id	sid	tid	token	lemma	pos
cana-1393	1	1	communications	communication	NOUN
cana-1393	1	2	on	on	ADP
cana-1393	1	3	applied	apply	VERB
cana-1393	1	4	nonlinear	nonlinear	ADJ
cana-1393	1	5	analysis	analysis	NOUN
cana-1393	1	6	issn	issn	NOUN
cana-1393	1	7	:	:	PUNCT
cana-1393	1	8	1074	1074	NUM
cana-1393	1	9	-	-	PUNCT
cana-1393	1	10	133x	133x	NUM
cana-1393	1	11	vol	vol	NOUN
cana-1393	1	12	31	31	NUM
cana-1393	1	13	no	no	NOUN
cana-1393	1	14	.	.	PUNCT
cana-1393	2	1	7s	7	NOUN
cana-1393	2	2	(	(	PUNCT
cana-1393	2	3	2024	2024	NUM
cana-1393	2	4	)	)	PUNCT
cana-1393	2	5	506	506	NUM
cana-1393	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1393	2	7	common	common	ADJ
cana-1393	2	8	fixed	fix	VERB
cana-1393	2	9	point	point	NOUN
cana-1393	2	10	theorems	theorem	NOUN
cana-1393	2	11	for	for	ADP
cana-1393	2	12	weakly	weakly	ADJ
cana-1393	2	13	compatible	compatible	ADJ
cana-1393	2	14	mappings	mapping	NOUN
cana-1393	2	15	in	in	ADP
cana-1393	2	16	multiplicative	multiplicative	ADJ
cana-1393	2	17	metric	metric	ADJ
cana-1393	2	18	space	space	NOUN
cana-1393	2	19	chiranjeevi	chiranjeevi	PROPN
cana-1393	2	20	perala	perala	PROPN
cana-1393	2	21	1	1	NUM
cana-1393	2	22	,	,	PUNCT
cana-1393	2	23	thirupathi	thirupathi	NOUN
cana-1393	2	24	thota	thota	ADJ
cana-1393	2	25	2	2	NUM
cana-1393	2	26	,	,	PUNCT
cana-1393	2	27	srinivas	srinivas	PROPN
cana-1393	2	28	veladi	veladi	NOUN
cana-1393	2	29	3	3	NUM
cana-1393	2	30	1	1	NUM
cana-1393	2	31	.	.	PUNCT
cana-1393	3	1	department	department	NOUN
cana-1393	3	2	of	of	ADP
cana-1393	3	3	mathematics	mathematics	PROPN
cana-1393	3	4	,	,	PUNCT
cana-1393	3	5	osmania	osmania	PROPN
cana-1393	3	6	university	university	PROPN
cana-1393	3	7	,	,	PUNCT
cana-1393	3	8	hyderabad	hyderabad	PROPN
cana-1393	3	9	,	,	PUNCT
cana-1393	3	10	telangana	telangana	PROPN
cana-1393	3	11	,	,	PUNCT
cana-1393	3	12	india	india	PROPN
cana-1393	3	13	,	,	PUNCT
cana-1393	3	14	email	email	NOUN
cana-1393	3	15	:	:	PUNCT
cana-1393	3	16	chiranjeeviperala@gmail.com	chiranjeeviperala@gmail.com	X
cana-1393	3	17	2	2	NUM
cana-1393	3	18	.department	.department	NOUN
cana-1393	3	19	of	of	ADP
cana-1393	3	20	mathematics	mathematic	NOUN
cana-1393	3	21	,	,	PUNCT
cana-1393	3	22	sreenidhi	sreenidhi	PROPN
cana-1393	3	23	institute	institute	PROPN
cana-1393	3	24	of	of	ADP
cana-1393	3	25	science	science	NOUN
cana-1393	3	26	and	and	CCONJ
cana-1393	3	27	technology	technology	NOUN
cana-1393	3	28	,	,	PUNCT
cana-1393	3	29	hyderabad	hyderabad	PROPN
cana-1393	3	30	,	,	PUNCT
cana-1393	3	31	telangana	telangana	PROPN
cana-1393	3	32	,	,	PUNCT
cana-1393	3	33	india	india	PROPN
cana-1393	3	34	email	email	NOUN
cana-1393	3	35	:	:	PUNCT
cana-1393	3	36	thotathirupathi1986@gmail.com	thotathirupathi1986@gmail.com	X
cana-1393	4	1	3	3	NUM
cana-1393	4	2	.department	.department	NOUN
cana-1393	4	3	of	of	ADP
cana-1393	4	4	mathematics	mathematic	NOUN
cana-1393	4	5	,	,	PUNCT
cana-1393	4	6	university	university	NOUN
cana-1393	4	7	college	college	NOUN
cana-1393	4	8	of	of	ADP
cana-1393	4	9	science	science	PROPN
cana-1393	4	10	,	,	PUNCT
cana-1393	4	11	osmania	osmania	PROPN
cana-1393	4	12	university	university	PROPN
cana-1393	4	13	,	,	PUNCT
cana-1393	4	14	hyderabad	hyderabad	PROPN
cana-1393	4	15	,	,	PUNCT
cana-1393	4	16	telangana	telangana	PROPN
cana-1393	4	17	,	,	PUNCT
cana-1393	4	18	india	india	PROPN
cana-1393	4	19	email:srinivasmaths4141@gmail.com	email:srinivasmaths4141@gmail.com	PROPN
cana-1393	4	20	article	article	NOUN
cana-1393	4	21	history	history	NOUN
cana-1393	4	22	:	:	PUNCT
cana-1393	4	23	received	receive	VERB
cana-1393	4	24	:	:	PUNCT
cana-1393	4	25	04	04	NUM
cana-1393	4	26	-	-	PUNCT
cana-1393	4	27	06	06	NUM
cana-1393	4	28	-	-	PUNCT
cana-1393	4	29	2024	2024	NUM
cana-1393	4	30	revised	revise	VERB
cana-1393	4	31	:	:	PUNCT
cana-1393	4	32	03	03	NUM
cana-1393	4	33	-	-	PUNCT
cana-1393	4	34	07	07	NUM
cana-1393	4	35	-	-	PUNCT
cana-1393	4	36	2024	2024	NUM
cana-1393	4	37	accepted	accept	VERB
cana-1393	4	38	:	:	PUNCT
cana-1393	4	39	30	30	NUM
cana-1393	4	40	-	-	SYM
cana-1393	4	41	07	07	NUM
cana-1393	4	42	-	-	PUNCT
cana-1393	4	43	2024	2024	NUM
cana-1393	4	44	abstract	abstract	NOUN
cana-1393	4	45	the	the	DET
cana-1393	4	46	aim	aim	NOUN
cana-1393	4	47	of	of	ADP
cana-1393	4	48	this	this	DET
cana-1393	4	49	paper	paper	NOUN
cana-1393	4	50	is	be	AUX
cana-1393	4	51	to	to	PART
cana-1393	4	52	establish	establish	VERB
cana-1393	4	53	three	three	NUM
cana-1393	4	54	common	common	ADJ
cana-1393	4	55	fixed	fix	VERB
cana-1393	4	56	point	point	NOUN
cana-1393	4	57	theorems	theorem	NOUN
cana-1393	4	58	in	in	ADP
cana-1393	4	59	multiplicative	multiplicative	ADJ
cana-1393	4	60	metric	metric	ADJ
cana-1393	4	61	space	space	NOUN
cana-1393	4	62	(	(	PUNCT
cana-1393	4	63	mms	mms	NOUN
cana-1393	4	64	)	)	PUNCT
cana-1393	4	65	.	.	PUNCT
cana-1393	5	1	by	by	ADP
cana-1393	5	2	utilizing	utilize	VERB
cana-1393	5	3	the	the	DET
cana-1393	5	4	conditions	condition	NOUN
cana-1393	5	5	concepts	concept	NOUN
cana-1393	5	6	of	of	ADP
cana-1393	5	7	non	non	ADJ
cana-1393	5	8	-	-	ADJ
cana-1393	5	9	continuous	continuous	ADJ
cana-1393	5	10	and	and	CCONJ
cana-1393	5	11	noncompatible	noncompatible	ADJ
cana-1393	5	12	mappings.the	mappings.the	DET
cana-1393	5	13	first	first	ADJ
cana-1393	5	14	theoem	theoem	NOUN
cana-1393	5	15	is	be	AUX
cana-1393	5	16	generated	generate	VERB
cana-1393	5	17	by	by	ADP
cana-1393	5	18	applying	apply	VERB
cana-1393	5	19	the	the	DET
cana-1393	5	20	concepts	concept	NOUN
cana-1393	5	21	of	of	ADP
cana-1393	5	22	semicompatible	semicompatible	ADJ
cana-1393	5	23	mapping	mapping	NOUN
cana-1393	5	24	,	,	PUNCT
cana-1393	5	25	wcm	wcm	NOUN
cana-1393	5	26	and	and	CCONJ
cana-1393	5	27	reciprocally	reciprocally	ADV
cana-1393	5	28	continuous	continuous	ADJ
cana-1393	5	29	mappings.the	mappings.the	DET
cana-1393	5	30	second	second	ADJ
cana-1393	5	31	theorem	theorem	NOUN
cana-1393	5	32	is	be	AUX
cana-1393	5	33	established	establish	VERB
cana-1393	5	34	by	by	ADP
cana-1393	5	35	using	use	VERB
cana-1393	5	36	the	the	DET
cana-1393	5	37	concepts	concept	NOUN
cana-1393	5	38	of	of	ADP
cana-1393	5	39	strongly	strongly	ADV
cana-1393	5	40	semi	semi	ADJ
cana-1393	5	41	compatible	compatible	ADJ
cana-1393	5	42	mappings	mapping	NOUN
cana-1393	5	43	,	,	PUNCT
cana-1393	5	44	conditionally	conditionally	ADV
cana-1393	5	45	reciprocally	reciprocally	VERB
cana-1393	5	46	continuous	continuous	ADJ
cana-1393	5	47	mappings	mapping	NOUN
cana-1393	5	48	and	and	CCONJ
cana-1393	5	49	and	and	CCONJ
cana-1393	5	50	owc	owc	NUM
cana-1393	5	51	mappings	mapping	NOUN
cana-1393	5	52	.	.	PUNCT
cana-1393	6	1	these	these	DET
cana-1393	6	2	conditions	condition	NOUN
cana-1393	6	3	are	be	AUX
cana-1393	6	4	weaker	weak	ADJ
cana-1393	6	5	than	than	ADP
cana-1393	6	6	the	the	DET
cana-1393	6	7	existing	exist	VERB
cana-1393	6	8	conditions	condition	NOUN
cana-1393	6	9	like	like	ADP
cana-1393	6	10	compatible	compatible	ADJ
cana-1393	6	11	mappings	mapping	NOUN
cana-1393	6	12	and	and	CCONJ
cana-1393	6	13	cotinuous	cotinuous	ADJ
cana-1393	6	14	which	which	PRON
cana-1393	6	15	generalizes	generalize	VERB
cana-1393	6	16	the	the	DET
cana-1393	6	17	theorem	theorem	NOUN
cana-1393	6	18	of	of	ADP
cana-1393	6	19	afrah	afrah	PROPN
cana-1393	6	20	a.	a.	PROPN
cana-1393	6	21	n.	n.	PROPN
cana-1393	6	22	abdou	abdou	PROPN
cana-1393	6	23	.	.	PUNCT
cana-1393	7	1	keywords	keyword	NOUN
cana-1393	7	2	:	:	PUNCT
cana-1393	7	3	multiplicative	multiplicative	ADJ
cana-1393	7	4	metric	metric	ADJ
cana-1393	7	5	space	space	NOUN
cana-1393	7	6	(	(	PUNCT
cana-1393	7	7	mms	mms	NOUN
cana-1393	7	8	)	)	PUNCT
cana-1393	7	9	,	,	PUNCT
cana-1393	7	10	fixed	fix	VERB
cana-1393	7	11	point	point	NOUN
cana-1393	7	12	,	,	PUNCT
cana-1393	7	13	semi	semi	ADJ
cana-1393	7	14	-	-	ADJ
cana-1393	7	15	compatible	compatible	ADJ
cana-1393	7	16	mapping	mapping	NOUN
cana-1393	7	17	,	,	PUNCT
cana-1393	7	18	reciprocally	reciprocally	ADV
cana-1393	7	19	continuous	continuous	ADJ
cana-1393	7	20	mappings	mapping	NOUN
cana-1393	7	21	,	,	PUNCT
cana-1393	7	22	weakly	weakly	ADV
cana-1393	7	23	compatible	compatible	ADJ
cana-1393	7	24	mapping	mapping	NOUN
cana-1393	7	25	,	,	PUNCT
cana-1393	7	26	strongly	strongly	ADV
cana-1393	7	27	semi	semi	ADJ
cana-1393	7	28	compatible	compatible	ADJ
cana-1393	7	29	mappings	mapping	NOUN
cana-1393	7	30	,	,	PUNCT
cana-1393	7	31	conditionally	conditionally	ADV
cana-1393	7	32	reciprocally	reciprocally	VERB
cana-1393	7	33	continuous	continuous	ADJ
cana-1393	7	34	mappings	mapping	NOUN
cana-1393	7	35	and	and	CCONJ
cana-1393	7	36	and	and	CCONJ
cana-1393	7	37	owc	owc	NUM
cana-1393	7	38	mappings	mapping	NOUN
cana-1393	7	39	.	.	PUNCT
cana-1393	8	1	2020	2020	NUM
cana-1393	8	2	mathematics	mathematic	NOUN
cana-1393	8	3	subject	subject	ADJ
cana-1393	8	4	classification	classification	NOUN
cana-1393	8	5	:	:	PUNCT
cana-1393	8	6	54h25	54h25	NUM
cana-1393	8	7	,	,	PUNCT
cana-1393	8	8	47h10	47h10	NUM
cana-1393	8	9	,	,	PUNCT
cana-1393	8	10	54e50	54e50	NOUN
cana-1393	8	11	.	.	PUNCT
cana-1393	9	1	1	1	X
cana-1393	9	2	.	.	X
cana-1393	9	3	introduction	introduction	NOUN
cana-1393	9	4	fixed	fix	VERB
cana-1393	9	5	point	point	NOUN
cana-1393	9	6	theory	theory	NOUN
cana-1393	9	7	is	be	AUX
cana-1393	9	8	one	one	NUM
cana-1393	9	9	of	of	ADP
cana-1393	9	10	the	the	DET
cana-1393	9	11	most	most	ADV
cana-1393	9	12	exciting	exciting	ADJ
cana-1393	9	13	problems	problem	NOUN
cana-1393	9	14	in	in	ADP
cana-1393	9	15	current	current	ADJ
cana-1393	9	16	mathematics	mathematic	NOUN
cana-1393	9	17	,	,	PUNCT
cana-1393	9	18	and	and	CCONJ
cana-1393	9	19	it	it	PRON
cana-1393	9	20	may	may	AUX
cana-1393	9	21	be	be	AUX
cana-1393	9	22	an	an	DET
cana-1393	9	23	existing	exist	VERB
cana-1393	9	24	area	area	NOUN
cana-1393	9	25	of	of	ADP
cana-1393	9	26	functional	functional	ADJ
cana-1393	9	27	analysis.furthermore	analysis.furthermore	NOUN
cana-1393	9	28	,	,	PUNCT
cana-1393	9	29	this	this	DET
cana-1393	9	30	topic	topic	NOUN
cana-1393	9	31	has	have	AUX
cana-1393	9	32	served	serve	VERB
cana-1393	9	33	as	as	ADP
cana-1393	9	34	a	a	DET
cana-1393	9	35	platform	platform	NOUN
cana-1393	9	36	for	for	ADP
cana-1393	9	37	various	various	ADJ
cana-1393	9	38	researchers	researcher	NOUN
cana-1393	9	39	during	during	ADP
cana-1393	9	40	the	the	DET
cana-1393	9	41	last	last	ADJ
cana-1393	9	42	several	several	ADJ
cana-1393	9	43	years	year	NOUN
cana-1393	9	44	.	.	PUNCT
cana-1393	10	1	within	within	ADP
cana-1393	10	2	the	the	DET
cana-1393	10	3	subject	subject	NOUN
cana-1393	10	4	of	of	ADP
cana-1393	10	5	analysis	analysis	NOUN
cana-1393	10	6	,	,	PUNCT
cana-1393	10	7	the	the	DET
cana-1393	10	8	theory	theory	NOUN
cana-1393	10	9	of	of	ADP
cana-1393	10	10	metric	metric	ADJ
cana-1393	10	11	spaces	space	NOUN
cana-1393	10	12	has	have	AUX
cana-1393	10	13	grown	grow	VERB
cana-1393	10	14	significantly.we	significantly.we	PRON
cana-1393	10	15	know	know	VERB
cana-1393	10	16	that	that	SCONJ
cana-1393	10	17	the	the	DET
cana-1393	10	18	set	set	NOUN
cana-1393	10	19	of	of	ADP
cana-1393	10	20	positive	positive	ADJ
cana-1393	10	21	real	real	ADJ
cana-1393	10	22	numbers	number	NOUN
cana-1393	10	23	is	be	AUX
cana-1393	10	24	not	not	PART
cana-1393	10	25	complete	complete	ADJ
cana-1393	10	26	in	in	ADP
cana-1393	10	27	metric	metric	ADJ
cana-1393	10	28	space	space	NOUN
cana-1393	10	29	.	.	PUNCT
cana-1393	11	1	inorder	inorder	NOUN
cana-1393	11	2	to	to	PART
cana-1393	11	3	overcome	overcome	VERB
cana-1393	11	4	this	this	DET
cana-1393	11	5	problem	problem	NOUN
cana-1393	11	6	the	the	DET
cana-1393	11	7	concept	concept	NOUN
cana-1393	11	8	known	know	VERB
cana-1393	11	9	as	as	ADP
cana-1393	11	10	mms	mms	NOUN
cana-1393	11	11	was	be	AUX
cana-1393	11	12	introduced	introduce	VERB
cana-1393	11	13	by	by	ADP
cana-1393	11	14	bashirove	bashirove	NOUN
cana-1393	11	15	in	in	ADP
cana-1393	11	16	2008	2008	NUM
cana-1393	11	17	.	.	PUNCT
cana-1393	12	1	further	far	ADV
cana-1393	12	2	ozavsar	ozavsar	VERB
cana-1393	12	3	and	and	CCONJ
cana-1393	12	4	cevikel	cevikel	VERB
cana-1393	12	5	in	in	ADP
cana-1393	12	6	2017	2017	NUM
cana-1393	12	7	investigated	investigate	VERB
cana-1393	12	8	and	and	CCONJ
cana-1393	12	9	developed	develop	VERB
cana-1393	12	10	the	the	DET
cana-1393	12	11	multiplicative	multiplicative	ADJ
cana-1393	12	12	contraction	contraction	NOUN
cana-1393	12	13	principle	principle	NOUN
cana-1393	12	14	and	and	CCONJ
cana-1393	12	15	proved	prove	VERB
cana-1393	12	16	some	some	DET
cana-1393	12	17	common	common	ADJ
cana-1393	12	18	fixed	fix	VERB
cana-1393	12	19	point	point	NOUN
cana-1393	12	20	results	result	NOUN
cana-1393	12	21	.	.	PUNCT
cana-1393	13	1	thereafter	thereafter	ADV
cana-1393	13	2	,	,	PUNCT
cana-1393	13	3	the	the	DET
cana-1393	13	4	theory	theory	NOUN
cana-1393	13	5	of	of	ADP
cana-1393	13	6	a	a	DET
cana-1393	13	7	multiplicative	multiplicative	ADJ
cana-1393	13	8	metric	metric	ADJ
cana-1393	13	9	space	space	NOUN
cana-1393	13	10	has	have	AUX
cana-1393	13	11	been	be	AUX
cana-1393	13	12	developed	develop	VERB
cana-1393	13	13	by	by	ADP
cana-1393	13	14	many	many	ADJ
cana-1393	13	15	authors[2,3,4,5,6,7,8,9].in	authors[2,3,4,5,6,7,8,9].in	PROPN
cana-1393	13	16	this	this	DET
cana-1393	13	17	process	process	NOUN
cana-1393	13	18	afrah	afrah	PROPN
cana-1393	13	19	a.	a.	PROPN
cana-1393	13	20	n.	n.	PROPN
cana-1393	13	21	abdou	abdou	PROPN
cana-1393	14	1	[	[	X
cana-1393	14	2	1	1	NUM
cana-1393	14	3	]	]	X
cana-1393	14	4	poved	pove	VERB
cana-1393	14	5	a	a	DET
cana-1393	14	6	theorem	theorem	NOUN
cana-1393	14	7	in	in	ADP
cana-1393	14	8	mms	mms	NOUN
cana-1393	14	9	in	in	ADP
cana-1393	14	10	2016.the	2016.the	DET
cana-1393	14	11	purpose	purpose	NOUN
cana-1393	14	12	of	of	ADP
cana-1393	14	13	this	this	DET
cana-1393	14	14	paper	paper	NOUN
cana-1393	14	15	is	be	AUX
cana-1393	14	16	to	to	PART
