two	NUM
cana-5900	124	19	points	point	NOUN
cana-5900	124	20	)	)	PUNCT
cana-5900	124	21	and	and	CCONJ
cana-5900	124	22	metric	metric	ADJ
cana-5900	124	23	projections	projection	NOUN
cana-5900	124	24	(	(	PUNCT
cana-5900	124	25	finding	find	VERB
cana-5900	124	26	the	the	DET
cana-5900	124	27	closest	close	ADJ
cana-5900	124	28	point	point	NOUN
cana-5900	124	29	in	in	ADP
cana-5900	124	30	a	a	DET
cana-5900	124	31	closed	closed	ADJ
cana-5900	124	32	set	set	NOUN
cana-5900	124	33	)	)	PUNCT
cana-5900	124	34	become	become	VERB
cana-5900	124	35	well	well	ADV
cana-5900	124	36	-	-	PUNCT
cana-5900	124	37	defined	define	VERB
cana-5900	124	38	and	and	CCONJ
cana-5900	124	39	possess	possess	NOUN
cana-5900	124	40	properties	property	NOUN
cana-5900	124	41	analogous	analogous	ADJ
cana-5900	124	42	to	to	ADP
cana-5900	124	43	their	their	PRON
cana-5900	124	44	counterparts	counterpart	NOUN
cana-5900	124	45	in	in	ADP
cana-5900	124	46	euclidean	euclidean	ADJ
cana-5900	124	47	space	space	NOUN
cana-5900	124	48	.	.	PUNCT
cana-5900	125	1	this	this	PRON
cana-5900	125	2	makes	make	VERB
cana-5900	125	3	them	they	PRON
cana-5900	125	4	particularly	particularly	ADV
cana-5900	125	5	relevant	relevant	ADJ
cana-5900	125	6	in	in	ADP
cana-5900	125	7	areas	area	NOUN
cana-5900	125	8	like	like	ADP
cana-5900	125	9	optimization	optimization	NOUN
cana-5900	125	10	,	,	PUNCT
cana-5900	125	11	fixed	fix	VERB
cana-5900	125	12	-	-	PUNCT
cana-5900	125	13	point	point	NOUN
cana-5900	125	14	theory	theory	NOUN
cana-5900	125	15	,	,	PUNCT
cana-5900	125	16	and	and	CCONJ
cana-5900	125	17	geometric	geometric	ADJ
cana-5900	125	18	group	group	NOUN
cana-5900	125	19	theory	theory	NOUN
cana-5900	125	20	.	.	PUNCT
cana-5900	126	1	examples	example	NOUN
cana-5900	126	2	of	of	ADP
cana-5900	126	3	convex	convex	NOUN
cana-5900	126	4	metric	metric	ADJ
cana-5900	126	5	spaces	space	NOUN
cana-5900	126	6	include	include	VERB
cana-5900	126	7	all	all	DET
cana-5900	126	8	normed	normed	ADJ
cana-5900	126	9	linear	linear	ADJ
cana-5900	126	10	spaces	space	NOUN
cana-5900	126	11	(	(	PUNCT
cana-5900	126	12	with	with	ADP
cana-5900	126	13	the	the	DET
cana-5900	126	14	metric	metric	NOUN
cana-5900	126	15	induced	induce	VERB
cana-5900	126	16	by	by	ADP
cana-5900	126	17	the	the	DET
cana-5900	126	18	norm	norm	NOUN
cana-5900	126	19	)	)	PUNCT
cana-5900	126	20	,	,	PUNCT
cana-5900	126	21	riemannian	riemannian	NOUN
cana-5900	126	22	manifolds	manifold	NOUN
cana-5900	126	23	(	(	PUNCT
cana-5900	126	24	where	where	SCONJ
cana-5900	126	25	geodesics	geodesic	NOUN
cana-5900	126	26	are	be	AUX
cana-5900	126	27	well	well	ADV
cana-5900	126	28	-	-	PUNCT
cana-5900	126	29	defined	define	VERB
cana-5900	126	30	)	)	PUNCT
cana-5900	126	31	,	,	PUNCT
cana-5900	126	32	and	and	CCONJ
cana-5900	126	33	cat(0	cat(0	ADJ
cana-5900	126	34	)	)	PUNCT
cana-5900	126	35	spaces	space	NOUN
cana-5900	126	36	,	,	PUNCT
cana-5900	126	37	which	which	PRON
cana-5900	126	38	communications	communication	NOUN
cana-5900	126	39	on	on	ADP
cana-5900	126	40	applied	apply	VERB
cana-5900	126	41	nonlinear	nonlinear	ADJ
cana-5900	126	42	analysis	analysis	NOUN
cana-5900	126	43	issn	issn	NOUN
cana-5900	126	44	:	:	PUNCT
cana-5900	126	45	1074	1074	NUM
cana-5900	126	46	-	-	PUNCT
cana-5900	126	47	133x	133x	NUM
cana-5900	126	48	vol	vol	NOUN
cana-5900	126	49	31	31	NUM
cana-5900	126	50	no	no	NOUN
cana-5900	126	51	.	.	PUNCT
cana-5900	127	1	8s	8s	PROPN
cana-5900	127	2	(	(	PUNCT
cana-5900	127	3	2024	2024	NUM
cana-5900	127	4	)	)	PUNCT
cana-5900	127	5	1102	1102	NUM
cana-5900	127	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5900	127	7	are	be	AUX
cana-5900	127	8	non	non	ADJ
cana-5900	127	9	-	-	ADJ
cana-5900	127	10	positively	positively	ADV
cana-5900	127	11	curved	curved	ADJ
cana-5900	127	12	metric	metric	ADJ
cana-5900	127	13	spaces	space	NOUN
cana-5900	127	14	.	.	PUNCT
cana-5900	128	1	on	on	ADP
cana-5900	128	2	the	the	DET
cana-5900	128	3	other	other	ADJ
cana-5900	128	4	hand	hand	NOUN
cana-5900	128	5	,	,	PUNCT
cana-5900	128	6	a	a	DET
cana-5900	128	7	discrete	discrete	ADJ
cana-5900	128	8	metric	metric	ADJ
cana-5900	128	9	space	space	NOUN
cana-5900	128	10	,	,	PUNCT
cana-5900	128	11	where	where	SCONJ
cana-5900	128	12	d(x	d(x	NOUN
cana-5900	128	13	,	,	PUNCT
cana-5900	128	14	y)=1	y)=1	PROPN
cana-5900	128	15	for	for	ADP
cana-5900	128	16	x	x	PUNCT
cana-5900	128	17	\neq	\neq	PROPN
cana-5900	128	18	y	y	PROPN
cana-5900	128	19	and	and	CCONJ
cana-5900	128	20	d(x	d(x	PROPN
cana-5900	128	21	,	,	PUNCT
cana-5900	128	22	x)=0	x)=0	PROPN
cana-5900	128	23	,	,	PUNCT
cana-5900	128	24	is	be	AUX
cana-5900	128	25	generally	generally	ADV
cana-5900	128	26	not	not	PART
cana-5900	128	27	convex	convex	ADJ
cana-5900	128	28	unless	unless	SCONJ
cana-5900	128	29	it	it	PRON
cana-5900	128	30	contains	contain	VERB
cana-5900	128	31	only	only	ADV
cana-5900	128	32	one	one	NUM
cana-5900	128	33	point	point	NOUN
cana-5900	128	34	,	,	PUNCT
cana-5900	128	35	as	as	SCONJ
cana-5900	128	36	there	there	PRON
cana-5900	128	37	are	be	VERB
cana-5900	128	38	no	no	DET
cana-5900	128	39	intermediate	intermediate	ADJ
cana-5900	128	40	points	point	NOUN
cana-5900	128	41	satisfying	satisfy	VERB
cana-5900	128	42	the	the	DET
cana-5900	128	43	metric	metric	ADJ
cana-5900	128	44	convexity	convexity	NOUN
cana-5900	128	45	condition	condition	NOUN
cana-5900	128	46	.	.	PUNCT
cana-5900	129	1	import	import	NOUN
cana-5900	129	2	numpy	numpy	NOUN
cana-5900	129	3	as	as	ADP
cana-5900	129	4	np	np	NOUN
cana-5900	129	5	#	#	NOUN
cana-5900	129	6	--1	--1	NOUN
cana-5900	129	7	.	.	PUNCT
cana-5900	130	1	define	define	VERB
cana-5900	130	2	metric	metric	ADJ
cana-5900	130	3	spaces	space	NOUN
cana-5900	130	4	(	(	PUNCT
cana-5900	130	5	via	via	ADP
cana-5900	130	6	their	their	PRON
cana-5900	130	7	distance	distance	NOUN
cana-5900	130	8	functions	function	NOUN
cana-5900	130	9	)	)	PUNCT
cana-5900	130	10	--	--	PUNCT
cana-5900	130	11	def	def	PROPN
cana-5900	130	12	euclidean_distance(p1	euclidean_distance(p1	NOUN
cana-5900	130	13	,	,	PUNCT
cana-5900	130	14	p2	p2	PROPN
cana-5900	130	15	):	):	PUNCT
cana-5900	130	16	return	return	NOUN
cana-5900	130	17	np.linalg.norm(np.array(p1	np.linalg.norm(np.array(p1	PROPN
cana-5900	130	18	)	)	PUNCT
cana-5900	130	19	np.array(p2	np.array(p2	PROPN
cana-5900	130	20	)	)	PUNCT
cana-5900	130	21	)	)	PUNCT
cana-5900	130	22	def	def	ADJ
cana-5900	130	23	manhattan_distance(p1	manhattan_distance(p1	NOUN
cana-5900	130	24	,	,	PUNCT
cana-5900	130	25	p2	p2	NOUN
cana-5900	130	26	):	):	PUNCT
cana-5900	130	27	return	return	NOUN
cana-5900	130	28	np.sum(np.abs(np.array(p1	np.sum(np.abs(np.array(p1	PROPN
cana-5900	130	29	)	)	PUNCT
cana-5900	130	30	np.array(p2	np.array(p2	PROPN
cana-5900	130	31	)	)	PUNCT
cana-5900	130	32	)	)	PUNCT
cana-5900	130	33	)	)	PUNCT
cana-5900	130	34	#	#	NOUN
cana-5900	130	35	--2	--2	NOUN
cana-5900	130	36	.	.	PUNCT
cana-5900	131	1	define	define	VERB
cana-5900	131	2	mappings	mapping	NOUN
cana-5900	131	3	--	--	PUNCT
cana-5900	131	4	#	#	NOUN
cana-5900	131	5	example	example	NOUN
cana-5900	131	6	1	1	NUM
cana-5900	131	7	:	:	PUNCT
cana-5900	131	8	contraction	contraction	NOUN
cana-5900	131	9	mapping	mapping	NOUN
cana-5900	131	10	(	(	PUNCT
cana-5900	131	11	for	for	ADP
cana-5900	131	12	banach	banach	ADV
cana-5900	131	13	fixed	fix	VERB
cana-5900	131	14	-	-	PUNCT
cana-5900	131	15	point	point	NOUN
cana-5900	131	16	theorem	theorem	NOUN
cana-5900	131	17	)	)	PUNCT
cana-5900	131	18	in	in	ADP
cana-5900	131	19	r^1	r^1	ADJ
cana-5900	131	20	def	def	ADJ
cana-5900	131	21	t1_contraction_1d(x	t1_contraction_1d(x	NOUN
cana-5900	131	22	):	):	PUNCT
cana-5900	131	23	#	#	NOUN
cana-5900	131	24	fixed	fix	VERB
cana-5900	131	25	point	point	NOUN
cana-5900	131	26	is	be	AUX
cana-5900	131	27	x	x	X
cana-5900	131	28	=	=	SYM
cana-5900	131	29	0.5x	0.5x	NUM
cana-5900	131	30	+	+	CCONJ
cana-5900	131	31	3	3	NUM
cana-5900	131	32	=	=	NOUN
cana-5900	131	33	>	>	X
cana-5900	131	34	0.5x	0.5x	NUM
cana-5900	131	35	=	=	SYM
cana-5900	131	36	3	3	NUM
cana-5900	131	37	=	=	SYM
cana-5900	131	38	>	>	X
cana-5900	131	39	x	x	PUNCT
cana-5900	132	1	=	=	SYM
cana-5900	132	2	6	6	NUM
cana-5900	132	3	return	return	VERB
cana-5900	132	4	0.5	0.5	NUM
cana-5900	132	5	*	*	PUNCT
cana-5900	132	6	x	x	PUNCT
cana-5900	133	1	+	+	CCONJ
cana-5900	133	2	3	3	NUM
cana-5900	133	3	#	#	NOUN
cana-5900	133	4	example	example	NOUN
cana-5900	133	5	2	2	NUM
cana-5900	133	6	:	:	PUNCT
cana-5900	133	7	contraction	contraction	NOUN
cana-5900	133	8	mapping	mapping	NOUN
cana-5900	133	9	in	in	ADP
cana-5900	133	10	r^2	r^2	PROPN
cana-5900	133	11	def	def	VERB
cana-5900	133	12	t2_contraction_2d(p	t2_contraction_2d(p	PROPN
cana-5900	133	13	):	):	PUNCT
cana-5900	133	14	x	x	X
cana-5900	133	15	,	,	PUNCT
cana-5900	133	16	y	y	PROPN
cana-5900	133	17	=	=	SYM
cana-5900	134	1	p	p	DET
cana-5900	134	2	#	#	NOUN
cana-5900	134	3	fixed	fix	VERB
cana-5900	134	4	point	point	NOUN
cana-5900	134	5	:	:	PUNCT
cana-5900	134	6	#	#	NOUN
cana-5900	134	7	x	x	NOUN
cana-5900	134	8	=	=	PUNCT
cana-5900	135	1	0.3x	0.3x	NOUN
cana-5900	136	1	+	+	NUM
cana-5900	136	2	0.1y	0.1y	NOUN
cana-5900	136	3	+	+	CCONJ
cana-5900	136	4	0.5	0.5	NUM
cana-5900	136	5	#	#	NOUN
cana-5900	136	6	y	y	NOUN
cana-5900	136	7	=	=	PUNCT
cana-5900	136	8	0.2x	0.2x	PROPN
cana-5900	137	1	+	+	CCONJ
cana-5900	137	2	0.4y	0.4y	NOUN
cana-5900	137	3	+	+	CCONJ
cana-5900	137	4	1.0	1.0	NUM
cana-5900	137	5	#	#	NOUN
cana-5900	137	6	this	this	PRON
cana-5900	137	7	is	be	AUX
cana-5900	137	8	a	a	DET
cana-5900	137	9	system	system	NOUN
cana-5900	137	10	of	of	ADP
cana-5900	137	11	linear	linear	PROPN
cana-5900	137	12	equations	equation	NOUN
cana-5900	137	13	,	,	PUNCT
cana-5900	137	14	can	can	AUX
cana-5900	137	15	solve	solve	VERB
cana-5900	137	16	for	for	ADP
cana-5900	137	17	fixed	fix	VERB
cana-5900	137	18	point	point	NOUN
cana-5900	137	19	.	.	PUNCT
cana-5900	138	1	#	#	NOUN
cana-5900	138	2	(	(	PUNCT
cana-5900	138	3	1	1	NUM
cana-5900	138	4	-	-	SYM
cana-5900	138	5	0.3)x	0.3)x	NUM
cana-5900	138	6	0.1y	0.1y	NOUN
cana-5900	138	7	=	=	SYM
cana-5900	138	8	0.5	0.5	NUM
cana-5900	138	9	=	=	SYM
cana-5900	138	10	>	>	X
cana-5900	138	11	0.7x	0.7x	NOUN
cana-5900	138	12	0.1y	0.1y	X
cana-5900	138	13	=	=	SYM
cana-5900	138	14	0.5	0.5	NUM
cana-5900	138	15	#	#	NOUN
cana-5900	138	16	-0.2x	-0.2x	NOUN
cana-5900	138	17	+	+	CCONJ
cana-5900	138	18	(	(	PUNCT
cana-5900	138	19	1	1	NUM
cana-5900	138	20	-	-	NUM
cana-5900	138	21	0.4)y	0.4)y	X
cana-5900	138	22	=	=	PUNCT
cana-5900	138	23	1.0	1.0	NUM
cana-5900	138	24	=	=	SYM
cana-5900	138	25	>	>	X
cana-5900	138	26	-0.2x	-0.2x	NOUN
cana-5900	139	1	+	+	CCONJ
cana-5900	139	2	0.6y	0.6y	NUM
cana-5900	139	3	=	=	SYM
cana-5900	139	4	1.0	1.0	NUM
cana-5900	139	5	communications	communication	NOUN
cana-5900	139	6	on	on	ADP
cana-5900	139	7	applied	apply	VERB
cana-5900	139	8	nonlinear	nonlinear	ADJ
cana-5900	139	9	analysis	analysis	NOUN
cana-5900	139	10	issn	issn	NOUN
cana-5900	139	11	:	:	PUNCT
cana-5900	139	12	1074	1074	NUM
cana-5900	139	13	-	-	PUNCT
cana-5900	139	14	133x	133x	NUM
cana-5900	139	15	vol	vol	NOUN
cana-5900	139	16	31	31	NUM
cana-5900	139	17	no	no	NOUN
cana-5900	139	18	.	.	PUNCT
cana-5900	140	1	8s	8s	PROPN
cana-5900	140	2	(	(	PUNCT
cana-5900	140	3	2024	2024	NUM
cana-5900	140	4	)	)	PUNCT
cana-5900	140	5	1103	1103	NUM
cana-5900	140	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5900	140	7	#	#	NOUN
cana-5900	140	8	solution	solution	NOUN
cana-5900	140	9	is	be	AUX
cana-5900	140	10	approx	approx	PROPN
cana-5900	140	11	x=1.0	x=1.0	PROPN
cana-5900	140	12	,	,	PUNCT
cana-5900	140	13	y=2.0	y=2.0	PROPN
cana-5900	140	14	(	(	PUNCT
cana-5900	140	15	you	you	PRON
cana-5900	140	16	can	can	AUX
cana-5900	140	17	verify	verify	VERB
cana-5900	140	18	by	by	ADP
cana-5900	140	19	plugging	plug	VERB
cana-5900	140	20	in	in	ADP
cana-5900	140	21	)	)	PUNCT
cana-5900	140	22	return	return	NOUN
cana-5900	140	23	[	[	PUNCT
cana-5900	140	24	0.3	0.3	NUM
cana-5900	140	25	*	*	PUNCT
cana-5900	140	26	x	x	PUNCT
cana-5900	141	1	+	+	NUM
cana-5900	141	2	0.1	0.1	NUM
cana-5900	141	3	*	*	PUNCT
cana-5900	141	4	y	y	PROPN
cana-5900	141	5	+	+	NUM
cana-5900	141	6	0.5	0.5	NUM
cana-5900	141	7	,	,	PUNCT
cana-5900	141	8	0.2	0.2	NUM
cana-5900	141	9	*	*	PUNCT
cana-5900	141	10	x	x	PUNCT
cana-5900	142	1	+	+	NUM
cana-5900	142	2	0.4	0.4	NUM
cana-5900	142	3	*	*	PUNCT
cana-5900	142	4	y	y	NOUN
cana-5900	142	5	+	+	CCONJ
cana-5900	142	6	1.0	1.0	NUM
cana-5900	142	7	]	]	SYM
cana-5900	142	8	#	#	NOUN
cana-5900	142	9	example	example	NOUN
cana-5900	142	10	3	3	NUM
cana-5900	142	11	:	:	PUNCT
cana-5900	142	12	nonexpansive	nonexpansive	ADJ
cana-5900	142	13	mapping	mapping	NOUN
cana-5900	142	14	(	(	PUNCT
cana-5900	142	15	for	for	ADP
cana-5900	142	16	mann	mann	PROPN
cana-5900	142	17	iteration	iteration	NOUN
cana-5900	142	18	)	)	PUNCT
cana-5900	142	19	in	in	ADP
cana-5900	142	20	r^1	r^1	ADJ
cana-5900	142	21	#	#	NOUN
cana-5900	142	22	this	this	PRON
cana-5900	142	23	is	be	AUX
cana-5900	142	24	a	a	DET
cana-5900	142	25	projection	projection	NOUN
cana-5900	142	26	mapping	mapping	NOUN
cana-5900	142	27	onto	onto	ADP
cana-5900	142	28	the	the	DET
cana-5900	142	29	interval	interval	NOUN
cana-5900	142	30	[	[	X
cana-5900	142	31	0	0	NUM
cana-5900	142	32	,	,	PUNCT
cana-5900	142	33	1	1	NUM
cana-5900	142	34	]	]	PUNCT
cana-5900	142	35	.	.	PUNCT
cana-5900	143	1	#	#	NOUN
cana-5900	143	2	fixed	fix	VERB
