id	sid	tid	token	lemma	pos
ejpam-3305	1	1	direct	direct	ADJ
ejpam-3305	1	2	estimates	estimate	NOUN
ejpam-3305	1	3	for	for	ADP
ejpam-3305	1	4	certain	certain	ADJ
ejpam-3305	1	5	integral	integral	ADJ
ejpam-3305	1	6	type	type	NOUN
ejpam-3305	1	7	operators	operator	NOUN
ejpam-3305	1	8	european	european	PROPN
ejpam-3305	1	9	journal	journal	PROPN
ejpam-3305	1	10	of	of	ADP
ejpam-3305	1	11	pure	pure	ADJ
ejpam-3305	1	12	and	and	CCONJ
ejpam-3305	1	13	applied	apply	VERB
ejpam-3305	1	14	mathematics	mathematic	NOUN
ejpam-3305	1	15	vol	vol	NOUN
ejpam-3305	1	16	.	.	PUNCT
ejpam-3305	2	1	11	11	NUM
ejpam-3305	2	2	,	,	PUNCT
ejpam-3305	2	3	no	no	INTJ
ejpam-3305	2	4	.	.	NOUN
ejpam-3305	2	5	4	4	NUM
ejpam-3305	2	6	,	,	PUNCT
ejpam-3305	2	7	2018	2018	NUM
ejpam-3305	2	8	,	,	PUNCT
ejpam-3305	2	9	958	958	NUM
ejpam-3305	2	10	-	-	SYM
ejpam-3305	2	11	975	975	NUM
ejpam-3305	2	12	issn	issn	PROPN
ejpam-3305	2	13	1307	1307	NUM
ejpam-3305	2	14	-	-	SYM
ejpam-3305	2	15	5543	5543	NUM
ejpam-3305	2	16	–	–	PUNCT
ejpam-3305	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3305	2	18	published	publish	VERB
ejpam-3305	2	19	by	by	ADP
ejpam-3305	2	20	new	new	PROPN
ejpam-3305	2	21	york	york	PROPN
ejpam-3305	2	22	business	business	PROPN
ejpam-3305	2	23	global	global	ADJ
ejpam-3305	2	24	direct	direct	ADJ
ejpam-3305	2	25	estimates	estimate	NOUN
ejpam-3305	2	26	for	for	ADP
ejpam-3305	2	27	certain	certain	ADJ
ejpam-3305	2	28	integral	integral	ADJ
ejpam-3305	2	29	type	type	NOUN
ejpam-3305	2	30	operators	operator	NOUN
ejpam-3305	2	31	alok	alok	PROPN
ejpam-3305	2	32	kumar1	kumar1	PROPN
ejpam-3305	2	33	,	,	PUNCT
ejpam-3305	2	34	dipti	dipti	PROPN
ejpam-3305	2	35	tapiawala2,3	tapiawala2,3	PROPN
ejpam-3305	2	36	,	,	PUNCT
ejpam-3305	2	37	lakshmi	lakshmi	NOUN
ejpam-3305	2	38	narayan	narayan	NOUN
ejpam-3305	2	39	mishra4,5,∗	mishra4,5,∗	PROPN
ejpam-3305	2	40	1	1	NUM
ejpam-3305	2	41	department	department	NOUN
ejpam-3305	2	42	of	of	ADP
ejpam-3305	2	43	computer	computer	NOUN
ejpam-3305	2	44	science	science	NOUN
ejpam-3305	2	45	,	,	PUNCT
ejpam-3305	2	46	dev	dev	PROPN
ejpam-3305	2	47	sanskriti	sanskriti	PROPN
ejpam-3305	2	48	vishwavidyalaya	vishwavidyalaya	PROPN
ejpam-3305	2	49	,	,	PUNCT
ejpam-3305	2	50	haridwar	haridwar	NOUN
ejpam-3305	2	51	249	249	NUM
ejpam-3305	2	52	411	411	NUM
ejpam-3305	2	53	,	,	PUNCT
ejpam-3305	2	54	uttarakhand	uttarakhand	PROPN
ejpam-3305	2	55	,	,	PUNCT
ejpam-3305	2	56	india	india	PROPN
ejpam-3305	2	57	2	2	NUM
ejpam-3305	2	58	department	department	NOUN
ejpam-3305	2	59	of	of	ADP
ejpam-3305	2	60	mathematics	mathematic	NOUN
ejpam-3305	2	61	,	,	PUNCT
ejpam-3305	2	62	c	c	PROPN
ejpam-3305	2	63	u	u	PROPN
ejpam-3305	2	64	shah	shah	PROPN
ejpam-3305	2	65	university	university	NOUN
ejpam-3305	2	66	,	,	PUNCT
ejpam-3305	2	67	surendranagar	surendranagar	NUM
ejpam-3305	2	68	-	-	PUNCT
ejpam-3305	2	69	ahmedabad	ahmedabad	NOUN
ejpam-3305	2	70	high	high	ADJ
ejpam-3305	2	71	way	way	NOUN
ejpam-3305	2	72	nr	nr	PROPN
ejpam-3305	2	73	kotharity	kotharity	PROPN
ejpam-3305	2	74	village	village	NOUN
ejpam-3305	2	75	,	,	PUNCT
ejpam-3305	2	76	wadhwan	wadhwan	PROPN
ejpam-3305	2	77	city	city	PROPN
ejpam-3305	2	78	363	363	NUM
ejpam-3305	2	79	030	030	NUM
ejpam-3305	2	80	,	,	PUNCT
ejpam-3305	2	81	surendranagar	surendranagar	NOUN
ejpam-3305	2	82	,	,	PUNCT
ejpam-3305	2	83	gujarat	gujarat	NOUN
ejpam-3305	2	84	,	,	PUNCT
ejpam-3305	2	85	india	india	PROPN
ejpam-3305	2	86	3	3	NUM
ejpam-3305	2	87	as	as	ADP
ejpam-3305	2	88	and	and	CCONJ
ejpam-3305	2	89	h	h	PROPN
ejpam-3305	2	90	department	department	PROPN
ejpam-3305	2	91	(	(	PUNCT
ejpam-3305	2	92	mathematics	mathematics	PROPN
ejpam-3305	2	93	)	)	PUNCT
ejpam-3305	2	94	,	,	PUNCT
ejpam-3305	2	95	sardar	sardar	PROPN
ejpam-3305	2	96	vallabhbhai	vallabhbhai	PROPN
ejpam-3305	2	97	patel	patel	PROPN
ejpam-3305	2	98	institute	institute	PROPN
ejpam-3305	2	99	of	of	ADP
ejpam-3305	2	100	technology	technology	PROPN
ejpam-3305	2	101	,	,	PUNCT
ejpam-3305	2	102	vasad	vasad	PROPN
ejpam-3305	2	103	388	388	NUM
ejpam-3305	2	104	306	306	NUM
ejpam-3305	2	105	,	,	PUNCT
ejpam-3305	2	106	anand	anand	NOUN
ejpam-3305	2	107	,	,	PUNCT
ejpam-3305	2	108	gujarat	gujarat	PROPN
ejpam-3305	2	109	,	,	PUNCT
ejpam-3305	2	110	india	india	PROPN
ejpam-3305	2	111	4	4	NUM
ejpam-3305	2	112	department	department	NOUN
ejpam-3305	2	113	of	of	ADP
ejpam-3305	2	114	mathematics	mathematic	NOUN
ejpam-3305	2	115	,	,	PUNCT
ejpam-3305	2	116	school	school	NOUN
ejpam-3305	2	117	of	of	ADP
ejpam-3305	2	118	advanced	advanced	ADJ
ejpam-3305	2	119	sciences	science	NOUN
ejpam-3305	2	120	,	,	PUNCT
ejpam-3305	2	121	vellore	vellore	PROPN
ejpam-3305	2	122	institute	institute	PROPN
ejpam-3305	2	123	of	of	ADP
ejpam-3305	2	124	technology	technology	PROPN
ejpam-3305	2	125	(	(	PUNCT
ejpam-3305	2	126	vit	vit	NOUN
ejpam-3305	2	127	)	)	PUNCT
ejpam-3305	2	128	university	university	NOUN
ejpam-3305	2	129	,	,	PUNCT
ejpam-3305	2	130	vellore	vellore	VERB
ejpam-3305	2	131	632	632	NUM
ejpam-3305	2	132	014	014	NUM
ejpam-3305	2	133	,	,	PUNCT
ejpam-3305	2	134	tamil	tamil	PROPN
ejpam-3305	2	135	nadu	nadu	PROPN
ejpam-3305	2	136	,	,	PUNCT
ejpam-3305	2	137	india	india	PROPN
ejpam-3305	2	138	5	5	NUM
ejpam-3305	2	139	l.	l.	PROPN
ejpam-3305	2	140	1627	1627	NUM
ejpam-3305	2	141	awadh	awadh	NOUN
ejpam-3305	2	142	puri	puri	PROPN
ejpam-3305	2	143	colony	colony	NOUN
ejpam-3305	2	144	,	,	PUNCT
ejpam-3305	2	145	beniganj	beniganj	ADJ
ejpam-3305	2	146	,	,	PUNCT
ejpam-3305	2	147	phase	phase	NOUN
ejpam-3305	2	148	iiird	iiird	NOUN
ejpam-3305	2	149	,	,	PUNCT
ejpam-3305	2	150	opposite	opposite	ADJ
ejpam-3305	2	151	industrial	industrial	ADJ
ejpam-3305	2	152	training	training	NOUN
ejpam-3305	2	153	institute	institute	NOUN
ejpam-3305	2	154	(	(	PUNCT
ejpam-3305	2	155	i.t.i	i.t.i	NOUN
ejpam-3305	2	156	.	.	PUNCT
ejpam-3305	2	157	)	)	PUNCT
ejpam-3305	2	158	,	,	PUNCT
ejpam-3305	2	159	ayodhya	ayodhya	PROPN
ejpam-3305	2	160	main	main	ADJ
ejpam-3305	2	161	road	road	NOUN
ejpam-3305	2	162	,	,	PUNCT
ejpam-3305	2	163	faizabad	faizabad	NOUN
ejpam-3305	2	164	224	224	NUM
ejpam-3305	2	165	001	001	NUM
ejpam-3305	2	166	,	,	PUNCT
ejpam-3305	2	167	uttar	uttar	PROPN
ejpam-3305	2	168	pradesh	pradesh	PROPN
ejpam-3305	2	169	,	,	PUNCT
ejpam-3305	2	170	india	india	PROPN
ejpam-3305	2	171	abstract	abstract	NOUN
ejpam-3305	2	172	.	.	PUNCT
ejpam-3305	3	1	in	in	ADP
ejpam-3305	3	2	this	this	DET
ejpam-3305	3	3	note	note	NOUN
ejpam-3305	3	4	,	,	PUNCT
ejpam-3305	3	5	we	we	PRON
ejpam-3305	3	6	study	study	VERB
ejpam-3305	3	7	approximation	approximation	NOUN
ejpam-3305	3	8	properties	property	NOUN
ejpam-3305	3	9	of	of	ADP
ejpam-3305	3	10	a	a	DET
ejpam-3305	3	11	family	family	NOUN
ejpam-3305	3	12	of	of	ADP
ejpam-3305	3	13	linear	linear	PROPN
ejpam-3305	3	14	positive	positive	ADJ
ejpam-3305	3	15	operators	operator	NOUN
ejpam-3305	3	16	and	and	CCONJ
ejpam-3305	3	17	establish	establish	VERB
ejpam-3305	3	18	asymptotic	asymptotic	ADJ
ejpam-3305	3	19	formula	formula	NOUN
ejpam-3305	3	20	,	,	PUNCT
ejpam-3305	3	21	rate	rate	NOUN
ejpam-3305	3	22	of	of	ADP
ejpam-3305	3	23	convergence	convergence	NOUN
ejpam-3305	3	24	,	,	PUNCT
ejpam-3305	3	25	local	local	ADJ
ejpam-3305	3	26	approximation	approximation	NOUN
ejpam-3305	3	27	theorem	theorem	NOUN
ejpam-3305	3	28	,	,	PUNCT
ejpam-3305	3	29	global	global	ADJ
ejpam-3305	3	30	approximation	approximation	NOUN
ejpam-3305	3	31	theorem	theorem	PROPN
ejpam-3305	3	32	,	,	PUNCT
ejpam-3305	3	33	weighted	weighted	ADJ
ejpam-3305	3	34	approximation	approximation	NOUN
ejpam-3305	3	35	theorem	theorem	NOUN
ejpam-3305	3	36	and	and	CCONJ
ejpam-3305	3	37	better	well	ADJ
ejpam-3305	3	38	approximation	approximation	NOUN
ejpam-3305	3	39	for	for	ADP
ejpam-3305	3	40	this	this	DET
ejpam-3305	3	41	family	family	NOUN
ejpam-3305	3	42	of	of	ADP
ejpam-3305	3	43	linear	linear	PROPN
ejpam-3305	3	44	positive	positive	ADJ
ejpam-3305	3	45	operators	operator	NOUN
ejpam-3305	3	46	.	.	PUNCT
ejpam-3305	4	1	2010	2010	NUM
ejpam-3305	4	2	mathematics	mathematic	NOUN
ejpam-3305	4	3	subject	subject	NOUN
ejpam-3305	4	4	classifications	classification	NOUN
ejpam-3305	4	5	:	:	PUNCT
ejpam-3305	4	6	41a25	41a25	NUM
ejpam-3305	4	7	,	,	PUNCT
ejpam-3305	4	8	26a15	26a15	NUM
ejpam-3305	4	9	,	,	PUNCT
ejpam-3305	4	10	40a35	40a35	DET
ejpam-3305	4	11	key	key	ADJ
ejpam-3305	4	12	words	word	NOUN
ejpam-3305	4	13	and	and	CCONJ
ejpam-3305	4	14	phrases	phrase	NOUN
ejpam-3305	4	15	:	:	PUNCT
ejpam-3305	4	16	global	global	ADJ
ejpam-3305	4	17	approximation	approximation	NOUN
ejpam-3305	4	18	,	,	PUNCT
ejpam-3305	4	19	voronovskaja	voronovskaja	PROPN
ejpam-3305	4	20	type	type	NOUN
ejpam-3305	4	21	theorem	theorem	PROPN
ejpam-3305	4	22	,	,	PUNCT
ejpam-3305	4	23	k	k	ADJ
ejpam-3305	4	24	-	-	ADJ
ejpam-3305	4	25	functional	functional	ADJ
ejpam-3305	4	26	,	,	PUNCT
ejpam-3305	4	27	modulus	modulus	NOUN
ejpam-3305	4	28	of	of	ADP
ejpam-3305	4	29	continuity	continuity	NOUN
ejpam-3305	4	30	,	,	PUNCT
ejpam-3305	4	31	weighted	weight	VERB
ejpam-3305	4	32	approximation	approximation	NOUN
ejpam-3305	4	33	1	1	NUM
ejpam-3305	4	34	.	.	PUNCT
ejpam-3305	5	1	introduction	introduction	NOUN
ejpam-3305	5	2	in	in	ADP
ejpam-3305	5	3	the	the	DET
ejpam-3305	5	4	year	year	NOUN
ejpam-3305	5	5	2008	2008	NUM
ejpam-3305	5	6	,	,	PUNCT
ejpam-3305	5	7	mihes.an	mihes.an	X
ejpam-3305	6	1	[	[	X
ejpam-3305	6	2	38	38	NUM
ejpam-3305	6	3	]	]	PUNCT
ejpam-3305	6	4	constructed	construct	VERB
ejpam-3305	6	5	an	an	DET
ejpam-3305	6	6	important	important	ADJ
ejpam-3305	6	7	generalization	generalization	NOUN
ejpam-3305	6	8	of	of	ADP
ejpam-3305	6	9	the	the	DET
ejpam-3305	6	10	wellknown	wellknown	ADJ
ejpam-3305	6	11	szász	szász	PUNCT
ejpam-3305	6	12	operators	operator	NOUN
ejpam-3305	6	13	depending	depend	VERB
ejpam-3305	6	14	on	on	ADP
ejpam-3305	6	15	α	α	PROPN
ejpam-3305	6	16	∈	∈	NOUN
ejpam-3305	6	17	r	r	NOUN
ejpam-3305	6	18	as	as	ADP
ejpam-3305	6	19	g(α)n	g(α)n	PROPN
ejpam-3305	6	20	(	(	PUNCT
ejpam-3305	6	21	f	f	PROPN
ejpam-3305	6	22	;	;	PUNCT
ejpam-3305	6	23	x	x	X
ejpam-3305	6	24	)	)	PUNCT
ejpam-3305	6	25	=	=	PUNCT
ejpam-3305	7	1	∞∑	∞∑	NUM
ejpam-3305	7	2	k=0	k=0	PUNCT
ejpam-3305	7	3	m	m	VERB
ejpam-3305	7	4	(	(	PUNCT
ejpam-3305	7	5	α	α	NOUN
ejpam-3305	7	6	)	)	PUNCT
ejpam-3305	7	7	n	n	CCONJ
ejpam-3305	7	8	,	,	PUNCT
ejpam-3305	7	9	k(x)f	k(x)f	PROPN
ejpam-3305	7	10	(	(	PUNCT
ejpam-3305	7	11	k	k	NOUN
ejpam-3305	7	12	n	n	PROPN
ejpam-3305	7	13	)	)	PUNCT
ejpam-3305	7	14	,	,	PUNCT
ejpam-3305	7	15	x	x	PUNCT
ejpam-3305	7	16	∈	∈	PROPN
ejpam-3305	8	1	[	[	X
ejpam-3305	8	2	0,∞	0,∞	NUM
ejpam-3305	8	3	)	)	PUNCT
ejpam-3305	8	4	(	(	PUNCT
ejpam-3305	8	5	1	1	X
ejpam-3305	8	6	)	)	PUNCT
ejpam-3305	8	7	where	where	SCONJ
ejpam-3305	8	8	m	m	VERB
ejpam-3305	8	9	(	(	PUNCT
ejpam-3305	8	10	α	α	NOUN
ejpam-3305	8	11	)	)	PUNCT
ejpam-3305	8	12	n	n	CCONJ
ejpam-3305	8	13	,	,	PUNCT
ejpam-3305	8	14	k(x	k(x	PROPN
ejpam-3305	8	15	)	)	PUNCT
ejpam-3305	8	16	=	=	SYM
ejpam-3305	8	17	(	(	PUNCT
ejpam-3305	8	18	α)k	α)k	NOUN
ejpam-3305	8	19	k	k	X
ejpam-3305	8	20	!	!	PUNCT
ejpam-3305	8	21	.	.	PUNCT
ejpam-3305	9	1	(	(	PUNCT
ejpam-3305	9	2	nxα	nxα	ADV
ejpam-3305	9	3	)	)	PUNCT
ejpam-3305	9	4	k	k	NOUN
ejpam-3305	9	5	(	(	PUNCT
ejpam-3305	9	6	1	1	NUM
ejpam-3305	9	7	+	+	NUM
ejpam-3305	9	8	nx	nx	PROPN
ejpam-3305	9	9	α	α	NOUN
ejpam-3305	9	10	)	)	PUNCT
ejpam-3305	9	11	α+k	α+k	NUM
ejpam-3305	9	12	,	,	PUNCT
ejpam-3305	9	13	∗corresponding	∗corresponde	VERB
ejpam-3305	9	14	author	author	NOUN
ejpam-3305	9	15	.	.	PUNCT
ejpam-3305	10	1	doi	doi	NOUN
ejpam-3305	10	2	:	:	PUNCT
ejpam-3305	10	3	https://doi.org/10.29020/nybg.ejpam.v11i4.3305	https://doi.org/10.29020/nybg.ejpam.v11i4.3305	ADJ
ejpam-3305	10	4	email	email	NOUN
ejpam-3305	10	5	addresses	address	NOUN
ejpam-3305	10	6	:	:	PUNCT
ejpam-3305	11	1	alokkpma@gmail.com	alokkpma@gmail.com	X
ejpam-3305	11	2	(	(	PUNCT
ejpam-3305	11	3	a.	a.	PROPN
ejpam-3305	11	4	kumar	kumar	PROPN
ejpam-3305	11	5	)	)	PUNCT
ejpam-3305	11	6	,	,	PUNCT
ejpam-3305	11	7	tapiawalad@yahoo.com	tapiawalad@yahoo.com	X
ejpam-3305	11	8	(	(	PUNCT
ejpam-3305	11	9	d.	d.	PROPN
ejpam-3305	11	10	tapiawala	tapiawala	PROPN
ejpam-3305	11	11	)	)	PUNCT
ejpam-3305	11	12	,	,	PUNCT
ejpam-3305	11	13	lakshminarayanmishra04@gmail.com	lakshminarayanmishra04@gmail.com	PROPN
ejpam-3305	11	14	,	,	PUNCT
ejpam-3305	11	15	l	l	NOUN
ejpam-3305	11	16	n	n	PRON
ejpam-3305	11	17	mishra@yahoo.co.in	mishra@yahoo.co.in	PROPN
ejpam-3305	11	18	(	(	PUNCT
ejpam-3305	11	19	l.	l.	PROPN
ejpam-3305	11	20	n.	n.	PROPN
ejpam-3305	11	21	mishra	mishra	PROPN
ejpam-3305	11	22	)	)	PUNCT
ejpam-3305	11	23	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3305	12	1	958	958	NUM
ejpam-3305	12	2	c	c	X
ejpam-3305	12	3	©	©	PROPN
ejpam-3305	12	4	2018	2018	NUM
ejpam-3305	12	5	ejpam	ejpam	VERB
ejpam-3305	12	6	all	all	DET
ejpam-3305	12	7	rights	right	NOUN
ejpam-3305	12	8	reserved	reserve	VERB
ejpam-3305	12	9	.	.	PUNCT
ejpam-3305	13	1	a.	a.	PROPN
ejpam-3305	13	2	kumar	kumar	PROPN
ejpam-3305	13	3	,	,	PUNCT
ejpam-3305	13	4	d.	d.	PROPN
ejpam-3305	13	5	tapiawala	tapiawala	PROPN
ejpam-3305	13	6	,	,	PUNCT
ejpam-3305	13	7	l.	l.	PROPN
ejpam-3305	13	8	n.	n.	PROPN
ejpam-3305	13	9	mishra	mishra	PROPN
ejpam-3305	13	10	/	/	SYM
ejpam-3305	13	11	eur	eur	PROPN
ejpam-3305	13	12	.	.	PUNCT
ejpam-3305	14	1	j.	j.	PROPN
ejpam-3305	14	2	pure	pure	PROPN
ejpam-3305	14	3	appl	appl	PROPN
ejpam-3305	14	4	.	.	PROPN
ejpam-3305	14	5	math	math	PROPN
ejpam-3305	14	6	,	,	PUNCT
ejpam-3305	14	7	11	11	NUM
ejpam-3305	14	8	(	(	PUNCT
ejpam-3305	14	9	4	4	NUM
ejpam-3305	14	10	)	)	PUNCT
ejpam-3305	14	11	(	(	PUNCT
ejpam-3305	14	12	2018	2018	NUM
ejpam-3305	14	13	)	)	PUNCT
ejpam-3305	14	14	,	,	PUNCT
ejpam-3305	14	15	958	958	NUM
ejpam-3305	14	16	-	-	SYM
ejpam-3305	14	17	975	975	NUM
ejpam-3305	14	18	959	959	NUM
ejpam-3305	14	19	and	and	CCONJ
ejpam-3305	14	20	(	(	PUNCT
ejpam-3305	14	21	α)k	α)k	NOUN
ejpam-3305	14	22	=	=	SYM
ejpam-3305	14	23	α(α	α(α	PROPN
ejpam-3305	14	24	+	+	NOUN
ejpam-3305	14	25	1)	1)	NUM
ejpam-3305	14	26	...	...	PUNCT
ejpam-3305	14	27	(α	(α	PUNCT
ejpam-3305	15	1	+	+	CCONJ
ejpam-3305	15	2	k	k	NOUN
ejpam-3305	15	3	−	−	NOUN
ejpam-3305	15	4	1	1	NUM
ejpam-3305	15	5	)	)	PUNCT
ejpam-3305	15	6	,	,	PUNCT
ejpam-3305	15	7	(	(	PUNCT
ejpam-3305	15	8	α)0	α)0	NOUN
ejpam-3305	15	9	=	=	NOUN
ejpam-3305	15	10	1	1	NUM
ejpam-3305	15	11	,	,	PUNCT
ejpam-3305	15	12	is	be	AUX
ejpam-3305	15	13	the	the	DET
ejpam-3305	15	14	rising	rise	VERB
ejpam-3305	15	15	factorial	factorial	NOUN
ejpam-3305	15	16	and	and	CCONJ
ejpam-3305	15	17	α	α	NOUN
ejpam-3305	16	1	+	+	CCONJ
ejpam-3305	16	2	nx	nx	X
ejpam-3305	16	3	>	>	X
ejpam-3305	16	4	0	0	PROPN
ejpam-3305	16	5	.	.	PUNCT
ejpam-3305	17	1	the	the	DET
ejpam-3305	17	2	operator	operator	NOUN
ejpam-3305	17	3	g(α)n	g(α)n	AUX
ejpam-3305	17	4	preserve	preserve	VERB
ejpam-3305	17	5	the	the	DET
ejpam-3305	17	6	linear	linear	ADJ
ejpam-3305	17	7	polynomials	polynomial	NOUN
ejpam-3305	17	8	,	,	PUNCT
ejpam-3305	17	9	and	and	CCONJ
ejpam-3305	17	10	for	for	ADP
ejpam-3305	17	11	special	special	ADJ
ejpam-3305	17	12	values	value	NOUN
ejpam-3305	17	13	of	of	ADP
ejpam-3305	17	14	α	α	NOUN
ejpam-3305	17	15	,	,	PUNCT
ejpam-3305	17	16	one	one	PRON
ejpam-3305	17	17	can	can	AUX
ejpam-3305	17	18	obtain	obtain	VERB
ejpam-3305	17	19	some	some	DET
ejpam-3305	17	20	well	well	ADV
ejpam-3305	17	21	-	-	PUNCT
ejpam-3305	17	22	known	know	VERB
ejpam-3305	17	23	operators	operator	NOUN
ejpam-3305	17	24	.	.	PUNCT
ejpam-3305	18	1	recently	recently	ADV
ejpam-3305	18	2	,	,	PUNCT
ejpam-3305	18	3	kajla	kajla	X
ejpam-3305	19	1	[	[	X
ejpam-3305	19	2	15	15	NUM
ejpam-3305	19	3	]	]	PUNCT
ejpam-3305	19	4	introduced	introduce	VERB
ejpam-3305	19	5	a	a	DET
ejpam-3305	19	6	new	new	ADJ
ejpam-3305	19	7	sequence	sequence	NOUN
ejpam-3305	19	8	of	of	ADP
ejpam-3305	19	9	summation	summation	NOUN
ejpam-3305	19	10	-	-	PUNCT
ejpam-3305	19	11	integral	integral	ADJ
ejpam-3305	19	12	type	type	NOUN
ejpam-3305	19	13	operators	operator	NOUN
ejpam-3305	19	14	and	and	CCONJ
ejpam-3305	19	15	established	establish	VERB
ejpam-3305	19	16	some	some	DET
ejpam-3305	19	17	approximation	approximation	NOUN
ejpam-3305	19	18	properties	property	NOUN
ejpam-3305	19	19	e.g.	e.g.	ADV
ejpam-3305	19	20	weighted	weight	VERB
ejpam-3305	19	21	approximation	approximation	NOUN
ejpam-3305	19	22	,	,	PUNCT
ejpam-3305	19	23	asymptotic	asymptotic	ADJ
ejpam-3305	19	24	formula	formula	NOUN
ejpam-3305	19	25	and	and	CCONJ
ejpam-3305	19	26	error	error	NOUN
ejpam-3305	19	27	estimation	estimation	NOUN
ejpam-3305	19	28	in	in	ADP
ejpam-3305	19	29	terms	term	NOUN
ejpam-3305	19	30	of	of	ADP
ejpam-3305	19	31	modulus	modulus	NOUN
ejpam-3305	19	32	of	of	ADP
ejpam-3305	19	33	smoothness	smoothness	NOUN
ejpam-3305	19	34	.	.	PUNCT
ejpam-3305	20	1	very	very	ADV
ejpam-3305	20	2	recently	recently	ADV
ejpam-3305	20	3	,	,	PUNCT
ejpam-3305	20	4	gupta	gupta	PROPN
ejpam-3305	20	5	and	and	CCONJ
ejpam-3305	20	6	agrawal	agrawal	PROPN
ejpam-3305	21	1	[	[	X
ejpam-3305	21	2	11	11	NUM
ejpam-3305	21	3	]	]	PUNCT
ejpam-3305	21	4	proposed	propose	VERB
ejpam-3305	21	5	the	the	DET
ejpam-3305	21	6	integral	integral	ADJ
ejpam-3305	21	7	modification	modification	NOUN
ejpam-3305	21	8	of	of	ADP
ejpam-3305	21	9	the	the	DET
ejpam-3305	21	10	operators	operator	NOUN
ejpam-3305	21	11	(	(	PUNCT
ejpam-3305	21	12	1	1	X
ejpam-3305	21	13	)	)	PUNCT
ejpam-3305	21	14	by	by	ADP
ejpam-3305	21	15	taking	take	VERB
ejpam-3305	21	16	weights	weight	NOUN
ejpam-3305	21	17	of	of	ADP
ejpam-3305	21	18	beta	beta	ADJ
ejpam-3305	21	19	basis	basis	NOUN
ejpam-3305	21	20	functions	function	NOUN
ejpam-3305	21	21	as	as	SCONJ
ejpam-3305	21	22	follows	follow	VERB
ejpam-3305	21	23	:	:	PUNCT
ejpam-3305	21	24	m	m	VERB
ejpam-3305	21	25	(	(	PUNCT
ejpam-3305	21	26	α	α	NOUN
ejpam-3305	21	27	)	)	PUNCT
ejpam-3305	21	28	n	n	PROPN
ejpam-3305	21	29	(	(	PUNCT
ejpam-3305	21	30	f	f	PROPN
ejpam-3305	21	31	;	;	PUNCT
ejpam-3305	21	32	x	x	X
ejpam-3305	21	33	)	)	PUNCT
ejpam-3305	21	34	=	=	PUNCT
ejpam-3305	22	1	∞∑	∞∑	NUM
ejpam-3305	22	2	k=1	k=1	PUNCT
ejpam-3305	22	3	m	m	VERB
ejpam-3305	22	4	(	(	PUNCT
ejpam-3305	22	5	α	α	NOUN
ejpam-3305	22	6	)	)	PUNCT
ejpam-3305	22	7	n	n	CCONJ
ejpam-3305	22	8	,	,	PUNCT
ejpam-3305	22	9	k(x	k(x	PROPN
ejpam-3305	22	10	)	)	PUNCT
ejpam-3305	22	11	∫	∫	PROPN
ejpam-3305	22	12	∞	∞	PROPN
ejpam-3305	22	13	0	0	NUM
ejpam-3305	22	14	bn	bn	PROPN
ejpam-3305	22	15	,	,	PUNCT
ejpam-3305	22	16	k(t)f(t)dt+	k(t)f(t)dt+	PROPN
ejpam-3305	22	17	(	(	PUNCT
ejpam-3305	22	18	α	α	X
ejpam-3305	22	19	α+	α+	X
ejpam-3305	22	20	nx	nx	NOUN
ejpam-3305	22	21	)	)	PUNCT
ejpam-3305	22	22	α	α	NOUN
ejpam-3305	22	23	f(0	f(0	NOUN
ejpam-3305	22	24	)	)	PUNCT
ejpam-3305	22	25	,	,	PUNCT
ejpam-3305	22	26	(	(	PUNCT
ejpam-3305	22	27	2	2	X
ejpam-3305	22	28	)	)	PUNCT
ejpam-3305	23	1	where	where	SCONJ
ejpam-3305	23	2	bn	bn	NOUN
ejpam-3305	23	3	,	,	PUNCT
ejpam-3305	23	4	k(t	k(t	PROPN
ejpam-3305	23	5	)	)	PUNCT
ejpam-3305	23	6	=	=	SYM
ejpam-3305	23	7	1	1	NUM
ejpam-3305	23	8	b(n+	b(n+	NUM
ejpam-3305	23	9	1	1	NUM
ejpam-3305	23	10	,	,	PUNCT
ejpam-3305	23	11	k	k	NOUN
ejpam-3305	23	12	)	)	PUNCT
ejpam-3305	23	13	.	.	PUNCT
ejpam-3305	24	1	tk−1	tk−1	INTJ
ejpam-3305	24	2	(	(	PUNCT
ejpam-3305	24	3	1	1	NUM
ejpam-3305	24	4	+	+	CCONJ
ejpam-3305	24	5	t)k+n+1	t)k+n+1	NUM
ejpam-3305	24	6	,	,	PUNCT
ejpam-3305	24	7	and	and	CCONJ
ejpam-3305	24	8	b(m	b(m	PROPN
ejpam-3305	24	9	,	,	PUNCT
ejpam-3305	24	10	n	n	CCONJ
ejpam-3305	24	11	)	)	PUNCT
ejpam-3305	24	12	being	be	AUX
ejpam-3305	24	13	the	the	DET
ejpam-3305	24	14	beta	beta	ADJ
ejpam-3305	24	15	function	function	NOUN
ejpam-3305	24	16	defined	define	VERB
ejpam-3305	24	17	as	as	ADP
ejpam-3305	24	18	b(m	b(m	PROPN
ejpam-3305	24	19	,	,	PUNCT
ejpam-3305	24	20	n	n	CCONJ
ejpam-3305	24	21	)	)	PUNCT
ejpam-3305	24	22	=	=	SYM
ejpam-3305	24	23	γ(m)γ(n	γ(m)γ(n	NUM
ejpam-3305	24	24	)	)	PUNCT
ejpam-3305	24	25	γ(m+	γ(m+	NUM
ejpam-3305	24	26	n	n	CCONJ
ejpam-3305	24	27	)	)	PUNCT
ejpam-3305	24	28	,	,	PUNCT
ejpam-3305	24	29	m	m	PROPN
ejpam-3305	24	30	,	,	PUNCT
ejpam-3305	24	31	n	n	PROPN
ejpam-3305	24	32	>	>	X
ejpam-3305	24	33	0	0	X
ejpam-3305	24	34	.	.	PUNCT
ejpam-3305	25	1	they	they	PRON
ejpam-3305	25	2	obtain	obtain	VERB
ejpam-3305	25	3	different	different	ADJ
ejpam-3305	25	4	approximation	approximation	NOUN
ejpam-3305	25	5	properties	property	NOUN
ejpam-3305	25	6	for	for	ADP
ejpam-3305	25	7	these	these	DET
ejpam-3305	25	8	operators	operator	NOUN
ejpam-3305	25	9	.	.	PUNCT
ejpam-3305	26	1	for	for	ADP
ejpam-3305	26	2	the	the	DET
ejpam-3305	26	3	different	different	ADJ
ejpam-3305	26	4	values	value	NOUN
ejpam-3305	26	5	of	of	ADP
ejpam-3305	26	6	α	α	NOUN
ejpam-3305	26	7	,	,	PUNCT
ejpam-3305	26	8	we	we	PRON
ejpam-3305	26	9	get	get	VERB
