id	sid	tid	token	lemma	pos
ejpam-6415	1	1	european	european	PROPN
ejpam-6415	1	2	journal	journal	PROPN
ejpam-6415	1	3	of	of	ADP
ejpam-6415	1	4	pure	pure	ADJ
ejpam-6415	1	5	and	and	CCONJ
ejpam-6415	1	6	applied	applied	ADJ
ejpam-6415	1	7	mathematics	mathematic	NOUN
ejpam-6415	1	8	2025	2025	NUM
ejpam-6415	1	9	,	,	PUNCT
ejpam-6415	1	10	vol	vol	NOUN
ejpam-6415	1	11	.	.	PROPN
ejpam-6415	1	12	18	18	NUM
ejpam-6415	1	13	,	,	PUNCT
ejpam-6415	1	14	issue	issue	NOUN
ejpam-6415	1	15	3	3	NUM
ejpam-6415	1	16	,	,	PUNCT
ejpam-6415	1	17	article	article	NOUN
ejpam-6415	1	18	number	number	NOUN
ejpam-6415	1	19	6415	6415	NUM
ejpam-6415	1	20	issn	issn	PROPN
ejpam-6415	1	21	1307	1307	NUM
ejpam-6415	1	22	-	-	SYM
ejpam-6415	1	23	5543	5543	NUM
ejpam-6415	1	24	–	–	PUNCT
ejpam-6415	1	25	ejpam.com	ejpam.com	X
ejpam-6415	1	26	published	publish	VERB
ejpam-6415	1	27	by	by	ADP
ejpam-6415	1	28	new	new	PROPN
ejpam-6415	1	29	york	york	PROPN
ejpam-6415	1	30	business	business	PROPN
ejpam-6415	1	31	global	global	ADJ
ejpam-6415	1	32	geometric	geometric	ADJ
ejpam-6415	1	33	properties	property	NOUN
ejpam-6415	1	34	of	of	ADP
ejpam-6415	1	35	a	a	DET
ejpam-6415	1	36	general	general	ADJ
ejpam-6415	1	37	subclass	subclass	NOUN
ejpam-6415	1	38	of	of	ADP
ejpam-6415	1	39	analytic	analytic	ADJ
ejpam-6415	1	40	functions	function	NOUN
ejpam-6415	1	41	involving	involve	VERB
ejpam-6415	1	42	multiplier	multipli	ADJ
ejpam-6415	1	43	operator	operator	NOUN
ejpam-6415	1	44	shasha	shasha	PROPN
ejpam-6415	1	45	han1,∗	han1,∗	PROPN
ejpam-6415	1	46	,	,	PUNCT
ejpam-6415	1	47	maisarah	maisarah	PROPN
ejpam-6415	1	48	haji	haji	PROPN
ejpam-6415	1	49	mohd2	mohd2	PROPN
ejpam-6415	1	50	,	,	PUNCT
ejpam-6415	1	51	mohamed	mohamed	PROPN
ejpam-6415	1	52	illafe1	illafe1	PROPN
ejpam-6415	1	53	1	1	NUM
ejpam-6415	1	54	mathematics	mathematics	PROPN
ejpam-6415	1	55	department	department	NOUN
ejpam-6415	1	56	,	,	PUNCT
ejpam-6415	1	57	school	school	NOUN
ejpam-6415	1	58	of	of	ADP
ejpam-6415	1	59	engineering	engineering	NOUN
ejpam-6415	1	60	,	,	PUNCT
ejpam-6415	1	61	mathematics	mathematic	NOUN
ejpam-6415	1	62	and	and	CCONJ
ejpam-6415	1	63	technology	technology	NOUN
ejpam-6415	1	64	,	,	PUNCT
ejpam-6415	1	65	navajo	navajo	PROPN
ejpam-6415	1	66	technical	technical	PROPN
ejpam-6415	1	67	university	university	PROPN
ejpam-6415	1	68	,	,	PUNCT
ejpam-6415	1	69	crownpoint	crownpoint	NOUN
ejpam-6415	1	70	,	,	PUNCT
ejpam-6415	1	71	new	new	PROPN
ejpam-6415	1	72	mexico	mexico	PROPN
ejpam-6415	1	73	,	,	PUNCT
ejpam-6415	1	74	united	united	PROPN
ejpam-6415	1	75	states	states	PROPN
ejpam-6415	1	76	2	2	NUM
ejpam-6415	1	77	school	school	NOUN
ejpam-6415	1	78	of	of	ADP
ejpam-6415	1	79	mathematical	mathematical	ADJ
ejpam-6415	1	80	sciences	science	NOUN
ejpam-6415	1	81	,	,	PUNCT
ejpam-6415	1	82	universiti	universiti	PROPN
ejpam-6415	1	83	sains	sain	NOUN
ejpam-6415	1	84	malaysia	malaysia	PROPN
ejpam-6415	1	85	,	,	PUNCT
ejpam-6415	1	86	penang	penang	PROPN
ejpam-6415	1	87	11800	11800	NUM
ejpam-6415	1	88	,	,	PUNCT
ejpam-6415	1	89	malaysia	malaysia	PROPN
ejpam-6415	1	90	abstract	abstract	NOUN
ejpam-6415	1	91	.	.	PUNCT
ejpam-6415	2	1	this	this	DET
ejpam-6415	2	2	paper	paper	NOUN
ejpam-6415	2	3	investigates	investigate	VERB
ejpam-6415	2	4	a	a	DET
ejpam-6415	2	5	general	general	ADJ
ejpam-6415	2	6	subclass	subclass	NOUN
ejpam-6415	2	7	of	of	ADP
ejpam-6415	2	8	analytic	analytic	ADJ
ejpam-6415	2	9	functions	function	NOUN
ejpam-6415	2	10	defined	define	VERB
ejpam-6415	2	11	in	in	ADP
ejpam-6415	2	12	the	the	DET
ejpam-6415	2	13	open	open	ADJ
ejpam-6415	2	14	unit	unit	NOUN
ejpam-6415	2	15	disk	disk	NOUN
ejpam-6415	2	16	involving	involve	VERB
ejpam-6415	2	17	a	a	DET
ejpam-6415	2	18	multiplier	multipli	ADJ
ejpam-6415	2	19	transformation	transformation	NOUN
ejpam-6415	2	20	.	.	PUNCT
ejpam-6415	3	1	employing	employ	VERB
ejpam-6415	3	2	the	the	DET
ejpam-6415	3	3	linear	linear	PROPN
ejpam-6415	3	4	approximation	approximation	NOUN
ejpam-6415	3	5	theorem	theorem	NOUN
ejpam-6415	3	6	,	,	PUNCT
ejpam-6415	3	7	we	we	PRON
ejpam-6415	3	8	present	present	VERB
ejpam-6415	3	9	sharp	sharp	ADJ
ejpam-6415	3	10	coefficient	coefficient	NOUN
ejpam-6415	3	11	estimates	estimate	NOUN
ejpam-6415	3	12	,	,	PUNCT
ejpam-6415	3	13	growth	growth	NOUN
ejpam-6415	3	14	and	and	CCONJ
ejpam-6415	3	15	distortion	distortion	NOUN
ejpam-6415	3	16	results	result	NOUN
ejpam-6415	3	17	,	,	PUNCT
ejpam-6415	3	18	and	and	CCONJ
ejpam-6415	3	19	radii	radii	VERB
ejpam-6415	3	20	for	for	ADP
ejpam-6415	3	21	geometric	geometric	ADJ
ejpam-6415	3	22	properties	property	NOUN
ejpam-6415	3	23	such	such	ADJ
ejpam-6415	3	24	as	as	ADP
ejpam-6415	3	25	close	close	ADJ
ejpam-6415	3	26	-	-	PUNCT
ejpam-6415	3	27	to	to	ADP
ejpam-6415	3	28	-	-	PUNCT
ejpam-6415	3	29	convexity	convexity	NOUN
ejpam-6415	3	30	,	,	PUNCT
ejpam-6415	3	31	starlikeness	starlikeness	NOUN
ejpam-6415	3	32	,	,	PUNCT
ejpam-6415	3	33	and	and	CCONJ
ejpam-6415	3	34	convexity	convexity	NOUN
ejpam-6415	3	35	.	.	PUNCT
ejpam-6415	4	1	our	our	PRON
ejpam-6415	4	2	approach	approach	NOUN
ejpam-6415	4	3	generalizes	generalize	VERB
ejpam-6415	4	4	several	several	ADJ
ejpam-6415	4	5	known	know	VERB
ejpam-6415	4	6	results	result	NOUN
ejpam-6415	4	7	.	.	PUNCT
ejpam-6415	5	1	2020	2020	NUM
ejpam-6415	5	2	mathematics	mathematic	NOUN
ejpam-6415	5	3	subject	subject	NOUN
ejpam-6415	5	4	classifications	classification	NOUN
ejpam-6415	5	5	:	:	PUNCT
ejpam-6415	5	6	30c45	30c45	NUM
ejpam-6415	5	7	key	key	ADJ
ejpam-6415	5	8	words	word	NOUN
ejpam-6415	5	9	and	and	CCONJ
ejpam-6415	5	10	phrases	phrase	NOUN
ejpam-6415	5	11	:	:	PUNCT
ejpam-6415	5	12	analytic	analytic	ADJ
ejpam-6415	5	13	functions	function	NOUN
ejpam-6415	5	14	,	,	PUNCT
ejpam-6415	5	15	linear	linear	ADJ
ejpam-6415	5	16	approximation	approximation	NOUN
ejpam-6415	5	17	,	,	PUNCT
ejpam-6415	5	18	geometric	geometric	ADJ
ejpam-6415	5	19	properties	property	NOUN
ejpam-6415	5	20	,	,	PUNCT
ejpam-6415	5	21	multiplier	multipli	ADJ
ejpam-6415	5	22	transformation	transformation	NOUN
ejpam-6415	5	23	,	,	PUNCT
ejpam-6415	5	24	coefficient	coefficient	NOUN
ejpam-6415	5	25	estimates	estimate	NOUN
ejpam-6415	5	26	,	,	PUNCT
ejpam-6415	5	27	starlikeness	starlikeness	NOUN
ejpam-6415	5	28	1	1	NUM
ejpam-6415	5	29	.	.	PUNCT
ejpam-6415	6	1	introduction	introduction	NOUN
ejpam-6415	6	2	let	let	VERB
ejpam-6415	6	3	u	u	PRON
ejpam-6415	6	4	=	=	PUNCT
ejpam-6415	6	5	{	{	PUNCT
ejpam-6415	6	6	z	z	PROPN
ejpam-6415	6	7	∈	∈	PROPN
ejpam-6415	6	8	c	c	NOUN
ejpam-6415	6	9	:	:	PUNCT
ejpam-6415	6	10	|z|	|z|	NOUN
ejpam-6415	6	11	<	<	X
ejpam-6415	6	12	1	1	NUM
ejpam-6415	6	13	}	}	PUNCT
ejpam-6415	6	14	denote	denote	VERB
ejpam-6415	6	15	the	the	DET
ejpam-6415	6	16	open	open	ADJ
ejpam-6415	6	17	unit	unit	NOUN
ejpam-6415	6	18	disk	disk	NOUN
ejpam-6415	6	19	.	.	PUNCT
ejpam-6415	7	1	define	define	VERB
ejpam-6415	7	2	a	a	PRON
ejpam-6415	7	3	as	as	SCONJ
ejpam-6415	7	4	the	the	DET
ejpam-6415	7	5	class	class	NOUN
ejpam-6415	7	6	of	of	ADP
ejpam-6415	7	7	functions	function	NOUN
ejpam-6415	7	8	analytic	analytic	ADJ
ejpam-6415	7	9	in	in	ADP
ejpam-6415	7	10	u	u	NOUN
ejpam-6415	7	11	with	with	ADP
ejpam-6415	7	12	the	the	DET
ejpam-6415	7	13	normalized	normalize	VERB
ejpam-6415	7	14	form	form	NOUN
ejpam-6415	7	15	f(z	f(z	NOUN
ejpam-6415	7	16	)	)	PUNCT
ejpam-6415	8	1	=	=	SYM
ejpam-6415	9	1	z	z	NOUN
ejpam-6415	10	1	+	+	NOUN
ejpam-6415	10	2	∞∑	∞∑	NUM
ejpam-6415	10	3	n=2	n=2	CCONJ
ejpam-6415	10	4	anz	anz	NOUN
ejpam-6415	10	5	n.	n.	NOUN
ejpam-6415	10	6	(	(	PUNCT
ejpam-6415	10	7	1	1	X
ejpam-6415	10	8	)	)	PUNCT
ejpam-6415	10	9	we	we	PRON
ejpam-6415	10	10	consider	consider	VERB
ejpam-6415	10	11	the	the	DET
ejpam-6415	10	12	subclass	subclass	NOUN
ejpam-6415	10	13	a∗	a∗	PROPN
ejpam-6415	10	14	⊂	⊂	PROPN
ejpam-6415	10	15	a	a	PRON
ejpam-6415	10	16	,	,	PUNCT
ejpam-6415	10	17	consisting	consist	VERB
ejpam-6415	10	18	of	of	ADP
ejpam-6415	10	19	functions	function	NOUN
ejpam-6415	10	20	with	with	ADP
ejpam-6415	10	21	non	non	ADJ
ejpam-6415	10	22	-	-	ADJ
ejpam-6415	10	23	positive	positive	ADJ
ejpam-6415	10	24	taylor	taylor	NOUN
ejpam-6415	10	25	coefficients	coefficient	NOUN
ejpam-6415	10	26	of	of	ADP
ejpam-6415	10	27	the	the	DET
ejpam-6415	10	28	form	form	NOUN
ejpam-6415	10	29	h(z	h(z	NOUN
ejpam-6415	10	30	)	)	PUNCT
ejpam-6415	10	31	=	=	SYM
ejpam-6415	11	1	z	z	NOUN
ejpam-6415	12	1	−	−	ADP
ejpam-6415	12	2	∞∑	∞∑	NUM
ejpam-6415	12	3	n=2	n=2	PRON
ejpam-6415	12	4	cnz	cnz	NOUN
ejpam-6415	12	5	n	n	CCONJ
ejpam-6415	12	6	,	,	PUNCT
ejpam-6415	12	7	cn	cn	X
ejpam-6415	12	8	≥	≥	PROPN
ejpam-6415	12	9	0	0	NUM
ejpam-6415	12	10	.	.	PUNCT
ejpam-6415	13	1	(	(	PUNCT
ejpam-6415	13	2	2	2	X
ejpam-6415	13	3	)	)	PUNCT
ejpam-6415	13	4	cho	cho	NOUN
ejpam-6415	13	5	and	and	CCONJ
ejpam-6415	13	6	srivastava	srivastava	PROPN
ejpam-6415	14	1	[	[	X
ejpam-6415	14	2	1	1	X
ejpam-6415	14	3	]	]	PUNCT
ejpam-6415	14	4	introduced	introduce	VERB
ejpam-6415	14	5	the	the	DET
ejpam-6415	14	6	generalized	generalize	VERB
ejpam-6415	14	7	multiplier	multipli	ADJ
ejpam-6415	14	8	transformation	transformation	NOUN
ejpam-6415	14	9	given	give	VERB
ejpam-6415	14	10	by	by	ADP
ejpam-6415	14	11	t	t	PROPN
ejpam-6415	14	12	r	r	NOUN
ejpam-6415	14	13	ν	ν	NOUN
ejpam-6415	14	14	f(z	f(z	PROPN
ejpam-6415	14	15	)	)	PUNCT
ejpam-6415	15	1	=	=	SYM
ejpam-6415	15	2	z	z	NOUN
ejpam-6415	16	1	+	+	NOUN
ejpam-6415	16	2	∞∑	∞∑	NUM
ejpam-6415	16	3	n=2	n=2	PRON
ejpam-6415	16	4	(	(	PUNCT
ejpam-6415	16	5	n+	n+	ADP
ejpam-6415	16	6	ν	ν	NOUN
ejpam-6415	16	7	1	1	NUM
ejpam-6415	16	8	+	+	CCONJ
ejpam-6415	16	9	ν	ν	NOUN
ejpam-6415	16	10	)	)	PUNCT
ejpam-6415	16	11	r	r	NOUN
ejpam-6415	16	12	cnz	cnz	NOUN
ejpam-6415	16	13	n	n	ADP
ejpam-6415	16	14	,	,	PUNCT
ejpam-6415	16	15	r	r	PROPN
ejpam-6415	16	16	∈	∈	PROPN
ejpam-6415	16	17	n0	n0	PROPN
ejpam-6415	16	18	,	,	PUNCT
ejpam-6415	16	19	ν	ν	X
ejpam-6415	16	20	≥	≥	NOUN
ejpam-6415	16	21	0	0	NUM
ejpam-6415	16	22	.	.	PUNCT
ejpam-6415	17	1	(	(	PUNCT
ejpam-6415	17	2	3	3	X
ejpam-6415	17	3	)	)	PUNCT
ejpam-6415	17	4	∗corresponding	∗corresponde	VERB
ejpam-6415	17	5	author	author	NOUN
ejpam-6415	17	6	.	.	PUNCT
ejpam-6415	18	1	doi	doi	NOUN
ejpam-6415	18	2	:	:	PUNCT
ejpam-6415	18	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6415	https://doi.org/10.29020/nybg.ejpam.v18i3.6415	NOUN
ejpam-6415	18	4	email	email	NOUN
ejpam-6415	18	5	addresses	address	VERB
ejpam-6415	18	6	:	:	PUNCT
ejpam-6415	18	7	hanshasha0532@student.usm.my	hanshasha0532@student.usm.my	PROPN
ejpam-6415	18	8	(	(	PUNCT
ejpam-6415	18	9	s.	s.	PROPN
ejpam-6415	18	10	han	han	PROPN
ejpam-6415	18	11	)	)	PUNCT
ejpam-6415	18	12	,	,	PUNCT
ejpam-6415	18	13	maisarah	maisarah	PROPN
ejpam-6415	18	14	hjmohd@usm.my	hjmohd@usm.my	X
ejpam-6415	19	1	(	(	PUNCT
ejpam-6415	19	2	m.	m.	NOUN
ejpam-6415	19	3	mohd	mohd	PROPN
ejpam-6415	19	4	)	)	PUNCT
ejpam-6415	19	5	,	,	PUNCT
ejpam-6415	19	6	millafe@navajotech.edu	millafe@navajotech.edu	PROPN
ejpam-6415	19	7	(	(	PUNCT
ejpam-6415	19	8	m.	m.	NOUN
ejpam-6415	19	9	illafe	illafe	NOUN
ejpam-6415	19	10	)	)	PUNCT
ejpam-6415	19	11	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6415	20	1	1	1	NUM
ejpam-6415	20	2	copyright	copyright	NOUN
ejpam-6415	20	3	:	:	PUNCT
ejpam-6415	20	4	©	©	PROPN
ejpam-6415	20	5	2025	2025	NUM
ejpam-6415	20	6	the	the	DET
ejpam-6415	20	7	author(s	author(s	NOUN
ejpam-6415	20	8	)	)	PUNCT
ejpam-6415	20	9	.	.	PUNCT
ejpam-6415	21	1	(	(	PUNCT
ejpam-6415	21	2	cc	cc	NOUN
ejpam-6415	21	3	by	by	ADP
ejpam-6415	21	4	-	-	PUNCT
ejpam-6415	21	5	nc	nc	PROPN
ejpam-6415	21	6	4.0	4.0	NUM
ejpam-6415	21	7	)	)	PUNCT
ejpam-6415	21	8	s.	s.	PROPN
ejpam-6415	21	9	han	han	PROPN
ejpam-6415	21	10	,	,	PUNCT
ejpam-6415	21	11	m.	m.	NOUN
ejpam-6415	21	12	h.	h.	PROPN
ejpam-6415	21	13	mohd	mohd	PROPN
ejpam-6415	21	14	,	,	PUNCT
ejpam-6415	21	15	m.	m.	NOUN
ejpam-6415	21	16	illafe	illafe	ADJ
ejpam-6415	21	17	/	/	SYM
ejpam-6415	21	18	eur	eur	PROPN
ejpam-6415	21	19	.	.	PUNCT
ejpam-6415	22	1	j.	j.	PROPN
ejpam-6415	22	2	pure	pure	PROPN
ejpam-6415	22	3	appl	appl	PROPN
ejpam-6415	22	4	.	.	PROPN
ejpam-6415	22	5	math	math	PROPN
ejpam-6415	22	6	,	,	PUNCT
ejpam-6415	22	7	18	18	NUM
ejpam-6415	22	8	(	(	PUNCT
ejpam-6415	22	9	3	3	NUM
ejpam-6415	22	10	)	)	PUNCT
ejpam-6415	22	11	(	(	PUNCT
ejpam-6415	22	12	2025	2025	NUM
ejpam-6415	22	13	)	)	PUNCT
ejpam-6415	22	14	,	,	PUNCT
ejpam-6415	22	15	6415	6415	NUM
ejpam-6415	22	16	2	2	NUM
ejpam-6415	22	17	of	of	ADP
ejpam-6415	22	18	9	9	NUM
ejpam-6415	22	19	this	this	DET
ejpam-6415	22	20	operator	operator	NOUN
ejpam-6415	22	21	generalizes	generalize	VERB
ejpam-6415	22	22	previous	previous	ADJ
ejpam-6415	22	23	cases	case	NOUN
ejpam-6415	22	24	.	.	PUNCT
ejpam-6415	23	1	for	for	ADP
ejpam-6415	23	2	instance	instance	NOUN
ejpam-6415	23	3	,	,	PUNCT
ejpam-6415	23	4	when	when	SCONJ
ejpam-6415	23	5	ν	ν	X
ejpam-6415	23	6	=	=	SYM
ejpam-6415	23	7	1	1	NUM
ejpam-6415	23	8	,	,	PUNCT
ejpam-6415	23	9	it	it	PRON
ejpam-6415	23	10	corresponds	correspond	VERB
ejpam-6415	23	11	to	to	ADP
ejpam-6415	23	12	the	the	DET
ejpam-6415	23	13	operator	operator	NOUN
ejpam-6415	23	14	studied	study	VERB
ejpam-6415	23	15	by	by	ADP
ejpam-6415	23	16	uralegaddi	uralegaddi	ADJ
ejpam-6415	23	17	and	and	CCONJ
ejpam-6415	23	18	somanatha	somanatha	NOUN
ejpam-6415	24	1	[	[	X
ejpam-6415	24	2	2	2	NUM
ejpam-6415	24	3	]	]	PUNCT
ejpam-6415	24	4	,	,	PUNCT
ejpam-6415	24	5	and	and	CCONJ
ejpam-6415	24	6	for	for	ADP
ejpam-6415	24	7	ν	ν	X
ejpam-6415	24	8	=	=	SYM
ejpam-6415	24	9	0	0	NUM
ejpam-6415	24	10	,	,	PUNCT
ejpam-6415	24	11	it	it	PRON
ejpam-6415	24	12	reduces	reduce	VERB
ejpam-6415	24	13	to	to	ADP
ejpam-6415	24	14	the	the	DET
ejpam-6415	24	15	classical	classical	ADJ
ejpam-6415	24	16	salagean	salagean	ADJ
ejpam-6415	24	17	operator	operator	NOUN
ejpam-6415	24	18	[	[	X
ejpam-6415	24	19	3	3	NUM
ejpam-6415	24	20	]	]	PUNCT
ejpam-6415	24	21	.	.	PUNCT
ejpam-6415	25	1	yousef	yousef	PROPN
ejpam-6415	25	2	et	et	PROPN
ejpam-6415	25	3	al	al	PROPN
ejpam-6415	25	4	.	.	PUNCT
ejpam-6415	26	1	[	[	X
ejpam-6415	26	2	4	4	X
ejpam-6415	26	3	]	]	PUNCT
ejpam-6415	26	4	defined	define	VERB
ejpam-6415	26	5	a	a	DET
ejpam-6415	26	6	general	general	ADJ
ejpam-6415	26	7	class	class	NOUN
ejpam-6415	26	8	of	of	ADP
ejpam-6415	26	9	analytic	analytic	ADJ
ejpam-6415	26	10	and	and	CCONJ
ejpam-6415	26	11	bi	bi	ADJ
ejpam-6415	26	12	-	-	ADJ
ejpam-6415	26	13	univalent	univalent	ADJ
ejpam-6415	26	14	functions	function	NOUN
ejpam-6415	26	15	denoted	denote	VERB
ejpam-6415	26	16	by	by	ADP
ejpam-6415	26	17	bτ	bτ	PROPN
ejpam-6415	26	18	σ(λ	σ(λ	PROPN
ejpam-6415	26	19	,	,	PUNCT
ejpam-6415	26	20	µ	µ	NOUN
ejpam-6415	26	21	,	,	PUNCT
ejpam-6415	26	22	δ;α	δ;α	NUM
ejpam-6415	26	23	)	)	PUNCT
ejpam-6415	26	24	,	,	PUNCT