cana-5900	143	3	points	point	NOUN
cana-5900	143	4	are	be	AUX
cana-5900	143	5	all	all	PRON
cana-5900	143	6	x	x	INTJ
cana-5900	143	7	in	in	ADP
cana-5900	143	8	[	[	X
cana-5900	143	9	0	0	NUM
cana-5900	143	10	,	,	PUNCT
cana-5900	143	11	1	1	NUM
cana-5900	143	12	]	]	PUNCT
cana-5900	143	13	.	.	PUNCT
cana-5900	144	1	def	def	ADJ
cana-5900	144	2	t3_nonexpansive_projection_1d(x	t3_nonexpansive_projection_1d(x	NOUN
cana-5900	144	3	):	):	PUNCT
cana-5900	144	4	return	return	NOUN
cana-5900	144	5	max(0	max(0	NOUN
cana-5900	144	6	,	,	PUNCT
cana-5900	144	7	min(x	min(x	PROPN
cana-5900	144	8	,	,	PUNCT
cana-5900	144	9	1	1	NUM
cana-5900	144	10	)	)	PUNCT
cana-5900	144	11	)	)	PUNCT
cana-5900	144	12	#	#	NOUN
cana-5900	144	13	--3	--3	NOUN
cana-5900	144	14	.	.	PUNCT
cana-5900	145	1	fixed	fix	VERB
cana-5900	145	2	-	-	PUNCT
cana-5900	145	3	point	point	NOUN
cana-5900	145	4	iteration	iteration	NOUN
cana-5900	145	5	functions	function	NOUN
cana-5900	145	6	--	--	PUNCT
cana-5900	145	7	def	def	ADJ
cana-5900	145	8	find_fixed_point_picard_iteration(mapping	find_fixed_point_picard_iteration(mapping	NOUN
cana-5900	145	9	,	,	PUNCT
cana-5900	145	10	initial_guess	initial_guess	PROPN
cana-5900	145	11	,	,	PUNCT
cana-5900	145	12	distance_metric	distance_metric	ADJ
cana-5900	145	13	,	,	PUNCT
cana-5900	145	14	tolerance=1e-7	tolerance=1e-7	NUM
cana-5900	145	15	,	,	PUNCT
cana-5900	145	16	max_iterations=1000	max_iterations=1000	NUM
cana-5900	145	17	):	):	PUNCT
cana-5900	145	18	current_point	current_point	NOUN
cana-5900	145	19	=	=	SYM
cana-5900	145	20	initial_guess	initial_guess	PROPN
cana-5900	145	21	for	for	ADP
cana-5900	145	22	i	i	PRON
cana-5900	145	23	in	in	ADP
cana-5900	145	24	range(max_iterations	range(max_iteration	NOUN
cana-5900	145	25	):	):	PUNCT
cana-5900	145	26	next_point	next_point	NOUN
cana-5900	145	27	=	=	SYM
cana-5900	145	28	mapping(current_point	mapping(current_point	NOUN
cana-5900	145	29	)	)	PUNCT
cana-5900	145	30	dist	dist	NOUN
cana-5900	145	31	=	=	SYM
cana-5900	145	32	distance_metric(current_point	distance_metric(current_point	NOUN
cana-5900	145	33	,	,	PUNCT
cana-5900	145	34	next_point	next_point	NOUN
cana-5900	145	35	)	)	PUNCT
cana-5900	145	36	if	if	SCONJ
cana-5900	145	37	dist	dist	NOUN
cana-5900	145	38	<	<	X
cana-5900	145	39	tolerance	tolerance	NOUN
cana-5900	145	40	:	:	PUNCT
cana-5900	145	41	print(f"picard	print(f"picard	ADJ
cana-5900	145	42	iteration	iteration	NOUN
cana-5900	145	43	converged	converge	VERB
cana-5900	145	44	in	in	ADP
cana-5900	145	45	{	{	PUNCT
cana-5900	145	46	i+1	i+1	NOUN
cana-5900	145	47	}	}	PUNCT
cana-5900	145	48	iterations	iteration	NOUN
cana-5900	145	49	.	.	PUNCT
cana-5900	146	1	final	final	ADJ
cana-5900	146	2	distance	distance	NOUN
cana-5900	146	3	:	:	PUNCT
cana-5900	146	4	{	{	PUNCT
cana-5900	146	5	dist:.8f	dist:.8f	NOUN
cana-5900	146	6	}	}	PUNCT
cana-5900	146	7	"	"	PUNCT
cana-5900	146	8	)	)	PUNCT
cana-5900	146	9	return	return	VERB
cana-5900	146	10	next_point	next_point	NOUN
cana-5900	146	11	current_point	current_point	NOUN
cana-5900	146	12	=	=	SYM
cana-5900	146	13	next_point	next_point	NOUN
cana-5900	146	14	print(f"picard	print(f"picard	ADJ
cana-5900	146	15	iteration	iteration	NOUN
cana-5900	146	16	did	do	AUX
cana-5900	146	17	not	not	PART
cana-5900	146	18	converge	converge	VERB
cana-5900	146	19	within	within	ADP
cana-5900	146	20	{	{	PUNCT
cana-5900	146	21	max_iterations	max_iteration	NOUN
cana-5900	146	22	}	}	PUNCT
cana-5900	146	23	iterations	iteration	NOUN
cana-5900	146	24	.	.	PUNCT
cana-5900	147	1	final	final	ADJ
cana-5900	147	2	distance	distance	NOUN
cana-5900	147	3	:	:	PUNCT
cana-5900	147	4	{	{	PUNCT
cana-5900	147	5	dist:.8f	dist:.8f	NOUN
cana-5900	147	6	}	}	PUNCT
cana-5900	147	7	"	"	PUNCT
cana-5900	147	8	)	)	PUNCT
cana-5900	147	9	return	return	VERB
cana-5900	147	10	none	none	NOUN
cana-5900	147	11	def	def	ADJ
cana-5900	147	12	find_fixed_point_mann_iteration(mapping	find_fixed_point_mann_iteration(mapping	NOUN
cana-5900	147	13	,	,	PUNCT
cana-5900	147	14	initial_guess	initial_guess	PROPN
cana-5900	147	15	,	,	PUNCT
cana-5900	147	16	distance_metric	distance_metric	ADJ
cana-5900	147	17	,	,	PUNCT
cana-5900	147	18	tolerance=1e-7	tolerance=1e-7	NUM
cana-5900	147	19	,	,	PUNCT
cana-5900	147	20	max_iterations=1000	max_iterations=1000	NUM
cana-5900	147	21	,	,	PUNCT
cana-5900	147	22	alpha=0.5	alpha=0.5	NUM
cana-5900	147	23	):	):	PUNCT
cana-5900	147	24	communications	communication	NOUN
cana-5900	147	25	on	on	ADP
cana-5900	147	26	applied	apply	VERB
cana-5900	147	27	nonlinear	nonlinear	ADJ
cana-5900	147	28	analysis	analysis	NOUN
cana-5900	147	29	issn	issn	NOUN
cana-5900	147	30	:	:	PUNCT
cana-5900	147	31	1074	1074	NUM
cana-5900	147	32	-	-	PUNCT
cana-5900	147	33	133x	133x	NUM
cana-5900	147	34	vol	vol	NOUN
cana-5900	147	35	31	31	NUM
cana-5900	147	36	no	no	NOUN
cana-5900	147	37	.	.	PUNCT
cana-5900	148	1	8s	8s	PROPN
cana-5900	148	2	(	(	PUNCT
cana-5900	148	3	2024	2024	NUM
cana-5900	148	4	)	)	PUNCT
cana-5900	148	5	1104	1104	NUM
cana-5900	148	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5900	148	7	current_point	current_point	NOUN
cana-5900	148	8	=	=	SYM
cana-5900	148	9	np.array(initial_guess	np.array(initial_guess	NOUN
cana-5900	148	10	)	)	PUNCT
cana-5900	148	11	for	for	ADP
cana-5900	148	12	i	i	PRON
cana-5900	148	13	in	in	ADP
cana-5900	148	14	range(max_iterations	range(max_iteration	NOUN
cana-5900	148	15	):	):	PUNCT
cana-5900	148	16	tx	tx	PROPN
cana-5900	148	17	=	=	SYM
cana-5900	148	18	np.array(mapping(current_point	np.array(mapping(current_point	NOUN
cana-5900	148	19	)	)	PUNCT
cana-5900	148	20	)	)	PUNCT
cana-5900	148	21	next_point	next_point	NOUN
cana-5900	148	22	=	=	PUNCT
cana-5900	148	23	(	(	PUNCT
cana-5900	148	24	1	1	NUM
cana-5900	148	25	alpha	alpha	NOUN
cana-5900	148	26	)	)	PUNCT
cana-5900	148	27	*	*	PUNCT
cana-5900	149	1	current_point	current_point	NOUN
cana-5900	149	2	+	+	CCONJ
cana-5900	149	3	alpha	alpha	NOUN
cana-5900	149	4	*	*	PUNCT
cana-5900	149	5	tx	tx	PROPN
cana-5900	149	6	dist	dist	NOUN
cana-5900	149	7	=	=	SYM
cana-5900	149	8	distance_metric(current_point	distance_metric(current_point	PROPN
cana-5900	149	9	,	,	PUNCT
cana-5900	149	10	next_point	next_point	NOUN
cana-5900	149	11	)	)	PUNCT
cana-5900	149	12	if	if	SCONJ
cana-5900	149	13	dist	dist	NOUN
cana-5900	149	14	<	<	X
cana-5900	149	15	tolerance	tolerance	NOUN
cana-5900	149	16	:	:	PUNCT
cana-5900	149	17	print(f"mann	print(f"mann	NOUN
cana-5900	149	18	iteration	iteration	NOUN
cana-5900	149	19	converged	converge	VERB
cana-5900	149	20	in	in	ADP
cana-5900	149	21	{	{	PUNCT
cana-5900	149	22	i+1	i+1	NOUN
cana-5900	149	23	}	}	PUNCT
cana-5900	149	24	iterations	iteration	NOUN
cana-5900	149	25	.	.	PUNCT
cana-5900	150	1	final	final	ADJ
cana-5900	150	2	distance	distance	NOUN
cana-5900	150	3	:	:	PUNCT
cana-5900	150	4	{	{	PUNCT
cana-5900	150	5	dist:.8f	dist:.8f	NOUN
cana-5900	150	6	}	}	PUNCT
cana-5900	150	7	"	"	PUNCT
cana-5900	150	8	)	)	PUNCT
cana-5900	150	9	return	return	VERB
cana-5900	150	10	next_point	next_point	NOUN
cana-5900	150	11	current_point	current_point	NOUN
cana-5900	150	12	=	=	SYM
cana-5900	150	13	next_point	next_point	NOUN
cana-5900	150	14	print(f"mann	print(f"mann	NOUN
cana-5900	150	15	iteration	iteration	NOUN
cana-5900	150	16	did	do	AUX
cana-5900	150	17	not	not	PART
cana-5900	150	18	converge	converge	VERB
cana-5900	150	19	within	within	ADP
cana-5900	150	20	{	{	PUNCT
cana-5900	150	21	max_iterations	max_iteration	NOUN
cana-5900	150	22	}	}	PUNCT
cana-5900	150	23	iterations	iteration	NOUN
cana-5900	150	24	.	.	PUNCT
cana-5900	151	1	final	final	ADJ
cana-5900	151	2	distance	distance	NOUN
cana-5900	151	3	:	:	PUNCT
cana-5900	151	4	{	{	PUNCT
cana-5900	151	5	dist:.8f	dist:.8f	NOUN
cana-5900	151	6	}	}	PUNCT
cana-5900	151	7	"	"	PUNCT
cana-5900	151	8	)	)	PUNCT
cana-5900	151	9	return	return	VERB
cana-5900	151	10	none	none	NOUN
cana-5900	151	11	#	#	NOUN
cana-5900	151	12	--4	--4	NOUN
cana-5900	151	13	.	.	PUNCT
cana-5900	152	1	demonstrations	demonstration	NOUN
cana-5900	152	2	--	--	PUNCT
cana-5900	152	3	print("--banach	print("--banach	VERB
cana-5900	152	4	fixed	fix	VERB
cana-5900	152	5	-	-	PUNCT
cana-5900	152	6	point	point	NOUN
cana-5900	152	7	theorem	theorem	ADJ
cana-5900	152	8	demonstration	demonstration	NOUN
cana-5900	152	9	(	(	PUNCT
cana-5900	152	10	contraction	contraction	NOUN
cana-5900	152	11	mapping	mapping	NOUN
cana-5900	152	12	)	)	PUNCT
cana-5900	152	13	---	---	PUNCT
cana-5900	152	14	"	"	PUNCT
cana-5900	152	15	)	)	PUNCT
cana-5900	152	16	#	#	NOUN
cana-5900	152	17	1d	1d	NUM
cana-5900	152	18	contraction	contraction	NOUN
cana-5900	152	19	initial_guess_1d	initial_guess_1d	NOUN
cana-5900	152	20	=	=	NOUN
cana-5900	152	21	0.0	0.0	NUM
cana-5900	152	22	fixed_point_1d	fixed_point_1d	NOUN
cana-5900	152	23	=	=	SYM
cana-5900	152	24	find_fixed_point_picard_iteration(t1_contraction_1d	find_fixed_point_picard_iteration(t1_contraction_1d	PROPN
cana-5900	152	25	,	,	PUNCT
cana-5900	152	26	initial_guess_1d	initial_guess_1d	NOUN
cana-5900	152	27	,	,	PUNCT
cana-5900	152	28	euclidean_distance	euclidean_distance	NOUN
cana-5900	152	29	)	)	PUNCT
cana-5900	152	30	print(f"fixed	print(f"fixe	VERB
cana-5900	152	31	point	point	NOUN
cana-5900	152	32	for	for	ADP
cana-5900	152	33	t1	t1	NOUN
cana-5900	152	34	:	:	PUNCT
cana-5900	152	35	{	{	PUNCT
cana-5900	152	36	fixed_point_1d}\n	fixed_point_1d}\n	NOUN
cana-5900	152	37	"	"	PUNCT
cana-5900	152	38	)	)	PUNCT
cana-5900	152	39	#	#	NOUN
cana-5900	152	40	2d	2d	NUM
cana-5900	152	41	contraction	contraction	NOUN
cana-5900	152	42	initial_guess_2d	initial_guess_2d	NOUN
cana-5900	152	43	=	=	PUNCT
cana-5900	153	1	[	[	X
cana-5900	153	2	0.0	0.0	NUM
cana-5900	153	3	,	,	PUNCT
cana-5900	153	4	0.0	0.0	NUM
cana-5900	153	5	]	]	SYM
cana-5900	153	6	fixed_point_2d	fixed_point_2d	NOUN
cana-5900	153	7	=	=	SYM
cana-5900	153	8	find_fixed_point_picard_iteration(t2_contraction_2d	find_fixed_point_picard_iteration(t2_contraction_2d	PROPN
cana-5900	153	9	,	,	PUNCT
cana-5900	153	10	initial_guess_2d	initial_guess_2d	ADJ
cana-5900	153	11	,	,	PUNCT
cana-5900	153	12	euclidean_distance	euclidean_distance	NOUN
cana-5900	153	13	)	)	PUNCT
cana-5900	153	14	print(f"fixed	print(f"fixe	VERB
cana-5900	153	15	point	point	NOUN
cana-5900	153	16	for	for	ADP
cana-5900	153	17	t2	t2	NOUN
cana-5900	153	18	:	:	PUNCT
cana-5900	153	19	{	{	PUNCT
cana-5900	153	20	fixed_point_2d}\n	fixed_point_2d}\n	NOUN
cana-5900	153	21	"	"	PUNCT
cana-5900	153	22	)	)	PUNCT
cana-5900	153	23	communications	communication	NOUN
cana-5900	153	24	on	on	ADP
cana-5900	153	25	applied	apply	VERB
cana-5900	153	26	nonlinear	nonlinear	ADJ
cana-5900	153	27	analysis	analysis	NOUN
cana-5900	153	28	issn	issn	NOUN
cana-5900	153	29	:	:	PUNCT
cana-5900	153	30	1074	1074	NUM
cana-5900	153	31	-	-	PUNCT
cana-5900	153	32	133x	133x	NUM
cana-5900	153	33	vol	vol	NOUN
cana-5900	153	34	31	31	NUM
cana-5900	153	35	no	no	NOUN
cana-5900	153	36	.	.	PUNCT
cana-5900	154	1	8s	8s	PROPN
cana-5900	154	2	(	(	PUNCT
cana-5900	154	3	2024	2024	NUM
cana-5900	154	4	)	)	PUNCT
cana-5900	154	5	1105	1105	NUM
cana-5900	154	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5900	154	7	print("--mann	print("--mann	PROPN
cana-5900	154	8	iteration	iteration	NOUN
cana-5900	154	9	demonstration	demonstration	NOUN
cana-5900	154	10	(	(	PUNCT
cana-5900	154	11	nonexpansive	nonexpansive	ADJ
cana-5900	154	12	mapping	mapping	NOUN
cana-5900	154	13	)	)	PUNCT
cana-5900	154	14	---	---	PUNCT
cana-5900	154	15	"	"	PUNCT
cana-5900	154	16	)	)	PUNCT
cana-5900	154	17	#	#	NOUN
cana-5900	154	18	for	for	ADP
cana-5900	154	19	mann	mann	PROPN
cana-5900	154	20	iteration	iteration	NOUN
cana-5900	154	21	,	,	PUNCT
cana-5900	154	22	we	we	PRON
cana-5900	154	23	assume	assume	VERB
cana-5900	154	24	the	the	DET
cana-5900	154	25	space	space	NOUN
cana-5900	154	26	is	be	AUX
cana-5900	154	27	convex	convex	ADJ
cana-5900	154	28	(	(	PUNCT
cana-5900	154	29	e.g.	e.g.	ADV
cana-5900	154	30	,	,	PUNCT
cana-5900	154	31	euclidean	euclidean	ADJ
cana-5900	154	32	space	space	NOUN
cana-5900	154	33	)	)	PUNCT
cana-5900	154	34	.	.	PUNCT
cana-5900	155	1	#	#	NOUN
cana-5900	155	2	the	the	DET
cana-5900	155	3	projection	projection	NOUN
cana-5900	155	4	mapping	mapping	NOUN
cana-5900	155	5	t3	t3	PROPN
cana-5900	155	6	has	have	AUX
cana-5900	155	7	fixed	fix	VERB
cana-5900	155	8	points	point	NOUN
cana-5900	155	9	in	in	ADP
cana-5900	155	10	[	[	X
cana-5900	155	11	0,1	0,1	NUM
cana-5900	155	12	]	]	PUNCT
cana-5900	155	13	.	.	PUNCT
cana-5900	156	1	if	if	SCONJ
cana-5900	156	2	we	we	PRON
cana-5900	156	3	start	start	VERB
cana-5900	156	4	outside	outside	ADV
cana-5900	156	5	,	,	PUNCT
cana-5900	156	6	it	it	PRON
cana-5900	156	7	should	should	AUX
cana-5900	156	8	converge	converge	VERB
cana-5900	156	9	to	to	ADP
cana-5900	156	10	the	the	DET
cana-5900	156	11	boundary	boundary	NOUN
cana-5900	156	12	.	.	PUNCT
cana-5900	157	1	initial_guess_proj	initial_guess_proj	PUNCT
cana-5900	158	1	=	=	NOUN
cana-5900	158	2	5.0	5.0	NUM
cana-5900	158	3	#	#	NOUN
cana-5900	158	4	start	start	NOUN
cana-5900	158	5	outside	outside	ADP
cana-5900	158	6	the	the	DET
cana-5900	158	7	fixed	fix	VERB
cana-5900	158	8	point	point	NOUN
cana-5900	158	9	set	set	VERB
cana-5900	158	10	[	[	X
cana-5900	158	11	0,1	0,1	NUM
cana-5900	158	12	]	]	PUNCT
cana-5900	158	13	fixed_point_proj	fixed_point_proj	PUNCT
cana-5900	159	1	=	=	SYM
