id	sid	tid	token	lemma	pos
cana-3958	1	1	communications	communication	NOUN
cana-3958	1	2	on	on	ADP
cana-3958	1	3	applied	apply	VERB
cana-3958	1	4	nonlinear	nonlinear	ADJ
cana-3958	1	5	analysis	analysis	NOUN
cana-3958	1	6	issn	issn	NOUN
cana-3958	1	7	:	:	PUNCT
cana-3958	1	8	1074	1074	NUM
cana-3958	1	9	-	-	PUNCT
cana-3958	1	10	133x	133x	NUM
cana-3958	1	11	vol	vol	NOUN
cana-3958	1	12	32	32	NUM
cana-3958	1	13	no	no	NOUN
cana-3958	1	14	.	.	PUNCT
cana-3958	2	1	9s	9s	NUM
cana-3958	2	2	(	(	PUNCT
cana-3958	2	3	2025	2025	NUM
cana-3958	2	4	)	)	PUNCT
cana-3958	2	5	466	466	NUM
cana-3958	3	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3958	3	2	subclass	subclass	NOUN
cana-3958	3	3	of	of	ADP
cana-3958	3	4	univalent	univalent	ADJ
cana-3958	3	5	functions	function	NOUN
cana-3958	3	6	involving	involve	VERB
cana-3958	3	7	raducanu	raducanu	NOUN
cana-3958	3	8	-	-	PUNCT
cana-3958	3	9	orhan	orhan	NOUN
cana-3958	3	10	differential	differential	ADJ
cana-3958	3	11	operator	operator	NOUN
cana-3958	3	12	connected	connect	VERB
cana-3958	3	13	with	with	ADP
cana-3958	3	14	pascal	pascal	ADJ
cana-3958	3	15	distribution	distribution	NOUN
cana-3958	3	16	series	series	NOUN
cana-3958	3	17	1saravanan	1saravanan	NUM
cana-3958	3	18	k	k	NOUN
cana-3958	3	19	,	,	PUNCT
cana-3958	3	20	2thirucheran	2thirucheran	NUM
cana-3958	3	21	m	m	NOUN
cana-3958	3	22	,	,	PUNCT
cana-3958	3	23	3bhuvaneswari	3bhuvaneswari	NUM
cana-3958	3	24	raja	raja	NOUN
cana-3958	3	25	,	,	PUNCT
cana-3958	3	26	4stalin	4stalin	PROPN
cana-3958	3	27	t	t	PROPN
cana-3958	3	28	,	,	PUNCT
cana-3958	3	29	5britto	5britto	PROPN
cana-3958	3	30	manoj	manoj	VERB
cana-3958	3	31	a	a	DET
cana-3958	3	32	1department	1department	NUM
cana-3958	3	33	of	of	ADP
cana-3958	3	34	mathematics	mathematic	NOUN
cana-3958	3	35	,	,	PUNCT
cana-3958	3	36	dr	dr	PROPN
cana-3958	3	37	ambedkar	ambedkar	PROPN
cana-3958	3	38	government	government	PROPN
cana-3958	3	39	arts	arts	PROPN
cana-3958	3	40	college	college	PROPN
cana-3958	3	41	,	,	PUNCT
cana-3958	3	42	chennai	chennai	PROPN
cana-3958	3	43	,	,	PUNCT
cana-3958	3	44	600	600	NUM
cana-3958	3	45	039	039	NUM
cana-3958	3	46	,	,	PUNCT
cana-3958	3	47	india	india	PROPN
cana-3958	3	48	.	.	PUNCT
cana-3958	4	1	saravanandagac@gmail.com	saravanandagac@gmail.com	X
cana-3958	5	1	2department	2department	NUM
cana-3958	5	2	of	of	ADP
cana-3958	5	3	mathematics	mathematic	NOUN
cana-3958	5	4	,	,	PUNCT
cana-3958	5	5	l	l	PROPN
cana-3958	5	6	n	n	PRON
cana-3958	5	7	government	government	NOUN
cana-3958	5	8	college	college	NOUN
cana-3958	5	9	,	,	PUNCT
cana-3958	5	10	ponneri	ponneri	NOUN
cana-3958	5	11	,	,	PUNCT
cana-3958	5	12	chennai	chennai	NOUN
cana-3958	5	13	,	,	PUNCT
cana-3958	5	14	601	601	NUM
cana-3958	5	15	204	204	NUM
cana-3958	5	16	,	,	PUNCT
cana-3958	5	17	india	india	PROPN
cana-3958	5	18	.	.	PUNCT
cana-3958	6	1	drthirucheran@gmail.com	drthirucheran@gmail.com	X
cana-3958	7	1	3department	3department	NUM
cana-3958	7	2	of	of	ADP
cana-3958	7	3	mathematics	mathematic	NOUN
cana-3958	7	4	,	,	PUNCT
cana-3958	7	5	aalim	aalim	PROPN
cana-3958	8	1	muhammed	muhamme	VERB
cana-3958	8	2	salegh	salegh	PROPN
cana-3958	8	3	college	college	PROPN
cana-3958	8	4	of	of	ADP
cana-3958	8	5	engineering	engineering	PROPN
cana-3958	8	6	,	,	PUNCT
cana-3958	8	7	chennai	chennai	PROPN
cana-3958	8	8	,	,	PUNCT
cana-3958	8	9	600	600	NUM
cana-3958	8	10	055	055	NUM
cana-3958	8	11	,	,	PUNCT
cana-3958	8	12	india	india	PROPN
cana-3958	8	13	.	.	PUNCT
cana-3958	9	1	rbrs1947@gmail.com	rbrs1947@gmail.com	PROPN
cana-3958	10	1	4department	4department	NUM
cana-3958	10	2	of	of	ADP
cana-3958	10	3	mathematics	mathematic	NOUN
cana-3958	10	4	,	,	PUNCT
cana-3958	10	5	vel	vel	PROPN
cana-3958	10	6	tech	tech	PROPN
cana-3958	10	7	rangarajan	rangarajan	PROPN
cana-3958	10	8	dr	dr	PROPN
cana-3958	10	9	sagunthala	sagunthala	PROPN
cana-3958	10	10	r	r	PROPN
cana-3958	10	11	&	&	CCONJ
cana-3958	10	12	d	d	PROPN
cana-3958	10	13	institute	institute	PROPN
cana-3958	10	14	of	of	ADP
cana-3958	10	15	science	science	NOUN
cana-3958	10	16	and	and	CCONJ
cana-3958	10	17	technology	technology	NOUN
cana-3958	10	18	,	,	PUNCT
cana-3958	10	19	chennai	chennai	PROPN
cana-3958	10	20	,	,	PUNCT
cana-3958	10	21	600	600	NUM
cana-3958	10	22	062	062	NUM
cana-3958	10	23	,	,	PUNCT
cana-3958	10	24	india	india	PROPN
cana-3958	10	25	.	.	PROPN
cana-3958	10	26	drstalint@veltech.edu.in	drstalint@veltech.edu.in	PROPN
cana-3958	10	27	,	,	PUNCT
cana-3958	10	28	https://orcid.org/0000-0002-8735-3567	https://orcid.org/0000-0002-8735-3567	VERB
cana-3958	10	29	5department	5department	NUM
cana-3958	10	30	of	of	ADP
cana-3958	10	31	advanced	advanced	ADJ
cana-3958	10	32	computer	computer	NOUN
cana-3958	10	33	science	science	NOUN
cana-3958	10	34	and	and	CCONJ
cana-3958	10	35	engineering	engineering	NOUN
cana-3958	10	36	,	,	PUNCT
cana-3958	10	37	vignan	vignan	NOUN
cana-3958	10	38	’s	’s	PART
cana-3958	10	39	foundation	foundation	PROPN
cana-3958	10	40	for	for	ADP
cana-3958	10	41	science	science	NOUN
cana-3958	10	42	,	,	PUNCT
cana-3958	10	43	technology	technology	NOUN
cana-3958	10	44	&	&	CCONJ
cana-3958	10	45	research	research	NOUN
cana-3958	10	46	,	,	PUNCT
cana-3958	10	47	guntur522213	guntur522213	PROPN
cana-3958	10	48	,	,	PUNCT
cana-3958	10	49	andhra	andhra	PROPN
cana-3958	10	50	pradesh	pradesh	PROPN
cana-3958	10	51	,	,	PUNCT
cana-3958	10	52	india	india	PROPN
cana-3958	10	53	.	.	PUNCT
cana-3958	11	1	brittomanoj@gmail.com	brittomanoj@gmail.com	X
cana-3958	11	2	article	article	NOUN
cana-3958	11	3	history	history	NOUN
cana-3958	11	4	:	:	PUNCT
cana-3958	11	5	received	receive	VERB
cana-3958	11	6	:	:	PUNCT
cana-3958	11	7	13	13	NUM
cana-3958	11	8	-	-	SYM
cana-3958	11	9	11	11	NUM
cana-3958	11	10	-	-	PUNCT
cana-3958	11	11	2024	2024	NUM
cana-3958	11	12	revised	revise	VERB
cana-3958	11	13	:	:	PUNCT
cana-3958	11	14	17	17	NUM
cana-3958	11	15	-	-	SYM
cana-3958	11	16	12	12	NUM
cana-3958	11	17	-	-	PUNCT
cana-3958	11	18	2024	2024	NUM
cana-3958	11	19	accepted	accept	VERB
cana-3958	11	20	:	:	PUNCT
cana-3958	11	21	20	20	NUM
cana-3958	11	22	-	-	SYM
cana-3958	11	23	01	01	NUM
cana-3958	11	24	-	-	PUNCT
cana-3958	11	25	2025	2025	NUM
cana-3958	11	26	abstract	abstract	NOUN
cana-3958	11	27	:	:	PUNCT
cana-3958	11	28	recent	recent	ADJ
cana-3958	11	29	years	year	NOUN
cana-3958	11	30	have	have	AUX
cana-3958	11	31	shown	show	VERB
cana-3958	11	32	us	we	PRON
cana-3958	11	33	how	how	SCONJ
cana-3958	11	34	fascinating	fascinating	ADJ
cana-3958	11	35	the	the	DET
cana-3958	11	36	univalent	univalent	ADJ
cana-3958	11	37	function	function	NOUN
cana-3958	11	38	is	be	AUX
cana-3958	11	39	many	many	ADJ
cana-3958	11	40	new	new	ADJ
cana-3958	11	41	publications	publication	NOUN
cana-3958	11	42	have	have	AUX
cana-3958	11	43	been	be	AUX
cana-3958	11	44	written	write	VERB
cana-3958	11	45	in	in	ADP
cana-3958	11	46	this	this	DET
cana-3958	11	47	field	field	NOUN
cana-3958	11	48	.	.	PUNCT
cana-3958	12	1	currently	currently	ADV
cana-3958	12	2	,	,	PUNCT
cana-3958	12	3	operators	operator	NOUN
cana-3958	12	4	of	of	ADP
cana-3958	12	5	normalized	normalize	VERB
cana-3958	12	6	analytic	analytic	ADJ
cana-3958	12	7	functions	function	NOUN
cana-3958	12	8	,	,	PUNCT
cana-3958	12	9	differential	differential	ADJ
cana-3958	12	10	and	and	CCONJ
cana-3958	12	11	integral	integral	ADJ
cana-3958	12	12	operators	operator	NOUN
cana-3958	12	13	are	be	AUX
cana-3958	12	14	highly	highly	ADV
cana-3958	12	15	sought	seek	VERB
cana-3958	12	16	after	after	ADP
cana-3958	12	17	.	.	PUNCT
cana-3958	13	1	numerous	numerous	ADJ
cana-3958	13	2	researchers	researcher	NOUN
cana-3958	13	3	have	have	AUX
cana-3958	13	4	examined	examine	VERB
cana-3958	13	5	and	and	CCONJ
cana-3958	13	6	debated	debate	VERB
cana-3958	13	7	a	a	DET
cana-3958	13	8	great	great	ADJ
cana-3958	13	9	deal	deal	NOUN
cana-3958	13	10	of	of	ADP
cana-3958	13	11	material	material	NOUN
cana-3958	13	12	for	for	ADP
cana-3958	13	13	the	the	DET
cana-3958	13	14	operators	operator	NOUN
cana-3958	13	15	.	.	PUNCT
cana-3958	14	1	this	this	DET
cana-3958	14	2	work	work	NOUN
cana-3958	14	3	introduces	introduce	VERB
cana-3958	14	4	a	a	DET
cana-3958	14	5	new	new	ADJ
cana-3958	14	6	subclass	subclass	NOUN
cana-3958	14	7	𝒫𝒬q	𝒫𝒬q	NOUN
cana-3958	14	8	,	,	PUNCT
cana-3958	14	9	δ	δ	PROPN
cana-3958	14	10	,	,	PUNCT
cana-3958	14	11	μ	μ	PROPN
cana-3958	14	12	n	n	CCONJ
cana-3958	14	13	,	,	PUNCT
cana-3958	14	14	r	r	NOUN
cana-3958	14	15	(	(	PUNCT
cana-3958	14	16	θ	θ	NOUN
cana-3958	14	17	)	)	PUNCT
cana-3958	14	18	of	of	ADP
cana-3958	14	19	the	the	DET
cana-3958	14	20	function	function	NOUN
cana-3958	14	21	class	class	NOUN
cana-3958	14	22	for	for	ADP
cana-3958	14	23	univalent	univalent	ADJ
cana-3958	14	24	functions	function	NOUN
cana-3958	14	25	defined	define	VERB
cana-3958	14	26	by	by	ADP
cana-3958	14	27	the	the	DET
cana-3958	14	28	raducanu	raducanu	PROPN
cana-3958	14	29	-	-	PUNCT
cana-3958	14	30	orhan	orhan	PROPN
cana-3958	14	31	differential	differential	ADJ
cana-3958	14	32	operator	operator	NOUN
cana-3958	14	33	connected	connect	VERB
cana-3958	14	34	with	with	ADP
cana-3958	14	35	pascal	pascal	ADJ
cana-3958	14	36	distribution	distribution	NOUN
cana-3958	14	37	series	series	NOUN
cana-3958	14	38	.	.	PUNCT
cana-3958	15	1	our	our	PRON
cana-3958	15	2	goal	goal	NOUN
cana-3958	15	3	in	in	ADP
cana-3958	15	4	this	this	DET
cana-3958	15	5	work	work	NOUN
cana-3958	15	6	is	be	AUX
cana-3958	15	7	to	to	PART
cana-3958	15	8	further	further	VERB
cana-3958	15	9	our	our	PRON
cana-3958	15	10	understanding	understanding	NOUN
cana-3958	15	11	and	and	CCONJ
cana-3958	15	12	make	make	VERB
cana-3958	15	13	inferences	inference	NOUN
cana-3958	15	14	regarding	regard	VERB
cana-3958	15	15	the	the	DET
cana-3958	15	16	functions	function	NOUN
cana-3958	15	17	that	that	PRON
cana-3958	15	18	are	be	AUX
cana-3958	15	19	a	a	DET
cana-3958	15	20	part	part	NOUN
cana-3958	15	21	of	of	ADP
cana-3958	15	22	these	these	DET
cana-3958	15	23	new	new	ADJ
cana-3958	15	24	subclass	subclass	NOUN
cana-3958	15	25	.	.	PUNCT
cana-3958	16	1	furthermore	furthermore	ADV
cana-3958	16	2	,	,	PUNCT
cana-3958	16	3	the	the	DET
cana-3958	16	4	convexity	convexity	NOUN
cana-3958	16	5	of	of	ADP
cana-3958	16	6	the	the	DET
cana-3958	16	7	subclass	subclass	NOUN
cana-3958	16	8	,	,	PUNCT
cana-3958	16	9	growth	growth	NOUN
cana-3958	16	10	and	and	CCONJ
cana-3958	16	11	distortion	distortion	NOUN
cana-3958	16	12	,	,	PUNCT
cana-3958	16	13	radius	radius	NOUN
cana-3958	16	14	of	of	ADP
cana-3958	16	15	starlike	starlike	NOUN
cana-3958	16	16	,	,	PUNCT
cana-3958	16	17	extreme	extreme	ADJ
cana-3958	16	18	points	point	NOUN
cana-3958	16	19	,	,	PUNCT
cana-3958	16	20	and	and	CCONJ
cana-3958	16	21	integral	integral	ADJ
cana-3958	16	22	means	mean	NOUN
cana-3958	16	23	of	of	ADP
cana-3958	16	24	inequalities	inequality	NOUN
cana-3958	16	25	are	be	AUX
cana-3958	16	26	obtained	obtain	VERB
cana-3958	16	27	.	.	PUNCT
cana-3958	17	1	all	all	DET
cana-3958	17	2	this	this	DET
cana-3958	17	3	research	research	NOUN
cana-3958	17	4	was	be	AUX
cana-3958	17	5	performed	perform	VERB
cana-3958	17	6	inside	inside	ADP
cana-3958	17	7	an	an	DET
cana-3958	17	8	open	open	ADJ
cana-3958	17	9	unit	unit	NOUN
cana-3958	17	10	disc	disc	NOUN
cana-3958	17	11	.	.	PUNCT
cana-3958	18	1	keywords	keyword	NOUN
cana-3958	18	2	:	:	PUNCT
cana-3958	18	3	analytic	analytic	ADJ
cana-3958	18	4	function	function	NOUN
cana-3958	18	5	,	,	PUNCT
cana-3958	18	6	univalent	univalent	ADJ
cana-3958	18	7	function	function	NOUN
cana-3958	18	8	,	,	PUNCT
cana-3958	18	9	differential	differential	NOUN
cana-3958	18	10	operator	operator	NOUN
cana-3958	18	11	,	,	PUNCT
cana-3958	18	12	subordination	subordination	NOUN
cana-3958	18	13	,	,	PUNCT
cana-3958	18	14	coefficient	coefficient	NOUN
cana-3958	18	15	inequality	inequality	NOUN
cana-3958	18	16	,	,	PUNCT
cana-3958	18	17	starlike	starlike	NOUN
cana-3958	18	18	and	and	CCONJ
cana-3958	18	19	convexity	convexity	NOUN
cana-3958	18	20	.	.	PUNCT
cana-3958	19	1	1	1	X
cana-3958	19	2	.	.	X
cana-3958	19	3	introduction	introduction	NOUN
cana-3958	19	4	consider	consider	VERB
cana-3958	19	5	that	that	SCONJ
cana-3958	19	6	the	the	DET
cana-3958	19	7	class	class	NOUN
cana-3958	19	8	𝒜	𝒜	NOUN
cana-3958	19	9	of	of	ADP
cana-3958	19	10	univalent	univalent	ADJ
cana-3958	19	11	function	function	NOUN
cana-3958	19	12	has	have	VERB
cana-3958	19	13	the	the	DET
cana-3958	19	14	following	follow	VERB
cana-3958	19	15	form	form	NOUN
cana-3958	19	16	𝑓(𝜉	𝑓(𝜉	PROPN
cana-3958	19	17	)	)	PUNCT
cana-3958	19	18	=	=	SYM
cana-3958	20	1	ξ	ξ	PROPN
cana-3958	21	1	+	+	CCONJ
cana-3958	21	2	∑	∑	PROPN
cana-3958	21	3	avξ	avξ	VERB
cana-3958	21	4	v,∞	v,∞	PROPN
cana-3958	21	5	v=2	v=2	PROPN
cana-3958	21	6	ξ	ξ	PRON
cana-3958	21	7	∈	∈	PROPN
cana-3958	21	8	𝕌	𝕌	PROPN
cana-3958	21	9	:	:	PUNCT
cana-3958	21	10	=	=	SYM
cana-3958	21	11	{	{	PUNCT
cana-3958	21	12	ξ	ξ	X
cana-3958	21	13	∈	∈	PROPN
cana-3958	21	14	ℂ	ℂ	PROPN
cana-3958	21	15	∶	∶	NOUN
cana-3958	21	16	|ξ|	|ξ|	NOUN
cana-3958	21	17	<	<	X
cana-3958	21	18	1	1	NUM
cana-3958	21	19	}	}	PUNCT
cana-3958	21	20	,	,	PUNCT
cana-3958	21	21	(	(	PUNCT
cana-3958	21	22	1	1	X
cana-3958	21	23	)	)	PUNCT
cana-3958	21	24	which	which	PRON
cana-3958	21	25	is	be	AUX
cana-3958	21	26	analytic	analytic	ADJ
cana-3958	21	27	in	in	ADP
cana-3958	21	28	the	the	DET
cana-3958	21	29	unit	unit	NOUN
cana-3958	21	30	disc	disc	NOUN
cana-3958	21	31	𝕌	𝕌	PROPN
cana-3958	21	32	,	,	PUNCT
cana-3958	21	33	and	and	CCONJ
cana-3958	21	34	𝑔(𝜉	𝑔(𝜉	PROPN
cana-3958	21	35	)	)	PUNCT
cana-3958	21	36	=	=	PUNCT
cana-3958	22	1	ξ	ξ	PROPN
cana-3958	22	2	+	+	CCONJ
cana-3958	22	3	∑	∑	ADP
cana-3958	22	4	bvξ	bvξ	VERB
cana-3958	22	5	v	v	ADP
cana-3958	22	6	,	,	PUNCT
cana-3958	22	7	ξϵ𝕌∞	ξϵ𝕌∞	PROPN
cana-3958	22	8	v=2	v=2	PROPN
cana-3958	22	9	(	(	PUNCT
cana-3958	22	10	2	2	NUM
cana-3958	22	11	)	)	PUNCT
cana-3958	22	12	then	then	ADV
cana-3958	22	13	the	the	DET
cana-3958	22	14	convolution	convolution	NOUN
cana-3958	22	15	of	of	ADP
cana-3958	22	16	(	(	PUNCT
cana-3958	22	17	1	1	NUM
cana-3958	22	18	)	)	PUNCT
cana-3958	22	19	and	and	CCONJ
cana-3958	22	20	(	(	PUNCT
cana-3958	22	21	2	2	X
cana-3958	22	22	)	)	PUNCT
cana-3958	22	23	is	be	AUX
cana-3958	22	24	represented	represent	VERB
cana-3958	22	25	by	by	ADP
cana-3958	22	26	(	(	PUNCT
cana-3958	22	27	𝑓	𝑓	DET
cana-3958	22	28	∗	∗	NOUN
cana-3958	22	29	𝑔)(𝜉	𝑔)(𝜉	NUM
cana-3958	22	30	)	)	PUNCT
cana-3958	22	31	=	=	PUNCT
cana-3958	23	1	ξ	ξ	X
cana-3958	23	2	+	+	CCONJ
cana-3958	23	3	∑	∑	ADP
cana-3958	23	4	avbvξ	avbvξ	VERB
cana-3958	23	5	v,∞	v,∞	PROPN
cana-3958	23	6	v=2	v=2	PROPN
cana-3958	23	7	ξ	ξ	PROPN
cana-3958	23	8	∈	∈	PROPN
cana-3958	23	9	𝕌	𝕌	PROPN
cana-3958	23	10	(	(	PUNCT
cana-3958	23	11	3	3	NUM
cana-3958	23	12	)	)	PUNCT
cana-3958	23	13	let	let	VERB
cana-3958	23	14	𝑓(𝜉	𝑓(𝜉	VERB
cana-3958	23	15	)	)	PUNCT
cana-3958	23	16	∈	∈	PROPN
cana-3958	23	17	𝐾(𝛼	𝐾(𝛼	NUM
cana-3958	23	18	)	)	PUNCT
cana-3958	23	19	then	then	ADV
cana-3958	23	20	𝑓(𝜉	𝑓(𝜉	PROPN
cana-3958	23	21	)	)	PUNCT
cana-3958	23	22	is	be	AUX
cana-3958	23	23	convex	convex	NOUN
cana-3958	23	24	of	of	ADP
cana-3958	23	25	order	order	NOUN
cana-3958	23	26	𝛼	𝛼	NOUN
cana-3958	23	27	,	,	PUNCT
cana-3958	23	28	(	(	PUNCT
cana-3958	23	29	0	0	NUM
cana-3958	23	30	≤	≤	NUM
cana-3958	23	31	𝛼	𝛼	X
cana-3958	23	32	<	<	X