ejpam-6415	26	25	characterized	characterize	VERB
ejpam-6415	26	26	by	by	ADP
ejpam-6415	26	27	the	the	DET
ejpam-6415	26	28	following	follow	VERB
ejpam-6415	26	29	differential	differential	ADJ
ejpam-6415	26	30	inequality	inequality	NOUN
ejpam-6415	26	31	ℜ	ℜ	PROPN
ejpam-6415	26	32	(	(	PUNCT
ejpam-6415	26	33	1−	1−	NUM
ejpam-6415	26	34	δ	δ	NOUN
ejpam-6415	26	35	)	)	PUNCT
ejpam-6415	26	36	(	(	PUNCT
ejpam-6415	26	37	f(z	f(z	PROPN
ejpam-6415	26	38	)	)	PUNCT
ejpam-6415	26	39	z	z	NOUN
ejpam-6415	26	40	)	)	PUNCT
ejpam-6415	26	41	τ	τ	PROPN
ejpam-6415	27	1	+	+	NUM
ejpam-6415	27	2	δ	δ	PROPN
ejpam-6415	27	3	(	(	PUNCT
ejpam-6415	27	4	f(z))′	f(z))′	PROPN
ejpam-6415	27	5	(	(	PUNCT
ejpam-6415	27	6	f(z	f(z	PROPN
ejpam-6415	27	7	)	)	PUNCT
ejpam-6415	27	8	z	z	NOUN
ejpam-6415	27	9	)	)	PUNCT
ejpam-6415	27	10	τ−1	τ−1	PROPN
ejpam-6415	28	1	+	+	PUNCT
ejpam-6415	28	2	λµz	λµz	PROPN
ejpam-6415	28	3	(	(	PUNCT
ejpam-6415	28	4	f(z))′′	f(z))′′	PROPN
ejpam-6415	28	5	)	)	PUNCT
ejpam-6415	28	6	>	>	X
ejpam-6415	28	7	α	α	X
ejpam-6415	28	8	,	,	PUNCT
ejpam-6415	28	9	(	(	PUNCT
ejpam-6415	28	10	4	4	NUM
ejpam-6415	28	11	)	)	PUNCT
ejpam-6415	28	12	where	where	SCONJ
ejpam-6415	28	13	δ	δ	PROPN
ejpam-6415	28	14	≥	≥	AUX
ejpam-6415	28	15	1	1	NUM
ejpam-6415	28	16	,	,	PUNCT
ejpam-6415	28	17	τ	τ	PROPN
ejpam-6415	28	18	≥	≥	NOUN
ejpam-6415	28	19	0	0	NUM
ejpam-6415	28	20	,	,	PUNCT
ejpam-6415	28	21	µ	µ	X
ejpam-6415	28	22	≥	≥	NOUN
ejpam-6415	28	23	0	0	NUM
ejpam-6415	28	24	,	,	PUNCT
ejpam-6415	28	25	0	0	NUM
ejpam-6415	28	26	≤	≤	NUM
ejpam-6415	28	27	α	α	NOUN
ejpam-6415	28	28	<	<	X
ejpam-6415	28	29	1	1	NUM
ejpam-6415	28	30	,	,	PUNCT
ejpam-6415	28	31	and	and	CCONJ
ejpam-6415	28	32	λ	λ	X
ejpam-6415	28	33	=	=	SYM
ejpam-6415	28	34	2δ+τ	2δ+τ	NUM
ejpam-6415	28	35	2δ+1	2δ+1	PROPN
ejpam-6415	28	36	.	.	PUNCT
ejpam-6415	29	1	this	this	DET
ejpam-6415	29	2	class	class	NOUN
ejpam-6415	29	3	has	have	AUX
ejpam-6415	29	4	been	be	AUX
ejpam-6415	29	5	the	the	DET
ejpam-6415	29	6	focus	focus	NOUN
ejpam-6415	29	7	of	of	ADP
ejpam-6415	29	8	some	some	DET
ejpam-6415	29	9	researchers	researcher	NOUN
ejpam-6415	29	10	in	in	ADP
ejpam-6415	29	11	numerous	numerous	ADJ
ejpam-6415	29	12	studies	study	NOUN
ejpam-6415	29	13	addressing	address	VERB
ejpam-6415	29	14	some	some	DET
ejpam-6415	29	15	bounding	bounding	NOUN
ejpam-6415	29	16	problem	problem	NOUN
ejpam-6415	29	17	such	such	ADJ
ejpam-6415	29	18	as	as	ADP
ejpam-6415	29	19	fekete	fekete	NOUN
ejpam-6415	29	20	-	-	PUNCT
ejpam-6415	29	21	szegö	szegö	PROPN
ejpam-6415	29	22	and	and	CCONJ
ejpam-6415	29	23	the	the	DET
ejpam-6415	29	24	second	second	ADJ
ejpam-6415	29	25	hankel	hankel	NOUN
ejpam-6415	29	26	determinate	determinate	NOUN
ejpam-6415	29	27	(	(	PUNCT
ejpam-6415	29	28	see	see	VERB
ejpam-6415	29	29	[	[	X
ejpam-6415	29	30	5–11	5–11	X
ejpam-6415	29	31	]	]	PUNCT
ejpam-6415	29	32	)	)	PUNCT
ejpam-6415	29	33	.	.	PUNCT
ejpam-6415	30	1	in	in	ADP
ejpam-6415	30	2	the	the	DET
ejpam-6415	30	3	current	current	ADJ
ejpam-6415	30	4	work	work	NOUN
ejpam-6415	30	5	,	,	PUNCT
ejpam-6415	30	6	we	we	PRON
ejpam-6415	30	7	adapt	adapt	VERB
ejpam-6415	30	8	the	the	DET
ejpam-6415	30	9	operator	operator	NOUN
ejpam-6415	30	10	t	t	NOUN
ejpam-6415	30	11	r	r	NOUN
ejpam-6415	30	12	ν	ν	X
ejpam-6415	30	13	h(z	h(z	NOUN
ejpam-6415	30	14	)	)	PUNCT
ejpam-6415	30	15	within	within	ADP
ejpam-6415	30	16	this	this	DET
ejpam-6415	30	17	framework	framework	NOUN
ejpam-6415	30	18	and	and	CCONJ
ejpam-6415	30	19	consider	consider	VERB
ejpam-6415	30	20	its	its	PRON
ejpam-6415	30	21	implications	implication	NOUN
ejpam-6415	30	22	in	in	ADP
ejpam-6415	30	23	analytic	analytic	ADJ
ejpam-6415	30	24	functions	function	NOUN
ejpam-6415	30	25	with	with	ADP
ejpam-6415	30	26	negative	negative	ADJ
ejpam-6415	30	27	coefficients	coefficient	NOUN
ejpam-6415	30	28	.	.	PUNCT
ejpam-6415	31	1	our	our	PRON
ejpam-6415	31	2	goal	goal	NOUN
ejpam-6415	31	3	is	be	AUX
ejpam-6415	31	4	to	to	PART
ejpam-6415	31	5	define	define	VERB
ejpam-6415	31	6	a	a	DET
ejpam-6415	31	7	refined	refined	ADJ
ejpam-6415	31	8	class	class	NOUN
ejpam-6415	31	9	bτ	bτ	NOUN
ejpam-6415	31	10	ν	ν	X
ejpam-6415	31	11	(	(	PUNCT
ejpam-6415	31	12	λ	λ	PROPN
ejpam-6415	31	13	,	,	PUNCT
ejpam-6415	31	14	µ	µ	NOUN
ejpam-6415	31	15	,	,	PUNCT
ejpam-6415	31	16	δ;α	δ;α	PRON
ejpam-6415	31	17	)	)	PUNCT
ejpam-6415	31	18	that	that	PRON
ejpam-6415	31	19	encapsulates	encapsulate	VERB
ejpam-6415	31	20	and	and	CCONJ
ejpam-6415	31	21	extends	extend	VERB
ejpam-6415	31	22	these	these	DET
ejpam-6415	31	23	concepts	concept	NOUN
ejpam-6415	31	24	,	,	PUNCT
ejpam-6415	31	25	forming	form	VERB
ejpam-6415	31	26	the	the	DET
ejpam-6415	31	27	basis	basis	NOUN
ejpam-6415	31	28	for	for	ADP
ejpam-6415	31	29	the	the	DET
ejpam-6415	31	30	investigations	investigation	NOUN
ejpam-6415	31	31	in	in	ADP
ejpam-6415	31	32	the	the	DET
ejpam-6415	31	33	following	follow	VERB
ejpam-6415	31	34	sections	section	NOUN
ejpam-6415	31	35	.	.	PUNCT
ejpam-6415	32	1	definition	definition	NOUN
ejpam-6415	32	2	1	1	NUM
ejpam-6415	32	3	.	.	PUNCT
ejpam-6415	33	1	let	let	VERB
ejpam-6415	33	2	z	z	NOUN
ejpam-6415	33	3	∈	∈	PROPN
ejpam-6415	33	4	u	u	NOUN
ejpam-6415	33	5	,	,	PUNCT
ejpam-6415	33	6	and	and	CCONJ
ejpam-6415	33	7	let	let	VERB
ejpam-6415	33	8	the	the	DET
ejpam-6415	33	9	parameters	parameter	NOUN
ejpam-6415	33	10	satisfy	satisfy	VERB
ejpam-6415	33	11	δ	δ	PROPN
ejpam-6415	33	12	≥	≥	NUM
ejpam-6415	33	13	1	1	NUM
ejpam-6415	33	14	,	,	PUNCT
ejpam-6415	33	15	τ	τ	PROPN
ejpam-6415	33	16	≥	≥	NOUN
ejpam-6415	33	17	0	0	NUM
ejpam-6415	33	18	,	,	PUNCT
ejpam-6415	33	19	µ	µ	X
ejpam-6415	33	20	≥	≥	NOUN
ejpam-6415	33	21	0	0	NUM
ejpam-6415	33	22	,	,	PUNCT
ejpam-6415	33	23	and	and	CCONJ
ejpam-6415	33	24	0	0	NUM
ejpam-6415	33	25	≤	≤	NUM
ejpam-6415	33	26	α	α	NOUN
ejpam-6415	33	27	<	<	X
ejpam-6415	33	28	1	1	NUM
ejpam-6415	33	29	.	.	PUNCT
ejpam-6415	34	1	a	a	DET
ejpam-6415	34	2	function	function	NOUN
ejpam-6415	34	3	f	f	PROPN
ejpam-6415	34	4	∈	∈	PROPN
ejpam-6415	34	5	a	a	DET
ejpam-6415	34	6	given	give	VERB
ejpam-6415	34	7	by	by	ADP
ejpam-6415	34	8	(	(	PUNCT
ejpam-6415	34	9	1	1	NUM
ejpam-6415	34	10	)	)	PUNCT
ejpam-6415	34	11	is	be	AUX
ejpam-6415	34	12	said	say	VERB
ejpam-6415	34	13	to	to	PART
ejpam-6415	34	14	belong	belong	VERB
ejpam-6415	34	15	to	to	ADP
ejpam-6415	34	16	the	the	DET
ejpam-6415	34	17	class	class	NOUN
ejpam-6415	34	18	bν(λ	bν(λ	NOUN
ejpam-6415	34	19	,	,	PUNCT
ejpam-6415	34	20	µ	µ	NOUN
ejpam-6415	34	21	,	,	PUNCT
ejpam-6415	34	22	δ	δ	PROPN
ejpam-6415	34	23	,	,	PUNCT
ejpam-6415	34	24	τ	τ	PROPN
ejpam-6415	34	25	;	;	PUNCT
ejpam-6415	34	26	α	α	X
ejpam-6415	34	27	)	)	PUNCT
ejpam-6415	34	28	if	if	SCONJ
ejpam-6415	34	29	the	the	DET
ejpam-6415	34	30	following	follow	VERB
ejpam-6415	34	31	condition	condition	NOUN
ejpam-6415	34	32	holds	hold	VERB
ejpam-6415	34	33	for	for	ADP
ejpam-6415	34	34	all	all	DET
ejpam-6415	34	35	z	z	NOUN
ejpam-6415	34	36	∈	∈	PROPN
ejpam-6415	34	37	u	u	NOUN
ejpam-6415	34	38	:	:	PUNCT
ejpam-6415	34	39	ℜ	ℜ	X
ejpam-6415	34	40	(	(	PUNCT
ejpam-6415	34	41	(	(	PUNCT
ejpam-6415	34	42	1−	1−	NUM
ejpam-6415	34	43	δ	δ	NOUN
ejpam-6415	34	44	)	)	PUNCT
ejpam-6415	34	45	(	(	PUNCT
ejpam-6415	34	46	t	t	NOUN
ejpam-6415	34	47	r	r	NOUN
ejpam-6415	34	48	ν	ν	X
ejpam-6415	34	49	f(z	f(z	PROPN
ejpam-6415	34	50	)	)	PUNCT
ejpam-6415	34	51	z	z	NOUN
ejpam-6415	34	52	)	)	PUNCT
ejpam-6415	35	1	τ	τ	PROPN
ejpam-6415	36	1	+	+	NUM
ejpam-6415	36	2	δ	δ	PROPN
ejpam-6415	36	3	(	(	PUNCT
ejpam-6415	36	4	t	t	NOUN
ejpam-6415	36	5	r	r	NOUN
ejpam-6415	36	6	ν	ν	NOUN
ejpam-6415	36	7	f(z	f(z	PROPN
ejpam-6415	36	8	)	)	PUNCT
ejpam-6415	36	9	)	)	PUNCT
ejpam-6415	37	1	′	′	NUM
ejpam-6415	38	1	(	(	PUNCT
ejpam-6415	38	2	t	t	NOUN
ejpam-6415	38	3	r	r	NOUN
ejpam-6415	38	4	ν	ν	X
ejpam-6415	38	5	f(z	f(z	PROPN
ejpam-6415	38	6	)	)	PUNCT
ejpam-6415	38	7	z	z	NOUN
ejpam-6415	38	8	)	)	PUNCT
ejpam-6415	38	9	τ−1	τ−1	PROPN
ejpam-6415	39	1	+	+	PUNCT
ejpam-6415	39	2	λµz	λµz	NOUN
ejpam-6415	39	3	(	(	PUNCT
ejpam-6415	39	4	t	t	NOUN
ejpam-6415	39	5	r	r	NOUN
ejpam-6415	39	6	ν	ν	NOUN
ejpam-6415	39	7	f(z	f(z	NOUN
ejpam-6415	39	8	)	)	PUNCT
ejpam-6415	39	9	)	)	PUNCT
ejpam-6415	40	1	′′	′′	PROPN
ejpam-6415	40	2	)	)	PUNCT
ejpam-6415	40	3	>	>	X
ejpam-6415	41	1	α	α	X
ejpam-6415	41	2	,	,	PUNCT
ejpam-6415	41	3	(	(	PUNCT
ejpam-6415	41	4	5	5	NUM
ejpam-6415	41	5	)	)	PUNCT
ejpam-6415	41	6	where	where	SCONJ
ejpam-6415	41	7	λ	λ	PROPN
ejpam-6415	41	8	=	=	SYM
ejpam-6415	41	9	2δ+τ	2δ+τ	NUM
ejpam-6415	41	10	2δ+1	2δ+1	PROPN
ejpam-6415	41	11	.	.	PUNCT
ejpam-6415	42	1	in	in	ADP
ejpam-6415	42	2	this	this	DET
ejpam-6415	42	3	paper	paper	NOUN
ejpam-6415	42	4	,	,	PUNCT
ejpam-6415	42	5	we	we	PRON
ejpam-6415	42	6	are	be	AUX
ejpam-6415	42	7	generalizing	generalize	VERB
ejpam-6415	42	8	the	the	DET
ejpam-6415	42	9	work	work	NOUN
ejpam-6415	42	10	that	that	PRON
ejpam-6415	42	11	illafe	illafe	NOUN
ejpam-6415	42	12	has	have	AUX
ejpam-6415	42	13	done	do	VERB
ejpam-6415	42	14	et	et	PROPN
ejpam-6415	42	15	al	al	PROPN
ejpam-6415	42	16	.	.	PUNCT
ejpam-6415	43	1	in	in	ADP
ejpam-6415	43	2	[	[	X
ejpam-6415	43	3	12	12	NUM
ejpam-6415	43	4	,	,	PUNCT
ejpam-6415	43	5	13	13	NUM
ejpam-6415	43	6	]	]	PUNCT
ejpam-6415	43	7	by	by	ADP
ejpam-6415	43	8	considering	consider	VERB
ejpam-6415	43	9	not	not	PART
ejpam-6415	43	10	to	to	PART
ejpam-6415	43	11	eliminate	eliminate	VERB
ejpam-6415	43	12	the	the	DET
ejpam-6415	43	13	parameter	parameter	NOUN
ejpam-6415	43	14	τ	τ	PROPN
ejpam-6415	43	15	.	.	PUNCT
ejpam-6415	44	1	furthermore	furthermore	ADV
ejpam-6415	44	2	,	,	PUNCT
ejpam-6415	44	3	let	let	VERB
ejpam-6415	44	4	b∗	b∗	ADJ
ejpam-6415	44	5	ν(λ	ν(λ	NOUN
ejpam-6415	44	6	,	,	PUNCT
ejpam-6415	44	7	µ	µ	NOUN
ejpam-6415	44	8	,	,	PUNCT
ejpam-6415	44	9	δ	δ	PROPN
ejpam-6415	44	10	,	,	PUNCT
ejpam-6415	44	11	τ	τ	PROPN
ejpam-6415	44	12	;	;	PUNCT
ejpam-6415	44	13	α	α	X
ejpam-6415	44	14	)	)	PUNCT
ejpam-6415	44	15	=	=	NOUN
ejpam-6415	44	16	bν(λ	bν(λ	NOUN
ejpam-6415	44	17	,	,	PUNCT
ejpam-6415	44	18	µ	µ	NOUN
ejpam-6415	44	19	,	,	PUNCT
ejpam-6415	44	20	δ	δ	PROPN
ejpam-6415	44	21	,	,	PUNCT
ejpam-6415	44	22	τ	τ	PROPN
ejpam-6415	44	23	;	;	PUNCT
ejpam-6415	44	24	α	α	X
ejpam-6415	44	25	)	)	PUNCT
ejpam-6415	44	26	∩	∩	NOUN
ejpam-6415	44	27	a∗.	a∗.	NOUN
ejpam-6415	44	28	lemma	lemma	PROPN
ejpam-6415	44	29	1	1	NUM
ejpam-6415	44	30	.	.	PUNCT
ejpam-6415	45	1	[	[	X
ejpam-6415	45	2	14	14	NUM
ejpam-6415	45	3	]	]	PUNCT
ejpam-6415	45	4	let	let	VERB
ejpam-6415	45	5	f(x	f(x	PROPN
ejpam-6415	45	6	)	)	PUNCT
ejpam-6415	45	7	be	be	AUX
ejpam-6415	45	8	a	a	DET
ejpam-6415	45	9	real	real	ADV
ejpam-6415	45	10	-	-	PUNCT
ejpam-6415	45	11	valued	value	VERB
ejpam-6415	45	12	function	function	NOUN
ejpam-6415	46	1	such	such	ADJ
ejpam-6415	46	2	that	that	SCONJ
ejpam-6415	46	3	|f(x)|	|f(x)|	NOUN
ejpam-6415	46	4	≪	≪	ADJ
ejpam-6415	46	5	1	1	NUM
ejpam-6415	46	6	,	,	PUNCT
ejpam-6415	46	7	and	and	CCONJ
ejpam-6415	46	8	let	let	VERB
ejpam-6415	46	9	n	n	PRON
ejpam-6415	46	10	∈	∈	PROPN
ejpam-6415	46	11	r.	r.	PROPN
ejpam-6415	46	12	then	then	ADV
ejpam-6415	46	13	,	,	PUNCT
ejpam-6415	46	14	the	the	DET
ejpam-6415	46	15	following	follow	VERB
ejpam-6415	46	16	linear	linear	ADJ
ejpam-6415	46	17	approximation	approximation	NOUN
ejpam-6415	46	18	holds	hold	VERB
ejpam-6415	46	19	(	(	PUNCT
ejpam-6415	46	20	1	1	NUM
ejpam-6415	46	21	+	+	X
ejpam-6415	46	22	f(x))n	f(x))n	PROPN
ejpam-6415	46	23	≈	≈	PROPN
ejpam-6415	46	24	1	1	NUM
ejpam-6415	46	25	+	+	NOUN
ejpam-6415	46	26	nf(x	nf(x	NOUN
ejpam-6415	46	27	)	)	PUNCT
ejpam-6415	46	28	up	up	ADP
ejpam-6415	46	29	to	to	ADP
ejpam-6415	46	30	first	first	ADJ
ejpam-6415	46	31	order	order	NOUN
ejpam-6415	46	32	in	in	ADP
ejpam-6415	46	33	f(x	f(x	PROPN
ejpam-6415	46	34	)	)	PUNCT
ejpam-6415	46	35	.	.	PUNCT
ejpam-6415	47	1	2	2	X
ejpam-6415	47	2	.	.	X
ejpam-6415	47	3	coefficient	coefficient	NOUN
ejpam-6415	47	4	bounds	bound	NOUN
ejpam-6415	47	5	and	and	CCONJ
ejpam-6415	47	6	characterization	characterization	NOUN
ejpam-6415	47	7	we	we	PRON
ejpam-6415	47	8	begin	begin	VERB
ejpam-6415	47	9	this	this	DET
ejpam-6415	47	10	section	section	NOUN
ejpam-6415	47	11	by	by	ADP
ejpam-6415	47	12	establishing	establish	VERB
ejpam-6415	47	13	a	a	DET
ejpam-6415	47	14	characterization	characterization	NOUN
ejpam-6415	47	15	result	result	NOUN
ejpam-6415	47	16	that	that	PRON
ejpam-6415	47	17	provides	provide	VERB
ejpam-6415	47	18	the	the	DET
ejpam-6415	47	19	necessary	necessary	ADJ
ejpam-6415	47	20	and	and	CCONJ
ejpam-6415	47	21	sufficient	sufficient	ADJ
ejpam-6415	47	22	conditions	condition	NOUN
ejpam-6415	47	23	for	for	ADP
ejpam-6415	47	24	a	a	DET
ejpam-6415	47	25	function	function	NOUN
ejpam-6415	47	26	to	to	PART
ejpam-6415	47	27	belong	belong	VERB
ejpam-6415	47	28	to	to	ADP
ejpam-6415	47	29	the	the	DET
ejpam-6415	47	30	class	class	NOUN
ejpam-6415	47	31	b∗	b∗	ADJ
ejpam-6415	47	32	ν(λ	ν(λ	NOUN
ejpam-6415	47	33	,	,	PUNCT
ejpam-6415	47	34	µ	µ	NOUN
ejpam-6415	47	35	,	,	PUNCT
ejpam-6415	47	36	δ	δ	PROPN
ejpam-6415	47	37	,	,	PUNCT
ejpam-6415	47	38	τ	τ	PROPN
ejpam-6415	47	39	;	;	PUNCT
ejpam-6415	47	40	α	α	X
ejpam-6415	47	41	)	)	PUNCT
ejpam-6415	47	42	.	.	PUNCT
ejpam-6415	48	1	we	we	PRON
ejpam-6415	48	2	begin	begin	VERB
ejpam-6415	48	3	this	this	DET
ejpam-6415	48	4	section	section	NOUN
ejpam-6415	48	5	by	by	ADP
ejpam-6415	48	6	establishing	establish	VERB
ejpam-6415	48	7	a	a	DET
ejpam-6415	48	8	characterization	characterization	NOUN
ejpam-6415	48	9	result	result	NOUN
ejpam-6415	48	10	that	that	PRON
ejpam-6415	48	11	provides	provide	VERB
ejpam-6415	48	12	the	the	DET
ejpam-6415	48	13	necessary	necessary	ADJ
ejpam-6415	48	14	and	and	CCONJ
ejpam-6415	48	15	sufficient	sufficient	ADJ
ejpam-6415	48	16	conditions	condition	NOUN
ejpam-6415	48	17	for	for	ADP
ejpam-6415	48	18	a	a	DET
ejpam-6415	48	19	function	function	NOUN
ejpam-6415	48	20	to	to	PART
ejpam-6415	48	21	belong	belong	VERB
ejpam-6415	48	22	to	to	ADP
ejpam-6415	48	23	the	the	DET
ejpam-6415	48	24	class	class	NOUN
ejpam-6415	48	25	b∗	b∗	ADJ
ejpam-6415	48	26	ν(λ	ν(λ	NOUN
ejpam-6415	48	27	,	,	PUNCT
ejpam-6415	48	28	µ	µ	NOUN
ejpam-6415	48	29	,	,	PUNCT
ejpam-6415	48	30	δ	δ	PROPN
ejpam-6415	48	31	,	,	PUNCT
ejpam-6415	48	32	τ	τ	PROPN
ejpam-6415	48	33	;	;	PUNCT
ejpam-6415	48	34	α	α	X
ejpam-6415	48	35	)	)	PUNCT
ejpam-6415	48	36	.	.	PUNCT
ejpam-6415	49	1	s.	s.	PROPN
ejpam-6415	49	2	han	han	PROPN
ejpam-6415	49	3	,	,	PUNCT
ejpam-6415	49	4	m.	m.	NOUN
ejpam-6415	49	5	h.	h.	PROPN
ejpam-6415	49	6	mohd	mohd	PROPN
ejpam-6415	49	7	,	,	PUNCT
ejpam-6415	49	8	m.	m.	NOUN
ejpam-6415	49	9	illafe	illafe	ADJ
ejpam-6415	49	10	/	/	SYM
ejpam-6415	49	11	eur	eur	PROPN
ejpam-6415	49	12	.	.	PUNCT
ejpam-6415	50	1	j.	j.	PROPN
ejpam-6415	50	2	pure	pure	PROPN
ejpam-6415	50	3	appl	appl	PROPN