cana-5900	159	2	find_fixed_point_mann_iteration(t3_nonexpansive_projection_1d	find_fixed_point_mann_iteration(t3_nonexpansive_projection_1d	PROPN
cana-5900	159	3	,	,	PUNCT
cana-5900	159	4	initial_guess_proj	initial_guess_proj	NUM
cana-5900	159	5	,	,	PUNCT
cana-5900	159	6	euclidean_distance	euclidean_distance	NOUN
cana-5900	159	7	,	,	PUNCT
cana-5900	159	8	alpha=0.5	alpha=0.5	NOUN
cana-5900	159	9	)	)	PUNCT
cana-5900	159	10	print(f"fixed	print(f"fixe	VERB
cana-5900	159	11	point	point	NOUN
cana-5900	159	12	for	for	ADP
cana-5900	159	13	t3	t3	PROPN
cana-5900	159	14	(	(	PUNCT
cana-5900	159	15	initial	initial	ADJ
cana-5900	159	16	guess	guess	NOUN
cana-5900	159	17	5.0	5.0	NUM
cana-5900	159	18	):	):	PUNCT
cana-5900	159	19	{	{	PUNCT
cana-5900	159	20	fixed_point_proj}\n	fixed_point_proj}\n	NOUN
cana-5900	159	21	"	"	PUNCT
cana-5900	159	22	)	)	PUNCT
cana-5900	159	23	initial_guess_proj_neg	initial_guess_proj_neg	PUNCT
cana-5900	160	1	=	=	SYM
cana-5900	160	2	-2.0	-2.0	ADJ
cana-5900	160	3	#	#	NOUN
cana-5900	160	4	start	start	NOUN
cana-5900	160	5	outside	outside	ADP
cana-5900	160	6	the	the	DET
cana-5900	160	7	fixed	fix	VERB
cana-5900	160	8	point	point	NOUN
cana-5900	160	9	set	set	VERB
cana-5900	160	10	[	[	X
cana-5900	160	11	0,1	0,1	NUM
cana-5900	160	12	]	]	X
cana-5900	160	13	fixed_point_proj_neg	fixed_point_proj_neg	PROPN
cana-5900	160	14	=	=	SYM
cana-5900	160	15	find_fixed_point_mann_iteration(t3_nonexpansive_projection_1d	find_fixed_point_mann_iteration(t3_nonexpansive_projection_1d	PROPN
cana-5900	160	16	,	,	PUNCT
cana-5900	160	17	initial_guess_proj_neg	initial_guess_proj_neg	NOUN
cana-5900	160	18	,	,	PUNCT
cana-5900	160	19	euclidean_distance	euclidean_distance	NOUN
cana-5900	160	20	,	,	PUNCT
cana-5900	160	21	alpha=0.5	alpha=0.5	NOUN
cana-5900	160	22	)	)	PUNCT
cana-5900	160	23	print(f"fixed	print(f"fixe	VERB
cana-5900	160	24	point	point	NOUN
cana-5900	160	25	for	for	ADP
cana-5900	160	26	t3	t3	PROPN
cana-5900	160	27	(	(	PUNCT
cana-5900	160	28	initial	initial	ADJ
cana-5900	160	29	guess	guess	NOUN
cana-5900	160	30	-2.0	-2.0	ADJ
cana-5900	160	31	):	):	PUNCT
cana-5900	160	32	{	{	PUNCT
cana-5900	160	33	fixed_point_proj_neg}\n	fixed_point_proj_neg}\n	NOUN
cana-5900	160	34	"	"	PUNCT
cana-5900	160	35	)	)	PUNCT
cana-5900	160	36	initial_guess_proj_inside	initial_guess_proj_inside	ADV
cana-5900	160	37	=	=	SYM
cana-5900	160	38	0.7	0.7	NUM
cana-5900	160	39	#	#	NOUN
cana-5900	160	40	start	start	NOUN
cana-5900	160	41	inside	inside	ADP
cana-5900	160	42	the	the	DET
cana-5900	160	43	fixed	fix	VERB
cana-5900	160	44	point	point	NOUN
cana-5900	160	45	set	set	VERB
cana-5900	160	46	[	[	X
cana-5900	160	47	0,1	0,1	NUM
cana-5900	160	48	]	]	PUNCT
cana-5900	160	49	fixed_point_proj_inside	fixed_point_proj_inside	NOUN
cana-5900	160	50	=	=	SYM
cana-5900	160	51	find_fixed_point_mann_iteration(t3_nonexpansive_projection_1d	find_fixed_point_mann_iteration(t3_nonexpansive_projection_1d	PROPN
cana-5900	160	52	,	,	PUNCT
cana-5900	160	53	initial_guess_proj_inside	initial_guess_proj_inside	NOUN
cana-5900	160	54	,	,	PUNCT
cana-5900	160	55	euclidean_distance	euclidean_distance	NOUN
cana-5900	160	56	,	,	PUNCT
cana-5900	160	57	alpha=0.5	alpha=0.5	NOUN
cana-5900	160	58	)	)	PUNCT
cana-5900	160	59	print(f"fixed	print(f"fixe	VERB
cana-5900	160	60	point	point	NOUN
cana-5900	160	61	for	for	ADP
cana-5900	160	62	t3	t3	PROPN
cana-5900	160	63	(	(	PUNCT
cana-5900	160	64	initial	initial	ADJ
cana-5900	160	65	guess	guess	NOUN
cana-5900	160	66	0.7	0.7	NUM
cana-5900	160	67	):	):	PUNCT
cana-5900	160	68	{	{	PUNCT
cana-5900	160	69	fixed_point_proj_inside}\n	fixed_point_proj_inside}\n	PROPN
cana-5900	160	70	"	"	PUNCT
cana-5900	160	71	)	)	PUNCT
cana-5900	160	72	the	the	DET
cana-5900	160	73	study	study	NOUN
cana-5900	160	74	of	of	ADP
cana-5900	160	75	convex	convex	PROPN
cana-5900	160	76	metric	metric	ADJ
cana-5900	160	77	spaces	space	NOUN
cana-5900	160	78	often	often	ADV
cana-5900	160	79	involves	involve	VERB
cana-5900	160	80	exploring	explore	VERB
cana-5900	160	81	properties	property	NOUN
cana-5900	160	82	related	relate	VERB
cana-5900	160	83	to	to	ADP
cana-5900	160	84	their	their	PRON
cana-5900	160	85	completeness	completeness	NOUN
cana-5900	160	86	,	,	PUNCT
cana-5900	160	87	compactness	compactness	NOUN
cana-5900	160	88	,	,	PUNCT
cana-5900	160	89	and	and	CCONJ
cana-5900	160	90	the	the	DET
cana-5900	160	91	existence	existence	NOUN
cana-5900	160	92	of	of	ADP
cana-5900	160	93	specific	specific	ADJ
cana-5900	160	94	types	type	NOUN
cana-5900	160	95	of	of	ADP
cana-5900	160	96	maps	map	NOUN
cana-5900	160	97	.	.	PUNCT
cana-5900	161	1	for	for	ADP
cana-5900	161	2	instance	instance	NOUN
cana-5900	161	3	,	,	PUNCT
cana-5900	161	4	the	the	DET
cana-5900	161	5	celebrated	celebrate	VERB
cana-5900	161	6	brouwer	brouwer	NOUN
cana-5900	161	7	fixed	fix	VERB
cana-5900	161	8	-	-	PUNCT
cana-5900	161	9	point	point	NOUN
cana-5900	161	10	theorem	theorem	NOUN
cana-5900	161	11	has	have	VERB
cana-5900	161	12	generalizations	generalization	NOUN
cana-5900	161	13	to	to	ADP
cana-5900	161	14	certain	certain	ADJ
cana-5900	161	15	types	type	NOUN
cana-5900	161	16	of	of	ADP
cana-5900	161	17	convex	convex	ADJ
cana-5900	161	18	metric	metric	ADJ
cana-5900	161	19	spaces	space	NOUN
cana-5900	161	20	.	.	PUNCT
cana-5900	162	1	moreover	moreover	ADV
cana-5900	162	2	,	,	PUNCT
cana-5900	162	3	the	the	DET
cana-5900	162	4	study	study	NOUN
cana-5900	162	5	of	of	ADP
cana-5900	162	6	geodesics	geodesic	NOUN
cana-5900	162	7	in	in	ADP
cana-5900	162	8	these	these	DET
cana-5900	162	9	spaces	space	NOUN
cana-5900	162	10	forms	form	VERB
cana-5900	162	11	a	a	DET
cana-5900	162	12	crucial	crucial	ADJ
cana-5900	162	13	part	part	NOUN
cana-5900	162	14	of	of	ADP
cana-5900	162	15	geometric	geometric	ADJ
cana-5900	162	16	analysis	analysis	NOUN
cana-5900	162	17	,	,	PUNCT
cana-5900	162	18	where	where	SCONJ
cana-5900	162	19	one	one	PRON
cana-5900	162	20	investigates	investigate	VERB
cana-5900	162	21	the	the	DET
cana-5900	162	22	behavior	behavior	NOUN
cana-5900	162	23	of	of	ADP
cana-5900	162	24	paths	path	NOUN
cana-5900	162	25	that	that	PRON
cana-5900	162	26	locally	locally	ADV
cana-5900	162	27	minimize	minimize	VERB
cana-5900	162	28	distance	distance	NOUN
cana-5900	162	29	.	.	PUNCT
cana-5900	163	1	convex	convex	PROPN
cana-5900	163	2	metric	metric	ADJ
cana-5900	163	3	spaces	space	NOUN
cana-5900	163	4	represent	represent	VERB
cana-5900	163	5	a	a	DET
cana-5900	163	6	powerful	powerful	ADJ
cana-5900	163	7	generalization	generalization	NOUN
cana-5900	163	8	of	of	ADP
cana-5900	163	9	the	the	DET
cana-5900	163	10	familiar	familiar	ADJ
cana-5900	163	11	geometric	geometric	ADJ
cana-5900	163	12	notions	notion	NOUN
cana-5900	163	13	of	of	ADP
cana-5900	163	14	“	"	PUNCT
cana-5900	163	15	straightness	straightness	NOUN
cana-5900	163	16	”	"	PUNCT
cana-5900	163	17	and	and	CCONJ
cana-5900	163	18	“	"	PUNCT
cana-5900	163	19	betweenness	betweenness	NOUN
cana-5900	163	20	”	"	PUNCT
cana-5900	163	21	from	from	ADP
cana-5900	163	22	euclidean	euclidean	ADJ
cana-5900	163	23	spaces	space	NOUN
cana-5900	163	24	to	to	ADP
cana-5900	163	25	a	a	DET
cana-5900	163	26	broader	broad	ADJ
cana-5900	163	27	class	class	NOUN
cana-5900	163	28	of	of	ADP
cana-5900	163	29	metric	metric	ADJ
cana-5900	163	30	spaces	space	NOUN
cana-5900	163	31	.	.	PUNCT
cana-5900	164	1	their	their	PRON
cana-5900	164	2	inherent	inherent	ADJ
cana-5900	164	3	geometric	geometric	ADJ
cana-5900	164	4	structure	structure	NOUN
cana-5900	164	5	provides	provide	VERB
cana-5900	164	6	a	a	DET
cana-5900	164	7	fertile	fertile	ADJ
cana-5900	164	8	ground	ground	NOUN
cana-5900	164	9	for	for	ADP
cana-5900	164	10	extending	extend	VERB
cana-5900	164	11	classical	classical	ADJ
cana-5900	164	12	results	result	NOUN
cana-5900	164	13	from	from	ADP
cana-5900	164	14	analysis	analysis	NOUN
cana-5900	164	15	and	and	CCONJ
cana-5900	164	16	geometry	geometry	NOUN
cana-5900	164	17	,	,	PUNCT
cana-5900	164	18	making	make	VERB
cana-5900	164	19	them	they	PRON
cana-5900	164	20	a	a	DET
cana-5900	164	21	fundamental	fundamental	ADJ
cana-5900	164	22	concept	concept	NOUN
cana-5900	164	23	with	with	ADP
cana-5900	164	24	wide	wide	ADV
cana-5900	164	25	-	-	PUNCT
cana-5900	164	26	ranging	range	VERB
cana-5900	164	27	applications	application	NOUN
cana-5900	164	28	across	across	ADP
cana-5900	164	29	various	various	ADJ
cana-5900	164	30	branches	branch	NOUN
cana-5900	164	31	of	of	ADP
cana-5900	164	32	mathematics	mathematic	NOUN
cana-5900	164	33	.	.	PUNCT
cana-5900	165	1	the	the	DET
cana-5900	165	2	concept	concept	NOUN
cana-5900	165	3	of	of	ADP
cana-5900	165	4	convexity	convexity	NOUN
cana-5900	165	5	in	in	ADP
cana-5900	165	6	a	a	DET
cana-5900	165	7	metric	metric	ADJ
cana-5900	165	8	setting	setting	NOUN
cana-5900	165	9	enriches	enrich	VERB
cana-5900	165	10	our	our	PRON
cana-5900	165	11	understanding	understanding	NOUN
cana-5900	165	12	of	of	ADP
cana-5900	165	13	the	the	DET
cana-5900	165	14	intrinsic	intrinsic	ADJ
cana-5900	165	15	geometry	geometry	NOUN
cana-5900	165	16	of	of	ADP
cana-5900	165	17	spaces	space	NOUN
cana-5900	165	18	and	and	CCONJ
cana-5900	165	19	provides	provide	VERB
cana-5900	165	20	tools	tool	NOUN
cana-5900	165	21	for	for	ADP
cana-5900	165	22	tackling	tackle	VERB
cana-5900	165	23	problems	problem	NOUN
cana-5900	165	24	in	in	ADP
cana-5900	165	25	diverse	diverse	ADJ
cana-5900	165	26	fields	field	NOUN
cana-5900	165	27	from	from	ADP
cana-5900	165	28	optimization	optimization	NOUN
cana-5900	165	29	to	to	ADP
cana-5900	165	30	theoretical	theoretical	ADJ
cana-5900	165	31	computer	computer	NOUN
cana-5900	165	32	science	science	NOUN
cana-5900	165	33	.	.	PUNCT
cana-5900	166	1	communications	communication	NOUN
cana-5900	166	2	on	on	ADP
cana-5900	166	3	applied	apply	VERB
cana-5900	166	4	nonlinear	nonlinear	ADJ
cana-5900	166	5	analysis	analysis	NOUN
cana-5900	166	6	issn	issn	NOUN
cana-5900	166	7	:	:	PUNCT
cana-5900	166	8	1074	1074	NUM
cana-5900	166	9	-	-	PUNCT
cana-5900	166	10	133x	133x	NUM
cana-5900	166	11	vol	vol	NOUN
cana-5900	166	12	31	31	NUM
cana-5900	166	13	no	no	NOUN
cana-5900	166	14	.	.	PUNCT
cana-5900	167	1	8s	8s	PROPN
cana-5900	167	2	(	(	PUNCT
cana-5900	167	3	2024	2024	NUM
cana-5900	167	4	)	)	PUNCT
cana-5900	167	5	1106	1106	NUM
cana-5900	167	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5900	167	7	fixed	fix	VERB
cana-5900	167	8	-	-	PUNCT
cana-5900	167	9	point	point	NOUN
cana-5900	167	10	problems	problem	NOUN
cana-5900	167	11	are	be	AUX
cana-5900	167	12	a	a	DET
cana-5900	167	13	cornerstone	cornerstone	NOUN
cana-5900	167	14	of	of	ADP
cana-5900	167	15	many	many	ADJ
cana-5900	167	16	scientific	scientific	ADJ
cana-5900	167	17	and	and	CCONJ
cana-5900	167	18	engineering	engineering	NOUN
cana-5900	167	19	disciplines	discipline	NOUN
cana-5900	167	20	.	.	PUNCT
cana-5900	168	1	at	at	ADP
cana-5900	168	2	their	their	PRON
cana-5900	168	3	heart	heart	NOUN
cana-5900	168	4	,	,	PUNCT
cana-5900	168	5	they	they	PRON
cana-5900	168	6	seek	seek	VERB
cana-5900	168	7	a	a	DET
cana-5900	168	8	value	value	NOUN
cana-5900	168	9	x	x	PUNCT
cana-5900	168	10	such	such	ADJ
cana-5900	168	11	that	that	SCONJ
cana-5900	168	12	f(x	f(x	NOUN
cana-5900	168	13	)	)	PUNCT
cana-5900	169	1	=	=	PUNCT
cana-5900	169	2	x	x	PUNCT
cana-5900	169	3	for	for	ADP
cana-5900	169	4	a	a	DET
cana-5900	169	5	given	give	VERB
cana-5900	169	6	function	function	NOUN
cana-5900	169	7	f.	f.	PROPN
cana-5900	169	8	while	while	SCONJ
cana-5900	169	9	seemingly	seemingly	ADV
cana-5900	169	10	simple	simple	ADJ
cana-5900	169	11	,	,	PUNCT
cana-5900	169	12	the	the	DET
cana-5900	169	13	existence	existence	NOUN
cana-5900	169	14	,	,	PUNCT
cana-5900	169	15	uniqueness	uniqueness	NOUN
cana-5900	169	16	,	,	PUNCT
cana-5900	169	17	and	and	CCONJ
cana-5900	169	18	efficient	efficient	ADJ
cana-5900	169	19	computation	computation	NOUN
cana-5900	169	20	of	of	ADP
cana-5900	169	21	such	such	ADJ
cana-5900	169	22	fixed	fix	VERB
cana-5900	169	23	points	point	NOUN
cana-5900	169	24	often	often	ADV
cana-5900	169	25	pose	pose	VERB
cana-5900	169	26	significant	significant	ADJ
cana-5900	169	27	challenges	challenge	NOUN
cana-5900	169	28	.	.	PUNCT
cana-5900	170	1	this	this	DET
cana-5900	170	2	essay	essay	NOUN
cana-5900	170	3	will	will	AUX
cana-5900	170	4	explore	explore	VERB
cana-5900	170	5	computational	computational	ADJ
cana-5900	170	6	approaches	approach	NOUN
cana-5900	170	7	to	to	ADP
cana-5900	170	8	solving	solve	VERB
cana-5900	170	9	fixed	fix	VERB
cana-5900	170	10	-	-	PUNCT
cana-5900	170	11	point	point	NOUN
cana-5900	170	12	problems	problem	NOUN
cana-5900	170	13	,	,	PUNCT
cana-5900	170	14	discussing	discuss	VERB
cana-5900	170	15	various	various	ADJ
cana-5900	170	16	techniques	technique	NOUN
cana-5900	170	17	ranging	range	VERB
cana-5900	170	18	from	from	ADP
cana-5900	170	19	classical	classical	ADJ
cana-5900	170	20	iterative	iterative	NOUN
cana-5900	170	21	methods	method	NOUN
cana-5900	170	22	to	to	ADP
cana-5900	170	23	more	more	ADJ
cana-5900	170	24	modern	modern	ADJ
cana-5900	170	25	numerical	numerical	ADJ
cana-5900	170	26	and	and	CCONJ
cana-5900	170	27	analytical	analytical	ADJ
cana-5900	170	28	strategies	strategy	NOUN
cana-5900	170	29	.	.	PUNCT
cana-5900	171	1	the	the	DET
cana-5900	171	2	simplicity	simplicity	NOUN
cana-5900	171	3	of	of	ADP
cana-5900	171	4	implementation	implementation	NOUN