cana-3958	23	33	1	1	NUM
cana-3958	23	34	)	)	PUNCT
cana-3958	23	35	in	in	ADP
cana-3958	23	36	𝕌	𝕌	PROPN
cana-3958	23	37	,	,	PUNCT
cana-3958	23	38	iff	iff	PROPN
cana-3958	23	39	𝑅𝑒	𝑅𝑒	PROPN
cana-3958	23	40	(	(	PUNCT
cana-3958	23	41	𝜉𝑓"(𝜉	𝜉𝑓"(𝜉	NOUN
cana-3958	23	42	)	)	PUNCT
cana-3958	23	43	𝑓′(𝜉	𝑓′(𝜉	PUNCT
cana-3958	24	1	+	+	NOUN
cana-3958	24	2	1	1	X
cana-3958	24	3	)	)	PUNCT
cana-3958	24	4	>	>	X
cana-3958	25	1	𝛼	𝛼	X
cana-3958	25	2	,	,	PUNCT
cana-3958	25	3	𝜉	𝜉	PROPN
cana-3958	25	4	∈	∈	PROPN
cana-3958	25	5	𝕌.	𝕌.	PROPN
cana-3958	25	6	let	let	VERB
cana-3958	25	7	𝑓(𝜉	𝑓(𝜉	PROPN
cana-3958	25	8	)	)	PUNCT
cana-3958	25	9	∈	∈	PROPN
cana-3958	25	10	𝑆∗(𝛼	𝑆∗(𝛼	ADJ
cana-3958	25	11	)	)	PUNCT
cana-3958	25	12	,	,	PUNCT
cana-3958	25	13	then	then	ADV
cana-3958	25	14	𝑓(𝜉	𝑓(𝜉	PROPN
cana-3958	25	15	)	)	PUNCT
cana-3958	25	16	is	be	AUX
cana-3958	25	17	starlike	starlike	NOUN
cana-3958	25	18	of	of	ADP
cana-3958	25	19	order	order	NOUN
cana-3958	25	20	𝛼	𝛼	NOUN
cana-3958	25	21	,	,	PUNCT
cana-3958	25	22	(	(	PUNCT
cana-3958	25	23	0	0	NUM
cana-3958	25	24	≤	≤	NUM
cana-3958	25	25	𝛼	𝛼	X
cana-3958	25	26	<	<	X
cana-3958	25	27	1	1	NUM
cana-3958	25	28	)	)	PUNCT
cana-3958	25	29	in	in	ADP
cana-3958	25	30	𝕌	𝕌	PROPN
cana-3958	25	31	,	,	PUNCT
cana-3958	25	32	iff	iff	PROPN
cana-3958	25	33	mailto:saravanandagac@gmail.com	mailto:saravanandagac@gmail.com	PROPN
cana-3958	25	34	mailto:drthirucheran@gmail.com	mailto:drthirucheran@gmail.com	X
cana-3958	26	1	mailto:rbrs1947@gmail.com	mailto:rbrs1947@gmail.com	PROPN
cana-3958	26	2	mailto:drstalint@veltech.edu.in	mailto:drstalint@veltech.edu.in	NOUN
cana-3958	26	3	https://orcid.org/0000-0002-8735-3567	https://orcid.org/0000-0002-8735-3567	ADJ
cana-3958	26	4	mailto:brittomanoj@gmail.com	mailto:brittomanoj@gmail.com	NOUN
cana-3958	26	5	communications	communication	NOUN
cana-3958	26	6	on	on	ADP
cana-3958	26	7	applied	apply	VERB
cana-3958	26	8	nonlinear	nonlinear	ADJ
cana-3958	26	9	analysis	analysis	NOUN
cana-3958	26	10	issn	issn	NOUN
cana-3958	26	11	:	:	PUNCT
cana-3958	26	12	1074	1074	NUM
cana-3958	26	13	-	-	PUNCT
cana-3958	26	14	133x	133x	NUM
cana-3958	26	15	vol	vol	NOUN
cana-3958	26	16	32	32	NUM
cana-3958	26	17	no	no	NOUN
cana-3958	26	18	.	.	PUNCT
cana-3958	27	1	9s	9s	NUM
cana-3958	27	2	(	(	PUNCT
cana-3958	27	3	2025	2025	NUM
cana-3958	27	4	)	)	PUNCT
cana-3958	27	5	467	467	NUM
cana-3958	27	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3958	27	7	𝑅𝑒	𝑅𝑒	PROPN
cana-3958	27	8	(	(	PUNCT
cana-3958	27	9	𝜉𝑓′(𝜉	𝜉𝑓′(𝜉	NOUN
cana-3958	27	10	)	)	PUNCT
cana-3958	27	11	𝑓(𝜉	𝑓(𝜉	PROPN
cana-3958	27	12	)	)	PUNCT
cana-3958	27	13	)	)	PUNCT
cana-3958	27	14	>	>	PUNCT
cana-3958	28	1	𝛼	𝛼	X
cana-3958	28	2	,	,	PUNCT
cana-3958	28	3	𝜉	𝜉	PROPN
cana-3958	28	4	∈	∈	PROPN
cana-3958	28	5	𝕌.	𝕌.	PROPN
cana-3958	28	6	the	the	DET
cana-3958	28	7	class	class	NOUN
cana-3958	28	8	𝐾(𝛼	𝐾(𝛼	ADP
cana-3958	28	9	)	)	PUNCT
cana-3958	28	10	and	and	CCONJ
cana-3958	28	11	𝑆∗(𝛼	𝑆∗(𝛼	ADJ
cana-3958	28	12	)	)	PUNCT
cana-3958	28	13	introduced	introduce	VERB
cana-3958	28	14	by	by	ADP
cana-3958	28	15	roberston	roberston	NOUN
cana-3958	28	16	[	[	X
cana-3958	28	17	10	10	NUM
cana-3958	28	18	]	]	PUNCT
cana-3958	28	19	.	.	PUNCT
cana-3958	29	1	after	after	SCONJ
cana-3958	29	2	that	that	DET
cana-3958	29	3	many	many	ADJ
cana-3958	29	4	authors	author	NOUN
cana-3958	29	5	introduced	introduce	VERB
cana-3958	29	6	the	the	DET
cana-3958	29	7	various	various	ADJ
cana-3958	29	8	subclass	subclass	NOUN
cana-3958	29	9	of	of	ADP
cana-3958	29	10	starlike	starlike	NOUN
cana-3958	29	11	and	and	CCONJ
cana-3958	29	12	convex	convex	NOUN
cana-3958	29	13	functions	function	NOUN
cana-3958	29	14	connected	connect	VERB
cana-3958	29	15	with	with	ADP
cana-3958	29	16	some	some	DET
cana-3958	29	17	differential	differential	ADJ
cana-3958	29	18	operators	operator	NOUN
cana-3958	29	19	.	.	PUNCT
cana-3958	30	1	the	the	DET
cana-3958	30	2	schwarz	schwarz	PROPN
cana-3958	30	3	function	function	NOUN
cana-3958	30	4	in	in	ADP
cana-3958	30	5	𝕌	𝕌	PROPN
cana-3958	30	6	,	,	PUNCT
cana-3958	30	7	ω(ξ	ω(ξ	NUM
cana-3958	30	8	)	)	PUNCT
cana-3958	30	9	exists	exist	VERB
cana-3958	30	10	if	if	SCONJ
cana-3958	30	11	and	and	CCONJ
cana-3958	30	12	only	only	ADV
cana-3958	30	13	if	if	SCONJ
cana-3958	30	14	𝑓(𝜉	𝑓(𝜉	PROPN
cana-3958	30	15	)	)	PUNCT
cana-3958	30	16	and	and	CCONJ
cana-3958	30	17	𝑔(𝜉	𝑔(𝜉	PROPN
cana-3958	30	18	)	)	PUNCT
cana-3958	30	19	are	be	AUX
cana-3958	30	20	analytic	analytic	ADJ
cana-3958	30	21	.	.	PUNCT
cana-3958	31	1	it	it	PRON
cana-3958	31	2	is	be	AUX
cana-3958	31	3	our	our	PRON
cana-3958	31	4	claim	claim	NOUN
cana-3958	31	5	that	that	SCONJ
cana-3958	31	6	𝑓(𝜉	𝑓(𝜉	PROPN
cana-3958	31	7	)	)	PUNCT
cana-3958	31	8	is	be	AUX
cana-3958	31	9	subordinate	subordinate	ADJ
cana-3958	31	10	to	to	ADP
cana-3958	31	11	𝑔(𝜉	𝑔(𝜉	PROPN
cana-3958	31	12	)	)	PUNCT
cana-3958	31	13	;	;	PUNCT
cana-3958	31	14	that	that	PRON
cana-3958	31	15	is	be	AUX
cana-3958	31	16	𝑓(𝜉	𝑓(𝜉	PROPN
cana-3958	31	17	)	)	PUNCT
cana-3958	31	18	≺	≺	NOUN
cana-3958	31	19	𝑔(𝜉	𝑔(𝜉	PROPN
cana-3958	31	20	)	)	PUNCT
cana-3958	31	21	.	.	PUNCT
cana-3958	32	1	in	in	ADP
cana-3958	32	2	this	this	DET
cana-3958	32	3	case	case	NOUN
cana-3958	32	4	,	,	PUNCT
cana-3958	32	5	ω(0	ω(0	PROPN
cana-3958	32	6	)	)	PUNCT
cana-3958	32	7	=	=	SYM
cana-3958	32	8	0	0	NUM
cana-3958	32	9	and	and	CCONJ
cana-3958	32	10	|ω|	|ω|	VERB
cana-3958	32	11	<	<	X
cana-3958	32	12	1	1	NUM
cana-3958	32	13	such	such	ADJ
cana-3958	32	14	that	that	PRON
cana-3958	32	15	𝑓(𝜉	𝑓(𝜉	PROPN
cana-3958	32	16	)	)	PUNCT
cana-3958	32	17	=	=	SYM
cana-3958	32	18	𝑔(𝜔(𝜉	𝑔(𝜔(𝜉	PROPN
cana-3958	32	19	)	)	PUNCT
cana-3958	32	20	)	)	PUNCT
cana-3958	32	21	as	as	SCONJ
cana-3958	32	22	proven	prove	VERB
cana-3958	32	23	,	,	PUNCT
cana-3958	32	24	𝑓(𝜉	𝑓(𝜉	PROPN
cana-3958	32	25	)	)	PUNCT
cana-3958	32	26	≺	≺	NOUN
cana-3958	32	27	𝑔(𝜉	𝑔(𝜉	PROPN
cana-3958	32	28	)	)	PUNCT
cana-3958	32	29	and	and	CCONJ
cana-3958	32	30	f(𝕌	f(𝕌	NUM
cana-3958	32	31	)	)	PUNCT
cana-3958	33	1	⊂	⊂	PROPN
cana-3958	33	2	g(𝕌	g(𝕌	PROPN
cana-3958	33	3	)	)	PUNCT
cana-3958	33	4	implied	imply	VERB
cana-3958	33	5	by	by	ADP
cana-3958	33	6	𝑓(0	𝑓(0	PROPN
cana-3958	33	7	)	)	PUNCT
cana-3958	33	8	=	=	SYM
cana-3958	33	9	𝑔(0	𝑔(0	PROPN
cana-3958	33	10	)	)	PUNCT
cana-3958	33	11	.	.	PUNCT
cana-3958	34	1	ma	ma	PROPN
cana-3958	34	2	and	and	CCONJ
cana-3958	34	3	minda	minda	PROPN
cana-3958	35	1	[	[	X
cana-3958	35	2	13	13	NUM
cana-3958	35	3	]	]	PUNCT
cana-3958	35	4	used	use	VERB
cana-3958	35	5	the	the	DET
cana-3958	35	6	idea	idea	NOUN
cana-3958	35	7	of	of	ADP
cana-3958	35	8	subordination	subordination	NOUN
cana-3958	35	9	to	to	PART
cana-3958	35	10	create	create	VERB
cana-3958	35	11	various	various	ADJ
cana-3958	35	12	sub	sub	NOUN
cana-3958	35	13	classes	class	NOUN
cana-3958	35	14	of	of	ADP
cana-3958	35	15	radii	radius	NOUN
cana-3958	35	16	of	of	ADP
cana-3958	35	17	convexity	convexity	NOUN
cana-3958	35	18	and	and	CCONJ
cana-3958	35	19	starlikeness	starlikeness	NOUN
cana-3958	35	20	.	.	PUNCT
cana-3958	36	1	to	to	PART
cana-3958	36	2	achieve	achieve	VERB
cana-3958	36	3	this	this	DET
cana-3958	36	4	goal	goal	NOUN
cana-3958	36	5	,	,	PUNCT
cana-3958	36	6	a	a	DET
cana-3958	36	7	univalent	univalent	ADJ
cana-3958	36	8	function	function	NOUN
cana-3958	36	9	ϕ(ξ	ϕ(ξ	PROPN
cana-3958	36	10	)	)	PUNCT
cana-3958	36	11	is	be	AUX
cana-3958	36	12	taken	take	VERB
cana-3958	36	13	into	into	ADP
cana-3958	36	14	consideration	consideration	NOUN
cana-3958	36	15	.	.	PUNCT
cana-3958	37	1	this	this	DET
cana-3958	37	2	function	function	NOUN
cana-3958	37	3	is	be	AUX
cana-3958	37	4	analytic	analytic	ADJ
cana-3958	37	5	and	and	CCONJ
cana-3958	37	6	defined	define	VERB
cana-3958	37	7	on	on	ADP
cana-3958	37	8	𝕌	𝕌	PROPN
cana-3958	37	9	with	with	ADP
cana-3958	37	10	a	a	DET
cana-3958	37	11	positive	positive	ADJ
cana-3958	37	12	real	real	ADJ
cana-3958	37	13	portion	portion	NOUN
cana-3958	37	14	,	,	PUNCT
cana-3958	37	15	such	such	ADJ
cana-3958	37	16	that	that	DET
cana-3958	37	17	ϕ′(0	ϕ′(0	NOUN
cana-3958	37	18	)	)	PUNCT
cana-3958	37	19	>	>	X
cana-3958	37	20	0	0	PUNCT
cana-3958	37	21	and	and	CCONJ
cana-3958	37	22	ϕ(0	ϕ(0	NOUN
cana-3958	37	23	)	)	PUNCT
cana-3958	38	1	=	=	NOUN
cana-3958	38	2	1	1	X
cana-3958	38	3	.	.	PUNCT
cana-3958	38	4	for	for	ADP
cana-3958	38	5	𝑓(ξ	𝑓(ξ	NOUN
cana-3958	38	6	)	)	PUNCT
cana-3958	38	7	ϵ	ϵ	PROPN
cana-3958	38	8	𝒜	𝒜	PROPN
cana-3958	38	9	,	,	PUNCT
cana-3958	38	10	raducanu	raducanu	NOUN
cana-3958	38	11	-	-	PUNCT
cana-3958	38	12	orhan	orhan	NOUN
cana-3958	38	13	[	[	X
cana-3958	38	14	4	4	X
cana-3958	38	15	]	]	PUNCT
cana-3958	38	16	introduced	introduce	VERB
cana-3958	38	17	the	the	DET
cana-3958	38	18	differential	differential	ADJ
cana-3958	38	19	operator	operator	NOUN
cana-3958	38	20	𝒬δ	𝒬δ	PROPN
cana-3958	38	21	,	,	PUNCT
cana-3958	38	22	μ	μ	PROPN
cana-3958	38	23	n	n	PRON
cana-3958	38	24	𝑓(ξ	𝑓(ξ	PROPN
cana-3958	38	25	)	)	PUNCT
cana-3958	38	26	=	=	SYM
cana-3958	39	1	𝒬δ	𝒬δ	PROPN
cana-3958	39	2	,	,	PUNCT
cana-3958	39	3	μ(𝒬δ	μ(𝒬δ	PROPN
cana-3958	39	4	,	,	PUNCT
cana-3958	39	5	μ	μ	PROPN
cana-3958	39	6	n−1	n−1	PROPN
cana-3958	39	7	)	)	PUNCT
cana-3958	39	8	=	=	SYM
cana-3958	40	1	ξ	ξ	PROPN
cana-3958	41	1	+	+	PUNCT
cana-3958	41	2	∑	∑	PUNCT
cana-3958	42	1	[	[	X
cana-3958	42	2	1	1	NUM
cana-3958	42	3	+	+	CCONJ
cana-3958	42	4	(	(	PUNCT
cana-3958	42	5	υ	υ	NOUN
cana-3958	42	6	−	−	PROPN
cana-3958	42	7	1)(δ	1)(δ	NUM
cana-3958	42	8	−	−	PROPN
cana-3958	42	9	μ	μ	PROPN
cana-3958	42	10	+	+	PROPN
cana-3958	42	11	υδμ)]n∞	υδμ)]n∞	PROPN
cana-3958	42	12	υ=2	υ=2	PROPN
cana-3958	42	13	avξ	avξ	PROPN
cana-3958	42	14	υ	υ	PROPN
cana-3958	42	15	,	,	PUNCT
cana-3958	42	16	(	(	PUNCT
cana-3958	42	17	4	4	NUM
cana-3958	42	18	)	)	PUNCT
cana-3958	42	19	where	where	SCONJ
cana-3958	42	20	n	n	PRON
cana-3958	42	21	∈	∈	PROPN
cana-3958	42	22	ℕ0=	ℕ0=	NOUN
cana-3958	42	23	ℕ∪0	ℕ∪0	NOUN
cana-3958	42	24	,	,	PUNCT
cana-3958	42	25	ℕ	ℕ	PROPN
cana-3958	42	26	=	=	SYM
cana-3958	42	27	{	{	PUNCT
cana-3958	42	28	1	1	NUM
cana-3958	42	29	,	,	PUNCT
cana-3958	42	30	2	2	NUM
cana-3958	42	31	,	,	PUNCT
cana-3958	42	32	...	...	PUNCT
cana-3958	42	33	,	,	PUNCT
cana-3958	42	34	}	}	PUNCT
cana-3958	42	35	,	,	PUNCT
cana-3958	42	36	µ	µ	X
cana-3958	42	37	,	,	PUNCT
cana-3958	42	38	δ	δ	PROPN
cana-3958	42	39	≥	≥	NUM
cana-3958	42	40	0	0	NUM
cana-3958	42	41	,	,	PUNCT
cana-3958	42	42	ξ	ξ	PROPN
cana-3958	42	43	∈	∈	PROPN
cana-3958	42	44	𝕌.	𝕌.	PROPN
cana-3958	42	45	remark	remark	NOUN
cana-3958	42	46	:	:	PUNCT
cana-3958	42	47	𝒬δ,0	𝒬δ,0	NOUN
cana-3958	42	48	n	n	X
cana-3958	42	49	=	=	X
cana-3958	42	50	𝒟n	𝒟n	PROPN
cana-3958	42	51	yields	yield	VERB
cana-3958	42	52	the	the	DET
cana-3958	42	53	operator	operator	NOUN
cana-3958	42	54	of	of	ADP
cana-3958	42	55	al	al	PROPN
cana-3958	42	56	-	-	PUNCT
cana-3958	42	57	oboudi	oboudi	ADJ
cana-3958	42	58	derivative	derivative	NOUN
cana-3958	42	59	[	[	X
cana-3958	42	60	5	5	NUM
cana-3958	42	61	]	]	PUNCT
cana-3958	42	62	,	,	PUNCT
cana-3958	42	63	𝒬1,0	𝒬1,0	PUNCT
cana-3958	42	64	n	n	CCONJ
cana-3958	42	65	=	=	X
cana-3958	42	66	𝒟n	𝒟n	PROPN
cana-3958	42	67	is	be	AUX
cana-3958	42	68	the	the	DET
cana-3958	42	69	salagean	salagean	ADJ
cana-3958	42	70	derivative	derivative	ADJ
cana-3958	42	71	operator	operator	NOUN
cana-3958	42	72	[	[	X
cana-3958	42	73	7	7	NUM
cana-3958	42	74	]	]	PUNCT
cana-3958	42	75	.	.	PUNCT
cana-3958	43	1	recent	recent	ADJ
cana-3958	43	2	studies	study	NOUN
cana-3958	43	3	have	have	AUX
cana-3958	43	4	focused	focus	VERB
cana-3958	43	5	on	on	ADP
cana-3958	43	6	a	a	DET
cana-3958	43	7	subclass	subclass	NOUN
cana-3958	43	8	of	of	ADP
cana-3958	43	9	univalent	univalent	ADJ
cana-3958	43	10	functions	function	NOUN
cana-3958	43	11	associated	associate	VERB
cana-3958	43	12	with	with	ADP
cana-3958	43	13	distribution	distribution	NOUN
cana-3958	43	14	series	series	NOUN
cana-3958	43	15	.	.	PUNCT
cana-3958	44	1	these	these	PRON
cana-3958	44	2	include	include	VERB
cana-3958	44	3	the	the	DET
cana-3958	44	4	borel	borel	NOUN
cana-3958	44	5	,	,	PUNCT
cana-3958	44	6	pascal	pascal	PROPN
cana-3958	44	7	,	,	PUNCT
cana-3958	44	8	binomial	binomial	ADJ
cana-3958	44	9	,	,	PUNCT
cana-3958	44	10	poisson	poisson	NOUN
cana-3958	44	11	,	,	PUNCT
cana-3958	44	12	geometric	geometric	ADJ
cana-3958	44	13	,	,	PUNCT
cana-3958	44	14	exponential	exponential	NOUN
cana-3958	44	15	,	,	PUNCT
cana-3958	44	16	and	and	CCONJ
cana-3958	44	17	generalized	generalized	ADJ
cana-3958	44	18	distributions	distribution	NOUN
cana-3958	44	19	as	as	ADV
cana-3958	44	20	well	well	ADV
cana-3958	44	21	as	as	ADP
cana-3958	44	22	a	a	DET
cana-3958	44	23	generalized	generalized	ADJ
cana-3958	44	24	discrete	discrete	ADJ
cana-3958	44	25	probability	probability	NOUN
cana-3958	44	26	distribution	distribution	NOUN
cana-3958	44	27	.	.	PUNCT
cana-3958	45	1	in	in	ADP
cana-3958	45	2	recent	recent	ADJ
cana-3958	45	3	years	year	NOUN
cana-3958	45	4	,	,	PUNCT
cana-3958	45	5	various	various	ADJ
cana-3958	45	6	sub	sub	NOUN
cana-3958	45	7	class	class	NOUN
cana-3958	45	8	of	of	ADP
cana-3958	45	9	univalent	univalent	ADJ
cana-3958	45	10	functions	function	NOUN
cana-3958	45	11	related	relate	VERB
cana-3958	45	12	to	to	ADP
cana-3958	45	13	pascal	pascal	ADJ
cana-3958	45	14	distribution	distribution	NOUN
cana-3958	45	15	series	series	NOUN
cana-3958	45	16	have	have	AUX
cana-3958	45	17	been	be	AUX
cana-3958	45	18	studied	study	VERB
cana-3958	45	19	by	by	ADP
cana-3958	45	20	the	the	DET
cana-3958	45	21	following	follow	VERB
cana-3958	45	22	authors	author	NOUN
cana-3958	45	23	,	,	PUNCT
cana-3958	45	24	b.a.frasin	b.a.frasin	PROPN
cana-3958	45	25	et	et	PROPN
cana-3958	45	26	al.[2	al.[2	PROPN
cana-3958	45	27	]	]	X
cana-3958	45	28	,	,	PUNCT
cana-3958	45	29	s.porwal	s.porwal	PUNCT
cana-3958	45	30	[	[	X
cana-3958	45	31	9	9	NUM
cana-3958	45	32	]	]	PUNCT
cana-3958	45	33	,	,	PUNCT
cana-3958	45	34	anitha	anitha	PROPN
cana-3958	45	35	lakshminarayanan	lakshminarayanan	INTJ
cana-3958	46	1	et	et	PROPN
cana-3958	46	2	al	al	PROPN
cana-3958	47	1	[	[	X
cana-3958	47	2	1	1	NUM
cana-3958	47	3	]	]	PUNCT
cana-3958	47	4	,	,	PUNCT
cana-3958	47	5	g.murugusundramoorthy	g.murugusundramoorthy	ADV
cana-3958	48	1	[	[	X
cana-3958	48	2	6	6	NUM
cana-3958	48	3	]	]	PUNCT
cana-3958	48	4	,	,	PUNCT
cana-3958	48	5	r.m.el	r.m.el	NOUN
cana-3958	48	6	-	-	PUNCT
cana-3958	48	7	ashwah	ashwah	NOUN
cana-3958	48	8	,	,	PUNCT
cana-3958	48	9	w.y.kota	w.y.kota	NOUN
cana-3958	48	10	[	[	X
cana-3958	48	11	10	10	NUM
cana-3958	48	12	]	]	PUNCT
cana-3958	48	13	,	,	PUNCT
cana-3958	48	14	t.bulboaca	t.bulboaca	NOUN
cana-3958	48	15	and	and	CCONJ
cana-3958	48	16	g.murugusundramoorthy	g.murugusundramoorthy	ADV
cana-3958	49	1	[	[	X
cana-3958	49	2	12	12	NUM
cana-3958	49	3	]	]	PUNCT
cana-3958	49	4	,	,	PUNCT
cana-3958	49	5	b.a.frasin	b.a.frasin	PROPN
cana-3958	49	6	et	et	PROPN
cana-3958	49	7	al	al	PROPN
cana-3958	49	8	.	.	PUNCT
cana-3958	50	1	[	[	X
cana-3958	50	2	3	3	NUM
cana-3958	50	3	]	]	PUNCT
cana-3958	50	4	.	.	PUNCT
cana-3958	51	1	by	by	ADP
cana-3958	51	2	examining	examine	VERB
cana-3958	51	3	the	the	DET
cana-3958	51	4	subclasses	subclass	NOUN
cana-3958	51	5	,	,	PUNCT
cana-3958	51	6	researchers	researcher	NOUN
cana-3958	51	7	hope	hope	VERB
cana-3958	51	8	to	to	PART
cana-3958	51	9	gain	gain	VERB
cana-3958	51	10	a	a	DET
cana-3958	51	11	deeper	deep	ADJ
cana-3958	51	12	understanding	understanding	NOUN