cana-1393	14	17	prove	prove	VERB
cana-1393	14	18	two	two	NUM
cana-1393	14	19	common	common	ADJ
cana-1393	14	20	fixed	fix	VERB
cana-1393	14	21	point	point	NOUN
cana-1393	14	22	theorems	theorem	NOUN
cana-1393	14	23	on	on	ADP
cana-1393	14	24	mms	mms	NOUN
cana-1393	14	25	utilizing	utilize	VERB
cana-1393	14	26	the	the	DET
cana-1393	14	27	concept	concept	NOUN
cana-1393	14	28	like	like	ADP
cana-1393	14	29	semi	semi	ADJ
cana-1393	14	30	-	-	ADJ
cana-1393	14	31	compatible	compatible	ADJ
cana-1393	14	32	mapping	mapping	NOUN
cana-1393	14	33	,	,	PUNCT
cana-1393	14	34	wcm	wcm	NOUN
cana-1393	14	35	,	,	PUNCT
cana-1393	14	36	reciprocally	reciprocally	ADV
cana-1393	14	37	continuous	continuous	ADJ
cana-1393	14	38	mappings	mapping	NOUN
cana-1393	14	39	,	,	PUNCT
cana-1393	14	40	strongly	strongly	ADV
cana-1393	14	41	semi	semi	ADJ
cana-1393	14	42	compatible	compatible	ADJ
cana-1393	14	43	mappings	mapping	NOUN
cana-1393	14	44	,	,	PUNCT
cana-1393	14	45	conditionally	conditionally	ADV
cana-1393	14	46	reciprocally	reciprocally	VERB
cana-1393	14	47	continuous	continuous	ADJ
cana-1393	14	48	mappings	mapping	NOUN
cana-1393	14	49	and	and	CCONJ
cana-1393	14	50	and	and	CCONJ
cana-1393	14	51	owc	owc	NUM
cana-1393	14	52	mappings	mapping	NOUN
cana-1393	14	53	.	.	PUNCT
cana-1393	15	1	additionally	additionally	ADV
cana-1393	15	2	we	we	PRON
cana-1393	15	3	provided	provide	VERB
cana-1393	15	4	three	three	NUM
cana-1393	15	5	examples	example	NOUN
cana-1393	15	6	to	to	PART
cana-1393	15	7	validate	validate	VERB
cana-1393	15	8	our	our	PRON
cana-1393	15	9	results	result	NOUN
cana-1393	15	10	.	.	PUNCT
cana-1393	16	1	we	we	PRON
cana-1393	16	2	first	first	ADV
cana-1393	16	3	provide	provide	VERB
cana-1393	16	4	some	some	DET
cana-1393	16	5	helpful	helpful	ADJ
cana-1393	16	6	definitions	definition	NOUN
cana-1393	16	7	and	and	CCONJ
cana-1393	16	8	examples	example	NOUN
cana-1393	16	9	before	before	ADP
cana-1393	16	10	presenting	present	VERB
cana-1393	16	11	our	our	PRON
cana-1393	16	12	findings	finding	NOUN
cana-1393	16	13	.	.	PUNCT
cana-1393	17	1	preliminaries	preliminary	NOUN
cana-1393	17	2	mailto:chiranjeeviperala@gmail.com	mailto:chiranjeeviperala@gmail.com	NOUN
cana-1393	17	3	communications	communication	NOUN
cana-1393	17	4	on	on	ADP
cana-1393	17	5	applied	apply	VERB
cana-1393	17	6	nonlinear	nonlinear	ADJ
cana-1393	17	7	analysis	analysis	NOUN
cana-1393	17	8	issn	issn	NOUN
cana-1393	17	9	:	:	PUNCT
cana-1393	17	10	1074	1074	NUM
cana-1393	17	11	-	-	PUNCT
cana-1393	17	12	133x	133x	NUM
cana-1393	17	13	vol	vol	NOUN
cana-1393	17	14	31	31	NUM
cana-1393	17	15	no	no	NOUN
cana-1393	17	16	.	.	PUNCT
cana-1393	18	1	7s	7	NOUN
cana-1393	18	2	(	(	PUNCT
cana-1393	18	3	2024	2024	NUM
cana-1393	18	4	)	)	PUNCT
cana-1393	18	5	507	507	NUM
cana-1393	18	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1393	18	7	definition	definition	NOUN
cana-1393	18	8	2.1	2.1	NUM
cana-1393	18	9	let	let	VERB
cana-1393	18	10	set	set	VERB
cana-1393	18	11	and	and	CCONJ
cana-1393	18	12	then	then	ADV
cana-1393	18	13	is	be	AUX
cana-1393	18	14	said	say	VERB
cana-1393	18	15	to	to	PART
cana-1393	18	16	be	be	AUX
cana-1393	18	17	mms	mms	ADJ
cana-1393	18	18	if	if	SCONJ
cana-1393	18	19	it	it	PRON
cana-1393	18	20	meets	meet	VERB
cana-1393	18	21	the	the	DET
cana-1393	18	22	requirements	requirement	NOUN
cana-1393	18	23	as	as	ADP
cana-1393	18	24	below	below	ADV
cana-1393	18	25	:	:	PUNCT
cana-1393	18	26	(	(	PUNCT
cana-1393	18	27	i	i	NOUN
cana-1393	18	28	)	)	PUNCT
cana-1393	18	29	for	for	ADP
cana-1393	18	30	all	all	PRON
cana-1393	18	31	and	and	CCONJ
cana-1393	18	32	(	(	PUNCT
cana-1393	18	33	ii	ii	NOUN
cana-1393	18	34	)	)	PUNCT
cana-1393	18	35	for	for	ADP
cana-1393	18	36	all	all	DET
cana-1393	18	37	(	(	PUNCT
cana-1393	18	38	iii	iii	NOUN
cana-1393	18	39	)	)	PUNCT
cana-1393	18	40	for	for	ADP
cana-1393	18	41	all	all	PRON
cana-1393	18	42	(	(	PUNCT
cana-1393	18	43	multiplicative	multiplicative	ADJ
cana-1393	18	44	triangle	triangle	NOUN
cana-1393	18	45	inequality	inequality	NOUN
cana-1393	18	46	)	)	PUNCT
cana-1393	18	47	definition	definition	NOUN
cana-1393	18	48	2.2	2.2	NUM
cana-1393	18	49	a	a	DET
cana-1393	18	50	sequence	sequence	NOUN
cana-1393	18	51	{	{	PUNCT
cana-1393	18	52	}	}	PUNCT
cana-1393	18	53	in	in	ADP
cana-1393	18	54	a	a	DET
cana-1393	18	55	mms	mms	NOUN
cana-1393	18	56	is	be	AUX
cana-1393	18	57	said	say	VERB
cana-1393	18	58	to	to	PART
cana-1393	18	59	be	be	AUX
cana-1393	18	60	(	(	PUNCT
cana-1393	18	61	i	i	NOUN
cana-1393	18	62	)	)	PUNCT
cana-1393	18	63	multiplicative	multiplicative	ADJ
cana-1393	18	64	convergent	convergent	NOUN
cana-1393	18	65	sequence	sequence	NOUN
cana-1393	18	66	to	to	PART
cana-1393	18	67	if	if	SCONJ
cana-1393	18	68	for	for	ADP
cana-1393	18	69	every	every	DET
cana-1393	18	70	multiplicative	multiplicative	ADJ
cana-1393	18	71	open	open	ADJ
cana-1393	18	72	ball	ball	NOUN
cana-1393	18	73	।	।	PROPN
cana-1393	18	74	,	,	PUNCT
cana-1393	18	75	thereexists	thereexist	VERB
cana-1393	18	76	a	a	DET
cana-1393	18	77	positive	positive	ADJ
cana-1393	18	78	integer	integer	NOUN
cana-1393	18	79	such	such	ADJ
cana-1393	18	80	that	that	PRON
cana-1393	18	81	for	for	ADP
cana-1393	18	82	all	all	DET
cana-1393	18	83	i.e	i.e	ADJ
cana-1393	18	84	(	(	PUNCT
cana-1393	18	85	)	)	PUNCT
cana-1393	18	86	as	as	ADP
cana-1393	18	87	.	.	PUNCT
cana-1393	19	1	(	(	PUNCT
cana-1393	19	2	ii	ii	NOUN
cana-1393	19	3	)	)	PUNCT
cana-1393	19	4	multiplicative	multiplicative	ADJ
cana-1393	19	5	cauchy	cauchy	NOUN
cana-1393	19	6	sequence	sequence	NOUN
cana-1393	19	7	if	if	SCONJ
cana-1393	19	8	for	for	ADP
cana-1393	19	9	all	all	PRON
cana-1393	19	10	such	such	ADJ
cana-1393	19	11	that	that	PRON
cana-1393	19	12	(	(	PUNCT
cana-1393	19	13	)	)	PUNCT
cana-1393	19	14	for	for	ADP
cana-1393	19	15	all	all	DET
cana-1393	19	16	i.e	i.e	ADJ
cana-1393	19	17	(	(	PUNCT
cana-1393	19	18	)	)	PUNCT
cana-1393	19	19	as	as	ADP
cana-1393	19	20	.	.	PUNCT
cana-1393	20	1	definition	definition	NOUN
cana-1393	20	2	2.3	2.3	NUM
cana-1393	20	3	the	the	DET
cana-1393	20	4	pair	pair	NOUN
cana-1393	20	5	of	of	ADP
cana-1393	20	6	mapping	mapping	NOUN
cana-1393	20	7	of	of	ADP
cana-1393	20	8	a	a	PRON
cana-1393	20	9	is	be	AUX
cana-1393	20	10	said	say	VERB
cana-1393	20	11	to	to	PART
cana-1393	20	12	be	be	AUX
cana-1393	20	13	(	(	PUNCT
cana-1393	20	14	i	i	NOUN
cana-1393	20	15	)	)	PUNCT
cana-1393	20	16	compatible	compatible	ADJ
cana-1393	20	17	if	if	SCONJ
cana-1393	20	18	(	(	PUNCT
cana-1393	20	19	)	)	PUNCT
cana-1393	20	20	,	,	PUNCT
cana-1393	20	21	whenever	whenever	SCONJ
cana-1393	20	22	a	a	DET
cana-1393	20	23	sequence	sequence	NOUN
cana-1393	20	24	{	{	PUNCT
cana-1393	20	25	}	}	PUNCT
cana-1393	20	26	in	in	ADP
cana-1393	20	27	like	like	ADP
cana-1393	20	28	that	that	PRON
cana-1393	20	29	for	for	ADP
cana-1393	20	30	some	some	PRON
cana-1393	20	31	.	.	PUNCT
cana-1393	21	1	(	(	PUNCT
cana-1393	21	2	ii	ii	NOUN
cana-1393	21	3	)	)	PUNCT
cana-1393	21	4	weakly	weakly	ADV
cana-1393	21	5	compatible	compatible	ADJ
cana-1393	21	6	if	if	SCONJ
cana-1393	21	7	for	for	ADP
cana-1393	21	8	some	some	DET
cana-1393	21	9	such	such	ADJ
cana-1393	21	10	that	that	PRON
cana-1393	21	11	.	.	PUNCT
cana-1393	22	1	(	(	PUNCT
cana-1393	22	2	iii	iii	NOUN
cana-1393	22	3	)	)	PUNCT
cana-1393	22	4	occasionally	occasionally	ADV
cana-1393	22	5	weakly	weakly	ADV
cana-1393	22	6	compatible	compatible	ADJ
cana-1393	22	7	if	if	SCONJ
cana-1393	22	8	for	for	ADP
cana-1393	22	9	such	such	ADJ
cana-1393	22	10	that	that	PRON
cana-1393	22	11	implies	imply	VERB
cana-1393	22	12	that	that	SCONJ
cana-1393	22	13	(	(	PUNCT
cana-1393	22	14	iii	iii	NOUN
cana-1393	22	15	)	)	PUNCT
cana-1393	22	16	reciprocally	reciprocally	ADV
cana-1393	22	17	continuous	continuous	ADJ
cana-1393	22	18	if	if	SCONJ
cana-1393	22	19	(	(	PUNCT
cana-1393	22	20	)	)	PUNCT
cana-1393	22	21	(	(	PUNCT
cana-1393	22	22	)	)	PUNCT
cana-1393	22	23	for	for	ADP
cana-1393	22	24	a	a	DET
cana-1393	22	25	sequence	sequence	NOUN
cana-1393	22	26	{	{	PUNCT
cana-1393	22	27	}	}	PUNCT
cana-1393	22	28	in	in	ADP
cana-1393	22	29	such	such	ADJ
cana-1393	22	30	that	that	PRON
cana-1393	22	31	for	for	SCONJ
cana-1393	22	32	some	some	DET
cana-1393	22	33	(	(	PUNCT
cana-1393	22	34	iv	iv	NOUN
cana-1393	22	35	)	)	PUNCT
cana-1393	22	36	semi	semi	ADV
cana-1393	22	37	compatible	compatible	ADJ
cana-1393	22	38	if	if	SCONJ
cana-1393	22	39	(	(	PUNCT
cana-1393	22	40	)	)	PUNCT
cana-1393	22	41	whenever	whenever	SCONJ
cana-1393	22	42	{	{	PUNCT
cana-1393	22	43	}	}	PUNCT
cana-1393	22	44	is	be	AUX
cana-1393	22	45	a	a	DET
cana-1393	22	46	sequence	sequence	NOUN
cana-1393	22	47	in	in	ADP
cana-1393	22	48	such	such	ADJ
cana-1393	22	49	that	that	PRON
cana-1393	22	50	for	for	SCONJ
cana-1393	22	51	some	some	DET
cana-1393	22	52	(	(	PUNCT
cana-1393	22	53	v	v	NOUN
cana-1393	22	54	)	)	PUNCT
cana-1393	22	55	conditionally	conditionally	ADV
cana-1393	22	56	semi	semi	ADV
cana-1393	22	57	compatible	compatible	ADJ
cana-1393	22	58	if	if	SCONJ
cana-1393	22	59	a	a	DET
cana-1393	22	60	sequence	sequence	NOUN
cana-1393	22	61	{	{	PUNCT
cana-1393	22	62	}	}	PUNCT
cana-1393	22	63	is	be	AUX
cana-1393	22	64	a	a	DET
cana-1393	22	65	sequence	sequence	NOUN
cana-1393	22	66	in	in	ADP
cana-1393	22	67	such	such	ADJ
cana-1393	22	68	that	that	PRON
cana-1393	22	69	is	be	AUX
cana-1393	22	70	non	non	X
cana-1393	22	71	empty	empty	ADJ
cana-1393	22	72	for	for	ADP
cana-1393	22	73	a	a	DET
cana-1393	22	74	sequence	sequence	NOUN
cana-1393	22	75	{	{	PUNCT
cana-1393	22	76	}	}	PUNCT
cana-1393	22	77	satisfying	satisfy	VERB
cana-1393	22	78	for	for	ADP
cana-1393	22	79	some	some	PRON
cana-1393	22	80	then	then	ADV
cana-1393	22	81	(	(	PUNCT
cana-1393	22	82	)	)	PUNCT
cana-1393	22	83	and	and	CCONJ
cana-1393	22	84	(	(	PUNCT
cana-1393	22	85	)	)	PUNCT
cana-1393	22	86	.	.	PUNCT
cana-1393	23	1	(	(	PUNCT
cana-1393	23	2	vi	vi	NOUN
cana-1393	23	3	)	)	PUNCT
cana-1393	23	4	strongly	strongly	ADV
cana-1393	23	5	semi	semi	ADJ
cana-1393	23	6	-	-	ADJ
cana-1393	23	7	compatible	compatible	ADJ
cana-1393	23	8	mappings	mapping	NOUN
cana-1393	23	9	if	if	SCONJ
cana-1393	23	10	they	they	PRON
cana-1393	23	11	satisfy	satisfy	VERB
cana-1393	23	12	owc	owc	PROPN
cana-1393	23	13	and	and	CCONJ
cana-1393	23	14	conditionally	conditionally	ADV
cana-1393	23	15	semi	semi	ADJ
cana-1393	23	16	-	-	ADJ
cana-1393	23	17	compatible	compatible	ADJ
cana-1393	23	18	property	property	NOUN
cana-1393	23	19	.	.	PUNCT
cana-1393	24	1	(	(	PUNCT
cana-1393	24	2	vii	vii	PROPN
cana-1393	24	3	)	)	PUNCT
cana-1393	24	4	conditionally	conditionally	ADV
cana-1393	24	5	reciprocally	reciprocally	ADV
cana-1393	24	6	continuous	continuous	ADJ
cana-1393	24	7	if	if	SCONJ
cana-1393	24	8	and	and	CCONJ
cana-1393	24	9	only	only	ADV
cana-1393	24	10	if	if	SCONJ
cana-1393	24	11	(	(	PUNCT
cana-1393	24	12	)	)	PUNCT
cana-1393	24	13	(	(	PUNCT
cana-1393	24	14	)	)	PUNCT
cana-1393	24	15	whenever	whenever	SCONJ
cana-1393	24	16	a	a	DET
cana-1393	24	17	sequence	sequence	NOUN
cana-1393	24	18	{	{	PUNCT
cana-1393	24	19	}	}	PUNCT
cana-1393	24	20	satisfying	satisfy	VERB
cana-1393	24	21	is	be	AUX
cana-1393	24	22	non	non	ADJ
cana-1393	24	23	-	-	ADJ
cana-1393	24	24	empty	empty	ADJ
cana-1393	24	25	there	there	PRON
cana-1393	24	26	exists	exist	VERB
cana-1393	24	27	another	another	DET
cana-1393	24	28	sequence	sequence	NOUN
cana-1393	24	29	{	{	PUNCT
cana-1393	24	30	}	}	PUNCT
cana-1393	24	31	satisfying	satisfy	VERB
cana-1393	24	32	=	=	PUNCT
cana-1393	24	33	as	as	SCONJ
cana-1393	24	34	now	now	ADV
cana-1393	24	35	we	we	PRON
cana-1393	24	36	present	present	VERB
cana-1393	24	37	the	the	DET
cana-1393	24	38	example	example	NOUN
cana-1393	24	39	for	for	ADP
cana-1393	24	40	strongly	strongly	ADV
cana-1393	24	41	semi	semi	ADJ
cana-1393	24	42	-	-	ADJ
cana-1393	24	43	compatible	compatible	ADJ
cana-1393	24	44	mappings	mapping	NOUN
cana-1393	24	45	and	and	CCONJ
cana-1393	24	46	conditionally	conditionally	ADV
cana-1393	24	47	reciprocally	reciprocally	VERB
cana-1393	24	48	continuous	continuous	ADJ
cana-1393	24	49	mappings	mapping	NOUN
cana-1393	24	50	.	.	PUNCT
cana-1393	24	51	example	example	NOUN
cana-1393	24	52	2.1	2.1	NUM
cana-1393	25	1	:	:	PUNCT
cana-1393	25	2	let	let	VERB
cana-1393	25	3	[	[	PUNCT
cana-1393	25	4	]	]	X
cana-1393	25	5	and	and	CCONJ
cana-1393	25	6	[	[	PUNCT
cana-1393	25	7	be	be	AUX
cana-1393	25	8	defined	define	VERB
cana-1393	25	9	as	as	ADP
cana-1393	25	10	|	|	ADV
cana-1393	25	11	|	|	ADV
cana-1393	25	12	then	then	ADV
cana-1393	25	13	is	be	AUX
cana-1393	25	14	a	a	DET
cana-1393	25	15	mms	mms	NOUN
cana-1393	25	16	.	.	PUNCT
cana-1393	26	1	communications	communication	NOUN
cana-1393	26	2	on	on	ADP
cana-1393	26	3	applied	apply	VERB
cana-1393	26	4	nonlinear	nonlinear	ADJ
cana-1393	26	5	analysis	analysis	NOUN
cana-1393	26	6	issn	issn	NOUN
cana-1393	26	7	:	:	PUNCT
cana-1393	26	8	1074	1074	NUM
cana-1393	26	9	-	-	PUNCT
cana-1393	26	10	133x	133x	NUM
cana-1393	26	11	vol	vol	NOUN
cana-1393	26	12	31	31	NUM
cana-1393	26	13	no	no	NOUN
cana-1393	26	14	.	.	PUNCT
cana-1393	27	1	7s	7	NOUN
cana-1393	27	2	(	(	PUNCT
cana-1393	27	3	2024	2024	NUM
cana-1393	27	4	)	)	PUNCT
cana-1393	27	5	508	508	NUM
cana-1393	27	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1393	27	7	define	define	VERB
cana-1393	27	8	the	the	DET
cana-1393	27	9	self	self	NOUN
cana-1393	27	10	-	-	PUNCT
cana-1393	27	11	mappings	mapping	NOUN
cana-1393	27	12	and	and	CCONJ
cana-1393	27	13	as	as	SCONJ
cana-1393	27	14	{	{	PUNCT
cana-1393	27	15	{	{	PUNCT
cana-1393	27	16	consider	consider	VERB
cana-1393	27	17	a	a	DET
cana-1393	27	18	sequence	sequence	NOUN
cana-1393	27	19	given	give	VERB
cana-1393	27	20	by	by	ADP
cana-1393	27	21	for	for	ADP
cana-1393	27	22	(	(	PUNCT
cana-1393	27	23	)	)	PUNCT
cana-1393	27	24	[	[	PUNCT
cana-1393	27	25	(	(	PUNCT