cana-5900	171	5	makes	make	VERB
cana-5900	171	6	it	it	PRON
cana-5900	171	7	highly	highly	ADV
cana-5900	171	8	attractive	attractive	ADJ
cana-5900	171	9	,	,	PUNCT
cana-5900	171	10	but	but	CCONJ
cana-5900	171	11	its	its	PRON
cana-5900	171	12	effectiveness	effectiveness	NOUN
cana-5900	171	13	is	be	AUX
cana-5900	171	14	contingent	contingent	ADJ
cana-5900	171	15	on	on	ADP
cana-5900	171	16	the	the	DET
cana-5900	171	17	contraction	contraction	NOUN
cana-5900	171	18	property	property	NOUN
cana-5900	171	19	,	,	PUNCT
cana-5900	171	20	which	which	PRON
cana-5900	171	21	might	might	AUX
cana-5900	171	22	not	not	PART
cana-5900	171	23	always	always	ADV
cana-5900	171	24	hold	hold	VERB
cana-5900	171	25	or	or	CCONJ
cana-5900	171	26	might	might	AUX
cana-5900	171	27	lead	lead	VERB
cana-5900	171	28	to	to	ADP
cana-5900	171	29	slow	slow	ADJ
cana-5900	171	30	convergence	convergence	NOUN
cana-5900	171	31	if	if	SCONJ
cana-5900	171	32	the	the	DET
cana-5900	171	33	contraction	contraction	NOUN
cana-5900	171	34	constant	constant	ADJ
cana-5900	171	35	is	be	AUX
cana-5900	171	36	close	close	ADJ
cana-5900	171	37	to	to	ADP
cana-5900	171	38	one	one	NUM
cana-5900	171	39	.	.	PUNCT
cana-5900	172	1	to	to	PART
cana-5900	172	2	address	address	VERB
cana-5900	172	3	the	the	DET
cana-5900	172	4	limitations	limitation	NOUN
cana-5900	172	5	of	of	ADP
cana-5900	172	6	simple	simple	ADJ
cana-5900	172	7	fixed	fix	VERB
cana-5900	172	8	-	-	PUNCT
cana-5900	172	9	point	point	NOUN
cana-5900	172	10	iteration	iteration	NOUN
cana-5900	172	11	,	,	PUNCT
cana-5900	172	12	several	several	ADJ
cana-5900	172	13	accelerated	accelerated	ADJ
cana-5900	172	14	and	and	CCONJ
cana-5900	172	15	refined	refined	ADJ
cana-5900	172	16	methods	method	NOUN
cana-5900	172	17	have	have	AUX
cana-5900	172	18	been	be	AUX
cana-5900	172	19	developed	develop	VERB
cana-5900	172	20	.	.	PUNCT
cana-5900	173	1	aitken	aitken	PROPN
cana-5900	173	2	’s	’s	PART
cana-5900	173	3	\delta^2	\delta^2	NUM
cana-5900	173	4	process	process	NOUN
cana-5900	173	5	is	be	AUX
cana-5900	173	6	a	a	DET
cana-5900	173	7	classic	classic	ADJ
cana-5900	173	8	technique	technique	NOUN
cana-5900	173	9	used	use	VERB
cana-5900	173	10	to	to	PART
cana-5900	173	11	accelerate	accelerate	VERB
cana-5900	173	12	the	the	DET
cana-5900	173	13	convergence	convergence	NOUN
cana-5900	173	14	of	of	ADP
cana-5900	173	15	linearly	linearly	ADV
cana-5900	173	16	convergent	convergent	ADJ
cana-5900	173	17	sequences	sequence	NOUN
cana-5900	173	18	,	,	PUNCT
cana-5900	173	19	including	include	VERB
cana-5900	173	20	those	those	PRON
cana-5900	173	21	generated	generate	VERB
cana-5900	173	22	by	by	ADP
cana-5900	173	23	fixed	fix	VERB
cana-5900	173	24	-	-	PUNCT
cana-5900	173	25	point	point	NOUN
cana-5900	173	26	iteration	iteration	NOUN
cana-5900	173	27	.	.	PUNCT
cana-5900	174	1	it	it	PRON
cana-5900	174	2	estimates	estimate	VERB
cana-5900	174	3	the	the	DET
cana-5900	174	4	limit	limit	NOUN
cana-5900	174	5	based	base	VERB
cana-5900	174	6	on	on	ADP
cana-5900	174	7	three	three	NUM
cana-5900	174	8	successive	successive	ADJ
cana-5900	174	9	terms	term	NOUN
cana-5900	174	10	of	of	ADP
cana-5900	174	11	the	the	DET
cana-5900	174	12	sequence	sequence	NOUN
cana-5900	174	13	,	,	PUNCT
cana-5900	174	14	often	often	ADV
cana-5900	174	15	significantly	significantly	ADV
cana-5900	174	16	improving	improve	VERB
cana-5900	174	17	the	the	DET
cana-5900	174	18	rate	rate	NOUN
cana-5900	174	19	of	of	ADP
cana-5900	174	20	convergence	convergence	NOUN
cana-5900	174	21	.	.	PUNCT
cana-5900	175	1	for	for	ADP
cana-5900	175	2	problems	problem	NOUN
cana-5900	175	3	where	where	SCONJ
cana-5900	175	4	the	the	DET
cana-5900	175	5	function	function	NOUN
cana-5900	175	6	f	f	PROPN
cana-5900	175	7	is	be	AUX
cana-5900	175	8	differentiable	differentiable	ADJ
cana-5900	175	9	,	,	PUNCT
cana-5900	175	10	newton	newton	PROPN
cana-5900	175	11	’s	’s	PART
cana-5900	175	12	method	method	NOUN
cana-5900	175	13	(	(	PUNCT
cana-5900	175	14	or	or	CCONJ
cana-5900	175	15	the	the	DET
cana-5900	175	16	newton	newton	PROPN
cana-5900	175	17	-	-	PUNCT
cana-5900	175	18	raphson	raphson	PROPN
cana-5900	175	19	method	method	NOUN
cana-5900	175	20	)	)	PUNCT
cana-5900	175	21	can	can	AUX
cana-5900	175	22	be	be	AUX
cana-5900	175	23	adapted	adapt	VERB
cana-5900	175	24	.	.	PUNCT
cana-5900	176	1	this	this	DET
cana-5900	176	2	method	method	NOUN
cana-5900	176	3	exhibits	exhibit	VERB
cana-5900	176	4	quadratic	quadratic	ADJ
cana-5900	176	5	convergence	convergence	NOUN
cana-5900	176	6	under	under	ADP
cana-5900	176	7	suitable	suitable	ADJ
cana-5900	176	8	conditions	condition	NOUN
cana-5900	176	9	,	,	PUNCT
cana-5900	176	10	making	make	VERB
cana-5900	176	11	it	it	PRON
cana-5900	176	12	exceptionally	exceptionally	ADV
cana-5900	176	13	fast	fast	ADV
cana-5900	176	14	when	when	SCONJ
cana-5900	176	15	applicable	applicable	ADJ
cana-5900	176	16	,	,	PUNCT
cana-5900	176	17	but	but	CCONJ
cana-5900	176	18	it	it	PRON
cana-5900	176	19	requires	require	VERB
cana-5900	176	20	the	the	DET
cana-5900	176	21	computation	computation	NOUN
cana-5900	176	22	of	of	ADP
cana-5900	176	23	the	the	DET
cana-5900	176	24	derivative	derivative	NOUN
cana-5900	176	25	and	and	CCONJ
cana-5900	176	26	can	can	AUX
cana-5900	176	27	be	be	AUX
cana-5900	176	28	sensitive	sensitive	ADJ
cana-5900	176	29	to	to	ADP
cana-5900	176	30	the	the	DET
cana-5900	176	31	initial	initial	ADJ
cana-5900	176	32	guess	guess	NOUN
cana-5900	176	33	.	.	PUNCT
cana-5900	177	1	beyond	beyond	ADP
cana-5900	177	2	these	these	DET
cana-5900	177	3	classical	classical	ADJ
cana-5900	177	4	techniques	technique	NOUN
cana-5900	177	5	,	,	PUNCT
cana-5900	177	6	quasi	quasi	ADJ
cana-5900	177	7	-	-	ADJ
cana-5900	177	8	newton	newton	PROPN
cana-5900	177	9	methods	method	NOUN
cana-5900	177	10	offer	offer	VERB
cana-5900	177	11	a	a	DET
cana-5900	177	12	powerful	powerful	ADJ
cana-5900	177	13	alternative	alternative	NOUN
cana-5900	177	14	when	when	SCONJ
cana-5900	177	15	analytical	analytical	ADJ
cana-5900	177	16	derivatives	derivative	NOUN
cana-5900	177	17	are	be	AUX
cana-5900	177	18	difficult	difficult	ADJ
cana-5900	177	19	or	or	CCONJ
cana-5900	177	20	impossible	impossible	ADJ
cana-5900	177	21	to	to	PART
cana-5900	177	22	obtain	obtain	VERB
cana-5900	177	23	.	.	PUNCT
cana-5900	178	1	these	these	DET
cana-5900	178	2	methods	method	NOUN
cana-5900	178	3	approximate	approximate	VERB
cana-5900	178	4	the	the	DET
cana-5900	178	5	derivative	derivative	NOUN
cana-5900	178	6	(	(	PUNCT
cana-5900	178	7	or	or	CCONJ
cana-5900	178	8	its	its	PRON
cana-5900	178	9	inverse	inverse	NOUN
cana-5900	178	10	)	)	PUNCT
cana-5900	178	11	using	use	VERB
cana-5900	178	12	information	information	NOUN
cana-5900	178	13	from	from	ADP
cana-5900	178	14	previous	previous	ADJ
cana-5900	178	15	iterations	iteration	NOUN
cana-5900	178	16	,	,	PUNCT
cana-5900	178	17	maintaining	maintain	VERB
cana-5900	178	18	a	a	DET
cana-5900	178	19	superlinear	superlinear	ADJ
cana-5900	178	20	convergence	convergence	NOUN
cana-5900	178	21	rate	rate	NOUN
cana-5900	178	22	while	while	SCONJ
cana-5900	178	23	avoiding	avoid	VERB
cana-5900	178	24	the	the	DET
cana-5900	178	25	computational	computational	ADJ
cana-5900	178	26	burden	burden	NOUN
cana-5900	178	27	of	of	ADP
cana-5900	178	28	exact	exact	ADJ
cana-5900	178	29	derivatives	derivative	NOUN
cana-5900	178	30	.	.	PUNCT
cana-5900	179	1	popular	popular	ADJ
cana-5900	179	2	examples	example	NOUN
cana-5900	179	3	include	include	VERB
cana-5900	179	4	the	the	DET
cana-5900	179	5	broyden	broyden	NOUN
cana-5900	179	6	’s	’s	PART
cana-5900	179	7	method	method	NOUN
cana-5900	179	8	,	,	PUNCT
cana-5900	179	9	which	which	PRON
cana-5900	179	10	is	be	AUX
cana-5900	179	11	particularly	particularly	ADV
cana-5900	179	12	useful	useful	ADJ
cana-5900	179	13	for	for	ADP
cana-5900	179	14	systems	system	NOUN
cana-5900	179	15	of	of	ADP
cana-5900	179	16	non	non	ADJ
cana-5900	179	17	-	-	ADJ
cana-5900	179	18	linear	linear	ADJ
cana-5900	179	19	equations	equation	NOUN
cana-5900	179	20	,	,	PUNCT
cana-5900	179	21	and	and	CCONJ
cana-5900	179	22	thus	thus	ADV
cana-5900	179	23	applicable	applicable	ADJ
cana-5900	179	24	to	to	ADP
cana-5900	179	25	multi	multi	ADJ
cana-5900	179	26	-	-	ADJ
cana-5900	179	27	dimensional	dimensional	ADJ
cana-5900	179	28	fixed	fix	VERB
cana-5900	179	29	-	-	PUNCT
cana-5900	179	30	point	point	NOUN
cana-5900	179	31	problems	problem	NOUN
cana-5900	179	32	.	.	PUNCT
cana-5900	180	1	for	for	ADP
cana-5900	180	2	higher	higher	ADV
cana-5900	180	3	-	-	PUNCT
cana-5900	180	4	dimensional	dimensional	ADJ
cana-5900	180	5	fixed	fix	VERB
cana-5900	180	6	-	-	PUNCT
cana-5900	180	7	point	point	NOUN
cana-5900	180	8	problems	problem	NOUN
cana-5900	180	9	,	,	PUNCT
cana-5900	180	10	where	where	SCONJ
cana-5900	180	11	x	x	PRON
cana-5900	180	12	is	be	AUX
cana-5900	180	13	a	a	DET
cana-5900	180	14	vector	vector	NOUN
cana-5900	180	15	and	and	CCONJ
cana-5900	180	16	f	f	PROPN
cana-5900	180	17	is	be	AUX
cana-5900	180	18	a	a	DET
cana-5900	180	19	vector	vector	NOUN
cana-5900	180	20	-	-	PUNCT
cana-5900	180	21	valued	value	VERB
cana-5900	180	22	function	function	NOUN
cana-5900	180	23	,	,	PUNCT
cana-5900	180	24	the	the	DET
cana-5900	180	25	computational	computational	ADJ
cana-5900	180	26	complexity	complexity	NOUN
cana-5900	180	27	increases	increase	VERB
cana-5900	180	28	significantly	significantly	ADV
cana-5900	180	29	.	.	PUNCT
cana-5900	181	1	homotopy	homotopy	NOUN
cana-5900	181	2	methods	method	NOUN
cana-5900	181	3	provide	provide	VERB
cana-5900	181	4	a	a	DET
cana-5900	181	5	robust	robust	ADJ
cana-5900	181	6	framework	framework	NOUN
cana-5900	181	7	for	for	ADP
cana-5900	181	8	solving	solve	VERB
cana-5900	181	9	such	such	ADJ
cana-5900	181	10	problems	problem	NOUN
cana-5900	181	11	.	.	PUNCT
cana-5900	182	1	the	the	DET
cana-5900	182	2	core	core	NOUN
cana-5900	182	3	idea	idea	NOUN
cana-5900	182	4	is	be	AUX
cana-5900	182	5	to	to	PART
cana-5900	182	6	embed	embed	VERB
cana-5900	182	7	the	the	DET
cana-5900	182	8	original	original	ADJ
cana-5900	182	9	problem	problem	NOUN
cana-5900	182	10	into	into	ADP
cana-5900	182	11	a	a	DET
cana-5900	182	12	family	family	NOUN
cana-5900	182	13	of	of	ADP
cana-5900	182	14	problems	problem	NOUN
cana-5900	182	15	parameterized	parameterize	VERB
cana-5900	182	16	by	by	ADP
cana-5900	182	17	a	a	DET
cana-5900	182	18	continuous	continuous	ADJ
cana-5900	182	19	variable	variable	NOUN
cana-5900	182	20	,	,	PUNCT
cana-5900	182	21	say	say	VERB
cana-5900	182	22	t	t	PROPN
cana-5900	182	23	\in	\in	PROPN
cana-5900	183	1	[	[	X
cana-5900	183	2	0	0	NUM
cana-5900	183	3	,	,	PUNCT
cana-5900	183	4	1	1	NUM
cana-5900	183	5	]	]	PUNCT
cana-5900	183	6	.	.	PUNCT
cana-5900	184	1	one	one	NUM
cana-5900	184	2	starts	start	VERB
cana-5900	184	3	with	with	ADP
cana-5900	184	4	a	a	DET
cana-5900	184	5	trivial	trivial	ADJ
cana-5900	184	6	problem	problem	NOUN
cana-5900	184	7	at	at	ADP
cana-5900	184	8	t=0	t=0	PRON
cana-5900	184	9	whose	whose	DET
cana-5900	184	10	solution	solution	NOUN
cana-5900	184	11	is	be	AUX
cana-5900	184	12	known	know	VERB
cana-5900	184	13	,	,	PUNCT
cana-5900	184	14	and	and	CCONJ
cana-5900	184	15	then	then	ADV
cana-5900	184	16	continuously	continuously	ADV
cana-5900	184	17	deforms	deform	VERB
cana-5900	184	18	it	it	PRON
cana-5900	184	19	to	to	ADP
cana-5900	184	20	the	the	DET
cana-5900	184	21	original	original	ADJ
cana-5900	184	22	problem	problem	NOUN
cana-5900	184	23	at	at	ADP
cana-5900	184	24	t=1	t=1	ADV
cana-5900	184	25	,	,	PUNCT
cana-5900	184	26	tracking	track	VERB
cana-5900	184	27	the	the	DET
cana-5900	184	28	solution	solution	NOUN
cana-5900	184	29	along	along	ADP
cana-5900	184	30	the	the	DET
cana-5900	184	31	path	path	NOUN
cana-5900	184	32	.	.	PUNCT
cana-5900	185	1	these	these	DET
cana-5900	185	2	methods	method	NOUN
cana-5900	185	3	are	be	AUX
cana-5900	185	4	generally	generally	ADV
cana-5900	185	5	more	more	ADV
cana-5900	185	6	globally	globally	ADV
cana-5900	185	7	convergent	convergent	ADJ
cana-5900	185	8	than	than	ADP
cana-5900	185	9	iterative	iterative	ADJ
cana-5900	185	10	methods	method	NOUN
cana-5900	185	11	,	,	PUNCT
cana-5900	185	12	as	as	SCONJ
cana-5900	185	13	they	they	PRON
cana-5900	185	14	can	can	AUX
cana-5900	185	15	overcome	overcome	VERB
cana-5900	185	16	difficulties	difficulty	NOUN
cana-5900	185	17	associated	associate	VERB
cana-5900	185	18	with	with	ADP
cana-5900	185	19	poor	poor	ADJ
cana-5900	185	20	initial	initial	ADJ
cana-5900	185	21	guesses	guess	NOUN
cana-5900	185	22	or	or	CCONJ
cana-5900	185	23	multiple	multiple	ADJ
cana-5900	185	24	solutions	solution	NOUN
cana-5900	185	25	.	.	PUNCT
cana-5900	186	1	in	in	ADP
cana-5900	186	2	situations	situation	NOUN
cana-5900	186	3	where	where	SCONJ
cana-5900	186	4	a	a	DET
cana-5900	186	5	closed	closed	ADJ
cana-5900	186	6	-	-	PUNCT
cana-5900	186	7	form	form	NOUN
cana-5900	186	8	solution	solution	NOUN
cana-5900	186	9	is	be	AUX
cana-5900	186	10	elusive	elusive	ADJ
cana-5900	186	11	and	and	CCONJ
cana-5900	186	12	traditional	traditional	ADJ
cana-5900	186	13	iterative	iterative	NOUN
cana-5900	186	14	methods	method	NOUN
cana-5900	186	15	struggle	struggle	NOUN
cana-5900	186	16	,	,	PUNCT
cana-5900	186	17	optimization	optimization	NOUN
cana-5900	186	18	-	-	PUNCT
cana-5900	186	19	based	base	VERB
cana-5900	186	20	approaches	approach	NOUN