ejpam-6415	50	4	.	.	PROPN
ejpam-6415	50	5	math	math	PROPN
ejpam-6415	50	6	,	,	PUNCT
ejpam-6415	50	7	18	18	NUM
ejpam-6415	50	8	(	(	PUNCT
ejpam-6415	50	9	3	3	NUM
ejpam-6415	50	10	)	)	PUNCT
ejpam-6415	50	11	(	(	PUNCT
ejpam-6415	50	12	2025	2025	NUM
ejpam-6415	50	13	)	)	PUNCT
ejpam-6415	50	14	,	,	PUNCT
ejpam-6415	50	15	6415	6415	NUM
ejpam-6415	50	16	3	3	NUM
ejpam-6415	50	17	of	of	ADP
ejpam-6415	50	18	9	9	NUM
ejpam-6415	50	19	theorem	theorem	NOUN
ejpam-6415	50	20	1	1	NUM
ejpam-6415	50	21	.	.	PUNCT
ejpam-6415	51	1	let	let	VERB
ejpam-6415	51	2	h	h	PRON
ejpam-6415	51	3	∈	∈	PROPN
ejpam-6415	51	4	a∗	a∗	PROPN
ejpam-6415	51	5	be	be	AUX
ejpam-6415	51	6	defined	define	VERB
ejpam-6415	51	7	by	by	ADP
ejpam-6415	51	8	the	the	DET
ejpam-6415	51	9	expansion	expansion	NOUN
ejpam-6415	51	10	h(z	h(z	NOUN
ejpam-6415	51	11	)	)	PUNCT
ejpam-6415	51	12	=	=	SYM
ejpam-6415	52	1	z	z	NOUN
ejpam-6415	53	1	−	−	ADP
ejpam-6415	53	2	∞∑	∞∑	NUM
ejpam-6415	53	3	n=2	n=2	PRON
ejpam-6415	53	4	cnz	cnz	NOUN
ejpam-6415	53	5	n.	n.	NOUN
ejpam-6415	53	6	then	then	ADV
ejpam-6415	53	7	h	h	NOUN
ejpam-6415	53	8	belongs	belong	VERB
ejpam-6415	53	9	to	to	ADP
ejpam-6415	53	10	the	the	DET
ejpam-6415	53	11	class	class	NOUN
ejpam-6415	53	12	b∗	b∗	ADJ
ejpam-6415	53	13	ν(λ	ν(λ	NOUN
ejpam-6415	53	14	,	,	PUNCT
ejpam-6415	53	15	µ	µ	NOUN
ejpam-6415	53	16	,	,	PUNCT
ejpam-6415	53	17	δ	δ	PROPN
ejpam-6415	53	18	,	,	PUNCT
ejpam-6415	53	19	τ	τ	PROPN
ejpam-6415	53	20	;	;	PUNCT
ejpam-6415	53	21	α	α	X
ejpam-6415	53	22	)	)	PUNCT
ejpam-6415	53	23	if	if	SCONJ
ejpam-6415	53	24	and	and	CCONJ
ejpam-6415	53	25	only	only	ADV
ejpam-6415	53	26	if	if	SCONJ
ejpam-6415	53	27	it	it	PRON
ejpam-6415	53	28	satisfies	satisfy	VERB
ejpam-6415	53	29	the	the	DET
ejpam-6415	53	30	condition	condition	NOUN
ejpam-6415	53	31	:	:	PUNCT
ejpam-6415	53	32	∞∑	∞∑	NUM
ejpam-6415	53	33	n=2	n=2	PRON
ejpam-6415	53	34	[	[	PUNCT
ejpam-6415	53	35	(	(	PUNCT
ejpam-6415	53	36	τ	τ	PROPN
ejpam-6415	53	37	−	−	PROPN
ejpam-6415	53	38	δ	δ	PROPN
ejpam-6415	53	39	+	+	CCONJ
ejpam-6415	53	40	nδ	nδ	PROPN
ejpam-6415	53	41	+	+	CCONJ
ejpam-6415	53	42	λµn(n−	λµn(n−	X
ejpam-6415	53	43	1	1	NUM
ejpam-6415	53	44	)	)	PUNCT
ejpam-6415	53	45	]	]	PUNCT
ejpam-6415	53	46	(	(	PUNCT
ejpam-6415	53	47	n+	n+	ADP
ejpam-6415	53	48	ν	ν	NOUN
ejpam-6415	53	49	1	1	NUM
ejpam-6415	53	50	+	+	CCONJ
ejpam-6415	53	51	ν	ν	NOUN
ejpam-6415	53	52	)	)	PUNCT
ejpam-6415	54	1	r	r	NOUN
ejpam-6415	54	2	cn	cn	NOUN
ejpam-6415	54	3	≤	≤	PROPN
ejpam-6415	54	4	1−	1−	NUM
ejpam-6415	54	5	α	α	NOUN
ejpam-6415	54	6	.	.	PUNCT
ejpam-6415	55	1	(	(	PUNCT
ejpam-6415	55	2	6	6	NUM
ejpam-6415	55	3	)	)	PUNCT
ejpam-6415	55	4	proof	proof	NOUN
ejpam-6415	55	5	.	.	PUNCT
ejpam-6415	56	1	from	from	ADP
ejpam-6415	56	2	the	the	DET
ejpam-6415	56	3	class	class	NOUN
ejpam-6415	56	4	condition	condition	NOUN
ejpam-6415	56	5	(	(	PUNCT
ejpam-6415	56	6	5	5	NUM
ejpam-6415	56	7	)	)	PUNCT
ejpam-6415	56	8	and	and	CCONJ
ejpam-6415	56	9	applying	apply	VERB
ejpam-6415	56	10	lemma	lemma	PROPN
ejpam-6415	56	11	1	1	NUM
ejpam-6415	56	12	,	,	PUNCT
ejpam-6415	56	13	we	we	PRON
ejpam-6415	56	14	can	can	AUX
ejpam-6415	56	15	write	write	VERB
ejpam-6415	56	16	ℜ	ℜ	PROPN
ejpam-6415	56	17	{	{	PUNCT
ejpam-6415	56	18	(	(	PUNCT
ejpam-6415	56	19	1−	1−	NUM
ejpam-6415	56	20	δ	δ	NOUN
ejpam-6415	56	21	)	)	PUNCT
ejpam-6415	56	22	(	(	PUNCT
ejpam-6415	56	23	t	t	NOUN
ejpam-6415	56	24	r	r	NOUN
ejpam-6415	56	25	ν	ν	X
ejpam-6415	56	26	h(z	h(z	NOUN
ejpam-6415	56	27	)	)	PUNCT
ejpam-6415	56	28	z	z	NOUN
ejpam-6415	56	29	)	)	PUNCT
ejpam-6415	56	30	τ	τ	PROPN
ejpam-6415	57	1	+	+	NUM
ejpam-6415	57	2	δ	δ	PROPN
ejpam-6415	57	3	(	(	PUNCT
ejpam-6415	57	4	t	t	NOUN
ejpam-6415	57	5	r	r	NOUN
ejpam-6415	57	6	ν	ν	X
ejpam-6415	57	7	h(z	h(z	NOUN
ejpam-6415	57	8	)	)	PUNCT
ejpam-6415	57	9	)	)	PUNCT
ejpam-6415	58	1	′	′	NUM
ejpam-6415	59	1	(	(	PUNCT
ejpam-6415	59	2	t	t	NOUN
ejpam-6415	59	3	r	r	NOUN
ejpam-6415	59	4	ν	ν	X
ejpam-6415	59	5	h(z	h(z	NOUN
ejpam-6415	59	6	)	)	PUNCT
ejpam-6415	59	7	z	z	NOUN
ejpam-6415	59	8	)	)	PUNCT
ejpam-6415	59	9	τ−1	τ−1	PROPN
ejpam-6415	60	1	+	+	PUNCT
ejpam-6415	60	2	λµz(t	λµz(t	PROPN
ejpam-6415	60	3	r	r	NOUN
ejpam-6415	60	4	ν	ν	X
ejpam-6415	60	5	h(z	h(z	NOUN
ejpam-6415	60	6	)	)	PUNCT
ejpam-6415	60	7	)	)	PUNCT
ejpam-6415	61	1	′′	′′	NOUN
ejpam-6415	61	2	}	}	PUNCT
ejpam-6415	61	3	=	=	SYM
ejpam-6415	61	4	ℜ	ℜ	PROPN
ejpam-6415	61	5	{	{	PUNCT
ejpam-6415	61	6	1	1	NUM
ejpam-6415	61	7	+	+	NUM
ejpam-6415	61	8	∞∑	∞∑	NUM
ejpam-6415	61	9	n=2	n=2	PRON
ejpam-6415	62	1	[	[	X
ejpam-6415	62	2	τ	τ	X
ejpam-6415	62	3	−	−	PROPN
ejpam-6415	62	4	δ	δ	PROPN
ejpam-6415	62	5	+	+	CCONJ
ejpam-6415	62	6	nδ	nδ	PROPN
ejpam-6415	62	7	+	+	CCONJ
ejpam-6415	62	8	λµn(n−	λµn(n−	X
ejpam-6415	62	9	1	1	NUM
ejpam-6415	62	10	)	)	PUNCT
ejpam-6415	62	11	]	]	PUNCT
ejpam-6415	63	1	(	(	PUNCT
ejpam-6415	63	2	n+	n+	ADP
ejpam-6415	63	3	ν	ν	NOUN
ejpam-6415	63	4	1	1	NUM
ejpam-6415	63	5	+	+	CCONJ
ejpam-6415	63	6	ν	ν	NOUN
ejpam-6415	63	7	)	)	PUNCT
ejpam-6415	63	8	r	r	NOUN
ejpam-6415	63	9	cnz	cnz	NOUN
ejpam-6415	63	10	n−1	n−1	PROPN
ejpam-6415	63	11	}	}	PUNCT
ejpam-6415	63	12	>	>	X
ejpam-6415	64	1	α	α	X
ejpam-6415	64	2	.	.	PUNCT
ejpam-6415	65	1	taking	take	VERB
ejpam-6415	65	2	the	the	DET
ejpam-6415	65	3	limit	limit	NOUN
ejpam-6415	65	4	as	as	ADP
ejpam-6415	65	5	z	z	PROPN
ejpam-6415	65	6	→	→	SYM
ejpam-6415	65	7	1−	1−	NUM
ejpam-6415	65	8	along	along	ADP
ejpam-6415	65	9	the	the	DET
ejpam-6415	65	10	real	real	ADJ
ejpam-6415	65	11	axis	axis	NOUN
ejpam-6415	65	12	yields	yield	VERB
ejpam-6415	65	13	the	the	DET
ejpam-6415	65	14	validity	validity	NOUN
ejpam-6415	65	15	of	of	ADP
ejpam-6415	65	16	inequality	inequality	NOUN
ejpam-6415	65	17	(	(	PUNCT
ejpam-6415	65	18	6	6	NUM
ejpam-6415	65	19	)	)	PUNCT
ejpam-6415	65	20	.	.	PUNCT
ejpam-6415	66	1	on	on	ADP
ejpam-6415	66	2	the	the	DET
ejpam-6415	66	3	other	other	ADJ
ejpam-6415	66	4	hand	hand	NOUN
ejpam-6415	66	5	,	,	PUNCT
ejpam-6415	66	6	assume	assume	VERB
ejpam-6415	66	7	inequality	inequality	NOUN
ejpam-6415	66	8	(	(	PUNCT
ejpam-6415	66	9	6	6	NUM
ejpam-6415	66	10	)	)	PUNCT
ejpam-6415	66	11	holds	hold	VERB
ejpam-6415	66	12	,	,	PUNCT
ejpam-6415	66	13	to	to	PART
ejpam-6415	66	14	prove	prove	VERB
ejpam-6415	66	15	h	h	NOUN
ejpam-6415	66	16	belongs	belong	VERB
ejpam-6415	66	17	to	to	ADP
ejpam-6415	66	18	class	class	NOUN
ejpam-6415	66	19	b∗	b∗	ADJ
ejpam-6415	66	20	ν(λ	ν(λ	NOUN
ejpam-6415	66	21	,	,	PUNCT
ejpam-6415	66	22	µ	µ	NOUN
ejpam-6415	66	23	,	,	PUNCT
ejpam-6415	66	24	δ	δ	PROPN
ejpam-6415	66	25	,	,	PUNCT
ejpam-6415	66	26	τ	τ	PROPN
ejpam-6415	66	27	;	;	PUNCT
ejpam-6415	66	28	α	α	X
ejpam-6415	66	29	)	)	PUNCT
ejpam-6415	66	30	,	,	PUNCT
ejpam-6415	66	31	we	we	PRON
ejpam-6415	66	32	need	need	VERB
ejpam-6415	66	33	to	to	PART
ejpam-6415	66	34	show	show	VERB
ejpam-6415	66	35	that	that	SCONJ
ejpam-6415	66	36	for	for	ADP
ejpam-6415	66	37	every	every	DET
ejpam-6415	66	38	z	z	NOUN
ejpam-6415	66	39	∈	∈	PROPN
ejpam-6415	66	40	u	u	NOUN
ejpam-6415	66	41	that	that	PRON
ejpam-6415	66	42	∣∣∣∣∣(1−	∣∣∣∣∣(1−	PROPN
ejpam-6415	66	43	δ	δ	PROPN
ejpam-6415	66	44	)	)	PUNCT
ejpam-6415	66	45	(	(	PUNCT
ejpam-6415	66	46	t	t	NOUN
ejpam-6415	66	47	r	r	NOUN
ejpam-6415	66	48	ν	ν	X
ejpam-6415	66	49	h(z	h(z	NOUN
ejpam-6415	66	50	)	)	PUNCT
ejpam-6415	66	51	z	z	NOUN
ejpam-6415	66	52	)	)	PUNCT
ejpam-6415	66	53	τ	τ	PROPN
ejpam-6415	67	1	+	+	NUM
ejpam-6415	67	2	δ	δ	PROPN
ejpam-6415	67	3	(	(	PUNCT
ejpam-6415	67	4	t	t	NOUN
ejpam-6415	67	5	r	r	NOUN
ejpam-6415	67	6	ν	ν	X
ejpam-6415	67	7	h(z	h(z	NOUN
ejpam-6415	67	8	)	)	PUNCT
ejpam-6415	67	9	)	)	PUNCT
ejpam-6415	68	1	′	′	NUM
ejpam-6415	69	1	(	(	PUNCT
ejpam-6415	69	2	t	t	NOUN
ejpam-6415	69	3	r	r	NOUN
ejpam-6415	69	4	ν	ν	X
ejpam-6415	69	5	h(z	h(z	NOUN
ejpam-6415	69	6	)	)	PUNCT
ejpam-6415	69	7	z	z	NOUN
ejpam-6415	69	8	)	)	PUNCT
ejpam-6415	69	9	τ−1	τ−1	PROPN
ejpam-6415	70	1	+	+	PUNCT
ejpam-6415	70	2	λµz	λµz	NOUN
ejpam-6415	70	3	(	(	PUNCT
ejpam-6415	70	4	t	t	NOUN
ejpam-6415	70	5	r	r	NOUN
ejpam-6415	70	6	ν	ν	X
ejpam-6415	70	7	h(z	h(z	NOUN
ejpam-6415	70	8	)	)	PUNCT
ejpam-6415	70	9	)	)	PUNCT
ejpam-6415	71	1	′′	′′	PROPN
ejpam-6415	71	2	−	−	NOUN
ejpam-6415	71	3	1	1	NUM
ejpam-6415	71	4	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6415	71	5	=	=	SYM
ejpam-6415	72	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6415	72	2	∞∑	∞∑	NUM
ejpam-6415	72	3	n=2	n=2	PUNCT
ejpam-6415	72	4	(	(	PUNCT
ejpam-6415	72	5	τ	τ	PROPN
ejpam-6415	72	6	−	−	PROPN
ejpam-6415	72	7	δ	δ	PROPN
ejpam-6415	72	8	+	+	CCONJ
ejpam-6415	72	9	nδ	nδ	PROPN
ejpam-6415	72	10	+	+	CCONJ
ejpam-6415	72	11	λµn(n−	λµn(n−	X
ejpam-6415	72	12	1	1	NUM
ejpam-6415	72	13	)	)	PUNCT
ejpam-6415	72	14	)	)	PUNCT
ejpam-6415	73	1	(	(	PUNCT
ejpam-6415	73	2	n+	n+	ADP
ejpam-6415	73	3	ν	ν	NOUN
ejpam-6415	73	4	1	1	NUM
ejpam-6415	73	5	+	+	CCONJ
ejpam-6415	73	6	ν	ν	NOUN
ejpam-6415	73	7	)	)	PUNCT
ejpam-6415	73	8	r	r	NOUN
ejpam-6415	73	9	cnz	cnz	NOUN
ejpam-6415	73	10	n−1	n−1	PROPN
ejpam-6415	73	11	∣∣∣∣∣	∣∣∣∣∣	NOUN
ejpam-6415	73	12	≤	≤	NOUN
ejpam-6415	74	1	∞∑	∞∑	NUM
ejpam-6415	74	2	n=2	n=2	PRON
ejpam-6415	74	3	(	(	PUNCT
ejpam-6415	74	4	τ	τ	PROPN
ejpam-6415	74	5	−	−	PROPN
ejpam-6415	74	6	δ	δ	PROPN
ejpam-6415	74	7	+	+	CCONJ
ejpam-6415	74	8	nδ	nδ	PROPN
ejpam-6415	74	9	+	+	CCONJ
ejpam-6415	74	10	λµn(n−	λµn(n−	X
ejpam-6415	74	11	1	1	NUM
ejpam-6415	74	12	)	)	PUNCT
ejpam-6415	74	13	)	)	PUNCT
ejpam-6415	74	14	(	(	PUNCT
ejpam-6415	74	15	n+	n+	ADP
ejpam-6415	74	16	ν	ν	NOUN
ejpam-6415	74	17	1	1	NUM
ejpam-6415	74	18	+	+	CCONJ
ejpam-6415	74	19	ν	ν	NOUN
ejpam-6415	74	20	)	)	PUNCT
ejpam-6415	74	21	r	r	NOUN
ejpam-6415	74	22	cn|z|n−1	cn|z|n−1	NUM
ejpam-6415	74	23	≤	≤	NOUN
ejpam-6415	74	24	∞∑	∞∑	NUM
ejpam-6415	74	25	n=2	n=2	PRON
ejpam-6415	74	26	(	(	PUNCT
ejpam-6415	74	27	τ	τ	PROPN
ejpam-6415	74	28	−	−	PROPN
ejpam-6415	74	29	δ	δ	PROPN
ejpam-6415	74	30	+	+	CCONJ
ejpam-6415	74	31	nδ	nδ	PROPN
ejpam-6415	74	32	+	+	CCONJ
ejpam-6415	74	33	λµn(n−	λµn(n−	X
ejpam-6415	74	34	1	1	NUM
ejpam-6415	74	35	)	)	PUNCT
ejpam-6415	74	36	)	)	PUNCT
ejpam-6415	74	37	(	(	PUNCT
ejpam-6415	74	38	n+	n+	ADP
ejpam-6415	74	39	ν	ν	NOUN
ejpam-6415	74	40	1	1	NUM
ejpam-6415	74	41	+	+	CCONJ
ejpam-6415	74	42	ν	ν	NOUN
ejpam-6415	74	43	)	)	PUNCT
ejpam-6415	74	44	r	r	NOUN
ejpam-6415	74	45	cn	cn	NOUN
ejpam-6415	74	46	≤	≤	PROPN
ejpam-6415	74	47	1−	1−	NUM
ejpam-6415	74	48	α	α	NOUN
ejpam-6415	74	49	.	.	PUNCT
ejpam-6415	75	1	this	this	PRON
ejpam-6415	75	2	completes	complete	VERB
ejpam-6415	75	3	the	the	DET
ejpam-6415	75	4	proof	proof	NOUN
ejpam-6415	75	5	.	.	PUNCT
ejpam-6415	76	1	corollary	corollary	ADJ
ejpam-6415	76	2	1	1	NUM
ejpam-6415	76	3	.	.	PUNCT
ejpam-6415	76	4	suppose	suppose	VERB
ejpam-6415	76	5	h(z	h(z	NOUN
ejpam-6415	76	6	)	)	PUNCT
ejpam-6415	76	7	,	,	PUNCT
ejpam-6415	76	8	as	as	SCONJ
ejpam-6415	76	9	defined	define	VERB
ejpam-6415	76	10	in	in	ADP
ejpam-6415	76	11	equation	equation	NOUN
ejpam-6415	76	12	(	(	PUNCT
ejpam-6415	76	13	2	2	NUM
ejpam-6415	76	14	)	)	PUNCT
ejpam-6415	76	15	,	,	PUNCT
ejpam-6415	76	16	belongs	belong	VERB
ejpam-6415	76	17	to	to	ADP
ejpam-6415	76	18	the	the	DET
ejpam-6415	76	19	class	class	NOUN
ejpam-6415	76	20	b∗	b∗	ADJ
ejpam-6415	76	21	ν(λ	ν(λ	NOUN
ejpam-6415	76	22	,	,	PUNCT
ejpam-6415	76	23	µ	µ	NOUN
ejpam-6415	76	24	,	,	PUNCT
ejpam-6415	76	25	δ	δ	PROPN
ejpam-6415	76	26	,	,	PUNCT
ejpam-6415	76	27	τ	τ	PROPN
ejpam-6415	76	28	;	;	PUNCT
ejpam-6415	76	29	α	α	X
ejpam-6415	76	30	)	)	PUNCT
ejpam-6415	76	31	.	.	PUNCT
ejpam-6415	77	1	then	then	ADV
ejpam-6415	77	2	cn	cn	PROPN
ejpam-6415	77	3	≤	≤	PROPN
ejpam-6415	77	4	1−	1−	NUM
ejpam-6415	78	1	α	α	PRON
ejpam-6415	79	1	[	[	X
ejpam-6415	79	2	τ	τ	X
ejpam-6415	79	3	−	−	PROPN
ejpam-6415	79	4	δ	δ	PROPN
ejpam-6415	79	5	+	+	CCONJ
ejpam-6415	79	6	nδ	nδ	PROPN
ejpam-6415	79	7	+	+	CCONJ
ejpam-6415	79	8	λµn(n−	λµn(n−	X
ejpam-6415	79	9	1	1	NUM
ejpam-6415	79	10	)	)	PUNCT
ejpam-6415	79	11	]	]	PUNCT
ejpam-6415	80	1	(	(	PUNCT
ejpam-6415	80	2	n+ν	n+ν	NUM
ejpam-6415	80	3	1+ν	1+ν	NUM
ejpam-6415	80	4	)	)	PUNCT
ejpam-6415	80	5	r	r	NOUN
ejpam-6415	80	6	,	,	PUNCT
ejpam-6415	80	7	n	n	CCONJ
ejpam-6415	80	8	≥	≥	NOUN
ejpam-6415	80	9	2	2	NUM
ejpam-6415	80	10	.	.	PUNCT
ejpam-6415	81	1	(	(	PUNCT
ejpam-6415	81	2	7	7	X
ejpam-6415	81	3	)	)	PUNCT
ejpam-6415	81	4	the	the	DET
ejpam-6415	81	5	bound	bound	ADJ
ejpam-6415	81	6	(	(	PUNCT
ejpam-6415	81	7	7	7	NUM
ejpam-6415	81	8	)	)	PUNCT
ejpam-6415	81	9	is	be	AUX
ejpam-6415	81	10	sharp	sharp	ADJ
ejpam-6415	81	11	and	and	CCONJ
ejpam-6415	81	12	attained	attain	VERB
ejpam-6415	81	13	by	by	ADP
ejpam-6415	81	14	the	the	DET
ejpam-6415	81	15	function	function	NOUN
ejpam-6415	81	16	h(z	h(z	NOUN
ejpam-6415	81	17	)	)	PUNCT
ejpam-6415	81	18	=	=	SYM
ejpam-6415	82	1	z	z	NOUN
ejpam-6415	83	1	−	−	PROPN
ejpam-6415	83	2	1−	1−	NUM
ejpam-6415	83	3	α	α	PRON
ejpam-6415	84	1	[	[	X
ejpam-6415	84	2	τ	τ	X
ejpam-6415	84	3	−	−	PROPN
ejpam-6415	84	4	δ	δ	PROPN
ejpam-6415	84	5	+	+	CCONJ
ejpam-6415	84	6	nδ	nδ	PROPN
ejpam-6415	84	7	+	+	CCONJ
ejpam-6415	84	8	λµn(n−	λµn(n−	X
ejpam-6415	84	9	1	1	NUM
ejpam-6415	84	10	)	)	PUNCT
ejpam-6415	84	11	]	]	PUNCT
ejpam-6415	85	1	(	(	PUNCT
ejpam-6415	85	2	n+ν	n+ν	NUM
ejpam-6415	85	3	1+ν	1+ν	NUM
ejpam-6415	85	4	)	)	PUNCT
ejpam-6415	85	5	r	r	NOUN
ejpam-6415	85	6	zn	zn	PROPN
ejpam-6415	85	7	.	.	PUNCT
ejpam-6415	85	8	s.	s.	PROPN
ejpam-6415	85	9	han	han	PROPN
ejpam-6415	85	10	,	,	PUNCT
ejpam-6415	85	11	m.	m.	NOUN
ejpam-6415	85	12	h.	h.	PROPN
ejpam-6415	85	13	mohd	mohd	PROPN
ejpam-6415	85	14	,	,	PUNCT
ejpam-6415	85	15	m.	m.	NOUN
ejpam-6415	85	16	illafe	illafe	ADJ
ejpam-6415	85	17	/	/	SYM
ejpam-6415	85	18	eur	eur	PROPN
ejpam-6415	85	19	.	.	PUNCT
ejpam-6415	86	1	j.	j.	PROPN
ejpam-6415	86	2	pure	pure	PROPN
ejpam-6415	86	3	appl	appl	PROPN
ejpam-6415	86	4	.	.	PROPN
ejpam-6415	86	5	math	math	PROPN
ejpam-6415	86	6	,	,	PUNCT
ejpam-6415	86	7	18	18	NUM
ejpam-6415	86	8	(	(	PUNCT
ejpam-6415	86	9	3	3	NUM
ejpam-6415	86	10	)	)	PUNCT
ejpam-6415	86	11	(	(	PUNCT
ejpam-6415	86	12	2025	2025	NUM
ejpam-6415	86	13	)	)	PUNCT
ejpam-6415	86	14	,	,	PUNCT
ejpam-6415	86	15	6415	6415	NUM
ejpam-6415	86	16	4	4	NUM
ejpam-6415	86	17	of	of	ADP
ejpam-6415	86	18	9	9	NUM
ejpam-6415	86	19	3	3	NUM
ejpam-6415	86	20	.	.	PUNCT
ejpam-6415	87	1	growth	growth	NOUN
ejpam-6415	87	2	and	and	CCONJ
ejpam-6415	87	3	distortion	distortion	NOUN
ejpam-6415	87	4	theorems	theorem	NOUN
ejpam-6415	87	5	in	in	ADP
ejpam-6415	87	6	this	this	DET
ejpam-6415	87	7	section	section	NOUN
ejpam-6415	87	8	,	,	PUNCT
ejpam-6415	87	9	we	we	PRON
ejpam-6415	87	10	obtain	obtain	VERB
ejpam-6415	87	11	upper	upper	ADJ
ejpam-6415	87	12	and	and	CCONJ
ejpam-6415	87	13	lower	low	ADJ
ejpam-6415	87	14	bounds	bound	NOUN
ejpam-6415	87	15	for	for	ADP