ejpam-3305	26	10	different	different	ADJ
ejpam-3305	26	11	special	special	ADJ
ejpam-3305	26	12	cases	case	NOUN
ejpam-3305	26	13	.	.	PUNCT
ejpam-3305	27	1	some	some	PRON
ejpam-3305	27	2	of	of	ADP
ejpam-3305	27	3	the	the	DET
ejpam-3305	27	4	special	special	ADJ
ejpam-3305	27	5	cases	case	NOUN
ejpam-3305	27	6	are	be	AUX
ejpam-3305	27	7	discussed	discuss	VERB
ejpam-3305	27	8	in	in	ADP
ejpam-3305	27	9	[	[	X
ejpam-3305	27	10	11	11	NUM
ejpam-3305	27	11	]	]	PUNCT
ejpam-3305	27	12	.	.	PUNCT
ejpam-3305	28	1	in	in	ADP
ejpam-3305	28	2	[	[	X
ejpam-3305	28	3	42	42	NUM
ejpam-3305	28	4	]	]	PUNCT
ejpam-3305	28	5	,	,	PUNCT
ejpam-3305	28	6	stancu	stancu	PROPN
ejpam-3305	28	7	introduced	introduce	VERB
ejpam-3305	28	8	and	and	CCONJ
ejpam-3305	28	9	investigated	investigate	VERB
ejpam-3305	28	10	a	a	DET
ejpam-3305	28	11	new	new	ADJ
ejpam-3305	28	12	parameter	parameter	NOUN
ejpam-3305	28	13	-	-	PUNCT
ejpam-3305	28	14	dependent	dependent	ADJ
ejpam-3305	28	15	linear	linear	ADJ
ejpam-3305	28	16	positive	positive	ADJ
ejpam-3305	28	17	operators	operator	NOUN
ejpam-3305	28	18	of	of	ADP
ejpam-3305	28	19	bernstein	bernstein	PROPN
ejpam-3305	28	20	type	type	PROPN
ejpam-3305	28	21	associated	associate	VERB
ejpam-3305	28	22	to	to	ADP
ejpam-3305	28	23	a	a	DET
ejpam-3305	28	24	function	function	NOUN
ejpam-3305	28	25	f	f	PROPN
ejpam-3305	28	26	∈	∈	PROPN
ejpam-3305	28	27	c[0	c[0	PROPN
ejpam-3305	28	28	,	,	PUNCT
ejpam-3305	28	29	1	1	NUM
ejpam-3305	28	30	]	]	PUNCT
ejpam-3305	28	31	.	.	PUNCT
ejpam-3305	29	1	the	the	DET
ejpam-3305	29	2	new	new	ADJ
ejpam-3305	29	3	construction	construction	NOUN
ejpam-3305	29	4	of	of	ADP
ejpam-3305	29	5	his	his	PRON
ejpam-3305	29	6	operators	operator	NOUN
ejpam-3305	29	7	shows	show	VERB
ejpam-3305	29	8	that	that	SCONJ
ejpam-3305	29	9	the	the	DET
ejpam-3305	29	10	new	new	ADJ
ejpam-3305	29	11	sequence	sequence	NOUN
ejpam-3305	29	12	of	of	ADP
ejpam-3305	29	13	bernstein	bernstein	PROPN
ejpam-3305	29	14	polynomials	polynomials	PROPN
ejpam-3305	29	15	present	present	VERB
ejpam-3305	29	16	a	a	DET
ejpam-3305	29	17	better	well	ADJ
ejpam-3305	29	18	approach	approach	NOUN
ejpam-3305	29	19	with	with	ADP
ejpam-3305	29	20	the	the	DET
ejpam-3305	29	21	suitable	suitable	ADJ
ejpam-3305	29	22	selection	selection	NOUN
ejpam-3305	29	23	of	of	ADP
ejpam-3305	29	24	the	the	DET
ejpam-3305	29	25	parameters	parameter	NOUN
ejpam-3305	29	26	.	.	PUNCT
ejpam-3305	30	1	in	in	ADP
ejpam-3305	30	2	the	the	DET
ejpam-3305	30	3	recent	recent	ADJ
ejpam-3305	30	4	years	year	NOUN
ejpam-3305	30	5	,	,	PUNCT
ejpam-3305	30	6	stancu	stancu	ADJ
ejpam-3305	30	7	type	type	NOUN
ejpam-3305	30	8	generalization	generalization	NOUN
ejpam-3305	30	9	of	of	ADP
ejpam-3305	30	10	the	the	DET
ejpam-3305	30	11	certain	certain	ADJ
ejpam-3305	30	12	operators	operator	NOUN
ejpam-3305	30	13	introduced	introduce	VERB
ejpam-3305	30	14	by	by	ADP
ejpam-3305	30	15	several	several	ADJ
ejpam-3305	30	16	researchers	researcher	NOUN
ejpam-3305	30	17	and	and	CCONJ
ejpam-3305	30	18	obtained	obtain	VERB
ejpam-3305	30	19	different	different	ADJ
ejpam-3305	30	20	type	type	NOUN
ejpam-3305	30	21	of	of	ADP
ejpam-3305	30	22	approximation	approximation	NOUN
ejpam-3305	30	23	properties	property	NOUN
ejpam-3305	30	24	of	of	ADP
ejpam-3305	30	25	many	many	ADJ
ejpam-3305	30	26	operators	operator	NOUN
ejpam-3305	30	27	,	,	PUNCT
ejpam-3305	30	28	we	we	PRON
ejpam-3305	30	29	refer	refer	VERB
ejpam-3305	30	30	some	some	PRON
ejpam-3305	30	31	of	of	ADP
ejpam-3305	30	32	the	the	DET
ejpam-3305	30	33	important	important	ADJ
ejpam-3305	30	34	papers	paper	NOUN
ejpam-3305	30	35	in	in	ADP
ejpam-3305	30	36	this	this	DET
ejpam-3305	30	37	direction	direction	NOUN
ejpam-3305	30	38	as	as	ADP
ejpam-3305	30	39	[	[	X
ejpam-3305	30	40	1	1	NUM
ejpam-3305	30	41	]	]	PUNCT
ejpam-3305	30	42	,	,	PUNCT
ejpam-3305	30	43	[	[	X
ejpam-3305	30	44	16	16	NUM
ejpam-3305	30	45	]	]	PUNCT
ejpam-3305	30	46	,	,	PUNCT
ejpam-3305	30	47	[	[	X
ejpam-3305	30	48	23	23	NUM
ejpam-3305	30	49	]	]	PUNCT
ejpam-3305	30	50	,	,	PUNCT
ejpam-3305	30	51	[	[	X
ejpam-3305	30	52	24	24	NUM
ejpam-3305	30	53	]	]	PUNCT
ejpam-3305	30	54	,	,	PUNCT
ejpam-3305	30	55	[	[	X
ejpam-3305	30	56	25	25	NUM
ejpam-3305	30	57	]	]	PUNCT
ejpam-3305	30	58	,	,	PUNCT
ejpam-3305	30	59	[	[	X
ejpam-3305	30	60	33	33	NUM
ejpam-3305	30	61	]	]	PUNCT
ejpam-3305	30	62	etc	etc	X
ejpam-3305	30	63	.	.	X
ejpam-3305	30	64	inspired	inspire	VERB
ejpam-3305	30	65	by	by	ADP
ejpam-3305	30	66	the	the	DET
ejpam-3305	30	67	above	above	ADJ
ejpam-3305	30	68	work	work	NOUN
ejpam-3305	30	69	,	,	PUNCT
ejpam-3305	30	70	we	we	PRON
ejpam-3305	30	71	introduce	introduce	VERB
ejpam-3305	30	72	the	the	DET
ejpam-3305	30	73	stancu	stancu	ADJ
ejpam-3305	30	74	type	type	NOUN
ejpam-3305	30	75	generalization	generalization	NOUN
ejpam-3305	30	76	of	of	ADP
ejpam-3305	30	77	the	the	DET
ejpam-3305	30	78	operators	operator	NOUN
ejpam-3305	30	79	(	(	PUNCT
ejpam-3305	30	80	2	2	NUM
ejpam-3305	30	81	):	):	PUNCT
ejpam-3305	30	82	m	m	VERB
ejpam-3305	30	83	(	(	PUNCT
ejpam-3305	30	84	β	β	X
ejpam-3305	30	85	,	,	PUNCT
ejpam-3305	30	86	γ	γ	NOUN
ejpam-3305	30	87	)	)	PUNCT
ejpam-3305	30	88	n	n	CCONJ
ejpam-3305	30	89	,	,	PUNCT
ejpam-3305	30	90	α	α	PROPN
ejpam-3305	30	91	(	(	PUNCT
ejpam-3305	30	92	f	f	NOUN
ejpam-3305	30	93	;	;	PUNCT
ejpam-3305	30	94	x	x	X
ejpam-3305	30	95	)	)	PUNCT
ejpam-3305	30	96	=	=	PUNCT
ejpam-3305	31	1	∞∑	∞∑	NUM
ejpam-3305	31	2	k=1	k=1	PUNCT
ejpam-3305	31	3	m	m	VERB
ejpam-3305	31	4	(	(	PUNCT
ejpam-3305	31	5	α	α	NOUN
ejpam-3305	31	6	)	)	PUNCT
ejpam-3305	31	7	n	n	CCONJ
ejpam-3305	31	8	,	,	PUNCT
ejpam-3305	31	9	k(x	k(x	PROPN
ejpam-3305	31	10	)	)	PUNCT
ejpam-3305	31	11	∫	∫	PROPN
ejpam-3305	31	12	∞	∞	PROPN
ejpam-3305	31	13	0	0	NUM
ejpam-3305	31	14	bn	bn	PROPN
ejpam-3305	31	15	,	,	PUNCT
ejpam-3305	31	16	k(t)f	k(t)f	PROPN
ejpam-3305	31	17	(	(	PUNCT
ejpam-3305	31	18	nt+	nt+	NOUN
ejpam-3305	31	19	β	β	X
ejpam-3305	31	20	n+	n+	X
ejpam-3305	31	21	γ	γ	NOUN
ejpam-3305	31	22	)	)	PUNCT
ejpam-3305	31	23	dt+	dt+	NOUN
ejpam-3305	31	24	(	(	PUNCT
ejpam-3305	31	25	α	α	X
ejpam-3305	31	26	α+	α+	X
ejpam-3305	31	27	nx	nx	PROPN
ejpam-3305	31	28	)	)	PUNCT
ejpam-3305	31	29	α	α	PROPN
ejpam-3305	31	30	f	f	X
ejpam-3305	31	31	(	(	PUNCT
ejpam-3305	31	32	β	β	X
ejpam-3305	31	33	n+	n+	X
ejpam-3305	31	34	γ	γ	PROPN
ejpam-3305	31	35	)	)	PUNCT
ejpam-3305	31	36	.	.	PUNCT
ejpam-3305	32	1	(	(	PUNCT
ejpam-3305	32	2	3	3	X
ejpam-3305	32	3	)	)	PUNCT
ejpam-3305	32	4	in	in	ADP
ejpam-3305	32	5	this	this	DET
ejpam-3305	32	6	present	present	ADJ
ejpam-3305	32	7	work	work	NOUN
ejpam-3305	32	8	,	,	PUNCT
ejpam-3305	32	9	our	our	PRON
ejpam-3305	32	10	focus	focus	NOUN
ejpam-3305	32	11	is	be	AUX
ejpam-3305	32	12	to	to	PART
ejpam-3305	32	13	study	study	VERB
ejpam-3305	32	14	the	the	DET
ejpam-3305	32	15	approximation	approximation	NOUN
ejpam-3305	32	16	properties	property	NOUN
ejpam-3305	32	17	of	of	ADP
ejpam-3305	32	18	the	the	DET
ejpam-3305	32	19	operators	operator	NOUN
ejpam-3305	32	20	(	(	PUNCT
ejpam-3305	32	21	3	3	X
ejpam-3305	32	22	)	)	PUNCT
ejpam-3305	32	23	in	in	ADP
ejpam-3305	32	24	terms	term	NOUN
ejpam-3305	32	25	of	of	ADP
ejpam-3305	32	26	first	first	ADJ
ejpam-3305	32	27	and	and	CCONJ
ejpam-3305	32	28	second	second	ADJ
ejpam-3305	32	29	order	order	NOUN
ejpam-3305	32	30	modulus	modulus	NOUN
ejpam-3305	32	31	of	of	ADP
ejpam-3305	32	32	continuity	continuity	NOUN
ejpam-3305	32	33	.	.	PUNCT
ejpam-3305	33	1	we	we	PRON
ejpam-3305	33	2	estimate	estimate	VERB
ejpam-3305	33	3	the	the	DET
ejpam-3305	33	4	rate	rate	NOUN
ejpam-3305	33	5	of	of	ADP
ejpam-3305	33	6	convergence	convergence	NOUN
ejpam-3305	33	7	of	of	ADP
ejpam-3305	33	8	these	these	DET
ejpam-3305	33	9	operators	operator	NOUN
ejpam-3305	33	10	in	in	ADP
ejpam-3305	33	11	terms	term	NOUN
ejpam-3305	33	12	of	of	ADP
ejpam-3305	33	13	modulus	modulus	NOUN
ejpam-3305	33	14	of	of	ADP
ejpam-3305	33	15	continuity	continuity	NOUN
ejpam-3305	33	16	.	.	PUNCT
ejpam-3305	34	1	furthermore	furthermore	ADV
ejpam-3305	34	2	,	,	PUNCT
ejpam-3305	34	3	we	we	PRON
ejpam-3305	34	4	investigate	investigate	VERB
ejpam-3305	34	5	weighted	weight	VERB
ejpam-3305	34	6	approximation	approximation	NOUN
ejpam-3305	34	7	theorems	theorem	NOUN
ejpam-3305	34	8	.	.	PUNCT
ejpam-3305	35	1	lastly	lastly	ADV
ejpam-3305	35	2	we	we	PRON
ejpam-3305	35	3	study	study	VERB
ejpam-3305	35	4	king	king	NOUN
ejpam-3305	35	5	type	type	NOUN
ejpam-3305	35	6	modification	modification	NOUN
ejpam-3305	35	7	of	of	ADP
ejpam-3305	35	8	the	the	DET
ejpam-3305	35	9	operators	operator	NOUN
ejpam-3305	35	10	(	(	PUNCT
ejpam-3305	35	11	3	3	NUM
ejpam-3305	35	12	)	)	PUNCT
ejpam-3305	35	13	.	.	PUNCT
ejpam-3305	36	1	a.	a.	PROPN
ejpam-3305	36	2	kumar	kumar	PROPN
ejpam-3305	36	3	,	,	PUNCT
ejpam-3305	36	4	d.	d.	PROPN
ejpam-3305	36	5	tapiawala	tapiawala	PROPN
ejpam-3305	36	6	,	,	PUNCT
ejpam-3305	36	7	l.	l.	PROPN
ejpam-3305	36	8	n.	n.	PROPN
ejpam-3305	36	9	mishra	mishra	PROPN
ejpam-3305	36	10	/	/	SYM
ejpam-3305	36	11	eur	eur	PROPN
ejpam-3305	36	12	.	.	PUNCT
ejpam-3305	37	1	j.	j.	PROPN
ejpam-3305	37	2	pure	pure	PROPN
ejpam-3305	37	3	appl	appl	PROPN
ejpam-3305	37	4	.	.	PROPN
ejpam-3305	37	5	math	math	PROPN
ejpam-3305	37	6	,	,	PUNCT
ejpam-3305	37	7	11	11	NUM
ejpam-3305	37	8	(	(	PUNCT
ejpam-3305	37	9	4	4	NUM
ejpam-3305	37	10	)	)	PUNCT
ejpam-3305	37	11	(	(	PUNCT
ejpam-3305	37	12	2018	2018	NUM
ejpam-3305	37	13	)	)	PUNCT
ejpam-3305	37	14	,	,	PUNCT
ejpam-3305	37	15	958	958	NUM
ejpam-3305	37	16	-	-	SYM
ejpam-3305	37	17	975	975	NUM
ejpam-3305	37	18	960	960	NUM
ejpam-3305	37	19	2	2	NUM
ejpam-3305	37	20	.	.	PUNCT
ejpam-3305	37	21	moment	moment	NOUN
ejpam-3305	37	22	estimates	estimate	NOUN
ejpam-3305	37	23	in	in	ADP
ejpam-3305	37	24	the	the	DET
ejpam-3305	37	25	sequel	sequel	NOUN
ejpam-3305	37	26	,	,	PUNCT
ejpam-3305	37	27	we	we	PRON
ejpam-3305	37	28	shall	shall	AUX
ejpam-3305	37	29	need	need	VERB
ejpam-3305	37	30	the	the	DET
ejpam-3305	37	31	following	follow	VERB
ejpam-3305	37	32	auxiliary	auxiliary	ADJ
ejpam-3305	37	33	results	result	NOUN
ejpam-3305	37	34	which	which	PRON
ejpam-3305	37	35	will	will	AUX
ejpam-3305	37	36	be	be	AUX
ejpam-3305	37	37	necessary	necessary	ADJ
ejpam-3305	37	38	to	to	PART
ejpam-3305	37	39	prove	prove	VERB
ejpam-3305	37	40	our	our	PRON
ejpam-3305	37	41	main	main	ADJ
ejpam-3305	37	42	results	result	NOUN
ejpam-3305	37	43	.	.	PUNCT
ejpam-3305	38	1	lemma	lemma	PROPN
ejpam-3305	38	2	1	1	NUM
ejpam-3305	38	3	.	.	PUNCT
ejpam-3305	39	1	[	[	X
ejpam-3305	39	2	11	11	NUM
ejpam-3305	39	3	]	]	PUNCT
ejpam-3305	39	4	for	for	ADP
ejpam-3305	39	5	the	the	DET
ejpam-3305	39	6	operators	operator	NOUN
ejpam-3305	39	7	m	m	VERB
ejpam-3305	39	8	(	(	PUNCT
ejpam-3305	39	9	α	α	NOUN
ejpam-3305	39	10	)	)	PUNCT
ejpam-3305	39	11	n	n	PROPN
ejpam-3305	39	12	(	(	PUNCT
ejpam-3305	39	13	f	f	PROPN
ejpam-3305	39	14	;	;	PUNCT
ejpam-3305	39	15	x	x	X
ejpam-3305	39	16	)	)	PUNCT
ejpam-3305	39	17	,	,	PUNCT
ejpam-3305	39	18	we	we	PRON
ejpam-3305	39	19	have	have	VERB
ejpam-3305	39	20	(	(	PUNCT
ejpam-3305	39	21	i	i	NOUN
ejpam-3305	39	22	)	)	PUNCT
ejpam-3305	39	23	m	m	VERB
ejpam-3305	39	24	(	(	PUNCT
ejpam-3305	39	25	α	α	NOUN
ejpam-3305	39	26	)	)	PUNCT
ejpam-3305	39	27	n	n	PROPN
ejpam-3305	39	28	(	(	PUNCT
ejpam-3305	39	29	1;x	1;x	NUM
ejpam-3305	39	30	)	)	PUNCT
ejpam-3305	39	31	=	=	SYM
ejpam-3305	39	32	1	1	NUM
ejpam-3305	39	33	,	,	PUNCT
ejpam-3305	39	34	(	(	PUNCT
ejpam-3305	39	35	ii	ii	NOUN
ejpam-3305	39	36	)	)	PUNCT
ejpam-3305	39	37	m	m	PROPN
ejpam-3305	39	38	(	(	PUNCT
ejpam-3305	39	39	α	α	NOUN
ejpam-3305	39	40	)	)	PUNCT
ejpam-3305	39	41	n	n	CCONJ
ejpam-3305	39	42	(	(	PUNCT
ejpam-3305	39	43	t;x	t;x	NUM
ejpam-3305	39	44	)	)	PUNCT
ejpam-3305	39	45	=	=	SYM
ejpam-3305	40	1	x	x	X
ejpam-3305	40	2	,	,	PUNCT
ejpam-3305	40	3	(	(	PUNCT
ejpam-3305	40	4	iii	iii	X
ejpam-3305	40	5	)	)	PUNCT
ejpam-3305	40	6	m	m	VERB
ejpam-3305	40	7	(	(	PUNCT
ejpam-3305	40	8	α	α	NOUN
ejpam-3305	40	9	)	)	PUNCT
ejpam-3305	40	10	n	n	CCONJ
ejpam-3305	40	11	(	(	PUNCT
ejpam-3305	40	12	t2;x	t2;x	PROPN
ejpam-3305	40	13	)	)	PUNCT
ejpam-3305	40	14	=	=	SYM
ejpam-3305	40	15	x[nx(α+	x[nx(α+	PROPN
ejpam-3305	40	16	1	1	NUM
ejpam-3305	40	17	)	)	PUNCT
ejpam-3305	41	1	+	+	CCONJ
ejpam-3305	41	2	2α	2α	NOUN
ejpam-3305	41	3	]	]	X
ejpam-3305	41	4	α(n−	α(n−	NUM
ejpam-3305	41	5	1	1	NUM
ejpam-3305	41	6	)	)	PUNCT
ejpam-3305	41	7	.	.	PUNCT
ejpam-3305	42	1	lemma	lemma	PROPN
ejpam-3305	42	2	2	2	NUM
ejpam-3305	42	3	.	.	X
ejpam-3305	43	1	for	for	ADP
ejpam-3305	43	2	the	the	DET
ejpam-3305	43	3	operators	operator	NOUN
ejpam-3305	43	4	m	m	VERB
ejpam-3305	43	5	(	(	PUNCT
ejpam-3305	43	6	β	β	X
ejpam-3305	43	7	,	,	PUNCT
ejpam-3305	43	8	γ	γ	NOUN
ejpam-3305	43	9	)	)	PUNCT
ejpam-3305	43	10	n	n	CCONJ
ejpam-3305	43	11	,	,	PUNCT
ejpam-3305	43	12	α	α	PROPN
ejpam-3305	43	13	(	(	PUNCT
ejpam-3305	43	14	f	f	NOUN
ejpam-3305	43	15	;	;	PUNCT
ejpam-3305	43	16	x	x	X
ejpam-3305	43	17	)	)	PUNCT
ejpam-3305	43	18	,	,	PUNCT
ejpam-3305	43	19	we	we	PRON
ejpam-3305	43	20	have	have	VERB
ejpam-3305	43	21	(	(	PUNCT
ejpam-3305	43	22	i	i	NOUN
ejpam-3305	43	23	)	)	PUNCT
ejpam-3305	43	24	m	m	VERB
ejpam-3305	43	25	(	(	PUNCT
ejpam-3305	43	26	β	β	X
ejpam-3305	43	27	,	,	PUNCT
ejpam-3305	43	28	γ	γ	NOUN
ejpam-3305	43	29	)	)	PUNCT
ejpam-3305	43	30	n	n	CCONJ
ejpam-3305	43	31	,	,	PUNCT
ejpam-3305	43	32	α	α	PROPN
ejpam-3305	43	33	(	(	PUNCT
ejpam-3305	43	34	1;x	1;x	NUM
ejpam-3305	43	35	)	)	PUNCT
ejpam-3305	43	36	=	=	SYM
ejpam-3305	43	37	1	1	NUM
ejpam-3305	43	38	,	,	PUNCT
ejpam-3305	43	39	(	(	PUNCT
ejpam-3305	43	40	ii	ii	NOUN
ejpam-3305	43	41	)	)	PUNCT
ejpam-3305	43	42	m	m	VERB
ejpam-3305	43	43	(	(	PUNCT
ejpam-3305	43	44	β	β	X
ejpam-3305	43	45	,	,	PUNCT
ejpam-3305	43	46	γ	γ	NOUN
ejpam-3305	43	47	)	)	PUNCT
ejpam-3305	43	48	n	n	CCONJ
ejpam-3305	43	49	,	,	PUNCT
ejpam-3305	43	50	α	α	PROPN
ejpam-3305	43	51	(	(	PUNCT
ejpam-3305	43	52	t;x	t;x	NUM
ejpam-3305	43	53	)	)	PUNCT
ejpam-3305	43	54	=	=	SYM
ejpam-3305	44	1	nx+	nx+	PROPN
ejpam-3305	44	2	β	β	X
ejpam-3305	44	3	n+	n+	X
ejpam-3305	44	4	γ	γ	X
ejpam-3305	44	5	,	,	PUNCT
ejpam-3305	44	6	(	(	PUNCT
ejpam-3305	44	7	iii	iii	X
ejpam-3305	44	8	)	)	PUNCT
ejpam-3305	44	9	m	m	VERB
ejpam-3305	44	10	(	(	PUNCT
ejpam-3305	44	11	β	β	X
ejpam-3305	44	12	,	,	PUNCT
ejpam-3305	44	13	γ	γ	NOUN
ejpam-3305	44	14	)	)	PUNCT
ejpam-3305	44	15	n	n	CCONJ
ejpam-3305	44	16	,	,	PUNCT
ejpam-3305	44	17	α	α	PROPN
ejpam-3305	44	18	(	(	PUNCT
ejpam-3305	44	19	t2;x	t2;x	PROPN
ejpam-3305	44	20	)	)	PUNCT
ejpam-3305	44	21	=	=	PRON
ejpam-3305	44	22	{	{	PUNCT
ejpam-3305	44	23	n3(α+	n3(α+	PROPN
ejpam-3305	44	24	1	1	NUM
ejpam-3305	44	25	)	)	PUNCT
ejpam-3305	44	26	α(n−	α(n−	NUM
ejpam-3305	44	27	1)(n+	1)(n+	NUM
ejpam-3305	44	28	γ)2	γ)2	NOUN
ejpam-3305	44	29	}	}	PUNCT
ejpam-3305	44	30	x2	x2	PROPN
ejpam-3305	45	1	+	+	PUNCT
ejpam-3305	45	2	{	{	PUNCT
ejpam-3305	45	3	2n2	2n2	NUM
ejpam-3305	45	4	+	+	CCONJ
ejpam-3305	45	5	2nβ(n−	2nβ(n−	NUM
ejpam-3305	45	6	1	1	NUM
ejpam-3305	45	7	)	)	PUNCT
ejpam-3305	45	8	(	(	PUNCT
ejpam-3305	45	9	n−	n−	NOUN
ejpam-3305	45	10	1)(n+	1)(n+	NUM
ejpam-3305	45	11	γ)2	γ)2	NOUN
ejpam-3305	45	12	}	}	PUNCT
ejpam-3305	45	13	x+	x+	ADJ
ejpam-3305	45	14	β2	β2	NOUN
ejpam-3305	45	15	(	(	PUNCT
ejpam-3305	45	16	n+	n+	X
ejpam-3305	45	17	γ)2	γ)2	NOUN
ejpam-3305	45	18	.	.	PUNCT
ejpam-3305	46	1	proof	proof	NOUN
ejpam-3305	46	2	.	.	PUNCT
ejpam-3305	47	1	for	for	ADP
ejpam-3305	47	2	x	x	PROPN
ejpam-3305	47	3	∈	∈	PROPN
ejpam-3305	47	4	[	[	X
ejpam-3305	47	5	0,∞	0,∞	NOUN
ejpam-3305	47	6	)	)	PUNCT
ejpam-3305	47	7	,	,	PUNCT
ejpam-3305	47	8	in	in	ADP
ejpam-3305	47	9	view	view	NOUN
ejpam-3305	47	10	of	of	ADP
ejpam-3305	47	11	lemma	lemma	PROPN
ejpam-3305	47	12	1	1	NUM
ejpam-3305	47	13	,	,	PUNCT
ejpam-3305	47	14	we	we	PRON
ejpam-3305	47	15	have	have	VERB
ejpam-3305	47	16	m	m	PROPN
ejpam-3305	47	17	(	(	PUNCT
ejpam-3305	47	18	β	β	X
ejpam-3305	47	19	,	,	PUNCT
ejpam-3305	47	20	γ	γ	NOUN
ejpam-3305	47	21	)	)	PUNCT
ejpam-3305	47	22	n	n	CCONJ
ejpam-3305	47	23	,	,	PUNCT
ejpam-3305	47	24	α	α	PROPN
ejpam-3305	47	25	(	(	PUNCT
ejpam-3305	47	26	1;x	1;x	NUM
ejpam-3305	47	27	)	)	PUNCT
ejpam-3305	47	28	=	=	SYM
ejpam-3305	48	1	1	1	X
ejpam-3305	48	2	.	.	PUNCT
ejpam-3305	49	1	the	the	DET
ejpam-3305	49	2	first	first	ADJ
ejpam-3305	49	3	order	order	NOUN
ejpam-3305	49	4	moment	moment	NOUN
ejpam-3305	49	5	is	be	AUX
ejpam-3305	49	6	given	give	VERB
ejpam-3305	49	7	by	by	ADP
ejpam-3305	49	8	m	m	PROPN
ejpam-3305	49	9	(	(	PUNCT
ejpam-3305	49	10	β	β	X
ejpam-3305	49	11	,	,	PUNCT
ejpam-3305	49	12	γ	γ	NOUN
ejpam-3305	49	13	)	)	PUNCT
ejpam-3305	49	14	n	n	CCONJ
ejpam-3305	49	15	,	,	PUNCT
ejpam-3305	49	16	α	α	PROPN
ejpam-3305	49	17	(	(	PUNCT
ejpam-3305	49	18	t;x	t;x	NUM
ejpam-3305	49	19	)	)	PUNCT
ejpam-3305	49	20	=	=	SYM
ejpam-3305	49	21	n	n	PROPN
ejpam-3305	49	22	n+	n+	PUNCT
ejpam-3305	49	23	γ	γ	X
ejpam-3305	49	24	m	m	PROPN
ejpam-3305	49	25	(	(	PUNCT
ejpam-3305	49	26	α	α	NOUN
ejpam-3305	49	27	)	)	PUNCT
ejpam-3305	49	28	n	n	CCONJ
ejpam-3305	49	29	(	(	PUNCT
ejpam-3305	49	30	t;x	t;x	NUM
ejpam-3305	49	31	)	)	PUNCT
ejpam-3305	49	32	+	+	CCONJ
ejpam-3305	49	33	β	β	X
ejpam-3305	49	34	n+	n+	X
ejpam-3305	49	35	γ	γ	X
ejpam-3305	49	36	=	=	SYM
ejpam-3305	49	37	nx+	nx+	PROPN
ejpam-3305	49	38	β	β	X
ejpam-3305	49	39	n+	n+	X
ejpam-3305	49	40	γ	γ	X
ejpam-3305	49	41	.	.	PUNCT
ejpam-3305	50	1	the	the	DET
ejpam-3305	50	2	second	second	ADJ
ejpam-3305	50	3	order	order	NOUN
ejpam-3305	50	4	moment	moment	NOUN
ejpam-3305	50	5	is	be	AUX
ejpam-3305	50	6	given	give	VERB
ejpam-3305	50	7	by	by	ADP
ejpam-3305	50	8	m	m	PROPN
ejpam-3305	50	9	(	(	PUNCT
ejpam-3305	50	10	β	β	X
ejpam-3305	50	11	,	,	PUNCT
ejpam-3305	50	12	γ	γ	NOUN
ejpam-3305	50	13	)	)	PUNCT
ejpam-3305	50	14	n	n	CCONJ
ejpam-3305	50	15	,	,	PUNCT
ejpam-3305	50	16	α	α	PROPN
ejpam-3305	50	17	(	(	PUNCT
ejpam-3305	50	18	t2;x	t2;x	PROPN
ejpam-3305	50	19	)	)	PUNCT
ejpam-3305	50	20	=	=	PUNCT
ejpam-3305	50	21	(	(	PUNCT
ejpam-3305	50	22	n	n	X
ejpam-3305	50	23	n+	n+	ADV
ejpam-3305	50	24	γ	γ	NOUN
ejpam-3305	50	25	)	)	PUNCT
ejpam-3305	50	26	2	2	NUM
ejpam-3305	50	27	m	m	NOUN
ejpam-3305	50	28	(	(	PUNCT
ejpam-3305	50	29	α	α	NOUN
ejpam-3305	50	30	)	)	PUNCT
ejpam-3305	50	31	n	n	CCONJ
ejpam-3305	50	32	(	(	PUNCT
ejpam-3305	50	33	t2;x	t2;x	PROPN
ejpam-3305	50	34	)	)	PUNCT
ejpam-3305	51	1	+	+	CCONJ
ejpam-3305	51	2	2nβ	2nβ	NOUN
ejpam-3305	51	3	(	(	PUNCT
ejpam-3305	51	4	n+	n+	NUM
ejpam-3305	51	5	γ)2	γ)2	PROPN
ejpam-3305	51	6	m	m	VERB
ejpam-3305	51	7	(	(	PUNCT
ejpam-3305	51	8	α	α	NOUN
ejpam-3305	51	9	)	)	PUNCT
ejpam-3305	51	10	n	n	CCONJ
ejpam-3305	51	11	(	(	PUNCT
ejpam-3305	51	12	t;x	t;x	NUM
ejpam-3305	51	13	)	)	PUNCT
ejpam-3305	51	14	+	+	CCONJ
ejpam-3305	51	15	(	(	PUNCT
ejpam-3305	51	16	β	β	X
ejpam-3305	51	17	n+	n+	X
ejpam-3305	51	18	γ	γ	X
ejpam-3305	51	19	)	)	PUNCT
ejpam-3305	51	20	2	2	NUM
ejpam-3305	51	21	=	=	SYM
ejpam-3305	51	22	{	{	PUNCT
ejpam-3305	51	23	n3(α+	n3(α+	PROPN
ejpam-3305	51	24	1	1	NUM
ejpam-3305	51	25	)	)	PUNCT
ejpam-3305	51	26	α(n−	α(n−	NUM
ejpam-3305	51	27	1)(n+	1)(n+	NUM
ejpam-3305	51	28	γ)2	γ)2	NOUN
ejpam-3305	51	29	}	}	PUNCT
ejpam-3305	51	30	x2	x2	PROPN
ejpam-3305	52	1	+	+	PUNCT
ejpam-3305	52	2	{	{	PUNCT
ejpam-3305	52	3	2n2	2n2	NUM
ejpam-3305	52	4	+	+	CCONJ
ejpam-3305	52	5	2nβ(n−	2nβ(n−	NUM
ejpam-3305	52	6	1	1	NUM
ejpam-3305	52	7	)	)	PUNCT
ejpam-3305	52	8	(	(	PUNCT
ejpam-3305	52	9	n−	n−	NOUN
ejpam-3305	52	10	1)(n+	1)(n+	NUM
ejpam-3305	52	11	γ)2	γ)2	NOUN
ejpam-3305	52	12	}	}	PUNCT
ejpam-3305	52	13	x+	x+	ADJ
ejpam-3305	52	14	β2	β2	NOUN
ejpam-3305	52	15	(	(	PUNCT
ejpam-3305	52	16	n+	n+	NOUN
ejpam-3305	52	17	γ)2	γ)2	NOUN
ejpam-3305	52	18	.	.	PUNCT
ejpam-3305	53	1	lemma	lemma	PROPN
ejpam-3305	53	2	3	3	X
ejpam-3305	53	3	.	.	X
ejpam-3305	54	1	for	for	ADP
ejpam-3305	54	2	f	f	PROPN
ejpam-3305	54	3	∈	∈	PROPN
ejpam-3305	54	4	cb[0,∞	cb[0,∞	PROPN
ejpam-3305	54	5	)	)	PUNCT
ejpam-3305	54	6	(	(	PUNCT
ejpam-3305	54	7	space	space	NOUN
ejpam-3305	54	8	of	of	ADP
ejpam-3305	54	9	all	all	DET
ejpam-3305	54	10	real	real	ADV
ejpam-3305	54	11	valued	value	VERB
ejpam-3305	54	12	bounded	bound	VERB
ejpam-3305	54	13	functions	function	NOUN
ejpam-3305	54	14	on	on	ADP
ejpam-3305	54	15	[	[	X
ejpam-3305	54	16	0,∞	0,∞	NOUN
ejpam-3305	54	17	)	)	PUNCT
ejpam-3305	54	18	endowed	endow	VERB
ejpam-3305	54	19	with	with	ADP
ejpam-3305	54	20	norm	norm	NOUN
ejpam-3305	55	1	‖	‖	PROPN
ejpam-3305	55	2	f	f	X
ejpam-3305	55	3	‖cb	‖cb	PUNCT
ejpam-3305	56	1	[	[	X
ejpam-3305	56	2	0,∞)=	0,∞)=	NOUN
ejpam-3305	56	3	sup	sup	NOUN
ejpam-3305	56	4	x∈[0,∞	x∈[0,∞	NOUN
ejpam-3305	56	5	)	)	PUNCT
ejpam-3305	56	6	|f(x)|	|f(x)|	NOUN
ejpam-3305	56	7	)	)	PUNCT
ejpam-3305	56	8	,	,	PUNCT
ejpam-3305	56	9	‖m	‖m	NOUN
ejpam-3305	56	10	(	(	PUNCT
ejpam-3305	56	11	β	β	X