cana-1393	27	26	)	)	PUNCT
cana-1393	27	27	]	]	PUNCT
cana-1393	27	28	and	and	CCONJ
cana-1393	27	29	(	(	PUNCT
cana-1393	27	30	)	)	PUNCT
cana-1393	27	31	.	.	PUNCT
cana-1393	28	1	therefore	therefore	ADV
cana-1393	28	2	is	be	AUX
cana-1393	28	3	non	non	ADJ
cana-1393	28	4	-	-	ADJ
cana-1393	28	5	empty	empty	ADJ
cana-1393	28	6	.	.	PUNCT
cana-1393	29	1	consider	consider	VERB
cana-1393	29	2	another	another	DET
cana-1393	29	3	sequence	sequence	NOUN
cana-1393	29	4	given	give	VERB
cana-1393	29	5	by	by	ADP
cana-1393	29	6	for	for	ADP
cana-1393	29	7	(	(	PUNCT
cana-1393	29	8	)	)	PUNCT
cana-1393	29	9	0	0	NUM
cana-1393	29	10	(	(	PUNCT
cana-1393	29	11	)	)	PUNCT
cana-1393	29	12	1	1	NUM
cana-1393	29	13	and	and	CCONJ
cana-1393	29	14	(	(	PUNCT
cana-1393	29	15	)	)	PUNCT
cana-1393	29	16	*	*	PUNCT
cana-1393	30	1	+	+	CCONJ
cana-1393	30	2	.	.	PUNCT
cana-1393	31	1	therefore	therefore	ADV
cana-1393	31	2	(	(	PUNCT
cana-1393	31	3	say	say	INTJ
cana-1393	31	4	)	)	PUNCT
cana-1393	31	5	.	.	PUNCT
cana-1393	32	1	this	this	PRON
cana-1393	32	2	gives	give	VERB
cana-1393	32	3	and	and	CCONJ
cana-1393	32	4	.	.	PUNCT
cana-1393	33	1	further	far	ADV
cana-1393	33	2	(	(	PUNCT
cana-1393	33	3	)	)	PUNCT
cana-1393	33	4	*	*	PUNCT
cana-1393	34	1	+	+	PUNCT
cana-1393	34	2	[	[	PUNCT
cana-1393	34	3	(	(	PUNCT
cana-1393	34	4	)	)	PUNCT
cana-1393	34	5	]	]	PUNCT
cana-1393	34	6	and	and	CCONJ
cana-1393	34	7	(	(	PUNCT
cana-1393	34	8	*	*	PUNCT
cana-1393	34	9	[	[	PUNCT
cana-1393	34	10	(	(	PUNCT
cana-1393	34	11	)	)	PUNCT
cana-1393	34	12	]	]	PUNCT
cana-1393	35	1	[	[	PUNCT
cana-1393	35	2	]	]	X
cana-1393	35	3	therefore	therefore	ADV
cana-1393	35	4	and	and	CCONJ
cana-1393	35	5	.	.	PUNCT
cana-1393	36	1	this	this	PRON
cana-1393	36	2	shows	show	VERB
cana-1393	36	3	that	that	SCONJ
cana-1393	36	4	the	the	DET
cana-1393	36	5	couple	couple	NOUN
cana-1393	36	6	is	be	AUX
cana-1393	36	7	conditionally	conditionally	ADV
cana-1393	36	8	semi	semi	ADJ
cana-1393	36	9	-	-	ADJ
cana-1393	36	10	compatible	compatible	ADJ
cana-1393	36	11	in	in	ADP
cana-1393	36	12	mms	mms	NOUN
cana-1393	36	13	.	.	PUNCT
cana-1393	37	1	now	now	ADV
cana-1393	37	2	and	and	CCONJ
cana-1393	37	3	,	,	PUNCT
cana-1393	37	4	showing	show	VERB
cana-1393	37	5	that	that	SCONJ
cana-1393	37	6	1,2	1,2	NUM
cana-1393	37	7	are	be	AUX
cana-1393	37	8	coincidence	coincidence	NOUN
cana-1393	37	9	points	point	NOUN
cana-1393	37	10	.	.	PUNCT
cana-1393	38	1	then	then	ADV
cana-1393	38	2	implies	imply	VERB
cana-1393	38	3	(	(	PUNCT
cana-1393	38	4	)	)	PUNCT
cana-1393	38	5	and	and	CCONJ
cana-1393	38	6	implies	imply	VERB
cana-1393	38	7	(	(	PUNCT
cana-1393	38	8	)	)	PUNCT
cana-1393	38	9	.	.	PUNCT
cana-1393	39	1	as	as	ADP
cana-1393	39	2	a	a	DET
cana-1393	39	3	result	result	NOUN
cana-1393	39	4	,	,	PUNCT
cana-1393	39	5	the	the	DET
cana-1393	39	6	two	two	NUM
cana-1393	39	7	self	self	NOUN
cana-1393	39	8	maps	map	NOUN
cana-1393	39	9	and	and	CCONJ
cana-1393	39	10	are	be	AUX
cana-1393	39	11	owc	owc	PROPN
cana-1393	39	12	.	.	PUNCT
cana-1393	40	1	therefore	therefore	ADV
cana-1393	40	2	the	the	DET
cana-1393	40	3	self	self	NOUN
cana-1393	40	4	maps	map	NOUN
cana-1393	40	5	and	and	CCONJ
cana-1393	40	6	are	be	AUX
cana-1393	40	7	strongly	strongly	ADV
cana-1393	40	8	semi	semi	ADJ
cana-1393	40	9	-	-	ADJ
cana-1393	40	10	compatible	compatible	ADJ
cana-1393	40	11	mappings	mapping	NOUN
cana-1393	40	12	in	in	ADP
cana-1393	40	13	mms	mms	NOUN
cana-1393	40	14	.	.	PUNCT
cana-1393	40	15	example	example	NOUN
cana-1393	40	16	2.2	2.2	NUM
cana-1393	40	17	:	:	PUNCT
cana-1393	40	18	let	let	VERB
cana-1393	40	19	[	[	PUNCT
cana-1393	40	20	]	]	X
cana-1393	40	21	and	and	CCONJ
cana-1393	40	22	[	[	PUNCT
cana-1393	40	23	be	be	AUX
cana-1393	40	24	defined	define	VERB
cana-1393	40	25	as	as	ADP
cana-1393	40	26	|	|	ADV
cana-1393	40	27	|	|	ADV
cana-1393	40	28	then	then	ADV
cana-1393	40	29	is	be	AUX
cana-1393	40	30	a	a	DET
cana-1393	40	31	mms	mms	NOUN
cana-1393	40	32	.	.	PUNCT
cana-1393	41	1	define	define	VERB
cana-1393	41	2	the	the	DET
cana-1393	41	3	self	self	NOUN
cana-1393	41	4	-	-	PUNCT
cana-1393	41	5	mappings	mapping	NOUN
cana-1393	41	6	and	and	CCONJ
cana-1393	41	7	as	as	SCONJ
cana-1393	41	8	2	2	NUM
cana-1393	41	9	{	{	PUNCT
cana-1393	41	10	communications	communication	NOUN
cana-1393	41	11	on	on	ADP
cana-1393	41	12	applied	apply	VERB
cana-1393	41	13	nonlinear	nonlinear	ADJ
cana-1393	41	14	analysis	analysis	NOUN
cana-1393	41	15	issn	issn	NOUN
cana-1393	41	16	:	:	PUNCT
cana-1393	41	17	1074	1074	NUM
cana-1393	41	18	-	-	PUNCT
cana-1393	41	19	133x	133x	NUM
cana-1393	41	20	vol	vol	NOUN
cana-1393	41	21	31	31	NUM
cana-1393	41	22	no	no	NOUN
cana-1393	41	23	.	.	PUNCT
cana-1393	42	1	7s	7	NOUN
cana-1393	42	2	(	(	PUNCT
cana-1393	42	3	2024	2024	NUM
cana-1393	42	4	)	)	PUNCT
cana-1393	42	5	509	509	NUM
cana-1393	42	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1393	42	7	consider	consider	VERB
cana-1393	42	8	a	a	DET
cana-1393	42	9	sequence	sequence	NOUN
cana-1393	42	10	sequences	sequence	NOUN
cana-1393	42	11	,	,	PUNCT
cana-1393	42	12	where	where	SCONJ
cana-1393	42	13	.	.	PUNCT
cana-1393	43	1	(	(	PUNCT
cana-1393	43	2	)	)	PUNCT
cana-1393	43	3	*	*	PUNCT
cana-1393	43	4	(	(	PUNCT
cana-1393	43	5	)	)	PUNCT
cana-1393	43	6	+	+	CCONJ
cana-1393	43	7	and	and	CCONJ
cana-1393	43	8	(	(	PUNCT
cana-1393	43	9	)	)	PUNCT
cana-1393	43	10	*	*	PUNCT
cana-1393	43	11	(	(	PUNCT
cana-1393	43	12	)	)	PUNCT
cana-1393	43	13	+	+	CCONJ
cana-1393	43	14	.	.	PUNCT
cana-1393	44	1	therefore	therefore	ADV
cana-1393	44	2	(	(	PUNCT
cana-1393	44	3	non	non	ADJ
cana-1393	44	4	-	-	ADJ
cana-1393	44	5	empty	empty	ADJ
cana-1393	44	6	)	)	PUNCT
cana-1393	44	7	.	.	PUNCT
cana-1393	45	1	furether	furether	PROPN
cana-1393	45	2	and	and	CCONJ
cana-1393	45	3	.	.	PUNCT
cana-1393	46	1	which	which	PRON
cana-1393	46	2	gives	give	VERB
cana-1393	46	3	.	.	PUNCT
cana-1393	47	1	hence	hence	ADV
cana-1393	47	2	the	the	DET
cana-1393	47	3	couple	couple	NOUN
cana-1393	47	4	is	be	AUX
cana-1393	47	5	not	not	PART
cana-1393	47	6	compatible	compatible	ADJ
cana-1393	47	7	.	.	PUNCT
cana-1393	48	1	consider	consider	VERB
cana-1393	48	2	a	a	DET
cana-1393	48	3	sequence	sequence	NOUN
cana-1393	48	4	sequences	sequence	NOUN
cana-1393	48	5	,	,	PUNCT
cana-1393	48	6	where	where	SCONJ
cana-1393	48	7	.	.	PUNCT
cana-1393	49	1	(	(	PUNCT
cana-1393	49	2	)	)	PUNCT
cana-1393	49	3	[	[	PUNCT
cana-1393	49	4	(	(	PUNCT
cana-1393	49	5	)	)	PUNCT
cana-1393	49	6	]	]	PUNCT
cana-1393	49	7	and	and	CCONJ
cana-1393	49	8	(	(	PUNCT
cana-1393	49	9	)	)	PUNCT
cana-1393	49	10	*	*	PUNCT
cana-1393	50	1	+	+	CCONJ
cana-1393	50	2	.	.	PUNCT
cana-1393	51	1	therefore	therefore	ADV
cana-1393	51	2	(	(	PUNCT
cana-1393	51	3	say	say	INTJ
cana-1393	51	4	)	)	PUNCT
cana-1393	51	5	.	.	PUNCT
cana-1393	52	1	furthermore	furthermore	ADV
cana-1393	52	2	(	(	PUNCT
cana-1393	52	3	)	)	PUNCT
cana-1393	52	4	and	and	CCONJ
cana-1393	52	5	(	(	PUNCT
cana-1393	52	6	)	)	PUNCT
cana-1393	52	7	.	.	PUNCT
cana-1393	53	1	also	also	ADV
cana-1393	53	2	we	we	PRON
cana-1393	53	3	absorve	absorve	VERB
cana-1393	53	4	that	that	SCONJ
cana-1393	53	5	thus	thus	ADV
cana-1393	53	6	but	but	CCONJ
cana-1393	53	7	.	.	PUNCT
cana-1393	54	1	hence	hence	ADV
cana-1393	54	2	two	two	NUM
cana-1393	54	3	self	self	NOUN
cana-1393	54	4	-	-	PUNCT
cana-1393	54	5	maps	map	NOUN
cana-1393	54	6	g	g	NOUN
cana-1393	55	1	and	and	CCONJ
cana-1393	55	2	i	i	PRON
cana-1393	55	3	are	be	AUX
cana-1393	55	4	conditionally	conditionally	ADV
cana-1393	55	5	reciprocally	reciprocally	ADV
cana-1393	55	6	continuous	continuous	ADJ
cana-1393	55	7	in	in	ADP
cana-1393	55	8	mms	mms	NOUN
cana-1393	55	9	.	.	PUNCT
cana-1393	56	1	afrah	afrah	PROPN
cana-1393	56	2	a.n.abdou	a.n.abdou	PROPN
cana-1393	57	1	[	[	X
cana-1393	57	2	1	1	X
cana-1393	57	3	]	]	PUNCT
cana-1393	57	4	established	establish	VERB
cana-1393	57	5	the	the	DET
cana-1393	57	6	following	following	ADJ
cana-1393	57	7	theorem	theorem	NOUN
cana-1393	57	8	in	in	ADP
cana-1393	57	9	mms	mms	PROPN
cana-1393	57	10	.	.	PUNCT
cana-1393	58	1	theorem	theorem	VERB
cana-1393	58	2	2.1	2.1	NUM
cana-1393	58	3	assume	assume	NOUN
cana-1393	58	4	that	that	PRON
cana-1393	58	5	is	be	AUX
cana-1393	58	6	a	a	DET
cana-1393	58	7	complete	complete	ADJ
cana-1393	58	8	mms	mms	NOUN
cana-1393	58	9	and	and	CCONJ
cana-1393	58	10	the	the	DET
cana-1393	58	11	mappings	mapping	NOUN
cana-1393	58	12	and	and	CCONJ
cana-1393	58	13	are	be	AUX
cana-1393	58	14	defined	define	VERB
cana-1393	58	15	on	on	ADP
cana-1393	58	16	such	such	ADJ
cana-1393	58	17	that	that	SCONJ
cana-1393	58	18	(	(	PUNCT
cana-1393	58	19	b1	b1	PROPN
cana-1393	58	20	)	)	PUNCT
cana-1393	58	21	(	(	PUNCT
cana-1393	58	22	b2	b2	NOUN
cana-1393	58	23	)	)	PUNCT
cana-1393	58	24	0	0	PUNCT
cana-1393	58	25	.	.	PUNCT
cana-1393	59	1	2	2	NUM
cana-1393	59	2	3/1	3/1	NUM
cana-1393	59	3	for	for	ADP
cana-1393	59	4	all	all	PRON
cana-1393	59	5	,	,	PUNCT
cana-1393	59	6	where	where	SCONJ
cana-1393	59	7	.	.	PUNCT
cana-1393	60	1	where	where	SCONJ
cana-1393	60	2	[	[	PUNCT
cana-1393	60	3	[	[	PUNCT
cana-1393	60	4	is	be	AUX
cana-1393	60	5	a	a	DET
cana-1393	60	6	continuous	continuous	ADJ
cana-1393	60	7	and	and	CCONJ
cana-1393	60	8	monotone	monotone	ADJ
cana-1393	60	9	increasing	increase	VERB
cana-1393	60	10	function	function	NOUN
cana-1393	60	11	such	such	ADJ
cana-1393	60	12	that	that	PRON
cana-1393	60	13	for	for	ADP
cana-1393	60	14	all	all	DET
cana-1393	60	15	(	(	PUNCT
cana-1393	60	16	b3	b3	PROPN
cana-1393	60	17	)	)	PUNCT
cana-1393	60	18	one	one	NUM
cana-1393	60	19	of	of	ADP
cana-1393	60	20	,	,	PUNCT
cana-1393	60	21	and	and	CCONJ
cana-1393	60	22	is	be	AUX
cana-1393	60	23	continuous	continuous	ADJ
cana-1393	60	24	(	(	PUNCT
cana-1393	60	25	b4	b4	NOUN
cana-1393	60	26	)	)	PUNCT
cana-1393	60	27	both	both	CCONJ
cana-1393	60	28	the	the	DET
cana-1393	60	29	pairs	pair	NOUN
cana-1393	60	30	and	and	CCONJ
cana-1393	60	31	are	be	AUX
cana-1393	60	32	compatible	compatible	ADJ
cana-1393	60	33	.	.	PUNCT
cana-1393	61	1	then	then	ADV
cana-1393	61	2	the	the	DET
cana-1393	61	3	four	four	NUM
cana-1393	61	4	maps	map	NOUN
cana-1393	61	5	and	and	CCONJ
cana-1393	61	6	share	share	VERB
cana-1393	61	7	a	a	DET
cana-1393	61	8	unique	unique	ADJ
cana-1393	61	9	common	common	ADJ
cana-1393	61	10	fixed	fix	VERB
cana-1393	61	11	point	point	NOUN
cana-1393	61	12	in	in	ADV
cana-1393	61	13	.	.	PUNCT
cana-1393	62	1	we	we	PRON
cana-1393	62	2	now	now	ADV
cana-1393	62	3	generalize	generalize	VERB
cana-1393	62	4	theorem	theorem	VERB
cana-1393	62	5	2.1	2.1	NUM
cana-1393	62	6	as	as	ADP
cana-1393	62	7	below	below	ADV
cana-1393	62	8	.	.	PUNCT
cana-1393	63	1	communications	communication	NOUN
cana-1393	63	2	on	on	ADP
cana-1393	63	3	applied	apply	VERB
cana-1393	63	4	nonlinear	nonlinear	ADJ
cana-1393	63	5	analysis	analysis	NOUN
cana-1393	63	6	issn	issn	NOUN
cana-1393	63	7	:	:	PUNCT
cana-1393	63	8	1074	1074	NUM
cana-1393	63	9	-	-	PUNCT
cana-1393	63	10	133x	133x	NUM
cana-1393	63	11	vol	vol	NOUN
cana-1393	63	12	31	31	NUM
cana-1393	63	13	no	no	NOUN
cana-1393	63	14	.	.	PUNCT
cana-1393	64	1	7s	7	NOUN
cana-1393	64	2	(	(	PUNCT
cana-1393	64	3	2024	2024	NUM
cana-1393	64	4	)	)	PUNCT
cana-1393	64	5	510	510	NUM
cana-1393	64	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1393	64	7	now	now	ADV
cana-1393	64	8	we	we	PRON
cana-1393	64	9	proceed	proceed	VERB
cana-1393	64	10	to	to	ADP
cana-1393	64	11	our	our	PRON
cana-1393	64	12	main	main	ADJ
cana-1393	64	13	result	result	NOUN
cana-1393	64	14	.	.	PUNCT
cana-1393	65	1	3	3	X
cana-1393	65	2	.	.	NOUN
cana-1393	65	3	results	result	NOUN
cana-1393	65	4	and	and	CCONJ
cana-1393	65	5	discussion	discussion	NOUN
cana-1393	65	6	3.1	3.1	NUM
cana-1393	65	7	theorem	theorem	NOUN
cana-1393	65	8	:	:	PUNCT
cana-1393	65	9	suppose	suppose	VERB
cana-1393	65	10	that	that	SCONJ
cana-1393	65	11	in	in	ADP
cana-1393	65	12	a	a	DET
cana-1393	65	13	complete	complete	ADJ
cana-1393	65	14	mms	mms	NOUN
cana-1393	65	15	,	,	PUNCT
cana-1393	65	16	the	the	DET
cana-1393	65	17	four	four	NUM
cana-1393	65	18	self	self	NOUN
cana-1393	65	19	-	-	PUNCT
cana-1393	65	20	mappings	mapping	NOUN
cana-1393	65	21	and	and	CCONJ
cana-1393	65	22	meeting	meet	VERB
cana-1393	65	23	the	the	DET
cana-1393	65	24	requirements	requirement	NOUN
cana-1393	65	25	(	(	PUNCT
cana-1393	65	26	c1	c1	PROPN
cana-1393	65	27	)	)	PUNCT
cana-1393	65	28	(	(	PUNCT
cana-1393	65	29	c2	c2	PROPN
cana-1393	65	30	)	)	PUNCT
cana-1393	65	31	0	0	NUM
cana-1393	65	32	.	.	PUNCT
cana-1393	66	1	2	2	NUM
cana-1393	66	2	3/1	3/1	NUM
cana-1393	66	3	for	for	ADP
cana-1393	66	4	all	all	PRON
cana-1393	66	5	,	,	PUNCT
cana-1393	66	6	where	where	SCONJ
cana-1393	66	7	.	.	PUNCT
cana-1393	67	1	where	where	SCONJ
cana-1393	67	2	[	[	PUNCT
cana-1393	67	3	[	[	PUNCT
cana-1393	67	4	is	be	AUX
cana-1393	67	5	a	a	DET
cana-1393	67	6	continuous	continuous	ADJ
cana-1393	67	7	and	and	CCONJ
cana-1393	67	8	monotone	monotone	ADJ
cana-1393	67	9	increasing	increase	VERB
cana-1393	67	10	function	function	NOUN
cana-1393	67	11	such	such	ADJ
cana-1393	67	12	that	that	PRON
cana-1393	67	13	for	for	ADP
cana-1393	67	14	all	all	DET
cana-1393	67	15	(	(	PUNCT
cana-1393	67	16	c3	c3	PROPN
cana-1393	67	17	)	)	PUNCT
cana-1393	67	18	the	the	DET
cana-1393	67	19	pair	pair	NOUN
cana-1393	67	20	is	be	AUX
cana-1393	67	21	reciprocally	reciprocally	ADV
cana-1393	67	22	continuous	continuous	ADJ
cana-1393	67	23	and	and	CCONJ
cana-1393	67	24	semi	semi	ADJ
cana-1393	67	25	-	-	ADJ
cana-1393	67	26	compatible	compatible	ADJ
cana-1393	67	27	(	(	PUNCT
cana-1393	67	28	c4	c4	NOUN
cana-1393	67	29	)	)	PUNCT
cana-1393	67	30	the	the	DET
cana-1393	67	31	pair	pair	NOUN
cana-1393	67	32	is	be	AUX
cana-1393	67	33	weakly	weakly	ADV
cana-1393	67	34	compatible	compatible	ADJ
cana-1393	67	35	mappings	mapping	NOUN
cana-1393	67	36	.	.	PUNCT
cana-1393	68	1	then	then	ADV