cana-5900	186	21	can	can	AUX
cana-5900	186	22	be	be	AUX
cana-5900	186	23	employed	employ	VERB
cana-5900	186	24	.	.	PUNCT
cana-5900	187	1	a	a	DET
cana-5900	187	2	fixed	fix	VERB
cana-5900	187	3	-	-	PUNCT
cana-5900	187	4	point	point	NOUN
cana-5900	187	5	problem	problem	NOUN
cana-5900	187	6	f(x	f(x	PROPN
cana-5900	187	7	)	)	PUNCT
cana-5900	188	1	=	=	PUNCT
cana-5900	188	2	x	x	X
cana-5900	188	3	can	can	AUX
cana-5900	188	4	be	be	AUX
cana-5900	188	5	rephrased	rephrase	VERB
cana-5900	188	6	as	as	ADP
cana-5900	188	7	finding	find	VERB
cana-5900	188	8	x	x	PUNCT
cana-5900	188	9	that	that	PRON
cana-5900	188	10	minimizes	minimize	VERB
cana-5900	188	11	the	the	DET
cana-5900	188	12	residual	residual	ADJ
cana-5900	188	13	\|f(x	\|f(x	PROPN
cana-5900	188	14	)	)	PUNCT
cana-5900	188	15	–	–	PUNCT
cana-5900	188	16	x\|	x\|	PROPN
cana-5900	188	17	.	.	PUNCT
cana-5900	189	1	this	this	PRON
cana-5900	189	2	transforms	transform	VERB
cana-5900	189	3	the	the	DET
cana-5900	189	4	problem	problem	NOUN
cana-5900	189	5	into	into	ADP
cana-5900	189	6	an	an	DET
cana-5900	189	7	unconstrained	unconstrained	ADJ
cana-5900	189	8	optimization	optimization	NOUN
cana-5900	189	9	problem	problem	NOUN
cana-5900	189	10	,	,	PUNCT
cana-5900	189	11	allowing	allow	VERB
cana-5900	189	12	the	the	DET
cana-5900	189	13	use	use	NOUN
cana-5900	189	14	of	of	ADP
cana-5900	189	15	a	a	DET
cana-5900	189	16	wide	wide	ADJ
cana-5900	189	17	array	array	NOUN
cana-5900	189	18	of	of	ADP
cana-5900	189	19	optimization	optimization	NOUN
cana-5900	189	20	algorithms	algorithm	NOUN
cana-5900	189	21	such	such	ADJ
cana-5900	189	22	as	as	ADP
cana-5900	189	23	gradient	gradient	ADJ
cana-5900	189	24	descent	descent	NOUN
cana-5900	189	25	,	,	PUNCT
cana-5900	189	26	conjugate	conjugate	ADJ
cana-5900	189	27	gradient	gradient	NOUN
cana-5900	189	28	,	,	PUNCT
cana-5900	189	29	or	or	CCONJ
cana-5900	189	30	more	more	ADV
cana-5900	189	31	sophisticated	sophisticated	ADJ
cana-5900	189	32	methods	method	NOUN
cana-5900	189	33	like	like	ADP
cana-5900	189	34	interior	interior	ADJ
cana-5900	189	35	-	-	PUNCT
cana-5900	189	36	point	point	NOUN
cana-5900	189	37	methods	method	NOUN
cana-5900	189	38	,	,	PUNCT
cana-5900	189	39	especially	especially	ADV
cana-5900	189	40	when	when	SCONJ
cana-5900	189	41	constraints	constraint	NOUN
cana-5900	189	42	are	be	AUX
cana-5900	189	43	involved	involve	VERB
cana-5900	189	44	.	.	PUNCT
cana-5900	190	1	communications	communication	NOUN
cana-5900	190	2	on	on	ADP
cana-5900	190	3	applied	apply	VERB
cana-5900	190	4	nonlinear	nonlinear	ADJ
cana-5900	190	5	analysis	analysis	NOUN
cana-5900	190	6	issn	issn	NOUN
cana-5900	190	7	:	:	PUNCT
cana-5900	190	8	1074	1074	NUM
cana-5900	190	9	-	-	PUNCT
cana-5900	190	10	133x	133x	NUM
cana-5900	190	11	vol	vol	NOUN
cana-5900	190	12	31	31	NUM
cana-5900	190	13	no	no	NOUN
cana-5900	190	14	.	.	PUNCT
cana-5900	191	1	8s	8s	PROPN
cana-5900	191	2	(	(	PUNCT
cana-5900	191	3	2024	2024	NUM
cana-5900	191	4	)	)	PUNCT
cana-5900	191	5	1107	1107	NUM
cana-5900	191	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5900	191	7	the	the	DET
cana-5900	191	8	advent	advent	NOUN
cana-5900	191	9	of	of	ADP
cana-5900	191	10	powerful	powerful	ADJ
cana-5900	191	11	computational	computational	ADJ
cana-5900	191	12	resources	resource	NOUN
cana-5900	191	13	has	have	AUX
cana-5900	191	14	also	also	ADV
cana-5900	191	15	led	lead	VERB
cana-5900	191	16	to	to	ADP
cana-5900	191	17	the	the	DET
cana-5900	191	18	rise	rise	NOUN
cana-5900	191	19	of	of	ADP
cana-5900	191	20	monte	monte	PROPN
cana-5900	191	21	carlo	carlo	PROPN
cana-5900	191	22	methods	method	NOUN
cana-5900	191	23	and	and	CCONJ
cana-5900	191	24	stochastic	stochastic	ADJ
cana-5900	191	25	approximation	approximation	NOUN
cana-5900	191	26	for	for	ADP
cana-5900	191	27	certain	certain	ADJ
cana-5900	191	28	types	type	NOUN
cana-5900	191	29	of	of	ADP
cana-5900	191	30	fixed	fix	VERB
cana-5900	191	31	-	-	PUNCT
cana-5900	191	32	point	point	NOUN
cana-5900	191	33	problems	problem	NOUN
cana-5900	191	34	,	,	PUNCT
cana-5900	191	35	particularly	particularly	ADV
cana-5900	191	36	those	those	PRON
cana-5900	191	37	arising	arise	VERB
cana-5900	191	38	in	in	ADP
cana-5900	191	39	stochastic	stochastic	ADJ
cana-5900	191	40	control	control	NOUN
cana-5900	191	41	,	,	PUNCT
cana-5900	191	42	finance	finance	NOUN
cana-5900	191	43	,	,	PUNCT
cana-5900	191	44	and	and	CCONJ
cana-5900	191	45	game	game	NOUN
cana-5900	191	46	theory	theory	NOUN
cana-5900	191	47	.	.	PUNCT
cana-5900	192	1	these	these	DET
cana-5900	192	2	methods	method	NOUN
cana-5900	192	3	use	use	VERB
cana-5900	192	4	random	random	ADJ
cana-5900	192	5	sampling	sampling	NOUN
cana-5900	192	6	to	to	ADP
cana-5900	192	7	approximate	approximate	ADJ
cana-5900	192	8	expectations	expectation	NOUN
cana-5900	192	9	or	or	CCONJ
cana-5900	192	10	functions	function	NOUN
cana-5900	192	11	,	,	PUNCT
cana-5900	192	12	leading	lead	VERB
cana-5900	192	13	to	to	ADP
cana-5900	192	14	iterative	iterative	NOUN
cana-5900	192	15	updates	update	NOUN
cana-5900	192	16	that	that	PRON
cana-5900	192	17	converge	converge	VERB
cana-5900	192	18	to	to	ADP
cana-5900	192	19	the	the	DET
cana-5900	192	20	fixed	fix	VERB
cana-5900	192	21	point	point	NOUN
cana-5900	192	22	in	in	ADP
cana-5900	192	23	a	a	DET
cana-5900	192	24	probabilistic	probabilistic	ADJ
cana-5900	192	25	sense	sense	NOUN
cana-5900	192	26	.	.	PUNCT
cana-5900	193	1	while	while	SCONJ
cana-5900	193	2	they	they	PRON
cana-5900	193	3	may	may	AUX
cana-5900	193	4	have	have	VERB
cana-5900	193	5	slower	slow	ADJ
cana-5900	193	6	convergence	convergence	NOUN
cana-5900	193	7	rates	rate	NOUN
cana-5900	193	8	in	in	ADP
cana-5900	193	9	deterministic	deterministic	ADJ
cana-5900	193	10	settings	setting	NOUN
cana-5900	193	11	,	,	PUNCT
cana-5900	193	12	they	they	PRON
cana-5900	193	13	are	be	AUX
cana-5900	193	14	invaluable	invaluable	ADJ
cana-5900	193	15	for	for	ADP
cana-5900	193	16	problems	problem	NOUN
cana-5900	193	17	with	with	ADP
cana-5900	193	18	high	high	ADJ
cana-5900	193	19	dimensionality	dimensionality	NOUN
cana-5900	193	20	or	or	CCONJ
cana-5900	193	21	inherent	inherent	ADJ
cana-5900	193	22	randomness	randomness	NOUN
cana-5900	193	23	.	.	PUNCT
cana-5900	194	1	the	the	DET
cana-5900	194	2	selection	selection	NOUN
cana-5900	194	3	of	of	ADP
cana-5900	194	4	a	a	DET
cana-5900	194	5	computational	computational	ADJ
cana-5900	194	6	approach	approach	NOUN
cana-5900	194	7	is	be	AUX
cana-5900	194	8	highly	highly	ADV
cana-5900	194	9	dependent	dependent	ADJ
cana-5900	194	10	on	on	ADP
cana-5900	194	11	the	the	DET
cana-5900	194	12	specific	specific	ADJ
cana-5900	194	13	characteristics	characteristic	NOUN
cana-5900	194	14	of	of	ADP
cana-5900	194	15	the	the	DET
cana-5900	194	16	fixed	fix	VERB
cana-5900	194	17	-	-	PUNCT
cana-5900	194	18	point	point	NOUN
cana-5900	194	19	problem	problem	NOUN
cana-5900	194	20	:	:	PUNCT
cana-5900	194	21	the	the	DET
cana-5900	194	22	dimension	dimension	NOUN
cana-5900	194	23	of	of	ADP
cana-5900	194	24	the	the	DET
cana-5900	194	25	space	space	NOUN
cana-5900	194	26	,	,	PUNCT
cana-5900	194	27	the	the	DET
cana-5900	194	28	smoothness	smoothness	NOUN
cana-5900	194	29	and	and	CCONJ
cana-5900	194	30	properties	property	NOUN
cana-5900	194	31	of	of	ADP
cana-5900	194	32	the	the	DET
cana-5900	194	33	function	function	NOUN
cana-5900	194	34	f	f	NOUN
cana-5900	194	35	,	,	PUNCT
cana-5900	194	36	the	the	DET
cana-5900	194	37	desired	desire	VERB
cana-5900	194	38	accuracy	accuracy	NOUN
cana-5900	194	39	,	,	PUNCT
cana-5900	194	40	and	and	CCONJ
cana-5900	194	41	the	the	DET
cana-5900	194	42	available	available	ADJ
cana-5900	194	43	computational	computational	ADJ
cana-5900	194	44	resources	resource	NOUN
cana-5900	194	45	.	.	PUNCT
cana-5900	195	1	a	a	DET
cana-5900	195	2	deep	deep	ADJ
cana-5900	195	3	understanding	understanding	NOUN
cana-5900	195	4	of	of	ADP
cana-5900	195	5	the	the	DET
cana-5900	195	6	theoretical	theoretical	ADJ
cana-5900	195	7	underpinnings	underpinning	NOUN
cana-5900	195	8	of	of	ADP
cana-5900	195	9	each	each	DET
cana-5900	195	10	method	method	NOUN
cana-5900	195	11	,	,	PUNCT
cana-5900	195	12	coupled	couple	VERB
cana-5900	195	13	with	with	ADP
cana-5900	195	14	practical	practical	ADJ
cana-5900	195	15	considerations	consideration	NOUN
cana-5900	195	16	,	,	PUNCT
cana-5900	195	17	is	be	AUX
cana-5900	195	18	crucial	crucial	ADJ
cana-5900	195	19	for	for	ADP
cana-5900	195	20	choosing	choose	VERB
cana-5900	195	21	the	the	DET
cana-5900	195	22	most	most	ADV
cana-5900	195	23	efficient	efficient	ADJ
cana-5900	195	24	and	and	CCONJ
cana-5900	195	25	reliable	reliable	ADJ
cana-5900	195	26	algorithm	algorithm	NOUN
cana-5900	195	27	.	.	PUNCT
cana-5900	196	1	the	the	DET
cana-5900	196	2	continuous	continuous	ADJ
cana-5900	196	3	development	development	NOUN
cana-5900	196	4	of	of	ADP
cana-5900	196	5	new	new	ADJ
cana-5900	196	6	algorithms	algorithm	NOUN
cana-5900	196	7	and	and	CCONJ
cana-5900	196	8	the	the	DET
cana-5900	196	9	increasing	increase	VERB
cana-5900	196	10	power	power	NOUN
cana-5900	196	11	of	of	ADP
cana-5900	196	12	computers	computer	NOUN
cana-5900	196	13	ensure	ensure	VERB
cana-5900	196	14	that	that	SCONJ
cana-5900	196	15	computational	computational	ADJ
cana-5900	196	16	approaches	approach	NOUN
cana-5900	196	17	to	to	ADP
cana-5900	196	18	fixed	fix	VERB
cana-5900	196	19	-	-	PUNCT
cana-5900	196	20	point	point	NOUN
cana-5900	196	21	problems	problem	NOUN
cana-5900	196	22	will	will	AUX
cana-5900	196	23	remain	remain	VERB
cana-5900	196	24	a	a	DET
cana-5900	196	25	vibrant	vibrant	ADJ
cana-5900	196	26	and	and	CCONJ
cana-5900	196	27	evolving	evolve	VERB
cana-5900	196	28	area	area	NOUN
cana-5900	196	29	of	of	ADP
cana-5900	196	30	research	research	NOUN
cana-5900	196	31	,	,	PUNCT
cana-5900	196	32	continually	continually	ADV
cana-5900	196	33	pushing	push	VERB
cana-5900	196	34	the	the	DET
cana-5900	196	35	boundaries	boundary	NOUN
cana-5900	196	36	of	of	ADP
cana-5900	196	37	what	what	PRON
cana-5900	196	38	is	be	AUX
cana-5900	196	39	numerically	numerically	ADV
cana-5900	196	40	tractable	tractable	ADJ
cana-5900	196	41	.	.	PUNCT
cana-5900	197	1	conclusion	conclusion	NOUN
cana-5900	197	2	the	the	DET
cana-5900	197	3	computational	computational	ADJ
cana-5900	197	4	approaches	approach	NOUN
cana-5900	197	5	to	to	ADP
cana-5900	197	6	fixed	fix	VERB
cana-5900	197	7	-	-	PUNCT
cana-5900	197	8	point	point	NOUN
cana-5900	197	9	problems	problem	NOUN
cana-5900	197	10	in	in	ADP
cana-5900	197	11	convex	convex	ADJ
cana-5900	197	12	metric	metric	ADJ
cana-5900	197	13	spaces	space	NOUN
cana-5900	197	14	,	,	PUNCT
cana-5900	197	15	as	as	ADP
cana-5900	197	16	a	a	DET
cana-5900	197	17	generalization	generalization	NOUN
cana-5900	197	18	of	of	ADP
cana-5900	197	19	the	the	DET
cana-5900	197	20	contraction	contraction	NOUN
cana-5900	197	21	principle	principle	NOUN
cana-5900	197	22	,	,	PUNCT
cana-5900	197	23	represent	represent	VERB
cana-5900	197	24	a	a	DET
cana-5900	197	25	powerful	powerful	ADJ
cana-5900	197	26	paradigm	paradigm	NOUN
cana-5900	197	27	for	for	ADP
cana-5900	197	28	solving	solve	VERB
cana-5900	197	29	a	a	DET
cana-5900	197	30	vast	vast	ADJ
cana-5900	197	31	array	array	NOUN
cana-5900	197	32	of	of	ADP
cana-5900	197	33	mathematical	mathematical	ADJ
cana-5900	197	34	and	and	CCONJ
cana-5900	197	35	real	real	ADJ
cana-5900	197	36	-	-	PUNCT
cana-5900	197	37	world	world	NOUN
cana-5900	197	38	challenges	challenge	NOUN
cana-5900	197	39	.	.	PUNCT
cana-5900	198	1	by	by	ADP
cana-5900	198	2	extending	extend	VERB
cana-5900	198	3	the	the	DET
cana-5900	198	4	fundamental	fundamental	ADJ
cana-5900	198	5	ideas	idea	NOUN
cana-5900	198	6	of	of	ADP
cana-5900	198	7	fixed	fix	VERB
cana-5900	198	8	-	-	PUNCT
cana-5900	198	9	point	point	NOUN
cana-5900	198	10	theory	theory	NOUN
cana-5900	198	11	to	to	ADP
cana-5900	198	12	broader	broad	ADJ
cana-5900	198	13	classes	class	NOUN
cana-5900	198	14	of	of	ADP
cana-5900	198	15	mappings	mapping	NOUN
cana-5900	198	16	and	and	CCONJ
cana-5900	198	17	leveraging	leverage	VERB
cana-5900	198	18	the	the	DET
cana-5900	198	19	geometric	geometric	ADJ
cana-5900	198	20	properties	property	NOUN
cana-5900	198	21	of	of	ADP
cana-5900	198	22	convex	convex	ADJ
cana-5900	198	23	spaces	space	NOUN
cana-5900	198	24	,	,	PUNCT
cana-5900	198	25	researchers	researcher	NOUN
cana-5900	198	26	have	have	AUX
cana-5900	198	27	developed	develop	VERB
cana-5900	198	28	sophisticated	sophisticated	ADJ
cana-5900	198	29	iterative	iterative	ADJ
cana-5900	198	30	algorithms	algorithm	NOUN
cana-5900	198	31	that	that	PRON
cana-5900	198	32	are	be	AUX
cana-5900	198	33	both	both	PRON
cana-5900	198	34	theoretically	theoretically	ADV
cana-5900	198	35	sound	sound	ADJ
cana-5900	198	36	and	and	CCONJ
cana-5900	198	37	practically	practically	ADV
cana-5900	198	38	effective	effective	ADJ
cana-5900	198	39	.	.	PUNCT
cana-5900	199	1	as	as	SCONJ
cana-5900	199	2	computational	computational	ADJ
cana-5900	199	3	power	power	NOUN
cana-5900	199	4	continues	continue	VERB
cana-5900	199	5	to	to	PART
cana-5900	199	6	grow	grow	VERB
cana-5900	199	7	and	and	CCONJ
cana-5900	199	8	the	the	DET
cana-5900	199	9	need	need	NOUN
cana-5900	199	10	for	for	ADP
cana-5900	199	11	robust	robust	ADJ
cana-5900	199	12	solutions	solution	NOUN
cana-5900	199	13	to	to	ADP
cana-5900	199	14	complex	complex	ADJ
cana-5900	199	15	problems	problem	NOUN