cana-3958	51	13	of	of	ADP
cana-3958	51	14	the	the	DET
cana-3958	51	15	structure	structure	NOUN
cana-3958	51	16	and	and	CCONJ
cana-3958	51	17	behaviour	behaviour	NOUN
cana-3958	51	18	of	of	ADP
cana-3958	51	19	analytic	analytic	ADJ
cana-3958	51	20	functions	function	NOUN
cana-3958	51	21	,	,	PUNCT
cana-3958	51	22	hence	hence	ADV
cana-3958	51	23	advancing	advance	VERB
cana-3958	51	24	their	their	PRON
cana-3958	51	25	knowledge	knowledge	NOUN
cana-3958	51	26	of	of	ADP
cana-3958	51	27	complex	complex	ADJ
cana-3958	51	28	analysis	analysis	NOUN
cana-3958	51	29	and	and	CCONJ
cana-3958	51	30	its	its	PRON
cana-3958	51	31	applications	application	NOUN
cana-3958	51	32	,	,	PUNCT
cana-3958	51	33	which	which	PRON
cana-3958	51	34	provides	provide	VERB
cana-3958	51	35	an	an	DET
cana-3958	51	36	extensive	extensive	ADJ
cana-3958	51	37	investigation	investigation	NOUN
cana-3958	51	38	of	of	ADP
cana-3958	51	39	this	this	DET
cana-3958	51	40	area	area	NOUN
cana-3958	51	41	of	of	ADP
cana-3958	51	42	study	study	NOUN
cana-3958	51	43	.	.	PUNCT
cana-3958	52	1	2	2	X
cana-3958	52	2	.	.	X
cana-3958	52	3	the	the	DET
cana-3958	52	4	subclass	subclass	NOUN
cana-3958	52	5	𝒫𝒬q	𝒫𝒬q	PROPN
cana-3958	52	6	,	,	PUNCT
cana-3958	52	7	δ	δ	PROPN
cana-3958	52	8	,	,	PUNCT
cana-3958	52	9	μ	μ	PROPN
cana-3958	52	10	n	n	CCONJ
cana-3958	52	11	,	,	PUNCT
cana-3958	52	12	r	r	NOUN
cana-3958	52	13	(	(	PUNCT
cana-3958	52	14	θ	θ	NOUN
cana-3958	52	15	)	)	PUNCT
cana-3958	52	16	the	the	DET
cana-3958	52	17	probabilities	probability	NOUN
cana-3958	52	18	(	(	PUNCT
cana-3958	52	19	1	1	NUM
cana-3958	52	20	−	−	NOUN
cana-3958	52	21	q)r	q)r	NOUN
cana-3958	52	22	,	,	PUNCT
cana-3958	52	23	q2r(r+1)(1−q)r	q2r(r+1)(1−q)r	PROPN
cana-3958	52	24	2	2	NUM
cana-3958	52	25	!	!	NUM
cana-3958	52	26	,	,	PUNCT
cana-3958	52	27	qr(1−q)r	qr(1−q)r	PROPN
cana-3958	52	28	1	1	X
cana-3958	52	29	!	!	NUM
cana-3958	52	30	,	,	PUNCT
cana-3958	52	31	q3r(r+1)(r+2)(1−q)r	q3r(r+1)(r+2)(1−q)r	PROPN
cana-3958	52	32	3	3	NUM
cana-3958	52	33	!	!	NUM
cana-3958	52	34	,	,	PUNCT
cana-3958	52	35	.	.	PUNCT
cana-3958	53	1	..	..	PUNCT
cana-3958	53	2	correspond	correspond	VERB
cana-3958	53	3	to	to	ADP
cana-3958	53	4	a	a	DET
cana-3958	53	5	variable	variable	NOUN
cana-3958	53	6	𝓍	𝓍	X
cana-3958	53	7	with	with	ADP
cana-3958	53	8	values	value	NOUN
cana-3958	53	9	of	of	ADP
cana-3958	53	10	0,1,2	0,1,2	NUM
cana-3958	53	11	,	,	PUNCT
cana-3958	53	12	and	and	CCONJ
cana-3958	53	13	3	3	NUM
cana-3958	53	14	,	,	PUNCT
cana-3958	53	15	respectively	respectively	ADV
cana-3958	53	16	,	,	PUNCT
cana-3958	53	17	where	where	SCONJ
cana-3958	53	18	𝑞	𝑞	NOUN
cana-3958	53	19	,	,	PUNCT
cana-3958	53	20	and	and	CCONJ
cana-3958	53	21	𝑟	𝑟	NOUN
cana-3958	53	22	are	be	AUX
cana-3958	53	23	called	call	VERB
cana-3958	53	24	the	the	DET
cana-3958	53	25	parameters	parameter	NOUN
cana-3958	53	26	,	,	PUNCT
cana-3958	53	27	and	and	CCONJ
cana-3958	53	28	thus	thus	ADV
cana-3958	53	29	𝒫(x	𝒫(x	X
cana-3958	53	30	=	=	SYM
cana-3958	53	31	𝓍	𝓍	X
cana-3958	53	32	)	)	PUNCT
cana-3958	53	33	=	=	SYM
cana-3958	54	1	(	(	PUNCT
cana-3958	54	2	n+r−1	n+r−1	PROPN
cana-3958	54	3	r−1	r−1	PROPN
cana-3958	54	4	)	)	PUNCT
cana-3958	55	1	q𝓍(1	q𝓍(1	PROPN
cana-3958	55	2	−	−	PROPN
cana-3958	55	3	q)r	q)r	NOUN
cana-3958	55	4	,	,	PUNCT
cana-3958	55	5	𝓍	𝓍	X
cana-3958	55	6	ϵ	ϵ	X
cana-3958	55	7	{	{	PUNCT
cana-3958	55	8	0,1,2,3	0,1,2,3	NUM
cana-3958	55	9	,	,	PUNCT
cana-3958	55	10	.	.	PUNCT
cana-3958	55	11	.	.	PUNCT
cana-3958	55	12	.	.	PUNCT
cana-3958	56	1	}	}	PUNCT
cana-3958	56	2	(	(	PUNCT
cana-3958	56	3	5	5	NUM
cana-3958	56	4	)	)	PUNCT
cana-3958	56	5	according	accord	VERB
cana-3958	56	6	to	to	ADP
cana-3958	56	7	s.m.el	s.m.el	NOUN
cana-3958	56	8	-	-	NOUN
cana-3958	56	9	deepa	deepa	NOUN
cana-3958	56	10	et	et	NOUN
cana-3958	56	11	al.[11],the	al.[11],the	DET
cana-3958	56	12	power	power	NOUN
cana-3958	56	13	series	series	NOUN
cana-3958	56	14	of	of	ADP
cana-3958	56	15	equation	equation	NOUN
cana-3958	56	16	(	(	PUNCT
cana-3958	56	17	6	6	NUM
cana-3958	56	18	)	)	PUNCT
cana-3958	56	19	is	be	AUX
cana-3958	56	20	examined	examine	VERB
cana-3958	56	21	,	,	PUNCT
cana-3958	56	22	with	with	ADP
cana-3958	56	23	its	its	PRON
cana-3958	56	24	coefficients	coefficient	NOUN
cana-3958	56	25	representing	represent	VERB
cana-3958	56	26	probabilities	probability	NOUN
cana-3958	56	27	of	of	ADP
cana-3958	56	28	the	the	DET
cana-3958	56	29	pascal	pascal	ADJ
cana-3958	56	30	distribution	distribution	NOUN
cana-3958	56	31	,	,	PUNCT
cana-3958	56	32	that	that	PRON
cana-3958	56	33	is	be	AUX
cana-3958	56	34	𝒫q	𝒫q	PROPN
cana-3958	56	35	r(ξ	r(ξ	NOUN
cana-3958	56	36	)	)	PUNCT
cana-3958	56	37	=	=	SYM
cana-3958	57	1	ξ	ξ	PROPN
cana-3958	57	2	+	+	CCONJ
cana-3958	57	3	∑	∑	PROPN
cana-3958	57	4	(	(	PUNCT
cana-3958	57	5	v+r−2	v+r−2	NOUN
cana-3958	57	6	r−1	r−1	PROPN
cana-3958	57	7	)	)	PUNCT
cana-3958	57	8	qv−1(1	qv−1(1	PROPN
cana-3958	57	9	−	−	PROPN
cana-3958	57	10	q)rξ	q)rξ	PROPN
cana-3958	57	11	v	v	NOUN
cana-3958	57	12	,	,	PUNCT
cana-3958	57	13	ξ	ξ	PROPN
cana-3958	57	14	ϵ	ϵ	X
cana-3958	57	15	𝕌	𝕌	PROPN
cana-3958	57	16	,	,	PUNCT
cana-3958	57	17	r	r	NOUN
cana-3958	57	18	≥	≥	NOUN
cana-3958	57	19	1	1	NUM
cana-3958	57	20	,	,	PUNCT
cana-3958	57	21	0	0	NUM
cana-3958	57	22	≤	≤	NUM
cana-3958	57	23	q	q	PROPN
cana-3958	57	24	≤	≤	NUM
cana-3958	57	25	1∞	1∞	NUM
cana-3958	57	26	v=2	v=2	NOUN
cana-3958	57	27	(	(	PUNCT
cana-3958	57	28	6	6	NUM
cana-3958	57	29	)	)	PUNCT
cana-3958	57	30	and	and	CCONJ
cana-3958	57	31	the	the	DET
cana-3958	57	32	linear	linear	ADJ
cana-3958	57	33	opeerator	opeerator	NOUN
cana-3958	57	34	𝒟q	𝒟q	NOUN
cana-3958	57	35	r	r	NOUN
cana-3958	57	36	:	:	PUNCT
cana-3958	57	37	𝒜	𝒜	NOUN
cana-3958	57	38	→	→	SYM
cana-3958	57	39	𝒜	𝒜	NOUN
cana-3958	57	40	is	be	AUX
cana-3958	57	41	defined	define	VERB
cana-3958	57	42	by	by	ADP
cana-3958	57	43	communications	communication	NOUN
cana-3958	57	44	on	on	ADP
cana-3958	57	45	applied	apply	VERB
cana-3958	57	46	nonlinear	nonlinear	ADJ
cana-3958	57	47	analysis	analysis	NOUN
cana-3958	57	48	issn	issn	NOUN
cana-3958	57	49	:	:	PUNCT
cana-3958	57	50	1074	1074	NUM
cana-3958	57	51	-	-	PUNCT
cana-3958	57	52	133x	133x	NUM
cana-3958	57	53	vol	vol	NOUN
cana-3958	57	54	32	32	NUM
cana-3958	57	55	no	no	NOUN
cana-3958	57	56	.	.	PUNCT
cana-3958	58	1	9s	9s	NUM
cana-3958	58	2	(	(	PUNCT
cana-3958	58	3	2025	2025	NUM
cana-3958	58	4	)	)	PUNCT
cana-3958	58	5	468	468	NUM
cana-3958	58	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3958	58	7	𝒟q	𝒟q	NOUN
cana-3958	58	8	r	r	NOUN
cana-3958	58	9	(	(	PUNCT
cana-3958	58	10	f(ξ	f(ξ	NOUN
cana-3958	58	11	)	)	PUNCT
cana-3958	58	12	)	)	PUNCT
cana-3958	59	1	=	=	PUNCT
cana-3958	60	1	𝒫q	𝒫q	NOUN
cana-3958	60	2	r	r	NOUN
cana-3958	60	3	∗	∗	NOUN
cana-3958	60	4	f(ξ	f(ξ	X
cana-3958	60	5	)	)	PUNCT
cana-3958	60	6	=	=	SYM
cana-3958	61	1	ξ	ξ	X
cana-3958	61	2	+	+	CCONJ
cana-3958	61	3	∑	∑	PUNCT
cana-3958	61	4	(	(	PUNCT
cana-3958	61	5	v+2−r	v+2−r	PROPN
cana-3958	61	6	r−1	r−1	PROPN
cana-3958	61	7	)	)	PUNCT
cana-3958	61	8	qv−1(1	qv−1(1	NOUN
cana-3958	61	9	−	−	PROPN
cana-3958	61	10	q)ravξ	q)ravξ	PROPN
cana-3958	61	11	v	v	PROPN
cana-3958	61	12	,	,	PUNCT
cana-3958	61	13	ξ	ξ	PROPN
cana-3958	61	14	∈	∈	PROPN
cana-3958	61	15	𝕌∞	𝕌∞	NOUN
cana-3958	61	16	v=2	v=2	PROPN
cana-3958	61	17	(	(	PUNCT
cana-3958	61	18	7	7	NUM
cana-3958	61	19	)	)	PUNCT
cana-3958	61	20	by	by	ADP
cana-3958	61	21	using	use	VERB
cana-3958	61	22	the	the	DET
cana-3958	61	23	convolution	convolution	NOUN
cana-3958	61	24	(	(	PUNCT
cana-3958	61	25	hadamard	hadamard	ADJ
cana-3958	61	26	product	product	NOUN
cana-3958	61	27	)	)	PUNCT
cana-3958	61	28	of	of	ADP
cana-3958	61	29	two	two	NUM
cana-3958	61	30	equations	equation	NOUN
cana-3958	61	31	(	(	PUNCT
cana-3958	61	32	4	4	NUM
cana-3958	61	33	)	)	PUNCT
cana-3958	61	34	and	and	CCONJ
cana-3958	61	35	(	(	PUNCT
cana-3958	61	36	7	7	NUM
cana-3958	61	37	)	)	PUNCT
cana-3958	61	38	,	,	PUNCT
cana-3958	61	39	the	the	DET
cana-3958	61	40	linear	linear	ADJ
cana-3958	61	41	operator	operator	NOUN
cana-3958	61	42	𝒫𝒟q	𝒫𝒟q	NOUN
cana-3958	61	43	,	,	PUNCT
cana-3958	61	44	δ	δ	PROPN
cana-3958	61	45	,	,	PUNCT
cana-3958	61	46	μ	μ	PROPN
cana-3958	61	47	n	n	CCONJ
cana-3958	61	48	,	,	PUNCT
cana-3958	61	49	r	r	NOUN
cana-3958	61	50	f(ξ	f(ξ	NOUN
cana-3958	61	51	)	)	PUNCT
cana-3958	61	52	∶	∶	NOUN
cana-3958	61	53	𝒜	𝒜	NOUN
cana-3958	61	54	→	→	SYM
cana-3958	61	55	𝒜	𝒜	NOUN
cana-3958	61	56	is	be	AUX
cana-3958	61	57	defined	define	VERB
cana-3958	61	58	by	by	ADP
cana-3958	61	59	𝒫𝒟q	𝒫𝒟q	PROPN
cana-3958	61	60	,	,	PUNCT
cana-3958	61	61	δ	δ	PROPN
cana-3958	61	62	,	,	PUNCT
cana-3958	61	63	μ	μ	PROPN
cana-3958	61	64	n	n	CCONJ
cana-3958	61	65	,	,	PUNCT
cana-3958	61	66	r	r	NOUN
cana-3958	61	67	f(ξ	f(ξ	NOUN
cana-3958	61	68	)	)	PUNCT
cana-3958	61	69	=	=	SYM
cana-3958	62	1	ξ	ξ	X
cana-3958	62	2	+	+	CCONJ
cana-3958	62	3	∑	∑	PUNCT
cana-3958	62	4	avcvξ	avcvξ	NOUN
cana-3958	62	5	v	v	NUM
cana-3958	62	6	,	,	PUNCT
cana-3958	62	7	∞	∞	PROPN
cana-3958	62	8	v=2	v=2	PROPN
cana-3958	62	9	(	(	PUNCT
cana-3958	62	10	8)	8)	NUM
cana-3958	62	11	where	where	SCONJ
cana-3958	62	12	cv	cv	NOUN
cana-3958	63	1	=	=	PUNCT
cana-3958	64	1	[	[	X
cana-3958	64	2	1	1	NUM
cana-3958	64	3	+	+	CCONJ
cana-3958	64	4	(	(	PUNCT
cana-3958	64	5	v	v	NOUN
cana-3958	64	6	−	−	PROPN
cana-3958	64	7	1)(δ	1)(δ	NUM
cana-3958	64	8	−	−	PROPN
cana-3958	64	9	μ	μ	PROPN
cana-3958	64	10	+	+	PROPN
cana-3958	64	11	vδμ)]n	vδμ)]n	ADJ
cana-3958	64	12	(	(	PUNCT
cana-3958	64	13	v+r−2	v+r−2	NOUN
cana-3958	64	14	r−1	r−1	PROPN
cana-3958	64	15	)	)	PUNCT
cana-3958	64	16	qv−1(1	qv−1(1	PROPN
cana-3958	64	17	−	−	PROPN
cana-3958	64	18	q)r	q)r	NOUN
cana-3958	64	19	.	.	PUNCT
cana-3958	65	1	the	the	DET
cana-3958	65	2	new	new	ADJ
cana-3958	65	3	subclass	subclass	NOUN
cana-3958	65	4	is	be	AUX
cana-3958	65	5	defined	define	VERB
cana-3958	65	6	in	in	ADP
cana-3958	65	7	the	the	DET
cana-3958	65	8	following	follow	VERB
cana-3958	65	9	definitions	definition	NOUN
cana-3958	65	10	:	:	PUNCT
cana-3958	65	11	definition	definition	NOUN
cana-3958	65	12	2.1	2.1	NUM
cana-3958	65	13	.	.	PUNCT
cana-3958	66	1	let	let	VERB
cana-3958	66	2	𝒫𝒟q	𝒫𝒟q	PROPN
cana-3958	66	3	,	,	PUNCT
cana-3958	66	4	δ	δ	PROPN
cana-3958	66	5	,	,	PUNCT
cana-3958	66	6	μ	μ	PROPN
cana-3958	66	7	n	n	CCONJ
cana-3958	66	8	,	,	PUNCT
cana-3958	66	9	r	r	NOUN
cana-3958	66	10	(	(	PUNCT
cana-3958	66	11	θ	θ	NOUN
cana-3958	66	12	)	)	PUNCT
cana-3958	66	13	represents	represent	VERB
cana-3958	66	14	a	a	DET
cana-3958	66	15	class	class	NOUN
cana-3958	66	16	of	of	ADP
cana-3958	66	17	f	f	PROPN
cana-3958	66	18	in	in	ADP
cana-3958	66	19	𝒜.	𝒜.	PROPN
cana-3958	66	20	then	then	ADV
cana-3958	66	21	re	re	VERB
cana-3958	66	22	(	(	PUNCT
cana-3958	66	23	1	1	NUM
cana-3958	66	24	+	+	SYM
cana-3958	66	25	1	1	NUM
cana-3958	66	26	b	b	X
cana-3958	66	27	(	(	PUNCT
cana-3958	66	28	ξ(𝒫𝒟q	ξ(𝒫𝒟q	PROPN
cana-3958	66	29	,	,	PUNCT
cana-3958	66	30	δ	δ	PROPN
cana-3958	66	31	,	,	PUNCT
cana-3958	66	32	μ	μ	PROPN
cana-3958	66	33	n	n	CCONJ
cana-3958	66	34	,	,	PUNCT
cana-3958	66	35	r	r	NOUN
cana-3958	66	36	f(ξ))′	f(ξ))′	PROPN
cana-3958	66	37	𝒫𝒟	𝒫𝒟	PROPN
cana-3958	66	38	q	q	NOUN
cana-3958	66	39	,	,	PUNCT
cana-3958	66	40	δ	δ	PROPN
cana-3958	66	41	,	,	PUNCT
cana-3958	66	42	μ	μ	PROPN
cana-3958	66	43	n	n	CCONJ
cana-3958	66	44	,	,	PUNCT
cana-3958	66	45	r	r	NOUN
cana-3958	66	46	f(ξ	f(ξ	NOUN
cana-3958	66	47	)	)	PUNCT
cana-3958	66	48	−	−	ADP
cana-3958	66	49	1	1	NUM
cana-3958	66	50	)	)	PUNCT
cana-3958	66	51	)	)	PUNCT
cana-3958	66	52	>	>	X
cana-3958	67	1	θ	θ	PROPN
cana-3958	67	2	(	(	PUNCT
cana-3958	67	3	9	9	NUM
cana-3958	67	4	)	)	PUNCT
cana-3958	67	5	where	where	SCONJ
cana-3958	67	6	r	r	NOUN
cana-3958	67	7	≥1	≥1	NUM
cana-3958	67	8	,	,	PUNCT
cana-3958	67	9	0	0	NUM
cana-3958	67	10	≤	≤	NUM
cana-3958	67	11	q	q	ADJ
cana-3958	67	12	≤	≤	NUM
cana-3958	67	13	1,µ	1,µ	NUM
cana-3958	67	14	,	,	PUNCT
cana-3958	67	15	δ	δ	PROPN
cana-3958	67	16	≥	≥	PRON
cana-3958	67	17	0,n	0,n	PROPN
cana-3958	67	18	∈	∈	PROPN
cana-3958	67	19	ℕ0	ℕ0	NOUN
cana-3958	67	20	0	0	NUM
cana-3958	68	1	≤	≤	NUM
cana-3958	68	2	θ	θ	PROPN
cana-3958	68	3	<	<	X
cana-3958	68	4	1	1	NUM
cana-3958	68	5	,	,	PUNCT
cana-3958	68	6	b	b	X
cana-3958	68	7	∈	∈	PROPN
cana-3958	68	8	ℂ	ℂ	PROPN
cana-3958	68	9	−	−	PROPN
cana-3958	68	10	{	{	PUNCT
cana-3958	68	11	0	0	NUM
cana-3958	68	12	}	}	PUNCT
cana-3958	68	13	,	,	PUNCT
cana-3958	68	14	and	and	CCONJ
cana-3958	68	15	ξ	ξ	X
cana-3958	68	16	∈	∈	PROPN
cana-3958	68	17	𝕌.	𝕌.	PROPN
cana-3958	68	18	theorem	theorem	VERB
cana-3958	68	19	2.2	2.2	NUM
cana-3958	68	20	(	(	PUNCT
cana-3958	68	21	coefficient	coefficient	NOUN
cana-3958	68	22	inequalities	inequality	NOUN
cana-3958	68	23	)	)	PUNCT
cana-3958	68	24	let	let	VERB
cana-3958	68	25	(	(	PUNCT
cana-3958	68	26	1	1	X
cana-3958	68	27	)	)	PUNCT
cana-3958	68	28	define	define	VERB
cana-3958	68	29	f(ξ	f(ξ	NOUN
cana-3958	68	30	)	)	PUNCT
cana-3958	68	31	∈	∈	NOUN
cana-3958	68	32	𝒫𝒬q	𝒫𝒬q	NOUN
cana-3958	68	33	,	,	PUNCT
cana-3958	68	34	δ	δ	PROPN
cana-3958	68	35	,	,	PUNCT
cana-3958	68	36	μ	μ	PROPN
cana-3958	68	37	n	n	CCONJ
cana-3958	68	38	,	,	PUNCT
cana-3958	68	39	r	r	NOUN
cana-3958	68	40	(	(	PUNCT
cana-3958	68	41	θ	θ	NOUN
cana-3958	68	42	)	)	PUNCT
cana-3958	68	43	.	.	PUNCT
cana-3958	69	1	then	then	ADV
cana-3958	69	2	∑	∑	ADV
cana-3958	69	3	ϕ	ϕ	PROPN
cana-3958	69	4	v	v	ADP
cana-3958	69	5	∞	∞	PROPN
cana-3958	69	6	v=2	v=2	PROPN
cana-3958	69	7	cv	cv	PROPN
cana-3958	69	8	|av|	|av|	PROPN
cana-3958	69	9	≤	≤	PROPN
cana-3958	69	10	(	(	PUNCT
cana-3958	69	11	1	1	NUM
cana-3958	69	12	−	−	PROPN
cana-3958	69	13	θ)|b|	θ)|b|	PROPN
cana-3958	69	14	,	,	PUNCT
cana-3958	69	15	(	(	PUNCT
cana-3958	69	16	10	10	NUM
cana-3958	69	17	)	)	PUNCT
cana-3958	69	18	where	where	SCONJ
cana-3958	69	19	ϕ	ϕ	PROPN
cana-3958	69	20	v	v	NOUN
cana-3958	69	21	=	=	SYM
cana-3958	69	22	|1	|1	NUM
cana-3958	69	23	−	−	PROPN
cana-3958	69	24	b	b	PROPN
cana-3958	69	25	−	−	PROPN
cana-3958	69	26	v	v	NOUN
cana-3958	69	27	+	+	CCONJ
cana-3958	69	28	θb|	θb|	NOUN
cana-3958	69	29	,	,	PUNCT
cana-3958	69	30	cv	cv	NOUN
cana-3958	69	31	=	=	PUNCT
cana-3958	70	1	[	[	X
cana-3958	70	2	1	1	NUM
cana-3958	70	3	+	+	CCONJ
cana-3958	70	4	(	(	PUNCT
cana-3958	70	5	v	v	NOUN
cana-3958	70	6	−	−	PROPN
cana-3958	70	7	1)(δ	1)(δ	NUM
cana-3958	70	8	−	−	PROPN
cana-3958	70	9	μ	μ	PROPN
cana-3958	70	10	+	+	PROPN
cana-3958	70	11	vδμ)]n	vδμ)]n	ADJ
cana-3958	70	12	(	(	PUNCT
cana-3958	70	13	v+r−2	v+r−2	NOUN
cana-3958	70	14	r−1	r−1	PROPN
cana-3958	70	15	)	)	PUNCT
cana-3958	70	16	qv−1(1	qv−1(1	PROPN
cana-3958	70	17	−	−	NOUN
cana-3958	70	18	q)r	q)r	NOUN
cana-3958	70	19	,	,	PUNCT
cana-3958	70	20	r	r	NOUN
cana-3958	70	21	≥	≥	NUM
cana-3958	70	22	1,0	1,0	NUM
cana-3958	70	23	≤	≤	NUM
cana-3958	70	24	q	q	PROPN
cana-3958	70	25	≤	≤	NUM
cana-3958	70	26	1	1	NUM
cana-3958	70	27	,	,	PUNCT
cana-3958	70	28	μ	μ	PROPN
cana-3958	70	29	,	,	PUNCT
cana-3958	70	30	δ	δ	PROPN
cana-3958	70	31	≥	≥	NOUN
cana-3958	70	32	0	0	NUM
cana-3958	70	33	,	,	PUNCT
cana-3958	70	34	n	n	PROPN
cana-3958	70	35	∈	∈	PROPN
cana-3958	70	36	ℕ0	ℕ0	NOUN
cana-3958	70	37	,	,	PUNCT
cana-3958	70	38	0	0	NUM
cana-3958	70	39	≤	≤	NUM
cana-3958	71	1	θ	θ	X
cana-3958	71	2	<	<	X
cana-3958	71	3	1	1	NUM
cana-3958	71	4	,	,	PUNCT
cana-3958	71	5	b	b	X
cana-3958	71	6	∈	∈	PROPN
cana-3958	71	7	ℂ	ℂ	PROPN
cana-3958	71	8	−	−	PROPN
cana-3958	71	9	{	{	PUNCT