ejpam-3305	56	12	,	,	PUNCT
ejpam-3305	56	13	γ	γ	NOUN
ejpam-3305	56	14	)	)	PUNCT
ejpam-3305	56	15	n	n	CCONJ
ejpam-3305	56	16	,	,	PUNCT
ejpam-3305	56	17	α	α	PROPN
ejpam-3305	56	18	(	(	PUNCT
ejpam-3305	56	19	f	f	X
ejpam-3305	56	20	)	)	PUNCT
ejpam-3305	56	21	‖≤‖	‖≤‖	PROPN
ejpam-3305	56	22	f	f	PROPN
ejpam-3305	56	23	‖	‖	PROPN
ejpam-3305	56	24	.	.	PUNCT
ejpam-3305	56	25	a.	a.	PROPN
ejpam-3305	56	26	kumar	kumar	PROPN
ejpam-3305	56	27	,	,	PUNCT
ejpam-3305	56	28	d.	d.	PROPN
ejpam-3305	56	29	tapiawala	tapiawala	PROPN
ejpam-3305	56	30	,	,	PUNCT
ejpam-3305	56	31	l.	l.	PROPN
ejpam-3305	56	32	n.	n.	PROPN
ejpam-3305	56	33	mishra	mishra	PROPN
ejpam-3305	56	34	/	/	SYM
ejpam-3305	56	35	eur	eur	PROPN
ejpam-3305	56	36	.	.	PUNCT
ejpam-3305	57	1	j.	j.	PROPN
ejpam-3305	57	2	pure	pure	PROPN
ejpam-3305	57	3	appl	appl	PROPN
ejpam-3305	57	4	.	.	PROPN
ejpam-3305	57	5	math	math	PROPN
ejpam-3305	57	6	,	,	PUNCT
ejpam-3305	57	7	11	11	NUM
ejpam-3305	57	8	(	(	PUNCT
ejpam-3305	57	9	4	4	NUM
ejpam-3305	57	10	)	)	PUNCT
ejpam-3305	57	11	(	(	PUNCT
ejpam-3305	57	12	2018	2018	NUM
ejpam-3305	57	13	)	)	PUNCT
ejpam-3305	57	14	,	,	PUNCT
ejpam-3305	57	15	958	958	NUM
ejpam-3305	57	16	-	-	SYM
ejpam-3305	57	17	975	975	NUM
ejpam-3305	57	18	961	961	NUM
ejpam-3305	57	19	proof	proof	NOUN
ejpam-3305	57	20	.	.	PUNCT
ejpam-3305	58	1	in	in	ADP
ejpam-3305	58	2	view	view	NOUN
ejpam-3305	58	3	of	of	ADP
ejpam-3305	58	4	(	(	PUNCT
ejpam-3305	58	5	3	3	NUM
ejpam-3305	58	6	)	)	PUNCT
ejpam-3305	58	7	and	and	CCONJ
ejpam-3305	58	8	lemma	lemma	PROPN
ejpam-3305	58	9	2	2	NUM
ejpam-3305	58	10	,	,	PUNCT
ejpam-3305	58	11	we	we	PRON
ejpam-3305	58	12	get	get	VERB
ejpam-3305	58	13	‖m	‖m	NOUN
ejpam-3305	58	14	(	(	PUNCT
ejpam-3305	58	15	β	β	X
ejpam-3305	58	16	,	,	PUNCT
ejpam-3305	58	17	γ	γ	NOUN
ejpam-3305	58	18	)	)	PUNCT
ejpam-3305	58	19	n	n	CCONJ
ejpam-3305	58	20	,	,	PUNCT
ejpam-3305	58	21	α	α	PROPN
ejpam-3305	58	22	(	(	PUNCT
ejpam-3305	58	23	f)‖	f)‖	ADJ
ejpam-3305	58	24	≤	≤	ADJ
ejpam-3305	58	25	‖f‖m	‖f‖m	NOUN
ejpam-3305	58	26	(	(	PUNCT
ejpam-3305	58	27	β	β	X
ejpam-3305	58	28	,	,	PUNCT
ejpam-3305	58	29	γ	γ	NOUN
ejpam-3305	58	30	)	)	PUNCT
ejpam-3305	58	31	n	n	CCONJ
ejpam-3305	58	32	,	,	PUNCT
ejpam-3305	58	33	α	α	PROPN
ejpam-3305	58	34	(	(	PUNCT
ejpam-3305	58	35	1;x	1;x	NUM
ejpam-3305	58	36	)	)	PUNCT
ejpam-3305	58	37	=	=	PRON
ejpam-3305	58	38	‖f‖.	‖f‖.	PART
ejpam-3305	58	39	remark	remark	NOUN
ejpam-3305	58	40	1	1	NUM
ejpam-3305	58	41	.	.	PUNCT
ejpam-3305	59	1	for	for	ADP
ejpam-3305	59	2	every	every	DET
ejpam-3305	59	3	x	x	SYM
ejpam-3305	59	4	∈	∈	PROPN
ejpam-3305	59	5	[	[	X
ejpam-3305	59	6	0,∞	0,∞	NOUN
ejpam-3305	59	7	)	)	PUNCT
ejpam-3305	59	8	,	,	PUNCT
ejpam-3305	59	9	we	we	PRON
ejpam-3305	59	10	have	have	VERB
ejpam-3305	59	11	m	m	PROPN
ejpam-3305	59	12	(	(	PUNCT
ejpam-3305	59	13	β	β	X
ejpam-3305	59	14	,	,	PUNCT
ejpam-3305	59	15	γ	γ	NOUN
ejpam-3305	59	16	)	)	PUNCT
ejpam-3305	59	17	n	n	CCONJ
ejpam-3305	59	18	,	,	PUNCT
ejpam-3305	59	19	α	α	X
ejpam-3305	59	20	(	(	PUNCT
ejpam-3305	59	21	(	(	PUNCT
ejpam-3305	59	22	t−	t−	PROPN
ejpam-3305	59	23	x);x	x);x	PROPN
ejpam-3305	59	24	)	)	PUNCT
ejpam-3305	59	25	=	=	PUNCT
ejpam-3305	60	1	β	β	X
ejpam-3305	60	2	−	−	NOUN
ejpam-3305	60	3	γx	γx	NOUN
ejpam-3305	60	4	n+	n+	ADP
ejpam-3305	60	5	γ	γ	X
ejpam-3305	60	6	and	and	CCONJ
ejpam-3305	60	7	m	m	PROPN
ejpam-3305	60	8	(	(	PUNCT
ejpam-3305	60	9	β	β	X
ejpam-3305	60	10	,	,	PUNCT
ejpam-3305	60	11	γ	γ	NOUN
ejpam-3305	60	12	)	)	PUNCT
ejpam-3305	60	13	n	n	CCONJ
ejpam-3305	60	14	,	,	PUNCT
ejpam-3305	60	15	α	α	X
ejpam-3305	60	16	(	(	PUNCT
ejpam-3305	60	17	(	(	PUNCT
ejpam-3305	60	18	t−	t−	PROPN
ejpam-3305	60	19	x)2;x	x)2;x	NUM
ejpam-3305	60	20	)	)	PUNCT
ejpam-3305	61	1	=	=	PRON
ejpam-3305	61	2	{	{	PUNCT
ejpam-3305	61	3	n2(n+	n2(n+	PROPN
ejpam-3305	61	4	α	α	X
ejpam-3305	61	5	)	)	PUNCT
ejpam-3305	61	6	+	+	CCONJ
ejpam-3305	61	7	αγ2(n−	αγ2(n−	NOUN
ejpam-3305	61	8	1	1	NUM
ejpam-3305	61	9	)	)	PUNCT
ejpam-3305	61	10	α(n−	α(n−	NUM
ejpam-3305	61	11	1)(n+	1)(n+	NUM
ejpam-3305	61	12	γ)2	γ)2	NOUN
ejpam-3305	61	13	}	}	PUNCT
ejpam-3305	61	14	x2	x2	PROPN
ejpam-3305	62	1	+	+	PUNCT
ejpam-3305	62	2	{	{	PUNCT
ejpam-3305	62	3	2n2	2n2	NUM
ejpam-3305	62	4	+	+	PUNCT
ejpam-3305	62	5	2βγ(1−	2βγ(1−	NUM
ejpam-3305	62	6	n	n	CCONJ
ejpam-3305	62	7	)	)	PUNCT
ejpam-3305	62	8	(	(	PUNCT
ejpam-3305	62	9	n−	n−	NOUN
ejpam-3305	62	10	1)(n+	1)(n+	NUM
ejpam-3305	62	11	γ)2	γ)2	NOUN
ejpam-3305	62	12	}	}	PUNCT
ejpam-3305	62	13	x+	x+	ADJ
ejpam-3305	62	14	β2	β2	NOUN
ejpam-3305	62	15	(	(	PUNCT
ejpam-3305	62	16	n+	n+	NOUN
ejpam-3305	62	17	γ)2	γ)2	NOUN
ejpam-3305	62	18	=	=	SYM
ejpam-3305	62	19	ξ(β	ξ(β	PROPN
ejpam-3305	62	20	,	,	PUNCT
ejpam-3305	62	21	γ)n	γ)n	X
ejpam-3305	62	22	,	,	PUNCT
ejpam-3305	62	23	α	α	PROPN
ejpam-3305	62	24	(	(	PUNCT
ejpam-3305	62	25	x	x	NOUN
ejpam-3305	62	26	)	)	PUNCT
ejpam-3305	62	27	.	.	PUNCT
ejpam-3305	63	1	3	3	X
ejpam-3305	63	2	.	.	X
ejpam-3305	63	3	main	main	ADJ
ejpam-3305	63	4	results	result	NOUN
ejpam-3305	63	5	throughout	throughout	ADP
ejpam-3305	63	6	this	this	DET
ejpam-3305	63	7	paper	paper	NOUN
ejpam-3305	63	8	,	,	PUNCT
ejpam-3305	63	9	we	we	PRON
ejpam-3305	63	10	assume	assume	VERB
ejpam-3305	63	11	that	that	SCONJ
ejpam-3305	63	12	α	α	PRON
ejpam-3305	63	13	=	=	SYM
ejpam-3305	63	14	α(n	α(n	NOUN
ejpam-3305	63	15	)	)	PUNCT
ejpam-3305	63	16	→	→	SYM
ejpam-3305	63	17	∞	∞	PROPN
ejpam-3305	63	18	,	,	PUNCT
ejpam-3305	63	19	as	as	ADP
ejpam-3305	63	20	n	n	PROPN
ejpam-3305	63	21	→	→	SYM
ejpam-3305	63	22	∞	∞	PROPN
ejpam-3305	63	23	and	and	CCONJ
ejpam-3305	63	24	lim	lim	PROPN
ejpam-3305	63	25	n→∞	n→∞	NUM
ejpam-3305	63	26	n	n	PRON
ejpam-3305	63	27	α(n	α(n	NOUN
ejpam-3305	63	28	)	)	PUNCT
ejpam-3305	63	29	=	=	SYM
ejpam-3305	63	30	l(∈	l(∈	ADJ
ejpam-3305	63	31	r	r	NOUN
ejpam-3305	63	32	)	)	PUNCT
ejpam-3305	63	33	.	.	PUNCT
ejpam-3305	64	1	let	let	VERB
ejpam-3305	64	2	ei(t	ei(t	PUNCT
ejpam-3305	64	3	)	)	PUNCT
ejpam-3305	65	1	=	=	SYM
ejpam-3305	65	2	ti	ti	X
ejpam-3305	65	3	,	,	PUNCT
ejpam-3305	65	4	i	i	NOUN
ejpam-3305	65	5	=	=	NOUN
ejpam-3305	65	6	0	0	NUM
ejpam-3305	65	7	,	,	PUNCT
ejpam-3305	65	8	1	1	NUM
ejpam-3305	65	9	,	,	PUNCT
ejpam-3305	65	10	2	2	NUM
ejpam-3305	65	11	.	.	X
ejpam-3305	65	12	theorem	theorem	NOUN
ejpam-3305	65	13	1	1	NUM
ejpam-3305	65	14	.	.	PUNCT
ejpam-3305	66	1	let	let	VERB
ejpam-3305	66	2	f	f	PROPN
ejpam-3305	66	3	∈	∈	PROPN
ejpam-3305	66	4	c[0,∞	c[0,∞	PROPN
ejpam-3305	66	5	)	)	PUNCT
ejpam-3305	66	6	.	.	PUNCT
ejpam-3305	67	1	then	then	ADV
ejpam-3305	67	2	lim	lim	PROPN
ejpam-3305	67	3	n→∞	n→∞	NUM
ejpam-3305	67	4	m	m	VERB
ejpam-3305	67	5	(	(	PUNCT
ejpam-3305	67	6	β	β	X
ejpam-3305	67	7	,	,	PUNCT
ejpam-3305	67	8	γ	γ	NOUN
ejpam-3305	67	9	)	)	PUNCT
ejpam-3305	67	10	n	n	CCONJ
ejpam-3305	67	11	,	,	PUNCT
ejpam-3305	67	12	α	α	PROPN
ejpam-3305	67	13	(	(	PUNCT
ejpam-3305	67	14	f	f	NOUN
ejpam-3305	67	15	;	;	PUNCT
ejpam-3305	67	16	x	x	X
ejpam-3305	67	17	)	)	PUNCT
ejpam-3305	67	18	=	=	SYM
ejpam-3305	67	19	f(x	f(x	PROPN
ejpam-3305	67	20	)	)	PUNCT
ejpam-3305	67	21	,	,	PUNCT
ejpam-3305	67	22	uniformly	uniformly	ADV
ejpam-3305	67	23	in	in	ADP
ejpam-3305	67	24	each	each	DET
ejpam-3305	67	25	compact	compact	ADJ
ejpam-3305	67	26	subset	subset	NOUN
ejpam-3305	67	27	of	of	ADP
ejpam-3305	67	28	[	[	X
ejpam-3305	67	29	0,∞	0,∞	NOUN
ejpam-3305	67	30	)	)	PUNCT
ejpam-3305	67	31	.	.	PUNCT
ejpam-3305	68	1	proof	proof	NOUN
ejpam-3305	68	2	.	.	PUNCT
ejpam-3305	69	1	in	in	ADP
ejpam-3305	69	2	view	view	NOUN
ejpam-3305	69	3	of	of	ADP
ejpam-3305	69	4	lemma	lemma	PROPN
ejpam-3305	69	5	2	2	NUM
ejpam-3305	69	6	,	,	PUNCT
ejpam-3305	69	7	we	we	PRON
ejpam-3305	69	8	get	get	VERB
ejpam-3305	69	9	lim	lim	PROPN
ejpam-3305	69	10	n→∞	n→∞	PRON
ejpam-3305	69	11	m	m	PROPN
ejpam-3305	69	12	(	(	PUNCT
ejpam-3305	69	13	β	β	X
ejpam-3305	69	14	,	,	PUNCT
ejpam-3305	69	15	γ	γ	NOUN
ejpam-3305	69	16	)	)	PUNCT
ejpam-3305	69	17	n	n	CCONJ
ejpam-3305	69	18	,	,	PUNCT
ejpam-3305	69	19	α	α	PROPN
ejpam-3305	69	20	(	(	PUNCT
ejpam-3305	69	21	ei;x	ei;x	NUM
ejpam-3305	69	22	)	)	PUNCT
ejpam-3305	69	23	=	=	SYM
ejpam-3305	69	24	xi	xi	PROPN
ejpam-3305	69	25	,	,	PUNCT
ejpam-3305	69	26	i	i	PRON
ejpam-3305	69	27	=	=	NOUN
ejpam-3305	69	28	0	0	NUM
ejpam-3305	69	29	,	,	PUNCT
ejpam-3305	69	30	1	1	NUM
ejpam-3305	69	31	,	,	PUNCT
ejpam-3305	69	32	2	2	NUM
ejpam-3305	69	33	,	,	PUNCT
ejpam-3305	69	34	uniformly	uniformly	ADV
ejpam-3305	69	35	in	in	ADP
ejpam-3305	69	36	each	each	DET
ejpam-3305	69	37	compact	compact	ADJ
ejpam-3305	69	38	subset	subset	NOUN
ejpam-3305	69	39	of	of	ADP
ejpam-3305	69	40	[	[	X
ejpam-3305	69	41	0,∞	0,∞	NOUN
ejpam-3305	69	42	)	)	PUNCT
ejpam-3305	69	43	.	.	PUNCT
ejpam-3305	70	1	applying	apply	VERB
ejpam-3305	70	2	bohman	bohman	NOUN
ejpam-3305	70	3	-	-	PUNCT
ejpam-3305	70	4	korovkin	korovkin	NOUN
ejpam-3305	70	5	theorem	theorem	PROPN
ejpam-3305	70	6	,	,	PUNCT
ejpam-3305	70	7	it	it	PRON
ejpam-3305	70	8	follows	follow	VERB
ejpam-3305	70	9	that	that	SCONJ
ejpam-3305	70	10	lim	lim	PROPN
ejpam-3305	70	11	n→∞	n→∞	PRON
ejpam-3305	70	12	m	m	VERB
ejpam-3305	70	13	(	(	PUNCT
ejpam-3305	70	14	β	β	X
ejpam-3305	70	15	,	,	PUNCT
ejpam-3305	70	16	γ	γ	NOUN
ejpam-3305	70	17	)	)	PUNCT
ejpam-3305	70	18	n	n	CCONJ
ejpam-3305	70	19	,	,	PUNCT
ejpam-3305	70	20	α	α	PROPN
ejpam-3305	70	21	(	(	PUNCT
ejpam-3305	70	22	f	f	NOUN
ejpam-3305	70	23	;	;	PUNCT
ejpam-3305	70	24	x	x	X
ejpam-3305	70	25	)	)	PUNCT
ejpam-3305	70	26	=	=	SYM
ejpam-3305	70	27	f(x	f(x	PROPN
ejpam-3305	70	28	)	)	PUNCT
ejpam-3305	70	29	,	,	PUNCT
ejpam-3305	70	30	uniformly	uniformly	ADV
ejpam-3305	70	31	in	in	ADP
ejpam-3305	70	32	each	each	DET
ejpam-3305	70	33	compact	compact	ADJ
ejpam-3305	70	34	subset	subset	NOUN
ejpam-3305	70	35	of	of	ADP
ejpam-3305	70	36	[	[	X
ejpam-3305	70	37	0,∞	0,∞	NOUN
ejpam-3305	70	38	)	)	PUNCT
ejpam-3305	70	39	.	.	PUNCT
ejpam-3305	71	1	3.1	3.1	NUM
ejpam-3305	71	2	.	.	PROPN
ejpam-3305	71	3	voronovskaja	voronovskaja	PROPN
ejpam-3305	71	4	type	type	PROPN
ejpam-3305	71	5	theorem	theorem	NOUN
ejpam-3305	71	6	in	in	ADP
ejpam-3305	71	7	this	this	DET
ejpam-3305	71	8	section	section	NOUN
ejpam-3305	71	9	we	we	PRON
ejpam-3305	71	10	prove	prove	VERB
ejpam-3305	71	11	voronvoskaja	voronvoskaja	ADJ
ejpam-3305	71	12	type	type	NOUN
ejpam-3305	71	13	asymptotic	asymptotic	ADJ
ejpam-3305	71	14	theorem	theorem	NOUN
ejpam-3305	71	15	for	for	ADP
ejpam-3305	71	16	the	the	DET
ejpam-3305	71	17	operators	operator	NOUN
ejpam-3305	71	18	m	m	VERB
ejpam-3305	71	19	(	(	PUNCT
ejpam-3305	71	20	β	β	X
ejpam-3305	71	21	,	,	PUNCT
ejpam-3305	71	22	γ	γ	NOUN
ejpam-3305	71	23	)	)	PUNCT
ejpam-3305	71	24	n	n	CCONJ
ejpam-3305	71	25	,	,	PUNCT
ejpam-3305	71	26	α	α	PROPN
ejpam-3305	71	27	.	.	PUNCT
ejpam-3305	72	1	theorem	theorem	NOUN
ejpam-3305	72	2	2	2	NUM
ejpam-3305	72	3	.	.	PUNCT
ejpam-3305	73	1	let	let	VERB
ejpam-3305	73	2	f	f	PRON
ejpam-3305	73	3	be	be	AUX
ejpam-3305	73	4	a	a	DET
ejpam-3305	73	5	bounded	bounded	ADJ
ejpam-3305	73	6	and	and	CCONJ
ejpam-3305	73	7	integrable	integrable	ADJ
ejpam-3305	73	8	function	function	NOUN
ejpam-3305	73	9	on	on	ADP
ejpam-3305	73	10	[	[	X
ejpam-3305	73	11	0,∞	0,∞	NOUN
ejpam-3305	73	12	)	)	PUNCT
ejpam-3305	73	13	,	,	PUNCT
ejpam-3305	73	14	second	second	ADJ
ejpam-3305	73	15	derivative	derivative	NOUN
ejpam-3305	73	16	of	of	ADP
ejpam-3305	73	17	f	f	PROPN
ejpam-3305	73	18	exists	exist	VERB
ejpam-3305	73	19	at	at	ADP
ejpam-3305	73	20	a	a	DET
ejpam-3305	73	21	fixed	fixed	ADJ
ejpam-3305	73	22	point	point	NOUN
ejpam-3305	73	23	x	x	X
ejpam-3305	73	24	∈	∈	PROPN
ejpam-3305	74	1	[	[	X
ejpam-3305	74	2	0,∞	0,∞	NOUN
ejpam-3305	74	3	)	)	PUNCT
ejpam-3305	74	4	,	,	PUNCT
ejpam-3305	74	5	then	then	ADV
ejpam-3305	74	6	lim	lim	PROPN
ejpam-3305	74	7	n→∞	n→∞	X
ejpam-3305	74	8	n	n	CCONJ
ejpam-3305	74	9	(	(	PUNCT
ejpam-3305	74	10	m	m	PROPN
ejpam-3305	74	11	(	(	PUNCT
ejpam-3305	74	12	β	β	X
ejpam-3305	74	13	,	,	PUNCT
ejpam-3305	74	14	γ	γ	NOUN
ejpam-3305	74	15	)	)	PUNCT
ejpam-3305	74	16	n	n	CCONJ
ejpam-3305	74	17	,	,	PUNCT
ejpam-3305	74	18	α	α	PROPN
ejpam-3305	74	19	(	(	PUNCT
ejpam-3305	74	20	f	f	PROPN
ejpam-3305	74	21	;	;	PUNCT
ejpam-3305	74	22	x)−	x)−	PROPN
ejpam-3305	74	23	f(x	f(x	PROPN
ejpam-3305	74	24	)	)	PUNCT
ejpam-3305	74	25	)	)	PUNCT
ejpam-3305	75	1	=	=	PUNCT
ejpam-3305	75	2	(	(	PUNCT
ejpam-3305	75	3	β	β	X
ejpam-3305	75	4	−	−	NOUN
ejpam-3305	75	5	γx)f	γx)f	NUM
ejpam-3305	75	6	′(x	′(x	NOUN
ejpam-3305	75	7	)	)	PUNCT
ejpam-3305	76	1	+	+	CCONJ
ejpam-3305	76	2	1	1	NUM
ejpam-3305	76	3	2	2	NUM
ejpam-3305	76	4	(	(	PUNCT
ejpam-3305	76	5	2x+	2x+	NUM
ejpam-3305	76	6	(	(	PUNCT
ejpam-3305	76	7	l	l	NOUN
ejpam-3305	76	8	+	+	SYM
ejpam-3305	76	9	1)x2	1)x2	NUM
ejpam-3305	76	10	)	)	PUNCT
ejpam-3305	76	11	f	f	PROPN
ejpam-3305	76	12	′′(x	′′(x	PROPN
ejpam-3305	76	13	)	)	PUNCT
ejpam-3305	76	14	.	.	PUNCT
ejpam-3305	77	1	proof	proof	NOUN
ejpam-3305	77	2	.	.	PUNCT
ejpam-3305	78	1	let	let	VERB
ejpam-3305	78	2	x	x	PUNCT
ejpam-3305	78	3	∈	∈	PROPN
ejpam-3305	79	1	[	[	X
ejpam-3305	79	2	0,∞	0,∞	NOUN
ejpam-3305	79	3	)	)	PUNCT
ejpam-3305	79	4	be	be	AUX
ejpam-3305	79	5	fixed	fix	VERB
ejpam-3305	79	6	.	.	PUNCT
ejpam-3305	80	1	using	use	VERB
ejpam-3305	80	2	taylor	taylor	PROPN
ejpam-3305	80	3	’s	’s	PART
ejpam-3305	80	4	expansion	expansion	NOUN
ejpam-3305	80	5	formula	formula	NOUN
ejpam-3305	80	6	of	of	ADP
ejpam-3305	80	7	function	function	NOUN
ejpam-3305	80	8	f	f	PROPN
ejpam-3305	80	9	,	,	PUNCT
ejpam-3305	80	10	it	it	PRON
ejpam-3305	80	11	follows	follow	VERB
ejpam-3305	80	12	f(t	f(t	PROPN
ejpam-3305	80	13	)	)	PUNCT
ejpam-3305	80	14	=	=	SYM
ejpam-3305	80	15	f(x	f(x	PROPN
ejpam-3305	80	16	)	)	PUNCT
ejpam-3305	81	1	+	+	CCONJ
ejpam-3305	81	2	(	(	PUNCT
ejpam-3305	81	3	t−	t−	PROPN
ejpam-3305	81	4	x)f	x)f	NOUN
ejpam-3305	81	5	′(x	′(x	NOUN
ejpam-3305	81	6	)	)	PUNCT
ejpam-3305	82	1	+	+	CCONJ
ejpam-3305	82	2	1	1	NUM
ejpam-3305	82	3	2	2	NUM
ejpam-3305	82	4	f	f	PROPN
ejpam-3305	82	5	′′(x)(t−	′′(x)(t−	X
ejpam-3305	82	6	x)2	x)2	VERB
ejpam-3305	82	7	+	+	CCONJ
ejpam-3305	82	8	r(t	r(t	NOUN
ejpam-3305	82	9	,	,	PUNCT
ejpam-3305	82	10	x)(t−	x)(t−	X
ejpam-3305	82	11	x)2	x)2	PROPN
ejpam-3305	82	12	,	,	PUNCT
ejpam-3305	82	13	(	(	PUNCT
ejpam-3305	82	14	4	4	X
ejpam-3305	82	15	)	)	PUNCT
ejpam-3305	82	16	a.	a.	NOUN
ejpam-3305	82	17	kumar	kumar	PROPN
ejpam-3305	82	18	,	,	PUNCT
ejpam-3305	82	19	d.	d.	PROPN
ejpam-3305	82	20	tapiawala	tapiawala	PROPN
ejpam-3305	82	21	,	,	PUNCT
ejpam-3305	82	22	l.	l.	PROPN
ejpam-3305	82	23	n.	n.	PROPN
ejpam-3305	82	24	mishra	mishra	PROPN
ejpam-3305	82	25	/	/	SYM
ejpam-3305	82	26	eur	eur	PROPN
ejpam-3305	82	27	.	.	PUNCT
ejpam-3305	83	1	j.	j.	PROPN
ejpam-3305	83	2	pure	pure	PROPN
ejpam-3305	83	3	appl	appl	PROPN
ejpam-3305	83	4	.	.	PROPN
ejpam-3305	83	5	math	math	PROPN
ejpam-3305	83	6	,	,	PUNCT
ejpam-3305	83	7	11	11	NUM
ejpam-3305	83	8	(	(	PUNCT
ejpam-3305	83	9	4	4	NUM
ejpam-3305	83	10	)	)	PUNCT
ejpam-3305	83	11	(	(	PUNCT
ejpam-3305	83	12	2018	2018	NUM
ejpam-3305	83	13	)	)	PUNCT
ejpam-3305	83	14	,	,	PUNCT
ejpam-3305	83	15	958	958	NUM
ejpam-3305	83	16	-	-	SYM
ejpam-3305	83	17	975	975	NUM
ejpam-3305	83	18	962	962	NUM
ejpam-3305	83	19	where	where	SCONJ
ejpam-3305	83	20	r(t	r(t	NOUN
ejpam-3305	83	21	,	,	PUNCT
ejpam-3305	83	22	x	x	X
ejpam-3305	83	23	)	)	PUNCT
ejpam-3305	83	24	is	be	AUX
ejpam-3305	83	25	a	a	DET
ejpam-3305	83	26	bounded	bounded	ADJ
ejpam-3305	83	27	function	function	NOUN
ejpam-3305	83	28	and	and	CCONJ
ejpam-3305	83	29	lim	lim	PROPN
ejpam-3305	83	30	t→x	t→x	PROPN
ejpam-3305	83	31	r(t	r(t	PROPN
ejpam-3305	83	32	,	,	PUNCT
ejpam-3305	83	33	x	x	NOUN
ejpam-3305	83	34	)	)	PUNCT
ejpam-3305	83	35	=	=	SYM
ejpam-3305	83	36	0	0	X
ejpam-3305	83	37	.	.	PUNCT
ejpam-3305	84	1	applying	apply	VERB
ejpam-3305	84	2	m	m	VERB
ejpam-3305	84	3	(	(	PUNCT
ejpam-3305	84	4	β	β	X
ejpam-3305	84	5	,	,	PUNCT
ejpam-3305	84	6	γ	γ	NOUN
ejpam-3305	84	7	)	)	PUNCT
ejpam-3305	84	8	n	n	CCONJ
ejpam-3305	84	9	,	,	PUNCT
ejpam-3305	84	10	α	α	PROPN
ejpam-3305	84	11	(	(	PUNCT
ejpam-3305	84	12	f	f	NOUN
ejpam-3305	84	13	;	;	PUNCT
ejpam-3305	84	14	x	x	X
ejpam-3305	84	15	)	)	PUNCT
ejpam-3305	84	16	on	on	ADP
ejpam-3305	84	17	both	both	DET
ejpam-3305	84	18	sides	side	NOUN
ejpam-3305	84	19	of	of	ADP
ejpam-3305	84	20	(	(	PUNCT
ejpam-3305	84	21	4	4	NUM
ejpam-3305	84	22	)	)	PUNCT
ejpam-3305	84	23	,	,	PUNCT
ejpam-3305	84	24	we	we	PRON
ejpam-3305	84	25	get	get	VERB
ejpam-3305	84	26	n	n	PRON
ejpam-3305	84	27	(	(	PUNCT
ejpam-3305	84	28	m	m	PROPN
ejpam-3305	84	29	(	(	PUNCT
ejpam-3305	84	30	β	β	X
ejpam-3305	84	31	,	,	PUNCT
ejpam-3305	84	32	γ	γ	NOUN
ejpam-3305	84	33	)	)	PUNCT
ejpam-3305	84	34	n	n	CCONJ
ejpam-3305	84	35	,	,	PUNCT
ejpam-3305	84	36	α	α	PROPN
ejpam-3305	84	37	(	(	PUNCT
ejpam-3305	84	38	f	f	PROPN
ejpam-3305	84	39	;	;	PUNCT
ejpam-3305	84	40	x)−	x)−	PROPN
ejpam-3305	84	41	f(x	f(x	PROPN
ejpam-3305	84	42	)	)	PUNCT
ejpam-3305	84	43	)	)	PUNCT
ejpam-3305	85	1	=	=	PUNCT
ejpam-3305	85	2	nf	nf	INTJ
ejpam-3305	85	3	′(x)m	′(x)m	PRON
ejpam-3305	85	4	(	(	PUNCT
ejpam-3305	85	5	β	β	X
ejpam-3305	85	6	,	,	PUNCT
ejpam-3305	85	7	γ	γ	NOUN
ejpam-3305	85	8	)	)	PUNCT
ejpam-3305	85	9	n	n	CCONJ
ejpam-3305	85	10	,	,	PUNCT
ejpam-3305	85	11	α	α	X
ejpam-3305	85	12	(	(	PUNCT
ejpam-3305	85	13	(	(	PUNCT
ejpam-3305	85	14	t−	t−	PROPN
ejpam-3305	85	15	x);x	x);x	PROPN
ejpam-3305	85	16	)	)	PUNCT
ejpam-3305	86	1	+	+	CCONJ
ejpam-3305	86	2	1	1	NUM
ejpam-3305	86	3	2	2	NUM
ejpam-3305	86	4	nf	nf	NOUN
ejpam-3305	86	5	′′(x)m	′′(x)m	X
ejpam-3305	86	6	(	(	PUNCT
ejpam-3305	86	7	β	β	X
ejpam-3305	86	8	,	,	PUNCT
ejpam-3305	86	9	γ	γ	NOUN
ejpam-3305	86	10	)	)	PUNCT
ejpam-3305	86	11	n	n	CCONJ
ejpam-3305	86	12	,	,	PUNCT
ejpam-3305	86	13	α	α	X
ejpam-3305	86	14	(	(	PUNCT
ejpam-3305	86	15	(	(	PUNCT
ejpam-3305	86	16	t−	t−	PROPN
ejpam-3305	86	17	x)2;x	x)2;x	NUM
ejpam-3305	86	18	)	)	PUNCT
ejpam-3305	87	1	+	+	X
ejpam-3305	87	2	nm	nm	PRON
ejpam-3305	87	3	(	(	PUNCT
ejpam-3305	87	4	β	β	X
ejpam-3305	87	5	,	,	PUNCT
ejpam-3305	87	6	γ	γ	NOUN
ejpam-3305	87	7	)	)	PUNCT
ejpam-3305	87	8	n	n	CCONJ
ejpam-3305	87	9	,	,	PUNCT
ejpam-3305	87	10	α	α	X
ejpam-3305	87	11	(	(	PUNCT
ejpam-3305	87	12	(	(	PUNCT
ejpam-3305	87	13	t−	t−	PROPN
ejpam-3305	87	14	x)2r(t	x)2r(t	NOUN
ejpam-3305	87	15	,	,	PUNCT
ejpam-3305	87	16	x);x	x);x	PROPN
ejpam-3305	87	17	)	)	PUNCT
ejpam-3305	87	18	.	.	PUNCT
ejpam-3305	88	1	in	in	ADP
ejpam-3305	88	2	view	view	NOUN
ejpam-3305	88	3	of	of	ADP
ejpam-3305	88	4	remark	remark	NOUN
ejpam-3305	88	5	1	1	NUM
ejpam-3305	88	6	,	,	PUNCT
ejpam-3305	88	7	we	we	PRON
ejpam-3305	88	8	have	have	VERB
ejpam-3305	88	9	lim	lim	PROPN
ejpam-3305	88	10	n→∞	n→∞	PRON
ejpam-3305	88	11	nm	nm	PROPN
ejpam-3305	88	12	(	(	PUNCT
ejpam-3305	88	13	β	β	X
ejpam-3305	88	14	,	,	PUNCT
ejpam-3305	88	15	γ	γ	NOUN
ejpam-3305	88	16	)	)	PUNCT
ejpam-3305	88	17	n	n	CCONJ
ejpam-3305	88	18	,	,	PUNCT
ejpam-3305	88	19	α	α	X
ejpam-3305	88	20	(	(	PUNCT
ejpam-3305	88	21	(	(	PUNCT
ejpam-3305	88	22	t−	t−	PROPN
ejpam-3305	88	23	x);x	x);x	PROPN
ejpam-3305	88	24	)	)	PUNCT
ejpam-3305	88	25	=	=	PUNCT
ejpam-3305	89	1	β	β	X
ejpam-3305	89	2	−	−	NOUN
ejpam-3305	89	3	γx	γx	NOUN
ejpam-3305	89	4	(	(	PUNCT
ejpam-3305	89	5	5	5	NUM
ejpam-3305	89	6	)	)	PUNCT
ejpam-3305	89	7	and	and	CCONJ
ejpam-3305	89	8	lim	lim	PROPN
ejpam-3305	89	9	n→∞	n→∞	PRON
ejpam-3305	89	10	nm	nm	PROPN
ejpam-3305	89	11	(	(	PUNCT
ejpam-3305	89	12	β	β	X
ejpam-3305	89	13	,	,	PUNCT
ejpam-3305	89	14	γ	γ	NOUN
ejpam-3305	89	15	)	)	PUNCT
ejpam-3305	89	16	n	n	CCONJ
ejpam-3305	89	17	,	,	PUNCT
ejpam-3305	89	18	α	α	X
ejpam-3305	89	19	(	(	PUNCT
ejpam-3305	89	20	(	(	PUNCT
ejpam-3305	89	21	t−	t−	PROPN
ejpam-3305	89	22	x)2;x	x)2;x	NUM
ejpam-3305	89	23	)	)	PUNCT
ejpam-3305	90	1	=	=	SYM
ejpam-3305	90	2	2x+	2x+	NUM
ejpam-3305	90	3	(	(	PUNCT
ejpam-3305	90	4	l	l	NOUN
ejpam-3305	91	1	+	+	PUNCT
ejpam-3305	91	2	1)x2	1)x2	NUM
ejpam-3305	91	3	.	.	PUNCT
ejpam-3305	92	1	(	(	PUNCT
ejpam-3305	92	2	6	6	NUM
ejpam-3305	92	3	)	)	PUNCT
ejpam-3305	92	4	now	now	ADV
ejpam-3305	92	5	,	,	PUNCT
ejpam-3305	92	6	we	we	PRON
ejpam-3305	92	7	shall	shall	AUX
ejpam-3305	92	8	show	show	VERB
ejpam-3305	92	9	that	that	SCONJ
ejpam-3305	92	10	lim	lim	PROPN
ejpam-3305	92	11	n→∞	n→∞	PRON
ejpam-3305	92	12	nm	nm	PROPN
ejpam-3305	92	13	(	(	PUNCT
ejpam-3305	92	14	β	β	X
ejpam-3305	92	15	,	,	PUNCT
ejpam-3305	92	16	γ	γ	NOUN
ejpam-3305	92	17	)	)	PUNCT
ejpam-3305	92	18	n	n	CCONJ
ejpam-3305	92	19	,	,	PUNCT
ejpam-3305	92	20	α	α	PROPN
ejpam-3305	92	21	(	(	PUNCT
ejpam-3305	92	22	r(t	r(t	NOUN
ejpam-3305	92	23	,	,	PUNCT
ejpam-3305	92	24	x)(t−	x)(t−	ADV
ejpam-3305	92	25	x)2;x	x)2;x	PUNCT
ejpam-3305	92	26	)	)	PUNCT
ejpam-3305	93	1	=	=	PUNCT
ejpam-3305	93	2	0	0	X
ejpam-3305	93	3	.	.	PUNCT
ejpam-3305	93	4	by	by	ADP
ejpam-3305	93	5	using	use	VERB
ejpam-3305	93	6	cauchy	cauchy	PROPN
