id	sid	tid	token	lemma	pos
ejpam-3018	1	1	european	european	PROPN
ejpam-3018	1	2	journal	journal	PROPN
ejpam-3018	1	3	of	of	ADP
ejpam-3018	1	4	pure	pure	ADJ
ejpam-3018	1	5	and	and	CCONJ
ejpam-3018	1	6	applied	apply	VERB
ejpam-3018	1	7	mathematics	mathematic	NOUN
ejpam-3018	1	8	vol	vol	NOUN
ejpam-3018	1	9	.	.	PROPN
ejpam-3018	2	1	10	10	NUM
ejpam-3018	2	2	,	,	PUNCT
ejpam-3018	2	3	no	no	INTJ
ejpam-3018	2	4	.	.	NOUN
ejpam-3018	2	5	4	4	NUM
ejpam-3018	2	6	,	,	PUNCT
ejpam-3018	2	7	2017	2017	NUM
ejpam-3018	2	8	,	,	PUNCT
ejpam-3018	2	9	890	890	NUM
ejpam-3018	2	10	-	-	SYM
ejpam-3018	2	11	907	907	NUM
ejpam-3018	2	12	issn	issn	PROPN
ejpam-3018	2	13	1307	1307	NUM
ejpam-3018	2	14	-	-	SYM
ejpam-3018	2	15	5543	5543	NUM
ejpam-3018	2	16	–	–	PUNCT
ejpam-3018	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3018	2	18	published	publish	VERB
ejpam-3018	2	19	by	by	ADP
ejpam-3018	2	20	new	new	PROPN
ejpam-3018	2	21	york	york	PROPN
ejpam-3018	2	22	business	business	PROPN
ejpam-3018	2	23	global	global	ADJ
ejpam-3018	2	24	stancu	stancu	PROPN
ejpam-3018	2	25	type	type	NOUN
ejpam-3018	2	26	generalization	generalization	NOUN
ejpam-3018	2	27	of	of	ADP
ejpam-3018	2	28	modified	modify	VERB
ejpam-3018	2	29	srivastava	srivastava	PROPN
ejpam-3018	2	30	-	-	PUNCT
ejpam-3018	2	31	gupta	gupta	PROPN
ejpam-3018	2	32	operators	operators	PROPN
ejpam-3018	2	33	alok	alok	PROPN
ejpam-3018	2	34	kumar1	kumar1	PROPN
ejpam-3018	2	35	,	,	PUNCT
ejpam-3018	2	36	vishnu	vishnu	PROPN
ejpam-3018	2	37	narayan	narayan	PROPN
ejpam-3018	2	38	mishra2,3,∗	mishra2,3,∗	PROPN
ejpam-3018	2	39	,	,	PUNCT
ejpam-3018	2	40	dipti	dipti	VERB
ejpam-3018	2	41	tapiawala4,5	tapiawala4,5	PROPN
ejpam-3018	2	42	1department	1department	NUM
ejpam-3018	2	43	of	of	ADP
ejpam-3018	2	44	computer	computer	NOUN
ejpam-3018	2	45	science	science	NOUN
ejpam-3018	2	46	,	,	PUNCT
ejpam-3018	2	47	dev	dev	PROPN
ejpam-3018	2	48	sanskriti	sanskriti	PROPN
ejpam-3018	2	49	vishwavidyalaya	vishwavidyalaya	PROPN
ejpam-3018	2	50	,	,	PUNCT
ejpam-3018	2	51	haridwar	haridwar	PROPN
ejpam-3018	2	52	,	,	PUNCT
ejpam-3018	2	53	uttarakhand	uttarakhand	PROPN
ejpam-3018	2	54	,	,	PUNCT
ejpam-3018	2	55	india	india	PROPN
ejpam-3018	2	56	2	2	NUM
ejpam-3018	2	57	department	department	NOUN
ejpam-3018	2	58	of	of	ADP
ejpam-3018	2	59	mathematics	mathematic	NOUN
ejpam-3018	2	60	,	,	PUNCT
ejpam-3018	2	61	indira	indira	PROPN
ejpam-3018	2	62	gandhi	gandhi	PROPN
ejpam-3018	2	63	national	national	PROPN
ejpam-3018	2	64	tribal	tribal	PROPN
ejpam-3018	2	65	university	university	PROPN
ejpam-3018	2	66	,	,	PUNCT
ejpam-3018	2	67	lalpur	lalpur	PROPN
ejpam-3018	2	68	,	,	PUNCT
ejpam-3018	2	69	amarkantak	amarkantak	PROPN
ejpam-3018	2	70	,	,	PUNCT
ejpam-3018	2	71	madhya	madhya	PROPN
ejpam-3018	2	72	pradesh	pradesh	PROPN
ejpam-3018	2	73	,	,	PUNCT
ejpam-3018	2	74	india	india	PROPN
ejpam-3018	2	75	3l	3l	NUM
ejpam-3018	2	76	.	.	PUNCT
ejpam-3018	3	1	1627	1627	NUM
ejpam-3018	3	2	awadh	awadh	PROPN
ejpam-3018	3	3	puri	puri	PROPN
ejpam-3018	3	4	colony	colony	NOUN
ejpam-3018	3	5	beniganj	beniganj	ADJ
ejpam-3018	3	6	,	,	PUNCT
ejpam-3018	3	7	phase	phase	NOUN
ejpam-3018	3	8	-	-	PUNCT
ejpam-3018	3	9	iii	iii	NOUN
ejpam-3018	3	10	,	,	PUNCT
ejpam-3018	3	11	opposite	opposite	ADJ
ejpam-3018	3	12	-	-	PUNCT
ejpam-3018	3	13	industrial	industrial	ADJ
ejpam-3018	3	14	training	training	NOUN
ejpam-3018	3	15	institute	institute	NOUN
ejpam-3018	3	16	(	(	PUNCT
ejpam-3018	3	17	i.t.i	i.t.i	NOUN
ejpam-3018	3	18	.	.	PUNCT
ejpam-3018	3	19	)	)	PUNCT
ejpam-3018	3	20	,	,	PUNCT
ejpam-3018	3	21	faizabad	faizabad	PROPN
ejpam-3018	3	22	,	,	PUNCT
ejpam-3018	3	23	uttar	uttar	PROPN
ejpam-3018	3	24	pradesh	pradesh	PROPN
ejpam-3018	3	25	,	,	PUNCT
ejpam-3018	3	26	india	india	PROPN
ejpam-3018	3	27	4department	4department	NUM
ejpam-3018	3	28	of	of	ADP
ejpam-3018	3	29	mathematics	mathematic	NOUN
ejpam-3018	3	30	,	,	PUNCT
ejpam-3018	3	31	c	c	PROPN
ejpam-3018	3	32	u	u	PROPN
ejpam-3018	3	33	shah	shah	PROPN
ejpam-3018	3	34	university	university	PROPN
ejpam-3018	3	35	,	,	PUNCT
ejpam-3018	3	36	gujarat	gujarat	PROPN
ejpam-3018	3	37	,	,	PUNCT
ejpam-3018	3	38	india	india	PROPN
ejpam-3018	3	39	5as	5as	PROPN
ejpam-3018	3	40	and	and	CCONJ
ejpam-3018	3	41	h	h	PROPN
ejpam-3018	3	42	department	department	PROPN
ejpam-3018	3	43	(	(	PUNCT
ejpam-3018	3	44	mathematics	mathematics	PROPN
ejpam-3018	3	45	)	)	PUNCT
ejpam-3018	3	46	,	,	PUNCT
ejpam-3018	3	47	sardar	sardar	PROPN
ejpam-3018	3	48	vallabhbhai	vallabhbhai	PROPN
ejpam-3018	3	49	patel	patel	PROPN
ejpam-3018	3	50	institute	institute	PROPN
ejpam-3018	3	51	of	of	ADP
ejpam-3018	3	52	technology	technology	PROPN
ejpam-3018	3	53	,	,	PUNCT
ejpam-3018	3	54	vasad	vasad	ADJ
ejpam-3018	3	55	,	,	PUNCT
ejpam-3018	3	56	gujarat	gujarat	PROPN
ejpam-3018	3	57	,	,	PUNCT
ejpam-3018	3	58	india	india	PROPN
ejpam-3018	3	59	abstract	abstract	NOUN
ejpam-3018	3	60	.	.	PUNCT
ejpam-3018	4	1	in	in	ADP
ejpam-3018	4	2	this	this	DET
ejpam-3018	4	3	paper	paper	NOUN
ejpam-3018	4	4	,	,	PUNCT
ejpam-3018	4	5	we	we	PRON
ejpam-3018	4	6	introduce	introduce	VERB
ejpam-3018	4	7	a	a	DET
ejpam-3018	4	8	stancu	stancu	ADJ
ejpam-3018	4	9	type	type	NOUN
ejpam-3018	4	10	generalization	generalization	NOUN
ejpam-3018	4	11	of	of	ADP
ejpam-3018	4	12	modified	modify	VERB
ejpam-3018	4	13	srivastava	srivastava	PROPN
ejpam-3018	4	14	-	-	PUNCT
ejpam-3018	4	15	gupta	gupta	PROPN
ejpam-3018	4	16	operators	operator	NOUN
ejpam-3018	4	17	.	.	PUNCT
ejpam-3018	5	1	we	we	PRON
ejpam-3018	5	2	obtain	obtain	VERB
ejpam-3018	5	3	the	the	DET
ejpam-3018	5	4	moments	moment	NOUN
ejpam-3018	5	5	of	of	ADP
ejpam-3018	5	6	the	the	DET
ejpam-3018	5	7	operators	operator	NOUN
ejpam-3018	5	8	and	and	CCONJ
ejpam-3018	5	9	then	then	ADV
ejpam-3018	5	10	prove	prove	VERB
ejpam-3018	5	11	the	the	DET
ejpam-3018	5	12	basic	basic	ADJ
ejpam-3018	5	13	convergence	convergence	NOUN
ejpam-3018	5	14	theorem	theorem	VERB
ejpam-3018	5	15	.	.	PUNCT
ejpam-3018	6	1	next	next	ADV
ejpam-3018	6	2	,	,	PUNCT
ejpam-3018	6	3	the	the	DET
ejpam-3018	6	4	voronovskaja	voronovskaja	NOUN
ejpam-3018	6	5	type	type	NOUN
ejpam-3018	6	6	asymptotic	asymptotic	ADJ
ejpam-3018	6	7	formula	formula	NOUN
ejpam-3018	6	8	and	and	CCONJ
ejpam-3018	6	9	some	some	DET
ejpam-3018	6	10	direct	direct	ADJ
ejpam-3018	6	11	results	result	NOUN
ejpam-3018	6	12	for	for	ADP
ejpam-3018	6	13	the	the	DET
ejpam-3018	6	14	above	above	ADJ
ejpam-3018	6	15	operators	operator	NOUN
ejpam-3018	6	16	are	be	AUX
ejpam-3018	6	17	discussed	discuss	VERB
ejpam-3018	6	18	.	.	PUNCT
ejpam-3018	7	1	also	also	ADV
ejpam-3018	7	2	,	,	PUNCT
ejpam-3018	7	3	the	the	DET
ejpam-3018	7	4	rate	rate	NOUN
ejpam-3018	7	5	of	of	ADP
ejpam-3018	7	6	convergence	convergence	NOUN
ejpam-3018	7	7	and	and	CCONJ
ejpam-3018	7	8	weighted	weighted	ADJ
ejpam-3018	7	9	approximation	approximation	NOUN
ejpam-3018	7	10	by	by	ADP
ejpam-3018	7	11	these	these	DET
ejpam-3018	7	12	operators	operator	NOUN
ejpam-3018	7	13	in	in	ADP
ejpam-3018	7	14	terms	term	NOUN
ejpam-3018	7	15	of	of	ADP
ejpam-3018	7	16	modulus	modulus	NOUN
ejpam-3018	7	17	of	of	ADP
ejpam-3018	7	18	continuity	continuity	NOUN
ejpam-3018	7	19	are	be	AUX
ejpam-3018	7	20	studied	study	VERB
ejpam-3018	7	21	.	.	PUNCT
ejpam-3018	8	1	then	then	ADV
ejpam-3018	8	2	,	,	PUNCT
ejpam-3018	8	3	we	we	PRON
ejpam-3018	8	4	obtain	obtain	VERB
ejpam-3018	8	5	point	point	ADV
ejpam-3018	8	6	-	-	PUNCT
ejpam-3018	8	7	wise	wise	ADJ
ejpam-3018	8	8	estimates	estimate	NOUN
ejpam-3018	8	9	using	use	VERB
ejpam-3018	8	10	the	the	DET
ejpam-3018	8	11	lipschitz	lipschitz	ADJ
ejpam-3018	8	12	type	type	NOUN
ejpam-3018	8	13	maximal	maximal	ADJ
ejpam-3018	8	14	function	function	NOUN
ejpam-3018	8	15	and	and	CCONJ
ejpam-3018	8	16	two	two	NUM
ejpam-3018	8	17	parameter	parameter	NOUN
ejpam-3018	8	18	lipschitz	lipschitz	NOUN
ejpam-3018	8	19	-	-	PUNCT
ejpam-3018	8	20	type	type	NOUN
ejpam-3018	8	21	space	space	NOUN
ejpam-3018	8	22	.	.	PUNCT
ejpam-3018	9	1	further	far	ADV
ejpam-3018	9	2	,	,	PUNCT
ejpam-3018	9	3	we	we	PRON
ejpam-3018	9	4	study	study	VERB
ejpam-3018	9	5	the	the	DET
ejpam-3018	9	6	a	a	PRON
ejpam-3018	9	7	-	-	PUNCT
ejpam-3018	9	8	statistical	statistical	ADJ
ejpam-3018	9	9	convergence	convergence	NOUN
ejpam-3018	9	10	of	of	ADP
ejpam-3018	9	11	these	these	DET
ejpam-3018	9	12	operators	operator	NOUN
ejpam-3018	9	13	.	.	PUNCT
ejpam-3018	10	1	lastly	lastly	ADV
ejpam-3018	10	2	,	,	PUNCT
ejpam-3018	10	3	we	we	PRON
ejpam-3018	10	4	give	give	VERB
ejpam-3018	10	5	better	well	ADJ
ejpam-3018	10	6	estimations	estimation	NOUN
ejpam-3018	10	7	of	of	ADP
ejpam-3018	10	8	the	the	DET
ejpam-3018	10	9	above	above	ADJ
ejpam-3018	10	10	operators	operator	NOUN
ejpam-3018	10	11	using	use	VERB
ejpam-3018	10	12	king	king	NOUN
ejpam-3018	10	13	type	type	NOUN
ejpam-3018	10	14	approach	approach	NOUN
ejpam-3018	10	15	.	.	PUNCT
ejpam-3018	11	1	2010	2010	NUM
ejpam-3018	11	2	mathematics	mathematic	NOUN
ejpam-3018	11	3	subject	subject	NOUN
ejpam-3018	11	4	classifications	classification	NOUN
ejpam-3018	11	5	:	:	PUNCT
ejpam-3018	11	6	41a25	41a25	NUM
ejpam-3018	11	7	,	,	PUNCT
ejpam-3018	11	8	26a15	26a15	NUM
ejpam-3018	11	9	,	,	PUNCT
ejpam-3018	11	10	40a35	40a35	NUM
ejpam-3018	11	11	.	.	PUNCT
ejpam-3018	12	1	key	key	ADJ
ejpam-3018	12	2	words	word	NOUN
ejpam-3018	12	3	and	and	CCONJ
ejpam-3018	12	4	phrases	phrase	NOUN
ejpam-3018	12	5	:	:	PUNCT
ejpam-3018	12	6	srivastava	srivastava	PROPN
ejpam-3018	12	7	-	-	PUNCT
ejpam-3018	12	8	gupta	gupta	PROPN
ejpam-3018	12	9	operators	operator	NOUN
ejpam-3018	12	10	,	,	PUNCT
ejpam-3018	12	11	rate	rate	NOUN
ejpam-3018	12	12	of	of	ADP
ejpam-3018	12	13	convergence	convergence	NOUN
ejpam-3018	12	14	,	,	PUNCT
ejpam-3018	12	15	modulus	modulus	NOUN
ejpam-3018	12	16	of	of	ADP
ejpam-3018	12	17	continuity	continuity	NOUN
ejpam-3018	12	18	,	,	PUNCT
ejpam-3018	12	19	weighted	weight	VERB
ejpam-3018	12	20	approximation	approximation	NOUN
ejpam-3018	12	21	,	,	PUNCT
ejpam-3018	12	22	pointwise	pointwise	NOUN
ejpam-3018	12	23	estimates	estimate	NOUN
ejpam-3018	12	24	,	,	PUNCT
ejpam-3018	12	25	a	a	DET
ejpam-3018	12	26	-	-	PUNCT
ejpam-3018	12	27	statistical	statistical	ADJ
ejpam-3018	12	28	convergence	convergence	NOUN
ejpam-3018	12	29	.	.	PUNCT
ejpam-3018	13	1	1	1	X
ejpam-3018	13	2	.	.	X
ejpam-3018	13	3	introduction	introduction	NOUN
ejpam-3018	13	4	in	in	ADP
ejpam-3018	13	5	the	the	DET
ejpam-3018	13	6	year	year	NOUN
ejpam-3018	13	7	2003	2003	NUM
ejpam-3018	13	8	,	,	PUNCT
ejpam-3018	13	9	srivastava	srivastava	PROPN
ejpam-3018	13	10	and	and	CCONJ
ejpam-3018	13	11	gupta	gupta	PROPN
ejpam-3018	13	12	[	[	X
ejpam-3018	13	13	33	33	NUM
ejpam-3018	13	14	]	]	PUNCT
ejpam-3018	13	15	introduced	introduce	VERB
ejpam-3018	13	16	a	a	DET
ejpam-3018	13	17	general	general	ADJ
ejpam-3018	13	18	family	family	NOUN
ejpam-3018	13	19	of	of	ADP
ejpam-3018	13	20	summationintegral	summationintegral	ADJ
ejpam-3018	13	21	type	type	NOUN
ejpam-3018	13	22	operators	operator	NOUN
ejpam-3018	13	23	{	{	PUNCT
ejpam-3018	13	24	gn	gn	PROPN
ejpam-3018	13	25	,	,	PUNCT
ejpam-3018	13	26	c	c	NOUN
ejpam-3018	13	27	}	}	PUNCT
ejpam-3018	13	28	which	which	PRON
ejpam-3018	13	29	includes	include	VERB
ejpam-3018	13	30	some	some	DET
ejpam-3018	13	31	well	well	ADV
ejpam-3018	13	32	-	-	PUNCT
ejpam-3018	13	33	known	know	VERB
ejpam-3018	13	34	operators	operator	NOUN
ejpam-3018	13	35	as	as	ADP
ejpam-3018	13	36	special	special	ADJ
ejpam-3018	13	37	cases	case	NOUN
ejpam-3018	13	38	.	.	PUNCT
ejpam-3018	14	1	they	they	PRON
ejpam-3018	14	2	obtained	obtain	VERB
ejpam-3018	14	3	the	the	DET
ejpam-3018	14	4	rate	rate	NOUN
ejpam-3018	14	5	of	of	ADP
ejpam-3018	14	6	convergence	convergence	NOUN
ejpam-3018	14	7	for	for	ADP
ejpam-3018	14	8	functions	function	NOUN
ejpam-3018	14	9	of	of	ADP
ejpam-3018	14	10	bounded	bounded	ADJ
ejpam-3018	14	11	variation	variation	NOUN
ejpam-3018	14	12	.	.	PUNCT
ejpam-3018	15	1	for	for	ADP
ejpam-3018	15	2	the	the	DET
ejpam-3018	15	3	details	detail	NOUN
ejpam-3018	15	4	of	of	ADP
ejpam-3018	15	5	special	special	ADJ
ejpam-3018	15	6	cases	case	NOUN
ejpam-3018	15	7	in	in	ADP
ejpam-3018	15	8	[	[	X
ejpam-3018	15	9	33	33	NUM
ejpam-3018	15	10	]	]	PUNCT
ejpam-3018	15	11	,	,	PUNCT
ejpam-3018	15	12	we	we	PRON
ejpam-3018	15	13	refer	refer	VERB
ejpam-3018	15	14	the	the	DET
ejpam-3018	15	15	readers	reader	NOUN
ejpam-3018	15	16	to	to	ADP
ejpam-3018	15	17	[	[	X
ejpam-3018	15	18	13	13	NUM
ejpam-3018	15	19	]	]	PUNCT
ejpam-3018	15	20	,	,	PUNCT
ejpam-3018	15	21	[	[	X
ejpam-3018	15	22	20	20	NUM
ejpam-3018	15	23	]	]	PUNCT
ejpam-3018	15	24	and	and	CCONJ
ejpam-3018	16	1	[	[	X
ejpam-3018	16	2	31	31	NUM
ejpam-3018	16	3	]	]	PUNCT
ejpam-3018	16	4	.	.	PUNCT
ejpam-3018	17	1	∗corresponding	∗corresponde	VERB
ejpam-3018	17	2	author	author	NOUN
ejpam-3018	17	3	.	.	PUNCT
ejpam-3018	18	1	email	email	NOUN
ejpam-3018	18	2	addresses	address	NOUN
ejpam-3018	18	3	:	:	PUNCT
ejpam-3018	18	4	alokkpma@gmail.com	alokkpma@gmail.com	X
ejpam-3018	18	5	(	(	PUNCT
ejpam-3018	18	6	a.	a.	PROPN
ejpam-3018	18	7	kumar	kumar	PROPN
ejpam-3018	18	8	)	)	PUNCT
ejpam-3018	18	9	,	,	PUNCT
ejpam-3018	18	10	vishnunarayanmishra@gmail.com	vishnunarayanmishra@gmail.com	X
ejpam-3018	18	11	(	(	PUNCT
ejpam-3018	18	12	v.	v.	ADP
ejpam-3018	18	13	n.	n.	PROPN
ejpam-3018	18	14	mishra	mishra	PROPN
ejpam-3018	18	15	)	)	PUNCT
ejpam-3018	18	16	,	,	PUNCT
ejpam-3018	19	1	tapiawalad@yahoo.com	tapiawalad@yahoo.com	X
ejpam-3018	19	2	(	(	PUNCT
ejpam-3018	19	3	d.	d.	PROPN
ejpam-3018	19	4	tapiawala	tapiawala	PROPN
ejpam-3018	19	5	)	)	PUNCT
ejpam-3018	19	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3018	20	1	890	890	NUM
ejpam-3018	20	2	c	c	X
ejpam-3018	20	3	©	©	PROPN
ejpam-3018	20	4	2017	2017	NUM
ejpam-3018	20	5	ejpam	ejpam	NOUN
ejpam-3018	20	6	all	all	DET
ejpam-3018	20	7	rights	right	NOUN
ejpam-3018	20	8	reserved	reserve	VERB
ejpam-3018	20	9	.	.	PUNCT
ejpam-3018	21	1	a.	a.	PROPN
ejpam-3018	21	2	kumar	kumar	PROPN
ejpam-3018	21	3	,	,	PUNCT
ejpam-3018	21	4	v.	v.	PROPN
ejpam-3018	21	5	n.	n.	PROPN
ejpam-3018	21	6	mishra	mishra	PROPN
ejpam-3018	21	7	,	,	PUNCT
ejpam-3018	21	8	d.	d.	PROPN
ejpam-3018	21	9	tapiawala	tapiawala	PROPN
ejpam-3018	21	10	/	/	SYM
ejpam-3018	21	11	eur	eur	PROPN
ejpam-3018	21	12	.	.	PUNCT
ejpam-3018	22	1	j.	j.	PROPN
ejpam-3018	22	2	pure	pure	PROPN
ejpam-3018	22	3	appl	appl	PROPN
ejpam-3018	22	4	.	.	PROPN
ejpam-3018	22	5	math	math	PROPN
ejpam-3018	22	6	,	,	PUNCT
ejpam-3018	22	7	10	10	NUM
ejpam-3018	22	8	(	(	PUNCT
ejpam-3018	22	9	4	4	NUM
ejpam-3018	22	10	)	)	PUNCT
ejpam-3018	22	11	(	(	PUNCT
ejpam-3018	22	12	2017	2017	NUM
ejpam-3018	22	13	)	)	PUNCT
ejpam-3018	22	14	,	,	PUNCT
ejpam-3018	22	15	890	890	NUM
ejpam-3018	22	16	-	-	SYM
ejpam-3018	22	17	907	907	NUM
ejpam-3018	22	18	891	891	NUM
ejpam-3018	22	19	for	for	ADP
ejpam-3018	22	20	f	f	PROPN
ejpam-3018	22	21	∈	∈	PROPN
ejpam-3018	22	22	cγ	cγ	NOUN
ejpam-3018	22	23	[	[	X
ejpam-3018	22	24	0,∞	0,∞	NOUN
ejpam-3018	22	25	)	)	PUNCT
ejpam-3018	22	26	:	:	PUNCT
ejpam-3018	23	1	=	=	PUNCT
ejpam-3018	23	2	{	{	PUNCT
ejpam-3018	23	3	f	f	PROPN
ejpam-3018	23	4	∈	∈	PROPN
ejpam-3018	23	5	c[0,∞	c[0,∞	PROPN
ejpam-3018	23	6	)	)	PUNCT
ejpam-3018	23	7	:	:	PUNCT
ejpam-3018	24	1	|f(t)|	|f(t)|	PROPN
ejpam-3018	24	2	≤m(1+t)γ	≤m(1+t)γ	PROPN
ejpam-3018	24	3	for	for	ADP
ejpam-3018	24	4	some	some	DET
ejpam-3018	24	5	m	m	NOUN
ejpam-3018	24	6	>	>	X
ejpam-3018	24	7	0	0	PROPN
ejpam-3018	24	8	,	,	PUNCT
ejpam-3018	24	9	γ	γ	X
ejpam-3018	24	10	>	>	X
ejpam-3018	24	11	0	0	NUM
ejpam-3018	24	12	}	}	PUNCT
ejpam-3018	24	13	,	,	PUNCT
ejpam-3018	24	14	srivastava	srivastava	PROPN
ejpam-3018	24	15	and	and	CCONJ
ejpam-3018	24	16	gupta	gupta	PROPN
ejpam-3018	24	17	proposed	propose	VERB
ejpam-3018	24	18	a	a	DET
ejpam-3018	24	19	certain	certain	ADJ
ejpam-3018	24	20	family	family	NOUN
ejpam-3018	24	21	of	of	ADP
ejpam-3018	24	22	positive	positive	ADJ
ejpam-3018	24	23	linear	linear	PROPN
ejpam-3018	24	24	operators	operator	NOUN
ejpam-3018	24	25	defined	define	VERB
ejpam-3018	24	26	by	by	ADP
ejpam-3018	24	27	gn	gn	PROPN
ejpam-3018	24	28	,	,	PUNCT
ejpam-3018	24	29	c(f	c(f	PROPN
ejpam-3018	24	30	;	;	PUNCT
ejpam-3018	24	31	x	x	X
ejpam-3018	24	32	)	)	PUNCT
ejpam-3018	24	33	=	=	SYM
ejpam-3018	25	1	n	n	PROPN
ejpam-3018	25	2	∞∑	∞∑	PROPN
ejpam-3018	25	3	k=1	k=1	PUNCT
ejpam-3018	25	4	pn	pn	PROPN
ejpam-3018	25	5	,	,	PUNCT
ejpam-3018	25	6	k(x	k(x	PROPN
ejpam-3018	25	7	,	,	PUNCT
ejpam-3018	25	8	c	c	NOUN
ejpam-3018	25	9	)	)	PUNCT
ejpam-3018	25	10	∫	∫	PROPN
ejpam-3018	25	11	∞	∞	PROPN
ejpam-3018	25	12	0	0	NUM
ejpam-3018	26	1	pn+c	pn+c	NOUN
ejpam-3018	26	2	,	,	PUNCT
ejpam-3018	26	3	k−1(t	k−1(t	PROPN
ejpam-3018	26	4	,	,	PUNCT
ejpam-3018	26	5	c)f(t)dt+	c)f(t)dt+	PROPN
ejpam-3018	26	6	pn,0(x	pn,0(x	PROPN
ejpam-3018	26	7	,	,	PUNCT
ejpam-3018	26	8	c)f(0	c)f(0	PROPN
ejpam-3018	26	9	)	)	PUNCT
ejpam-3018	26	10	,	,	PUNCT
ejpam-3018	26	11	(	(	PUNCT
ejpam-3018	26	12	1	1	X
ejpam-3018	26	13	)	)	PUNCT
ejpam-3018	27	1	where	where	SCONJ
ejpam-3018	27	2	pn	pn	PROPN
ejpam-3018	27	3	,	,	PUNCT
ejpam-3018	27	4	k(x	k(x	PROPN
ejpam-3018	27	5	,	,	PUNCT
ejpam-3018	27	6	c	c	NOUN
ejpam-3018	27	7	)	)	PUNCT
ejpam-3018	27	8	=	=	SYM
ejpam-3018	27	9	(	(	PUNCT
ejpam-3018	27	10	−x)k	−x)k	NOUN
ejpam-3018	27	11	k	k	X
ejpam-3018	27	12	!	!	PUNCT
ejpam-3018	27	13	φ(k)n	φ(k)n	PROPN
ejpam-3018	27	14	,	,	PUNCT
ejpam-3018	27	15	c(x	c(x	NOUN
ejpam-3018	27	16	)	)	PUNCT
ejpam-3018	27	17	(	(	PUNCT
ejpam-3018	27	18	2	2	NUM
ejpam-3018	27	19	)	)	PUNCT
ejpam-3018	27	20	and	and	CCONJ
ejpam-3018	27	21	φn	φn	NOUN
ejpam-3018	27	22	,	,	PUNCT
ejpam-3018	27	23	c(x	c(x	NOUN
ejpam-3018	27	24	)	)	PUNCT
ejpam-3018	27	25	=	=	PRON
ejpam-3018	27	26	{	{	PUNCT
ejpam-3018	27	27	e−nx	e−nx	NOUN
ejpam-3018	27	28	,	,	PUNCT
ejpam-3018	27	29	c	c	NOUN
ejpam-3018	27	30	=	=	SYM
ejpam-3018	27	31	0	0	NUM
ejpam-3018	27	32	,	,	PUNCT
ejpam-3018	27	33	(	(	PUNCT
ejpam-3018	27	34	1	1	NUM
ejpam-3018	27	35	+	+	CCONJ
ejpam-3018	27	36	cx)−n	cx)−n	PROPN
ejpam-3018	27	37	/	/	SYM
ejpam-3018	27	38	c	c	NOUN
ejpam-3018	27	39	,	,	PUNCT
ejpam-3018	27	40	c	c	PROPN
ejpam-3018	27	41	∈	∈	PROPN
ejpam-3018	27	42	n	n	X
ejpam-3018	27	43	.	.	PUNCT
ejpam-3018	28	1	verma	verma	PROPN
ejpam-3018	28	2	and	and	CCONJ
ejpam-3018	28	3	agrawal	agrawal	PROPN
ejpam-3018	29	1	[	[	X
ejpam-3018	29	2	35	35	NUM
ejpam-3018	29	3	]	]	PUNCT
ejpam-3018	29	4	introduced	introduce	VERB
ejpam-3018	29	5	the	the	DET
ejpam-3018	29	6	generalized	generalized	ADJ
ejpam-3018	29	7	form	form	NOUN
ejpam-3018	29	8	of	of	ADP
ejpam-3018	29	9	the	the	DET
ejpam-3018	29	10	operators	operator	NOUN
ejpam-3018	29	11	(	(	PUNCT
ejpam-3018	29	12	1	1	X
ejpam-3018	29	13	)	)	PUNCT
ejpam-3018	29	14	and	and	CCONJ
ejpam-3018	29	15	studied	study	VERB
ejpam-3018	29	16	some	some	PRON
ejpam-3018	29	17	of	of	ADP
ejpam-3018	29	18	its	its	PRON
ejpam-3018	29	19	approximation	approximation	NOUN
ejpam-3018	29	20	properties	property	NOUN
ejpam-3018	29	21	.	.	PUNCT
ejpam-3018	30	1	deo	deo	NOUN
ejpam-3018	31	1	[	[	X
ejpam-3018	31	2	3	3	NUM
ejpam-3018	31	3	]	]	PUNCT
ejpam-3018	31	4	gave	give	VERB
ejpam-3018	31	5	a	a	DET
ejpam-3018	31	6	modification	modification	NOUN
ejpam-3018	31	7	of	of	ADP
ejpam-3018	31	8	these	these	DET
ejpam-3018	31	9	operators	operator	NOUN
ejpam-3018	31	10	and	and	CCONJ
ejpam-3018	31	11	established	establish	VERB
ejpam-3018	31	12	the	the	DET
ejpam-3018	31	13	rate	rate	NOUN
ejpam-3018	31	14	of	of	ADP
ejpam-3018	31	15	convergence	convergence	NOUN
ejpam-3018	31	16	and	and	CCONJ
ejpam-3018	31	17	voronovskaja	voronovskaja	NOUN
ejpam-3018	31	18	type	type	NOUN
ejpam-3018	31	19	asymptotic	asymptotic	ADJ
ejpam-3018	31	20	result	result	NOUN
ejpam-3018	31	21	.	.	PUNCT
ejpam-3018	32	1	recently	recently	ADV
ejpam-3018	32	2	,	,	PUNCT
ejpam-3018	32	3	acar	acar	VERB
ejpam-3018	32	4	et	et	PROPN
ejpam-3018	32	5	al	al	PROPN
ejpam-3018	32	6	.	.	PUNCT
ejpam-3018	33	1	[	[	X
ejpam-3018	33	2	1	1	X
ejpam-3018	33	3	]	]	PUNCT
ejpam-3018	33	4	introduced	introduce	VERB
ejpam-3018	33	5	stancu	stancu	ADJ
ejpam-3018	33	6	type	type	NOUN
ejpam-3018	33	7	generalization	generalization	NOUN
ejpam-3018	33	8	of	of	ADP
ejpam-3018	33	9	the	the	DET
ejpam-3018	33	10	operators	operator	NOUN
ejpam-3018	33	11	(	(	PUNCT
ejpam-3018	33	12	1	1	X
ejpam-3018	33	13	)	)	PUNCT
ejpam-3018	33	14	and	and	CCONJ
ejpam-3018	33	15	obtained	obtain	VERB
ejpam-3018	33	16	an	an	DET
ejpam-3018	33	17	estimate	estimate	NOUN
ejpam-3018	33	18	of	of	ADP
ejpam-3018	33	19	the	the	DET
ejpam-3018	33	20	rate	rate	NOUN
ejpam-3018	33	21	of	of	ADP
ejpam-3018	33	22	convergence	convergence	NOUN
ejpam-3018	33	23	for	for	ADP
ejpam-3018	33	24	functions	function	NOUN
ejpam-3018	33	25	having	have	VERB
ejpam-3018	33	26	derivatives	derivative	NOUN
ejpam-3018	33	27	of	of	ADP
ejpam-3018	33	28	bounded	bounded	ADJ
ejpam-3018	33	29	variation	variation	NOUN
ejpam-3018	33	30	and	and	CCONJ
ejpam-3018	33	31	also	also	ADV
ejpam-3018	33	32	studied	study	VERB
ejpam-3018	33	33	the	the	DET
ejpam-3018	33	34	simultaneous	simultaneous	ADJ
ejpam-3018	33	35	approximation	approximation	NOUN
ejpam-3018	33	36	for	for	ADP
ejpam-3018	33	37	these	these	DET
ejpam-3018	33	38	operators	operator	NOUN
ejpam-3018	33	39	.	.	PUNCT
ejpam-3018	34	1	yadav	yadav	PROPN
ejpam-3018	35	1	[	[	X
ejpam-3018	35	2	36	36	NUM
ejpam-3018	35	3	]	]	PUNCT
ejpam-3018	35	4	proposed	propose	VERB
ejpam-3018	35	5	the	the	DET
ejpam-3018	35	6	modification	modification	NOUN
ejpam-3018	35	7	of	of	ADP
ejpam-3018	35	8	the	the	DET
ejpam-3018	35	9	operators	operator	NOUN
ejpam-3018	35	10	(	(	PUNCT
ejpam-3018	35	11	1	1	X
ejpam-3018	35	12	)	)	PUNCT
ejpam-3018	35	13	using	use	VERB
ejpam-3018	35	14	the	the	DET
ejpam-3018	35	15	king	king	NOUN
ejpam-3018	35	16	approach	approach	NOUN
ejpam-3018	35	17	as	as	ADP
ejpam-3018	35	18	g∗n	g∗n	X
ejpam-3018	35	19	,	,	PUNCT
ejpam-3018	35	20	c(f	c(f	PROPN
ejpam-3018	35	21	;	;	PUNCT
ejpam-3018	35	22	x	x	X
ejpam-3018	35	23	)	)	PUNCT
ejpam-3018	35	24	=	=	SYM
ejpam-3018	36	1	n	n	PROPN
ejpam-3018	36	2	∞∑	∞∑	PROPN
ejpam-3018	36	3	k=1	k=1	PUNCT
ejpam-3018	36	4	pn	pn	PROPN
ejpam-3018	36	5	,	,	PUNCT
ejpam-3018	36	6	k(x	k(x	PROPN
ejpam-3018	36	7	,	,	PUNCT
ejpam-3018	36	8	c	c	NOUN
ejpam-3018	36	9	)	)	PUNCT
ejpam-3018	36	10	∫	∫	PROPN
ejpam-3018	36	11	∞	∞	PROPN
ejpam-3018	36	12	0	0	NUM
ejpam-3018	37	1	pn+c	pn+c	NOUN
ejpam-3018	37	2	,	,	PUNCT
ejpam-3018	37	3	k−1(t	k−1(t	PROPN
ejpam-3018	37	4	,	,	PUNCT
ejpam-3018	37	5	c)f	c)f	NOUN
ejpam-3018	37	6	(	(	PUNCT
ejpam-3018	37	7	(	(	PUNCT
ejpam-3018	37	8	n−	n−	NOUN
ejpam-3018	37	9	c)t	c)t	X
ejpam-3018	37	10	n	n	CCONJ
ejpam-3018	37	11	)	)	PUNCT
ejpam-3018	37	12	dt+	dt+	NOUN
ejpam-3018	37	13	pn,0(x	pn,0(x	NOUN
ejpam-3018	37	14	,	,	PUNCT
ejpam-3018	37	15	c)f(0	c)f(0	PROPN
ejpam-3018	37	16	)	)	PUNCT
ejpam-3018	37	17	(	(	PUNCT
ejpam-3018	37	18	3	3	X
ejpam-3018	37	19	)	)	PUNCT
ejpam-3018	38	1	and	and	CCONJ
ejpam-3018	38	2	studied	study	VERB
ejpam-3018	38	3	its	its	PRON
ejpam-3018	38	4	moment	moment	NOUN
ejpam-3018	38	5	estimates	estimate	NOUN
ejpam-3018	38	6	,	,	PUNCT
ejpam-3018	38	7	direct	direct	ADJ
ejpam-3018	38	8	estimate	estimate	NOUN
ejpam-3018	38	9	,	,	PUNCT
ejpam-3018	38	10	asymptotic	asymptotic	ADJ
ejpam-3018	38	11	formula	formula	NOUN
ejpam-3018	38	12	and	and	CCONJ
ejpam-3018	38	13	statistical	statistical	ADJ
ejpam-3018	38	14	convergence	convergence	NOUN
ejpam-3018	38	15	.	.	PUNCT
ejpam-3018	39	1	recently	recently	ADV
ejpam-3018	39	2	,	,	PUNCT
ejpam-3018	39	3	maheshwari	maheshwari	PROPN
ejpam-3018	39	4	[	[	X
ejpam-3018	39	5	22	22	NUM
ejpam-3018	39	6	]	]	PUNCT
ejpam-3018	39	7	obtained	obtain	VERB
ejpam-3018	39	8	the	the	DET
ejpam-3018	39	9	rate	rate	NOUN
ejpam-3018	39	10	of	of	ADP
ejpam-3018	39	11	convergence	convergence	NOUN
ejpam-3018	39	12	for	for	SCONJ
ejpam-3018	39	13	the	the	DET
ejpam-3018	39	14	functions	function	NOUN
ejpam-3018	39	15	having	having	AUX
ejpam-3018	39	16	bounded	bound	VERB
ejpam-3018	39	17	derivatives	derivative	NOUN
ejpam-3018	39	18	on	on	ADP
ejpam-3018	39	19	every	every	DET
ejpam-3018	39	20	finite	finite	ADJ
ejpam-3018	39	21	subinterval	subinterval	NOUN
ejpam-3018	39	22	of	of	ADP
ejpam-3018	39	23	[	[	X
ejpam-3018	39	24	0,∞	0,∞	NOUN
ejpam-3018	39	25	)	)	PUNCT
ejpam-3018	39	26	for	for	ADP
ejpam-3018	39	27	the	the	DET
ejpam-3018	39	28	operators	operator	NOUN
ejpam-3018	39	29	(	(	PUNCT
ejpam-3018	39	30	3	3	NUM
ejpam-3018	39	31	)	)	PUNCT
ejpam-3018	39	32	.	.	PUNCT
ejpam-3018	40	1	very	very	ADV
ejpam-3018	40	2	recently	recently	ADV
ejpam-3018	40	3	,	,	PUNCT
ejpam-3018	40	4	neer	neer	NOUN
ejpam-3018	40	5	et	et	PROPN
ejpam-3018	40	6	al	al	PROPN
ejpam-3018	40	7	.	.	PUNCT
ejpam-3018	41	1	[	[	X
ejpam-3018	41	2	29	29	NUM
ejpam-3018	41	3	]	]	PUNCT
ejpam-3018	41	4	introduced	introduce	VERB
ejpam-3018	41	5	the	the	DET
ejpam-3018	41	6	bezier	bezier	ADJ
ejpam-3018	41	7	variant	variant	NOUN
ejpam-3018	41	8	of	of	ADP
ejpam-3018	41	9	the	the	DET
ejpam-3018	41	10	operators	operator	NOUN
ejpam-3018	41	11	(	(	PUNCT
ejpam-3018	41	12	3	3	NUM
ejpam-3018	41	13	)	)	PUNCT
ejpam-3018	41	14	and	and	CCONJ
ejpam-3018	41	15	studied	study	VERB
ejpam-3018	41	16	the	the	DET
ejpam-3018	41	17	direct	direct	ADJ
ejpam-3018	41	18	approximation	approximation	NOUN
ejpam-3018	41	19	result	result	NOUN
ejpam-3018	41	20	and	and	CCONJ
ejpam-3018	41	21	estimate	estimate	NOUN
ejpam-3018	41	22	of	of	ADP
ejpam-3018	41	23	the	the	DET
ejpam-3018	41	24	rate	rate	NOUN
ejpam-3018	41	25	of	of	ADP
ejpam-3018	41	26	convergence	convergence	NOUN
ejpam-3018	41	27	of	of	ADP
ejpam-3018	41	28	these	these	DET
ejpam-3018	41	29	operators	operator	NOUN
ejpam-3018	41	30	for	for	ADP
ejpam-3018	41	31	functions	function	NOUN
ejpam-3018	41	32	of	of	ADP
ejpam-3018	41	33	bounded	bounded	ADJ
ejpam-3018	41	34	variation	variation	NOUN
ejpam-3018	41	35	.	.	PUNCT
ejpam-3018	42	1	in	in	ADP
ejpam-3018	42	2	[	[	X
ejpam-3018	42	3	34	34	NUM
ejpam-3018	42	4	]	]	PUNCT
ejpam-3018	42	5	,	,	PUNCT
ejpam-3018	42	6	stancu	stancu	PROPN
ejpam-3018	42	7	introduced	introduce	VERB
ejpam-3018	42	8	the	the	DET
ejpam-3018	42	9	positive	positive	ADJ
ejpam-3018	42	10	linear	linear	PROPN
ejpam-3018	42	11	operators	operator	NOUN
ejpam-3018	42	12	p	p	X
ejpam-3018	42	13	(	(	PUNCT
ejpam-3018	42	14	α	α	X
ejpam-3018	42	15	,	,	PUNCT
ejpam-3018	42	16	β	β	NOUN
ejpam-3018	42	17	)	)	PUNCT
ejpam-3018	42	18	n	n	CCONJ
ejpam-3018	42	19	:	:	PUNCT
ejpam-3018	42	20	c[0	c[0	PROPN
ejpam-3018	42	21	,	,	PUNCT
ejpam-3018	42	22	1	1	NUM
ejpam-3018	42	23	]	]	PUNCT
ejpam-3018	42	24	→	→	X
ejpam-3018	42	25	c[0	c[0	PROPN
ejpam-3018	42	26	,	,	PUNCT
ejpam-3018	42	27	1	1	NUM
ejpam-3018	42	28	]	]	PUNCT
ejpam-3018	42	29	by	by	ADP
ejpam-3018	42	30	modifying	modify	VERB
ejpam-3018	42	31	the	the	DET
ejpam-3018	42	32	bernstein	bernstein	PROPN
ejpam-3018	42	33	polynomial	polynomial	PROPN
ejpam-3018	42	34	as	as	ADP
ejpam-3018	42	35	p	p	PROPN
ejpam-3018	42	36	(	(	PUNCT
ejpam-3018	42	37	α	α	NOUN
ejpam-3018	42	38	,	,	PUNCT
ejpam-3018	42	39	β	β	NOUN
ejpam-3018	42	40	)	)	PUNCT
ejpam-3018	42	41	n	n	PROPN
ejpam-3018	42	42	(	(	PUNCT
ejpam-3018	42	43	f	f	PROPN
ejpam-3018	42	44	;	;	PUNCT
ejpam-3018	42	45	x	x	X
ejpam-3018	42	46	)	)	PUNCT
ejpam-3018	43	1	=	=	SYM
ejpam-3018	43	2	n∑	n∑	PROPN
ejpam-3018	43	3	k=0	k=0	PROPN
ejpam-3018	43	4	bn	bn	PROPN
ejpam-3018	43	5	,	,	PUNCT
ejpam-3018	43	6	k(x)f	k(x)f	PROPN
ejpam-3018	43	7	(	(	PUNCT
ejpam-3018	43	8	k	k	PROPN
ejpam-3018	43	9	+	+	CCONJ
ejpam-3018	43	10	α	α	PROPN
ejpam-3018	43	11	n+	n+	X
ejpam-3018	43	12	β	β	X
ejpam-3018	43	13	)	)	PUNCT
ejpam-3018	43	14	,	,	PUNCT
ejpam-3018	44	1	where	where	SCONJ
ejpam-3018	44	2	bn	bn	NOUN
ejpam-3018	44	3	,	,	PUNCT
ejpam-3018	44	4	k(x	k(x	PROPN
ejpam-3018	44	5	)	)	PUNCT
ejpam-3018	44	6	=	=	PUNCT
ejpam-3018	44	7	(	(	PUNCT
ejpam-3018	44	8	n	n	X
ejpam-3018	44	9	k	k	NOUN
ejpam-3018	44	10	)	)	PUNCT
ejpam-3018	44	11	xk(1	xk(1	PROPN
ejpam-3018	44	12	−	−	PROPN
ejpam-3018	44	13	x)n−k	x)n−k	PROPN
ejpam-3018	44	14	,	,	PUNCT
ejpam-3018	44	15	x	x	PUNCT
ejpam-3018	44	16	∈	∈	PROPN
ejpam-3018	45	1	[	[	X
ejpam-3018	45	2	0	0	NUM
ejpam-3018	45	3	,	,	PUNCT
ejpam-3018	45	4	1	1	NUM
ejpam-3018	45	5	]	]	PUNCT
ejpam-3018	45	6	is	be	AUX
ejpam-3018	45	7	the	the	DET
ejpam-3018	45	8	bernstein	bernstein	PROPN
ejpam-3018	45	9	basis	basis	NOUN
ejpam-3018	45	10	function	function	NOUN
ejpam-3018	45	11	and	and	CCONJ
ejpam-3018	45	12	α	α	NOUN
ejpam-3018	45	13	,	,	PUNCT
ejpam-3018	45	14	β	β	X
ejpam-3018	45	15	are	be	AUX
ejpam-3018	45	16	any	any	DET
ejpam-3018	45	17	two	two	NUM
ejpam-3018	45	18	real	real	ADJ
ejpam-3018	45	19	numbers	number	NOUN
ejpam-3018	45	20	which	which	PRON
ejpam-3018	45	21	satisfy	satisfy	VERB
ejpam-3018	45	22	the	the	DET
ejpam-3018	45	23	condition	condition	NOUN
ejpam-3018	45	24	that	that	SCONJ
ejpam-3018	45	25	0	0	NUM
ejpam-3018	45	26	≤	≤	NUM
ejpam-3018	45	27	α	α	NOUN
ejpam-3018	45	28	≤	≤	NOUN
ejpam-3018	45	29	β	β	X
ejpam-3018	45	30	.	.	PUNCT
ejpam-3018	46	1	in	in	ADP
ejpam-3018	46	2	the	the	DET
ejpam-3018	46	3	recent	recent	ADJ
ejpam-3018	46	4	years	year	NOUN
ejpam-3018	46	5	,	,	PUNCT
ejpam-3018	46	6	stancu	stancu	ADJ
ejpam-3018	46	7	type	type	NOUN
ejpam-3018	46	8	generalization	generalization	NOUN
ejpam-3018	46	9	of	of	ADP
ejpam-3018	46	10	the	the	DET
ejpam-3018	46	11	certain	certain	ADJ
ejpam-3018	46	12	operators	operator	NOUN
ejpam-3018	46	13	introduced	introduce	VERB
ejpam-3018	46	14	by	by	ADP
ejpam-3018	46	15	several	several	ADJ
ejpam-3018	46	16	researchers	researcher	NOUN
ejpam-3018	46	17	and	and	CCONJ
ejpam-3018	46	18	obtained	obtain	VERB
ejpam-3018	46	19	different	different	ADJ
ejpam-3018	46	20	type	type	NOUN
ejpam-3018	46	21	of	of	ADP
ejpam-3018	46	22	approximation	approximation	NOUN
ejpam-3018	46	23	properties	property	NOUN
ejpam-3018	46	24	of	of	ADP
ejpam-3018	46	25	many	many	ADJ
ejpam-3018	46	26	operators	operator	NOUN
ejpam-3018	46	27	,	,	PUNCT
ejpam-3018	46	28	we	we	PRON
ejpam-3018	46	29	refer	refer	VERB
ejpam-3018	46	30	some	some	PRON
ejpam-3018	46	31	of	of	ADP
ejpam-3018	46	32	the	the	DET
ejpam-3018	46	33	important	important	ADJ
ejpam-3018	46	34	papers	paper	NOUN
ejpam-3018	46	35	in	in	ADP
ejpam-3018	46	36	this	this	DET
ejpam-3018	46	37	direction	direction	NOUN
ejpam-3018	46	38	as	as	ADP
ejpam-3018	46	39	[	[	X
ejpam-3018	46	40	1	1	NUM
ejpam-3018	46	41	]	]	PUNCT
ejpam-3018	46	42	,	,	PUNCT
ejpam-3018	47	1	[	[	X
ejpam-3018	47	2	2	2	NUM
ejpam-3018	47	3	]	]	PUNCT
ejpam-3018	47	4	,	,	PUNCT
ejpam-3018	47	5	[	[	X
ejpam-3018	47	6	32	32	NUM
ejpam-3018	47	7	]	]	SYM
ejpam-3018	47	8	etc	etc	X
ejpam-3018	47	9	.	.	X
ejpam-3018	47	10	a.	a.	PROPN
ejpam-3018	47	11	kumar	kumar	PROPN
ejpam-3018	47	12	,	,	PUNCT
ejpam-3018	47	13	v.	v.	PROPN
ejpam-3018	47	14	n.	n.	PROPN
ejpam-3018	47	15	mishra	mishra	PROPN
ejpam-3018	47	16	,	,	PUNCT
ejpam-3018	47	17	d.	d.	PROPN
ejpam-3018	47	18	tapiawala	tapiawala	PROPN
ejpam-3018	47	19	/	/	SYM
ejpam-3018	47	20	eur	eur	PROPN
ejpam-3018	47	21	.	.	PUNCT
ejpam-3018	48	1	j.	j.	PROPN
ejpam-3018	48	2	pure	pure	PROPN
ejpam-3018	48	3	appl	appl	PROPN
ejpam-3018	48	4	.	.	PROPN
ejpam-3018	48	5	math	math	PROPN
ejpam-3018	48	6	,	,	PUNCT
ejpam-3018	48	7	10	10	NUM
ejpam-3018	48	8	(	(	PUNCT
ejpam-3018	48	9	4	4	NUM
ejpam-3018	48	10	)	)	PUNCT
ejpam-3018	48	11	(	(	PUNCT
ejpam-3018	48	12	2017	2017	NUM
ejpam-3018	48	13	)	)	PUNCT
ejpam-3018	48	14	,	,	PUNCT
ejpam-3018	48	15	890	890	NUM
ejpam-3018	48	16	-	-	SYM
ejpam-3018	48	17	907	907	NUM
ejpam-3018	48	18	892	892	NUM
ejpam-3018	48	19	for	for	ADP
ejpam-3018	48	20	f	f	PROPN
ejpam-3018	48	21	∈	∈	PROPN
ejpam-3018	48	22	cγ	cγ	NOUN
ejpam-3018	48	23	[	[	X
ejpam-3018	48	24	0,∞	0,∞	NOUN
ejpam-3018	48	25	)	)	PUNCT
ejpam-3018	48	26	,	,	PUNCT
ejpam-3018	48	27	0	0	NUM
ejpam-3018	48	28	≤	≤	NUM
ejpam-3018	48	29	α	α	NOUN
ejpam-3018	48	30	≤	≤	NOUN
ejpam-3018	48	31	β	β	NOUN
ejpam-3018	48	32	we	we	PRON
ejpam-3018	48	33	introduce	introduce	VERB
ejpam-3018	48	34	the	the	DET
ejpam-3018	48	35	following	follow	VERB
ejpam-3018	48	36	stancu	stancu	ADJ
ejpam-3018	48	37	type	type	NOUN
ejpam-3018	48	38	generalization	generalization	NOUN
ejpam-3018	48	39	of	of	ADP
ejpam-3018	48	40	the	the	DET
ejpam-3018	48	41	operators	operator	NOUN