ejpam-6415	87	16	|h(z)|	|h(z)|	NOUN
ejpam-6415	87	17	and	and	CCONJ
ejpam-6415	87	18	|h′(z)|	|h′(z)|	NUM
ejpam-6415	87	19	when	when	SCONJ
ejpam-6415	87	20	h	h	NOUN
ejpam-6415	87	21	belongs	belong	VERB
ejpam-6415	87	22	to	to	ADP
ejpam-6415	87	23	the	the	DET
ejpam-6415	87	24	class	class	NOUN
ejpam-6415	87	25	b∗	b∗	ADJ
ejpam-6415	87	26	ν(λ	ν(λ	NOUN
ejpam-6415	87	27	,	,	PUNCT
ejpam-6415	87	28	µ	µ	NOUN
ejpam-6415	87	29	,	,	PUNCT
ejpam-6415	87	30	δ	δ	PROPN
ejpam-6415	87	31	,	,	PUNCT
ejpam-6415	87	32	τ	τ	PROPN
ejpam-6415	87	33	;	;	PUNCT
ejpam-6415	87	34	α	α	X
ejpam-6415	87	35	)	)	PUNCT
ejpam-6415	87	36	.	.	PUNCT
ejpam-6415	88	1	theorem	theorem	NOUN
ejpam-6415	88	2	2	2	NUM
ejpam-6415	88	3	.	.	PUNCT
ejpam-6415	88	4	let	let	VERB
ejpam-6415	88	5	h(z	h(z	NOUN
ejpam-6415	88	6	)	)	PUNCT
ejpam-6415	88	7	=	=	SYM
ejpam-6415	88	8	z	z	NOUN
ejpam-6415	88	9	−	−	NOUN
ejpam-6415	88	10	∑∞	∑∞	NOUN
ejpam-6415	88	11	n=2	n=2	PRON
ejpam-6415	88	12	cnz	cnz	NOUN
ejpam-6415	88	13	n	n	PRON
ejpam-6415	88	14	be	be	AUX
ejpam-6415	88	15	in	in	ADP
ejpam-6415	88	16	the	the	DET
ejpam-6415	88	17	class	class	NOUN
ejpam-6415	88	18	b∗	b∗	ADJ
ejpam-6415	88	19	ν(λ	ν(λ	NOUN
ejpam-6415	88	20	,	,	PUNCT
ejpam-6415	88	21	µ	µ	NOUN
ejpam-6415	88	22	,	,	PUNCT
ejpam-6415	88	23	δ	δ	PROPN
ejpam-6415	88	24	,	,	PUNCT
ejpam-6415	88	25	τ	τ	PROPN
ejpam-6415	88	26	;	;	PUNCT
ejpam-6415	88	27	α	α	X
ejpam-6415	88	28	)	)	PUNCT
ejpam-6415	88	29	.	.	PUNCT
ejpam-6415	89	1	then	then	ADV
ejpam-6415	89	2	,	,	PUNCT
ejpam-6415	89	3	for	for	ADP
ejpam-6415	89	4	|z|	|z|	NOUN
ejpam-6415	89	5	=	=	SYM
ejpam-6415	89	6	t	t	X
ejpam-6415	89	7	<	<	X
ejpam-6415	89	8	1	1	NUM
ejpam-6415	89	9	,	,	PUNCT
ejpam-6415	89	10	the	the	DET
ejpam-6415	89	11	following	follow	VERB
ejpam-6415	89	12	bounds	bound	NOUN
ejpam-6415	89	13	hold	hold	VERB
ejpam-6415	89	14	|h(z)|	|h(z)|	NOUN
ejpam-6415	89	15	∈	∈	PROPN
ejpam-6415	89	16	[	[	PUNCT
ejpam-6415	89	17	t−at2	t−at2	PROPN
ejpam-6415	89	18	,	,	PUNCT
ejpam-6415	89	19	t+at2	t+at2	X
ejpam-6415	89	20	]	]	PUNCT
ejpam-6415	89	21	,	,	PUNCT
ejpam-6415	89	22	(	(	PUNCT
ejpam-6415	89	23	8)	8)	NUM
ejpam-6415	89	24	where	where	SCONJ
ejpam-6415	89	25	a	a	DET
ejpam-6415	89	26	=	=	SYM
ejpam-6415	89	27	1−	1−	NUM
ejpam-6415	89	28	α	α	NOUN
ejpam-6415	89	29	(	(	PUNCT
ejpam-6415	89	30	τ	τ	PROPN
ejpam-6415	89	31	+	+	CCONJ
ejpam-6415	89	32	δ	δ	PROPN
ejpam-6415	89	33	+	+	CCONJ
ejpam-6415	89	34	2λµ)(2+ν	2λµ)(2+ν	NUM
ejpam-6415	89	35	1+ν	1+ν	NUM
ejpam-6415	89	36	)	)	PUNCT
ejpam-6415	90	1	r	r	NOUN
ejpam-6415	90	2	.	.	PUNCT
ejpam-6415	91	1	the	the	DET
ejpam-6415	91	2	bound	bind	VERB
ejpam-6415	91	3	given	give	VERB
ejpam-6415	91	4	by	by	ADP
ejpam-6415	91	5	inequality	inequality	NOUN
ejpam-6415	91	6	(	(	PUNCT
ejpam-6415	91	7	8)	8)	NUM
ejpam-6415	91	8	is	be	AUX
ejpam-6415	91	9	sharp	sharp	ADJ
ejpam-6415	91	10	,	,	PUNCT
ejpam-6415	91	11	and	and	CCONJ
ejpam-6415	91	12	equality	equality	NOUN
ejpam-6415	91	13	is	be	AUX
ejpam-6415	91	14	attained	attain	VERB
ejpam-6415	91	15	for	for	ADP
ejpam-6415	91	16	the	the	DET
ejpam-6415	91	17	function	function	NOUN
ejpam-6415	91	18	f(z	f(z	PROPN
ejpam-6415	91	19	)	)	PUNCT
ejpam-6415	92	1	=	=	SYM
ejpam-6415	92	2	z	z	NOUN
ejpam-6415	92	3	−az2	−az2	PROPN
ejpam-6415	92	4	.	.	PUNCT
ejpam-6415	92	5	proof	proof	NOUN
ejpam-6415	92	6	.	.	PUNCT
ejpam-6415	93	1	let	let	VERB
ejpam-6415	93	2	h(z	h(z	NOUN
ejpam-6415	93	3	)	)	PUNCT
ejpam-6415	93	4	∈	∈	NOUN
ejpam-6415	93	5	b∗	b∗	ADJ
ejpam-6415	93	6	ν(λ	ν(λ	NOUN
ejpam-6415	93	7	,	,	PUNCT
ejpam-6415	93	8	µ	µ	NOUN
ejpam-6415	93	9	,	,	PUNCT
ejpam-6415	93	10	δ	δ	PROPN
ejpam-6415	93	11	,	,	PUNCT
ejpam-6415	93	12	τ	τ	PROPN
ejpam-6415	93	13	;	;	PUNCT
ejpam-6415	93	14	α	α	X
ejpam-6415	93	15	)	)	PUNCT
ejpam-6415	93	16	be	be	AUX
ejpam-6415	93	17	defined	define	VERB
ejpam-6415	93	18	by	by	ADP
ejpam-6415	93	19	(	(	PUNCT
ejpam-6415	93	20	2	2	NUM
ejpam-6415	93	21	)	)	PUNCT
ejpam-6415	93	22	.	.	PUNCT
ejpam-6415	94	1	assume	assume	VERB
ejpam-6415	94	2	|z|	|z|	NOUN
ejpam-6415	94	3	=	=	SYM
ejpam-6415	94	4	t	t	X
ejpam-6415	94	5	<	<	X
ejpam-6415	94	6	1	1	NUM
ejpam-6415	94	7	.	.	PUNCT
ejpam-6415	95	1	then	then	ADV
ejpam-6415	95	2	,	,	PUNCT
ejpam-6415	95	3	|h(z)|	|h(z)|	ADP
ejpam-6415	95	4	≤	≤	NOUN
ejpam-6415	95	5	|z|+	|z|+	NOUN
ejpam-6415	95	6	∞∑	∞∑	NUM
ejpam-6415	95	7	n=2	n=2	ADV
ejpam-6415	95	8	cn|z|n	cn|z|n	NOUN
ejpam-6415	95	9	≤	≤	NOUN
ejpam-6415	95	10	t+	t+	PUNCT
ejpam-6415	95	11	t2	t2	NOUN
ejpam-6415	95	12	∞∑	∞∑	PROPN
ejpam-6415	95	13	n=2	n=2	X
ejpam-6415	95	14	cn	cn	PROPN
ejpam-6415	95	15	.	.	PUNCT
ejpam-6415	96	1	then	then	ADV
ejpam-6415	96	2	,	,	PUNCT
ejpam-6415	96	3	∞∑	∞∑	NUM
ejpam-6415	96	4	n=2	n=2	PRON
ejpam-6415	97	1	[	[	X
ejpam-6415	97	2	τ	τ	X
ejpam-6415	97	3	−	−	PROPN
ejpam-6415	97	4	δ	δ	PROPN
ejpam-6415	97	5	+	+	CCONJ
ejpam-6415	97	6	nδ	nδ	PROPN
ejpam-6415	97	7	+	+	CCONJ
ejpam-6415	97	8	λµn(n−	λµn(n−	X
ejpam-6415	97	9	1	1	NUM
ejpam-6415	97	10	)	)	PUNCT
ejpam-6415	97	11	]	]	PUNCT
ejpam-6415	98	1	(	(	PUNCT
ejpam-6415	98	2	n+	n+	ADP
ejpam-6415	98	3	ν	ν	NOUN
ejpam-6415	98	4	1	1	NUM
ejpam-6415	98	5	+	+	CCONJ
ejpam-6415	98	6	ν	ν	NOUN
ejpam-6415	98	7	)	)	PUNCT
ejpam-6415	98	8	r	r	NOUN
ejpam-6415	98	9	cn	cn	NOUN
ejpam-6415	98	10	≤	≤	NOUN
ejpam-6415	98	11	1−	1−	NUM
ejpam-6415	98	12	α	α	NOUN
ejpam-6415	98	13	equivalently	equivalently	ADV
ejpam-6415	98	14	,	,	PUNCT
ejpam-6415	98	15	∞∑	∞∑	PROPN
ejpam-6415	98	16	n=2	n=2	ADV
ejpam-6415	98	17	cn	cn	VERB
ejpam-6415	98	18	≤	≤	NOUN
ejpam-6415	98	19	1−	1−	NUM
ejpam-6415	98	20	α	α	NOUN
ejpam-6415	99	1	[	[	X
ejpam-6415	99	2	τ	τ	X
ejpam-6415	99	3	−	−	PROPN
ejpam-6415	99	4	δ	δ	PROPN
ejpam-6415	99	5	+	+	CCONJ
ejpam-6415	99	6	nδ	nδ	PROPN
ejpam-6415	99	7	+	+	CCONJ
ejpam-6415	99	8	λµn(n+	λµn(n+	PROPN
ejpam-6415	99	9	1	1	NUM
ejpam-6415	99	10	)	)	PUNCT
ejpam-6415	99	11	]	]	PUNCT
ejpam-6415	100	1	(	(	PUNCT
ejpam-6415	100	2	n+ν	n+ν	NUM
ejpam-6415	100	3	1+ν	1+ν	NUM
ejpam-6415	100	4	)	)	PUNCT
ejpam-6415	100	5	r	r	NOUN
ejpam-6415	100	6	≤	≤	NOUN
ejpam-6415	100	7	1−	1−	NUM
ejpam-6415	100	8	α	α	NOUN
ejpam-6415	100	9	(	(	PUNCT
ejpam-6415	100	10	τ	τ	PROPN
ejpam-6415	100	11	+	+	CCONJ
ejpam-6415	100	12	δ	δ	PROPN
ejpam-6415	100	13	+	+	CCONJ
ejpam-6415	100	14	2λµ	2λµ	NOUN
ejpam-6415	100	15	)	)	PUNCT
ejpam-6415	100	16	(	(	PUNCT
ejpam-6415	100	17	2+ν	2+ν	NUM
ejpam-6415	100	18	1+ν	1+ν	NUM
ejpam-6415	100	19	)	)	PUNCT
ejpam-6415	100	20	r	r	NOUN
ejpam-6415	100	21	.	.	PUNCT
ejpam-6415	101	1	hence	hence	ADV
ejpam-6415	101	2	,	,	PUNCT
ejpam-6415	101	3	|h(z)|	|h(z)|	ADP
ejpam-6415	101	4	≤	≤	NUM
ejpam-6415	101	5	t+	t+	PUNCT
ejpam-6415	101	6	1−	1−	NUM
ejpam-6415	101	7	α	α	NOUN
ejpam-6415	101	8	(	(	PUNCT
ejpam-6415	101	9	τ	τ	PROPN
ejpam-6415	101	10	+	+	CCONJ
ejpam-6415	101	11	δ	δ	PROPN
ejpam-6415	101	12	+	+	CCONJ
ejpam-6415	101	13	2λµ	2λµ	NOUN
ejpam-6415	101	14	)	)	PUNCT
ejpam-6415	101	15	(	(	PUNCT
ejpam-6415	101	16	2+ν	2+ν	NUM
ejpam-6415	101	17	1+ν	1+ν	NUM
ejpam-6415	101	18	)	)	PUNCT
ejpam-6415	101	19	r	r	NOUN
ejpam-6415	101	20	t2	t2	NOUN
ejpam-6415	101	21	similarly	similarly	ADV
ejpam-6415	101	22	,	,	PUNCT
ejpam-6415	101	23	we	we	PRON
ejpam-6415	101	24	can	can	AUX
ejpam-6415	101	25	apply	apply	VERB
ejpam-6415	101	26	the	the	DET
ejpam-6415	101	27	same	same	ADJ
ejpam-6415	101	28	argument	argument	NOUN
ejpam-6415	101	29	for	for	SCONJ
ejpam-6415	101	30	the	the	DET
ejpam-6415	101	31	lower	lower	ADV
ejpam-6415	101	32	bound	bind	VERB
ejpam-6415	101	33	|h(z)|	|h(z)|	NOUN
ejpam-6415	101	34	≥	≥	NOUN
ejpam-6415	101	35	|z|	|z|	VERB
ejpam-6415	101	36	−	−	ADP
ejpam-6415	101	37	∞∑	∞∑	NUM
ejpam-6415	101	38	n=2	n=2	PRON
ejpam-6415	101	39	cn|z|n	cn|z|n	NOUN
ejpam-6415	101	40	≥	≥	NOUN
ejpam-6415	101	41	t−	t−	PROPN
ejpam-6415	101	42	1−	1−	NUM
ejpam-6415	101	43	α	α	NOUN
ejpam-6415	101	44	(	(	PUNCT
ejpam-6415	101	45	τ	τ	PROPN
ejpam-6415	101	46	+	+	CCONJ
ejpam-6415	101	47	δ	δ	PROPN
ejpam-6415	101	48	+	+	CCONJ
ejpam-6415	101	49	2λµ	2λµ	NOUN
ejpam-6415	101	50	)	)	PUNCT
ejpam-6415	101	51	(	(	PUNCT
ejpam-6415	101	52	2+ν	2+ν	NUM
ejpam-6415	101	53	1+ν	1+ν	NUM
ejpam-6415	101	54	)	)	PUNCT
ejpam-6415	101	55	r	r	NOUN
ejpam-6415	101	56	t2	t2	NOUN
ejpam-6415	101	57	.	.	PUNCT
ejpam-6415	102	1	therefore	therefore	ADV
ejpam-6415	102	2	,	,	PUNCT
ejpam-6415	102	3	the	the	DET
ejpam-6415	102	4	estimate	estimate	NOUN
ejpam-6415	102	5	in	in	ADP
ejpam-6415	102	6	theorem	theorem	ADJ
ejpam-6415	102	7	2	2	NUM
ejpam-6415	102	8	follows	follow	VERB
ejpam-6415	102	9	.	.	PUNCT
ejpam-6415	103	1	s.	s.	PROPN
ejpam-6415	103	2	han	han	PROPN
ejpam-6415	103	3	,	,	PUNCT
ejpam-6415	103	4	m.	m.	NOUN
ejpam-6415	103	5	h.	h.	PROPN
ejpam-6415	103	6	mohd	mohd	PROPN
ejpam-6415	103	7	,	,	PUNCT
ejpam-6415	103	8	m.	m.	NOUN
ejpam-6415	103	9	illafe	illafe	ADJ
ejpam-6415	103	10	/	/	SYM
ejpam-6415	103	11	eur	eur	PROPN
ejpam-6415	103	12	.	.	PUNCT
ejpam-6415	104	1	j.	j.	PROPN
ejpam-6415	104	2	pure	pure	PROPN
ejpam-6415	104	3	appl	appl	PROPN
ejpam-6415	104	4	.	.	PROPN
ejpam-6415	104	5	math	math	PROPN
ejpam-6415	104	6	,	,	PUNCT
ejpam-6415	104	7	18	18	NUM
ejpam-6415	104	8	(	(	PUNCT
ejpam-6415	104	9	3	3	NUM
ejpam-6415	104	10	)	)	PUNCT
ejpam-6415	104	11	(	(	PUNCT
ejpam-6415	104	12	2025	2025	NUM
ejpam-6415	104	13	)	)	PUNCT
ejpam-6415	104	14	,	,	PUNCT
ejpam-6415	104	15	6415	6415	NUM
ejpam-6415	104	16	5	5	NUM
ejpam-6415	104	17	of	of	ADP
ejpam-6415	104	18	9	9	NUM
ejpam-6415	104	19	theorem	theorem	NOUN
ejpam-6415	104	20	3	3	NUM
ejpam-6415	104	21	.	.	PUNCT
ejpam-6415	104	22	let	let	VERB
ejpam-6415	104	23	h(z	h(z	NOUN
ejpam-6415	104	24	)	)	PUNCT
ejpam-6415	104	25	be	be	AUX
ejpam-6415	104	26	in	in	ADP
ejpam-6415	104	27	the	the	DET
ejpam-6415	104	28	class	class	NOUN
ejpam-6415	104	29	b∗	b∗	ADJ
ejpam-6415	104	30	ν(λ	ν(λ	NOUN
ejpam-6415	104	31	,	,	PUNCT
ejpam-6415	104	32	µ	µ	NOUN
ejpam-6415	104	33	,	,	PUNCT
ejpam-6415	104	34	δ	δ	PROPN
ejpam-6415	104	35	,	,	PUNCT
ejpam-6415	104	36	τ	τ	PROPN
ejpam-6415	104	37	;	;	PUNCT
ejpam-6415	104	38	α	α	X
ejpam-6415	104	39	)	)	PUNCT
ejpam-6415	104	40	.	.	PUNCT
ejpam-6415	105	1	then	then	ADV
ejpam-6415	105	2	,	,	PUNCT
ejpam-6415	105	3	for	for	ADP
ejpam-6415	105	4	|z|	|z|	NOUN
ejpam-6415	105	5	=	=	SYM
ejpam-6415	105	6	t	t	X
ejpam-6415	105	7	<	<	X
ejpam-6415	105	8	1	1	NUM
ejpam-6415	105	9	,	,	PUNCT
ejpam-6415	105	10	the	the	DET
ejpam-6415	105	11	h′(z	h′(z	NOUN
ejpam-6415	105	12	)	)	PUNCT
ejpam-6415	105	13	satisfies	satisfy	VERB
ejpam-6415	105	14	the	the	DET
ejpam-6415	105	15	inequality	inequality	NOUN
ejpam-6415	105	16	1−bt	1−bt	NUM
ejpam-6415	105	17	≤	≤	NOUN
ejpam-6415	105	18	|h′(z)|	|h′(z)|	PRON
ejpam-6415	105	19	≤	≤	NUM
ejpam-6415	105	20	1	1	NUM
ejpam-6415	106	1	+	+	NOUN
ejpam-6415	106	2	bt	bt	ADJ
ejpam-6415	106	3	,	,	PUNCT
ejpam-6415	106	4	(	(	PUNCT
ejpam-6415	106	5	9	9	NUM
ejpam-6415	106	6	)	)	PUNCT
ejpam-6415	106	7	where	where	SCONJ
ejpam-6415	106	8	b	b	NOUN
ejpam-6415	106	9	=	=	SYM
ejpam-6415	106	10	2(1−	2(1−	NUM
ejpam-6415	106	11	α	α	X
ejpam-6415	106	12	)	)	PUNCT
ejpam-6415	106	13	(	(	PUNCT
ejpam-6415	106	14	τ	τ	X
ejpam-6415	106	15	+	+	CCONJ
ejpam-6415	106	16	δ	δ	PROPN
ejpam-6415	106	17	+	+	CCONJ
ejpam-6415	106	18	2λµ	2λµ	NOUN
ejpam-6415	106	19	)	)	PUNCT
ejpam-6415	106	20	(	(	PUNCT
ejpam-6415	106	21	2+ν	2+ν	NUM
ejpam-6415	106	22	1+ν	1+ν	NUM
ejpam-6415	106	23	)	)	PUNCT
ejpam-6415	106	24	r	r	NOUN
ejpam-6415	106	25	.	.	PUNCT
ejpam-6415	107	1	the	the	DET
ejpam-6415	107	2	bounds	bound	NOUN
ejpam-6415	107	3	are	be	AUX
ejpam-6415	107	4	sharp	sharp	ADJ
ejpam-6415	107	5	,	,	PUNCT
ejpam-6415	107	6	and	and	CCONJ
ejpam-6415	107	7	equality	equality	NOUN
ejpam-6415	107	8	in	in	ADP
ejpam-6415	107	9	(	(	PUNCT
ejpam-6415	107	10	9	9	NUM
ejpam-6415	107	11	)	)	PUNCT
ejpam-6415	107	12	is	be	AUX
ejpam-6415	107	13	attained	attain	VERB
ejpam-6415	107	14	by	by	ADP
ejpam-6415	107	15	the	the	DET
ejpam-6415	107	16	function	function	NOUN
ejpam-6415	107	17	h(z	h(z	NOUN
ejpam-6415	107	18	)	)	PUNCT
ejpam-6415	107	19	=	=	SYM
ejpam-6415	108	1	z	z	NOUN
ejpam-6415	109	1	−	−	PROPN
ejpam-6415	109	2	1−	1−	NUM
ejpam-6415	109	3	α	α	NOUN
ejpam-6415	109	4	(	(	PUNCT
ejpam-6415	109	5	τ	τ	PROPN
ejpam-6415	109	6	+	+	CCONJ
ejpam-6415	109	7	δ	δ	PROPN
ejpam-6415	109	8	+	+	CCONJ
ejpam-6415	109	9	2λµ	2λµ	NOUN
ejpam-6415	109	10	)	)	PUNCT
ejpam-6415	109	11	(	(	PUNCT
ejpam-6415	109	12	2+ν	2+ν	NUM
ejpam-6415	109	13	1+ν	1+ν	NUM
ejpam-6415	109	14	)	)	PUNCT
ejpam-6415	109	15	r	r	NOUN
ejpam-6415	109	16	z2	z2	PROPN
ejpam-6415	109	17	.	.	PUNCT
ejpam-6415	110	1	proof	proof	NOUN
ejpam-6415	110	2	.	.	PUNCT
ejpam-6415	111	1	a	a	DET
ejpam-6415	111	2	similar	similar	ADJ
ejpam-6415	111	3	argument	argument	NOUN
ejpam-6415	111	4	as	as	ADP
ejpam-6415	111	5	in	in	ADP
ejpam-6415	111	6	the	the	DET
ejpam-6415	111	7	proof	proof	NOUN
ejpam-6415	111	8	of	of	ADP
ejpam-6415	111	9	theorem	theorem	ADJ
ejpam-6415	111	10	3.1	3.1	NUM
ejpam-6415	111	11	can	can	AUX
ejpam-6415	111	12	be	be	AUX
ejpam-6415	111	13	applied	apply	VERB
ejpam-6415	111	14	here	here	ADV
ejpam-6415	111	15	by	by	ADP
ejpam-6415	111	16	considering	consider	VERB
ejpam-6415	111	17	the	the	DET
ejpam-6415	111	18	derivative	derivative	NOUN
ejpam-6415	111	19	of	of	ADP
ejpam-6415	111	20	f	f	PROPN
ejpam-6415	111	21	.	.	PUNCT
ejpam-6415	112	1	4	4	X
ejpam-6415	112	2	.	.	X
ejpam-6415	112	3	closure	closure	NOUN
ejpam-6415	112	4	properties	property	NOUN
ejpam-6415	112	5	in	in	ADP
ejpam-6415	112	6	this	this	DET
ejpam-6415	112	7	section	section	NOUN
ejpam-6415	112	8	,	,	PUNCT
ejpam-6415	112	9	we	we	PRON
ejpam-6415	112	10	establish	establish	VERB
ejpam-6415	112	11	that	that	SCONJ
ejpam-6415	112	12	the	the	DET
ejpam-6415	112	13	class	class	NOUN
ejpam-6415	112	14	b∗	b∗	ADJ
ejpam-6415	112	15	ν(λ	ν(λ	NOUN
ejpam-6415	112	16	,	,	PUNCT
ejpam-6415	112	17	µ	µ	NOUN
ejpam-6415	112	18	,	,	PUNCT
ejpam-6415	112	19	δ	δ	PROPN
ejpam-6415	112	20	,	,	PUNCT
ejpam-6415	112	21	τ	τ	PROPN
ejpam-6415	112	22	;	;	PUNCT
ejpam-6415	112	23	α	α	X
ejpam-6415	112	24	)	)	PUNCT
ejpam-6415	112	25	is	be	AUX
ejpam-6415	112	26	closed	close	VERB
ejpam-6415	112	27	under	under	ADP
ejpam-6415	112	28	convex	convex	NOUN
ejpam-6415	112	29	combinations	combination	NOUN
ejpam-6415	112	30	and	and	CCONJ
ejpam-6415	112	31	averaging	averaging	NOUN
ejpam-6415	112	32	.	.	PUNCT
ejpam-6415	113	1	this	this	PRON
ejpam-6415	113	2	follows	follow	VERB
ejpam-6415	113	3	naturally	naturally	ADV
ejpam-6415	113	4	from	from	ADP
ejpam-6415	113	5	the	the	DET
ejpam-6415	113	6	linearity	linearity	NOUN
ejpam-6415	113	7	of	of	ADP
ejpam-6415	113	8	the	the	DET
ejpam-6415	113	9	operator	operator	NOUN
ejpam-6415	113	10	t	t	NOUN
ejpam-6415	113	11	r	r	NOUN
ejpam-6415	113	12	ν	ν	X
ejpam-6415	113	13	h(z	h(z	NOUN
ejpam-6415	113	14	)	)	PUNCT
ejpam-6415	113	15	and	and	CCONJ