cana-1393	68	2	there	there	PRON
cana-1393	68	3	exists	exist	VERB
cana-1393	68	4	a	a	DET
cana-1393	68	5	unique	unique	ADJ
cana-1393	68	6	common	common	ADJ
cana-1393	68	7	fixed	fix	VERB
cana-1393	68	8	point	point	NOUN
cana-1393	68	9	for	for	ADP
cana-1393	68	10	the	the	DET
cana-1393	68	11	above	above	ADJ
cana-1393	68	12	mappings	mapping	NOUN
cana-1393	68	13	.	.	PUNCT
cana-1393	69	1	proof	proof	NOUN
cana-1393	69	2	:	:	PUNCT
cana-1393	69	3	since	since	SCONJ
cana-1393	69	4	by	by	ADV
cana-1393	69	5	,	,	PUNCT
cana-1393	69	6	we	we	PRON
cana-1393	69	7	can	can	AUX
cana-1393	69	8	consider	consider	VERB
cana-1393	69	9	a	a	DET
cana-1393	69	10	point	point	NOUN
cana-1393	69	11	there	there	PRON
cana-1393	69	12	exists	exist	VERB
cana-1393	69	13	such	such	ADJ
cana-1393	69	14	that	that	SCONJ
cana-1393	69	15	at	at	ADP
cana-1393	69	16	this	this	PRON
cana-1393	69	17	a	a	DET
cana-1393	69	18	point	point	NOUN
cana-1393	69	19	in	in	ADP
cana-1393	69	20	and	and	CCONJ
cana-1393	69	21	so	so	ADV
cana-1393	69	22	on	on	ADV
cana-1393	69	23	.	.	PUNCT
cana-1393	70	1	likewise	likewise	ADV
cana-1393	70	2	,	,	PUNCT
cana-1393	70	3	we	we	PRON
cana-1393	70	4	are	be	AUX
cana-1393	70	5	able	able	ADJ
cana-1393	70	6	to	to	PART
cana-1393	70	7	define	define	VERB
cana-1393	70	8	;	;	PUNCT
cana-1393	70	9	for	for	ADP
cana-1393	70	10	now	now	ADV
cana-1393	70	11	it	it	PRON
cana-1393	70	12	is	be	AUX
cana-1393	70	13	possible	possible	ADJ
cana-1393	70	14	to	to	PART
cana-1393	70	15	establish	establish	VERB
cana-1393	70	16	that	that	SCONJ
cana-1393	70	17	th	th	NUM
cana-1393	70	18	e	e	NOUN
cana-1393	70	19	sequence	sequence	NOUN
cana-1393	70	20	{	{	PUNCT
cana-1393	70	21	}	}	PUNCT
cana-1393	70	22	(	(	PUNCT
cana-1393	70	23	)	)	PUNCT
cana-1393	70	24	(	(	PUNCT
cana-1393	70	25	)	)	PUNCT
cana-1393	70	26	0	0	NUM
cana-1393	70	27	.	.	X
cana-1393	71	1	2	2	NUM
cana-1393	71	2	(	(	PUNCT
cana-1393	71	3	)	)	PUNCT
cana-1393	71	4	(	(	PUNCT
cana-1393	71	5	)	)	PUNCT
cana-1393	71	6	(	(	PUNCT
cana-1393	71	7	)	)	PUNCT
cana-1393	71	8	(	(	PUNCT
cana-1393	71	9	)	)	PUNCT
cana-1393	71	10	(	(	PUNCT
cana-1393	71	11	)	)	PUNCT
cana-1393	71	12	(	(	PUNCT
cana-1393	71	13	)	)	PUNCT
cana-1393	71	14	(	(	PUNCT
cana-1393	71	15	)	)	PUNCT
cana-1393	71	16	3/1	3/1	NUM
cana-1393	71	17	[	[	PUNCT
cana-1393	71	18	(	(	PUNCT
cana-1393	71	19	{	{	PUNCT
cana-1393	71	20	(	(	PUNCT
cana-1393	71	21	)	)	PUNCT
cana-1393	71	22	(	(	PUNCT
cana-1393	71	23	)	)	PUNCT
cana-1393	71	24	(	(	PUNCT
cana-1393	71	25	)	)	PUNCT
cana-1393	71	26	}	}	PUNCT
cana-1393	71	27	)	)	PUNCT
cana-1393	71	28	]	]	PUNCT
cana-1393	72	1	[	[	PUNCT
cana-1393	72	2	(	(	PUNCT
cana-1393	72	3	{	{	PUNCT
cana-1393	72	4	(	(	PUNCT
cana-1393	72	5	)	)	PUNCT
cana-1393	72	6	(	(	PUNCT
cana-1393	72	7	)	)	PUNCT
cana-1393	72	8	}	}	PUNCT
cana-1393	72	9	)	)	PUNCT
cana-1393	72	10	]	]	PUNCT
cana-1393	73	1	[	[	PUNCT
cana-1393	73	2	(	(	PUNCT
cana-1393	73	3	)	)	PUNCT
cana-1393	73	4	]	]	PUNCT
cana-1393	73	5	.	.	PUNCT
cana-1393	74	1	[	[	PUNCT
cana-1393	74	2	(	(	PUNCT
cana-1393	74	3	)	)	PUNCT
cana-1393	74	4	]	]	PUNCT
cana-1393	74	5	which	which	PRON
cana-1393	74	6	implies	imply	VERB
cana-1393	74	7	that	that	PRON
cana-1393	74	8	(	(	PUNCT
cana-1393	74	9	)	)	PUNCT
cana-1393	74	10	[	[	PUNCT
cana-1393	74	11	(	(	PUNCT
cana-1393	74	12	)	)	PUNCT
cana-1393	74	13	]	]	PUNCT
cana-1393	75	1	[	[	PUNCT
cana-1393	75	2	(	(	PUNCT
cana-1393	75	3	)	)	PUNCT
cana-1393	75	4	]	]	PUNCT
cana-1393	75	5	where	where	SCONJ
cana-1393	75	6	.	.	PUNCT
cana-1393	75	7	similaly	similaly	PROPN
cana-1393	75	8	,	,	PUNCT
cana-1393	75	9	we	we	PRON
cana-1393	75	10	have	have	AUX
cana-1393	75	11	(	(	PUNCT
cana-1393	75	12	)	)	PUNCT
cana-1393	75	13	(	(	PUNCT
cana-1393	75	14	)	)	PUNCT
cana-1393	75	15	communications	communication	NOUN
cana-1393	75	16	on	on	ADP
cana-1393	75	17	applied	apply	VERB
cana-1393	75	18	nonlinear	nonlinear	ADJ
cana-1393	75	19	analysis	analysis	NOUN
cana-1393	75	20	issn	issn	NOUN
cana-1393	75	21	:	:	PUNCT
cana-1393	75	22	1074	1074	NUM
cana-1393	75	23	-	-	PUNCT
cana-1393	75	24	133x	133x	NUM
cana-1393	75	25	vol	vol	NOUN
cana-1393	75	26	31	31	NUM
cana-1393	75	27	no	no	NOUN
cana-1393	75	28	.	.	PUNCT
cana-1393	76	1	7s	7	NOUN
cana-1393	76	2	(	(	PUNCT
cana-1393	76	3	2024	2024	NUM
cana-1393	76	4	)	)	PUNCT
cana-1393	76	5	511	511	NUM
cana-1393	76	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1393	76	7	0	0	PUNCT
cana-1393	76	8	.	.	SYM
cana-1393	76	9	2	2	NUM
cana-1393	76	10	(	(	PUNCT
cana-1393	76	11	)	)	PUNCT
cana-1393	76	12	(	(	PUNCT
cana-1393	76	13	)	)	PUNCT
cana-1393	76	14	(	(	PUNCT
cana-1393	76	15	)	)	PUNCT
cana-1393	76	16	(	(	PUNCT
cana-1393	76	17	)	)	PUNCT
cana-1393	76	18	(	(	PUNCT
cana-1393	76	19	)	)	PUNCT
cana-1393	76	20	(	(	PUNCT
cana-1393	76	21	)	)	PUNCT
cana-1393	76	22	(	(	PUNCT
cana-1393	76	23	)	)	PUNCT
cana-1393	76	24	3/1	3/1	NUM
cana-1393	76	25	[	[	PUNCT
cana-1393	76	26	(	(	PUNCT
cana-1393	76	27	{	{	PUNCT
cana-1393	76	28	(	(	PUNCT
cana-1393	76	29	)	)	PUNCT
cana-1393	76	30	(	(	PUNCT
cana-1393	76	31	)	)	PUNCT
cana-1393	76	32	(	(	PUNCT
cana-1393	76	33	)	)	PUNCT
cana-1393	76	34	}	}	PUNCT
cana-1393	76	35	)	)	PUNCT
cana-1393	76	36	]	]	PUNCT
cana-1393	77	1	[	[	PUNCT
cana-1393	77	2	(	(	PUNCT
cana-1393	77	3	{	{	PUNCT
cana-1393	77	4	(	(	PUNCT
cana-1393	77	5	)	)	PUNCT
cana-1393	77	6	(	(	PUNCT
cana-1393	77	7	)	)	PUNCT
cana-1393	77	8	}	}	PUNCT
cana-1393	77	9	)	)	PUNCT
cana-1393	77	10	]	]	PUNCT
cana-1393	78	1	[	[	PUNCT
cana-1393	78	2	(	(	PUNCT
cana-1393	78	3	)	)	PUNCT
cana-1393	78	4	]	]	PUNCT
cana-1393	78	5	.	.	PUNCT
cana-1393	79	1	[	[	PUNCT
cana-1393	79	2	(	(	PUNCT
cana-1393	79	3	)	)	PUNCT
cana-1393	79	4	]	]	PUNCT
cana-1393	79	5	which	which	PRON
cana-1393	79	6	implies	imply	VERB
cana-1393	79	7	that	that	PRON
cana-1393	79	8	(	(	PUNCT
cana-1393	79	9	)	)	PUNCT
cana-1393	79	10	[	[	PUNCT
cana-1393	79	11	(	(	PUNCT
cana-1393	79	12	)	)	PUNCT
cana-1393	79	13	]	]	PUNCT
cana-1393	79	14	[	[	PUNCT
cana-1393	79	15	(	(	PUNCT
cana-1393	79	16	)	)	PUNCT
cana-1393	79	17	]	]	PUNCT
cana-1393	79	18	thus	thus	ADV
cana-1393	79	19	it	it	PRON
cana-1393	79	20	follows	follow	VERB
cana-1393	79	21	that	that	SCONJ
cana-1393	79	22	,	,	PUNCT
cana-1393	79	23	for	for	ADP
cana-1393	79	24	all	all	PRON
cana-1393	79	25	(	(	PUNCT
cana-1393	79	26	)	)	PUNCT
cana-1393	79	27	[	[	PUNCT
cana-1393	79	28	(	(	PUNCT
cana-1393	79	29	)	)	PUNCT
cana-1393	79	30	]	]	PUNCT
cana-1393	79	31	[	[	PUNCT
cana-1393	79	32	(	(	PUNCT
cana-1393	79	33	)	)	PUNCT
cana-1393	79	34	]	]	PUNCT
cana-1393	79	35	[	[	PUNCT
cana-1393	79	36	]	]	X
cana-1393	79	37	therefore	therefore	ADV
cana-1393	79	38	,	,	PUNCT
cana-1393	79	39	with	with	ADP
cana-1393	79	40	,	,	PUNCT
cana-1393	79	41	by	by	ADP
cana-1393	79	42	the	the	DET
cana-1393	79	43	multiplicative	multiplicative	ADJ
cana-1393	79	44	triangle	triangle	NOUN
cana-1393	79	45	inequality	inequality	NOUN
cana-1393	79	46	,	,	PUNCT
cana-1393	79	47	we	we	PRON
cana-1393	79	48	obtain	obtain	VERB
cana-1393	79	49	(	(	PUNCT
cana-1393	79	50	)	)	PUNCT
cana-1393	79	51	(	(	PUNCT
cana-1393	79	52	)	)	PUNCT
cana-1393	79	53	(	(	PUNCT
cana-1393	79	54	)	)	PUNCT
cana-1393	80	1	[	[	PUNCT
cana-1393	80	2	]	]	X
cana-1393	80	3	[	[	PUNCT
cana-1393	80	4	]	]	X
cana-1393	80	5	[	[	PUNCT
cana-1393	80	6	]	]	X
cana-1393	80	7	[	[	X
cana-1393	80	8	]	]	X
cana-1393	80	9	.	.	PUNCT
cana-1393	81	1	which	which	PRON
cana-1393	81	2	means	mean	VERB
cana-1393	81	3	that	that	SCONJ
cana-1393	81	4	(	(	PUNCT
cana-1393	81	5	)	)	PUNCT
cana-1393	81	6	as	as	ADP
cana-1393	81	7	.	.	PUNCT
cana-1393	82	1	hence	hence	ADV
cana-1393	82	2	{	{	PUNCT
cana-1393	82	3	}	}	PUNCT
cana-1393	82	4	is	be	AUX
cana-1393	82	5	multiplicative	multiplicative	ADJ
cana-1393	82	6	cauchy	cauchy	ADJ
cana-1393	82	7	sequence	sequence	NOUN
cana-1393	82	8	.	.	PUNCT
cana-1393	83	1	by	by	ADP
cana-1393	83	2	the	the	DET
cana-1393	83	3	completeness	completeness	NOUN
cana-1393	83	4	of	of	ADP
cana-1393	83	5	as	as	ADV
cana-1393	83	6	accordingly	accordingly	ADV
cana-1393	83	7	,	,	PUNCT
cana-1393	83	8	the	the	DET
cana-1393	83	9	sequences	sequence	NOUN
cana-1393	83	10	as	as	ADP
cana-1393	83	11	by	by	ADP
cana-1393	83	12	(	(	PUNCT
cana-1393	83	13	c3	c3	PROPN
cana-1393	83	14	)	)	PUNCT
cana-1393	83	15	the	the	DET
cana-1393	83	16	couple	couple	NOUN
cana-1393	83	17	is	be	AUX
cana-1393	83	18	reciprocally	reciprocally	ADV
cana-1393	83	19	continuous	continuous	ADJ
cana-1393	83	20	(	(	PUNCT
cana-1393	83	21	)	)	PUNCT
cana-1393	83	22	(	(	PUNCT
cana-1393	83	23	)	)	PUNCT
cana-1393	83	24	(	(	PUNCT
cana-1393	83	25	1	1	X
cana-1393	83	26	)	)	PUNCT
cana-1393	83	27	also	also	ADV
cana-1393	83	28	the	the	DET
cana-1393	83	29	couple	couple	NOUN
cana-1393	83	30	is	be	AUX
cana-1393	83	31	semi	semi	ADJ
cana-1393	83	32	-	-	ADJ
cana-1393	83	33	compatible	compatible	ADJ
cana-1393	83	34	,	,	PUNCT
cana-1393	83	35	we	we	PRON
cana-1393	83	36	have	have	VERB
cana-1393	83	37	(	(	PUNCT
cana-1393	83	38	)	)	PUNCT
cana-1393	83	39	(	(	PUNCT
cana-1393	83	40	2	2	NUM
cana-1393	83	41	)	)	PUNCT
cana-1393	83	42	from	from	ADP
cana-1393	83	43	(	(	PUNCT
cana-1393	83	44	1	1	NUM
cana-1393	83	45	)	)	PUNCT
cana-1393	83	46	and	and	CCONJ
cana-1393	83	47	(	(	PUNCT
cana-1393	83	48	2	2	X
cana-1393	83	49	)	)	PUNCT
cana-1393	83	50	we	we	PRON
cana-1393	83	51	get	get	VERB
cana-1393	83	52	(	(	PUNCT
cana-1393	83	53	3	3	NUM
cana-1393	83	54	)	)	PUNCT
cana-1393	83	55	since	since	SCONJ
cana-1393	83	56	which	which	PRON
cana-1393	83	57	gives	give	VERB
cana-1393	83	58	then	then	ADV
cana-1393	83	59	thereexists	thereexist	NOUN
cana-1393	83	60	such	such	ADJ
cana-1393	83	61	that	that	SCONJ
cana-1393	83	62	since	since	SCONJ
cana-1393	83	63	as	as	ADP
cana-1393	83	64	.	.	PUNCT
cana-1393	84	1	which	which	PRON
cana-1393	84	2	implies	imply	VERB
cana-1393	84	3	(	(	PUNCT
cana-1393	84	4	4	4	X
cana-1393	84	5	)	)	PUNCT
cana-1393	84	6	now	now	ADV
cana-1393	84	7	we	we	PRON
cana-1393	84	8	prove	prove	VERB
cana-1393	84	9	that	that	SCONJ
cana-1393	84	10	putting	put	VERB
cana-1393	84	11	and	and	CCONJ
cana-1393	84	12	in	in	ADP
cana-1393	84	13	(	(	PUNCT
cana-1393	84	14	c2	c2	PROPN
cana-1393	84	15	)	)	PUNCT
cana-1393	84	16	we	we	PRON
cana-1393	84	17	have	have	VERB
cana-1393	84	18	(	(	PUNCT
cana-1393	84	19	)	)	PUNCT
cana-1393	85	1	0	0	NUM
cana-1393	85	2	.	.	X
cana-1393	86	1	2	2	NUM
cana-1393	86	2	(	(	PUNCT
cana-1393	86	3	)	)	PUNCT
cana-1393	86	4	(	(	PUNCT
cana-1393	86	5	)	)	PUNCT
cana-1393	86	6	(	(	PUNCT
cana-1393	86	7	)	)	PUNCT
cana-1393	86	8	(	(	PUNCT
cana-1393	86	9	)	)	PUNCT
cana-1393	86	10	(	(	PUNCT
cana-1393	86	11	)	)	PUNCT
cana-1393	86	12	(	(	PUNCT
cana-1393	86	13	)	)	PUNCT
cana-1393	86	14	3/1	3/1	NUM
cana-1393	86	15	communications	communication	NOUN
cana-1393	86	16	on	on	ADP
cana-1393	86	17	applied	apply	VERB
cana-1393	86	18	nonlinear	nonlinear	ADJ
cana-1393	86	19	analysis	analysis	NOUN
cana-1393	86	20	issn	issn	NOUN
cana-1393	86	21	:	:	PUNCT
cana-1393	86	22	1074	1074	NUM
cana-1393	86	23	-	-	PUNCT
cana-1393	86	24	133x	133x	NUM
cana-1393	86	25	vol	vol	NOUN
cana-1393	86	26	31	31	NUM
cana-1393	86	27	no	no	NOUN
cana-1393	86	28	.	.	PUNCT
cana-1393	87	1	7s	7	NOUN
cana-1393	87	2	(	(	PUNCT
cana-1393	87	3	2024	2024	NUM
cana-1393	87	4	)	)	PUNCT
cana-1393	87	5	512	512	NUM
cana-1393	87	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1393	87	7	0	0	NUM
cana-1393	87	8	.	.	PUNCT
cana-1393	87	9	2	2	NUM
cana-1393	87	10	3/1	3/1	NUM
cana-1393	87	11	[	[	PUNCT
cana-1393	87	12	(	(	PUNCT
cana-1393	87	13	)	)	PUNCT
cana-1393	87	14	]	]	PUNCT
cana-1393	88	1	[	[	PUNCT
cana-1393	88	2	(	(	PUNCT
cana-1393	88	3	)	)	PUNCT
cana-1393	88	4	]	]	PUNCT
cana-1393	88	5	which	which	PRON
cana-1393	88	6	gives	give	VERB
cana-1393	88	7	.	.	PUNCT
cana-1393	89	1	therefore	therefore	ADV
cana-1393	89	2	since	since	SCONJ
cana-1393	89	3	the	the	DET
cana-1393	89	4	couple	couple	NOUN
cana-1393	89	5	is	be	AUX
cana-1393	89	6	wcm	wcm	NOUN
cana-1393	89	7	and	and	CCONJ
cana-1393	89	8	is	be	AUX
cana-1393	89	9	coincidence	coincidence	NOUN
cana-1393	89	10	point	point	NOUN
cana-1393	89	11	then	then	ADV
cana-1393	89	12	we	we	PRON
cana-1393	89	13	have	have	VERB
cana-1393	89	14	.	.	PUNCT
cana-1393	90	1	(	(	PUNCT
cana-1393	90	2	5	5	X
cana-1393	90	3	)	)	PUNCT
cana-1393	90	4	putting	put	VERB
cana-1393	90	5	and	and	CCONJ
cana-1393	90	6	in	in	ADP
cana-1393	90	7	(	(	PUNCT
cana-1393	90	8	c2	c2	PROPN
cana-1393	90	9	)	)	PUNCT
cana-1393	90	10	we	we	PRON
cana-1393	90	11	have	have	VERB
cana-1393	90	12	(	(	PUNCT
cana-1393	90	13	)	)	PUNCT
cana-1393	90	14	0	0	NUM
cana-1393	90	15	.	.	X
cana-1393	91	1	2	2	NUM
cana-1393	91	2	(	(	PUNCT
cana-1393	91	3	)	)	PUNCT
cana-1393	91	4	(	(	PUNCT
cana-1393	91	5	)	)	PUNCT
cana-1393	91	6	(	(	PUNCT
cana-1393	91	7	)	)	PUNCT
cana-1393	91	8	(	(	PUNCT
cana-1393	91	9	)	)	PUNCT
cana-1393	91	10	(	(	PUNCT
cana-1393	91	11	)	)	PUNCT
cana-1393	91	12	(	(	PUNCT
cana-1393	91	13	)	)	PUNCT
cana-1393	92	1	3/1	3/1	NUM
cana-1393	92	2	0	0	NUM
cana-1393	92	3	.	.	PUNCT
cana-1393	92	4	2	2	NUM
cana-1393	92	5	3/1	3/1	NUM
cana-1393	92	6	[	[	PUNCT
cana-1393	92	7	(	(	PUNCT
cana-1393	92	8	)	)	PUNCT
cana-1393	92	9	]	]	PUNCT
cana-1393	93	1	[	[	PUNCT
cana-1393	93	2	]	]	X
cana-1393	93	3	which	which	PRON
cana-1393	93	4	implies	imply	VERB
cana-1393	93	5	(	(	PUNCT
cana-1393	93	6	6	6	NUM
cana-1393	93	7	)	)	PUNCT
cana-1393	93	8	from	from	ADP
cana-1393	93	9	(	(	PUNCT
cana-1393	93	10	5	5	NUM
cana-1393	93	11	)	)	PUNCT
cana-1393	93	12	and	and	CCONJ
cana-1393	93	13	(	(	PUNCT
cana-1393	93	14	6	6	X
cana-1393	93	15	)	)	PUNCT
cana-1393	93	16	we	we	PRON
cana-1393	93	17	obtain	obtain	VERB
cana-1393	93	18	.	.	PUNCT
cana-1393	94	1	(	(	PUNCT
cana-1393	94	2	7	7	X
cana-1393	94	3	)	)	PUNCT
cana-1393	94	4	in	in	ADP
cana-1393	94	5	the	the	DET
cana-1393	94	6	inequality	inequality	NOUN
cana-1393	94	7	(	(	PUNCT
cana-1393	94	8	c2	c2	PROPN