cana-5900	199	16	intensifies	intensifie	NOUN
cana-5900	199	17	,	,	PUNCT
cana-5900	199	18	this	this	DET
cana-5900	199	19	field	field	NOUN
cana-5900	199	20	will	will	AUX
cana-5900	199	21	undoubtedly	undoubtedly	ADV
cana-5900	199	22	remain	remain	VERB
cana-5900	199	23	a	a	DET
cana-5900	199	24	cornerstone	cornerstone	NOUN
cana-5900	199	25	of	of	ADP
cana-5900	199	26	applied	apply	VERB
cana-5900	199	27	mathematics	mathematic	NOUN
cana-5900	199	28	,	,	PUNCT
cana-5900	199	29	offering	offer	VERB
cana-5900	199	30	innovative	innovative	ADJ
cana-5900	199	31	tools	tool	NOUN
cana-5900	199	32	for	for	ADP
cana-5900	199	33	analysis	analysis	NOUN
cana-5900	199	34	,	,	PUNCT
cana-5900	199	35	optimization	optimization	NOUN
cana-5900	199	36	,	,	PUNCT
cana-5900	199	37	and	and	CCONJ
cana-5900	199	38	problem	problem	NOUN
cana-5900	199	39	-	-	PUNCT
cana-5900	199	40	solving	solving	NOUN
cana-5900	199	41	across	across	ADP
cana-5900	199	42	diverse	diverse	ADJ
cana-5900	199	43	scientific	scientific	ADJ
cana-5900	199	44	and	and	CCONJ
cana-5900	199	45	engineering	engineering	NOUN
cana-5900	199	46	disciplines	discipline	NOUN
cana-5900	199	47	.	.	PUNCT
cana-5900	200	1	references	reference	NOUN
cana-5900	200	2	1	1	NUM
cana-5900	200	3	.	.	PUNCT
cana-5900	200	4	banach	banach	NOUN
cana-5900	200	5	,	,	PUNCT
cana-5900	200	6	s.	s.	PROPN
cana-5900	200	7	sur	sur	PROPN
cana-5900	200	8	les	les	PROPN
cana-5900	200	9	opérations	opération	NOUN
cana-5900	200	10	dans	dan	NOUN
cana-5900	200	11	les	les	X
cana-5900	200	12	ensembles	ensemble	NOUN
cana-5900	200	13	abstraits	abstrait	NOUN
cana-5900	200	14	et	et	PROPN
cana-5900	200	15	leur	leur	X
cana-5900	200	16	application	application	PROPN
cana-5900	200	17	aux	aux	PROPN
cana-5900	200	18	équations	équations	PROPN
cana-5900	200	19	intégrales	intégrale	NOUN
cana-5900	200	20	.	.	PUNCT
cana-5900	201	1	fundam	fundam	PROPN
cana-5900	201	2	.	.	PUNCT
cana-5900	201	3	math	math	NOUN
cana-5900	201	4	.	.	PUNCT
cana-5900	202	1	2022	2022	NUM
cana-5900	202	2	,	,	PUNCT
cana-5900	202	3	3	3	NUM
cana-5900	202	4	,	,	PUNCT
cana-5900	202	5	133–181	133–181	NUM
cana-5900	202	6	.	.	PUNCT
cana-5900	203	1	2	2	X
cana-5900	203	2	.	.	X
cana-5900	203	3	kannan	kannan	PROPN
cana-5900	203	4	,	,	PUNCT
cana-5900	203	5	r.	r.	VERB
cana-5900	203	6	some	some	DET
cana-5900	203	7	results	result	NOUN
cana-5900	203	8	on	on	ADP
cana-5900	203	9	fixed	fix	VERB
cana-5900	203	10	points	point	NOUN
cana-5900	203	11	.	.	PUNCT
cana-5900	204	1	bull	bull	NOUN
cana-5900	204	2	.	.	PUNCT
cana-5900	205	1	calcutta	calcutta	PROPN
cana-5900	205	2	math	math	PROPN
cana-5900	205	3	.	.	PUNCT
cana-5900	206	1	soc	soc	PROPN
cana-5900	206	2	.	.	PUNCT
cana-5900	207	1	2021	2021	NUM
cana-5900	207	2	,	,	PUNCT
cana-5900	207	3	60	60	NUM
cana-5900	207	4	,	,	PUNCT
cana-5900	207	5	71–76	71–76	NUM
cana-5900	207	6	.	.	NOUN
cana-5900	208	1	3	3	NUM
cana-5900	208	2	.	.	X
cana-5900	208	3	hardy	hardy	ADJ
cana-5900	208	4	,	,	PUNCT
cana-5900	208	5	g.e	g.e	PROPN
cana-5900	208	6	.	.	PROPN
cana-5900	208	7	;	;	PUNCT
cana-5900	209	1	rogers	rogers	PROPN
cana-5900	209	2	,	,	PUNCT
cana-5900	209	3	t.d	t.d	PROPN
cana-5900	209	4	.	.	PUNCT
cana-5900	210	1	a	a	DET
cana-5900	210	2	generalization	generalization	NOUN
cana-5900	210	3	of	of	ADP
cana-5900	210	4	a	a	DET
cana-5900	210	5	fixed	fix	VERB
cana-5900	210	6	point	point	NOUN
cana-5900	210	7	theorem	theorem	NOUN
cana-5900	210	8	of	of	ADP
cana-5900	210	9	reich	reich	PROPN
cana-5900	210	10	.	.	PUNCT
cana-5900	211	1	can	can	AUX
cana-5900	211	2	.	.	PUNCT
cana-5900	212	1	math	math	NOUN
cana-5900	212	2	.	.	PUNCT
cana-5900	213	1	bull	bull	NOUN
cana-5900	213	2	.	.	PUNCT
cana-5900	214	1	2020	2020	NUM
cana-5900	214	2	,	,	PUNCT
cana-5900	214	3	16	16	NUM
cana-5900	214	4	,	,	PUNCT
cana-5900	214	5	201–206	201–206	NUM
cana-5900	214	6	.	.	NOUN
cana-5900	214	7	4	4	NUM
cana-5900	214	8	.	.	X
cana-5900	214	9	samet	samet	PROPN
cana-5900	214	10	,	,	PUNCT
cana-5900	214	11	b.	b.	PROPN
cana-5900	214	12	;	;	PUNCT
cana-5900	214	13	vetro	vetro	PROPN
cana-5900	214	14	,	,	PUNCT
cana-5900	214	15	c.	c.	NOUN
cana-5900	214	16	;	;	PUNCT
cana-5900	214	17	vetro	vetro	PROPN
cana-5900	214	18	,	,	PUNCT
cana-5900	215	1	p.	p.	PROPN
cana-5900	215	2	fixed	fix	VERB
cana-5900	215	3	point	point	NOUN
cana-5900	215	4	theorems	theorem	NOUN
cana-5900	215	5	for	for	ADP
cana-5900	215	6	α	α	NOUN
cana-5900	215	7	-	-	PUNCT
cana-5900	215	8	ψ	ψ	NOUN
cana-5900	215	9	-	-	ADJ
cana-5900	215	10	contractive	contractive	ADJ
cana-5900	215	11	type	type	NOUN
cana-5900	215	12	mappings	mapping	NOUN
cana-5900	215	13	.	.	PUNCT
cana-5900	216	1	nonlinear	nonlinear	ADJ
cana-5900	216	2	anal	anal	PROPN
cana-5900	216	3	.	.	PUNCT
cana-5900	217	1	theory	theory	NOUN
cana-5900	217	2	methods	method	NOUN
cana-5900	217	3	appl	appl	PROPN
cana-5900	217	4	.	.	PUNCT
cana-5900	218	1	2022	2022	NUM
cana-5900	218	2	,	,	PUNCT
cana-5900	218	3	75	75	NUM
cana-5900	218	4	,	,	PUNCT
cana-5900	218	5	2154–2165	2154–2165	NUM
cana-5900	218	6	.	.	NOUN
cana-5900	218	7	5	5	NUM
cana-5900	218	8	.	.	X
cana-5900	219	1	wardowski	wardowski	PROPN
cana-5900	219	2	,	,	PUNCT
cana-5900	219	3	d.	d.	PROPN
cana-5900	219	4	fixed	fix	VERB
cana-5900	219	5	points	point	NOUN
cana-5900	219	6	of	of	ADP
cana-5900	219	7	a	a	DET
cana-5900	219	8	new	new	ADJ
cana-5900	219	9	type	type	NOUN
cana-5900	219	10	of	of	ADP
cana-5900	219	11	contractive	contractive	ADJ
cana-5900	219	12	mappings	mapping	NOUN
cana-5900	219	13	in	in	ADP
cana-5900	219	14	complete	complete	ADJ
cana-5900	219	15	metric	metric	ADJ
cana-5900	219	16	spaces	space	NOUN
cana-5900	219	17	.	.	PUNCT
cana-5900	220	1	fixed	fix	VERB
cana-5900	220	2	point	point	NOUN
cana-5900	220	3	theory	theory	NOUN
cana-5900	220	4	appl	appl	NOUN
cana-5900	220	5	.	.	PUNCT
cana-5900	221	1	2022	2022	NUM
cana-5900	221	2	,	,	PUNCT
cana-5900	221	3	2012	2012	NUM
cana-5900	221	4	,	,	PUNCT
cana-5900	221	5	94	94	NUM
cana-5900	221	6	.	.	PUNCT
cana-5900	222	1	communications	communication	NOUN
cana-5900	222	2	on	on	ADP
cana-5900	222	3	applied	apply	VERB
cana-5900	222	4	nonlinear	nonlinear	ADJ
cana-5900	222	5	analysis	analysis	NOUN
cana-5900	222	6	issn	issn	NOUN
cana-5900	222	7	:	:	PUNCT
cana-5900	222	8	1074	1074	NUM
cana-5900	222	9	-	-	PUNCT
cana-5900	222	10	133x	133x	NUM
cana-5900	222	11	vol	vol	NOUN
cana-5900	222	12	31	31	NUM
cana-5900	222	13	no	no	NOUN
cana-5900	222	14	.	.	PUNCT
cana-5900	223	1	8s	8s	PROPN
cana-5900	223	2	(	(	PUNCT
cana-5900	223	3	2024	2024	NUM
cana-5900	223	4	)	)	PUNCT
cana-5900	223	5	1108	1108	NUM
cana-5900	223	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5900	223	7	6	6	X
cana-5900	223	8	.	.	PUNCT
cana-5900	223	9	karapınar	karapınar	PROPN
cana-5900	223	10	,	,	PUNCT
cana-5900	223	11	e.	e.	PROPN
cana-5900	223	12	revisiting	revisit	VERB
cana-5900	223	13	the	the	DET
cana-5900	223	14	kannan	kannan	PROPN
cana-5900	223	15	type	type	NOUN
cana-5900	223	16	contractions	contraction	NOUN
cana-5900	223	17	via	via	ADP
cana-5900	223	18	interpolation	interpolation	NOUN
cana-5900	223	19	.	.	PUNCT
cana-5900	224	1	adv	adv	PROPN
cana-5900	224	2	.	.	PUNCT
cana-5900	224	3	theory	theory	PROPN
cana-5900	224	4	nonlinear	nonlinear	PROPN
cana-5900	224	5	anal	anal	NOUN
cana-5900	224	6	.	.	PUNCT
cana-5900	225	1	its	its	PRON
cana-5900	225	2	appl	appl	NOUN
cana-5900	225	3	.	.	PROPN
cana-5900	225	4	2021	2021	NUM
cana-5900	225	5	,	,	PUNCT
cana-5900	225	6	2	2	NUM
cana-5900	225	7	,	,	PUNCT
cana-5900	225	8	85–87	85–87	NUM
cana-5900	225	9	.	.	PUNCT
cana-5900	226	1	7	7	X
cana-5900	226	2	.	.	X
cana-5900	226	3	karapınar	karapınar	PROPN
cana-5900	226	4	,	,	PUNCT
cana-5900	226	5	e.	e.	PROPN
cana-5900	226	6	;	;	PUNCT
cana-5900	226	7	alqahtani	alqahtani	ADJ
cana-5900	226	8	,	,	PUNCT
cana-5900	226	9	o.	o.	PROPN
cana-5900	226	10	;	;	PUNCT
cana-5900	226	11	aydi	aydi	VERB
cana-5900	226	12	,	,	PUNCT
cana-5900	226	13	h.	h.	PROPN
cana-5900	226	14	on	on	ADP
cana-5900	226	15	interpolative	interpolative	ADJ
cana-5900	226	16	hardy	hardy	ADJ
cana-5900	226	17	-	-	PUNCT
cana-5900	226	18	rogers	rogers	NOUN
cana-5900	226	19	type	type	NOUN
cana-5900	226	20	contractions	contraction	NOUN
cana-5900	226	21	.	.	PUNCT
cana-5900	227	1	symmetry	symmetry	NOUN
cana-5900	227	2	2020	2020	NUM
cana-5900	227	3	,	,	PUNCT
cana-5900	227	4	11	11	NUM
cana-5900	227	5	,	,	PUNCT
cana-5900	227	6	8	8	NUM
cana-5900	227	7	.	.	NOUN
cana-5900	227	8	8	8	NUM
cana-5900	227	9	.	.	X
cana-5900	227	10	bakhtin	bakhtin	PROPN
cana-5900	227	11	,	,	PUNCT
cana-5900	227	12	i.a	i.a	PROPN
cana-5900	227	13	.	.	PROPN
cana-5900	228	1	the	the	DET
cana-5900	228	2	contraction	contraction	NOUN
cana-5900	228	3	mapping	map	VERB
cana-5900	228	4	principle	principle	NOUN
cana-5900	228	5	in	in	ADP
cana-5900	228	6	quasimetric	quasimetric	ADJ
cana-5900	228	7	spaces	space	NOUN
cana-5900	228	8	.	.	PUNCT
cana-5900	229	1	funct	funct	ADJ
cana-5900	229	2	.	.	PUNCT
cana-5900	230	1	anal	anal	PROPN
cana-5900	230	2	.	.	PUNCT
cana-5900	231	1	2020	2020	NUM
cana-5900	231	2	,	,	PUNCT
cana-5900	231	3	30	30	NUM
cana-5900	231	4	,	,	PUNCT
cana-5900	231	5	26–37	26–37	NUM
cana-5900	231	6	.	.	PUNCT
cana-5900	232	1	9	9	NUM
cana-5900	232	2	.	.	X
cana-5900	232	3	matthews	matthews	PROPN
cana-5900	232	4	,	,	PUNCT
cana-5900	232	5	s.g	s.g	PROPN
cana-5900	232	6	.	.	PROPN
cana-5900	232	7	partial	partial	ADJ
cana-5900	232	8	metric	metric	ADJ
cana-5900	232	9	topology	topology	NOUN
cana-5900	232	10	.	.	PUNCT
cana-5900	233	1	ann	ann	PROPN
cana-5900	233	2	.	.	PUNCT
cana-5900	233	3	n.	n.	PROPN
cana-5900	233	4	y.	y.	PROPN
cana-5900	233	5	acad	acad	PROPN
cana-5900	233	6	.	.	PUNCT
cana-5900	234	1	sci	sci	PROPN
cana-5900	234	2	.	.	PROPN
cana-5900	234	3	2021	2021	NUM
cana-5900	234	4	,	,	PUNCT
cana-5900	234	5	728	728	NUM
cana-5900	234	6	,	,	PUNCT
cana-5900	234	7	183–197	183–197	NUM
cana-5900	234	8	.	.	PUNCT
cana-5900	234	9	10	10	NUM
cana-5900	234	10	.	.	PUNCT
cana-5900	235	1	hitzler	hitzler	ADJ
cana-5900	235	2	,	,	PUNCT
cana-5900	235	3	p.	p.	NOUN
cana-5900	235	4	;	;	PUNCT
cana-5900	235	5	seda	seda	PROPN
cana-5900	235	6	,	,	PUNCT
cana-5900	235	7	a.k	a.k	PROPN
cana-5900	235	8	.	.	PROPN
cana-5900	235	9	dislocated	dislocated	ADJ
cana-5900	235	10	topologies	topology	NOUN
cana-5900	235	11	.	.	PUNCT
cana-5900	236	1	j.	j.	PROPN
cana-5900	236	2	electr	electr	PROPN
cana-5900	236	3	.	.	PUNCT
cana-5900	237	1	eng	eng	PROPN
cana-5900	237	2	.	.	PROPN
cana-5900	237	3	2020	2020	NUM
cana-5900	237	4	,	,	PUNCT
cana-5900	237	5	51	51	NUM
cana-5900	237	6	,	,	PUNCT
cana-5900	237	7	3–7	3–7	NUM
cana-5900	237	8	.	.	PUNCT
cana-5900	237	9	11	11	NUM
cana-5900	237	10	.	.	PUNCT
cana-5900	238	1	mustafa	mustafa	PROPN
cana-5900	238	2	,	,	PUNCT
cana-5900	238	3	z.	z.	PROPN
cana-5900	238	4	;	;	PUNCT
cana-5900	238	5	sims	sim	NOUN
cana-5900	238	6	,	,	PUNCT
cana-5900	238	7	b.	b.	PROPN
cana-5900	238	8	a	a	DET
cana-5900	238	9	new	new	ADJ
cana-5900	238	10	approach	approach	NOUN
cana-5900	238	11	to	to	ADP
cana-5900	238	12	generalized	generalize	VERB
cana-5900	238	13	metric	metric	ADJ
cana-5900	238	14	spaces	space	NOUN
cana-5900	238	15	.	.	PUNCT
cana-5900	239	1	j.	j.	PROPN
cana-5900	239	2	nonlinear	nonlinear	PROPN
cana-5900	239	3	convex	convex	PROPN
cana-5900	239	4	anal	anal	NOUN
cana-5900	239	5	.	.	PUNCT
cana-5900	239	6	2021	2021	NUM
cana-5900	239	7	,	,	PUNCT
cana-5900	239	8	7	7	NUM
cana-5900	239	9	,	,	PUNCT
cana-5900	239	10	289–297	289–297	NUM
cana-5900	239	11	.	.	PUNCT
cana-5900	240	1	12	12	NUM
cana-5900	240	2	.	.	PUNCT
cana-5900	240	3	jain	jain	PROPN
cana-5900	240	4	,	,	PUNCT
cana-5900	240	5	k.	k.	PROPN
cana-5900	240	6	;	;	PUNCT
cana-5900	240	7	kaur	kaur	PROPN
cana-5900	240	8	,	,	PUNCT
cana-5900	240	9	j.	j.	PROPN
cana-5900	240	10	a	a	DET
cana-5900	240	11	generalization	generalization	NOUN
cana-5900	240	12	of	of	ADP
cana-5900	240	13	g	g	NOUN
cana-5900	240	14	-	-	PUNCT
cana-5900	240	15	metric	metric	ADJ
cana-5900	240	16	spaces	space	NOUN
cana-5900	240	17	and	and	CCONJ
cana-5900	240	18	related	relate	VERB
cana-5900	240	19	fixed	fix	VERB
cana-5900	240	20	point	point	NOUN
cana-5900	240	21	theorems	theorem	NOUN
cana-5900	240	22	.	.	PUNCT
cana-5900	241	1	math	math	PROPN
cana-5900	241	2	.	.	PUNCT
cana-5900	242	1	inequalities	inequalities	PROPN
cana-5900	242	2	appl	appl	PROPN
cana-5900	242	3	.	.	PUNCT
cana-5900	243	1	2023	2023	NUM
cana-5900	243	2	,	,	PUNCT
cana-5900	243	3	22	22	NUM
cana-5900	243	4	,	,	PUNCT
cana-5900	243	5	1145–1160	1145–1160	NUM
cana-5900	243	6	.	.	NOUN
cana-5900	243	7	13	13	NUM
cana-5900	243	8	.	.	PUNCT
cana-5900	244	1	jleli	jleli	ADJ
cana-5900	244	2	,	,	PUNCT
cana-5900	244	3	m.	m.	NOUN
cana-5900	244	4	;	;	PUNCT
cana-5900	244	5	samet	samet	PROPN
cana-5900	244	6	,	,	PUNCT
cana-5900	244	7	b.	b.	PROPN
cana-5900	245	1	on	on	ADP
cana-5900	245	2	banach	banach	NOUN
cana-5900	245	3	’s	’s	PART
cana-5900	245	4	fixed	fix	VERB
cana-5900	245	5	point	point	NOUN
cana-5900	245	6	theorem	theorem	VERB
cana-5900	245	7	in	in	ADP
cana-5900	245	8	perturbed	perturb	VERB
cana-5900	245	9	metric	metric	ADJ
cana-5900	245	10	spaces	space	NOUN
cana-5900	245	11	.	.	PUNCT
cana-5900	246	1	j.	j.	PROPN
cana-5900	246	2	appl	appl	PROPN
cana-5900	246	3	.	.	PROPN
cana-5900	247	1	anal	anal	PROPN
cana-5900	247	2	.	.	PUNCT
cana-5900	248	1	comput	comput	NOUN
cana-5900	248	2	.	.	PUNCT
cana-5900	249	1	2023	2023	NUM
cana-5900	249	2	,	,	PUNCT
cana-5900	249	3	15	15	NUM