ejpam-6415	113	16	the	the	DET
ejpam-6415	113	17	sub	sub	ADJ
ejpam-6415	113	18	-	-	ADJ
ejpam-6415	113	19	additive	additive	ADJ
ejpam-6415	113	20	behavior	behavior	NOUN
ejpam-6415	113	21	of	of	ADP
ejpam-6415	113	22	the	the	DET
ejpam-6415	113	23	defining	define	VERB
ejpam-6415	113	24	inequality	inequality	NOUN
ejpam-6415	113	25	.	.	PUNCT
ejpam-6415	114	1	theorem	theorem	ADJ
ejpam-6415	114	2	4	4	NUM
ejpam-6415	114	3	.	.	PUNCT
ejpam-6415	114	4	let	let	VERB
ejpam-6415	114	5	hj(z	hj(z	NOUN
ejpam-6415	114	6	)	)	PUNCT
ejpam-6415	114	7	=	=	SYM
ejpam-6415	114	8	z	z	NOUN
ejpam-6415	114	9	−	−	NOUN
ejpam-6415	114	10	∑∞	∑∞	NOUN
ejpam-6415	114	11	n=2	n=2	X
ejpam-6415	114	12	cnjz	cnjz	VERB
ejpam-6415	114	13	n	n	PRON
ejpam-6415	114	14	∈	∈	NOUN
ejpam-6415	114	15	b∗	b∗	ADJ
ejpam-6415	114	16	ν(λ	ν(λ	NOUN
ejpam-6415	114	17	,	,	PUNCT
ejpam-6415	114	18	µ	µ	NOUN
ejpam-6415	114	19	,	,	PUNCT
ejpam-6415	114	20	δ	δ	PROPN
ejpam-6415	114	21	,	,	PUNCT
ejpam-6415	114	22	τ	τ	PROPN
ejpam-6415	114	23	;	;	PUNCT
ejpam-6415	114	24	α	α	X
ejpam-6415	114	25	)	)	PUNCT
ejpam-6415	114	26	for	for	ADP
ejpam-6415	114	27	j	j	PROPN
ejpam-6415	114	28	=	=	SYM
ejpam-6415	114	29	1	1	NUM
ejpam-6415	114	30	,	,	PUNCT
ejpam-6415	114	31	2	2	NUM
ejpam-6415	114	32	,	,	PUNCT
ejpam-6415	114	33	.	.	PUNCT
ejpam-6415	114	34	.	.	PUNCT
ejpam-6415	115	1	.	.	PUNCT
ejpam-6415	116	1	,	,	PUNCT
ejpam-6415	116	2	n	n	X
ejpam-6415	116	3	.	.	PUNCT
ejpam-6415	117	1	then	then	ADV
ejpam-6415	117	2	the	the	DET
ejpam-6415	117	3	average	average	ADJ
ejpam-6415	117	4	function	function	NOUN
ejpam-6415	117	5	h(z	h(z	NOUN
ejpam-6415	117	6	)	)	PUNCT
ejpam-6415	117	7	:	:	PUNCT
ejpam-6415	117	8	=	=	SYM
ejpam-6415	117	9	1	1	NUM
ejpam-6415	117	10	n	n	NUM
ejpam-6415	117	11	n∑	n∑	PROPN
ejpam-6415	117	12	j=1	j=1	NOUN
ejpam-6415	117	13	hj(z	hj(z	X
ejpam-6415	117	14	)	)	PUNCT
ejpam-6415	117	15	=	=	SYM
ejpam-6415	117	16	z	z	NOUN
ejpam-6415	118	1	−	−	ADP
ejpam-6415	118	2	∞∑	∞∑	NUM
ejpam-6415	118	3	n=2	n=2	ADV
ejpam-6415	118	4			PROPN
ejpam-6415	118	5	1	1	NUM
ejpam-6415	118	6	n	n	NOUN
ejpam-6415	118	7	n∑	n∑	NOUN
ejpam-6415	118	8	j=1	j=1	PROPN
ejpam-6415	118	9	cnj	cnj	PROPN
ejpam-6415	119	1			PROPN
ejpam-6415	119	2	zn	zn	PROPN
ejpam-6415	119	3	also	also	ADV
ejpam-6415	119	4	belongs	belong	VERB
ejpam-6415	119	5	to	to	ADP
ejpam-6415	119	6	the	the	DET
ejpam-6415	119	7	class	class	NOUN
ejpam-6415	119	8	b∗	b∗	ADJ
ejpam-6415	119	9	ν(λ	ν(λ	NOUN
ejpam-6415	119	10	,	,	PUNCT
ejpam-6415	119	11	µ	µ	NOUN
ejpam-6415	119	12	,	,	PUNCT
ejpam-6415	119	13	δ	δ	PROPN
ejpam-6415	119	14	,	,	PUNCT
ejpam-6415	119	15	τ	τ	PROPN
ejpam-6415	119	16	;	;	PUNCT
ejpam-6415	119	17	α	α	X
ejpam-6415	119	18	)	)	PUNCT
ejpam-6415	119	19	.	.	PUNCT
ejpam-6415	120	1	proof	proof	NOUN
ejpam-6415	120	2	.	.	PUNCT
ejpam-6415	121	1	let	let	VERB
ejpam-6415	121	2	bn	bn	INTJ
ejpam-6415	121	3	=	=	SYM
ejpam-6415	121	4	1	1	NUM
ejpam-6415	121	5	n	n	NOUN
ejpam-6415	121	6	∑n	∑n	PROPN
ejpam-6415	121	7	j=1	j=1	PROPN
ejpam-6415	121	8	cnj	cnj	PROPN
ejpam-6415	121	9	.	.	PUNCT
ejpam-6415	122	1	then	then	ADV
ejpam-6415	122	2	,	,	PUNCT
ejpam-6415	122	3	using	use	VERB
ejpam-6415	122	4	linearity	linearity	NOUN
ejpam-6415	122	5	and	and	CCONJ
ejpam-6415	122	6	convexity	convexity	NOUN
ejpam-6415	122	7	of	of	ADP
ejpam-6415	122	8	the	the	DET
ejpam-6415	122	9	modulus	modulus	NOUN
ejpam-6415	122	10	∞∑	∞∑	PROPN
ejpam-6415	122	11	n=2	n=2	PRON
ejpam-6415	122	12	[	[	X
ejpam-6415	122	13	τ	τ	X
ejpam-6415	122	14	−	−	PROPN
ejpam-6415	122	15	δ	δ	PROPN
ejpam-6415	122	16	+	+	CCONJ
ejpam-6415	122	17	nδ	nδ	PROPN
ejpam-6415	122	18	+	+	CCONJ
ejpam-6415	122	19	λµn(n−	λµn(n−	X
ejpam-6415	122	20	1	1	NUM
ejpam-6415	122	21	)	)	PUNCT
ejpam-6415	122	22	]	]	PUNCT
ejpam-6415	122	23	(	(	PUNCT
ejpam-6415	122	24	n+	n+	ADP
ejpam-6415	122	25	ν	ν	NOUN
ejpam-6415	122	26	1	1	NUM
ejpam-6415	122	27	+	+	CCONJ
ejpam-6415	122	28	ν	ν	NOUN
ejpam-6415	122	29	)	)	PUNCT
ejpam-6415	122	30	r	r	NOUN
ejpam-6415	122	31	bn	bn	NOUN
ejpam-6415	122	32	=	=	SYM
ejpam-6415	122	33	∞∑	∞∑	NUM
ejpam-6415	122	34	n=2	n=2	PRON
ejpam-6415	123	1	[	[	X
ejpam-6415	123	2	τ	τ	X
ejpam-6415	123	3	−	−	PROPN
ejpam-6415	123	4	δ	δ	PROPN
ejpam-6415	123	5	+	+	CCONJ
ejpam-6415	123	6	nδ	nδ	PROPN
ejpam-6415	123	7	+	+	CCONJ
ejpam-6415	123	8	λµn(n−	λµn(n−	X
ejpam-6415	123	9	1	1	NUM
ejpam-6415	123	10	)	)	PUNCT
ejpam-6415	123	11	]	]	PUNCT
ejpam-6415	123	12	(	(	PUNCT
ejpam-6415	123	13	n+	n+	ADP
ejpam-6415	123	14	ν	ν	NOUN
ejpam-6415	123	15	1	1	NUM
ejpam-6415	123	16	+	+	CCONJ
ejpam-6415	123	17	ν	ν	NOUN
ejpam-6415	123	18	)	)	PUNCT
ejpam-6415	123	19	r	r	NOUN
ejpam-6415	123	20			PROPN
ejpam-6415	123	21	1	1	NUM
ejpam-6415	123	22	n	n	NOUN
ejpam-6415	123	23	n∑	n∑	NOUN
ejpam-6415	123	24	j=1	j=1	PROPN
ejpam-6415	123	25	cnj	cnj	NOUN
ejpam-6415	124	1			PROPN
ejpam-6415	124	2	=	=	SYM
ejpam-6415	124	3	1	1	NUM
ejpam-6415	124	4	n	n	NUM
ejpam-6415	124	5	n∑	n∑	NOUN
ejpam-6415	124	6	j=1	j=1	NOUN
ejpam-6415	124	7	(	(	PUNCT
ejpam-6415	124	8	∞∑	∞∑	NUM
ejpam-6415	124	9	n=2	n=2	PRON
ejpam-6415	125	1	[	[	X
ejpam-6415	125	2	τ	τ	X
ejpam-6415	125	3	−	−	PROPN
ejpam-6415	125	4	δ	δ	PROPN
ejpam-6415	125	5	+	+	CCONJ
ejpam-6415	125	6	nδ	nδ	PROPN
ejpam-6415	125	7	+	+	CCONJ
ejpam-6415	125	8	λµn(n−	λµn(n−	X
ejpam-6415	125	9	1	1	NUM
ejpam-6415	125	10	)	)	PUNCT
ejpam-6415	125	11	]	]	PUNCT
ejpam-6415	125	12	(	(	PUNCT
ejpam-6415	125	13	n+	n+	ADP
ejpam-6415	125	14	ν	ν	NOUN
ejpam-6415	125	15	1	1	NUM
ejpam-6415	125	16	+	+	CCONJ
ejpam-6415	125	17	ν	ν	NOUN
ejpam-6415	125	18	)	)	PUNCT
ejpam-6415	125	19	r	r	NOUN
ejpam-6415	125	20	cnj	cnj	NOUN
ejpam-6415	125	21	)	)	PUNCT
ejpam-6415	125	22	≤	≤	ADV
ejpam-6415	126	1	1	1	NUM
ejpam-6415	126	2	n	n	NOUN
ejpam-6415	126	3	n∑	n∑	NOUN
ejpam-6415	126	4	j=1	j=1	NOUN
ejpam-6415	126	5	(	(	PUNCT
ejpam-6415	126	6	1−	1−	NUM
ejpam-6415	126	7	α	α	NOUN
ejpam-6415	126	8	)	)	PUNCT
ejpam-6415	126	9	=	=	SYM
ejpam-6415	127	1	1−	1−	NUM
ejpam-6415	127	2	α	α	NOUN
ejpam-6415	127	3	hence	hence	ADV
ejpam-6415	127	4	,	,	PUNCT
ejpam-6415	127	5	h	h	NOUN
ejpam-6415	127	6	∈	∈	NOUN
ejpam-6415	127	7	b∗	b∗	ADJ
ejpam-6415	127	8	ν(λ	ν(λ	NOUN
ejpam-6415	127	9	,	,	PUNCT
ejpam-6415	127	10	µ	µ	NOUN
ejpam-6415	127	11	,	,	PUNCT
ejpam-6415	127	12	δ	δ	PROPN
ejpam-6415	127	13	,	,	PUNCT
ejpam-6415	127	14	τ	τ	PROPN
ejpam-6415	127	15	;	;	PUNCT
ejpam-6415	127	16	α	α	X
ejpam-6415	127	17	)	)	PUNCT
ejpam-6415	127	18	.	.	PUNCT
ejpam-6415	128	1	s.	s.	PROPN
ejpam-6415	128	2	han	han	PROPN
ejpam-6415	128	3	,	,	PUNCT
ejpam-6415	128	4	m.	m.	NOUN
ejpam-6415	128	5	h.	h.	PROPN
ejpam-6415	128	6	mohd	mohd	PROPN
ejpam-6415	128	7	,	,	PUNCT
ejpam-6415	128	8	m.	m.	NOUN
ejpam-6415	128	9	illafe	illafe	ADJ
ejpam-6415	128	10	/	/	SYM
ejpam-6415	128	11	eur	eur	PROPN
ejpam-6415	128	12	.	.	PUNCT
ejpam-6415	129	1	j.	j.	PROPN
ejpam-6415	129	2	pure	pure	PROPN
ejpam-6415	129	3	appl	appl	PROPN
ejpam-6415	129	4	.	.	PROPN
ejpam-6415	129	5	math	math	PROPN
ejpam-6415	129	6	,	,	PUNCT
ejpam-6415	129	7	18	18	NUM
ejpam-6415	129	8	(	(	PUNCT
ejpam-6415	129	9	3	3	NUM
ejpam-6415	129	10	)	)	PUNCT
ejpam-6415	129	11	(	(	PUNCT
ejpam-6415	129	12	2025	2025	NUM
ejpam-6415	129	13	)	)	PUNCT
ejpam-6415	129	14	,	,	PUNCT
ejpam-6415	129	15	6415	6415	NUM
ejpam-6415	129	16	6	6	NUM
ejpam-6415	129	17	of	of	ADP
ejpam-6415	129	18	9	9	NUM
ejpam-6415	129	19	theorem	theorem	NOUN
ejpam-6415	129	20	5	5	NUM
ejpam-6415	129	21	.	.	PUNCT
ejpam-6415	130	1	the	the	DET
ejpam-6415	130	2	class	class	NOUN
ejpam-6415	130	3	b∗	b∗	ADJ
ejpam-6415	130	4	ν(λ	ν(λ	NOUN
ejpam-6415	130	5	,	,	PUNCT
ejpam-6415	130	6	µ	µ	NOUN
ejpam-6415	130	7	,	,	PUNCT
ejpam-6415	130	8	δ	δ	PROPN
ejpam-6415	130	9	,	,	PUNCT
ejpam-6415	130	10	τ	τ	PROPN
ejpam-6415	130	11	;	;	PUNCT
ejpam-6415	130	12	α	α	X
ejpam-6415	130	13	)	)	PUNCT
ejpam-6415	130	14	is	be	AUX
ejpam-6415	130	15	convex	convex	ADJ
ejpam-6415	130	16	for	for	ADP
ejpam-6415	130	17	any	any	DET
ejpam-6415	130	18	h1	h1	NOUN
ejpam-6415	130	19	,	,	PUNCT
ejpam-6415	130	20	h2	h2	PROPN
ejpam-6415	130	21	∈	∈	PROPN
ejpam-6415	130	22	b∗	b∗	ADJ
ejpam-6415	130	23	ν(λ	ν(λ	NOUN
ejpam-6415	130	24	,	,	PUNCT
ejpam-6415	130	25	µ	µ	NOUN
ejpam-6415	130	26	,	,	PUNCT
ejpam-6415	130	27	δ	δ	PROPN
ejpam-6415	130	28	,	,	PUNCT
ejpam-6415	130	29	τ	τ	PROPN
ejpam-6415	130	30	;	;	PUNCT
ejpam-6415	130	31	α	α	X
ejpam-6415	130	32	)	)	PUNCT
ejpam-6415	130	33	and	and	CCONJ
ejpam-6415	130	34	any	any	DET
ejpam-6415	130	35	0	0	NUM
ejpam-6415	130	36	≤	≤	NUM
ejpam-6415	130	37	ω	ω	NUM
ejpam-6415	130	38	≤	≤	NUM
ejpam-6415	130	39	1	1	NUM
ejpam-6415	130	40	,	,	PUNCT
ejpam-6415	130	41	the	the	DET
ejpam-6415	130	42	function	function	NOUN
ejpam-6415	130	43	t	t	PROPN
ejpam-6415	130	44	(	(	PUNCT
ejpam-6415	130	45	z	z	NOUN
ejpam-6415	130	46	)	)	PUNCT
ejpam-6415	130	47	:	:	PUNCT
ejpam-6415	130	48	=	=	SYM
ejpam-6415	130	49	ωh1(z	ωh1(z	PROPN
ejpam-6415	130	50	)	)	PUNCT
ejpam-6415	130	51	+	+	CCONJ
ejpam-6415	130	52	(	(	PUNCT
ejpam-6415	130	53	1−	1−	NUM
ejpam-6415	130	54	ω)h2(z	ω)h2(z	NOUN
ejpam-6415	130	55	)	)	PUNCT
ejpam-6415	130	56	also	also	ADV
ejpam-6415	130	57	belongs	belong	VERB
ejpam-6415	130	58	to	to	ADP
ejpam-6415	130	59	b∗	b∗	ADJ
ejpam-6415	130	60	ν(λ	ν(λ	NOUN
ejpam-6415	130	61	,	,	PUNCT
ejpam-6415	130	62	µ	µ	NOUN
ejpam-6415	130	63	,	,	PUNCT
ejpam-6415	130	64	δ	δ	PROPN
ejpam-6415	130	65	,	,	PUNCT
ejpam-6415	130	66	τ	τ	PROPN
ejpam-6415	130	67	;	;	PUNCT
ejpam-6415	130	68	α	α	X
ejpam-6415	130	69	)	)	PUNCT
ejpam-6415	130	70	.	.	PUNCT
ejpam-6415	131	1	proof	proof	NOUN
ejpam-6415	131	2	.	.	PUNCT
ejpam-6415	132	1	let	let	VERB
ejpam-6415	132	2	hj(z	hj(z	NOUN
ejpam-6415	132	3	)	)	PUNCT
ejpam-6415	132	4	=	=	SYM
ejpam-6415	133	1	z	z	NOUN
ejpam-6415	134	1	−	−	ADP
ejpam-6415	134	2	∞∑	∞∑	NUM
ejpam-6415	134	3	n=2	n=2	AUX
ejpam-6415	134	4	cnjz	cnjz	NOUN
ejpam-6415	134	5	n	n	CCONJ
ejpam-6415	134	6	,	,	PUNCT
ejpam-6415	134	7	j	j	PROPN
ejpam-6415	134	8	=	=	SYM
ejpam-6415	134	9	1	1	NUM
ejpam-6415	134	10	,	,	PUNCT
ejpam-6415	134	11	2	2	NUM
ejpam-6415	134	12	and	and	CCONJ
ejpam-6415	134	13	define	define	VERB
ejpam-6415	134	14	t	t	PROPN
ejpam-6415	134	15	(	(	PUNCT
ejpam-6415	134	16	z	z	NOUN
ejpam-6415	134	17	)	)	PUNCT
ejpam-6415	134	18	=	=	PUNCT
ejpam-6415	135	1	z	z	NOUN
ejpam-6415	136	1	−	−	PROPN
ejpam-6415	136	2	∞∑	∞∑	NOUN
ejpam-6415	136	3	n=2	n=2	PRON
ejpam-6415	137	1	[	[	X
ejpam-6415	137	2	ωcn1	ωcn1	NOUN
ejpam-6415	137	3	+	+	CCONJ
ejpam-6415	137	4	(	(	PUNCT
ejpam-6415	137	5	1−	1−	NUM
ejpam-6415	137	6	ω)cn2	ω)cn2	NOUN
ejpam-6415	137	7	]	]	X
ejpam-6415	137	8	z	z	X
ejpam-6415	137	9	n.	n.	NOUN
ejpam-6415	137	10	as	as	ADP
ejpam-6415	137	11	before	before	ADV
ejpam-6415	137	12	,	,	PUNCT
ejpam-6415	137	13	the	the	DET
ejpam-6415	137	14	inequality	inequality	NOUN
ejpam-6415	137	15	becomes	become	VERB
ejpam-6415	137	16	∞∑	∞∑	PROPN
ejpam-6415	137	17	n=2	n=2	PRON
ejpam-6415	137	18	[	[	X
ejpam-6415	137	19	τ	τ	X
ejpam-6415	137	20	−	−	PROPN
ejpam-6415	137	21	δ	δ	PROPN
ejpam-6415	137	22	+	+	CCONJ
ejpam-6415	137	23	nδ	nδ	PROPN
ejpam-6415	137	24	+	+	CCONJ
ejpam-6415	137	25	λµn(n−	λµn(n−	X
ejpam-6415	137	26	1	1	NUM
ejpam-6415	137	27	)	)	PUNCT
ejpam-6415	137	28	]	]	PUNCT
ejpam-6415	138	1	(	(	PUNCT
ejpam-6415	138	2	n+	n+	ADP
ejpam-6415	138	3	ν	ν	NOUN
ejpam-6415	138	4	1	1	NUM
ejpam-6415	138	5	+	+	CCONJ
ejpam-6415	138	6	ν	ν	NOUN
ejpam-6415	138	7	)	)	PUNCT
ejpam-6415	138	8	r	r	NOUN
ejpam-6415	138	9	[	[	X
ejpam-6415	138	10	wcn1	wcn1	NOUN
ejpam-6415	138	11	+	+	CCONJ
ejpam-6415	138	12	(	(	PUNCT
ejpam-6415	138	13	1−	1−	NUM
ejpam-6415	138	14	w)cn2	w)cn2	NOUN
ejpam-6415	138	15	]	]	PUNCT
ejpam-6415	138	16	=	=	PUNCT
ejpam-6415	139	1	w	w	ADP
ejpam-6415	139	2	∞∑	∞∑	NUM
ejpam-6415	139	3	n=2	n=2	PRON
ejpam-6415	140	1	[	[	X
ejpam-6415	140	2	τ	τ	X
ejpam-6415	140	3	−	−	PROPN
ejpam-6415	140	4	δ	δ	PROPN
ejpam-6415	140	5	+	+	CCONJ
ejpam-6415	140	6	nδ	nδ	PROPN
ejpam-6415	140	7	+	+	CCONJ
ejpam-6415	140	8	λµn(n−	λµn(n−	X
ejpam-6415	140	9	1	1	NUM
ejpam-6415	140	10	)	)	PUNCT
ejpam-6415	140	11	]	]	PUNCT
ejpam-6415	141	1	(	(	PUNCT
ejpam-6415	141	2	n+	n+	ADP
ejpam-6415	141	3	ν	ν	NOUN
ejpam-6415	141	4	1	1	NUM
ejpam-6415	141	5	+	+	CCONJ
ejpam-6415	141	6	ν	ν	NOUN
ejpam-6415	141	7	)	)	PUNCT
ejpam-6415	141	8	r	r	NOUN
ejpam-6415	141	9	cn1	cn1	NOUN
ejpam-6415	141	10	+	+	CCONJ
ejpam-6415	141	11	(	(	PUNCT
ejpam-6415	141	12	1−	1−	NUM
ejpam-6415	141	13	w	w	NOUN
ejpam-6415	141	14	)	)	PUNCT
ejpam-6415	141	15	∞∑	∞∑	NUM
ejpam-6415	141	16	n=3	n=3	PUNCT
ejpam-6415	142	1	[	[	X
ejpam-6415	142	2	τ	τ	X
ejpam-6415	142	3	−	−	PROPN
ejpam-6415	142	4	δ	δ	PROPN
ejpam-6415	142	5	+	+	CCONJ
ejpam-6415	142	6	nδ	nδ	PROPN
ejpam-6415	142	7	+	+	CCONJ
ejpam-6415	142	8	λµn(n−	λµn(n−	X
ejpam-6415	142	9	1	1	NUM
ejpam-6415	142	10	)	)	PUNCT
ejpam-6415	142	11	]	]	PUNCT
ejpam-6415	142	12	(	(	PUNCT
ejpam-6415	142	13	n+	n+	ADP
ejpam-6415	142	14	ν	ν	NOUN
ejpam-6415	142	15	1	1	NUM
ejpam-6415	142	16	+	+	CCONJ
ejpam-6415	142	17	ν	ν	NOUN
ejpam-6415	142	18	)	)	PUNCT
ejpam-6415	142	19	r	r	NOUN
ejpam-6415	142	20	cn2	cn2	NOUN
ejpam-6415	142	21	≤	≤	PROPN
ejpam-6415	142	22	w(1−	w(1−	NOUN
ejpam-6415	142	23	α	α	X
ejpam-6415	142	24	)	)	PUNCT
ejpam-6415	142	25	+	+	CCONJ
ejpam-6415	142	26	(	(	PUNCT
ejpam-6415	142	27	1−	1−	NUM
ejpam-6415	142	28	w)(1−	w)(1−	NOUN
ejpam-6415	142	29	α	α	NOUN
ejpam-6415	142	30	)	)	PUNCT
ejpam-6415	142	31	=	=	SYM
ejpam-6415	143	1	1−	1−	NUM
ejpam-6415	143	2	α	α	PRON
ejpam-6415	143	3	thus	thus	ADV
ejpam-6415	143	4	t	t	X
ejpam-6415	143	5	∈	∈	PROPN
ejpam-6415	143	6	b∗	b∗	ADJ
ejpam-6415	143	7	ν(λ	ν(λ	NOUN
ejpam-6415	143	8	,	,	PUNCT
ejpam-6415	143	9	µ	µ	NOUN
ejpam-6415	143	10	,	,	PUNCT
ejpam-6415	143	11	δ	δ	PROPN
ejpam-6415	143	12	,	,	PUNCT
ejpam-6415	143	13	τ	τ	PROPN
ejpam-6415	143	14	;	;	PUNCT
ejpam-6415	143	15	α	α	X
ejpam-6415	143	16	)	)	PUNCT
ejpam-6415	143	17	.	.	PUNCT
ejpam-6415	144	1	5	5	X
ejpam-6415	144	2	.	.	X
ejpam-6415	144	3	radii	radius	NOUN
ejpam-6415	144	4	of	of	ADP
ejpam-6415	144	5	close	close	NOUN
ejpam-6415	144	6	-	-	PUNCT
ejpam-6415	144	7	to	to	ADP
ejpam-6415	144	8	-	-	PUNCT
ejpam-6415	144	9	convexity	convexity	NOUN
ejpam-6415	144	10	,	,	PUNCT
ejpam-6415	144	11	starlikeness	starlikeness	NOUN
ejpam-6415	144	12	,	,	PUNCT
ejpam-6415	144	13	and	and	CCONJ
ejpam-6415	144	14	convexity	convexity	NOUN
ejpam-6415	144	15	let	let	VERB
ejpam-6415	144	16	us	we	PRON
ejpam-6415	144	17	now	now	ADV
ejpam-6415	144	18	derive	derive	VERB
ejpam-6415	144	19	the	the	DET
ejpam-6415	144	20	radii	radius	NOUN
ejpam-6415	144	21	within	within	ADP
ejpam-6415	144	22	which	which	PRON
ejpam-6415	144	23	a	a	DET
ejpam-6415	144	24	function	function	NOUN
ejpam-6415	144	25	h	h	NOUN
ejpam-6415	144	26	∈	∈	NOUN
ejpam-6415	144	27	b∗	b∗	ADJ
ejpam-6415	144	28	ν(λ	ν(λ	NOUN
ejpam-6415	144	29	,	,	PUNCT
ejpam-6415	144	30	µ	µ	NOUN