cana-3958	71	10	0}and	0}and	NUM
cana-3958	71	11	ξ	ξ	PROPN
cana-3958	71	12	∈	∈	PROPN
cana-3958	71	13	𝕌.	𝕌.	PROPN
cana-3958	71	14	proof	proof	NOUN
cana-3958	71	15	:	:	PUNCT
cana-3958	71	16	let	let	VERB
cana-3958	71	17	f(z	f(z	NUM
cana-3958	71	18	)	)	PUNCT
cana-3958	71	19	=	=	SYM
cana-3958	72	1	1	1	NUM
cana-3958	72	2	+	+	SYM
cana-3958	72	3	1	1	NUM
cana-3958	72	4	b	b	X
cana-3958	72	5	(	(	PUNCT
cana-3958	72	6	ξ(𝒫𝒟q	ξ(𝒫𝒟q	PROPN
cana-3958	72	7	,	,	PUNCT
cana-3958	72	8	δ	δ	PROPN
cana-3958	72	9	,	,	PUNCT
cana-3958	72	10	μ	μ	PROPN
cana-3958	72	11	n	n	CCONJ
cana-3958	72	12	,	,	PUNCT
cana-3958	72	13	r	r	NOUN
cana-3958	72	14	f(ξ))′	f(ξ))′	PROPN
cana-3958	72	15	𝒫𝒟	𝒫𝒟	PROPN
cana-3958	72	16	q	q	NOUN
cana-3958	72	17	,	,	PUNCT
cana-3958	72	18	δ	δ	PROPN
cana-3958	72	19	,	,	PUNCT
cana-3958	72	20	μ	μ	PROPN
cana-3958	72	21	n	n	CCONJ
cana-3958	72	22	,	,	PUNCT
cana-3958	72	23	r	r	NOUN
cana-3958	72	24	f(ξ	f(ξ	NOUN
cana-3958	72	25	)	)	PUNCT
cana-3958	72	26	−	−	ADP
cana-3958	72	27	1	1	NUM
cana-3958	72	28	)	)	PUNCT
cana-3958	72	29	–	–	PUNCT
cana-3958	72	30	θ	θ	NOUN
cana-3958	72	31	,	,	PUNCT
cana-3958	72	32	=	=	SYM
cana-3958	72	33	1	1	NUM
cana-3958	72	34	+	+	CCONJ
cana-3958	72	35	(	(	PUNCT
cana-3958	72	36	ξ(𝒫𝒟q	ξ(𝒫𝒟q	PROPN
cana-3958	72	37	,	,	PUNCT
cana-3958	72	38	δ	δ	PROPN
cana-3958	72	39	,	,	PUNCT
cana-3958	72	40	μ	μ	PROPN
cana-3958	72	41	n	n	CCONJ
cana-3958	72	42	,	,	PUNCT
cana-3958	72	43	r	r	NOUN
cana-3958	72	44	f(ξ))′	f(ξ))′	PROPN
cana-3958	72	45	𝒫𝒟	𝒫𝒟	PROPN
cana-3958	72	46	q	q	NOUN
cana-3958	72	47	,	,	PUNCT
cana-3958	72	48	δ	δ	PROPN
cana-3958	72	49	,	,	PUNCT
cana-3958	72	50	μ	μ	PROPN
cana-3958	72	51	n	n	CCONJ
cana-3958	72	52	,	,	PUNCT
cana-3958	72	53	r	r	NOUN
cana-3958	72	54	f(ξ	f(ξ	NOUN
cana-3958	72	55	)	)	PUNCT
cana-3958	72	56	−	−	PROPN
cana-3958	72	57	1	1	NUM
cana-3958	72	58	b	b	NOUN
cana-3958	72	59	)	)	PUNCT
cana-3958	72	60	–	–	PUNCT
cana-3958	72	61	θ	θ	X
cana-3958	72	62	=	=	SYM
cana-3958	72	63	1	1	NUM
cana-3958	72	64	+	+	CCONJ
cana-3958	72	65	(	(	PUNCT
cana-3958	72	66	ξ	ξ	X
cana-3958	72	67	(	(	PUNCT
cana-3958	72	68	𝒫𝒟q	𝒫𝒟q	PROPN
cana-3958	72	69	,	,	PUNCT
cana-3958	72	70	δ	δ	PROPN
cana-3958	72	71	,	,	PUNCT
cana-3958	72	72	μ	μ	PROPN
cana-3958	72	73	n	n	CCONJ
cana-3958	72	74	,	,	PUNCT
cana-3958	72	75	r	r	NOUN
cana-3958	72	76	f(ξ	f(ξ	PROPN
cana-3958	72	77	)	)	PUNCT
cana-3958	72	78	)	)	PUNCT
cana-3958	72	79	′	′	NUM
cana-3958	73	1	−	−	PROPN
cana-3958	73	2	b𝒫𝒟q	b𝒫𝒟q	PROPN
cana-3958	73	3	,	,	PUNCT
cana-3958	73	4	δ	δ	PROPN
cana-3958	73	5	,	,	PUNCT
cana-3958	73	6	μ	μ	PROPN
cana-3958	73	7	n	n	CCONJ
cana-3958	73	8	,	,	PUNCT
cana-3958	73	9	r	r	NOUN
cana-3958	73	10	f(ξ	f(ξ	NOUN
cana-3958	73	11	)	)	PUNCT
cana-3958	73	12	−	−	NOUN
cana-3958	73	13	θb𝒫𝒟q	θb𝒫𝒟q	PROPN
cana-3958	73	14	,	,	PUNCT
cana-3958	73	15	δ	δ	PROPN
cana-3958	73	16	,	,	PUNCT
cana-3958	73	17	μ	μ	PROPN
cana-3958	73	18	n	n	CCONJ
cana-3958	73	19	,	,	PUNCT
cana-3958	73	20	r	r	NOUN
cana-3958	73	21	f(ξ	f(ξ	NOUN
cana-3958	73	22	)	)	PUNCT
cana-3958	73	23	b𝒫𝒟q	b𝒫𝒟q	PROPN
cana-3958	73	24	,	,	PUNCT
cana-3958	73	25	δ	δ	PROPN
cana-3958	73	26	,	,	PUNCT
cana-3958	73	27	μ	μ	PROPN
cana-3958	73	28	n	n	CCONJ
cana-3958	73	29	,	,	PUNCT
cana-3958	73	30	r	r	NOUN
cana-3958	73	31	f(ξ	f(ξ	PROPN
cana-3958	73	32	)	)	PUNCT
cana-3958	73	33	)	)	PUNCT
cana-3958	73	34	by	by	ADP
cana-3958	73	35	the	the	DET
cana-3958	73	36	condition	condition	NOUN
cana-3958	73	37	of	of	ADP
cana-3958	73	38	the	the	DET
cana-3958	73	39	class	class	NOUN
cana-3958	73	40	,	,	PUNCT
cana-3958	73	41	f(z	f(z	PROPN
cana-3958	73	42	)	)	PUNCT
cana-3958	73	43	≺	≺	NOUN
cana-3958	73	44	1+z	1+z	NUM
cana-3958	73	45	1−z	1−z	NUM
cana-3958	73	46	.	.	PUNCT
cana-3958	74	1	a	a	DET
cana-3958	74	2	schwarz	schwarz	PROPN
cana-3958	74	3	function	function	NOUN
cana-3958	74	4	ω(z	ω(z	PUNCT
cana-3958	74	5	)	)	PUNCT
cana-3958	74	6	exist	exist	VERB
cana-3958	74	7	,	,	PUNCT
cana-3958	74	8	and	and	CCONJ
cana-3958	74	9	ω(0	ω(0	NUM
cana-3958	74	10	)	)	PUNCT
cana-3958	74	11	=	=	SYM
cana-3958	74	12	0	0	NUM
cana-3958	74	13	as	as	ADP
cana-3958	74	14	f(z	f(z	NOUN
cana-3958	74	15	)	)	PUNCT
cana-3958	74	16	=	=	PUNCT
cana-3958	75	1	1+ω(z	1+ω(z	ADJ
cana-3958	75	2	)	)	PUNCT
cana-3958	75	3	1−ω(z	1−ω(z	NUM
cana-3958	75	4	)	)	PUNCT
cana-3958	75	5	,	,	PUNCT
cana-3958	75	6	where	where	SCONJ
cana-3958	75	7	|ω|	|ω|	ADP
cana-3958	75	8	<	<	X
cana-3958	75	9	1	1	NUM
cana-3958	75	10	.	.	PUNCT
cana-3958	76	1	∴	∴	NOUN
cana-3958	76	2	ω(z	ω(z	PROPN
cana-3958	76	3	)	)	PUNCT
cana-3958	77	1	=	=	SYM
cana-3958	77	2	f(z)−1	f(z)−1	ADJ
cana-3958	77	3	f(z)+1	f(z)+1	NOUN
cana-3958	77	4	.	.	PUNCT
cana-3958	78	1	we	we	PRON
cana-3958	78	2	know	know	VERB
cana-3958	78	3	that	that	SCONJ
cana-3958	78	4	|	|	NOUN
cana-3958	78	5	ω(z)|	ω(z)|	ADV
cana-3958	78	6	=	=	PUNCT
cana-3958	79	1	|	|	ADV
cana-3958	79	2	f(z)−1	f(z)−1	ADJ
cana-3958	79	3	f(z)+1	f(z)+1	NOUN
cana-3958	79	4	|	|	ADV
cana-3958	79	5	<	<	X
cana-3958	79	6	1	1	X
cana-3958	79	7	.	.	PUNCT
cana-3958	80	1	then	then	ADV
cana-3958	80	2	communications	communication	NOUN
cana-3958	80	3	on	on	ADP
cana-3958	80	4	applied	apply	VERB
cana-3958	80	5	nonlinear	nonlinear	ADJ
cana-3958	80	6	analysis	analysis	NOUN
cana-3958	80	7	issn	issn	NOUN
cana-3958	80	8	:	:	PUNCT
cana-3958	80	9	1074	1074	NUM
cana-3958	80	10	-	-	PUNCT
cana-3958	80	11	133x	133x	NUM
cana-3958	80	12	vol	vol	NOUN
cana-3958	80	13	32	32	NUM
cana-3958	80	14	no	no	NOUN
cana-3958	80	15	.	.	PUNCT
cana-3958	81	1	9s	9s	NUM
cana-3958	81	2	(	(	PUNCT
cana-3958	81	3	2025	2025	NUM
cana-3958	81	4	)	)	PUNCT
cana-3958	81	5	469	469	NUM
cana-3958	81	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3958	81	7	|	|	ADV
cana-3958	81	8	f(z)−1	f(z)−1	ADJ
cana-3958	81	9	f(z)+1	f(z)+1	NOUN
cana-3958	81	10	|	|	ADV
cana-3958	81	11	=	=	PUNCT
cana-3958	82	1	|	|	ADV
cana-3958	82	2	ξ(𝒫𝒟q	ξ(𝒫𝒟q	PROPN
cana-3958	82	3	,	,	PUNCT
cana-3958	82	4	δ	δ	PROPN
cana-3958	82	5	,	,	PUNCT
cana-3958	82	6	μ	μ	PROPN
cana-3958	82	7	n	n	CCONJ
cana-3958	82	8	,	,	PUNCT
cana-3958	82	9	r	r	NOUN
cana-3958	82	10	f(ξ	f(ξ	PROPN
cana-3958	82	11	)	)	PUNCT
cana-3958	82	12	)	)	PUNCT
cana-3958	82	13	′	′	NUM
cana-3958	83	1	−(1+θb)𝒫𝒟q	−(1+θb)𝒫𝒟q	PROPN
cana-3958	83	2	,	,	PUNCT
cana-3958	83	3	δ	δ	PROPN
cana-3958	83	4	,	,	PUNCT
cana-3958	83	5	μ	μ	PROPN
cana-3958	83	6	n	n	CCONJ
cana-3958	83	7	,	,	PUNCT
cana-3958	83	8	r	r	NOUN
cana-3958	83	9	f(ξ	f(ξ	PROPN
cana-3958	83	10	)	)	PUNCT
cana-3958	83	11	ξ(𝒫𝒟	ξ(𝒫𝒟	PROPN
cana-3958	83	12	q	q	PROPN
cana-3958	83	13	,	,	PUNCT
cana-3958	83	14	δ	δ	PROPN
cana-3958	83	15	,	,	PUNCT
cana-3958	83	16	μ	μ	PROPN
cana-3958	83	17	n	n	CCONJ
cana-3958	83	18	,	,	PUNCT
cana-3958	83	19	r	r	NOUN
cana-3958	83	20	f(ξ	f(ξ	PROPN
cana-3958	83	21	)	)	PUNCT
cana-3958	83	22	)	)	PUNCT
cana-3958	84	1	′	′	NUM
cana-3958	85	1	−(1+θb−2b)𝒫𝒟	−(1+θb−2b)𝒫𝒟	PUNCT
cana-3958	85	2	q	q	NOUN
cana-3958	85	3	,	,	PUNCT
cana-3958	85	4	δ	δ	PROPN
cana-3958	85	5	,	,	PUNCT
cana-3958	85	6	μ	μ	PROPN
cana-3958	85	7	n	n	CCONJ
cana-3958	85	8	,	,	PUNCT
cana-3958	85	9	r	r	NOUN
cana-3958	85	10	f(ξ	f(ξ	NOUN
cana-3958	85	11	)	)	PUNCT
cana-3958	86	1	|	|	ADV
cana-3958	86	2	=	=	SYM
cana-3958	87	1	|	|	ADV
cana-3958	87	2	z+∑	z+∑	NUM
cana-3958	87	3	vcvavzv∞	vcvavzv∞	PUNCT
cana-3958	87	4	v=2	v=2	X
cana-3958	87	5	−(1+θb)z−∑	−(1+θb)z−∑	X
cana-3958	87	6	(	(	PUNCT
cana-3958	87	7	1+θb)∞	1+θb)∞	NUM
cana-3958	87	8	v=2	v=2	PART
cana-3958	87	9	cvavzv	cvavzv	VERB
cana-3958	87	10	z+∑	z+∑	NOUN
cana-3958	87	11	vcvavzv∞	vcvavzv∞	NOUN
cana-3958	87	12	k=2	k=2	PROPN
cana-3958	88	1	−(1+θb−2b)z−∑	−(1+θb−2b)z−∑	X
cana-3958	88	2	(	(	PUNCT
cana-3958	88	3	1+θb−2b)cvavzv∞	1+θb−2b)cvavzv∞	X
cana-3958	88	4	v=2	v=2	X
cana-3958	88	5	|	|	NOUN
cana-3958	88	6	=	=	PUNCT
cana-3958	88	7	|	|	ADV
cana-3958	88	8	θb+∑	θb+∑	NOUN
cana-3958	88	9	(	(	PUNCT
cana-3958	88	10	1+θb−v)cvavzv−1∞	1+θb−v)cvavzv−1∞	PROPN
cana-3958	88	11	v=2	v=2	SYM
cana-3958	88	12	(	(	PUNCT
cana-3958	88	13	2−θ)b+∑	2−θ)b+∑	NUM
cana-3958	88	14	(	(	PUNCT
cana-3958	88	15	1+θb−2b−v)c	1+θb−2b−v)c	NUM
cana-3958	88	16	v	v	NOUN
cana-3958	88	17	avzv−1∞	avzv−1∞	NOUN
cana-3958	88	18	v=2	v=2	PROPN
cana-3958	88	19	|	|	ADV
cana-3958	88	20	≤	≤	NUM
cana-3958	88	21	|	|	ADV
cana-3958	88	22	θ|b|+∑	θ|b|+∑	VERB
cana-3958	88	23	|(1+θb−v||cvav||zv−1|∞	|(1+θb−v||cvav||zv−1|∞	PROPN
cana-3958	88	24	v=2	v=2	PROPN
cana-3958	88	25	(	(	PUNCT
cana-3958	88	26	2−θ)|b|−∑	2−θ)|b|−∑	PROPN
cana-3958	88	27	|(1+θb−2b−v)||cvav||zv−1|∞	|(1+θb−2b−v)||cvav||zv−1|∞	PROPN
cana-3958	88	28	v=2	v=2	PROPN
cana-3958	88	29	|	|	NOUN
cana-3958	88	30	.	.	PUNCT
cana-3958	89	1	which	which	PRON
cana-3958	89	2	is	be	AUX
cana-3958	89	3	bounded	bound	VERB
cana-3958	89	4	by	by	ADP
cana-3958	89	5	1	1	NUM
cana-3958	89	6	,	,	PUNCT
cana-3958	89	7	if	if	SCONJ
cana-3958	89	8	θ|b|	θ|b|	NOUN
cana-3958	89	9	+	+	CCONJ
cana-3958	89	10	∑	∑	PROPN
cana-3958	89	11	|(1	|(1	PROPN
cana-3958	89	12	+	+	PROPN
cana-3958	89	13	θb	θb	ADP
cana-3958	89	14	−	−	PROPN
cana-3958	89	15	v)|cv|av|	v)|cv|av|	NOUN
cana-3958	89	16	≤	≤	NUM
cana-3958	89	17	(	(	PUNCT
cana-3958	89	18	2	2	NUM
cana-3958	89	19	−	−	NOUN
cana-3958	89	20	θ)|b|	θ)|b|	PROPN
cana-3958	90	1	−	−	NOUN
cana-3958	90	2	∑	∑	PUNCT
cana-3958	91	1	|(1	|(1	PROPN
cana-3958	91	2	+	+	PROPN
cana-3958	91	3	θb	θb	ADP
cana-3958	91	4	−	−	PROPN
cana-3958	91	5	2b	2b	NOUN
cana-3958	91	6	−	−	PROPN
cana-3958	91	7	v)|∞	v)|∞	NUM
cana-3958	91	8	v=2	v=2	PROPN
cana-3958	91	9	∞	∞	PROPN
cana-3958	91	10	v=2	v=2	PROPN
cana-3958	91	11	cv|av|	cv|av|	PROPN
cana-3958	91	12	.	.	PUNCT
cana-3958	91	13	∑|(1	∑|(1	NOUN
cana-3958	92	1	+	+	CCONJ
cana-3958	92	2	θb	θb	ADP
cana-3958	92	3	−	−	PROPN
cana-3958	92	4	b	b	PROPN
cana-3958	92	5	−	−	PROPN
cana-3958	92	6	v)|cv|av|	v)|cv|av|	NOUN
cana-3958	92	7	≤	≤	NUM
cana-3958	92	8	(	(	PUNCT
cana-3958	92	9	1	1	NUM
cana-3958	92	10	−	−	PROPN
cana-3958	92	11	θ)|b|	θ)|b|	PROPN
cana-3958	92	12	.	.	PUNCT
cana-3958	93	1	∞	∞	NUM
cana-3958	94	1	v=2	v=2	PROPN
cana-3958	94	2	hence	hence	ADV
cana-3958	94	3	equation	equation	NOUN
cana-3958	94	4	(	(	PUNCT
cana-3958	94	5	10	10	NUM
cana-3958	94	6	)	)	PUNCT
cana-3958	94	7	holds	hold	VERB
cana-3958	94	8	.	.	PUNCT
cana-3958	95	1	corollary	corollary	ADJ
cana-3958	95	2	2.3	2.3	NUM
cana-3958	95	3	let	let	VERB
cana-3958	95	4	f	f	PROPN
cana-3958	95	5	∈	∈	PROPN
cana-3958	95	6	𝒫𝒬q	𝒫𝒬q	PROPN
cana-3958	95	7	,	,	PUNCT
cana-3958	95	8	δ	δ	PROPN
cana-3958	95	9	,	,	PUNCT
cana-3958	95	10	μ	μ	PROPN
cana-3958	95	11	n	n	CCONJ
cana-3958	95	12	,	,	PUNCT
cana-3958	95	13	r	r	NOUN
cana-3958	95	14	(	(	PUNCT
cana-3958	95	15	θ	θ	NOUN
cana-3958	95	16	)	)	PUNCT
cana-3958	95	17	then	then	ADV
cana-3958	95	18	we	we	PRON
cana-3958	95	19	have	have	VERB
cana-3958	95	20	av	av	PROPN
cana-3958	95	21	≤	≤	NUM
cana-3958	95	22	(	(	PUNCT
cana-3958	95	23	1−θ)|b|	1−θ)|b|	NUM
cana-3958	95	24	ϕ	ϕ	NOUN
cana-3958	95	25	v	v	ADP
cana-3958	95	26	cv	cv	PROPN
cana-3958	95	27	and	and	CCONJ
cana-3958	95	28	f(ξ	f(ξ	NOUN
cana-3958	95	29	)	)	PUNCT
cana-3958	95	30	=	=	SYM
cana-3958	96	1	ξ	ξ	X
cana-3958	97	1	+	+	PUNCT
cana-3958	97	2	(	(	PUNCT
cana-3958	97	3	1−θ)|b|	1−θ)|b|	NUM
cana-3958	97	4	ϕ	ϕ	NOUN
cana-3958	97	5	v	v	NUM
cana-3958	97	6	cv	cv	PROPN
cana-3958	97	7	ξ	ξ	PROPN
cana-3958	97	8	v	v	PROPN
cana-3958	97	9	,	,	PUNCT
cana-3958	97	10	v	v	NOUN
cana-3958	97	11	=	=	SYM
cana-3958	97	12	2,3,4	2,3,4	NUM
cana-3958	97	13	,	,	PUNCT
cana-3958	97	14	.	.	PUNCT
cana-3958	97	15	..	..	PUNCT
cana-3958	98	1	(	(	PUNCT
cana-3958	98	2	11	11	X
cana-3958	98	3	)	)	PUNCT
cana-3958	98	4	equals	equal	VERB
cana-3958	98	5	itself	itself	PRON
cana-3958	98	6	.	.	PUNCT
cana-3958	99	1	the	the	DET
cana-3958	99	2	function	function	NOUN
cana-3958	99	3	f	f	PROPN
cana-3958	99	4	ϵ𝒜	ϵ𝒜	NOUN
cana-3958	99	5	is	be	AUX
cana-3958	99	6	the	the	DET
cana-3958	99	7	subclass	subclass	ADJ
cana-3958	99	8	𝒫𝒬q	𝒫𝒬q	NOUN
cana-3958	99	9	,	,	PUNCT
cana-3958	99	10	δ	δ	PROPN
cana-3958	99	11	,	,	PUNCT
cana-3958	99	12	μ	μ	PROPN
cana-3958	99	13	n	n	CCONJ
cana-3958	99	14	,	,	PUNCT
cana-3958	99	15	r	r	NOUN
cana-3958	99	16	(	(	PUNCT
cana-3958	99	17	θ	θ	NOUN
cana-3958	99	18	)	)	PUNCT
cana-3958	99	19	∁	∁	PROPN
cana-3958	99	20	𝒫𝒬q	𝒫𝒬q	NOUN
cana-3958	99	21	,	,	PUNCT
cana-3958	99	22	δ	δ	PROPN
cana-3958	99	23	,	,	PUNCT
cana-3958	99	24	μ	μ	PROPN
cana-3958	99	25	n	n	CCONJ
cana-3958	99	26	,	,	PUNCT
cana-3958	99	27	r	r	NOUN
cana-3958	99	28	(	(	PUNCT
cana-3958	99	29	θ	θ	NOUN
cana-3958	99	30	)	)	PUNCT
cana-3958	99	31	,	,	PUNCT
cana-3958	99	32	which	which	PRON
cana-3958	99	33	we	we	PRON
cana-3958	99	34	define	define	VERB
cana-3958	99	35	.	.	PUNCT
cana-3958	100	1	the	the	DET
cana-3958	100	2	extreme	extreme	ADJ
cana-3958	100	3	points	point	NOUN
cana-3958	100	4	of	of	ADP
cana-3958	100	5	the	the	DET
cana-3958	100	6	subclass	subclass	NOUN
cana-3958	100	7	𝒫𝒬q	𝒫𝒬q	NOUN
cana-3958	100	8	,	,	PUNCT
cana-3958	100	9	δ	δ	PROPN
cana-3958	100	10	,	,	PUNCT
cana-3958	100	11	μ	μ	PROPN
cana-3958	100	12	n	n	CCONJ
cana-3958	100	13	,	,	PUNCT
cana-3958	100	14	r	r	NOUN
cana-3958	100	15	(	(	PUNCT
cana-3958	100	16	θ	θ	NOUN
cana-3958	100	17	)	)	PUNCT
cana-3958	100	18	are	be	AUX
cana-3958	100	19	now	now	ADV
cana-3958	100	20	determined	determine	VERB
cana-3958	100	21	.	.	PUNCT
cana-3958	101	1	theorem	theorem	VERB
cana-3958	101	2	2.4(extreme	2.4(extreme	NUM
cana-3958	101	3	points	point	NOUN
cana-3958	101	4	)	)	PUNCT
cana-3958	101	5	let	let	VERB
cana-3958	101	6	f1(ξ	f1(ξ	PRON
cana-3958	101	7	)	)	PUNCT
cana-3958	101	8	=	=	SYM
cana-3958	101	9	ξ	ξ	NOUN
cana-3958	101	10	,	,	PUNCT
cana-3958	101	11	fv(ξ	fv(ξ	NOUN
cana-3958	101	12	)	)	PUNCT
cana-3958	101	13	=	=	SYM
cana-3958	102	1	ξ	ξ	X
cana-3958	102	2	+	+	NUM
cana-3958	102	3	∑	∑	PROPN
cana-3958	102	4	η	η	PROPN
cana-3958	102	5	v	v	X
cana-3958	102	6	(	(	PUNCT
cana-3958	102	7	1−θ)|b|	1−θ)|b|	NUM
cana-3958	102	8	ϕ	ϕ	NOUN
cana-3958	102	9	v	v	NUM
cana-3958	102	10	cv	cv	PROPN
cana-3958	102	11	∞	∞	PROPN
cana-3958	102	12	v=2	v=2	PROPN
cana-3958	102	13	ξ	ξ	PROPN
cana-3958	102	14	v	v	NOUN
cana-3958	102	15	,	,	PUNCT
cana-3958	102	16	v	v	PRON
cana-3958	102	17	≥	≥	NOUN
cana-3958	102	18	2	2	NUM
cana-3958	102	19	.	.	PUNCT
cana-3958	103	1	then	then	ADV
cana-3958	103	2	f	f	PROPN
cana-3958	103	3	ϵ	ϵ	X
cana-3958	103	4	𝒫𝒬q	𝒫𝒬q	PROPN
cana-3958	103	5	,	,	PUNCT
cana-3958	103	6	δ	δ	PROPN
cana-3958	103	7	,	,	PUNCT
cana-3958	103	8	μ	μ	PROPN
cana-3958	103	9	n	n	CCONJ
cana-3958	103	10	,	,	PUNCT
cana-3958	103	11	r	r	NOUN
cana-3958	103	12	(	(	PUNCT
cana-3958	103	13	θ	θ	NOUN
cana-3958	103	14	)	)	PUNCT
cana-3958	103	15	strictly	strictly	ADV
cana-3958	103	16	if	if	SCONJ
cana-3958	103	17	f(ξ	f(ξ	NOUN
cana-3958	103	18	)	)	PUNCT
cana-3958	103	19	=	=	SYM
cana-3958	103	20	∑	∑	PUNCT
cana-3958	103	21	η	η	PROPN
cana-3958	103	22	v	v	ADP
cana-3958	103	23	fv(ξ)∞	fv(ξ)∞	PROPN
cana-3958	103	24	v=1	v=1	X
cana-3958	103	25	,	,	PUNCT
cana-3958	103	26	where	where	SCONJ
cana-3958	103	27	η	η	PROPN
cana-3958	103	28	v	v	ADP
cana-3958	103	29	>	>	X
cana-3958	103	30	0	0	NUM
cana-3958	104	1	and	and	CCONJ
cana-3958	104	2	∑	∑	PUNCT
cana-3958	104	3	η	η	PROPN
cana-3958	104	4	v	v	X
cana-3958	104	5	=	=	SYM
cana-3958	104	6	1∞	1∞	NUM
cana-3958	104	7	v=1	v=1	X
cana-3958	104	8	.	.	PUNCT
cana-3958	105	1	proof	proof	NOUN
cana-3958	105	2	:	:	PUNCT
cana-3958	105	3	let	let	VERB
cana-3958	105	4	f(ξ	f(ξ	NOUN
cana-3958	105	5	)	)	PUNCT
cana-3958	105	6	=	=	SYM
cana-3958	105	7	∑	∑	PUNCT