cana-5900	249	4	,	,	PUNCT
cana-5900	249	5	993–1001	993–1001	NUM
cana-5900	249	6	.	.	PUNCT
cana-5900	250	1	14	14	NUM
cana-5900	250	2	.	.	PUNCT
cana-5900	251	1	takahashi	takahashi	PROPN
cana-5900	251	2	,	,	PUNCT
cana-5900	251	3	w.	w.	PROPN
cana-5900	251	4	a	a	DET
cana-5900	251	5	convexity	convexity	NOUN
cana-5900	251	6	in	in	ADP
cana-5900	251	7	metric	metric	ADJ
cana-5900	251	8	spaces	space	NOUN
cana-5900	251	9	and	and	CCONJ
cana-5900	251	10	nonexpansive	nonexpansive	ADJ
cana-5900	251	11	mappings	mapping	NOUN
cana-5900	251	12	.	.	PUNCT
cana-5900	252	1	kodai	kodai	PROPN
cana-5900	252	2	math	math	PROPN
cana-5900	252	3	.	.	PUNCT
cana-5900	253	1	semin	semin	PROPN
cana-5900	253	2	.	.	PUNCT
cana-5900	254	1	rep	rep	PROPN
cana-5900	254	2	.	.	PROPN
cana-5900	254	3	2024	2024	NUM
cana-5900	254	4	,	,	PUNCT
cana-5900	254	5	22	22	NUM
cana-5900	254	6	,	,	PUNCT
cana-5900	254	7	142–149	142–149	NUM
cana-5900	254	8	.	.	NOUN
cana-5900	254	9	15	15	NUM
cana-5900	254	10	.	.	PUNCT
cana-5900	255	1	ding	ding	NOUN
cana-5900	255	2	,	,	PUNCT
cana-5900	255	3	x.p	x.p	PROPN
cana-5900	255	4	.	.	PUNCT
cana-5900	255	5	iteration	iteration	NOUN
cana-5900	255	6	processes	process	NOUN
cana-5900	255	7	for	for	ADP
cana-5900	255	8	nonlinear	nonlinear	ADJ
cana-5900	255	9	mappings	mapping	NOUN
cana-5900	255	10	in	in	ADP
cana-5900	255	11	convex	convex	ADJ
cana-5900	255	12	metric	metric	ADJ
cana-5900	255	13	spaces	space	NOUN
cana-5900	255	14	.	.	PUNCT
cana-5900	256	1	j.	j.	PROPN
cana-5900	256	2	math	math	PROPN
cana-5900	256	3	.	.	PUNCT
cana-5900	257	1	anal	anal	PROPN
cana-5900	257	2	.	.	PUNCT
cana-5900	257	3	appl	appl	PROPN
cana-5900	257	4	.	.	PROPN
cana-5900	257	5	2024	2024	NUM
cana-5900	257	6	,	,	PUNCT
cana-5900	257	7	132	132	NUM
cana-5900	257	8	,	,	PUNCT
cana-5900	257	9	114–122	114–122	NUM
cana-5900	257	10	.	.	NOUN
cana-5900	257	11	16	16	NUM
cana-5900	257	12	.	.	PUNCT
cana-5900	258	1	adewale	adewale	PROPN
cana-5900	258	2	,	,	PUNCT
cana-5900	258	3	o.	o.	PROPN
cana-5900	258	4	k.	k.	PROPN
cana-5900	258	5	and	and	CCONJ
cana-5900	258	6	osawaru	osawaru	PROPN
cana-5900	258	7	,	,	PUNCT
cana-5900	258	8	k.	k.	PROPN
cana-5900	258	9	(	(	PUNCT
cana-5900	258	10	2019	2019	NUM
cana-5900	258	11	)	)	PUNCT
cana-5900	258	12	g	g	NOUN
cana-5900	258	13	-	-	PUNCT
cana-5900	258	14	cone	cone	NOUN
cana-5900	258	15	metric	metric	ADJ
cana-5900	258	16	spaces	space	NOUN
cana-5900	258	17	over	over	ADP
cana-5900	258	18	banach	banach	NOUN
cana-5900	258	19	algebras	algebra	NOUN
cana-5900	258	20	and	and	CCONJ
cana-5900	258	21	some	some	DET
cana-5900	258	22	fixed	fix	VERB
cana-5900	258	23	point	point	NOUN
cana-5900	258	24	results	result	NOUN
cana-5900	258	25	.	.	PUNCT
cana-5900	259	1	international	international	ADJ
cana-5900	259	2	journal	journal	PROPN
cana-5900	259	3	of	of	ADP
cana-5900	259	4	mathematical	mathematical	ADJ
cana-5900	259	5	analysis	analysis	NOUN
cana-5900	259	6	and	and	CCONJ
cana-5900	259	7	optimization	optimization	NOUN
cana-5900	259	8	,	,	PUNCT
cana-5900	259	9	2019(2	2019(2	NUM
cana-5900	259	10	)	)	PUNCT
cana-5900	259	11	,	,	PUNCT
cana-5900	259	12	546	546	NUM
cana-5900	259	13	-	-	SYM
cana-5900	259	14	557	557	NUM
cana-5900	259	15	.	.	PUNCT
cana-5900	260	1	17	17	NUM
cana-5900	260	2	.	.	PUNCT
cana-5900	261	1	adewale	adewale	PROPN
cana-5900	261	2	,	,	PUNCT
cana-5900	261	3	o.	o.	PROPN
cana-5900	261	4	k.	k.	PROPN
cana-5900	261	5	,	,	PUNCT
cana-5900	261	6	ayodele	ayodele	PROPN
cana-5900	261	7	s.	s.	PROPN
cana-5900	261	8	o.	o.	PROPN
cana-5900	261	9	,	,	PUNCT
cana-5900	261	10	oyelade	oyelade	NOUN
cana-5900	261	11	b.	b.	PROPN
cana-5900	261	12	e.	e.	PROPN
cana-5900	261	13	and	and	CCONJ
cana-5900	261	14	aribike	aribike	PROPN
cana-5900	261	15	e.	e.	PROPN
cana-5900	261	16	e.	e.	PROPN
cana-5900	261	17	(	(	PUNCT
cana-5900	261	18	2024	2024	NUM
cana-5900	261	19	)	)	PUNCT
cana-5900	261	20	.	.	PUNCT
cana-5900	262	1	equivalence	equivalence	NOUN
cana-5900	262	2	of	of	ADP
cana-5900	262	3	some	some	DET
cana-5900	262	4	results	result	NOUN
cana-5900	262	5	and	and	CCONJ
cana-5900	262	6	fixed	fix	VERB
cana-5900	262	7	-	-	PUNCT
cana-5900	262	8	point	point	NOUN
cana-5900	262	9	theorems	theorem	NOUN
cana-5900	262	10	in	in	ADP
cana-5900	262	11	s	s	NOUN
cana-5900	262	12	-	-	PUNCT
cana-5900	262	13	multiplicative	multiplicative	ADJ
cana-5900	262	14	metric	metric	ADJ
cana-5900	262	15	spaces	space	NOUN
cana-5900	262	16	.	.	PUNCT
cana-5900	263	1	fixed	fix	VERB
cana-5900	263	2	point	point	NOUN
cana-5900	263	3	theory	theory	NOUN
cana-5900	263	4	and	and	CCONJ
cana-5900	263	5	algorithms	algorithm	NOUN
cana-5900	263	6	for	for	ADP
cana-5900	263	7	sciences	science	NOUN
cana-5900	263	8	and	and	CCONJ
cana-5900	263	9	engineering	engineering	NOUN
cana-5900	263	10	,	,	PUNCT
cana-5900	263	11	1	1	NUM
cana-5900	263	12	-	-	SYM
cana-5900	263	13	13	13	NUM
cana-5900	263	14	.	.	PUNCT
cana-5900	263	15	18	18	NUM
cana-5900	263	16	.	.	PUNCT
cana-5900	264	1	adewale	adewale	PROPN
cana-5900	264	2	,	,	PUNCT
cana-5900	264	3	o.	o.	PROPN
cana-5900	264	4	k.	k.	PROPN
cana-5900	264	5	and	and	CCONJ
cana-5900	264	6	iluno	iluno	PROPN
cana-5900	264	7	c.	c.	PROPN
cana-5900	264	8	(	(	PUNCT
cana-5900	264	9	2022	2022	NUM
cana-5900	264	10	)	)	PUNCT
cana-5900	264	11	.	.	PUNCT
cana-5900	265	1	fixed	fix	VERB
cana-5900	265	2	point	point	NOUN
cana-5900	265	3	theorems	theorem	NOUN
cana-5900	265	4	on	on	ADP
cana-5900	265	5	rectangular	rectangular	ADJ
cana-5900	265	6	s	s	ADJ
cana-5900	265	7	-	-	ADJ
cana-5900	265	8	metric	metric	ADJ
cana-5900	265	9	spaces	space	NOUN
cana-5900	265	10	,	,	PUNCT
cana-5900	265	11	scientific	scientific	ADJ
cana-5900	265	12	african	african	ADJ
cana-5900	265	13	,	,	PUNCT
cana-5900	265	14	16	16	NUM
cana-5900	265	15	,	,	PUNCT
cana-5900	265	16	1	1	NUM
cana-5900	265	17	-	-	SYM
cana-5900	265	18	10	10	NUM
cana-5900	265	19	.	.	PUNCT
cana-5900	266	1	19	19	NUM
cana-5900	266	2	.	.	PUNCT
cana-5900	267	1	adewale	adewale	PROPN
cana-5900	267	2	o.	o.	PROPN
cana-5900	267	3	k.	k.	PROPN
cana-5900	267	4	,	,	PUNCT
cana-5900	268	1	olaleru	olaleru	INTJ
cana-5900	268	2	j.	j.	PROPN
cana-5900	268	3	o.	o.	PROPN
cana-5900	268	4	and	and	CCONJ
cana-5900	268	5	akewe	akewe	PROPN
cana-5900	268	6	h.	h.	PROPN
cana-5900	268	7	,	,	PUNCT
cana-5900	268	8	fixed	fix	VERB
cana-5900	268	9	point	point	NOUN
cana-5900	268	10	theorems	theorem	NOUN
cana-5900	268	11	of	of	ADP
cana-5900	268	12	zamfirescu	zamfirescu	PROPN
cana-5900	268	13	’s	’s	PART
cana-5900	268	14	type	type	NOUN
cana-5900	268	15	in	in	ADP
cana-5900	268	16	complex	complex	NOUN
cana-5900	268	17	valued	value	VERB
cana-5900	268	18	gb	gb	ADV
cana-5900	268	19	-	-	PUNCT
cana-5900	268	20	metric	metric	ADJ
cana-5900	268	21	spaces	space	NOUN
cana-5900	268	22	,	,	PUNCT
cana-5900	268	23	transactions	transaction	NOUN
cana-5900	268	24	of	of	ADP
cana-5900	268	25	the	the	DET
cana-5900	268	26	nigerian	nigerian	ADJ
cana-5900	268	27	association	association	PROPN
cana-5900	268	28	of	of	ADP
cana-5900	268	29	mathematical	mathematical	ADJ
cana-5900	268	30	physics	physics	NOUN
cana-5900	268	31	,	,	PUNCT
cana-5900	268	32	vol	vol	NOUN
cana-5900	268	33	.	.	PROPN
cana-5900	268	34	8	8	NUM
cana-5900	268	35	,	,	PUNCT
cana-5900	268	36	no	no	INTJ
cana-5900	268	37	.	.	NOUN
cana-5900	268	38	1	1	NUM
cana-5900	268	39	,	,	PUNCT
cana-5900	268	40	(	(	PUNCT
cana-5900	268	41	2019	2019	NUM
cana-5900	268	42	)	)	PUNCT
cana-5900	268	43	,	,	PUNCT
cana-5900	268	44	5	5	NUM
cana-5900	268	45	-	-	SYM
cana-5900	268	46	10	10	NUM
cana-5900	268	47	.	.	PUNCT
cana-5900	268	48	20	20	NUM
cana-5900	268	49	.	.	PUNCT
cana-5900	269	1	adewale	adewale	PROPN
cana-5900	269	2	o.	o.	PROPN
cana-5900	269	3	k.	k.	PROPN
cana-5900	269	4	,	,	PUNCT
cana-5900	269	5	olaleru	olaleru	INTJ
cana-5900	269	6	j.	j.	PROPN
cana-5900	269	7	o.	o.	PROPN
cana-5900	269	8	and	and	CCONJ
cana-5900	269	9	akewe	akewe	VERB
cana-5900	269	10	h.	h.	PROPN
cana-5900	269	11	(	(	PUNCT
cana-5900	269	12	2019	2019	NUM
cana-5900	269	13	)	)	PUNCT
cana-5900	269	14	.	.	PUNCT
cana-5900	270	1	fixed	fix	VERB
cana-5900	270	2	point	point	NOUN
cana-5900	270	3	theorems	theorem	NOUN
cana-5900	270	4	on	on	ADP
cana-5900	270	5	a	a	DET
cana-5900	270	6	quaternion	quaternion	NOUN
cana-5900	270	7	valued	value	VERB
cana-5900	270	8	g	g	NOUN
cana-5900	270	9	-	-	PUNCT
cana-5900	270	10	metric	metric	ADJ
cana-5900	270	11	spaces	space	NOUN
cana-5900	270	12	,	,	PUNCT
cana-5900	270	13	communications	communication	NOUN
cana-5900	270	14	in	in	ADP
cana-5900	270	15	nonlinear	nonlinear	ADJ
cana-5900	270	16	analysis	analysis	NOUN
cana-5900	270	17	,	,	PUNCT
cana-5900	270	18	7	7	NUM
cana-5900	270	19	,	,	PUNCT
cana-5900	270	20	73	73	NUM
cana-5900	270	21	-	-	SYM
cana-5900	270	22	81	81	NUM
cana-5900	270	23	.	.	PUNCT
cana-5900	271	1	21	21	NUM
cana-5900	271	2	.	.	PUNCT
cana-5900	272	1	adewale	adewale	PROPN
cana-5900	272	2	o.	o.	PROPN
cana-5900	272	3	k.	k.	PROPN
cana-5900	272	4	,	,	PUNCT
cana-5900	272	5	olaleru	olaleru	INTJ
cana-5900	272	6	j.	j.	PROPN
cana-5900	272	7	o.	o.	PROPN
cana-5900	272	8	and	and	CCONJ
cana-5900	272	9	akewe	akewe	PROPN
cana-5900	272	10	h.	h.	PROPN
cana-5900	272	11	(	(	PUNCT
cana-5900	272	12	2020	2020	NUM
cana-5900	272	13	)	)	PUNCT
cana-5900	272	14	.	.	PUNCT
cana-5900	273	1	on	on	ADP
cana-5900	273	2	quasiconvex	quasiconvex	NOUN
cana-5900	273	3	metric	metric	ADJ
cana-5900	273	4	spaces	space	NOUN
cana-5900	273	5	,	,	PUNCT
cana-5900	273	6	advanced	advanced	ADJ
cana-5900	273	7	fixed	fix	VERB
cana-5900	273	8	point	point	NOUN
cana-5900	273	9	theory	theory	NOUN
cana-5900	273	10	,	,	PUNCT
cana-5900	273	11	10	10	NUM
cana-5900	273	12	,	,	PUNCT
cana-5900	273	13	1	1	NUM
cana-5900	273	14	-	-	SYM
cana-5900	273	15	11	11	NUM
cana-5900	273	16	.	.	PUNCT
cana-5900	273	17	22	22	NUM
cana-5900	273	18	.	.	PUNCT
cana-5900	274	1	adewale	adewale	PROPN
cana-5900	274	2	o.	o.	PROPN
cana-5900	274	3	k.	k.	PROPN
cana-5900	274	4	,	,	PUNCT
cana-5900	275	1	olaleru	olaleru	PROPN
cana-5900	275	2	j.	j.	PROPN
cana-5900	275	3	o.	o.	PROPN
cana-5900	275	4	,	,	PUNCT
cana-5900	275	5	olaoluwa	olaoluwa	PROPN
cana-5900	275	6	h.	h.	PROPN
cana-5900	275	7	and	and	CCONJ
cana-5900	275	8	akewe	akewe	PROPN
cana-5900	275	9	h.	h.	PROPN
cana-5900	275	10	(	(	PUNCT
cana-5900	275	11	2019	2019	NUM
cana-5900	275	12	)	)	PUNCT
cana-5900	275	13	.	.	PUNCT
cana-5900	276	1	fixed	fix	VERB
cana-5900	276	2	point	point	NOUN
cana-5900	276	3	theorems	theorem	NOUN
cana-5900	276	4	on	on	ADP
cana-5900	276	5	a	a	DET
cana-5900	276	6	γ	γ	X
cana-5900	276	7	-	-	PUNCT
cana-5900	276	8	generalized	generalize	VERB
cana-5900	276	9	quasi	quasi	ADJ
cana-5900	276	10	-	-	ADJ
cana-5900	276	11	metric	metric	ADJ
cana-5900	276	12	spaces	space	NOUN
cana-5900	276	13	,	,	PUNCT
cana-5900	276	14	creative	creative	ADJ
cana-5900	276	15	mathematical	mathematical	ADJ
cana-5900	276	16	and	and	CCONJ
cana-5900	276	17	informatics	informatic	NOUN
cana-5900	276	18	,	,	PUNCT
cana-5900	276	19	28	28	NUM
cana-5900	276	20	,	,	PUNCT
cana-5900	276	21	135	135	NUM
cana-5900	276	22	-	-	SYM
cana-5900	276	23	142	142	NUM
cana-5900	276	24	.	.	PUNCT
cana-5900	277	1	communications	communication	NOUN
cana-5900	277	2	on	on	ADP
cana-5900	277	3	applied	apply	VERB
cana-5900	277	4	nonlinear	nonlinear	ADJ
cana-5900	277	5	analysis	analysis	NOUN
cana-5900	277	6	issn	issn	NOUN
cana-5900	277	7	:	:	PUNCT
cana-5900	277	8	1074	1074	NUM
cana-5900	277	9	-	-	PUNCT
cana-5900	277	10	133x	133x	NUM
cana-5900	277	11	vol	vol	NOUN
cana-5900	277	12	31	31	NUM
cana-5900	277	13	no	no	NOUN
cana-5900	277	14	.	.	PUNCT
cana-5900	278	1	8s	8s	PROPN
cana-5900	278	2	(	(	PUNCT
cana-5900	278	3	2024	2024	NUM
cana-5900	278	4	)	)	PUNCT
cana-5900	278	5	1109	1109	NUM
cana-5900	278	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-5900	278	7	23	23	NUM
cana-5900	278	8	.	.	PUNCT
cana-5900	279	1	adewale	adewale	PROPN
cana-5900	279	2	o.	o.	PROPN
cana-5900	279	3	k.	k.	PROPN
cana-5900	279	4	,	,	PUNCT
cana-5900	279	5	umudu	umudu	PROPN
cana-5900	279	6	j.	j.	PROPN
cana-5900	279	7	c.	c.	PROPN
cana-5900	279	8	and	and	CCONJ
cana-5900	279	9	mogbademu	mogbademu	PROPN
cana-5900	279	10	a.	a.	PROPN
cana-5900	279	11	a.	a.	NOUN
cana-5900	279	12	(	(	PUNCT
cana-5900	279	13	2020	2020	NUM
cana-5900	279	14	)	)	PUNCT
cana-5900	279	15	.	.	PUNCT
cana-5900	280	1	fixed	fix	VERB
cana-5900	280	2	point	point	NOUN
cana-5900	280	3	theorems	theorem	NOUN
cana-5900	280	4	on	on	ADP
cana-5900	280	5	apmetric	apmetric	ADJ
cana-5900	280	6	spaces	space	NOUN
cana-5900	280	7	with	with	ADP
cana-5900	280	8	an	an	DET
cana-5900	280	9	application	application	NOUN
cana-5900	280	10	,	,	PUNCT
cana-5900	280	11	international	international	ADJ
cana-5900	280	12	journal	journal	NOUN
cana-5900	280	13	of	of	ADP
cana-5900	280	14	mathematical	mathematical	ADJ
cana-5900	280	15	analysis	analysis	NOUN
cana-5900	280	16	and	and	CCONJ
cana-5900	280	17	optimization	optimization	NOUN
cana-5900	280	18	,	,	PUNCT
cana-5900	280	19	2020(1	2020(1	NUM
cana-5900	280	20	)	)	PUNCT
cana-5900	280	21	,	,	PUNCT
cana-5900	280	22	657	657	NUM
cana-5900	280	23	-	-	SYM
cana-5900	280	24	668	668	NUM
cana-5900	280	25	.	.	NOUN
cana-5900	280	26	24	24	NUM
cana-5900	280	27	.	.	PUNCT
cana-5900	280	28	ansari	ansari	PROPN
cana-5900	280	29	a.	a.	PROPN
cana-5900	280	30	h.	h.	PROPN
cana-5900	280	31	,	,	PUNCT
cana-5900	280	32	ege	ege	PROPN
cana-5900	280	33	o.	o.	NOUN
cana-5900	280	34	and	and	CCONJ