ejpam-3018	48	42	(	(	PUNCT
ejpam-3018	48	43	3	3	NUM
ejpam-3018	48	44	):	):	PUNCT
ejpam-3018	48	45	g∗(α	g∗(α	PROPN
ejpam-3018	48	46	,	,	PUNCT
ejpam-3018	48	47	β)n	β)n	NOUN
ejpam-3018	48	48	,	,	PUNCT
ejpam-3018	48	49	c	c	PROPN
ejpam-3018	48	50	(	(	PUNCT
ejpam-3018	48	51	f	f	PROPN
ejpam-3018	48	52	;	;	PUNCT
ejpam-3018	48	53	x	x	X
ejpam-3018	48	54	)	)	PUNCT
ejpam-3018	48	55	=	=	SYM
ejpam-3018	49	1	n	n	PROPN
ejpam-3018	49	2	∞∑	∞∑	PROPN
ejpam-3018	49	3	k=1	k=1	PUNCT
ejpam-3018	49	4	pn	pn	PROPN
ejpam-3018	49	5	,	,	PUNCT
ejpam-3018	49	6	k(x	k(x	PROPN
ejpam-3018	49	7	,	,	PUNCT
ejpam-3018	49	8	c	c	NOUN
ejpam-3018	49	9	)	)	PUNCT
ejpam-3018	49	10	∫	∫	PROPN
ejpam-3018	49	11	∞	∞	PROPN
ejpam-3018	49	12	0	0	NUM
ejpam-3018	50	1	pn+c	pn+c	NOUN
ejpam-3018	50	2	,	,	PUNCT
ejpam-3018	50	3	k−1(t	k−1(t	PROPN
ejpam-3018	50	4	,	,	PUNCT
ejpam-3018	50	5	c)f	c)f	NOUN
ejpam-3018	50	6	(	(	PUNCT
ejpam-3018	50	7	(	(	PUNCT
ejpam-3018	50	8	n−	n−	NOUN
ejpam-3018	50	9	c)t+	c)t+	VERB
ejpam-3018	50	10	α	α	NUM
ejpam-3018	50	11	n+	n+	NUM
ejpam-3018	50	12	β	β	X
ejpam-3018	50	13	)	)	PUNCT
ejpam-3018	50	14	dt	dt	PROPN
ejpam-3018	51	1	+	+	PUNCT
ejpam-3018	51	2	pn,0(x	pn,0(x	PROPN
ejpam-3018	51	3	,	,	PUNCT
ejpam-3018	51	4	c)f	c)f	PUNCT
ejpam-3018	51	5	(	(	PUNCT
ejpam-3018	51	6	α	α	NOUN
ejpam-3018	51	7	n+	n+	X
ejpam-3018	51	8	β	β	X
ejpam-3018	51	9	)	)	PUNCT
ejpam-3018	51	10	(	(	PUNCT
ejpam-3018	51	11	4	4	X
ejpam-3018	51	12	)	)	PUNCT
ejpam-3018	51	13	for	for	ADP
ejpam-3018	51	14	α	α	NOUN
ejpam-3018	51	15	=	=	SYM
ejpam-3018	51	16	β	β	X
ejpam-3018	51	17	=	=	SYM
ejpam-3018	51	18	0	0	NUM
ejpam-3018	51	19	,	,	PUNCT
ejpam-3018	51	20	we	we	PRON
ejpam-3018	51	21	denote	denote	VERB
ejpam-3018	51	22	g	g	PROPN
ejpam-3018	51	23	∗(α	∗(α	PROPN
ejpam-3018	51	24	,	,	PUNCT
ejpam-3018	51	25	β	β	NOUN
ejpam-3018	51	26	)	)	PUNCT
ejpam-3018	51	27	n	n	CCONJ
ejpam-3018	51	28	,	,	PUNCT
ejpam-3018	51	29	c	c	PROPN
ejpam-3018	51	30	(	(	PUNCT
ejpam-3018	51	31	f	f	PROPN
ejpam-3018	51	32	;	;	PUNCT
ejpam-3018	51	33	x	x	X
ejpam-3018	51	34	)	)	PUNCT
ejpam-3018	51	35	by	by	ADP
ejpam-3018	51	36	g∗n	g∗n	PROPN
ejpam-3018	51	37	,	,	PUNCT
ejpam-3018	51	38	c(f	c(f	PROPN
ejpam-3018	51	39	;	;	PUNCT
ejpam-3018	51	40	x	x	X
ejpam-3018	51	41	)	)	PUNCT
ejpam-3018	51	42	.	.	PUNCT
ejpam-3018	52	1	the	the	DET
ejpam-3018	52	2	goal	goal	NOUN
ejpam-3018	52	3	of	of	ADP
ejpam-3018	52	4	the	the	DET
ejpam-3018	52	5	present	present	ADJ
ejpam-3018	52	6	paper	paper	NOUN
ejpam-3018	52	7	is	be	AUX
ejpam-3018	52	8	to	to	PART
ejpam-3018	52	9	study	study	VERB
ejpam-3018	52	10	the	the	DET
ejpam-3018	52	11	basic	basic	ADJ
ejpam-3018	52	12	convergence	convergence	NOUN
ejpam-3018	52	13	theorem	theorem	NOUN
ejpam-3018	52	14	,	,	PUNCT
ejpam-3018	52	15	voronovskaja	voronovskaja	NOUN
ejpam-3018	52	16	type	type	NOUN
ejpam-3018	52	17	asymptotic	asymptotic	ADJ
ejpam-3018	52	18	result	result	NOUN
ejpam-3018	52	19	,	,	PUNCT
ejpam-3018	52	20	local	local	ADJ
ejpam-3018	52	21	approximation	approximation	NOUN
ejpam-3018	52	22	theorem	theorem	NOUN
ejpam-3018	52	23	,	,	PUNCT
ejpam-3018	52	24	rate	rate	NOUN
ejpam-3018	52	25	of	of	ADP
ejpam-3018	52	26	convergence	convergence	NOUN
ejpam-3018	52	27	,	,	PUNCT
ejpam-3018	52	28	weighted	weighted	ADJ
ejpam-3018	52	29	approximation	approximation	NOUN
ejpam-3018	52	30	,	,	PUNCT
ejpam-3018	52	31	pointwise	pointwise	NOUN
ejpam-3018	52	32	estimation	estimation	NOUN
ejpam-3018	52	33	and	and	CCONJ
ejpam-3018	52	34	a	a	DET
ejpam-3018	52	35	-	-	PUNCT
ejpam-3018	52	36	statistical	statistical	ADJ
ejpam-3018	52	37	convergence	convergence	NOUN
ejpam-3018	52	38	of	of	ADP
ejpam-3018	52	39	the	the	DET
ejpam-3018	52	40	operators	operator	NOUN
ejpam-3018	52	41	(	(	PUNCT
ejpam-3018	52	42	4	4	NUM
ejpam-3018	52	43	)	)	PUNCT
ejpam-3018	52	44	.	.	PUNCT
ejpam-3018	53	1	further	far	ADV
ejpam-3018	53	2	,	,	PUNCT
ejpam-3018	53	3	to	to	PART
ejpam-3018	53	4	obtain	obtain	VERB
ejpam-3018	53	5	better	well	ADJ
ejpam-3018	53	6	approximation	approximation	NOUN
ejpam-3018	53	7	,	,	PUNCT
ejpam-3018	53	8	we	we	PRON
ejpam-3018	53	9	also	also	ADV
ejpam-3018	53	10	propose	propose	VERB
ejpam-3018	53	11	modification	modification	NOUN
ejpam-3018	53	12	of	of	ADP
ejpam-3018	53	13	the	the	DET
ejpam-3018	53	14	operators	operator	NOUN
ejpam-3018	53	15	(	(	PUNCT
ejpam-3018	53	16	4	4	X
ejpam-3018	53	17	)	)	PUNCT
ejpam-3018	53	18	using	use	VERB
ejpam-3018	53	19	king	king	NOUN
ejpam-3018	53	20	type	type	NOUN
ejpam-3018	53	21	approach	approach	NOUN
ejpam-3018	53	22	.	.	PUNCT
ejpam-3018	54	1	2	2	X
ejpam-3018	54	2	.	.	X
ejpam-3018	54	3	moment	moment	NOUN
ejpam-3018	54	4	estimates	estimate	VERB
ejpam-3018	54	5	lemma	lemma	PROPN
ejpam-3018	54	6	1	1	X
ejpam-3018	54	7	.	.	PUNCT
ejpam-3018	55	1	[	[	X
ejpam-3018	55	2	36	36	NUM
ejpam-3018	55	3	]	]	PUNCT
ejpam-3018	55	4	for	for	ADP
ejpam-3018	55	5	g∗n	g∗n	PROPN
ejpam-3018	55	6	,	,	PUNCT
ejpam-3018	55	7	c(t	c(t	PROPN
ejpam-3018	55	8	m;x	m;x	PROPN
ejpam-3018	55	9	)	)	PUNCT
ejpam-3018	55	10	,	,	PUNCT
ejpam-3018	55	11	m	m	VERB
ejpam-3018	55	12	=	=	NOUN
ejpam-3018	55	13	0	0	NUM
ejpam-3018	55	14	,	,	PUNCT
ejpam-3018	55	15	1	1	NUM
ejpam-3018	55	16	,	,	PUNCT
ejpam-3018	55	17	2	2	NUM
ejpam-3018	55	18	,	,	PUNCT
ejpam-3018	55	19	one	one	NUM
ejpam-3018	55	20	has	have	VERB
ejpam-3018	55	21	(	(	PUNCT
ejpam-3018	55	22	i	i	NOUN
ejpam-3018	55	23	)	)	PUNCT
ejpam-3018	55	24	g∗n	g∗n	PROPN
ejpam-3018	55	25	,	,	PUNCT
ejpam-3018	55	26	c(1;x	c(1;x	PRON
ejpam-3018	55	27	)	)	PUNCT
ejpam-3018	55	28	=	=	SYM
ejpam-3018	55	29	1	1	NUM
ejpam-3018	55	30	;	;	PUNCT
ejpam-3018	55	31	(	(	PUNCT
ejpam-3018	55	32	ii	ii	NOUN
ejpam-3018	55	33	)	)	PUNCT
ejpam-3018	55	34	g∗n	g∗n	PROPN
ejpam-3018	55	35	,	,	PUNCT
ejpam-3018	55	36	c(t;x	c(t;x	X
ejpam-3018	55	37	)	)	PUNCT
ejpam-3018	55	38	=	=	SYM
ejpam-3018	56	1	x	x	X
ejpam-3018	56	2	;	;	PUNCT
ejpam-3018	56	3	(	(	PUNCT
ejpam-3018	56	4	iii	iii	NOUN
ejpam-3018	56	5	)	)	PUNCT
ejpam-3018	56	6	g∗n	g∗n	NOUN
ejpam-3018	56	7	,	,	PUNCT
ejpam-3018	56	8	c(t	c(t	PROPN
ejpam-3018	56	9	2;x	2;x	NUM
ejpam-3018	56	10	)	)	PUNCT
ejpam-3018	56	11	=	=	SYM
ejpam-3018	56	12	(	(	PUNCT
ejpam-3018	56	13	n2−c2)x2	n2−c2)x2	X
ejpam-3018	56	14	+	+	ADJ
ejpam-3018	56	15	2x(n−c	2x(n−c	NUM
ejpam-3018	56	16	)	)	PUNCT
ejpam-3018	56	17	n(n−2c	n(n−2c	PROPN
ejpam-3018	56	18	)	)	PUNCT
ejpam-3018	56	19	,	,	PUNCT
ejpam-3018	56	20	for	for	ADP
ejpam-3018	56	21	n	n	PROPN
ejpam-3018	56	22	>	>	X
ejpam-3018	56	23	2c	2c	NOUN
ejpam-3018	56	24	.	.	PUNCT
ejpam-3018	57	1	lemma	lemma	PROPN
ejpam-3018	57	2	2	2	NUM
ejpam-3018	57	3	.	.	X
ejpam-3018	58	1	for	for	ADP
ejpam-3018	58	2	the	the	DET
ejpam-3018	58	3	operators	operator	NOUN
ejpam-3018	58	4	g	g	PROPN
ejpam-3018	58	5	∗(α	∗(α	PROPN
ejpam-3018	58	6	,	,	PUNCT
ejpam-3018	58	7	β	β	NOUN
ejpam-3018	58	8	)	)	PUNCT
ejpam-3018	58	9	n	n	CCONJ
ejpam-3018	58	10	,	,	PUNCT
ejpam-3018	58	11	c	c	PROPN
ejpam-3018	58	12	(	(	PUNCT
ejpam-3018	58	13	f	f	PROPN
ejpam-3018	58	14	;	;	PUNCT
ejpam-3018	58	15	x	x	X
ejpam-3018	58	16	)	)	PUNCT
ejpam-3018	58	17	as	as	SCONJ
ejpam-3018	58	18	defined	define	VERB
ejpam-3018	58	19	in	in	ADP
ejpam-3018	58	20	(	(	PUNCT
ejpam-3018	58	21	4	4	NUM
ejpam-3018	58	22	)	)	PUNCT
ejpam-3018	58	23	,	,	PUNCT
ejpam-3018	58	24	the	the	DET
ejpam-3018	58	25	following	follow	VERB
ejpam-3018	58	26	equalities	equality	NOUN
ejpam-3018	58	27	hold	hold	VERB
ejpam-3018	58	28	:	:	PUNCT
ejpam-3018	58	29	(	(	PUNCT
ejpam-3018	58	30	i	i	NOUN
ejpam-3018	58	31	)	)	PUNCT
ejpam-3018	58	32	g	g	PROPN
ejpam-3018	58	33	∗(α	∗(α	PROPN
ejpam-3018	58	34	,	,	PUNCT
ejpam-3018	58	35	β	β	NOUN
ejpam-3018	58	36	)	)	PUNCT
ejpam-3018	58	37	n	n	CCONJ
ejpam-3018	58	38	,	,	PUNCT
ejpam-3018	58	39	c	c	PROPN
ejpam-3018	58	40	(	(	PUNCT
ejpam-3018	58	41	1;x	1;x	NUM
ejpam-3018	58	42	)	)	PUNCT
ejpam-3018	58	43	=	=	SYM
ejpam-3018	58	44	1	1	NUM
ejpam-3018	58	45	;	;	PUNCT
ejpam-3018	58	46	(	(	PUNCT
ejpam-3018	58	47	ii	ii	NOUN
ejpam-3018	58	48	)	)	PUNCT
ejpam-3018	58	49	g	g	PROPN
ejpam-3018	58	50	∗(α	∗(α	PROPN
ejpam-3018	58	51	,	,	PUNCT
ejpam-3018	58	52	β	β	NOUN
ejpam-3018	58	53	)	)	PUNCT
ejpam-3018	58	54	n	n	CCONJ
ejpam-3018	58	55	,	,	PUNCT
ejpam-3018	58	56	c	c	X
ejpam-3018	58	57	(	(	PUNCT
ejpam-3018	58	58	t;x	t;x	NUM
ejpam-3018	58	59	)	)	PUNCT
ejpam-3018	59	1	=	=	SYM
ejpam-3018	59	2	nx+α	nx+α	PROPN
ejpam-3018	59	3	n+β	n+β	NUM
ejpam-3018	59	4	;	;	PUNCT
ejpam-3018	59	5	(	(	PUNCT
ejpam-3018	59	6	iii	iii	X
ejpam-3018	59	7	)	)	PUNCT
ejpam-3018	59	8	g	g	PROPN
ejpam-3018	59	9	∗(α	∗(α	PROPN
ejpam-3018	59	10	,	,	PUNCT
ejpam-3018	59	11	β	β	NOUN
ejpam-3018	59	12	)	)	PUNCT
ejpam-3018	59	13	n	n	CCONJ
ejpam-3018	59	14	,	,	PUNCT
ejpam-3018	59	15	c	c	X
ejpam-3018	59	16	(	(	PUNCT
ejpam-3018	59	17	t2;x	t2;x	PROPN
ejpam-3018	59	18	)	)	PUNCT
ejpam-3018	59	19	=	=	SYM
ejpam-3018	59	20	{	{	PUNCT
ejpam-3018	59	21	n(n2−c2	n(n2−c2	NOUN
ejpam-3018	59	22	)	)	PUNCT
ejpam-3018	59	23	(	(	PUNCT
ejpam-3018	59	24	n−2c)(n+β)2	n−2c)(n+β)2	NOUN
ejpam-3018	59	25	}	}	PUNCT
ejpam-3018	59	26	x2	x2	PROPN
ejpam-3018	60	1	+	+	CCONJ
ejpam-3018	60	2	{	{	PUNCT
ejpam-3018	60	3	2n((n−c)+α(n−2c	2n((n−c)+α(n−2c	NUM
ejpam-3018	60	4	)	)	PUNCT
ejpam-3018	60	5	)	)	PUNCT
ejpam-3018	61	1	(	(	PUNCT
ejpam-3018	61	2	n−2c)(n+β)2	n−2c)(n+β)2	NOUN
ejpam-3018	61	3	}	}	PUNCT
ejpam-3018	61	4	x+	x+	ADJ
ejpam-3018	61	5	α2	α2	NOUN
ejpam-3018	61	6	(	(	PUNCT
ejpam-3018	61	7	n+β)2	n+β)2	PROPN
ejpam-3018	61	8	,	,	PUNCT
ejpam-3018	61	9	for	for	ADP
ejpam-3018	61	10	n	n	X
ejpam-3018	61	11	>	>	X
ejpam-3018	61	12	2c	2c	NOUN
ejpam-3018	61	13	.	.	PUNCT
ejpam-3018	62	1	proof	proof	NOUN
ejpam-3018	62	2	.	.	PUNCT
ejpam-3018	63	1	for	for	ADP
ejpam-3018	63	2	x	x	PROPN
ejpam-3018	63	3	∈	∈	PROPN
ejpam-3018	63	4	[	[	X
ejpam-3018	63	5	0,∞	0,∞	NOUN
ejpam-3018	63	6	)	)	PUNCT
ejpam-3018	63	7	,	,	PUNCT
ejpam-3018	63	8	in	in	ADP
ejpam-3018	63	9	view	view	NOUN
ejpam-3018	63	10	of	of	ADP
ejpam-3018	63	11	lemma	lemma	PROPN
ejpam-3018	63	12	1	1	NUM
ejpam-3018	63	13	,	,	PUNCT
ejpam-3018	63	14	we	we	PRON
ejpam-3018	63	15	have	have	VERB
ejpam-3018	63	16	g∗(α	g∗(α	PROPN
ejpam-3018	63	17	,	,	PUNCT
ejpam-3018	63	18	β)n	β)n	ADJ
ejpam-3018	63	19	,	,	PUNCT
ejpam-3018	63	20	c	c	PROPN
ejpam-3018	63	21	(	(	PUNCT
ejpam-3018	63	22	1;x	1;x	NUM
ejpam-3018	63	23	)	)	PUNCT
ejpam-3018	63	24	=	=	SYM
ejpam-3018	64	1	1	1	X
ejpam-3018	64	2	.	.	PUNCT
ejpam-3018	65	1	next	next	ADV
ejpam-3018	65	2	,	,	PUNCT
ejpam-3018	65	3	for	for	ADP
ejpam-3018	65	4	f(t	f(t	NOUN
ejpam-3018	65	5	)	)	PUNCT
ejpam-3018	65	6	=	=	SYM
ejpam-3018	65	7	t	t	PROPN
ejpam-3018	65	8	,	,	PUNCT
ejpam-3018	65	9	again	again	ADV
ejpam-3018	65	10	applying	apply	VERB
ejpam-3018	65	11	lemma	lemma	PROPN
ejpam-3018	65	12	1	1	NUM
ejpam-3018	65	13	,	,	PUNCT
ejpam-3018	65	14	we	we	PRON
ejpam-3018	65	15	get	get	VERB
ejpam-3018	65	16	g∗(α	g∗(α	PROPN
ejpam-3018	65	17	,	,	PUNCT
ejpam-3018	65	18	β)n	β)n	ADJ
ejpam-3018	65	19	,	,	PUNCT
ejpam-3018	65	20	c	c	PROPN
ejpam-3018	65	21	(	(	PUNCT
ejpam-3018	65	22	t;x	t;x	NUM
ejpam-3018	65	23	)	)	PUNCT
ejpam-3018	65	24	=	=	SYM
ejpam-3018	66	1	n	n	PROPN
ejpam-3018	66	2	∞∑	∞∑	PROPN
ejpam-3018	66	3	k=1	k=1	PUNCT
ejpam-3018	66	4	pn	pn	PROPN
ejpam-3018	66	5	,	,	PUNCT
ejpam-3018	66	6	k(x	k(x	PROPN
ejpam-3018	66	7	,	,	PUNCT
ejpam-3018	66	8	c	c	NOUN
ejpam-3018	66	9	)	)	PUNCT
ejpam-3018	66	10	∫	∫	PROPN
ejpam-3018	66	11	∞	∞	PROPN
ejpam-3018	66	12	0	0	NUM
ejpam-3018	67	1	pn+c	pn+c	NOUN
ejpam-3018	67	2	,	,	PUNCT
ejpam-3018	67	3	k−1(t	k−1(t	PROPN
ejpam-3018	67	4	,	,	PUNCT
ejpam-3018	67	5	c	c	X
ejpam-3018	67	6	)	)	PUNCT
ejpam-3018	67	7	(	(	PUNCT
ejpam-3018	67	8	(	(	PUNCT
ejpam-3018	67	9	n−	n−	NOUN
ejpam-3018	67	10	c)t+	c)t+	VERB
ejpam-3018	67	11	α	α	NUM
ejpam-3018	67	12	n+	n+	NUM
ejpam-3018	68	1	β	β	X
ejpam-3018	68	2	)	)	PUNCT
ejpam-3018	68	3	dt+	dt+	NOUN
ejpam-3018	68	4	pn,0(x	pn,0(x	NOUN
ejpam-3018	68	5	,	,	PUNCT
ejpam-3018	68	6	c	c	NOUN
ejpam-3018	68	7	)	)	PUNCT
ejpam-3018	68	8	(	(	PUNCT
ejpam-3018	68	9	α	α	NOUN
ejpam-3018	68	10	n+	n+	X
ejpam-3018	68	11	β	β	X
ejpam-3018	68	12	)	)	PUNCT
ejpam-3018	69	1	=	=	SYM
ejpam-3018	69	2	n	n	PROPN
ejpam-3018	69	3	n+	n+	X
ejpam-3018	69	4	β	β	X
ejpam-3018	69	5	g∗n	g∗n	PROPN
ejpam-3018	69	6	,	,	PUNCT
ejpam-3018	69	7	c(t	c(t	PROPN
ejpam-3018	69	8	,	,	PUNCT
ejpam-3018	69	9	x	x	NOUN
ejpam-3018	69	10	)	)	PUNCT
ejpam-3018	70	1	+	+	CCONJ
ejpam-3018	70	2	α	α	NOUN
ejpam-3018	70	3	n+	n+	X
ejpam-3018	70	4	β	β	X
ejpam-3018	70	5	=	=	SYM
ejpam-3018	70	6	nx+	nx+	PROPN
ejpam-3018	70	7	α	α	NOUN
ejpam-3018	70	8	n+	n+	X
ejpam-3018	70	9	β	β	X
ejpam-3018	70	10	a.	a.	NOUN
ejpam-3018	70	11	kumar	kumar	PROPN
ejpam-3018	70	12	,	,	PUNCT
ejpam-3018	70	13	v.	v.	PROPN
ejpam-3018	70	14	n.	n.	PROPN
ejpam-3018	70	15	mishra	mishra	PROPN
ejpam-3018	70	16	,	,	PUNCT
ejpam-3018	70	17	d.	d.	PROPN
ejpam-3018	70	18	tapiawala	tapiawala	PROPN
ejpam-3018	70	19	/	/	SYM
ejpam-3018	70	20	eur	eur	PROPN
ejpam-3018	70	21	.	.	PUNCT
ejpam-3018	71	1	j.	j.	PROPN
ejpam-3018	71	2	pure	pure	PROPN
ejpam-3018	71	3	appl	appl	PROPN
ejpam-3018	71	4	.	.	PROPN
ejpam-3018	71	5	math	math	PROPN
ejpam-3018	71	6	,	,	PUNCT
ejpam-3018	71	7	10	10	NUM
ejpam-3018	71	8	(	(	PUNCT
ejpam-3018	71	9	4	4	NUM
ejpam-3018	71	10	)	)	PUNCT
ejpam-3018	71	11	(	(	PUNCT
ejpam-3018	71	12	2017	2017	NUM
ejpam-3018	71	13	)	)	PUNCT
ejpam-3018	71	14	,	,	PUNCT
ejpam-3018	71	15	890	890	NUM
ejpam-3018	71	16	-	-	SYM
ejpam-3018	71	17	907	907	NUM
ejpam-3018	71	18	893	893	NUM
ejpam-3018	71	19	proceeding	proceeding	NOUN
ejpam-3018	71	20	similarly	similarly	ADV
ejpam-3018	71	21	,	,	PUNCT
ejpam-3018	71	22	we	we	PRON
ejpam-3018	71	23	have	have	VERB
ejpam-3018	71	24	g∗(α	g∗(α	PROPN
ejpam-3018	71	25	,	,	PUNCT
ejpam-3018	71	26	β)n	β)n	ADJ
ejpam-3018	71	27	,	,	PUNCT
ejpam-3018	71	28	c	c	X
ejpam-3018	71	29	(	(	PUNCT
ejpam-3018	71	30	t2;x	t2;x	PROPN
ejpam-3018	71	31	)	)	PUNCT
ejpam-3018	71	32	=	=	SYM
ejpam-3018	72	1	n	n	PROPN
ejpam-3018	72	2	∞∑	∞∑	PROPN
ejpam-3018	72	3	k=1	k=1	PUNCT
ejpam-3018	72	4	pn	pn	PROPN
ejpam-3018	72	5	,	,	PUNCT
ejpam-3018	72	6	k(x	k(x	PROPN
ejpam-3018	72	7	,	,	PUNCT
ejpam-3018	72	8	c	c	NOUN
ejpam-3018	72	9	)	)	PUNCT
ejpam-3018	72	10	∫	∫	PROPN
ejpam-3018	73	1	∞	∞	PROPN
ejpam-3018	73	2	0	0	NUM
ejpam-3018	73	3	pn+c	pn+c	NOUN
ejpam-3018	73	4	,	,	PUNCT
ejpam-3018	73	5	k−1(t	k−1(t	PROPN
ejpam-3018	73	6	,	,	PUNCT
ejpam-3018	73	7	c	c	X
ejpam-3018	73	8	)	)	PUNCT
ejpam-3018	73	9	(	(	PUNCT
ejpam-3018	73	10	(	(	PUNCT
ejpam-3018	73	11	n−	n−	NOUN
ejpam-3018	73	12	c)t+	c)t+	VERB
ejpam-3018	73	13	α	α	NUM
ejpam-3018	73	14	n+	n+	X
ejpam-3018	73	15	β	β	X
ejpam-3018	73	16	)	)	PUNCT
ejpam-3018	73	17	2	2	NUM
ejpam-3018	73	18	dt+	dt+	NOUN
ejpam-3018	73	19	pn,0(x	pn,0(x	NOUN
ejpam-3018	73	20	,	,	PUNCT
ejpam-3018	73	21	c	c	NOUN
ejpam-3018	73	22	)	)	PUNCT
ejpam-3018	73	23	(	(	PUNCT
ejpam-3018	73	24	α	α	NOUN
ejpam-3018	73	25	n+	n+	X
ejpam-3018	73	26	β	β	X
ejpam-3018	73	27	)	)	PUNCT
ejpam-3018	73	28	2	2	NUM
ejpam-3018	73	29	=	=	SYM
ejpam-3018	73	30	(	(	PUNCT
ejpam-3018	73	31	n	n	X
ejpam-3018	73	32	n+	n+	X
ejpam-3018	73	33	β	β	X
ejpam-3018	73	34	)	)	PUNCT
ejpam-3018	73	35	2	2	NUM
ejpam-3018	73	36	g∗n	g∗n	NOUN
ejpam-3018	73	37	,	,	PUNCT
ejpam-3018	73	38	c(t	c(t	PROPN
ejpam-3018	73	39	2	2	NUM
ejpam-3018	73	40	,	,	PUNCT
ejpam-3018	73	41	x	x	NOUN
ejpam-3018	73	42	)	)	PUNCT
ejpam-3018	73	43	+	+	CCONJ
ejpam-3018	73	44	2nα	2nα	ADJ
ejpam-3018	73	45	(	(	PUNCT
ejpam-3018	73	46	n+	n+	X
ejpam-3018	73	47	β)2	β)2	X
ejpam-3018	73	48	g∗n	g∗n	X
ejpam-3018	73	49	,	,	PUNCT
ejpam-3018	73	50	c(t	c(t	PROPN
ejpam-3018	73	51	,	,	PUNCT
ejpam-3018	73	52	x	x	NOUN
ejpam-3018	73	53	)	)	PUNCT
ejpam-3018	74	1	+	+	CCONJ
ejpam-3018	74	2	(	(	PUNCT
ejpam-3018	74	3	α	α	NOUN
ejpam-3018	74	4	n+	n+	X
ejpam-3018	74	5	β	β	X
ejpam-3018	74	6	)	)	PUNCT
ejpam-3018	74	7	2	2	NUM
ejpam-3018	74	8	=	=	SYM
ejpam-3018	74	9	{	{	PUNCT
ejpam-3018	74	10	n(n2	n(n2	NOUN
ejpam-3018	74	11	−	−	PROPN
ejpam-3018	74	12	c2	c2	PROPN
ejpam-3018	74	13	)	)	PUNCT
ejpam-3018	74	14	(	(	PUNCT
ejpam-3018	74	15	n−	n−	NOUN
ejpam-3018	74	16	2c)(n+	2c)(n+	NUM
ejpam-3018	74	17	β)2	β)2	ADV
ejpam-3018	74	18	}	}	PUNCT
ejpam-3018	74	19	x2	x2	PROPN
ejpam-3018	75	1	+	+	CCONJ
ejpam-3018	75	2	{	{	PUNCT
ejpam-3018	75	3	2n((n−	2n((n−	NUM
ejpam-3018	75	4	c	c	NOUN
ejpam-3018	75	5	)	)	PUNCT
ejpam-3018	75	6	+	+	CCONJ
ejpam-3018	75	7	α(n−	α(n−	NUM
ejpam-3018	75	8	2c	2c	NUM
ejpam-3018	75	9	)	)	PUNCT
ejpam-3018	75	10	)	)	PUNCT
ejpam-3018	76	1	(	(	PUNCT
ejpam-3018	76	2	n−	n−	NOUN
ejpam-3018	76	3	2c)(n+	2c)(n+	NUM
ejpam-3018	76	4	β)2	β)2	ADV
ejpam-3018	76	5	}	}	PUNCT
ejpam-3018	76	6	x+	x+	ADJ
ejpam-3018	76	7	α2	α2	PROPN
ejpam-3018	76	8	(	(	PUNCT
ejpam-3018	76	9	n+	n+	X
ejpam-3018	76	10	β)2	β)2	X
ejpam-3018	76	11	.	.	PUNCT
ejpam-3018	77	1	lemma	lemma	PROPN
ejpam-3018	77	2	3	3	X
ejpam-3018	77	3	.	.	X
ejpam-3018	78	1	for	for	ADP
ejpam-3018	78	2	f	f	PROPN
ejpam-3018	78	3	∈	∈	PROPN
ejpam-3018	78	4	cb[0,∞	cb[0,∞	PROPN
ejpam-3018	78	5	)	)	PUNCT
ejpam-3018	78	6	(	(	PUNCT
ejpam-3018	78	7	space	space	NOUN
ejpam-3018	78	8	of	of	ADP
ejpam-3018	78	9	all	all	DET
ejpam-3018	78	10	bounded	bounded	ADJ
ejpam-3018	78	11	and	and	CCONJ
ejpam-3018	78	12	continuous	continuous	ADJ
ejpam-3018	78	13	functions	function	NOUN
ejpam-3018	78	14	on	on	ADP
ejpam-3018	78	15	[	[	X
ejpam-3018	78	16	0,∞	0,∞	NOUN
ejpam-3018	78	17	)	)	PUNCT
ejpam-3018	78	18	endowed	endow	VERB
ejpam-3018	78	19	with	with	ADP
ejpam-3018	78	20	norm	norm	NOUN
ejpam-3018	78	21	‖	‖	PROPN
ejpam-3018	78	22	f	f	PROPN
ejpam-3018	78	23	‖=	‖=	PROPN
ejpam-3018	78	24	sup{|f(x)|	sup{|f(x)|	PROPN
ejpam-3018	78	25	:	:	PUNCT
ejpam-3018	78	26	x	x	PUNCT
ejpam-3018	78	27	∈	∈	PROPN
ejpam-3018	79	1	[	[	X
ejpam-3018	79	2	0,∞	0,∞	NOUN
ejpam-3018	79	3	)	)	PUNCT
ejpam-3018	79	4	}	}	PUNCT
ejpam-3018	79	5	)	)	PUNCT
ejpam-3018	79	6	,	,	PUNCT
ejpam-3018	79	7	‖	‖	PROPN
ejpam-3018	79	8	g∗(α	g∗(α	PROPN
ejpam-3018	79	9	,	,	PUNCT
ejpam-3018	79	10	β)n	β)n	NOUN
ejpam-3018	79	11	,	,	PUNCT
ejpam-3018	79	12	c	c	PROPN
ejpam-3018	79	13	(	(	PUNCT
ejpam-3018	79	14	f	f	PROPN
ejpam-3018	79	15	;	;	PUNCT
ejpam-3018	79	16	x	x	X
ejpam-3018	79	17	)	)	PUNCT
ejpam-3018	79	18	‖≤‖	‖≤‖	NOUN
ejpam-3018	79	19	f	f	NOUN
ejpam-3018	79	20	‖.	‖.	NUM
ejpam-3018	79	21	proof	proof	NOUN
ejpam-3018	79	22	.	.	PUNCT
ejpam-3018	80	1	in	in	ADP
ejpam-3018	80	2	view	view	NOUN
ejpam-3018	80	3	of	of	ADP
ejpam-3018	80	4	(	(	PUNCT
ejpam-3018	80	5	4	4	NUM
ejpam-3018	80	6	)	)	PUNCT
ejpam-3018	80	7	and	and	CCONJ
ejpam-3018	80	8	lemma	lemma	PROPN
ejpam-3018	80	9	2	2	NUM
ejpam-3018	80	10	,	,	PUNCT
ejpam-3018	80	11	the	the	DET
ejpam-3018	80	12	proof	proof	NOUN
ejpam-3018	80	13	of	of	ADP
ejpam-3018	80	14	this	this	DET
ejpam-3018	80	15	lemma	lemma	PROPN
ejpam-3018	80	16	easily	easily	ADV
ejpam-3018	80	17	follows	follow	VERB
ejpam-3018	80	18	.	.	PUNCT
ejpam-3018	81	1	remark	remark	PROPN
ejpam-3018	81	2	1	1	NUM
ejpam-3018	81	3	.	.	PUNCT
ejpam-3018	82	1	for	for	ADP
ejpam-3018	82	2	every	every	DET
ejpam-3018	82	3	x	x	PUNCT
ejpam-3018	82	4	≥	≥	NOUN
ejpam-3018	82	5	0	0	NUM
ejpam-3018	82	6	,	,	PUNCT
ejpam-3018	82	7	n	n	PROPN
ejpam-3018	82	8	>	>	X
ejpam-3018	82	9	2c	2c	NOUN
ejpam-3018	82	10	,	,	PUNCT
ejpam-3018	82	11	we	we	PRON
ejpam-3018	82	12	have	have	VERB
ejpam-3018	82	13	g∗(α	g∗(α	PROPN
ejpam-3018	82	14	,	,	PUNCT
ejpam-3018	82	15	β)n	β)n	ADJ
ejpam-3018	82	16	,	,	PUNCT
ejpam-3018	82	17	c	c	NOUN
ejpam-3018	82	18	(	(	PUNCT
ejpam-3018	82	19	(	(	PUNCT
ejpam-3018	82	20	t−	t−	PROPN
ejpam-3018	82	21	x);x	x);x	PROPN
ejpam-3018	82	22	)	)	PUNCT
ejpam-3018	82	23	=	=	PUNCT
ejpam-3018	83	1	α−	α−	ADP
ejpam-3018	83	2	βx	βx	PRON
ejpam-3018	83	3	n+	n+	X
ejpam-3018	83	4	β	β	X
ejpam-3018	83	5	,	,	PUNCT
ejpam-3018	83	6	and	and	CCONJ
ejpam-3018	83	7	g∗(α	g∗(α	PROPN
ejpam-3018	83	8	,	,	PUNCT
ejpam-3018	83	9	β)n	β)n	NOUN
ejpam-3018	83	10	,	,	PUNCT
ejpam-3018	83	11	c	c	PROPN
ejpam-3018	83	12	(	(	PUNCT
ejpam-3018	83	13	(	(	PUNCT
ejpam-3018	83	14	t−	t−	PROPN
ejpam-3018	83	15	x)2;x	x)2;x	NUM
ejpam-3018	83	16	)	)	PUNCT
ejpam-3018	83	17	=	=	PRON
ejpam-3018	83	18	{	{	PUNCT
ejpam-3018	83	19	nc(2n−	nc(2n−	PROPN
ejpam-3018	83	20	c	c	X
ejpam-3018	83	21	)	)	PUNCT
ejpam-3018	83	22	+	+	CCONJ
ejpam-3018	83	23	β2(n−	β2(n−	NUM
ejpam-3018	83	24	2c	2c	NUM
ejpam-3018	83	25	)	)	PUNCT
ejpam-3018	83	26	(	(	PUNCT
ejpam-3018	83	27	n−	n−	NOUN
ejpam-3018	83	28	2c)(n+	2c)(n+	NUM
ejpam-3018	83	29	β)2	β)2	ADV
ejpam-3018	83	30	}	}	PUNCT
ejpam-3018	83	31	x2	x2	NOUN
ejpam-3018	84	1	+	+	CCONJ
ejpam-3018	84	2	{	{	PUNCT
ejpam-3018	84	3	2n(n−	2n(n−	NUM
ejpam-3018	84	4	c)−	c)−	PROPN
ejpam-3018	84	5	2αβ(n−	2αβ(n−	NUM
ejpam-3018	84	6	2c	2c	NUM
ejpam-3018	84	7	)	)	PUNCT
ejpam-3018	84	8	(	(	PUNCT
ejpam-3018	84	9	n−	n−	NOUN
ejpam-3018	84	10	2c)(n+	2c)(n+	NUM
ejpam-3018	84	11	β)2	β)2	ADV
ejpam-3018	84	12	}	}	PUNCT
ejpam-3018	84	13	x+	x+	ADJ
ejpam-3018	84	14	α2	α2	PROPN
ejpam-3018	84	15	(	(	PUNCT
ejpam-3018	84	16	n+	n+	X
ejpam-3018	84	17	β)2	β)2	NOUN
ejpam-3018	84	18	,	,	PUNCT
ejpam-3018	84	19	n	n	PROPN
ejpam-3018	84	20	>	>	X
ejpam-3018	84	21	2c	2c	NUM
ejpam-3018	84	22	=	=	SYM
ejpam-3018	84	23	γ(α	γ(α	PROPN
ejpam-3018	84	24	,	,	PUNCT
ejpam-3018	84	25	β)n	β)n	NOUN
ejpam-3018	84	26	,	,	PUNCT
ejpam-3018	84	27	c	c	PROPN
ejpam-3018	84	28	(	(	PUNCT
ejpam-3018	84	29	x	x	NOUN
ejpam-3018	84	30	)	)	PUNCT
ejpam-3018	84	31	,	,	PUNCT
ejpam-3018	84	32	(	(	PUNCT
ejpam-3018	84	33	say	say	INTJ
ejpam-3018	84	34	)	)	PUNCT
ejpam-3018	84	35	.	.	PUNCT
ejpam-3018	85	1	3	3	X
ejpam-3018	85	2	.	.	X
ejpam-3018	85	3	main	main	ADJ
ejpam-3018	85	4	results	result	NOUN
ejpam-3018	85	5	theorem	theorem	VERB
ejpam-3018	85	6	4	4	NUM
ejpam-3018	85	7	.	.	PUNCT
ejpam-3018	86	1	(	(	PUNCT
ejpam-3018	86	2	voronovskaja	voronovskaja	PROPN
ejpam-3018	86	3	type	type	NOUN
ejpam-3018	86	4	theorem	theorem	VERB
ejpam-3018	86	5	)	)	PUNCT
ejpam-3018	86	6	let	let	VERB
ejpam-3018	86	7	f	f	PROPN
ejpam-3018	86	8	∈	∈	PROPN
ejpam-3018	86	9	cb[0,∞	cb[0,∞	PROPN
ejpam-3018	86	10	)	)	PUNCT
ejpam-3018	86	11	.	.	PUNCT
ejpam-3018	87	1	if	if	SCONJ
ejpam-3018	87	2	f	f	PROPN
ejpam-3018	87	3	′	′	PROPN
ejpam-3018	87	4	,	,	PUNCT
ejpam-3018	87	5	f	f	PROPN
ejpam-3018	88	1	′′	′′	PROPN
ejpam-3018	88	2	exists	exist	VERB
ejpam-3018	88	3	at	at	ADP
ejpam-3018	88	4	a	a	DET
ejpam-3018	88	5	fixed	fixed	ADJ
ejpam-3018	88	6	point	point	NOUN
ejpam-3018	88	7	x	x	X
ejpam-3018	88	8	∈	∈	PROPN
ejpam-3018	89	1	[	[	X
ejpam-3018	89	2	0,∞	0,∞	NOUN
ejpam-3018	89	3	)	)	PUNCT
ejpam-3018	89	4	,	,	PUNCT
ejpam-3018	89	5	we	we	PRON
ejpam-3018	89	6	have	have	VERB
ejpam-3018	89	7	lim	lim	PROPN
ejpam-3018	89	8	n→∞	n→∞	NUM
ejpam-3018	89	9	n	n	PROPN
ejpam-3018	89	10	(	(	PUNCT
ejpam-3018	89	11	g∗(α	g∗(α	PROPN
ejpam-3018	89	12	,	,	PUNCT
ejpam-3018	89	13	β)n	β)n	NOUN
ejpam-3018	89	14	,	,	PUNCT
ejpam-3018	89	15	c	c	PROPN
ejpam-3018	89	16	(	(	PUNCT
ejpam-3018	89	17	f	f	PROPN
ejpam-3018	89	18	;	;	PUNCT
ejpam-3018	89	19	x)−	x)−	PROPN
ejpam-3018	89	20	f(x	f(x	PROPN
ejpam-3018	89	21	)	)	PUNCT
ejpam-3018	89	22	)	)	PUNCT
ejpam-3018	90	1	=	=	PUNCT
ejpam-3018	90	2	(	(	PUNCT
ejpam-3018	90	3	α−	α−	ADP
ejpam-3018	90	4	βx)f	βx)f	SYM
ejpam-3018	90	5	′(x	′(x	NOUN
ejpam-3018	90	6	)	)	PUNCT
ejpam-3018	91	1	+	+	CCONJ
ejpam-3018	91	2	x(1	x(1	PROPN
ejpam-3018	91	3	+	+	CCONJ
ejpam-3018	91	4	cx)f	cx)f	PROPN
ejpam-3018	91	5	′′(x	′′(x	NOUN
ejpam-3018	91	6	)	)	PUNCT
ejpam-3018	91	7	.	.	PUNCT
ejpam-3018	92	1	proof	proof	NOUN
ejpam-3018	92	2	.	.	PUNCT
ejpam-3018	93	1	let	let	VERB
ejpam-3018	93	2	x	x	PUNCT
ejpam-3018	93	3	∈	∈	PROPN
ejpam-3018	94	1	[	[	X
ejpam-3018	94	2	0,∞	0,∞	NOUN
ejpam-3018	94	3	)	)	PUNCT
ejpam-3018	94	4	be	be	AUX
ejpam-3018	94	5	fixed	fix	VERB
ejpam-3018	94	6	.	.	PUNCT
ejpam-3018	95	1	from	from	ADP
ejpam-3018	95	2	the	the	DET
ejpam-3018	95	3	taylor	taylor	PROPN
ejpam-3018	95	4	’s	’s	PART
ejpam-3018	95	5	theorem	theorem	PROPN
ejpam-3018	95	6	,	,	PUNCT
ejpam-3018	95	7	we	we	PRON
ejpam-3018	95	8	may	may	AUX
ejpam-3018	95	9	write	write	VERB
ejpam-3018	95	10	f(t	f(t	NOUN
ejpam-3018	95	11	)	)	PUNCT
ejpam-3018	95	12	=	=	SYM
ejpam-3018	95	13	f(x	f(x	PROPN
ejpam-3018	95	14	)	)	PUNCT
ejpam-3018	96	1	+	+	CCONJ
ejpam-3018	96	2	(	(	PUNCT
ejpam-3018	96	3	t−	t−	PROPN
ejpam-3018	96	4	x)f	x)f	NOUN
ejpam-3018	96	5	′(x	′(x	NOUN
ejpam-3018	96	6	)	)	PUNCT
ejpam-3018	97	1	+	+	CCONJ
ejpam-3018	97	2	1	1	NUM
ejpam-3018	97	3	2	2	NUM
ejpam-3018	97	4	f	f	PROPN
ejpam-3018	97	5	′′(x)(t−	′′(x)(t−	X
ejpam-3018	97	6	x)2	x)2	VERB
ejpam-3018	97	7	+	+	CCONJ
ejpam-3018	97	8	ξ(t	ξ(t	NOUN
ejpam-3018	97	9	,	,	PUNCT
ejpam-3018	97	10	x)(t−	x)(t−	X
ejpam-3018	97	11	x)2	x)2	PROPN
ejpam-3018	97	12	,	,	PUNCT
ejpam-3018	97	13	(	(	PUNCT
ejpam-3018	97	14	5	5	X
ejpam-3018	97	15	)	)	PUNCT
ejpam-3018	97	16	where	where	SCONJ
ejpam-3018	97	17	ξ(t	ξ(t	NOUN
ejpam-3018	97	18	,	,	PUNCT
ejpam-3018	97	19	x	x	PRON
ejpam-3018	97	20	)	)	PUNCT
ejpam-3018	97	21	is	be	AUX
ejpam-3018	97	22	the	the	DET
ejpam-3018	97	23	peano	peano	NOUN
ejpam-3018	97	24	form	form	NOUN
ejpam-3018	97	25	of	of	ADP
ejpam-3018	97	26	the	the	DET
ejpam-3018	97	27	remainder	remainder	NOUN
ejpam-3018	97	28	and	and	CCONJ
ejpam-3018	97	29	lim	lim	PROPN
ejpam-3018	97	30	t→x	t→x	NUM
ejpam-3018	97	31	ξ(t	ξ(t	PROPN
ejpam-3018	97	32	,	,	PUNCT
ejpam-3018	97	33	x	x	X
ejpam-3018	97	34	)	)	PUNCT
ejpam-3018	98	1	=	=	SYM
ejpam-3018	98	2	0	0	X
ejpam-3018	98	3	.	.	PUNCT
ejpam-3018	98	4	applying	apply	VERB
ejpam-3018	98	5	g	g	PROPN
ejpam-3018	98	6	∗(α	∗(α	PROPN
ejpam-3018	98	7	,	,	PUNCT
ejpam-3018	98	8	β	β	NOUN
ejpam-3018	98	9	)	)	PUNCT
ejpam-3018	98	10	n	n	CCONJ
ejpam-3018	98	11	,	,	PUNCT
ejpam-3018	98	12	c	c	PROPN
ejpam-3018	98	13	(	(	PUNCT
ejpam-3018	98	14	f	f	X
ejpam-3018	98	15	,	,	PUNCT
ejpam-3018	98	16	x	x	NOUN
ejpam-3018	98	17	)	)	PUNCT
ejpam-3018	98	18	on	on	ADP
ejpam-3018	98	19	both	both	DET
ejpam-3018	98	20	sides	side	NOUN
ejpam-3018	98	21	of	of	ADP
ejpam-3018	98	22	(	(	PUNCT
ejpam-3018	98	23	5	5	NUM
ejpam-3018	98	24	)	)	PUNCT
ejpam-3018	98	25	,	,	PUNCT
ejpam-3018	98	26	we	we	PRON
ejpam-3018	98	27	have	have	VERB
ejpam-3018	98	28	n	n	PROPN
ejpam-3018	98	29	(	(	PUNCT
ejpam-3018	98	30	g∗(α	g∗(α	PROPN
ejpam-3018	98	31	,	,	PUNCT
ejpam-3018	98	32	β)n	β)n	NOUN
ejpam-3018	98	33	,	,	PUNCT
ejpam-3018	98	34	c	c	PROPN
ejpam-3018	98	35	(	(	PUNCT
ejpam-3018	98	36	f	f	PROPN
ejpam-3018	98	37	;	;	PUNCT
ejpam-3018	98	38	x)−	x)−	PROPN
ejpam-3018	98	39	f(x	f(x	PROPN
ejpam-3018	98	40	)	)	PUNCT
ejpam-3018	98	41	)	)	PUNCT
ejpam-3018	99	1	=	=	PUNCT
ejpam-3018	99	2	nf	nf	PROPN
ejpam-3018	100	1	′(x)g∗(α	′(x)g∗(α	NUM
ejpam-3018	100	2	,	,	PUNCT
ejpam-3018	100	3	β)n	β)n	NOUN
ejpam-3018	100	4	,	,	PUNCT
ejpam-3018	100	5	c	c	NOUN
ejpam-3018	100	6	(	(	PUNCT
ejpam-3018	100	7	(	(	PUNCT
ejpam-3018	100	8	t−	t−	PROPN
ejpam-3018	100	9	x);x	x);x	PROPN
ejpam-3018	100	10	)	)	PUNCT
ejpam-3018	101	1	+	+	CCONJ
ejpam-3018	101	2	1	1	NUM
ejpam-3018	101	3	2	2	NUM
ejpam-3018	101	4	nf	nf	NOUN
ejpam-3018	101	5	′′(x)g∗(α	′′(x)g∗(α	NOUN
ejpam-3018	101	6	,	,	PUNCT
ejpam-3018	101	7	β)n	β)n	NOUN
ejpam-3018	101	8	,	,	PUNCT
ejpam-3018	101	9	c	c	PROPN
ejpam-3018	101	10	(	(	PUNCT
ejpam-3018	101	11	(	(	PUNCT
ejpam-3018	101	12	t−	t−	PROPN
ejpam-3018	101	13	x)2;x	x)2;x	NUM
ejpam-3018	101	14	)	)	PUNCT
ejpam-3018	101	15	a.	a.	PROPN
ejpam-3018	101	16	kumar	kumar	PROPN
ejpam-3018	101	17	,	,	PUNCT
ejpam-3018	101	18	v.	v.	PROPN
ejpam-3018	101	19	n.	n.	PROPN
ejpam-3018	101	20	mishra	mishra	PROPN
ejpam-3018	101	21	,	,	PUNCT
ejpam-3018	101	22	d.	d.	PROPN
ejpam-3018	101	23	tapiawala	tapiawala	PROPN
ejpam-3018	101	24	/	/	SYM
ejpam-3018	101	25	eur	eur	PROPN
ejpam-3018	101	26	.	.	PUNCT
ejpam-3018	102	1	j.	j.	PROPN
ejpam-3018	102	2	pure	pure	PROPN
ejpam-3018	102	3	appl	appl	PROPN
ejpam-3018	102	4	.	.	PROPN
ejpam-3018	102	5	math	math	PROPN
ejpam-3018	102	6	,	,	PUNCT
ejpam-3018	102	7	10	10	NUM
ejpam-3018	102	8	(	(	PUNCT
ejpam-3018	102	9	4	4	NUM
ejpam-3018	102	10	)	)	PUNCT
ejpam-3018	102	11	(	(	PUNCT
ejpam-3018	102	12	2017	2017	NUM
ejpam-3018	102	13	)	)	PUNCT
ejpam-3018	102	14	,	,	PUNCT
ejpam-3018	102	15	890	890	NUM
ejpam-3018	102	16	-	-	SYM
ejpam-3018	102	17	907	907	NUM
ejpam-3018	102	18	894	894	NUM
ejpam-3018	102	19	+	+	NOUN
ejpam-3018	102	20	ng∗(α	ng∗(α	ADJ
ejpam-3018	102	21	,	,	PUNCT
ejpam-3018	102	22	β)n	β)n	ADJ
ejpam-3018	102	23	,	,	PUNCT
ejpam-3018	102	24	c	c	PROPN
ejpam-3018	102	25	(	(	PUNCT
ejpam-3018	102	26	(	(	PUNCT
ejpam-3018	102	27	t−	t−	PROPN
ejpam-3018	102	28	x)2ξ(t	x)2ξ(t	PROPN
ejpam-3018	102	29	,	,	PUNCT
ejpam-3018	102	30	x);x	x);x	PROPN
ejpam-3018	102	31	)	)	PUNCT
ejpam-3018	102	32	.	.	PUNCT
ejpam-3018	103	1	in	in	ADP
ejpam-3018	103	2	view	view	NOUN
ejpam-3018	103	3	of	of	ADP
ejpam-3018	103	4	remark	remark	NOUN
ejpam-3018	103	5	1	1	NUM
ejpam-3018	103	6	,	,	PUNCT
ejpam-3018	103	7	we	we	PRON
ejpam-3018	103	8	have	have	VERB
ejpam-3018	103	9	lim	lim	PROPN
ejpam-3018	103	10	n→∞	n→∞	PRON
ejpam-3018	103	11	ng∗(α	ng∗(α	PROPN
ejpam-3018	103	12	,	,	PUNCT
ejpam-3018	103	13	β)n	β)n	ADJ
ejpam-3018	103	14	,	,	PUNCT
ejpam-3018	103	15	c	c	NOUN
ejpam-3018	103	16	(	(	PUNCT
ejpam-3018	103	17	(	(	PUNCT
ejpam-3018	103	18	t−	t−	PROPN
ejpam-3018	103	19	x);x	x);x	PROPN
ejpam-3018	103	20	)	)	PUNCT
ejpam-3018	103	21	=	=	PUNCT
ejpam-3018	104	1	α−	α−	ADP
ejpam-3018	104	2	βx	βx	PROPN
ejpam-3018	104	3	(	(	PUNCT
ejpam-3018	104	4	6	6	NUM
ejpam-3018	104	5	)	)	PUNCT
ejpam-3018	104	6	and	and	CCONJ
ejpam-3018	104	7	lim	lim	PROPN
ejpam-3018	104	8	n→∞	n→∞	NUM
ejpam-3018	104	9	ng∗(α	ng∗(α	PROPN
ejpam-3018	104	10	,	,	PUNCT
ejpam-3018	104	11	β)n	β)n	ADJ
ejpam-3018	104	12	,	,	PUNCT
ejpam-3018	104	13	c	c	PROPN
ejpam-3018	104	14	(	(	PUNCT
ejpam-3018	104	15	(	(	PUNCT
ejpam-3018	104	16	t−	t−	PROPN
ejpam-3018	104	17	x)2;x	x)2;x	NUM
ejpam-3018	104	18	)	)	PUNCT
ejpam-3018	104	19	=	=	SYM
ejpam-3018	104	20	2x(1	2x(1	NUM
ejpam-3018	104	21	+	+	NUM
ejpam-3018	104	22	cx	cx	NOUN
ejpam-3018	104	23	)	)	PUNCT
ejpam-3018	104	24	.	.	PUNCT
ejpam-3018	105	1	(	(	PUNCT
ejpam-3018	105	2	7	7	X
ejpam-3018	105	3	)	)	PUNCT
ejpam-3018	105	4	now	now	ADV
ejpam-3018	105	5	,	,	PUNCT
ejpam-3018	105	6	we	we	PRON
ejpam-3018	105	7	shall	shall	AUX
ejpam-3018	105	8	show	show	VERB
ejpam-3018	105	9	that	that	SCONJ
ejpam-3018	105	10	lim	lim	PROPN
ejpam-3018	105	11	n→∞	n→∞	PRON
ejpam-3018	105	12	ng∗(α	ng∗(α	PROPN
ejpam-3018	105	13	,	,	PUNCT
ejpam-3018	105	14	β)n	β)n	ADJ
ejpam-3018	105	15	,	,	PUNCT
ejpam-3018	105	16	c	c	PROPN
ejpam-3018	105	17	(	(	PUNCT
ejpam-3018	105	18	ξ(t	ξ(t	ADP
ejpam-3018	105	19	,	,	PUNCT
ejpam-3018	105	20	x)(t−	x)(t−	NOUN
ejpam-3018	105	21	x)2;x	x)2;x	PUNCT
ejpam-3018	105	22	)	)	PUNCT
ejpam-3018	106	1	=	=	PUNCT
ejpam-3018	106	2	0	0	NUM
ejpam-3018	106	3	by	by	ADP
ejpam-3018	106	4	using	use	VERB
ejpam-3018	106	5	cauchy	cauchy	PROPN
ejpam-3018	106	6	-	-	PUNCT
ejpam-3018	106	7	schwarz	schwarz	PROPN
ejpam-3018	106	8	inequality	inequality	NOUN
ejpam-3018	106	9	,	,	PUNCT
ejpam-3018	106	10	we	we	PRON
ejpam-3018	106	11	have	have	VERB
ejpam-3018	106	12	g∗(α	g∗(α	PROPN
ejpam-3018	106	13	,	,	PUNCT
ejpam-3018	106	14	β)n	β)n	ADJ
ejpam-3018	106	15	,	,	PUNCT
ejpam-3018	106	16	c	c	PROPN
ejpam-3018	106	17	(	(	PUNCT
ejpam-3018	106	18	ξ(t	ξ(t	ADP
ejpam-3018	106	19	,	,	PUNCT
ejpam-3018	106	20	x)(t−	x)(t−	NOUN
ejpam-3018	106	21	x)2;x	x)2;x	PUNCT
ejpam-3018	106	22	)	)	PUNCT
ejpam-3018	106	23	≤	≤	NOUN
ejpam-3018	107	1	√	√	ADP
ejpam-3018	107	2	g	g	PROPN
ejpam-3018	107	3	∗(α	∗(α	PROPN
ejpam-3018	107	4	,	,	PUNCT
ejpam-3018	107	5	β	β	NOUN
ejpam-3018	107	6	)	)	PUNCT
ejpam-3018	107	7	n	n	CCONJ
ejpam-3018	107	8	,	,	PUNCT
ejpam-3018	107	9	c	c	PROPN
ejpam-3018	107	10	(	(	PUNCT
ejpam-3018	107	11	ξ2(t	ξ2(t	PROPN
ejpam-3018	107	12	,	,	PUNCT
ejpam-3018	107	13	x);x	x);x	ADJ
ejpam-3018	107	14	)	)	PUNCT
ejpam-3018	107	15	√	√	PUNCT
ejpam-3018	108	1	g	g	PROPN
ejpam-3018	108	2	∗(α	∗(α	PROPN
ejpam-3018	108	3	,	,	PUNCT
ejpam-3018	108	4	β	β	NOUN
ejpam-3018	108	5	)	)	PUNCT
ejpam-3018	108	6	n	n	CCONJ
ejpam-3018	108	7	,	,	PUNCT
ejpam-3018	108	8	c	c	X
ejpam-3018	108	9	(	(	PUNCT
ejpam-3018	108	10	(	(	PUNCT
ejpam-3018	108	11	t−	t−	PROPN
ejpam-3018	108	12	x)4;x	x)4;x	NUM
ejpam-3018	108	13	)	)	PUNCT
ejpam-3018	108	14	.	.	PUNCT
ejpam-3018	109	1	(	(	PUNCT
ejpam-3018	109	2	8)	8)	NUM
ejpam-3018	109	3	we	we	PRON
ejpam-3018	109	4	observe	observe	VERB