cana-3958	105	8	η	η	PROPN
cana-3958	105	9	v	v	PROPN
cana-3958	105	10	fv(ξ	fv(ξ	NOUN
cana-3958	105	11	)	)	PUNCT
cana-3958	105	12	∞	∞	PROPN
cana-3958	105	13	v=1	v=1	X
cana-3958	106	1	=	=	SYM
cana-3958	106	2	ξ	ξ	PROPN
cana-3958	106	3	+	+	PROPN
cana-3958	106	4	∑	∑	PROPN
cana-3958	106	5	η	η	PROPN
cana-3958	106	6	v	v	X
cana-3958	106	7	(	(	PUNCT
cana-3958	106	8	1	1	NUM
cana-3958	106	9	−	−	PROPN
cana-3958	106	10	θ)|b|	θ)|b|	PROPN
cana-3958	106	11	ϕ	ϕ	NOUN
cana-3958	106	12	v	v	ADP
cana-3958	106	13	cv	cv	PROPN
cana-3958	106	14	∞	∞	PROPN
cana-3958	106	15	v=2	v=2	PROPN
cana-3958	106	16	ξ	ξ	X
cana-3958	106	17	v	v	NOUN
cana-3958	106	18	=	=	PUNCT
cana-3958	106	19	∑	∑	PROPN
cana-3958	106	20	η	η	PROPN
cana-3958	106	21	v	v	X
cana-3958	106	22	(	(	PUNCT
cana-3958	106	23	1	1	NUM
cana-3958	106	24	−	−	PROPN
cana-3958	106	25	θ)|b|	θ)|b|	PROPN
cana-3958	106	26	ϕ	ϕ	NOUN
cana-3958	106	27	v	v	ADP
cana-3958	106	28	cv	cv	PROPN
cana-3958	106	29	∞	∞	PROPN
cana-3958	106	30	v=2	v=2	PROPN
cana-3958	106	31	ϕ	ϕ	PROPN
cana-3958	106	32	v	v	NUM
cana-3958	106	33	cv	cv	NOUN
cana-3958	106	34	communications	communication	NOUN
cana-3958	106	35	on	on	ADP
cana-3958	106	36	applied	apply	VERB
cana-3958	106	37	nonlinear	nonlinear	ADJ
cana-3958	106	38	analysis	analysis	NOUN
cana-3958	106	39	issn	issn	NOUN
cana-3958	106	40	:	:	PUNCT
cana-3958	106	41	1074	1074	NUM
cana-3958	106	42	-	-	PUNCT
cana-3958	106	43	133x	133x	NUM
cana-3958	106	44	vol	vol	NOUN
cana-3958	106	45	32	32	NUM
cana-3958	106	46	no	no	NOUN
cana-3958	106	47	.	.	PUNCT
cana-3958	107	1	9s	9s	NUM
cana-3958	107	2	(	(	PUNCT
cana-3958	107	3	2025	2025	NUM
cana-3958	107	4	)	)	PUNCT
cana-3958	107	5	470	470	NUM
cana-3958	107	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3958	107	7	=	=	PUNCT
cana-3958	107	8	(	(	PUNCT
cana-3958	107	9	1	1	NUM
cana-3958	107	10	−	−	PROPN
cana-3958	107	11	θ|b|	θ|b|	VERB
cana-3958	107	12	∑	∑	PUNCT
cana-3958	107	13	η	η	PROPN
cana-3958	107	14	v	v	ADP
cana-3958	107	15	∞	∞	PROPN
cana-3958	107	16	v=1	v=1	X
cana-3958	107	17	=	=	PUNCT
cana-3958	107	18	(	(	PUNCT
cana-3958	107	19	1	1	NUM
cana-3958	107	20	−	−	PROPN
cana-3958	107	21	θ	θ	PROPN
cana-3958	107	22	)	)	PUNCT
cana-3958	108	1	|b|(1	|b|(1	PROPN
cana-3958	108	2	−	−	PROPN
cana-3958	108	3	η	η	PROPN
cana-3958	108	4	1	1	NUM
cana-3958	108	5	)	)	PUNCT
cana-3958	108	6	<	<	X
cana-3958	108	7	(	(	PUNCT
cana-3958	108	8	1	1	NUM
cana-3958	108	9	−	−	PROPN
cana-3958	108	10	θ)|b|	θ)|b|	PROPN
cana-3958	108	11	,	,	PUNCT
cana-3958	108	12	which	which	PRON
cana-3958	108	13	shows	show	VERB
cana-3958	108	14	that	that	SCONJ
cana-3958	108	15	f	f	PROPN
cana-3958	108	16	ϵ	ϵ	X
cana-3958	108	17	𝒫𝒬q	𝒫𝒬q	PROPN
cana-3958	108	18	,	,	PUNCT
cana-3958	108	19	δ	δ	PROPN
cana-3958	108	20	,	,	PUNCT
cana-3958	108	21	μ	μ	PROPN
cana-3958	108	22	n	n	CCONJ
cana-3958	108	23	,	,	PUNCT
cana-3958	108	24	r	r	NOUN
cana-3958	108	25	(	(	PUNCT
cana-3958	108	26	θ	θ	NOUN
cana-3958	108	27	)	)	PUNCT
cana-3958	108	28	.	.	PUNCT
cana-3958	109	1	conversely	conversely	ADV
cana-3958	109	2	,	,	PUNCT
cana-3958	109	3	suppose	suppose	VERB
cana-3958	109	4	that	that	SCONJ
cana-3958	109	5	f	f	PROPN
cana-3958	109	6	ϵ	ϵ	X
cana-3958	109	7	𝒫𝒬q	𝒫𝒬q	PROPN
cana-3958	109	8	,	,	PUNCT
cana-3958	109	9	δ	δ	PROPN
cana-3958	109	10	,	,	PUNCT
cana-3958	109	11	μ	μ	PROPN
cana-3958	109	12	n	n	CCONJ
cana-3958	109	13	,	,	PUNCT
cana-3958	109	14	r	r	NOUN
cana-3958	109	15	(	(	PUNCT
cana-3958	109	16	θ	θ	NOUN
cana-3958	109	17	)	)	PUNCT
cana-3958	109	18	.	.	PUNCT
cana-3958	110	1	since	since	SCONJ
cana-3958	110	2	|av|	|av|	PROPN
cana-3958	110	3	≤	≤	NOUN
cana-3958	110	4	(	(	PUNCT
cana-3958	110	5	1−θ)|b|	1−θ)|b|	NUM
cana-3958	110	6	ϕ	ϕ	NOUN
cana-3958	110	7	v	v	X
cana-3958	110	8	cv	cv	PROPN
cana-3958	110	9	,	,	PUNCT
cana-3958	110	10	v	v	NOUN
cana-3958	110	11	=	=	SYM
cana-3958	110	12	2,3	2,3	NUM
cana-3958	110	13	,	,	PUNCT
cana-3958	110	14	..	..	PUNCT
cana-3958	110	15	let	let	VERB
cana-3958	110	16	η	η	PROPN
cana-3958	110	17	v	v	ADP
cana-3958	110	18	≤	≤	PROPN
cana-3958	110	19	ϕ	ϕ	PROPN
cana-3958	110	20	v	v	X
cana-3958	110	21	cv	cv	PROPN
cana-3958	110	22	(	(	PUNCT
cana-3958	110	23	1	1	NUM
cana-3958	110	24	−	−	PROPN
cana-3958	110	25	θ)|b|	θ)|b|	PROPN
cana-3958	110	26	,	,	PUNCT
cana-3958	110	27	η	η	PROPN
cana-3958	110	28	1	1	NUM
cana-3958	110	29	=	=	SYM
cana-3958	110	30	1	1	NUM
cana-3958	110	31	−	−	NUM
cana-3958	110	32	∑	∑	PUNCT
cana-3958	110	33	η	η	PROPN
cana-3958	110	34	v	v	ADP
cana-3958	110	35	∞	∞	PROPN
cana-3958	110	36	v=2	v=2	PROPN
cana-3958	110	37	.	.	PUNCT
cana-3958	111	1	then	then	ADV
cana-3958	111	2	we	we	PRON
cana-3958	111	3	obtain	obtain	VERB
cana-3958	111	4	f(ξ	f(ξ	NOUN
cana-3958	111	5	)	)	PUNCT
cana-3958	111	6	=	=	SYM
cana-3958	111	7	∑	∑	PUNCT
cana-3958	111	8	η	η	PROPN
cana-3958	111	9	v	v	ADP
cana-3958	111	10	fv(ξ)∞	fv(ξ)∞	PROPN
cana-3958	111	11	v=1	v=1	X
cana-3958	111	12	.	.	PUNCT
cana-3958	112	1	definition	definition	NOUN
cana-3958	112	2	2.5.(little	2.5.(little	NUM
cana-3958	112	3	wood	wood	NOUN
cana-3958	112	4	subordination	subordination	NOUN
cana-3958	112	5	theorem	theorem	VERB
cana-3958	112	6	[	[	X
cana-3958	112	7	8	8	NUM
cana-3958	112	8	]	]	PUNCT
cana-3958	112	9	)	)	PUNCT
cana-3958	112	10	considering	consider	VERB
cana-3958	112	11	that	that	SCONJ
cana-3958	112	12	f	f	PROPN
cana-3958	112	13	and	and	CCONJ
cana-3958	112	14	g	g	PROPN
cana-3958	112	15	in	in	ADP
cana-3958	112	16	𝕌	𝕌	PROPN
cana-3958	112	17	are	be	AUX
cana-3958	112	18	analytic	analytic	ADJ
cana-3958	112	19	and	and	CCONJ
cana-3958	112	20	that	that	SCONJ
cana-3958	112	21	f(ξ)≺g(ξ	f(ξ)≺g(ξ	PROPN
cana-3958	112	22	)	)	PUNCT
cana-3958	112	23	,	,	PUNCT
cana-3958	112	24	then	then	ADV
cana-3958	112	25	∫	∫	PROPN
cana-3958	113	1	|f(ξ)|μ2π	|f(ξ)|μ2π	PROPN
cana-3958	113	2	0	0	NUM
cana-3958	114	1	dθ	dθ	PROPN
cana-3958	114	2	≤	≤	PROPN
cana-3958	114	3	∫	∫	PROPN
cana-3958	114	4	|g(ξ)|μ	|g(ξ)|μ	PROPN
cana-3958	114	5	dθ	dθ	PROPN
cana-3958	114	6	,	,	PUNCT
cana-3958	114	7	μ	μ	PROPN
cana-3958	114	8	>	>	X
cana-3958	114	9	0	0	PROPN
cana-3958	114	10	,	,	PUNCT
cana-3958	114	11	2π	2π	PROPN
cana-3958	114	12	0	0	NUM
cana-3958	114	13	and	and	CCONJ
cana-3958	114	14	ξ	ξ	X
cana-3958	114	15	=	=	SYM
cana-3958	114	16	reiθ	reiθ	PROPN
cana-3958	114	17	,	,	PUNCT
cana-3958	114	18	0	0	PUNCT
cana-3958	114	19	<	<	X
cana-3958	114	20	r	r	X
cana-3958	114	21	<	<	X
cana-3958	114	22	1	1	NUM
cana-3958	114	23	.	.	PUNCT
cana-3958	114	24	theorem	theorem	ADJ
cana-3958	114	25	2.6(integral	2.6(integral	ADJ
cana-3958	114	26	means	mean	NOUN
cana-3958	114	27	of	of	ADP
cana-3958	114	28	inequalities	inequality	NOUN
cana-3958	114	29	)	)	PUNCT
cana-3958	114	30	if	if	SCONJ
cana-3958	114	31	f	f	PROPN
cana-3958	114	32	ϵ	ϵ	X
cana-3958	114	33	𝒫𝒬q	𝒫𝒬q	PROPN
cana-3958	114	34	,	,	PUNCT
cana-3958	114	35	δ	δ	PROPN
cana-3958	114	36	,	,	PUNCT
cana-3958	114	37	μ	μ	PROPN
cana-3958	114	38	n	n	CCONJ
cana-3958	114	39	,	,	PUNCT
cana-3958	114	40	r	r	NOUN
cana-3958	114	41	(	(	PUNCT
cana-3958	114	42	θ	θ	NOUN
cana-3958	114	43	)	)	PUNCT
cana-3958	114	44	and	and	CCONJ
cana-3958	114	45	suppose	suppose	VERB
cana-3958	114	46	that	that	SCONJ
cana-3958	114	47	g(ξ	g(ξ	PROPN
cana-3958	114	48	)	)	PUNCT
cana-3958	114	49	=	=	SYM
cana-3958	115	1	ξ	ξ	PROPN
cana-3958	116	1	+	+	CCONJ
cana-3958	116	2	(	(	PUNCT
cana-3958	116	3	1−θ)|b|εv	1−θ)|b|εv	NUM
cana-3958	116	4	ϕ	ϕ	X
cana-3958	116	5	v	v	NUM
cana-3958	116	6	cv	cv	PROPN
cana-3958	116	7	ξ	ξ	PROPN
cana-3958	116	8	v	v	PROPN
cana-3958	116	9	,	,	PUNCT
cana-3958	116	10	v	v	NOUN
cana-3958	116	11	=	=	SYM
cana-3958	116	12	2,3	2,3	NUM
cana-3958	116	13	,	,	PUNCT
cana-3958	116	14	.	.	PUNCT
cana-3958	116	15	.	.	PUNCT
cana-3958	116	16	.	.	PUNCT
cana-3958	117	1	,	,	PUNCT
cana-3958	117	2	|εv|	|εv|	NOUN
cana-3958	117	3	=	=	SYM
cana-3958	118	1	1	1	X
cana-3958	118	2	.	.	PUNCT
cana-3958	119	1	if	if	SCONJ
cana-3958	119	2	ω(ξ	ω(ξ	NOUN
cana-3958	119	3	)	)	PUNCT
cana-3958	119	4	is	be	AUX
cana-3958	119	5	real	real	ADJ
cana-3958	119	6	it	it	PRON
cana-3958	119	7	is	be	AUX
cana-3958	119	8	given	give	VERB
cana-3958	119	9	by	by	ADP
cana-3958	119	10	(	(	PUNCT
cana-3958	119	11	ω(ξ))v−1	ω(ξ))v−1	NUM
cana-3958	119	12	=	=	SYM
cana-3958	119	13	ϕ	ϕ	X
cana-3958	119	14	v	v	X
cana-3958	119	15	cv	cv	PROPN
cana-3958	119	16	(	(	PUNCT
cana-3958	119	17	1−θ)|b|εv	1−θ)|b|εv	NUM
cana-3958	119	18	∑	∑	ADV
cana-3958	119	19	avξ	avξ	ADP
cana-3958	119	20	v−1∞	v−1∞	PROPN
cana-3958	119	21	v=2	v=2	PROPN
cana-3958	119	22	.	.	PUNCT
cana-3958	120	1	then∫	then∫	NOUN
cana-3958	121	1	|f(ξ)|μ2π	|f(ξ)|μ2π	PROPN
cana-3958	121	2	0	0	NUM
cana-3958	122	1	dθ	dθ	PROPN
cana-3958	122	2	≤	≤	PROPN
cana-3958	122	3	∫	∫	PROPN
cana-3958	122	4	|g(ξ)|μ	|g(ξ)|μ	PROPN
cana-3958	122	5	dθ	dθ	PROPN
cana-3958	122	6	,	,	PUNCT
cana-3958	122	7	for	for	ADP
cana-3958	122	8	ξ	ξ	PROPN
cana-3958	122	9	=	=	SYM
cana-3958	122	10	reiθ	reiθ	PROPN
cana-3958	122	11	,	,	PUNCT
cana-3958	122	12	0	0	PUNCT
cana-3958	122	13	<	<	X
cana-3958	122	14	r	r	X
cana-3958	122	15	<	<	X
cana-3958	122	16	1	1	NUM
cana-3958	122	17	,	,	PUNCT
cana-3958	122	18	μ	μ	PROPN
cana-3958	122	19	>	>	X
cana-3958	122	20	0	0	PUNCT
cana-3958	122	21	2π	2π	NOUN
cana-3958	122	22	0	0	NUM
cana-3958	122	23	.	.	PUNCT
cana-3958	123	1	we	we	PRON
cana-3958	123	2	need	need	VERB
cana-3958	123	3	to	to	PART
cana-3958	123	4	demonstrate	demonstrate	VERB
cana-3958	123	5	that	that	SCONJ
cana-3958	123	6	to	to	PART
cana-3958	123	7	finish	finish	VERB
cana-3958	123	8	the	the	DET
cana-3958	123	9	theorem	theorem	ADJ
cana-3958	123	10	∫	∫	PROPN
cana-3958	123	11	|1	|1	X
cana-3958	124	1	+	+	CCONJ
cana-3958	124	2	∑	∑	PROPN
cana-3958	124	3	av	av	PROPN
cana-3958	124	4	∞	∞	NUM
cana-3958	124	5	v=2	v=2	PROPN
cana-3958	124	6	ξ	ξ	PROPN
cana-3958	124	7	v−1|	v−1|	PROPN
cana-3958	124	8	μ	μ	PROPN
cana-3958	124	9	dθ	dθ	PROPN
cana-3958	124	10	≤	≤	ADJ
cana-3958	124	11	2π	2π	PROPN
cana-3958	124	12	0	0	NUM
cana-3958	124	13	∫	∫	NUM
cana-3958	124	14	|1	|1	X
cana-3958	125	1	+	+	CCONJ
cana-3958	125	2	(	(	PUNCT
cana-3958	125	3	1	1	NUM
cana-3958	125	4	−	−	PROPN
cana-3958	125	5	θ)|b|	θ)|b|	PROPN
cana-3958	126	1	ϵv	ϵv	PRON
cana-3958	126	2	ϕ	ϕ	NOUN
cana-3958	126	3	v	v	NUM
cana-3958	126	4	cv	cv	PROPN
cana-3958	126	5	ξv−1|	ξv−1|	PROPN
cana-3958	126	6	μ	μ	PROPN
cana-3958	126	7	dθ	dθ	PROPN
cana-3958	126	8	.	.	PUNCT
cana-3958	127	1	2π	2π	PROPN
cana-3958	127	2	0	0	NUM
cana-3958	128	1	the	the	DET
cana-3958	128	2	littlewood	littlewood	PROPN
cana-3958	128	3	subordination	subordination	NOUN
cana-3958	128	4	theorem	theorem	NOUN
cana-3958	128	5	can	can	AUX
cana-3958	128	6	be	be	AUX
cana-3958	128	7	used	use	VERB
cana-3958	128	8	to	to	PART
cana-3958	128	9	demonstrate	demonstrate	VERB
cana-3958	128	10	that	that	SCONJ
cana-3958	128	11	1	1	NUM
cana-3958	129	1	+	+	CCONJ
cana-3958	129	2	∑	∑	ADV
cana-3958	129	3	avξ	avξ	ADP
cana-3958	129	4	v−1	v−1	PROPN
cana-3958	129	5	∞	∞	PROPN
cana-3958	129	6	v=2	v=2	PROPN
cana-3958	129	7	≺	≺	NOUN
cana-3958	129	8	1	1	NUM
cana-3958	129	9	+	+	CCONJ
cana-3958	129	10	(	(	PUNCT
cana-3958	129	11	1	1	NUM
cana-3958	129	12	+	+	CCONJ
cana-3958	129	13	θ)bϵv	θ)bϵv	PROPN
cana-3958	129	14	ϕ	ϕ	X
cana-3958	129	15	v	v	ADP
cana-3958	129	16	cv	cv	PROPN
cana-3958	129	17	ξ	ξ	PROPN
cana-3958	129	18	v−1	v−1	PROPN
cana-3958	129	19	.	.	PUNCT
cana-3958	130	1	let	let	VERB
cana-3958	130	2	1	1	NUM
cana-3958	131	1	+	+	CCONJ
cana-3958	131	2	∑	∑	ADV
cana-3958	131	3	avξ	avξ	ADP
cana-3958	131	4	v−1	v−1	PROPN
cana-3958	131	5	∞	∞	PROPN
cana-3958	131	6	v=2	v=2	PROPN
cana-3958	131	7	≺	≺	NOUN
cana-3958	131	8	1	1	NUM
cana-3958	131	9	+	+	CCONJ
cana-3958	131	10	(	(	PUNCT
cana-3958	131	11	1	1	NUM
cana-3958	131	12	+	+	X
cana-3958	131	13	θ)|b|ϵv	θ)|b|ϵv	NOUN
cana-3958	131	14	ϕ	ϕ	PROPN
cana-3958	131	15	v	v	X
cana-3958	131	16	cv	cv	PROPN
cana-3958	131	17	(	(	PUNCT
cana-3958	131	18	ω(ξ))v−1	ω(ξ))v−1	NUM
cana-3958	131	19	therefore	therefore	ADV
cana-3958	131	20	(	(	PUNCT
cana-3958	131	21	ω(ξ))v−1	ω(ξ))v−1	NUM
cana-3958	131	22	=	=	SYM
cana-3958	131	23	ϕ	ϕ	X
cana-3958	131	24	v	v	X
cana-3958	131	25	cv	cv	PROPN
cana-3958	131	26	(	(	PUNCT
cana-3958	131	27	1−θ)|b|ϵv	1−θ)|b|ϵv	NUM
cana-3958	131	28	∑	∑	ADV
cana-3958	131	29	avξ	avξ	ADP
cana-3958	131	30	v−1∞	v−1∞	PROPN
cana-3958	131	31	v=2	v=2	PROPN
cana-3958	131	32	communications	communication	NOUN
cana-3958	131	33	on	on	ADP
cana-3958	131	34	applied	apply	VERB
cana-3958	131	35	nonlinear	nonlinear	ADJ
cana-3958	131	36	analysis	analysis	NOUN
cana-3958	131	37	issn	issn	NOUN
cana-3958	131	38	:	:	PUNCT
cana-3958	131	39	1074	1074	NUM
cana-3958	131	40	-	-	PUNCT
cana-3958	131	41	133x	133x	NUM
cana-3958	131	42	vol	vol	NOUN
cana-3958	131	43	32	32	NUM
cana-3958	131	44	no	no	NOUN
cana-3958	131	45	.	.	PUNCT
cana-3958	132	1	9s	9s	NUM
cana-3958	132	2	(	(	PUNCT
cana-3958	132	3	2025	2025	NUM
cana-3958	132	4	)	)	PUNCT
cana-3958	132	5	471	471	NUM
cana-3958	132	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3958	132	7	hence	hence	ADV
cana-3958	132	8	ω(0)=0	ω(0)=0	NUM
cana-3958	132	9	.	.	PUNCT
cana-3958	133	1	furthermore	furthermore	ADV
cana-3958	133	2	,	,	PUNCT
cana-3958	133	3	if	if	SCONJ
cana-3958	133	4	fϵ𝒜	fϵ𝒜	PROPN
cana-3958	133	5	satisfy	satisfy	VERB
cana-3958	133	6	ϕ	ϕ	PROPN
cana-3958	133	7	v	v	ADP
cana-3958	133	8	cv	cv	PROPN
cana-3958	133	9	≤	≤	PROPN
cana-3958	133	10	(	(	PUNCT
cana-3958	133	11	1	1	NUM
cana-3958	133	12	−	−	PROPN
cana-3958	133	13	θ)|b|	θ)|b|	PROPN
cana-3958	133	14	.	.	PUNCT
cana-3958	134	1	|ω(ξ)|v−1	|ω(ξ)|v−1	NOUN
cana-3958	134	2	=	=	PUNCT
cana-3958	135	1	|	|	ADV
cana-3958	135	2	ϕ	ϕ	X
cana-3958	135	3	v	v	X
cana-3958	135	4	cv	cv	PROPN
cana-3958	135	5	(	(	PUNCT
cana-3958	135	6	1	1	NUM
cana-3958	135	7	−	−	PROPN
cana-3958	135	8	θ)|b|ϵv	θ)|b|ϵv	NUM
cana-3958	135	9	|	|	ADV
cana-3958	135	10	∑|av|	∑|av|	PROPN
cana-3958	135	11	∞	∞	PROPN
cana-3958	135	12	v=2	v=2	X
cana-3958	135	13	|ξv−1|	|ξv−1|	PROPN
cana-3958	135	14	≤	≤	NOUN
cana-3958	135	15	|ξ|	|ξ|	PROPN
cana-3958	135	16	<	<	X
cana-3958	135	17	1	1	NUM
cana-3958	135	18	.	.	PUNCT
cana-3958	135	19	theorem	theorem	VERB
cana-3958	135	20	2.7(convex	2.7(convex	NUM
cana-3958	135	21	of	of	ADP
cana-3958	135	22	order	order	NOUN
cana-3958	135	23	𝛉	𝛉	X
cana-3958	135	24	)	)	PUNCT
cana-3958	135	25	let	let	VERB
cana-3958	135	26	f	f	PROPN
cana-3958	135	27	ϵ	ϵ	X
cana-3958	135	28	𝒫𝒬q	𝒫𝒬q	PROPN
cana-3958	135	29	,	,	PUNCT
cana-3958	135	30	δ	δ	PROPN
cana-3958	135	31	,	,	PUNCT
cana-3958	135	32	μ	μ	PROPN
cana-3958	135	33	n	n	CCONJ
cana-3958	135	34	,	,	PUNCT
cana-3958	135	35	r	r	NOUN
cana-3958	135	36	(	(	PUNCT
cana-3958	135	37	θ	θ	NOUN
cana-3958	135	38	)	)	PUNCT
cana-3958	135	39	.	.	PUNCT
cana-3958	136	1	then	then	ADV
cana-3958	136	2	𝑓	𝑓	PRON
cana-3958	136	3	is	be	AUX
cana-3958	136	4	convex	convex	NOUN
cana-3958	136	5	of	of	ADP
cana-3958	136	6	order	order	NOUN
cana-3958	136	7	θ	θ	PROPN
cana-3958	136	8	in	in	ADP
cana-3958	136	9	|ξ|	|ξ|	PROPN
cana-3958	136	10	<	<	X
cana-3958	136	11	r3	r3	PROPN
cana-3958	136	12	,	,	PUNCT
cana-3958	136	13	wℎere	wℎere	ADP
cana-3958	136	14	r3	r3	NOUN
cana-3958	136	15	:	:	PUNCT
cana-3958	136	16	=	=	SYM
cana-3958	136	17	inf	inf	PROPN
cana-3958	136	18	(	(	PUNCT
cana-3958	136	19	(	(	PUNCT
cana-3958	136	20	1−θ)ϕ	1−θ)ϕ	PROPN
cana-3958	136	21	v	v	NOUN
cana-3958	136	22	cv	cv	PROPN
cana-3958	136	23	v(v−θ)(1−θ)|b|	v(v−θ)(1−θ)|b|	X
cana-3958	136	24	)	)	PUNCT
cana-3958	136	25	1	1	NUM