ejpam-6415	144	31	,	,	PUNCT
ejpam-6415	144	32	δ	δ	PROPN
ejpam-6415	144	33	,	,	PUNCT
ejpam-6415	144	34	τ	τ	PROPN
ejpam-6415	144	35	;	;	PUNCT
ejpam-6415	144	36	α	α	X
ejpam-6415	144	37	)	)	PUNCT
ejpam-6415	144	38	exhibits	exhibit	VERB
ejpam-6415	144	39	the	the	DET
ejpam-6415	144	40	standard	standard	ADJ
ejpam-6415	144	41	geometric	geometric	ADJ
ejpam-6415	144	42	behaviors	behavior	NOUN
ejpam-6415	144	43	of	of	ADP
ejpam-6415	144	44	close	close	NOUN
ejpam-6415	144	45	-	-	PUNCT
ejpam-6415	144	46	to	to	ADP
ejpam-6415	144	47	-	-	PUNCT
ejpam-6415	144	48	convexity	convexity	NOUN
ejpam-6415	144	49	,	,	PUNCT
ejpam-6415	144	50	starlikeness	starlikeness	NOUN
ejpam-6415	144	51	,	,	PUNCT
ejpam-6415	144	52	and	and	CCONJ
ejpam-6415	144	53	convexity	convexity	NOUN
ejpam-6415	144	54	.	.	PUNCT
ejpam-6415	145	1	let	let	VERB
ejpam-6415	145	2	a	a	DET
ejpam-6415	145	3	denote	denote	NOUN
ejpam-6415	145	4	the	the	DET
ejpam-6415	145	5	class	class	NOUN
ejpam-6415	145	6	of	of	ADP
ejpam-6415	145	7	normalized	normalize	VERB
ejpam-6415	145	8	analytic	analytic	ADJ
ejpam-6415	145	9	functions	function	NOUN
ejpam-6415	145	10	in	in	ADP
ejpam-6415	145	11	the	the	DET
ejpam-6415	145	12	unit	unit	NOUN
ejpam-6415	145	13	disk	disk	NOUN
ejpam-6415	145	14	u.	u.	NOUN
ejpam-6415	145	15	for	for	ADP
ejpam-6415	145	16	0	0	NUM
ejpam-6415	145	17	≤	≤	NOUN
ejpam-6415	145	18	β	β	X
ejpam-6415	145	19	<	<	X
ejpam-6415	145	20	1	1	NUM
ejpam-6415	145	21	,	,	PUNCT
ejpam-6415	145	22	we	we	PRON
ejpam-6415	145	23	define	define	VERB
ejpam-6415	145	24	the	the	DET
ejpam-6415	145	25	following	follow	VERB
ejpam-6415	145	26	important	important	ADJ
ejpam-6415	145	27	subclasses	subclass	NOUN
ejpam-6415	145	28	:	:	PUNCT
ejpam-6415	145	29	•	•	ADP
ejpam-6415	145	30	the	the	DET
ejpam-6415	145	31	class	class	NOUN
ejpam-6415	145	32	of	of	ADP
ejpam-6415	145	33	close	close	NOUN
ejpam-6415	145	34	-	-	PUNCT
ejpam-6415	145	35	to	to	ADP
ejpam-6415	145	36	-	-	PUNCT
ejpam-6415	145	37	convex	convex	NOUN
ejpam-6415	145	38	functions	function	NOUN
ejpam-6415	145	39	of	of	ADP
ejpam-6415	145	40	order	order	NOUN
ejpam-6415	145	41	β	β	X
ejpam-6415	145	42	c(β	c(β	PROPN
ejpam-6415	145	43	)	)	PUNCT
ejpam-6415	145	44	=	=	PRON
ejpam-6415	145	45	{	{	PUNCT
ejpam-6415	145	46	h	h	NOUN
ejpam-6415	145	47	∈	∈	PROPN
ejpam-6415	146	1	a	a	DET
ejpam-6415	146	2	:	:	PUNCT
ejpam-6415	146	3	re	re	X
ejpam-6415	146	4	{	{	PUNCT
ejpam-6415	146	5	h′(z	h′(z	PROPN
ejpam-6415	146	6	)	)	PUNCT
ejpam-6415	146	7	}	}	PUNCT
ejpam-6415	146	8	>	>	X
ejpam-6415	146	9	β	β	X
ejpam-6415	146	10	}	}	PUNCT
ejpam-6415	146	11	•	•	ADP
ejpam-6415	146	12	the	the	DET
ejpam-6415	146	13	class	class	NOUN
ejpam-6415	146	14	of	of	ADP
ejpam-6415	146	15	starlike	starlike	NOUN
ejpam-6415	146	16	functions	function	NOUN
ejpam-6415	146	17	of	of	ADP
ejpam-6415	146	18	order	order	NOUN
ejpam-6415	146	19	β	β	X
ejpam-6415	146	20	s∗(β	s∗(β	PROPN
ejpam-6415	146	21	)	)	PUNCT
ejpam-6415	146	22	=	=	PRON
ejpam-6415	146	23	{	{	PUNCT
ejpam-6415	146	24	h	h	NOUN
ejpam-6415	146	25	∈	∈	PROPN
ejpam-6415	146	26	a	a	DET
ejpam-6415	146	27	:	:	PUNCT
ejpam-6415	146	28	re	re	X
ejpam-6415	146	29	{	{	PUNCT
ejpam-6415	146	30	zh′(z	zh′(z	NOUN
ejpam-6415	146	31	)	)	PUNCT
ejpam-6415	146	32	h(z	h(z	NOUN
ejpam-6415	146	33	)	)	PUNCT
ejpam-6415	146	34	}	}	PUNCT
ejpam-6415	146	35	>	>	X
ejpam-6415	146	36	β	β	X
ejpam-6415	146	37	}	}	PUNCT
ejpam-6415	146	38	•	•	ADP
ejpam-6415	146	39	the	the	DET
ejpam-6415	146	40	class	class	NOUN
ejpam-6415	146	41	of	of	ADP
ejpam-6415	146	42	convex	convex	NOUN
ejpam-6415	146	43	functions	function	NOUN
ejpam-6415	146	44	of	of	ADP
ejpam-6415	146	45	order	order	NOUN
ejpam-6415	146	46	β	β	X
ejpam-6415	146	47	k(β	k(β	NOUN
ejpam-6415	146	48	)	)	PUNCT
ejpam-6415	146	49	=	=	PRON
ejpam-6415	146	50	{	{	PUNCT
ejpam-6415	146	51	h	h	NOUN
ejpam-6415	146	52	∈	∈	PROPN
ejpam-6415	146	53	a	a	DET
ejpam-6415	146	54	:	:	PUNCT
ejpam-6415	146	55	re	re	X
ejpam-6415	146	56	{	{	PUNCT
ejpam-6415	146	57	1	1	NUM
ejpam-6415	146	58	+	+	NUM
ejpam-6415	146	59	zh′′(z	zh′′(z	NUM
ejpam-6415	146	60	)	)	PUNCT
ejpam-6415	146	61	h′(z	h′(z	PROPN
ejpam-6415	146	62	)	)	PUNCT
ejpam-6415	146	63	}	}	PUNCT
ejpam-6415	146	64	>	>	X
ejpam-6415	146	65	β	β	X
ejpam-6415	146	66	}	}	PUNCT
ejpam-6415	146	67	s.	s.	PROPN
ejpam-6415	146	68	han	han	PROPN
ejpam-6415	146	69	,	,	PUNCT
ejpam-6415	146	70	m.	m.	NOUN
ejpam-6415	146	71	h.	h.	PROPN
ejpam-6415	146	72	mohd	mohd	PROPN
ejpam-6415	146	73	,	,	PUNCT
ejpam-6415	146	74	m.	m.	NOUN
ejpam-6415	146	75	illafe	illafe	ADJ
ejpam-6415	146	76	/	/	SYM
ejpam-6415	146	77	eur	eur	PROPN
ejpam-6415	146	78	.	.	PUNCT
ejpam-6415	147	1	j.	j.	PROPN
ejpam-6415	147	2	pure	pure	PROPN
ejpam-6415	147	3	appl	appl	PROPN
ejpam-6415	147	4	.	.	PROPN
ejpam-6415	147	5	math	math	PROPN
ejpam-6415	147	6	,	,	PUNCT
ejpam-6415	147	7	18	18	NUM
ejpam-6415	147	8	(	(	PUNCT
ejpam-6415	147	9	3	3	NUM
ejpam-6415	147	10	)	)	PUNCT
ejpam-6415	147	11	(	(	PUNCT
ejpam-6415	147	12	2025	2025	NUM
ejpam-6415	147	13	)	)	PUNCT
ejpam-6415	147	14	,	,	PUNCT
ejpam-6415	147	15	6415	6415	NUM
ejpam-6415	147	16	7	7	NUM
ejpam-6415	147	17	of	of	ADP
ejpam-6415	147	18	9	9	NUM
ejpam-6415	147	19	in	in	ADP
ejpam-6415	147	20	the	the	DET
ejpam-6415	147	21	following	following	NOUN
ejpam-6415	147	22	,	,	PUNCT
ejpam-6415	147	23	we	we	PRON
ejpam-6415	147	24	aim	aim	VERB
ejpam-6415	147	25	to	to	PART
ejpam-6415	147	26	determine	determine	VERB
ejpam-6415	147	27	these	these	DET
ejpam-6415	147	28	properties	property	NOUN
ejpam-6415	147	29	for	for	ADP
ejpam-6415	147	30	functions	function	NOUN
ejpam-6415	147	31	belonging	belong	VERB
ejpam-6415	147	32	to	to	ADP
ejpam-6415	147	33	the	the	DET
ejpam-6415	147	34	class	class	NOUN
ejpam-6415	147	35	b∗	b∗	ADJ
ejpam-6415	147	36	ν(λ	ν(λ	NOUN
ejpam-6415	147	37	,	,	PUNCT
ejpam-6415	147	38	µ	µ	NOUN
ejpam-6415	147	39	,	,	PUNCT
ejpam-6415	147	40	δ	δ	PROPN
ejpam-6415	147	41	,	,	PUNCT
ejpam-6415	147	42	τ	τ	PROPN
ejpam-6415	147	43	;	;	PUNCT
ejpam-6415	147	44	α	α	X
ejpam-6415	147	45	)	)	PUNCT
ejpam-6415	147	46	.	.	PUNCT
ejpam-6415	148	1	close	close	ADJ
ejpam-6415	148	2	-	-	PUNCT
ejpam-6415	148	3	to	to	ADP
ejpam-6415	148	4	-	-	PUNCT
ejpam-6415	148	5	convexity	convexity	NOUN
ejpam-6415	148	6	radius	radius	NOUN
ejpam-6415	148	7	theorem	theorem	VERB
ejpam-6415	148	8	6	6	NUM
ejpam-6415	148	9	.	.	PUNCT
ejpam-6415	149	1	let	let	VERB
ejpam-6415	149	2	h	h	PRON
ejpam-6415	149	3	∈	∈	PROPN
ejpam-6415	149	4	b∗	b∗	ADJ
ejpam-6415	149	5	ν(λ	ν(λ	NOUN
ejpam-6415	149	6	,	,	PUNCT
ejpam-6415	149	7	µ	µ	NOUN
ejpam-6415	149	8	,	,	PUNCT
ejpam-6415	149	9	δ	δ	PROPN
ejpam-6415	149	10	,	,	PUNCT
ejpam-6415	149	11	τ	τ	PROPN
ejpam-6415	149	12	;	;	PUNCT
ejpam-6415	149	13	α	α	X
ejpam-6415	149	14	)	)	PUNCT
ejpam-6415	149	15	.	.	PUNCT
ejpam-6415	150	1	then	then	ADV
ejpam-6415	150	2	h	h	PROPN
ejpam-6415	150	3	∈	∈	PROPN
ejpam-6415	150	4	c(β	c(β	PROPN
ejpam-6415	150	5	)	)	PUNCT
ejpam-6415	150	6	in	in	ADP
ejpam-6415	150	7	the	the	DET
ejpam-6415	150	8	disk	disk	NOUN
ejpam-6415	150	9	|z|	|z|	NOUN
ejpam-6415	150	10	<	<	X
ejpam-6415	150	11	r1	r1	PROPN
ejpam-6415	150	12	,	,	PUNCT
ejpam-6415	150	13	where	where	SCONJ
ejpam-6415	150	14	r1	r1	PROPN
ejpam-6415	150	15	=	=	PUNCT
ejpam-6415	150	16	inf	inf	PROPN
ejpam-6415	151	1	n≥2	n≥2	PROPN
ejpam-6415	151	2	(1−	(1−	PROPN
ejpam-6415	151	3	β	β	X
ejpam-6415	151	4	)	)	PUNCT
ejpam-6415	152	1	[	[	X
ejpam-6415	152	2	(	(	PUNCT
ejpam-6415	152	3	τ	τ	PROPN
ejpam-6415	152	4	−	−	PROPN
ejpam-6415	152	5	δ	δ	PROPN
ejpam-6415	152	6	)	)	PUNCT
ejpam-6415	152	7	+	+	NUM
ejpam-6415	152	8	nδ	nδ	NOUN
ejpam-6415	152	9	+	+	NOUN
ejpam-6415	152	10	λµn(n−	λµn(n−	X
ejpam-6415	152	11	1	1	NUM
ejpam-6415	152	12	)	)	PUNCT
ejpam-6415	152	13	]	]	PUNCT
ejpam-6415	152	14	(	(	PUNCT
ejpam-6415	152	15	n+ν	n+ν	NUM
ejpam-6415	152	16	1+ν	1+ν	NUM
ejpam-6415	152	17	)	)	PUNCT
ejpam-6415	152	18	r	r	NOUN
ejpam-6415	152	19	n(1−	n(1−	PROPN
ejpam-6415	152	20	α	α	NOUN
ejpam-6415	152	21	)	)	PUNCT
ejpam-6415	152	22			NOUN
ejpam-6415	152	23	1/(n−1	1/(n−1	NUM
ejpam-6415	152	24	)	)	PUNCT
ejpam-6415	152	25	.	.	PUNCT
ejpam-6415	153	1	(	(	PUNCT
ejpam-6415	153	2	10	10	NUM
ejpam-6415	153	3	)	)	PUNCT
ejpam-6415	153	4	proof	proof	NOUN
ejpam-6415	153	5	.	.	PUNCT
ejpam-6415	154	1	for	for	ADP
ejpam-6415	154	2	h(z	h(z	NOUN
ejpam-6415	154	3	)	)	PUNCT
ejpam-6415	154	4	=	=	SYM
ejpam-6415	154	5	z	z	NOUN
ejpam-6415	154	6	−	−	NOUN
ejpam-6415	154	7	∑∞	∑∞	NOUN
ejpam-6415	154	8	n=2	n=2	PRON
ejpam-6415	154	9	cnz	cnz	NOUN
ejpam-6415	154	10	n	n	CCONJ
ejpam-6415	154	11	,	,	PUNCT
ejpam-6415	154	12	we	we	PRON
ejpam-6415	154	13	have	have	VERB
ejpam-6415	154	14	h′(z	h′(z	NOUN
ejpam-6415	154	15	)	)	PUNCT
ejpam-6415	155	1	=	=	SYM
ejpam-6415	156	1	1−	1−	NUM
ejpam-6415	156	2	∞∑	∞∑	NUM
ejpam-6415	156	3	n=2	n=2	X
ejpam-6415	156	4	ncnz	ncnz	NOUN
ejpam-6415	156	5	n−1	n−1	PROPN
ejpam-6415	156	6	.	.	PROPN
ejpam-6415	156	7	to	to	PART
ejpam-6415	156	8	ensure	ensure	VERB
ejpam-6415	156	9	ℜ{h′(z	ℜ{h′(z	NOUN
ejpam-6415	156	10	)	)	PUNCT
ejpam-6415	156	11	}	}	PUNCT
ejpam-6415	156	12	>	>	X
ejpam-6415	156	13	β	β	X
ejpam-6415	156	14	,	,	PUNCT
ejpam-6415	156	15	it	it	PRON
ejpam-6415	156	16	is	be	AUX
ejpam-6415	156	17	sufficient	sufficient	ADJ
ejpam-6415	156	18	that	that	SCONJ
ejpam-6415	156	19	|h′(z)−	|h′(z)−	NOUN
ejpam-6415	156	20	1|	1|	NUM
ejpam-6415	156	21	≤	≤	NOUN
ejpam-6415	156	22	1−	1−	NUM
ejpam-6415	156	23	β	β	X
ejpam-6415	156	24	for	for	ADP
ejpam-6415	156	25	z	z	PROPN
ejpam-6415	156	26	∈	∈	PROPN
ejpam-6415	156	27	u.	u.	NOUN
ejpam-6415	156	28	that	that	PRON
ejpam-6415	156	29	is	be	AUX
ejpam-6415	156	30	,	,	PUNCT
ejpam-6415	156	31	∞∑	∞∑	PROPN
ejpam-6415	156	32	n=2	n=2	PRON
ejpam-6415	156	33	ncnr	ncnr	ADJ
ejpam-6415	156	34	n−1	n−1	PROPN
ejpam-6415	156	35	≤	≤	NOUN
ejpam-6415	156	36	1−	1−	NUM
ejpam-6415	156	37	β	β	NOUN
ejpam-6415	156	38	.	.	PUNCT
ejpam-6415	157	1	using	use	VERB
ejpam-6415	157	2	the	the	DET
ejpam-6415	157	3	coefficient	coefficient	NOUN
ejpam-6415	157	4	bound	bind	VERB
ejpam-6415	157	5	property	property	NOUN
ejpam-6415	157	6	represented	represent	VERB
ejpam-6415	157	7	by	by	ADP
ejpam-6415	157	8	theorem	theorem	NOUN
ejpam-6415	157	9	1	1	NUM
ejpam-6415	157	10	,	,	PUNCT
ejpam-6415	157	11	we	we	PRON
ejpam-6415	157	12	get	get	VERB
ejpam-6415	157	13	n|z|n−1	n|z|n−1	ADJ
ejpam-6415	157	14	≤	≤	NOUN
ejpam-6415	157	15	(	(	PUNCT
ejpam-6415	157	16	1−	1−	NUM
ejpam-6415	157	17	β)[τ	β)[τ	NUM
ejpam-6415	157	18	−	−	PROPN
ejpam-6415	157	19	δ	δ	NOUN
ejpam-6415	157	20	+	+	CCONJ
ejpam-6415	157	21	nδ	nδ	PROPN
ejpam-6415	157	22	+	+	CCONJ
ejpam-6415	157	23	λµn(n−	λµn(n−	X
ejpam-6415	157	24	1	1	NUM
ejpam-6415	157	25	)	)	PUNCT
ejpam-6415	157	26	]	]	PUNCT
ejpam-6415	158	1	(	(	PUNCT
ejpam-6415	158	2	n+ν	n+ν	NUM
ejpam-6415	158	3	1+ν	1+ν	NUM
ejpam-6415	158	4	)	)	PUNCT
ejpam-6415	158	5	r	r	NOUN
ejpam-6415	158	6	1−	1−	NUM
ejpam-6415	159	1	α	α	NOUN
ejpam-6415	159	2	|z|	|z|	VERB
ejpam-6415	159	3	≤	≤	NUM
ejpam-6415	159	4	inf	inf	NOUN
ejpam-6415	159	5	n≥2	n≥2	PROPN
ejpam-6415	159	6	(1−	(1−	PROPN
ejpam-6415	159	7	β	β	X
ejpam-6415	159	8	)	)	PUNCT
ejpam-6415	160	1	[	[	X
ejpam-6415	160	2	(	(	PUNCT
ejpam-6415	160	3	τ	τ	PROPN
ejpam-6415	160	4	−	−	PROPN
ejpam-6415	160	5	δ	δ	PROPN
ejpam-6415	160	6	)	)	PUNCT
ejpam-6415	160	7	+	+	NUM
ejpam-6415	160	8	nδ	nδ	NOUN
ejpam-6415	160	9	+	+	NOUN
ejpam-6415	160	10	λµn(n−	λµn(n−	X
ejpam-6415	160	11	1	1	NUM
ejpam-6415	160	12	)	)	PUNCT
ejpam-6415	160	13	]	]	PUNCT
ejpam-6415	160	14	(	(	PUNCT
ejpam-6415	160	15	n+ν	n+ν	NUM
ejpam-6415	160	16	1+ν	1+ν	NUM
ejpam-6415	160	17	)	)	PUNCT
ejpam-6415	160	18	r	r	NOUN
ejpam-6415	160	19	n(1−	n(1−	PROPN
ejpam-6415	160	20	α	α	NOUN
ejpam-6415	160	21	)	)	PUNCT
ejpam-6415	160	22			NOUN
ejpam-6415	160	23	1/(n−1	1/(n−1	NUM
ejpam-6415	160	24	)	)	PUNCT
ejpam-6415	160	25	,	,	PUNCT
ejpam-6415	160	26	(	(	PUNCT
ejpam-6415	160	27	11	11	NUM
ejpam-6415	160	28	)	)	PUNCT
ejpam-6415	160	29	which	which	PRON
ejpam-6415	160	30	yields	yield	VERB
ejpam-6415	160	31	the	the	DET
ejpam-6415	160	32	radius	radius	NOUN
ejpam-6415	160	33	in	in	ADP
ejpam-6415	160	34	(	(	PUNCT
ejpam-6415	160	35	10	10	NUM
ejpam-6415	160	36	)	)	PUNCT
ejpam-6415	160	37	.	.	PUNCT
ejpam-6415	161	1	starlikeness	starlikeness	ADJ
ejpam-6415	161	2	radius	radius	NOUN
ejpam-6415	161	3	theorem	theorem	VERB
ejpam-6415	161	4	7	7	NUM
ejpam-6415	161	5	.	.	PUNCT
ejpam-6415	162	1	if	if	SCONJ
ejpam-6415	162	2	h	h	NOUN
ejpam-6415	162	3	∈	∈	PROPN
ejpam-6415	162	4	b∗	b∗	ADJ
ejpam-6415	162	5	ν(λ	ν(λ	NOUN
ejpam-6415	162	6	,	,	PUNCT
ejpam-6415	162	7	µ	µ	NOUN
ejpam-6415	162	8	,	,	PUNCT
ejpam-6415	162	9	δ	δ	PROPN
ejpam-6415	162	10	,	,	PUNCT
ejpam-6415	162	11	τ	τ	PROPN
ejpam-6415	162	12	;	;	PUNCT
ejpam-6415	162	13	α	α	X
ejpam-6415	162	14	)	)	PUNCT
ejpam-6415	162	15	,	,	PUNCT
ejpam-6415	162	16	then	then	ADV
ejpam-6415	162	17	h	h	PROPN
ejpam-6415	162	18	is	be	AUX
ejpam-6415	162	19	starlike	starlike	NOUN
ejpam-6415	162	20	of	of	SCONJ
ejpam-6415	162	21	order	order	NOUN
ejpam-6415	162	22	β	β	X
ejpam-6415	162	23	in	in	ADP
ejpam-6415	162	24	the	the	DET
ejpam-6415	162	25	disk	disk	NOUN
ejpam-6415	162	26	|z|	|z|	NOUN
ejpam-6415	162	27	<	<	X
ejpam-6415	162	28	r2	r2	NOUN
ejpam-6415	162	29	,	,	PUNCT
ejpam-6415	162	30	where	where	SCONJ
ejpam-6415	162	31	r2	r2	PROPN
ejpam-6415	162	32	=	=	PROPN
ejpam-6415	162	33	inf	inf	PROPN
ejpam-6415	162	34	n≥2	n≥2	PROPN
ejpam-6415	162	35	(1−	(1−	PROPN
ejpam-6415	162	36	β	β	X
ejpam-6415	162	37	)	)	PUNCT
ejpam-6415	163	1	[	[	X
ejpam-6415	163	2	(	(	PUNCT
ejpam-6415	163	3	τ	τ	PROPN
ejpam-6415	163	4	−	−	PROPN
ejpam-6415	163	5	δ	δ	PROPN
ejpam-6415	163	6	)	)	PUNCT
ejpam-6415	163	7	+	+	NUM
ejpam-6415	163	8	nδ	nδ	NOUN
ejpam-6415	163	9	+	+	NOUN
ejpam-6415	163	10	λµn(n−	λµn(n−	X
ejpam-6415	163	11	1	1	NUM
ejpam-6415	163	12	)	)	PUNCT
ejpam-6415	163	13	]	]	PUNCT
ejpam-6415	163	14	(	(	PUNCT
ejpam-6415	163	15	n+ν	n+ν	NUM
ejpam-6415	163	16	1+ν	1+ν	NUM
ejpam-6415	163	17	)	)	PUNCT
ejpam-6415	163	18	r	r	NOUN
ejpam-6415	163	19	(	(	PUNCT
ejpam-6415	163	20	n−	n−	NOUN
ejpam-6415	163	21	β)(1−	β)(1−	NOUN
ejpam-6415	163	22	α	α	X
ejpam-6415	163	23	)	)	PUNCT
ejpam-6415	163	24			NOUN
ejpam-6415	163	25	1/(n−1	1/(n−1	NUM
ejpam-6415	163	26	)	)	PUNCT
ejpam-6415	163	27	.	.	PUNCT
ejpam-6415	164	1	(	(	PUNCT
ejpam-6415	164	2	12	12	NUM
ejpam-6415	164	3	)	)	PUNCT
ejpam-6415	164	4	s.	s.	PROPN
ejpam-6415	164	5	han	han	PROPN
ejpam-6415	164	6	,	,	PUNCT
ejpam-6415	164	7	m.	m.	NOUN
ejpam-6415	164	8	h.	h.	PROPN
ejpam-6415	164	9	mohd	mohd	PROPN
ejpam-6415	164	10	,	,	PUNCT
ejpam-6415	164	11	m.	m.	NOUN
ejpam-6415	164	12	illafe	illafe	ADJ
ejpam-6415	164	13	/	/	SYM
ejpam-6415	164	14	eur	eur	PROPN
ejpam-6415	164	15	.	.	PUNCT
ejpam-6415	165	1	j.	j.	PROPN