ejpam-3018	109	5	that	that	SCONJ
ejpam-3018	109	6	ξ2(x	ξ2(x	NOUN
ejpam-3018	109	7	,	,	PUNCT
ejpam-3018	109	8	x	x	NOUN
ejpam-3018	109	9	)	)	PUNCT
ejpam-3018	109	10	=	=	SYM
ejpam-3018	109	11	0	0	NUM
ejpam-3018	109	12	and	and	CCONJ
ejpam-3018	109	13	ξ2	ξ2	PROPN
ejpam-3018	109	14	(	(	PUNCT
ejpam-3018	109	15	.	.	NUM
ejpam-3018	109	16	,	,	PUNCT
ejpam-3018	109	17	x	x	X
ejpam-3018	109	18	)	)	PUNCT
ejpam-3018	109	19	∈	∈	PROPN
ejpam-3018	109	20	cb[0,∞	cb[0,∞	PROPN
ejpam-3018	109	21	)	)	PUNCT
ejpam-3018	109	22	.	.	PUNCT
ejpam-3018	110	1	then	then	ADV
ejpam-3018	110	2	,	,	PUNCT
ejpam-3018	110	3	it	it	PRON
ejpam-3018	110	4	follows	follow	VERB
ejpam-3018	110	5	that	that	SCONJ
ejpam-3018	110	6	lim	lim	PROPN
ejpam-3018	110	7	n→∞	n→∞	NUM
ejpam-3018	110	8	g∗(α	g∗(α	PROPN
ejpam-3018	110	9	,	,	PUNCT
ejpam-3018	110	10	β)n	β)n	NOUN
ejpam-3018	110	11	,	,	PUNCT
ejpam-3018	110	12	c	c	PROPN
ejpam-3018	110	13	(	(	PUNCT
ejpam-3018	110	14	ξ2(t	ξ2(t	PROPN
ejpam-3018	110	15	,	,	PUNCT
ejpam-3018	110	16	x);x	x);x	ADJ
ejpam-3018	110	17	)	)	PUNCT
ejpam-3018	110	18	=	=	SYM
ejpam-3018	110	19	ξ2(x	ξ2(x	PROPN
ejpam-3018	110	20	,	,	PUNCT
ejpam-3018	110	21	x	x	NOUN
ejpam-3018	110	22	)	)	PUNCT
ejpam-3018	110	23	=	=	SYM
ejpam-3018	110	24	0	0	NUM
ejpam-3018	110	25	,	,	PUNCT
ejpam-3018	110	26	(	(	PUNCT
ejpam-3018	110	27	9	9	X
ejpam-3018	110	28	)	)	PUNCT
ejpam-3018	110	29	in	in	ADP
ejpam-3018	110	30	view	view	NOUN
ejpam-3018	110	31	of	of	ADP
ejpam-3018	110	32	fact	fact	NOUN
ejpam-3018	110	33	that	that	SCONJ
ejpam-3018	110	34	g	g	PROPN
ejpam-3018	110	35	∗(α	∗(α	PROPN
ejpam-3018	110	36	,	,	PUNCT
ejpam-3018	110	37	β	β	NOUN
ejpam-3018	110	38	)	)	PUNCT
ejpam-3018	110	39	n	n	CCONJ
ejpam-3018	110	40	,	,	PUNCT
ejpam-3018	110	41	c	c	X
ejpam-3018	110	42	(	(	PUNCT
ejpam-3018	110	43	(	(	PUNCT
ejpam-3018	110	44	t−	t−	PROPN
ejpam-3018	110	45	x)4;x	x)4;x	NUM
ejpam-3018	110	46	)	)	PUNCT
ejpam-3018	111	1	=	=	SYM
ejpam-3018	111	2	o	o	X
ejpam-3018	111	3	(	(	PUNCT
ejpam-3018	111	4	1	1	NUM
ejpam-3018	111	5	n2	n2	NOUN
ejpam-3018	111	6	)	)	PUNCT
ejpam-3018	111	7	.	.	PUNCT
ejpam-3018	112	1	now	now	ADV
ejpam-3018	112	2	,	,	PUNCT
ejpam-3018	112	3	from	from	ADP
ejpam-3018	112	4	(	(	PUNCT
ejpam-3018	112	5	8)	8)	NUM
ejpam-3018	112	6	and	and	CCONJ
ejpam-3018	112	7	(	(	PUNCT
ejpam-3018	112	8	9	9	X
ejpam-3018	112	9	)	)	PUNCT
ejpam-3018	112	10	we	we	PRON
ejpam-3018	112	11	obtain	obtain	VERB
ejpam-3018	112	12	lim	lim	PROPN
ejpam-3018	112	13	n→∞	n→∞	PRON
ejpam-3018	112	14	ng∗(α	ng∗(α	ADJ
ejpam-3018	112	15	,	,	PUNCT
ejpam-3018	112	16	β)n	β)n	ADJ
ejpam-3018	112	17	,	,	PUNCT
ejpam-3018	112	18	c	c	PROPN
ejpam-3018	112	19	(	(	PUNCT
ejpam-3018	112	20	ξ(t	ξ(t	ADP
ejpam-3018	112	21	,	,	PUNCT
ejpam-3018	112	22	x)(t−	x)(t−	NOUN
ejpam-3018	112	23	x)2;x	x)2;x	PUNCT
ejpam-3018	112	24	)	)	PUNCT
ejpam-3018	113	1	=	=	PUNCT
ejpam-3018	113	2	0	0	X
ejpam-3018	113	3	.	.	PUNCT
ejpam-3018	114	1	(	(	PUNCT
ejpam-3018	114	2	10	10	NUM
ejpam-3018	114	3	)	)	PUNCT
ejpam-3018	114	4	from	from	ADP
ejpam-3018	114	5	(	(	PUNCT
ejpam-3018	114	6	6	6	NUM
ejpam-3018	114	7	)	)	PUNCT
ejpam-3018	114	8	,	,	PUNCT
ejpam-3018	114	9	(	(	PUNCT
ejpam-3018	114	10	7	7	X
ejpam-3018	114	11	)	)	PUNCT
ejpam-3018	114	12	and	and	CCONJ
ejpam-3018	114	13	(	(	PUNCT
ejpam-3018	114	14	10	10	NUM
ejpam-3018	114	15	)	)	PUNCT
ejpam-3018	114	16	,	,	PUNCT
ejpam-3018	114	17	we	we	PRON
ejpam-3018	114	18	get	get	VERB
ejpam-3018	114	19	the	the	DET
ejpam-3018	114	20	required	require	VERB
ejpam-3018	114	21	result	result	NOUN
ejpam-3018	114	22	.	.	PUNCT
ejpam-3018	115	1	3.1	3.1	NUM
ejpam-3018	115	2	.	.	PUNCT
ejpam-3018	115	3	local	local	ADJ
ejpam-3018	115	4	approximation	approximation	NOUN
ejpam-3018	115	5	for	for	ADP
ejpam-3018	115	6	cb[0,∞	cb[0,∞	PROPN
ejpam-3018	115	7	)	)	PUNCT
ejpam-3018	115	8	,	,	PUNCT
ejpam-3018	115	9	let	let	VERB
ejpam-3018	115	10	us	we	PRON
ejpam-3018	115	11	consider	consider	VERB
ejpam-3018	115	12	the	the	PRON
ejpam-3018	115	13	following	follow	VERB
ejpam-3018	115	14	k	k	ADJ
ejpam-3018	115	15	-	-	ADJ
ejpam-3018	115	16	functional	functional	ADJ
ejpam-3018	115	17	:	:	PUNCT
ejpam-3018	115	18	k2(f	k2(f	PROPN
ejpam-3018	115	19	,	,	PUNCT
ejpam-3018	115	20	δ	δ	NOUN
ejpam-3018	115	21	)	)	PUNCT
ejpam-3018	115	22	=	=	PROPN
ejpam-3018	115	23	inf	inf	PROPN
ejpam-3018	115	24	g∈w	g∈w	PROPN
ejpam-3018	115	25	2	2	NUM
ejpam-3018	115	26	{	{	PUNCT
ejpam-3018	115	27	‖	‖	PROPN
ejpam-3018	115	28	f	f	PROPN
ejpam-3018	116	1	−	−	PROPN
ejpam-3018	116	2	g	g	PROPN
ejpam-3018	116	3	‖	‖	PROPN
ejpam-3018	116	4	+	+	PROPN
ejpam-3018	116	5	δ	δ	PROPN
ejpam-3018	116	6	‖	‖	PROPN
ejpam-3018	116	7	g′′	g′′	PROPN
ejpam-3018	116	8	‖	‖	PROPN
ejpam-3018	116	9	}	}	PUNCT
ejpam-3018	116	10	,	,	PUNCT
ejpam-3018	116	11	where	where	SCONJ
ejpam-3018	116	12	δ	δ	PROPN
ejpam-3018	116	13	>	>	X
ejpam-3018	116	14	0	0	PUNCT
ejpam-3018	117	1	and	and	CCONJ
ejpam-3018	117	2	w	w	PROPN
ejpam-3018	117	3	2	2	NUM
ejpam-3018	117	4	=	=	SYM
ejpam-3018	117	5	{	{	PUNCT
ejpam-3018	117	6	g	g	PROPN
ejpam-3018	117	7	∈	∈	PROPN
ejpam-3018	117	8	cb[0,∞	cb[0,∞	PROPN
ejpam-3018	117	9	)	)	PUNCT
ejpam-3018	117	10	:	:	PUNCT
ejpam-3018	117	11	g′	g′	NOUN
ejpam-3018	117	12	,	,	PUNCT
ejpam-3018	117	13	g	g	PROPN
ejpam-3018	117	14	′′	′′	PROPN
ejpam-3018	117	15	∈	∈	PROPN
ejpam-3018	117	16	cb[0,∞	cb[0,∞	PROPN
ejpam-3018	117	17	)	)	PUNCT
ejpam-3018	117	18	}	}	PUNCT
ejpam-3018	117	19	.	.	PUNCT
ejpam-3018	118	1	by	by	ADP
ejpam-3018	118	2	,	,	PUNCT
ejpam-3018	118	3	p.	p.	NOUN
ejpam-3018	118	4	177	177	NUM
ejpam-3018	118	5	,	,	PUNCT
ejpam-3018	118	6	theorem	theorem	VERB
ejpam-3018	118	7	2.4	2.4	NUM
ejpam-3018	118	8	in	in	ADP
ejpam-3018	118	9	[	[	X
ejpam-3018	118	10	4	4	NUM
ejpam-3018	118	11	]	]	PUNCT
ejpam-3018	118	12	,	,	PUNCT
ejpam-3018	118	13	there	there	PRON
ejpam-3018	118	14	exists	exist	VERB
ejpam-3018	118	15	an	an	DET
ejpam-3018	118	16	absolute	absolute	ADJ
ejpam-3018	118	17	constant	constant	ADJ
ejpam-3018	118	18	c	c	NOUN
ejpam-3018	118	19	>	>	X
ejpam-3018	118	20	0	0	NUM
ejpam-3018	119	1	such	such	ADJ
ejpam-3018	119	2	that	that	SCONJ
ejpam-3018	119	3	k2(f	k2(f	PROPN
ejpam-3018	119	4	,	,	PUNCT
ejpam-3018	119	5	δ	δ	PROPN
ejpam-3018	119	6	)	)	PUNCT
ejpam-3018	119	7	≤	≤	PUNCT
ejpam-3018	119	8	cω2(f	cω2(f	PROPN
ejpam-3018	119	9	,	,	PUNCT
ejpam-3018	119	10	√	√	PROPN
ejpam-3018	119	11	δ	δ	PROPN
ejpam-3018	119	12	)	)	PUNCT
ejpam-3018	119	13	,	,	PUNCT
ejpam-3018	119	14	(	(	PUNCT
ejpam-3018	119	15	11	11	NUM
ejpam-3018	119	16	)	)	PUNCT
ejpam-3018	119	17	where	where	SCONJ
ejpam-3018	119	18	ω2(f	ω2(f	X
ejpam-3018	119	19	,	,	PUNCT
ejpam-3018	119	20	√	√	NUM
ejpam-3018	119	21	δ	δ	NOUN
ejpam-3018	119	22	)	)	PUNCT
ejpam-3018	119	23	=	=	SYM
ejpam-3018	119	24	sup	sup	NOUN
ejpam-3018	119	25	0	0	NUM
ejpam-3018	119	26	<	<	X
ejpam-3018	119	27	h≤	h≤	PRON
ejpam-3018	119	28	√	√	ADJ
ejpam-3018	119	29	δ	δ	PROPN
ejpam-3018	119	30	sup	sup	NOUN
ejpam-3018	119	31	x∈[0,∞	x∈[0,∞	PUNCT
ejpam-3018	119	32	)	)	PUNCT
ejpam-3018	119	33	|	|	ADV
ejpam-3018	119	34	f(x+	f(x+	VERB
ejpam-3018	119	35	2h)−	2h)−	ADV
ejpam-3018	119	36	2f(x+	2f(x+	ADJ
ejpam-3018	119	37	h	h	NOUN
ejpam-3018	119	38	)	)	PUNCT
ejpam-3018	120	1	+	+	CCONJ
ejpam-3018	120	2	f(x	f(x	PROPN
ejpam-3018	120	3	)	)	PUNCT
ejpam-3018	120	4	|	|	ADV
ejpam-3018	120	5	a.	a.	NOUN
ejpam-3018	120	6	kumar	kumar	PROPN
ejpam-3018	120	7	,	,	PUNCT
ejpam-3018	120	8	v.	v.	PROPN
ejpam-3018	120	9	n.	n.	PROPN
ejpam-3018	120	10	mishra	mishra	PROPN
ejpam-3018	120	11	,	,	PUNCT
ejpam-3018	120	12	d.	d.	PROPN
ejpam-3018	120	13	tapiawala	tapiawala	PROPN
ejpam-3018	120	14	/	/	SYM
ejpam-3018	120	15	eur	eur	PROPN
ejpam-3018	120	16	.	.	PUNCT
ejpam-3018	121	1	j.	j.	PROPN
ejpam-3018	121	2	pure	pure	PROPN
ejpam-3018	121	3	appl	appl	PROPN
ejpam-3018	121	4	.	.	PROPN
ejpam-3018	121	5	math	math	PROPN
ejpam-3018	121	6	,	,	PUNCT
ejpam-3018	121	7	10	10	NUM
ejpam-3018	121	8	(	(	PUNCT
ejpam-3018	121	9	4	4	NUM
ejpam-3018	121	10	)	)	PUNCT
ejpam-3018	121	11	(	(	PUNCT
ejpam-3018	121	12	2017	2017	NUM
ejpam-3018	121	13	)	)	PUNCT
ejpam-3018	121	14	,	,	PUNCT
ejpam-3018	121	15	890	890	NUM
ejpam-3018	121	16	-	-	SYM
ejpam-3018	121	17	907	907	NUM
ejpam-3018	121	18	895	895	NUM
ejpam-3018	121	19	is	be	AUX
ejpam-3018	121	20	the	the	DET
ejpam-3018	121	21	second	second	ADJ
ejpam-3018	121	22	order	order	NOUN
ejpam-3018	121	23	modulus	modulus	NOUN
ejpam-3018	121	24	of	of	ADP
ejpam-3018	121	25	smoothness	smoothness	NOUN
ejpam-3018	121	26	of	of	ADP
ejpam-3018	121	27	f	f	PROPN
ejpam-3018	121	28	.	.	PUNCT
ejpam-3018	122	1	by	by	ADP
ejpam-3018	122	2	ω(f	ω(f	PROPN
ejpam-3018	122	3	,	,	PUNCT
ejpam-3018	122	4	δ	δ	PROPN
ejpam-3018	122	5	)	)	PUNCT
ejpam-3018	122	6	=	=	SYM
ejpam-3018	122	7	sup	sup	NOUN
ejpam-3018	122	8	0	0	NUM
ejpam-3018	122	9	<	<	X
ejpam-3018	122	10	h≤δ	h≤δ	PROPN
ejpam-3018	122	11	sup	sup	PROPN
ejpam-3018	122	12	x∈[0,∞	x∈[0,∞	NUM
ejpam-3018	122	13	)	)	PUNCT
ejpam-3018	122	14	|	|	ADV
ejpam-3018	122	15	f(x+	f(x+	VERB
ejpam-3018	122	16	h)−	h)−	PROPN
ejpam-3018	122	17	f(x	f(x	PROPN
ejpam-3018	122	18	)	)	PUNCT
ejpam-3018	123	1	|	|	ADV
ejpam-3018	123	2	,	,	PUNCT
ejpam-3018	123	3	we	we	PRON
ejpam-3018	123	4	denote	denote	VERB
ejpam-3018	123	5	the	the	DET
ejpam-3018	123	6	usual	usual	ADJ
ejpam-3018	123	7	modulus	modulus	NOUN
ejpam-3018	123	8	of	of	ADP
ejpam-3018	123	9	continuity	continuity	NOUN
ejpam-3018	123	10	of	of	ADP
ejpam-3018	123	11	f	f	PROPN
ejpam-3018	123	12	∈	∈	PROPN
ejpam-3018	123	13	cb[0,∞	cb[0,∞	PROPN
ejpam-3018	123	14	)	)	PUNCT
ejpam-3018	123	15	.	.	PUNCT
ejpam-3018	124	1	theorem	theorem	NOUN
ejpam-3018	124	2	5	5	NUM
ejpam-3018	124	3	.	.	PUNCT
ejpam-3018	125	1	let	let	VERB
ejpam-3018	125	2	f	f	PROPN
ejpam-3018	125	3	∈	∈	PROPN
ejpam-3018	125	4	cb[0,∞	cb[0,∞	PROPN
ejpam-3018	125	5	)	)	PUNCT
ejpam-3018	125	6	.	.	PUNCT
ejpam-3018	126	1	then	then	ADV
ejpam-3018	126	2	,	,	PUNCT
ejpam-3018	126	3	for	for	ADP
ejpam-3018	126	4	every	every	DET
ejpam-3018	126	5	x	x	SYM
ejpam-3018	126	6	∈	∈	PROPN
ejpam-3018	126	7	[	[	X
ejpam-3018	126	8	0,∞	0,∞	NOUN
ejpam-3018	126	9	)	)	PUNCT
ejpam-3018	126	10	,	,	PUNCT
ejpam-3018	126	11	we	we	PRON
ejpam-3018	126	12	have	have	VERB
ejpam-3018	126	13	|	|	ADV
ejpam-3018	126	14	g∗(α	g∗(α	NOUN
ejpam-3018	126	15	,	,	PUNCT
ejpam-3018	126	16	β)n	β)n	NOUN
ejpam-3018	126	17	,	,	PUNCT
ejpam-3018	126	18	c	c	PROPN
ejpam-3018	126	19	(	(	PUNCT
ejpam-3018	126	20	f	f	PROPN
ejpam-3018	126	21	;	;	PUNCT
ejpam-3018	126	22	x)−	x)−	PROPN
ejpam-3018	126	23	f(x	f(x	PROPN
ejpam-3018	126	24	)	)	PUNCT
ejpam-3018	127	1	|	|	ADV
ejpam-3018	127	2	≤	≤	NUM
ejpam-3018	127	3	cω2	cω2	NOUN
ejpam-3018	127	4	(	(	PUNCT
ejpam-3018	127	5	f	f	X
ejpam-3018	127	6	,	,	PUNCT
ejpam-3018	127	7	δ(α	δ(α	ADJ
ejpam-3018	127	8	,	,	PUNCT
ejpam-3018	127	9	β)n	β)n	ADJ
ejpam-3018	127	10	,	,	PUNCT
ejpam-3018	127	11	c	c	PROPN
ejpam-3018	127	12	(	(	PUNCT
ejpam-3018	127	13	x	x	NOUN
ejpam-3018	127	14	)	)	PUNCT
ejpam-3018	127	15	)	)	PUNCT
ejpam-3018	128	1	+	+	CCONJ
ejpam-3018	128	2	ω	ω	NUM
ejpam-3018	128	3	(	(	PUNCT
ejpam-3018	128	4	f	f	X
ejpam-3018	128	5	,	,	PUNCT
ejpam-3018	128	6	|α−	|α−	PROPN
ejpam-3018	128	7	βx|	βx|	NUM
ejpam-3018	128	8	n+	n+	X
ejpam-3018	128	9	β	β	X
ejpam-3018	128	10	)	)	PUNCT
ejpam-3018	128	11	,	,	PUNCT
ejpam-3018	128	12	where	where	SCONJ
ejpam-3018	128	13	c	c	NOUN
ejpam-3018	128	14	is	be	AUX
ejpam-3018	128	15	an	an	DET
ejpam-3018	128	16	absolute	absolute	ADJ
ejpam-3018	128	17	constant	constant	ADJ
ejpam-3018	128	18	and	and	CCONJ
ejpam-3018	128	19	δ(α	δ(α	NOUN
ejpam-3018	128	20	,	,	PUNCT
ejpam-3018	128	21	β)n	β)n	ADJ
ejpam-3018	128	22	,	,	PUNCT
ejpam-3018	128	23	c	c	PROPN
ejpam-3018	128	24	(	(	PUNCT
ejpam-3018	128	25	x	x	NOUN
ejpam-3018	128	26	)	)	PUNCT
ejpam-3018	128	27	=	=	SYM
ejpam-3018	128	28	(	(	PUNCT
ejpam-3018	128	29	g∗(α	g∗(α	PROPN
ejpam-3018	128	30	,	,	PUNCT
ejpam-3018	128	31	β)n	β)n	NOUN
ejpam-3018	128	32	,	,	PUNCT
ejpam-3018	128	33	c	c	NOUN
ejpam-3018	128	34	(	(	PUNCT
ejpam-3018	128	35	(	(	PUNCT
ejpam-3018	128	36	t−	t−	PROPN
ejpam-3018	128	37	x)2;x	x)2;x	NUM
ejpam-3018	128	38	)	)	PUNCT
ejpam-3018	129	1	+	+	CCONJ
ejpam-3018	129	2	(	(	PUNCT
ejpam-3018	129	3	α−	α−	ADP
ejpam-3018	129	4	βx	βx	PRON
ejpam-3018	129	5	n+	n+	X
ejpam-3018	129	6	β	β	X
ejpam-3018	129	7	)	)	PUNCT
ejpam-3018	129	8	2)1/2	2)1/2	NUM
ejpam-3018	129	9	.	.	PUNCT
ejpam-3018	130	1	proof	proof	NOUN
ejpam-3018	130	2	.	.	PUNCT
ejpam-3018	131	1	for	for	ADP
ejpam-3018	131	2	x	x	PROPN
ejpam-3018	131	3	∈	∈	PROPN
ejpam-3018	131	4	[	[	X
ejpam-3018	131	5	0,∞	0,∞	NOUN
ejpam-3018	131	6	)	)	PUNCT
ejpam-3018	131	7	,	,	PUNCT
ejpam-3018	131	8	we	we	PRON
ejpam-3018	131	9	consider	consider	VERB
ejpam-3018	131	10	the	the	DET
ejpam-3018	131	11	auxiliary	auxiliary	ADJ
ejpam-3018	131	12	operators	operator	NOUN
ejpam-3018	131	13	g	g	PROPN
ejpam-3018	131	14	∗(α	∗(α	PROPN
ejpam-3018	131	15	,	,	PUNCT
ejpam-3018	131	16	β	β	NOUN
ejpam-3018	131	17	)	)	PUNCT
ejpam-3018	131	18	n	n	CCONJ
ejpam-3018	131	19	,	,	PUNCT
ejpam-3018	132	1	c	c	PROPN
ejpam-3018	132	2	defined	define	VERB
ejpam-3018	132	3	by	by	ADP
ejpam-3018	132	4	g	g	PROPN
ejpam-3018	132	5	∗(α	∗(α	PROPN
ejpam-3018	132	6	,	,	PUNCT
ejpam-3018	132	7	β	β	NOUN
ejpam-3018	132	8	)	)	PUNCT
ejpam-3018	132	9	n	n	CCONJ
ejpam-3018	132	10	,	,	PUNCT
ejpam-3018	132	11	c	c	PROPN
ejpam-3018	132	12	(	(	PUNCT
ejpam-3018	132	13	f	f	NOUN
ejpam-3018	132	14	;	;	PUNCT
ejpam-3018	132	15	x	x	X
ejpam-3018	132	16	)	)	PUNCT
ejpam-3018	132	17	=	=	SYM
ejpam-3018	132	18	g∗(α	g∗(α	NOUN
ejpam-3018	132	19	,	,	PUNCT
ejpam-3018	132	20	β)n	β)n	NOUN
ejpam-3018	132	21	,	,	PUNCT
ejpam-3018	132	22	c	c	PROPN
ejpam-3018	132	23	(	(	PUNCT
ejpam-3018	132	24	f	f	PROPN
ejpam-3018	132	25	;	;	PUNCT
ejpam-3018	132	26	x)−	x)−	PROPN
ejpam-3018	132	27	f	f	PROPN
ejpam-3018	132	28	(	(	PUNCT
ejpam-3018	132	29	nx+	nx+	PROPN
ejpam-3018	132	30	α	α	PROPN
ejpam-3018	132	31	n+	n+	X
ejpam-3018	132	32	β	β	X
ejpam-3018	132	33	)	)	PUNCT
ejpam-3018	133	1	+	+	CCONJ
ejpam-3018	133	2	f(x	f(x	PROPN
ejpam-3018	133	3	)	)	PUNCT
ejpam-3018	133	4	.	.	PUNCT
ejpam-3018	134	1	(	(	PUNCT
ejpam-3018	134	2	12	12	NUM
ejpam-3018	134	3	)	)	PUNCT
ejpam-3018	134	4	from	from	ADP
ejpam-3018	134	5	lemma	lemma	PROPN
ejpam-3018	134	6	2	2	NUM
ejpam-3018	134	7	,	,	PUNCT
ejpam-3018	134	8	we	we	PRON
ejpam-3018	134	9	observe	observe	VERB
ejpam-3018	134	10	that	that	SCONJ
ejpam-3018	134	11	the	the	DET
ejpam-3018	134	12	operators	operator	NOUN
ejpam-3018	134	13	g	g	PROPN
ejpam-3018	134	14	∗(α	∗(α	PROPN
ejpam-3018	134	15	,	,	PUNCT
ejpam-3018	134	16	β	β	NOUN
ejpam-3018	134	17	)	)	PUNCT
ejpam-3018	134	18	n	n	CCONJ
ejpam-3018	134	19	,	,	PUNCT
ejpam-3018	134	20	c	c	PROPN
ejpam-3018	134	21	are	be	AUX
ejpam-3018	134	22	linear	linear	ADJ
ejpam-3018	134	23	and	and	CCONJ
ejpam-3018	134	24	reproduce	reproduce	VERB
ejpam-3018	134	25	the	the	DET
ejpam-3018	134	26	linear	linear	ADJ
ejpam-3018	134	27	functions	function	NOUN
ejpam-3018	134	28	.	.	PUNCT
ejpam-3018	135	1	hence	hence	ADV
ejpam-3018	135	2	g	g	PROPN
ejpam-3018	135	3	∗(α	∗(α	PROPN
ejpam-3018	135	4	,	,	PUNCT
ejpam-3018	135	5	β	β	NOUN
ejpam-3018	135	6	)	)	PUNCT
ejpam-3018	135	7	n	n	CCONJ
ejpam-3018	135	8	,	,	PUNCT
ejpam-3018	135	9	c	c	X
ejpam-3018	135	10	(	(	PUNCT
ejpam-3018	135	11	(	(	PUNCT
ejpam-3018	135	12	t−	t−	PROPN
ejpam-3018	135	13	x);x	x);x	PROPN
ejpam-3018	135	14	)	)	PUNCT
ejpam-3018	135	15	=	=	SYM
ejpam-3018	136	1	0	0	X
ejpam-3018	136	2	.	.	PUNCT
ejpam-3018	137	1	(	(	PUNCT
ejpam-3018	137	2	13	13	NUM
ejpam-3018	137	3	)	)	PUNCT
ejpam-3018	137	4	let	let	VERB
ejpam-3018	137	5	g	g	PROPN
ejpam-3018	137	6	∈w	∈w	PROPN
ejpam-3018	137	7	2	2	X
ejpam-3018	137	8	.	.	PUNCT
ejpam-3018	138	1	by	by	ADP
ejpam-3018	138	2	taylor	taylor	PROPN
ejpam-3018	138	3	’s	’s	PART
ejpam-3018	138	4	theorem	theorem	PROPN
ejpam-3018	138	5	,	,	PUNCT
ejpam-3018	138	6	we	we	PRON
ejpam-3018	138	7	have	have	VERB
ejpam-3018	138	8	g(t	g(t	PROPN
ejpam-3018	138	9	)	)	PUNCT
ejpam-3018	139	1	=	=	SYM
ejpam-3018	139	2	g(x	g(x	NOUN
ejpam-3018	139	3	)	)	PUNCT
ejpam-3018	140	1	+	+	CCONJ
ejpam-3018	140	2	(	(	PUNCT
ejpam-3018	140	3	t−	t−	PROPN
ejpam-3018	140	4	x)g′(x	x)g′(x	PROPN
ejpam-3018	140	5	)	)	PUNCT
ejpam-3018	141	1	+	+	NUM
ejpam-3018	141	2	∫	∫	PROPN
ejpam-3018	141	3	t	t	NOUN
ejpam-3018	141	4	x	x	X
ejpam-3018	141	5	(	(	PUNCT
ejpam-3018	141	6	t−	t−	PROPN
ejpam-3018	141	7	v)g′′(v)dv	v)g′′(v)dv	PROPN
ejpam-3018	141	8	,	,	PUNCT
ejpam-3018	141	9	t	t	PROPN
ejpam-3018	141	10	∈	∈	PROPN
ejpam-3018	142	1	[	[	X
ejpam-3018	142	2	0,∞	0,∞	NOUN
ejpam-3018	142	3	)	)	PUNCT
ejpam-3018	142	4	.	.	PUNCT
ejpam-3018	143	1	applying	apply	VERB
ejpam-3018	143	2	g	g	PROPN
ejpam-3018	143	3	∗(α	∗(α	PROPN
ejpam-3018	143	4	,	,	PUNCT
ejpam-3018	143	5	β	β	NOUN
ejpam-3018	143	6	)	)	PUNCT
ejpam-3018	143	7	n	n	CCONJ
ejpam-3018	143	8	,	,	PUNCT
ejpam-3018	143	9	c	c	PROPN
ejpam-3018	143	10	on	on	ADP
ejpam-3018	143	11	both	both	DET
ejpam-3018	143	12	sides	side	NOUN
ejpam-3018	143	13	of	of	ADP
ejpam-3018	143	14	the	the	DET
ejpam-3018	143	15	above	above	ADJ
ejpam-3018	143	16	equation	equation	NOUN
ejpam-3018	143	17	and	and	CCONJ
ejpam-3018	143	18	using	use	VERB
ejpam-3018	143	19	(	(	PUNCT
ejpam-3018	143	20	13	13	NUM
ejpam-3018	143	21	)	)	PUNCT
ejpam-3018	143	22	,	,	PUNCT
ejpam-3018	143	23	we	we	PRON
ejpam-3018	143	24	have	have	VERB
ejpam-3018	143	25	g	g	PROPN
ejpam-3018	143	26	∗(α	∗(α	PROPN
ejpam-3018	143	27	,	,	PUNCT
ejpam-3018	143	28	β	β	NOUN
ejpam-3018	143	29	)	)	PUNCT
ejpam-3018	143	30	n	n	CCONJ
ejpam-3018	143	31	,	,	PUNCT
ejpam-3018	143	32	c	c	PROPN
ejpam-3018	143	33	(	(	PUNCT
ejpam-3018	143	34	g;x	g;x	NUM
ejpam-3018	143	35	)	)	PUNCT
ejpam-3018	143	36	=	=	SYM
ejpam-3018	144	1	g(x	g(x	NOUN
ejpam-3018	144	2	)	)	PUNCT
ejpam-3018	145	1	+	+	ADP
ejpam-3018	145	2	g	g	PROPN
ejpam-3018	145	3	∗(α	∗(α	PROPN
ejpam-3018	145	4	,	,	PUNCT
ejpam-3018	145	5	β	β	NOUN
ejpam-3018	145	6	)	)	PUNCT
ejpam-3018	145	7	n	n	CCONJ
ejpam-3018	145	8	,	,	PUNCT
ejpam-3018	145	9	c	c	PROPN
ejpam-3018	145	10	(	(	PUNCT
ejpam-3018	145	11	∫	∫	PROPN
ejpam-3018	145	12	t	t	PROPN
ejpam-3018	145	13	x	x	X
ejpam-3018	145	14	(	(	PUNCT
ejpam-3018	145	15	t−	t−	PROPN
ejpam-3018	145	16	v)g′′(v)dv;x	v)g′′(v)dv;x	PROPN
ejpam-3018	145	17	)	)	PUNCT
ejpam-3018	145	18	.	.	PUNCT
ejpam-3018	146	1	thus	thus	ADV
ejpam-3018	146	2	,	,	PUNCT
ejpam-3018	146	3	by	by	ADP
ejpam-3018	146	4	(	(	PUNCT
ejpam-3018	146	5	12	12	NUM
ejpam-3018	146	6	)	)	PUNCT
ejpam-3018	146	7	we	we	PRON
ejpam-3018	146	8	get	get	VERB
ejpam-3018	146	9	|g∗(α	|g∗(α	PROPN
ejpam-3018	146	10	,	,	PUNCT
ejpam-3018	146	11	β)n	β)n	ADJ
ejpam-3018	146	12	,	,	PUNCT
ejpam-3018	146	13	c	c	PROPN
ejpam-3018	146	14	(	(	PUNCT
ejpam-3018	146	15	g;x)−	g;x)−	PROPN
ejpam-3018	146	16	g(x)|	g(x)|	VERB
ejpam-3018	146	17	≤	≤	NUM
ejpam-3018	146	18	g∗(α	g∗(α	NOUN
ejpam-3018	146	19	,	,	PUNCT
ejpam-3018	146	20	β)n	β)n	NOUN
ejpam-3018	146	21	,	,	PUNCT
ejpam-3018	146	22	c	c	PROPN
ejpam-3018	146	23	(	(	PUNCT
ejpam-3018	146	24	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3018	146	25	∫	∫	PROPN
ejpam-3018	146	26	t	t	PROPN
ejpam-3018	146	27	x	x	X
ejpam-3018	146	28	(	(	PUNCT
ejpam-3018	146	29	t−	t−	ADJ
ejpam-3018	146	30	v)g	v)g	NOUN
ejpam-3018	147	1	′′	′′	PROPN
ejpam-3018	147	2	(	(	PUNCT
ejpam-3018	147	3	v)dv	v)dv	PROPN
ejpam-3018	147	4	∣∣∣∣;x)+	∣∣∣∣;x)+	NOUN
ejpam-3018	147	5	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3018	147	6	∫	∫	PROPN
ejpam-3018	147	7	nx+α	nx+α	PROPN
ejpam-3018	147	8	n+β	n+β	NUM
ejpam-3018	147	9	x	x	X
ejpam-3018	147	10	(	(	PUNCT
ejpam-3018	147	11	nx+	nx+	PROPN
ejpam-3018	147	12	α	α	X
ejpam-3018	147	13	n+	n+	PUNCT
ejpam-3018	147	14	β	β	NOUN
ejpam-3018	147	15	−	−	NUM
ejpam-3018	147	16	v	v	NOUN
ejpam-3018	147	17	)	)	PUNCT
ejpam-3018	147	18	g	g	PROPN
ejpam-3018	147	19	′′	′′	PROPN
ejpam-3018	147	20	(	(	PUNCT
ejpam-3018	147	21	v)dv	v)dv	PROPN
ejpam-3018	147	22	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3018	147	23	≤	≤	ADJ
ejpam-3018	147	24	g∗(α	g∗(α	PROPN
ejpam-3018	147	25	,	,	PUNCT
ejpam-3018	147	26	β)n	β)n	NOUN
ejpam-3018	147	27	,	,	PUNCT
ejpam-3018	147	28	c	c	PROPN
ejpam-3018	147	29	(	(	PUNCT
ejpam-3018	147	30	∫	∫	PROPN
ejpam-3018	147	31	t	t	PROPN
ejpam-3018	147	32	x	x	PROPN
ejpam-3018	147	33	|t−	|t−	PROPN
ejpam-3018	147	34	v||g′′(v)|dv;x	v||g′′(v)|dv;x	NOUN
ejpam-3018	147	35	)	)	PUNCT
ejpam-3018	148	1	+	+	CCONJ
ejpam-3018	149	1	∫	∫	PROPN
ejpam-3018	149	2	nx+α	nx+α	PROPN
ejpam-3018	149	3	n+β	n+β	NUM
ejpam-3018	149	4	x	x	X
ejpam-3018	149	5	∣∣∣∣nx+	∣∣∣∣nx+	PROPN
ejpam-3018	149	6	α	α	NOUN
ejpam-3018	149	7	n+	n+	PUNCT
ejpam-3018	149	8	β	β	NOUN
ejpam-3018	149	9	−	−	NOUN
ejpam-3018	149	10	v	v	ADP
ejpam-3018	149	11	∣∣∣∣|g′′(v)|dv	∣∣∣∣|g′′(v)|dv	PROPN
ejpam-3018	149	12	a.	a.	NOUN
ejpam-3018	149	13	kumar	kumar	PROPN
ejpam-3018	149	14	,	,	PUNCT
ejpam-3018	149	15	v.	v.	PROPN
ejpam-3018	149	16	n.	n.	PROPN
ejpam-3018	149	17	mishra	mishra	PROPN
ejpam-3018	149	18	,	,	PUNCT
ejpam-3018	149	19	d.	d.	PROPN
ejpam-3018	149	20	tapiawala	tapiawala	PROPN
ejpam-3018	149	21	/	/	SYM
ejpam-3018	149	22	eur	eur	PROPN
ejpam-3018	149	23	.	.	PUNCT
ejpam-3018	150	1	j.	j.	PROPN
ejpam-3018	150	2	pure	pure	PROPN
ejpam-3018	150	3	appl	appl	PROPN
ejpam-3018	150	4	.	.	PROPN
ejpam-3018	150	5	math	math	PROPN
ejpam-3018	150	6	,	,	PUNCT
ejpam-3018	150	7	10	10	NUM
ejpam-3018	150	8	(	(	PUNCT
ejpam-3018	150	9	4	4	NUM
ejpam-3018	150	10	)	)	PUNCT
ejpam-3018	150	11	(	(	PUNCT
ejpam-3018	150	12	2017	2017	NUM
ejpam-3018	150	13	)	)	PUNCT
ejpam-3018	150	14	,	,	PUNCT
ejpam-3018	150	15	890	890	NUM
ejpam-3018	150	16	-	-	SYM
ejpam-3018	150	17	907	907	NUM
ejpam-3018	150	18	896	896	NUM
ejpam-3018	150	19	≤	≤	NOUN
ejpam-3018	150	20	[	[	PUNCT
ejpam-3018	150	21	g∗(α	g∗(α	PROPN
ejpam-3018	150	22	,	,	PUNCT
ejpam-3018	150	23	β)n	β)n	NOUN
ejpam-3018	150	24	,	,	PUNCT
ejpam-3018	150	25	c	c	NOUN
ejpam-3018	150	26	(	(	PUNCT
ejpam-3018	150	27	(	(	PUNCT
ejpam-3018	150	28	t−	t−	PROPN
ejpam-3018	150	29	x)2;x	x)2;x	NUM
ejpam-3018	150	30	)	)	PUNCT
ejpam-3018	151	1	+	+	CCONJ
ejpam-3018	151	2	(	(	PUNCT
ejpam-3018	151	3	α−	α−	ADP
ejpam-3018	151	4	βx	βx	PRON
ejpam-3018	151	5	n+	n+	X
ejpam-3018	151	6	β	β	X
ejpam-3018	151	7	)	)	PUNCT
ejpam-3018	151	8	2	2	NUM
ejpam-3018	151	9	]	]	PUNCT
ejpam-3018	151	10	‖	‖	PROPN
ejpam-3018	151	11	g′′	g′′	PROPN
ejpam-3018	151	12	‖	‖	PROPN
ejpam-3018	151	13	≤	≤	NOUN
ejpam-3018	151	14	(	(	PUNCT
ejpam-3018	151	15	δ(α	δ(α	NOUN
ejpam-3018	151	16	,	,	PUNCT
ejpam-3018	151	17	β)n	β)n	ADJ
ejpam-3018	151	18	,	,	PUNCT
ejpam-3018	151	19	c	c	PROPN
ejpam-3018	151	20	(	(	PUNCT
ejpam-3018	151	21	x	x	NOUN
ejpam-3018	151	22	)	)	PUNCT
ejpam-3018	151	23	)	)	PUNCT
ejpam-3018	151	24	2	2	NUM
ejpam-3018	151	25	‖	‖	PROPN
ejpam-3018	151	26	g′′	g′′	PROPN
ejpam-3018	151	27	‖	‖	PROPN
ejpam-3018	151	28	.	.	PUNCT
ejpam-3018	152	1	(	(	PUNCT
ejpam-3018	152	2	14	14	NUM
ejpam-3018	152	3	)	)	PUNCT
ejpam-3018	152	4	on	on	ADP
ejpam-3018	152	5	other	other	ADJ
ejpam-3018	152	6	hand	hand	NOUN
ejpam-3018	152	7	,	,	PUNCT
ejpam-3018	152	8	by	by	ADP
ejpam-3018	152	9	(	(	PUNCT
ejpam-3018	152	10	12	12	NUM
ejpam-3018	152	11	)	)	PUNCT
ejpam-3018	152	12	and	and	CCONJ
ejpam-3018	152	13	lemma	lemma	PROPN
ejpam-3018	152	14	3	3	NUM
ejpam-3018	152	15	,	,	PUNCT
ejpam-3018	152	16	we	we	PRON
ejpam-3018	152	17	have	have	VERB
ejpam-3018	152	18	|g∗(α	|g∗(α	PROPN
ejpam-3018	152	19	,	,	PUNCT
ejpam-3018	152	20	β)n	β)n	ADJ
ejpam-3018	152	21	,	,	PUNCT
ejpam-3018	152	22	c	c	PROPN
ejpam-3018	152	23	(	(	PUNCT
ejpam-3018	152	24	f	f	PROPN
ejpam-3018	152	25	;	;	PUNCT
ejpam-3018	152	26	x)|	x)|	PROPN
ejpam-3018	152	27	≤	≤	NUM
ejpam-3018	152	28	3	3	NUM
ejpam-3018	152	29	‖	‖	PROPN
ejpam-3018	152	30	f	f	PROPN
ejpam-3018	152	31	‖	‖	PROPN
ejpam-3018	152	32	.	.	PUNCT
ejpam-3018	153	1	(	(	PUNCT
ejpam-3018	153	2	15	15	X
ejpam-3018	153	3	)	)	PUNCT
ejpam-3018	153	4	using	use	VERB
ejpam-3018	153	5	(	(	PUNCT
ejpam-3018	153	6	14	14	NUM
ejpam-3018	153	7	)	)	PUNCT
ejpam-3018	153	8	and	and	CCONJ
ejpam-3018	153	9	(	(	PUNCT
ejpam-3018	153	10	15	15	NUM
ejpam-3018	153	11	)	)	PUNCT
ejpam-3018	153	12	in	in	ADP
ejpam-3018	153	13	(	(	PUNCT
ejpam-3018	153	14	12	12	NUM
ejpam-3018	153	15	)	)	PUNCT
ejpam-3018	153	16	,	,	PUNCT
ejpam-3018	153	17	we	we	PRON
ejpam-3018	153	18	obtain	obtain	VERB
ejpam-3018	153	19	|g∗(α	|g∗(α	NOUN
ejpam-3018	153	20	,	,	PUNCT
ejpam-3018	153	21	β)n	β)n	NOUN
ejpam-3018	153	22	,	,	PUNCT
ejpam-3018	153	23	c	c	PROPN
ejpam-3018	153	24	(	(	PUNCT
ejpam-3018	153	25	f	f	PROPN
ejpam-3018	153	26	;	;	PUNCT
ejpam-3018	153	27	x)−	x)−	PROPN
ejpam-3018	153	28	f(x)|	f(x)|	VERB
ejpam-3018	153	29	≤	≤	NUM
ejpam-3018	153	30	|g∗(α	|g∗(α	PROPN
ejpam-3018	153	31	,	,	PUNCT
ejpam-3018	153	32	β)n	β)n	NOUN
ejpam-3018	153	33	,	,	PUNCT
ejpam-3018	153	34	c	c	PROPN
ejpam-3018	153	35	(	(	PUNCT
ejpam-3018	153	36	f	f	PROPN
ejpam-3018	153	37	−	−	PROPN
ejpam-3018	153	38	g;x)|+	g;x)|+	PROPN
ejpam-3018	153	39	|(f	|(f	PROPN
ejpam-3018	154	1	−	−	PROPN
ejpam-3018	154	2	g)(x)|+	g)(x)|+	PROPN
ejpam-3018	154	3	|g∗(α	|g∗(α	PROPN
ejpam-3018	154	4	,	,	PUNCT
ejpam-3018	154	5	β)n	β)n	NOUN
ejpam-3018	154	6	,	,	PUNCT
ejpam-3018	154	7	c	c	PROPN
ejpam-3018	154	8	(	(	PUNCT
ejpam-3018	154	9	g;x)−	g;x)−	PROPN
ejpam-3018	154	10	g(x)|	g(x)|	VERB
ejpam-3018	154	11	+	+	CCONJ
ejpam-3018	154	12	∣∣∣∣f	∣∣∣∣f	ADJ
ejpam-3018	154	13	(	(	PUNCT
ejpam-3018	154	14	nx+	nx+	PROPN
ejpam-3018	154	15	α	α	PROPN
ejpam-3018	154	16	n+	n+	X
ejpam-3018	154	17	β	β	X
ejpam-3018	154	18	)	)	PUNCT
ejpam-3018	155	1	−	−	ADP
ejpam-3018	155	2	f(x	f(x	PROPN
ejpam-3018	155	3	)	)	PUNCT
ejpam-3018	156	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3018	156	2	≤	≤	NUM
ejpam-3018	156	3	4	4	NUM
ejpam-3018	156	4	‖	‖	PROPN
ejpam-3018	156	5	f	f	NOUN
ejpam-3018	156	6	−	−	PROPN
ejpam-3018	156	7	g	g	PROPN
ejpam-3018	156	8	‖	‖	PROPN
ejpam-3018	157	1	+	+	CCONJ
ejpam-3018	158	1	(	(	PUNCT
ejpam-3018	158	2	δ(α	δ(α	NOUN
ejpam-3018	158	3	,	,	PUNCT
ejpam-3018	158	4	β)n	β)n	ADJ
ejpam-3018	158	5	,	,	PUNCT
ejpam-3018	158	6	c	c	PROPN
ejpam-3018	158	7	(	(	PUNCT
ejpam-3018	158	8	x	x	NOUN
ejpam-3018	158	9	)	)	PUNCT
ejpam-3018	158	10	)	)	PUNCT
ejpam-3018	159	1	2	2	NUM
ejpam-3018	159	2	‖	‖	PROPN
ejpam-3018	159	3	g′′	g′′	PROPN
ejpam-3018	159	4	‖	‖	PROPN
ejpam-3018	159	5	+	+	PROPN
ejpam-3018	159	6	∣∣∣∣f	∣∣∣∣f	PROPN
ejpam-3018	159	7	(	(	PUNCT
ejpam-3018	159	8	nx+	nx+	PROPN
ejpam-3018	159	9	α	α	PROPN
ejpam-3018	159	10	n+	n+	X
ejpam-3018	159	11	β	β	X
ejpam-3018	159	12	)	)	PUNCT
ejpam-3018	159	13	−	−	ADP
ejpam-3018	159	14	f(x	f(x	PROPN
ejpam-3018	159	15	)	)	PUNCT
ejpam-3018	159	16	∣∣∣∣.	∣∣∣∣.	PROPN
ejpam-3018	159	17	hence	hence	ADV
ejpam-3018	159	18	,	,	PUNCT
ejpam-3018	159	19	taking	take	VERB
ejpam-3018	159	20	infimum	infimum	ADV
ejpam-3018	159	21	on	on	ADP
ejpam-3018	159	22	the	the	DET
ejpam-3018	159	23	right	right	ADJ
ejpam-3018	159	24	hand	hand	NOUN
ejpam-3018	159	25	side	side	NOUN
ejpam-3018	159	26	over	over	ADP
ejpam-3018	159	27	all	all	DET
ejpam-3018	159	28	g	g	NOUN
ejpam-3018	159	29	∈w	∈w	NOUN
ejpam-3018	159	30	2	2	NUM
ejpam-3018	159	31	,	,	PUNCT
ejpam-3018	159	32	we	we	PRON
ejpam-3018	159	33	get	get	VERB
ejpam-3018	159	34	|	|	ADV
ejpam-3018	159	35	g∗(α	g∗(α	NOUN
ejpam-3018	159	36	,	,	PUNCT
ejpam-3018	159	37	β)n	β)n	NOUN
ejpam-3018	159	38	,	,	PUNCT
ejpam-3018	159	39	c	c	PROPN
ejpam-3018	159	40	(	(	PUNCT
ejpam-3018	159	41	f	f	PROPN
ejpam-3018	159	42	;	;	PUNCT
ejpam-3018	159	43	x)−	x)−	PROPN
ejpam-3018	159	44	f(x	f(x	PROPN
ejpam-3018	159	45	)	)	PUNCT
ejpam-3018	160	1	|	|	ADV
ejpam-3018	160	2	≤	≤	NUM
ejpam-3018	160	3	k2	k2	X
ejpam-3018	160	4	(	(	PUNCT
ejpam-3018	160	5	f	f	PROPN
ejpam-3018	160	6	,	,	PUNCT
ejpam-3018	160	7	(	(	PUNCT
ejpam-3018	160	8	δ(α	δ(α	NOUN
ejpam-3018	160	9	,	,	PUNCT
ejpam-3018	160	10	β)n	β)n	ADJ
ejpam-3018	160	11	,	,	PUNCT
ejpam-3018	160	12	c	c	PROPN
ejpam-3018	160	13	(	(	PUNCT
ejpam-3018	160	14	x))2	x))2	PROPN
ejpam-3018	160	15	)	)	PUNCT
ejpam-3018	161	1	+	+	CCONJ
ejpam-3018	161	2	ω	ω	NUM
ejpam-3018	161	3	(	(	PUNCT
ejpam-3018	161	4	f	f	X
ejpam-3018	161	5	,	,	PUNCT
ejpam-3018	161	6	|α−	|α−	PROPN
ejpam-3018	161	7	βx|	βx|	NUM
ejpam-3018	161	8	n+	n+	X
ejpam-3018	161	9	β	β	NOUN
ejpam-3018	161	10	)	)	PUNCT
ejpam-3018	161	11	.	.	PUNCT
ejpam-3018	162	1	in	in	ADP
ejpam-3018	162	2	view	view	NOUN
ejpam-3018	162	3	of	of	ADP
ejpam-3018	162	4	(	(	PUNCT
ejpam-3018	162	5	11	11	NUM
ejpam-3018	162	6	)	)	PUNCT
ejpam-3018	162	7	,	,	PUNCT
ejpam-3018	162	8	we	we	PRON
ejpam-3018	162	9	get	get	VERB
ejpam-3018	162	10	|	|	ADV
ejpam-3018	162	11	g∗(α	g∗(α	NOUN
ejpam-3018	162	12	,	,	PUNCT
ejpam-3018	162	13	β)n	β)n	NOUN
ejpam-3018	162	14	,	,	PUNCT
ejpam-3018	162	15	c	c	PROPN
ejpam-3018	162	16	(	(	PUNCT
ejpam-3018	162	17	f	f	PROPN
ejpam-3018	162	18	;	;	PUNCT
ejpam-3018	162	19	x)−	x)−	PROPN
ejpam-3018	162	20	f(x	f(x	PROPN
ejpam-3018	162	21	)	)	PUNCT
ejpam-3018	163	1	|	|	ADV
ejpam-3018	163	2	≤	≤	NUM
ejpam-3018	163	3	cω2	cω2	NOUN
ejpam-3018	163	4	(	(	PUNCT
ejpam-3018	163	5	f	f	X
ejpam-3018	163	6	,	,	PUNCT
ejpam-3018	163	7	δ(α	δ(α	ADJ
ejpam-3018	163	8	,	,	PUNCT
ejpam-3018	163	9	β)n	β)n	ADJ
ejpam-3018	163	10	,	,	PUNCT
ejpam-3018	163	11	c	c	PROPN
ejpam-3018	163	12	(	(	PUNCT
ejpam-3018	163	13	x	x	NOUN
ejpam-3018	163	14	)	)	PUNCT
ejpam-3018	163	15	)	)	PUNCT
ejpam-3018	164	1	+	+	CCONJ
ejpam-3018	164	2	ω	ω	NUM
ejpam-3018	164	3	(	(	PUNCT
ejpam-3018	164	4	f	f	X
ejpam-3018	164	5	,	,	PUNCT
ejpam-3018	164	6	|α−	|α−	PROPN
ejpam-3018	164	7	βx|	βx|	NUM
ejpam-3018	164	8	n+	n+	X
ejpam-3018	164	9	β	β	NOUN
ejpam-3018	164	10	)	)	PUNCT
ejpam-3018	164	11	.	.	PUNCT
ejpam-3018	165	1	hence	hence	ADV
ejpam-3018	165	2	,	,	PUNCT
ejpam-3018	165	3	the	the	DET
ejpam-3018	165	4	proof	proof	NOUN
ejpam-3018	165	5	is	be	AUX
ejpam-3018	165	6	completed	complete	VERB
ejpam-3018	165	7	.	.	PUNCT
ejpam-3018	166	1	3.2	3.2	NUM
ejpam-3018	166	2	.	.	PUNCT
ejpam-3018	167	1	rate	rate	NOUN
ejpam-3018	167	2	of	of	ADP
ejpam-3018	167	3	convergence	convergence	NOUN
ejpam-3018	167	4	let	let	AUX
ejpam-3018	167	5	ωb(f	ωb(f	NUM
ejpam-3018	167	6	,	,	PUNCT
ejpam-3018	167	7	δ	δ	PROPN
ejpam-3018	167	8	)	)	PUNCT
ejpam-3018	167	9	denote	denote	VERB
ejpam-3018	167	10	the	the	DET
ejpam-3018	167	11	modulus	modulus	NOUN
ejpam-3018	167	12	of	of	ADP
ejpam-3018	167	13	continuity	continuity	NOUN
ejpam-3018	167	14	of	of	ADP
ejpam-3018	167	15	f	f	PROPN
ejpam-3018	167	16	on	on	ADP
ejpam-3018	167	17	the	the	DET
ejpam-3018	167	18	closed	closed	ADJ
ejpam-3018	167	19	interval	interval	NOUN
ejpam-3018	167	20	[	[	X
ejpam-3018	167	21	0	0	NUM
ejpam-3018	167	22	,	,	PUNCT
ejpam-3018	167	23	b	b	NOUN
ejpam-3018	167	24	]	]	X
ejpam-3018	167	25	,	,	PUNCT
ejpam-3018	167	26	b	b	X
ejpam-3018	167	27	>	>	X
ejpam-3018	167	28	0	0	NUM
ejpam-3018	167	29	,	,	PUNCT
ejpam-3018	167	30	and	and	CCONJ
ejpam-3018	167	31	defined	define	VERB
ejpam-3018	167	32	as	as	ADP
ejpam-3018	167	33	ωb(f	ωb(f	NOUN
ejpam-3018	167	34	,	,	PUNCT
ejpam-3018	167	35	δ	δ	PROPN
ejpam-3018	167	36	)	)	PUNCT
ejpam-3018	167	37	=	=	SYM
ejpam-3018	167	38	sup	sup	NUM
ejpam-3018	167	39	|t−x|≤δ	|t−x|≤δ	NOUN
ejpam-3018	167	40	sup	sup	NOUN
ejpam-3018	167	41	x	x	NOUN
ejpam-3018	167	42	,	,	PUNCT
ejpam-3018	167	43	t∈[0,b	t∈[0,b	PROPN
ejpam-3018	167	44	]	]	X
ejpam-3018	167	45	|f(t)−	|f(t)−	PROPN
ejpam-3018	167	46	f(x)|	f(x)|	VERB
ejpam-3018	167	47	.	.	PUNCT
ejpam-3018	168	1	we	we	PRON
ejpam-3018	168	2	observe	observe	VERB
ejpam-3018	168	3	that	that	SCONJ
ejpam-3018	168	4	for	for	ADP
ejpam-3018	168	5	a	a	DET
ejpam-3018	168	6	function	function	NOUN
ejpam-3018	168	7	f	f	PROPN
ejpam-3018	168	8	∈	∈	PROPN
ejpam-3018	168	9	cb[0,∞	cb[0,∞	PROPN
ejpam-3018	168	10	)	)	PUNCT
ejpam-3018	168	11	,	,	PUNCT
ejpam-3018	168	12	the	the	DET
ejpam-3018	168	13	modulus	modulus	NOUN
ejpam-3018	168	14	of	of	ADP
ejpam-3018	168	15	continuity	continuity	NOUN
ejpam-3018	168	16	ωb(f	ωb(f	NOUN
ejpam-3018	168	17	,	,	PUNCT
ejpam-3018	168	18	δ	δ	PROPN
ejpam-3018	168	19	)	)	PUNCT
ejpam-3018	168	20	tends	tend	VERB
ejpam-3018	168	21	to	to	ADP
ejpam-3018	168	22	zero	zero	NUM
ejpam-3018	168	23	.	.	PUNCT
ejpam-3018	169	1	now	now	ADV
ejpam-3018	169	2	,	,	PUNCT
ejpam-3018	169	3	we	we	PRON
ejpam-3018	169	4	give	give	VERB
ejpam-3018	169	5	a	a	DET
ejpam-3018	169	6	rate	rate	NOUN