cana-1393	94	9	)	)	PUNCT
cana-1393	94	10	putting	putting	NOUN
cana-1393	94	11	and	and	CCONJ
cana-1393	94	12	0	0	NUM
cana-1393	94	13	.	.	PUNCT
cana-1393	94	14	2	2	NUM
cana-1393	94	15	3/1	3/1	NUM
cana-1393	94	16	0	0	NUM
cana-1393	94	17	.	.	PUNCT
cana-1393	94	18	2	2	NUM
cana-1393	94	19	3/1	3/1	NUM
cana-1393	94	20	[	[	PUNCT
cana-1393	94	21	(	(	PUNCT
cana-1393	94	22	)	)	PUNCT
cana-1393	94	23	]	]	PUNCT
cana-1393	95	1	[	[	PUNCT
cana-1393	95	2	]	]	X
cana-1393	95	3	which	which	PRON
cana-1393	95	4	implies	imply	VERB
cana-1393	95	5	(	(	PUNCT
cana-1393	95	6	8)	8)	NUM
cana-1393	95	7	from	from	ADP
cana-1393	95	8	(	(	PUNCT
cana-1393	95	9	3	3	NUM
cana-1393	95	10	)	)	PUNCT
cana-1393	95	11	and	and	CCONJ
cana-1393	95	12	(	(	PUNCT
cana-1393	95	13	8)	8)	NUM
cana-1393	95	14	it	it	PRON
cana-1393	95	15	gives	give	VERB
cana-1393	95	16	(	(	PUNCT
cana-1393	95	17	9	9	NUM
cana-1393	95	18	)	)	PUNCT
cana-1393	95	19	from	from	ADP
cana-1393	95	20	(	(	PUNCT
cana-1393	95	21	7	7	NUM
cana-1393	95	22	)	)	PUNCT
cana-1393	95	23	and	and	CCONJ
cana-1393	95	24	(	(	PUNCT
cana-1393	95	25	9	9	X
cana-1393	95	26	)	)	PUNCT
cana-1393	95	27	we	we	PRON
cana-1393	95	28	have	have	VERB
cana-1393	95	29	.	.	PUNCT
cana-1393	96	1	this	this	PRON
cana-1393	96	2	demonstrates	demonstrate	VERB
cana-1393	96	3	that	that	SCONJ
cana-1393	96	4	the	the	DET
cana-1393	96	5	common	common	ADJ
cana-1393	96	6	fixed	fix	VERB
cana-1393	96	7	point	point	NOUN
cana-1393	96	8	for	for	SCONJ
cana-1393	96	9	the	the	DET
cana-1393	96	10	maps	map	NOUN
cana-1393	96	11	above	above	ADV
cana-1393	96	12	is	be	AUX
cana-1393	96	13	.	.	PUNCT
cana-1393	97	1	for	for	ADP
cana-1393	97	2	uniqueness	uniqueness	NOUN
cana-1393	97	3	:	:	PUNCT
cana-1393	97	4	assume	assume	VERB
cana-1393	97	5	that	that	PRON
cana-1393	97	6	be	be	AUX
cana-1393	97	7	another	another	DET
cana-1393	97	8	fixed	fix	VERB
cana-1393	97	9	point	point	NOUN
cana-1393	97	10	then	then	ADV
cana-1393	97	11	communications	communication	NOUN
cana-1393	97	12	on	on	ADP
cana-1393	97	13	applied	apply	VERB
cana-1393	97	14	nonlinear	nonlinear	ADJ
cana-1393	97	15	analysis	analysis	NOUN
cana-1393	97	16	issn	issn	NOUN
cana-1393	97	17	:	:	PUNCT
cana-1393	97	18	1074	1074	NUM
cana-1393	97	19	-	-	PUNCT
cana-1393	97	20	133x	133x	NUM
cana-1393	97	21	vol	vol	NOUN
cana-1393	97	22	31	31	NUM
cana-1393	97	23	no	no	NOUN
cana-1393	97	24	.	.	PUNCT
cana-1393	98	1	7s	7	NOUN
cana-1393	98	2	(	(	PUNCT
cana-1393	98	3	2024	2024	NUM
cana-1393	98	4	)	)	PUNCT
cana-1393	98	5	513	513	NUM
cana-1393	99	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-1393	99	2	putting	putting	NOUN
cana-1393	99	3	and	and	CCONJ
cana-1393	99	4	in	in	ADP
cana-1393	99	5	0	0	NUM
cana-1393	99	6	.	.	PUNCT
cana-1393	100	1	2	2	NUM
cana-1393	100	2	3/1	3/1	NUM
cana-1393	100	3	0	0	NUM
cana-1393	100	4	.	.	PUNCT
cana-1393	100	5	2	2	NUM
cana-1393	100	6	3/1	3/1	NUM
cana-1393	100	7	[	[	PUNCT
cana-1393	100	8	(	(	PUNCT
cana-1393	100	9	)	)	PUNCT
cana-1393	100	10	]	]	PUNCT
cana-1393	101	1	[	[	PUNCT
cana-1393	101	2	]	]	X
cana-1393	101	3	,	,	PUNCT
cana-1393	101	4	a	a	DET
cana-1393	101	5	contradiction	contradiction	NOUN
cana-1393	101	6	which	which	PRON
cana-1393	101	7	implies	imply	VERB
cana-1393	101	8	.	.	PUNCT
cana-1393	102	1	this	this	PRON
cana-1393	102	2	demonstrates	demonstrate	VERB
cana-1393	102	3	is	be	AUX
cana-1393	102	4	the	the	DET
cana-1393	102	5	unique	unique	ADJ
cana-1393	102	6	common	common	ADJ
cana-1393	102	7	fixed	fix	VERB
cana-1393	102	8	point	point	NOUN
cana-1393	102	9	of	of	ADP
cana-1393	102	10	four	four	NUM
cana-1393	102	11	self	self	NOUN
cana-1393	102	12	-	-	PUNCT
cana-1393	102	13	mappings	mapping	NOUN
cana-1393	102	14	.	.	PUNCT
cana-1393	103	1	3.1	3.1	NUM
cana-1393	103	2	example	example	NOUN
cana-1393	103	3	:	:	PUNCT
cana-1393	103	4	suppose	suppose	VERB
cana-1393	103	5	[	[	PUNCT
cana-1393	103	6	]	]	X
cana-1393	103	7	be	be	AUX
cana-1393	103	8	defined	define	VERB
cana-1393	103	9	in	in	ADP
cana-1393	103	10	mms	mms	NOUN
cana-1393	103	11	with	with	ADP
cana-1393	103	12	|	|	ADV
cana-1393	103	13	|	|	ADV
cana-1393	103	14	.	.	PUNCT
cana-1393	104	1	we	we	PRON
cana-1393	104	2	define	define	VERB
cana-1393	104	3	self	self	NOUN
cana-1393	104	4	-	-	PUNCT
cana-1393	104	5	mappings	mapping	NOUN
cana-1393	104	6	and	and	CCONJ
cana-1393	104	7	as	as	ADP
cana-1393	104	8	{	{	PUNCT
cana-1393	104	9	{	{	PUNCT
cana-1393	104	10	{	{	PUNCT
cana-1393	104	11	and	and	CCONJ
cana-1393	104	12	{	{	PUNCT
cana-1393	104	13	clearly	clearly	ADV
cana-1393	104	14	*	*	PUNCT
cana-1393	104	15	+	+	PUNCT
cana-1393	104	16	(	(	PUNCT
cana-1393	104	17	]	]	PUNCT
cana-1393	104	18	(	(	PUNCT
cana-1393	104	19	]	]	PUNCT
cana-1393	104	20	*	*	PUNCT
cana-1393	105	1	+	+	PUNCT
cana-1393	105	2	(	(	PUNCT
cana-1393	105	3	+	+	NOUN
cana-1393	105	4	*	*	PUNCT
cana-1393	105	5	+	+	PUNCT
cana-1393	105	6	and	and	CCONJ
cana-1393	105	7	*	*	PUNCT
cana-1393	105	8	+	+	PUNCT
cana-1393	105	9	(	(	PUNCT
cana-1393	105	10	+	+	NOUN
cana-1393	105	11	*	*	PUNCT
cana-1393	105	12	+	+	PUNCT
cana-1393	105	13	*	*	PUNCT
cana-1393	105	14	+	+	PUNCT
cana-1393	105	15	(	(	PUNCT
cana-1393	105	16	+	+	NOUN
cana-1393	105	17	*	*	PUNCT
cana-1393	105	18	+	+	CCONJ
cana-1393	105	19	so	so	SCONJ
cana-1393	105	20	that	that	SCONJ
cana-1393	105	21	condition	condition	NOUN
cana-1393	105	22	is	be	AUX
cana-1393	105	23	fulfilled	fulfil	VERB
cana-1393	105	24	.	.	PUNCT
cana-1393	106	1	suppose	suppose	VERB
cana-1393	106	2	we	we	PRON
cana-1393	106	3	have	have	VERB
cana-1393	106	4	a	a	DET
cana-1393	106	5	sequence	sequence	NOUN
cana-1393	106	6	,	,	PUNCT
cana-1393	106	7	for	for	ADV
cana-1393	106	8	.	.	PUNCT
cana-1393	107	1	now	now	ADV
cana-1393	107	2	(	(	PUNCT
cana-1393	107	3	)	)	PUNCT
cana-1393	107	4	*	*	PUNCT
cana-1393	107	5	(	(	PUNCT
cana-1393	107	6	)	)	PUNCT
cana-1393	107	7	+	+	CCONJ
cana-1393	107	8	and	and	CCONJ
cana-1393	107	9	(	(	PUNCT
cana-1393	107	10	)	)	PUNCT
cana-1393	107	11	0	0	NUM
cana-1393	107	12	(	(	PUNCT
cana-1393	107	13	)	)	PUNCT
cana-1393	107	14	1	1	X
cana-1393	107	15	.	.	PUNCT
cana-1393	108	1	this	this	PRON
cana-1393	108	2	gives	give	VERB
cana-1393	108	3	also	also	ADV
cana-1393	108	4	(	(	PUNCT
cana-1393	108	5	)	)	PUNCT
cana-1393	108	6	[	[	PUNCT
cana-1393	108	7	(	(	PUNCT
cana-1393	108	8	)	)	PUNCT
cana-1393	108	9	]	]	PUNCT
cana-1393	108	10	and	and	CCONJ
cana-1393	108	11	(	(	PUNCT
cana-1393	108	12	)	)	PUNCT
cana-1393	108	13	[	[	PUNCT
cana-1393	108	14	(	(	PUNCT
cana-1393	108	15	)	)	PUNCT
cana-1393	108	16	(	(	PUNCT
cana-1393	108	17	)	)	PUNCT
cana-1393	108	18	]	]	PUNCT
cana-1393	108	19	.	.	PUNCT
cana-1393	109	1	communications	communication	NOUN
cana-1393	109	2	on	on	ADP
cana-1393	109	3	applied	apply	VERB
cana-1393	109	4	nonlinear	nonlinear	ADJ
cana-1393	109	5	analysis	analysis	NOUN
cana-1393	109	6	issn	issn	NOUN
cana-1393	109	7	:	:	PUNCT
cana-1393	109	8	1074	1074	NUM
cana-1393	109	9	-	-	PUNCT
cana-1393	109	10	133x	133x	NUM
cana-1393	109	11	vol	vol	NOUN
cana-1393	109	12	31	31	NUM
cana-1393	109	13	no	no	NOUN
cana-1393	109	14	.	.	PUNCT
cana-1393	110	1	7s	7	NOUN
cana-1393	110	2	(	(	PUNCT
cana-1393	110	3	2024	2024	NUM
cana-1393	110	4	)	)	PUNCT
cana-1393	110	5	514	514	NUM
cana-1393	110	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1393	111	1	this	this	PRON
cana-1393	111	2	gives	give	VERB
cana-1393	111	3	therefore	therefore	ADV
cana-1393	111	4	also	also	ADV
cana-1393	111	5	(	(	PUNCT
cana-1393	111	6	)	)	PUNCT
cana-1393	111	7	(	(	PUNCT
cana-1393	111	8	)	)	PUNCT
cana-1393	111	9	.	.	PUNCT
cana-1393	112	1	this	this	PRON
cana-1393	112	2	implies	imply	VERB
cana-1393	112	3	(	(	PUNCT
cana-1393	112	4	)	)	PUNCT
cana-1393	112	5	(	(	PUNCT
cana-1393	112	6	(	(	PUNCT
cana-1393	112	7	)	)	PUNCT
cana-1393	112	8	(	(	PUNCT
cana-1393	112	9	)	)	PUNCT
cana-1393	112	10	*	*	PUNCT
cana-1393	113	1	*	*	PUNCT
cana-1393	114	1	+	+	PUNCT
cana-1393	114	2	*	*	PUNCT
cana-1393	115	1	+	+	CCONJ
cana-1393	115	2	and	and	CCONJ
cana-1393	115	3	(	(	PUNCT
cana-1393	115	4	)	)	PUNCT
cana-1393	115	5	[	[	PUNCT
cana-1393	115	6	(	(	PUNCT
cana-1393	115	7	)	)	PUNCT
cana-1393	115	8	]	]	PUNCT
cana-1393	116	1	*	*	PUNCT
cana-1393	117	1	+	+	PUNCT
cana-1393	117	2	[	[	PUNCT
cana-1393	117	3	(	(	PUNCT
cana-1393	117	4	)	)	PUNCT
cana-1393	117	5	(	(	PUNCT
cana-1393	117	6	)	)	PUNCT
cana-1393	117	7	]	]	PUNCT
cana-1393	117	8	.	.	PUNCT
cana-1393	118	1	this	this	PRON
cana-1393	118	2	implies	imply	VERB
cana-1393	118	3	(	(	PUNCT
cana-1393	118	4	)	)	PUNCT
cana-1393	118	5	and	and	CCONJ
cana-1393	118	6	(	(	PUNCT
cana-1393	118	7	)	)	PUNCT
cana-1393	118	8	.	.	PUNCT
cana-1393	119	1	this	this	PRON
cana-1393	119	2	proves	prove	VERB
cana-1393	119	3	that	that	SCONJ
cana-1393	119	4	the	the	DET
cana-1393	119	5	couple	couple	NOUN
cana-1393	119	6	is	be	AUX
cana-1393	119	7	reciprocally	reciprocally	ADV
cana-1393	119	8	continuous	continuous	ADJ
cana-1393	119	9	and	and	CCONJ
cana-1393	119	10	semi	semi	ADJ
cana-1393	119	11	-	-	ADJ
cana-1393	119	12	compatible	compatible	ADJ
cana-1393	119	13	in	in	ADP
cana-1393	119	14	mms	mms	NOUN
cana-1393	119	15	.	.	PUNCT
cana-1393	120	1	further	far	ADV
cana-1393	120	2	(	(	PUNCT
cana-1393	120	3	)	)	PUNCT
cana-1393	120	4	(	(	PUNCT
cana-1393	120	5	)	)	PUNCT
cana-1393	121	1	which	which	PRON
cana-1393	121	2	imliies	imliie	VERB
cana-1393	121	3	that	that	PRON
cana-1393	121	4	is	be	AUX
cana-1393	121	5	the	the	DET
cana-1393	121	6	coincidence	coincidence	NOUN
cana-1393	121	7	point	point	NOUN
cana-1393	121	8	of	of	ADP
cana-1393	121	9	and	and	CCONJ
cana-1393	121	10	.	.	PUNCT
cana-1393	122	1	hence	hence	ADV
cana-1393	122	2	(	(	PUNCT
cana-1393	122	3	)	)	PUNCT
cana-1393	122	4	(	(	PUNCT
cana-1393	122	5	)	)	PUNCT
cana-1393	122	6	and	and	CCONJ
cana-1393	122	7	(	(	PUNCT
cana-1393	122	8	)	)	PUNCT
cana-1393	122	9	(	(	PUNCT
cana-1393	122	10	)	)	PUNCT
cana-1393	122	11	which	which	PRON
cana-1393	122	12	gives	give	VERB
cana-1393	122	13	(	(	PUNCT
cana-1393	122	14	(	(	PUNCT
cana-1393	122	15	)	)	PUNCT
cana-1393	122	16	(	(	PUNCT
cana-1393	122	17	)	)	PUNCT
cana-1393	122	18	*	*	PUNCT
cana-1393	122	19	hence	hence	ADV
cana-1393	122	20	the	the	DET
cana-1393	122	21	couple	couple	NOUN
cana-1393	122	22	is	be	AUX
cana-1393	122	23	weakly	weakly	ADV
cana-1393	122	24	compatible	compatible	ADJ
cana-1393	122	25	mappings	mapping	NOUN
cana-1393	122	26	.	.	PUNCT
cana-1393	123	1	but	but	CCONJ
cana-1393	123	2	(	(	PUNCT
cana-1393	123	3	)	)	PUNCT
cana-1393	123	4	0	0	NUM
cana-1393	124	1	(	(	PUNCT
cana-1393	124	2	)	)	PUNCT
cana-1393	124	3	1	1	NUM
cana-1393	124	4	*	*	PUNCT
cana-1393	125	1	+	+	NUM
cana-1393	125	2	0	0	NUM
cana-1393	125	3	(	(	PUNCT
cana-1393	125	4	)	)	PUNCT
cana-1393	125	5	(	(	PUNCT
cana-1393	125	6	)	)	PUNCT
cana-1393	125	7	1	1	NUM
cana-1393	125	8	and	and	CCONJ
cana-1393	125	9	(	(	PUNCT
cana-1393	125	10	)	)	PUNCT
cana-1393	125	11	0	0	NUM
cana-1393	126	1	(	(	PUNCT
cana-1393	126	2	)	)	PUNCT
cana-1393	126	3	1	1	NUM
cana-1393	126	4	*	*	PUNCT
cana-1393	126	5	(	(	PUNCT
cana-1393	126	6	)	)	PUNCT
cana-1393	126	7	+	+	CCONJ
cana-1393	126	8	[	[	PUNCT
cana-1393	126	9	(	(	PUNCT
cana-1393	126	10	(	(	PUNCT
cana-1393	126	11	)	)	PUNCT
cana-1393	126	12	*	*	PUNCT
cana-1393	126	13	]	]	PUNCT
cana-1393	126	14	.	.	PUNCT
cana-1393	127	1	similarly	similarly	ADV
cana-1393	127	2	(	(	PUNCT
cana-1393	127	3	)	)	PUNCT
cana-1393	127	4	.	.	PUNCT
cana-1393	128	1	(	(	PUNCT
cana-1393	128	2	)	)	PUNCT
cana-1393	128	3	/	/	PUNCT
cana-1393	129	1	*	*	PUNCT
cana-1393	130	1	+	+	NUM
cana-1393	130	2	0	0	NUM
cana-1393	130	3	(	(	PUNCT
cana-1393	130	4	)	)	PUNCT
cana-1393	130	5	1	1	NUM
cana-1393	130	6	and	and	CCONJ
cana-1393	130	7	communications	communication	NOUN
cana-1393	130	8	on	on	ADP
cana-1393	130	9	applied	apply	VERB
cana-1393	130	10	nonlinear	nonlinear	ADJ
cana-1393	130	11	analysis	analysis	NOUN
cana-1393	130	12	issn	issn	NOUN
cana-1393	130	13	:	:	PUNCT
cana-1393	130	14	1074	1074	NUM
cana-1393	130	15	-	-	PUNCT
cana-1393	130	16	133x	133x	NUM
cana-1393	130	17	vol	vol	NOUN
cana-1393	130	18	31	31	NUM
cana-1393	130	19	no	no	NOUN
cana-1393	130	20	.	.	PUNCT
cana-1393	131	1	7s	7	NOUN
cana-1393	131	2	(	(	PUNCT
cana-1393	131	3	2024	2024	NUM
cana-1393	131	4	)	)	PUNCT
cana-1393	131	5	515	515	NUM
cana-1393	131	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1393	131	7	(	(	PUNCT
cana-1393	131	8	*	*	PUNCT
cana-1393	131	9	[	[	PUNCT
cana-1393	131	10	(	(	PUNCT
cana-1393	131	11	)	)	PUNCT
cana-1393	131	12	]	]	PUNCT
cana-1393	132	1	[	[	PUNCT
cana-1393	132	2	]	]	X
cana-1393	132	3	[	[	PUNCT
cana-1393	132	4	(	(	PUNCT
cana-1393	132	5	)	)	PUNCT
cana-1393	132	6	]	]	PUNCT
cana-1393	132	7	therefore	therefore	ADV
cana-1393	132	8	(	(	PUNCT
cana-1393	132	9	)	)	PUNCT
cana-1393	132	10	and	and	CCONJ
cana-1393	132	11	(	(	PUNCT
cana-1393	132	12	)	)	PUNCT
cana-1393	132	13	.	.	PUNCT
cana-1393	133	1	demonstrating	demonstrate	VERB
cana-1393	133	2	that	that	SCONJ
cana-1393	133	3	the	the	DET
cana-1393	133	4	compatibility	compatibility	NOUN
cana-1393	133	5	condition	condition	NOUN
cana-1393	133	6	is	be	AUX
cana-1393	133	7	not	not	PART
cana-1393	133	8	satisfied	satisfied	ADJ
cana-1393	133	9	.	.	PUNCT
cana-1393	134	1	also	also	ADV
cana-1393	134	2	(	(	PUNCT
cana-1393	134	3	)	)	PUNCT
cana-1393	134	4	(	(	PUNCT
cana-1393	134	5	)	)	PUNCT
cana-1393	134	6	(	(	PUNCT
cana-1393	134	7	)	)	PUNCT
cana-1393	134	8	(	(	PUNCT
cana-1393	134	9	)	)	PUNCT
cana-1393	134	10	.	.	PUNCT
cana-1393	135	1	it	it	PRON
cana-1393	135	2	has	have	AUX
cana-1393	135	3	been	be	AUX
cana-1393	135	4	observed	observe	VERB
cana-1393	135	5	that	that	SCONJ
cana-1393	135	6	the	the	DET
cana-1393	135	7	unique	unique	ADJ
cana-1393	135	8	common	common	ADJ
cana-1393	135	9	fixed	fix	VERB
cana-1393	135	10	point	point	NOUN
cana-1393	135	11	to	to	ADP
cana-1393	135	12	four	four	NUM
cana-1393	135	13	self	self	NOUN
cana-1393	135	14	-	-	PUNCT