ejpam-3305	93	7	-	-	PUNCT
ejpam-3305	93	8	schwarz	schwarz	PROPN
ejpam-3305	93	9	inequality	inequality	NOUN
ejpam-3305	93	10	,	,	PUNCT
ejpam-3305	93	11	we	we	PRON
ejpam-3305	93	12	have	have	VERB
ejpam-3305	93	13	m	m	PROPN
ejpam-3305	93	14	(	(	PUNCT
ejpam-3305	93	15	β	β	X
ejpam-3305	93	16	,	,	PUNCT
ejpam-3305	93	17	γ	γ	NOUN
ejpam-3305	93	18	)	)	PUNCT
ejpam-3305	93	19	n	n	CCONJ
ejpam-3305	93	20	,	,	PUNCT
ejpam-3305	93	21	α	α	PROPN
ejpam-3305	93	22	(	(	PUNCT
ejpam-3305	93	23	r(t	r(t	NOUN
ejpam-3305	93	24	,	,	PUNCT
ejpam-3305	93	25	x)(t−	x)(t−	PROPN
ejpam-3305	93	26	x)2;x	x)2;x	NUM
ejpam-3305	93	27	)	)	PUNCT
ejpam-3305	93	28	≤	≤	NOUN
ejpam-3305	94	1	(	(	PUNCT
ejpam-3305	94	2	m	m	PROPN
ejpam-3305	94	3	(	(	PUNCT
ejpam-3305	94	4	β	β	X
ejpam-3305	94	5	,	,	PUNCT
ejpam-3305	94	6	γ	γ	NOUN
ejpam-3305	94	7	)	)	PUNCT
ejpam-3305	94	8	n	n	CCONJ
ejpam-3305	94	9	,	,	PUNCT
ejpam-3305	94	10	α	α	PROPN
ejpam-3305	94	11	(	(	PUNCT
ejpam-3305	94	12	r2(t	r2(t	PROPN
ejpam-3305	94	13	,	,	PUNCT
ejpam-3305	94	14	x);x	x);x	ADJ
ejpam-3305	94	15	)	)	PUNCT
ejpam-3305	94	16	)	)	PUNCT
ejpam-3305	94	17	1/2	1/2	NUM
ejpam-3305	94	18	(	(	PUNCT
ejpam-3305	94	19	m	m	PROPN
ejpam-3305	94	20	(	(	PUNCT
ejpam-3305	94	21	β	β	X
ejpam-3305	94	22	,	,	PUNCT
ejpam-3305	94	23	γ	γ	NOUN
ejpam-3305	94	24	)	)	PUNCT
ejpam-3305	94	25	n	n	CCONJ
ejpam-3305	94	26	,	,	PUNCT
ejpam-3305	94	27	α	α	X
ejpam-3305	94	28	(	(	PUNCT
ejpam-3305	94	29	(	(	PUNCT
ejpam-3305	94	30	t−	t−	PROPN
ejpam-3305	94	31	x)4;x	x)4;x	NUM
ejpam-3305	94	32	)	)	PUNCT
ejpam-3305	94	33	)	)	PUNCT
ejpam-3305	94	34	1/2	1/2	NUM
ejpam-3305	94	35	.	.	PUNCT
ejpam-3305	95	1	(	(	PUNCT
ejpam-3305	95	2	7	7	X
ejpam-3305	95	3	)	)	PUNCT
ejpam-3305	95	4	we	we	PRON
ejpam-3305	95	5	observe	observe	VERB
ejpam-3305	95	6	that	that	SCONJ
ejpam-3305	95	7	r2(x	r2(x	PROPN
ejpam-3305	95	8	,	,	PUNCT
ejpam-3305	95	9	x	x	NOUN
ejpam-3305	95	10	)	)	PUNCT
ejpam-3305	95	11	=	=	SYM
ejpam-3305	95	12	0	0	NUM
ejpam-3305	95	13	and	and	CCONJ
ejpam-3305	95	14	r2	r2	PROPN
ejpam-3305	95	15	(	(	PUNCT
ejpam-3305	95	16	.	.	NUM
ejpam-3305	95	17	,	,	PUNCT
ejpam-3305	95	18	x	x	X
ejpam-3305	95	19	)	)	PUNCT
ejpam-3305	95	20	∈	∈	PROPN
ejpam-3305	95	21	cb[0,∞	cb[0,∞	PROPN
ejpam-3305	95	22	)	)	PUNCT
ejpam-3305	95	23	.	.	PUNCT
ejpam-3305	96	1	then	then	ADV
ejpam-3305	96	2	,	,	PUNCT
ejpam-3305	96	3	it	it	PRON
ejpam-3305	96	4	follows	follow	VERB
ejpam-3305	96	5	that	that	SCONJ
ejpam-3305	96	6	lim	lim	PROPN
ejpam-3305	96	7	n→∞	n→∞	PRON
ejpam-3305	96	8	m	m	VERB
ejpam-3305	96	9	(	(	PUNCT
ejpam-3305	96	10	β	β	X
ejpam-3305	96	11	,	,	PUNCT
ejpam-3305	96	12	γ	γ	NOUN
ejpam-3305	96	13	)	)	PUNCT
ejpam-3305	96	14	n	n	CCONJ
ejpam-3305	96	15	,	,	PUNCT
ejpam-3305	96	16	α	α	PROPN
ejpam-3305	96	17	(	(	PUNCT
ejpam-3305	96	18	r2(t	r2(t	PROPN
ejpam-3305	96	19	,	,	PUNCT
ejpam-3305	96	20	x);x	x);x	ADJ
ejpam-3305	96	21	)	)	PUNCT
ejpam-3305	96	22	=	=	SYM
ejpam-3305	97	1	r2(x	r2(x	PROPN
ejpam-3305	97	2	,	,	PUNCT
ejpam-3305	97	3	x	x	NOUN
ejpam-3305	97	4	)	)	PUNCT
ejpam-3305	97	5	=	=	SYM
ejpam-3305	97	6	0	0	X
ejpam-3305	97	7	.	.	PUNCT
ejpam-3305	98	1	(	(	PUNCT
ejpam-3305	98	2	8)	8)	NUM
ejpam-3305	98	3	now	now	ADV
ejpam-3305	98	4	,	,	PUNCT
ejpam-3305	98	5	from	from	ADP
ejpam-3305	98	6	(	(	PUNCT
ejpam-3305	98	7	7	7	NUM
ejpam-3305	98	8	)	)	PUNCT
ejpam-3305	98	9	and	and	CCONJ
ejpam-3305	98	10	(	(	PUNCT
ejpam-3305	98	11	8)	8)	NUM
ejpam-3305	98	12	we	we	PRON
ejpam-3305	98	13	obtain	obtain	VERB
ejpam-3305	98	14	lim	lim	PROPN
ejpam-3305	98	15	n→∞	n→∞	NUM
ejpam-3305	98	16	nm	nm	PROPN
ejpam-3305	98	17	(	(	PUNCT
ejpam-3305	98	18	β	β	X
ejpam-3305	98	19	,	,	PUNCT
ejpam-3305	98	20	γ	γ	NOUN
ejpam-3305	98	21	)	)	PUNCT
ejpam-3305	98	22	n	n	CCONJ
ejpam-3305	98	23	,	,	PUNCT
ejpam-3305	98	24	α	α	PROPN
ejpam-3305	98	25	(	(	PUNCT
ejpam-3305	98	26	r(t	r(t	NOUN
ejpam-3305	98	27	,	,	PUNCT
ejpam-3305	98	28	x)(t−	x)(t−	ADV
ejpam-3305	98	29	x)2;x	x)2;x	PUNCT
ejpam-3305	98	30	)	)	PUNCT
ejpam-3305	99	1	=	=	PUNCT
ejpam-3305	99	2	0	0	X
ejpam-3305	99	3	.	.	PUNCT
ejpam-3305	100	1	(	(	PUNCT
ejpam-3305	100	2	9	9	NUM
ejpam-3305	100	3	)	)	PUNCT
ejpam-3305	100	4	from	from	ADP
ejpam-3305	100	5	(	(	PUNCT
ejpam-3305	100	6	5	5	NUM
ejpam-3305	100	7	)	)	PUNCT
ejpam-3305	100	8	,	,	PUNCT
ejpam-3305	100	9	(	(	PUNCT
ejpam-3305	100	10	6	6	NUM
ejpam-3305	100	11	)	)	PUNCT
ejpam-3305	100	12	and	and	CCONJ
ejpam-3305	100	13	(	(	PUNCT
ejpam-3305	100	14	9	9	NUM
ejpam-3305	100	15	)	)	PUNCT
ejpam-3305	100	16	,	,	PUNCT
ejpam-3305	100	17	we	we	PRON
ejpam-3305	100	18	get	get	VERB
ejpam-3305	100	19	the	the	DET
ejpam-3305	100	20	required	require	VERB
ejpam-3305	100	21	result	result	NOUN
ejpam-3305	100	22	.	.	PUNCT
ejpam-3305	101	1	3.2	3.2	NUM
ejpam-3305	101	2	.	.	PUNCT
ejpam-3305	102	1	local	local	ADJ
ejpam-3305	102	2	approximation	approximation	NOUN
ejpam-3305	102	3	for	for	ADP
ejpam-3305	102	4	cb[0,∞	cb[0,∞	PROPN
ejpam-3305	102	5	)	)	PUNCT
ejpam-3305	102	6	,	,	PUNCT
ejpam-3305	102	7	let	let	VERB
ejpam-3305	102	8	us	we	PRON
ejpam-3305	102	9	consider	consider	VERB
ejpam-3305	102	10	the	the	PRON
ejpam-3305	102	11	following	follow	VERB
ejpam-3305	102	12	k	k	ADJ
ejpam-3305	102	13	-	-	ADJ
ejpam-3305	102	14	functional	functional	ADJ
ejpam-3305	102	15	:	:	PUNCT
ejpam-3305	102	16	k2(f	k2(f	PROPN
ejpam-3305	102	17	,	,	PUNCT
ejpam-3305	102	18	δ	δ	NOUN
ejpam-3305	102	19	)	)	PUNCT
ejpam-3305	102	20	=	=	PROPN
ejpam-3305	102	21	inf	inf	PROPN
ejpam-3305	102	22	g∈w	g∈w	PROPN
ejpam-3305	102	23	2	2	NUM
ejpam-3305	102	24	{	{	PUNCT
ejpam-3305	102	25	‖	‖	PROPN
ejpam-3305	102	26	f	f	PROPN
ejpam-3305	103	1	−	−	PROPN
ejpam-3305	103	2	g	g	PROPN
ejpam-3305	103	3	‖	‖	PROPN
ejpam-3305	103	4	+	+	PROPN
ejpam-3305	103	5	δ	δ	PROPN
ejpam-3305	103	6	‖	‖	PROPN
ejpam-3305	103	7	g′′	g′′	PROPN
ejpam-3305	103	8	‖	‖	PROPN
ejpam-3305	103	9	}	}	PUNCT
ejpam-3305	103	10	,	,	PUNCT
ejpam-3305	103	11	where	where	SCONJ
ejpam-3305	103	12	δ	δ	PROPN
ejpam-3305	103	13	>	>	X
ejpam-3305	103	14	0	0	PUNCT
ejpam-3305	104	1	and	and	CCONJ
ejpam-3305	104	2	w	w	PROPN
ejpam-3305	104	3	2	2	NUM
ejpam-3305	104	4	=	=	SYM
ejpam-3305	104	5	{	{	PUNCT
ejpam-3305	104	6	g	g	PROPN
ejpam-3305	104	7	∈	∈	PROPN
ejpam-3305	104	8	cb[0,∞	cb[0,∞	PROPN
ejpam-3305	104	9	)	)	PUNCT
ejpam-3305	104	10	:	:	PUNCT
ejpam-3305	104	11	g′	g′	NOUN
ejpam-3305	104	12	,	,	PUNCT
ejpam-3305	104	13	g′′	g′′	PROPN
ejpam-3305	104	14	∈	∈	PROPN
ejpam-3305	104	15	cb[0,∞	cb[0,∞	PROPN
ejpam-3305	104	16	)	)	PUNCT
ejpam-3305	104	17	}	}	PUNCT
ejpam-3305	104	18	.	.	PUNCT
ejpam-3305	105	1	by	by	ADP
ejpam-3305	105	2	,	,	PUNCT
ejpam-3305	105	3	p.	p.	NOUN
ejpam-3305	105	4	177	177	NUM
ejpam-3305	105	5	,	,	PUNCT
ejpam-3305	105	6	theorem	theorem	VERB
ejpam-3305	105	7	2.4	2.4	NUM
ejpam-3305	105	8	in	in	ADP
ejpam-3305	105	9	[	[	X
ejpam-3305	105	10	2	2	NUM
ejpam-3305	105	11	]	]	PUNCT
ejpam-3305	105	12	,	,	PUNCT
ejpam-3305	105	13	there	there	PRON
ejpam-3305	105	14	exists	exist	VERB
ejpam-3305	105	15	an	an	DET
ejpam-3305	105	16	absolute	absolute	ADJ
ejpam-3305	105	17	constant	constant	ADJ
ejpam-3305	105	18	m	m	NOUN
ejpam-3305	105	19	>	>	X
ejpam-3305	105	20	0	0	NUM
ejpam-3305	106	1	such	such	ADJ
ejpam-3305	106	2	that	that	SCONJ
ejpam-3305	106	3	k2(f	k2(f	PROPN
ejpam-3305	106	4	,	,	PUNCT
ejpam-3305	106	5	δ	δ	PROPN
ejpam-3305	106	6	)	)	PUNCT
ejpam-3305	106	7	≤mω2(f	≤mω2(f	VERB
ejpam-3305	106	8	,	,	PUNCT
ejpam-3305	106	9	√	√	PROPN
ejpam-3305	106	10	δ	δ	PROPN
ejpam-3305	106	11	)	)	PUNCT
ejpam-3305	106	12	,	,	PUNCT
ejpam-3305	107	1	(	(	PUNCT
ejpam-3305	107	2	10	10	NUM
ejpam-3305	107	3	)	)	PUNCT
ejpam-3305	107	4	a.	a.	NOUN
ejpam-3305	107	5	kumar	kumar	PROPN
ejpam-3305	107	6	,	,	PUNCT
ejpam-3305	107	7	d.	d.	PROPN
ejpam-3305	107	8	tapiawala	tapiawala	PROPN
ejpam-3305	107	9	,	,	PUNCT
ejpam-3305	107	10	l.	l.	PROPN
ejpam-3305	107	11	n.	n.	PROPN
ejpam-3305	107	12	mishra	mishra	PROPN
ejpam-3305	107	13	/	/	SYM
ejpam-3305	107	14	eur	eur	PROPN
ejpam-3305	107	15	.	.	PUNCT
ejpam-3305	108	1	j.	j.	PROPN
ejpam-3305	108	2	pure	pure	PROPN
ejpam-3305	108	3	appl	appl	PROPN
ejpam-3305	108	4	.	.	PROPN
ejpam-3305	108	5	math	math	PROPN
ejpam-3305	108	6	,	,	PUNCT
ejpam-3305	108	7	11	11	NUM
ejpam-3305	108	8	(	(	PUNCT
ejpam-3305	108	9	4	4	NUM
ejpam-3305	108	10	)	)	PUNCT
ejpam-3305	108	11	(	(	PUNCT
ejpam-3305	108	12	2018	2018	NUM
ejpam-3305	108	13	)	)	PUNCT
ejpam-3305	108	14	,	,	PUNCT
ejpam-3305	108	15	958	958	NUM
ejpam-3305	108	16	-	-	SYM
ejpam-3305	108	17	975	975	NUM
ejpam-3305	108	18	963	963	NUM
ejpam-3305	108	19	where	where	SCONJ
ejpam-3305	108	20	ω2(f	ω2(f	X
ejpam-3305	108	21	,	,	PUNCT
ejpam-3305	108	22	√	√	NUM
ejpam-3305	108	23	δ	δ	NOUN
ejpam-3305	108	24	)	)	PUNCT
ejpam-3305	108	25	=	=	SYM
ejpam-3305	109	1	sup	sup	NOUN
ejpam-3305	109	2	0	0	NUM
ejpam-3305	109	3	<	<	X
ejpam-3305	109	4	h≤	h≤	PRON
ejpam-3305	109	5	√	√	ADJ
ejpam-3305	109	6	δ	δ	PROPN
ejpam-3305	109	7	sup	sup	NOUN
ejpam-3305	109	8	x∈[0,∞	x∈[0,∞	PUNCT
ejpam-3305	109	9	)	)	PUNCT
ejpam-3305	109	10	|	|	ADV
ejpam-3305	109	11	f(x+	f(x+	VERB
ejpam-3305	109	12	2h)−	2h)−	ADV
ejpam-3305	109	13	2f(x+	2f(x+	ADJ
ejpam-3305	109	14	h	h	NOUN
ejpam-3305	109	15	)	)	PUNCT
ejpam-3305	110	1	+	+	CCONJ
ejpam-3305	110	2	f(x	f(x	PROPN
ejpam-3305	110	3	)	)	PUNCT
ejpam-3305	110	4	|	|	ADV
ejpam-3305	110	5	is	be	AUX
ejpam-3305	110	6	the	the	DET
ejpam-3305	110	7	second	second	ADJ
ejpam-3305	110	8	order	order	NOUN
ejpam-3305	110	9	modulus	modulus	NOUN
ejpam-3305	110	10	of	of	ADP
ejpam-3305	110	11	smoothness	smoothness	NOUN
ejpam-3305	110	12	of	of	ADP
ejpam-3305	110	13	f	f	PROPN
ejpam-3305	110	14	.	.	PUNCT
ejpam-3305	111	1	by	by	ADP
ejpam-3305	111	2	ω(f	ω(f	PROPN
ejpam-3305	111	3	,	,	PUNCT
ejpam-3305	111	4	δ	δ	PROPN
ejpam-3305	111	5	)	)	PUNCT
ejpam-3305	111	6	=	=	SYM
ejpam-3305	111	7	sup	sup	NOUN
ejpam-3305	111	8	0	0	NUM
ejpam-3305	111	9	<	<	X
ejpam-3305	111	10	h≤δ	h≤δ	PROPN
ejpam-3305	111	11	sup	sup	PROPN
ejpam-3305	111	12	x∈[0,∞	x∈[0,∞	NUM
ejpam-3305	111	13	)	)	PUNCT
ejpam-3305	111	14	|	|	ADV
ejpam-3305	111	15	f(x+	f(x+	VERB
ejpam-3305	111	16	h)−	h)−	PROPN
ejpam-3305	111	17	f(x	f(x	PROPN
ejpam-3305	111	18	)	)	PUNCT
ejpam-3305	112	1	|	|	ADV
ejpam-3305	112	2	,	,	PUNCT
ejpam-3305	112	3	we	we	PRON
ejpam-3305	112	4	denote	denote	VERB
ejpam-3305	112	5	the	the	DET
ejpam-3305	112	6	first	first	ADJ
ejpam-3305	112	7	order	order	NOUN
ejpam-3305	112	8	modulus	modulus	NOUN
ejpam-3305	112	9	of	of	ADP
ejpam-3305	112	10	continuity	continuity	NOUN
ejpam-3305	112	11	of	of	ADP
ejpam-3305	112	12	f	f	PROPN
ejpam-3305	112	13	∈	∈	PROPN
ejpam-3305	112	14	cb[0,∞	cb[0,∞	PROPN
ejpam-3305	112	15	)	)	PUNCT
ejpam-3305	112	16	.	.	PUNCT
ejpam-3305	113	1	theorem	theorem	NOUN
ejpam-3305	113	2	3	3	X
ejpam-3305	113	3	.	.	PUNCT
ejpam-3305	114	1	let	let	VERB
ejpam-3305	114	2	f	f	PROPN
ejpam-3305	114	3	∈	∈	PROPN
ejpam-3305	114	4	cb[0,∞	cb[0,∞	PROPN
ejpam-3305	114	5	)	)	PUNCT
ejpam-3305	114	6	.	.	PUNCT
ejpam-3305	115	1	then	then	ADV
ejpam-3305	115	2	,	,	PUNCT
ejpam-3305	115	3	for	for	ADP
ejpam-3305	115	4	every	every	DET
ejpam-3305	115	5	x	x	SYM
ejpam-3305	115	6	∈	∈	PROPN
ejpam-3305	115	7	[	[	X
ejpam-3305	115	8	0,∞	0,∞	NOUN
ejpam-3305	115	9	)	)	PUNCT
ejpam-3305	115	10	,	,	PUNCT
ejpam-3305	115	11	we	we	PRON
ejpam-3305	115	12	have	have	VERB
ejpam-3305	115	13	|m	|m	NOUN
ejpam-3305	115	14	(	(	PUNCT
ejpam-3305	115	15	β	β	X
ejpam-3305	115	16	,	,	PUNCT
ejpam-3305	115	17	γ	γ	NOUN
ejpam-3305	115	18	)	)	PUNCT
ejpam-3305	115	19	n	n	CCONJ
ejpam-3305	115	20	,	,	PUNCT
ejpam-3305	115	21	α	α	PROPN
ejpam-3305	115	22	(	(	PUNCT
ejpam-3305	115	23	f	f	PROPN
ejpam-3305	115	24	;	;	PUNCT
ejpam-3305	115	25	x)−	x)−	PROPN
ejpam-3305	115	26	f(x	f(x	PROPN
ejpam-3305	115	27	)	)	PUNCT
ejpam-3305	115	28	|	|	ADV
ejpam-3305	115	29	≤	≤	NUM
ejpam-3305	115	30	mω2	mω2	NOUN
ejpam-3305	115	31	(	(	PUNCT
ejpam-3305	115	32	f	f	X
ejpam-3305	115	33	,	,	PUNCT
ejpam-3305	115	34	ζ(β	ζ(β	PROPN
ejpam-3305	115	35	,	,	PUNCT
ejpam-3305	115	36	γ)n	γ)n	X
ejpam-3305	115	37	,	,	PUNCT
ejpam-3305	115	38	α	α	PROPN
ejpam-3305	115	39	(	(	PUNCT
ejpam-3305	115	40	x	x	NOUN
ejpam-3305	115	41	)	)	PUNCT
ejpam-3305	115	42	)	)	PUNCT
ejpam-3305	116	1	+	+	CCONJ
ejpam-3305	116	2	ω	ω	NUM
ejpam-3305	116	3	(	(	PUNCT
ejpam-3305	116	4	f	f	PROPN
ejpam-3305	116	5	,	,	PUNCT
ejpam-3305	116	6	|β	|β	VERB
ejpam-3305	116	7	−	−	PROPN
ejpam-3305	117	1	γx|	γx|	VERB
ejpam-3305	117	2	n+	n+	NUM
ejpam-3305	117	3	γ	γ	NOUN
ejpam-3305	117	4	)	)	PUNCT
ejpam-3305	117	5	,	,	PUNCT
ejpam-3305	117	6	where	where	SCONJ
ejpam-3305	117	7	m	m	NOUN
ejpam-3305	117	8	is	be	AUX
ejpam-3305	117	9	a	a	DET
ejpam-3305	117	10	positive	positive	ADJ
ejpam-3305	117	11	constant	constant	NOUN
ejpam-3305	117	12	and	and	CCONJ
ejpam-3305	117	13	ζ(β	ζ(β	NOUN
ejpam-3305	117	14	,	,	PUNCT
ejpam-3305	117	15	γ)n	γ)n	X
ejpam-3305	117	16	,	,	PUNCT
ejpam-3305	117	17	α	α	PROPN
ejpam-3305	117	18	(	(	PUNCT
ejpam-3305	117	19	x	x	NOUN
ejpam-3305	117	20	)	)	PUNCT
ejpam-3305	117	21	=	=	SYM
ejpam-3305	117	22	(	(	PUNCT
ejpam-3305	117	23	ξ(β	ξ(β	PROPN
ejpam-3305	117	24	,	,	PUNCT
ejpam-3305	117	25	γ)n	γ)n	X
ejpam-3305	117	26	,	,	PUNCT
ejpam-3305	117	27	α	α	PROPN
ejpam-3305	117	28	(	(	PUNCT
ejpam-3305	117	29	x	x	NOUN
ejpam-3305	117	30	)	)	PUNCT
ejpam-3305	118	1	+	+	CCONJ
ejpam-3305	118	2	(	(	PUNCT
ejpam-3305	118	3	β	β	X
ejpam-3305	118	4	−	−	NOUN
ejpam-3305	118	5	γx	γx	NOUN
ejpam-3305	118	6	n+	n+	PUNCT
ejpam-3305	118	7	γ	γ	PROPN
ejpam-3305	118	8	)	)	PUNCT
ejpam-3305	118	9	2)1/2	2)1/2	PROPN
ejpam-3305	118	10	.	.	PUNCT
ejpam-3305	119	1	proof	proof	NOUN
ejpam-3305	119	2	.	.	PUNCT
ejpam-3305	120	1	for	for	ADP
ejpam-3305	120	2	x	x	PROPN
ejpam-3305	120	3	∈	∈	PROPN
ejpam-3305	120	4	[	[	X
ejpam-3305	120	5	0,∞	0,∞	NOUN
ejpam-3305	120	6	)	)	PUNCT
ejpam-3305	120	7	,	,	PUNCT
ejpam-3305	120	8	we	we	PRON
ejpam-3305	120	9	consider	consider	VERB
ejpam-3305	120	10	the	the	DET
ejpam-3305	120	11	auxiliary	auxiliary	ADJ
ejpam-3305	120	12	operators	operator	NOUN
ejpam-3305	120	13	m	m	VERB
ejpam-3305	120	14	(	(	PUNCT
ejpam-3305	120	15	β	β	X
ejpam-3305	120	16	,	,	PUNCT
ejpam-3305	120	17	γ	γ	NOUN
ejpam-3305	120	18	)	)	PUNCT
ejpam-3305	120	19	n	n	CCONJ
ejpam-3305	120	20	,	,	PUNCT
ejpam-3305	120	21	α	α	PRON
ejpam-3305	120	22	defined	define	VERB
ejpam-3305	120	23	by	by	ADP
ejpam-3305	120	24	m	m	PROPN
ejpam-3305	120	25	(	(	PUNCT
ejpam-3305	120	26	β	β	X
ejpam-3305	120	27	,	,	PUNCT
ejpam-3305	120	28	γ	γ	NOUN
ejpam-3305	120	29	)	)	PUNCT
ejpam-3305	120	30	n	n	CCONJ
ejpam-3305	120	31	,	,	PUNCT
ejpam-3305	120	32	α	α	PROPN
ejpam-3305	120	33	(	(	PUNCT
ejpam-3305	120	34	f	f	NOUN
ejpam-3305	120	35	;	;	PUNCT
ejpam-3305	120	36	x	x	X
ejpam-3305	120	37	)	)	PUNCT
ejpam-3305	121	1	=	=	SYM
ejpam-3305	121	2	m	m	PROPN
ejpam-3305	121	3	(	(	PUNCT
ejpam-3305	121	4	β	β	X
ejpam-3305	121	5	,	,	PUNCT
ejpam-3305	121	6	γ	γ	NOUN
ejpam-3305	121	7	)	)	PUNCT
ejpam-3305	121	8	n	n	CCONJ
ejpam-3305	121	9	,	,	PUNCT
ejpam-3305	121	10	α	α	PROPN
ejpam-3305	121	11	(	(	PUNCT
ejpam-3305	121	12	f	f	PROPN
ejpam-3305	121	13	;	;	PUNCT
ejpam-3305	121	14	x)−	x)−	PROPN
ejpam-3305	121	15	f	f	PROPN
ejpam-3305	121	16	(	(	PUNCT
ejpam-3305	121	17	nx+	nx+	PROPN
ejpam-3305	121	18	β	β	X
ejpam-3305	121	19	n+	n+	X
ejpam-3305	121	20	γ	γ	X
ejpam-3305	121	21	)	)	PUNCT
ejpam-3305	121	22	+	+	CCONJ
ejpam-3305	121	23	f(x	f(x	PROPN
ejpam-3305	121	24	)	)	PUNCT
ejpam-3305	121	25	.	.	PUNCT
ejpam-3305	122	1	(	(	PUNCT
ejpam-3305	122	2	11	11	NUM
ejpam-3305	122	3	)	)	PUNCT
ejpam-3305	122	4	from	from	ADP
ejpam-3305	122	5	lemma	lemma	PROPN
ejpam-3305	122	6	2	2	NUM
ejpam-3305	122	7	,	,	PUNCT
ejpam-3305	122	8	we	we	PRON
ejpam-3305	122	9	observe	observe	VERB
ejpam-3305	122	10	that	that	SCONJ
ejpam-3305	122	11	the	the	DET
ejpam-3305	122	12	operators	operator	NOUN
ejpam-3305	122	13	m	m	VERB
ejpam-3305	122	14	(	(	PUNCT
ejpam-3305	122	15	β	β	X
ejpam-3305	122	16	,	,	PUNCT
ejpam-3305	122	17	γ	γ	NOUN
ejpam-3305	122	18	)	)	PUNCT
ejpam-3305	122	19	n	n	CCONJ
ejpam-3305	122	20	,	,	PUNCT
ejpam-3305	122	21	α	α	PROPN
ejpam-3305	122	22	are	be	AUX
ejpam-3305	122	23	linear	linear	ADJ
ejpam-3305	122	24	and	and	CCONJ
ejpam-3305	122	25	reproduce	reproduce	VERB
ejpam-3305	122	26	the	the	DET
ejpam-3305	122	27	linear	linear	ADJ
ejpam-3305	122	28	functions	function	NOUN
ejpam-3305	122	29	.	.	PUNCT
ejpam-3305	123	1	hence	hence	ADV
ejpam-3305	123	2	m	m	PROPN
ejpam-3305	123	3	(	(	PUNCT
ejpam-3305	123	4	β	β	X
ejpam-3305	123	5	,	,	PUNCT
ejpam-3305	123	6	γ	γ	NOUN
ejpam-3305	123	7	)	)	PUNCT
ejpam-3305	123	8	n	n	CCONJ
ejpam-3305	123	9	,	,	PUNCT
ejpam-3305	123	10	α	α	X
ejpam-3305	123	11	(	(	PUNCT
ejpam-3305	123	12	(	(	PUNCT
ejpam-3305	123	13	t−	t−	PROPN
ejpam-3305	123	14	x);x	x);x	PROPN
ejpam-3305	123	15	)	)	PUNCT
ejpam-3305	123	16	=	=	SYM
ejpam-3305	124	1	0	0	X
ejpam-3305	124	2	.	.	PUNCT
ejpam-3305	125	1	(	(	PUNCT
ejpam-3305	125	2	12	12	NUM
ejpam-3305	125	3	)	)	PUNCT
ejpam-3305	125	4	let	let	VERB
ejpam-3305	125	5	g	g	PROPN
ejpam-3305	125	6	∈w	∈w	NOUN
ejpam-3305	125	7	2	2	NUM
ejpam-3305	125	8	and	and	CCONJ
ejpam-3305	125	9	x	x	NOUN
ejpam-3305	125	10	,	,	PUNCT
ejpam-3305	125	11	t	t	PROPN
ejpam-3305	125	12	∈	∈	PROPN
ejpam-3305	126	1	[	[	X
ejpam-3305	126	2	0,∞	0,∞	NOUN
ejpam-3305	126	3	)	)	PUNCT
ejpam-3305	126	4	.	.	PUNCT
ejpam-3305	127	1	by	by	ADP
ejpam-3305	127	2	taylor	taylor	PROPN
ejpam-3305	127	3	’s	’s	PART
ejpam-3305	127	4	expansion	expansion	NOUN
ejpam-3305	127	5	we	we	PRON
ejpam-3305	127	6	have	have	VERB
ejpam-3305	127	7	g(t	g(t	PROPN
ejpam-3305	127	8	)	)	PUNCT
ejpam-3305	128	1	=	=	SYM
ejpam-3305	128	2	g(x	g(x	NOUN
ejpam-3305	128	3	)	)	PUNCT
ejpam-3305	129	1	+	+	CCONJ
ejpam-3305	129	2	(	(	PUNCT
ejpam-3305	129	3	t−	t−	PROPN
ejpam-3305	129	4	x)g′(x	x)g′(x	PROPN
ejpam-3305	129	5	)	)	PUNCT
ejpam-3305	130	1	+	+	NUM
ejpam-3305	130	2	∫	∫	PROPN
ejpam-3305	130	3	t	t	NOUN
ejpam-3305	130	4	x	x	X
ejpam-3305	130	5	(	(	PUNCT
ejpam-3305	130	6	t−	t−	PROPN
ejpam-3305	130	7	v)g′′(v)dv	v)g′′(v)dv	PROPN
ejpam-3305	130	8	.	.	PUNCT
ejpam-3305	131	1	applying	apply	VERB
ejpam-3305	131	2	m	m	VERB
ejpam-3305	131	3	(	(	PUNCT
ejpam-3305	131	4	β	β	X
ejpam-3305	131	5	,	,	PUNCT
ejpam-3305	131	6	γ	γ	NOUN
ejpam-3305	131	7	)	)	PUNCT
ejpam-3305	131	8	n	n	CCONJ
ejpam-3305	131	9	,	,	PUNCT
ejpam-3305	131	10	α	α	NOUN
ejpam-3305	131	11	on	on	ADP
ejpam-3305	131	12	both	both	DET
ejpam-3305	131	13	sides	side	NOUN
ejpam-3305	131	14	of	of	ADP
ejpam-3305	131	15	the	the	DET
ejpam-3305	131	16	above	above	ADJ
ejpam-3305	131	17	equation	equation	NOUN
ejpam-3305	131	18	and	and	CCONJ
ejpam-3305	131	19	using	use	VERB
ejpam-3305	131	20	(	(	PUNCT
ejpam-3305	131	21	12	12	NUM
ejpam-3305	131	22	)	)	PUNCT
ejpam-3305	131	23	,	,	PUNCT
ejpam-3305	131	24	we	we	PRON
ejpam-3305	131	25	get	get	VERB
ejpam-3305	131	26	m	m	VERB
ejpam-3305	131	27	(	(	PUNCT
ejpam-3305	131	28	β	β	X
ejpam-3305	131	29	,	,	PUNCT
ejpam-3305	131	30	γ	γ	NOUN
ejpam-3305	131	31	)	)	PUNCT
ejpam-3305	131	32	n	n	CCONJ
ejpam-3305	131	33	,	,	PUNCT
ejpam-3305	131	34	α	α	PROPN
ejpam-3305	131	35	(	(	PUNCT
ejpam-3305	131	36	g;x)−	g;x)−	PROPN
ejpam-3305	131	37	g(x	g(x	PROPN
ejpam-3305	131	38	)	)	PUNCT
ejpam-3305	132	1	=	=	PUNCT
ejpam-3305	132	2	m	m	PROPN
ejpam-3305	132	3	(	(	PUNCT
ejpam-3305	132	4	β	β	X
ejpam-3305	132	5	,	,	PUNCT
ejpam-3305	132	6	γ	γ	NOUN
ejpam-3305	132	7	)	)	PUNCT
ejpam-3305	132	8	n	n	CCONJ
ejpam-3305	132	9	,	,	PUNCT
ejpam-3305	132	10	α	α	PROPN
ejpam-3305	132	11	(	(	PUNCT
ejpam-3305	132	12	∫	∫	PROPN
ejpam-3305	132	13	t	t	PROPN
ejpam-3305	132	14	x	x	X
ejpam-3305	132	15	(	(	PUNCT
ejpam-3305	132	16	t−	t−	PROPN
ejpam-3305	132	17	v)g′′(v)dv;x	v)g′′(v)dv;x	PROPN
ejpam-3305	132	18	)	)	PUNCT
ejpam-3305	132	19	.	.	PUNCT
ejpam-3305	133	1	thus	thus	ADV
ejpam-3305	133	2	,	,	PUNCT
ejpam-3305	133	3	by	by	ADP
ejpam-3305	133	4	(	(	PUNCT
ejpam-3305	133	5	11	11	NUM
ejpam-3305	133	6	)	)	PUNCT
ejpam-3305	133	7	we	we	PRON
ejpam-3305	133	8	get	get	VERB
ejpam-3305	133	9	|m	|m	NOUN
ejpam-3305	133	10	(	(	PUNCT
ejpam-3305	133	11	β	β	X
ejpam-3305	133	12	,	,	PUNCT
ejpam-3305	133	13	γ	γ	NOUN
ejpam-3305	133	14	)	)	PUNCT
ejpam-3305	133	15	n	n	CCONJ
ejpam-3305	133	16	,	,	PUNCT
ejpam-3305	133	17	α	α	PROPN
ejpam-3305	133	18	(	(	PUNCT
ejpam-3305	133	19	g;x)−	g;x)−	PROPN
ejpam-3305	133	20	g(x)|	g(x)|	VERB
ejpam-3305	133	21	≤	≤	NUM
ejpam-3305	133	22	m	m	VERB
ejpam-3305	133	23	(	(	PUNCT
ejpam-3305	133	24	β	β	X
ejpam-3305	133	25	,	,	PUNCT
ejpam-3305	133	26	γ	γ	NOUN
ejpam-3305	133	27	)	)	PUNCT
ejpam-3305	133	28	n	n	CCONJ
ejpam-3305	133	29	,	,	PUNCT
ejpam-3305	133	30	α	α	PROPN
ejpam-3305	133	31	(	(	PUNCT
ejpam-3305	133	32	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3305	133	33	∫	∫	PROPN
ejpam-3305	133	34	t	t	PROPN
ejpam-3305	133	35	x	x	X
ejpam-3305	133	36	(	(	PUNCT
ejpam-3305	133	37	t−	t−	PROPN