ejpam-3018	169	7	of	of	ADP
ejpam-3018	169	8	convergence	convergence	NOUN
ejpam-3018	169	9	theorem	theorem	NOUN
ejpam-3018	169	10	for	for	ADP
ejpam-3018	169	11	the	the	DET
ejpam-3018	169	12	operators	operator	NOUN
ejpam-3018	169	13	g	g	PROPN
ejpam-3018	169	14	∗(α	∗(α	PROPN
ejpam-3018	169	15	,	,	PUNCT
ejpam-3018	169	16	β	β	NOUN
ejpam-3018	169	17	)	)	PUNCT
ejpam-3018	169	18	n	n	CCONJ
ejpam-3018	169	19	,	,	PUNCT
ejpam-3018	169	20	c	c	PROPN
ejpam-3018	169	21	.	.	PUNCT
ejpam-3018	170	1	theorem	theorem	NOUN
ejpam-3018	170	2	6	6	NUM
ejpam-3018	170	3	.	.	PUNCT
ejpam-3018	171	1	let	let	VERB
ejpam-3018	171	2	f	f	PROPN
ejpam-3018	171	3	∈	∈	PROPN
ejpam-3018	171	4	cb[0,∞	cb[0,∞	PROPN
ejpam-3018	171	5	)	)	PUNCT
ejpam-3018	171	6	and	and	CCONJ
ejpam-3018	171	7	ωb+1(f	ωb+1(f	PROPN
ejpam-3018	171	8	,	,	PUNCT
ejpam-3018	171	9	δ	δ	PROPN
ejpam-3018	171	10	)	)	PUNCT
ejpam-3018	171	11	be	be	VERB
ejpam-3018	171	12	its	its	PRON
ejpam-3018	171	13	modulus	modulus	NOUN
ejpam-3018	171	14	of	of	ADP
ejpam-3018	171	15	continuity	continuity	NOUN
ejpam-3018	171	16	on	on	ADP
ejpam-3018	171	17	the	the	DET
ejpam-3018	171	18	finite	finite	ADJ
ejpam-3018	171	19	interval	interval	NOUN
ejpam-3018	172	1	[	[	X
ejpam-3018	172	2	0	0	NUM
ejpam-3018	172	3	,	,	PUNCT
ejpam-3018	172	4	b+	b+	X
ejpam-3018	172	5	1	1	NUM
ejpam-3018	172	6	]	]	PUNCT
ejpam-3018	172	7	⊂	⊂	PROPN
ejpam-3018	173	1	[	[	X
ejpam-3018	173	2	0,∞	0,∞	NOUN
ejpam-3018	173	3	)	)	PUNCT
ejpam-3018	173	4	,	,	PUNCT
ejpam-3018	174	1	where	where	SCONJ
ejpam-3018	174	2	b	b	X
ejpam-3018	174	3	>	>	X
ejpam-3018	174	4	0	0	NUM
ejpam-3018	174	5	.	.	PUNCT
ejpam-3018	175	1	then	then	ADV
ejpam-3018	175	2	,	,	PUNCT
ejpam-3018	175	3	for	for	ADP
ejpam-3018	175	4	every	every	DET
ejpam-3018	175	5	n	n	NOUN
ejpam-3018	175	6	>	>	X
ejpam-3018	175	7	2c	2c	NUM
ejpam-3018	175	8	,	,	PUNCT
ejpam-3018	175	9	|g∗(α	|g∗(α	PROPN
ejpam-3018	175	10	,	,	PUNCT
ejpam-3018	175	11	β)n	β)n	NOUN
ejpam-3018	175	12	,	,	PUNCT
ejpam-3018	175	13	c	c	PROPN
ejpam-3018	175	14	(	(	PUNCT
ejpam-3018	175	15	f	f	PROPN
ejpam-3018	175	16	;	;	PUNCT
ejpam-3018	175	17	x)−	x)−	PROPN
ejpam-3018	175	18	f(x)|	f(x)|	VERB
ejpam-3018	175	19	≤	≤	NUM
ejpam-3018	175	20	4mf	4mf	NOUN
ejpam-3018	175	21	(	(	PUNCT
ejpam-3018	175	22	1	1	NUM
ejpam-3018	175	23	+	+	CCONJ
ejpam-3018	175	24	b2)γ(α	b2)γ(α	ADJ
ejpam-3018	175	25	,	,	PUNCT
ejpam-3018	175	26	β)n	β)n	ADJ
ejpam-3018	175	27	,	,	PUNCT
ejpam-3018	175	28	c	c	PROPN
ejpam-3018	175	29	(	(	PUNCT
ejpam-3018	175	30	x	x	X
ejpam-3018	175	31	)	)	PUNCT
ejpam-3018	175	32	+	+	CCONJ
ejpam-3018	176	1	2ωb+1	2ωb+1	NUM
ejpam-3018	176	2	(	(	PUNCT
ejpam-3018	176	3	f	f	X
ejpam-3018	176	4	,	,	PUNCT
ejpam-3018	176	5	√	√	PROPN
ejpam-3018	176	6	γ	γ	PROPN
ejpam-3018	176	7	(	(	PUNCT
ejpam-3018	176	8	α	α	NOUN
ejpam-3018	176	9	,	,	PUNCT
ejpam-3018	176	10	β	β	NOUN
ejpam-3018	176	11	)	)	PUNCT
ejpam-3018	176	12	n	n	CCONJ
ejpam-3018	176	13	,	,	PUNCT
ejpam-3018	176	14	c	c	PROPN
ejpam-3018	176	15	(	(	PUNCT
ejpam-3018	176	16	x	x	NOUN
ejpam-3018	176	17	)	)	PUNCT
ejpam-3018	176	18	)	)	PUNCT
ejpam-3018	176	19	,	,	PUNCT
ejpam-3018	176	20	where	where	SCONJ
ejpam-3018	176	21	γ	γ	X
ejpam-3018	176	22	(	(	PUNCT
ejpam-3018	176	23	α	α	PROPN
ejpam-3018	176	24	,	,	PUNCT
ejpam-3018	176	25	β	β	NOUN
ejpam-3018	176	26	)	)	PUNCT
ejpam-3018	176	27	n	n	CCONJ
ejpam-3018	176	28	,	,	PUNCT
ejpam-3018	176	29	c	c	PROPN
ejpam-3018	176	30	(	(	PUNCT
ejpam-3018	176	31	x	x	X
ejpam-3018	176	32	)	)	PUNCT
ejpam-3018	176	33	is	be	AUX
ejpam-3018	176	34	defined	define	VERB
ejpam-3018	176	35	in	in	ADP
ejpam-3018	176	36	remark	remark	NOUN
ejpam-3018	176	37	1	1	NUM
ejpam-3018	176	38	and	and	CCONJ
ejpam-3018	176	39	mf	mf	PROPN
ejpam-3018	176	40	is	be	AUX
ejpam-3018	176	41	a	a	DET
ejpam-3018	176	42	constant	constant	ADJ
ejpam-3018	176	43	depending	depend	VERB
ejpam-3018	176	44	only	only	ADV
ejpam-3018	176	45	on	on	ADP
ejpam-3018	176	46	f.	f.	PROPN
ejpam-3018	176	47	a.	a.	PROPN
ejpam-3018	176	48	kumar	kumar	PROPN
ejpam-3018	176	49	,	,	PUNCT
ejpam-3018	176	50	v.	v.	PROPN
ejpam-3018	176	51	n.	n.	PROPN
ejpam-3018	176	52	mishra	mishra	PROPN
ejpam-3018	176	53	,	,	PUNCT
ejpam-3018	176	54	d.	d.	PROPN
ejpam-3018	176	55	tapiawala	tapiawala	PROPN
ejpam-3018	176	56	/	/	SYM
ejpam-3018	176	57	eur	eur	PROPN
ejpam-3018	176	58	.	.	PUNCT
ejpam-3018	177	1	j.	j.	PROPN
ejpam-3018	177	2	pure	pure	PROPN
ejpam-3018	177	3	appl	appl	PROPN
ejpam-3018	177	4	.	.	PROPN
ejpam-3018	177	5	math	math	PROPN
ejpam-3018	177	6	,	,	PUNCT
ejpam-3018	177	7	10	10	NUM
ejpam-3018	177	8	(	(	PUNCT
ejpam-3018	177	9	4	4	NUM
ejpam-3018	177	10	)	)	PUNCT
ejpam-3018	177	11	(	(	PUNCT
ejpam-3018	177	12	2017	2017	NUM
ejpam-3018	177	13	)	)	PUNCT
ejpam-3018	177	14	,	,	PUNCT
ejpam-3018	177	15	890	890	NUM
ejpam-3018	177	16	-	-	SYM
ejpam-3018	177	17	907	907	NUM
ejpam-3018	177	18	897	897	NUM
ejpam-3018	177	19	proof	proof	NOUN
ejpam-3018	177	20	.	.	PUNCT
ejpam-3018	178	1	for	for	ADP
ejpam-3018	178	2	x	x	PROPN
ejpam-3018	178	3	∈	∈	PROPN
ejpam-3018	178	4	[	[	X
ejpam-3018	178	5	0	0	NUM
ejpam-3018	178	6	,	,	PUNCT
ejpam-3018	178	7	b	b	NOUN
ejpam-3018	178	8	]	]	PUNCT
ejpam-3018	178	9	and	and	CCONJ
ejpam-3018	178	10	t	t	PROPN
ejpam-3018	178	11	>	>	X
ejpam-3018	178	12	b+	b+	X
ejpam-3018	178	13	1	1	NUM
ejpam-3018	178	14	.	.	PUNCT
ejpam-3018	179	1	since	since	SCONJ
ejpam-3018	179	2	t−	t−	PROPN
ejpam-3018	179	3	x	x	SYM
ejpam-3018	179	4	>	>	X
ejpam-3018	179	5	1	1	NUM
ejpam-3018	179	6	,	,	PUNCT
ejpam-3018	179	7	we	we	PRON
ejpam-3018	179	8	have	have	VERB
ejpam-3018	179	9	|f(t)−	|f(t)−	PROPN
ejpam-3018	179	10	f(x)|	f(x)|	VERB
ejpam-3018	179	11	≤mf	≤mf	NOUN
ejpam-3018	179	12	(	(	PUNCT
ejpam-3018	179	13	2	2	NUM
ejpam-3018	180	1	+	+	NUM
ejpam-3018	180	2	t2	t2	NOUN
ejpam-3018	180	3	+	+	CCONJ
ejpam-3018	180	4	x2	x2	ADJ
ejpam-3018	180	5	)	)	PUNCT
ejpam-3018	180	6	≤mf	≤mf	NOUN
ejpam-3018	180	7	(	(	PUNCT
ejpam-3018	180	8	t−	t−	PROPN
ejpam-3018	180	9	x)2(2	x)2(2	PROPN
ejpam-3018	181	1	+	+	NUM
ejpam-3018	181	2	2x+	2x+	NUM
ejpam-3018	181	3	2x2	2x2	NUM
ejpam-3018	181	4	)	)	PUNCT
ejpam-3018	181	5	≤	≤	NUM
ejpam-3018	181	6	4mf	4mf	NOUN
ejpam-3018	181	7	(	(	PUNCT
ejpam-3018	181	8	1	1	NUM
ejpam-3018	181	9	+	+	NUM
ejpam-3018	181	10	b2)(t−	b2)(t−	NOUN
ejpam-3018	181	11	x)2	x)2	NOUN
ejpam-3018	181	12	.	.	PUNCT
ejpam-3018	182	1	for	for	ADP
ejpam-3018	182	2	x	x	PROPN
ejpam-3018	182	3	∈	∈	PROPN
ejpam-3018	182	4	[	[	X
ejpam-3018	182	5	0	0	NUM
ejpam-3018	182	6	,	,	PUNCT
ejpam-3018	182	7	b	b	NOUN
ejpam-3018	182	8	]	]	PUNCT
ejpam-3018	182	9	and	and	CCONJ
ejpam-3018	182	10	t	t	PROPN
ejpam-3018	182	11	≤	≤	NUM
ejpam-3018	182	12	b+	b+	ADJ
ejpam-3018	182	13	1	1	NUM
ejpam-3018	182	14	,	,	PUNCT
ejpam-3018	182	15	we	we	PRON
ejpam-3018	182	16	have	have	VERB
ejpam-3018	182	17	|f(t)−	|f(t)−	PROPN
ejpam-3018	182	18	f(x)|	f(x)|	VERB
ejpam-3018	182	19	≤	≤	ADJ
ejpam-3018	182	20	ωb+1(f	ωb+1(f	PROPN
ejpam-3018	182	21	,	,	PUNCT
ejpam-3018	182	22	|t−	|t−	PROPN
ejpam-3018	182	23	x|	x|	PROPN
ejpam-3018	182	24	)	)	PUNCT
ejpam-3018	182	25	≤	≤	NOUN
ejpam-3018	182	26	(	(	PUNCT
ejpam-3018	182	27	1	1	NUM
ejpam-3018	182	28	+	+	NUM
ejpam-3018	182	29	|t−	|t−	PROPN
ejpam-3018	182	30	x|	x|	PROPN
ejpam-3018	182	31	δ	δ	PROPN
ejpam-3018	182	32	)	)	PUNCT
ejpam-3018	182	33	ωb+1(f	ωb+1(f	PROPN
ejpam-3018	182	34	,	,	PUNCT
ejpam-3018	182	35	δ	δ	PROPN
ejpam-3018	182	36	)	)	PUNCT
ejpam-3018	182	37	,	,	PUNCT
ejpam-3018	182	38	δ	δ	PROPN
ejpam-3018	182	39	>	>	X
ejpam-3018	182	40	0	0	X
ejpam-3018	182	41	.	.	PUNCT
ejpam-3018	183	1	from	from	ADP
ejpam-3018	183	2	the	the	DET
ejpam-3018	183	3	above	above	NOUN
ejpam-3018	183	4	,	,	PUNCT
ejpam-3018	183	5	we	we	PRON
ejpam-3018	183	6	have	have	VERB
ejpam-3018	183	7	|f(t)−	|f(t)−	PROPN
ejpam-3018	183	8	f(x)|	f(x)|	VERB
ejpam-3018	183	9	≤	≤	ADJ
ejpam-3018	183	10	4mf	4mf	NOUN
ejpam-3018	183	11	(	(	PUNCT
ejpam-3018	183	12	1	1	NUM
ejpam-3018	183	13	+	+	NUM
ejpam-3018	183	14	b2)(t−	b2)(t−	NOUN
ejpam-3018	183	15	x)2	x)2	VERB
ejpam-3018	184	1	+	+	CCONJ
ejpam-3018	184	2	(	(	PUNCT
ejpam-3018	184	3	1	1	NUM
ejpam-3018	184	4	+	+	NUM
ejpam-3018	184	5	|t−	|t−	PROPN
ejpam-3018	184	6	x|	x|	PROPN
ejpam-3018	184	7	δ	δ	PROPN
ejpam-3018	184	8	)	)	PUNCT
ejpam-3018	184	9	ωb+1(f	ωb+1(f	PROPN
ejpam-3018	184	10	,	,	PUNCT
ejpam-3018	184	11	δ	δ	PROPN
ejpam-3018	184	12	)	)	PUNCT
ejpam-3018	184	13	,	,	PUNCT
ejpam-3018	184	14	δ	δ	PROPN
ejpam-3018	184	15	>	>	X
ejpam-3018	184	16	0	0	PROPN
ejpam-3018	184	17	.	.	PUNCT
ejpam-3018	185	1	thus	thus	ADV
ejpam-3018	185	2	,	,	PUNCT
ejpam-3018	185	3	by	by	ADP
ejpam-3018	185	4	applying	apply	VERB
ejpam-3018	185	5	cauchy	cauchy	NOUN
ejpam-3018	185	6	-	-	PUNCT
ejpam-3018	185	7	schwarz	schwarz	PROPN
ejpam-3018	185	8	inequality	inequality	NOUN
ejpam-3018	185	9	,	,	PUNCT
ejpam-3018	185	10	we	we	PRON
ejpam-3018	185	11	have	have	VERB
ejpam-3018	185	12	|g∗(α	|g∗(α	PROPN
ejpam-3018	185	13	,	,	PUNCT
ejpam-3018	185	14	β)n	β)n	ADJ
ejpam-3018	185	15	,	,	PUNCT
ejpam-3018	185	16	c	c	PROPN
ejpam-3018	185	17	(	(	PUNCT
ejpam-3018	185	18	f	f	PROPN
ejpam-3018	185	19	;	;	PUNCT
ejpam-3018	185	20	x)−	x)−	PROPN
ejpam-3018	185	21	f(x)|	f(x)|	VERB
ejpam-3018	185	22	≤	≤	NUM
ejpam-3018	185	23	4mf	4mf	NOUN
ejpam-3018	185	24	(	(	PUNCT
ejpam-3018	185	25	1	1	NUM
ejpam-3018	185	26	+	+	CCONJ
ejpam-3018	185	27	b2)(g∗(α	b2)(g∗(α	X
ejpam-3018	185	28	,	,	PUNCT
ejpam-3018	185	29	β)n	β)n	ADJ
ejpam-3018	185	30	,	,	PUNCT
ejpam-3018	185	31	c	c	PROPN
ejpam-3018	185	32	(	(	PUNCT
ejpam-3018	185	33	t−	t−	PROPN
ejpam-3018	185	34	x)2;x	x)2;x	NUM
ejpam-3018	185	35	)	)	PUNCT
ejpam-3018	186	1	+	+	NOUN
ejpam-3018	186	2	ωb+1(f	ωb+1(f	PROPN
ejpam-3018	186	3	,	,	PUNCT
ejpam-3018	186	4	δ	δ	PROPN
ejpam-3018	186	5	)	)	PUNCT
ejpam-3018	186	6	(	(	PUNCT
ejpam-3018	186	7	1	1	NUM
ejpam-3018	186	8	+	+	SYM
ejpam-3018	186	9	1	1	NUM
ejpam-3018	186	10	δ	δ	PROPN
ejpam-3018	186	11	(	(	PUNCT
ejpam-3018	186	12	g∗(α	g∗(α	PROPN
ejpam-3018	186	13	,	,	PUNCT
ejpam-3018	186	14	β)n	β)n	NOUN
ejpam-3018	186	15	,	,	PUNCT
ejpam-3018	186	16	c	c	PROPN
ejpam-3018	186	17	(	(	PUNCT
ejpam-3018	186	18	t−	t−	PROPN
ejpam-3018	186	19	x)2;x	x)2;x	NUM
ejpam-3018	186	20	)	)	PUNCT
ejpam-3018	186	21	1	1	NUM
ejpam-3018	186	22	2	2	NUM
ejpam-3018	186	23	)	)	PUNCT
ejpam-3018	186	24	≤	≤	NOUN
ejpam-3018	186	25	4mf	4mf	NOUN
ejpam-3018	186	26	(	(	PUNCT
ejpam-3018	186	27	1	1	NUM
ejpam-3018	186	28	+	+	CCONJ
ejpam-3018	186	29	b2)γ(α	b2)γ(α	ADJ
ejpam-3018	186	30	,	,	PUNCT
ejpam-3018	186	31	β)n	β)n	ADJ
ejpam-3018	186	32	,	,	PUNCT
ejpam-3018	186	33	c	c	PROPN
ejpam-3018	186	34	(	(	PUNCT
ejpam-3018	186	35	x	x	X
ejpam-3018	186	36	)	)	PUNCT
ejpam-3018	186	37	+	+	CCONJ
ejpam-3018	186	38	2ωb+1	2ωb+1	NUM
ejpam-3018	186	39	(	(	PUNCT
ejpam-3018	186	40	f	f	X
ejpam-3018	186	41	,	,	PUNCT
ejpam-3018	186	42	√	√	PROPN
ejpam-3018	186	43	γ	γ	PROPN
ejpam-3018	186	44	(	(	PUNCT
ejpam-3018	186	45	α	α	NOUN
ejpam-3018	186	46	,	,	PUNCT
ejpam-3018	186	47	β	β	NOUN
ejpam-3018	186	48	)	)	PUNCT
ejpam-3018	186	49	n	n	CCONJ
ejpam-3018	186	50	,	,	PUNCT
ejpam-3018	186	51	c	c	PROPN
ejpam-3018	186	52	(	(	PUNCT
ejpam-3018	186	53	x	x	NOUN
ejpam-3018	186	54	)	)	PUNCT
ejpam-3018	186	55	)	)	PUNCT
ejpam-3018	186	56	,	,	PUNCT
ejpam-3018	186	57	on	on	ADP
ejpam-3018	186	58	choosing	choose	VERB
ejpam-3018	186	59	δ	δ	PROPN
ejpam-3018	186	60	=	=	PROPN
ejpam-3018	186	61	√	√	PROPN
ejpam-3018	186	62	γ	γ	PROPN
ejpam-3018	186	63	(	(	PUNCT
ejpam-3018	186	64	α	α	NOUN
ejpam-3018	186	65	,	,	PUNCT
ejpam-3018	186	66	β	β	NOUN
ejpam-3018	186	67	)	)	PUNCT
ejpam-3018	186	68	n	n	CCONJ
ejpam-3018	186	69	,	,	PUNCT
ejpam-3018	186	70	c	c	PROPN
ejpam-3018	186	71	(	(	PUNCT
ejpam-3018	186	72	x	x	NOUN
ejpam-3018	186	73	)	)	PUNCT
ejpam-3018	186	74	.	.	PUNCT
ejpam-3018	187	1	this	this	PRON
ejpam-3018	187	2	completes	complete	VERB
ejpam-3018	187	3	the	the	DET
ejpam-3018	187	4	proof	proof	NOUN
ejpam-3018	187	5	of	of	ADP
ejpam-3018	187	6	the	the	DET
ejpam-3018	187	7	theorem	theorem	NOUN
ejpam-3018	187	8	.	.	PROPN
ejpam-3018	187	9	3.3	3.3	NUM
ejpam-3018	187	10	.	.	PUNCT
ejpam-3018	188	1	weighted	weight	VERB
ejpam-3018	188	2	approximation	approximation	NOUN
ejpam-3018	188	3	.	.	PUNCT
ejpam-3018	189	1	let	let	VERB
ejpam-3018	189	2	cν	cν	NOUN
ejpam-3018	189	3	be	be	AUX
ejpam-3018	189	4	the	the	DET
ejpam-3018	189	5	space	space	NOUN
ejpam-3018	189	6	of	of	ADP
ejpam-3018	189	7	all	all	DET
ejpam-3018	189	8	continuous	continuous	ADJ
ejpam-3018	189	9	functions	function	NOUN
ejpam-3018	189	10	on	on	ADP
ejpam-3018	189	11	[	[	X
ejpam-3018	189	12	0,∞	0,∞	NOUN
ejpam-3018	189	13	)	)	PUNCT
ejpam-3018	189	14	with	with	ADP
ejpam-3018	189	15	the	the	DET
ejpam-3018	189	16	norm	norm	NOUN
ejpam-3018	189	17	‖	‖	PROPN
ejpam-3018	189	18	f	f	PROPN
ejpam-3018	189	19	‖ν=	‖ν=	PROPN
ejpam-3018	189	20	sup	sup	NOUN
ejpam-3018	189	21	x∈[0,∞	x∈[0,∞	NOUN
ejpam-3018	189	22	)	)	PUNCT
ejpam-3018	189	23	|f(x)|	|f(x)|	PROPN
ejpam-3018	189	24	ν(x	ν(x	PROPN
ejpam-3018	189	25	)	)	PUNCT
ejpam-3018	189	26	and	and	CCONJ
ejpam-3018	189	27	c0	c0	PROPN
ejpam-3018	189	28	ν	ν	PROPN
ejpam-3018	190	1	=	=	PUNCT
ejpam-3018	190	2	{	{	PUNCT
ejpam-3018	190	3	f	f	PROPN
ejpam-3018	190	4	∈	∈	PROPN
ejpam-3018	190	5	cν	cν	NOUN
ejpam-3018	190	6	:	:	PUNCT
ejpam-3018	190	7	lim	lim	PROPN
ejpam-3018	190	8	x→∞	x→∞	NUM
ejpam-3018	191	1	|f(x)|	|f(x)|	PROPN
ejpam-3018	191	2	ν(x	ν(x	PROPN
ejpam-3018	191	3	)	)	PUNCT
ejpam-3018	192	1	<	<	X
ejpam-3018	192	2	∞	∞	NUM
ejpam-3018	192	3	}	}	PUNCT
ejpam-3018	192	4	,	,	PUNCT
ejpam-3018	192	5	where	where	SCONJ
ejpam-3018	192	6	ν(x	ν(x	PROPN
ejpam-3018	192	7	)	)	PUNCT
ejpam-3018	192	8	is	be	AUX
ejpam-3018	192	9	a	a	DET
ejpam-3018	192	10	weight	weight	NOUN
ejpam-3018	192	11	function	function	NOUN
ejpam-3018	192	12	.	.	PUNCT
ejpam-3018	193	1	in	in	ADP
ejpam-3018	193	2	what	what	PRON
ejpam-3018	193	3	follows	follow	VERB
ejpam-3018	193	4	we	we	PRON
ejpam-3018	193	5	consider	consider	VERB
ejpam-3018	193	6	ν(x	ν(x	NOUN
ejpam-3018	193	7	)	)	PUNCT
ejpam-3018	193	8	=	=	SYM
ejpam-3018	193	9	1	1	NUM
ejpam-3018	193	10	+	+	CCONJ
ejpam-3018	193	11	x2	x2	PROPN
ejpam-3018	193	12	.	.	PUNCT
ejpam-3018	193	13	theorem	theorem	VERB
ejpam-3018	193	14	7	7	NUM
ejpam-3018	193	15	.	.	X
ejpam-3018	193	16	for	for	ADP
ejpam-3018	193	17	each	each	DET
ejpam-3018	193	18	f	f	PROPN
ejpam-3018	193	19	∈	∈	PROPN
ejpam-3018	193	20	c0	c0	PROPN
ejpam-3018	193	21	ν	ν	PROPN
ejpam-3018	193	22	,	,	PUNCT
ejpam-3018	193	23	we	we	PRON
ejpam-3018	193	24	have	have	VERB
ejpam-3018	193	25	lim	lim	PROPN
ejpam-3018	193	26	n→∞	n→∞	X
ejpam-3018	193	27	‖	‖	PROPN
ejpam-3018	193	28	g∗(α	g∗(α	PROPN
ejpam-3018	193	29	,	,	PUNCT
ejpam-3018	193	30	β)n	β)n	NOUN
ejpam-3018	193	31	,	,	PUNCT
ejpam-3018	193	32	c	c	PROPN
ejpam-3018	193	33	(	(	PUNCT
ejpam-3018	193	34	f)−	f)−	PROPN
ejpam-3018	193	35	f	f	X
ejpam-3018	193	36	‖ν=	‖ν=	PROPN
ejpam-3018	193	37	0	0	NUM
ejpam-3018	193	38	.	.	PUNCT
ejpam-3018	194	1	proof	proof	NOUN
ejpam-3018	194	2	.	.	PUNCT
ejpam-3018	195	1	from	from	ADP
ejpam-3018	195	2	[	[	X
ejpam-3018	195	3	8	8	NUM
ejpam-3018	195	4	]	]	PUNCT
ejpam-3018	195	5	,	,	PUNCT
ejpam-3018	195	6	we	we	PRON
ejpam-3018	195	7	know	know	VERB
ejpam-3018	195	8	that	that	SCONJ
ejpam-3018	195	9	it	it	PRON
ejpam-3018	195	10	is	be	AUX
ejpam-3018	195	11	sufficient	sufficient	ADJ
ejpam-3018	195	12	to	to	PART
ejpam-3018	195	13	verify	verify	VERB
ejpam-3018	195	14	the	the	DET
ejpam-3018	195	15	following	follow	VERB
ejpam-3018	195	16	three	three	NUM
ejpam-3018	195	17	conditions	condition	NOUN
ejpam-3018	195	18	lim	lim	PROPN
ejpam-3018	195	19	n→∞	n→∞	NUM
ejpam-3018	195	20	‖	‖	PROPN
ejpam-3018	195	21	g∗(α	g∗(α	PROPN
ejpam-3018	195	22	,	,	PUNCT
ejpam-3018	195	23	β)n	β)n	NOUN
ejpam-3018	195	24	,	,	PUNCT
ejpam-3018	195	25	c	c	PROPN
ejpam-3018	195	26	(	(	PUNCT
ejpam-3018	195	27	tk;x)−	tk;x)−	PROPN
ejpam-3018	195	28	xk	xk	PROPN
ejpam-3018	195	29	‖ν=	‖ν=	PROPN
ejpam-3018	195	30	0	0	NUM
ejpam-3018	195	31	,	,	PUNCT
ejpam-3018	195	32	k	k	NOUN
ejpam-3018	195	33	=	=	SYM
ejpam-3018	195	34	0	0	NUM
ejpam-3018	195	35	,	,	PUNCT
ejpam-3018	195	36	1	1	NUM
ejpam-3018	195	37	,	,	PUNCT
ejpam-3018	195	38	2	2	NUM
ejpam-3018	195	39	.	.	PUNCT
ejpam-3018	196	1	(	(	PUNCT
ejpam-3018	196	2	16	16	NUM
ejpam-3018	196	3	)	)	PUNCT
ejpam-3018	196	4	since	since	SCONJ
ejpam-3018	196	5	g	g	PROPN
ejpam-3018	196	6	∗(α	∗(α	PROPN
ejpam-3018	196	7	,	,	PUNCT
ejpam-3018	196	8	β	β	NOUN
ejpam-3018	196	9	)	)	PUNCT
ejpam-3018	196	10	n	n	CCONJ
ejpam-3018	196	11	,	,	PUNCT
ejpam-3018	196	12	c	c	PROPN
ejpam-3018	196	13	(	(	PUNCT
ejpam-3018	196	14	1;x	1;x	NUM
ejpam-3018	196	15	)	)	PUNCT
ejpam-3018	196	16	=	=	SYM
ejpam-3018	196	17	1	1	NUM
ejpam-3018	196	18	,	,	PUNCT
ejpam-3018	196	19	the	the	DET
ejpam-3018	196	20	condition	condition	NOUN
ejpam-3018	196	21	in	in	ADP
ejpam-3018	196	22	(	(	PUNCT
ejpam-3018	196	23	16	16	NUM
ejpam-3018	196	24	)	)	PUNCT
ejpam-3018	196	25	holds	hold	VERB
ejpam-3018	196	26	for	for	ADP
ejpam-3018	196	27	k	k	PROPN
ejpam-3018	196	28	=	=	SYM
ejpam-3018	196	29	0	0	PROPN
ejpam-3018	196	30	.	.	PUNCT
ejpam-3018	197	1	by	by	ADP
ejpam-3018	197	2	lemma	lemma	PROPN
ejpam-3018	197	3	2	2	NUM
ejpam-3018	197	4	,	,	PUNCT
ejpam-3018	197	5	we	we	PRON
ejpam-3018	197	6	have	have	VERB
ejpam-3018	197	7	‖	‖	ADJ
ejpam-3018	197	8	g∗(α	g∗(α	PROPN
ejpam-3018	197	9	,	,	PUNCT
ejpam-3018	197	10	β)n	β)n	NOUN
ejpam-3018	197	11	,	,	PUNCT
ejpam-3018	197	12	c	c	PROPN
ejpam-3018	197	13	(	(	PUNCT
ejpam-3018	197	14	t;x)−	t;x)−	PROPN
ejpam-3018	197	15	x	x	SYM
ejpam-3018	197	16	)	)	PUNCT
ejpam-3018	197	17	‖ν	‖ν	NOUN
ejpam-3018	197	18	=	=	NOUN
ejpam-3018	198	1	sup	sup	NOUN
ejpam-3018	198	2	x∈[0,∞	x∈[0,∞	NUM
ejpam-3018	198	3	)	)	PUNCT
ejpam-3018	198	4	|g∗(α	|g∗(α	PROPN
ejpam-3018	198	5	,	,	PUNCT
ejpam-3018	198	6	β)n	β)n	NOUN
ejpam-3018	198	7	,	,	PUNCT
ejpam-3018	198	8	c	c	PROPN
ejpam-3018	198	9	(	(	PUNCT
ejpam-3018	198	10	t;x)−	t;x)−	PROPN
ejpam-3018	198	11	x|	x|	PROPN
ejpam-3018	198	12	1	1	NUM
ejpam-3018	199	1	+	+	CCONJ
ejpam-3018	199	2	x2	x2	PROPN
ejpam-3018	199	3	a.	a.	NOUN
ejpam-3018	199	4	kumar	kumar	PROPN
ejpam-3018	199	5	,	,	PUNCT
ejpam-3018	199	6	v.	v.	PROPN
ejpam-3018	199	7	n.	n.	PROPN
ejpam-3018	199	8	mishra	mishra	PROPN
ejpam-3018	199	9	,	,	PUNCT
ejpam-3018	199	10	d.	d.	PROPN
ejpam-3018	199	11	tapiawala	tapiawala	PROPN
ejpam-3018	199	12	/	/	SYM
ejpam-3018	199	13	eur	eur	PROPN
ejpam-3018	199	14	.	.	PUNCT
ejpam-3018	200	1	j.	j.	PROPN
ejpam-3018	200	2	pure	pure	PROPN
ejpam-3018	200	3	appl	appl	PROPN
ejpam-3018	200	4	.	.	PROPN
ejpam-3018	200	5	math	math	PROPN
ejpam-3018	200	6	,	,	PUNCT
ejpam-3018	200	7	10	10	NUM
ejpam-3018	200	8	(	(	PUNCT
ejpam-3018	200	9	4	4	NUM
ejpam-3018	200	10	)	)	PUNCT
ejpam-3018	200	11	(	(	PUNCT
ejpam-3018	200	12	2017	2017	NUM
ejpam-3018	200	13	)	)	PUNCT
ejpam-3018	200	14	,	,	PUNCT
ejpam-3018	200	15	890	890	NUM
ejpam-3018	200	16	-	-	SYM
ejpam-3018	200	17	907	907	NUM
ejpam-3018	200	18	898	898	NUM
ejpam-3018	200	19	≤	≤	NOUN
ejpam-3018	200	20	β	β	X
ejpam-3018	200	21	n+	n+	X
ejpam-3018	200	22	β	β	X
ejpam-3018	200	23	sup	sup	NOUN
ejpam-3018	200	24	x∈[0,∞	x∈[0,∞	NUM
ejpam-3018	200	25	)	)	PUNCT
ejpam-3018	200	26	x	x	SYM
ejpam-3018	201	1	1	1	NUM
ejpam-3018	201	2	+	+	NUM
ejpam-3018	201	3	x2	x2	PROPN
ejpam-3018	202	1	+	+	CCONJ
ejpam-3018	202	2	α	α	NOUN
ejpam-3018	202	3	n+	n+	PUNCT
ejpam-3018	202	4	β	β	X
ejpam-3018	202	5	sup	sup	NOUN
ejpam-3018	202	6	x∈[0,∞	x∈[0,∞	PROPN
ejpam-3018	202	7	)	)	PUNCT
ejpam-3018	202	8	1	1	NUM
ejpam-3018	202	9	1	1	NUM
ejpam-3018	202	10	+	+	NUM
ejpam-3018	202	11	x2	x2	ADJ
ejpam-3018	202	12	≤	≤	NOUN
ejpam-3018	202	13	α+	α+	PUNCT
ejpam-3018	202	14	β	β	X
ejpam-3018	202	15	n+	n+	X
ejpam-3018	202	16	β	β	X
ejpam-3018	202	17	,	,	PUNCT
ejpam-3018	202	18	which	which	PRON
ejpam-3018	202	19	implies	imply	VERB
ejpam-3018	202	20	that	that	SCONJ
ejpam-3018	202	21	the	the	DET
ejpam-3018	202	22	condition	condition	NOUN
ejpam-3018	202	23	in	in	ADP
ejpam-3018	202	24	(	(	PUNCT
ejpam-3018	202	25	16	16	NUM
ejpam-3018	202	26	)	)	PUNCT
ejpam-3018	202	27	holds	hold	VERB
ejpam-3018	202	28	for	for	ADP
ejpam-3018	202	29	k	k	PROPN
ejpam-3018	202	30	=	=	SYM
ejpam-3018	202	31	1	1	X
ejpam-3018	202	32	.	.	PUNCT
ejpam-3018	203	1	similarly	similarly	ADV
ejpam-3018	203	2	,	,	PUNCT
ejpam-3018	203	3	we	we	PRON
ejpam-3018	203	4	can	can	AUX
ejpam-3018	203	5	write	write	VERB
ejpam-3018	203	6	for	for	ADP
ejpam-3018	203	7	n	n	PROPN
ejpam-3018	203	8	>	>	X
ejpam-3018	203	9	2c	2c	NUM
ejpam-3018	203	10	‖	‖	PROPN
ejpam-3018	203	11	g∗(α	g∗(α	PROPN
ejpam-3018	203	12	,	,	PUNCT
ejpam-3018	203	13	β)n	β)n	NOUN
ejpam-3018	203	14	,	,	PUNCT
ejpam-3018	203	15	c	c	PROPN
ejpam-3018	203	16	(	(	PUNCT
ejpam-3018	203	17	t2;x)−	t2;x)−	NOUN
ejpam-3018	203	18	x2	x2	PROPN
ejpam-3018	203	19	‖ν	‖ν	PROPN
ejpam-3018	204	1	=	=	NOUN
ejpam-3018	204	2	sup	sup	NOUN
ejpam-3018	204	3	x∈[0,∞	x∈[0,∞	NOUN
ejpam-3018	204	4	)	)	PUNCT
ejpam-3018	204	5	|g∗(α	|g∗(α	PROPN
ejpam-3018	204	6	,	,	PUNCT
ejpam-3018	204	7	β)n	β)n	NOUN
ejpam-3018	204	8	,	,	PUNCT
ejpam-3018	204	9	c	c	PROPN
ejpam-3018	204	10	(	(	PUNCT
ejpam-3018	204	11	t2;x)−	t2;x)−	NOUN
ejpam-3018	204	12	x2|	x2|	PROPN
ejpam-3018	204	13	1	1	NUM
ejpam-3018	205	1	+	+	NUM
ejpam-3018	205	2	x2	x2	ADJ
ejpam-3018	205	3	≤	≤	PROPN
ejpam-3018	205	4	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3018	205	5	n(n2	n(n2	NOUN
ejpam-3018	205	6	−	−	PROPN
ejpam-3018	205	7	c2	c2	PROPN
ejpam-3018	205	8	)	)	PUNCT
ejpam-3018	205	9	(	(	PUNCT
ejpam-3018	205	10	n−	n−	NOUN
ejpam-3018	205	11	2c)(n+	2c)(n+	NUM
ejpam-3018	205	12	β)2	β)2	ADV
ejpam-3018	205	13	−	−	PROPN
ejpam-3018	205	14	1	1	NUM
ejpam-3018	205	15	∣∣∣∣+	∣∣∣∣+	NOUN
ejpam-3018	205	16	∣∣∣∣2n((n−	∣∣∣∣2n((n−	PROPN
ejpam-3018	205	17	c	c	NOUN
ejpam-3018	205	18	)	)	PUNCT
ejpam-3018	205	19	+	+	CCONJ
ejpam-3018	205	20	α(n−	α(n−	NUM
ejpam-3018	205	21	2c	2c	NUM
ejpam-3018	205	22	)	)	PUNCT
ejpam-3018	205	23	)	)	PUNCT
ejpam-3018	206	1	(	(	PUNCT
ejpam-3018	206	2	n−	n−	NOUN
ejpam-3018	206	3	2c)(n+	2c)(n+	NUM
ejpam-3018	206	4	β)2	β)2	ADV
ejpam-3018	206	5	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3018	206	6	+	+	CCONJ
ejpam-3018	206	7	α2	α2	ADJ
ejpam-3018	206	8	(	(	PUNCT
ejpam-3018	206	9	n+	n+	X
ejpam-3018	206	10	β)2	β)2	NOUN
ejpam-3018	206	11	,	,	PUNCT
ejpam-3018	206	12	which	which	PRON
ejpam-3018	206	13	implies	imply	VERB
ejpam-3018	206	14	that	that	SCONJ
ejpam-3018	206	15	lim	lim	PROPN
ejpam-3018	206	16	n→∞	n→∞	PRON
ejpam-3018	206	17	‖	‖	PROPN
ejpam-3018	206	18	g∗(α	g∗(α	PROPN
ejpam-3018	206	19	,	,	PUNCT
ejpam-3018	206	20	β)n	β)n	NOUN
ejpam-3018	206	21	,	,	PUNCT
ejpam-3018	206	22	c	c	PROPN
ejpam-3018	206	23	(	(	PUNCT
ejpam-3018	206	24	t2;x)−	t2;x)−	NOUN
ejpam-3018	206	25	x2	x2	PROPN
ejpam-3018	206	26	‖ν=	‖ν=	PROPN
ejpam-3018	206	27	0	0	NUM
ejpam-3018	206	28	,	,	PUNCT
ejpam-3018	206	29	the	the	DET
ejpam-3018	206	30	equation	equation	NOUN
ejpam-3018	206	31	(	(	PUNCT
ejpam-3018	206	32	16	16	NUM
ejpam-3018	206	33	)	)	PUNCT
ejpam-3018	206	34	holds	hold	VERB
ejpam-3018	206	35	for	for	ADP
ejpam-3018	206	36	k	k	PROPN
ejpam-3018	206	37	=	=	SYM
ejpam-3018	206	38	2	2	X
ejpam-3018	206	39	.	.	PUNCT
ejpam-3018	207	1	this	this	PRON
ejpam-3018	207	2	completes	complete	VERB
ejpam-3018	207	3	the	the	DET
ejpam-3018	207	4	proof	proof	NOUN
ejpam-3018	207	5	of	of	ADP
ejpam-3018	207	6	theorem	theorem	PROPN
ejpam-3018	207	7	.	.	PUNCT
ejpam-3018	208	1	now	now	ADV
ejpam-3018	208	2	we	we	PRON
ejpam-3018	208	3	give	give	VERB
ejpam-3018	208	4	the	the	DET
ejpam-3018	208	5	following	following	NOUN
ejpam-3018	208	6	theorem	theorem	NOUN
ejpam-3018	208	7	to	to	PART
ejpam-3018	208	8	approximate	approximate	VERB
ejpam-3018	208	9	all	all	DET
ejpam-3018	208	10	functions	function	NOUN
ejpam-3018	208	11	in	in	ADP
ejpam-3018	208	12	c0	c0	PROPN
ejpam-3018	208	13	ν	ν	PROPN
ejpam-3018	208	14	.	.	PUNCT
ejpam-3018	209	1	such	such	ADJ
ejpam-3018	209	2	type	type	NOUN
ejpam-3018	209	3	of	of	ADP
ejpam-3018	209	4	results	result	NOUN
ejpam-3018	209	5	are	be	AUX
ejpam-3018	209	6	given	give	VERB
ejpam-3018	209	7	in	in	ADP
ejpam-3018	209	8	[	[	NOUN
ejpam-3018	209	9	9	9	NUM
ejpam-3018	209	10	]	]	PUNCT
ejpam-3018	209	11	for	for	ADP
ejpam-3018	209	12	locally	locally	ADV
ejpam-3018	209	13	integrable	integrable	ADJ
ejpam-3018	209	14	functions	function	NOUN
ejpam-3018	209	15	.	.	PUNCT
ejpam-3018	210	1	theorem	theorem	VERB
ejpam-3018	210	2	8	8	NUM
ejpam-3018	210	3	.	.	PUNCT
ejpam-3018	211	1	for	for	ADP
ejpam-3018	211	2	each	each	DET
ejpam-3018	211	3	f	f	PROPN
ejpam-3018	211	4	∈	∈	PROPN
ejpam-3018	211	5	c0	c0	PROPN
ejpam-3018	211	6	ν	ν	PROPN
ejpam-3018	211	7	and	and	CCONJ
ejpam-3018	211	8	σ	σ	PROPN
ejpam-3018	211	9	>	>	X
ejpam-3018	211	10	0	0	NUM
ejpam-3018	211	11	,	,	PUNCT
ejpam-3018	211	12	we	we	PRON
ejpam-3018	211	13	have	have	VERB
ejpam-3018	211	14	lim	lim	PROPN
ejpam-3018	211	15	n→∞	n→∞	NUM
ejpam-3018	211	16	sup	sup	NOUN
ejpam-3018	211	17	x∈[0,∞	x∈[0,∞	NUM
ejpam-3018	211	18	)	)	PUNCT
ejpam-3018	211	19	|g∗(α	|g∗(α	PROPN
ejpam-3018	211	20	,	,	PUNCT
ejpam-3018	211	21	β)n	β)n	NOUN
ejpam-3018	211	22	,	,	PUNCT
ejpam-3018	211	23	c	c	PROPN
ejpam-3018	211	24	(	(	PUNCT
ejpam-3018	211	25	f	f	PROPN
ejpam-3018	211	26	;	;	PUNCT
ejpam-3018	211	27	x)−	x)−	PROPN
ejpam-3018	211	28	f(x)|	f(x)|	PUNCT
ejpam-3018	211	29	(	(	PUNCT
ejpam-3018	211	30	1	1	NUM
ejpam-3018	212	1	+	+	CCONJ
ejpam-3018	212	2	x2)σ+1	x2)σ+1	PROPN
ejpam-3018	212	3	=	=	SYM
ejpam-3018	212	4	0	0	X
ejpam-3018	212	5	.	.	PUNCT
ejpam-3018	212	6	proof	proof	NOUN
ejpam-3018	212	7	.	.	PUNCT
ejpam-3018	213	1	for	for	ADP
ejpam-3018	213	2	any	any	DET
ejpam-3018	213	3	fixed	fix	VERB
ejpam-3018	213	4	x0	x0	PROPN
ejpam-3018	213	5	>	>	X
ejpam-3018	213	6	0	0	NUM
ejpam-3018	213	7	,	,	PUNCT
ejpam-3018	213	8	sup	sup	NOUN
ejpam-3018	213	9	x∈[0,∞	x∈[0,∞	NOUN
ejpam-3018	213	10	)	)	PUNCT
ejpam-3018	213	11	|g∗(α	|g∗(α	PROPN
ejpam-3018	213	12	,	,	PUNCT
ejpam-3018	213	13	β)n	β)n	NOUN
ejpam-3018	213	14	,	,	PUNCT
ejpam-3018	213	15	c	c	PROPN
ejpam-3018	213	16	(	(	PUNCT
ejpam-3018	213	17	f	f	PROPN
ejpam-3018	213	18	;	;	PUNCT
ejpam-3018	213	19	x)−	x)−	PROPN
ejpam-3018	213	20	f(x)|	f(x)|	PUNCT
ejpam-3018	213	21	(	(	PUNCT
ejpam-3018	213	22	1	1	NUM
ejpam-3018	213	23	+	+	CCONJ
ejpam-3018	213	24	x2)σ+1	x2)σ+1	PROPN
ejpam-3018	213	25	=	=	PUNCT
ejpam-3018	213	26	sup	sup	NOUN
ejpam-3018	213	27	x≤x0	x≤x0	PROPN
ejpam-3018	213	28	|g∗(α	|g∗(α	PROPN
ejpam-3018	213	29	,	,	PUNCT
ejpam-3018	213	30	β)n	β)n	NOUN
ejpam-3018	213	31	,	,	PUNCT
ejpam-3018	213	32	c	c	PROPN
ejpam-3018	213	33	(	(	PUNCT
ejpam-3018	213	34	f	f	PROPN
ejpam-3018	213	35	;	;	PUNCT
ejpam-3018	213	36	x)−	x)−	PROPN
ejpam-3018	213	37	f(x)|	f(x)|	PUNCT
ejpam-3018	213	38	(	(	PUNCT
ejpam-3018	213	39	1	1	NUM
ejpam-3018	213	40	+	+	CCONJ
ejpam-3018	213	41	x2)σ+1	x2)σ+1	PROPN
ejpam-3018	214	1	+	+	NUM
ejpam-3018	214	2	sup	sup	NOUN
ejpam-3018	214	3	x	x	SYM
ejpam-3018	214	4	>	>	X
ejpam-3018	214	5	x0	x0	PROPN
ejpam-3018	214	6	|g∗(α	|g∗(α	PROPN
ejpam-3018	214	7	,	,	PUNCT
ejpam-3018	214	8	β)n	β)n	NOUN
ejpam-3018	214	9	,	,	PUNCT
ejpam-3018	214	10	c	c	PROPN
ejpam-3018	214	11	(	(	PUNCT
ejpam-3018	214	12	f	f	PROPN
ejpam-3018	214	13	;	;	PUNCT
ejpam-3018	214	14	x)−	x)−	PROPN
ejpam-3018	214	15	f(x)|	f(x)|	PUNCT
ejpam-3018	214	16	(	(	PUNCT
ejpam-3018	214	17	1	1	NUM
ejpam-3018	214	18	+	+	CCONJ
ejpam-3018	214	19	x2)σ+1	x2)σ+1	PROPN
ejpam-3018	214	20	sup	sup	NOUN
ejpam-3018	214	21	x∈[0,∞	x∈[0,∞	NUM
ejpam-3018	214	22	)	)	PUNCT
ejpam-3018	214	23	|g∗(α	|g∗(α	PROPN
ejpam-3018	214	24	,	,	PUNCT
ejpam-3018	214	25	β)n	β)n	NOUN
ejpam-3018	214	26	,	,	PUNCT
ejpam-3018	214	27	c	c	PROPN
ejpam-3018	214	28	(	(	PUNCT
ejpam-3018	214	29	f	f	PROPN
ejpam-3018	214	30	;	;	PUNCT
ejpam-3018	214	31	x)−	x)−	PROPN
ejpam-3018	214	32	f(x)|	f(x)|	PUNCT
ejpam-3018	214	33	(	(	PUNCT
ejpam-3018	214	34	1	1	NUM
ejpam-3018	214	35	+	+	CCONJ
ejpam-3018	214	36	x2)σ+1	x2)σ+1	PROPN
ejpam-3018	214	37	≤	≤	NUM
ejpam-3018	214	38	‖	‖	ADJ
ejpam-3018	214	39	g∗(α	g∗(α	PROPN
ejpam-3018	214	40	,	,	PUNCT
ejpam-3018	214	41	β)n	β)n	NOUN
ejpam-3018	214	42	,	,	PUNCT
ejpam-3018	214	43	c	c	PROPN
ejpam-3018	214	44	(	(	PUNCT
ejpam-3018	214	45	f)−	f)−	PROPN
ejpam-3018	214	46	f	f	X
ejpam-3018	215	1	‖c[0,x0	‖c[0,x0	X
ejpam-3018	215	2	]	]	X
ejpam-3018	216	1	+	+	CCONJ
ejpam-3018	216	2	‖	‖	PROPN
ejpam-3018	216	3	f	f	PROPN
ejpam-3018	216	4	‖ν	‖ν	PROPN
ejpam-3018	216	5	sup	sup	NOUN
ejpam-3018	216	6	x	x	PROPN
ejpam-3018	216	7	>	>	X
ejpam-3018	216	8	x0	x0	PROPN
ejpam-3018	216	9	|g∗(α	|g∗(α	PROPN
ejpam-3018	216	10	,	,	PUNCT
ejpam-3018	216	11	β)n	β)n	NOUN
ejpam-3018	216	12	,	,	PUNCT
ejpam-3018	216	13	c	c	X
ejpam-3018	216	14	(	(	PUNCT
ejpam-3018	216	15	1	1	NUM
ejpam-3018	216	16	+	+	NUM
ejpam-3018	216	17	t2;x)|	t2;x)|	NUM
ejpam-3018	216	18	(	(	PUNCT
ejpam-3018	216	19	1	1	NUM
ejpam-3018	216	20	+	+	CCONJ
ejpam-3018	216	21	x2)σ+1	x2)σ+1	PROPN
ejpam-3018	217	1	+	+	NUM
ejpam-3018	217	2	sup	sup	NOUN
ejpam-3018	217	3	x	x	SYM
ejpam-3018	217	4	>	>	X
ejpam-3018	217	5	x0	x0	PROPN
ejpam-3018	217	6	|f(x)|	|f(x)|	NOUN
ejpam-3018	217	7	(	(	PUNCT
ejpam-3018	217	8	1	1	NUM
ejpam-3018	218	1	+	+	CCONJ
ejpam-3018	218	2	x2)σ+1	x2)σ+1	PROPN
ejpam-3018	218	3	.	.	PUNCT
ejpam-3018	219	1	the	the	DET
ejpam-3018	219	2	first	first	ADJ
ejpam-3018	219	3	term	term	NOUN
ejpam-3018	219	4	of	of	ADP
ejpam-3018	219	5	the	the	DET
ejpam-3018	219	6	above	above	ADJ
ejpam-3018	219	7	inequality	inequality	NOUN
ejpam-3018	219	8	tends	tend	VERB
ejpam-3018	219	9	to	to	ADP
ejpam-3018	219	10	zero	zero	NUM
ejpam-3018	219	11	from	from	ADP
ejpam-3018	219	12	theorem	theorem	ADJ
ejpam-3018	219	13	6	6	NUM
ejpam-3018	219	14	.	.	PUNCT
ejpam-3018	219	15	by	by	ADP
ejpam-3018	219	16	lemma	lemma	PROPN
ejpam-3018	219	17	2	2	NUM
ejpam-3018	219	18	,	,	PUNCT
ejpam-3018	219	19	for	for	ADP
ejpam-3018	219	20	any	any	DET
ejpam-3018	219	21	fixed	fix	VERB
ejpam-3018	219	22	x0	x0	PROPN
ejpam-3018	219	23	>	>	X
ejpam-3018	219	24	0	0	PROPN
ejpam-3018	219	25	,	,	PUNCT
ejpam-3018	219	26	it	it	PRON
ejpam-3018	219	27	is	be	AUX
ejpam-3018	219	28	easily	easily	ADV
ejpam-3018	219	29	prove	prove	VERB
ejpam-3018	219	30	that	that	SCONJ
ejpam-3018	219	31	sup	sup	NOUN
ejpam-3018	219	32	x	x	X
ejpam-3018	219	33	>	>	X
ejpam-3018	219	34	x0	x0	PROPN
ejpam-3018	219	35	|g∗(α	|g∗(α	PROPN
ejpam-3018	219	36	,	,	PUNCT
ejpam-3018	219	37	β)n	β)n	NOUN
ejpam-3018	219	38	,	,	PUNCT
ejpam-3018	219	39	c	c	X
ejpam-3018	219	40	(	(	PUNCT
ejpam-3018	219	41	1	1	NUM
ejpam-3018	219	42	+	+	NUM
ejpam-3018	219	43	t2;x)|	t2;x)|	NUM
ejpam-3018	219	44	(	(	PUNCT
ejpam-3018	219	45	1	1	NUM
ejpam-3018	219	46	+	+	CCONJ
ejpam-3018	219	47	x2)σ+1	x2)σ+1	PROPN
ejpam-3018	219	48	→	→	SYM
ejpam-3018	219	49	0	0	PUNCT
ejpam-3018	219	50	as	as	ADP
ejpam-3018	219	51	n	n	PROPN
ejpam-3018	219	52	→	→	SYM
ejpam-3018	219	53	∞.	∞.	PROPN
ejpam-3018	219	54	we	we	PRON
ejpam-3018	219	55	can	can	AUX
ejpam-3018	219	56	choose	choose	VERB
ejpam-3018	219	57	x0	x0	PROPN
ejpam-3018	219	58	>	>	X
ejpam-3018	219	59	0	0	PUNCT
ejpam-3018	220	1	so	so	ADV
ejpam-3018	220	2	large	large	ADJ
ejpam-3018	220	3	that	that	SCONJ
ejpam-3018	220	4	the	the	DET
ejpam-3018	220	5	last	last	ADJ
ejpam-3018	220	6	part	part	NOUN
ejpam-3018	220	7	of	of	ADP
ejpam-3018	220	8	the	the	DET
ejpam-3018	220	9	above	above	ADJ
ejpam-3018	220	10	inequality	inequality	NOUN
ejpam-3018	220	11	can	can	AUX
ejpam-3018	220	12	be	be	AUX
ejpam-3018	220	13	small	small	ADJ
ejpam-3018	220	14	.	.	PUNCT
ejpam-3018	221	1	hence	hence	ADV
ejpam-3018	221	2	the	the	DET
ejpam-3018	221	3	proof	proof	NOUN
ejpam-3018	221	4	is	be	AUX
ejpam-3018	221	5	completed	complete	VERB
ejpam-3018	221	6	.	.	PUNCT
ejpam-3018	222	1	a.	a.	PROPN
ejpam-3018	222	2	kumar	kumar	PROPN
ejpam-3018	222	3	,	,	PUNCT
ejpam-3018	222	4	v.	v.	PROPN
ejpam-3018	222	5	n.	n.	PROPN
ejpam-3018	222	6	mishra	mishra	PROPN
ejpam-3018	222	7	,	,	PUNCT
ejpam-3018	222	8	d.	d.	PROPN
ejpam-3018	222	9	tapiawala	tapiawala	PROPN
ejpam-3018	222	10	/	/	SYM
ejpam-3018	222	11	eur	eur	PROPN
ejpam-3018	222	12	.	.	PUNCT
ejpam-3018	223	1	j.	j.	PROPN
ejpam-3018	223	2	pure	pure	PROPN
ejpam-3018	223	3	appl	appl	PROPN
ejpam-3018	223	4	.	.	PROPN
ejpam-3018	223	5	math	math	PROPN
ejpam-3018	223	6	,	,	PUNCT
ejpam-3018	223	7	10	10	NUM
ejpam-3018	223	8	(	(	PUNCT