cana-1393	135	15	mapping	mapping	NOUN
cana-1393	135	16	and	and	CCONJ
cana-1393	135	17	is	be	AUX
cana-1393	135	18	.	.	PUNCT
cana-1393	136	1	we	we	PRON
cana-1393	136	2	now	now	ADV
cana-1393	136	3	demonstrate	demonstrate	VERB
cana-1393	136	4	another	another	DET
cana-1393	136	5	theorem	theorem	NOUN
cana-1393	136	6	on	on	ADP
cana-1393	136	7	mms	mms	NOUN
cana-1393	136	8	.	.	PUNCT
cana-1393	137	1	3.2	3.2	NUM
cana-1393	137	2	theorem	theorem	VERB
cana-1393	137	3	:	:	PUNCT
cana-1393	137	4	suppose	suppose	VERB
cana-1393	137	5	that	that	SCONJ
cana-1393	137	6	in	in	ADP
cana-1393	137	7	a	a	DET
cana-1393	137	8	complete	complete	ADJ
cana-1393	137	9	mms	mms	NOUN
cana-1393	137	10	,	,	PUNCT
cana-1393	137	11	the	the	DET
cana-1393	137	12	four	four	NUM
cana-1393	137	13	self	self	NOUN
cana-1393	137	14	-	-	PUNCT
cana-1393	137	15	mappings	mapping	NOUN
cana-1393	137	16	and	and	CCONJ
cana-1393	137	17	meeting	meet	VERB
cana-1393	137	18	the	the	DET
cana-1393	137	19	requirements	requirement	NOUN
cana-1393	137	20	(	(	PUNCT
cana-1393	137	21	d1	d1	NOUN
cana-1393	137	22	)	)	PUNCT
cana-1393	137	23	(	(	PUNCT
cana-1393	137	24	d2	d2	PROPN
cana-1393	137	25	)	)	PUNCT
cana-1393	137	26	0	0	NUM
cana-1393	137	27	.	.	PUNCT
cana-1393	138	1	2	2	NUM
cana-1393	138	2	3/1	3/1	NUM
cana-1393	138	3	for	for	ADP
cana-1393	138	4	all	all	PRON
cana-1393	138	5	,	,	PUNCT
cana-1393	138	6	where	where	SCONJ
cana-1393	138	7	.	.	PUNCT
cana-1393	139	1	where	where	SCONJ
cana-1393	139	2	[	[	PUNCT
cana-1393	139	3	[	[	PUNCT
cana-1393	139	4	is	be	AUX
cana-1393	139	5	a	a	DET
cana-1393	139	6	continuous	continuous	ADJ
cana-1393	139	7	and	and	CCONJ
cana-1393	139	8	monotone	monotone	ADJ
cana-1393	139	9	increasing	increase	VERB
cana-1393	139	10	function	function	NOUN
cana-1393	139	11	such	such	ADJ
cana-1393	139	12	that	that	PRON
cana-1393	139	13	for	for	ADP
cana-1393	139	14	all	all	DET
cana-1393	139	15	(	(	PUNCT
cana-1393	139	16	d3	d3	PROPN
cana-1393	139	17	)	)	PUNCT
cana-1393	139	18	the	the	DET
cana-1393	139	19	pair	pair	NOUN
cana-1393	139	20	is	be	AUX
cana-1393	139	21	strongly	strongly	ADV
cana-1393	139	22	semi	semi	ADJ
cana-1393	139	23	-	-	ADJ
cana-1393	139	24	compatible	compatible	ADJ
cana-1393	139	25	and	and	CCONJ
cana-1393	139	26	conditinally	conditinally	ADV
cana-1393	139	27	reciprocally	reciprocally	ADV
cana-1393	139	28	continuous	continuous	ADJ
cana-1393	139	29	(	(	PUNCT
cana-1393	139	30	d4	d4	PROPN
cana-1393	139	31	)	)	PUNCT
cana-1393	139	32	the	the	DET
cana-1393	139	33	pair	pair	NOUN
cana-1393	139	34	is	be	AUX
cana-1393	139	35	owc	owc	PROPN
cana-1393	139	36	.	.	PUNCT
cana-1393	140	1	then	then	ADV
cana-1393	140	2	there	there	PRON
cana-1393	140	3	exists	exist	VERB
cana-1393	140	4	a	a	DET
cana-1393	140	5	unique	unique	ADJ
cana-1393	140	6	common	common	ADJ
cana-1393	140	7	fixed	fix	VERB
cana-1393	140	8	point	point	NOUN
cana-1393	140	9	for	for	ADP
cana-1393	140	10	the	the	DET
cana-1393	140	11	above	above	ADJ
cana-1393	140	12	mappings	mapping	NOUN
cana-1393	140	13	.	.	PUNCT
cana-1393	141	1	proof	proof	NOUN
cana-1393	141	2	:	:	PUNCT
cana-1393	141	3	as	as	ADP
cana-1393	141	4	in	in	ADP
cana-1393	141	5	theorem	theorem	NOUN
cana-1393	141	6	(	(	PUNCT
cana-1393	141	7	3.1	3.1	NUM
cana-1393	141	8	)	)	PUNCT
cana-1393	141	9	,	,	PUNCT
cana-1393	141	10	is	be	AUX
cana-1393	141	11	cauchy	cauchy	ADJ
cana-1393	141	12	sequence	sequence	NOUN
cana-1393	141	13	.	.	PUNCT
cana-1393	142	1	by	by	ADP
cana-1393	142	2	the	the	DET
cana-1393	142	3	completeness	completeness	NOUN
cana-1393	142	4	of	of	ADP
cana-1393	142	5	as	as	ADV
cana-1393	142	6	accordingly	accordingly	ADV
cana-1393	142	7	,	,	PUNCT
cana-1393	142	8	the	the	DET
cana-1393	142	9	sequences	sequence	NOUN
cana-1393	142	10	as	as	ADP
cana-1393	142	11	by	by	ADP
cana-1393	142	12	(	(	PUNCT
cana-1393	142	13	d3	d3	PROPN
cana-1393	142	14	)	)	PUNCT
cana-1393	142	15	the	the	DET
cana-1393	142	16	couple	couple	NOUN
cana-1393	142	17	is	be	AUX
cana-1393	142	18	strongly	strongly	ADV
cana-1393	142	19	semi	semi	ADJ
cana-1393	142	20	-	-	ADJ
cana-1393	142	21	compatible	compatible	ADJ
cana-1393	142	22	whenever	whenever	SCONJ
cana-1393	142	23	(	(	PUNCT
cana-1393	142	24	)	)	PUNCT
cana-1393	142	25	(	(	PUNCT
cana-1393	142	26	)	)	PUNCT
cana-1393	142	27	(	(	PUNCT
cana-1393	142	28	nonempty	nonempty	NOUN
cana-1393	142	29	)	)	PUNCT
cana-1393	142	30	implies	imply	VERB
cana-1393	142	31	is	be	AUX
cana-1393	142	32	a	a	DET
cana-1393	142	33	sequence	sequence	NOUN
cana-1393	142	34	in	in	ADP
cana-1393	142	35	so	so	SCONJ
cana-1393	142	36	that	that	DET
cana-1393	142	37	forsome	forsome	NOUN
cana-1393	142	38	then	then	ADV
cana-1393	142	39	and	and	CCONJ
cana-1393	142	40	as	as	ADP
cana-1393	142	41	(	(	PUNCT
cana-1393	142	42	1	1	NUM
cana-1393	142	43	)	)	PUNCT
cana-1393	142	44	also	also	ADV
cana-1393	142	45	the	the	DET
cana-1393	142	46	coulple	coulple	NOUN
cana-1393	142	47	is	be	AUX
cana-1393	142	48	conditinally	conditinally	ADV
cana-1393	142	49	reciprocally	reciprocally	ADV
cana-1393	142	50	continuous	continuous	ADJ
cana-1393	142	51	implies	implie	NOUN
cana-1393	142	52	and	and	CCONJ
cana-1393	142	53	as	as	ADP
cana-1393	142	54	(	(	PUNCT
cana-1393	142	55	2	2	NUM
cana-1393	142	56	)	)	PUNCT
cana-1393	142	57	from	from	ADP
cana-1393	142	58	(	(	PUNCT
cana-1393	142	59	1	1	NUM
cana-1393	142	60	)	)	PUNCT
cana-1393	142	61	and	and	CCONJ
cana-1393	142	62	(	(	PUNCT
cana-1393	142	63	2	2	X
cana-1393	142	64	)	)	PUNCT
cana-1393	142	65	it	it	PRON
cana-1393	142	66	gives	give	VERB
cana-1393	142	67	(	(	PUNCT
cana-1393	142	68	3	3	NUM
cana-1393	142	69	)	)	PUNCT
cana-1393	142	70	since	since	SCONJ
cana-1393	142	71	implies	imply	VERB
cana-1393	142	72	such	such	ADJ
cana-1393	142	73	that	that	SCONJ
cana-1393	142	74	communications	communication	NOUN
cana-1393	142	75	on	on	ADP
cana-1393	142	76	applied	apply	VERB
cana-1393	142	77	nonlinear	nonlinear	ADJ
cana-1393	142	78	analysis	analysis	NOUN
cana-1393	142	79	issn	issn	NOUN
cana-1393	142	80	:	:	PUNCT
cana-1393	142	81	1074	1074	NUM
cana-1393	142	82	-	-	PUNCT
cana-1393	142	83	133x	133x	NUM
cana-1393	142	84	vol	vol	NOUN
cana-1393	142	85	31	31	NUM
cana-1393	142	86	no	no	NOUN
cana-1393	142	87	.	.	PUNCT
cana-1393	143	1	7s	7	NOUN
cana-1393	143	2	(	(	PUNCT
cana-1393	143	3	2024	2024	NUM
cana-1393	143	4	)	)	PUNCT
cana-1393	143	5	516	516	NUM
cana-1393	143	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1393	143	7	therefore	therefore	ADV
cana-1393	143	8	.	.	PUNCT
cana-1393	144	1	(	(	PUNCT
cana-1393	144	2	4	4	X
cana-1393	144	3	)	)	PUNCT
cana-1393	144	4	now	now	ADV
cana-1393	144	5	we	we	PRON
cana-1393	144	6	show	show	VERB
cana-1393	144	7	that	that	PRON
cana-1393	144	8	.	.	PUNCT
cana-1393	145	1	in	in	ADP
cana-1393	145	2	the	the	DET
cana-1393	145	3	inequality	inequality	NOUN
cana-1393	145	4	putting	put	VERB
cana-1393	145	5	and	and	CCONJ
cana-1393	145	6	0	0	NUM
cana-1393	145	7	.	.	PUNCT
cana-1393	145	8	2	2	NUM
cana-1393	145	9	3/1	3/1	NUM
cana-1393	145	10	0	0	NUM
cana-1393	145	11	.	.	PUNCT
cana-1393	145	12	2	2	NUM
cana-1393	145	13	3/1	3/1	NUM
cana-1393	145	14	[	[	PUNCT
cana-1393	145	15	(	(	PUNCT
cana-1393	145	16	)	)	PUNCT
cana-1393	145	17	]	]	PUNCT
cana-1393	145	18	[	[	PUNCT
cana-1393	145	19	]	]	X
cana-1393	145	20	which	which	PRON
cana-1393	145	21	implies	imply	VERB
cana-1393	145	22	(	(	PUNCT
cana-1393	145	23	5	5	NUM
cana-1393	145	24	)	)	PUNCT
cana-1393	145	25	from	from	ADP
cana-1393	145	26	(	(	PUNCT
cana-1393	145	27	4	4	NUM
cana-1393	145	28	)	)	PUNCT
cana-1393	145	29	and	and	CCONJ
cana-1393	145	30	(	(	PUNCT
cana-1393	145	31	5	5	X
cana-1393	145	32	)	)	PUNCT
cana-1393	145	33	it	it	PRON
cana-1393	145	34	gives	give	VERB
cana-1393	145	35	(	(	PUNCT
cana-1393	145	36	say	say	INTJ
cana-1393	145	37	)	)	PUNCT
cana-1393	145	38	.	.	PUNCT
cana-1393	146	1	(	(	PUNCT
cana-1393	146	2	6	6	NUM
cana-1393	146	3	)	)	PUNCT
cana-1393	146	4	but	but	CCONJ
cana-1393	146	5	the	the	DET
cana-1393	146	6	couple	couple	NOUN
cana-1393	146	7	is	be	AUX
cana-1393	146	8	strongly	strongly	ADV
cana-1393	146	9	semi	semi	ADJ
cana-1393	146	10	-	-	ADJ
cana-1393	146	11	compatible	compatible	ADJ
cana-1393	146	12	mappings	mapping	NOUN
cana-1393	146	13	and	and	CCONJ
cana-1393	146	14	implies	imply	VERB
cana-1393	146	15	.	.	PUNCT
cana-1393	147	1	since	since	SCONJ
cana-1393	147	2	the	the	DET
cana-1393	147	3	couple	couple	NOUN
cana-1393	147	4	is	be	AUX
cana-1393	147	5	owc	owc	NOUN
cana-1393	147	6	implies	implie	NOUN
cana-1393	147	7	which	which	PRON
cana-1393	147	8	gives	give	VERB
cana-1393	147	9	implies	implie	NOUN
cana-1393	147	10	.	.	PUNCT
cana-1393	148	1	now	now	ADV
cana-1393	148	2	we	we	PRON
cana-1393	148	3	show	show	VERB
cana-1393	148	4	that	that	PRON
cana-1393	148	5	.	.	PUNCT
cana-1393	149	1	in	in	ADP
cana-1393	149	2	the	the	DET
cana-1393	149	3	inequality	inequality	NOUN
cana-1393	149	4	(	(	PUNCT
cana-1393	149	5	d2	d2	PROPN
cana-1393	149	6	)	)	PUNCT
cana-1393	149	7	putting	putting	NOUN
cana-1393	149	8	and	and	CCONJ
cana-1393	149	9	0	0	NUM
cana-1393	149	10	.	.	PUNCT
cana-1393	149	11	2	2	NUM
cana-1393	149	12	3/1	3/1	NUM
cana-1393	149	13	as	as	SCONJ
cana-1393	149	14	this	this	PRON
cana-1393	149	15	implies	imply	VERB
cana-1393	149	16	0	0	NUM
cana-1393	149	17	.	.	PUNCT
cana-1393	149	18	2	2	NUM
cana-1393	149	19	3/1	3/1	NUM
cana-1393	149	20	[	[	PUNCT
cana-1393	149	21	(	(	PUNCT
cana-1393	149	22	)	)	PUNCT
cana-1393	149	23	]	]	PUNCT
cana-1393	150	1	[	[	PUNCT
cana-1393	150	2	]	]	PUNCT
cana-1393	150	3	implies	imply	VERB
cana-1393	150	4	.	.	PUNCT
cana-1393	151	1	therefore	therefore	ADV
cana-1393	151	2	(	(	PUNCT
cana-1393	151	3	7	7	X
cana-1393	151	4	)	)	PUNCT
cana-1393	151	5	now	now	ADV
cana-1393	151	6	we	we	PRON
cana-1393	151	7	show	show	VERB
cana-1393	151	8	that	that	SCONJ
cana-1393	151	9	in	in	ADP
cana-1393	151	10	the	the	DET
cana-1393	151	11	inequality	inequality	NOUN
cana-1393	151	12	(	(	PUNCT
cana-1393	151	13	d2	d2	PROPN
cana-1393	151	14	)	)	PUNCT
cana-1393	151	15	putting	putting	NOUN
cana-1393	151	16	and	and	CCONJ
cana-1393	151	17	communications	communication	NOUN
cana-1393	151	18	on	on	ADP
cana-1393	151	19	applied	apply	VERB
cana-1393	151	20	nonlinear	nonlinear	ADJ
cana-1393	151	21	analysis	analysis	NOUN
cana-1393	151	22	issn	issn	NOUN
cana-1393	151	23	:	:	PUNCT
cana-1393	151	24	1074	1074	NUM
cana-1393	151	25	-	-	PUNCT
cana-1393	151	26	133x	133x	NUM
cana-1393	151	27	vol	vol	NOUN
cana-1393	151	28	31	31	NUM
cana-1393	151	29	no	no	NOUN
cana-1393	151	30	.	.	PUNCT
cana-1393	152	1	7s	7	NOUN
cana-1393	152	2	(	(	PUNCT
cana-1393	152	3	2024	2024	NUM
cana-1393	152	4	)	)	PUNCT
cana-1393	152	5	517	517	NUM
cana-1393	152	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1393	152	7	0	0	NUM
cana-1393	152	8	.	.	PUNCT
cana-1393	152	9	2	2	NUM
cana-1393	152	10	3/1	3/1	NUM
cana-1393	152	11	as	as	SCONJ
cana-1393	152	12	this	this	PRON
cana-1393	152	13	implies	imply	VERB
cana-1393	152	14	0	0	NUM
cana-1393	152	15	.	.	PUNCT
cana-1393	152	16	2	2	NUM
cana-1393	152	17	3/1	3/1	NUM
cana-1393	152	18	[	[	PUNCT
cana-1393	152	19	(	(	PUNCT
cana-1393	152	20	)	)	PUNCT
cana-1393	152	21	]	]	PUNCT
cana-1393	153	1	[	[	PUNCT
cana-1393	153	2	]	]	PUNCT
cana-1393	153	3	implies	imply	VERB
cana-1393	153	4	.	.	PUNCT
cana-1393	154	1	therefore	therefore	ADV
cana-1393	154	2	(	(	PUNCT
cana-1393	154	3	8)	8)	NUM
cana-1393	154	4	from	from	ADP
cana-1393	154	5	(	(	PUNCT
cana-1393	154	6	7	7	NUM
cana-1393	154	7	)	)	PUNCT
cana-1393	154	8	and	and	CCONJ
cana-1393	154	9	(	(	PUNCT
cana-1393	154	10	8)	8)	NUM
cana-1393	154	11	we	we	PRON
cana-1393	154	12	get	get	VERB
cana-1393	154	13	.	.	PUNCT
cana-1393	154	14	thus	thus	ADV
cana-1393	154	15	is	be	AUX
cana-1393	154	16	a	a	DET
cana-1393	154	17	fixed	fix	VERB
cana-1393	154	18	point	point	NOUN
cana-1393	154	19	that	that	PRON
cana-1393	154	20	is	be	AUX
cana-1393	154	21	common	common	ADJ
cana-1393	154	22	to	to	ADP
cana-1393	154	23	all	all	DET
cana-1393	154	24	four	four	NUM
cana-1393	154	25	self	self	NOUN
cana-1393	154	26	-	-	PUNCT
cana-1393	154	27	maps	map	NOUN
cana-1393	154	28	and	and	CCONJ
cana-1393	154	29	.	.	PUNCT
cana-1393	155	1	for	for	ADP
cana-1393	155	2	uniqueness	uniqueness	NOUN
cana-1393	155	3	:	:	PUNCT
cana-1393	155	4	assume	assume	VERB
cana-1393	155	5	that	that	PRON
cana-1393	155	6	be	be	AUX
cana-1393	155	7	another	another	DET
cana-1393	155	8	fixed	fix	VERB
cana-1393	155	9	point	point	NOUN
cana-1393	155	10	then	then	ADV
cana-1393	155	11	putting	put	VERB
cana-1393	155	12	and	and	CCONJ
cana-1393	155	13	in	in	ADP
cana-1393	155	14	0	0	NUM
cana-1393	155	15	.	.	PUNCT
cana-1393	155	16	2	2	NUM
cana-1393	155	17	3/1	3/1	NUM
cana-1393	155	18	0	0	NUM
cana-1393	155	19	.	.	PUNCT
cana-1393	155	20	2	2	NUM
cana-1393	155	21	3/1	3/1	NUM
cana-1393	155	22	[	[	PUNCT
cana-1393	155	23	(	(	PUNCT
cana-1393	155	24	)	)	PUNCT
cana-1393	155	25	]	]	PUNCT
cana-1393	156	1	[	[	PUNCT
cana-1393	156	2	]	]	X
cana-1393	156	3	,	,	PUNCT
cana-1393	156	4	a	a	DET
cana-1393	156	5	contradiction	contradiction	NOUN
cana-1393	156	6	which	which	PRON
cana-1393	156	7	implies	imply	VERB
cana-1393	156	8	.	.	PUNCT
cana-1393	157	1	this	this	PRON
cana-1393	157	2	demonstrates	demonstrate	VERB
cana-1393	157	3	is	be	AUX
cana-1393	157	4	the	the	DET
cana-1393	157	5	unique	unique	ADJ
cana-1393	157	6	common	common	ADJ
cana-1393	157	7	fixed	fix	VERB
cana-1393	157	8	point	point	NOUN
cana-1393	157	9	of	of	ADP
cana-1393	157	10	four	four	NUM
cana-1393	157	11	self	self	NOUN
cana-1393	157	12	-	-	PUNCT
cana-1393	157	13	mappings	mapping	NOUN
cana-1393	157	14	.	.	PUNCT
cana-1393	158	1	3.2	3.2	NUM
cana-1393	158	2	example	example	NOUN
cana-1393	158	3	:	:	PUNCT
cana-1393	158	4	suppose	suppose	VERB
cana-1393	158	5	[	[	PUNCT
cana-1393	158	6	]	]	X
cana-1393	158	7	be	be	AUX
cana-1393	158	8	defined	define	VERB
cana-1393	158	9	in	in	ADP