ejpam-3305	133	38	v)g′′(v)dv	v)g′′(v)dv	PROPN
ejpam-3305	133	39	∣∣∣∣;x)+	∣∣∣∣;x)+	NOUN
ejpam-3305	133	40	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3305	133	41	∫	∫	PROPN
ejpam-3305	133	42	nx+β	nx+β	PROPN
ejpam-3305	133	43	n+γ	n+γ	PROPN
ejpam-3305	133	44	x	x	PUNCT
ejpam-3305	133	45	(	(	PUNCT
ejpam-3305	133	46	nx+	nx+	ADJ
ejpam-3305	133	47	β	β	X
ejpam-3305	133	48	n+	n+	X
ejpam-3305	133	49	γ	γ	PROPN
ejpam-3305	133	50	−	−	PROPN
ejpam-3305	133	51	v	v	NOUN
ejpam-3305	133	52	)	)	PUNCT
ejpam-3305	133	53	g′′(v)dv	g′′(v)dv	NOUN
ejpam-3305	133	54	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3305	133	55	a.	a.	NOUN
ejpam-3305	133	56	kumar	kumar	PROPN
ejpam-3305	133	57	,	,	PUNCT
ejpam-3305	133	58	d.	d.	PROPN
ejpam-3305	133	59	tapiawala	tapiawala	PROPN
ejpam-3305	133	60	,	,	PUNCT
ejpam-3305	133	61	l.	l.	PROPN
ejpam-3305	133	62	n.	n.	PROPN
ejpam-3305	133	63	mishra	mishra	PROPN
ejpam-3305	133	64	/	/	SYM
ejpam-3305	133	65	eur	eur	PROPN
ejpam-3305	133	66	.	.	PUNCT
ejpam-3305	134	1	j.	j.	PROPN
ejpam-3305	134	2	pure	pure	PROPN
ejpam-3305	134	3	appl	appl	PROPN
ejpam-3305	134	4	.	.	PROPN
ejpam-3305	134	5	math	math	PROPN
ejpam-3305	134	6	,	,	PUNCT
ejpam-3305	134	7	11	11	NUM
ejpam-3305	134	8	(	(	PUNCT
ejpam-3305	134	9	4	4	NUM
ejpam-3305	134	10	)	)	PUNCT
ejpam-3305	134	11	(	(	PUNCT
ejpam-3305	134	12	2018	2018	NUM
ejpam-3305	134	13	)	)	PUNCT
ejpam-3305	134	14	,	,	PUNCT
ejpam-3305	134	15	958	958	NUM
ejpam-3305	134	16	-	-	SYM
ejpam-3305	134	17	975	975	NUM
ejpam-3305	134	18	964	964	NUM
ejpam-3305	134	19	≤	≤	NOUN
ejpam-3305	134	20	(	(	PUNCT
ejpam-3305	134	21	ξ(β	ξ(β	PROPN
ejpam-3305	134	22	,	,	PUNCT
ejpam-3305	134	23	γ)n	γ)n	X
ejpam-3305	134	24	,	,	PUNCT
ejpam-3305	134	25	α	α	PROPN
ejpam-3305	134	26	(	(	PUNCT
ejpam-3305	134	27	x	x	NOUN
ejpam-3305	134	28	)	)	PUNCT
ejpam-3305	135	1	+	+	CCONJ
ejpam-3305	135	2	(	(	PUNCT
ejpam-3305	135	3	β	β	X
ejpam-3305	135	4	−	−	NOUN
ejpam-3305	135	5	γx	γx	NOUN
ejpam-3305	135	6	n+	n+	PUNCT
ejpam-3305	135	7	γ	γ	NOUN
ejpam-3305	135	8	)	)	PUNCT
ejpam-3305	135	9	2	2	NUM
ejpam-3305	135	10	)	)	PUNCT
ejpam-3305	135	11	‖	‖	PROPN
ejpam-3305	135	12	g′′	g′′	PROPN
ejpam-3305	135	13	‖	‖	PROPN
ejpam-3305	135	14	≤	≤	NOUN
ejpam-3305	135	15	(	(	PUNCT
ejpam-3305	135	16	ζ(β	ζ(β	PROPN
ejpam-3305	135	17	,	,	PUNCT
ejpam-3305	135	18	γ)n	γ)n	X
ejpam-3305	135	19	,	,	PUNCT
ejpam-3305	135	20	α	α	PROPN
ejpam-3305	135	21	(	(	PUNCT
ejpam-3305	135	22	x	x	NOUN
ejpam-3305	135	23	)	)	PUNCT
ejpam-3305	135	24	)	)	PUNCT
ejpam-3305	135	25	2	2	NUM
ejpam-3305	135	26	‖	‖	PROPN
ejpam-3305	135	27	g′′	g′′	PROPN
ejpam-3305	135	28	‖	‖	PROPN
ejpam-3305	135	29	.	.	PUNCT
ejpam-3305	136	1	(	(	PUNCT
ejpam-3305	136	2	13	13	NUM
ejpam-3305	136	3	)	)	PUNCT
ejpam-3305	136	4	on	on	ADP
ejpam-3305	136	5	other	other	ADJ
ejpam-3305	136	6	hand	hand	NOUN
ejpam-3305	136	7	,	,	PUNCT
ejpam-3305	136	8	by	by	ADP
ejpam-3305	136	9	(	(	PUNCT
ejpam-3305	136	10	11	11	NUM
ejpam-3305	136	11	)	)	PUNCT
ejpam-3305	136	12	and	and	CCONJ
ejpam-3305	136	13	lemma	lemma	PROPN
ejpam-3305	136	14	3	3	NUM
ejpam-3305	136	15	,	,	PUNCT
ejpam-3305	136	16	we	we	PRON
ejpam-3305	136	17	have	have	VERB
ejpam-3305	136	18	|m	|m	NOUN
ejpam-3305	136	19	(	(	PUNCT
ejpam-3305	136	20	β	β	X
ejpam-3305	136	21	,	,	PUNCT
ejpam-3305	136	22	γ	γ	NOUN
ejpam-3305	136	23	)	)	PUNCT
ejpam-3305	136	24	n	n	CCONJ
ejpam-3305	136	25	,	,	PUNCT
ejpam-3305	136	26	α	α	PROPN
ejpam-3305	136	27	(	(	PUNCT
ejpam-3305	136	28	f	f	PROPN
ejpam-3305	136	29	;	;	PUNCT
ejpam-3305	137	1	x)|	x)|	PROPN
ejpam-3305	137	2	≤	≤	PROPN
ejpam-3305	137	3	‖	‖	PROPN
ejpam-3305	137	4	f	f	PROPN
ejpam-3305	137	5	‖	‖	PROPN
ejpam-3305	137	6	.	.	PUNCT
ejpam-3305	138	1	(	(	PUNCT
ejpam-3305	138	2	14	14	NUM
ejpam-3305	138	3	)	)	PUNCT
ejpam-3305	138	4	using	use	VERB
ejpam-3305	138	5	(	(	PUNCT
ejpam-3305	138	6	13	13	NUM
ejpam-3305	138	7	)	)	PUNCT
ejpam-3305	138	8	and	and	CCONJ
ejpam-3305	138	9	(	(	PUNCT
ejpam-3305	138	10	14	14	NUM
ejpam-3305	138	11	)	)	PUNCT
ejpam-3305	138	12	in	in	ADP
ejpam-3305	138	13	(	(	PUNCT
ejpam-3305	138	14	11	11	NUM
ejpam-3305	138	15	)	)	PUNCT
ejpam-3305	138	16	,	,	PUNCT
ejpam-3305	138	17	we	we	PRON
ejpam-3305	138	18	obtain	obtain	VERB
ejpam-3305	138	19	|m	|m	NOUN
ejpam-3305	138	20	(	(	PUNCT
ejpam-3305	138	21	β	β	X
ejpam-3305	138	22	,	,	PUNCT
ejpam-3305	138	23	γ	γ	NOUN
ejpam-3305	138	24	)	)	PUNCT
ejpam-3305	138	25	n	n	CCONJ
ejpam-3305	138	26	,	,	PUNCT
ejpam-3305	138	27	α	α	PROPN
ejpam-3305	138	28	(	(	PUNCT
ejpam-3305	138	29	f	f	X
ejpam-3305	138	30	;	;	PUNCT
ejpam-3305	138	31	x)−	x)−	PROPN
ejpam-3305	138	32	f(x)|	f(x)|	VERB
ejpam-3305	138	33	≤	≤	NUM
ejpam-3305	138	34	|m	|m	NOUN
ejpam-3305	138	35	(	(	PUNCT
ejpam-3305	138	36	β	β	X
ejpam-3305	138	37	,	,	PUNCT
ejpam-3305	138	38	γ	γ	NOUN
ejpam-3305	138	39	)	)	PUNCT
ejpam-3305	138	40	n	n	CCONJ
ejpam-3305	138	41	,	,	PUNCT
ejpam-3305	138	42	α	α	PROPN
ejpam-3305	138	43	(	(	PUNCT
ejpam-3305	138	44	f	f	NOUN
ejpam-3305	138	45	−	−	PROPN
ejpam-3305	138	46	g;x)|+	g;x)|+	PROPN
ejpam-3305	138	47	|(f	|(f	PROPN
ejpam-3305	139	1	−	−	PROPN
ejpam-3305	140	1	g)(x)|+	g)(x)|+	NOUN
ejpam-3305	141	1	|m	|m	NOUN
ejpam-3305	141	2	(	(	PUNCT
ejpam-3305	141	3	β	β	X
ejpam-3305	141	4	,	,	PUNCT
ejpam-3305	141	5	γ	γ	NOUN
ejpam-3305	141	6	)	)	PUNCT
ejpam-3305	141	7	n	n	CCONJ
ejpam-3305	141	8	,	,	PUNCT
ejpam-3305	141	9	α	α	PROPN
ejpam-3305	141	10	(	(	PUNCT
ejpam-3305	141	11	g;x)−	g;x)−	PROPN
ejpam-3305	141	12	g(x)|+	g(x)|+	PROPN
ejpam-3305	141	13	∣∣∣∣f	∣∣∣∣f	PROPN
ejpam-3305	141	14	(	(	PUNCT
ejpam-3305	141	15	nx+	nx+	PROPN
ejpam-3305	141	16	β	β	X
ejpam-3305	141	17	n+	n+	X
ejpam-3305	141	18	γ	γ	PROPN
ejpam-3305	141	19	)	)	PUNCT
ejpam-3305	141	20	−	−	PROPN
ejpam-3305	141	21	f(x	f(x	PROPN
ejpam-3305	141	22	)	)	PUNCT
ejpam-3305	141	23	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3305	141	24	≤	≤	NUM
ejpam-3305	141	25	2	2	NUM
ejpam-3305	141	26	‖	‖	PROPN
ejpam-3305	141	27	f	f	NOUN
ejpam-3305	141	28	−	−	PROPN
ejpam-3305	141	29	g	g	PROPN
ejpam-3305	141	30	‖	‖	PROPN
ejpam-3305	141	31	+	+	CCONJ
ejpam-3305	141	32	(	(	PUNCT
ejpam-3305	141	33	ζ(β	ζ(β	PROPN
ejpam-3305	141	34	,	,	PUNCT
ejpam-3305	141	35	γ)n	γ)n	X
ejpam-3305	141	36	,	,	PUNCT
ejpam-3305	141	37	α	α	PROPN
ejpam-3305	141	38	(	(	PUNCT
ejpam-3305	141	39	x	x	NOUN
ejpam-3305	141	40	)	)	PUNCT
ejpam-3305	141	41	)	)	PUNCT
ejpam-3305	142	1	2	2	NUM
ejpam-3305	142	2	‖	‖	PROPN
ejpam-3305	142	3	g′′	g′′	PROPN
ejpam-3305	142	4	‖	‖	PROPN
ejpam-3305	142	5	+	+	PROPN
ejpam-3305	142	6	∣∣∣∣f	∣∣∣∣f	PROPN
ejpam-3305	142	7	(	(	PUNCT
ejpam-3305	142	8	nx+	nx+	PROPN
ejpam-3305	142	9	β	β	X
ejpam-3305	142	10	n+	n+	X
ejpam-3305	142	11	γ	γ	PROPN
ejpam-3305	142	12	)	)	PUNCT
ejpam-3305	142	13	−	−	PROPN
ejpam-3305	142	14	f(x	f(x	PROPN
ejpam-3305	142	15	)	)	PUNCT
ejpam-3305	142	16	∣∣∣∣.	∣∣∣∣.	NOUN
ejpam-3305	142	17	taking	take	VERB
ejpam-3305	142	18	infimum	infimum	ADV
ejpam-3305	142	19	over	over	ADP
ejpam-3305	142	20	all	all	DET
ejpam-3305	142	21	g	g	NOUN
ejpam-3305	142	22	∈w	∈w	NOUN
ejpam-3305	142	23	2	2	NUM
ejpam-3305	142	24	,	,	PUNCT
ejpam-3305	142	25	we	we	PRON
ejpam-3305	142	26	get	get	VERB
ejpam-3305	142	27	|m	|m	NOUN
ejpam-3305	142	28	(	(	PUNCT
ejpam-3305	142	29	β	β	X
ejpam-3305	142	30	,	,	PUNCT
ejpam-3305	142	31	γ	γ	NOUN
ejpam-3305	142	32	)	)	PUNCT
ejpam-3305	142	33	n	n	CCONJ
ejpam-3305	142	34	,	,	PUNCT
ejpam-3305	142	35	α	α	PROPN
ejpam-3305	142	36	(	(	PUNCT
ejpam-3305	142	37	f	f	PROPN
ejpam-3305	142	38	;	;	PUNCT
ejpam-3305	142	39	x)−	x)−	PROPN
ejpam-3305	142	40	f(x	f(x	PROPN
ejpam-3305	142	41	)	)	PUNCT
ejpam-3305	142	42	|	|	ADV
ejpam-3305	142	43	≤	≤	NUM
ejpam-3305	142	44	k2	k2	X
ejpam-3305	142	45	(	(	PUNCT
ejpam-3305	142	46	f	f	X
ejpam-3305	142	47	,	,	PUNCT
ejpam-3305	142	48	(	(	PUNCT
ejpam-3305	142	49	ζ(β	ζ(β	NOUN
ejpam-3305	142	50	,	,	PUNCT
ejpam-3305	142	51	γ)n	γ)n	X
ejpam-3305	142	52	,	,	PUNCT
ejpam-3305	142	53	α	α	PROPN
ejpam-3305	142	54	(	(	PUNCT
ejpam-3305	142	55	x))2	x))2	PROPN
ejpam-3305	142	56	)	)	PUNCT
ejpam-3305	143	1	+	+	CCONJ
ejpam-3305	143	2	ω	ω	NUM
ejpam-3305	143	3	(	(	PUNCT
ejpam-3305	143	4	f	f	PROPN
ejpam-3305	143	5	,	,	PUNCT
ejpam-3305	143	6	|β	|β	VERB
ejpam-3305	143	7	−	−	PROPN
ejpam-3305	144	1	γx|	γx|	VERB
ejpam-3305	144	2	n+	n+	NUM
ejpam-3305	144	3	γ	γ	NOUN
ejpam-3305	144	4	)	)	PUNCT
ejpam-3305	144	5	.	.	PUNCT
ejpam-3305	145	1	in	in	ADP
ejpam-3305	145	2	view	view	NOUN
ejpam-3305	145	3	of	of	ADP
ejpam-3305	145	4	(	(	PUNCT
ejpam-3305	145	5	10	10	NUM
ejpam-3305	145	6	)	)	PUNCT
ejpam-3305	145	7	,	,	PUNCT
ejpam-3305	145	8	we	we	PRON
ejpam-3305	145	9	get	get	VERB
ejpam-3305	145	10	|m	|m	NOUN
ejpam-3305	145	11	(	(	PUNCT
ejpam-3305	145	12	β	β	X
ejpam-3305	145	13	,	,	PUNCT
ejpam-3305	145	14	γ	γ	NOUN
ejpam-3305	145	15	)	)	PUNCT
ejpam-3305	145	16	n	n	CCONJ
ejpam-3305	145	17	,	,	PUNCT
ejpam-3305	145	18	α	α	PROPN
ejpam-3305	145	19	(	(	PUNCT
ejpam-3305	145	20	f	f	PROPN
ejpam-3305	145	21	;	;	PUNCT
ejpam-3305	145	22	x)−	x)−	PROPN
ejpam-3305	145	23	f(x	f(x	PROPN
ejpam-3305	145	24	)	)	PUNCT
ejpam-3305	145	25	|	|	ADV
ejpam-3305	145	26	≤	≤	NUM
ejpam-3305	145	27	mω2	mω2	NOUN
ejpam-3305	145	28	(	(	PUNCT
ejpam-3305	145	29	f	f	X
ejpam-3305	145	30	,	,	PUNCT
ejpam-3305	145	31	ζ(β	ζ(β	PROPN
ejpam-3305	145	32	,	,	PUNCT
ejpam-3305	145	33	γ)n	γ)n	X
ejpam-3305	145	34	,	,	PUNCT
ejpam-3305	145	35	α	α	PROPN
ejpam-3305	145	36	(	(	PUNCT
ejpam-3305	145	37	x	x	NOUN
ejpam-3305	145	38	)	)	PUNCT
ejpam-3305	145	39	)	)	PUNCT
ejpam-3305	146	1	+	+	CCONJ
ejpam-3305	146	2	ω	ω	NUM
ejpam-3305	146	3	(	(	PUNCT
ejpam-3305	146	4	f	f	PROPN
ejpam-3305	146	5	,	,	PUNCT
ejpam-3305	146	6	|β	|β	VERB
ejpam-3305	146	7	−	−	PROPN
ejpam-3305	147	1	γx|	γx|	VERB
ejpam-3305	147	2	n+	n+	NUM
ejpam-3305	147	3	γ	γ	NOUN
ejpam-3305	147	4	)	)	PUNCT
ejpam-3305	147	5	,	,	PUNCT
ejpam-3305	147	6	which	which	PRON
ejpam-3305	147	7	proves	prove	VERB
ejpam-3305	147	8	the	the	DET
ejpam-3305	147	9	theorem	theorem	NOUN
ejpam-3305	147	10	.	.	PUNCT
ejpam-3305	148	1	let	let	VERB
ejpam-3305	148	2	a1	a1	PROPN
ejpam-3305	148	3	,	,	PUNCT
ejpam-3305	148	4	a2	a2	PROPN
ejpam-3305	148	5	>	>	X
ejpam-3305	148	6	0	0	PUNCT
ejpam-3305	148	7	be	be	AUX
ejpam-3305	148	8	fixed	fix	VERB
ejpam-3305	148	9	.	.	PUNCT
ejpam-3305	149	1	we	we	PRON
ejpam-3305	149	2	define	define	VERB
ejpam-3305	149	3	the	the	DET
ejpam-3305	149	4	following	follow	VERB
ejpam-3305	149	5	lipschitz	lipschitz	ADJ
ejpam-3305	149	6	-	-	PUNCT
ejpam-3305	149	7	type	type	NOUN
ejpam-3305	149	8	space	space	NOUN
ejpam-3305	149	9	(	(	PUNCT
ejpam-3305	149	10	see	see	VERB
ejpam-3305	149	11	[	[	X
ejpam-3305	149	12	39	39	NUM
ejpam-3305	149	13	]	]	PUNCT
ejpam-3305	149	14	):	):	PUNCT
ejpam-3305	149	15	lip	lip	NOUN
ejpam-3305	149	16	(	(	PUNCT
ejpam-3305	149	17	a1,a2	a1,a2	PROPN
ejpam-3305	149	18	)	)	PUNCT
ejpam-3305	149	19	m	m	VERB
ejpam-3305	150	1	(	(	PUNCT
ejpam-3305	150	2	r	r	NOUN
ejpam-3305	150	3	)	)	PUNCT
ejpam-3305	150	4	=	=	PUNCT
ejpam-3305	151	1	(	(	PUNCT
ejpam-3305	151	2	f	f	PROPN
ejpam-3305	151	3	∈	∈	PROPN
ejpam-3305	151	4	c[0,∞	c[0,∞	PROPN
ejpam-3305	151	5	)	)	PUNCT
ejpam-3305	151	6	:	:	PUNCT
ejpam-3305	151	7	|f(t)−	|f(t)−	PROPN
ejpam-3305	151	8	f(x)|	f(x)|	VERB
ejpam-3305	151	9	≤m	≤m	NOUN
ejpam-3305	151	10	|t−	|t−	PROPN
ejpam-3305	151	11	x|r	x|r	PUNCT
ejpam-3305	152	1	(	(	PUNCT
ejpam-3305	152	2	t+	t+	NOUN
ejpam-3305	152	3	a1x2	a1x2	X
ejpam-3305	152	4	+	+	CCONJ
ejpam-3305	152	5	a2x)r/2	a2x)r/2	ADJ
ejpam-3305	152	6	;	;	PUNCT
ejpam-3305	152	7	x	x	X
ejpam-3305	152	8	,	,	PUNCT
ejpam-3305	152	9	t	t	PROPN
ejpam-3305	152	10	∈	∈	PROPN
ejpam-3305	153	1	[	[	X
ejpam-3305	153	2	0,∞	0,∞	NOUN
ejpam-3305	153	3	)	)	PUNCT
ejpam-3305	153	4	)	)	PUNCT
ejpam-3305	154	1	,	,	PUNCT
ejpam-3305	154	2	where	where	SCONJ
ejpam-3305	154	3	m	m	NOUN
ejpam-3305	154	4	is	be	AUX
ejpam-3305	154	5	any	any	DET
ejpam-3305	154	6	positive	positive	ADJ
ejpam-3305	154	7	constant	constant	ADJ
ejpam-3305	154	8	and	and	CCONJ
ejpam-3305	154	9	0	0	NUM
ejpam-3305	154	10	<	<	X
ejpam-3305	154	11	r	r	NOUN
ejpam-3305	154	12	≤	≤	NUM
ejpam-3305	154	13	1	1	NUM
ejpam-3305	154	14	.	.	PUNCT
ejpam-3305	154	15	theorem	theorem	NOUN
ejpam-3305	154	16	4	4	NUM
ejpam-3305	154	17	.	.	PUNCT
ejpam-3305	155	1	let	let	VERB
ejpam-3305	155	2	f	f	PROPN
ejpam-3305	155	3	∈	∈	PROPN
ejpam-3305	155	4	lip(a1,a2)m	lip(a1,a2)m	NOUN
ejpam-3305	155	5	(	(	PUNCT
ejpam-3305	155	6	r	r	NOUN
ejpam-3305	155	7	)	)	PUNCT
ejpam-3305	155	8	.	.	PUNCT
ejpam-3305	156	1	then	then	ADV
ejpam-3305	156	2	,	,	PUNCT
ejpam-3305	156	3	for	for	ADP
ejpam-3305	156	4	all	all	PRON
ejpam-3305	156	5	x	x	SYM
ejpam-3305	156	6	>	>	X
ejpam-3305	156	7	0	0	NUM
ejpam-3305	156	8	,	,	PUNCT
ejpam-3305	156	9	we	we	PRON
ejpam-3305	156	10	have	have	VERB
ejpam-3305	156	11	|m	|m	NOUN
ejpam-3305	156	12	(	(	PUNCT
ejpam-3305	156	13	β	β	X
ejpam-3305	156	14	,	,	PUNCT
ejpam-3305	156	15	γ	γ	NOUN
ejpam-3305	156	16	)	)	PUNCT
ejpam-3305	156	17	n	n	CCONJ
ejpam-3305	156	18	,	,	PUNCT
ejpam-3305	156	19	α	α	PROPN
ejpam-3305	156	20	(	(	PUNCT
ejpam-3305	156	21	f	f	X
ejpam-3305	156	22	;	;	PUNCT
ejpam-3305	157	1	x)−	x)−	PROPN
ejpam-3305	157	2	f(x)|	f(x)|	VERB
ejpam-3305	157	3	≤m	≤m	NOUN
ejpam-3305	157	4	(	(	PUNCT
ejpam-3305	157	5	ξ	ξ	X
ejpam-3305	157	6	(	(	PUNCT
ejpam-3305	157	7	β	β	X
ejpam-3305	157	8	,	,	PUNCT
ejpam-3305	157	9	γ	γ	NOUN
ejpam-3305	157	10	)	)	PUNCT
ejpam-3305	157	11	n	n	CCONJ
ejpam-3305	157	12	,	,	PUNCT
ejpam-3305	157	13	α	α	PROPN
ejpam-3305	157	14	(	(	PUNCT
ejpam-3305	157	15	x	x	X
ejpam-3305	157	16	)	)	PUNCT
ejpam-3305	157	17	a1x2	a1x2	X
ejpam-3305	158	1	+	+	CCONJ
ejpam-3305	158	2	a2x	a2x	NOUN
ejpam-3305	158	3	)	)	PUNCT
ejpam-3305	158	4	r/2	r/2	X
ejpam-3305	158	5	.	.	PUNCT
ejpam-3305	159	1	proof	proof	NOUN
ejpam-3305	159	2	.	.	PUNCT
ejpam-3305	160	1	first	first	ADV
ejpam-3305	160	2	we	we	PRON
ejpam-3305	160	3	prove	prove	VERB
ejpam-3305	160	4	the	the	DET
ejpam-3305	160	5	theorem	theorem	NOUN
ejpam-3305	160	6	for	for	ADP
ejpam-3305	160	7	r	r	NOUN
ejpam-3305	160	8	=	=	SYM
ejpam-3305	160	9	1	1	NUM
ejpam-3305	160	10	.	.	PUNCT
ejpam-3305	161	1	then	then	ADV
ejpam-3305	161	2	,	,	PUNCT
ejpam-3305	161	3	for	for	ADP
ejpam-3305	161	4	f	f	PROPN
ejpam-3305	161	5	∈	∈	PROPN
ejpam-3305	161	6	lip(a1,a2)m	lip(a1,a2)m	NOUN
ejpam-3305	161	7	(	(	PUNCT
ejpam-3305	161	8	1	1	NUM
ejpam-3305	161	9	)	)	PUNCT
ejpam-3305	161	10	,	,	PUNCT
ejpam-3305	161	11	and	and	CCONJ
ejpam-3305	161	12	x	x	X
ejpam-3305	161	13	>	>	X
ejpam-3305	161	14	0	0	NUM
ejpam-3305	161	15	,	,	PUNCT
ejpam-3305	161	16	we	we	PRON
ejpam-3305	161	17	have	have	VERB
ejpam-3305	161	18	|m	|m	NOUN
ejpam-3305	161	19	(	(	PUNCT
ejpam-3305	161	20	β	β	X
ejpam-3305	161	21	,	,	PUNCT
ejpam-3305	161	22	γ	γ	NOUN
ejpam-3305	161	23	)	)	PUNCT
ejpam-3305	161	24	n	n	CCONJ
ejpam-3305	161	25	,	,	PUNCT
ejpam-3305	161	26	α	α	PROPN
ejpam-3305	161	27	(	(	PUNCT
ejpam-3305	161	28	f	f	X
ejpam-3305	161	29	;	;	PUNCT
ejpam-3305	161	30	x)−	x)−	PROPN
ejpam-3305	161	31	f(x)|	f(x)|	VERB
ejpam-3305	161	32	≤	≤	NUM
ejpam-3305	161	33	m	m	VERB
ejpam-3305	161	34	(	(	PUNCT
ejpam-3305	161	35	β	β	X
ejpam-3305	161	36	,	,	PUNCT
ejpam-3305	161	37	γ	γ	NOUN
ejpam-3305	161	38	)	)	PUNCT
ejpam-3305	161	39	n	n	CCONJ
ejpam-3305	161	40	,	,	PUNCT
ejpam-3305	161	41	α	α	PROPN
ejpam-3305	161	42	(	(	PUNCT
ejpam-3305	161	43	|f(t)−	|f(t)−	PROPN
ejpam-3305	161	44	f(x)|;x	f(x)|;x	NOUN
ejpam-3305	161	45	)	)	PUNCT
ejpam-3305	161	46	≤	≤	NUM
ejpam-3305	161	47	mm	mm	INTJ
ejpam-3305	161	48	(	(	PUNCT
ejpam-3305	161	49	β	β	X
ejpam-3305	161	50	,	,	PUNCT
ejpam-3305	161	51	γ	γ	NOUN
ejpam-3305	161	52	)	)	PUNCT
ejpam-3305	161	53	n	n	CCONJ
ejpam-3305	161	54	,	,	PUNCT
ejpam-3305	161	55	α	α	PROPN
ejpam-3305	161	56	(	(	PUNCT
ejpam-3305	161	57	|t−	|t−	PROPN
ejpam-3305	161	58	x|	x|	PROPN
ejpam-3305	161	59	(	(	PUNCT
ejpam-3305	161	60	t+	t+	NOUN
ejpam-3305	161	61	a1x2	a1x2	X
ejpam-3305	161	62	+	+	CCONJ
ejpam-3305	161	63	a2x)1/2	a2x)1/2	VERB
ejpam-3305	161	64	;	;	PUNCT
ejpam-3305	161	65	x	x	X
ejpam-3305	161	66	)	)	PUNCT
ejpam-3305	161	67	a.	a.	PROPN
ejpam-3305	161	68	kumar	kumar	PROPN
ejpam-3305	161	69	,	,	PUNCT
ejpam-3305	161	70	d.	d.	PROPN
ejpam-3305	161	71	tapiawala	tapiawala	PROPN
ejpam-3305	161	72	,	,	PUNCT
ejpam-3305	161	73	l.	l.	PROPN
ejpam-3305	161	74	n.	n.	PROPN
ejpam-3305	161	75	mishra	mishra	PROPN
ejpam-3305	161	76	/	/	SYM
ejpam-3305	161	77	eur	eur	PROPN
ejpam-3305	161	78	.	.	PUNCT
ejpam-3305	162	1	j.	j.	PROPN
ejpam-3305	162	2	pure	pure	PROPN
ejpam-3305	162	3	appl	appl	PROPN
ejpam-3305	162	4	.	.	PROPN
ejpam-3305	162	5	math	math	PROPN
ejpam-3305	162	6	,	,	PUNCT
ejpam-3305	162	7	11	11	NUM
ejpam-3305	162	8	(	(	PUNCT
ejpam-3305	162	9	4	4	NUM
ejpam-3305	162	10	)	)	PUNCT
ejpam-3305	162	11	(	(	PUNCT
ejpam-3305	162	12	2018	2018	NUM
ejpam-3305	162	13	)	)	PUNCT
ejpam-3305	162	14	,	,	PUNCT
ejpam-3305	162	15	958	958	NUM
ejpam-3305	162	16	-	-	SYM
ejpam-3305	162	17	975	975	NUM
ejpam-3305	162	18	965	965	NUM
ejpam-3305	162	19	≤	≤	NUM
ejpam-3305	162	20	m	m	VERB
ejpam-3305	162	21	(	(	PUNCT
ejpam-3305	162	22	a1x2	a1x2	X
ejpam-3305	162	23	+	+	CCONJ
ejpam-3305	162	24	a2x)1/2	a2x)1/2	NOUN
ejpam-3305	162	25	m	m	VERB
ejpam-3305	162	26	(	(	PUNCT
ejpam-3305	162	27	β	β	X
ejpam-3305	162	28	,	,	PUNCT
ejpam-3305	162	29	γ	γ	NOUN
ejpam-3305	162	30	)	)	PUNCT
ejpam-3305	162	31	n	n	CCONJ
ejpam-3305	162	32	,	,	PUNCT
ejpam-3305	162	33	α	α	PROPN
ejpam-3305	162	34	(	(	PUNCT
ejpam-3305	162	35	|t−	|t−	PROPN
ejpam-3305	162	36	x|;x	x|;x	PROPN
ejpam-3305	162	37	)	)	PUNCT
ejpam-3305	162	38	.	.	PUNCT
ejpam-3305	163	1	applying	apply	VERB
ejpam-3305	163	2	cauchy	cauchy	NOUN
ejpam-3305	163	3	-	-	PUNCT
ejpam-3305	163	4	schwarz	schwarz	PROPN
ejpam-3305	163	5	inequality	inequality	NOUN
ejpam-3305	163	6	,	,	PUNCT
ejpam-3305	163	7	we	we	PRON
ejpam-3305	163	8	get	get	VERB
ejpam-3305	163	9	|m	|m	NOUN
ejpam-3305	163	10	(	(	PUNCT
ejpam-3305	163	11	β	β	X
ejpam-3305	163	12	,	,	PUNCT
ejpam-3305	163	13	γ	γ	NOUN
ejpam-3305	163	14	)	)	PUNCT
ejpam-3305	163	15	n	n	CCONJ
ejpam-3305	163	16	,	,	PUNCT
ejpam-3305	163	17	α	α	PROPN
ejpam-3305	163	18	(	(	PUNCT
ejpam-3305	163	19	f	f	X
ejpam-3305	163	20	;	;	PUNCT
ejpam-3305	163	21	x)−	x)−	PROPN
ejpam-3305	163	22	f(x)|	f(x)|	VERB
ejpam-3305	163	23	≤	≤	NUM
ejpam-3305	163	24	m	m	VERB
ejpam-3305	163	25	(	(	PUNCT
ejpam-3305	163	26	a1x2	a1x2	X
ejpam-3305	164	1	+	+	X
ejpam-3305	164	2	a2x)1/2	a2x)1/2	PROPN
ejpam-3305	164	3	(	(	PUNCT
ejpam-3305	164	4	m	m	PROPN
ejpam-3305	164	5	(	(	PUNCT
ejpam-3305	164	6	β	β	X
ejpam-3305	164	7	,	,	PUNCT
ejpam-3305	164	8	γ	γ	NOUN
ejpam-3305	164	9	)	)	PUNCT
ejpam-3305	164	10	n	n	CCONJ
ejpam-3305	164	11	,	,	PUNCT
ejpam-3305	164	12	α	α	X
ejpam-3305	164	13	(	(	PUNCT
ejpam-3305	164	14	(	(	PUNCT
ejpam-3305	164	15	t−	t−	PROPN
ejpam-3305	164	16	x)2;x	x)2;x	NUM
ejpam-3305	164	17	)	)	PUNCT
ejpam-3305	164	18	)	)	PUNCT
ejpam-3305	165	1	1/2	1/2	NUM
ejpam-3305	165	2	≤	≤	NUM
ejpam-3305	165	3	m	m	VERB
ejpam-3305	165	4	(	(	PUNCT
ejpam-3305	165	5	ξ	ξ	X
ejpam-3305	165	6	(	(	PUNCT
ejpam-3305	165	7	β	β	X
ejpam-3305	165	8	,	,	PUNCT
ejpam-3305	165	9	γ	γ	NOUN
ejpam-3305	165	10	)	)	PUNCT
ejpam-3305	165	11	n	n	CCONJ
ejpam-3305	165	12	,	,	PUNCT
ejpam-3305	165	13	α	α	PROPN
ejpam-3305	165	14	(	(	PUNCT
ejpam-3305	165	15	x	x	X
ejpam-3305	165	16	)	)	PUNCT
ejpam-3305	165	17	a1x2	a1x2	X
ejpam-3305	166	1	+	+	CCONJ
ejpam-3305	166	2	a2x	a2x	PROPN
ejpam-3305	166	3	)	)	PUNCT
ejpam-3305	166	4	1/2	1/2	NUM
ejpam-3305	166	5	.	.	PUNCT
ejpam-3305	167	1	thus	thus	ADV
ejpam-3305	167	2	the	the	DET
ejpam-3305	167	3	result	result	NOUN
ejpam-3305	167	4	holds	hold	VERB
ejpam-3305	167	5	for	for	ADP
ejpam-3305	167	6	r	r	NOUN
ejpam-3305	167	7	=	=	SYM
ejpam-3305	167	8	1	1	NUM
ejpam-3305	167	9	.	.	PUNCT
ejpam-3305	168	1	now	now	ADV
ejpam-3305	168	2	,	,	PUNCT
ejpam-3305	168	3	we	we	PRON
ejpam-3305	168	4	prove	prove	VERB
ejpam-3305	168	5	that	that	SCONJ
ejpam-3305	168	6	the	the	DET
ejpam-3305	168	7	result	result	NOUN
ejpam-3305	168	8	is	be	AUX
ejpam-3305	168	9	true	true	ADJ
ejpam-3305	168	10	for	for	ADP
ejpam-3305	168	11	0	0	NUM
ejpam-3305	168	12	<	<	X
ejpam-3305	168	13	r	r	X
ejpam-3305	168	14	<	<	X
ejpam-3305	168	15	1	1	NUM
ejpam-3305	168	16	.	.	PUNCT
ejpam-3305	169	1	then	then	ADV
ejpam-3305	169	2	,	,	PUNCT
ejpam-3305	169	3	for	for	ADP
ejpam-3305	169	4	f	f	PROPN
ejpam-3305	169	5	∈	∈	PROPN
ejpam-3305	169	6	lip(a1,a2)m	lip(a1,a2)m	NOUN
ejpam-3305	169	7	(	(	PUNCT
ejpam-3305	169	8	r	r	NOUN
ejpam-3305	169	9	)	)	PUNCT
ejpam-3305	169	10	,	,	PUNCT
ejpam-3305	169	11	and	and	CCONJ
ejpam-3305	169	12	x	x	X
ejpam-3305	169	13	>	>	X
ejpam-3305	169	14	0	0	NUM
ejpam-3305	169	15	,	,	PUNCT
ejpam-3305	169	16	we	we	PRON
ejpam-3305	169	17	get	get	VERB
ejpam-3305	169	18	|m	|m	NOUN
ejpam-3305	169	19	(	(	PUNCT
ejpam-3305	169	20	β	β	X
ejpam-3305	169	21	,	,	PUNCT