ejpam-3018	223	9	4	4	NUM
ejpam-3018	223	10	)	)	PUNCT
ejpam-3018	223	11	(	(	PUNCT
ejpam-3018	223	12	2017	2017	NUM
ejpam-3018	223	13	)	)	PUNCT
ejpam-3018	223	14	,	,	PUNCT
ejpam-3018	223	15	890	890	NUM
ejpam-3018	223	16	-	-	SYM
ejpam-3018	223	17	907	907	NUM
ejpam-3018	223	18	899	899	NUM
ejpam-3018	223	19	3.4	3.4	NUM
ejpam-3018	223	20	.	.	PUNCT
ejpam-3018	224	1	pointwise	pointwise	NOUN
ejpam-3018	224	2	estimates	estimate	NOUN
ejpam-3018	224	3	in	in	ADP
ejpam-3018	224	4	this	this	DET
ejpam-3018	224	5	section	section	NOUN
ejpam-3018	224	6	,	,	PUNCT
ejpam-3018	224	7	we	we	PRON
ejpam-3018	224	8	establish	establish	VERB
ejpam-3018	224	9	some	some	DET
ejpam-3018	224	10	pointwise	pointwise	ADJ
ejpam-3018	224	11	estimates	estimate	NOUN
ejpam-3018	224	12	of	of	ADP
ejpam-3018	224	13	the	the	DET
ejpam-3018	224	14	rate	rate	NOUN
ejpam-3018	224	15	of	of	ADP
ejpam-3018	224	16	convergence	convergence	NOUN
ejpam-3018	224	17	of	of	ADP
ejpam-3018	224	18	the	the	DET
ejpam-3018	224	19	operators	operator	NOUN
ejpam-3018	224	20	g	g	PROPN
ejpam-3018	224	21	∗(α	∗(α	PROPN
ejpam-3018	224	22	,	,	PUNCT
ejpam-3018	224	23	β	β	NOUN
ejpam-3018	224	24	)	)	PUNCT
ejpam-3018	224	25	n	n	CCONJ
ejpam-3018	224	26	,	,	PUNCT
ejpam-3018	224	27	c	c	NOUN
ejpam-3018	224	28	.	.	PUNCT
ejpam-3018	225	1	first	first	ADV
ejpam-3018	225	2	,	,	PUNCT
ejpam-3018	225	3	we	we	PRON
ejpam-3018	225	4	give	give	VERB
ejpam-3018	225	5	the	the	DET
ejpam-3018	225	6	relationship	relationship	NOUN
ejpam-3018	225	7	between	between	ADP
ejpam-3018	225	8	the	the	DET
ejpam-3018	225	9	local	local	ADJ
ejpam-3018	225	10	smoothness	smoothness	NOUN
ejpam-3018	225	11	of	of	ADP
ejpam-3018	225	12	f	f	PROPN
ejpam-3018	225	13	and	and	CCONJ
ejpam-3018	225	14	local	local	ADJ
ejpam-3018	225	15	approximation	approximation	NOUN
ejpam-3018	225	16	.	.	PUNCT
ejpam-3018	226	1	we	we	PRON
ejpam-3018	226	2	know	know	VERB
ejpam-3018	226	3	that	that	SCONJ
ejpam-3018	226	4	a	a	DET
ejpam-3018	226	5	function	function	NOUN
ejpam-3018	226	6	f	f	PROPN
ejpam-3018	226	7	∈	∈	PROPN
ejpam-3018	226	8	c[0,∞	c[0,∞	PROPN
ejpam-3018	226	9	)	)	PUNCT
ejpam-3018	226	10	is	be	AUX
ejpam-3018	226	11	in	in	ADP
ejpam-3018	226	12	lipm	lipm	NOUN
ejpam-3018	226	13	(	(	PUNCT
ejpam-3018	226	14	α	α	NOUN
ejpam-3018	226	15	)	)	PUNCT
ejpam-3018	226	16	on	on	ADP
ejpam-3018	226	17	e	e	PROPN
ejpam-3018	226	18	,	,	PUNCT
ejpam-3018	226	19	α	α	PROPN
ejpam-3018	226	20	∈	∈	PROPN
ejpam-3018	226	21	(	(	PUNCT
ejpam-3018	226	22	0	0	NUM
ejpam-3018	226	23	,	,	PUNCT
ejpam-3018	226	24	1	1	NUM
ejpam-3018	226	25	]	]	PUNCT
ejpam-3018	226	26	,	,	PUNCT
ejpam-3018	226	27	e⊂	e⊂	VERB
ejpam-3018	227	1	[	[	X
ejpam-3018	227	2	0,∞	0,∞	X
ejpam-3018	227	3	)	)	PUNCT
ejpam-3018	227	4	if	if	SCONJ
ejpam-3018	227	5	it	it	PRON
ejpam-3018	227	6	satisfies	satisfy	VERB
ejpam-3018	227	7	the	the	DET
ejpam-3018	227	8	condition	condition	NOUN
ejpam-3018	227	9	|f(t)−	|f(t)−	ADJ
ejpam-3018	227	10	f(x)|	f(x)|	VERB
ejpam-3018	227	11	≤m	≤m	PROPN
ejpam-3018	227	12	|t−	|t−	PROPN
ejpam-3018	227	13	x|α	x|α	PROPN
ejpam-3018	227	14	,	,	PUNCT
ejpam-3018	227	15	t	t	PROPN
ejpam-3018	227	16	∈	∈	PROPN
ejpam-3018	228	1	[	[	X
ejpam-3018	228	2	0,∞	0,∞	NUM
ejpam-3018	228	3	)	)	PUNCT
ejpam-3018	228	4	and	and	CCONJ
ejpam-3018	228	5	x	x	PUNCT
ejpam-3018	228	6	∈	∈	PROPN
ejpam-3018	228	7	e	e	NOUN
ejpam-3018	228	8	,	,	PUNCT
ejpam-3018	228	9	where	where	SCONJ
ejpam-3018	228	10	m	m	NOUN
ejpam-3018	228	11	is	be	AUX
ejpam-3018	228	12	a	a	DET
ejpam-3018	228	13	constant	constant	ADJ
ejpam-3018	228	14	depending	depend	VERB
ejpam-3018	228	15	only	only	ADV
ejpam-3018	228	16	on	on	ADP
ejpam-3018	228	17	α	α	PROPN
ejpam-3018	228	18	and	and	CCONJ
ejpam-3018	228	19	f	f	PROPN
ejpam-3018	228	20	.	.	PUNCT
ejpam-3018	229	1	theorem	theorem	VERB
ejpam-3018	229	2	9	9	NUM
ejpam-3018	229	3	.	.	PUNCT
ejpam-3018	230	1	let	let	VERB
ejpam-3018	230	2	f	f	PROPN
ejpam-3018	230	3	∈	∈	PROPN
ejpam-3018	230	4	c[0,∞	c[0,∞	PROPN
ejpam-3018	230	5	)	)	PUNCT
ejpam-3018	230	6	∩	∩	NOUN
ejpam-3018	230	7	lipm	lipm	NOUN
ejpam-3018	230	8	(	(	PUNCT
ejpam-3018	230	9	α	α	NOUN
ejpam-3018	230	10	)	)	PUNCT
ejpam-3018	230	11	,	,	PUNCT
ejpam-3018	231	1	e	e	PROPN
ejpam-3018	231	2	⊂	⊂	PROPN
ejpam-3018	232	1	[	[	X
ejpam-3018	232	2	0,∞	0,∞	NUM
ejpam-3018	232	3	)	)	PUNCT
ejpam-3018	232	4	and	and	CCONJ
ejpam-3018	232	5	α	α	PRON
ejpam-3018	232	6	∈	∈	PROPN
ejpam-3018	232	7	(	(	PUNCT
ejpam-3018	232	8	0	0	NUM
ejpam-3018	232	9	,	,	PUNCT
ejpam-3018	232	10	1	1	NUM
ejpam-3018	232	11	]	]	PUNCT
ejpam-3018	232	12	.	.	PUNCT
ejpam-3018	233	1	then	then	ADV
ejpam-3018	233	2	,	,	PUNCT
ejpam-3018	233	3	we	we	PRON
ejpam-3018	233	4	have	have	VERB
ejpam-3018	233	5	|g∗(α	|g∗(α	PROPN
ejpam-3018	233	6	,	,	PUNCT
ejpam-3018	233	7	β)n	β)n	ADJ
ejpam-3018	233	8	,	,	PUNCT
ejpam-3018	233	9	c	c	PROPN
ejpam-3018	233	10	(	(	PUNCT
ejpam-3018	233	11	f	f	PROPN
ejpam-3018	233	12	;	;	PUNCT
ejpam-3018	233	13	x)−	x)−	PROPN
ejpam-3018	233	14	f(x)|	f(x)|	VERB
ejpam-3018	233	15	≤	≤	NUM
ejpam-3018	233	16	m	m	VERB
ejpam-3018	233	17	(	(	PUNCT
ejpam-3018	233	18	(	(	PUNCT
ejpam-3018	233	19	γ(α	γ(α	NOUN
ejpam-3018	233	20	,	,	PUNCT
ejpam-3018	233	21	β)n	β)n	NOUN
ejpam-3018	233	22	,	,	PUNCT
ejpam-3018	233	23	c	c	PROPN
ejpam-3018	233	24	(	(	PUNCT
ejpam-3018	233	25	x	x	NOUN
ejpam-3018	233	26	)	)	PUNCT
ejpam-3018	233	27	)	)	PUNCT
ejpam-3018	233	28	α/2	α/2	NOUN
ejpam-3018	233	29	+	+	CCONJ
ejpam-3018	233	30	2dα(x	2dα(x	NUM
ejpam-3018	233	31	,	,	PUNCT
ejpam-3018	233	32	e	e	NOUN
ejpam-3018	233	33	)	)	PUNCT
ejpam-3018	233	34	)	)	PUNCT
ejpam-3018	233	35	,	,	PUNCT
ejpam-3018	233	36	x	x	PUNCT
ejpam-3018	233	37	∈	∈	PROPN
ejpam-3018	234	1	[	[	X
ejpam-3018	234	2	0,∞	0,∞	NOUN
ejpam-3018	234	3	)	)	PUNCT
ejpam-3018	234	4	,	,	PUNCT
ejpam-3018	234	5	where	where	SCONJ
ejpam-3018	234	6	m	m	NOUN
ejpam-3018	234	7	is	be	AUX
ejpam-3018	234	8	a	a	DET
ejpam-3018	234	9	constant	constant	ADJ
ejpam-3018	234	10	depending	depend	VERB
ejpam-3018	234	11	on	on	ADP
ejpam-3018	234	12	α	α	PROPN
ejpam-3018	234	13	and	and	CCONJ
ejpam-3018	234	14	f	f	PROPN
ejpam-3018	234	15	and	and	CCONJ
ejpam-3018	234	16	d(x	d(x	PROPN
ejpam-3018	234	17	,	,	PUNCT
ejpam-3018	234	18	e	e	NOUN
ejpam-3018	234	19	)	)	PUNCT
ejpam-3018	234	20	is	be	AUX
ejpam-3018	234	21	the	the	DET
ejpam-3018	234	22	distance	distance	NOUN
ejpam-3018	234	23	between	between	ADP
ejpam-3018	234	24	x	x	PUNCT
ejpam-3018	234	25	and	and	CCONJ
ejpam-3018	234	26	e	e	NOUN
ejpam-3018	234	27	defined	define	VERB
ejpam-3018	234	28	as	as	ADP
ejpam-3018	234	29	d(x	d(x	PROPN
ejpam-3018	234	30	,	,	PUNCT
ejpam-3018	234	31	e	e	NOUN
ejpam-3018	234	32	)	)	PUNCT
ejpam-3018	234	33	=	=	SYM
ejpam-3018	235	1	inf{|t−	inf{|t−	PROPN
ejpam-3018	235	2	x|	x|	NOUN
ejpam-3018	235	3	:	:	PUNCT
ejpam-3018	236	1	t	t	PROPN
ejpam-3018	236	2	∈	∈	PROPN
ejpam-3018	236	3	e	e	X
ejpam-3018	236	4	}	}	PUNCT
ejpam-3018	236	5	.	.	PUNCT
ejpam-3018	237	1	proof	proof	NOUN
ejpam-3018	237	2	.	.	PUNCT
ejpam-3018	238	1	let	let	VERB
ejpam-3018	238	2	e	e	PRON
ejpam-3018	238	3	be	be	AUX
ejpam-3018	238	4	the	the	DET
ejpam-3018	238	5	closure	closure	NOUN
ejpam-3018	238	6	of	of	ADP
ejpam-3018	238	7	e	e	NOUN
ejpam-3018	238	8	in	in	ADP
ejpam-3018	238	9	[	[	X
ejpam-3018	238	10	0,∞	0,∞	NOUN
ejpam-3018	238	11	)	)	PUNCT
ejpam-3018	238	12	.	.	PUNCT
ejpam-3018	239	1	then	then	ADV
ejpam-3018	239	2	,	,	PUNCT
ejpam-3018	239	3	there	there	PRON
ejpam-3018	239	4	exists	exist	VERB
ejpam-3018	239	5	at	at	ADV
ejpam-3018	239	6	least	least	ADV
ejpam-3018	239	7	one	one	NUM
ejpam-3018	239	8	point	point	NOUN
ejpam-3018	239	9	x0	x0	PROPN
ejpam-3018	239	10	∈	∈	PROPN
ejpam-3018	239	11	e	e	NOUN
ejpam-3018	239	12	such	such	ADJ
ejpam-3018	239	13	that	that	DET
ejpam-3018	239	14	d(x	d(x	NOUN
ejpam-3018	239	15	,	,	PUNCT
ejpam-3018	239	16	e	e	NOUN
ejpam-3018	239	17	)	)	PUNCT
ejpam-3018	239	18	=	=	SYM
ejpam-3018	239	19	|x−	|x−	PROPN
ejpam-3018	239	20	x0|	x0|	PROPN
ejpam-3018	239	21	.	.	PUNCT
ejpam-3018	240	1	by	by	ADP
ejpam-3018	240	2	our	our	PRON
ejpam-3018	240	3	hypothesis	hypothesis	NOUN
ejpam-3018	240	4	and	and	CCONJ
ejpam-3018	240	5	the	the	DET
ejpam-3018	240	6	monotonicity	monotonicity	NOUN
ejpam-3018	240	7	of	of	ADP
ejpam-3018	240	8	g	g	PROPN
ejpam-3018	240	9	∗(α	∗(α	PROPN
ejpam-3018	240	10	,	,	PUNCT
ejpam-3018	240	11	β	β	NOUN
ejpam-3018	240	12	)	)	PUNCT
ejpam-3018	240	13	n	n	CCONJ
ejpam-3018	240	14	,	,	PUNCT
ejpam-3018	240	15	c	c	X
ejpam-3018	240	16	,	,	PUNCT
ejpam-3018	240	17	we	we	PRON
ejpam-3018	240	18	get	get	VERB
ejpam-3018	240	19	|g∗(α	|g∗(α	PROPN
ejpam-3018	240	20	,	,	PUNCT
ejpam-3018	240	21	β)n	β)n	ADJ
ejpam-3018	240	22	,	,	PUNCT
ejpam-3018	240	23	c	c	PROPN
ejpam-3018	240	24	(	(	PUNCT
ejpam-3018	240	25	f	f	PROPN
ejpam-3018	240	26	;	;	PUNCT
ejpam-3018	240	27	x)−	x)−	PROPN
ejpam-3018	240	28	f(x)|	f(x)|	VERB
ejpam-3018	240	29	≤	≤	ADJ
ejpam-3018	240	30	g∗(α	g∗(α	NOUN
ejpam-3018	240	31	,	,	PUNCT
ejpam-3018	240	32	β)n	β)n	NOUN
ejpam-3018	240	33	,	,	PUNCT
ejpam-3018	240	34	c	c	PROPN
ejpam-3018	240	35	(	(	PUNCT
ejpam-3018	240	36	|f(t)−	|f(t)−	PROPN
ejpam-3018	240	37	f(x0)|;x	f(x0)|;x	PRON
ejpam-3018	240	38	)	)	PUNCT
ejpam-3018	241	1	+	+	ADV
ejpam-3018	241	2	g∗(α	g∗(α	NOUN
ejpam-3018	241	3	,	,	PUNCT
ejpam-3018	241	4	β)n	β)n	NOUN
ejpam-3018	241	5	,	,	PUNCT
ejpam-3018	241	6	c	c	PROPN
ejpam-3018	241	7	(	(	PUNCT
ejpam-3018	241	8	|f(x)−	|f(x)−	NOUN
ejpam-3018	241	9	f(x0)|;x	f(x0)|;x	NOUN
ejpam-3018	241	10	)	)	PUNCT
ejpam-3018	241	11	≤	≤	NUM
ejpam-3018	241	12	m	m	VERB
ejpam-3018	241	13	(	(	PUNCT
ejpam-3018	241	14	g∗(α	g∗(α	PROPN
ejpam-3018	241	15	,	,	PUNCT
ejpam-3018	241	16	β)n	β)n	NOUN
ejpam-3018	241	17	,	,	PUNCT
ejpam-3018	241	18	c	c	PROPN
ejpam-3018	241	19	(	(	PUNCT
ejpam-3018	241	20	|t−	|t−	PROPN
ejpam-3018	241	21	x0|α;x	x0|α;x	PROPN
ejpam-3018	241	22	)	)	PUNCT
ejpam-3018	242	1	+	+	NUM
ejpam-3018	242	2	|x−	|x−	NOUN
ejpam-3018	242	3	x0|α	x0|α	PROPN
ejpam-3018	242	4	)	)	PUNCT
ejpam-3018	243	1	≤	≤	NUM
ejpam-3018	243	2	m	m	VERB
ejpam-3018	243	3	(	(	PUNCT
ejpam-3018	243	4	g∗(α	g∗(α	PROPN
ejpam-3018	243	5	,	,	PUNCT
ejpam-3018	243	6	β)n	β)n	NOUN
ejpam-3018	243	7	,	,	PUNCT
ejpam-3018	243	8	c	c	PROPN
ejpam-3018	243	9	(	(	PUNCT
ejpam-3018	243	10	|t−	|t−	PROPN
ejpam-3018	243	11	x|α;x	x|α;x	PROPN
ejpam-3018	243	12	)	)	PUNCT
ejpam-3018	244	1	+	+	CCONJ
ejpam-3018	244	2	2|x−	2|x−	NUM
ejpam-3018	244	3	x0|α	x0|α	PRON
ejpam-3018	244	4	)	)	PUNCT
ejpam-3018	244	5	.	.	PUNCT
ejpam-3018	245	1	now	now	ADV
ejpam-3018	245	2	,	,	PUNCT
ejpam-3018	245	3	applying	apply	VERB
ejpam-3018	245	4	hölder	hölder	NOUN
ejpam-3018	245	5	’s	’s	PART
ejpam-3018	245	6	inequality	inequality	NOUN
ejpam-3018	245	7	with	with	ADP
ejpam-3018	245	8	p	p	NOUN
ejpam-3018	245	9	=	=	PROPN
ejpam-3018	245	10	2	2	NUM
ejpam-3018	245	11	α	α	NOUN
ejpam-3018	245	12	and	and	CCONJ
ejpam-3018	245	13	1	1	NUM
ejpam-3018	245	14	q	q	NOUN
ejpam-3018	245	15	=	=	SYM
ejpam-3018	245	16	1−	1−	NUM
ejpam-3018	245	17	1	1	NUM
ejpam-3018	245	18	p	p	NOUN
ejpam-3018	245	19	,	,	PUNCT
ejpam-3018	245	20	we	we	PRON
ejpam-3018	245	21	obtain	obtain	VERB
ejpam-3018	245	22	|g∗(α	|g∗(α	NOUN
ejpam-3018	245	23	,	,	PUNCT
ejpam-3018	245	24	β)n	β)n	ADJ
ejpam-3018	245	25	,	,	PUNCT
ejpam-3018	245	26	c	c	NOUN
ejpam-3018	245	27	(	(	PUNCT
ejpam-3018	245	28	(	(	PUNCT
ejpam-3018	245	29	f	f	X
ejpam-3018	245	30	;	;	PUNCT
ejpam-3018	246	1	x)−	x)−	PROPN
ejpam-3018	246	2	f(x)|	f(x)|	VERB
ejpam-3018	246	3	≤m	≤m	NOUN
ejpam-3018	246	4	(	(	PUNCT
ejpam-3018	246	5	{	{	PUNCT
ejpam-3018	246	6	g∗(α	g∗(α	PROPN
ejpam-3018	246	7	,	,	PUNCT
ejpam-3018	246	8	β)n	β)n	NOUN
ejpam-3018	246	9	,	,	PUNCT
ejpam-3018	246	10	c	c	PROPN
ejpam-3018	246	11	(	(	PUNCT
ejpam-3018	246	12	|t−	|t−	PROPN
ejpam-3018	246	13	x|2;x)}α/2	x|2;x)}α/2	PROPN
ejpam-3018	247	1	+	+	CCONJ
ejpam-3018	247	2	2dα(x	2dα(x	NUM
ejpam-3018	247	3	,	,	PUNCT
ejpam-3018	247	4	e	e	NOUN
ejpam-3018	247	5	)	)	PUNCT
ejpam-3018	247	6	)	)	PUNCT
ejpam-3018	247	7	,	,	PUNCT
ejpam-3018	248	1	from	from	ADP
ejpam-3018	248	2	which	which	PRON
ejpam-3018	248	3	the	the	DET
ejpam-3018	248	4	desired	desire	VERB
ejpam-3018	248	5	result	result	NOUN
ejpam-3018	248	6	immediate	immediate	ADJ
ejpam-3018	248	7	.	.	PUNCT
ejpam-3018	249	1	next	next	ADV
ejpam-3018	249	2	,	,	PUNCT
ejpam-3018	249	3	we	we	PRON
ejpam-3018	249	4	obtain	obtain	VERB
ejpam-3018	249	5	the	the	DET
ejpam-3018	249	6	local	local	ADJ
ejpam-3018	249	7	direct	direct	ADJ
ejpam-3018	249	8	estimate	estimate	NOUN
ejpam-3018	249	9	of	of	ADP
ejpam-3018	249	10	the	the	DET
ejpam-3018	249	11	operators	operator	NOUN
ejpam-3018	249	12	defined	define	VERB
ejpam-3018	249	13	in	in	ADP
ejpam-3018	249	14	(	(	PUNCT
ejpam-3018	249	15	4	4	NUM
ejpam-3018	249	16	)	)	PUNCT
ejpam-3018	249	17	,	,	PUNCT
ejpam-3018	249	18	using	use	VERB
ejpam-3018	249	19	the	the	DET
ejpam-3018	249	20	lipschitz	lipschitz	ADJ
ejpam-3018	249	21	-	-	PUNCT
ejpam-3018	249	22	type	type	NOUN
ejpam-3018	249	23	maximal	maximal	ADJ
ejpam-3018	249	24	function	function	NOUN
ejpam-3018	249	25	of	of	ADP
ejpam-3018	249	26	order	order	NOUN
ejpam-3018	249	27	α	α	PRON
ejpam-3018	249	28	introduced	introduce	VERB
ejpam-3018	249	29	by	by	ADP
ejpam-3018	249	30	b.	b.	PROPN
ejpam-3018	249	31	lenze	lenze	PROPN
ejpam-3018	250	1	[	[	X
ejpam-3018	250	2	19	19	NUM
ejpam-3018	250	3	]	]	PUNCT
ejpam-3018	250	4	as	as	ADP
ejpam-3018	250	5	ω̃α(f	ω̃α(f	PROPN
ejpam-3018	250	6	,	,	PUNCT
ejpam-3018	250	7	x	x	NOUN
ejpam-3018	250	8	)	)	PUNCT
ejpam-3018	250	9	=	=	SYM
ejpam-3018	250	10	sup	sup	NOUN
ejpam-3018	250	11	t6	t6	PROPN
ejpam-3018	250	12	=	=	PROPN
ejpam-3018	250	13	x	x	PROPN
ejpam-3018	250	14	,	,	PUNCT
ejpam-3018	250	15	t∈[0,∞	t∈[0,∞	NOUN
ejpam-3018	250	16	)	)	PUNCT
ejpam-3018	250	17	|f(t)−	|f(t)−	PROPN
ejpam-3018	250	18	f(x)|	f(x)|	VERB
ejpam-3018	250	19	|t−	|t−	PROPN
ejpam-3018	250	20	x|α	x|α	PUNCT
ejpam-3018	251	1	,	,	PUNCT
ejpam-3018	251	2	x	x	PUNCT
ejpam-3018	251	3	∈	∈	PROPN
ejpam-3018	251	4	[	[	X
ejpam-3018	251	5	0,∞	0,∞	NOUN
ejpam-3018	251	6	)	)	PUNCT
ejpam-3018	251	7	and	and	CCONJ
ejpam-3018	251	8	α	α	PRON
ejpam-3018	251	9	∈	∈	PROPN
ejpam-3018	251	10	(	(	PUNCT
ejpam-3018	251	11	0	0	NUM
ejpam-3018	251	12	,	,	PUNCT
ejpam-3018	251	13	1	1	NUM
ejpam-3018	251	14	]	]	PUNCT
ejpam-3018	251	15	.	.	PUNCT
ejpam-3018	252	1	(	(	PUNCT
ejpam-3018	252	2	17	17	NUM
ejpam-3018	252	3	)	)	PUNCT
ejpam-3018	252	4	a.	a.	NOUN
ejpam-3018	252	5	kumar	kumar	PROPN
ejpam-3018	252	6	,	,	PUNCT
ejpam-3018	252	7	v.	v.	PROPN
ejpam-3018	252	8	n.	n.	PROPN
ejpam-3018	252	9	mishra	mishra	PROPN
ejpam-3018	252	10	,	,	PUNCT
ejpam-3018	252	11	d.	d.	PROPN
ejpam-3018	252	12	tapiawala	tapiawala	PROPN
ejpam-3018	252	13	/	/	SYM
ejpam-3018	252	14	eur	eur	PROPN
ejpam-3018	252	15	.	.	PUNCT
ejpam-3018	253	1	j.	j.	PROPN
ejpam-3018	253	2	pure	pure	PROPN
ejpam-3018	253	3	appl	appl	PROPN
ejpam-3018	253	4	.	.	PROPN
ejpam-3018	253	5	math	math	PROPN
ejpam-3018	253	6	,	,	PUNCT
ejpam-3018	253	7	10	10	NUM
ejpam-3018	253	8	(	(	PUNCT
ejpam-3018	253	9	4	4	NUM
ejpam-3018	253	10	)	)	PUNCT
ejpam-3018	253	11	(	(	PUNCT
ejpam-3018	253	12	2017	2017	NUM
ejpam-3018	253	13	)	)	PUNCT
ejpam-3018	253	14	,	,	PUNCT
ejpam-3018	253	15	890	890	NUM
ejpam-3018	253	16	-	-	SYM
ejpam-3018	253	17	907	907	NUM
ejpam-3018	253	18	900	900	NUM
ejpam-3018	253	19	theorem	theorem	NOUN
ejpam-3018	253	20	10	10	NUM
ejpam-3018	253	21	.	.	PUNCT
ejpam-3018	254	1	let	let	VERB
ejpam-3018	254	2	f	f	PROPN
ejpam-3018	254	3	∈	∈	PROPN
ejpam-3018	254	4	cb[0,∞	cb[0,∞	PROPN
ejpam-3018	254	5	)	)	PUNCT
ejpam-3018	254	6	and	and	CCONJ
ejpam-3018	254	7	0	0	NUM
ejpam-3018	254	8	<	<	X
ejpam-3018	254	9	α	α	X
ejpam-3018	254	10	≤	≤	NUM
ejpam-3018	254	11	1	1	NUM
ejpam-3018	254	12	.	.	PUNCT
ejpam-3018	255	1	then	then	ADV
ejpam-3018	255	2	,	,	PUNCT
ejpam-3018	255	3	for	for	ADP
ejpam-3018	255	4	all	all	DET
ejpam-3018	255	5	x	x	SYM
ejpam-3018	255	6	∈	∈	PROPN
ejpam-3018	256	1	[	[	X
ejpam-3018	256	2	0,∞	0,∞	NOUN
ejpam-3018	256	3	)	)	PUNCT
ejpam-3018	256	4	we	we	PRON
ejpam-3018	256	5	have	have	VERB
ejpam-3018	256	6	|g∗(α	|g∗(α	PROPN
ejpam-3018	256	7	,	,	PUNCT
ejpam-3018	256	8	β)n	β)n	ADJ
ejpam-3018	256	9	,	,	PUNCT
ejpam-3018	256	10	c	c	PROPN
ejpam-3018	256	11	(	(	PUNCT
ejpam-3018	256	12	f	f	PROPN
ejpam-3018	256	13	;	;	PUNCT
ejpam-3018	256	14	x)−	x)−	PROPN
ejpam-3018	256	15	f(x)|	f(x)|	VERB
ejpam-3018	256	16	≤	≤	NUM
ejpam-3018	256	17	ω̃α(f	ω̃α(f	NOUN
ejpam-3018	256	18	,	,	PUNCT
ejpam-3018	256	19	x	x	X
ejpam-3018	256	20	)	)	PUNCT
ejpam-3018	256	21	(	(	PUNCT
ejpam-3018	256	22	γ(α	γ(α	PROPN
ejpam-3018	256	23	,	,	PUNCT
ejpam-3018	256	24	β)n	β)n	NOUN
ejpam-3018	256	25	,	,	PUNCT
ejpam-3018	256	26	c	c	PROPN
ejpam-3018	256	27	(	(	PUNCT
ejpam-3018	256	28	x	x	NOUN
ejpam-3018	256	29	)	)	PUNCT
ejpam-3018	256	30	)	)	PUNCT
ejpam-3018	256	31	α/2	α/2	NOUN
ejpam-3018	256	32	.	.	PUNCT
ejpam-3018	257	1	proof	proof	NOUN
ejpam-3018	257	2	.	.	PUNCT
ejpam-3018	258	1	from	from	ADP
ejpam-3018	258	2	the	the	DET
ejpam-3018	258	3	equation	equation	NOUN
ejpam-3018	258	4	(	(	PUNCT
ejpam-3018	258	5	17	17	NUM
ejpam-3018	258	6	)	)	PUNCT
ejpam-3018	258	7	,	,	PUNCT
ejpam-3018	258	8	we	we	PRON
ejpam-3018	258	9	have	have	VERB
ejpam-3018	258	10	|g∗(α	|g∗(α	PROPN
ejpam-3018	258	11	,	,	PUNCT
ejpam-3018	258	12	β)n	β)n	ADJ
ejpam-3018	258	13	,	,	PUNCT
ejpam-3018	258	14	c	c	PROPN
ejpam-3018	258	15	(	(	PUNCT
ejpam-3018	258	16	f	f	PROPN
ejpam-3018	258	17	;	;	PUNCT
ejpam-3018	258	18	x)−	x)−	PROPN
ejpam-3018	258	19	f(x)|	f(x)|	VERB
ejpam-3018	258	20	≤	≤	NUM
ejpam-3018	258	21	ω̃α(f	ω̃α(f	NOUN
ejpam-3018	258	22	,	,	PUNCT
ejpam-3018	258	23	x)g∗(α	x)g∗(α	NUM
ejpam-3018	258	24	,	,	PUNCT
ejpam-3018	258	25	β)n	β)n	NOUN
ejpam-3018	258	26	,	,	PUNCT
ejpam-3018	258	27	c	c	PROPN
ejpam-3018	258	28	(	(	PUNCT
ejpam-3018	258	29	|t−	|t−	PROPN
ejpam-3018	258	30	x|α;x	x|α;x	PROPN
ejpam-3018	258	31	)	)	PUNCT
ejpam-3018	258	32	.	.	PUNCT
ejpam-3018	259	1	applying	apply	VERB
ejpam-3018	259	2	the	the	DET
ejpam-3018	259	3	hölder	hölder	NOUN
ejpam-3018	259	4	’s	’s	PART
ejpam-3018	259	5	inequality	inequality	NOUN
ejpam-3018	259	6	with	with	ADP
ejpam-3018	259	7	p	p	NOUN
ejpam-3018	259	8	=	=	PROPN
ejpam-3018	259	9	2	2	NUM
ejpam-3018	259	10	α	α	NOUN
ejpam-3018	259	11	and	and	CCONJ
ejpam-3018	259	12	1	1	NUM
ejpam-3018	259	13	q	q	NOUN
ejpam-3018	259	14	=	=	SYM
ejpam-3018	259	15	1−	1−	NUM
ejpam-3018	259	16	1	1	NUM
ejpam-3018	259	17	p	p	NOUN
ejpam-3018	259	18	,	,	PUNCT
ejpam-3018	259	19	we	we	PRON
ejpam-3018	259	20	get	get	VERB
ejpam-3018	259	21	|g∗(α	|g∗(α	PROPN
ejpam-3018	259	22	,	,	PUNCT
ejpam-3018	259	23	β)n	β)n	ADJ
ejpam-3018	259	24	,	,	PUNCT
ejpam-3018	259	25	c	c	PROPN
ejpam-3018	259	26	(	(	PUNCT
ejpam-3018	259	27	f	f	PROPN
ejpam-3018	259	28	;	;	PUNCT
ejpam-3018	259	29	x)−	x)−	PROPN
ejpam-3018	259	30	f(x)|	f(x)|	VERB
ejpam-3018	259	31	≤	≤	NUM
ejpam-3018	259	32	ω̃α(f	ω̃α(f	NOUN
ejpam-3018	259	33	,	,	PUNCT
ejpam-3018	259	34	x)g∗(α	x)g∗(α	NUM
ejpam-3018	259	35	,	,	PUNCT
ejpam-3018	259	36	β)n	β)n	NOUN
ejpam-3018	259	37	,	,	PUNCT
ejpam-3018	259	38	c	c	NOUN
ejpam-3018	259	39	(	(	PUNCT
ejpam-3018	259	40	(	(	PUNCT
ejpam-3018	259	41	t−	t−	PROPN
ejpam-3018	259	42	x)2;x	x)2;x	NUM
ejpam-3018	259	43	)	)	PUNCT
ejpam-3018	260	1	α	α	PROPN
ejpam-3018	260	2	2	2	NUM
ejpam-3018	260	3	≤	≤	NUM
ejpam-3018	260	4	ω̃α(f	ω̃α(f	NOUN
ejpam-3018	260	5	,	,	PUNCT
ejpam-3018	260	6	x	x	X
ejpam-3018	260	7	)	)	PUNCT
ejpam-3018	260	8	(	(	PUNCT
ejpam-3018	260	9	γ(α	γ(α	PROPN
ejpam-3018	260	10	,	,	PUNCT
ejpam-3018	260	11	β)n	β)n	NOUN
ejpam-3018	260	12	,	,	PUNCT
ejpam-3018	260	13	c	c	PROPN
ejpam-3018	260	14	(	(	PUNCT
ejpam-3018	260	15	x	x	NOUN
ejpam-3018	260	16	)	)	PUNCT
ejpam-3018	260	17	)	)	PUNCT
ejpam-3018	260	18	α/2	α/2	NUM
ejpam-3018	260	19	.	.	PUNCT
ejpam-3018	261	1	thus	thus	ADV
ejpam-3018	261	2	,	,	PUNCT
ejpam-3018	261	3	the	the	DET
ejpam-3018	261	4	proof	proof	NOUN
ejpam-3018	261	5	is	be	AUX
ejpam-3018	261	6	completed	complete	VERB
ejpam-3018	261	7	.	.	PUNCT
ejpam-3018	262	1	for	for	ADP
ejpam-3018	262	2	a	a	DET
ejpam-3018	262	3	,	,	PUNCT
ejpam-3018	262	4	b	b	X
ejpam-3018	262	5	>	>	X
ejpam-3018	262	6	0	0	NUM
ejpam-3018	262	7	,	,	PUNCT
ejpam-3018	262	8	özarslan	özarslan	PROPN
ejpam-3018	262	9	and	and	CCONJ
ejpam-3018	262	10	aktuğlu	aktuğlu	PROPN
ejpam-3018	262	11	[	[	X
ejpam-3018	262	12	30	30	NUM
ejpam-3018	262	13	]	]	PUNCT
ejpam-3018	262	14	consider	consider	VERB
ejpam-3018	262	15	the	the	DET
ejpam-3018	262	16	lipschitz	lipschitz	NOUN
ejpam-3018	262	17	-	-	PUNCT
ejpam-3018	262	18	type	type	NOUN
ejpam-3018	262	19	space	space	NOUN
ejpam-3018	262	20	with	with	ADP
ejpam-3018	262	21	two	two	NUM
ejpam-3018	262	22	parameters	parameter	NOUN
ejpam-3018	262	23	:	:	PUNCT
ejpam-3018	262	24	lip	lip	NOUN
ejpam-3018	262	25	(	(	PUNCT
ejpam-3018	262	26	a	a	DET
ejpam-3018	262	27	,	,	PUNCT
ejpam-3018	262	28	b	b	NOUN
ejpam-3018	262	29	)	)	PUNCT
ejpam-3018	262	30	m	m	VERB
ejpam-3018	262	31	(	(	PUNCT
ejpam-3018	262	32	α	α	NOUN
ejpam-3018	262	33	)	)	PUNCT
ejpam-3018	262	34	=	=	PUNCT
ejpam-3018	263	1	(	(	PUNCT
ejpam-3018	263	2	f	f	PROPN
ejpam-3018	263	3	∈	∈	PROPN
ejpam-3018	263	4	c[0,∞	c[0,∞	PROPN
ejpam-3018	263	5	)	)	PUNCT
ejpam-3018	263	6	:	:	PUNCT
ejpam-3018	263	7	|f(t)−	|f(t)−	PROPN
ejpam-3018	263	8	f(x)|	f(x)|	VERB
ejpam-3018	263	9	≤m	≤m	PROPN
ejpam-3018	263	10	|t−	|t−	PROPN
ejpam-3018	263	11	x|α	x|α	PUNCT
ejpam-3018	264	1	(	(	PUNCT
ejpam-3018	264	2	t+	t+	NOUN
ejpam-3018	264	3	ax2	ax2	NOUN
ejpam-3018	264	4	+	+	CCONJ
ejpam-3018	264	5	bx)α/2	bx)α/2	ADP
ejpam-3018	264	6	;	;	PUNCT
ejpam-3018	264	7	x	x	X
ejpam-3018	264	8	,	,	PUNCT
ejpam-3018	264	9	t	t	PROPN
ejpam-3018	264	10	∈	∈	PROPN
ejpam-3018	265	1	[	[	X
ejpam-3018	265	2	0,∞	0,∞	NOUN
ejpam-3018	265	3	)	)	PUNCT
ejpam-3018	265	4	)	)	PUNCT
ejpam-3018	266	1	,	,	PUNCT
ejpam-3018	266	2	where	where	SCONJ
ejpam-3018	266	3	m	m	NOUN
ejpam-3018	266	4	is	be	AUX
ejpam-3018	266	5	any	any	DET
ejpam-3018	266	6	positive	positive	ADJ
ejpam-3018	266	7	constant	constant	ADJ
ejpam-3018	266	8	and	and	CCONJ
ejpam-3018	266	9	0	0	NUM
ejpam-3018	266	10	<	<	X
ejpam-3018	266	11	α	α	PROPN
ejpam-3018	266	12	≤	≤	NUM
ejpam-3018	266	13	1	1	NUM
ejpam-3018	266	14	.	.	PUNCT
ejpam-3018	267	1	theorem	theorem	VERB
ejpam-3018	267	2	11	11	NUM
ejpam-3018	267	3	.	.	PUNCT
ejpam-3018	268	1	for	for	ADP
ejpam-3018	268	2	f	f	PROPN
ejpam-3018	268	3	∈	∈	PROPN
ejpam-3018	268	4	lip(a	lip(a	PROPN
ejpam-3018	268	5	,	,	PUNCT
ejpam-3018	268	6	b)m	b)m	X
ejpam-3018	268	7	(	(	PUNCT
ejpam-3018	268	8	α	α	NOUN
ejpam-3018	268	9	)	)	PUNCT
ejpam-3018	268	10	.	.	PUNCT
ejpam-3018	269	1	then	then	ADV
ejpam-3018	269	2	,	,	PUNCT
ejpam-3018	269	3	for	for	ADP
ejpam-3018	269	4	all	all	PRON
ejpam-3018	269	5	x	x	SYM
ejpam-3018	269	6	>	>	X
ejpam-3018	269	7	0	0	NUM
ejpam-3018	269	8	,	,	PUNCT
ejpam-3018	269	9	we	we	PRON
ejpam-3018	269	10	have	have	VERB
ejpam-3018	269	11	|g∗(α	|g∗(α	PROPN
ejpam-3018	269	12	,	,	PUNCT
ejpam-3018	269	13	β)n	β)n	ADJ
ejpam-3018	269	14	,	,	PUNCT
ejpam-3018	269	15	c	c	PROPN
ejpam-3018	269	16	(	(	PUNCT
ejpam-3018	269	17	f	f	PROPN
ejpam-3018	269	18	;	;	PUNCT
ejpam-3018	269	19	x)−	x)−	PROPN
ejpam-3018	269	20	f(x)|	f(x)|	VERB
ejpam-3018	269	21	≤m	≤m	NOUN
ejpam-3018	269	22	(	(	PUNCT
ejpam-3018	269	23	γ	γ	X
ejpam-3018	269	24	(	(	PUNCT
ejpam-3018	269	25	α	α	PROPN
ejpam-3018	269	26	,	,	PUNCT
ejpam-3018	269	27	β	β	NOUN
ejpam-3018	269	28	)	)	PUNCT
ejpam-3018	269	29	n	n	CCONJ
ejpam-3018	269	30	,	,	PUNCT
ejpam-3018	269	31	c	c	PROPN
ejpam-3018	269	32	(	(	PUNCT
ejpam-3018	269	33	x	x	NOUN
ejpam-3018	269	34	)	)	PUNCT
ejpam-3018	269	35	ax2	ax2	NOUN
ejpam-3018	269	36	+	+	CCONJ
ejpam-3018	269	37	bx	bx	PROPN
ejpam-3018	269	38	)	)	PUNCT
ejpam-3018	269	39	α/2	α/2	X
ejpam-3018	269	40	.	.	PUNCT
ejpam-3018	270	1	proof	proof	NOUN
ejpam-3018	270	2	.	.	PUNCT
ejpam-3018	271	1	first	first	ADV
ejpam-3018	271	2	we	we	PRON
ejpam-3018	271	3	prove	prove	VERB
ejpam-3018	271	4	the	the	DET
ejpam-3018	271	5	theorem	theorem	NOUN
ejpam-3018	271	6	for	for	ADP
ejpam-3018	271	7	α	α	NOUN
ejpam-3018	271	8	=	=	SYM
ejpam-3018	271	9	1	1	NUM
ejpam-3018	271	10	.	.	PUNCT
ejpam-3018	272	1	then	then	ADV
ejpam-3018	272	2	,	,	PUNCT
ejpam-3018	272	3	for	for	ADP
ejpam-3018	272	4	f	f	PROPN
ejpam-3018	272	5	∈	∈	PROPN
ejpam-3018	272	6	lip(a	lip(a	PROPN
ejpam-3018	272	7	,	,	PUNCT
ejpam-3018	272	8	b)m	b)m	X
ejpam-3018	272	9	(	(	PUNCT
ejpam-3018	272	10	1	1	NUM
ejpam-3018	272	11	)	)	PUNCT
ejpam-3018	272	12	,	,	PUNCT
ejpam-3018	272	13	and	and	CCONJ
ejpam-3018	272	14	x	x	PUNCT
ejpam-3018	272	15	∈	∈	PROPN
ejpam-3018	273	1	[	[	X
ejpam-3018	273	2	0,∞	0,∞	NOUN
ejpam-3018	273	3	)	)	PUNCT
ejpam-3018	273	4	,	,	PUNCT
ejpam-3018	273	5	we	we	PRON
ejpam-3018	273	6	have	have	VERB
ejpam-3018	273	7	|g∗(α	|g∗(α	PROPN
ejpam-3018	273	8	,	,	PUNCT
ejpam-3018	273	9	β)n	β)n	ADJ
ejpam-3018	273	10	,	,	PUNCT
ejpam-3018	273	11	c	c	PROPN
ejpam-3018	273	12	(	(	PUNCT
ejpam-3018	273	13	f	f	PROPN
ejpam-3018	273	14	;	;	PUNCT
ejpam-3018	273	15	x)−	x)−	PROPN
ejpam-3018	273	16	f(x)|	f(x)|	VERB
ejpam-3018	273	17	≤	≤	ADJ
ejpam-3018	273	18	g∗(α	g∗(α	NOUN
ejpam-3018	273	19	,	,	PUNCT
ejpam-3018	273	20	β)n	β)n	NOUN
ejpam-3018	273	21	,	,	PUNCT
ejpam-3018	273	22	c	c	PROPN
ejpam-3018	273	23	(	(	PUNCT
ejpam-3018	273	24	|f(t)−	|f(t)−	ADP
ejpam-3018	273	25	f(x)|;x	f(x)|;x	NOUN
ejpam-3018	273	26	)	)	PUNCT
ejpam-3018	273	27	≤	≤	NOUN
ejpam-3018	273	28	mg∗(α	mg∗(α	NUM
ejpam-3018	273	29	,	,	PUNCT
ejpam-3018	273	30	β)n	β)n	ADJ
ejpam-3018	273	31	,	,	PUNCT
ejpam-3018	273	32	c	c	PROPN
ejpam-3018	273	33	(	(	PUNCT
ejpam-3018	273	34	|t−	|t−	PROPN
ejpam-3018	273	35	x|	x|	PROPN
ejpam-3018	273	36	(	(	PUNCT
ejpam-3018	273	37	t+	t+	NOUN
ejpam-3018	273	38	ax2	ax2	NOUN
ejpam-3018	273	39	+	+	CCONJ
ejpam-3018	273	40	bx)1/2	bx)1/2	PROPN
ejpam-3018	273	41	;	;	PUNCT
ejpam-3018	273	42	x	x	SYM
ejpam-3018	273	43	)	)	PUNCT
ejpam-3018	273	44	≤	≤	NUM
ejpam-3018	274	1	m	m	VERB
ejpam-3018	274	2	(	(	PUNCT
ejpam-3018	274	3	ax2	ax2	NOUN
ejpam-3018	274	4	+	+	CCONJ
ejpam-3018	274	5	bx)1/2	bx)1/2	PROPN
ejpam-3018	274	6	g∗(α	g∗(α	PROPN
ejpam-3018	274	7	,	,	PUNCT
ejpam-3018	274	8	β)n	β)n	NOUN
ejpam-3018	274	9	,	,	PUNCT
ejpam-3018	274	10	c	c	PROPN
ejpam-3018	274	11	(	(	PUNCT
ejpam-3018	274	12	|t−	|t−	PROPN
ejpam-3018	274	13	x|;x	x|;x	PROPN
ejpam-3018	274	14	)	)	PUNCT
ejpam-3018	274	15	.	.	PUNCT
ejpam-3018	275	1	applying	apply	VERB
ejpam-3018	275	2	cauchy	cauchy	NOUN
ejpam-3018	275	3	-	-	PUNCT
ejpam-3018	275	4	schwarz	schwarz	PROPN
ejpam-3018	275	5	inequality	inequality	NOUN
ejpam-3018	275	6	,	,	PUNCT
ejpam-3018	275	7	we	we	PRON
ejpam-3018	275	8	get	get	VERB
ejpam-3018	275	9	|g∗(α	|g∗(α	PROPN
ejpam-3018	275	10	,	,	PUNCT
ejpam-3018	275	11	β)n	β)n	ADJ
ejpam-3018	275	12	,	,	PUNCT
ejpam-3018	275	13	c	c	PROPN
ejpam-3018	275	14	(	(	PUNCT
ejpam-3018	275	15	f	f	PROPN
ejpam-3018	275	16	;	;	PUNCT
ejpam-3018	275	17	x)−	x)−	PROPN
ejpam-3018	275	18	f(x)|	f(x)|	VERB
ejpam-3018	275	19	≤	≤	NUM
ejpam-3018	275	20	m	m	PROPN
ejpam-3018	275	21	(	(	PUNCT
ejpam-3018	275	22	ax2	ax2	NOUN
ejpam-3018	275	23	+	+	CCONJ
ejpam-3018	275	24	bx)1/2	bx)1/2	PROPN
ejpam-3018	275	25	(	(	PUNCT
ejpam-3018	275	26	g∗(α	g∗(α	PROPN
ejpam-3018	275	27	,	,	PUNCT
ejpam-3018	275	28	β)n	β)n	NOUN
ejpam-3018	275	29	,	,	PUNCT
ejpam-3018	275	30	c	c	NOUN
ejpam-3018	275	31	(	(	PUNCT
ejpam-3018	275	32	(	(	PUNCT
ejpam-3018	275	33	t−	t−	PROPN
ejpam-3018	275	34	x)2;x	x)2;x	NUM
ejpam-3018	275	35	)	)	PUNCT
ejpam-3018	275	36	)	)	PUNCT
ejpam-3018	276	1	1/2	1/2	NUM
ejpam-3018	276	2	≤	≤	NUM
ejpam-3018	276	3	m	m	VERB
ejpam-3018	276	4	(	(	PUNCT
ejpam-3018	276	5	γ	γ	X
ejpam-3018	276	6	(	(	PUNCT
ejpam-3018	276	7	α	α	PROPN
ejpam-3018	276	8	,	,	PUNCT
ejpam-3018	276	9	β	β	NOUN
ejpam-3018	276	10	)	)	PUNCT
ejpam-3018	276	11	n	n	CCONJ
ejpam-3018	276	12	,	,	PUNCT
ejpam-3018	276	13	c	c	PROPN
ejpam-3018	276	14	(	(	PUNCT
ejpam-3018	276	15	x	x	NOUN
ejpam-3018	276	16	)	)	PUNCT
ejpam-3018	276	17	ax2	ax2	NOUN
ejpam-3018	276	18	+	+	CCONJ
ejpam-3018	276	19	bx	bx	PROPN
ejpam-3018	276	20	)	)	PUNCT
ejpam-3018	276	21	1/2	1/2	NUM
ejpam-3018	276	22	.	.	PUNCT
ejpam-3018	277	1	a.	a.	PROPN
ejpam-3018	277	2	kumar	kumar	PROPN
ejpam-3018	277	3	,	,	PUNCT
ejpam-3018	277	4	v.	v.	PROPN
ejpam-3018	277	5	n.	n.	PROPN
ejpam-3018	277	6	mishra	mishra	PROPN
ejpam-3018	277	7	,	,	PUNCT
ejpam-3018	277	8	d.	d.	PROPN
ejpam-3018	277	9	tapiawala	tapiawala	PROPN
ejpam-3018	277	10	/	/	SYM
ejpam-3018	277	11	eur	eur	PROPN
ejpam-3018	277	12	.	.	PUNCT
ejpam-3018	278	1	j.	j.	PROPN
ejpam-3018	278	2	pure	pure	PROPN
ejpam-3018	278	3	appl	appl	PROPN
ejpam-3018	278	4	.	.	PROPN
ejpam-3018	278	5	math	math	PROPN
ejpam-3018	278	6	,	,	PUNCT
ejpam-3018	278	7	10	10	NUM
ejpam-3018	278	8	(	(	PUNCT
ejpam-3018	278	9	4	4	NUM
ejpam-3018	278	10	)	)	PUNCT
ejpam-3018	278	11	(	(	PUNCT
ejpam-3018	278	12	2017	2017	NUM
ejpam-3018	278	13	)	)	PUNCT
ejpam-3018	278	14	,	,	PUNCT
ejpam-3018	278	15	890	890	NUM
ejpam-3018	278	16	-	-	SYM
ejpam-3018	278	17	907	907	NUM
ejpam-3018	278	18	901	901	NUM
ejpam-3018	278	19	thus	thus	ADV
ejpam-3018	278	20	the	the	DET
ejpam-3018	278	21	result	result	NOUN
ejpam-3018	278	22	holds	hold	VERB
ejpam-3018	278	23	for	for	ADP
ejpam-3018	278	24	α	α	NOUN
ejpam-3018	278	25	=	=	SYM
ejpam-3018	278	26	1	1	NUM
ejpam-3018	278	27	.	.	PUNCT
ejpam-3018	279	1	now	now	ADV
ejpam-3018	279	2	,	,	PUNCT
ejpam-3018	279	3	we	we	PRON
ejpam-3018	279	4	prove	prove	VERB
ejpam-3018	279	5	that	that	SCONJ
ejpam-3018	279	6	the	the	DET
ejpam-3018	279	7	result	result	NOUN
ejpam-3018	279	8	is	be	AUX
ejpam-3018	279	9	true	true	ADJ
ejpam-3018	279	10	for	for	ADP
ejpam-3018	279	11	0	0	NUM
ejpam-3018	279	12	<	<	X
ejpam-3018	279	13	α	α	X
ejpam-3018	279	14	<	<	X
ejpam-3018	279	15	1	1	NUM
ejpam-3018	279	16	.	.	PUNCT
ejpam-3018	280	1	then	then	ADV
ejpam-3018	280	2	,	,	PUNCT
ejpam-3018	280	3	for	for	ADP
ejpam-3018	280	4	f	f	PROPN
ejpam-3018	280	5	∈	∈	PROPN
ejpam-3018	280	6	lip	lip	NOUN
ejpam-3018	280	7	(	(	PUNCT
ejpam-3018	280	8	a	a	DET
ejpam-3018	280	9	,	,	PUNCT
ejpam-3018	280	10	b	b	NOUN
ejpam-3018	280	11	)	)	PUNCT
ejpam-3018	280	12	m	m	VERB
ejpam-3018	280	13	(	(	PUNCT
ejpam-3018	280	14	α	α	NOUN
ejpam-3018	280	15	)	)	PUNCT
ejpam-3018	280	16	,	,	PUNCT
ejpam-3018	280	17	and	and	CCONJ
ejpam-3018	280	18	x	x	PUNCT
ejpam-3018	280	19	∈	∈	PROPN
ejpam-3018	281	1	[	[	X
ejpam-3018	281	2	0,∞	0,∞	NOUN
ejpam-3018	281	3	)	)	PUNCT
ejpam-3018	281	4	,	,	PUNCT
ejpam-3018	281	5	we	we	PRON
ejpam-3018	281	6	get	get	VERB
ejpam-3018	281	7	|g∗(α	|g∗(α	PROPN
ejpam-3018	281	8	,	,	PUNCT
ejpam-3018	281	9	β)n	β)n	ADJ
ejpam-3018	281	10	,	,	PUNCT
ejpam-3018	281	11	c	c	PROPN
ejpam-3018	281	12	(	(	PUNCT
ejpam-3018	281	13	f	f	PROPN
ejpam-3018	281	14	;	;	PUNCT
ejpam-3018	281	15	x)−	x)−	PROPN
ejpam-3018	281	16	f(x)|	f(x)|	VERB
ejpam-3018	281	17	≤	≤	NUM
ejpam-3018	281	18	m	m	PROPN
ejpam-3018	281	19	(	(	PUNCT
ejpam-3018	281	20	ax2	ax2	NOUN
ejpam-3018	281	21	+	+	CCONJ
ejpam-3018	281	22	bx)α/2	bx)α/2	PUNCT
ejpam-3018	281	23	g∗(α	g∗(α	NOUN
ejpam-3018	281	24	,	,	PUNCT
ejpam-3018	281	25	β)n	β)n	NOUN
ejpam-3018	281	26	,	,	PUNCT
ejpam-3018	281	27	c	c	PROPN
ejpam-3018	281	28	(	(	PUNCT
ejpam-3018	281	29	|t−	|t−	PROPN
ejpam-3018	281	30	x|α;x	x|α;x	PROPN
ejpam-3018	281	31	)	)	PUNCT
ejpam-3018	281	32	.	.	PUNCT
ejpam-3018	282	1	taking	take	VERB
ejpam-3018	282	2	p	p	NOUN
ejpam-3018	282	3	=	=	NOUN
ejpam-3018	282	4	1	1	NUM
ejpam-3018	282	5	α	α	NOUN
ejpam-3018	282	6	and	and	CCONJ
ejpam-3018	282	7	q	q	NOUN
ejpam-3018	283	1	=	=	SYM
ejpam-3018	283	2	p	p	PROPN
ejpam-3018	283	3	p−1	p−1	PROPN
ejpam-3018	283	4	,	,	PUNCT
ejpam-3018	283	5	applying	apply	VERB
ejpam-3018	283	6	the	the	DET
ejpam-3018	283	7	hölders	hölder	NOUN
ejpam-3018	283	8	inequality	inequality	NOUN
ejpam-3018	283	9	,	,	PUNCT
ejpam-3018	283	10	we	we	PRON
ejpam-3018	283	11	have	have	VERB
ejpam-3018	283	12	|g∗(α	|g∗(α	PROPN
ejpam-3018	283	13	,	,	PUNCT
ejpam-3018	283	14	β)n	β)n	ADJ
ejpam-3018	283	15	,	,	PUNCT
ejpam-3018	283	16	c	c	PROPN
ejpam-3018	283	17	(	(	PUNCT
ejpam-3018	283	18	f	f	PROPN
ejpam-3018	283	19	;	;	PUNCT
ejpam-3018	283	20	x)−	x)−	PROPN
ejpam-3018	283	21	f(x)|	f(x)|	VERB
ejpam-3018	283	22	≤	≤	NUM
ejpam-3018	283	23	m	m	PROPN
ejpam-3018	283	24	(	(	PUNCT
ejpam-3018	283	25	ax2	ax2	NOUN
ejpam-3018	283	26	+	+	CCONJ