cana-3958	136	26	v−1	v−1	PROPN
cana-3958	136	27	,	,	PUNCT
cana-3958	136	28	(	(	PUNCT
cana-3958	136	29	v	v	NOUN
cana-3958	136	30	≥2	≥2	NOUN
cana-3958	136	31	)	)	PUNCT
cana-3958	136	32	(	(	PUNCT
cana-3958	136	33	12	12	X
cana-3958	136	34	)	)	PUNCT
cana-3958	136	35	proof	proof	NOUN
cana-3958	136	36	:	:	PUNCT
cana-3958	136	37	if	if	SCONJ
cana-3958	136	38	|ξ|	|ξ|	PROPN
cana-3958	136	39	<	<	X
cana-3958	136	40	r3	r3	PROPN
cana-3958	136	41	and	and	CCONJ
cana-3958	136	42	the	the	DET
cana-3958	136	43	inequality	inequality	NOUN
cana-3958	136	44	(	(	PUNCT
cana-3958	136	45	12	12	NUM
cana-3958	136	46	)	)	PUNCT
cana-3958	136	47	are	be	AUX
cana-3958	136	48	valid	valid	ADJ
cana-3958	136	49	,	,	PUNCT
cana-3958	136	50	it	it	PRON
cana-3958	136	51	is	be	AUX
cana-3958	136	52	demonstrated	demonstrate	VERB
cana-3958	136	53	that	that	SCONJ
cana-3958	136	54	|	|	ADV
cana-3958	136	55	ξf"(ξ	ξf"(ξ	NOUN
cana-3958	136	56	)	)	PUNCT
cana-3958	136	57	f′(ξ	f′(ξ	PROPN
cana-3958	136	58	)	)	PUNCT
cana-3958	136	59	|	|	ADV
cana-3958	136	60	≤	≤	NUM
cana-3958	136	61	1	1	NUM
cana-3958	136	62	−	−	PROPN
cana-3958	136	63	θ	θ	PROPN
cana-3958	136	64	.	.	PUNCT
cana-3958	137	1	(	(	PUNCT
cana-3958	137	2	13	13	NUM
cana-3958	137	3	)	)	PUNCT
cana-3958	137	4	it	it	PRON
cana-3958	137	5	is	be	AUX
cana-3958	137	6	adequate	adequate	ADJ
cana-3958	137	7	to	to	PART
cana-3958	137	8	show	show	VERB
cana-3958	137	9	that	that	SCONJ
cana-3958	137	10	|ξ|	|ξ|	PROPN
cana-3958	137	11	≤	≤	X
cana-3958	137	12	(	(	PUNCT
cana-3958	137	13	(	(	PUNCT
cana-3958	137	14	1	1	NUM
cana-3958	137	15	−	−	NOUN
cana-3958	137	16	θ)ϕ	θ)ϕ	NOUN
cana-3958	137	17	v	v	X
cana-3958	137	18	cv	cv	PROPN
cana-3958	137	19	v(v	v(v	PROPN
cana-3958	137	20	−	−	PROPN
cana-3958	137	21	θ)(1	θ)(1	ADP
cana-3958	138	1	−	−	PROPN
cana-3958	138	2	θ)|b|	θ)|b|	PROPN
cana-3958	138	3	)	)	PUNCT
cana-3958	138	4	1	1	NUM
cana-3958	138	5	v−1	v−1	PROPN
cana-3958	138	6	,	,	PUNCT
cana-3958	138	7	(	(	PUNCT
cana-3958	138	8	v	v	PRON
cana-3958	138	9	≥	≥	NOUN
cana-3958	138	10	2	2	NUM
cana-3958	138	11	)	)	PUNCT
cana-3958	138	12	.	.	PUNCT
cana-3958	139	1	from	from	ADP
cana-3958	139	2	(	(	PUNCT
cana-3958	139	3	13	13	NUM
cana-3958	139	4	)	)	PUNCT
cana-3958	139	5	,	,	PUNCT
cana-3958	139	6	we	we	PRON
cana-3958	139	7	obtain	obtain	VERB
cana-3958	139	8	|	|	ADV
cana-3958	139	9	∑	∑	PROPN
cana-3958	139	10	v(v	v(v	PROPN
cana-3958	139	11	−	−	PROPN
cana-3958	140	1	1)avξ	1)avξ	NUM
cana-3958	140	2	v−1∞	v−1∞	PROPN
cana-3958	140	3	v=2	v=2	PROPN
cana-3958	140	4	1	1	NUM
cana-3958	140	5	+	+	NOUN
cana-3958	140	6	∑	∑	PROPN
cana-3958	140	7	vavξ	vavξ	PROPN
cana-3958	140	8	v−1∞	v−1∞	PROPN
cana-3958	140	9	v=2	v=2	PROPN
cana-3958	140	10	|	|	ADV
cana-3958	140	11	≤	≤	NUM
cana-3958	140	12	1	1	NUM
cana-3958	140	13	−	−	NUM
cana-3958	140	14	θ	θ	X
cana-3958	140	15	.	.	PUNCT
cana-3958	141	1	∑(v(v	∑(v(v	VERB
cana-3958	141	2	−	−	NOUN
cana-3958	142	1	1)avξ	1)avξ	NUM
cana-3958	142	2	v−1	v−1	PROPN
cana-3958	142	3	∞	∞	NUM
cana-3958	143	1	v=2	v=2	PROPN
cana-3958	143	2	≤	≤	ADV
cana-3958	143	3	1	1	NUM
cana-3958	143	4	+	+	NUM
cana-3958	143	5	∑	∑	NOUN
cana-3958	143	6	vavξ	vavξ	NOUN
cana-3958	143	7	v−1	v−1	PROPN
cana-3958	143	8	∞	∞	PROPN
cana-3958	143	9	v=2	v=2	PROPN
cana-3958	143	10	−	−	NUM
cana-3958	143	11	θ	θ	NOUN
cana-3958	143	12	−	−	PROPN
cana-3958	143	13	θ	θ	X
cana-3958	143	14	∑	∑	PUNCT
cana-3958	143	15	vav|ξ|v−1	vav|ξ|v−1	NUM
cana-3958	143	16	∞	∞	NUM
cana-3958	143	17	v=2	v=2	PROPN
cana-3958	143	18	∑	∑	PUNCT
cana-3958	143	19	(	(	PUNCT
cana-3958	143	20	v2	v2	VERB
cana-3958	143	21	−	−	PROPN
cana-3958	143	22	θv)av|ξ|v−1	θv)av|ξ|v−1	PROPN
cana-3958	143	23	≤	≤	NUM
cana-3958	143	24	(	(	PUNCT
cana-3958	143	25	1	1	NUM
cana-3958	143	26	−	−	NOUN
cana-3958	143	27	θ)∞	θ)∞	NOUN
cana-3958	143	28	v=2	v=2	PROPN
cana-3958	143	29	.	.	PUNCT
cana-3958	144	1	|ξ|	|ξ|	PROPN
cana-3958	144	2	≤	≤	NOUN
cana-3958	144	3	(	(	PUNCT
cana-3958	144	4	1−θ	1−θ	X
cana-3958	144	5	(	(	PUNCT
cana-3958	144	6	v2−θv)av	v2−θv)av	PROPN
cana-3958	144	7	)	)	PUNCT
cana-3958	144	8	1	1	NUM
cana-3958	145	1	v−1	v−1	PROPN
cana-3958	145	2	,	,	PUNCT
cana-3958	145	3	(	(	PUNCT
cana-3958	145	4	v	v	X
cana-3958	145	5	≥	≥	NOUN
cana-3958	145	6	2	2	NUM
cana-3958	145	7	)	)	PUNCT
cana-3958	145	8	.	.	PUNCT
cana-3958	146	1	|ξ|	|ξ|	PROPN
cana-3958	146	2	≤	≤	NOUN
cana-3958	146	3	(	(	PUNCT
cana-3958	146	4	(	(	PUNCT
cana-3958	146	5	1−θ)ϕ	1−θ)ϕ	PROPN
cana-3958	146	6	v	v	NOUN
cana-3958	146	7	cv	cv	PROPN
cana-3958	146	8	v(v−θ)(1−θ)|b|	v(v−θ)(1−θ)|b|	X
cana-3958	146	9	)	)	PUNCT
cana-3958	146	10	1	1	NUM
cana-3958	146	11	v−1	v−1	PROPN
cana-3958	146	12	.	.	PUNCT
cana-3958	147	1	theorem	theorem	VERB
cana-3958	147	2	2.8	2.8	NUM
cana-3958	147	3	(	(	PUNCT
cana-3958	147	4	starlike	starlike	NOUN
cana-3958	147	5	of	of	ADP
cana-3958	147	6	order	order	NOUN
cana-3958	147	7	𝛉	𝛉	NOUN
cana-3958	147	8	)	)	PUNCT
cana-3958	147	9	let	let	VERB
cana-3958	147	10	f	f	PROPN
cana-3958	147	11	ϵ	ϵ	X
cana-3958	147	12	𝒫	𝒫	PROPN
cana-3958	147	13	𝒬q	𝒬q	PROPN
cana-3958	147	14	,	,	PUNCT
cana-3958	147	15	δ	δ	PROPN
cana-3958	147	16	,	,	PUNCT
cana-3958	147	17	μ	μ	PROPN
cana-3958	147	18	n	n	CCONJ
cana-3958	147	19	,	,	PUNCT
cana-3958	147	20	r	r	NOUN
cana-3958	147	21	(	(	PUNCT
cana-3958	147	22	θ	θ	NOUN
cana-3958	147	23	)	)	PUNCT
cana-3958	147	24	.	.	PUNCT
cana-3958	148	1	then	then	ADV
cana-3958	148	2	f	f	PROPN
cana-3958	148	3	is	be	AUX
cana-3958	148	4	starlike	starlike	NOUN
cana-3958	148	5	of	of	ADP
cana-3958	148	6	order	order	NOUN
cana-3958	148	7	θ	θ	PROPN
cana-3958	148	8	in	in	ADP
cana-3958	148	9	|ξ|	|ξ|	PROPN
cana-3958	148	10	<	<	X
cana-3958	148	11	r2	r2	PROPN
cana-3958	148	12	,	,	PUNCT
cana-3958	148	13	where	where	SCONJ
cana-3958	148	14	r2	r2	PROPN
cana-3958	148	15	:	:	PUNCT
cana-3958	148	16	=	=	SYM
cana-3958	148	17	inf	inf	PROPN
cana-3958	148	18	(	(	PUNCT
cana-3958	148	19	(	(	PUNCT
cana-3958	148	20	1−θ)ϕ	1−θ)ϕ	PROPN
cana-3958	148	21	v	v	NUM
cana-3958	148	22	cv	cv	PROPN
cana-3958	148	23	(	(	PUNCT
cana-3958	148	24	v−θ)(1−θ)|b|	v−θ)(1−θ)|b|	PROPN
cana-3958	148	25	)	)	PUNCT
cana-3958	148	26	1	1	NUM
cana-3958	149	1	v−1	v−1	PROPN
cana-3958	149	2	,	,	PUNCT
cana-3958	149	3	(	(	PUNCT
cana-3958	149	4	v	v	X
cana-3958	149	5	≥	≥	NOUN
cana-3958	149	6	2	2	NUM
cana-3958	149	7	)	)	PUNCT
cana-3958	149	8	(	(	PUNCT
cana-3958	149	9	14	14	X
cana-3958	149	10	)	)	PUNCT
cana-3958	149	11	proof	proof	NOUN
cana-3958	149	12	:	:	PUNCT
cana-3958	149	13	if	if	SCONJ
cana-3958	149	14	|ξ|<r2	|ξ|<r2	PROPN
cana-3958	149	15	and	and	CCONJ
cana-3958	149	16	the	the	DET
cana-3958	149	17	inequality	inequality	NOUN
cana-3958	149	18	(	(	PUNCT
cana-3958	149	19	14	14	NUM
cana-3958	149	20	)	)	PUNCT
cana-3958	149	21	are	be	AUX
cana-3958	149	22	valid	valid	ADJ
cana-3958	149	23	it	it	PRON
cana-3958	149	24	is	be	AUX
cana-3958	149	25	demonstrated	demonstrate	VERB
cana-3958	149	26	that	that	SCONJ
cana-3958	149	27	|	|	ADV
cana-3958	149	28	ξf′(ξ	ξf′(ξ	PROPN
cana-3958	149	29	)	)	PUNCT
cana-3958	149	30	f(ξ	f(ξ	NOUN
cana-3958	149	31	)	)	PUNCT
cana-3958	150	1	−	−	ADP
cana-3958	150	2	1|	1|	NUM
cana-3958	151	1	≤	≤	NUM
cana-3958	151	2	1	1	NUM
cana-3958	151	3	−	−	PROPN
cana-3958	151	4	θ	θ	PROPN
cana-3958	151	5	(	(	PUNCT
cana-3958	151	6	15	15	NUM
cana-3958	151	7	)	)	PUNCT
cana-3958	151	8	it	it	PRON
cana-3958	151	9	is	be	AUX
cana-3958	151	10	adequate	adequate	ADJ
cana-3958	151	11	to	to	PART
cana-3958	151	12	show	show	VERB
cana-3958	151	13	that	that	SCONJ
cana-3958	151	14	communications	communication	NOUN
cana-3958	151	15	on	on	ADP
cana-3958	151	16	applied	apply	VERB
cana-3958	151	17	nonlinear	nonlinear	ADJ
cana-3958	151	18	analysis	analysis	NOUN
cana-3958	151	19	issn	issn	NOUN
cana-3958	151	20	:	:	PUNCT
cana-3958	151	21	1074	1074	NUM
cana-3958	151	22	-	-	PUNCT
cana-3958	151	23	133x	133x	NUM
cana-3958	151	24	vol	vol	NOUN
cana-3958	151	25	32	32	NUM
cana-3958	151	26	no	no	NOUN
cana-3958	151	27	.	.	PUNCT
cana-3958	152	1	9s	9s	NUM
cana-3958	152	2	(	(	PUNCT
cana-3958	152	3	2025	2025	NUM
cana-3958	152	4	)	)	PUNCT
cana-3958	152	5	472	472	NUM
cana-3958	153	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3958	153	2	|ξ|	|ξ|	PROPN
cana-3958	153	3	≤	≤	X
cana-3958	153	4	(	(	PUNCT
cana-3958	153	5	(	(	PUNCT
cana-3958	153	6	1−θ)ϕ	1−θ)ϕ	PROPN
cana-3958	153	7	v	v	NUM
cana-3958	153	8	cv	cv	PROPN
cana-3958	153	9	(	(	PUNCT
cana-3958	153	10	v−θ)(1−θ)|b|	v−θ)(1−θ)|b|	PROPN
cana-3958	153	11	)	)	PUNCT
cana-3958	153	12	1	1	NUM
cana-3958	154	1	v−1	v−1	PROPN
cana-3958	154	2	,	,	PUNCT
cana-3958	154	3	(	(	PUNCT
cana-3958	154	4	v	v	NOUN
cana-3958	154	5	≥2	≥2	NOUN
cana-3958	154	6	)	)	PUNCT
cana-3958	154	7	from	from	ADP
cana-3958	154	8	(	(	PUNCT
cana-3958	154	9	15	15	NUM
cana-3958	154	10	)	)	PUNCT
cana-3958	154	11	,	,	PUNCT
cana-3958	154	12	we	we	PRON
cana-3958	154	13	obtain	obtain	VERB
cana-3958	154	14	|	|	ADV
cana-3958	154	15	ξ	ξ	X
cana-3958	155	1	+	+	NUM
cana-3958	155	2	∑	∑	PROPN
cana-3958	155	3	vav	vav	PROPN
cana-3958	155	4	ξ	ξ	X
cana-3958	155	5	v∞	v∞	X
cana-3958	155	6	v=2	v=2	PROPN
cana-3958	155	7	ξ	ξ	PROPN
cana-3958	155	8	+	+	PROPN
cana-3958	155	9	∑	∑	PROPN
cana-3958	155	10	av	av	PROPN
cana-3958	155	11	∞	∞	NUM
cana-3958	155	12	v=2	v=2	PROPN
cana-3958	155	13	ξ	ξ	PRON
cana-3958	155	14	v	v	ADP
cana-3958	155	15	−	−	PROPN
cana-3958	155	16	1|	1|	NUM
cana-3958	155	17	≤	≤	NUM
cana-3958	155	18	1	1	NUM
cana-3958	155	19	−	−	NOUN
cana-3958	155	20	θ	θ	PROPN
cana-3958	156	1	∑(1	∑(1	NOUN
cana-3958	156	2	−	−	PROPN
cana-3958	157	1	v)av|ξ|v−1	v)av|ξ|v−1	PRON
cana-3958	157	2	∞	∞	PROPN
cana-3958	157	3	v=2	v=2	PROPN
cana-3958	157	4	≤	≤	NUM
cana-3958	157	5	(	(	PUNCT
cana-3958	157	6	θ	θ	NOUN
cana-3958	157	7	−	−	PROPN
cana-3958	157	8	1)(1	1)(1	NUM
cana-3958	157	9	+	+	CCONJ
cana-3958	157	10	∑	∑	PUNCT
cana-3958	157	11	av|ξ|v−1	av|ξ|v−1	NUM
cana-3958	157	12	∞	∞	NUM
cana-3958	157	13	v=2	v=2	PROPN
cana-3958	157	14	)	)	PUNCT
cana-3958	157	15	∑	∑	PUNCT
cana-3958	157	16	(	(	PUNCT
cana-3958	157	17	θ	θ	PROPN
cana-3958	157	18	−	−	PROPN
cana-3958	157	19	v)av|ξ|v−1∞	v)av|ξ|v−1∞	NUM
cana-3958	157	20	v=2	v=2	SYM
cana-3958	157	21	≤	≤	NUM
cana-3958	157	22	(	(	PUNCT
cana-3958	157	23	θ	θ	X
cana-3958	157	24	−	−	PROPN
cana-3958	157	25	1)ξ	1)ξ	NUM
cana-3958	157	26	.	.	PUNCT
cana-3958	158	1	|ξ|	|ξ|	PROPN
cana-3958	158	2	≤	≤	NOUN
cana-3958	158	3	(	(	PUNCT
cana-3958	158	4	(	(	PUNCT
cana-3958	158	5	1−θ)ϕ	1−θ)ϕ	PROPN
cana-3958	158	6	v	v	NUM
cana-3958	158	7	cv	cv	PROPN
cana-3958	158	8	(	(	PUNCT
cana-3958	158	9	v−θ)(1−θ)|b|	v−θ)(1−θ)|b|	PROPN
cana-3958	158	10	)	)	PUNCT
cana-3958	158	11	1	1	NUM
cana-3958	159	1	v−1	v−1	PROPN
cana-3958	159	2	,	,	PUNCT
cana-3958	159	3	(	(	PUNCT
cana-3958	159	4	v	v	X
cana-3958	159	5	≥	≥	NOUN
cana-3958	159	6	2	2	NUM
cana-3958	159	7	)	)	PUNCT
cana-3958	159	8	.	.	PUNCT
cana-3958	160	1	theorem	theorem	VERB
cana-3958	160	2	2.9(close	2.9(close	NUM
cana-3958	160	3	-	-	PUNCT
cana-3958	160	4	to	to	PART
cana-3958	160	5	convex	convex	NOUN
cana-3958	160	6	of	of	ADP
cana-3958	160	7	order	order	NOUN
cana-3958	160	8	𝛉	𝛉	NOUN
cana-3958	160	9	)	)	PUNCT
cana-3958	160	10	let	let	VERB
cana-3958	160	11	fϵ	fϵ	ADP
cana-3958	160	12	𝒫𝒬q	𝒫𝒬q	NOUN
cana-3958	160	13	,	,	PUNCT
cana-3958	160	14	δ	δ	PROPN
cana-3958	160	15	,	,	PUNCT
cana-3958	160	16	μ	μ	PROPN
cana-3958	160	17	n	n	CCONJ
cana-3958	160	18	,	,	PUNCT
cana-3958	160	19	r	r	NOUN
cana-3958	160	20	(	(	PUNCT
cana-3958	160	21	θ	θ	NOUN
cana-3958	160	22	)	)	PUNCT
cana-3958	160	23	,	,	PUNCT
cana-3958	160	24	then	then	ADV
cana-3958	160	25	f	f	PROPN
cana-3958	160	26	is	be	AUX
cana-3958	160	27	close	close	ADJ
cana-3958	160	28	-	-	PUNCT
cana-3958	160	29	to	to	ADP
cana-3958	160	30	-	-	PUNCT
cana-3958	160	31	convex	convex	NOUN
cana-3958	160	32	of	of	ADP
cana-3958	160	33	order	order	NOUN
cana-3958	160	34	θ	θ	X
cana-3958	160	35	(	(	PUNCT
cana-3958	160	36	0	0	NUM
cana-3958	160	37	≤	≤	NUM
cana-3958	160	38	θ	θ	X
cana-3958	160	39	<	<	X
cana-3958	160	40	1	1	NUM
cana-3958	160	41	)	)	PUNCT
cana-3958	160	42	in	in	ADP
cana-3958	160	43	the	the	DET
cana-3958	160	44	disc	disc	NOUN
cana-3958	160	45	|ξ|	|ξ|	PROPN
cana-3958	160	46	<	<	X
cana-3958	160	47	r3	r3	PROPN
cana-3958	160	48	,	,	PUNCT
cana-3958	160	49	were	be	AUX
cana-3958	160	50	r3	r3	NOUN
cana-3958	160	51	:	:	PUNCT
cana-3958	160	52	=	=	SYM
cana-3958	160	53	inf	inf	PROPN
cana-3958	160	54	(	(	PUNCT
cana-3958	160	55	(	(	PUNCT
cana-3958	160	56	1−θ)ϕ	1−θ)ϕ	PROPN
cana-3958	160	57	v	v	NUM
cana-3958	160	58	cv	cv	PROPN
cana-3958	160	59	(	(	PUNCT
cana-3958	160	60	v(1−θ)|b|	v(1−θ)|b|	PROPN
cana-3958	160	61	)	)	PUNCT
cana-3958	160	62	1	1	NUM
cana-3958	161	1	v−1	v−1	PROPN
cana-3958	161	2	,	,	PUNCT
cana-3958	161	3	(	(	PUNCT
cana-3958	161	4	v	v	X
cana-3958	161	5	≥	≥	NOUN
cana-3958	161	6	2	2	NUM
cana-3958	161	7	)	)	PUNCT
cana-3958	161	8	(	(	PUNCT
cana-3958	161	9	16	16	X
cana-3958	161	10	)	)	PUNCT
cana-3958	161	11	proof	proof	NOUN
cana-3958	161	12	:	:	PUNCT
cana-3958	161	13	if	if	SCONJ
cana-3958	161	14	|ξ|	|ξ|	PROPN
cana-3958	161	15	<	<	X
cana-3958	161	16	r3	r3	PROPN
cana-3958	161	17	and	and	CCONJ
cana-3958	161	18	the	the	DET
cana-3958	161	19	inequality	inequality	NOUN
cana-3958	161	20	(	(	PUNCT
cana-3958	161	21	16	16	NUM
cana-3958	161	22	)	)	PUNCT
cana-3958	161	23	are	be	AUX
cana-3958	161	24	valid	valid	ADJ
cana-3958	161	25	,	,	PUNCT
cana-3958	161	26	it	it	PRON
cana-3958	161	27	is	be	AUX
cana-3958	161	28	demonstrated	demonstrate	VERB
cana-3958	161	29	that	that	SCONJ
cana-3958	161	30	|f′(ξ	|f′(ξ	NOUN
cana-3958	161	31	)	)	PUNCT
cana-3958	161	32	−	−	PROPN
cana-3958	162	1	1|	1|	NUM
cana-3958	162	2	<	<	X
cana-3958	162	3	1	1	NUM
cana-3958	162	4	−	−	PROPN
cana-3958	162	5	θ	θ	PROPN
cana-3958	162	6	.	.	PUNCT
cana-3958	163	1	(	(	PUNCT
cana-3958	163	2	17	17	NUM
cana-3958	163	3	)	)	PUNCT
cana-3958	163	4	it	it	PRON
cana-3958	163	5	is	be	AUX
cana-3958	163	6	adequate	adequate	ADJ
cana-3958	163	7	to	to	PART
cana-3958	163	8	show	show	VERB
cana-3958	163	9	that	that	SCONJ
cana-3958	163	10	|ξ|	|ξ|	PROPN
cana-3958	163	11	≤	≤	X
cana-3958	163	12	(	(	PUNCT
cana-3958	163	13	(	(	PUNCT
cana-3958	163	14	1−θ)ϕ	1−θ)ϕ	PROPN
cana-3958	163	15	v	v	NUM
cana-3958	163	16	cv	cv	PROPN
cana-3958	163	17	(	(	PUNCT
cana-3958	163	18	v)(1−θ)|b|	v)(1−θ)|b|	PROPN
cana-3958	163	19	)	)	PUNCT
cana-3958	163	20	1	1	NUM
cana-3958	164	1	v−1	v−1	PROPN
cana-3958	164	2	,	,	PUNCT
cana-3958	164	3	(	(	PUNCT
cana-3958	164	4	v	v	NOUN
cana-3958	164	5	≥2	≥2	NOUN
cana-3958	164	6	)	)	PUNCT
cana-3958	164	7	from	from	ADP
cana-3958	164	8	(	(	PUNCT
cana-3958	164	9	17	17	NUM
cana-3958	164	10	)	)	PUNCT
cana-3958	164	11	,	,	PUNCT
cana-3958	164	12	we	we	PRON
cana-3958	164	13	obtain	obtain	VERB
cana-3958	164	14	|1	|1	PRON
cana-3958	165	1	+	+	NOUN
cana-3958	165	2	∑	∑	NOUN
cana-3958	165	3	vavξ	vavξ	NOUN
cana-3958	165	4	v−1	v−1	PROPN
cana-3958	165	5	−	−	NUM
cana-3958	165	6	1	1	NUM
cana-3958	165	7	∞	∞	PROPN
cana-3958	165	8	v=2	v=2	PROPN
cana-3958	166	1	|	|	ADV
cana-3958	166	2	<	<	X
cana-3958	166	3	1	1	NUM
cana-3958	166	4	−	−	PROPN
cana-3958	166	5	θ	θ	X
cana-3958	166	6	∑	∑	PUNCT
cana-3958	166	7	vav|ξ|v−1	vav|ξ|v−1	NUM
cana-3958	166	8	∞	∞	PROPN
cana-3958	166	9	v=2	v=2	X
cana-3958	166	10	<	<	X
cana-3958	166	11	1	1	NUM
cana-3958	166	12	−	−	NUM
cana-3958	166	13	θ	θ	NOUN
cana-3958	166	14	|ξ|v−1	|ξ|v−1	X
cana-3958	166	15	<	<	X
cana-3958	166	16	1	1	NUM
cana-3958	166	17	−	−	NUM