ejpam-3305	169	22	γ	γ	NOUN
ejpam-3305	169	23	)	)	PUNCT
ejpam-3305	169	24	n	n	CCONJ
ejpam-3305	169	25	,	,	PUNCT
ejpam-3305	169	26	α	α	PROPN
ejpam-3305	169	27	(	(	PUNCT
ejpam-3305	169	28	f	f	X
ejpam-3305	169	29	;	;	PUNCT
ejpam-3305	169	30	x)−	x)−	PROPN
ejpam-3305	169	31	f(x)|	f(x)|	VERB
ejpam-3305	169	32	≤	≤	NUM
ejpam-3305	169	33	m	m	VERB
ejpam-3305	169	34	(	(	PUNCT
ejpam-3305	169	35	a1x2	a1x2	X
ejpam-3305	169	36	+	+	CCONJ
ejpam-3305	169	37	a2x)r/2	a2x)r/2	PROPN
ejpam-3305	169	38	m	m	ADJ
ejpam-3305	169	39	(	(	PUNCT
ejpam-3305	169	40	β	β	X
ejpam-3305	169	41	,	,	PUNCT
ejpam-3305	169	42	γ	γ	NOUN
ejpam-3305	169	43	)	)	PUNCT
ejpam-3305	169	44	n	n	CCONJ
ejpam-3305	169	45	,	,	PUNCT
ejpam-3305	169	46	α	α	PROPN
ejpam-3305	169	47	(	(	PUNCT
ejpam-3305	169	48	|t−	|t−	PROPN
ejpam-3305	169	49	x|r;x	x|r;x	PROPN
ejpam-3305	169	50	)	)	PUNCT
ejpam-3305	169	51	.	.	PUNCT
ejpam-3305	170	1	taking	take	VERB
ejpam-3305	170	2	p	p	NOUN
ejpam-3305	170	3	=	=	SYM
ejpam-3305	170	4	1	1	NUM
ejpam-3305	170	5	r	r	NOUN
ejpam-3305	170	6	and	and	CCONJ
ejpam-3305	170	7	q	q	NOUN
ejpam-3305	171	1	=	=	SYM
ejpam-3305	171	2	p	p	PROPN
ejpam-3305	171	3	p−1	p−1	PROPN
ejpam-3305	171	4	,	,	PUNCT
ejpam-3305	171	5	applying	apply	VERB
ejpam-3305	171	6	the	the	DET
ejpam-3305	171	7	hölders	hölder	NOUN
ejpam-3305	171	8	inequality	inequality	NOUN
ejpam-3305	171	9	,	,	PUNCT
ejpam-3305	171	10	we	we	PRON
ejpam-3305	171	11	have	have	VERB
ejpam-3305	171	12	|m	|m	NOUN
ejpam-3305	171	13	(	(	PUNCT
ejpam-3305	171	14	β	β	X
ejpam-3305	171	15	,	,	PUNCT
ejpam-3305	171	16	γ	γ	NOUN
ejpam-3305	171	17	)	)	PUNCT
ejpam-3305	171	18	n	n	CCONJ
ejpam-3305	171	19	,	,	PUNCT
ejpam-3305	171	20	α	α	PROPN
ejpam-3305	171	21	(	(	PUNCT
ejpam-3305	171	22	f	f	X
ejpam-3305	171	23	;	;	PUNCT
ejpam-3305	171	24	x)−	x)−	PROPN
ejpam-3305	171	25	f(x)|	f(x)|	VERB
ejpam-3305	171	26	≤	≤	NUM
ejpam-3305	171	27	m	m	VERB
ejpam-3305	171	28	(	(	PUNCT
ejpam-3305	171	29	a1x2	a1x2	X
ejpam-3305	172	1	+	+	CCONJ
ejpam-3305	172	2	a2x)r/2	a2x)r/2	ADJ
ejpam-3305	172	3	(	(	PUNCT
ejpam-3305	172	4	m	m	VERB
ejpam-3305	172	5	(	(	PUNCT
ejpam-3305	172	6	β	β	X
ejpam-3305	172	7	,	,	PUNCT
ejpam-3305	172	8	γ	γ	NOUN
ejpam-3305	172	9	)	)	PUNCT
ejpam-3305	172	10	n	n	CCONJ
ejpam-3305	172	11	,	,	PUNCT
ejpam-3305	172	12	α	α	PROPN
ejpam-3305	172	13	(	(	PUNCT
ejpam-3305	172	14	|t−	|t−	PROPN
ejpam-3305	172	15	x|;x	x|;x	PROPN
ejpam-3305	172	16	)	)	PUNCT
ejpam-3305	172	17	)	)	PUNCT
ejpam-3305	173	1	r	r	NOUN
ejpam-3305	173	2	.	.	PUNCT
ejpam-3305	174	1	finally	finally	ADV
ejpam-3305	174	2	by	by	ADP
ejpam-3305	174	3	cauchy	cauchy	PROPN
ejpam-3305	174	4	-	-	PUNCT
ejpam-3305	174	5	schwarz	schwarz	PROPN
ejpam-3305	174	6	inequality	inequality	NOUN
ejpam-3305	174	7	,	,	PUNCT
ejpam-3305	174	8	we	we	PRON
ejpam-3305	174	9	get	get	VERB
ejpam-3305	174	10	|m	|m	NOUN
ejpam-3305	174	11	(	(	PUNCT
ejpam-3305	174	12	β	β	X
ejpam-3305	174	13	,	,	PUNCT
ejpam-3305	174	14	γ	γ	NOUN
ejpam-3305	174	15	)	)	PUNCT
ejpam-3305	174	16	n	n	CCONJ
ejpam-3305	174	17	,	,	PUNCT
ejpam-3305	174	18	α	α	PROPN
ejpam-3305	174	19	(	(	PUNCT
ejpam-3305	174	20	f	f	X
ejpam-3305	174	21	;	;	PUNCT
ejpam-3305	174	22	x)−	x)−	PROPN
ejpam-3305	174	23	f(x)|	f(x)|	VERB
ejpam-3305	174	24	≤	≤	NUM
ejpam-3305	174	25	m	m	VERB
ejpam-3305	174	26	(	(	PUNCT
ejpam-3305	174	27	ξ	ξ	X
ejpam-3305	174	28	(	(	PUNCT
ejpam-3305	174	29	β	β	X
ejpam-3305	174	30	,	,	PUNCT
ejpam-3305	174	31	γ	γ	NOUN
ejpam-3305	174	32	)	)	PUNCT
ejpam-3305	174	33	n	n	CCONJ
ejpam-3305	174	34	,	,	PUNCT
ejpam-3305	174	35	α	α	PROPN
ejpam-3305	174	36	(	(	PUNCT
ejpam-3305	174	37	x	x	X
ejpam-3305	174	38	)	)	PUNCT
ejpam-3305	174	39	a1x2	a1x2	X
ejpam-3305	175	1	+	+	CCONJ
ejpam-3305	175	2	a2x	a2x	NOUN
ejpam-3305	175	3	)	)	PUNCT
ejpam-3305	175	4	r/2	r/2	PROPN
ejpam-3305	175	5	.	.	PUNCT
ejpam-3305	176	1	thus	thus	ADV
ejpam-3305	176	2	,	,	PUNCT
ejpam-3305	176	3	the	the	DET
ejpam-3305	176	4	proof	proof	NOUN
ejpam-3305	176	5	is	be	AUX
ejpam-3305	176	6	completed	complete	VERB
ejpam-3305	176	7	.	.	PUNCT
ejpam-3305	177	1	3.3	3.3	NUM
ejpam-3305	177	2	.	.	PUNCT
ejpam-3305	178	1	global	global	ADJ
ejpam-3305	178	2	approximation	approximation	NOUN
ejpam-3305	178	3	in	in	ADP
ejpam-3305	178	4	this	this	DET
ejpam-3305	178	5	section	section	NOUN
ejpam-3305	178	6	,	,	PUNCT
ejpam-3305	178	7	the	the	DET
ejpam-3305	178	8	first	first	ADJ
ejpam-3305	178	9	and	and	CCONJ
ejpam-3305	178	10	the	the	DET
ejpam-3305	178	11	second	second	ADJ
ejpam-3305	178	12	order	order	NOUN
ejpam-3305	178	13	ditzian	ditzian	NOUN
ejpam-3305	178	14	-	-	PUNCT
ejpam-3305	178	15	totik	totik	NOUN
ejpam-3305	178	16	moduli	modulus	NOUN
ejpam-3305	178	17	of	of	ADP
ejpam-3305	178	18	smoothness	smoothness	NOUN
ejpam-3305	178	19	are	be	AUX
ejpam-3305	178	20	defined	define	VERB
ejpam-3305	178	21	as	as	ADP
ejpam-3305	178	22	ω̄φ(f	ω̄φ(f	NOUN
ejpam-3305	178	23	,	,	PUNCT
ejpam-3305	178	24	δ	δ	NOUN
ejpam-3305	178	25	)	)	PUNCT
ejpam-3305	179	1	=	=	SYM
ejpam-3305	179	2	sup	sup	NUM
ejpam-3305	179	3	0<|h|≤δ	0<|h|≤δ	NOUN
ejpam-3305	179	4	sup	sup	NOUN
ejpam-3305	179	5	x+hφ(x)∈[0,∞	x+hφ(x)∈[0,∞	PUNCT
ejpam-3305	179	6	)	)	PUNCT
ejpam-3305	180	1	|	|	ADV
ejpam-3305	180	2	f(x+	f(x+	ADP
ejpam-3305	180	3	hφ(x))−	hφ(x))−	ADJ
ejpam-3305	180	4	f(x	f(x	PROPN
ejpam-3305	180	5	)	)	PUNCT
ejpam-3305	180	6	|	|	ADV
ejpam-3305	180	7	and	and	CCONJ
ejpam-3305	180	8	ω2,φ(f	ω2,φ(f	NOUN
ejpam-3305	180	9	,	,	PUNCT
ejpam-3305	180	10	√	√	PROPN
ejpam-3305	180	11	δ	δ	NOUN
ejpam-3305	180	12	)	)	PUNCT
ejpam-3305	180	13	=	=	PUNCT
ejpam-3305	181	1	sup	sup	NOUN
ejpam-3305	181	2	0<|h|≤	0<|h|≤	NOUN
ejpam-3305	181	3	√	√	NUM
ejpam-3305	181	4	δ	δ	PROPN
ejpam-3305	181	5	sup	sup	NOUN
ejpam-3305	181	6	x±hφ(x)∈[0,∞	x±hφ(x)∈[0,∞	PROPN
ejpam-3305	181	7	)	)	PUNCT
ejpam-3305	181	8	|	|	ADV
ejpam-3305	181	9	f(x+	f(x+	ADP
ejpam-3305	181	10	hφ(x))−	hφ(x))−	PROPN
ejpam-3305	181	11	2f(x	2f(x	PROPN
ejpam-3305	181	12	)	)	PUNCT
ejpam-3305	182	1	+	+	CCONJ
ejpam-3305	182	2	f(x−	f(x−	NOUN
ejpam-3305	182	3	hφ(x	hφ(x	NOUN
ejpam-3305	182	4	)	)	PUNCT
ejpam-3305	182	5	)	)	PUNCT
ejpam-3305	183	1	|	|	ADV
ejpam-3305	183	2	,	,	PUNCT
ejpam-3305	183	3	respectively	respectively	ADV
ejpam-3305	183	4	and	and	CCONJ
ejpam-3305	183	5	the	the	DET
ejpam-3305	183	6	corresponding	corresponding	ADJ
ejpam-3305	183	7	k	k	ADJ
ejpam-3305	183	8	-	-	ADJ
ejpam-3305	183	9	functional	functional	ADJ
ejpam-3305	183	10	is	be	AUX
ejpam-3305	183	11	k2,φ(f	k2,φ(f	X
ejpam-3305	183	12	,	,	PUNCT
ejpam-3305	183	13	δ	δ	NOUN
ejpam-3305	183	14	)	)	PUNCT
ejpam-3305	183	15	=	=	PROPN
ejpam-3305	183	16	inf	inf	PROPN
ejpam-3305	183	17	g∈w	g∈w	PROPN
ejpam-3305	183	18	2(φ	2(φ	NUM
ejpam-3305	183	19	)	)	PUNCT
ejpam-3305	183	20	{	{	PUNCT
ejpam-3305	183	21	‖	‖	PROPN
ejpam-3305	183	22	f	f	PROPN
ejpam-3305	183	23	−	−	PROPN
ejpam-3305	183	24	g	g	PROPN
ejpam-3305	183	25	‖	‖	PROPN
ejpam-3305	183	26	+	+	PROPN
ejpam-3305	183	27	δ	δ	PROPN
ejpam-3305	183	28	‖	‖	PROPN
ejpam-3305	183	29	φ2g′′	φ2g′′	PROPN
ejpam-3305	183	30	‖	‖	PROPN
ejpam-3305	183	31	}	}	PUNCT
ejpam-3305	183	32	,	,	PUNCT
ejpam-3305	183	33	a.	a.	PROPN
ejpam-3305	183	34	kumar	kumar	PROPN
ejpam-3305	183	35	,	,	PUNCT
ejpam-3305	183	36	d.	d.	PROPN
ejpam-3305	183	37	tapiawala	tapiawala	PROPN
ejpam-3305	183	38	,	,	PUNCT
ejpam-3305	183	39	l.	l.	PROPN
ejpam-3305	183	40	n.	n.	PROPN
ejpam-3305	183	41	mishra	mishra	PROPN
ejpam-3305	183	42	/	/	SYM
ejpam-3305	183	43	eur	eur	PROPN
ejpam-3305	183	44	.	.	PUNCT
ejpam-3305	184	1	j.	j.	PROPN
ejpam-3305	184	2	pure	pure	PROPN
ejpam-3305	184	3	appl	appl	PROPN
ejpam-3305	184	4	.	.	PROPN
ejpam-3305	184	5	math	math	PROPN
ejpam-3305	184	6	,	,	PUNCT
ejpam-3305	184	7	11	11	NUM
ejpam-3305	184	8	(	(	PUNCT
ejpam-3305	184	9	4	4	NUM
ejpam-3305	184	10	)	)	PUNCT
ejpam-3305	184	11	(	(	PUNCT
ejpam-3305	184	12	2018	2018	NUM
ejpam-3305	184	13	)	)	PUNCT
ejpam-3305	184	14	,	,	PUNCT
ejpam-3305	184	15	958	958	NUM
ejpam-3305	184	16	-	-	SYM
ejpam-3305	184	17	975	975	NUM
ejpam-3305	184	18	966	966	NUM
ejpam-3305	185	1	where	where	SCONJ
ejpam-3305	185	2	δ	δ	X
ejpam-3305	185	3	>	>	X
ejpam-3305	185	4	0	0	PUNCT
ejpam-3305	186	1	and	and	CCONJ
ejpam-3305	186	2	w	w	PROPN
ejpam-3305	186	3	2(φ	2(φ	NUM
ejpam-3305	186	4	)	)	PUNCT
ejpam-3305	187	1	=	=	PRON
ejpam-3305	187	2	{	{	PUNCT
ejpam-3305	187	3	g	g	PROPN
ejpam-3305	187	4	∈	∈	PROPN
ejpam-3305	187	5	cb[0,∞	cb[0,∞	PROPN
ejpam-3305	187	6	)	)	PUNCT
ejpam-3305	187	7	:	:	PUNCT
ejpam-3305	187	8	g′	g′	NOUN
ejpam-3305	187	9	∈	∈	PROPN
ejpam-3305	187	10	ac[0,∞	ac[0,∞	PROPN
ejpam-3305	187	11	)	)	PUNCT
ejpam-3305	187	12	,	,	PUNCT
ejpam-3305	187	13	φ2g′′	φ2g′′	PROPN
ejpam-3305	187	14	∈	∈	PROPN
ejpam-3305	187	15	cb[0,∞	cb[0,∞	PROPN
ejpam-3305	187	16	)	)	PUNCT
ejpam-3305	187	17	}	}	PUNCT
ejpam-3305	187	18	and	and	CCONJ
ejpam-3305	187	19	g′	g′	NOUN
ejpam-3305	187	20	∈	∈	PROPN
ejpam-3305	187	21	ac[0,∞	ac[0,∞	NOUN
ejpam-3305	187	22	)	)	PUNCT
ejpam-3305	187	23	means	mean	VERB
ejpam-3305	187	24	that	that	SCONJ
ejpam-3305	187	25	g′	g′	NOUN
ejpam-3305	187	26	is	be	AUX
ejpam-3305	187	27	absolutely	absolutely	ADV
ejpam-3305	187	28	continuous	continuous	ADJ
ejpam-3305	187	29	on	on	ADP
ejpam-3305	187	30	[	[	X
ejpam-3305	187	31	0,∞	0,∞	NOUN
ejpam-3305	187	32	)	)	PUNCT
ejpam-3305	187	33	.	.	PUNCT
ejpam-3305	188	1	it	it	PRON
ejpam-3305	188	2	is	be	AUX
ejpam-3305	188	3	well	well	ADV
ejpam-3305	188	4	known	know	VERB
ejpam-3305	188	5	that	that	SCONJ
ejpam-3305	188	6	(	(	PUNCT
ejpam-3305	188	7	see	see	VERB
ejpam-3305	188	8	[	[	X
ejpam-3305	188	9	3	3	NUM
ejpam-3305	188	10	]	]	SYM
ejpam-3305	188	11	)	)	PUNCT
ejpam-3305	188	12	k2,φ(f	k2,φ(f	PROPN
ejpam-3305	188	13	,	,	PUNCT
ejpam-3305	188	14	δ	δ	NOUN
ejpam-3305	188	15	)	)	PUNCT
ejpam-3305	188	16	∼	∼	NOUN
ejpam-3305	188	17	ω2,φ(f	ω2,φ(f	NOUN
ejpam-3305	188	18	,	,	PUNCT
ejpam-3305	188	19	√	√	PROPN
ejpam-3305	188	20	δ	δ	PROPN
ejpam-3305	188	21	)	)	PUNCT
ejpam-3305	188	22	which	which	PRON
ejpam-3305	188	23	means	mean	VERB
ejpam-3305	188	24	that	that	SCONJ
ejpam-3305	188	25	there	there	PRON
ejpam-3305	188	26	exist	exist	VERB
ejpam-3305	188	27	an	an	DET
ejpam-3305	188	28	absolute	absolute	ADJ
ejpam-3305	188	29	constant	constant	ADJ
ejpam-3305	188	30	m	m	NOUN
ejpam-3305	188	31	>	>	X
ejpam-3305	188	32	0	0	NUM
ejpam-3305	189	1	such	such	ADJ
ejpam-3305	189	2	that	that	SCONJ
ejpam-3305	189	3	m−1ω2,φ(f	m−1ω2,φ(f	NOUN
ejpam-3305	189	4	,	,	PUNCT
ejpam-3305	189	5	√	√	PROPN
ejpam-3305	189	6	δ	δ	NOUN
ejpam-3305	189	7	)	)	PUNCT
ejpam-3305	189	8	≤	≤	PUNCT
ejpam-3305	190	1	k2,φ(f	k2,φ(f	PROPN
ejpam-3305	190	2	,	,	PUNCT
ejpam-3305	190	3	δ	δ	PROPN
ejpam-3305	190	4	)	)	PUNCT
ejpam-3305	190	5	≤mω2,φ(f	≤mω2,φ(f	PROPN
ejpam-3305	190	6	,	,	PUNCT
ejpam-3305	190	7	√	√	NUM
ejpam-3305	190	8	δ	δ	PROPN
ejpam-3305	190	9	)	)	PUNCT
ejpam-3305	190	10	.	.	PUNCT
ejpam-3305	191	1	(	(	PUNCT
ejpam-3305	191	2	15	15	NUM
ejpam-3305	191	3	)	)	PUNCT
ejpam-3305	191	4	in	in	ADP
ejpam-3305	191	5	the	the	DET
ejpam-3305	191	6	following	following	NOUN
ejpam-3305	191	7	we	we	PRON
ejpam-3305	191	8	will	will	AUX
ejpam-3305	191	9	consider	consider	VERB
ejpam-3305	191	10	φ(x	φ(x	NOUN
ejpam-3305	191	11	)	)	PUNCT
ejpam-3305	191	12	=	=	SYM
ejpam-3305	192	1	1	1	NUM
ejpam-3305	192	2	+	+	CCONJ
ejpam-3305	192	3	x2	x2	PROPN
ejpam-3305	192	4	.	.	PUNCT
ejpam-3305	193	1	theorem	theorem	VERB
ejpam-3305	193	2	5	5	NUM
ejpam-3305	193	3	.	.	PUNCT
ejpam-3305	194	1	let	let	VERB
ejpam-3305	194	2	f	f	PROPN
ejpam-3305	194	3	∈	∈	PROPN
ejpam-3305	194	4	cb[0,∞	cb[0,∞	PROPN
ejpam-3305	194	5	)	)	PUNCT
ejpam-3305	194	6	and	and	CCONJ
ejpam-3305	194	7	x	x	PUNCT
ejpam-3305	194	8	∈	∈	PROPN
ejpam-3305	195	1	[	[	X
ejpam-3305	195	2	0,∞	0,∞	NOUN
ejpam-3305	195	3	)	)	PUNCT
ejpam-3305	195	4	.	.	PUNCT
ejpam-3305	196	1	then	then	ADV
ejpam-3305	196	2	,	,	PUNCT
ejpam-3305	196	3	there	there	PRON
ejpam-3305	196	4	exist	exist	VERB
ejpam-3305	196	5	an	an	DET
ejpam-3305	196	6	absolute	absolute	ADJ
ejpam-3305	196	7	constant	constant	ADJ
ejpam-3305	196	8	m	m	NOUN
ejpam-3305	196	9	>	>	X
ejpam-3305	196	10	0	0	NUM
ejpam-3305	197	1	such	such	ADJ
ejpam-3305	197	2	that	that	SCONJ
ejpam-3305	197	3	|m	|m	NOUN
ejpam-3305	197	4	(	(	PUNCT
ejpam-3305	197	5	β	β	X
ejpam-3305	197	6	,	,	PUNCT
ejpam-3305	197	7	γ	γ	NOUN
ejpam-3305	197	8	)	)	PUNCT
ejpam-3305	197	9	n	n	CCONJ
ejpam-3305	197	10	,	,	PUNCT
ejpam-3305	197	11	α	α	PROPN
ejpam-3305	197	12	(	(	PUNCT
ejpam-3305	197	13	f	f	PROPN
ejpam-3305	197	14	;	;	PUNCT
ejpam-3305	197	15	x)−	x)−	PROPN
ejpam-3305	197	16	f(x	f(x	PROPN
ejpam-3305	197	17	)	)	PUNCT
ejpam-3305	197	18	|≤	|≤	PROPN
ejpam-3305	197	19	4k2,φ	4k2,φ	NUM
ejpam-3305	197	20	(	(	PUNCT
ejpam-3305	197	21	f	f	X
ejpam-3305	197	22	,	,	PUNCT
ejpam-3305	197	23	m	m	PROPN
ejpam-3305	197	24	2n	2n	NUM
ejpam-3305	197	25	)	)	PUNCT
ejpam-3305	198	1	+	+	PUNCT
ejpam-3305	198	2	ω̄φ	ω̄φ	NUM
ejpam-3305	198	3	(	(	PUNCT
ejpam-3305	198	4	f	f	X
ejpam-3305	198	5	,	,	PUNCT
ejpam-3305	198	6	√	√	NOUN
ejpam-3305	198	7	m	m	VERB
ejpam-3305	198	8	n	n	NOUN
ejpam-3305	198	9	)	)	PUNCT
ejpam-3305	198	10	,	,	PUNCT
ejpam-3305	198	11	for	for	ADP
ejpam-3305	198	12	n	n	PRON
ejpam-3305	198	13	sufficiently	sufficiently	ADV
ejpam-3305	198	14	large	large	ADJ
ejpam-3305	198	15	.	.	PUNCT
ejpam-3305	199	1	proof	proof	NOUN
ejpam-3305	199	2	.	.	PUNCT
ejpam-3305	200	1	let	let	VERB
ejpam-3305	200	2	g	g	PROPN
ejpam-3305	200	3	∈w	∈w	PROPN
ejpam-3305	200	4	2(φ	2(φ	NUM
ejpam-3305	200	5	)	)	PUNCT
ejpam-3305	200	6	.	.	PUNCT
ejpam-3305	201	1	applying	apply	VERB
ejpam-3305	201	2	taylor	taylor	PROPN
ejpam-3305	201	3	’s	’s	PART
ejpam-3305	201	4	expansion	expansion	NOUN
ejpam-3305	201	5	,	,	PUNCT
ejpam-3305	201	6	we	we	PRON
ejpam-3305	201	7	may	may	AUX
ejpam-3305	201	8	write	write	VERB
ejpam-3305	201	9	g(t	g(t	PROPN
ejpam-3305	201	10	)	)	PUNCT
ejpam-3305	202	1	=	=	SYM
ejpam-3305	202	2	g(x	g(x	NOUN
ejpam-3305	202	3	)	)	PUNCT
ejpam-3305	203	1	+	+	CCONJ
ejpam-3305	203	2	(	(	PUNCT
ejpam-3305	203	3	t−	t−	PROPN
ejpam-3305	203	4	x)g′(x	x)g′(x	PROPN
ejpam-3305	203	5	)	)	PUNCT
ejpam-3305	204	1	+	+	NUM
ejpam-3305	204	2	∫	∫	PROPN
ejpam-3305	204	3	t	t	NOUN
ejpam-3305	204	4	x	x	X
ejpam-3305	204	5	(	(	PUNCT
ejpam-3305	204	6	t−	t−	PROPN
ejpam-3305	204	7	v)g′′(v)dv	v)g′′(v)dv	PROPN
ejpam-3305	204	8	.	.	PUNCT
ejpam-3305	205	1	applying	apply	VERB
ejpam-3305	205	2	m	m	VERB
ejpam-3305	205	3	(	(	PUNCT
ejpam-3305	205	4	β	β	X
ejpam-3305	205	5	,	,	PUNCT
ejpam-3305	205	6	γ	γ	NOUN
ejpam-3305	205	7	)	)	PUNCT
ejpam-3305	205	8	n	n	CCONJ
ejpam-3305	205	9	,	,	PUNCT
ejpam-3305	205	10	α	α	NOUN
ejpam-3305	205	11	on	on	ADP
ejpam-3305	205	12	both	both	DET
ejpam-3305	205	13	sides	side	NOUN
ejpam-3305	205	14	of	of	ADP
ejpam-3305	205	15	the	the	DET
ejpam-3305	205	16	above	above	ADJ
ejpam-3305	205	17	equation	equation	NOUN
ejpam-3305	205	18	,	,	PUNCT
ejpam-3305	205	19	we	we	PRON
ejpam-3305	205	20	get	get	VERB
ejpam-3305	205	21	|m	|m	NOUN
ejpam-3305	205	22	(	(	PUNCT
ejpam-3305	205	23	β	β	X
ejpam-3305	205	24	,	,	PUNCT
ejpam-3305	205	25	γ	γ	NOUN
ejpam-3305	205	26	)	)	PUNCT
ejpam-3305	205	27	n	n	CCONJ
ejpam-3305	205	28	,	,	PUNCT
ejpam-3305	205	29	α	α	PROPN
ejpam-3305	205	30	(	(	PUNCT
ejpam-3305	205	31	g;x)−	g;x)−	PROPN
ejpam-3305	205	32	g(x)|	g(x)|	VERB
ejpam-3305	205	33	≤	≤	NUM
ejpam-3305	205	34	m	m	VERB
ejpam-3305	205	35	(	(	PUNCT
ejpam-3305	205	36	β	β	X
ejpam-3305	205	37	,	,	PUNCT
ejpam-3305	205	38	γ	γ	NOUN
ejpam-3305	205	39	)	)	PUNCT
ejpam-3305	205	40	n	n	CCONJ
ejpam-3305	205	41	,	,	PUNCT
ejpam-3305	205	42	α	α	PROPN
ejpam-3305	205	43	(	(	PUNCT
ejpam-3305	205	44	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3305	205	45	∫	∫	PROPN
ejpam-3305	205	46	t	t	PROPN
ejpam-3305	205	47	x	x	PROPN
ejpam-3305	205	48	|t−	|t−	PROPN
ejpam-3305	205	49	v||g′′(v)|dv	v||g′′(v)|dv	NOUN
ejpam-3305	205	50	∣∣∣∣;x)+	∣∣∣∣;x)+	NOUN
ejpam-3305	205	51	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3305	205	52	∫	∫	PROPN
ejpam-3305	205	53	nx+β	nx+β	PROPN
ejpam-3305	205	54	n+γ	n+γ	PROPN
ejpam-3305	205	55	x	x	X
ejpam-3305	206	1	∣∣∣∣nx+	∣∣∣∣nx+	PROPN
ejpam-3305	206	2	β	β	X
ejpam-3305	206	3	n+	n+	ADP
ejpam-3305	206	4	γ	γ	NOUN
ejpam-3305	206	5	−	−	PROPN
ejpam-3305	206	6	v	v	ADP
ejpam-3305	206	7	∣∣∣∣|g′′(v)|dv	∣∣∣∣|g′′(v)|dv	PROPN
ejpam-3305	206	8	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3305	206	9	≤	≤	NUM
ejpam-3305	206	10	‖	‖	PROPN
ejpam-3305	206	11	φ2g′′	φ2g′′	PROPN
ejpam-3305	206	12	‖	‖	PROPN
ejpam-3305	206	13	φ2(x	φ2(x	NOUN
ejpam-3305	206	14	)	)	PUNCT
ejpam-3305	206	15	(	(	PUNCT
ejpam-3305	206	16	ξ(β	ξ(β	PROPN
ejpam-3305	206	17	,	,	PUNCT
ejpam-3305	206	18	γ)n	γ)n	X
ejpam-3305	206	19	,	,	PUNCT
ejpam-3305	206	20	α	α	PROPN
ejpam-3305	206	21	(	(	PUNCT
ejpam-3305	206	22	x	x	NOUN
ejpam-3305	206	23	)	)	PUNCT
ejpam-3305	206	24	+	+	CCONJ
ejpam-3305	206	25	(	(	PUNCT
ejpam-3305	206	26	β	β	X
ejpam-3305	206	27	−	−	NOUN
ejpam-3305	206	28	γx	γx	NOUN
ejpam-3305	206	29	n+	n+	PUNCT
ejpam-3305	206	30	γ	γ	NOUN
ejpam-3305	206	31	)	)	PUNCT
ejpam-3305	206	32	2	2	NUM
ejpam-3305	206	33	)	)	PUNCT
ejpam-3305	206	34	.	.	PUNCT
ejpam-3305	207	1	(	(	PUNCT
ejpam-3305	207	2	16	16	NUM
ejpam-3305	207	3	)	)	PUNCT
ejpam-3305	207	4	in	in	ADP
ejpam-3305	207	5	view	view	NOUN
ejpam-3305	207	6	of	of	ADP
ejpam-3305	207	7	remark	remark	NOUN
ejpam-3305	207	8	1	1	NUM
ejpam-3305	207	9	,	,	PUNCT
ejpam-3305	207	10	it	it	PRON
ejpam-3305	207	11	follows	follow	VERB
ejpam-3305	207	12	that	that	SCONJ
ejpam-3305	207	13	there	there	PRON
ejpam-3305	207	14	exist	exist	VERB
ejpam-3305	207	15	a	a	DET
ejpam-3305	207	16	positive	positive	ADJ
ejpam-3305	207	17	constant	constant	ADJ
ejpam-3305	207	18	m	m	NOUN
ejpam-3305	207	19	>	>	X
ejpam-3305	207	20	0	0	NUM
ejpam-3305	207	21	such	such	ADJ
ejpam-3305	207	22	that	that	SCONJ
ejpam-3305	207	23	ξ	ξ	PROPN
ejpam-3305	207	24	(	(	PUNCT
ejpam-3305	207	25	β	β	X
ejpam-3305	207	26	,	,	PUNCT
ejpam-3305	207	27	γ	γ	NOUN
ejpam-3305	207	28	)	)	PUNCT
ejpam-3305	207	29	n	n	CCONJ
ejpam-3305	207	30	,	,	PUNCT
ejpam-3305	207	31	α	α	PROPN
ejpam-3305	207	32	(	(	PUNCT
ejpam-3305	207	33	x	x	NOUN
ejpam-3305	207	34	)	)	PUNCT
ejpam-3305	207	35	φ2(x	φ2(x	NUM
ejpam-3305	207	36	)	)	PUNCT
ejpam-3305	207	37	≤	≤	NUM
ejpam-3305	207	38	m	m	VERB
ejpam-3305	207	39	n	n	PRON
ejpam-3305	207	40	,	,	PUNCT
ejpam-3305	207	41	1	1	NUM
ejpam-3305	207	42	φ2(x	φ2(x	NUM
ejpam-3305	207	43	)	)	PUNCT
ejpam-3305	207	44	(	(	PUNCT
ejpam-3305	207	45	β	β	X
ejpam-3305	207	46	−	−	NOUN
ejpam-3305	207	47	γx	γx	NOUN
ejpam-3305	207	48	n+	n+	PUNCT
ejpam-3305	207	49	γ	γ	NOUN
ejpam-3305	207	50	)	)	PUNCT
ejpam-3305	207	51	2	2	NUM
ejpam-3305	207	52	≤	≤	NUM
ejpam-3305	207	53	m	m	VERB
ejpam-3305	207	54	n2	n2	NOUN
ejpam-3305	207	55	.	.	PUNCT
ejpam-3305	208	1	thus	thus	ADV
ejpam-3305	208	2	,	,	PUNCT
ejpam-3305	208	3	|m	|m	NOUN
ejpam-3305	208	4	(	(	PUNCT
ejpam-3305	208	5	β	β	X
ejpam-3305	208	6	,	,	PUNCT
ejpam-3305	208	7	γ	γ	NOUN
ejpam-3305	208	8	)	)	PUNCT
ejpam-3305	208	9	n	n	CCONJ
ejpam-3305	208	10	,	,	PUNCT
ejpam-3305	208	11	α	α	PROPN
ejpam-3305	208	12	(	(	PUNCT
ejpam-3305	208	13	g;x)−	g;x)−	PROPN
ejpam-3305	208	14	g(x)|	g(x)|	NOUN
ejpam-3305	208	15	≤m	≤m	PROPN
ejpam-3305	208	16	‖	‖	ADJ
ejpam-3305	208	17	φ2g′′	φ2g′′	PROPN
ejpam-3305	208	18	‖	‖	PROPN
ejpam-3305	208	19	(	(	PUNCT
ejpam-3305	208	20	1	1	NUM
ejpam-3305	208	21	n	n	NOUN
ejpam-3305	208	22	+	+	CCONJ
ejpam-3305	208	23	1	1	NUM
ejpam-3305	208	24	n2	n2	ADJ
ejpam-3305	208	25	)	)	PUNCT
ejpam-3305	208	26	≤	≤	NUM
ejpam-3305	208	27	2	2	NUM
ejpam-3305	208	28	m	m	NOUN
ejpam-3305	208	29	n	n	NUM
ejpam-3305	208	30	‖	‖	PROPN
ejpam-3305	208	31	φ2g′′	φ2g′′	PROPN
ejpam-3305	208	32	‖	‖	PROPN
ejpam-3305	208	33	.	.	PUNCT
ejpam-3305	209	1	now	now	ADV
ejpam-3305	209	2	,	,	PUNCT
ejpam-3305	209	3	|m	|m	NOUN
ejpam-3305	209	4	(	(	PUNCT
ejpam-3305	209	5	β	β	X
ejpam-3305	209	6	,	,	PUNCT
ejpam-3305	209	7	γ	γ	NOUN
ejpam-3305	209	8	)	)	PUNCT
ejpam-3305	209	9	n	n	CCONJ
ejpam-3305	209	10	,	,	PUNCT
ejpam-3305	209	11	α	α	PROPN
ejpam-3305	209	12	(	(	PUNCT
ejpam-3305	209	13	f	f	X
ejpam-3305	209	14	;	;	PUNCT
ejpam-3305	209	15	x)−	x)−	PROPN
ejpam-3305	209	16	f(x)|	f(x)|	VERB
ejpam-3305	209	17	≤	≤	NUM
ejpam-3305	209	18	|m	|m	NOUN
ejpam-3305	209	19	(	(	PUNCT
ejpam-3305	209	20	β	β	X
ejpam-3305	209	21	,	,	PUNCT
ejpam-3305	209	22	γ	γ	NOUN
ejpam-3305	209	23	)	)	PUNCT
ejpam-3305	209	24	n	n	CCONJ
ejpam-3305	209	25	,	,	PUNCT
ejpam-3305	209	26	α	α	PROPN
ejpam-3305	209	27	(	(	PUNCT
ejpam-3305	209	28	f	f	NOUN
ejpam-3305	209	29	−	−	PROPN
ejpam-3305	209	30	g;x)|+	g;x)|+	PROPN
ejpam-3305	209	31	|(f	|(f	PROPN
ejpam-3305	210	1	−	−	PROPN
ejpam-3305	211	1	g)(x)|+	g)(x)|+	NOUN
ejpam-3305	212	1	|m	|m	NOUN
ejpam-3305	212	2	(	(	PUNCT
ejpam-3305	212	3	β	β	X
ejpam-3305	212	4	,	,	PUNCT
ejpam-3305	212	5	γ	γ	NOUN
ejpam-3305	212	6	)	)	PUNCT