ejpam-3018	283	27	bx)α/2	bx)α/2	PUNCT
ejpam-3018	283	28	(	(	PUNCT
ejpam-3018	283	29	g∗(α	g∗(α	PROPN
ejpam-3018	283	30	,	,	PUNCT
ejpam-3018	283	31	β)n	β)n	NOUN
ejpam-3018	283	32	,	,	PUNCT
ejpam-3018	283	33	c	c	PROPN
ejpam-3018	283	34	(	(	PUNCT
ejpam-3018	283	35	|t−	|t−	PROPN
ejpam-3018	283	36	x|;x	x|;x	PROPN
ejpam-3018	283	37	)	)	PUNCT
ejpam-3018	283	38	)	)	PUNCT
ejpam-3018	284	1	α	α	X
ejpam-3018	284	2	.	.	PUNCT
ejpam-3018	285	1	finally	finally	ADV
ejpam-3018	285	2	by	by	ADP
ejpam-3018	285	3	cauchy	cauchy	PROPN
ejpam-3018	285	4	-	-	PUNCT
ejpam-3018	285	5	schwarz	schwarz	PROPN
ejpam-3018	285	6	inequality	inequality	NOUN
ejpam-3018	285	7	,	,	PUNCT
ejpam-3018	285	8	we	we	PRON
ejpam-3018	285	9	get	get	VERB
ejpam-3018	285	10	|g∗(α	|g∗(α	PROPN
ejpam-3018	285	11	,	,	PUNCT
ejpam-3018	285	12	β)n	β)n	ADJ
ejpam-3018	285	13	,	,	PUNCT
ejpam-3018	285	14	c	c	PROPN
ejpam-3018	285	15	(	(	PUNCT
ejpam-3018	285	16	f	f	PROPN
ejpam-3018	285	17	;	;	PUNCT
ejpam-3018	285	18	x)−	x)−	PROPN
ejpam-3018	285	19	f(x)|	f(x)|	VERB
ejpam-3018	285	20	≤	≤	NUM
ejpam-3018	285	21	m	m	VERB
ejpam-3018	285	22	(	(	PUNCT
ejpam-3018	285	23	γ	γ	X
ejpam-3018	285	24	(	(	PUNCT
ejpam-3018	285	25	α	α	PROPN
ejpam-3018	285	26	,	,	PUNCT
ejpam-3018	285	27	β	β	NOUN
ejpam-3018	285	28	)	)	PUNCT
ejpam-3018	285	29	n	n	CCONJ
ejpam-3018	285	30	,	,	PUNCT
ejpam-3018	285	31	c	c	PROPN
ejpam-3018	285	32	(	(	PUNCT
ejpam-3018	285	33	x	x	NOUN
ejpam-3018	285	34	)	)	PUNCT
ejpam-3018	285	35	ax2	ax2	NOUN
ejpam-3018	285	36	+	+	CCONJ
ejpam-3018	285	37	bx	bx	PROPN
ejpam-3018	285	38	)	)	PUNCT
ejpam-3018	285	39	α/2	α/2	NUM
ejpam-3018	285	40	.	.	PUNCT
ejpam-3018	286	1	thus	thus	ADV
ejpam-3018	286	2	,	,	PUNCT
ejpam-3018	286	3	the	the	DET
ejpam-3018	286	4	proof	proof	NOUN
ejpam-3018	286	5	is	be	AUX
ejpam-3018	286	6	completed	complete	VERB
ejpam-3018	286	7	.	.	PUNCT
ejpam-3018	287	1	3.5	3.5	NUM
ejpam-3018	287	2	.	.	PUNCT
ejpam-3018	288	1	statistical	statistical	ADJ
ejpam-3018	288	2	convergence	convergence	NOUN
ejpam-3018	288	3	let	let	VERB
ejpam-3018	288	4	a	a	DET
ejpam-3018	288	5	=	=	SYM
ejpam-3018	288	6	(	(	PUNCT
ejpam-3018	288	7	ank	ank	PROPN
ejpam-3018	288	8	)	)	PUNCT
ejpam-3018	288	9	,	,	PUNCT
ejpam-3018	288	10	(	(	PUNCT
ejpam-3018	288	11	n	n	X
ejpam-3018	288	12	,	,	PUNCT
ejpam-3018	288	13	k	k	PROPN
ejpam-3018	288	14	∈	∈	PROPN
ejpam-3018	288	15	n	n	CCONJ
ejpam-3018	288	16	)	)	PUNCT
ejpam-3018	288	17	,	,	PUNCT
ejpam-3018	288	18	be	be	AUX
ejpam-3018	288	19	a	a	DET
ejpam-3018	288	20	non	non	ADJ
ejpam-3018	288	21	-	-	ADJ
ejpam-3018	288	22	negative	negative	ADJ
ejpam-3018	288	23	infinite	infinite	ADJ
ejpam-3018	288	24	summability	summability	NOUN
ejpam-3018	288	25	matrix	matrix	NOUN
ejpam-3018	288	26	.	.	PUNCT
ejpam-3018	289	1	for	for	ADP
ejpam-3018	289	2	a	a	DET
ejpam-3018	289	3	given	give	VERB
ejpam-3018	289	4	sequence	sequence	NOUN
ejpam-3018	289	5	x	x	NOUN
ejpam-3018	289	6	:	:	PUNCT
ejpam-3018	289	7	=	=	SYM
ejpam-3018	289	8	(	(	PUNCT
ejpam-3018	289	9	x)n	x)n	PROPN
ejpam-3018	289	10	,	,	PUNCT
ejpam-3018	289	11	the	the	DET
ejpam-3018	289	12	a	a	DET
ejpam-3018	289	13	-	-	PUNCT
ejpam-3018	289	14	transform	transform	NOUN
ejpam-3018	289	15	of	of	ADP
ejpam-3018	289	16	x	x	PUNCT
ejpam-3018	289	17	denoted	denote	VERB
ejpam-3018	289	18	by	by	ADP
ejpam-3018	289	19	ax	ax	NOUN
ejpam-3018	289	20	:	:	PUNCT
ejpam-3018	289	21	(	(	PUNCT
ejpam-3018	289	22	(	(	PUNCT
ejpam-3018	289	23	ax)n	ax)n	PROPN
ejpam-3018	289	24	)	)	PUNCT
ejpam-3018	289	25	is	be	AUX
ejpam-3018	289	26	defined	define	VERB
ejpam-3018	289	27	as	as	ADP
ejpam-3018	289	28	(	(	PUNCT
ejpam-3018	289	29	ax)n	ax)n	PROPN
ejpam-3018	289	30	=	=	PROPN
ejpam-3018	289	31	∞∑	∞∑	NUM
ejpam-3018	289	32	k=1	k=1	PROPN
ejpam-3018	289	33	ankxk	ankxk	PROPN
ejpam-3018	289	34	provided	provide	VERB
ejpam-3018	289	35	the	the	DET
ejpam-3018	289	36	series	series	NOUN
ejpam-3018	289	37	converges	converge	VERB
ejpam-3018	289	38	for	for	ADP
ejpam-3018	289	39	each	each	DET
ejpam-3018	289	40	n.	n.	NOUN
ejpam-3018	289	41	a	a	PRON
ejpam-3018	289	42	is	be	AUX
ejpam-3018	289	43	said	say	VERB
ejpam-3018	289	44	to	to	PART
ejpam-3018	289	45	be	be	AUX
ejpam-3018	289	46	regular	regular	ADJ
ejpam-3018	289	47	if	if	SCONJ
ejpam-3018	289	48	lim	lim	PROPN
ejpam-3018	289	49	n	n	PROPN
ejpam-3018	289	50	(	(	PUNCT
ejpam-3018	289	51	ax)n	ax)n	PROPN
ejpam-3018	289	52	=	=	PUNCT
ejpam-3018	290	1	l	l	NOUN
ejpam-3018	290	2	whenever	whenever	SCONJ
ejpam-3018	290	3	lim	lim	PROPN
ejpam-3018	290	4	n	n	PROPN
ejpam-3018	290	5	xn	xn	PROPN
ejpam-3018	290	6	=	=	SYM
ejpam-3018	290	7	l.	l.	PROPN
ejpam-3018	290	8	the	the	DET
ejpam-3018	290	9	sequence	sequence	NOUN
ejpam-3018	290	10	x	x	NOUN
ejpam-3018	290	11	=	=	PUNCT
ejpam-3018	290	12	(	(	PUNCT
ejpam-3018	290	13	x)n	x)n	PROPN
ejpam-3018	290	14	is	be	AUX
ejpam-3018	290	15	said	say	VERB
ejpam-3018	290	16	to	to	PART
ejpam-3018	290	17	be	be	AUX
ejpam-3018	290	18	a	a	DET
ejpam-3018	290	19	astatistically	astatistically	ADV
ejpam-3018	290	20	convergent	convergent	ADJ
ejpam-3018	290	21	to	to	ADP
ejpam-3018	290	22	l	l	PROPN
ejpam-3018	290	23	i.e.	i.e.	X
ejpam-3018	290	24	sta	sta	X
ejpam-3018	291	1	−	−	PROPN
ejpam-3018	291	2	lim	lim	PROPN
ejpam-3018	291	3	n	n	PROPN
ejpam-3018	291	4	(	(	PUNCT
ejpam-3018	291	5	x)n	x)n	PUNCT
ejpam-3018	291	6	=	=	PUNCT
ejpam-3018	292	1	l	l	NOUN
ejpam-3018	292	2	if	if	SCONJ
ejpam-3018	292	3	for	for	ADP
ejpam-3018	292	4	every	every	DET
ejpam-3018	292	5	ε	ε	PROPN
ejpam-3018	292	6	>	>	X
ejpam-3018	292	7	0	0	PROPN
ejpam-3018	292	8	,	,	PUNCT
ejpam-3018	292	9	lim	lim	PROPN
ejpam-3018	292	10	n	n	PROPN
ejpam-3018	292	11	∑	∑	PROPN
ejpam-3018	292	12	k:|xk−l|≥ε	k:|xk−l|≥ε	PROPN
ejpam-3018	292	13	ank	ank	PROPN
ejpam-3018	292	14	=	=	SYM
ejpam-3018	292	15	0	0	PROPN
ejpam-3018	292	16	.	.	PUNCT
ejpam-3018	293	1	if	if	SCONJ
ejpam-3018	293	2	we	we	PRON
ejpam-3018	293	3	replace	replace	VERB
ejpam-3018	293	4	a	a	PRON
ejpam-3018	293	5	by	by	ADP
ejpam-3018	293	6	c1	c1	NOUN
ejpam-3018	293	7	then	then	ADV
ejpam-3018	293	8	a	a	PRON
ejpam-3018	293	9	is	be	AUX
ejpam-3018	293	10	a	a	DET
ejpam-3018	293	11	cesáro	cesáro	ADJ
ejpam-3018	293	12	matrix	matrix	NOUN
ejpam-3018	293	13	of	of	ADP
ejpam-3018	293	14	order	order	NOUN
ejpam-3018	293	15	one	one	NUM
ejpam-3018	293	16	and	and	CCONJ
ejpam-3018	293	17	astatistical	astatistical	ADJ
ejpam-3018	293	18	convergence	convergence	NOUN
ejpam-3018	293	19	is	be	AUX
ejpam-3018	293	20	reduced	reduce	VERB
ejpam-3018	293	21	to	to	ADP
ejpam-3018	293	22	the	the	DET
ejpam-3018	293	23	statistical	statistical	ADJ
ejpam-3018	293	24	convergence	convergence	NOUN
ejpam-3018	293	25	.	.	PUNCT
ejpam-3018	294	1	similarly	similarly	ADV
ejpam-3018	294	2	,	,	PUNCT
ejpam-3018	294	3	if	if	SCONJ
ejpam-3018	294	4	a	a	PRON
ejpam-3018	294	5	=	=	X
ejpam-3018	294	6	i	i	PROPN
ejpam-3018	294	7	,	,	PUNCT
ejpam-3018	294	8	the	the	DET
ejpam-3018	294	9	identity	identity	NOUN
ejpam-3018	294	10	matrix	matrix	NOUN
ejpam-3018	294	11	,	,	PUNCT
ejpam-3018	294	12	then	then	ADV
ejpam-3018	294	13	astatistical	astatistical	ADJ
ejpam-3018	294	14	convergence	convergence	NOUN
ejpam-3018	294	15	coincides	coincide	VERB
ejpam-3018	294	16	with	with	ADP
ejpam-3018	294	17	the	the	DET
ejpam-3018	294	18	ordinary	ordinary	ADJ
ejpam-3018	294	19	convergence	convergence	NOUN
ejpam-3018	294	20	.	.	PUNCT
ejpam-3018	295	1	it	it	PRON
ejpam-3018	295	2	is	be	AUX
ejpam-3018	295	3	to	to	PART
ejpam-3018	295	4	be	be	AUX
ejpam-3018	295	5	noted	note	VERB
ejpam-3018	295	6	that	that	SCONJ
ejpam-3018	295	7	the	the	DET
ejpam-3018	295	8	concept	concept	NOUN
ejpam-3018	295	9	of	of	ADP
ejpam-3018	295	10	a	a	DET
ejpam-3018	295	11	-	-	PUNCT
ejpam-3018	295	12	statistical	statistical	ADJ
ejpam-3018	295	13	convergence	convergence	NOUN
ejpam-3018	295	14	may	may	AUX
ejpam-3018	295	15	also	also	ADV
ejpam-3018	295	16	be	be	AUX
ejpam-3018	295	17	given	give	VERB
ejpam-3018	295	18	in	in	ADP
ejpam-3018	295	19	normed	normed	ADJ
ejpam-3018	295	20	spaces	space	NOUN
ejpam-3018	295	21	.	.	PUNCT
ejpam-3018	296	1	many	many	ADJ
ejpam-3018	296	2	researchers	researcher	NOUN
ejpam-3018	296	3	have	have	AUX
ejpam-3018	296	4	investigated	investigate	VERB
ejpam-3018	296	5	the	the	DET
ejpam-3018	296	6	statistical	statistical	ADJ
ejpam-3018	296	7	convergence	convergence	NOUN
ejpam-3018	296	8	properties	property	NOUN
ejpam-3018	296	9	for	for	ADP
ejpam-3018	296	10	several	several	ADJ
ejpam-3018	296	11	sequences	sequence	NOUN
ejpam-3018	296	12	and	and	CCONJ
ejpam-3018	296	13	classes	class	NOUN
ejpam-3018	296	14	of	of	ADP
ejpam-3018	296	15	linear	linear	ADJ
ejpam-3018	296	16	positive	positive	ADJ
ejpam-3018	296	17	operators	operator	NOUN
ejpam-3018	296	18	(	(	PUNCT
ejpam-3018	296	19	see	see	VERB
ejpam-3018	296	20	[	[	X
ejpam-3018	296	21	5	5	NUM
ejpam-3018	296	22	]	]	PUNCT
ejpam-3018	296	23	,	,	PUNCT
ejpam-3018	296	24	[	[	X
ejpam-3018	296	25	6	6	NUM
ejpam-3018	296	26	]	]	PUNCT
ejpam-3018	296	27	,	,	PUNCT
ejpam-3018	296	28	[	[	X
ejpam-3018	296	29	7	7	NUM
ejpam-3018	296	30	]	]	PUNCT
ejpam-3018	296	31	,	,	PUNCT
ejpam-3018	296	32	[	[	X
ejpam-3018	296	33	10	10	NUM
ejpam-3018	296	34	]	]	PUNCT
ejpam-3018	296	35	,	,	PUNCT
ejpam-3018	296	36	[	[	X
ejpam-3018	296	37	23	23	NUM
ejpam-3018	296	38	]	]	PUNCT
ejpam-3018	296	39	,	,	PUNCT
ejpam-3018	296	40	[	[	X
ejpam-3018	296	41	28	28	NUM
ejpam-3018	296	42	]	]	PUNCT
ejpam-3018	296	43	)	)	PUNCT
ejpam-3018	296	44	.	.	PUNCT
ejpam-3018	297	1	in	in	ADP
ejpam-3018	297	2	the	the	DET
ejpam-3018	297	3	following	following	ADJ
ejpam-3018	297	4	result	result	NOUN
ejpam-3018	297	5	we	we	PRON
ejpam-3018	297	6	prove	prove	VERB
ejpam-3018	297	7	a	a	DET
ejpam-3018	297	8	weighted	weighted	ADJ
ejpam-3018	297	9	korovkin	korovkin	NOUN
ejpam-3018	297	10	theorem	theorem	NOUN
ejpam-3018	297	11	via	via	ADP
ejpam-3018	297	12	a	a	DET
ejpam-3018	297	13	-	-	PUNCT
ejpam-3018	297	14	statistical	statistical	ADJ
ejpam-3018	297	15	convergence	convergence	NOUN
ejpam-3018	297	16	.	.	PUNCT
ejpam-3018	298	1	throughout	throughout	ADP
ejpam-3018	298	2	this	this	DET
ejpam-3018	298	3	section	section	NOUN
ejpam-3018	298	4	,	,	PUNCT
ejpam-3018	298	5	let	let	VERB
ejpam-3018	298	6	us	we	PRON
ejpam-3018	298	7	assume	assume	VERB
ejpam-3018	298	8	that	that	SCONJ
ejpam-3018	298	9	ei(t	ei(t	ADV
ejpam-3018	298	10	)	)	PUNCT
ejpam-3018	298	11	=	=	SYM
ejpam-3018	298	12	ti	ti	NOUN
ejpam-3018	298	13	,	,	PUNCT
ejpam-3018	298	14	i	i	NOUN
ejpam-3018	298	15	=	=	NOUN
ejpam-3018	298	16	0	0	NUM
ejpam-3018	298	17	,	,	PUNCT
ejpam-3018	298	18	1	1	NUM
ejpam-3018	298	19	,	,	PUNCT
ejpam-3018	298	20	2	2	NUM
ejpam-3018	298	21	.	.	X
ejpam-3018	298	22	theorem	theorem	NOUN
ejpam-3018	298	23	12	12	NUM
ejpam-3018	298	24	.	.	PUNCT
ejpam-3018	299	1	let	let	AUX
ejpam-3018	299	2	(	(	PUNCT
ejpam-3018	299	3	ank	ank	PROPN
ejpam-3018	299	4	)	)	PUNCT
ejpam-3018	299	5	be	be	AUX
ejpam-3018	299	6	a	a	DET
ejpam-3018	299	7	non	non	ADJ
ejpam-3018	299	8	-	-	ADJ
ejpam-3018	299	9	negative	negative	ADJ
ejpam-3018	299	10	regular	regular	ADJ
ejpam-3018	299	11	infinite	infinite	ADJ
ejpam-3018	299	12	summability	summability	NOUN
ejpam-3018	299	13	matrix	matrix	NOUN
ejpam-3018	299	14	and	and	CCONJ
ejpam-3018	299	15	x	x	PUNCT
ejpam-3018	299	16	∈	∈	PROPN
ejpam-3018	300	1	[	[	X
ejpam-3018	300	2	0,∞	0,∞	NOUN
ejpam-3018	300	3	)	)	PUNCT
ejpam-3018	300	4	.	.	PUNCT
ejpam-3018	301	1	let	let	VERB
ejpam-3018	301	2	νς	νς	PROPN
ejpam-3018	301	3	≥	≥	PROPN
ejpam-3018	301	4	1	1	NUM
ejpam-3018	301	5	be	be	AUX
ejpam-3018	301	6	a	a	DET
ejpam-3018	301	7	continuous	continuous	ADJ
ejpam-3018	301	8	function	function	NOUN
ejpam-3018	301	9	such	such	ADJ
ejpam-3018	301	10	that	that	SCONJ
ejpam-3018	301	11	lim	lim	PROPN
ejpam-3018	301	12	x→∞	x→∞	NUM
ejpam-3018	301	13	ν(x	ν(x	PROPN
ejpam-3018	301	14	)	)	PUNCT
ejpam-3018	301	15	νς(x	νς(x	PUNCT
ejpam-3018	301	16	)	)	PUNCT
ejpam-3018	302	1	=	=	SYM
ejpam-3018	302	2	0	0	X
ejpam-3018	302	3	.	.	PUNCT
ejpam-3018	302	4	a.	a.	PROPN
ejpam-3018	302	5	kumar	kumar	PROPN
ejpam-3018	302	6	,	,	PUNCT
ejpam-3018	302	7	v.	v.	PROPN
ejpam-3018	302	8	n.	n.	PROPN
ejpam-3018	302	9	mishra	mishra	PROPN
ejpam-3018	302	10	,	,	PUNCT
ejpam-3018	302	11	d.	d.	PROPN
ejpam-3018	302	12	tapiawala	tapiawala	PROPN
ejpam-3018	302	13	/	/	SYM
ejpam-3018	302	14	eur	eur	PROPN
ejpam-3018	302	15	.	.	PUNCT
ejpam-3018	303	1	j.	j.	PROPN
ejpam-3018	303	2	pure	pure	PROPN
ejpam-3018	303	3	appl	appl	PROPN
ejpam-3018	303	4	.	.	PROPN
ejpam-3018	303	5	math	math	PROPN
ejpam-3018	303	6	,	,	PUNCT
ejpam-3018	303	7	10	10	NUM
ejpam-3018	303	8	(	(	PUNCT
ejpam-3018	303	9	4	4	NUM
ejpam-3018	303	10	)	)	PUNCT
ejpam-3018	303	11	(	(	PUNCT
ejpam-3018	303	12	2017	2017	NUM
ejpam-3018	303	13	)	)	PUNCT
ejpam-3018	303	14	,	,	PUNCT
ejpam-3018	303	15	890	890	NUM
ejpam-3018	303	16	-	-	SYM
ejpam-3018	303	17	907	907	NUM
ejpam-3018	303	18	902	902	NUM
ejpam-3018	303	19	then	then	ADV
ejpam-3018	303	20	,	,	PUNCT
ejpam-3018	303	21	for	for	ADP
ejpam-3018	303	22	all	all	DET
ejpam-3018	303	23	f	f	PROPN
ejpam-3018	303	24	∈	∈	PROPN
ejpam-3018	303	25	c0	c0	PROPN
ejpam-3018	303	26	ν	ν	PROPN
ejpam-3018	303	27	,	,	PUNCT
ejpam-3018	303	28	we	we	PRON
ejpam-3018	303	29	have	have	VERB
ejpam-3018	303	30	sta	sta	NOUN
ejpam-3018	303	31	−	−	PROPN
ejpam-3018	303	32	lim	lim	PROPN
ejpam-3018	303	33	n	n	PROPN
ejpam-3018	303	34	‖	‖	PROPN
ejpam-3018	303	35	g∗(α	g∗(α	PROPN
ejpam-3018	303	36	,	,	PUNCT
ejpam-3018	303	37	β)n	β)n	NOUN
ejpam-3018	303	38	,	,	PUNCT
ejpam-3018	303	39	c	c	PROPN
ejpam-3018	303	40	(	(	PUNCT
ejpam-3018	303	41	f)−	f)−	PROPN
ejpam-3018	303	42	f	f	PROPN
ejpam-3018	303	43	‖νς=	‖νς=	PROPN
ejpam-3018	303	44	0	0	NUM
ejpam-3018	303	45	.	.	PUNCT
ejpam-3018	304	1	proof	proof	NOUN
ejpam-3018	304	2	.	.	PUNCT
ejpam-3018	305	1	from	from	ADP
ejpam-3018	305	2	(	(	PUNCT
ejpam-3018	305	3	[	[	X
ejpam-3018	305	4	7	7	X
ejpam-3018	305	5	]	]	PUNCT
ejpam-3018	305	6	p.	p.	NOUN
ejpam-3018	305	7	195	195	NUM
ejpam-3018	305	8	,	,	PUNCT
ejpam-3018	305	9	th	th	X
ejpam-3018	305	10	.	.	NOUN
ejpam-3018	305	11	6	6	NUM
ejpam-3018	305	12	)	)	PUNCT
ejpam-3018	305	13	,	,	PUNCT
ejpam-3018	305	14	it	it	PRON
ejpam-3018	305	15	is	be	AUX
ejpam-3018	305	16	enough	enough	ADJ
ejpam-3018	305	17	to	to	PART
ejpam-3018	305	18	show	show	VERB
ejpam-3018	305	19	that	that	DET
ejpam-3018	305	20	sta	sta	NOUN
ejpam-3018	305	21	−	−	PROPN
ejpam-3018	305	22	lim	lim	PROPN
ejpam-3018	305	23	n	n	PROPN
ejpam-3018	305	24	‖	‖	PROPN
ejpam-3018	305	25	g∗(α	g∗(α	PROPN
ejpam-3018	305	26	,	,	PUNCT
ejpam-3018	305	27	β)n	β)n	NOUN
ejpam-3018	305	28	,	,	PUNCT
ejpam-3018	305	29	c	c	PROPN
ejpam-3018	305	30	(	(	PUNCT
ejpam-3018	305	31	ei)−	ei)−	X
ejpam-3018	305	32	ei	ei	ADP
ejpam-3018	305	33	‖ν=	‖ν=	PROPN
ejpam-3018	305	34	0	0	NUM
ejpam-3018	305	35	.	.	PUNCT
ejpam-3018	306	1	from	from	ADP
ejpam-3018	306	2	lemma	lemma	PROPN
ejpam-3018	306	3	2	2	NUM
ejpam-3018	306	4	,	,	PUNCT
ejpam-3018	306	5	we	we	PRON
ejpam-3018	306	6	get	get	VERB
ejpam-3018	306	7	sta	sta	NOUN
ejpam-3018	307	1	−	−	PROPN
ejpam-3018	307	2	lim	lim	PROPN
ejpam-3018	307	3	n	n	PROPN
ejpam-3018	307	4	‖	‖	PROPN
ejpam-3018	307	5	g∗(α	g∗(α	PROPN
ejpam-3018	307	6	,	,	PUNCT
ejpam-3018	307	7	β)n	β)n	NOUN
ejpam-3018	307	8	,	,	PUNCT
ejpam-3018	307	9	c	c	PROPN
ejpam-3018	307	10	(	(	PUNCT
ejpam-3018	307	11	e0)−	e0)−	PROPN
ejpam-3018	307	12	e0	e0	PROPN
ejpam-3018	307	13	‖ν=	‖ν=	PROPN
ejpam-3018	307	14	0	0	NUM
ejpam-3018	307	15	.	.	PUNCT
ejpam-3018	308	1	again	again	ADV
ejpam-3018	308	2	by	by	ADP
ejpam-3018	308	3	using	use	VERB
ejpam-3018	308	4	lemma	lemma	PROPN
ejpam-3018	308	5	2	2	NUM
ejpam-3018	308	6	,	,	PUNCT
ejpam-3018	308	7	we	we	PRON
ejpam-3018	308	8	have	have	VERB
ejpam-3018	308	9	‖	‖	ADJ
ejpam-3018	308	10	g∗(α	g∗(α	PROPN
ejpam-3018	308	11	,	,	PUNCT
ejpam-3018	308	12	β)n	β)n	NOUN
ejpam-3018	308	13	,	,	PUNCT
ejpam-3018	308	14	c	c	PROPN
ejpam-3018	308	15	(	(	PUNCT
ejpam-3018	308	16	e1)−	e1)−	NOUN
ejpam-3018	308	17	e1	e1	NOUN
ejpam-3018	308	18	‖ν	‖ν	PROPN
ejpam-3018	308	19	≤	≤	PROPN
ejpam-3018	309	1	β	β	X
ejpam-3018	309	2	(	(	PUNCT
ejpam-3018	309	3	n+	n+	X
ejpam-3018	309	4	β	β	X
ejpam-3018	309	5	)	)	PUNCT
ejpam-3018	309	6	sup	sup	NOUN
ejpam-3018	309	7	x∈[0,∞	x∈[0,∞	NUM
ejpam-3018	309	8	)	)	PUNCT
ejpam-3018	309	9	x	x	SYM
ejpam-3018	309	10	1	1	NUM
ejpam-3018	310	1	+	+	NUM
ejpam-3018	310	2	x2	x2	PROPN
ejpam-3018	311	1	+	+	CCONJ
ejpam-3018	311	2	α	α	NOUN
ejpam-3018	311	3	n+	n+	PUNCT
ejpam-3018	311	4	β	β	X
ejpam-3018	311	5	sup	sup	NOUN
ejpam-3018	311	6	x∈[0,∞	x∈[0,∞	PROPN
ejpam-3018	311	7	)	)	PUNCT
ejpam-3018	311	8	1	1	NUM
ejpam-3018	311	9	1	1	NUM
ejpam-3018	311	10	+	+	NUM
ejpam-3018	311	11	x2	x2	ADJ
ejpam-3018	311	12	≤	≤	NOUN
ejpam-3018	311	13	α+	α+	PUNCT
ejpam-3018	311	14	β	β	X
ejpam-3018	311	15	n+	n+	X
ejpam-3018	312	1	β	β	X
ejpam-3018	312	2	.	.	PUNCT
ejpam-3018	313	1	for	for	ADP
ejpam-3018	313	2	any	any	DET
ejpam-3018	313	3	given	give	VERB
ejpam-3018	313	4	ε	ε	PROPN
ejpam-3018	313	5	>	>	X
ejpam-3018	313	6	0	0	PROPN
ejpam-3018	313	7	,	,	PUNCT
ejpam-3018	313	8	let	let	VERB
ejpam-3018	313	9	us	we	PRON
ejpam-3018	313	10	define	define	VERB
ejpam-3018	313	11	the	the	DET
ejpam-3018	313	12	following	follow	VERB
ejpam-3018	313	13	sets	set	NOUN
ejpam-3018	313	14	:	:	PUNCT
ejpam-3018	313	15	s	s	VERB
ejpam-3018	313	16	:	:	PUNCT
ejpam-3018	313	17	=	=	SYM
ejpam-3018	313	18	{	{	PUNCT
ejpam-3018	313	19	n	n	CCONJ
ejpam-3018	313	20	:	:	PUNCT
ejpam-3018	314	1	‖	‖	PROPN
ejpam-3018	314	2	g∗(α	g∗(α	PROPN
ejpam-3018	314	3	,	,	PUNCT
ejpam-3018	314	4	β)n	β)n	NOUN
ejpam-3018	314	5	,	,	PUNCT
ejpam-3018	314	6	c	c	PROPN
ejpam-3018	314	7	(	(	PUNCT
ejpam-3018	314	8	e1)−	e1)−	AUX
ejpam-3018	314	9	e1	e1	PROPN
ejpam-3018	314	10	‖ν≥	‖ν≥	VERB
ejpam-3018	314	11	ε	ε	PROPN
ejpam-3018	314	12	}	}	PUNCT
ejpam-3018	314	13	,	,	PUNCT
ejpam-3018	314	14	s1	s1	NOUN
ejpam-3018	314	15	:	:	PUNCT
ejpam-3018	314	16	=	=	X
ejpam-3018	314	17	{	{	PUNCT
ejpam-3018	314	18	n	n	NOUN
ejpam-3018	314	19	:	:	PUNCT
ejpam-3018	314	20	α	α	NOUN
ejpam-3018	314	21	n+	n+	X
ejpam-3018	314	22	β	β	X
ejpam-3018	314	23	≥	≥	NOUN
ejpam-3018	314	24	ε	ε	PROPN
ejpam-3018	314	25	2	2	NUM
ejpam-3018	314	26	}	}	PUNCT
ejpam-3018	314	27	and	and	CCONJ
ejpam-3018	314	28	s2	s2	VERB
ejpam-3018	314	29	:	:	PUNCT
ejpam-3018	314	30	=	=	X
ejpam-3018	314	31	{	{	PUNCT
ejpam-3018	314	32	n	n	NOUN
ejpam-3018	314	33	:	:	PUNCT
ejpam-3018	314	34	β	β	X
ejpam-3018	314	35	n+	n+	NUM
ejpam-3018	314	36	β	β	X
ejpam-3018	314	37	≥	≥	NOUN
ejpam-3018	314	38	ε	ε	PROPN
ejpam-3018	314	39	2	2	NUM
ejpam-3018	314	40	}	}	PUNCT
ejpam-3018	314	41	.	.	PUNCT
ejpam-3018	315	1	then	then	ADV
ejpam-3018	315	2	,	,	PUNCT
ejpam-3018	315	3	we	we	PRON
ejpam-3018	315	4	get	get	VERB
ejpam-3018	315	5	s	s	PRON
ejpam-3018	315	6	⊆	⊆	NUM
ejpam-3018	315	7	s1	s1	NOUN
ejpam-3018	315	8	∪	∪	ADP
ejpam-3018	315	9	s2	s2	NOUN
ejpam-3018	315	10	which	which	PRON
ejpam-3018	315	11	implies	imply	VERB
ejpam-3018	315	12	that∑	that∑	NOUN
ejpam-3018	315	13	k∈s	k∈s	VERB
ejpam-3018	315	14	ank	ank	PROPN
ejpam-3018	315	15	≤	≤	PROPN
ejpam-3018	315	16	∑	∑	PROPN
ejpam-3018	315	17	k∈s1	k∈s1	PROPN
ejpam-3018	315	18	ank	ank	PROPN
ejpam-3018	316	1	+	+	PROPN
ejpam-3018	316	2	∑	∑	PROPN
ejpam-3018	316	3	k∈s2	k∈s2	PROPN
ejpam-3018	316	4	ank	ank	PROPN
ejpam-3018	316	5	and	and	CCONJ
ejpam-3018	316	6	hence	hence	ADV
ejpam-3018	316	7	sta	sta	PROPN
ejpam-3018	316	8	−	−	PROPN
ejpam-3018	316	9	lim	lim	PROPN
ejpam-3018	316	10	n	n	PROPN
ejpam-3018	316	11	‖	‖	PROPN
ejpam-3018	316	12	g∗(α	g∗(α	PROPN
ejpam-3018	316	13	,	,	PUNCT
ejpam-3018	316	14	β)n	β)n	NOUN
ejpam-3018	316	15	,	,	PUNCT
ejpam-3018	316	16	c	c	PROPN
ejpam-3018	316	17	(	(	PUNCT
ejpam-3018	316	18	e1)−	e1)−	PROPN
ejpam-3018	316	19	e1	e1	VERB
ejpam-3018	316	20	‖ν=	‖ν=	PROPN
ejpam-3018	316	21	0	0	NUM
ejpam-3018	316	22	.	.	PUNCT
ejpam-3018	317	1	similarly	similarly	ADV
ejpam-3018	317	2	,	,	PUNCT
ejpam-3018	317	3	we	we	PRON
ejpam-3018	317	4	have	have	VERB
ejpam-3018	317	5	‖	‖	ADJ
ejpam-3018	317	6	g∗(α	g∗(α	PROPN
ejpam-3018	317	7	,	,	PUNCT
ejpam-3018	317	8	β)n	β)n	NOUN
ejpam-3018	317	9	,	,	PUNCT
ejpam-3018	317	10	c	c	PROPN
ejpam-3018	317	11	(	(	PUNCT
ejpam-3018	317	12	e2)−	e2)−	PROPN
ejpam-3018	317	13	e2	e2	PROPN
ejpam-3018	317	14	‖ν	‖ν	PROPN
ejpam-3018	317	15	≤	≤	PROPN
ejpam-3018	317	16	(	(	PUNCT
ejpam-3018	317	17	n(n2	n(n2	NOUN
ejpam-3018	317	18	−	−	PROPN
ejpam-3018	317	19	c2	c2	PROPN
ejpam-3018	317	20	)	)	PUNCT
ejpam-3018	317	21	(	(	PUNCT
ejpam-3018	317	22	n−	n−	NOUN
ejpam-3018	317	23	2c)(n+	2c)(n+	NUM
ejpam-3018	317	24	β)2	β)2	ADV
ejpam-3018	317	25	−	−	PROPN
ejpam-3018	317	26	1	1	NUM
ejpam-3018	317	27	)	)	PUNCT
ejpam-3018	317	28	+	+	CCONJ
ejpam-3018	317	29	2n((n−	2n((n−	NUM
ejpam-3018	317	30	c	c	X
ejpam-3018	317	31	)	)	PUNCT
ejpam-3018	318	1	+	+	CCONJ
ejpam-3018	318	2	α(n−	α(n−	NUM
ejpam-3018	318	3	2c	2c	NUM
ejpam-3018	318	4	)	)	PUNCT
ejpam-3018	318	5	)	)	PUNCT
ejpam-3018	319	1	(	(	PUNCT
ejpam-3018	319	2	n−	n−	NOUN
ejpam-3018	319	3	2c)(n+	2c)(n+	NUM
ejpam-3018	319	4	β)2	β)2	X
ejpam-3018	319	5	+	+	X
ejpam-3018	319	6	α2	α2	ADJ
ejpam-3018	319	7	(	(	PUNCT
ejpam-3018	319	8	n+	n+	X
ejpam-3018	319	9	β)2	β)2	X
ejpam-3018	319	10	.	.	PUNCT
ejpam-3018	320	1	now	now	ADV
ejpam-3018	320	2	,	,	PUNCT
ejpam-3018	320	3	we	we	PRON
ejpam-3018	320	4	define	define	VERB
ejpam-3018	320	5	the	the	DET
ejpam-3018	320	6	following	follow	VERB
ejpam-3018	320	7	sets	set	NOUN
ejpam-3018	320	8	:	:	PUNCT
ejpam-3018	320	9	u	u	NOUN
ejpam-3018	320	10	:	:	PUNCT
ejpam-3018	320	11	=	=	SYM
ejpam-3018	320	12	{	{	PUNCT
ejpam-3018	320	13	n	n	CCONJ
ejpam-3018	320	14	:	:	PUNCT
ejpam-3018	320	15	‖	‖	PROPN
ejpam-3018	320	16	g∗(α	g∗(α	PROPN
ejpam-3018	320	17	,	,	PUNCT
ejpam-3018	320	18	β)n	β)n	NOUN
ejpam-3018	320	19	,	,	PUNCT
ejpam-3018	320	20	c	c	PROPN
ejpam-3018	320	21	(	(	PUNCT
ejpam-3018	320	22	e2)−	e2)−	PROPN
ejpam-3018	320	23	e2	e2	PROPN
ejpam-3018	320	24	‖ν≥	‖ν≥	VERB
ejpam-3018	320	25	ε	ε	PROPN
ejpam-3018	320	26	}	}	PUNCT
ejpam-3018	320	27	,	,	PUNCT
ejpam-3018	320	28	a.	a.	PROPN
ejpam-3018	320	29	kumar	kumar	PROPN
ejpam-3018	320	30	,	,	PUNCT
ejpam-3018	320	31	v.	v.	PROPN
ejpam-3018	320	32	n.	n.	PROPN
ejpam-3018	320	33	mishra	mishra	PROPN
ejpam-3018	320	34	,	,	PUNCT
ejpam-3018	320	35	d.	d.	PROPN
ejpam-3018	320	36	tapiawala	tapiawala	PROPN
ejpam-3018	320	37	/	/	SYM
ejpam-3018	320	38	eur	eur	PROPN
ejpam-3018	320	39	.	.	PUNCT
ejpam-3018	321	1	j.	j.	PROPN
ejpam-3018	321	2	pure	pure	PROPN
ejpam-3018	321	3	appl	appl	PROPN
ejpam-3018	321	4	.	.	PROPN
ejpam-3018	321	5	math	math	PROPN
ejpam-3018	321	6	,	,	PUNCT
ejpam-3018	321	7	10	10	NUM
ejpam-3018	321	8	(	(	PUNCT
ejpam-3018	321	9	4	4	NUM
ejpam-3018	321	10	)	)	PUNCT
ejpam-3018	321	11	(	(	PUNCT
ejpam-3018	321	12	2017	2017	NUM
ejpam-3018	321	13	)	)	PUNCT
ejpam-3018	321	14	,	,	PUNCT
ejpam-3018	321	15	890	890	NUM
ejpam-3018	321	16	-	-	SYM
ejpam-3018	321	17	907	907	NUM
ejpam-3018	321	18	903	903	NUM
ejpam-3018	321	19	u1	u1	NOUN
ejpam-3018	321	20	:	:	PUNCT
ejpam-3018	321	21	=	=	SYM
ejpam-3018	321	22	{	{	PUNCT
ejpam-3018	321	23	n	n	NOUN
ejpam-3018	321	24	:	:	PUNCT
ejpam-3018	321	25	(	(	PUNCT
ejpam-3018	321	26	n(n2	n(n2	NOUN
ejpam-3018	321	27	−	−	PROPN
ejpam-3018	321	28	c2	c2	PROPN
ejpam-3018	321	29	)	)	PUNCT
ejpam-3018	321	30	(	(	PUNCT
ejpam-3018	321	31	n−	n−	NOUN
ejpam-3018	321	32	2c)(n+	2c)(n+	NUM
ejpam-3018	321	33	β)2	β)2	ADV
ejpam-3018	321	34	−	−	PROPN
ejpam-3018	321	35	1	1	NUM
ejpam-3018	321	36	)	)	PUNCT
ejpam-3018	321	37	≥	≥	NOUN
ejpam-3018	321	38	ε	ε	PROPN
ejpam-3018	321	39	3	3	NUM
ejpam-3018	321	40	}	}	PUNCT
ejpam-3018	321	41	,	,	PUNCT
ejpam-3018	321	42	u2	u2	NOUN
ejpam-3018	321	43	:	:	PUNCT
ejpam-3018	321	44	=	=	X
ejpam-3018	321	45	{	{	PUNCT
ejpam-3018	321	46	n	n	CCONJ
ejpam-3018	321	47	:	:	PUNCT
ejpam-3018	321	48	2n((n−	2n((n−	NUM
ejpam-3018	321	49	c	c	X
ejpam-3018	321	50	)	)	PUNCT
ejpam-3018	322	1	+	+	CCONJ
ejpam-3018	322	2	α(n−	α(n−	NUM
ejpam-3018	322	3	2c	2c	NUM
ejpam-3018	322	4	)	)	PUNCT
ejpam-3018	322	5	)	)	PUNCT
ejpam-3018	323	1	(	(	PUNCT
ejpam-3018	323	2	n−	n−	NOUN
ejpam-3018	323	3	2c)(n+	2c)(n+	NUM
ejpam-3018	323	4	β)2	β)2	ADV
ejpam-3018	323	5	≥	≥	X
ejpam-3018	323	6	ε	ε	PROPN
ejpam-3018	323	7	3	3	NUM
ejpam-3018	323	8	}	}	PUNCT
ejpam-3018	323	9	and	and	CCONJ
ejpam-3018	323	10	u3	u3	NOUN
ejpam-3018	323	11	:	:	PUNCT
ejpam-3018	323	12	=	=	SYM
ejpam-3018	323	13	{	{	PUNCT
ejpam-3018	323	14	n	n	NOUN
ejpam-3018	323	15	:	:	PUNCT
ejpam-3018	323	16	α2	α2	PROPN
ejpam-3018	323	17	(	(	PUNCT
ejpam-3018	323	18	n+	n+	X
ejpam-3018	323	19	β)2	β)2	X
ejpam-3018	323	20	≥	≥	X
ejpam-3018	323	21	ε	ε	PROPN
ejpam-3018	323	22	3	3	NUM
ejpam-3018	323	23	}	}	PUNCT
ejpam-3018	323	24	.	.	PUNCT
ejpam-3018	324	1	then	then	ADV
ejpam-3018	324	2	,	,	PUNCT
ejpam-3018	324	3	we	we	PRON
ejpam-3018	324	4	get	get	VERB
ejpam-3018	324	5	u	u	NOUN
ejpam-3018	324	6	⊆	⊆	NUM
ejpam-3018	324	7	u1	u1	NOUN
ejpam-3018	324	8	∪	∪	ADP
ejpam-3018	324	9	u2	u2	PROPN
ejpam-3018	324	10	∪	∪	NOUN
ejpam-3018	324	11	u3	u3	NOUN
ejpam-3018	324	12	which	which	PRON
ejpam-3018	324	13	implies	imply	VERB
ejpam-3018	324	14	that∑	that∑	NOUN
ejpam-3018	324	15	k∈u	k∈u	VERB
ejpam-3018	324	16	ank	ank	PROPN
ejpam-3018	324	17	≤	≤	PROPN
ejpam-3018	324	18	∑	∑	PUNCT
ejpam-3018	324	19	k∈u1	k∈u1	PROPN
ejpam-3018	324	20	ank	ank	PROPN
ejpam-3018	325	1	+	+	CCONJ
ejpam-3018	325	2	∑	∑	PROPN
ejpam-3018	325	3	k∈u2	k∈u2	PROPN
ejpam-3018	325	4	ank	ank	PROPN
ejpam-3018	325	5	+	+	PROPN
ejpam-3018	325	6	∑	∑	PROPN
ejpam-3018	325	7	k∈u3	k∈u3	PROPN
ejpam-3018	325	8	ank	ank	PROPN
ejpam-3018	325	9	and	and	CCONJ
ejpam-3018	325	10	hence	hence	ADV
ejpam-3018	325	11	sta	sta	NOUN
ejpam-3018	326	1	−	−	PROPN
ejpam-3018	326	2	lim	lim	PROPN
ejpam-3018	326	3	n	n	PROPN
ejpam-3018	326	4	‖	‖	PROPN
ejpam-3018	326	5	g∗(α	g∗(α	PROPN
ejpam-3018	326	6	,	,	PUNCT
ejpam-3018	326	7	β)n	β)n	NOUN
ejpam-3018	326	8	,	,	PUNCT
ejpam-3018	326	9	c	c	PROPN
ejpam-3018	326	10	(	(	PUNCT
ejpam-3018	326	11	e2)−	e2)−	PROPN
ejpam-3018	326	12	e2	e2	PROPN
ejpam-3018	326	13	‖ν=	‖ν=	PROPN
ejpam-3018	326	14	0	0	NUM
ejpam-3018	326	15	.	.	PUNCT
ejpam-3018	327	1	this	this	PRON
ejpam-3018	327	2	completes	complete	VERB
ejpam-3018	327	3	the	the	DET
ejpam-3018	327	4	proof	proof	NOUN
ejpam-3018	327	5	of	of	ADP
ejpam-3018	327	6	the	the	DET
ejpam-3018	327	7	theorem	theorem	NOUN
ejpam-3018	327	8	.	.	PROPN
ejpam-3018	327	9	4	4	X
ejpam-3018	327	10	.	.	X
ejpam-3018	328	1	better	well	ADJ
ejpam-3018	328	2	estimates	estimate	NOUN
ejpam-3018	328	3	it	it	PRON
ejpam-3018	328	4	is	be	AUX
ejpam-3018	328	5	well	well	ADV
ejpam-3018	328	6	known	know	VERB
ejpam-3018	328	7	that	that	SCONJ
ejpam-3018	328	8	the	the	DET
ejpam-3018	328	9	classical	classical	ADJ
ejpam-3018	328	10	bernstein	bernstein	PROPN
ejpam-3018	328	11	polynomial	polynomial	PROPN
ejpam-3018	328	12	preserve	preserve	NOUN
ejpam-3018	328	13	constant	constant	ADJ
ejpam-3018	328	14	as	as	ADV
ejpam-3018	328	15	well	well	ADV
ejpam-3018	328	16	as	as	ADP
ejpam-3018	328	17	linear	linear	ADJ
ejpam-3018	328	18	functions	function	NOUN
ejpam-3018	328	19	.	.	PUNCT
ejpam-3018	329	1	to	to	PART
ejpam-3018	329	2	make	make	VERB
ejpam-3018	329	3	the	the	DET
ejpam-3018	329	4	convergence	convergence	NOUN
ejpam-3018	329	5	faster	fast	ADV
ejpam-3018	329	6	,	,	PUNCT
ejpam-3018	329	7	king	king	NOUN
ejpam-3018	329	8	[	[	X
ejpam-3018	329	9	18	18	NUM
ejpam-3018	329	10	]	]	PUNCT
ejpam-3018	329	11	proposed	propose	VERB
ejpam-3018	329	12	an	an	DET
ejpam-3018	329	13	approach	approach	NOUN
ejpam-3018	329	14	to	to	PART
ejpam-3018	329	15	modify	modify	VERB
ejpam-3018	329	16	the	the	DET
ejpam-3018	329	17	bernstein	bernstein	PROPN
ejpam-3018	329	18	polynomial	polynomial	PROPN
ejpam-3018	329	19	,	,	PUNCT
ejpam-3018	329	20	so	so	SCONJ
ejpam-3018	329	21	that	that	SCONJ
ejpam-3018	329	22	the	the	DET
ejpam-3018	329	23	sequence	sequence	NOUN
ejpam-3018	329	24	preserve	preserve	VERB
ejpam-3018	329	25	test	test	NOUN
ejpam-3018	329	26	functions	function	NOUN
ejpam-3018	329	27	e0	e0	PROPN
ejpam-3018	329	28	and	and	CCONJ
ejpam-3018	329	29	e2	e2	PROPN
ejpam-3018	329	30	,	,	PUNCT
ejpam-3018	329	31	where	where	SCONJ
ejpam-3018	329	32	ei(t	ei(t	NUM
ejpam-3018	329	33	)	)	PUNCT
ejpam-3018	330	1	=	=	SYM
ejpam-3018	330	2	ti	ti	X
ejpam-3018	330	3	,	,	PUNCT
ejpam-3018	330	4	i	i	NOUN
ejpam-3018	330	5	=	=	NOUN
ejpam-3018	330	6	0	0	NUM
ejpam-3018	330	7	,	,	PUNCT
ejpam-3018	330	8	1	1	NUM
ejpam-3018	330	9	,	,	PUNCT
ejpam-3018	330	10	2	2	NUM
ejpam-3018	330	11	.	.	PUNCT
ejpam-3018	330	12	as	as	ADP
ejpam-3018	330	13	the	the	DET
ejpam-3018	330	14	operator	operator	NOUN
ejpam-3018	330	15	g	g	PROPN
ejpam-3018	330	16	∗(α	∗(α	PROPN
ejpam-3018	330	17	,	,	PUNCT
ejpam-3018	330	18	β	β	NOUN
ejpam-3018	330	19	)	)	PUNCT
ejpam-3018	330	20	n	n	CCONJ
ejpam-3018	330	21	,	,	PUNCT
ejpam-3018	330	22	c	c	PROPN
ejpam-3018	330	23	(	(	PUNCT
ejpam-3018	330	24	f	f	NOUN
ejpam-3018	330	25	;	;	PUNCT
ejpam-3018	330	26	x	x	X
ejpam-3018	330	27	)	)	PUNCT
ejpam-3018	330	28	defined	define	VERB
ejpam-3018	330	29	in	in	ADP
ejpam-3018	330	30	(	(	PUNCT
ejpam-3018	330	31	4	4	X
ejpam-3018	330	32	)	)	PUNCT
ejpam-3018	330	33	preserve	preserve	VERB
ejpam-3018	330	34	only	only	ADV
ejpam-3018	330	35	the	the	DET
ejpam-3018	330	36	constant	constant	ADJ
ejpam-3018	330	37	functions	function	NOUN
ejpam-3018	330	38	so	so	ADV
ejpam-3018	330	39	further	further	ADJ
ejpam-3018	330	40	modification	modification	NOUN
ejpam-3018	330	41	of	of	ADP
ejpam-3018	330	42	these	these	DET
ejpam-3018	330	43	operators	operator	NOUN
ejpam-3018	330	44	is	be	AUX
ejpam-3018	330	45	proposed	propose	VERB
ejpam-3018	330	46	to	to	PART
ejpam-3018	330	47	be	be	AUX
ejpam-3018	330	48	made	make	VERB
ejpam-3018	330	49	so	so	SCONJ
ejpam-3018	330	50	that	that	SCONJ
ejpam-3018	330	51	the	the	DET
ejpam-3018	330	52	modified	modify	VERB
ejpam-3018	330	53	operators	operator	NOUN
ejpam-3018	330	54	preserve	preserve	VERB
ejpam-3018	330	55	the	the	DET
ejpam-3018	330	56	constant	constant	ADJ
ejpam-3018	330	57	as	as	ADV
ejpam-3018	330	58	well	well	ADV
ejpam-3018	330	59	as	as	ADP
ejpam-3018	330	60	linear	linear	ADJ
ejpam-3018	330	61	functions	function	NOUN
ejpam-3018	330	62	.	.	PUNCT
ejpam-3018	331	1	for	for	ADP
ejpam-3018	331	2	this	this	DET
ejpam-3018	331	3	purpose	purpose	NOUN
ejpam-3018	331	4	the	the	DET
ejpam-3018	331	5	modification	modification	NOUN
ejpam-3018	331	6	of	of	ADP
ejpam-3018	331	7	(	(	PUNCT
ejpam-3018	331	8	4	4	NUM
ejpam-3018	331	9	)	)	PUNCT
ejpam-3018	331	10	is	be	AUX
ejpam-3018	331	11	defined	define	VERB
ejpam-3018	331	12	as	as	ADP
ejpam-3018	331	13	g	g	PROPN
ejpam-3018	331	14	∗(α	∗(α	PROPN
ejpam-3018	331	15	,	,	PUNCT
ejpam-3018	331	16	β	β	NOUN
ejpam-3018	331	17	)	)	PUNCT
ejpam-3018	331	18	n	n	CCONJ
ejpam-3018	331	19	,	,	PUNCT
ejpam-3018	331	20	c	c	PROPN
ejpam-3018	331	21	(	(	PUNCT
ejpam-3018	331	22	f	f	NOUN
ejpam-3018	331	23	;	;	PUNCT
ejpam-3018	331	24	x	x	X
ejpam-3018	331	25	)	)	PUNCT
ejpam-3018	331	26	=	=	SYM
ejpam-3018	332	1	n	n	PROPN
ejpam-3018	332	2	∞∑	∞∑	PROPN
ejpam-3018	332	3	k=1	k=1	PUNCT
ejpam-3018	332	4	pn	pn	PROPN
ejpam-3018	332	5	,	,	PUNCT
ejpam-3018	332	6	k(rn(x	k(rn(x	PROPN
ejpam-3018	332	7	)	)	PUNCT
ejpam-3018	332	8	,	,	PUNCT
ejpam-3018	332	9	c	c	X
ejpam-3018	332	10	)	)	PUNCT
ejpam-3018	332	11	∫	∫	PROPN
ejpam-3018	333	1	∞	∞	PROPN
ejpam-3018	333	2	0	0	NUM
ejpam-3018	333	3	pn+c	pn+c	NOUN
ejpam-3018	333	4	,	,	PUNCT
ejpam-3018	333	5	k−1(t	k−1(t	PROPN
ejpam-3018	333	6	,	,	PUNCT
ejpam-3018	333	7	c)f	c)f	NOUN
ejpam-3018	333	8	(	(	PUNCT
ejpam-3018	333	9	(	(	PUNCT
ejpam-3018	333	10	n−	n−	NOUN
ejpam-3018	333	11	c)t+	c)t+	VERB
ejpam-3018	333	12	α	α	NUM
ejpam-3018	333	13	n+	n+	NUM
ejpam-3018	333	14	β	β	X
ejpam-3018	333	15	)	)	PUNCT
ejpam-3018	333	16	dt	dt	PUNCT
ejpam-3018	334	1	+	+	NOUN
ejpam-3018	334	2	pn,0(rn(x	pn,0(rn(x	PROPN
ejpam-3018	334	3	)	)	PUNCT
ejpam-3018	334	4	,	,	PUNCT
ejpam-3018	334	5	c)f	c)f	NOUN
ejpam-3018	334	6	(	(	PUNCT
ejpam-3018	334	7	α	α	NOUN
ejpam-3018	334	8	n+	n+	X
ejpam-3018	334	9	β	β	X
ejpam-3018	334	10	)	)	PUNCT
ejpam-3018	334	11	,	,	PUNCT
ejpam-3018	334	12	(	(	PUNCT
ejpam-3018	334	13	18	18	NUM
ejpam-3018	334	14	)	)	PUNCT
ejpam-3018	334	15	where	where	SCONJ
ejpam-3018	334	16	rn(x	rn(x	X