cana-3958	166	18	θ	θ	PROPN
cana-3958	166	19	vav	vav	PROPN
cana-3958	166	20	|ξ|	|ξ|	PROPN
cana-3958	166	21	≤	≤	NUM
cana-3958	166	22	(	(	PUNCT
cana-3958	166	23	(	(	PUNCT
cana-3958	166	24	1−θ)ϕ	1−θ)ϕ	PROPN
cana-3958	166	25	v	v	NUM
cana-3958	166	26	cv	cv	PROPN
cana-3958	166	27	(	(	PUNCT
cana-3958	166	28	v)(1−θ)|b|	v)(1−θ)|b|	PROPN
cana-3958	166	29	)	)	PUNCT
cana-3958	166	30	1	1	NUM
cana-3958	167	1	v−1	v−1	PROPN
cana-3958	167	2	,	,	PUNCT
cana-3958	167	3	(	(	PUNCT
cana-3958	167	4	v	v	ADP
cana-3958	167	5	≥2	≥2	NUM
cana-3958	167	6	)	)	PUNCT
cana-3958	167	7	.	.	PUNCT
cana-3958	168	1	communications	communication	NOUN
cana-3958	168	2	on	on	ADP
cana-3958	168	3	applied	apply	VERB
cana-3958	168	4	nonlinear	nonlinear	ADJ
cana-3958	168	5	analysis	analysis	NOUN
cana-3958	168	6	issn	issn	NOUN
cana-3958	168	7	:	:	PUNCT
cana-3958	168	8	1074	1074	NUM
cana-3958	168	9	-	-	PUNCT
cana-3958	168	10	133x	133x	NUM
cana-3958	168	11	vol	vol	NOUN
cana-3958	168	12	32	32	NUM
cana-3958	168	13	no	no	NOUN
cana-3958	168	14	.	.	PUNCT
cana-3958	169	1	9s	9s	NUM
cana-3958	169	2	(	(	PUNCT
cana-3958	169	3	2025	2025	NUM
cana-3958	169	4	)	)	PUNCT
cana-3958	169	5	473	473	NUM
cana-3958	169	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3958	169	7	theorem	theorem	VERB
cana-3958	169	8	2.10	2.10	NUM
cana-3958	169	9	(	(	PUNCT
cana-3958	169	10	growth	growth	NOUN
cana-3958	169	11	theorem	theorem	VERB
cana-3958	169	12	)	)	PUNCT
cana-3958	169	13	let	let	VERB
cana-3958	169	14	f(ξ	f(ξ	NOUN
cana-3958	170	1	=	=	SYM
cana-3958	170	2	ξ	ξ	PROPN
cana-3958	170	3	+	+	PROPN
cana-3958	170	4	∑	∑	PROPN
cana-3958	170	5	|av|ξv	|av|ξv	NUM
cana-3958	170	6	∞	∞	NUM
cana-3958	170	7	v=2	v=2	PROPN
cana-3958	170	8	belongs	belong	VERB
cana-3958	170	9	to	to	ADP
cana-3958	170	10	class	class	NOUN
cana-3958	170	11	f	f	PROPN
cana-3958	170	12	ϵ	ϵ	X
cana-3958	170	13	𝒫𝒬q	𝒫𝒬q	PROPN
cana-3958	170	14	,	,	PUNCT
cana-3958	170	15	δ	δ	PROPN
cana-3958	170	16	,	,	PUNCT
cana-3958	170	17	μ	μ	PROPN
cana-3958	170	18	n	n	CCONJ
cana-3958	170	19	,	,	PUNCT
cana-3958	170	20	r	r	NOUN
cana-3958	170	21	(	(	PUNCT
cana-3958	170	22	θ	θ	NOUN
cana-3958	170	23	)	)	PUNCT
cana-3958	170	24	.	.	PUNCT
cana-3958	171	1	then	then	ADV
cana-3958	171	2	for|ξ|	for|ξ|	PROPN
cana-3958	171	3	=	=	SYM
cana-3958	171	4	r∗	r∗	PROPN
cana-3958	171	5	,	,	PUNCT
cana-3958	171	6	we	we	PRON
cana-3958	171	7	ℎave	ℎave	VERB
cana-3958	171	8	r∗	r∗	PROPN
cana-3958	171	9	−	−	PROPN
cana-3958	172	1	(	(	PUNCT
cana-3958	172	2	1−θ)|b|	1−θ)|b|	NUM
cana-3958	172	3	|(θb−b−1)|c2	|(θb−b−1)|c2	NOUN
cana-3958	172	4	r∗2	r∗2	ADJ
cana-3958	172	5	≤	≤	PUNCT
cana-3958	172	6	|f(ξ)|	|f(ξ)|	NOUN
cana-3958	172	7	≤	≤	NUM
cana-3958	172	8	r∗	r∗	NOUN
cana-3958	173	1	+	+	CCONJ
cana-3958	173	2	(	(	PUNCT
cana-3958	173	3	1+θ)|b|	1+θ)|b|	NUM
cana-3958	173	4	|(θb−b−1)|c2	|(θb−b−1)|c2	ADV
cana-3958	173	5	r∗2	r∗2	ADJ
cana-3958	173	6	,	,	PUNCT
cana-3958	173	7	(	(	PUNCT
cana-3958	173	8	18	18	NUM
cana-3958	173	9	)	)	PUNCT
cana-3958	173	10	where	where	SCONJ
cana-3958	173	11	c2	c2	PROPN
cana-3958	173	12	=	=	SYM
cana-3958	173	13	(	(	PUNCT
cana-3958	173	14	1	1	NUM
cana-3958	173	15	+	+	CCONJ
cana-3958	173	16	(	(	PUNCT
cana-3958	173	17	δ	δ	PROPN
cana-3958	173	18	−	−	PROPN
cana-3958	173	19	μ	μ	PROPN
cana-3958	173	20	+	+	PROPN
cana-3958	174	1	2δμ))nrq(1	2δμ))nrq(1	ADJ
cana-3958	174	2	−	−	NOUN
cana-3958	174	3	q)r	q)r	NOUN
cana-3958	174	4	.	.	PUNCT
cana-3958	175	1	proof	proof	NOUN
cana-3958	175	2	:	:	PUNCT
cana-3958	175	3	since	since	SCONJ
cana-3958	175	4	av	av	PROPN
cana-3958	175	5	≤	≤	X
cana-3958	175	6	(	(	PUNCT
cana-3958	175	7	1	1	NUM
cana-3958	175	8	−	−	PROPN
cana-3958	175	9	θ)|b|	θ)|b|	PROPN
cana-3958	175	10	ϕ	ϕ	NOUN
cana-3958	175	11	v	v	NUM
cana-3958	175	12	cv	cv	NOUN
cana-3958	175	13	f(ξ	f(ξ	PROPN
cana-3958	175	14	)	)	PUNCT
cana-3958	175	15	=	=	SYM
cana-3958	176	1	ξ	ξ	PROPN
cana-3958	177	1	+	+	CCONJ
cana-3958	177	2	∑	∑	PROPN
cana-3958	177	3	avξ	avξ	ADP
cana-3958	177	4	v∞	v∞	X
cana-3958	177	5	v=2	v=2	ADP
cana-3958	177	6	|f(ξ)|	|f(ξ)|	ADJ
cana-3958	177	7	≤	≤	NUM
cana-3958	177	8	r∗	r∗	NOUN
cana-3958	177	9	+	+	CCONJ
cana-3958	177	10	∑	∑	PUNCT
cana-3958	177	11	av(r	av(r	PUNCT
cana-3958	177	12	∗)v	∗)v	PROPN
cana-3958	177	13	∞	∞	NUM
cana-3958	177	14	v=2	v=2	PROPN
cana-3958	177	15	|f(ξ)|	|f(ξ)|	ADJ
cana-3958	177	16	≤	≤	NUM
cana-3958	177	17	r∗	r∗	NOUN
cana-3958	177	18	+	+	CCONJ
cana-3958	177	19	(	(	PUNCT
cana-3958	177	20	∑	∑	INTJ
cana-3958	177	21	(	(	PUNCT
cana-3958	177	22	1−θ)|b|	1−θ)|b|	NUM
cana-3958	177	23	ϕ	ϕ	NOUN
cana-3958	177	24	v	v	NUM
cana-3958	177	25	cv	cv	PROPN
cana-3958	177	26	∞	∞	PROPN
cana-3958	177	27	v=2	v=2	PROPN
cana-3958	177	28	)	)	PUNCT
cana-3958	178	1	(	(	PUNCT
cana-3958	178	2	r	r	NOUN
cana-3958	178	3	∗)v	∗)v	PROPN
cana-3958	178	4	.	.	PUNCT
cana-3958	179	1	|f(ξ)|	|f(ξ)|	ADJ
cana-3958	179	2	≤	≤	NUM
cana-3958	179	3	r∗	r∗	NOUN
cana-3958	179	4	+	+	CCONJ
cana-3958	179	5	(	(	PUNCT
cana-3958	179	6	(	(	PUNCT
cana-3958	179	7	1−θ)|b|	1−θ)|b|	NUM
cana-3958	179	8	ϕ	ϕ	NOUN
cana-3958	179	9	v	v	X
cana-3958	179	10	cv	cv	PROPN
cana-3958	179	11	)	)	PUNCT
cana-3958	179	12	(	(	PUNCT
cana-3958	179	13	r	r	NOUN
cana-3958	179	14	∗)v	∗)v	PROPN
cana-3958	179	15	.	.	PUNCT
cana-3958	180	1	|f(ξ)|	|f(ξ)|	ADJ
cana-3958	180	2	≤	≤	NUM
cana-3958	180	3	r∗	r∗	NOUN
cana-3958	180	4	+	+	CCONJ
cana-3958	180	5	(	(	PUNCT
cana-3958	180	6	(	(	PUNCT
cana-3958	180	7	1−θ)|b|	1−θ)|b|	NUM
cana-3958	180	8	|(θb−b−1)|c2	|(θb−b−1)|c2	NUM
cana-3958	180	9	)	)	PUNCT
cana-3958	180	10	(	(	PUNCT
cana-3958	180	11	r	r	NOUN
cana-3958	180	12	∗)2	∗)2	PROPN
cana-3958	180	13	.	.	PUNCT
cana-3958	181	1	similarly	similarly	ADV
cana-3958	181	2	,	,	PUNCT
cana-3958	181	3	|f(ξ)|	|f(ξ)|	ADJ
cana-3958	181	4	≥	≥	NUM
cana-3958	181	5	r∗	r∗	NOUN
cana-3958	181	6	−	−	PROPN
cana-3958	182	1	(	(	PUNCT
cana-3958	182	2	(	(	PUNCT
cana-3958	182	3	1−θ)|b|	1−θ)|b|	NUM
cana-3958	182	4	|(θb−b−1)|c2	|(θb−b−1)|c2	NUM
cana-3958	182	5	)	)	PUNCT
cana-3958	183	1	(	(	PUNCT
cana-3958	183	2	r	r	NOUN
cana-3958	183	3	∗)2	∗)2	PROPN
cana-3958	183	4	.	.	PUNCT
cana-3958	184	1	theorem	theorem	PROPN
cana-3958	184	2	2.11(distortion	2.11(distortion	NUM
cana-3958	184	3	theorem	theorem	ADJ
cana-3958	184	4	)	)	PUNCT
cana-3958	184	5	let	let	VERB
cana-3958	184	6	f(ξ	f(ξ	NOUN
cana-3958	184	7	)	)	PUNCT
cana-3958	184	8	=	=	SYM
cana-3958	185	1	ξ	ξ	PROPN
cana-3958	185	2	+	+	CCONJ
cana-3958	185	3	∑	∑	PROPN
cana-3958	185	4	|av|∞	|av|∞	PROPN
cana-3958	185	5	v=2	v=2	SYM
cana-3958	185	6	ξ	ξ	PRON
cana-3958	185	7	v	v	NOUN
cana-3958	185	8	belong	belong	VERB
cana-3958	185	9	to	to	ADP
cana-3958	185	10	class	class	NOUN
cana-3958	185	11	f	f	PROPN
cana-3958	185	12	ϵ𝒫𝒬q	ϵ𝒫𝒬q	PROPN
cana-3958	185	13	,	,	PUNCT
cana-3958	185	14	δ	δ	PROPN
cana-3958	185	15	,	,	PUNCT
cana-3958	185	16	μ	μ	PROPN
cana-3958	185	17	n	n	CCONJ
cana-3958	185	18	,	,	PUNCT
cana-3958	185	19	r	r	NOUN
cana-3958	185	20	(	(	PUNCT
cana-3958	185	21	θ	θ	NOUN
cana-3958	185	22	)	)	PUNCT
cana-3958	185	23	,	,	PUNCT
cana-3958	185	24	then	then	ADV
cana-3958	185	25	for	for	ADP
cana-3958	185	26	|ξ|	|ξ|	PROPN
cana-3958	185	27	=	=	SYM
cana-3958	185	28	r∗	r∗	PROPN
cana-3958	185	29	,	,	PUNCT
cana-3958	185	30	we	we	PRON
cana-3958	185	31	have	have	VERB
cana-3958	185	32	1	1	NUM
cana-3958	185	33	−	−	NOUN
cana-3958	185	34	2(1−θ)|b|	2(1−θ)|b|	NUM
cana-3958	185	35	|(θb−b−1)|c2	|(θb−b−1)|c2	NOUN
cana-3958	185	36	r∗	r∗	VERB
cana-3958	185	37	≤	≤	ADV
cana-3958	185	38	|f′(ξ)|	|f′(ξ)|	NUM
cana-3958	185	39	≤	≤	NUM
cana-3958	185	40	1	1	NUM
cana-3958	185	41	+	+	NUM
cana-3958	185	42	2(1−θ)|b|	2(1−θ)|b|	NUM
cana-3958	185	43	|(θb−b−1)|c2	|(θb−b−1)|c2	NOUN
cana-3958	185	44	r∗	r∗	ADJ
cana-3958	185	45	(	(	PUNCT
cana-3958	185	46	19	19	NUM
cana-3958	185	47	)	)	PUNCT
cana-3958	185	48	proof	proof	NOUN
cana-3958	185	49	.	.	PUNCT
cana-3958	186	1	since	since	SCONJ
cana-3958	186	2	av	av	PROPN
cana-3958	186	3	≤	≤	X
cana-3958	186	4	(	(	PUNCT
cana-3958	186	5	1	1	NUM
cana-3958	186	6	−	−	PROPN
cana-3958	186	7	θ)|b|	θ)|b|	PROPN
cana-3958	186	8	ϕ	ϕ	NOUN
cana-3958	186	9	v	v	NUM
cana-3958	186	10	cv	cv	NOUN
cana-3958	186	11	f(ξ	f(ξ	PROPN
cana-3958	186	12	)	)	PUNCT
cana-3958	186	13	=	=	SYM
cana-3958	186	14	ξ	ξ	X
cana-3958	186	15	∑	∑	PROPN
cana-3958	186	16	avξ	avξ	ADP
cana-3958	186	17	v∞	v∞	PROPN
cana-3958	186	18	v=2	v=2	PROPN
cana-3958	186	19	|fξ)|	|fξ)|	NOUN
cana-3958	186	20	≤	≤	NUM
cana-3958	186	21	1	1	NUM
cana-3958	186	22	+	+	NUM
cana-3958	186	23	∑	∑	ADP
cana-3958	186	24	vav|ξ|v−1	vav|ξ|v−1	NUM
cana-3958	186	25	∞	∞	NUM
cana-3958	186	26	v=2	v=2	PROPN
cana-3958	186	27	|f′ξ)|	|f′ξ)|	NOUN
cana-3958	186	28	≤	≤	NUM
cana-3958	186	29	1	1	NUM
cana-3958	186	30	+	+	NUM
cana-3958	186	31	2(1	2(1	NUM
cana-3958	186	32	−	−	NOUN
cana-3958	186	33	θ)|b|	θ)|b|	PROPN
cana-3958	186	34	|(θb	|(θb	NUM
cana-3958	186	35	−	−	NOUN
cana-3958	186	36	b	b	NOUN
cana-3958	186	37	−	−	PROPN
cana-3958	186	38	1)|c2	1)|c2	NOUN
cana-3958	186	39	r∗	r∗	NOUN
cana-3958	186	40	similarly	similarly	ADV
cana-3958	186	41	communications	communication	NOUN
cana-3958	186	42	on	on	ADP
cana-3958	186	43	applied	apply	VERB
cana-3958	186	44	nonlinear	nonlinear	ADJ
cana-3958	186	45	analysis	analysis	NOUN
cana-3958	186	46	issn	issn	NOUN
cana-3958	186	47	:	:	PUNCT
cana-3958	186	48	1074	1074	NUM
cana-3958	186	49	-	-	PUNCT
cana-3958	186	50	133x	133x	NUM
cana-3958	186	51	vol	vol	NOUN
cana-3958	186	52	32	32	NUM
cana-3958	186	53	no	no	NOUN
cana-3958	186	54	.	.	PUNCT
cana-3958	187	1	9s	9s	NUM
cana-3958	187	2	(	(	PUNCT
cana-3958	187	3	2025	2025	NUM
cana-3958	187	4	)	)	PUNCT
cana-3958	187	5	474	474	NUM
cana-3958	187	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3958	187	7	|f′ξ)|	|f′ξ)|	NOUN
cana-3958	187	8	≥	≥	NOUN
cana-3958	187	9	1	1	NUM
cana-3958	187	10	+	+	NUM
cana-3958	187	11	2(1	2(1	NUM
cana-3958	187	12	−	−	NOUN
cana-3958	187	13	θ)|b|	θ)|b|	PROPN
cana-3958	187	14	|(θb	|(θb	NUM
cana-3958	187	15	−	−	NOUN
cana-3958	187	16	b	b	NOUN
cana-3958	187	17	−	−	NOUN
cana-3958	187	18	1)|c2	1)|c2	NUM
cana-3958	187	19	r∗.	r∗.	NOUN
cana-3958	187	20	3	3	NUM
cana-3958	187	21	.	.	X
cana-3958	187	22	conclusion	conclusion	NOUN
cana-3958	187	23	in	in	ADP
cana-3958	187	24	conclusion	conclusion	NOUN
cana-3958	187	25	,	,	PUNCT
cana-3958	187	26	this	this	DET
cana-3958	187	27	study	study	NOUN
cana-3958	187	28	has	have	AUX
cana-3958	187	29	provided	provide	VERB
cana-3958	187	30	a	a	DET
cana-3958	187	31	thorough	thorough	ADJ
cana-3958	187	32	examination	examination	NOUN
cana-3958	187	33	of	of	ADP
cana-3958	187	34	the	the	DET
cana-3958	187	35	coefficient	coefficient	NOUN
cana-3958	187	36	challenges	challenge	VERB
cana-3958	187	37	inherent	inherent	ADJ
cana-3958	187	38	in	in	ADP
cana-3958	187	39	the	the	DET
cana-3958	187	40	newly	newly	ADV
cana-3958	187	41	defined	define	VERB
cana-3958	187	42	subclass	subclass	NOUN
cana-3958	187	43	of	of	ADP
cana-3958	187	44	univalent	univalent	ADJ
cana-3958	187	45	functions	function	NOUN
cana-3958	187	46	in	in	ADP
cana-3958	187	47	u	u	NOUN
cana-3958	187	48	,	,	PUNCT
cana-3958	187	49	as	as	SCONJ
cana-3958	187	50	outlined	outline	VERB
cana-3958	187	51	in	in	ADP
cana-3958	187	52	definition	definition	NOUN
cana-3958	187	53	(	(	PUNCT
cana-3958	187	54	2.1	2.1	NUM
cana-3958	187	55	)	)	PUNCT
cana-3958	187	56	.	.	PUNCT
cana-3958	188	1	key	key	ADJ
cana-3958	188	2	properties	property	NOUN
cana-3958	188	3	such	such	ADJ
cana-3958	188	4	as	as	ADP
cana-3958	188	5	the	the	DET
cana-3958	188	6	radius	radius	NOUN
cana-3958	188	7	of	of	ADP
cana-3958	188	8	starlikeness	starlikeness	NOUN
cana-3958	188	9	,	,	PUNCT
cana-3958	188	10	extreme	extreme	ADJ
cana-3958	188	11	points	point	NOUN
cana-3958	188	12	,	,	PUNCT
cana-3958	188	13	development	development	NOUN
cana-3958	188	14	and	and	CCONJ
cana-3958	188	15	distortion	distortion	NOUN
cana-3958	188	16	,	,	PUNCT
cana-3958	188	17	convexity	convexity	NOUN
cana-3958	188	18	,	,	PUNCT
cana-3958	188	19	and	and	CCONJ
cana-3958	188	20	integral	integral	ADJ
cana-3958	188	21	means	mean	NOUN
cana-3958	188	22	of	of	ADP
cana-3958	188	23	inequalities	inequality	NOUN
cana-3958	188	24	were	be	AUX
cana-3958	188	25	explored	explore	VERB
cana-3958	188	26	,	,	PUNCT
cana-3958	188	27	enhancing	enhance	VERB
cana-3958	188	28	our	our	PRON
cana-3958	188	29	understanding	understanding	NOUN
cana-3958	188	30	of	of	ADP
cana-3958	188	31	the	the	DET
cana-3958	188	32	subclass	subclass	NOUN
cana-3958	188	33	's	's	PART
cana-3958	188	34	behaviour	behaviour	NOUN
cana-3958	188	35	.	.	PUNCT
cana-3958	189	1	the	the	DET
cana-3958	189	2	findings	finding	NOUN
cana-3958	189	3	contribute	contribute	VERB
cana-3958	189	4	valuable	valuable	ADJ
cana-3958	189	5	insights	insight	NOUN
cana-3958	189	6	into	into	ADP
cana-3958	189	7	the	the	DET
cana-3958	189	8	composition	composition	NOUN
cana-3958	189	9	and	and	CCONJ
cana-3958	189	10	properties	property	NOUN
cana-3958	189	11	of	of	ADP
cana-3958	189	12	analytic	analytic	ADJ
cana-3958	189	13	functions	function	NOUN
cana-3958	189	14	.	.	PUNCT
cana-3958	190	1	moreover	moreover	ADV
cana-3958	190	2	,	,	PUNCT
cana-3958	190	3	the	the	DET
cana-3958	190	4	study	study	NOUN
cana-3958	190	5	suggests	suggest	VERB
cana-3958	190	6	promising	promise	VERB
cana-3958	190	7	directions	direction	NOUN
cana-3958	190	8	for	for	ADP
cana-3958	190	9	future	future	ADJ
cana-3958	190	10	research	research	NOUN
cana-3958	190	11	,	,	PUNCT
cana-3958	190	12	including	include	VERB
cana-3958	190	13	the	the	DET
cana-3958	190	14	analysis	analysis	NOUN
cana-3958	190	15	of	of	ADP
cana-3958	190	16	hankel	hankel	NOUN
cana-3958	190	17	determinants	determinant	NOUN
cana-3958	190	18	for	for	ADP
cana-3958	190	19	orders	order	NOUN
cana-3958	190	20	between	between	ADP
cana-3958	190	21	two	two	NUM
cana-3958	190	22	and	and	CCONJ
cana-3958	190	23	three	three	NUM
cana-3958	190	24	,	,	PUNCT
cana-3958	190	25	as	as	ADV
cana-3958	190	26	well	well	ADV
cana-3958	190	27	as	as	ADP
cana-3958	190	28	further	further	ADJ
cana-3958	190	29	investigations	investigation	NOUN
cana-3958	190	30	and	and	CCONJ
cana-3958	190	31	estimates	estimate	NOUN
cana-3958	190	32	related	relate	VERB
cana-3958	190	33	to	to	ADP
cana-3958	190	34	the	the	DET
cana-3958	190	35	fekete	fekete	NOUN
cana-3958	190	36	-	-	PUNCT
cana-3958	190	37	szegö	szegö	ADJ
cana-3958	190	38	functional	functional	ADJ
cana-3958	190	39	problem	problem	NOUN
cana-3958	190	40	.	.	PUNCT
cana-3958	191	1	these	these	DET
cana-3958	191	2	avenues	avenue	NOUN
cana-3958	191	3	present	present	VERB
cana-3958	191	4	exciting	exciting	ADJ
cana-3958	191	5	opportunities	opportunity	NOUN
cana-3958	191	6	for	for	ADP
cana-3958	191	7	advancing	advance	VERB
cana-3958	191	8	the	the	DET
cana-3958	191	9	field	field	NOUN
cana-3958	191	10	.	.	PUNCT
cana-3958	192	1	references	reference	NOUN
cana-3958	192	2	[	[	X
cana-3958	192	3	1	1	NUM
cana-3958	192	4	]	]	X
cana-3958	192	5	anitha	anitha	PROPN
cana-3958	192	6	lakshminarayanan	lakshminarayanan	PROPN
cana-3958	192	7	,	,	PUNCT
cana-3958	192	8	ramachandran	ramachandran	PROPN
cana-3958	192	9	chellakutti	chellakutti	PROPN
cana-3958	192	10	,	,	PUNCT
cana-3958	192	11	bul	bul	PROPN
cana-3958	192	12	boaca	boaca	PROPN
cana-3958	192	13	teodor	teodor	ADV
cana-3958	192	14	,	,	PUNCT
cana-3958	192	15	certain	certain	ADJ
cana-3958	192	16	subclasses	subclass	NOUN
cana-3958	192	17	of	of	ADP