cana-1393	158	10	mms	mms	NOUN
cana-1393	158	11	with	with	ADP
cana-1393	158	12	|	|	ADV
cana-1393	158	13	|	|	ADV
cana-1393	158	14	.	.	PUNCT
cana-1393	159	1	we	we	PRON
cana-1393	159	2	define	define	VERB
cana-1393	159	3	self	self	NOUN
cana-1393	159	4	-	-	PUNCT
cana-1393	159	5	mappings	mapping	NOUN
cana-1393	159	6	and	and	CCONJ
cana-1393	159	7	as	as	SCONJ
cana-1393	159	8	{	{	PUNCT
cana-1393	159	9	{	{	PUNCT
cana-1393	159	10	communications	communication	NOUN
cana-1393	159	11	on	on	ADP
cana-1393	159	12	applied	apply	VERB
cana-1393	159	13	nonlinear	nonlinear	ADJ
cana-1393	159	14	analysis	analysis	NOUN
cana-1393	159	15	issn	issn	NOUN
cana-1393	159	16	:	:	PUNCT
cana-1393	159	17	1074	1074	NUM
cana-1393	159	18	-	-	PUNCT
cana-1393	159	19	133x	133x	NUM
cana-1393	159	20	vol	vol	NOUN
cana-1393	159	21	31	31	NUM
cana-1393	159	22	no	no	NOUN
cana-1393	159	23	.	.	PUNCT
cana-1393	160	1	7s	7	NOUN
cana-1393	160	2	(	(	PUNCT
cana-1393	160	3	2024	2024	NUM
cana-1393	160	4	)	)	PUNCT
cana-1393	160	5	518	518	NUM
cana-1393	160	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1393	160	7	{	{	PUNCT
cana-1393	160	8	and	and	CCONJ
cana-1393	160	9	{	{	PUNCT
cana-1393	160	10	clearly	clearly	ADV
cana-1393	160	11	*	*	PUNCT
cana-1393	161	1	+	+	CCONJ
cana-1393	161	2	,	,	PUNCT
cana-1393	161	3	*	*	PUNCT
cana-1393	162	1	+	+	PUNCT
cana-1393	163	1	*	*	PUNCT
cana-1393	163	2	+	+	NUM
cana-1393	163	3	*	*	PUNCT
cana-1393	163	4	)	)	PUNCT
cana-1393	164	1	*	*	PUNCT
cana-1393	165	1	+	+	PUNCT
cana-1393	165	2	and	and	CCONJ
cana-1393	165	3	*	*	PUNCT
cana-1393	165	4	+	+	PUNCT
cana-1393	165	5	*	*	PUNCT
cana-1393	165	6	)	)	PUNCT
cana-1393	166	1	*	*	PUNCT
cana-1393	167	1	+	+	PUNCT
cana-1393	167	2	*	*	PUNCT
cana-1393	168	1	+	+	PUNCT
cana-1393	168	2	[	[	PUNCT
cana-1393	168	3	[	[	PUNCT
cana-1393	168	4	so	so	SCONJ
cana-1393	168	5	that	that	SCONJ
cana-1393	168	6	condition	condition	NOUN
cana-1393	168	7	(	(	PUNCT
cana-1393	168	8	d1	d1	NOUN
cana-1393	168	9	)	)	PUNCT
cana-1393	168	10	is	be	AUX
cana-1393	168	11	fulfilled	fulfil	VERB
cana-1393	168	12	.	.	PUNCT
cana-1393	169	1	suppose	suppose	VERB
cana-1393	169	2	we	we	PRON
cana-1393	169	3	have	have	VERB
cana-1393	169	4	a	a	DET
cana-1393	169	5	sequence	sequence	NOUN
cana-1393	169	6	,	,	PUNCT
cana-1393	169	7	for	for	ADV
cana-1393	169	8	.	.	PUNCT
cana-1393	170	1	now	now	ADV
cana-1393	170	2	(	(	PUNCT
cana-1393	170	3	)	)	PUNCT
cana-1393	170	4	0	0	NUM
cana-1393	171	1	(	(	PUNCT
cana-1393	171	2	)	)	PUNCT
cana-1393	171	3	(	(	PUNCT
cana-1393	171	4	)	)	PUNCT
cana-1393	171	5	1	1	NUM
cana-1393	171	6	and	and	CCONJ
cana-1393	171	7	(	(	PUNCT
cana-1393	171	8	)	)	PUNCT
cana-1393	171	9	0	0	NUM
cana-1393	172	1	(	(	PUNCT
cana-1393	172	2	)	)	PUNCT
cana-1393	172	3	1	1	X
cana-1393	172	4	.	.	PUNCT
cana-1393	173	1	this	this	PRON
cana-1393	173	2	gives	give	VERB
cana-1393	173	3	and	and	CCONJ
cana-1393	173	4	.	.	PUNCT
cana-1393	174	1	(	(	PUNCT
cana-1393	174	2	)	)	PUNCT
cana-1393	174	3	.	.	PUNCT
cana-1393	175	1	(	(	PUNCT
cana-1393	175	2	)	)	PUNCT
cana-1393	175	3	/	/	PUNCT
cana-1393	176	1	*	*	PUNCT
cana-1393	176	2	+	+	NUM
cana-1393	176	3	0	0	NUM
cana-1393	176	4	(	(	PUNCT
cana-1393	176	5	)	)	PUNCT
cana-1393	176	6	(	(	PUNCT
cana-1393	176	7	)	)	PUNCT
cana-1393	176	8	1	1	NUM
cana-1393	176	9	and	and	CCONJ
cana-1393	176	10	(	(	PUNCT
cana-1393	176	11	*	*	PUNCT
cana-1393	176	12	[	[	PUNCT
cana-1393	176	13	(	(	PUNCT
cana-1393	176	14	)	)	PUNCT
cana-1393	176	15	(	(	PUNCT
cana-1393	176	16	)	)	PUNCT
cana-1393	176	17	]	]	PUNCT
cana-1393	177	1	[	[	PUNCT
cana-1393	177	2	(	(	PUNCT
cana-1393	177	3	.	.	PUNCT
cana-1393	177	4	(	(	PUNCT
cana-1393	177	5	)	)	PUNCT
cana-1393	177	6	/	/	SYM
cana-1393	177	7	)	)	PUNCT
cana-1393	177	8	]	]	PUNCT
cana-1393	177	9	(	(	PUNCT
cana-1393	177	10	)	)	PUNCT
cana-1393	177	11	.	.	PUNCT
cana-1393	178	1	now	now	ADV
cana-1393	178	2	take	take	VERB
cana-1393	178	3	another	another	DET
cana-1393	178	4	sequence	sequence	NOUN
cana-1393	178	5	,	,	PUNCT
cana-1393	178	6	for	for	ADV
cana-1393	178	7	.	.	PUNCT
cana-1393	179	1	now	now	ADV
cana-1393	179	2	(	(	PUNCT
cana-1393	179	3	)	)	PUNCT
cana-1393	179	4	0	0	NUM
cana-1393	180	1	(	(	PUNCT
cana-1393	180	2	)	)	PUNCT
cana-1393	180	3	1	1	NUM
cana-1393	180	4	and	and	CCONJ
cana-1393	180	5	(	(	PUNCT
cana-1393	180	6	)	)	PUNCT
cana-1393	180	7	0	0	NUM
cana-1393	181	1	(	(	PUNCT
cana-1393	181	2	)	)	PUNCT
cana-1393	181	3	(	(	PUNCT
cana-1393	181	4	)	)	PUNCT
cana-1393	181	5	1	1	X
cana-1393	181	6	.	.	PUNCT
cana-1393	182	1	communications	communication	NOUN
cana-1393	182	2	on	on	ADP
cana-1393	182	3	applied	apply	VERB
cana-1393	182	4	nonlinear	nonlinear	ADJ
cana-1393	182	5	analysis	analysis	NOUN
cana-1393	182	6	issn	issn	NOUN
cana-1393	182	7	:	:	PUNCT
cana-1393	182	8	1074	1074	NUM
cana-1393	182	9	-	-	PUNCT
cana-1393	182	10	133x	133x	NUM
cana-1393	182	11	vol	vol	NOUN
cana-1393	182	12	31	31	NUM
cana-1393	182	13	no	no	NOUN
cana-1393	182	14	.	.	PUNCT
cana-1393	183	1	7s	7	NOUN
cana-1393	183	2	(	(	PUNCT
cana-1393	183	3	2024	2024	NUM
cana-1393	183	4	)	)	PUNCT
cana-1393	183	5	519	519	NUM
cana-1393	183	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1393	183	7	this	this	PRON
cana-1393	183	8	gives	give	VERB
cana-1393	183	9	and	and	CCONJ
cana-1393	183	10	.	.	PUNCT
cana-1393	184	1	(	(	PUNCT
cana-1393	184	2	)	)	PUNCT
cana-1393	184	3	.	.	PUNCT
cana-1393	185	1	(	(	PUNCT
cana-1393	185	2	)	)	PUNCT
cana-1393	185	3	(	(	PUNCT
cana-1393	185	4	)	)	PUNCT
cana-1393	185	5	/	/	PUNCT
cana-1393	185	6	.	.	PUNCT
cana-1393	186	1	(	(	PUNCT
cana-1393	186	2	)	)	PUNCT
cana-1393	186	3	(	(	PUNCT
cana-1393	186	4	)	)	PUNCT
cana-1393	186	5	/	/	PUNCT
cana-1393	187	1	*	*	PUNCT
cana-1393	188	1	+	+	PUNCT
cana-1393	188	2	*	*	PUNCT
cana-1393	188	3	+	+	NUM
cana-1393	188	4	0	0	NUM
cana-1393	188	5	(	(	PUNCT
cana-1393	188	6	)	)	PUNCT
cana-1393	188	7	(	(	PUNCT
cana-1393	188	8	)	)	PUNCT
cana-1393	188	9	1	1	NUM
cana-1393	188	10	and	and	CCONJ
cana-1393	188	11	(	(	PUNCT
cana-1393	188	12	)	)	PUNCT
cana-1393	188	13	0	0	NUM
cana-1393	188	14	(	(	PUNCT
cana-1393	188	15	)	)	PUNCT
cana-1393	188	16	(	(	PUNCT
cana-1393	188	17	)	)	PUNCT
cana-1393	188	18	1	1	NUM
cana-1393	188	19	[	[	PUNCT
cana-1393	188	20	(	(	PUNCT
cana-1393	188	21	.	.	PUNCT
cana-1393	188	22	(	(	PUNCT
cana-1393	188	23	)	)	PUNCT
cana-1393	188	24	/	/	SYM
cana-1393	188	25	)	)	PUNCT
cana-1393	188	26	]	]	PUNCT
cana-1393	188	27	also	also	ADV
cana-1393	188	28	(	(	PUNCT
cana-1393	188	29	)	)	PUNCT
cana-1393	188	30	and	and	CCONJ
cana-1393	188	31	(	(	PUNCT
cana-1393	188	32	)	)	PUNCT
cana-1393	188	33	this	this	PRON
cana-1393	188	34	shows	show	VERB
cana-1393	188	35	that	that	SCONJ
cana-1393	188	36	the	the	DET
cana-1393	188	37	self	self	NOUN
cana-1393	188	38	-	-	PUNCT
cana-1393	188	39	maps	map	NOUN
cana-1393	188	40	and	and	CCONJ
cana-1393	188	41	are	be	AUX
cana-1393	188	42	conditionally	conditionally	ADV
cana-1393	188	43	reciprocally	reciprocally	ADV
cana-1393	188	44	continuous	continuous	ADJ
cana-1393	188	45	in	in	ADP
cana-1393	188	46	mms	mms	NOUN
cana-1393	188	47	.	.	PUNCT
cana-1393	189	1	similarly	similarly	ADV
cana-1393	189	2	(	(	PUNCT
cana-1393	189	3	)	)	PUNCT
cana-1393	189	4	and	and	CCONJ
cana-1393	189	5	(	(	PUNCT
cana-1393	189	6	)	)	PUNCT
cana-1393	189	7	this	this	PRON
cana-1393	189	8	shows	show	VERB
cana-1393	189	9	that	that	SCONJ
cana-1393	189	10	the	the	DET
cana-1393	189	11	self	self	NOUN
cana-1393	189	12	-	-	PUNCT
cana-1393	189	13	maps	map	NOUN
cana-1393	189	14	and	and	CCONJ
cana-1393	189	15	are	be	AUX
cana-1393	189	16	conditionally	conditionally	ADV
cana-1393	189	17	semi	semi	ADV
cana-1393	189	18	compatible	compatible	ADJ
cana-1393	189	19	in	in	ADP
cana-1393	189	20	mms	mms	NOUN
cana-1393	189	21	.	.	PUNCT
cana-1393	190	1	moreover	moreover	ADV
cana-1393	190	2	and	and	CCONJ
cana-1393	190	3	are	be	AUX
cana-1393	190	4	coincidence	coincidence	NOUN
cana-1393	190	5	points	point	NOUN
cana-1393	190	6	(	(	PUNCT
cana-1393	190	7	(	(	PUNCT
cana-1393	190	8	)	)	PUNCT
cana-1393	190	9	(	(	PUNCT
cana-1393	190	10	)	)	PUNCT
cana-1393	190	11	*	*	PUNCT
cana-1393	190	12	implies	imply	VERB
cana-1393	190	13	(	(	PUNCT
cana-1393	190	14	(	(	PUNCT
cana-1393	190	15	)	)	PUNCT
cana-1393	190	16	(	(	PUNCT
cana-1393	190	17	)	)	PUNCT
cana-1393	190	18	*	*	PUNCT
cana-1393	190	19	,	,	PUNCT
cana-1393	190	20	but	but	CCONJ
cana-1393	190	21	(	(	PUNCT
cana-1393	190	22	)	)	PUNCT
cana-1393	190	23	and	and	CCONJ
cana-1393	190	24	(	(	PUNCT
cana-1393	190	25	)	)	PUNCT
cana-1393	190	26	.	.	PUNCT
cana-1393	191	1	as	as	ADP
cana-1393	191	2	a	a	DET
cana-1393	191	3	result	result	NOUN
cana-1393	191	4	,	,	PUNCT
cana-1393	191	5	the	the	DET
cana-1393	191	6	couple	couple	NOUN
cana-1393	191	7	satisfies	satisfy	VERB
cana-1393	191	8	owc	owc	PROPN
cana-1393	191	9	.	.	PUNCT
cana-1393	192	1	therefore	therefore	ADV
cana-1393	192	2	the	the	DET
cana-1393	192	3	self	self	NOUN
cana-1393	192	4	-	-	PUNCT
cana-1393	192	5	maps	map	NOUN
cana-1393	192	6	and	and	CCONJ
cana-1393	192	7	t	t	PROPN
cana-1393	192	8	are	be	AUX
cana-1393	192	9	strongly	strongly	ADV
cana-1393	192	10	semi	semi	ADJ
cana-1393	192	11	compatible	compatible	ADJ
cana-1393	192	12	mappings	mapping	NOUN
cana-1393	192	13	in	in	ADP
cana-1393	192	14	mms	mms	NOUN
cana-1393	192	15	.	.	PUNCT
cana-1393	193	1	but	but	CCONJ
cana-1393	193	2	(	(	PUNCT
cana-1393	193	3	)	)	PUNCT
cana-1393	193	4	0	0	NUM
cana-1393	194	1	(	(	PUNCT
cana-1393	194	2	)	)	PUNCT
cana-1393	194	3	1	1	NUM
cana-1393	194	4	*	*	PUNCT
cana-1393	195	1	+	+	PUNCT
cana-1393	195	2	[	[	PUNCT
cana-1393	195	3	(	(	PUNCT
cana-1393	195	4	(	(	PUNCT
cana-1393	195	5	)	)	PUNCT
cana-1393	195	6	*	*	PUNCT
cana-1393	195	7	]	]	PUNCT
cana-1393	195	8	and	and	CCONJ
cana-1393	195	9	(	(	PUNCT
cana-1393	195	10	*	*	PUNCT
cana-1393	195	11	[	[	PUNCT
cana-1393	195	12	(	(	PUNCT
cana-1393	195	13	)	)	PUNCT
cana-1393	195	14	]	]	PUNCT
cana-1393	196	1	[	[	PUNCT
cana-1393	196	2	]	]	X
cana-1393	196	3	[	[	PUNCT
cana-1393	196	4	(	(	PUNCT
cana-1393	196	5	)	)	PUNCT
cana-1393	196	6	]	]	PUNCT
cana-1393	196	7	communications	communication	NOUN
cana-1393	196	8	on	on	ADP
cana-1393	196	9	applied	apply	VERB
cana-1393	196	10	nonlinear	nonlinear	ADJ
cana-1393	196	11	analysis	analysis	NOUN
cana-1393	196	12	issn	issn	NOUN
cana-1393	196	13	:	:	PUNCT
cana-1393	196	14	1074	1074	NUM
cana-1393	196	15	-	-	PUNCT
cana-1393	196	16	133x	133x	NUM
cana-1393	196	17	vol	vol	NOUN
cana-1393	196	18	31	31	NUM
cana-1393	196	19	no	no	NOUN
cana-1393	196	20	.	.	PUNCT
cana-1393	197	1	7s	7	NOUN
cana-1393	197	2	(	(	PUNCT
cana-1393	197	3	2024	2024	NUM
cana-1393	197	4	)	)	PUNCT
cana-1393	197	5	520	520	NUM
cana-1393	197	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1393	197	7	similarly	similarly	ADV
cana-1393	197	8	(	(	PUNCT
cana-1393	197	9	)	)	PUNCT
cana-1393	197	10	.	.	PUNCT
cana-1393	198	1	(	(	PUNCT
cana-1393	198	2	)	)	PUNCT
cana-1393	198	3	/	/	PUNCT
cana-1393	199	1	*	*	PUNCT
cana-1393	200	1	+	+	PUNCT
cana-1393	200	2	*	*	PUNCT
cana-1393	200	3	(	(	PUNCT
cana-1393	200	4	)	)	PUNCT
cana-1393	200	5	+	+	CCONJ
cana-1393	200	6	and	and	CCONJ
cana-1393	200	7	(	(	PUNCT
cana-1393	200	8	*	*	PUNCT
cana-1393	200	9	[	[	PUNCT
cana-1393	200	10	(	(	PUNCT
cana-1393	200	11	*	*	SYM
cana-1393	200	12	]	]	X
cana-1393	201	1	[	[	PUNCT
cana-1393	201	2	]	]	X
cana-1393	201	3	[	[	PUNCT
cana-1393	201	4	.	.	PUNCT
cana-1393	201	5	(	(	PUNCT
cana-1393	201	6	)	)	PUNCT
cana-1393	201	7	/	/	SYM
cana-1393	201	8	]	]	PUNCT
cana-1393	201	9	therefore	therefore	ADV
cana-1393	201	10	(	(	PUNCT
cana-1393	201	11	)	)	PUNCT
cana-1393	201	12	and	and	CCONJ
cana-1393	201	13	(	(	PUNCT
cana-1393	201	14	)	)	PUNCT
cana-1393	201	15	.	.	PUNCT
cana-1393	202	1	demonstrating	demonstrate	VERB
cana-1393	202	2	that	that	SCONJ
cana-1393	202	3	the	the	DET
cana-1393	202	4	compatibility	compatibility	NOUN
cana-1393	202	5	condition	condition	NOUN
cana-1393	202	6	is	be	AUX
cana-1393	202	7	not	not	PART
cana-1393	202	8	satisfied	satisfied	ADJ
cana-1393	202	9	.	.	PUNCT
cana-1393	203	1	further	far	ADV
cana-1393	203	2	(	(	PUNCT
cana-1393	203	3	)	)	PUNCT
cana-1393	203	4	(	(	PUNCT
cana-1393	203	5	)	)	PUNCT
cana-1393	203	6	which	which	PRON
cana-1393	203	7	imliies	imliie	VERB
cana-1393	203	8	that	that	PRON
cana-1393	203	9	is	be	AUX
cana-1393	203	10	the	the	DET
cana-1393	203	11	coincidence	coincidence	NOUN
cana-1393	203	12	point	point	NOUN
cana-1393	203	13	of	of	ADP
cana-1393	203	14	and	and	CCONJ
cana-1393	203	15	.	.	PUNCT
cana-1393	204	1	(	(	PUNCT
cana-1393	204	2	)	)	PUNCT
cana-1393	204	3	(	(	PUNCT
cana-1393	204	4	)	)	PUNCT
cana-1393	204	5	which	which	PRON
cana-1393	204	6	imliies	imliie	VERB
cana-1393	204	7	that	that	PRON
cana-1393	204	8	is	be	AUX
cana-1393	204	9	the	the	DET
cana-1393	204	10	coincidence	coincidence	NOUN
cana-1393	204	11	point	point	NOUN
cana-1393	204	12	of	of	ADP
cana-1393	204	13	and	and	CCONJ
cana-1393	204	14	.	.	PUNCT
cana-1393	205	1	hence	hence	ADV
cana-1393	205	2	(	(	PUNCT
cana-1393	205	3	)	)	PUNCT
cana-1393	205	4	(	(	PUNCT
cana-1393	205	5	)	)	PUNCT
cana-1393	205	6	and	and	CCONJ
cana-1393	205	7	(	(	PUNCT
cana-1393	205	8	)	)	PUNCT
cana-1393	205	9	(	(	PUNCT
cana-1393	205	10	)	)	PUNCT
cana-1393	205	11	which	which	PRON
cana-1393	205	12	gives	give	VERB
cana-1393	205	13	(	(	PUNCT
cana-1393	205	14	(	(	PUNCT
cana-1393	205	15	)	)	PUNCT
cana-1393	205	16	(	(	PUNCT
cana-1393	205	17	)	)	PUNCT
cana-1393	205	18	*	*	PUNCT
cana-1393	206	1	also	also	ADV
cana-1393	206	2	(	(	PUNCT
cana-1393	206	3	)	)	PUNCT
cana-1393	206	4	(	(	PUNCT
cana-1393	206	5	)	)	PUNCT
cana-1393	206	6	and	and	CCONJ
cana-1393	206	7	(	(	PUNCT
cana-1393	206	8	)	)	PUNCT
cana-1393	206	9	(	(	PUNCT
cana-1393	206	10	)	)	PUNCT
cana-1393	206	11	which	which	PRON
cana-1393	206	12	gives	give	VERB
cana-1393	206	13	(	(	PUNCT
cana-1393	206	14	(	(	PUNCT
cana-1393	206	15	)	)	PUNCT