ejpam-6415	165	2	pure	pure	PROPN
ejpam-6415	165	3	appl	appl	PROPN
ejpam-6415	165	4	.	.	PROPN
ejpam-6415	165	5	math	math	PROPN
ejpam-6415	165	6	,	,	PUNCT
ejpam-6415	165	7	18	18	NUM
ejpam-6415	165	8	(	(	PUNCT
ejpam-6415	165	9	3	3	NUM
ejpam-6415	165	10	)	)	PUNCT
ejpam-6415	165	11	(	(	PUNCT
ejpam-6415	165	12	2025	2025	NUM
ejpam-6415	165	13	)	)	PUNCT
ejpam-6415	165	14	,	,	PUNCT
ejpam-6415	165	15	6415	6415	NUM
ejpam-6415	165	16	8	8	NUM
ejpam-6415	165	17	of	of	ADP
ejpam-6415	165	18	9	9	NUM
ejpam-6415	165	19	proof	proof	NOUN
ejpam-6415	165	20	.	.	PUNCT
ejpam-6415	166	1	using	use	VERB
ejpam-6415	166	2	similar	similar	ADJ
ejpam-6415	166	3	argument	argument	NOUN
ejpam-6415	166	4	in	in	ADP
ejpam-6415	166	5	the	the	DET
ejpam-6415	166	6	previous	previous	ADJ
ejpam-6415	166	7	theorem	theorem	NOUN
ejpam-6415	166	8	,	,	PUNCT
ejpam-6415	166	9	we	we	PRON
ejpam-6415	166	10	can	can	AUX
ejpam-6415	166	11	write∣∣∣∣zf	write∣∣∣∣zf	PROPN
ejpam-6415	166	12	′(z	′(z	NOUN
ejpam-6415	166	13	)	)	PUNCT
ejpam-6415	166	14	f(z	f(z	PROPN
ejpam-6415	166	15	)	)	PUNCT
ejpam-6415	166	16	−	−	PROPN
ejpam-6415	166	17	1	1	NUM
ejpam-6415	166	18	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6415	166	19	=	=	PUNCT
ejpam-6415	166	20	∣∣∣∣∑∞	∣∣∣∣∑∞	VERB
ejpam-6415	166	21	n=2(n−	n=2(n−	PROPN
ejpam-6415	166	22	1)anz	1)anz	NUM
ejpam-6415	166	23	n−1	n−1	PROPN
ejpam-6415	166	24	1−	1−	NUM
ejpam-6415	166	25	∑∞	∑∞	NOUN
ejpam-6415	166	26	n=2	n=2	PUNCT
ejpam-6415	166	27	anz	anz	PROPN
ejpam-6415	166	28	n−1	n−1	PROPN
ejpam-6415	166	29	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6415	166	30	≤	≤	NOUN
ejpam-6415	166	31	∑∞	∑∞	NOUN
ejpam-6415	166	32	n=2(n−	n=2(n−	PROPN
ejpam-6415	166	33	1)an|z|n−1	1)an|z|n−1	PROPN
ejpam-6415	166	34	1−	1−	NUM
ejpam-6415	166	35	∑∞	∑∞	NOUN
ejpam-6415	166	36	n=2	n=2	AUX
ejpam-6415	166	37	an|z|n−1	an|z|n−1	VERB
ejpam-6415	166	38	≤	≤	NUM
ejpam-6415	166	39	1−	1−	NUM
ejpam-6415	166	40	β	β	X
ejpam-6415	166	41	(	(	PUNCT
ejpam-6415	166	42	n−	n−	NOUN
ejpam-6415	166	43	β)|z|n−1	β)|z|n−1	SYM
ejpam-6415	166	44	≤	≤	NUM
ejpam-6415	166	45	(	(	PUNCT
ejpam-6415	166	46	1−	1−	NUM
ejpam-6415	166	47	β	β	X
ejpam-6415	166	48	)	)	PUNCT
ejpam-6415	167	1	[	[	X
ejpam-6415	167	2	τ	τ	X
ejpam-6415	167	3	−	−	PROPN
ejpam-6415	167	4	δ	δ	PROPN
ejpam-6415	167	5	+	+	CCONJ
ejpam-6415	167	6	nδ	nδ	PROPN
ejpam-6415	167	7	+	+	CCONJ
ejpam-6415	167	8	λµn(n−	λµn(n−	X
ejpam-6415	167	9	1	1	NUM
ejpam-6415	167	10	)	)	PUNCT
ejpam-6415	167	11	]	]	PUNCT
ejpam-6415	168	1	(	(	PUNCT
ejpam-6415	168	2	n+ν	n+ν	NUM
ejpam-6415	168	3	1+ν	1+ν	NUM
ejpam-6415	168	4	)	)	PUNCT
ejpam-6415	168	5	r	r	NOUN
ejpam-6415	168	6	1−	1−	NUM
ejpam-6415	169	1	α	α	NOUN
ejpam-6415	169	2	|z|	|z|	VERB
ejpam-6415	169	3	≤	≤	NUM
ejpam-6415	169	4	inf	inf	NOUN
ejpam-6415	169	5	n≥2	n≥2	PROPN
ejpam-6415	169	6	(1−	(1−	PROPN
ejpam-6415	169	7	β	β	X
ejpam-6415	169	8	)	)	PUNCT
ejpam-6415	170	1	[	[	X
ejpam-6415	170	2	(	(	PUNCT
ejpam-6415	170	3	τ	τ	PROPN
ejpam-6415	170	4	−	−	PROPN
ejpam-6415	170	5	δ	δ	PROPN
ejpam-6415	170	6	)	)	PUNCT
ejpam-6415	170	7	+	+	NUM
ejpam-6415	170	8	nδ	nδ	NOUN
ejpam-6415	170	9	+	+	NOUN
ejpam-6415	170	10	λµn(n−	λµn(n−	X
ejpam-6415	170	11	1	1	NUM
ejpam-6415	170	12	)	)	PUNCT
ejpam-6415	170	13	]	]	PUNCT
ejpam-6415	170	14	(	(	PUNCT
ejpam-6415	170	15	n+ν	n+ν	NUM
ejpam-6415	170	16	1+ν	1+ν	NUM
ejpam-6415	170	17	)	)	PUNCT
ejpam-6415	170	18	r	r	NOUN
ejpam-6415	170	19	(	(	PUNCT
ejpam-6415	170	20	n−	n−	NOUN
ejpam-6415	170	21	β)(1−	β)(1−	NOUN
ejpam-6415	170	22	α	α	X
ejpam-6415	170	23	)	)	PUNCT
ejpam-6415	170	24			NOUN
ejpam-6415	170	25	1/(n−1	1/(n−1	NUM
ejpam-6415	170	26	)	)	PUNCT
ejpam-6415	170	27	.	.	PUNCT
ejpam-6415	171	1	(	(	PUNCT
ejpam-6415	171	2	13	13	X
ejpam-6415	171	3	)	)	PUNCT
ejpam-6415	171	4	convexity	convexity	NOUN
ejpam-6415	171	5	radius	radius	NOUN
ejpam-6415	171	6	theorem	theorem	VERB
ejpam-6415	171	7	8	8	NUM
ejpam-6415	171	8	.	.	PUNCT
ejpam-6415	172	1	if	if	SCONJ
ejpam-6415	172	2	h	h	NOUN
ejpam-6415	172	3	∈	∈	PROPN
ejpam-6415	172	4	b∗	b∗	ADJ
ejpam-6415	172	5	ν(λ	ν(λ	NOUN
ejpam-6415	172	6	,	,	PUNCT
ejpam-6415	172	7	µ	µ	NOUN
ejpam-6415	172	8	,	,	PUNCT
ejpam-6415	172	9	δ	δ	PROPN
ejpam-6415	172	10	,	,	PUNCT
ejpam-6415	172	11	τ	τ	PROPN
ejpam-6415	172	12	;	;	PUNCT
ejpam-6415	172	13	α	α	X
ejpam-6415	172	14	)	)	PUNCT
ejpam-6415	172	15	,	,	PUNCT
ejpam-6415	172	16	then	then	ADV
ejpam-6415	172	17	h	h	PROPN
ejpam-6415	172	18	is	be	AUX
ejpam-6415	172	19	convex	convex	ADJ
ejpam-6415	172	20	of	of	ADP
ejpam-6415	172	21	order	order	NOUN
ejpam-6415	172	22	β	β	X
ejpam-6415	172	23	in	in	ADP
ejpam-6415	172	24	the	the	DET
ejpam-6415	172	25	disk	disk	NOUN
ejpam-6415	172	26	|z|	|z|	NOUN
ejpam-6415	172	27	<	<	X
ejpam-6415	172	28	r3	r3	PROPN
ejpam-6415	172	29	,	,	PUNCT
ejpam-6415	172	30	where	where	SCONJ
ejpam-6415	172	31	r3	r3	PROPN
ejpam-6415	172	32	=	=	SYM
ejpam-6415	172	33	inf	inf	PROPN
ejpam-6415	172	34	n≥2	n≥2	PROPN
ejpam-6415	172	35	(1−	(1−	PROPN
ejpam-6415	172	36	β	β	X
ejpam-6415	172	37	)	)	PUNCT
ejpam-6415	173	1	[	[	X
ejpam-6415	173	2	(	(	PUNCT
ejpam-6415	173	3	τ	τ	PROPN
ejpam-6415	173	4	−	−	PROPN
ejpam-6415	173	5	δ	δ	PROPN
ejpam-6415	173	6	)	)	PUNCT
ejpam-6415	173	7	+	+	NUM
ejpam-6415	173	8	nδ	nδ	NOUN
ejpam-6415	173	9	+	+	NOUN
ejpam-6415	173	10	λµn(n−	λµn(n−	X
ejpam-6415	173	11	1	1	NUM
ejpam-6415	173	12	)	)	PUNCT
ejpam-6415	173	13	]	]	PUNCT
ejpam-6415	173	14	(	(	PUNCT
ejpam-6415	173	15	n+ν	n+ν	NUM
ejpam-6415	173	16	1+ν	1+ν	NUM
ejpam-6415	173	17	)	)	PUNCT
ejpam-6415	173	18	r	r	NOUN
ejpam-6415	173	19	n(n−	n(n−	PROPN
ejpam-6415	173	20	β)(1−	β)(1−	NOUN
ejpam-6415	173	21	α	α	NOUN
ejpam-6415	173	22	)	)	PUNCT
ejpam-6415	173	23			NOUN
ejpam-6415	173	24	1/(n−1	1/(n−1	NUM
ejpam-6415	173	25	)	)	PUNCT
ejpam-6415	173	26	.	.	PUNCT
ejpam-6415	174	1	(	(	PUNCT
ejpam-6415	174	2	14	14	NUM
ejpam-6415	174	3	)	)	PUNCT
ejpam-6415	174	4	proof	proof	NOUN
ejpam-6415	174	5	.	.	PUNCT
ejpam-6415	175	1	following	follow	VERB
ejpam-6415	175	2	arguments	argument	NOUN
ejpam-6415	175	3	analogous	analogous	ADJ
ejpam-6415	175	4	to	to	ADP
ejpam-6415	175	5	those	those	PRON
ejpam-6415	175	6	of	of	ADP
ejpam-6415	175	7	theorems	theorem	NOUN
ejpam-6415	175	8	5.1	5.1	NUM
ejpam-6415	175	9	and	and	CCONJ
ejpam-6415	175	10	5.2	5.2	NUM
ejpam-6415	175	11	,	,	PUNCT
ejpam-6415	175	12	we	we	PRON
ejpam-6415	175	13	obtain	obtain	VERB
ejpam-6415	175	14	the	the	DET
ejpam-6415	175	15	expression	expression	NOUN
ejpam-6415	175	16	for	for	ADP
ejpam-6415	175	17	the	the	DET
ejpam-6415	175	18	radius	radius	NOUN
ejpam-6415	175	19	given	give	VERB
ejpam-6415	175	20	in	in	ADP
ejpam-6415	175	21	(	(	PUNCT
ejpam-6415	175	22	14	14	NUM
ejpam-6415	175	23	)	)	PUNCT
ejpam-6415	175	24	.	.	PUNCT
ejpam-6415	176	1	6	6	X
ejpam-6415	176	2	.	.	X
ejpam-6415	176	3	conclusion	conclusion	NOUN
ejpam-6415	176	4	in	in	ADP
ejpam-6415	176	5	this	this	DET
ejpam-6415	176	6	paper	paper	NOUN
ejpam-6415	176	7	,	,	PUNCT
ejpam-6415	176	8	we	we	PRON
ejpam-6415	176	9	introduce	introduce	VERB
ejpam-6415	176	10	a	a	DET
ejpam-6415	176	11	new	new	ADJ
ejpam-6415	176	12	subclass	subclass	NOUN
ejpam-6415	176	13	of	of	ADP
ejpam-6415	176	14	analytic	analytic	ADJ
ejpam-6415	176	15	functions	function	NOUN
ejpam-6415	176	16	b∗	b∗	ADJ
ejpam-6415	176	17	ν(λ	ν(λ	NOUN
ejpam-6415	176	18	,	,	PUNCT
ejpam-6415	176	19	µ	µ	NOUN
ejpam-6415	176	20	,	,	PUNCT
ejpam-6415	176	21	δ	δ	PROPN
ejpam-6415	176	22	,	,	PUNCT
ejpam-6415	176	23	τ	τ	PROPN
ejpam-6415	176	24	;	;	PUNCT
ejpam-6415	176	25	α	α	X
ejpam-6415	176	26	)	)	PUNCT
ejpam-6415	176	27	,	,	PUNCT
ejpam-6415	176	28	which	which	PRON
ejpam-6415	176	29	is	be	AUX
ejpam-6415	176	30	defined	define	VERB
ejpam-6415	176	31	by	by	ADP
ejpam-6415	176	32	a	a	DET
ejpam-6415	176	33	generalized	generalize	VERB
ejpam-6415	176	34	multiplier	multipli	ADJ
ejpam-6415	176	35	operator	operator	NOUN
ejpam-6415	176	36	t	t	NOUN
ejpam-6415	176	37	r	r	NOUN
ejpam-6415	176	38	ν	ν	NOUN
ejpam-6415	176	39	.	.	PUNCT
ejpam-6415	177	1	we	we	PRON
ejpam-6415	177	2	derive	derive	VERB
ejpam-6415	177	3	sharp	sharp	ADJ
ejpam-6415	177	4	coefficient	coefficient	NOUN
ejpam-6415	177	5	estimates	estimate	NOUN
ejpam-6415	177	6	,	,	PUNCT
ejpam-6415	177	7	establish	establish	VERB
ejpam-6415	177	8	growth	growth	NOUN
ejpam-6415	177	9	and	and	CCONJ
ejpam-6415	177	10	distortion	distortion	NOUN
ejpam-6415	177	11	theorems	theorem	NOUN
ejpam-6415	177	12	,	,	PUNCT
ejpam-6415	177	13	and	and	CCONJ
ejpam-6415	177	14	determine	determine	VERB
ejpam-6415	177	15	the	the	DET
ejpam-6415	177	16	radii	radius	NOUN
ejpam-6415	177	17	of	of	ADP
ejpam-6415	177	18	close	close	NOUN
ejpam-6415	177	19	-	-	PUNCT
ejpam-6415	177	20	to	to	ADP
ejpam-6415	177	21	-	-	PUNCT
ejpam-6415	177	22	convexity	convexity	NOUN
ejpam-6415	177	23	,	,	PUNCT
ejpam-6415	177	24	starlikeness	starlikeness	NOUN
ejpam-6415	177	25	,	,	PUNCT
ejpam-6415	177	26	and	and	CCONJ
ejpam-6415	177	27	convexity	convexity	NOUN
ejpam-6415	177	28	.	.	PUNCT
ejpam-6415	178	1	the	the	DET
ejpam-6415	178	2	proposed	propose	VERB
ejpam-6415	178	3	class	class	NOUN
ejpam-6415	178	4	unifies	unify	VERB
ejpam-6415	178	5	and	and	CCONJ
ejpam-6415	178	6	generalizes	generalize	VERB
ejpam-6415	178	7	several	several	ADJ
ejpam-6415	178	8	well	well	ADV
ejpam-6415	178	9	-	-	PUNCT
ejpam-6415	178	10	known	know	VERB
ejpam-6415	178	11	subclasses	subclass	NOUN
ejpam-6415	178	12	in	in	ADP
ejpam-6415	178	13	geometric	geometric	ADJ
ejpam-6415	178	14	function	function	NOUN
ejpam-6415	178	15	theory	theory	NOUN
ejpam-6415	178	16	.	.	PUNCT
ejpam-6415	179	1	potential	potential	ADJ
ejpam-6415	179	2	directions	direction	NOUN
ejpam-6415	179	3	for	for	ADP
ejpam-6415	179	4	future	future	ADJ
ejpam-6415	179	5	work	work	NOUN
ejpam-6415	179	6	include	include	VERB
ejpam-6415	179	7	exploring	explore	VERB
ejpam-6415	179	8	inclusion	inclusion	NOUN
ejpam-6415	179	9	relationships	relationship	NOUN
ejpam-6415	179	10	,	,	PUNCT
ejpam-6415	179	11	neighborhood	neighborhood	NOUN
ejpam-6415	179	12	properties	property	NOUN
ejpam-6415	179	13	,	,	PUNCT
ejpam-6415	179	14	and	and	CCONJ
ejpam-6415	179	15	the	the	DET
ejpam-6415	179	16	behavior	behavior	NOUN
ejpam-6415	179	17	of	of	ADP
ejpam-6415	179	18	partial	partial	ADJ
ejpam-6415	179	19	sums	sum	NOUN
ejpam-6415	179	20	within	within	ADP
ejpam-6415	179	21	this	this	DET
ejpam-6415	179	22	class	class	NOUN
ejpam-6415	179	23	.	.	PUNCT
ejpam-6415	180	1	conflict	conflict	NOUN
ejpam-6415	180	2	of	of	ADP
ejpam-6415	180	3	interest	interest	NOUN
ejpam-6415	180	4	the	the	DET
ejpam-6415	180	5	authors	author	NOUN
ejpam-6415	180	6	declare	declare	VERB
ejpam-6415	180	7	that	that	SCONJ
ejpam-6415	180	8	there	there	PRON
ejpam-6415	180	9	are	be	VERB
ejpam-6415	180	10	no	no	DET
ejpam-6415	180	11	conflicts	conflict	NOUN
ejpam-6415	180	12	of	of	ADP
ejpam-6415	180	13	interest	interest	NOUN
ejpam-6415	180	14	.	.	PUNCT
ejpam-6415	181	1	s.	s.	PROPN
ejpam-6415	181	2	han	han	PROPN
ejpam-6415	181	3	,	,	PUNCT
ejpam-6415	181	4	m.	m.	NOUN
ejpam-6415	181	5	h.	h.	PROPN
ejpam-6415	181	6	mohd	mohd	PROPN
ejpam-6415	181	7	,	,	PUNCT
ejpam-6415	181	8	m.	m.	NOUN
ejpam-6415	181	9	illafe	illafe	ADJ
ejpam-6415	181	10	/	/	SYM
ejpam-6415	181	11	eur	eur	PROPN
ejpam-6415	181	12	.	.	PUNCT
ejpam-6415	182	1	j.	j.	PROPN
ejpam-6415	182	2	pure	pure	PROPN
ejpam-6415	182	3	appl	appl	PROPN
ejpam-6415	182	4	.	.	PROPN
ejpam-6415	182	5	math	math	PROPN
ejpam-6415	182	6	,	,	PUNCT
ejpam-6415	182	7	18	18	NUM
ejpam-6415	182	8	(	(	PUNCT
ejpam-6415	182	9	3	3	NUM
ejpam-6415	182	10	)	)	PUNCT
ejpam-6415	182	11	(	(	PUNCT
ejpam-6415	182	12	2025	2025	NUM
ejpam-6415	182	13	)	)	PUNCT
ejpam-6415	182	14	,	,	PUNCT
ejpam-6415	182	15	6415	6415	NUM
ejpam-6415	182	16	9	9	NUM
ejpam-6415	182	17	of	of	ADP
ejpam-6415	182	18	9	9	NUM
ejpam-6415	182	19	references	reference	NOUN
ejpam-6415	182	20	[	[	X
ejpam-6415	182	21	1	1	NUM
ejpam-6415	182	22	]	]	X
ejpam-6415	182	23	n.	n.	PROPN
ejpam-6415	182	24	e.	e.	PROPN
ejpam-6415	182	25	cho	cho	PROPN
ejpam-6415	182	26	and	and	CCONJ
ejpam-6415	182	27	h.	h.	PROPN
ejpam-6415	182	28	m.	m.	PROPN
ejpam-6415	182	29	srivastava	srivastava	PROPN
ejpam-6415	182	30	.	.	PUNCT
ejpam-6415	183	1	argument	argument	NOUN
ejpam-6415	183	2	estimates	estimate	NOUN
ejpam-6415	183	3	of	of	ADP
ejpam-6415	183	4	certain	certain	ADJ
ejpam-6415	183	5	analytic	analytic	ADJ
ejpam-6415	183	6	functions	function	NOUN
ejpam-6415	183	7	defined	define	VERB
ejpam-6415	183	8	by	by	ADP
ejpam-6415	183	9	a	a	DET
ejpam-6415	183	10	class	class	NOUN
ejpam-6415	183	11	of	of	ADP
ejpam-6415	183	12	multiplier	multipli	ADJ
ejpam-6415	183	13	transformations	transformation	NOUN
ejpam-6415	183	14	.	.	PUNCT
ejpam-6415	184	1	mathematical	mathematical	ADJ
ejpam-6415	184	2	and	and	CCONJ
ejpam-6415	184	3	computer	computer	NOUN
ejpam-6415	184	4	modelling	modelling	NOUN
ejpam-6415	184	5	,	,	PUNCT
ejpam-6415	184	6	37(1–2):39–49	37(1–2):39–49	NUM
ejpam-6415	184	7	,	,	PUNCT
ejpam-6415	184	8	2003	2003	NUM
ejpam-6415	184	9	.	.	PUNCT
ejpam-6415	185	1	[	[	X
ejpam-6415	185	2	2	2	NUM
ejpam-6415	185	3	]	]	X
ejpam-6415	185	4	b.	b.	PROPN
ejpam-6415	185	5	a.	a.	PROPN
ejpam-6415	185	6	uralegaddi	uralegaddi	PROPN
ejpam-6415	185	7	and	and	CCONJ
ejpam-6415	185	8	c.	c.	PROPN
ejpam-6415	185	9	somanatha	somanatha	PROPN
ejpam-6415	185	10	.	.	PUNCT
ejpam-6415	186	1	certain	certain	ADJ
ejpam-6415	186	2	classes	class	NOUN
ejpam-6415	186	3	of	of	ADP
ejpam-6415	186	4	univalent	univalent	ADJ
ejpam-6415	186	5	functions	function	NOUN
ejpam-6415	186	6	.	.	PUNCT
ejpam-6415	187	1	in	in	ADP
ejpam-6415	187	2	current	current	ADJ
ejpam-6415	187	3	topics	topic	NOUN
ejpam-6415	187	4	in	in	ADP
ejpam-6415	187	5	analytic	analytic	ADJ
ejpam-6415	187	6	function	function	NOUN
ejpam-6415	187	7	theory	theory	NOUN
ejpam-6415	187	8	,	,	PUNCT
ejpam-6415	187	9	pages	page	NOUN
ejpam-6415	187	10	371–374	371–374	NUM
ejpam-6415	187	11	,	,	PUNCT
ejpam-6415	187	12	1992	1992	NUM
ejpam-6415	187	13	.	.	PUNCT
ejpam-6415	188	1	[	[	X
ejpam-6415	188	2	3	3	X
ejpam-6415	188	3	]	]	X
ejpam-6415	188	4	g.	g.	PROPN
ejpam-6415	188	5	s.	s.	PROPN
ejpam-6415	188	6	sălăgean	sălăgean	PROPN
ejpam-6415	188	7	.	.	PUNCT
ejpam-6415	189	1	subclasses	subclass	NOUN
ejpam-6415	189	2	of	of	ADP
ejpam-6415	189	3	univalent	univalent	ADJ
ejpam-6415	189	4	functions	function	NOUN
ejpam-6415	189	5	.	.	PUNCT
ejpam-6415	190	1	in	in	ADP
ejpam-6415	190	2	complex	complex	ADJ
ejpam-6415	190	3	analysis	analysis	NOUN
ejpam-6415	190	4	:	:	PUNCT
ejpam-6415	190	5	fifth	fifth	ADJ
ejpam-6415	190	6	romanian	romanian	ADJ
ejpam-6415	190	7	-	-	PUNCT
ejpam-6415	190	8	finnish	finnish	ADJ
ejpam-6415	190	9	seminar	seminar	NOUN
ejpam-6415	190	10	,	,	PUNCT
ejpam-6415	190	11	pages	page	NOUN