cana-3958	192	18	spirallike	spirallike	ADJ
cana-3958	192	19	univalent	univalent	ADJ
cana-3958	192	20	functions	function	NOUN
cana-3958	192	21	related	relate	VERB
cana-3958	192	22	to	to	ADP
cana-3958	192	23	poisson	poisson	NOUN
cana-3958	192	24	distribution	distribution	NOUN
cana-3958	192	25	series	series	NOUN
cana-3958	192	26	,	,	PUNCT
cana-3958	192	27	turkish	turkish	ADJ
cana-3958	192	28	j.	j.	PROPN
cana-3958	192	29	math	math	PROPN
cana-3958	192	30	.	.	PUNCT
cana-3958	192	31	,	,	PUNCT
cana-3958	192	32	45(3	45(3	NUM
cana-3958	192	33	)	)	PUNCT
cana-3958	192	34	,	,	PUNCT
cana-3958	192	35	1449	1449	NUM
cana-3958	192	36	-	-	SYM
cana-3958	192	37	1458	1458	NUM
cana-3958	192	38	,	,	PUNCT
cana-3958	192	39	(	(	PUNCT
cana-3958	192	40	2021	2021	NUM
cana-3958	192	41	)	)	PUNCT
cana-3958	192	42	.	.	PUNCT
cana-3958	193	1	[	[	X
cana-3958	193	2	2	2	X
cana-3958	193	3	]	]	X
cana-3958	193	4	b.	b.	PROPN
cana-3958	193	5	a.	a.	PROPN
cana-3958	193	6	frasin	frasin	PROPN
cana-3958	193	7	,	,	PUNCT
cana-3958	193	8	on	on	ADP
cana-3958	193	9	certain	certain	ADJ
cana-3958	193	10	subclasses	subclass	NOUN
cana-3958	193	11	of	of	ADP
cana-3958	193	12	analytic	analytic	ADJ
cana-3958	193	13	functions	function	NOUN
cana-3958	193	14	associated	associate	VERB
cana-3958	193	15	with	with	ADP
cana-3958	193	16	poisson	poisson	NOUN
cana-3958	193	17	distribution	distribution	NOUN
cana-3958	193	18	series	series	NOUN
cana-3958	193	19	,	,	PUNCT
cana-3958	193	20	acta	acta	PROPN
cana-3958	193	21	univ	univ	PROPN
cana-3958	193	22	.	.	PUNCT
cana-3958	194	1	sapientiae	sapientiae	PROPN
cana-3958	194	2	math	math	PROPN
cana-3958	194	3	.	.	PUNCT
cana-3958	194	4	,	,	PUNCT
cana-3958	194	5	11(1	11(1	NUM
cana-3958	194	6	)	)	PUNCT
cana-3958	194	7	,	,	PUNCT
cana-3958	194	8	78	78	NUM
cana-3958	194	9	-	-	SYM
cana-3958	194	10	86	86	NUM
cana-3958	194	11	,	,	PUNCT
cana-3958	194	12	(	(	PUNCT
cana-3958	194	13	2019	2019	NUM
cana-3958	194	14	)	)	PUNCT
cana-3958	194	15	.	.	PUNCT
cana-3958	195	1	[	[	X
cana-3958	195	2	3	3	X
cana-3958	195	3	]	]	X
cana-3958	195	4	b.a	b.a	PROPN
cana-3958	195	5	.	.	PROPN
cana-3958	195	6	frasin	frasin	PROPN
cana-3958	195	7	,	,	PUNCT
cana-3958	195	8	g.	g.	PROPN
cana-3958	195	9	murugusundaramoorthy	murugusundaramoorthy	PROPN
cana-3958	195	10	,	,	PUNCT
cana-3958	195	11	sibel	sibel	PROPN
cana-3958	195	12	yalçin	yalçin	NOUN
cana-3958	195	13	,	,	PUNCT
cana-3958	195	14	subclass	subclass	NOUN
cana-3958	195	15	of	of	ADP
cana-3958	195	16	analytic	analytic	ADJ
cana-3958	195	17	functions	function	NOUN
cana-3958	195	18	associated	associate	VERB
cana-3958	195	19	with	with	ADP
cana-3958	195	20	pascal	pascal	ADJ
cana-3958	195	21	distribution	distribution	NOUN
cana-3958	195	22	series	series	NOUN
cana-3958	195	23	,	,	PUNCT
cana-3958	195	24	series	series	PROPN
cana-3958	195	25	iii	iii	PROPN
cana-3958	195	26	matematics	matematic	NOUN
cana-3958	195	27	,	,	PUNCT
cana-3958	195	28	informatics	informatic	NOUN
cana-3958	195	29	,	,	PUNCT
cana-3958	195	30	physics	physics	NOUN
cana-3958	195	31	,	,	PUNCT
cana-3958	195	32	13(62	13(62	NUM
cana-3958	195	33	)	)	PUNCT
cana-3958	195	34	,	,	PUNCT
cana-3958	195	35	521	521	NUM
cana-3958	195	36	-	-	SYM
cana-3958	195	37	528	528	NUM
cana-3958	195	38	,	,	PUNCT
cana-3958	195	39	(	(	PUNCT
cana-3958	195	40	2021	2021	NUM
cana-3958	195	41	)	)	PUNCT
cana-3958	195	42	.	.	PUNCT
cana-3958	196	1	[	[	X
cana-3958	196	2	4	4	X
cana-3958	196	3	]	]	X
cana-3958	196	4	d.	d.	PROPN
cana-3958	196	5	raducanu	raducanu	PROPN
cana-3958	196	6	and	and	CCONJ
cana-3958	196	7	h.	h.	PROPN
cana-3958	196	8	orhan	orhan	PROPN
cana-3958	196	9	,	,	PUNCT
cana-3958	196	10	subclass	subclass	NOUN
cana-3958	196	11	of	of	ADP
cana-3958	196	12	analytic	analytic	ADJ
cana-3958	196	13	functions	function	NOUN
cana-3958	196	14	defined	define	VERB
cana-3958	196	15	by	by	ADP
cana-3958	196	16	a	a	DET
cana-3958	196	17	generalized	generalize	VERB
cana-3958	196	18	differential	differential	NOUN
cana-3958	196	19	operator	operator	NOUN
cana-3958	196	20	,	,	PUNCT
cana-3958	196	21	international	international	ADJ
cana-3958	196	22	journal	journal	NOUN
cana-3958	196	23	of	of	ADP
cana-3958	196	24	mathematics	mathematics	PROPN
cana-3958	196	25	and	and	CCONJ
cana-3958	196	26	mathematical	mathematical	ADJ
cana-3958	196	27	analysis	analysis	NOUN
cana-3958	196	28	,	,	PUNCT
cana-3958	196	29	4(1	4(1	X
cana-3958	196	30	-	-	SYM
cana-3958	196	31	4	4	NUM
cana-3958	196	32	)	)	PUNCT
cana-3958	196	33	,	,	PUNCT
cana-3958	196	34	1	1	NUM
cana-3958	196	35	-	-	SYM
cana-3958	196	36	15	15	NUM
cana-3958	196	37	,	,	PUNCT
cana-3958	196	38	(	(	PUNCT
cana-3958	196	39	2010	2010	NUM
cana-3958	196	40	)	)	PUNCT
cana-3958	196	41	.	.	PUNCT
cana-3958	197	1	[	[	X
cana-3958	197	2	5	5	X
cana-3958	197	3	]	]	PUNCT
cana-3958	197	4	f.	f.	PROPN
cana-3958	197	5	m.	m.	PROPN
cana-3958	197	6	al	al	PROPN
cana-3958	197	7	-	-	PUNCT
cana-3958	197	8	oboudi	oboudi	NOUN
cana-3958	197	9	,	,	PUNCT
cana-3958	197	10	on	on	ADP
cana-3958	197	11	univalent	univalent	ADJ
cana-3958	197	12	functions	function	NOUN
cana-3958	197	13	defined	define	VERB
cana-3958	197	14	by	by	ADP
cana-3958	197	15	a	a	DET
cana-3958	197	16	generalized	generalize	VERB
cana-3958	197	17	salagean	salagean	ADJ
cana-3958	197	18	operator	operator	NOUN
cana-3958	197	19	,	,	PUNCT
cana-3958	197	20	international	international	ADJ
cana-3958	197	21	journal	journal	NOUN
cana-3958	197	22	of	of	ADP
cana-3958	197	23	mathematics	mathematics	PROPN
cana-3958	197	24	and	and	CCONJ
cana-3958	197	25	mathematical	mathematical	ADJ
cana-3958	197	26	sciences	science	NOUN
cana-3958	197	27	,	,	PUNCT
cana-3958	197	28	2004(27	2004(27	NUM
cana-3958	197	29	)	)	PUNCT
cana-3958	197	30	,	,	PUNCT
cana-3958	197	31	1429	1429	NUM
cana-3958	197	32	-	-	SYM
cana-3958	197	33	1436	1436	NUM
cana-3958	197	34	,	,	PUNCT
cana-3958	197	35	(	(	PUNCT
cana-3958	197	36	2004	2004	NUM
cana-3958	197	37	)	)	PUNCT
cana-3958	197	38	.	.	PUNCT
cana-3958	198	1	[	[	X
cana-3958	198	2	6	6	NUM
cana-3958	198	3	]	]	X
cana-3958	198	4	g.	g.	PROPN
cana-3958	198	5	murugusundaramoorthy	murugusundaramoorthy	ADJ
cana-3958	198	6	,	,	PUNCT
cana-3958	198	7	subclasses	subclass	NOUN
cana-3958	198	8	of	of	ADP
cana-3958	198	9	starlike	starlike	NOUN
cana-3958	198	10	and	and	CCONJ
cana-3958	198	11	convex	convex	NOUN
cana-3958	198	12	functions	function	NOUN
cana-3958	198	13	involving	involve	VERB
cana-3958	198	14	poisson	poisson	NOUN
cana-3958	198	15	distribution	distribution	NOUN
cana-3958	198	16	series	series	NOUN
cana-3958	198	17	,	,	PUNCT
cana-3958	198	18	afr	afr	PROPN
cana-3958	198	19	.	.	PUNCT
cana-3958	198	20	mat	mat	PROPN
cana-3958	198	21	.	.	PROPN
cana-3958	198	22	,	,	PUNCT
cana-3958	198	23	28(7	28(7	NUM
cana-3958	198	24	-	-	SYM
cana-3958	198	25	8)	8)	NUM
cana-3958	198	26	,	,	PUNCT
cana-3958	198	27	1357	1357	NUM
cana-3958	198	28	-	-	SYM
cana-3958	198	29	1366	1366	NUM
cana-3958	198	30	,	,	PUNCT
cana-3958	198	31	(	(	PUNCT
cana-3958	198	32	2017	2017	NUM
cana-3958	198	33	)	)	PUNCT
cana-3958	198	34	.	.	PUNCT
cana-3958	199	1	[	[	X
cana-3958	199	2	7	7	X
cana-3958	199	3	]	]	X
cana-3958	199	4	g.	g.	PROPN
cana-3958	199	5	salagean	salagean	PROPN
cana-3958	199	6	,	,	PUNCT
cana-3958	199	7	subclasses	subclass	NOUN
cana-3958	199	8	of	of	ADP
cana-3958	199	9	univalent	univalent	ADJ
cana-3958	199	10	functions	function	NOUN
cana-3958	199	11	,	,	PUNCT
cana-3958	199	12	lecture	lecture	NOUN
cana-3958	199	13	notes	note	NOUN
cana-3958	199	14	in	in	ADP
cana-3958	199	15	maths	math	NOUN
cana-3958	199	16	,	,	PUNCT
cana-3958	199	17	springerverlag	springerverlag	NOUN
cana-3958	199	18	,	,	PUNCT
cana-3958	199	19	berlin	berlin	PROPN
cana-3958	199	20	,	,	PUNCT
cana-3958	199	21	1013	1013	NUM
cana-3958	199	22	,	,	PUNCT
cana-3958	199	23	362	362	NUM
cana-3958	199	24	-	-	SYM
cana-3958	199	25	372	372	NUM
cana-3958	199	26	,	,	PUNCT
cana-3958	199	27	(	(	PUNCT
cana-3958	199	28	1983	1983	NUM
cana-3958	199	29	)	)	PUNCT
cana-3958	199	30	.	.	PUNCT
cana-3958	200	1	[	[	X
cana-3958	200	2	8	8	X
cana-3958	200	3	]	]	PUNCT
cana-3958	200	4	j.	j.	PROPN
cana-3958	200	5	e.	e.	PROPN
cana-3958	200	6	littlewood	littlewood	PROPN
cana-3958	200	7	,	,	PUNCT
cana-3958	200	8	on	on	ADP
cana-3958	200	9	inequalities	inequality	NOUN
cana-3958	200	10	in	in	ADP
cana-3958	200	11	the	the	DET
cana-3958	200	12	theory	theory	NOUN
cana-3958	200	13	of	of	ADP
cana-3958	200	14	functions	function	NOUN
cana-3958	200	15	,	,	PUNCT
cana-3958	200	16	proceedings	proceeding	NOUN
cana-3958	200	17	of	of	ADP
cana-3958	200	18	london	london	PROPN
cana-3958	200	19	mathematical	mathematical	ADJ
cana-3958	200	20	society	society	NOUN
cana-3958	200	21	,	,	PUNCT
cana-3958	200	22	23(1	23(1	NUM
cana-3958	200	23	)	)	PUNCT
cana-3958	200	24	,	,	PUNCT
cana-3958	200	25	481519	481519	NUM
cana-3958	200	26	,	,	PUNCT
cana-3958	200	27	(	(	PUNCT
cana-3958	200	28	1925	1925	NUM
cana-3958	200	29	)	)	PUNCT
cana-3958	200	30	.	.	PUNCT
cana-3958	201	1	[	[	X
cana-3958	201	2	9	9	NUM
cana-3958	201	3	]	]	X
cana-3958	201	4	porwal	porwal	NOUN
cana-3958	201	5	saurabh	saurabh	PROPN
cana-3958	201	6	,	,	PUNCT
cana-3958	201	7	kumar	kumar	PROPN
cana-3958	201	8	manish	manish	PROPN
cana-3958	201	9	,	,	PUNCT
cana-3958	201	10	a	a	DET
cana-3958	201	11	unifed	unifed	ADJ
cana-3958	201	12	study	study	NOUN
cana-3958	201	13	on	on	ADP
cana-3958	201	14	star	star	NOUN
cana-3958	201	15	like	like	ADP
cana-3958	201	16	and	and	CCONJ
cana-3958	201	17	convex	convex	NOUN
cana-3958	201	18	functions	function	NOUN
cana-3958	201	19	associated	associate	VERB
cana-3958	201	20	with	with	ADP
cana-3958	201	21	poisson	poisson	NOUN
cana-3958	201	22	distribution	distribution	NOUN
cana-3958	201	23	series	series	NOUN
cana-3958	201	24	,	,	PUNCT
cana-3958	201	25	afr	afr	PROPN
cana-3958	201	26	.	.	PUNCT
cana-3958	201	27	mat	mat	PROPN
cana-3958	201	28	.	.	PROPN
cana-3958	201	29	,	,	PUNCT
cana-3958	201	30	27(5	27(5	PROPN
cana-3958	201	31	-	-	PUNCT
cana-3958	201	32	6	6	NUM
cana-3958	201	33	)	)	PUNCT
cana-3958	201	34	,	,	PUNCT
cana-3958	201	35	1021	1021	NUM
cana-3958	201	36	-1027	-1027	NOUN
cana-3958	201	37	,	,	PUNCT
cana-3958	201	38	(	(	PUNCT
cana-3958	201	39	2016	2016	NUM
cana-3958	201	40	)	)	PUNCT
cana-3958	201	41	.	.	PUNCT
cana-3958	202	1	[	[	X
cana-3958	202	2	10	10	NUM
cana-3958	202	3	]	]	X
cana-3958	202	4	r.	r.	PROPN
cana-3958	202	5	m.	m.	PROPN
cana-3958	203	1	el	el	PROPN
cana-3958	203	2	-	-	PUNCT
cana-3958	203	3	ashwah	ashwah	NOUN
cana-3958	203	4	,	,	PUNCT
cana-3958	203	5	w.	w.	PROPN
cana-3958	203	6	y.	y.	PROPN
cana-3958	203	7	kota	kota	PROPN
cana-3958	203	8	,	,	PUNCT
cana-3958	203	9	some	some	DET
cana-3958	203	10	condition	condition	NOUN
cana-3958	203	11	on	on	ADP
cana-3958	203	12	a	a	DET
cana-3958	203	13	poisson	poisson	NOUN
cana-3958	203	14	distribution	distribution	NOUN
cana-3958	203	15	series	series	NOUN
cana-3958	203	16	to	to	PART
cana-3958	203	17	be	be	AUX
cana-3958	203	18	in	in	ADP
cana-3958	203	19	subclasses	subclass	NOUN
cana-3958	203	20	of	of	ADP
cana-3958	203	21	univalent	univalent	ADJ
cana-3958	203	22	functions	function	NOUN
cana-3958	203	23	,	,	PUNCT
cana-3958	203	24	acta	acta	PROPN
cana-3958	203	25	universitatis	universitatis	PROPN
cana-3958	203	26	apulensis	apulensis	NOUN
cana-3958	203	27	,	,	PUNCT
cana-3958	203	28	51	51	NUM
cana-3958	203	29	,	,	PUNCT
cana-3958	203	30	89	89	NUM
cana-3958	203	31	-	-	SYM
cana-3958	203	32	103	103	NUM
cana-3958	203	33	,	,	PUNCT
cana-3958	203	34	(	(	PUNCT
cana-3958	203	35	2017	2017	NUM
cana-3958	203	36	)	)	PUNCT
cana-3958	203	37	.	.	PUNCT
cana-3958	204	1	[	[	X
cana-3958	204	2	11	11	NUM
cana-3958	204	3	]	]	PUNCT
cana-3958	204	4	s.	s.	PROPN
cana-3958	204	5	m.	m.	PROPN
cana-3958	204	6	el	el	PROPN
cana-3958	204	7	-	-	PUNCT
cana-3958	204	8	deeb	deeb	PROPN
cana-3958	204	9	,	,	PUNCT
cana-3958	204	10	t.	t.	NOUN
cana-3958	204	11	bulboaca	bulboaca	NOUN
cana-3958	204	12	and	and	CCONJ
cana-3958	204	13	j.	j.	PROPN
cana-3958	204	14	dziok	dziok	PROPN
cana-3958	204	15	,	,	PUNCT
cana-3958	204	16	pascal	pascal	ADJ
cana-3958	204	17	distribution	distribution	NOUN
cana-3958	204	18	series	series	NOUN
cana-3958	204	19	connected	connect	VERB
cana-3958	204	20	with	with	ADP
cana-3958	204	21	certain	certain	ADJ
cana-3958	204	22	subclasses	subclass	NOUN
cana-3958	204	23	of	of	ADP
cana-3958	204	24	univalent	univalent	ADJ
cana-3958	204	25	functions	function	NOUN
cana-3958	204	26	,	,	PUNCT
cana-3958	204	27	kyungpook	kyungpook	NOUN
cana-3958	204	28	math	math	NOUN
cana-3958	204	29	.	.	PUNCT
cana-3958	205	1	j.	j.	PROPN
cana-3958	205	2	,	,	PUNCT
cana-3958	205	3	59	59	NUM
cana-3958	205	4	,	,	PUNCT
cana-3958	205	5	301	301	NUM
cana-3958	205	6	-	-	SYM
cana-3958	205	7	314	314	NUM
cana-3958	205	8	,	,	PUNCT
cana-3958	205	9	(	(	PUNCT
cana-3958	205	10	2019	2019	NUM
cana-3958	205	11	)	)	PUNCT
cana-3958	205	12	.	.	PUNCT
cana-3958	206	1	[	[	X
cana-3958	206	2	12	12	NUM
cana-3958	206	3	]	]	PUNCT
cana-3958	206	4	t.	t.	NOUN
cana-3958	206	5	bulboaca	bulboaca	NOUN
cana-3958	206	6	and	and	CCONJ
cana-3958	206	7	g.	g.	PROPN
cana-3958	206	8	murugusundaramoorthy	murugusundaramoorthy	ADJ
cana-3958	206	9	,	,	PUNCT
cana-3958	206	10	univalent	univalent	ADJ
cana-3958	206	11	functions	function	NOUN
cana-3958	206	12	with	with	ADP
cana-3958	206	13	positive	positive	ADJ
cana-3958	206	14	co	co	NOUN
cana-3958	206	15	-	-	ADJ
cana-3958	206	16	efficient	efficient	ADJ
cana-3958	206	17	involving	involve	VERB
cana-3958	206	18	pascal	pascal	ADJ
cana-3958	206	19	distribution	distribution	NOUN
cana-3958	206	20	series	series	NOUN
cana-3958	206	21	,	,	PUNCT
cana-3958	206	22	commun	commun	PROPN
cana-3958	206	23	.	.	PUNCT
cana-3958	207	1	korean	korean	ADJ
cana-3958	207	2	math	math	PROPN
cana-3958	207	3	.	.	PUNCT
cana-3958	208	1	soc	soc	PROPN
cana-3958	208	2	.	.	PUNCT
cana-3958	208	3	,	,	PUNCT
cana-3958	208	4	35(3	35(3	NUM
cana-3958	208	5	)	)	PUNCT
cana-3958	208	6	,	,	PUNCT
cana-3958	208	7	867	867	NUM
cana-3958	208	8	-	-	SYM
cana-3958	208	9	877	877	NUM
cana-3958	208	10	,	,	PUNCT
cana-3958	208	11	(	(	PUNCT
cana-3958	208	12	2020	2020	NUM
cana-3958	208	13	)	)	PUNCT
cana-3958	208	14	.	.	PUNCT
cana-3958	209	1	[	[	X
cana-3958	209	2	13	13	NUM
cana-3958	209	3	]	]	X
cana-3958	209	4	w.	w.	PROPN
cana-3958	209	5	ma	ma	PROPN
cana-3958	209	6	and	and	CCONJ
cana-3958	209	7	d.	d.	PROPN
cana-3958	209	8	minda	minda	PROPN
cana-3958	209	9	,	,	PUNCT
cana-3958	209	10	a	a	DET
cana-3958	209	11	unified	unified	ADJ
cana-3958	209	12	treatment	treatment	NOUN
cana-3958	209	13	of	of	ADP
cana-3958	209	14	some	some	DET
cana-3958	209	15	special	special	ADJ
cana-3958	209	16	classes	class	NOUN
cana-3958	209	17	of	of	ADP
cana-3958	209	18	univalent	univalent	ADJ
cana-3958	209	19	functions	function	NOUN
cana-3958	209	20	,	,	PUNCT
cana-3958	209	21	proc	proc	NOUN
cana-3958	209	22	.	.	PUNCT
cana-3958	210	1	of	of	ADP
cana-3958	210	2	the	the	DET
cana-3958	210	3	conf	conf	NOUN
cana-3958	210	4	.	.	PUNCT
cana-3958	211	1	on	on	ADP
cana-3958	211	2	complex	complex	ADJ
cana-3958	211	3	analysis	analysis	NOUN
cana-3958	211	4	,	,	PUNCT
cana-3958	211	5	157	157	NUM
cana-3958	211	6	-	-	SYM
cana-3958	211	7	169	169	NUM
cana-3958	211	8	,	,	PUNCT
cana-3958	211	9	(	(	PUNCT
cana-3958	211	10	1994	1994	NUM
cana-3958	211	11	)	)	PUNCT
cana-3958	211	12	.	.	PUNCT