cana-1393	206	16	(	(	PUNCT
cana-1393	206	17	)	)	PUNCT
cana-1393	206	18	*	*	PUNCT
cana-1393	206	19	.	.	PUNCT
cana-1393	207	1	hence	hence	ADV
cana-1393	207	2	the	the	DET
cana-1393	207	3	couple	couple	NOUN
cana-1393	207	4	and	and	CCONJ
cana-1393	207	5	are	be	AUX
cana-1393	207	6	weakly	weakly	ADV
cana-1393	207	7	compatible	compatible	ADJ
cana-1393	207	8	mappings	mapping	NOUN
cana-1393	207	9	but	but	CCONJ
cana-1393	207	10	not	not	PART
cana-1393	207	11	compatible	compatible	ADJ
cana-1393	207	12	.	.	PUNCT
cana-1393	208	1	also	also	ADV
cana-1393	208	2	(	(	PUNCT
cana-1393	208	3	)	)	PUNCT
cana-1393	208	4	(	(	PUNCT
cana-1393	208	5	)	)	PUNCT
cana-1393	208	6	(	(	PUNCT
cana-1393	208	7	)	)	PUNCT
cana-1393	208	8	(	(	PUNCT
cana-1393	208	9	)	)	PUNCT
cana-1393	208	10	.	.	PUNCT
cana-1393	209	1	it	it	PRON
cana-1393	209	2	has	have	AUX
cana-1393	209	3	been	be	AUX
cana-1393	209	4	observed	observe	VERB
cana-1393	209	5	that	that	SCONJ
cana-1393	209	6	the	the	DET
cana-1393	209	7	unique	unique	ADJ
cana-1393	209	8	common	common	ADJ
cana-1393	209	9	fixed	fix	VERB
cana-1393	209	10	point	point	NOUN
cana-1393	209	11	to	to	ADP
cana-1393	209	12	four	four	NUM
cana-1393	209	13	self	self	NOUN
cana-1393	209	14	-	-	PUNCT
cana-1393	209	15	mapping	mapping	NOUN
cana-1393	209	16	and	and	CCONJ
cana-1393	209	17	is	be	AUX
cana-1393	209	18	.	.	PUNCT
cana-1393	210	1	4	4	X
cana-1393	210	2	.	.	X
cana-1393	210	3	conclusion	conclusion	NOUN
cana-1393	210	4	in	in	ADP
cana-1393	210	5	this	this	DET
cana-1393	210	6	paper	paper	NOUN
cana-1393	210	7	the	the	DET
cana-1393	210	8	concepts	concept	NOUN
cana-1393	210	9	of	of	ADP
cana-1393	210	10	semi	semi	ADJ
cana-1393	210	11	-	-	ADJ
cana-1393	210	12	compatible	compatible	ADJ
cana-1393	210	13	mapping	mapping	NOUN
cana-1393	210	14	,	,	PUNCT
cana-1393	210	15	wcm	wcm	NOUN
cana-1393	210	16	,	,	PUNCT
cana-1393	210	17	reciprocally	reciprocally	ADV
cana-1393	210	18	continuous	continuous	ADJ
cana-1393	210	19	,	,	PUNCT
cana-1393	210	20	conditionally	conditionally	ADV
cana-1393	210	21	reciprocally	reciprocally	ADV
cana-1393	210	22	continuous	continuous	ADJ
cana-1393	210	23	mappings	mapping	NOUN
cana-1393	210	24	and	and	CCONJ
cana-1393	210	25	and	and	CCONJ
cana-1393	210	26	owc	owc	NUM
cana-1393	210	27	mappings	mapping	NOUN
cana-1393	210	28	are	be	AUX
cana-1393	210	29	used	use	VERB
cana-1393	210	30	for	for	ADP
cana-1393	210	31	obtaining	obtain	VERB
cana-1393	210	32	the	the	DET
cana-1393	210	33	generalization	generalization	NOUN
cana-1393	210	34	of	of	ADP
cana-1393	210	35	existing	exist	VERB
cana-1393	210	36	common	common	ADJ
cana-1393	210	37	fixed	fix	VERB
cana-1393	210	38	point	point	NOUN
cana-1393	210	39	theorems	theorem	NOUN
cana-1393	210	40	proved	prove	VERB
cana-1393	210	41	in	in	ADP
cana-1393	210	42	[	[	X
cana-1393	210	43	1	1	X
cana-1393	210	44	]	]	PUNCT
cana-1393	210	45	which	which	PRON
cana-1393	210	46	are	be	AUX
cana-1393	210	47	weaker	weak	ADJ
cana-1393	210	48	than	than	ADP
cana-1393	210	49	those	those	DET
cana-1393	210	50	classes	class	NOUN
cana-1393	210	51	of	of	ADP
cana-1393	210	52	compatible	compatible	ADJ
cana-1393	210	53	mappings	mapping	NOUN
cana-1393	210	54	and	and	CCONJ
cana-1393	210	55	continuous	continuous	ADJ
cana-1393	210	56	mappings	mapping	NOUN
cana-1393	210	57	.	.	PUNCT
cana-1393	211	1	further	far	ADV
cana-1393	211	2	,	,	PUNCT
cana-1393	211	3	these	these	DET
cana-1393	211	4	results	result	NOUN
cana-1393	211	5	are	be	AUX
cana-1393	211	6	also	also	ADV
cana-1393	211	7	substantiated	substantiate	VERB
cana-1393	211	8	with	with	ADP
cana-1393	211	9	appropriate	appropriate	ADJ
cana-1393	211	10	examples	example	NOUN
cana-1393	211	11	.	.	PUNCT
cana-1393	212	1	references	reference	NOUN
cana-1393	212	2	:	:	PUNCT
cana-1393	213	1	[	[	X
cana-1393	213	2	1	1	NUM
cana-1393	213	3	]	]	X
cana-1393	213	4	abdou	abdou	PROPN
cana-1393	213	5	,	,	PUNCT
cana-1393	213	6	afrah	afrah	PROPN
cana-1393	213	7	an	an	PROPN
cana-1393	213	8	.	.	PUNCT
cana-1393	214	1	"	"	PUNCT
cana-1393	214	2	common	common	ADJ
cana-1393	214	3	fixed	fix	VERB
cana-1393	214	4	point	point	NOUN
cana-1393	214	5	results	result	NOUN
cana-1393	214	6	for	for	ADP
cana-1393	214	7	compatible	compatible	ADJ
cana-1393	214	8	-	-	PUNCT
cana-1393	214	9	type	type	NOUN
cana-1393	214	10	mappings	mapping	NOUN
cana-1393	214	11	in	in	ADP
cana-1393	214	12	multiplicative	multiplicative	ADJ
cana-1393	214	13	metric	metric	ADJ
cana-1393	214	14	spaces	space	NOUN
cana-1393	214	15	.	.	PUNCT
cana-1393	214	16	"	"	PUNCT
cana-1393	215	1	j.	j.	PROPN
cana-1393	215	2	nonlinear	nonlinear	PROPN
cana-1393	215	3	sci	sci	PROPN
cana-1393	215	4	.	.	PUNCT
cana-1393	215	5	appl	appl	PROPN
cana-1393	215	6	9	9	NUM
cana-1393	215	7	(	(	PUNCT
cana-1393	215	8	2016	2016	NUM
cana-1393	215	9	):	):	PUNCT
cana-1393	215	10	2244	2244	NUM
cana-1393	215	11	-	-	SYM
cana-1393	215	12	2257	2257	NUM
cana-1393	215	13	.	.	PUNCT
cana-1393	216	1	[	[	X
cana-1393	216	2	2	2	NUM
cana-1393	216	3	]	]	SYM
cana-1393	216	4	b	b	NOUN
cana-1393	216	5	vijayabaskerreddy	vijayabaskerreddy	NOUN
cana-1393	216	6	and	and	CCONJ
cana-1393	216	7	v	v	ADP
cana-1393	216	8	srinivas	srinivas	PROPN
cana-1393	216	9	fixed	fix	VERB
cana-1393	216	10	point	point	NOUN
cana-1393	216	11	results	result	NOUN
cana-1393	216	12	on	on	ADP
cana-1393	216	13	multiplicative	multiplicative	ADJ
cana-1393	216	14	semi	semi	ADJ
cana-1393	216	15	-	-	ADJ
cana-1393	216	16	metric	metric	ADJ
cana-1393	216	17	space	space	NOUN
cana-1393	216	18	.	.	PUNCT
cana-1393	217	1	journal	journal	NOUN
cana-1393	217	2	of	of	ADP
cana-1393	217	3	scientific	scientific	ADJ
cana-1393	217	4	research	research	NOUN
cana-1393	217	5	,	,	PUNCT
cana-1393	217	6	12(3):341–348	12(3):341–348	PROPN
cana-1393	217	7	,	,	PUNCT
cana-1393	217	8	2020	2020	NUM
cana-1393	217	9	.	.	PUNCT
cana-1393	218	1	http://dx.doi.org/10.3329/jsr.v12i3.44754	http://dx.doi.org/10.3329/jsr.v12i3.44754	PROPN
cana-1393	218	2	[	[	X
cana-1393	218	3	3	3	NUM
cana-1393	218	4	]	]	PUNCT
cana-1393	218	5	kidane	kidane	PROPN
cana-1393	218	6	koyas	koyas	PROPN
cana-1393	218	7	,	,	PUNCT
cana-1393	218	8	alemayehu	alemayehu	PROPN
cana-1393	218	9	gebre	gebre	NOUN
cana-1393	218	10	,	,	PUNCT
cana-1393	218	11	and	and	CCONJ
cana-1393	218	12	aynalem	aynalem	PROPN
cana-1393	218	13	kassaye	kassaye	NOUN
cana-1393	218	14	.	.	PUNCT
cana-1393	219	1	a	a	DET
cana-1393	219	2	common	common	ADJ
cana-1393	219	3	fixed	fix	VERB
cana-1393	219	4	point	point	NOUN
cana-1393	219	5	theorem	theorem	NOUN
cana-1393	219	6	for	for	ADP
cana-1393	219	7	generalized	generalized	ADJ
cana-1393	219	8	weakly	weakly	ADJ
cana-1393	219	9	contractive	contractive	ADJ
cana-1393	219	10	mappings	mapping	NOUN
cana-1393	219	11	in	in	ADP
cana-1393	219	12	multiplicative	multiplicative	ADJ
cana-1393	219	13	metric	metric	ADJ
cana-1393	219	14	spaces	space	NOUN
cana-1393	219	15	.	.	PUNCT
cana-1393	220	1	advances	advance	NOUN
cana-1393	220	2	in	in	ADP
cana-1393	220	3	the	the	DET
cana-1393	220	4	theory	theory	NOUN
cana-1393	220	5	of	of	ADP
cana-1393	220	6	nonlinear	nonlinear	ADJ
cana-1393	220	7	analysis	analysis	NOUN
cana-1393	220	8	and	and	CCONJ
cana-1393	220	9	its	its	PRON
cana-1393	220	10	application	application	NOUN
cana-1393	220	11	,	,	PUNCT
cana-1393	220	12	4(1):1–13	4(1):1–13	PROPN
cana-1393	220	13	,	,	PUNCT
cana-1393	220	14	2020	2020	NUM
cana-1393	220	15	.	.	PUNCT
cana-1393	221	1	https://doi.org/10.31197/atnaa.573903	https://doi.org/10.31197/atnaa.573903	VERB
cana-1393	222	1	[	[	X
cana-1393	222	2	4	4	X
cana-1393	222	3	]	]	PUNCT
cana-1393	222	4	b.vijayabaskerreddy	b.vijayabaskerreddy	NOUN
cana-1393	222	5	and	and	CCONJ
cana-1393	222	6	v.	v.	ADP
cana-1393	222	7	srinivas	srinivas	PROPN
cana-1393	222	8	.	.	PUNCT
cana-1393	223	1	some	some	DET
cana-1393	223	2	results	result	NOUN
cana-1393	223	3	in	in	ADP
cana-1393	223	4	multiplicative	multiplicative	ADJ
cana-1393	223	5	metric	metric	ADJ
cana-1393	223	6	space	space	NOUN
cana-1393	223	7	using	use	VERB
cana-1393	223	8	absorbing	absorb	VERB
cana-1393	223	9	mappings	mapping	NOUN
cana-1393	223	10	.	.	PUNCT
cana-1393	224	1	indian	indian	ADJ
cana-1393	224	2	journal	journal	PROPN
cana-1393	224	3	of	of	ADP
cana-1393	224	4	science	science	NOUN
cana-1393	224	5	and	and	CCONJ
cana-1393	224	6	technology	technology	NOUN
cana-1393	224	7	,	,	PUNCT
cana-1393	224	8	13(39	13(39	NUM
cana-1393	224	9	):	):	PUNCT
cana-1393	224	10	4161–4167	4161–4167	NUM
cana-1393	224	11	,	,	PUNCT
cana-1393	224	12	2020	2020	NUM
cana-1393	224	13	.	.	PUNCT
cana-1393	225	1	https://doi.org/10.17485/ijst/v13i39.1629	https://doi.org/10.17485/ijst/v13i39.1629	PROPN
cana-1393	225	2	communications	communication	NOUN
cana-1393	225	3	on	on	ADP
cana-1393	225	4	applied	apply	VERB
cana-1393	225	5	nonlinear	nonlinear	ADJ
cana-1393	225	6	analysis	analysis	NOUN
cana-1393	225	7	issn	issn	NOUN
cana-1393	225	8	:	:	PUNCT
cana-1393	225	9	1074	1074	NUM
cana-1393	225	10	-	-	PUNCT
cana-1393	225	11	133x	133x	NUM
cana-1393	225	12	vol	vol	NOUN
cana-1393	225	13	31	31	NUM
cana-1393	225	14	no	no	NOUN
cana-1393	225	15	.	.	PUNCT
cana-1393	226	1	7s	7	NOUN
cana-1393	226	2	(	(	PUNCT
cana-1393	226	3	2024	2024	NUM
cana-1393	226	4	)	)	PUNCT
cana-1393	226	5	521	521	NUM
cana-1393	226	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1393	227	1	[	[	X
cana-1393	227	2	5	5	NUM
cana-1393	227	3	]	]	SYM
cana-1393	227	4	v.srinivas	v.srinivas	NOUN
cana-1393	227	5	and	and	CCONJ
cana-1393	227	6	k.mallaiah	k.mallaiah	PROPN
cana-1393	227	7	.	.	PUNCT
cana-1393	228	1	a	a	DET
cana-1393	228	2	result	result	NOUN
cana-1393	228	3	on	on	ADP
cana-1393	228	4	multiplicative	multiplicative	ADJ
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cana-1393	229	1	j.	j.	PROPN
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cana-1393	230	2	.	.	PUNCT
cana-1393	231	1	sci	sci	PROPN
cana-1393	231	2	.	.	PROPN
cana-1393	231	3	,	,	PUNCT
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cana-1393	240	2	.	.	PUNCT
cana-1393	241	1	sci	sci	PROPN
cana-1393	241	2	.	.	PROPN
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cana-1393	241	5	,	,	PUNCT
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cana-1393	241	7	.	.	PUNCT
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cana-1393	243	2	8	8	NUM
cana-1393	243	3	]	]	X
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cana-1393	243	5	,	,	PUNCT
cana-1393	243	6	t.	t.	PROPN
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cana-1393	245	9	-	-	PUNCT
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cana-1393	245	11	,	,	PUNCT
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cana-1393	245	13	.	.	PUNCT
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cana-1393	246	4	]	]	PUNCT
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cana-1393	246	22	,	,	PUNCT
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cana-1393	246	24	.	.	PUNCT
cana-1393	247	1	j.	j.	PROPN
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cana-1393	248	7	)	)	PUNCT
cana-1393	248	8	(	(	PUNCT
cana-1393	248	9	2021	2021	NUM
cana-1393	248	10	)	)	PUNCT
cana-1393	248	11	,	,	PUNCT
cana-1393	248	12	915	915	NUM
cana-1393	248	13	-	-	SYM
cana-1393	248	14	928	928	NUM
cana-1393	248	15	.	.	PUNCT
cana-1393	249	1	doi	doi	NOUN
cana-1393	249	2	:	:	PUNCT
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cana-1393	250	1	[	[	X
cana-1393	250	2	10	10	NUM
cana-1393	250	3	]	]	X
cana-1393	250	4	hussain	hussain	PROPN
cana-1393	250	5	,	,	PUNCT
cana-1393	250	6	baqir	baqir	PROPN
cana-1393	250	7	,	,	PUNCT
cana-1393	250	8	et	et	PROPN
cana-1393	250	9	al	al	PROPN
cana-1393	250	10	.	.	PUNCT
cana-1393	251	1	"	"	PUNCT
cana-1393	251	2	some	some	DET
cana-1393	251	3	coupled	couple	VERB
cana-1393	251	4	fixed	fix	VERB
cana-1393	251	5	point	point	NOUN
cana-1393	251	6	theorems	theorem	NOUN
cana-1393	251	7	on	on	ADP
cana-1393	251	8	multiplicative	multiplicative	ADJ
cana-1393	251	9	metric	metric	ADJ
cana-1393	251	10	spaces	space	NOUN
cana-1393	251	11	with	with	ADP
cana-1393	251	12	an	an	DET
cana-1393	251	13	application	application	NOUN
cana-1393	251	14	.	.	PUNCT
cana-1393	251	15	"	"	PUNCT
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cana-1393	251	19	(	(	PUNCT
cana-1393	251	20	2022	2022	NUM
cana-1393	251	21	):	):	PUNCT
cana-1393	251	22	14631	14631	NUM
cana-1393	251	23	-	-	SYM
cana-1393	251	24	14651	14651	NUM
cana-1393	251	25	.	.	PUNCT
cana-1393	252	1	doi:10.3934	doi:10.3934	NOUN
cana-1393	252	2	/	/	SYM
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cana-1393	252	4	.	.	PUNCT
cana-1393	253	1	[	[	X
cana-1393	253	2	11	11	NUM
cana-1393	253	3	]	]	PUNCT
cana-1393	253	4	m.verma	m.verma	NUM
cana-1393	253	5	,	,	PUNCT
cana-1393	253	6	p.	p.	PROPN
cana-1393	253	7	kumar	kumar	PROPN
cana-1393	253	8	,	,	PUNCT
cana-1393	253	9	and	and	CCONJ
cana-1393	253	10	n.	n.	PROPN
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cana-1393	254	3	point	point	NOUN
cana-1393	254	4	theorems	theorem	NOUN
cana-1393	254	5	using	use	VERB
cana-1393	254	6	weakly	weakly	ADJ
cana-1393	254	7	compaible	compaible	ADJ
cana-1393	254	8	mapsin	mapsin	NOUN
cana-1393	254	9	multiplicative	multiplicative	ADJ
cana-1393	254	10	metric	metric	ADJ
cana-1393	254	11	spaces	space	NOUN
cana-1393	254	12	.	.	PUNCT
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cana-1393	255	6	and	and	CCONJ
cana-1393	255	7	applications	application	NOUN
cana-1393	255	8	,	,	PUNCT
cana-1393	255	9	9(1):284–292	9(1):284–292	NOUN
cana-1393	255	10	,	,	PUNCT
cana-1393	255	11	2021	2021	NUM
cana-1393	255	12	.	.	PUNCT
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cana-1393	256	5	http://math-frac.org/journals/ejmaa/	http://math-frac.org/journals/ejmaa/	NOUN
cana-1393	256	6	http://math-frac.org/journals/ejmaa/	http://math-frac.org/journals/ejmaa/	NOUN