ejpam-6415	190	12	362–372	362–372	NUM
ejpam-6415	190	13	.	.	PUNCT
ejpam-6415	190	14	springer	springer	NOUN
ejpam-6415	190	15	,	,	PUNCT
ejpam-6415	190	16	1981	1981	NUM
ejpam-6415	190	17	.	.	PUNCT
ejpam-6415	191	1	[	[	X
ejpam-6415	191	2	4	4	X
ejpam-6415	191	3	]	]	PUNCT
ejpam-6415	191	4	f.	f.	PROPN
ejpam-6415	191	5	yousef	yousef	PROPN
ejpam-6415	191	6	,	,	PUNCT
ejpam-6415	191	7	s.	s.	PROPN
ejpam-6415	191	8	alroud	alroud	PROPN
ejpam-6415	191	9	,	,	PUNCT
ejpam-6415	191	10	and	and	CCONJ
ejpam-6415	191	11	m.	m.	NOUN
ejpam-6415	191	12	illafe	illafe	ADJ
ejpam-6415	191	13	.	.	PUNCT
ejpam-6415	192	1	new	new	ADJ
ejpam-6415	192	2	subclasses	subclass	NOUN
ejpam-6415	192	3	of	of	ADP
ejpam-6415	192	4	analytic	analytic	ADJ
ejpam-6415	192	5	and	and	CCONJ
ejpam-6415	192	6	bi	bi	ADJ
ejpam-6415	192	7	-	-	ADJ
ejpam-6415	192	8	univalent	univalent	ADJ
ejpam-6415	192	9	functions	function	NOUN
ejpam-6415	192	10	endowed	endow	VERB
ejpam-6415	192	11	with	with	ADP
ejpam-6415	192	12	coefficient	coefficient	NOUN
ejpam-6415	192	13	estimate	estimate	NOUN
ejpam-6415	192	14	problems	problem	NOUN
ejpam-6415	192	15	.	.	PUNCT
ejpam-6415	193	1	analysis	analysis	NOUN
ejpam-6415	193	2	and	and	CCONJ
ejpam-6415	193	3	mathematical	mathematical	ADJ
ejpam-6415	193	4	physics	physics	NOUN
ejpam-6415	193	5	,	,	PUNCT
ejpam-6415	193	6	11:1–12	11:1–12	NUM
ejpam-6415	193	7	,	,	PUNCT
ejpam-6415	193	8	2021	2021	NUM
ejpam-6415	193	9	.	.	PUNCT
ejpam-6415	194	1	[	[	X
ejpam-6415	194	2	5	5	NUM
ejpam-6415	194	3	]	]	PUNCT
ejpam-6415	194	4	m.	m.	NOUN
ejpam-6415	194	5	illafe	illafe	NOUN
ejpam-6415	194	6	,	,	PUNCT
ejpam-6415	194	7	a.	a.	PROPN
ejpam-6415	194	8	amourah	amourah	PROPN
ejpam-6415	194	9	,	,	PUNCT
ejpam-6415	194	10	and	and	CCONJ
ejpam-6415	194	11	m.	m.	PROPN
ejpam-6415	194	12	haji	haji	PROPN
ejpam-6415	194	13	mohd	mohd	PROPN
ejpam-6415	194	14	.	.	PUNCT
ejpam-6415	195	1	coefficient	coefficient	NOUN
ejpam-6415	195	2	estimates	estimate	NOUN
ejpam-6415	195	3	and	and	CCONJ
ejpam-6415	195	4	fekete	fekete	PROPN
ejpam-6415	195	5	–	–	PUNCT
ejpam-6415	195	6	szegö	szegö	ADJ
ejpam-6415	195	7	inequalities	inequality	NOUN
ejpam-6415	195	8	for	for	ADP
ejpam-6415	195	9	a	a	DET
ejpam-6415	195	10	subclass	subclass	NOUN
ejpam-6415	195	11	of	of	ADP
ejpam-6415	195	12	analytic	analytic	ADJ
ejpam-6415	195	13	and	and	CCONJ
ejpam-6415	195	14	bi	bi	ADJ
ejpam-6415	195	15	-	-	ADJ
ejpam-6415	195	16	univalent	univalent	ADJ
ejpam-6415	195	17	functions	function	NOUN
ejpam-6415	195	18	.	.	PUNCT
ejpam-6415	196	1	axioms	axiom	NOUN
ejpam-6415	196	2	,	,	PUNCT
ejpam-6415	196	3	11(4):147	11(4):147	NUM
ejpam-6415	196	4	,	,	PUNCT
ejpam-6415	196	5	2022	2022	NUM
ejpam-6415	196	6	.	.	PUNCT
ejpam-6415	197	1	[	[	X
ejpam-6415	197	2	6	6	NUM
ejpam-6415	197	3	]	]	PUNCT
ejpam-6415	197	4	m.	m.	NOUN
ejpam-6415	197	5	illafe	illafe	NOUN
ejpam-6415	197	6	,	,	PUNCT
ejpam-6415	197	7	m.	m.	NOUN
ejpam-6415	197	8	h.	h.	PROPN
ejpam-6415	197	9	mohd	mohd	PROPN
ejpam-6415	197	10	,	,	PUNCT
ejpam-6415	197	11	f.	f.	PROPN
ejpam-6415	197	12	yousef	yousef	PROPN
ejpam-6415	197	13	,	,	PUNCT
ejpam-6415	197	14	and	and	CCONJ
ejpam-6415	197	15	s.	s.	PROPN
ejpam-6415	197	16	supramaniam	supramaniam	PROPN
ejpam-6415	197	17	.	.	PUNCT
ejpam-6415	198	1	a	a	DET
ejpam-6415	198	2	subclass	subclass	NOUN
ejpam-6415	198	3	of	of	ADP
ejpam-6415	198	4	bi	bi	ADJ
ejpam-6415	198	5	-	-	ADJ
ejpam-6415	198	6	univalent	univalent	ADJ
ejpam-6415	198	7	functions	function	NOUN
ejpam-6415	198	8	defined	define	VERB
ejpam-6415	198	9	by	by	ADP
ejpam-6415	198	10	a	a	DET
ejpam-6415	198	11	symmetric	symmetric	ADJ
ejpam-6415	198	12	q	q	ADJ
ejpam-6415	198	13	-	-	ADJ
ejpam-6415	198	14	derivative	derivative	ADJ
ejpam-6415	198	15	operator	operator	NOUN
ejpam-6415	198	16	and	and	CCONJ
ejpam-6415	198	17	gegenbauer	gegenbauer	NOUN
ejpam-6415	198	18	polynomials	polynomial	NOUN
ejpam-6415	198	19	.	.	PUNCT
ejpam-6415	199	1	european	european	PROPN
ejpam-6415	199	2	journal	journal	PROPN
ejpam-6415	199	3	of	of	ADP
ejpam-6415	199	4	pure	pure	ADJ
ejpam-6415	199	5	and	and	CCONJ
ejpam-6415	199	6	applied	applied	ADJ
ejpam-6415	199	7	mathematics	mathematic	NOUN
ejpam-6415	199	8	,	,	PUNCT
ejpam-6415	199	9	17(4):2467–2480	17(4):2467–2480	NUM
ejpam-6415	199	10	,	,	PUNCT
ejpam-6415	199	11	2024	2024	NUM
ejpam-6415	199	12	.	.	PUNCT
ejpam-6415	200	1	[	[	X
ejpam-6415	200	2	7	7	X
ejpam-6415	200	3	]	]	PUNCT
ejpam-6415	200	4	m.	m.	NOUN
ejpam-6415	200	5	illafe	illafe	NOUN
ejpam-6415	200	6	,	,	PUNCT
ejpam-6415	200	7	f.	f.	PROPN
ejpam-6415	200	8	yousef	yousef	PROPN
ejpam-6415	200	9	,	,	PUNCT
ejpam-6415	200	10	m.	m.	NOUN
ejpam-6415	200	11	h.	h.	PROPN
ejpam-6415	200	12	mohd	mohd	PROPN
ejpam-6415	200	13	,	,	PUNCT
ejpam-6415	200	14	and	and	CCONJ
ejpam-6415	200	15	s.	s.	PROPN
ejpam-6415	200	16	supramaniam	supramaniam	PROPN
ejpam-6415	200	17	.	.	PUNCT
ejpam-6415	201	1	initial	initial	ADJ
ejpam-6415	201	2	coefficients	coefficient	NOUN
ejpam-6415	201	3	estimates	estimate	NOUN
ejpam-6415	201	4	and	and	CCONJ
ejpam-6415	201	5	fekete	fekete	PROPN
ejpam-6415	201	6	–	–	PUNCT
ejpam-6415	201	7	szegö	szegö	VERB
ejpam-6415	201	8	inequality	inequality	NOUN
ejpam-6415	201	9	problem	problem	NOUN
ejpam-6415	201	10	for	for	ADP
ejpam-6415	201	11	a	a	DET
ejpam-6415	201	12	general	general	ADJ
ejpam-6415	201	13	subclass	subclass	NOUN
ejpam-6415	201	14	of	of	ADP
ejpam-6415	201	15	bi	bi	ADJ
ejpam-6415	201	16	-	-	ADJ
ejpam-6415	201	17	univalent	univalent	ADJ
ejpam-6415	201	18	functions	function	NOUN
ejpam-6415	201	19	defined	define	VERB
ejpam-6415	201	20	by	by	ADP
ejpam-6415	201	21	subordination	subordination	NOUN
ejpam-6415	201	22	.	.	PUNCT
ejpam-6415	202	1	axioms	axiom	NOUN
ejpam-6415	202	2	,	,	PUNCT
ejpam-6415	202	3	12(3):235	12(3):235	NUM
ejpam-6415	202	4	,	,	PUNCT
ejpam-6415	202	5	2023	2023	NUM
ejpam-6415	202	6	.	.	PUNCT
ejpam-6415	203	1	[	[	X
ejpam-6415	203	2	8	8	NUM
ejpam-6415	203	3	]	]	PUNCT
ejpam-6415	203	4	m.	m.	NOUN
ejpam-6415	203	5	illafe	illafe	NOUN
ejpam-6415	203	6	and	and	CCONJ
ejpam-6415	203	7	a.	a.	NOUN
ejpam-6415	203	8	a.	a.	PROPN
ejpam-6415	203	9	amourah	amourah	PROPN
ejpam-6415	203	10	.	.	PUNCT
ejpam-6415	204	1	coefficient	coefficient	NOUN
ejpam-6415	204	2	estimates	estimate	NOUN
ejpam-6415	204	3	and	and	CCONJ
ejpam-6415	204	4	fekete	fekete	PROPN
ejpam-6415	204	5	–	–	PUNCT
ejpam-6415	204	6	szegö	szegö	ADJ
ejpam-6415	204	7	functional	functional	ADJ
ejpam-6415	204	8	inequalities	inequality	NOUN
ejpam-6415	204	9	for	for	ADP
ejpam-6415	204	10	a	a	DET
ejpam-6415	204	11	certain	certain	ADJ
ejpam-6415	204	12	subclass	subclass	NOUN
ejpam-6415	204	13	of	of	ADP
ejpam-6415	204	14	analytic	analytic	ADJ
ejpam-6415	204	15	and	and	CCONJ
ejpam-6415	204	16	bi	bi	ADJ
ejpam-6415	204	17	-	-	ADJ
ejpam-6415	204	18	univalent	univalent	ADJ
ejpam-6415	204	19	functions	function	NOUN
ejpam-6415	204	20	.	.	PUNCT
ejpam-6415	205	1	axioms	axiom	NOUN
ejpam-6415	205	2	,	,	PUNCT
ejpam-6415	205	3	11(4):147	11(4):147	NUM
ejpam-6415	205	4	,	,	PUNCT
ejpam-6415	205	5	2022	2022	NUM
ejpam-6415	205	6	.	.	PUNCT
ejpam-6415	206	1	[	[	X
ejpam-6415	206	2	9	9	NUM
ejpam-6415	206	3	]	]	PUNCT
ejpam-6415	206	4	a.	a.	NOUN
ejpam-6415	206	5	amourah	amourah	PROPN
ejpam-6415	206	6	and	and	CCONJ
ejpam-6415	206	7	m.	m.	NOUN
ejpam-6415	206	8	illafe	illafe	ADJ
ejpam-6415	206	9	.	.	PUNCT
ejpam-6415	207	1	a	a	DET
ejpam-6415	207	2	comprehensive	comprehensive	ADJ
ejpam-6415	207	3	subclass	subclass	NOUN
ejpam-6415	207	4	of	of	ADP
ejpam-6415	207	5	analytic	analytic	ADJ
ejpam-6415	207	6	and	and	CCONJ
ejpam-6415	207	7	bi	bi	ADJ
ejpam-6415	207	8	-	-	ADJ
ejpam-6415	207	9	univalent	univalent	ADJ
ejpam-6415	207	10	functions	function	NOUN
ejpam-6415	207	11	associated	associate	VERB
ejpam-6415	207	12	with	with	ADP
ejpam-6415	207	13	subordination	subordination	NOUN
ejpam-6415	207	14	.	.	PUNCT
ejpam-6415	208	1	palestine	palestine	PROPN
ejpam-6415	208	2	journal	journal	PROPN
ejpam-6415	208	3	of	of	ADP
ejpam-6415	208	4	mathematics	mathematic	NOUN
ejpam-6415	208	5	,	,	PUNCT
ejpam-6415	208	6	9(1):187	9(1):187	NUM
ejpam-6415	208	7	–	–	PUNCT
ejpam-6415	208	8	193	193	NUM
ejpam-6415	208	9	,	,	PUNCT
ejpam-6415	208	10	2022	2022	NUM
ejpam-6415	208	11	.	.	PUNCT
ejpam-6415	209	1	[	[	X
ejpam-6415	209	2	10	10	NUM
ejpam-6415	209	3	]	]	X
ejpam-6415	209	4	f.	f.	PROPN
ejpam-6415	209	5	yousef	yousef	PROPN
ejpam-6415	209	6	,	,	PUNCT
ejpam-6415	209	7	s.	s.	PROPN
ejpam-6415	209	8	alroud	alroud	PROPN
ejpam-6415	209	9	,	,	PUNCT
ejpam-6415	209	10	and	and	CCONJ
ejpam-6415	209	11	m.	m.	NOUN
ejpam-6415	209	12	illafe	illafe	ADJ
ejpam-6415	209	13	.	.	PUNCT
ejpam-6415	210	1	a	a	DET
ejpam-6415	210	2	comprehensive	comprehensive	ADJ
ejpam-6415	210	3	subclass	subclass	NOUN
ejpam-6415	210	4	of	of	ADP
ejpam-6415	210	5	bi	bi	ADJ
ejpam-6415	210	6	-	-	ADJ
ejpam-6415	210	7	univalent	univalent	ADJ
ejpam-6415	210	8	functions	function	NOUN
ejpam-6415	210	9	associated	associate	VERB
ejpam-6415	210	10	with	with	ADP
ejpam-6415	210	11	chebyshev	chebyshev	NOUN
ejpam-6415	210	12	polynomials	polynomial	NOUN
ejpam-6415	210	13	of	of	ADP
ejpam-6415	210	14	the	the	DET
ejpam-6415	210	15	second	second	ADJ
ejpam-6415	210	16	kind	kind	NOUN
ejpam-6415	210	17	.	.	PUNCT
ejpam-6415	211	1	analysis	analysis	NOUN
ejpam-6415	211	2	and	and	CCONJ
ejpam-6415	211	3	mathematical	mathematical	ADJ
ejpam-6415	211	4	physics	physics	NOUN
ejpam-6415	211	5	,	,	PUNCT
ejpam-6415	211	6	26:329–339	26:329–339	NUM
ejpam-6415	211	7	,	,	PUNCT
ejpam-6415	211	8	2019	2019	NUM
ejpam-6415	211	9	.	.	PUNCT
ejpam-6415	212	1	[	[	X
ejpam-6415	212	2	11	11	NUM
ejpam-6415	212	3	]	]	PUNCT
ejpam-6415	212	4	m.	m.	NOUN
ejpam-6415	212	5	illafe	illafe	NOUN
ejpam-6415	212	6	,	,	PUNCT
ejpam-6415	212	7	m.	m.	NOUN
ejpam-6415	212	8	h.	h.	PROPN
ejpam-6415	212	9	mohd	mohd	PROPN
ejpam-6415	212	10	,	,	PUNCT
ejpam-6415	212	11	and	and	CCONJ
ejpam-6415	212	12	f.	f.	PROPN
ejpam-6415	212	13	yousef	yousef	PROPN
ejpam-6415	212	14	.	.	PUNCT
ejpam-6415	213	1	bounds	bound	VERB
ejpam-6415	213	2	for	for	ADP
ejpam-6415	213	3	the	the	DET
ejpam-6415	213	4	second	second	ADJ
ejpam-6415	213	5	hankel	hankel	NOUN
ejpam-6415	213	6	determinant	determinant	ADJ
ejpam-6415	213	7	of	of	ADP
ejpam-6415	213	8	a	a	DET
ejpam-6415	213	9	general	general	ADJ
ejpam-6415	213	10	subclass	subclass	NOUN
ejpam-6415	213	11	of	of	ADP
ejpam-6415	213	12	bi	bi	ADJ
ejpam-6415	213	13	-	-	ADJ
ejpam-6415	213	14	univalent	univalent	ADJ
ejpam-6415	213	15	functions	function	NOUN
ejpam-6415	213	16	.	.	PUNCT
ejpam-6415	214	1	international	international	ADJ
ejpam-6415	214	2	journal	journal	PROPN
ejpam-6415	214	3	of	of	ADP
ejpam-6415	214	4	mathematics	mathematics	PROPN
ejpam-6415	214	5	engineering	engineering	NOUN
ejpam-6415	214	6	and	and	CCONJ
ejpam-6415	214	7	management	management	NOUN
ejpam-6415	214	8	science	science	NOUN
ejpam-6415	214	9	,	,	PUNCT
ejpam-6415	214	10	9:1226–1239	9:1226–1239	NUM
ejpam-6415	214	11	,	,	PUNCT
ejpam-6415	214	12	2024	2024	NUM
ejpam-6415	214	13	.	.	PUNCT
ejpam-6415	215	1	[	[	X
ejpam-6415	215	2	12	12	NUM
ejpam-6415	215	3	]	]	PUNCT
ejpam-6415	215	4	m.	m.	NOUN
ejpam-6415	215	5	illafe	illafe	NOUN
ejpam-6415	215	6	,	,	PUNCT
ejpam-6415	215	7	m.	m.	NOUN
ejpam-6415	215	8	h.	h.	PROPN
ejpam-6415	215	9	mohd	mohd	PROPN
ejpam-6415	215	10	,	,	PUNCT
ejpam-6415	215	11	f.	f.	PROPN
ejpam-6415	215	12	yousef	yousef	PROPN
ejpam-6415	215	13	,	,	PUNCT
ejpam-6415	215	14	and	and	CCONJ
ejpam-6415	215	15	s.	s.	PROPN
ejpam-6415	215	16	supramaniam	supramaniam	PROPN
ejpam-6415	215	17	.	.	PUNCT
ejpam-6415	216	1	investigating	investigate	VERB
ejpam-6415	216	2	inclusion	inclusion	NOUN
ejpam-6415	216	3	,	,	PUNCT
ejpam-6415	216	4	neighborhood	neighborhood	NOUN
ejpam-6415	216	5	,	,	PUNCT
ejpam-6415	216	6	and	and	CCONJ
ejpam-6415	216	7	partial	partial	ADJ
ejpam-6415	216	8	sums	sum	VERB
ejpam-6415	216	9	properties	property	NOUN
ejpam-6415	216	10	for	for	ADP
ejpam-6415	216	11	a	a	DET
ejpam-6415	216	12	general	general	ADJ
ejpam-6415	216	13	subclass	subclass	NOUN
ejpam-6415	216	14	of	of	ADP
ejpam-6415	216	15	analytic	analytic	ADJ
ejpam-6415	216	16	functions	function	NOUN
ejpam-6415	216	17	.	.	PUNCT
ejpam-6415	217	1	international	international	ADJ
ejpam-6415	217	2	journal	journal	PROPN
ejpam-6415	217	3	of	of	ADP
ejpam-6415	217	4	neutrosophic	neutrosophic	ADJ
ejpam-6415	217	5	science	science	NOUN
ejpam-6415	217	6	,	,	PUNCT
ejpam-6415	217	7	25(3):501–510	25(3):501–510	NUM
ejpam-6415	217	8	,	,	PUNCT
ejpam-6415	217	9	2024	2024	NUM
ejpam-6415	217	10	.	.	PUNCT
ejpam-6415	218	1	[	[	X
ejpam-6415	218	2	13	13	NUM
ejpam-6415	218	3	]	]	PUNCT
ejpam-6415	218	4	m.	m.	NOUN
ejpam-6415	218	5	illafe	illafe	NOUN
ejpam-6415	218	6	,	,	PUNCT
ejpam-6415	218	7	f.	f.	PROPN
ejpam-6415	218	8	yousef	yousef	PROPN
ejpam-6415	218	9	,	,	PUNCT
ejpam-6415	218	10	m.	m.	NOUN
ejpam-6415	218	11	h.	h.	PROPN
ejpam-6415	218	12	mohd	mohd	PROPN
ejpam-6415	218	13	,	,	PUNCT
ejpam-6415	218	14	and	and	CCONJ
ejpam-6415	218	15	s.	s.	PROPN
ejpam-6415	218	16	supramaniam	supramaniam	PROPN
ejpam-6415	218	17	.	.	PUNCT
ejpam-6415	219	1	fundamental	fundamental	ADJ
ejpam-6415	219	2	properties	property	NOUN
ejpam-6415	219	3	of	of	ADP
ejpam-6415	219	4	a	a	DET
ejpam-6415	219	5	class	class	NOUN
ejpam-6415	219	6	of	of	ADP
ejpam-6415	219	7	analytic	analytic	ADJ
ejpam-6415	219	8	functions	function	NOUN
ejpam-6415	219	9	defined	define	VERB
ejpam-6415	219	10	by	by	ADP
ejpam-6415	219	11	a	a	DET
ejpam-6415	219	12	generalized	generalize	VERB
ejpam-6415	219	13	multiplier	multipli	ADJ
ejpam-6415	219	14	transformation	transformation	NOUN
ejpam-6415	219	15	operator	operator	NOUN
ejpam-6415	219	16	.	.	PUNCT
ejpam-6415	220	1	international	international	ADJ
ejpam-6415	220	2	journal	journal	PROPN
ejpam-6415	220	3	of	of	ADP
ejpam-6415	220	4	mathematics	mathematic	NOUN
ejpam-6415	220	5	and	and	CCONJ
ejpam-6415	220	6	computer	computer	NOUN
ejpam-6415	220	7	science	science	NOUN
ejpam-6415	220	8	,	,	PUNCT
ejpam-6415	220	9	19(4):1203–1211	19(4):1203–1211	NUM
ejpam-6415	220	10	,	,	PUNCT
ejpam-6415	220	11	2024	2024	NUM
ejpam-6415	220	12	.	.	PUNCT
ejpam-6415	221	1	[	[	X
ejpam-6415	221	2	14	14	NUM
ejpam-6415	221	3	]	]	X
ejpam-6415	221	4	j.	j.	PROPN
ejpam-6415	221	5	stewart	stewart	PROPN
ejpam-6415	221	6	.	.	PUNCT
ejpam-6415	222	1	tayler	tayler	PROPN
ejpam-6415	222	2	and	and	CCONJ
ejpam-6415	222	3	maclaurin	maclaurin	PROPN
ejpam-6415	222	4	series	series	NOUN
ejpam-6415	222	5	.	.	PUNCT
ejpam-6415	223	1	cengage	cengage	PROPN
ejpam-6415	223	2	learning	learning	PROPN
ejpam-6415	223	3	,	,	PUNCT
ejpam-6415	223	4	8th	8th	ADJ
ejpam-6415	223	5	edition	edition	NOUN
ejpam-6415	223	6	,	,	PUNCT
ejpam-6415	223	7	2016	2016	NUM
ejpam-6415	223	8	.	.	PUNCT