cana-5900	280	35	radenovic	radenovic	PROPN
cana-5900	280	36	s.	s.	PROPN
cana-5900	280	37	(	(	PUNCT
cana-5900	280	38	2018	2018	NUM
cana-5900	280	39	)	)	PUNCT
cana-5900	280	40	.	.	PUNCT
cana-5900	281	1	some	some	DET
cana-5900	281	2	fixed	fix	VERB
cana-5900	281	3	point	point	NOUN
cana-5900	281	4	results	result	NOUN
cana-5900	281	5	on	on	ADP
cana-5900	281	6	complex	complex	ADJ
cana-5900	281	7	valued	value	VERB
cana-5900	281	8	gb	gb	ADV
cana-5900	281	9	-	-	PUNCT
cana-5900	281	10	metric	metric	ADJ
cana-5900	281	11	spaces	space	NOUN
cana-5900	281	12	,	,	PUNCT
cana-5900	281	13	revista	revista	PROPN
cana-5900	281	14	de	de	X
cana-5900	281	15	la	la	PROPN
cana-5900	281	16	real	real	PROPN
cana-5900	281	17	academia	academia	PROPN
cana-5900	281	18	de	de	PROPN
cana-5900	281	19	ciencias	ciencias	PROPN
cana-5900	281	20	exactas	exacta	NOUN
cana-5900	281	21	,	,	PUNCT
cana-5900	281	22	fisicas	fisicas	PROPN
cana-5900	281	23	y	y	PROPN
cana-5900	281	24	naturales	naturales	PROPN
cana-5900	281	25	,	,	PUNCT
cana-5900	281	26	seria	seria	PROPN
cana-5900	281	27	a.	a.	PROPN
cana-5900	281	28	matematicas	matematicas	PROPN
cana-5900	281	29	,	,	PUNCT
cana-5900	281	30	112(2	112(2	NUM
cana-5900	281	31	)	)	PUNCT
cana-5900	281	32	,	,	PUNCT
cana-5900	281	33	463472	463472	NUM
cana-5900	281	34	.	.	PUNCT
cana-5900	282	1	25	25	NUM
cana-5900	282	2	.	.	X
cana-5900	283	1	ege	ege	PROPN
cana-5900	283	2	,	,	PUNCT
cana-5900	283	3	o.	o.	PROPN
cana-5900	283	4	and	and	CCONJ
cana-5900	283	5	karaca	karaca	PROPN
cana-5900	283	6	,	,	PUNCT
cana-5900	283	7	i.	i.	PROPN
cana-5900	283	8	(	(	PUNCT
cana-5900	283	9	2018	2018	NUM
cana-5900	283	10	)	)	PUNCT
cana-5900	283	11	.	.	PUNCT
cana-5900	284	1	common	common	ADJ
cana-5900	284	2	fixed	fix	VERB
cana-5900	284	3	point	point	NOUN
cana-5900	284	4	results	result	NOUN
cana-5900	284	5	on	on	ADP
cana-5900	284	6	complex	complex	ADJ
cana-5900	284	7	valued	value	VERB
cana-5900	284	8	gb	gb	ADV
cana-5900	284	9	-	-	PUNCT
cana-5900	284	10	metric	metric	ADJ
cana-5900	284	11	spaces	space	NOUN
cana-5900	284	12	,	,	PUNCT
cana-5900	284	13	thai	thai	PROPN
cana-5900	284	14	journal	journal	PROPN
cana-5900	284	15	of	of	ADP
cana-5900	284	16	mathematics	mathematics	PROPN
cana-5900	284	17	,	,	PUNCT
cana-5900	284	18	16(3	16(3	NOUN
cana-5900	284	19	)	)	PUNCT
cana-5900	284	20	,	,	PUNCT
cana-5900	284	21	775	775	NUM
cana-5900	284	22	-	-	SYM
cana-5900	284	23	787	787	NUM
cana-5900	284	24	.	.	NUM
cana-5900	285	1	26	26	NUM
cana-5900	285	2	.	.	PUNCT
cana-5900	286	1	ege	ege	PROPN
cana-5900	286	2	,	,	PUNCT
cana-5900	286	3	o.	o.	NOUN
cana-5900	286	4	,	,	PUNCT
cana-5900	286	5	park	park	NOUN
cana-5900	286	6	,	,	PUNCT
cana-5900	286	7	c.	c.	PROPN
cana-5900	286	8	and	and	CCONJ
cana-5900	286	9	ansari	ansari	ADJ
cana-5900	286	10	,	,	PUNCT
cana-5900	286	11	a.	a.	PROPN
cana-5900	286	12	h.	h.	PROPN
cana-5900	286	13	(	(	PUNCT
cana-5900	286	14	2020	2020	NUM
cana-5900	286	15	)	)	PUNCT
cana-5900	286	16	.	.	PUNCT
cana-5900	287	1	a	a	DET
cana-5900	287	2	different	different	ADJ
cana-5900	287	3	approach	approach	NOUN
cana-5900	287	4	to	to	ADP
cana-5900	287	5	complex	complex	ADJ
cana-5900	287	6	valued	value	VERB
cana-5900	287	7	gbmetric	gbmetric	ADJ
cana-5900	287	8	spaces	space	NOUN
cana-5900	287	9	,	,	PUNCT
cana-5900	287	10	advances	advance	NOUN
cana-5900	287	11	in	in	ADP
cana-5900	287	12	difference	difference	NOUN
cana-5900	287	13	equations	equation	NOUN
cana-5900	287	14	,	,	PUNCT
cana-5900	287	15	152	152	NUM
cana-5900	287	16	,	,	PUNCT
cana-5900	287	17	1	1	NUM
cana-5900	287	18	-	-	SYM
cana-5900	287	19	13	13	NUM
cana-5900	287	20	,	,	PUNCT
cana-5900	287	21	https://doi.org/10.1186/s13662-020-02605-0	https://doi.org/10.1186/s13662-020-02605-0	NUM
cana-5900	287	22	.	.	PUNCT
cana-5900	288	1	27	27	NUM
cana-5900	288	2	.	.	X
cana-5900	289	1	ege	ege	PROPN
cana-5900	289	2	,	,	PUNCT
cana-5900	289	3	o.	o.	NOUN
cana-5900	289	4	(	(	PUNCT
cana-5900	289	5	2017	2017	NUM
cana-5900	289	6	)	)	PUNCT
cana-5900	289	7	.	.	PUNCT
cana-5900	290	1	some	some	DET
cana-5900	290	2	fixed	fix	VERB
cana-5900	290	3	point	point	NOUN
cana-5900	290	4	theorems	theorem	NOUN
cana-5900	290	5	in	in	ADP
cana-5900	290	6	complex	complex	NOUN
cana-5900	290	7	valued	value	VERB
cana-5900	290	8	gb	gb	ADV
cana-5900	290	9	-	-	PUNCT
cana-5900	290	10	metric	metric	ADJ
cana-5900	290	11	spaces	space	NOUN
cana-5900	290	12	.	.	PUNCT
cana-5900	291	1	journal	journal	PROPN
cana-5900	291	2	of	of	ADP
cana-5900	291	3	nonlinear	nonlinear	ADJ
cana-5900	291	4	and	and	CCONJ
cana-5900	291	5	convex	convex	ADJ
cana-5900	291	6	analysis	analysis	NOUN
cana-5900	291	7	,	,	PUNCT
cana-5900	291	8	18(11	18(11	NUM
cana-5900	291	9	)	)	PUNCT
cana-5900	291	10	,	,	PUNCT
cana-5900	291	11	1997	1997	NUM
cana-5900	291	12	-	-	SYM
cana-5900	291	13	2005	2005	NUM
cana-5900	291	14	.	.	PUNCT
cana-5900	292	1	28	28	NUM
cana-5900	292	2	.	.	X
cana-5900	293	1	ege	ege	PROPN
cana-5900	293	2	,	,	PUNCT
cana-5900	293	3	o.	o.	PROPN
cana-5900	293	4	(	(	PUNCT
cana-5900	293	5	2016	2016	NUM
cana-5900	293	6	)	)	PUNCT
cana-5900	293	7	.	.	PUNCT
cana-5900	294	1	complex	complex	PROPN
cana-5900	294	2	valued	value	VERB
cana-5900	294	3	gb	gb	ADV
cana-5900	294	4	-	-	PUNCT
cana-5900	294	5	metric	metric	ADJ
cana-5900	294	6	spaces	space	NOUN
cana-5900	294	7	,	,	PUNCT
cana-5900	294	8	journal	journal	NOUN
cana-5900	294	9	of	of	ADP
cana-5900	294	10	computational	computational	ADJ
cana-5900	294	11	analysis	analysis	NOUN
cana-5900	294	12	and	and	CCONJ
cana-5900	294	13	applications	application	NOUN
cana-5900	294	14	,	,	PUNCT
cana-5900	294	15	21(2	21(2	NUM
cana-5900	294	16	)	)	PUNCT
cana-5900	294	17	,	,	PUNCT
cana-5900	294	18	363	363	NUM
cana-5900	294	19	-	-	SYM
cana-5900	294	20	368	368	NUM
cana-5900	294	21	.	.	PUNCT
cana-5900	295	1	29	29	NUM
cana-5900	295	2	.	.	X
cana-5900	296	1	ege	ege	PROPN
cana-5900	296	2	,	,	PUNCT
cana-5900	296	3	o.	o.	NOUN
cana-5900	296	4	(	(	PUNCT
cana-5900	296	5	2015	2015	NUM
cana-5900	296	6	)	)	PUNCT
cana-5900	296	7	.	.	PUNCT
cana-5900	297	1	complex	complex	PROPN
cana-5900	297	2	valued	value	VERB
cana-5900	297	3	rectangular	rectangular	ADJ
cana-5900	297	4	b	b	X
cana-5900	297	5	-	-	ADJ
cana-5900	297	6	metric	metric	ADJ
cana-5900	297	7	spaces	space	NOUN
cana-5900	297	8	and	and	CCONJ
cana-5900	297	9	an	an	DET
cana-5900	297	10	application	application	NOUN
cana-5900	297	11	to	to	ADP
cana-5900	297	12	linear	linear	PROPN
cana-5900	297	13	equations	equation	NOUN
cana-5900	297	14	.	.	PUNCT
cana-5900	298	1	journal	journal	PROPN
cana-5900	298	2	of	of	ADP
cana-5900	298	3	nonlinear	nonlinear	ADJ
cana-5900	298	4	science	science	NOUN
cana-5900	298	5	and	and	CCONJ
cana-5900	298	6	applications	application	NOUN
cana-5900	298	7	,	,	PUNCT
cana-5900	298	8	8(6	8(6	NUM
cana-5900	298	9	)	)	PUNCT
cana-5900	298	10	,	,	PUNCT
cana-5900	298	11	1014	1014	NUM
cana-5900	298	12	-	-	SYM
cana-5900	298	13	1021	1021	NUM
cana-5900	298	14	.	.	PUNCT
cana-5900	299	1	30	30	NUM
cana-5900	299	2	.	.	PUNCT
cana-5900	300	1	iqbal	iqbal	PROPN
cana-5900	300	2	,	,	PUNCT
cana-5900	300	3	m.	m.	NOUN
cana-5900	300	4	,	,	PUNCT
cana-5900	300	5	batool	batool	NOUN
cana-5900	300	6	,	,	PUNCT
cana-5900	300	7	a.	a.	NOUN
cana-5900	300	8	,	,	PUNCT
cana-5900	300	9	ege	ege	PROPN
cana-5900	300	10	,	,	PUNCT
cana-5900	300	11	o.	o.	NOUN
cana-5900	300	12	and	and	CCONJ
cana-5900	300	13	de	de	PROPN
cana-5900	300	14	la	la	X
cana-5900	300	15	sen	sen	PROPN
cana-5900	300	16	,	,	PUNCT
cana-5900	300	17	m.	m.	NOUN
cana-5900	300	18	(	(	PUNCT
cana-5900	300	19	2020	2020	NUM
cana-5900	300	20	)	)	PUNCT
cana-5900	300	21	.	.	PUNCT
cana-5900	301	1	fixed	fix	VERB
cana-5900	301	2	point	point	NOUN
cana-5900	301	3	of	of	ADP
cana-5900	301	4	almost	almost	ADV
cana-5900	301	5	contraction	contraction	NOUN
cana-5900	301	6	in	in	ADP
cana-5900	301	7	b	b	ADJ
cana-5900	301	8	-	-	ADJ
cana-5900	301	9	metric	metric	ADJ
cana-5900	301	10	spaces	space	NOUN
cana-5900	301	11	,	,	PUNCT
cana-5900	301	12	journal	journal	NOUN
cana-5900	301	13	of	of	ADP
cana-5900	301	14	mathematics	mathematic	NOUN
cana-5900	301	15	,	,	PUNCT
cana-5900	301	16	3218134	3218134	NUM
cana-5900	301	17	,	,	PUNCT
cana-5900	301	18	1	1	NUM
cana-5900	301	19	-	-	SYM
cana-5900	301	20	6	6	NUM
cana-5900	301	21	,	,	PUNCT
cana-5900	301	22	https://doi.org/10.1155/2020/3218134	https://doi.org/10.1155/2020/3218134	NOUN
cana-5900	301	23	.	.	PUNCT
cana-5900	302	1	31	31	NUM
cana-5900	302	2	.	.	PUNCT
cana-5900	302	3	isik	isik	PROPN
cana-5900	302	4	,	,	PUNCT
cana-5900	302	5	h.	h.	PROPN
cana-5900	302	6	,	,	PUNCT
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cana-5900	302	8	,	,	PUNCT
cana-5900	302	9	b.	b.	PROPN
cana-5900	302	10	,	,	PUNCT
cana-5900	302	11	parvaneh	parvaneh	NOUN
cana-5900	302	12	,	,	PUNCT
cana-5900	302	13	v.	v.	PROPN
cana-5900	302	14	and	and	CCONJ
cana-5900	302	15	park	park	NOUN
cana-5900	302	16	,	,	PUNCT
cana-5900	302	17	c.	c.	PROPN
cana-5900	302	18	(	(	PUNCT
cana-5900	302	19	2020	2020	NUM
cana-5900	302	20	)	)	PUNCT
cana-5900	302	21	.	.	PUNCT
cana-5900	303	1	extended	extend	VERB
cana-5900	303	2	quasi	quasi	ADJ
cana-5900	303	3	bmetric	bmetric	NOUN
cana-5900	303	4	-	-	PUNCT
cana-5900	303	5	like	like	ADJ
cana-5900	303	6	spaces	space	NOUN
cana-5900	303	7	and	and	CCONJ
cana-5900	303	8	some	some	DET
cana-5900	303	9	fixed	fix	VERB
cana-5900	303	10	point	point	NOUN
cana-5900	303	11	theorems	theorem	NOUN
cana-5900	303	12	for	for	ADP
cana-5900	303	13	contractive	contractive	ADJ
cana-5900	303	14	mappings	mapping	NOUN
cana-5900	303	15	,	,	PUNCT
cana-5900	303	16	appl	appl	PROPN
cana-5900	303	17	.	.	PROPN
cana-5900	303	18	math	math	NOUN
cana-5900	303	19	.	.	PUNCT
cana-5900	304	1	e	e	X
cana-5900	304	2	-	-	NOUN
cana-5900	304	3	notes	note	NOUN
cana-5900	304	4	,	,	PUNCT
cana-5900	304	5	20	20	NUM
cana-5900	304	6	,	,	PUNCT
cana-5900	304	7	204	204	NUM
cana-5900	304	8	-	-	SYM
cana-5900	304	9	214	214	NUM
cana-5900	304	10	.	.	PUNCT
cana-5900	305	1	32	32	NUM
cana-5900	305	2	.	.	PUNCT
cana-5900	306	1	mitrovic	mitrovic	PROPN
cana-5900	306	2	,	,	PUNCT
cana-5900	306	3	z.	z.	PROPN
cana-5900	306	4	d.	d.	PROPN
cana-5900	306	5	,	,	PUNCT
cana-5900	306	6	isik	isik	PROPN
cana-5900	306	7	,	,	PUNCT
cana-5900	306	8	h.	h.	PROPN
cana-5900	306	9	and	and	CCONJ
cana-5900	306	10	radenovic	radenovic	PROPN
cana-5900	306	11	,	,	PUNCT
cana-5900	306	12	s.	s.	PROPN
cana-5900	306	13	(	(	PUNCT
cana-5900	306	14	2020	2020	NUM
cana-5900	306	15	)	)	PUNCT
cana-5900	306	16	.	.	PUNCT
cana-5900	307	1	the	the	DET
cana-5900	307	2	new	new	ADJ
cana-5900	307	3	results	result	NOUN
cana-5900	307	4	in	in	ADP
cana-5900	307	5	extended	extended	ADJ
cana-5900	307	6	b	b	X
cana-5900	307	7	-	-	ADJ
cana-5900	307	8	metric	metric	ADJ
cana-5900	307	9	spaces	space	NOUN
cana-5900	307	10	and	and	CCONJ
cana-5900	307	11	applications	application	NOUN
cana-5900	307	12	.	.	PUNCT
cana-5900	308	1	int	int	NOUN
cana-5900	308	2	.	.	PUNCT
cana-5900	309	1	j.	j.	PROPN
cana-5900	309	2	nonlinear	nonlinear	PROPN
cana-5900	309	3	anal	anal	PROPN
cana-5900	309	4	.	.	PUNCT
cana-5900	310	1	appl	appl	PROPN
cana-5900	310	2	.	.	PROPN
cana-5900	310	3	,	,	PUNCT
cana-5900	310	4	11(1	11(1	NUM
cana-5900	310	5	)	)	PUNCT
cana-5900	310	6	,	,	PUNCT
cana-5900	310	7	473	473	NUM
cana-5900	310	8	-	-	SYM
cana-5900	310	9	482	482	NUM
cana-5900	310	10	.	.	PUNCT
cana-5900	310	11	33	33	NUM
cana-5900	310	12	.	.	PUNCT
cana-5900	311	1	mustafa	mustafa	PROPN
cana-5900	311	2	,	,	PUNCT
cana-5900	311	3	z.	z.	PROPN
cana-5900	311	4	,	,	PUNCT
cana-5900	311	5	shahkoohi	shahkoohi	PROPN
cana-5900	311	6	,	,	PUNCT
cana-5900	311	7	r.	r.	PROPN
cana-5900	311	8	j.	j.	PROPN
cana-5900	311	9	,	,	PUNCT
cana-5900	311	10	parvaneh	parvaneh	PROPN
cana-5900	311	11	,	,	PUNCT
cana-5900	311	12	v.	v.	PROPN
cana-5900	311	13	,	,	PUNCT
cana-5900	311	14	kadelburg	kadelburg	PROPN
cana-5900	311	15	,	,	PUNCT
cana-5900	311	16	z.	z.	PROPN
cana-5900	311	17	and	and	CCONJ
cana-5900	311	18	jaradat	jaradat	PROPN
cana-5900	311	19	,	,	PUNCT
cana-5900	311	20	m.	m.	NOUN
cana-5900	311	21	m.	m.	NOUN
cana-5900	311	22	m.	m.	NOUN
cana-5900	311	23	(	(	PUNCT
cana-5900	311	24	2019	2019	NUM
cana-5900	311	25	)	)	PUNCT
cana-5900	311	26	.	.	PUNCT
cana-5900	312	1	ordered	order	VERB
cana-5900	312	2	sp	sp	NOUN
cana-5900	312	3	-	-	PUNCT
cana-5900	312	4	metric	metric	ADJ
cana-5900	312	5	spaces	space	NOUN
cana-5900	312	6	and	and	CCONJ
cana-5900	312	7	some	some	DET
cana-5900	312	8	fixed	fix	VERB
cana-5900	312	9	point	point	NOUN
cana-5900	312	10	theorems	theorem	NOUN
cana-5900	312	11	for	for	ADP
cana-5900	312	12	contractive	contractive	ADJ
cana-5900	312	13	mappings	mapping	NOUN
cana-5900	312	14	with	with	ADP
cana-5900	312	15	application	application	NOUN
cana-5900	312	16	to	to	ADP
cana-5900	312	17	periodic	periodic	ADJ
cana-5900	312	18	boundary	boundary	ADJ
cana-5900	312	19	value	value	NOUN
cana-5900	312	20	problems	problem	NOUN
cana-5900	312	21	.	.	PUNCT
cana-5900	313	1	fixed	fix	VERB
cana-5900	313	2	point	point	NOUN
cana-5900	313	3	theory	theory	NOUN
cana-5900	313	4	and	and	CCONJ
cana-5900	313	5	applications	application	NOUN
cana-5900	313	6	,	,	PUNCT
cana-5900	313	7	20	20	NUM
cana-5900	313	8	.	.	PUNCT
cana-5900	313	9	https://doi.org/10.1186/s13662-020-02605-0	https://doi.org/10.1186/s13662-020-02605-0	PROPN
cana-5900	313	10	https://doi.org/10.1155/2020/3218134	https://doi.org/10.1155/2020/3218134	PROPN