ejpam-3305	212	7	n	n	CCONJ
ejpam-3305	212	8	,	,	PUNCT
ejpam-3305	212	9	α	α	PROPN
ejpam-3305	212	10	(	(	PUNCT
ejpam-3305	212	11	g;x)−	g;x)−	PROPN
ejpam-3305	212	12	g(x)|+	g(x)|+	PROPN
ejpam-3305	212	13	∣∣∣∣f	∣∣∣∣f	PROPN
ejpam-3305	212	14	(	(	PUNCT
ejpam-3305	212	15	nx+	nx+	PROPN
ejpam-3305	212	16	β	β	X
ejpam-3305	212	17	n+	n+	X
ejpam-3305	212	18	γ	γ	PROPN
ejpam-3305	212	19	)	)	PUNCT
ejpam-3305	212	20	−	−	PROPN
ejpam-3305	212	21	f(x	f(x	PROPN
ejpam-3305	212	22	)	)	PUNCT
ejpam-3305	212	23	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3305	212	24	a.	a.	NOUN
ejpam-3305	212	25	kumar	kumar	PROPN
ejpam-3305	212	26	,	,	PUNCT
ejpam-3305	212	27	d.	d.	PROPN
ejpam-3305	212	28	tapiawala	tapiawala	PROPN
ejpam-3305	212	29	,	,	PUNCT
ejpam-3305	212	30	l.	l.	PROPN
ejpam-3305	212	31	n.	n.	PROPN
ejpam-3305	212	32	mishra	mishra	PROPN
ejpam-3305	212	33	/	/	SYM
ejpam-3305	212	34	eur	eur	PROPN
ejpam-3305	212	35	.	.	PUNCT
ejpam-3305	213	1	j.	j.	PROPN
ejpam-3305	213	2	pure	pure	PROPN
ejpam-3305	213	3	appl	appl	PROPN
ejpam-3305	213	4	.	.	PROPN
ejpam-3305	213	5	math	math	PROPN
ejpam-3305	213	6	,	,	PUNCT
ejpam-3305	213	7	11	11	NUM
ejpam-3305	213	8	(	(	PUNCT
ejpam-3305	213	9	4	4	NUM
ejpam-3305	213	10	)	)	PUNCT
ejpam-3305	213	11	(	(	PUNCT
ejpam-3305	213	12	2018	2018	NUM
ejpam-3305	213	13	)	)	PUNCT
ejpam-3305	213	14	,	,	PUNCT
ejpam-3305	213	15	958	958	NUM
ejpam-3305	213	16	-	-	SYM
ejpam-3305	213	17	975	975	NUM
ejpam-3305	213	18	967	967	NUM
ejpam-3305	213	19	≤	≤	NOUN
ejpam-3305	213	20	4	4	NUM
ejpam-3305	213	21	‖	‖	PROPN
ejpam-3305	213	22	f	f	NOUN
ejpam-3305	213	23	−	−	PROPN
ejpam-3305	213	24	g	g	PROPN
ejpam-3305	213	25	‖	‖	PROPN
ejpam-3305	214	1	+	+	PROPN
ejpam-3305	214	2	2	2	NUM
ejpam-3305	214	3	m	m	NOUN
ejpam-3305	214	4	n	n	ADJ
ejpam-3305	214	5	‖	‖	ADJ
ejpam-3305	214	6	φ2g′′	φ2g′′	PROPN
ejpam-3305	214	7	‖	‖	PROPN
ejpam-3305	214	8	+	+	CCONJ
ejpam-3305	214	9	∣∣∣∣f	∣∣∣∣f	PROPN
ejpam-3305	214	10	(	(	PUNCT
ejpam-3305	214	11	nx+	nx+	PROPN
ejpam-3305	214	12	β	β	X
ejpam-3305	214	13	n+	n+	X
ejpam-3305	214	14	γ	γ	PROPN
ejpam-3305	214	15	)	)	PUNCT
ejpam-3305	214	16	−	−	PROPN
ejpam-3305	214	17	f(x	f(x	PROPN
ejpam-3305	214	18	)	)	PUNCT
ejpam-3305	214	19	∣∣∣∣.	∣∣∣∣.	PROPN
ejpam-3305	214	20	also	also	ADV
ejpam-3305	214	21	,	,	PUNCT
ejpam-3305	214	22	we	we	PRON
ejpam-3305	214	23	obtain∣∣∣∣f	obtain∣∣∣∣f	NOUN
ejpam-3305	214	24	(	(	PUNCT
ejpam-3305	214	25	nx+	nx+	PROPN
ejpam-3305	214	26	β	β	X
ejpam-3305	214	27	n+	n+	X
ejpam-3305	214	28	γ	γ	PROPN
ejpam-3305	214	29	)	)	PUNCT
ejpam-3305	214	30	−	−	PROPN
ejpam-3305	214	31	f(x	f(x	PROPN
ejpam-3305	214	32	)	)	PUNCT
ejpam-3305	214	33	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3305	214	34	=	=	SYM
ejpam-3305	214	35	∣∣∣∣f	∣∣∣∣f	PROPN
ejpam-3305	214	36	(	(	PUNCT
ejpam-3305	214	37	x+	x+	X
ejpam-3305	214	38	φ(x	φ(x	NOUN
ejpam-3305	214	39	)	)	PUNCT
ejpam-3305	214	40	nx+β	nx+β	NOUN
ejpam-3305	214	41	n+γ	n+γ	ADV
ejpam-3305	214	42	−	−	NOUN
ejpam-3305	214	43	x	x	SYM
ejpam-3305	214	44	φ(x	φ(x	NOUN
ejpam-3305	214	45	)	)	PUNCT
ejpam-3305	214	46	)	)	PUNCT
ejpam-3305	215	1	−	−	PROPN
ejpam-3305	215	2	f(x	f(x	PROPN
ejpam-3305	215	3	)	)	PUNCT
ejpam-3305	215	4	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3305	215	5	≤	≤	NUM
ejpam-3305	215	6	sup	sup	NOUN
ejpam-3305	215	7	∣∣∣∣f	∣∣∣∣f	NOUN
ejpam-3305	215	8	(	(	PUNCT
ejpam-3305	215	9	x+	x+	X
ejpam-3305	215	10	φ(x	φ(x	NOUN
ejpam-3305	215	11	)	)	PUNCT
ejpam-3305	215	12	β−γx	β−γx	NOUN
ejpam-3305	215	13	n+γ	n+γ	X
ejpam-3305	215	14	φ(x	φ(x	NOUN
ejpam-3305	215	15	)	)	PUNCT
ejpam-3305	215	16	)	)	PUNCT
ejpam-3305	216	1	−	−	PROPN
ejpam-3305	216	2	f(x	f(x	PROPN
ejpam-3305	216	3	)	)	PUNCT
ejpam-3305	216	4	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3305	216	5	≤	≤	NUM
ejpam-3305	217	1	ω̄φ	ω̄φ	PROPN
ejpam-3305	217	2	(	(	PUNCT
ejpam-3305	217	3	f	f	X
ejpam-3305	217	4	,	,	PUNCT
ejpam-3305	217	5	√	√	NOUN
ejpam-3305	217	6	m	m	VERB
ejpam-3305	217	7	n	n	NOUN
ejpam-3305	217	8	)	)	PUNCT
ejpam-3305	217	9	.	.	PUNCT
ejpam-3305	218	1	using	use	VERB
ejpam-3305	218	2	the	the	DET
ejpam-3305	218	3	above	above	ADJ
ejpam-3305	218	4	equations	equation	NOUN
ejpam-3305	218	5	,	,	PUNCT
ejpam-3305	218	6	we	we	PRON
ejpam-3305	218	7	get	get	VERB
ejpam-3305	218	8	|m	|m	NOUN
ejpam-3305	218	9	(	(	PUNCT
ejpam-3305	218	10	β	β	X
ejpam-3305	218	11	,	,	PUNCT
ejpam-3305	218	12	γ	γ	NOUN
ejpam-3305	218	13	)	)	PUNCT
ejpam-3305	218	14	n	n	CCONJ
ejpam-3305	218	15	,	,	PUNCT
ejpam-3305	218	16	α	α	PROPN
ejpam-3305	218	17	(	(	PUNCT
ejpam-3305	218	18	f	f	PROPN
ejpam-3305	218	19	;	;	PUNCT
ejpam-3305	218	20	x)−	x)−	PROPN
ejpam-3305	218	21	f(x	f(x	PROPN
ejpam-3305	218	22	)	)	PUNCT
ejpam-3305	218	23	|	|	ADV
ejpam-3305	218	24	≤	≤	NUM
ejpam-3305	218	25	4	4	NUM
ejpam-3305	218	26	(	(	PUNCT
ejpam-3305	218	27	‖	‖	PROPN
ejpam-3305	218	28	f	f	NOUN
ejpam-3305	218	29	−	−	PROPN
ejpam-3305	218	30	g	g	PROPN
ejpam-3305	218	31	‖	‖	PROPN
ejpam-3305	218	32	+	+	PROPN
ejpam-3305	218	33	m	m	VERB
ejpam-3305	218	34	2n	2n	NUM
ejpam-3305	218	35	‖	‖	ADJ
ejpam-3305	218	36	φ2g′′	φ2g′′	PROPN
ejpam-3305	218	37	‖	‖	PROPN
ejpam-3305	218	38	)	)	PUNCT
ejpam-3305	219	1	+	+	CCONJ
ejpam-3305	219	2	ω̄φ	ω̄φ	NUM
ejpam-3305	219	3	(	(	PUNCT
ejpam-3305	219	4	f	f	X
ejpam-3305	219	5	,	,	PUNCT
ejpam-3305	219	6	√	√	NOUN
ejpam-3305	219	7	m	m	VERB
ejpam-3305	219	8	n	n	NOUN
ejpam-3305	219	9	)	)	PUNCT
ejpam-3305	219	10	.	.	PUNCT
ejpam-3305	220	1	now	now	ADV
ejpam-3305	220	2	,	,	PUNCT
ejpam-3305	220	3	applying	apply	VERB
ejpam-3305	220	4	(	(	PUNCT
ejpam-3305	220	5	15	15	NUM
ejpam-3305	220	6	)	)	PUNCT
ejpam-3305	220	7	,	,	PUNCT
ejpam-3305	220	8	the	the	DET
ejpam-3305	220	9	theorem	theorem	NOUN
ejpam-3305	220	10	is	be	AUX
ejpam-3305	220	11	completed	complete	VERB
ejpam-3305	220	12	.	.	PUNCT
ejpam-3305	221	1	3.4	3.4	NUM
ejpam-3305	221	2	.	.	PUNCT
ejpam-3305	221	3	rate	rate	NOUN
ejpam-3305	221	4	of	of	ADP
ejpam-3305	221	5	convergence	convergence	NOUN
ejpam-3305	221	6	let	let	VERB
ejpam-3305	221	7	ωa(f	ωa(f	NOUN
ejpam-3305	221	8	,	,	PUNCT
ejpam-3305	221	9	δ	δ	PROPN
ejpam-3305	221	10	)	)	PUNCT
ejpam-3305	221	11	denote	denote	VERB
ejpam-3305	221	12	the	the	DET
ejpam-3305	221	13	usual	usual	ADJ
ejpam-3305	221	14	modulus	modulus	NOUN
ejpam-3305	221	15	of	of	ADP
ejpam-3305	221	16	continuity	continuity	NOUN
ejpam-3305	221	17	of	of	ADP
ejpam-3305	221	18	f	f	PROPN
ejpam-3305	221	19	on	on	ADP
ejpam-3305	221	20	the	the	DET
ejpam-3305	221	21	closed	closed	ADJ
ejpam-3305	221	22	interval	interval	NOUN
ejpam-3305	222	1	[	[	X
ejpam-3305	222	2	0	0	NUM
ejpam-3305	222	3	,	,	PUNCT
ejpam-3305	222	4	a	a	PRON
ejpam-3305	222	5	]	]	X
ejpam-3305	222	6	,	,	PUNCT
ejpam-3305	222	7	a	a	DET
ejpam-3305	222	8	>	>	X
ejpam-3305	222	9	0	0	NUM
ejpam-3305	222	10	,	,	PUNCT
ejpam-3305	222	11	and	and	CCONJ
ejpam-3305	222	12	defined	define	VERB
ejpam-3305	222	13	as	as	ADP
ejpam-3305	222	14	ωa(f	ωa(f	NOUN
ejpam-3305	222	15	,	,	PUNCT
ejpam-3305	222	16	δ	δ	PROPN
ejpam-3305	222	17	)	)	PUNCT
ejpam-3305	222	18	=	=	SYM
ejpam-3305	222	19	sup	sup	NUM
ejpam-3305	222	20	|t−x|≤δ	|t−x|≤δ	NOUN
ejpam-3305	222	21	sup	sup	NOUN
ejpam-3305	222	22	x	x	NOUN
ejpam-3305	222	23	,	,	PUNCT
ejpam-3305	222	24	t∈[0,a	t∈[0,a	X
ejpam-3305	222	25	]	]	X
ejpam-3305	222	26	|f(t)−	|f(t)−	PROPN
ejpam-3305	222	27	f(x)|	f(x)|	VERB
ejpam-3305	222	28	.	.	PUNCT
ejpam-3305	223	1	we	we	PRON
ejpam-3305	223	2	observe	observe	VERB
ejpam-3305	223	3	that	that	SCONJ
ejpam-3305	223	4	for	for	ADP
ejpam-3305	223	5	a	a	DET
ejpam-3305	223	6	function	function	NOUN
ejpam-3305	223	7	f	f	PROPN
ejpam-3305	223	8	∈	∈	PROPN
ejpam-3305	223	9	cb[0,∞	cb[0,∞	PROPN
ejpam-3305	223	10	)	)	PUNCT
ejpam-3305	223	11	,	,	PUNCT
ejpam-3305	223	12	the	the	DET
ejpam-3305	223	13	modulus	modulus	NOUN
ejpam-3305	223	14	of	of	ADP
ejpam-3305	223	15	continuity	continuity	NOUN
ejpam-3305	223	16	ωa(f	ωa(f	NOUN
ejpam-3305	223	17	,	,	PUNCT
ejpam-3305	223	18	δ	δ	PROPN
ejpam-3305	223	19	)	)	PUNCT
ejpam-3305	223	20	tends	tend	VERB
ejpam-3305	223	21	to	to	ADP
ejpam-3305	223	22	zero	zero	NUM
ejpam-3305	223	23	.	.	PUNCT
ejpam-3305	224	1	now	now	ADV
ejpam-3305	224	2	,	,	PUNCT
ejpam-3305	224	3	we	we	PRON
ejpam-3305	224	4	give	give	VERB
ejpam-3305	224	5	a	a	DET
ejpam-3305	224	6	rate	rate	NOUN
ejpam-3305	224	7	of	of	ADP
ejpam-3305	224	8	convergence	convergence	NOUN
ejpam-3305	224	9	theorem	theorem	NOUN
ejpam-3305	224	10	for	for	ADP
ejpam-3305	224	11	the	the	DET
ejpam-3305	224	12	operators	operator	NOUN
ejpam-3305	224	13	m	m	VERB
ejpam-3305	224	14	(	(	PUNCT
ejpam-3305	224	15	β	β	X
ejpam-3305	224	16	,	,	PUNCT
ejpam-3305	224	17	γ	γ	NOUN
ejpam-3305	224	18	)	)	PUNCT
ejpam-3305	224	19	n	n	CCONJ
ejpam-3305	224	20	,	,	PUNCT
ejpam-3305	224	21	α	α	PROPN
ejpam-3305	224	22	.	.	PUNCT
ejpam-3305	225	1	theorem	theorem	VERB
ejpam-3305	225	2	6	6	NUM
ejpam-3305	225	3	.	.	PUNCT
ejpam-3305	226	1	let	let	VERB
ejpam-3305	226	2	f	f	PROPN
ejpam-3305	226	3	∈	∈	PROPN
ejpam-3305	226	4	cb[0,∞	cb[0,∞	PROPN
ejpam-3305	226	5	)	)	PUNCT
ejpam-3305	226	6	and	and	CCONJ
ejpam-3305	226	7	ωa+1(f	ωa+1(f	PROPN
ejpam-3305	226	8	,	,	PUNCT
ejpam-3305	226	9	δ	δ	PROPN
ejpam-3305	226	10	)	)	PUNCT
ejpam-3305	226	11	be	be	VERB
ejpam-3305	226	12	its	its	PRON
ejpam-3305	226	13	modulus	modulus	NOUN
ejpam-3305	226	14	of	of	ADP
ejpam-3305	226	15	continuity	continuity	NOUN
ejpam-3305	226	16	on	on	ADP
ejpam-3305	226	17	the	the	DET
ejpam-3305	226	18	finite	finite	ADJ
ejpam-3305	226	19	interval	interval	NOUN
ejpam-3305	227	1	[	[	X
ejpam-3305	227	2	0	0	NUM
ejpam-3305	227	3	,	,	PUNCT
ejpam-3305	227	4	a+	a+	X
ejpam-3305	227	5	1	1	X
ejpam-3305	227	6	]	]	PUNCT
ejpam-3305	227	7	⊂	⊂	PROPN
ejpam-3305	228	1	[	[	X
ejpam-3305	228	2	0,∞	0,∞	NOUN
ejpam-3305	228	3	)	)	PUNCT
ejpam-3305	228	4	,	,	PUNCT
ejpam-3305	229	1	where	where	SCONJ
ejpam-3305	229	2	a	a	DET
ejpam-3305	229	3	>	>	X
ejpam-3305	229	4	0	0	NUM
ejpam-3305	229	5	.	.	PUNCT
ejpam-3305	230	1	then	then	ADV
ejpam-3305	230	2	,	,	PUNCT
ejpam-3305	230	3	we	we	PRON
ejpam-3305	230	4	have	have	VERB
ejpam-3305	230	5	|m	|m	NOUN
ejpam-3305	230	6	(	(	PUNCT
ejpam-3305	230	7	β	β	X
ejpam-3305	230	8	,	,	PUNCT
ejpam-3305	230	9	γ	γ	NOUN
ejpam-3305	230	10	)	)	PUNCT
ejpam-3305	230	11	n	n	CCONJ
ejpam-3305	230	12	,	,	PUNCT
ejpam-3305	230	13	α	α	PROPN
ejpam-3305	230	14	(	(	PUNCT
ejpam-3305	230	15	f	f	X
ejpam-3305	230	16	;	;	PUNCT
ejpam-3305	230	17	x)−	x)−	PROPN
ejpam-3305	230	18	f(x)|	f(x)|	VERB
ejpam-3305	230	19	≤	≤	ADJ
ejpam-3305	230	20	6mf	6mf	NOUN
ejpam-3305	230	21	(	(	PUNCT
ejpam-3305	230	22	1	1	NUM
ejpam-3305	230	23	+	+	CCONJ
ejpam-3305	230	24	a2)ξ(β	a2)ξ(β	ADJ
ejpam-3305	230	25	,	,	PUNCT
ejpam-3305	230	26	γ)n	γ)n	X
ejpam-3305	230	27	,	,	PUNCT
ejpam-3305	230	28	α	α	PROPN
ejpam-3305	230	29	(	(	PUNCT
ejpam-3305	230	30	a	a	NOUN
ejpam-3305	230	31	)	)	PUNCT
ejpam-3305	230	32	+	+	NOUN
ejpam-3305	230	33	2ωa+1	2ωa+1	NUM
ejpam-3305	230	34	(	(	PUNCT
ejpam-3305	230	35	f	f	X
ejpam-3305	230	36	,	,	PUNCT
ejpam-3305	230	37	√	√	PROPN
ejpam-3305	230	38	ξ	ξ	PROPN
ejpam-3305	230	39	(	(	PUNCT
ejpam-3305	230	40	β	β	X
ejpam-3305	230	41	,	,	PUNCT
ejpam-3305	230	42	γ	γ	NOUN
ejpam-3305	230	43	)	)	PUNCT
ejpam-3305	230	44	n	n	CCONJ
ejpam-3305	230	45	,	,	PUNCT
ejpam-3305	230	46	α	α	PROPN
ejpam-3305	230	47	(	(	PUNCT
ejpam-3305	230	48	a	a	NOUN
ejpam-3305	230	49	)	)	PUNCT
ejpam-3305	230	50	)	)	PUNCT
ejpam-3305	230	51	,	,	PUNCT
ejpam-3305	230	52	where	where	SCONJ
ejpam-3305	230	53	ξ	ξ	X
ejpam-3305	230	54	(	(	PUNCT
ejpam-3305	230	55	β	β	X
ejpam-3305	230	56	,	,	PUNCT
ejpam-3305	230	57	γ	γ	NOUN
ejpam-3305	230	58	)	)	PUNCT
ejpam-3305	230	59	n	n	CCONJ
ejpam-3305	230	60	,	,	PUNCT
ejpam-3305	230	61	α	α	PROPN
ejpam-3305	230	62	(	(	PUNCT
ejpam-3305	230	63	a	a	NOUN
ejpam-3305	230	64	)	)	PUNCT
ejpam-3305	230	65	is	be	AUX
ejpam-3305	230	66	defined	define	VERB
ejpam-3305	230	67	in	in	ADP
ejpam-3305	230	68	remark	remark	NOUN
ejpam-3305	230	69	1	1	NUM
ejpam-3305	230	70	and	and	CCONJ
ejpam-3305	230	71	mf	mf	PROPN
ejpam-3305	230	72	is	be	AUX
ejpam-3305	230	73	a	a	DET
ejpam-3305	230	74	constant	constant	ADJ
ejpam-3305	230	75	depending	depend	VERB
ejpam-3305	230	76	only	only	ADV
ejpam-3305	230	77	on	on	ADP
ejpam-3305	230	78	f	f	PROPN
ejpam-3305	230	79	.	.	PUNCT
ejpam-3305	231	1	proof	proof	NOUN
ejpam-3305	231	2	.	.	PUNCT
ejpam-3305	232	1	for	for	ADP
ejpam-3305	232	2	x	x	PROPN
ejpam-3305	232	3	∈	∈	PROPN
ejpam-3305	232	4	[	[	X
ejpam-3305	232	5	0	0	NUM
ejpam-3305	232	6	,	,	PUNCT
ejpam-3305	232	7	a	a	PRON
ejpam-3305	232	8	]	]	X
ejpam-3305	232	9	and	and	CCONJ
ejpam-3305	232	10	t	t	X
ejpam-3305	232	11	>	>	PUNCT
ejpam-3305	232	12	a+	a+	PUNCT
ejpam-3305	232	13	1	1	X
ejpam-3305	232	14	.	.	PUNCT
ejpam-3305	233	1	since	since	SCONJ
ejpam-3305	233	2	t−	t−	PROPN
ejpam-3305	233	3	x	x	SYM
ejpam-3305	233	4	>	>	X
ejpam-3305	233	5	1	1	NUM
ejpam-3305	233	6	,	,	PUNCT
ejpam-3305	233	7	we	we	PRON
ejpam-3305	233	8	have	have	VERB
ejpam-3305	233	9	|f(t)−	|f(t)−	PROPN
ejpam-3305	233	10	f(x)|	f(x)|	VERB
ejpam-3305	234	1	≤	≤	ADJ
ejpam-3305	234	2	mf	mf	NOUN
ejpam-3305	234	3	(	(	PUNCT
ejpam-3305	234	4	2	2	NUM
ejpam-3305	234	5	+	+	NUM
ejpam-3305	234	6	x2	x2	PROPN
ejpam-3305	234	7	+	+	CCONJ
ejpam-3305	234	8	t2	t2	NOUN
ejpam-3305	234	9	)	)	PUNCT
ejpam-3305	234	10	≤	≤	NOUN
ejpam-3305	234	11	mf	mf	X
ejpam-3305	234	12	(	(	PUNCT
ejpam-3305	234	13	t−	t−	PROPN
ejpam-3305	234	14	x)2(2	x)2(2	PROPN
ejpam-3305	235	1	+	+	NUM
ejpam-3305	235	2	3x2	3x2	NUM
ejpam-3305	235	3	+	+	CCONJ
ejpam-3305	235	4	2(t−	2(t−	NUM
ejpam-3305	235	5	x)2	x)2	NOUN
ejpam-3305	235	6	)	)	PUNCT
ejpam-3305	235	7	≤	≤	NUM
ejpam-3305	235	8	6mf	6mf	NOUN
ejpam-3305	235	9	(	(	PUNCT
ejpam-3305	235	10	1	1	NUM
ejpam-3305	235	11	+	+	NUM
ejpam-3305	235	12	a2)(t−	a2)(t−	ADJ
ejpam-3305	235	13	x)2	x)2	PROPN
ejpam-3305	235	14	.	.	PUNCT
ejpam-3305	236	1	a.	a.	PROPN
ejpam-3305	236	2	kumar	kumar	PROPN
ejpam-3305	236	3	,	,	PUNCT
ejpam-3305	236	4	d.	d.	PROPN
ejpam-3305	236	5	tapiawala	tapiawala	PROPN
ejpam-3305	236	6	,	,	PUNCT
ejpam-3305	236	7	l.	l.	PROPN
ejpam-3305	236	8	n.	n.	PROPN
ejpam-3305	236	9	mishra	mishra	PROPN
ejpam-3305	236	10	/	/	SYM
ejpam-3305	236	11	eur	eur	PROPN
ejpam-3305	236	12	.	.	PUNCT
ejpam-3305	237	1	j.	j.	PROPN
ejpam-3305	237	2	pure	pure	PROPN
ejpam-3305	237	3	appl	appl	PROPN
ejpam-3305	237	4	.	.	PROPN
ejpam-3305	237	5	math	math	PROPN
ejpam-3305	237	6	,	,	PUNCT
ejpam-3305	237	7	11	11	NUM
ejpam-3305	237	8	(	(	PUNCT
ejpam-3305	237	9	4	4	NUM
ejpam-3305	237	10	)	)	PUNCT
ejpam-3305	237	11	(	(	PUNCT
ejpam-3305	237	12	2018	2018	NUM
ejpam-3305	237	13	)	)	PUNCT
ejpam-3305	237	14	,	,	PUNCT
ejpam-3305	237	15	958	958	NUM
ejpam-3305	237	16	-	-	SYM
ejpam-3305	237	17	975	975	NUM
ejpam-3305	237	18	968	968	NUM
ejpam-3305	237	19	for	for	ADP
ejpam-3305	237	20	x	x	PUNCT
ejpam-3305	237	21	∈	∈	PROPN
ejpam-3305	238	1	[	[	X
ejpam-3305	238	2	0	0	NUM
ejpam-3305	238	3	,	,	PUNCT
ejpam-3305	238	4	a	a	PRON
ejpam-3305	238	5	]	]	X
ejpam-3305	238	6	and	and	CCONJ
ejpam-3305	238	7	t	t	X
ejpam-3305	238	8	≤	≤	NUM
ejpam-3305	238	9	a+	a+	PUNCT
ejpam-3305	238	10	1	1	NUM
ejpam-3305	238	11	,	,	PUNCT
ejpam-3305	238	12	we	we	PRON
ejpam-3305	238	13	have	have	VERB
ejpam-3305	238	14	|f(t)−	|f(t)−	PROPN
ejpam-3305	238	15	f(x)|	f(x)|	VERB
ejpam-3305	238	16	≤	≤	ADJ
ejpam-3305	238	17	ωa+1(f	ωa+1(f	PROPN
ejpam-3305	238	18	,	,	PUNCT
ejpam-3305	238	19	|t−	|t−	PROPN
ejpam-3305	238	20	x|	x|	PROPN
ejpam-3305	238	21	)	)	PUNCT
ejpam-3305	238	22	≤	≤	NOUN
ejpam-3305	238	23	(	(	PUNCT
ejpam-3305	238	24	1	1	NUM
ejpam-3305	238	25	+	+	NUM
ejpam-3305	239	1	|t−	|t−	PROPN
ejpam-3305	239	2	x|	x|	PROPN
ejpam-3305	239	3	δ	δ	PROPN
ejpam-3305	239	4	)	)	PUNCT
ejpam-3305	239	5	ωa+1(f	ωa+1(f	PROPN
ejpam-3305	239	6	,	,	PUNCT
ejpam-3305	239	7	δ	δ	PROPN
ejpam-3305	239	8	)	)	PUNCT
ejpam-3305	239	9	with	with	ADP
ejpam-3305	239	10	δ	δ	PROPN
ejpam-3305	239	11	>	>	X
ejpam-3305	239	12	0	0	PROPN
ejpam-3305	239	13	.	.	PUNCT
ejpam-3305	240	1	from	from	ADP
ejpam-3305	240	2	the	the	DET
ejpam-3305	240	3	above	above	NOUN
ejpam-3305	240	4	,	,	PUNCT
ejpam-3305	240	5	we	we	PRON
ejpam-3305	240	6	have	have	VERB
ejpam-3305	240	7	|f(t)−	|f(t)−	PROPN
ejpam-3305	240	8	f(x)|	f(x)|	VERB
ejpam-3305	240	9	≤	≤	ADJ
ejpam-3305	240	10	6mf	6mf	NOUN
ejpam-3305	240	11	(	(	PUNCT
ejpam-3305	240	12	1	1	NUM
ejpam-3305	240	13	+	+	NUM
ejpam-3305	240	14	a2)(t−	a2)(t−	ADJ
ejpam-3305	240	15	x)2	x)2	VERB
ejpam-3305	241	1	+	+	CCONJ
ejpam-3305	241	2	(	(	PUNCT
ejpam-3305	241	3	1	1	NUM
ejpam-3305	241	4	+	+	NUM
ejpam-3305	241	5	|t−	|t−	PROPN
ejpam-3305	241	6	x|	x|	PROPN
ejpam-3305	241	7	δ	δ	PROPN
ejpam-3305	241	8	)	)	PUNCT
ejpam-3305	242	1	ωa+1(f	ωa+1(f	PROPN
ejpam-3305	242	2	,	,	PUNCT
ejpam-3305	242	3	δ	δ	PROPN
ejpam-3305	242	4	)	)	PUNCT
ejpam-3305	242	5	,	,	PUNCT
ejpam-3305	242	6	for	for	ADP
ejpam-3305	242	7	x	x	PROPN
ejpam-3305	242	8	∈	∈	PROPN
ejpam-3305	243	1	[	[	X
ejpam-3305	243	2	0	0	NUM
ejpam-3305	243	3	,	,	PUNCT
ejpam-3305	243	4	a	a	PRON
ejpam-3305	243	5	]	]	X
ejpam-3305	243	6	and	and	CCONJ
ejpam-3305	243	7	t	t	PROPN
ejpam-3305	243	8	≥	≥	NUM
ejpam-3305	243	9	0	0	NUM
ejpam-3305	243	10	.	.	PUNCT
ejpam-3305	244	1	thus	thus	ADV
ejpam-3305	244	2	|m	|m	NOUN
ejpam-3305	244	3	(	(	PUNCT
ejpam-3305	244	4	β	β	X
ejpam-3305	244	5	,	,	PUNCT
ejpam-3305	244	6	γ	γ	NOUN
ejpam-3305	244	7	)	)	PUNCT
ejpam-3305	244	8	n	n	CCONJ
ejpam-3305	244	9	,	,	PUNCT
ejpam-3305	244	10	α	α	PROPN
ejpam-3305	244	11	(	(	PUNCT
ejpam-3305	244	12	f	f	X
ejpam-3305	244	13	;	;	PUNCT
ejpam-3305	244	14	x)−	x)−	PROPN
ejpam-3305	244	15	f(x)|	f(x)|	VERB
ejpam-3305	244	16	≤	≤	ADJ
ejpam-3305	244	17	6mf	6mf	NOUN
ejpam-3305	244	18	(	(	PUNCT
ejpam-3305	244	19	1	1	NUM
ejpam-3305	244	20	+	+	CCONJ
ejpam-3305	244	21	a2)(m	a2)(m	PROPN
ejpam-3305	244	22	(	(	PUNCT
ejpam-3305	244	23	β	β	X
ejpam-3305	244	24	,	,	PUNCT
ejpam-3305	244	25	γ	γ	NOUN
ejpam-3305	244	26	)	)	PUNCT
ejpam-3305	244	27	n	n	CCONJ
ejpam-3305	244	28	,	,	PUNCT
ejpam-3305	244	29	α	α	PROPN
ejpam-3305	244	30	(	(	PUNCT
ejpam-3305	244	31	t−	t−	PROPN
ejpam-3305	244	32	x)2;x	x)2;x	NUM
ejpam-3305	244	33	)	)	PUNCT
ejpam-3305	245	1	+	+	PROPN
ejpam-3305	245	2	ωa+1(f	ωa+1(f	PROPN
ejpam-3305	245	3	,	,	PUNCT
ejpam-3305	245	4	δ	δ	PROPN
ejpam-3305	245	5	)	)	PUNCT
ejpam-3305	245	6	(	(	PUNCT
ejpam-3305	245	7	1	1	NUM
ejpam-3305	245	8	+	+	SYM
ejpam-3305	245	9	1	1	NUM
ejpam-3305	245	10	δ	δ	PROPN
ejpam-3305	245	11	(	(	PUNCT
ejpam-3305	245	12	m	m	PROPN
ejpam-3305	245	13	(	(	PUNCT
ejpam-3305	245	14	β	β	X
ejpam-3305	245	15	,	,	PUNCT
ejpam-3305	245	16	γ	γ	NOUN
ejpam-3305	245	17	)	)	PUNCT
ejpam-3305	245	18	n	n	CCONJ
ejpam-3305	245	19	,	,	PUNCT
ejpam-3305	245	20	α	α	PROPN
ejpam-3305	245	21	(	(	PUNCT
ejpam-3305	245	22	t−	t−	PROPN
ejpam-3305	245	23	x)2;x	x)2;x	NUM
ejpam-3305	245	24	)	)	PUNCT
ejpam-3305	245	25	1	1	NUM
ejpam-3305	245	26	2	2	NUM
ejpam-3305	245	27	)	)	PUNCT
ejpam-3305	245	28	.	.	PUNCT
ejpam-3305	246	1	applying	apply	VERB
ejpam-3305	246	2	cauchy	cauchy	PROPN
ejpam-3305	246	3	-	-	PUNCT
ejpam-3305	246	4	schwarz	schwarz	PROPN
ejpam-3305	246	5	’s	’s	PART
ejpam-3305	246	6	inequality	inequality	NOUN
ejpam-3305	246	7	,	,	PUNCT
ejpam-3305	246	8	we	we	PRON
ejpam-3305	246	9	get	get	VERB
ejpam-3305	246	10	|m	|m	NOUN
ejpam-3305	246	11	(	(	PUNCT
ejpam-3305	246	12	β	β	X
ejpam-3305	246	13	,	,	PUNCT
ejpam-3305	246	14	γ	γ	NOUN
ejpam-3305	246	15	)	)	PUNCT
ejpam-3305	246	16	n	n	CCONJ
ejpam-3305	246	17	,	,	PUNCT
ejpam-3305	246	18	α	α	PROPN
ejpam-3305	246	19	(	(	PUNCT
ejpam-3305	246	20	f	f	X
ejpam-3305	246	21	;	;	PUNCT
ejpam-3305	246	22	x)−	x)−	PROPN
ejpam-3305	246	23	f(x)|	f(x)|	VERB
ejpam-3305	246	24	≤	≤	ADJ
ejpam-3305	246	25	6mf	6mf	NOUN
ejpam-3305	246	26	(	(	PUNCT
ejpam-3305	246	27	1	1	NUM
ejpam-3305	246	28	+	+	CCONJ
ejpam-3305	246	29	a2)ξ(β	a2)ξ(β	ADJ
ejpam-3305	246	30	,	,	PUNCT
ejpam-3305	246	31	γ)n	γ)n	X
ejpam-3305	246	32	,	,	PUNCT
ejpam-3305	246	33	α	α	PROPN
ejpam-3305	246	34	(	(	PUNCT
ejpam-3305	246	35	a	a	NOUN
ejpam-3305	246	36	)	)	PUNCT
ejpam-3305	246	37	+	+	NOUN
ejpam-3305	246	38	2ωa+1	2ωa+1	NUM
ejpam-3305	246	39	(	(	PUNCT
ejpam-3305	246	40	f	f	X
ejpam-3305	246	41	,	,	PUNCT
ejpam-3305	246	42	√	√	PROPN
ejpam-3305	246	43	ξ	ξ	PROPN
ejpam-3305	246	44	(	(	PUNCT
ejpam-3305	246	45	β	β	X
ejpam-3305	246	46	,	,	PUNCT
ejpam-3305	246	47	γ	γ	NOUN
ejpam-3305	246	48	)	)	PUNCT
ejpam-3305	246	49	n	n	CCONJ
ejpam-3305	246	50	,	,	PUNCT
ejpam-3305	246	51	α	α	PROPN
ejpam-3305	246	52	(	(	PUNCT
ejpam-3305	246	53	a	a	NOUN
ejpam-3305	246	54	)	)	PUNCT
ejpam-3305	246	55	)	)	PUNCT
ejpam-3305	246	56	,	,	PUNCT
ejpam-3305	246	57	on	on	ADP
ejpam-3305	246	58	choosing	choose	VERB
ejpam-3305	246	59	δ	δ	PROPN
ejpam-3305	246	60	=	=	PUNCT
ejpam-3305	246	61	√	√	PROPN
ejpam-3305	246	62	ξ	ξ	X
ejpam-3305	246	63	(	(	PUNCT