ejpam-3018	334	17	)	)	PUNCT
ejpam-3018	334	18	=	=	SYM
ejpam-3018	334	19	(	(	PUNCT
ejpam-3018	334	20	n+β)x−α	n+β)x−α	PUNCT
ejpam-3018	334	21	n	n	CCONJ
ejpam-3018	334	22	for	for	ADP
ejpam-3018	334	23	x	x	PROPN
ejpam-3018	334	24	∈	∈	PROPN
ejpam-3018	334	25	in	in	ADP
ejpam-3018	334	26	=	=	PUNCT
ejpam-3018	334	27	[	[	PUNCT
ejpam-3018	334	28	α	α	X
ejpam-3018	334	29	n+β	n+β	NUM
ejpam-3018	334	30	,	,	PUNCT
ejpam-3018	334	31	∞	∞	PROPN
ejpam-3018	334	32	)	)	PUNCT
ejpam-3018	334	33	and	and	CCONJ
ejpam-3018	334	34	n	n	CCONJ
ejpam-3018	334	35	>	>	X
ejpam-3018	334	36	2c	2c	NUM
ejpam-3018	334	37	.	.	PUNCT
ejpam-3018	335	1	lemma	lemma	PROPN
ejpam-3018	335	2	13	13	NUM
ejpam-3018	335	3	.	.	PUNCT
ejpam-3018	336	1	for	for	ADP
ejpam-3018	336	2	each	each	DET
ejpam-3018	336	3	x	x	SYM
ejpam-3018	336	4	∈	∈	NOUN
ejpam-3018	336	5	in	in	ADP
ejpam-3018	336	6	,	,	PUNCT
ejpam-3018	336	7	by	by	ADP
ejpam-3018	336	8	simple	simple	ADJ
ejpam-3018	336	9	computations	computation	NOUN
ejpam-3018	336	10	,	,	PUNCT
ejpam-3018	336	11	we	we	PRON
ejpam-3018	336	12	have	have	VERB
ejpam-3018	336	13	(	(	PUNCT
ejpam-3018	336	14	i	i	NOUN
ejpam-3018	336	15	)	)	PUNCT
ejpam-3018	336	16	g	g	PROPN
ejpam-3018	336	17	∗(α	∗(α	PROPN
ejpam-3018	336	18	,	,	PUNCT
ejpam-3018	336	19	β	β	NOUN
ejpam-3018	336	20	)	)	PUNCT
ejpam-3018	336	21	n	n	CCONJ
ejpam-3018	336	22	,	,	PUNCT
ejpam-3018	336	23	c	c	PROPN
ejpam-3018	336	24	(	(	PUNCT
ejpam-3018	336	25	1;x	1;x	NUM
ejpam-3018	336	26	)	)	PUNCT
ejpam-3018	336	27	=	=	SYM
ejpam-3018	336	28	1	1	NUM
ejpam-3018	336	29	;	;	PUNCT
ejpam-3018	337	1	(	(	PUNCT
ejpam-3018	337	2	ii	ii	NOUN
ejpam-3018	337	3	)	)	PUNCT
ejpam-3018	337	4	g	g	PROPN
ejpam-3018	337	5	∗(α	∗(α	PROPN
ejpam-3018	337	6	,	,	PUNCT
ejpam-3018	337	7	β	β	NOUN
ejpam-3018	337	8	)	)	PUNCT
ejpam-3018	337	9	n	n	CCONJ
ejpam-3018	337	10	,	,	PUNCT
ejpam-3018	337	11	c	c	X
ejpam-3018	337	12	(	(	PUNCT
ejpam-3018	337	13	t;x	t;x	NUM
ejpam-3018	337	14	)	)	PUNCT
ejpam-3018	337	15	=	=	SYM
ejpam-3018	338	1	x	x	X
ejpam-3018	338	2	;	;	PUNCT
ejpam-3018	338	3	a.	a.	PROPN
ejpam-3018	338	4	kumar	kumar	PROPN
ejpam-3018	338	5	,	,	PUNCT
ejpam-3018	338	6	v.	v.	PROPN
ejpam-3018	338	7	n.	n.	PROPN
ejpam-3018	338	8	mishra	mishra	PROPN
ejpam-3018	338	9	,	,	PUNCT
ejpam-3018	338	10	d.	d.	PROPN
ejpam-3018	338	11	tapiawala	tapiawala	PROPN
ejpam-3018	338	12	/	/	SYM
ejpam-3018	338	13	eur	eur	PROPN
ejpam-3018	338	14	.	.	PUNCT
ejpam-3018	339	1	j.	j.	PROPN
ejpam-3018	339	2	pure	pure	PROPN
ejpam-3018	339	3	appl	appl	PROPN
ejpam-3018	339	4	.	.	PROPN
ejpam-3018	339	5	math	math	PROPN
ejpam-3018	339	6	,	,	PUNCT
ejpam-3018	339	7	10	10	NUM
ejpam-3018	339	8	(	(	PUNCT
ejpam-3018	339	9	4	4	NUM
ejpam-3018	339	10	)	)	PUNCT
ejpam-3018	339	11	(	(	PUNCT
ejpam-3018	339	12	2017	2017	NUM
ejpam-3018	339	13	)	)	PUNCT
ejpam-3018	339	14	,	,	PUNCT
ejpam-3018	339	15	890	890	NUM
ejpam-3018	339	16	-	-	SYM
ejpam-3018	339	17	907	907	NUM
ejpam-3018	339	18	904	904	NUM
ejpam-3018	339	19	(	(	PUNCT
ejpam-3018	339	20	iii	iii	NOUN
ejpam-3018	339	21	)	)	PUNCT
ejpam-3018	339	22	g	g	PROPN
ejpam-3018	339	23	∗(α	∗(α	PROPN
ejpam-3018	339	24	,	,	PUNCT
ejpam-3018	339	25	β	β	NOUN
ejpam-3018	339	26	)	)	PUNCT
ejpam-3018	339	27	n	n	CCONJ
ejpam-3018	339	28	,	,	PUNCT
ejpam-3018	339	29	c	c	X
ejpam-3018	339	30	(	(	PUNCT
ejpam-3018	339	31	t2;x	t2;x	PROPN
ejpam-3018	339	32	)	)	PUNCT
ejpam-3018	339	33	=	=	SYM
ejpam-3018	340	1	(	(	PUNCT
ejpam-3018	340	2	n2	n2	ADJ
ejpam-3018	340	3	−	−	PROPN
ejpam-3018	340	4	c2	c2	PROPN
ejpam-3018	340	5	)	)	PUNCT
ejpam-3018	340	6	n(n−	n(n−	PROPN
ejpam-3018	340	7	2c	2c	NUM
ejpam-3018	340	8	)	)	PUNCT
ejpam-3018	340	9	x2	x2	PROPN
ejpam-3018	340	10	+	+	NUM
ejpam-3018	340	11	2n(n−	2n(n−	NUM
ejpam-3018	340	12	c)−	c)−	PROPN
ejpam-3018	340	13	2αc(2n−	2αc(2n−	NUM
ejpam-3018	340	14	c	c	NOUN
ejpam-3018	340	15	)	)	PUNCT
ejpam-3018	340	16	n(n−	n(n−	NOUN
ejpam-3018	340	17	2c)(n+	2c)(n+	NUM
ejpam-3018	340	18	β	β	NOUN
ejpam-3018	340	19	)	)	PUNCT
ejpam-3018	340	20	x+	x+	PUNCT
ejpam-3018	340	21	α2c(2n−	α2c(2n−	PROPN
ejpam-3018	340	22	c)−	c)−	PROPN
ejpam-3018	340	23	2αn(n−	2αn(n−	NUM
ejpam-3018	340	24	c	c	NOUN
ejpam-3018	340	25	)	)	PUNCT
ejpam-3018	340	26	n(n−	n(n−	NOUN
ejpam-3018	340	27	2c)(n+	2c)(n+	NUM
ejpam-3018	340	28	β)2	β)2	ADV
ejpam-3018	340	29	.	.	PUNCT
ejpam-3018	341	1	consequently	consequently	ADV
ejpam-3018	341	2	,	,	PUNCT
ejpam-3018	341	3	for	for	ADP
ejpam-3018	341	4	each	each	DET
ejpam-3018	341	5	x	x	SYM
ejpam-3018	341	6	∈	∈	PROPN
ejpam-3018	341	7	in	in	ADV
ejpam-3018	341	8	,	,	PUNCT
ejpam-3018	341	9	we	we	PRON
ejpam-3018	341	10	have	have	VERB
ejpam-3018	341	11	the	the	DET
ejpam-3018	341	12	following	follow	VERB
ejpam-3018	341	13	equalities	equality	NOUN
ejpam-3018	341	14	g	g	PROPN
ejpam-3018	341	15	∗(α	∗(α	PROPN
ejpam-3018	341	16	,	,	PUNCT
ejpam-3018	341	17	β	β	NOUN
ejpam-3018	341	18	)	)	PUNCT
ejpam-3018	341	19	n	n	CCONJ
ejpam-3018	341	20	,	,	PUNCT
ejpam-3018	341	21	c	c	PROPN
ejpam-3018	341	22	(	(	PUNCT
ejpam-3018	341	23	t−	t−	PROPN
ejpam-3018	341	24	x;x	x;x	NUM
ejpam-3018	341	25	)	)	PUNCT
ejpam-3018	342	1	=	=	PUNCT
ejpam-3018	342	2	0	0	NUM
ejpam-3018	343	1	g	g	PROPN
ejpam-3018	343	2	∗(α	∗(α	PROPN
ejpam-3018	343	3	,	,	PUNCT
ejpam-3018	343	4	β	β	NOUN
ejpam-3018	343	5	)	)	PUNCT
ejpam-3018	343	6	n	n	CCONJ
ejpam-3018	343	7	,	,	PUNCT
ejpam-3018	343	8	c	c	X
ejpam-3018	343	9	(	(	PUNCT
ejpam-3018	343	10	(	(	PUNCT
ejpam-3018	343	11	t−	t−	PROPN
ejpam-3018	343	12	x)2;x	x)2;x	NUM
ejpam-3018	343	13	)	)	PUNCT
ejpam-3018	343	14	=	=	VERB
ejpam-3018	344	1	c(2n−	c(2n−	NUM
ejpam-3018	344	2	c	c	NOUN
ejpam-3018	344	3	)	)	PUNCT
ejpam-3018	344	4	n(n−	n(n−	PROPN
ejpam-3018	344	5	2c	2c	NUM
ejpam-3018	344	6	)	)	PUNCT
ejpam-3018	344	7	x2	x2	PROPN
ejpam-3018	345	1	+	+	CCONJ
ejpam-3018	345	2	2n(n−	2n(n−	NUM
ejpam-3018	345	3	c)−	c)−	PROPN
ejpam-3018	345	4	2cα(2n−	2cα(2n−	NUM
ejpam-3018	345	5	c	c	X
ejpam-3018	345	6	)	)	PUNCT
ejpam-3018	345	7	n(n−	n(n−	NOUN
ejpam-3018	345	8	2c)(n+	2c)(n+	NUM
ejpam-3018	345	9	β	β	NOUN
ejpam-3018	345	10	)	)	PUNCT
ejpam-3018	345	11	x	x	PUNCT
ejpam-3018	346	1	+	+	CCONJ
ejpam-3018	346	2	α2c(2n−	α2c(2n−	PROPN
ejpam-3018	346	3	c)−	c)−	PROPN
ejpam-3018	346	4	2αn(n−	2αn(n−	NUM
ejpam-3018	346	5	c	c	NOUN
ejpam-3018	346	6	)	)	PUNCT
ejpam-3018	346	7	n(n−	n(n−	NOUN
ejpam-3018	346	8	2c)(n+	2c)(n+	NUM
ejpam-3018	346	9	β)2	β)2	NOUN
ejpam-3018	346	10	=	=	NOUN
ejpam-3018	346	11	ζ(α	ζ(α	PROPN
ejpam-3018	346	12	,	,	PUNCT
ejpam-3018	346	13	β)n	β)n	NOUN
ejpam-3018	346	14	,	,	PUNCT
ejpam-3018	346	15	c	c	PROPN
ejpam-3018	346	16	(	(	PUNCT
ejpam-3018	346	17	x	x	NOUN
ejpam-3018	346	18	)	)	PUNCT
ejpam-3018	346	19	,	,	PUNCT
ejpam-3018	346	20	(	(	PUNCT
ejpam-3018	346	21	say	say	INTJ
ejpam-3018	346	22	)	)	PUNCT
ejpam-3018	346	23	.	.	PUNCT
ejpam-3018	347	1	(	(	PUNCT
ejpam-3018	347	2	19	19	NUM
ejpam-3018	347	3	)	)	PUNCT
ejpam-3018	347	4	theorem	theorem	VERB
ejpam-3018	347	5	14	14	NUM
ejpam-3018	347	6	.	.	PUNCT
ejpam-3018	348	1	let	let	VERB
ejpam-3018	348	2	f	f	PROPN
ejpam-3018	348	3	∈	∈	PROPN
ejpam-3018	348	4	cb(in	cb(in	PROPN
ejpam-3018	348	5	)	)	PUNCT
ejpam-3018	348	6	and	and	CCONJ
ejpam-3018	348	7	x	x	PUNCT
ejpam-3018	348	8	∈	∈	NOUN
ejpam-3018	348	9	in	in	ADP
ejpam-3018	348	10	.	.	PUNCT
ejpam-3018	349	1	then	then	ADV
ejpam-3018	349	2	for	for	ADP
ejpam-3018	349	3	n	n	PROPN
ejpam-3018	349	4	>	>	X
ejpam-3018	349	5	2c	2c	NOUN
ejpam-3018	349	6	,	,	PUNCT
ejpam-3018	349	7	there	there	PRON
ejpam-3018	349	8	exists	exist	VERB
ejpam-3018	349	9	a	a	DET
ejpam-3018	349	10	positive	positive	ADJ
ejpam-3018	349	11	constant	constant	ADJ
ejpam-3018	349	12	c	c	NOUN
ejpam-3018	349	13	′	′	NUM
ejpam-3018	349	14	such	such	ADJ
ejpam-3018	350	1	that	that	SCONJ
ejpam-3018	350	2	|g∗(α	|g∗(α	PROPN
ejpam-3018	350	3	,	,	PUNCT
ejpam-3018	350	4	β)n	β)n	NOUN
ejpam-3018	350	5	,	,	PUNCT
ejpam-3018	350	6	c	c	PROPN
ejpam-3018	350	7	(	(	PUNCT
ejpam-3018	350	8	f	f	PROPN
ejpam-3018	350	9	;	;	PUNCT
ejpam-3018	350	10	x)−	x)−	PROPN
ejpam-3018	350	11	f(x)|	f(x)|	VERB
ejpam-3018	350	12	≤	≤	NUM
ejpam-3018	350	13	c	c	NOUN
ejpam-3018	350	14	′ω2	′ω2	NUM
ejpam-3018	350	15	(	(	PUNCT
ejpam-3018	350	16	f	f	X
ejpam-3018	350	17	,	,	PUNCT
ejpam-3018	350	18	√	√	VERB
ejpam-3018	350	19	ζ	ζ	NOUN
ejpam-3018	350	20	(	(	PUNCT
ejpam-3018	350	21	α	α	NOUN
ejpam-3018	350	22	,	,	PUNCT
ejpam-3018	350	23	β	β	NOUN
ejpam-3018	350	24	)	)	PUNCT
ejpam-3018	350	25	n	n	CCONJ
ejpam-3018	350	26	,	,	PUNCT
ejpam-3018	350	27	c	c	PROPN
ejpam-3018	350	28	(	(	PUNCT
ejpam-3018	350	29	x	x	NOUN
ejpam-3018	350	30	)	)	PUNCT
ejpam-3018	350	31	)	)	PUNCT
ejpam-3018	350	32	,	,	PUNCT
ejpam-3018	350	33	where	where	SCONJ
ejpam-3018	350	34	ζ	ζ	X
ejpam-3018	350	35	(	(	PUNCT
ejpam-3018	350	36	α	α	NOUN
ejpam-3018	350	37	,	,	PUNCT
ejpam-3018	350	38	β	β	NOUN
ejpam-3018	350	39	)	)	PUNCT
ejpam-3018	350	40	n	n	CCONJ
ejpam-3018	350	41	,	,	PUNCT
ejpam-3018	350	42	c	c	PROPN
ejpam-3018	350	43	(	(	PUNCT
ejpam-3018	350	44	x	x	X
ejpam-3018	350	45	)	)	PUNCT
ejpam-3018	350	46	is	be	AUX
ejpam-3018	350	47	given	give	VERB
ejpam-3018	350	48	by	by	ADP
ejpam-3018	350	49	(	(	PUNCT
ejpam-3018	350	50	19	19	NUM
ejpam-3018	350	51	)	)	PUNCT
ejpam-3018	350	52	.	.	PUNCT
ejpam-3018	351	1	proof	proof	NOUN
ejpam-3018	351	2	.	.	PUNCT
ejpam-3018	352	1	let	let	VERB
ejpam-3018	352	2	g	g	PROPN
ejpam-3018	352	3	∈w	∈w	NOUN
ejpam-3018	352	4	2	2	NUM
ejpam-3018	352	5	and	and	CCONJ
ejpam-3018	352	6	x	x	NOUN
ejpam-3018	352	7	,	,	PUNCT
ejpam-3018	352	8	t	t	PROPN
ejpam-3018	352	9	∈	∈	PROPN
ejpam-3018	352	10	in	in	ADP
ejpam-3018	352	11	.	.	PUNCT
ejpam-3018	353	1	using	use	VERB
ejpam-3018	353	2	the	the	DET
ejpam-3018	353	3	taylor	taylor	PROPN
ejpam-3018	353	4	’s	’s	PART
ejpam-3018	353	5	expansion	expansion	NOUN
ejpam-3018	353	6	we	we	PRON
ejpam-3018	353	7	have	have	VERB
ejpam-3018	353	8	g(t	g(t	PROPN
ejpam-3018	353	9	)	)	PUNCT
ejpam-3018	354	1	=	=	SYM
ejpam-3018	354	2	g(x	g(x	NOUN
ejpam-3018	354	3	)	)	PUNCT
ejpam-3018	355	1	+	+	CCONJ
ejpam-3018	355	2	(	(	PUNCT
ejpam-3018	355	3	t−	t−	PROPN
ejpam-3018	355	4	x)g′(x	x)g′(x	PROPN
ejpam-3018	355	5	)	)	PUNCT
ejpam-3018	356	1	+	+	NUM
ejpam-3018	356	2	∫	∫	PROPN
ejpam-3018	356	3	t	t	NOUN
ejpam-3018	356	4	x	x	X
ejpam-3018	356	5	(	(	PUNCT
ejpam-3018	356	6	t−	t−	PROPN
ejpam-3018	356	7	v)g′′(v)dv	v)g′′(v)dv	PROPN
ejpam-3018	356	8	.	.	PUNCT
ejpam-3018	357	1	applying	apply	VERB
ejpam-3018	357	2	g	g	PROPN
ejpam-3018	357	3	∗(α	∗(α	PROPN
ejpam-3018	357	4	,	,	PUNCT
ejpam-3018	357	5	β	β	NOUN
ejpam-3018	357	6	)	)	PUNCT
ejpam-3018	357	7	n	n	CCONJ
ejpam-3018	357	8	,	,	PUNCT
ejpam-3018	357	9	c	c	PROPN
ejpam-3018	357	10	on	on	ADP
ejpam-3018	357	11	both	both	DET
ejpam-3018	357	12	sides	side	NOUN
ejpam-3018	357	13	and	and	CCONJ
ejpam-3018	357	14	using	use	VERB
ejpam-3018	357	15	lemma	lemma	PROPN
ejpam-3018	357	16	13	13	NUM
ejpam-3018	357	17	,	,	PUNCT
ejpam-3018	357	18	we	we	PRON
ejpam-3018	357	19	get	get	VERB
ejpam-3018	357	20	g	g	PROPN
ejpam-3018	357	21	∗(α	∗(α	PROPN
ejpam-3018	357	22	,	,	PUNCT
ejpam-3018	357	23	β	β	NOUN
ejpam-3018	357	24	)	)	PUNCT
ejpam-3018	357	25	n	n	CCONJ
ejpam-3018	357	26	,	,	PUNCT
ejpam-3018	357	27	c	c	PROPN
ejpam-3018	357	28	(	(	PUNCT
ejpam-3018	357	29	g;x)−	g;x)−	PROPN
ejpam-3018	357	30	g(x	g(x	PROPN
ejpam-3018	357	31	)	)	PUNCT
ejpam-3018	358	1	=	=	SYM
ejpam-3018	358	2	g	g	PROPN
ejpam-3018	358	3	∗(α	∗(α	PROPN
ejpam-3018	358	4	,	,	PUNCT
ejpam-3018	358	5	β	β	NOUN
ejpam-3018	358	6	)	)	PUNCT
ejpam-3018	358	7	n	n	CCONJ
ejpam-3018	358	8	,	,	PUNCT
ejpam-3018	358	9	c	c	PROPN
ejpam-3018	358	10	(	(	PUNCT
ejpam-3018	358	11	∫	∫	PROPN
ejpam-3018	358	12	t	t	PROPN
ejpam-3018	358	13	x	x	X
ejpam-3018	358	14	(	(	PUNCT
ejpam-3018	358	15	t−	t−	PROPN
ejpam-3018	358	16	v)g′′(v)dv;x	v)g′′(v)dv;x	PROPN
ejpam-3018	358	17	)	)	PUNCT
ejpam-3018	358	18	.	.	PUNCT
ejpam-3018	359	1	obviously	obviously	ADV
ejpam-3018	359	2	,	,	PUNCT
ejpam-3018	359	3	we	we	PRON
ejpam-3018	359	4	have	have	VERB
ejpam-3018	359	5	∣∣∣∣∫	∣∣∣∣∫	DET
ejpam-3018	359	6	t	t	NOUN
ejpam-3018	359	7	x	x	SYM
ejpam-3018	359	8	(	(	PUNCT
ejpam-3018	359	9	t−	t−	PROPN
ejpam-3018	359	10	v)g′′(v)dv	v)g′′(v)dv	PROPN
ejpam-3018	359	11	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3018	359	12	≤	≤	NOUN
ejpam-3018	359	13	(	(	PUNCT
ejpam-3018	359	14	t−	t−	PROPN
ejpam-3018	359	15	x)2‖g′′‖.	x)2‖g′′‖.	PROPN
ejpam-3018	359	16	therefore	therefore	ADV
ejpam-3018	359	17	|	|	ADV
ejpam-3018	359	18	g∗(α	g∗(α	PROPN
ejpam-3018	359	19	,	,	PUNCT
ejpam-3018	359	20	β)n	β)n	NOUN
ejpam-3018	359	21	,	,	PUNCT
ejpam-3018	359	22	c	c	PROPN
ejpam-3018	359	23	(	(	PUNCT
ejpam-3018	359	24	g;x)−	g;x)−	PROPN
ejpam-3018	359	25	g(x	g(x	PROPN
ejpam-3018	359	26	)	)	PUNCT
ejpam-3018	359	27	|≤	|≤	PROPN
ejpam-3018	359	28	g∗(α	g∗(α	PROPN
ejpam-3018	359	29	,	,	PUNCT
ejpam-3018	359	30	β)n	β)n	NOUN
ejpam-3018	359	31	,	,	PUNCT
ejpam-3018	359	32	c	c	NOUN
ejpam-3018	359	33	(	(	PUNCT
ejpam-3018	359	34	(	(	PUNCT
ejpam-3018	359	35	t−	t−	PROPN
ejpam-3018	359	36	x)2;x	x)2;x	NUM
ejpam-3018	359	37	)	)	PUNCT
ejpam-3018	360	1	‖	‖	PROPN
ejpam-3018	360	2	g′′	g′′	PROPN
ejpam-3018	360	3	‖=	‖=	PROPN
ejpam-3018	360	4	ζ(α	ζ(α	PROPN
ejpam-3018	360	5	,	,	PUNCT
ejpam-3018	360	6	β)n	β)n	NOUN
ejpam-3018	360	7	,	,	PUNCT
ejpam-3018	360	8	c	c	PROPN
ejpam-3018	360	9	(	(	PUNCT
ejpam-3018	360	10	x	x	X
ejpam-3018	360	11	)	)	PUNCT
ejpam-3018	360	12	‖	‖	PROPN
ejpam-3018	360	13	g′′	g′′	PROPN
ejpam-3018	360	14	‖	‖	PROPN
ejpam-3018	360	15	.	.	PUNCT
ejpam-3018	361	1	since	since	SCONJ
ejpam-3018	361	2	|	|	ADV
ejpam-3018	361	3	g∗(α	g∗(α	PROPN
ejpam-3018	361	4	,	,	PUNCT
ejpam-3018	361	5	β)n	β)n	NOUN
ejpam-3018	361	6	,	,	PUNCT
ejpam-3018	361	7	c	c	PROPN
ejpam-3018	361	8	(	(	PUNCT
ejpam-3018	361	9	f	f	PROPN
ejpam-3018	361	10	;	;	PUNCT
ejpam-3018	361	11	x	x	X
ejpam-3018	361	12	)	)	PUNCT
ejpam-3018	361	13	|≤	|≤	PROPN
ejpam-3018	361	14	‖f‖	‖f‖	PROPN
ejpam-3018	361	15	,	,	PUNCT
ejpam-3018	361	16	we	we	PRON
ejpam-3018	361	17	get	get	VERB
ejpam-3018	361	18	|	|	ADV
ejpam-3018	361	19	g∗(α	g∗(α	NOUN
ejpam-3018	361	20	,	,	PUNCT
ejpam-3018	361	21	β)n	β)n	NOUN
ejpam-3018	361	22	,	,	PUNCT
ejpam-3018	361	23	c	c	PROPN
ejpam-3018	361	24	(	(	PUNCT
ejpam-3018	361	25	f	f	PROPN
ejpam-3018	361	26	;	;	PUNCT
ejpam-3018	361	27	x)−	x)−	PROPN
ejpam-3018	361	28	f(x	f(x	PROPN
ejpam-3018	361	29	)	)	PUNCT
ejpam-3018	362	1	|	|	ADV
ejpam-3018	362	2	≤	≤	PUNCT
ejpam-3018	362	3	|	|	ADV
ejpam-3018	362	4	g∗(α	g∗(α	PROPN
ejpam-3018	362	5	,	,	PUNCT
ejpam-3018	362	6	β)n	β)n	NOUN
ejpam-3018	362	7	,	,	PUNCT
ejpam-3018	362	8	c	c	PROPN
ejpam-3018	362	9	(	(	PUNCT
ejpam-3018	362	10	f	f	PROPN
ejpam-3018	362	11	−	−	PROPN
ejpam-3018	363	1	g;x	g;x	PROPN
ejpam-3018	363	2	)	)	PUNCT
ejpam-3018	364	1	|	|	ADV
ejpam-3018	365	1	+	+	CCONJ
ejpam-3018	366	1	|	|	ADV
ejpam-3018	366	2	(	(	PUNCT
ejpam-3018	366	3	f	f	PROPN
ejpam-3018	366	4	−	−	PROPN
ejpam-3018	366	5	g)(x	g)(x	PROPN
ejpam-3018	366	6	)	)	PUNCT
ejpam-3018	366	7	|	|	ADV
ejpam-3018	367	1	+	+	CCONJ
ejpam-3018	367	2	|	|	ADV
ejpam-3018	367	3	g∗(α	g∗(α	NOUN
ejpam-3018	367	4	,	,	PUNCT
ejpam-3018	367	5	β)n	β)n	NOUN
ejpam-3018	367	6	,	,	PUNCT
ejpam-3018	367	7	c	c	PROPN
ejpam-3018	367	8	(	(	PUNCT
ejpam-3018	367	9	g;x)−	g;x)−	PROPN
ejpam-3018	367	10	g(x	g(x	PROPN
ejpam-3018	367	11	)	)	PUNCT
ejpam-3018	367	12	|	|	ADV
ejpam-3018	367	13	≤	≤	ADV
ejpam-3018	367	14	2‖f	2‖f	NUM
ejpam-3018	367	15	−	−	PROPN
ejpam-3018	367	16	g‖+	g‖+	PROPN
ejpam-3018	367	17	ζ(α	ζ(α	PROPN
ejpam-3018	367	18	,	,	PUNCT
ejpam-3018	367	19	β)n	β)n	NOUN
ejpam-3018	367	20	,	,	PUNCT
ejpam-3018	367	21	c	c	PROPN
ejpam-3018	367	22	(	(	PUNCT
ejpam-3018	367	23	x)‖g′′‖.	x)‖g′′‖.	NOUN
ejpam-3018	367	24	finally	finally	ADV
ejpam-3018	367	25	,	,	PUNCT
ejpam-3018	367	26	taking	take	VERB
ejpam-3018	367	27	the	the	DET
ejpam-3018	367	28	infimum	infimum	NOUN
ejpam-3018	367	29	over	over	ADP
ejpam-3018	367	30	all	all	PRON
ejpam-3018	367	31	g	g	NOUN
ejpam-3018	367	32	∈w	∈w	NOUN
ejpam-3018	367	33	2	2	NUM
ejpam-3018	367	34	and	and	CCONJ
ejpam-3018	367	35	using	use	VERB
ejpam-3018	367	36	(	(	PUNCT
ejpam-3018	367	37	11	11	NUM
ejpam-3018	367	38	)	)	PUNCT
ejpam-3018	367	39	we	we	PRON
ejpam-3018	367	40	obtain	obtain	VERB
ejpam-3018	367	41	|	|	ADV
ejpam-3018	367	42	g∗(α	g∗(α	NOUN
ejpam-3018	367	43	,	,	PUNCT
ejpam-3018	367	44	β)n	β)n	NOUN
ejpam-3018	367	45	,	,	PUNCT
ejpam-3018	367	46	c	c	PROPN
ejpam-3018	367	47	(	(	PUNCT
ejpam-3018	367	48	f	f	PROPN
ejpam-3018	367	49	;	;	PUNCT
ejpam-3018	367	50	x)−	x)−	PROPN
ejpam-3018	367	51	f(x	f(x	PROPN
ejpam-3018	367	52	)	)	PUNCT
ejpam-3018	368	1	|≤	|≤	PROPN
ejpam-3018	368	2	c	c	PROPN
ejpam-3018	368	3	′ω2	′ω2	NUM
ejpam-3018	368	4	(	(	PUNCT
ejpam-3018	368	5	f	f	X
ejpam-3018	368	6	,	,	PUNCT
ejpam-3018	368	7	√	√	VERB
ejpam-3018	368	8	ζ	ζ	NOUN
ejpam-3018	368	9	(	(	PUNCT
ejpam-3018	368	10	α	α	NOUN
ejpam-3018	368	11	,	,	PUNCT
ejpam-3018	368	12	β	β	NOUN
ejpam-3018	368	13	)	)	PUNCT
ejpam-3018	368	14	n	n	CCONJ
ejpam-3018	368	15	,	,	PUNCT
ejpam-3018	368	16	c	c	PROPN
ejpam-3018	368	17	(	(	PUNCT
ejpam-3018	368	18	x	x	NOUN
ejpam-3018	368	19	)	)	PUNCT
ejpam-3018	368	20	)	)	PUNCT
ejpam-3018	368	21	,	,	PUNCT
ejpam-3018	368	22	which	which	PRON
ejpam-3018	368	23	proves	prove	VERB
ejpam-3018	368	24	the	the	DET
ejpam-3018	368	25	theorem	theorem	PROPN
ejpam-3018	368	26	.	.	PROPN
ejpam-3018	369	1	references	reference	NOUN
ejpam-3018	369	2	905	905	NUM
ejpam-3018	369	3	theorem	theorem	VERB
ejpam-3018	369	4	15	15	NUM
ejpam-3018	369	5	.	.	PUNCT
ejpam-3018	370	1	let	let	VERB
ejpam-3018	370	2	f	f	PROPN
ejpam-3018	370	3	∈	∈	PROPN
ejpam-3018	370	4	cb(in	cb(in	PROPN
ejpam-3018	370	5	)	)	PUNCT
ejpam-3018	370	6	.	.	PUNCT
ejpam-3018	371	1	if	if	SCONJ
ejpam-3018	371	2	f	f	PROPN
ejpam-3018	371	3	′	′	PROPN
ejpam-3018	371	4	,	,	PUNCT
ejpam-3018	371	5	f	f	PROPN
ejpam-3018	372	1	′′	′′	PROPN
ejpam-3018	372	2	exists	exist	VERB
ejpam-3018	372	3	at	at	ADP
ejpam-3018	372	4	a	a	DET
ejpam-3018	372	5	fixed	fixed	ADJ
ejpam-3018	372	6	point	point	NOUN
ejpam-3018	372	7	x	x	X
ejpam-3018	372	8	∈	∈	NOUN
ejpam-3018	372	9	in	in	ADP
ejpam-3018	372	10	,	,	PUNCT
ejpam-3018	372	11	then	then	ADV
ejpam-3018	372	12	we	we	PRON
ejpam-3018	372	13	have	have	VERB
ejpam-3018	372	14	lim	lim	PROPN
ejpam-3018	372	15	n→∞	n→∞	NUM
ejpam-3018	372	16	n	n	CCONJ
ejpam-3018	372	17	(	(	PUNCT
ejpam-3018	372	18	g	g	PROPN
ejpam-3018	372	19	∗(α	∗(α	PROPN
ejpam-3018	372	20	,	,	PUNCT
ejpam-3018	372	21	β	β	NOUN
ejpam-3018	372	22	)	)	PUNCT
ejpam-3018	372	23	n	n	CCONJ
ejpam-3018	372	24	,	,	PUNCT
ejpam-3018	372	25	c	c	PROPN
ejpam-3018	372	26	(	(	PUNCT
ejpam-3018	372	27	f	f	PROPN
ejpam-3018	372	28	;	;	PUNCT
ejpam-3018	372	29	x)−	x)−	PROPN
ejpam-3018	372	30	f(x	f(x	PROPN
ejpam-3018	372	31	)	)	PUNCT
ejpam-3018	372	32	)	)	PUNCT
ejpam-3018	373	1	=	=	PUNCT
ejpam-3018	373	2	x(1	x(1	PROPN
ejpam-3018	373	3	+	+	PUNCT
ejpam-3018	373	4	cx)f	cx)f	PROPN
ejpam-3018	373	5	′′(x	′′(x	NOUN
ejpam-3018	373	6	)	)	PUNCT
ejpam-3018	373	7	.	.	PUNCT
ejpam-3018	374	1	the	the	DET
ejpam-3018	374	2	proof	proof	NOUN
ejpam-3018	374	3	follows	follow	VERB
ejpam-3018	374	4	along	along	ADP
ejpam-3018	374	5	the	the	DET
ejpam-3018	374	6	lines	line	NOUN
ejpam-3018	374	7	of	of	ADP
ejpam-3018	374	8	theorem	theorem	ADJ
ejpam-3018	374	9	4	4	NUM
ejpam-3018	374	10	.	.	PUNCT
ejpam-3018	375	1	acknowledgements	acknowledgement	NOUN
ejpam-3018	375	2	the	the	DET
ejpam-3018	375	3	authors	author	NOUN
ejpam-3018	375	4	are	be	AUX
ejpam-3018	375	5	thankful	thankful	ADJ
ejpam-3018	375	6	to	to	ADP
ejpam-3018	375	7	the	the	DET
ejpam-3018	375	8	reviewer	reviewer	NOUN
ejpam-3018	375	9	,	,	PUNCT
ejpam-3018	375	10	for	for	ADP
ejpam-3018	375	11	his	his	PRON
ejpam-3018	375	12	/	/	SYM
ejpam-3018	375	13	her	her	PRON
ejpam-3018	375	14	critical	critical	ADJ
ejpam-3018	375	15	suggestion	suggestion	NOUN
ejpam-3018	375	16	,	,	PUNCT
ejpam-3018	375	17	for	for	ADP
ejpam-3018	375	18	the	the	DET
ejpam-3018	375	19	overall	overall	ADJ
ejpam-3018	375	20	improvement	improvement	NOUN
ejpam-3018	375	21	of	of	ADP
ejpam-3018	375	22	the	the	DET
ejpam-3018	375	23	paper	paper	NOUN
ejpam-3018	375	24	.	.	PUNCT
ejpam-3018	376	1	references	reference	NOUN
ejpam-3018	376	2	[	[	X
ejpam-3018	376	3	1	1	X
ejpam-3018	376	4	]	]	PUNCT
ejpam-3018	376	5	t.	t.	NOUN
ejpam-3018	376	6	acar	acar	NOUN
ejpam-3018	376	7	,	,	PUNCT
ejpam-3018	376	8	l.n	l.n	PROPN
ejpam-3018	376	9	.	.	PROPN
ejpam-3018	376	10	mishra	mishra	PROPN
ejpam-3018	376	11	and	and	CCONJ
ejpam-3018	376	12	v.n	v.n	PROPN
ejpam-3018	376	13	.	.	PROPN
ejpam-3018	376	14	mishra	mishra	PROPN
ejpam-3018	376	15	,	,	PUNCT
ejpam-3018	376	16	simultaneous	simultaneous	ADJ
ejpam-3018	376	17	approximation	approximation	NOUN
ejpam-3018	376	18	for	for	ADP
ejpam-3018	376	19	generalized	generalized	ADJ
ejpam-3018	376	20	srivastava	srivastava	PROPN
ejpam-3018	376	21	-	-	PUNCT
ejpam-3018	376	22	gupta	gupta	PROPN
ejpam-3018	376	23	operators	operator	NOUN
ejpam-3018	376	24	,	,	PUNCT
ejpam-3018	376	25	j.	j.	PROPN
ejpam-3018	376	26	funct	funct	PROPN
ejpam-3018	376	27	.	.	PUNCT
ejpam-3018	377	1	spaces	space	NOUN
ejpam-3018	377	2	,	,	PUNCT
ejpam-3018	377	3	article	article	NOUN
ejpam-3018	377	4	i	i	PROPN
ejpam-3018	377	5	d	d	PROPN
ejpam-3018	377	6	936308	936308	NUM
ejpam-3018	377	7	,	,	PUNCT
ejpam-3018	377	8	11	11	NUM
ejpam-3018	377	9	pages	page	NOUN
ejpam-3018	377	10	,	,	PUNCT
ejpam-3018	377	11	2015	2015	NUM
ejpam-3018	377	12	.	.	PUNCT
ejpam-3018	378	1	[	[	X
ejpam-3018	378	2	2	2	NUM
ejpam-3018	378	3	]	]	X
ejpam-3018	378	4	p.n	p.n	PROPN
ejpam-3018	378	5	.	.	PROPN
ejpam-3018	378	6	agrawal	agrawal	PROPN
ejpam-3018	378	7	,	,	PUNCT
ejpam-3018	378	8	a.	a.	NOUN
ejpam-3018	378	9	sathish	sathish	PROPN
ejpam-3018	378	10	kumar	kumar	PROPN
ejpam-3018	378	11	and	and	CCONJ
ejpam-3018	378	12	t.a.k	t.a.k	NOUN
ejpam-3018	378	13	.	.	PUNCT
ejpam-3018	379	1	sinha	sinha	PROPN
ejpam-3018	379	2	,	,	PUNCT
ejpam-3018	379	3	stancu	stancu	ADJ
ejpam-3018	379	4	type	type	NOUN
ejpam-3018	379	5	generalization	generalization	NOUN
ejpam-3018	379	6	of	of	ADP
ejpam-3018	379	7	modified	modified	ADJ
ejpam-3018	379	8	schurer	schurer	NOUN
ejpam-3018	379	9	operators	operator	NOUN
ejpam-3018	379	10	based	base	VERB
ejpam-3018	379	11	on	on	ADP
ejpam-3018	379	12	q	q	ADJ
ejpam-3018	379	13	-	-	PUNCT
ejpam-3018	379	14	integers	integer	NOUN
ejpam-3018	379	15	,	,	PUNCT
ejpam-3018	379	16	appl	appl	PROPN
ejpam-3018	379	17	.	.	PROPN
ejpam-3018	379	18	math	math	NOUN
ejpam-3018	379	19	.	.	PUNCT
ejpam-3018	380	1	comput	comput	NOUN
ejpam-3018	380	2	.	.	PUNCT
ejpam-3018	381	1	226	226	NUM
ejpam-3018	381	2	,	,	PUNCT
ejpam-3018	381	3	765	765	NUM
ejpam-3018	381	4	-	-	SYM
ejpam-3018	381	5	776	776	NUM
ejpam-3018	381	6	,	,	PUNCT
ejpam-3018	381	7	2014	2014	NUM
ejpam-3018	381	8	.	.	PUNCT
ejpam-3018	382	1	[	[	X
ejpam-3018	382	2	3	3	X
ejpam-3018	382	3	]	]	X
ejpam-3018	382	4	n.	n.	PROPN
ejpam-3018	382	5	deo	deo	PROPN
ejpam-3018	382	6	,	,	PUNCT
ejpam-3018	382	7	faster	fast	ADJ
ejpam-3018	382	8	rate	rate	NOUN
ejpam-3018	382	9	of	of	ADP
ejpam-3018	382	10	convergence	convergence	NOUN
ejpam-3018	382	11	on	on	ADP
ejpam-3018	382	12	srivastava	srivastava	PROPN
ejpam-3018	382	13	-	-	PUNCT
ejpam-3018	382	14	gupta	gupta	PROPN
ejpam-3018	382	15	operators	operator	NOUN
ejpam-3018	382	16	,	,	PUNCT
ejpam-3018	382	17	appl	appl	PROPN
ejpam-3018	382	18	.	.	PROPN
ejpam-3018	382	19	math	math	NOUN
ejpam-3018	382	20	.	.	PUNCT
ejpam-3018	383	1	comput	comput	NOUN
ejpam-3018	383	2	.	.	PUNCT
ejpam-3018	384	1	218	218	NUM
ejpam-3018	384	2	,	,	PUNCT
ejpam-3018	384	3	10486	10486	NUM
ejpam-3018	384	4	-	-	SYM
ejpam-3018	384	5	10491	10491	NUM
ejpam-3018	384	6	,	,	PUNCT
ejpam-3018	384	7	2012	2012	NUM
ejpam-3018	384	8	.	.	PUNCT
ejpam-3018	385	1	[	[	X
ejpam-3018	385	2	4	4	NUM
ejpam-3018	385	3	]	]	X
ejpam-3018	385	4	r.a	r.a	PROPN
ejpam-3018	385	5	.	.	PROPN
ejpam-3018	385	6	devore	devore	PROPN
ejpam-3018	385	7	and	and	CCONJ
ejpam-3018	385	8	g.g	g.g	PROPN
ejpam-3018	385	9	.	.	PROPN
ejpam-3018	385	10	lorentz	lorentz	PROPN
ejpam-3018	385	11	,	,	PUNCT
ejpam-3018	385	12	constructive	constructive	ADJ
ejpam-3018	385	13	approximation	approximation	NOUN
ejpam-3018	385	14	,	,	PUNCT
ejpam-3018	385	15	springer	springer	NOUN
ejpam-3018	385	16	,	,	PUNCT
ejpam-3018	385	17	berlin	berlin	PROPN
ejpam-3018	385	18	(	(	PUNCT
ejpam-3018	385	19	1993	1993	NUM
ejpam-3018	385	20	)	)	PUNCT
ejpam-3018	385	21	.	.	PUNCT
ejpam-3018	386	1	[	[	X
ejpam-3018	386	2	5	5	X
ejpam-3018	386	3	]	]	X
ejpam-3018	386	4	e.e	e.e	PROPN
ejpam-3018	386	5	.	.	PROPN
ejpam-3018	386	6	duman	duman	PROPN
ejpam-3018	386	7	and	and	CCONJ
ejpam-3018	386	8	o.	o.	PROPN
ejpam-3018	386	9	duman	duman	PROPN
ejpam-3018	386	10	,	,	PUNCT
ejpam-3018	386	11	statistical	statistical	ADJ
ejpam-3018	386	12	approximation	approximation	NOUN
ejpam-3018	386	13	properties	property	NOUN
ejpam-3018	386	14	of	of	ADP
ejpam-3018	386	15	high	high	ADJ
ejpam-3018	386	16	order	order	NOUN
ejpam-3018	386	17	operators	operator	NOUN
ejpam-3018	386	18	constructed	construct	VERB
ejpam-3018	386	19	with	with	ADP
ejpam-3018	386	20	the	the	DET
ejpam-3018	386	21	chan	chan	PROPN
ejpam-3018	386	22	-	-	PUNCT
ejpam-3018	386	23	chayan	chayan	NOUN
ejpam-3018	386	24	-	-	PUNCT
ejpam-3018	386	25	srivastava	srivastava	PROPN
ejpam-3018	386	26	polynomials	polynomials	PROPN
ejpam-3018	386	27	,	,	PUNCT
ejpam-3018	386	28	appl	appl	PROPN
ejpam-3018	386	29	.	.	PROPN
ejpam-3018	386	30	math	math	NOUN
ejpam-3018	386	31	.	.	PUNCT
ejpam-3018	387	1	comput	comput	NOUN
ejpam-3018	387	2	.	.	PUNCT
ejpam-3018	388	1	218	218	NUM
ejpam-3018	388	2	,	,	PUNCT
ejpam-3018	388	3	1927	1927	NUM
ejpam-3018	388	4	-	-	SYM
ejpam-3018	388	5	1933	1933	NUM
ejpam-3018	388	6	,	,	PUNCT
ejpam-3018	388	7	2011	2011	NUM
ejpam-3018	388	8	.	.	PUNCT
ejpam-3018	389	1	[	[	X
ejpam-3018	389	2	6	6	NUM
ejpam-3018	389	3	]	]	X
ejpam-3018	389	4	e.e	e.e	PROPN
ejpam-3018	389	5	.	.	PROPN
ejpam-3018	389	6	duman	duman	PROPN
ejpam-3018	389	7	,	,	PUNCT
ejpam-3018	389	8	o.	o.	PROPN
ejpam-3018	389	9	duman	duman	PROPN
ejpam-3018	389	10	and	and	CCONJ
ejpam-3018	389	11	h.	h.	PROPN
ejpam-3018	389	12	m.	m.	PROPN
ejpam-3018	389	13	srivastava	srivastava	PROPN
ejpam-3018	389	14	,	,	PUNCT
ejpam-3018	389	15	statistical	statistical	ADJ
ejpam-3018	389	16	approximation	approximation	NOUN
ejpam-3018	389	17	of	of	ADP
ejpam-3018	389	18	certain	certain	ADJ
ejpam-3018	389	19	positive	positive	ADJ
ejpam-3018	389	20	linear	linear	PROPN
ejpam-3018	389	21	operators	operator	NOUN
ejpam-3018	389	22	constructed	construct	VERB
ejpam-3018	389	23	by	by	ADP
ejpam-3018	389	24	means	mean	NOUN
ejpam-3018	389	25	of	of	ADP
ejpam-3018	389	26	the	the	DET
ejpam-3018	389	27	chan	chan	PROPN
ejpam-3018	389	28	-	-	PUNCT
ejpam-3018	389	29	chayan	chayan	NOUN
ejpam-3018	389	30	-	-	PUNCT
ejpam-3018	389	31	srivastava	srivastava	PROPN
ejpam-3018	389	32	polynomials	polynomial	NOUN
ejpam-3018	389	33	.	.	PUNCT
ejpam-3018	390	1	appl	appl	PROPN
ejpam-3018	390	2	,	,	PUNCT
ejpam-3018	390	3	math	math	NOUN
ejpam-3018	390	4	.	.	PUNCT
ejpam-3018	391	1	comput	comput	NOUN
ejpam-3018	391	2	.	.	PUNCT
ejpam-3018	392	1	182	182	NUM
ejpam-3018	392	2	,	,	PUNCT
ejpam-3018	392	3	231	231	NUM
ejpam-3018	392	4	-	-	SYM
ejpam-3018	392	5	222	222	NUM
ejpam-3018	392	6	,	,	PUNCT
ejpam-3018	392	7	2006	2006	NUM
ejpam-3018	392	8	.	.	PUNCT
ejpam-3018	393	1	[	[	X
ejpam-3018	393	2	7	7	X
ejpam-3018	393	3	]	]	X
ejpam-3018	393	4	o.	o.	PROPN
ejpam-3018	393	5	duman	duman	PROPN
ejpam-3018	393	6	and	and	CCONJ
ejpam-3018	393	7	c.	c.	PROPN
ejpam-3018	393	8	orhan	orhan	PROPN
ejpam-3018	393	9	,	,	PUNCT
ejpam-3018	393	10	statistical	statistical	ADJ
ejpam-3018	393	11	approximation	approximation	NOUN
ejpam-3018	393	12	by	by	ADP
ejpam-3018	393	13	positive	positive	ADJ
ejpam-3018	393	14	linear	linear	PROPN
ejpam-3018	393	15	operators	operator	NOUN
ejpam-3018	393	16	,	,	PUNCT
ejpam-3018	393	17	studia	studia	PROPN
ejpam-3018	393	18	math	math	NOUN
ejpam-3018	393	19	.	.	PUNCT
ejpam-3018	394	1	161(2	161(2	NUM
ejpam-3018	394	2	)	)	PUNCT
ejpam-3018	394	3	,	,	PUNCT
ejpam-3018	394	4	187	187	NUM
ejpam-3018	394	5	-	-	SYM
ejpam-3018	394	6	197	197	NUM
ejpam-3018	394	7	,	,	PUNCT
ejpam-3018	394	8	2004	2004	NUM
ejpam-3018	394	9	.	.	PUNCT
ejpam-3018	395	1	[	[	X
ejpam-3018	395	2	8	8	NUM
ejpam-3018	395	3	]	]	X
ejpam-3018	395	4	a.d	a.d	PROPN
ejpam-3018	395	5	.	.	PROPN
ejpam-3018	395	6	gadjiev	gadjiev	PROPN
ejpam-3018	395	7	,	,	PUNCT
ejpam-3018	395	8	theorems	theorem	NOUN
ejpam-3018	395	9	of	of	ADP
ejpam-3018	395	10	the	the	DET
ejpam-3018	395	11	type	type	NOUN
ejpam-3018	395	12	of	of	ADP
ejpam-3018	395	13	p.	p.	PROPN
ejpam-3018	395	14	p.	p.	PROPN
ejpam-3018	396	1	korovkin	korovkin	PROPN
ejpam-3018	396	2	’s	’s	PART
ejpam-3018	396	3	theorems	theorem	NOUN
ejpam-3018	396	4	,	,	PUNCT
ejpam-3018	396	5	matematicheskie	matematicheskie	NOUN
ejpam-3018	396	6	zametki	zametki	NOUN
ejpam-3018	396	7	,	,	PUNCT
ejpam-3018	396	8	20(5	20(5	NUM
ejpam-3018	396	9	)	)	PUNCT
ejpam-3018	396	10	,	,	PUNCT
ejpam-3018	396	11	781	781	NUM
ejpam-3018	396	12	-	-	SYM
ejpam-3018	396	13	786	786	NUM
ejpam-3018	396	14	,	,	PUNCT
ejpam-3018	396	15	1976	1976	NUM
ejpam-3018	396	16	.	.	PUNCT
ejpam-3018	397	1	[	[	X
ejpam-3018	397	2	9	9	NUM
ejpam-3018	397	3	]	]	X
ejpam-3018	397	4	a.d	a.d	PROPN
ejpam-3018	397	5	.	.	PROPN
ejpam-3018	397	6	gadjiev	gadjiev	PROPN
ejpam-3018	397	7	,	,	PUNCT
ejpam-3018	397	8	r.o	r.o	PROPN
ejpam-3018	397	9	.	.	PROPN
ejpam-3018	397	10	efendiyev	efendiyev	PROPN
ejpam-3018	397	11	and	and	CCONJ
ejpam-3018	397	12	e.	e.	PROPN
ejpam-3018	397	13	ibikli	ibikli	PROPN
ejpam-3018	397	14	,	,	PUNCT
ejpam-3018	397	15	on	on	ADP
ejpam-3018	397	16	korovkin	korovkin	NOUN
ejpam-3018	397	17	type	type	NOUN
ejpam-3018	397	18	theorem	theorem	VERB
ejpam-3018	397	19	in	in	ADP
ejpam-3018	397	20	the	the	DET
ejpam-3018	397	21	space	space	NOUN
ejpam-3018	397	22	of	of	ADP
ejpam-3018	397	23	locally	locally	ADV
ejpam-3018	397	24	integrable	integrable	ADJ
ejpam-3018	397	25	functions	function	NOUN
ejpam-3018	397	26	,	,	PUNCT
ejpam-3018	397	27	czechoslovak	czechoslovak	ADJ
ejpam-3018	397	28	math	math	NOUN
ejpam-3018	397	29	.	.	PUNCT
ejpam-3018	398	1	j.	j.	PROPN
ejpam-3018	398	2	1(128	1(128	PROPN
ejpam-3018	398	3	)	)	PUNCT
ejpam-3018	398	4	,	,	PUNCT
ejpam-3018	398	5	45	45	NUM
ejpam-3018	398	6	-	-	SYM
ejpam-3018	398	7	53	53	NUM
ejpam-3018	398	8	,	,	PUNCT
ejpam-3018	398	9	2003	2003	NUM
ejpam-3018	398	10	.	.	PUNCT
ejpam-3018	399	1	[	[	X
ejpam-3018	399	2	10	10	NUM
ejpam-3018	399	3	]	]	X
ejpam-3018	399	4	a.d	a.d	PROPN
ejpam-3018	399	5	.	.	PROPN
ejpam-3018	399	6	gadjiev	gadjiev	PROPN
ejpam-3018	399	7	and	and	CCONJ
ejpam-3018	399	8	c.	c.	PROPN
ejpam-3018	399	9	orhan	orhan	PROPN
ejpam-3018	399	10	,	,	PUNCT
ejpam-3018	399	11	some	some	DET
ejpam-3018	399	12	approximation	approximation	NOUN
ejpam-3018	399	13	theorems	theorem	NOUN
ejpam-3018	399	14	via	via	ADP
ejpam-3018	399	15	statistical	statistical	ADJ
ejpam-3018	399	16	convergence	convergence	NOUN
ejpam-3018	399	17	,	,	PUNCT
ejpam-3018	399	18	rocky	rocky	ADJ
ejpam-3018	399	19	mountain	mountain	NOUN
ejpam-3018	399	20	.	.	PUNCT
ejpam-3018	400	1	j.	j.	PROPN
ejpam-3018	400	2	math	math	PROPN
ejpam-3018	400	3	.	.	PUNCT
ejpam-3018	401	1	32(1	32(1	NUM
ejpam-3018	401	2	)	)	PUNCT
ejpam-3018	401	3	,	,	PUNCT
ejpam-3018	401	4	129	129	NUM
ejpam-3018	401	5	-	-	SYM
ejpam-3018	401	6	138	138	NUM
ejpam-3018	401	7	,	,	PUNCT
ejpam-3018	401	8	2002	2002	NUM
ejpam-3018	401	9	.	.	PUNCT
ejpam-3018	402	1	references	reference	NOUN
ejpam-3018	402	2	906	906	NUM
ejpam-3018	402	3	[	[	SYM
ejpam-3018	402	4	11	11	NUM
ejpam-3018	402	5	]	]	X
ejpam-3018	402	6	a.r	a.r	PROPN
ejpam-3018	402	7	.	.	PROPN
ejpam-3018	402	8	gairola	gairola	PROPN
ejpam-3018	402	9	,	,	PUNCT
ejpam-3018	402	10	deepmala	deepmala	NOUN
ejpam-3018	402	11	and	and	CCONJ
ejpam-3018	402	12	l.n	l.n	PROPN
ejpam-3018	402	13	.	.	PROPN
ejpam-3018	402	14	mishra	mishra	PROPN
ejpam-3018	402	15	,	,	PUNCT
ejpam-3018	402	16	on	on	ADP
ejpam-3018	402	17	the	the	DET
ejpam-3018	402	18	q	q	NOUN
ejpam-3018	402	19	-	-	PUNCT
ejpam-3018	402	20	derivatives	derivative	NOUN
ejpam-3018	402	21	of	of	ADP
ejpam-3018	402	22	a	a	DET
ejpam-3018	402	23	certain	certain	ADJ
ejpam-3018	402	24	linear	linear	ADJ
ejpam-3018	402	25	positive	positive	ADJ
ejpam-3018	402	26	operators	operator	NOUN
ejpam-3018	402	27	,	,	PUNCT
ejpam-3018	402	28	iranian	iranian	ADJ
ejpam-3018	402	29	journal	journal	PROPN
ejpam-3018	402	30	of	of	ADP
ejpam-3018	402	31	science	science	NOUN
ejpam-3018	402	32	and	and	CCONJ
ejpam-3018	402	33	technology	technology	NOUN
ejpam-3018	402	34	,	,	PUNCT
ejpam-3018	402	35	transactions	transaction	VERB
ejpam-3018	402	36	a	a	DET
ejpam-3018	402	37	:	:	PUNCT
ejpam-3018	402	38	science	science	NOUN
ejpam-3018	402	39	,	,	PUNCT
ejpam-3018	402	40	(	(	PUNCT
ejpam-3018	402	41	2017	2017	NUM
ejpam-3018	402	42	)	)	PUNCT
ejpam-3018	402	43	,	,	PUNCT
ejpam-3018	402	44	doi	doi	X
ejpam-3018	402	45	10.1007	10.1007	NUM
ejpam-3018	402	46	/	/	SYM
ejpam-3018	402	47	s40995	s40995	VERB
ejpam-3018	402	48	-	-	PUNCT
ejpam-3018	402	49	017	017	NUM
ejpam-3018	402	50	-	-	PUNCT
ejpam-3018	402	51	0227	0227	NUM
ejpam-3018	402	52	-	-	SYM
ejpam-3018	402	53	8	8	NUM
ejpam-3018	402	54	.	.	PUNCT
ejpam-3018	403	1	[	[	X
ejpam-3018	403	2	12	12	NUM
ejpam-3018	403	3	]	]	X
ejpam-3018	403	4	a.r	a.r	PROPN
ejpam-3018	403	5	.	.	PROPN
ejpam-3018	403	6	gairola	gairola	PROPN
ejpam-3018	403	7	,	,	PUNCT
ejpam-3018	403	8	deepmala	deepmala	NOUN
ejpam-3018	403	9	and	and	CCONJ
ejpam-3018	403	10	l.n	l.n	PROPN
ejpam-3018	403	11	.	.	PROPN
ejpam-3018	403	12	mishra	mishra	PROPN
ejpam-3018	403	13	,	,	PUNCT
ejpam-3018	403	14	rate	rate	NOUN
ejpam-3018	403	15	of	of	ADP
ejpam-3018	403	16	approximation	approximation	NOUN
ejpam-3018	403	17	by	by	ADP
ejpam-3018	403	18	finite	finite	ADJ
ejpam-3018	403	19	iterates	iterate	NOUN
ejpam-3018	403	20	of	of	ADP
ejpam-3018	403	21	q	q	NOUN
ejpam-3018	403	22	-	-	PUNCT
ejpam-3018	403	23	durrmeyer	durrmeyer	NOUN
ejpam-3018	403	24	operators	operator	NOUN
ejpam-3018	403	25	,	,	PUNCT
ejpam-3018	403	26	proc	proc	PROPN
ejpam-3018	403	27	.	.	PUNCT
ejpam-3018	404	1	natl	natl	PROPN
ejpam-3018	404	2	.	.	PUNCT
ejpam-3018	405	1	acad	acad	PROPN
ejpam-3018	405	2	.	.	PUNCT
ejpam-3018	406	1	sci	sci	PROPN
ejpam-3018	406	2	.	.	PROPN
ejpam-3018	406	3	,	,	PUNCT
ejpam-3018	406	4	india	india	PROPN
ejpam-3018	406	5	,	,	PUNCT
ejpam-3018	406	6	sect	sect	NOUN
ejpam-3018	406	7	.	.	PUNCT
ejpam-3018	407	1	a	a	DET
ejpam-3018	407	2	phys	phy	NOUN
ejpam-3018	407	3	.	.	PUNCT
ejpam-3018	408	1	sci	sci	PROPN
ejpam-3018	408	2	.	.	PUNCT
ejpam-3018	408	3	(	(	PUNCT
ejpam-3018	408	4	april	april	PROPN
ejpam-3018	408	5	-	-	PUNCT
ejpam-3018	408	6	june	june	PROPN
ejpam-3018	408	7	2016	2016	NUM
ejpam-3018	408	8	)	)	PUNCT
ejpam-3018	408	9	86(2):229	86(2):229	NUM
ejpam-3018	408	10	-	-	SYM
ejpam-3018	408	11	234	234	NUM
ejpam-3018	408	12	(	(	PUNCT
ejpam-3018	408	13	2016	2016	NUM
ejpam-3018	408	14	)	)	PUNCT
ejpam-3018	408	15	.	.	PUNCT
ejpam-3018	409	1	doi	doi	NOUN
ejpam-3018	409	2	:	:	PUNCT
ejpam-3018	409	3	10.1007	10.1007	NUM
ejpam-3018	409	4	/	/	SYM
ejpam-3018	409	5	s40010	s40010	NOUN
ejpam-3018	409	6	-	-	PUNCT
ejpam-3018	409	7	016	016	NUM
ejpam-3018	409	8	-	-	PUNCT
ejpam-3018	409	9	0267	0267	NUM
ejpam-3018	409	10	-	-	PUNCT
ejpam-3018	409	11	z	z	NOUN
ejpam-3018	410	1	[	[	X
ejpam-3018	410	2	13	13	NUM
ejpam-3018	410	3	]	]	X
ejpam-3018	410	4	v.	v.	CCONJ
ejpam-3018	410	5	gupta	gupta	PROPN
ejpam-3018	410	6	,	,	PUNCT
ejpam-3018	410	7	m.k	m.k	PROPN
ejpam-3018	410	8	.	.	PUNCT
ejpam-3018	410	9	gupta	gupta	PROPN
ejpam-3018	410	10	and	and	CCONJ
ejpam-3018	410	11	v.	v.	ADP
ejpam-3018	410	12	vasishtha	vasishtha	ADJ
ejpam-3018	410	13	,	,	PUNCT
ejpam-3018	410	14	simultaneous	simultaneous	ADJ
ejpam-3018	410	15	approximation	approximation	NOUN
ejpam-3018	410	16	by	by	ADP
ejpam-3018	410	17	summationintegral	summationintegral	ADJ
ejpam-3018	410	18	type	type	NOUN
ejpam-3018	410	19	operators	operator	NOUN
ejpam-3018	410	20	,	,	PUNCT
ejpam-3018	410	21	nonlinear	nonlinear	ADJ
ejpam-3018	410	22	funct	funct	NOUN
ejpam-3018	410	23	.	.	PUNCT
ejpam-3018	411	1	anal	anal	PROPN
ejpam-3018	411	2	.	.	PUNCT
ejpam-3018	411	3	appl	appl	PROPN
ejpam-3018	411	4	.	.	PUNCT
ejpam-3018	412	1	8(3	8(3	NUM
ejpam-3018	412	2	)	)	PUNCT
ejpam-3018	412	3	,	,	PUNCT
ejpam-3018	412	4	399	399	NUM
ejpam-3018	412	5	-	-	SYM
ejpam-3018	412	6	412	412	NUM
ejpam-3018	412	7	,	,	PUNCT
ejpam-3018	412	8	2003	2003	NUM
ejpam-3018	412	9	.	.	PUNCT
ejpam-3018	413	1	[	[	X
ejpam-3018	413	2	14	14	NUM
ejpam-3018	413	3	]	]	X
ejpam-3018	413	4	r.b	r.b	PROPN
ejpam-3018	413	5	.	.	PROPN
ejpam-3018	413	6	gandhi	gandhi	PROPN
ejpam-3018	413	7	,	,	PUNCT
ejpam-3018	413	8	deepmala	deepmala	PROPN
ejpam-3018	413	9	and	and	CCONJ
ejpam-3018	413	10	v.n	v.n	PROPN
ejpam-3018	413	11	.	.	PROPN
ejpam-3018	413	12	mishra	mishra	PROPN
ejpam-3018	413	13	,	,	PUNCT
ejpam-3018	413	14	local	local	ADJ
ejpam-3018	413	15	and	and	CCONJ
ejpam-3018	413	16	global	global	ADJ
ejpam-3018	413	17	results	result	NOUN
ejpam-3018	413	18	for	for	ADP
ejpam-3018	413	19	modified	modify	VERB
ejpam-3018	413	20	szászmirakjan	szászmirakjan	PROPN
ejpam-3018	413	21	operators	operator	NOUN
ejpam-3018	413	22	,	,	PUNCT
ejpam-3018	413	23	math	math	NOUN
ejpam-3018	413	24	.	.	PUNCT
ejpam-3018	413	25	method	method	PROPN
ejpam-3018	413	26	.	.	PUNCT
ejpam-3018	414	1	appl	appl	PROPN
ejpam-3018	414	2	.	.	PUNCT
ejpam-3018	415	1	sci	sci	PROPN
ejpam-3018	415	2	.	.	PUNCT
ejpam-3018	416	1	(	(	PUNCT
ejpam-3018	416	2	2016	2016	NUM
ejpam-3018	416	3	)	)	PUNCT
ejpam-3018	416	4	,	,	PUNCT
ejpam-3018	416	5	doi	doi	NOUN
ejpam-3018	416	6	:	:	PUNCT
ejpam-3018	416	7	10.1002	10.1002	NUM
ejpam-3018	416	8	/	/	SYM
ejpam-3018	416	9	mma.4171	mma.4171	NOUN
ejpam-3018	416	10	.	.	PUNCT
ejpam-3018	417	1	[	[	X
ejpam-3018	417	2	15	15	NUM
ejpam-3018	417	3	]	]	X
ejpam-3018	417	4	alok	alok	PROPN
ejpam-3018	417	5	kumar	kumar	PROPN
ejpam-3018	417	6	,	,	PUNCT
ejpam-3018	417	7	voronovskaja	voronovskaja	AUX
ejpam-3018	417	8	type	type	VERB
ejpam-3018	417	9	asymptotic	asymptotic	ADJ
ejpam-3018	417	10	approximation	approximation	NOUN
ejpam-3018	417	11	by	by	ADP
ejpam-3018	417	12	general	general	ADJ
ejpam-3018	417	13	gamma	gamma	PROPN
ejpam-3018	417	14	type	type	NOUN
ejpam-3018	417	15	operators	operator	NOUN
ejpam-3018	417	16	,	,	PUNCT
ejpam-3018	417	17	int	int	NOUN
ejpam-3018	417	18	.	.	PUNCT
ejpam-3018	418	1	j.	j.	PROPN
ejpam-3018	418	2	of	of	ADP
ejpam-3018	418	3	mathematics	mathematics	PROPN
ejpam-3018	418	4	and	and	CCONJ
ejpam-3018	418	5	its	its	PRON
ejpam-3018	418	6	applications	application	NOUN
ejpam-3018	418	7	3(4	3(4	NOUN
ejpam-3018	418	8	-	-	SYM
ejpam-3018	418	9	b	b	NOUN
ejpam-3018	418	10	)	)	PUNCT
ejpam-3018	418	11	,	,	PUNCT
ejpam-3018	418	12	71	71	NUM
ejpam-3018	418	13	-	-	SYM
ejpam-3018	418	14	78	78	NUM
ejpam-3018	418	15	,	,	PUNCT
ejpam-3018	418	16	2015	2015	NUM
ejpam-3018	418	17	.	.	PUNCT
ejpam-3018	419	1	[	[	X
ejpam-3018	419	2	16	16	NUM
ejpam-3018	419	3	]	]	X
ejpam-3018	419	4	alok	alok	PROPN
ejpam-3018	419	5	kumar	kumar	PROPN
ejpam-3018	419	6	and	and	CCONJ
ejpam-3018	419	7	d.	d.	PROPN
ejpam-3018	419	8	k.	k.	PROPN
ejpam-3018	419	9	vishwakarma	vishwakarma	PROPN
ejpam-3018	419	10	,	,	PUNCT
ejpam-3018	419	11	global	global	ADJ
ejpam-3018	419	12	approximation	approximation	NOUN
ejpam-3018	419	13	theorems	theorem	NOUN
ejpam-3018	419	14	for	for	ADP
ejpam-3018	419	15	general	general	ADJ
ejpam-3018	419	16	gamma	gamma	NOUN
ejpam-3018	419	17	type	type	NOUN
ejpam-3018	419	18	operators	operator	NOUN
ejpam-3018	419	19	,	,	PUNCT
ejpam-3018	419	20	int	int	NOUN
ejpam-3018	419	21	.	.	PUNCT
ejpam-3018	420	1	j.	j.	PROPN
ejpam-3018	420	2	of	of	ADP
ejpam-3018	420	3	adv	adv	PROPN
ejpam-3018	420	4	.	.	PUNCT
ejpam-3018	421	1	in	in	ADP
ejpam-3018	421	2	appl	appl	PROPN
ejpam-3018	421	3	.	.	PUNCT
ejpam-3018	421	4	math	math	PROPN
ejpam-3018	421	5	.	.	PUNCT
ejpam-3018	422	1	and	and	CCONJ
ejpam-3018	422	2	mech	mech	NOUN
ejpam-3018	422	3	.	.	PUNCT
ejpam-3018	423	1	3(2	3(2	NUM
ejpam-3018	423	2	)	)	PUNCT
ejpam-3018	423	3	,	,	PUNCT
ejpam-3018	423	4	77	77	NUM
ejpam-3018	423	5	-	-	SYM
ejpam-3018	423	6	83	83	NUM
ejpam-3018	423	7	,	,	PUNCT
ejpam-3018	423	8	2015	2015	NUM
ejpam-3018	423	9	.	.	PUNCT
ejpam-3018	424	1	[	[	X
ejpam-3018	424	2	17	17	NUM
ejpam-3018	424	3	]	]	X
ejpam-3018	424	4	alok	alok	PROPN
ejpam-3018	424	5	kumar	kumar	PROPN
ejpam-3018	424	6	,	,	PUNCT
ejpam-3018	424	7	artee	artee	PROPN
ejpam-3018	424	8	and	and	CCONJ
ejpam-3018	424	9	d.	d.	PROPN
ejpam-3018	424	10	k.	k.	PROPN
ejpam-3018	424	11	vishwakarma	vishwakarma	PROPN
ejpam-3018	424	12	,	,	PUNCT
ejpam-3018	424	13	approximation	approximation	NOUN
ejpam-3018	424	14	properties	property	NOUN
ejpam-3018	424	15	of	of	ADP
ejpam-3018	424	16	general	general	ADJ
ejpam-3018	424	17	gamma	gamma	NOUN
ejpam-3018	424	18	type	type	NOUN
ejpam-3018	424	19	operators	operator	NOUN
ejpam-3018	424	20	in	in	ADP
ejpam-3018	424	21	polynomial	polynomial	ADJ
ejpam-3018	424	22	weighted	weight	VERB
ejpam-3018	424	23	space	space	NOUN
ejpam-3018	424	24	,	,	PUNCT
ejpam-3018	424	25	int	int	NOUN
ejpam-3018	424	26	.	.	PUNCT
ejpam-3018	425	1	j.	j.	PROPN
ejpam-3018	425	2	adv	adv	PROPN
ejpam-3018	425	3	.	.	PUNCT
ejpam-3018	425	4	appl	appl	PROPN
ejpam-3018	425	5	.	.	PROPN
ejpam-3018	425	6	math	math	PROPN
ejpam-3018	425	7	.	.	PUNCT
ejpam-3018	426	1	and	and	CCONJ
ejpam-3018	426	2	mech	mech	NOUN
ejpam-3018	426	3	.	.	PUNCT
ejpam-3018	427	1	4(3	4(3	NUM
ejpam-3018	427	2	)	)	PUNCT
ejpam-3018	427	3	,	,	PUNCT
ejpam-3018	427	4	7	7	NUM
ejpam-3018	427	5	-	-	SYM
ejpam-3018	427	6	13	13	NUM
ejpam-3018	427	7	,	,	PUNCT
ejpam-3018	427	8	2017	2017	NUM
ejpam-3018	427	9	.	.	PUNCT
ejpam-3018	428	1	[	[	X
ejpam-3018	428	2	18	18	NUM
ejpam-3018	428	3	]	]	X
ejpam-3018	428	4	j.p	j.p	PROPN
ejpam-3018	428	5	.	.	PROPN
ejpam-3018	428	6	king	king	PROPN
ejpam-3018	428	7	,	,	PUNCT
ejpam-3018	428	8	positive	positive	ADJ
ejpam-3018	428	9	linear	linear	NOUN
ejpam-3018	428	10	operators	operator	NOUN
ejpam-3018	428	11	which	which	PRON
ejpam-3018	428	12	preserve	preserve	VERB
ejpam-3018	428	13	x2	x2	PROPN
ejpam-3018	428	14	,	,	PUNCT
ejpam-3018	428	15	acta	acta	PROPN
ejpam-3018	428	16	math	math	PROPN
ejpam-3018	428	17	.	.	PUNCT
ejpam-3018	429	1	hungar	hungar	NOUN
ejpam-3018	429	2	.	.	PUNCT
ejpam-3018	430	1	99(3	99(3	NUM
ejpam-3018	430	2	)	)	PUNCT
ejpam-3018	430	3	,	,	PUNCT
ejpam-3018	430	4	203	203	NUM
ejpam-3018	430	5	-	-	SYM
ejpam-3018	430	6	208	208	NUM
ejpam-3018	430	7	,	,	PUNCT
ejpam-3018	430	8	2003	2003	NUM
ejpam-3018	430	9	.	.	PUNCT
ejpam-3018	431	1	[	[	X
ejpam-3018	431	2	19	19	NUM
ejpam-3018	431	3	]	]	PUNCT
ejpam-3018	431	4	b.	b.	PROPN
ejpam-3018	431	5	lenze	lenze	PROPN
ejpam-3018	431	6	,	,	PUNCT
ejpam-3018	431	7	on	on	ADP
ejpam-3018	431	8	lipschitz	lipschitz	NOUN
ejpam-3018	431	9	type	type	NOUN
ejpam-3018	431	10	maximal	maximal	ADJ
ejpam-3018	431	11	functions	function	NOUN
ejpam-3018	431	12	and	and	CCONJ
ejpam-3018	431	13	their	their	PRON
ejpam-3018	431	14	smoothness	smoothness	ADJ
ejpam-3018	431	15	spaces	space	NOUN
ejpam-3018	431	16	,	,	PUNCT
ejpam-3018	431	17	nederl	nederl	PROPN
ejpam-3018	431	18	.	.	PUNCT
ejpam-3018	431	19	akad	akad	NOUN
ejpam-3018	431	20	.	.	PUNCT
ejpam-3018	432	1	indag	indag	PROPN
ejpam-3018	432	2	.	.	PUNCT
ejpam-3018	433	1	math	math	NOUN
ejpam-3018	433	2	.	.	PUNCT
ejpam-3018	434	1	50	50	NUM
ejpam-3018	434	2	,	,	PUNCT
ejpam-3018	434	3	53	53	NUM
ejpam-3018	434	4	-	-	SYM
ejpam-3018	434	5	63	63	NUM
ejpam-3018	434	6	,	,	PUNCT
ejpam-3018	434	7	1988	1988	NUM
ejpam-3018	434	8	.	.	PUNCT
ejpam-3018	435	1	[	[	X
ejpam-3018	435	2	20	20	NUM
ejpam-3018	435	3	]	]	X
ejpam-3018	435	4	c.p	c.p	PROPN
ejpam-3018	435	5	.	.	PROPN
ejpam-3018	436	1	may	may	AUX
ejpam-3018	436	2	,	,	PUNCT
ejpam-3018	436	3	on	on	ADP
ejpam-3018	436	4	phillips	phillips	PROPN
ejpam-3018	436	5	operators	operators	PROPN
ejpam-3018	436	6	,	,	PUNCT
ejpam-3018	436	7	j.	j.	PROPN
ejpam-3018	436	8	approx	approx	PROPN
ejpam-3018	436	9	.	.	PUNCT
ejpam-3018	437	1	theory	theory	NOUN
ejpam-3018	437	2	,	,	PUNCT
ejpam-3018	437	3	20	20	NUM
ejpam-3018	437	4	,	,	PUNCT
ejpam-3018	437	5	315	315	NUM
ejpam-3018	437	6	-	-	SYM
ejpam-3018	437	7	332	332	NUM
ejpam-3018	437	8	,	,	PUNCT
ejpam-3018	437	9	1977	1977	NUM
ejpam-3018	437	10	.	.	PUNCT
ejpam-3018	438	1	[	[	X
ejpam-3018	438	2	21	21	NUM
ejpam-3018	438	3	]	]	X
ejpam-3018	438	4	l.n	l.n	PROPN
ejpam-3018	438	5	.	.	PROPN
ejpam-3018	438	6	mishra	mishra	PROPN
ejpam-3018	438	7	,	,	PUNCT
ejpam-3018	438	8	on	on	ADP
ejpam-3018	438	9	existence	existence	NOUN
ejpam-3018	438	10	and	and	CCONJ
ejpam-3018	438	11	behavior	behavior	NOUN
ejpam-3018	438	12	of	of	ADP
ejpam-3018	438	13	solutions	solution	NOUN
ejpam-3018	438	14	to	to	ADP
ejpam-3018	438	15	some	some	DET
ejpam-3018	438	16	nonlinear	nonlinear	ADJ
ejpam-3018	438	17	integral	integral	ADJ
ejpam-3018	438	18	equations	equation	NOUN
ejpam-3018	438	19	with	with	ADP
ejpam-3018	438	20	applications	application	NOUN
ejpam-3018	438	21	,	,	PUNCT
ejpam-3018	438	22	ph.d	ph.d	PROPN
ejpam-3018	438	23	.	.	PUNCT
ejpam-3018	439	1	thesis	thesis	NOUN
ejpam-3018	439	2	(	(	PUNCT
ejpam-3018	439	3	2017	2017	NUM
ejpam-3018	439	4	)	)	PUNCT
ejpam-3018	439	5	,	,	PUNCT
ejpam-3018	439	6	national	national	PROPN
ejpam-3018	439	7	institute	institute	PROPN
ejpam-3018	439	8	of	of	ADP
ejpam-3018	439	9	technology	technology	PROPN
ejpam-3018	439	10	,	,	PUNCT
ejpam-3018	439	11	silchar	silchar	PROPN
ejpam-3018	439	12	788	788	NUM
ejpam-3018	439	13	010	010	NUM
ejpam-3018	439	14	,	,	PUNCT
ejpam-3018	439	15	assam	assam	PROPN
ejpam-3018	439	16	,	,	PUNCT
ejpam-3018	439	17	india	india	PROPN
ejpam-3018	439	18	.	.	PUNCT
ejpam-3018	440	1	[	[	X
ejpam-3018	440	2	22	22	NUM
ejpam-3018	440	3	]	]	X
ejpam-3018	440	4	p.	p.	PROPN
ejpam-3018	440	5	maheshwari(sharma	maheshwari(sharma	PROPN
ejpam-3018	440	6	)	)	PUNCT
ejpam-3018	440	7	,	,	PUNCT
ejpam-3018	440	8	on	on	ADP
ejpam-3018	440	9	modified	modify	VERB
ejpam-3018	440	10	srivastava	srivastava	PROPN
ejpam-3018	440	11	-	-	PUNCT
ejpam-3018	440	12	gupta	gupta	PROPN
ejpam-3018	440	13	operators	operator	NOUN
ejpam-3018	440	14	,	,	PUNCT
ejpam-3018	440	15	filomat	filomat	NOUN
ejpam-3018	440	16	,	,	PUNCT
ejpam-3018	440	17	29:6	29:6	NUM
ejpam-3018	440	18	,	,	PUNCT
ejpam-3018	440	19	1173	1173	NUM
ejpam-3018	440	20	-	-	SYM
ejpam-3018	440	21	1177	1177	NUM
ejpam-3018	440	22	,	,	PUNCT
ejpam-3018	440	23	2015	2015	NUM
ejpam-3018	440	24	.	.	PUNCT
ejpam-3018	441	1	[	[	X
ejpam-3018	441	2	23	23	NUM
ejpam-3018	441	3	]	]	X
ejpam-3018	441	4	v.n	v.n	PROPN
ejpam-3018	441	5	.	.	PROPN
ejpam-3018	441	6	mishra	mishra	PROPN
ejpam-3018	441	7	,	,	PUNCT
ejpam-3018	441	8	p.	p.	PROPN
ejpam-3018	441	9	sharma	sharma	PROPN
ejpam-3018	441	10	and	and	CCONJ
ejpam-3018	441	11	l.n	l.n	PROPN
ejpam-3018	441	12	.	.	PROPN
ejpam-3018	441	13	mishra	mishra	PROPN
ejpam-3018	441	14	,	,	PUNCT
ejpam-3018	441	15	on	on	ADP
ejpam-3018	441	16	statistical	statistical	ADJ
ejpam-3018	441	17	approximation	approximation	NOUN
ejpam-3018	441	18	properties	property	NOUN
ejpam-3018	441	19	of	of	ADP
ejpam-3018	441	20	q	q	NOUN
ejpam-3018	441	21	-	-	PUNCT
ejpam-3018	441	22	baskakov	baskakov	PROPN
ejpam-3018	441	23	-	-	PUNCT
ejpam-3018	441	24	szász	szász	NUM
ejpam-3018	441	25	-	-	PUNCT
ejpam-3018	441	26	stancu	stancu	ADJ
ejpam-3018	441	27	operators	operator	NOUN
ejpam-3018	441	28	,	,	PUNCT
ejpam-3018	441	29	journal	journal	NOUN
ejpam-3018	441	30	of	of	ADP
ejpam-3018	441	31	egyptian	egyptian	PROPN
ejpam-3018	441	32	mathematical	mathematical	PROPN
ejpam-3018	441	33	society	society	NOUN
ejpam-3018	441	34	,	,	PUNCT
ejpam-3018	441	35	vol	vol	NOUN
ejpam-3018	441	36	.	.	PROPN
ejpam-3018	441	37	24	24	NUM
ejpam-3018	441	38	,	,	PUNCT
ejpam-3018	441	39	issue	issue	NOUN
ejpam-3018	441	40	3	3	NUM
ejpam-3018	441	41	,	,	PUNCT
ejpam-3018	441	42	2016	2016	NUM
ejpam-3018	441	43	,	,	PUNCT
ejpam-3018	441	44	pp	pp	ADJ
ejpam-3018	441	45	.	.	PUNCT
ejpam-3018	442	1	396	396	NUM
ejpam-3018	442	2	-	-	SYM
ejpam-3018	442	3	401	401	NUM
ejpam-3018	442	4	.	.	PUNCT
ejpam-3018	443	1	doi	doi	NOUN
ejpam-3018	443	2	:	:	PUNCT
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ejpam-3018	443	4	/	/	SYM
ejpam-3018	443	5	j.joems.2015.07.005	j.joems.2015.07.005	PROPN
ejpam-3018	443	6	.	.	PUNCT
ejpam-3018	444	1	[	[	X
ejpam-3018	444	2	24	24	NUM
ejpam-3018	444	3	]	]	X
ejpam-3018	444	4	v.n	v.n	PROPN
ejpam-3018	444	5	.	.	PROPN
ejpam-3018	444	6	mishra	mishra	PROPN
ejpam-3018	444	7	,	,	PUNCT
ejpam-3018	444	8	k.	k.	PROPN
ejpam-3018	444	9	khatri	khatri	PROPN
ejpam-3018	444	10	,	,	PUNCT
ejpam-3018	444	11	l.n	l.n	PROPN
ejpam-3018	444	12	.	.	PROPN
ejpam-3018	444	13	mishra	mishra	PROPN
ejpam-3018	444	14	and	and	CCONJ
ejpam-3018	444	15	deepmala	deepmala	PROPN
ejpam-3018	444	16	,	,	PUNCT
ejpam-3018	444	17	inverse	inverse	NOUN
ejpam-3018	444	18	result	result	NOUN
ejpam-3018	444	19	in	in	ADP
ejpam-3018	444	20	simultaneous	simultaneous	ADJ
ejpam-3018	444	21	approximation	approximation	NOUN
ejpam-3018	444	22	by	by	ADP
ejpam-3018	444	23	baskakov	baskakov	PROPN
ejpam-3018	444	24	-	-	PUNCT
ejpam-3018	444	25	durrmeyer	durrmeyer	NOUN
ejpam-3018	444	26	-	-	PUNCT
ejpam-3018	444	27	stancu	stancu	PROPN
ejpam-3018	444	28	operators	operator	NOUN
ejpam-3018	444	29	,	,	PUNCT
ejpam-3018	444	30	journal	journal	NOUN
ejpam-3018	444	31	of	of	ADP
ejpam-3018	444	32	inequalities	inequality	NOUN
ejpam-3018	444	33	and	and	CCONJ
ejpam-3018	444	34	applications	application	NOUN
ejpam-3018	444	35	2013	2013	NUM
ejpam-3018	444	36	,	,	PUNCT
ejpam-3018	444	37	2013:586	2013:586	NUM
ejpam-3018	444	38	.	.	PUNCT
ejpam-3018	444	39	doi:10.1186/1029	doi:10.1186/1029	VERB
ejpam-3018	444	40	-	-	PROPN
ejpam-3018	444	41	242x-2013	242x-2013	NUM
ejpam-3018	444	42	-	-	PUNCT
ejpam-3018	444	43	586	586	NUM
ejpam-3018	444	44	.	.	PUNCT
ejpam-3018	444	45	references	reference	NOUN
ejpam-3018	444	46	907	907	NUM
ejpam-3018	445	1	[	[	X
ejpam-3018	445	2	25	25	NUM
ejpam-3018	445	3	]	]	X
ejpam-3018	445	4	v.n	v.n	PROPN
ejpam-3018	445	5	.	.	PROPN
ejpam-3018	445	6	mishra	mishra	PROPN
ejpam-3018	445	7	,	,	PUNCT
ejpam-3018	445	8	h.h	h.h	PROPN
ejpam-3018	445	9	.	.	PROPN
ejpam-3018	445	10	khan	khan	PROPN
ejpam-3018	445	11	,	,	PUNCT
ejpam-3018	445	12	k.	k.	PROPN
ejpam-3018	445	13	khatri	khatri	PROPN
ejpam-3018	445	14	and	and	CCONJ
ejpam-3018	445	15	l.n	l.n	PROPN
ejpam-3018	445	16	.	.	PROPN
ejpam-3018	445	17	mishra	mishra	PROPN
ejpam-3018	445	18	,	,	PUNCT
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ejpam-3018	445	20	representation	representation	NOUN
ejpam-3018	445	21	for	for	ADP
ejpam-3018	445	22	baskakov	baskakov	PROPN
ejpam-3018	445	23	-	-	PUNCT
ejpam-3018	445	24	durrmeyer	durrmeyer	NOUN
ejpam-3018	445	25	-	-	PUNCT
ejpam-3018	445	26	stancu	stancu	NOUN
ejpam-3018	445	27	type	type	NOUN
ejpam-3018	445	28	operators	operator	NOUN
ejpam-3018	445	29	,	,	PUNCT
ejpam-3018	445	30	bulletin	bulletin	NOUN
ejpam-3018	445	31	of	of	ADP
ejpam-3018	445	32	mathematical	mathematical	ADJ
ejpam-3018	445	33	analysis	analysis	NOUN
ejpam-3018	445	34	and	and	CCONJ
ejpam-3018	445	35	applications	application	NOUN
ejpam-3018	445	36	,	,	PUNCT
ejpam-3018	445	37	volume	volume	NOUN
ejpam-3018	445	38	5	5	NUM
ejpam-3018	445	39	issue	issue	NOUN
ejpam-3018	445	40	3	3	NUM
ejpam-3018	445	41	(	(	PUNCT
ejpam-3018	445	42	2013	2013	NUM
ejpam-3018	445	43	)	)	PUNCT
ejpam-3018	445	44	,	,	PUNCT
ejpam-3018	445	45	pages	page	NOUN
ejpam-3018	445	46	18	18	NUM
ejpam-3018	445	47	-	-	SYM
ejpam-3018	445	48	26	26	NUM
ejpam-3018	445	49	.	.	PUNCT
ejpam-3018	446	1	[	[	X
ejpam-3018	446	2	26	26	NUM
ejpam-3018	446	3	]	]	X
ejpam-3018	446	4	v.n	v.n	PROPN
ejpam-3018	446	5	.	.	PROPN
ejpam-3018	446	6	mishra	mishra	PROPN
ejpam-3018	446	7	,	,	PUNCT
ejpam-3018	446	8	k.	k.	PROPN
ejpam-3018	446	9	khatri	khatri	PROPN
ejpam-3018	446	10	and	and	CCONJ
ejpam-3018	446	11	l.n	l.n	PROPN
ejpam-3018	446	12	.	.	PROPN
ejpam-3018	446	13	mishra	mishra	PROPN
ejpam-3018	446	14	,	,	PUNCT
ejpam-3018	446	15	on	on	ADP
ejpam-3018	446	16	simultaneous	simultaneous	ADJ
ejpam-3018	446	17	approximation	approximation	NOUN
ejpam-3018	446	18	for	for	ADP
ejpam-3018	446	19	baskakov	baskakov	PROPN
ejpam-3018	446	20	-	-	PUNCT
ejpam-3018	446	21	durrmeyer	durrmeyer	NOUN
ejpam-3018	446	22	-	-	PUNCT
ejpam-3018	446	23	stancu	stancu	NOUN
ejpam-3018	446	24	type	type	NOUN
ejpam-3018	446	25	operators	operator	NOUN
ejpam-3018	446	26	,	,	PUNCT
ejpam-3018	446	27	journal	journal	NOUN
ejpam-3018	446	28	of	of	ADP
ejpam-3018	446	29	ultra	ultra	ADJ
ejpam-3018	446	30	scientist	scientist	NOUN
ejpam-3018	446	31	of	of	ADP
ejpam-3018	446	32	physical	physical	ADJ
ejpam-3018	446	33	sciences	science	NOUN
ejpam-3018	446	34	,	,	PUNCT
ejpam-3018	446	35	vol	vol	NOUN
ejpam-3018	446	36	.	.	PROPN
ejpam-3018	446	37	24	24	NUM
ejpam-3018	446	38	,	,	PUNCT
ejpam-3018	446	39	no	no	INTJ
ejpam-3018	446	40	.	.	PUNCT
ejpam-3018	447	1	(	(	PUNCT
ejpam-3018	447	2	3	3	X
ejpam-3018	447	3	)	)	PUNCT
ejpam-3018	447	4	a	a	PRON
ejpam-3018	447	5	,	,	PUNCT
ejpam-3018	447	6	2012	2012	NUM
ejpam-3018	447	7	,	,	PUNCT
ejpam-3018	447	8	pp	pp	ADJ
ejpam-3018	447	9	.	.	PUNCT
ejpam-3018	448	1	567	567	NUM
ejpam-3018	448	2	-	-	SYM
ejpam-3018	448	3	577	577	NUM
ejpam-3018	448	4	.	.	PUNCT
ejpam-3018	449	1	[	[	X
ejpam-3018	449	2	27	27	NUM
ejpam-3018	449	3	]	]	X
ejpam-3018	449	4	v.n	v.n	PROPN
ejpam-3018	449	5	.	.	PROPN
ejpam-3018	449	6	mishra	mishra	PROPN
ejpam-3018	449	7	,	,	PUNCT
ejpam-3018	449	8	k.	k.	PROPN
ejpam-3018	449	9	khatri	khatri	PROPN
ejpam-3018	449	10	and	and	CCONJ
ejpam-3018	449	11	l.n	l.n	PROPN
ejpam-3018	449	12	.	.	PROPN
ejpam-3018	449	13	mishra	mishra	PROPN
ejpam-3018	449	14	,	,	PUNCT
ejpam-3018	449	15	some	some	DET
ejpam-3018	449	16	approximation	approximation	NOUN
ejpam-3018	449	17	properties	property	NOUN
ejpam-3018	449	18	of	of	ADP
ejpam-3018	449	19	qbaskakov	qbaskakov	NOUN
ejpam-3018	449	20	-	-	PUNCT
ejpam-3018	449	21	beta	beta	NOUN
ejpam-3018	449	22	-	-	PUNCT
ejpam-3018	449	23	stancu	stancu	NOUN
ejpam-3018	449	24	type	type	NOUN
ejpam-3018	449	25	operators	operator	NOUN
ejpam-3018	449	26	,	,	PUNCT
ejpam-3018	449	27	journal	journal	NOUN
ejpam-3018	449	28	of	of	ADP
ejpam-3018	449	29	calculus	calculus	NOUN
ejpam-3018	449	30	of	of	ADP
ejpam-3018	449	31	variations	variation	NOUN
ejpam-3018	449	32	,	,	PUNCT
ejpam-3018	449	33	volume	volume	NOUN
ejpam-3018	449	34	2013	2013	NUM
ejpam-3018	449	35	,	,	PUNCT
ejpam-3018	449	36	article	article	NOUN
ejpam-3018	449	37	i	i	PROPN
ejpam-3018	449	38	d	d	PROPN
ejpam-3018	449	39	814824	814824	NUM
ejpam-3018	449	40	,	,	PUNCT
ejpam-3018	449	41	8	8	NUM
ejpam-3018	449	42	pages	page	NOUN
ejpam-3018	449	43	.	.	PUNCT
ejpam-3018	450	1	http://dx.doi.org/10.1155/2013/814824	http://dx.doi.org/10.1155/2013/814824	PROPN
ejpam-3018	451	1	[	[	X
ejpam-3018	451	2	28	28	NUM
ejpam-3018	451	3	]	]	X
ejpam-3018	451	4	v.n	v.n	PROPN
ejpam-3018	451	5	.	.	PROPN
ejpam-3018	451	6	mishra	mishra	PROPN
ejpam-3018	451	7	,	,	PUNCT
ejpam-3018	451	8	k.	k.	PROPN
ejpam-3018	451	9	khatri	khatri	PROPN
ejpam-3018	451	10	and	and	CCONJ
ejpam-3018	451	11	l.n	l.n	PROPN
ejpam-3018	451	12	.	.	PROPN
ejpam-3018	451	13	mishra	mishra	PROPN
ejpam-3018	451	14	,	,	PUNCT
ejpam-3018	451	15	statistical	statistical	ADJ
ejpam-3018	451	16	approximation	approximation	NOUN
ejpam-3018	451	17	by	by	ADP
ejpam-3018	451	18	kantorovichtype	kantorovichtype	NOUN
ejpam-3018	451	19	discrete	discrete	ADJ
ejpam-3018	451	20	q	q	ADJ
ejpam-3018	451	21	-	-	PUNCT
ejpam-3018	451	22	beta	beta	ADJ
ejpam-3018	451	23	operators	operator	NOUN
ejpam-3018	451	24	,	,	PUNCT
ejpam-3018	451	25	advances	advance	NOUN
ejpam-3018	451	26	in	in	ADP
ejpam-3018	451	27	difference	difference	NOUN
ejpam-3018	451	28	equations	equation	NOUN
ejpam-3018	451	29	2013	2013	NUM
ejpam-3018	451	30	,	,	PUNCT
ejpam-3018	451	31	2013:345	2013:345	NUM
ejpam-3018	451	32	,	,	PUNCT
ejpam-3018	451	33	doi	doi	NOUN
ejpam-3018	451	34	:	:	PUNCT
ejpam-3018	451	35	10.1186/10.1186/1687	10.1186/10.1186/1687	NUM
ejpam-3018	451	36	-	-	PUNCT
ejpam-3018	451	37	1847	1847	NUM
ejpam-3018	451	38	-	-	PUNCT
ejpam-3018	451	39	2013	2013	NUM
ejpam-3018	451	40	-	-	SYM
ejpam-3018	451	41	345	345	NUM
ejpam-3018	451	42	.	.	PUNCT
ejpam-3018	452	1	[	[	X
ejpam-3018	452	2	29	29	NUM
ejpam-3018	452	3	]	]	PUNCT
ejpam-3018	452	4	t.	t.	PROPN
ejpam-3018	452	5	neer	neer	PROPN
ejpam-3018	452	6	,	,	PUNCT
ejpam-3018	452	7	n.	n.	NOUN
ejpam-3018	452	8	ispir	ispir	PROPN
ejpam-3018	452	9	and	and	CCONJ
ejpam-3018	452	10	p.n	p.n	PROPN
ejpam-3018	452	11	.	.	PROPN
ejpam-3018	452	12	agrawal	agrawal	PROPN
ejpam-3018	452	13	,	,	PUNCT
ejpam-3018	452	14	bezier	bezier	ADJ
ejpam-3018	452	15	variant	variant	NOUN
ejpam-3018	452	16	of	of	ADP
ejpam-3018	452	17	modified	modified	ADJ
ejpam-3018	452	18	srivastava	srivastava	PROPN
ejpam-3018	452	19	-	-	PUNCT
ejpam-3018	452	20	gupta	gupta	PROPN
ejpam-3018	452	21	operators	operator	NOUN
ejpam-3018	452	22	,	,	PUNCT
ejpam-3018	452	23	revista	revista	X
ejpam-3018	452	24	de	de	X
ejpam-3018	452	25	la	la	PROPN
ejpam-3018	452	26	unión	unión	PROPN
ejpam-3018	452	27	matemática	matemática	PROPN
ejpam-3018	452	28	argentina	argentina	PROPN
ejpam-3018	452	29	,	,	PUNCT
ejpam-3018	452	30	2017	2017	NUM
ejpam-3018	452	31	.	.	PUNCT
ejpam-3018	453	1	[	[	X
ejpam-3018	453	2	30	30	NUM
ejpam-3018	453	3	]	]	X
ejpam-3018	453	4	m.	m.	NOUN
ejpam-3018	453	5	a.	a.	PROPN
ejpam-3018	453	6	özarslan	özarslan	PROPN
ejpam-3018	453	7	and	and	CCONJ
ejpam-3018	453	8	h.	h.	PROPN
ejpam-3018	453	9	aktuǧlu	aktuǧlu	PROPN
ejpam-3018	453	10	,	,	PUNCT
ejpam-3018	453	11	local	local	ADJ
ejpam-3018	453	12	approximation	approximation	NOUN
ejpam-3018	453	13	for	for	ADP
ejpam-3018	453	14	certain	certain	ADJ
ejpam-3018	453	15	king	king	NOUN
ejpam-3018	453	16	type	type	NOUN
ejpam-3018	453	17	operators	operator	NOUN
ejpam-3018	453	18	,	,	PUNCT
ejpam-3018	453	19	filomat	filomat	PROPN
ejpam-3018	453	20	,	,	PUNCT
ejpam-3018	453	21	27:1	27:1	NUM
ejpam-3018	453	22	,	,	PUNCT
ejpam-3018	453	23	173	173	NUM
ejpam-3018	453	24	-	-	SYM
ejpam-3018	453	25	181	181	NUM
ejpam-3018	453	26	,	,	PUNCT
ejpam-3018	453	27	2013	2013	NUM
ejpam-3018	453	28	.	.	PUNCT
ejpam-3018	454	1	[	[	X
ejpam-3018	454	2	31	31	NUM
ejpam-3018	454	3	]	]	X
ejpam-3018	454	4	r.s	r.s	PROPN
ejpam-3018	454	5	.	.	PROPN
ejpam-3018	454	6	phillips	phillips	PROPN
ejpam-3018	454	7	,	,	PUNCT
ejpam-3018	454	8	an	an	DET
ejpam-3018	454	9	inversion	inversion	NOUN
ejpam-3018	454	10	formula	formula	NOUN
ejpam-3018	454	11	for	for	ADP
ejpam-3018	454	12	semi	semi	NOUN
ejpam-3018	454	13	-	-	NOUN
ejpam-3018	454	14	groups	group	NOUN
ejpam-3018	454	15	of	of	ADP
ejpam-3018	454	16	linear	linear	PROPN
ejpam-3018	454	17	operators	operator	NOUN
ejpam-3018	454	18	,	,	PUNCT
ejpam-3018	454	19	ann	ann	PROPN
ejpam-3018	454	20	.	.	PROPN
ejpam-3018	454	21	of	of	ADP
ejpam-3018	454	22	math	math	NOUN
ejpam-3018	454	23	.	.	PUNCT
ejpam-3018	455	1	(	(	PUNCT
ejpam-3018	455	2	ser-2	ser-2	ADV
ejpam-3018	455	3	)	)	PUNCT
ejpam-3018	455	4	352	352	NUM
ejpam-3018	455	5	-	-	SYM
ejpam-3018	455	6	356	356	NUM
ejpam-3018	455	7	,	,	PUNCT
ejpam-3018	455	8	1954	1954	NUM
ejpam-3018	455	9	.	.	PUNCT
ejpam-3018	456	1	[	[	X
ejpam-3018	456	2	32	32	NUM
ejpam-3018	456	3	]	]	PUNCT
ejpam-3018	456	4	p.	p.	NOUN
ejpam-3018	456	5	patel	patel	PROPN
ejpam-3018	456	6	and	and	CCONJ
ejpam-3018	456	7	v.n	v.n	PROPN
ejpam-3018	456	8	.	.	PROPN
ejpam-3018	456	9	mishra	mishra	PROPN
ejpam-3018	456	10	,	,	PUNCT
ejpam-3018	456	11	approximation	approximation	NOUN
ejpam-3018	456	12	properties	property	NOUN
ejpam-3018	456	13	of	of	ADP
ejpam-3018	456	14	certain	certain	ADJ
ejpam-3018	456	15	summation	summation	NOUN
ejpam-3018	456	16	integral	integral	ADJ
ejpam-3018	456	17	type	type	NOUN
ejpam-3018	456	18	operators	operator	NOUN
ejpam-3018	456	19	,	,	PUNCT
ejpam-3018	456	20	demonstratio	demonstratio	PROPN
ejpam-3018	456	21	mathematica	mathematica	PROPN
ejpam-3018	456	22	vol	vol	PROPN
ejpam-3018	456	23	.	.	PUNCT
ejpam-3018	457	1	xlviii	xlviii	PROPN
ejpam-3018	458	1	no	no	INTJ
ejpam-3018	458	2	.	.	PROPN
ejpam-3018	458	3	1	1	NUM
ejpam-3018	458	4	,	,	PUNCT
ejpam-3018	458	5	2015	2015	NUM
ejpam-3018	458	6	.	.	PUNCT
ejpam-3018	459	1	[	[	X
ejpam-3018	459	2	33	33	NUM
ejpam-3018	459	3	]	]	X
ejpam-3018	459	4	h.m	h.m	PROPN
ejpam-3018	459	5	.	.	PROPN
ejpam-3018	459	6	srivastava	srivastava	PROPN
ejpam-3018	459	7	and	and	CCONJ
ejpam-3018	459	8	v.	v.	ADP
ejpam-3018	459	9	gupta	gupta	PROPN
ejpam-3018	459	10	,	,	PUNCT
ejpam-3018	459	11	a	a	DET
ejpam-3018	459	12	certain	certain	ADJ
ejpam-3018	459	13	family	family	NOUN
ejpam-3018	459	14	of	of	ADP
ejpam-3018	459	15	summation	summation	NOUN
ejpam-3018	459	16	-	-	PUNCT
ejpam-3018	459	17	integral	integral	ADJ
ejpam-3018	459	18	type	type	NOUN
ejpam-3018	459	19	operators	operator	NOUN
ejpam-3018	459	20	,	,	PUNCT
ejpam-3018	459	21	math	math	NOUN
ejpam-3018	459	22	.	.	PUNCT
ejpam-3018	460	1	comput	comput	NOUN
ejpam-3018	460	2	.	.	PUNCT
ejpam-3018	461	1	modelling	model	VERB
ejpam-3018	461	2	37	37	NUM
ejpam-3018	461	3	,	,	PUNCT
ejpam-3018	461	4	1307	1307	NUM
ejpam-3018	461	5	-	-	SYM
ejpam-3018	461	6	1315	1315	NUM
ejpam-3018	461	7	,	,	PUNCT
ejpam-3018	461	8	2003	2003	NUM
ejpam-3018	461	9	.	.	PUNCT
ejpam-3018	462	1	[	[	X
ejpam-3018	462	2	34	34	NUM
ejpam-3018	462	3	]	]	X
ejpam-3018	462	4	d.d	d.d	PROPN
ejpam-3018	462	5	.	.	PROPN
ejpam-3018	462	6	stancu	stancu	PROPN
ejpam-3018	462	7	,	,	PUNCT
ejpam-3018	462	8	approximation	approximation	NOUN
ejpam-3018	462	9	of	of	ADP
ejpam-3018	462	10	functions	function	NOUN
ejpam-3018	462	11	by	by	ADP
ejpam-3018	462	12	a	a	DET
ejpam-3018	462	13	new	new	ADJ
ejpam-3018	462	14	class	class	NOUN
ejpam-3018	462	15	of	of	ADP
ejpam-3018	462	16	linear	linear	ADJ
ejpam-3018	462	17	polynomial	polynomial	ADJ
ejpam-3018	462	18	operators	operator	NOUN
ejpam-3018	462	19	,	,	PUNCT
ejpam-3018	462	20	rev	rev	PROPN
ejpam-3018	462	21	.	.	PROPN
ejpam-3018	462	22	roum	roum	PROPN
ejpam-3018	462	23	.	.	PUNCT
ejpam-3018	463	1	math	math	NOUN
ejpam-3018	463	2	.	.	PUNCT
ejpam-3018	464	1	pures	pure	NOUN
ejpam-3018	464	2	appl	appl	PROPN
ejpam-3018	464	3	.	.	PUNCT
ejpam-3018	464	4	13(8	13(8	NUM
ejpam-3018	464	5	)	)	PUNCT
ejpam-3018	464	6	,	,	PUNCT
ejpam-3018	464	7	1173	1173	NUM
ejpam-3018	464	8	-	-	SYM
ejpam-3018	464	9	1194	1194	NUM
ejpam-3018	464	10	,	,	PUNCT
ejpam-3018	464	11	1968	1968	NUM
ejpam-3018	464	12	.	.	PUNCT
ejpam-3018	465	1	[	[	X
ejpam-3018	465	2	35	35	NUM
ejpam-3018	465	3	]	]	X
ejpam-3018	465	4	d.k	d.k	PROPN
ejpam-3018	465	5	.	.	PROPN
ejpam-3018	465	6	verma	verma	PROPN
ejpam-3018	465	7	and	and	CCONJ
ejpam-3018	465	8	p.n	p.n	PROPN
ejpam-3018	465	9	.	.	PROPN
ejpam-3018	465	10	agrawal	agrawal	PROPN
ejpam-3018	465	11	,	,	PUNCT
ejpam-3018	465	12	convergence	convergence	NOUN
ejpam-3018	465	13	in	in	ADP
ejpam-3018	465	14	simultaneous	simultaneous	ADJ
ejpam-3018	465	15	approximation	approximation	NOUN
ejpam-3018	465	16	for	for	ADP
ejpam-3018	465	17	srivastava	srivastava	PROPN
ejpam-3018	465	18	-	-	PUNCT
ejpam-3018	465	19	gupta	gupta	PROPN
ejpam-3018	465	20	operators	operator	NOUN
ejpam-3018	465	21	,	,	PUNCT
ejpam-3018	465	22	math	math	NOUN
ejpam-3018	465	23	.	.	PUNCT
ejpam-3018	466	1	sci	sci	PROPN
ejpam-3018	466	2	.	.	PROPN
ejpam-3018	467	1	6	6	NUM
ejpam-3018	467	2	-	-	SYM
ejpam-3018	467	3	22	22	NUM
ejpam-3018	467	4	,	,	PUNCT
ejpam-3018	467	5	2012	2012	NUM
ejpam-3018	467	6	.	.	PUNCT
ejpam-3018	468	1	[	[	X
ejpam-3018	468	2	36	36	NUM
ejpam-3018	468	3	]	]	X
ejpam-3018	468	4	r.	r.	PROPN
ejpam-3018	468	5	yadav	yadav	PROPN
ejpam-3018	468	6	,	,	PUNCT
ejpam-3018	468	7	approximation	approximation	NOUN
ejpam-3018	468	8	by	by	ADP
ejpam-3018	468	9	modified	modify	VERB
ejpam-3018	468	10	srivastava	srivastava	PROPN
ejpam-3018	468	11	-	-	PUNCT
ejpam-3018	468	12	gupta	gupta	PROPN
ejpam-3018	468	13	operators	operator	NOUN
ejpam-3018	468	14	,	,	PUNCT
ejpam-3018	468	15	appl	appl	PROPN
ejpam-3018	468	16	.	.	PROPN
ejpam-3018	468	17	math	math	PROPN
ejpam-3018	468	18	.	.	PUNCT
ejpam-3018	469	1	comput	comput	NOUN
ejpam-3018	469	2	.	.	PUNCT
ejpam-3018	470	1	226	226	NUM
ejpam-3018	470	2	,	,	PUNCT
ejpam-3018	470	3	61	61	NUM
ejpam-3018	470	4	-	-	SYM
ejpam-3018	470	5	66	66	NUM
ejpam-3018	470	6	,	,	PUNCT
ejpam-3018	470	7	2014	2014	NUM
ejpam-3018	470	8	.	.	PUNCT