ejpam-3305	246	64	β	β	X
ejpam-3305	246	65	,	,	PUNCT
ejpam-3305	246	66	γ	γ	NOUN
ejpam-3305	246	67	)	)	PUNCT
ejpam-3305	246	68	n	n	CCONJ
ejpam-3305	246	69	,	,	PUNCT
ejpam-3305	246	70	α	α	PROPN
ejpam-3305	246	71	(	(	PUNCT
ejpam-3305	246	72	a	a	NOUN
ejpam-3305	246	73	)	)	PUNCT
ejpam-3305	246	74	.	.	PUNCT
ejpam-3305	247	1	this	this	PRON
ejpam-3305	247	2	completes	complete	VERB
ejpam-3305	247	3	the	the	DET
ejpam-3305	247	4	proof	proof	NOUN
ejpam-3305	247	5	of	of	ADP
ejpam-3305	247	6	theorem	theorem	PROPN
ejpam-3305	247	7	.	.	PROPN
ejpam-3305	247	8	3.5	3.5	NUM
ejpam-3305	247	9	.	.	PUNCT
ejpam-3305	248	1	weighted	weight	VERB
ejpam-3305	248	2	approximation	approximation	NOUN
ejpam-3305	248	3	in	in	ADP
ejpam-3305	248	4	this	this	DET
ejpam-3305	248	5	section	section	NOUN
ejpam-3305	248	6	we	we	PRON
ejpam-3305	248	7	give	give	VERB
ejpam-3305	248	8	some	some	DET
ejpam-3305	248	9	weighted	weighted	ADJ
ejpam-3305	248	10	approximation	approximation	NOUN
ejpam-3305	248	11	properties	property	NOUN
ejpam-3305	248	12	of	of	ADP
ejpam-3305	248	13	the	the	DET
ejpam-3305	248	14	operators	operator	NOUN
ejpam-3305	248	15	m	m	VERB
ejpam-3305	248	16	(	(	PUNCT
ejpam-3305	248	17	β	β	X
ejpam-3305	248	18	,	,	PUNCT
ejpam-3305	248	19	γ	γ	NOUN
ejpam-3305	248	20	)	)	PUNCT
ejpam-3305	248	21	n	n	CCONJ
ejpam-3305	248	22	,	,	PUNCT
ejpam-3305	248	23	α	α	X
ejpam-3305	248	24	.	.	PUNCT
ejpam-3305	249	1	we	we	PRON
ejpam-3305	249	2	do	do	VERB
ejpam-3305	249	3	this	this	PRON
ejpam-3305	249	4	for	for	ADP
ejpam-3305	249	5	the	the	DET
ejpam-3305	249	6	following	follow	VERB
ejpam-3305	249	7	class	class	NOUN
ejpam-3305	249	8	of	of	ADP
ejpam-3305	249	9	continuous	continuous	ADJ
ejpam-3305	249	10	functions	function	NOUN
ejpam-3305	249	11	defined	define	VERB
ejpam-3305	249	12	on	on	ADP
ejpam-3305	249	13	[	[	X
ejpam-3305	249	14	0,∞	0,∞	NOUN
ejpam-3305	249	15	)	)	PUNCT
ejpam-3305	249	16	.	.	PUNCT
ejpam-3305	250	1	let	let	VERB
ejpam-3305	250	2	bν	bν	PRON
ejpam-3305	250	3	[	[	X
ejpam-3305	250	4	0,∞	0,∞	X
ejpam-3305	250	5	)	)	PUNCT
ejpam-3305	250	6	denote	denote	VERB
ejpam-3305	250	7	the	the	DET
ejpam-3305	250	8	weighted	weighted	ADJ
ejpam-3305	250	9	space	space	NOUN
ejpam-3305	250	10	of	of	ADP
ejpam-3305	250	11	real	real	ADV
ejpam-3305	250	12	-	-	PUNCT
ejpam-3305	250	13	valued	value	VERB
ejpam-3305	250	14	functions	function	NOUN
ejpam-3305	250	15	f	f	PRON
ejpam-3305	250	16	defined	define	VERB
ejpam-3305	250	17	on	on	ADP
ejpam-3305	250	18	[	[	X
ejpam-3305	250	19	0,∞	0,∞	NOUN
ejpam-3305	250	20	)	)	PUNCT
ejpam-3305	250	21	with	with	ADP
ejpam-3305	250	22	the	the	DET
ejpam-3305	250	23	property	property	NOUN
ejpam-3305	250	24	|f(x)|	|f(x)|	PROPN
ejpam-3305	250	25	≤mfν(x	≤mfν(x	PROPN
ejpam-3305	250	26	)	)	PUNCT
ejpam-3305	250	27	for	for	ADP
ejpam-3305	250	28	all	all	DET
ejpam-3305	250	29	x	x	SYM
ejpam-3305	250	30	∈	∈	PROPN
ejpam-3305	250	31	[	[	X
ejpam-3305	250	32	0,∞	0,∞	NOUN
ejpam-3305	250	33	)	)	PUNCT
ejpam-3305	250	34	,	,	PUNCT
ejpam-3305	250	35	where	where	SCONJ
ejpam-3305	250	36	ν(x	ν(x	X
ejpam-3305	250	37	)	)	PUNCT
ejpam-3305	250	38	=	=	SYM
ejpam-3305	251	1	1	1	NUM
ejpam-3305	252	1	+	+	CCONJ
ejpam-3305	252	2	x2	x2	NOUN
ejpam-3305	252	3	is	be	AUX
ejpam-3305	252	4	a	a	DET
ejpam-3305	252	5	weight	weight	NOUN
ejpam-3305	252	6	function	function	NOUN
ejpam-3305	252	7	and	and	CCONJ
ejpam-3305	252	8	mf	mf	NOUN
ejpam-3305	252	9	is	be	AUX
ejpam-3305	252	10	a	a	DET
ejpam-3305	252	11	constant	constant	ADJ
ejpam-3305	252	12	depending	depend	VERB
ejpam-3305	252	13	on	on	ADP
ejpam-3305	252	14	the	the	DET
ejpam-3305	252	15	function	function	NOUN
ejpam-3305	252	16	f	f	PROPN
ejpam-3305	252	17	.	.	PUNCT
ejpam-3305	253	1	we	we	PRON
ejpam-3305	253	2	also	also	ADV
ejpam-3305	253	3	consider	consider	VERB
ejpam-3305	253	4	the	the	DET
ejpam-3305	253	5	weighted	weight	VERB
ejpam-3305	253	6	subspace	subspace	NOUN
ejpam-3305	253	7	cν	cν	NOUN
ejpam-3305	254	1	[	[	X
ejpam-3305	254	2	0,∞	0,∞	NOUN
ejpam-3305	254	3	)	)	PUNCT
ejpam-3305	254	4	of	of	ADP
ejpam-3305	254	5	bν	bν	PROPN
ejpam-3305	254	6	[	[	X
ejpam-3305	254	7	0,∞	0,∞	NOUN
ejpam-3305	254	8	)	)	PUNCT
ejpam-3305	254	9	given	give	VERB
ejpam-3305	254	10	by	by	ADP
ejpam-3305	254	11	cν	cν	NOUN
ejpam-3305	255	1	[	[	X
ejpam-3305	255	2	0,∞	0,∞	NOUN
ejpam-3305	255	3	)	)	PUNCT
ejpam-3305	255	4	=	=	PRON
ejpam-3305	256	1	{	{	PUNCT
ejpam-3305	256	2	f	f	PROPN
ejpam-3305	256	3	∈	∈	PROPN
ejpam-3305	256	4	bν	bν	PROPN
ejpam-3305	257	1	[	[	X
ejpam-3305	257	2	0,∞	0,∞	NUM
ejpam-3305	257	3	)	)	PUNCT
ejpam-3305	257	4	:	:	PUNCT
ejpam-3305	258	1	f	f	PROPN
ejpam-3305	258	2	is	be	AUX
ejpam-3305	258	3	continuous	continuous	ADJ
ejpam-3305	258	4	on	on	ADP
ejpam-3305	258	5	[	[	X
ejpam-3305	258	6	0,∞	0,∞	NOUN
ejpam-3305	258	7	)	)	PUNCT
ejpam-3305	258	8	}	}	PUNCT
ejpam-3305	258	9	and	and	CCONJ
ejpam-3305	258	10	c∗ν	c∗ν	NUM
ejpam-3305	258	11	[	[	X
ejpam-3305	258	12	0,∞	0,∞	NOUN
ejpam-3305	258	13	)	)	PUNCT
ejpam-3305	258	14	denotes	denote	VERB
ejpam-3305	258	15	the	the	DET
ejpam-3305	258	16	subspace	subspace	NOUN
ejpam-3305	258	17	of	of	ADP
ejpam-3305	258	18	all	all	DET
ejpam-3305	258	19	functions	function	NOUN
ejpam-3305	258	20	f	f	PROPN
ejpam-3305	258	21	∈	∈	PROPN
ejpam-3305	258	22	cν	cν	NOUN
ejpam-3305	259	1	[	[	X
ejpam-3305	259	2	0,∞	0,∞	NOUN
ejpam-3305	259	3	)	)	PUNCT
ejpam-3305	259	4	for	for	ADP
ejpam-3305	259	5	which	which	PRON
ejpam-3305	259	6	lim	lim	NOUN
ejpam-3305	259	7	|x|→∞	|x|→∞	NOUN
ejpam-3305	259	8	f(x	f(x	PROPN
ejpam-3305	259	9	)	)	PUNCT
ejpam-3305	260	1	ν(x	ν(x	PROPN
ejpam-3305	260	2	)	)	PUNCT
ejpam-3305	260	3	exists	exist	VERB
ejpam-3305	260	4	finitely	finitely	ADV
ejpam-3305	260	5	.	.	PUNCT
ejpam-3305	261	1	it	it	PRON
ejpam-3305	261	2	is	be	AUX
ejpam-3305	261	3	obvious	obvious	ADJ
ejpam-3305	261	4	that	that	SCONJ
ejpam-3305	261	5	c∗ν	c∗ν	PUNCT
ejpam-3305	262	1	[	[	X
ejpam-3305	262	2	0,∞	0,∞	X
ejpam-3305	262	3	)	)	PUNCT
ejpam-3305	263	1	⊂	⊂	PRON
ejpam-3305	263	2	cν	cν	X
ejpam-3305	264	1	[	[	X
ejpam-3305	264	2	0,∞	0,∞	NOUN
ejpam-3305	264	3	)	)	PUNCT
ejpam-3305	265	1	⊂	⊂	PROPN
ejpam-3305	265	2	bν	bν	PROPN
ejpam-3305	266	1	[	[	X
ejpam-3305	266	2	0,∞	0,∞	NUM
ejpam-3305	266	3	)	)	PUNCT
ejpam-3305	266	4	.	.	PUNCT
ejpam-3305	267	1	the	the	DET
ejpam-3305	267	2	space	space	NOUN
ejpam-3305	267	3	bν	bν	PROPN
ejpam-3305	268	1	[	[	X
ejpam-3305	268	2	0,∞	0,∞	NUM
ejpam-3305	268	3	)	)	PUNCT
ejpam-3305	268	4	is	be	AUX
ejpam-3305	268	5	a	a	DET
ejpam-3305	268	6	normed	normed	ADJ
ejpam-3305	268	7	linear	linear	ADJ
ejpam-3305	268	8	space	space	NOUN
ejpam-3305	268	9	with	with	ADP
ejpam-3305	268	10	the	the	DET
ejpam-3305	268	11	following	follow	VERB
ejpam-3305	268	12	norm	norm	NOUN
ejpam-3305	268	13	:	:	PUNCT
ejpam-3305	268	14	‖	‖	PROPN
ejpam-3305	268	15	f	f	PROPN
ejpam-3305	268	16	‖ν=	‖ν=	PROPN
ejpam-3305	268	17	sup	sup	NOUN
ejpam-3305	268	18	x∈[0,∞	x∈[0,∞	NOUN
ejpam-3305	268	19	)	)	PUNCT
ejpam-3305	268	20	|f(x)|	|f(x)|	PROPN
ejpam-3305	268	21	ν(x	ν(x	PROPN
ejpam-3305	268	22	)	)	PUNCT
ejpam-3305	268	23	.	.	PUNCT
ejpam-3305	269	1	theorem	theorem	VERB
ejpam-3305	269	2	7	7	NUM
ejpam-3305	269	3	.	.	X
ejpam-3305	269	4	for	for	ADP
ejpam-3305	269	5	each	each	DET
ejpam-3305	269	6	f	f	PROPN
ejpam-3305	269	7	∈	∈	PROPN
ejpam-3305	269	8	c∗ν	c∗ν	PUNCT
ejpam-3305	270	1	[	[	X
ejpam-3305	270	2	0,∞	0,∞	NOUN
ejpam-3305	270	3	)	)	PUNCT
ejpam-3305	270	4	,	,	PUNCT
ejpam-3305	270	5	we	we	PRON
ejpam-3305	270	6	have	have	VERB
ejpam-3305	270	7	lim	lim	PROPN
ejpam-3305	270	8	n→∞	n→∞	PRON
ejpam-3305	270	9	‖m	‖m	NOUN
ejpam-3305	270	10	(	(	PUNCT
ejpam-3305	270	11	β	β	X
ejpam-3305	270	12	,	,	PUNCT
ejpam-3305	270	13	γ	γ	NOUN
ejpam-3305	270	14	)	)	PUNCT
ejpam-3305	270	15	n	n	CCONJ
ejpam-3305	270	16	,	,	PUNCT
ejpam-3305	270	17	α	α	PROPN
ejpam-3305	270	18	(	(	PUNCT
ejpam-3305	270	19	f)−	f)−	PROPN
ejpam-3305	270	20	f	f	X
ejpam-3305	270	21	‖ν=	‖ν=	PROPN
ejpam-3305	270	22	0	0	NUM
ejpam-3305	270	23	.	.	PUNCT
ejpam-3305	270	24	a.	a.	PROPN
ejpam-3305	270	25	kumar	kumar	PROPN
ejpam-3305	270	26	,	,	PUNCT
ejpam-3305	270	27	d.	d.	PROPN
ejpam-3305	270	28	tapiawala	tapiawala	PROPN
ejpam-3305	270	29	,	,	PUNCT
ejpam-3305	270	30	l.	l.	PROPN
ejpam-3305	270	31	n.	n.	PROPN
ejpam-3305	270	32	mishra	mishra	PROPN
ejpam-3305	270	33	/	/	SYM
ejpam-3305	270	34	eur	eur	PROPN
ejpam-3305	270	35	.	.	PUNCT
ejpam-3305	271	1	j.	j.	PROPN
ejpam-3305	271	2	pure	pure	PROPN
ejpam-3305	271	3	appl	appl	PROPN
ejpam-3305	271	4	.	.	PROPN
ejpam-3305	271	5	math	math	PROPN
ejpam-3305	271	6	,	,	PUNCT
ejpam-3305	271	7	11	11	NUM
ejpam-3305	271	8	(	(	PUNCT
ejpam-3305	271	9	4	4	NUM
ejpam-3305	271	10	)	)	PUNCT
ejpam-3305	271	11	(	(	PUNCT
ejpam-3305	271	12	2018	2018	NUM
ejpam-3305	271	13	)	)	PUNCT
ejpam-3305	271	14	,	,	PUNCT
ejpam-3305	271	15	958	958	NUM
ejpam-3305	271	16	-	-	SYM
ejpam-3305	271	17	975	975	NUM
ejpam-3305	271	18	969	969	NUM
ejpam-3305	271	19	proof	proof	NOUN
ejpam-3305	271	20	.	.	PUNCT
ejpam-3305	272	1	from	from	ADP
ejpam-3305	272	2	[	[	X
ejpam-3305	272	3	6	6	NUM
ejpam-3305	272	4	]	]	PUNCT
ejpam-3305	272	5	,	,	PUNCT
ejpam-3305	272	6	we	we	PRON
ejpam-3305	272	7	know	know	VERB
ejpam-3305	272	8	that	that	SCONJ
ejpam-3305	272	9	it	it	PRON
ejpam-3305	272	10	is	be	AUX
ejpam-3305	272	11	sufficient	sufficient	ADJ
ejpam-3305	272	12	to	to	PART
ejpam-3305	272	13	verify	verify	VERB
ejpam-3305	272	14	the	the	DET
ejpam-3305	272	15	following	follow	VERB
ejpam-3305	272	16	three	three	NUM
ejpam-3305	272	17	conditions	condition	NOUN
ejpam-3305	272	18	lim	lim	PROPN
ejpam-3305	272	19	n→∞	n→∞	PRON
ejpam-3305	272	20	‖m	‖m	NOUN
ejpam-3305	272	21	(	(	PUNCT
ejpam-3305	272	22	β	β	X
ejpam-3305	272	23	,	,	PUNCT
ejpam-3305	272	24	γ	γ	NOUN
ejpam-3305	272	25	)	)	PUNCT
ejpam-3305	272	26	n	n	CCONJ
ejpam-3305	272	27	,	,	PUNCT
ejpam-3305	272	28	α	α	PROPN
ejpam-3305	272	29	(	(	PUNCT
ejpam-3305	272	30	ei)−	ei)−	NOUN
ejpam-3305	272	31	ei	ei	ADP
ejpam-3305	272	32	‖ν=	‖ν=	PROPN
ejpam-3305	272	33	0	0	NUM
ejpam-3305	272	34	,	,	PUNCT
ejpam-3305	272	35	i	i	PRON
ejpam-3305	272	36	=	=	NOUN
ejpam-3305	272	37	0	0	NUM
ejpam-3305	272	38	,	,	PUNCT
ejpam-3305	272	39	1	1	NUM
ejpam-3305	272	40	,	,	PUNCT
ejpam-3305	272	41	2	2	NUM
ejpam-3305	272	42	.	.	PUNCT
ejpam-3305	272	43	(	(	PUNCT
ejpam-3305	272	44	17	17	NUM
ejpam-3305	272	45	)	)	PUNCT
ejpam-3305	272	46	since	since	SCONJ
ejpam-3305	272	47	m	m	PROPN
ejpam-3305	272	48	(	(	PUNCT
ejpam-3305	272	49	β	β	X
ejpam-3305	272	50	,	,	PUNCT
ejpam-3305	272	51	γ	γ	NOUN
ejpam-3305	272	52	)	)	PUNCT
ejpam-3305	272	53	n	n	CCONJ
ejpam-3305	272	54	,	,	PUNCT
ejpam-3305	272	55	α	α	PROPN
ejpam-3305	272	56	(	(	PUNCT
ejpam-3305	272	57	1;x	1;x	NUM
ejpam-3305	272	58	)	)	PUNCT
ejpam-3305	272	59	=	=	SYM
ejpam-3305	272	60	1	1	NUM
ejpam-3305	272	61	,	,	PUNCT
ejpam-3305	272	62	the	the	DET
ejpam-3305	272	63	condition	condition	NOUN
ejpam-3305	272	64	in	in	ADP
ejpam-3305	272	65	(	(	PUNCT
ejpam-3305	272	66	17	17	NUM
ejpam-3305	272	67	)	)	PUNCT
ejpam-3305	272	68	holds	hold	VERB
ejpam-3305	272	69	true	true	ADJ
ejpam-3305	272	70	for	for	ADP
ejpam-3305	272	71	i	i	PROPN
ejpam-3305	272	72	=	=	NOUN
ejpam-3305	272	73	0	0	X
ejpam-3305	272	74	.	.	PUNCT
ejpam-3305	273	1	by	by	ADP
ejpam-3305	273	2	lemma	lemma	PROPN
ejpam-3305	273	3	2	2	NUM
ejpam-3305	273	4	,	,	PUNCT
ejpam-3305	273	5	we	we	PRON
ejpam-3305	273	6	have	have	VERB
ejpam-3305	273	7	‖m	‖m	NOUN
ejpam-3305	273	8	(	(	PUNCT
ejpam-3305	273	9	β	β	X
ejpam-3305	273	10	,	,	PUNCT
ejpam-3305	273	11	γ	γ	NOUN
ejpam-3305	273	12	)	)	PUNCT
ejpam-3305	273	13	n	n	CCONJ
ejpam-3305	273	14	,	,	PUNCT
ejpam-3305	273	15	α	α	PROPN
ejpam-3305	273	16	(	(	PUNCT
ejpam-3305	273	17	t)−	t)−	PROPN
ejpam-3305	273	18	x	x	PUNCT
ejpam-3305	273	19	‖ν	‖ν	NOUN
ejpam-3305	273	20	=	=	NOUN
ejpam-3305	273	21	sup	sup	NOUN
ejpam-3305	273	22	x∈[0,∞	x∈[0,∞	NOUN
ejpam-3305	273	23	)	)	PUNCT
ejpam-3305	274	1	|m	|m	NOUN
ejpam-3305	274	2	(	(	PUNCT
ejpam-3305	274	3	β	β	X
ejpam-3305	274	4	,	,	PUNCT
ejpam-3305	274	5	γ	γ	NOUN
ejpam-3305	274	6	)	)	PUNCT
ejpam-3305	274	7	n	n	CCONJ
ejpam-3305	274	8	,	,	PUNCT
ejpam-3305	274	9	α	α	PROPN
ejpam-3305	274	10	(	(	PUNCT
ejpam-3305	274	11	t;x)−	t;x)−	PROPN
ejpam-3305	274	12	x|	x|	PROPN
ejpam-3305	274	13	1	1	NUM
ejpam-3305	274	14	+	+	CCONJ
ejpam-3305	274	15	x2	x2	ADJ
ejpam-3305	274	16	≤	≤	NUM
ejpam-3305	274	17	γ	γ	X
ejpam-3305	274	18	n+	n+	PUNCT
ejpam-3305	274	19	γ	γ	X
ejpam-3305	274	20	sup	sup	NOUN
ejpam-3305	274	21	x∈[0,∞	x∈[0,∞	NUM
ejpam-3305	274	22	)	)	PUNCT
ejpam-3305	275	1	(	(	PUNCT
ejpam-3305	275	2	x	x	SYM
ejpam-3305	275	3	1	1	NUM
ejpam-3305	275	4	+	+	NUM
ejpam-3305	275	5	x2	x2	NOUN
ejpam-3305	275	6	)	)	PUNCT
ejpam-3305	275	7	+	+	CCONJ
ejpam-3305	275	8	β	β	X
ejpam-3305	275	9	n+	n+	X
ejpam-3305	275	10	γ	γ	X
ejpam-3305	275	11	sup	sup	NOUN
ejpam-3305	275	12	x∈[0,∞	x∈[0,∞	NUM
ejpam-3305	275	13	)	)	PUNCT
ejpam-3305	275	14	(	(	PUNCT
ejpam-3305	275	15	1	1	NUM
ejpam-3305	275	16	1	1	NUM
ejpam-3305	275	17	+	+	NUM
ejpam-3305	275	18	x2	x2	NOUN
ejpam-3305	275	19	)	)	PUNCT
ejpam-3305	275	20	≤	≤	NOUN
ejpam-3305	276	1	β	β	X
ejpam-3305	276	2	+	+	X
ejpam-3305	276	3	γ	γ	X
ejpam-3305	276	4	n+	n+	ADP
ejpam-3305	276	5	γ	γ	NOUN
ejpam-3305	276	6	which	which	PRON
ejpam-3305	276	7	implies	imply	VERB
ejpam-3305	276	8	that	that	SCONJ
ejpam-3305	276	9	lim	lim	PROPN
ejpam-3305	276	10	n→∞	n→∞	PRON
ejpam-3305	276	11	‖m	‖m	NOUN
ejpam-3305	276	12	(	(	PUNCT
ejpam-3305	276	13	β	β	X
ejpam-3305	276	14	,	,	PUNCT
ejpam-3305	276	15	γ	γ	NOUN
ejpam-3305	276	16	)	)	PUNCT
ejpam-3305	276	17	n	n	CCONJ
ejpam-3305	276	18	,	,	PUNCT
ejpam-3305	276	19	α	α	PROPN
ejpam-3305	276	20	(	(	PUNCT
ejpam-3305	276	21	t)−	t)−	PROPN
ejpam-3305	276	22	x	x	SYM
ejpam-3305	276	23	‖ν=	‖ν=	PROPN
ejpam-3305	276	24	0	0	NUM
ejpam-3305	276	25	.	.	PUNCT
ejpam-3305	277	1	again	again	ADV
ejpam-3305	277	2	by	by	ADP
ejpam-3305	277	3	lemma	lemma	PROPN
ejpam-3305	277	4	2	2	NUM
ejpam-3305	277	5	,	,	PUNCT
ejpam-3305	277	6	we	we	PRON
ejpam-3305	277	7	have	have	VERB
ejpam-3305	277	8	‖m	‖m	NOUN
ejpam-3305	277	9	(	(	PUNCT
ejpam-3305	277	10	β	β	X
ejpam-3305	277	11	,	,	PUNCT
ejpam-3305	277	12	γ	γ	NOUN
ejpam-3305	277	13	)	)	PUNCT
ejpam-3305	277	14	n	n	CCONJ
ejpam-3305	277	15	,	,	PUNCT
ejpam-3305	277	16	α	α	X
ejpam-3305	277	17	(	(	PUNCT
ejpam-3305	277	18	t2)−	t2)−	VERB
ejpam-3305	277	19	x2	x2	NOUN
ejpam-3305	277	20	‖ν	‖ν	NOUN
ejpam-3305	277	21	=	=	NOUN
ejpam-3305	277	22	sup	sup	NOUN
ejpam-3305	277	23	x∈[0,∞	x∈[0,∞	NOUN
ejpam-3305	277	24	)	)	PUNCT
ejpam-3305	278	1	|m	|m	NOUN
ejpam-3305	278	2	(	(	PUNCT
ejpam-3305	278	3	β	β	X
ejpam-3305	278	4	,	,	PUNCT
ejpam-3305	278	5	γ	γ	NOUN
ejpam-3305	278	6	)	)	PUNCT
ejpam-3305	278	7	n	n	CCONJ
ejpam-3305	278	8	,	,	PUNCT
ejpam-3305	278	9	α	α	PROPN
ejpam-3305	278	10	(	(	PUNCT
ejpam-3305	278	11	t2;x)−	t2;x)−	NOUN
ejpam-3305	278	12	x2|	x2|	PROPN
ejpam-3305	278	13	1	1	NUM
ejpam-3305	279	1	+	+	NUM
ejpam-3305	279	2	x2	x2	PROPN
ejpam-3305	279	3	≤	≤	PROPN
ejpam-3305	279	4	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3305	279	5	n3(α+	n3(α+	PROPN
ejpam-3305	279	6	1	1	NUM
ejpam-3305	279	7	)	)	PUNCT
ejpam-3305	279	8	α(n−	α(n−	NUM
ejpam-3305	279	9	1)(n+	1)(n+	NUM
ejpam-3305	279	10	γ)2	γ)2	NOUN
ejpam-3305	279	11	−	−	NOUN
ejpam-3305	279	12	1	1	NUM
ejpam-3305	279	13	∣∣∣∣+	∣∣∣∣+	NOUN
ejpam-3305	279	14	∣∣∣∣2n2	∣∣∣∣2n2	NOUN
ejpam-3305	279	15	+	+	CCONJ
ejpam-3305	279	16	2nβ(n−	2nβ(n−	NUM
ejpam-3305	279	17	1	1	NUM
ejpam-3305	279	18	)	)	PUNCT
ejpam-3305	279	19	(	(	PUNCT
ejpam-3305	279	20	n−	n−	NOUN
ejpam-3305	279	21	1)(n+	1)(n+	NUM
ejpam-3305	279	22	γ)2	γ)2	NOUN
ejpam-3305	279	23	∣∣∣∣+	∣∣∣∣+	PROPN
ejpam-3305	279	24	β2	β2	PROPN
ejpam-3305	279	25	(	(	PUNCT
ejpam-3305	279	26	n+	n+	X
ejpam-3305	279	27	γ)2	γ)2	NOUN
ejpam-3305	279	28	,	,	PUNCT
ejpam-3305	279	29	which	which	PRON
ejpam-3305	279	30	implies	imply	VERB
ejpam-3305	279	31	that	that	SCONJ
ejpam-3305	279	32	lim	lim	PROPN
ejpam-3305	279	33	n→∞	n→∞	PRON
ejpam-3305	279	34	‖m	‖m	NOUN
ejpam-3305	279	35	(	(	PUNCT
ejpam-3305	279	36	β	β	X
ejpam-3305	279	37	,	,	PUNCT
ejpam-3305	279	38	γ	γ	NOUN
ejpam-3305	279	39	)	)	PUNCT
ejpam-3305	279	40	n	n	CCONJ
ejpam-3305	279	41	,	,	PUNCT
ejpam-3305	279	42	α	α	X
ejpam-3305	279	43	(	(	PUNCT
ejpam-3305	279	44	t2)−	t2)−	VERB
ejpam-3305	279	45	x2	x2	NOUN
ejpam-3305	279	46	‖ν=	‖ν=	PROPN
ejpam-3305	279	47	0	0	NUM
ejpam-3305	279	48	.	.	PUNCT
ejpam-3305	280	1	this	this	PRON
ejpam-3305	280	2	completes	complete	VERB
ejpam-3305	280	3	the	the	DET
ejpam-3305	280	4	proof	proof	NOUN
ejpam-3305	280	5	of	of	ADP
ejpam-3305	280	6	theorem	theorem	ADJ
ejpam-3305	280	7	.	.	PROPN
ejpam-3305	280	8	3.6	3.6	NUM
ejpam-3305	280	9	.	.	PUNCT
ejpam-3305	281	1	weighted	weight	VERB
ejpam-3305	281	2	lp	lp	ADJ
ejpam-3305	281	3	-	-	PUNCT
ejpam-3305	281	4	approximation	approximation	NOUN
ejpam-3305	281	5	let	let	VERB
ejpam-3305	281	6	w	w	NOUN
ejpam-3305	281	7	be	be	AUX
ejpam-3305	281	8	positive	positive	ADJ
ejpam-3305	281	9	continuous	continuous	ADJ
ejpam-3305	281	10	function	function	NOUN
ejpam-3305	281	11	on	on	ADP
ejpam-3305	281	12	real	real	ADJ
ejpam-3305	281	13	axis	axis	NOUN
ejpam-3305	282	1	[	[	X
ejpam-3305	282	2	0,∞	0,∞	NOUN
ejpam-3305	282	3	)	)	PUNCT
ejpam-3305	282	4	satisfying	satisfy	VERB
ejpam-3305	282	5	the	the	DET
ejpam-3305	282	6	condition∫	condition∫	NOUN
ejpam-3305	282	7	∞	∞	NOUN
ejpam-3305	282	8	0	0	NUM
ejpam-3305	283	1	x2pw(x)dx	x2pw(x)dx	PROPN
ejpam-3305	283	2	<	<	X
ejpam-3305	283	3	∞.	∞.	NOUN
ejpam-3305	283	4	we	we	PRON
ejpam-3305	283	5	denote	denote	VERB
ejpam-3305	283	6	by	by	ADP
ejpam-3305	283	7	lp	lp	NOUN
ejpam-3305	283	8	,	,	PUNCT
ejpam-3305	283	9	w[0,∞)(1	w[0,∞)(1	NOUN
ejpam-3305	283	10	≤	≤	PUNCT
ejpam-3305	284	1	p	p	X
ejpam-3305	284	2	<	<	X
ejpam-3305	284	3	∞	∞	NOUN
ejpam-3305	284	4	)	)	PUNCT
ejpam-3305	284	5	the	the	DET
ejpam-3305	284	6	linear	linear	ADJ
ejpam-3305	284	7	space	space	NOUN
ejpam-3305	284	8	of	of	ADP
ejpam-3305	284	9	p	p	NOUN
ejpam-3305	284	10	-	-	PUNCT
ejpam-3305	284	11	absolutely	absolutely	ADV
ejpam-3305	284	12	integrable	integrable	ADJ
ejpam-3305	284	13	on	on	ADP
ejpam-3305	284	14	[	[	X
ejpam-3305	284	15	0,∞	0,∞	NOUN
ejpam-3305	284	16	)	)	PUNCT
ejpam-3305	284	17	with	with	ADP
ejpam-3305	284	18	respect	respect	NOUN
ejpam-3305	284	19	to	to	ADP
ejpam-3305	284	20	the	the	DET
ejpam-3305	284	21	weight	weight	NOUN
ejpam-3305	284	22	function	function	NOUN
ejpam-3305	284	23	w	w	PROPN
ejpam-3305	284	24	lp	lp	PROPN
ejpam-3305	284	25	,	,	PUNCT
ejpam-3305	284	26	w[0,∞	w[0,∞	NUM
ejpam-3305	284	27	)	)	PUNCT
ejpam-3305	285	1	=	=	PRON
ejpam-3305	285	2	{	{	PUNCT
ejpam-3305	285	3	f	f	X
ejpam-3305	285	4	:	:	PUNCT
ejpam-3305	286	1	[	[	X
ejpam-3305	286	2	0,∞)→	0,∞)→	NOUN
ejpam-3305	286	3	r	r	NOUN
ejpam-3305	286	4	,	,	PUNCT
ejpam-3305	286	5	‖f‖p	‖f‖p	NOUN
ejpam-3305	286	6	,	,	PUNCT
ejpam-3305	286	7	w	w	NOUN
ejpam-3305	286	8	=	=	SYM
ejpam-3305	286	9	(	(	PUNCT
ejpam-3305	286	10	∫	∫	PROPN
ejpam-3305	286	11	∞	∞	PROPN
ejpam-3305	286	12	0	0	NUM
ejpam-3305	286	13	|f(x)|pw(x)dx	|f(x)|pw(x)dx	ADJ
ejpam-3305	286	14	)	)	PUNCT
ejpam-3305	286	15	1	1	NUM
ejpam-3305	287	1	p	p	NOUN
ejpam-3305	287	2	<	<	X
ejpam-3305	287	3	∞	∞	NUM
ejpam-3305	287	4	}	}	PUNCT
ejpam-3305	287	5	.	.	PUNCT
ejpam-3305	288	1	theorem	theorem	ADJ
ejpam-3305	288	2	8	8	NUM
ejpam-3305	288	3	.	.	PUNCT
ejpam-3305	289	1	[	[	X
ejpam-3305	289	2	8	8	NUM
ejpam-3305	289	3	]	]	X
ejpam-3305	289	4	let	let	VERB
ejpam-3305	289	5	(	(	PUNCT
ejpam-3305	289	6	ln)n≥1	ln)n≥1	NOUN
ejpam-3305	289	7	be	be	AUX
ejpam-3305	289	8	a	a	DET
ejpam-3305	289	9	uniformly	uniformly	ADV
ejpam-3305	289	10	bounded	bound	VERB
ejpam-3305	289	11	sequence	sequence	NOUN
ejpam-3305	289	12	of	of	ADP
ejpam-3305	289	13	positive	positive	ADJ
ejpam-3305	289	14	linear	linear	PROPN
ejpam-3305	289	15	operators	operator	NOUN
ejpam-3305	289	16	from	from	ADP
ejpam-3305	289	17	lp	lp	NOUN
ejpam-3305	289	18	,	,	PUNCT
ejpam-3305	289	19	w[0,∞	w[0,∞	NUM
ejpam-3305	289	20	)	)	PUNCT
ejpam-3305	289	21	into	into	ADP
ejpam-3305	289	22	lp	lp	NOUN
ejpam-3305	289	23	,	,	PUNCT
ejpam-3305	289	24	w[0,∞	w[0,∞	NUM
ejpam-3305	289	25	)	)	PUNCT
ejpam-3305	289	26	,	,	PUNCT
ejpam-3305	289	27	satisfying	satisfy	VERB
ejpam-3305	289	28	the	the	DET
ejpam-3305	289	29	conditions	condition	NOUN
ejpam-3305	289	30	lim	lim	PROPN
ejpam-3305	289	31	n→∞	n→∞	PRON
ejpam-3305	289	32	‖	‖	PROPN
ejpam-3305	289	33	ln(tk)−	ln(tk)−	PROPN
ejpam-3305	289	34	xk	xk	PROPN
ejpam-3305	289	35	‖p	‖p	PROPN
ejpam-3305	289	36	,	,	PUNCT
ejpam-3305	289	37	w=	w=	NOUN
ejpam-3305	289	38	0	0	NUM
ejpam-3305	289	39	,	,	PUNCT
ejpam-3305	289	40	k	k	NOUN
ejpam-3305	289	41	=	=	SYM
ejpam-3305	289	42	0	0	NUM
ejpam-3305	289	43	,	,	PUNCT
ejpam-3305	289	44	1	1	NUM
ejpam-3305	289	45	,	,	PUNCT
ejpam-3305	289	46	2	2	NUM
ejpam-3305	289	47	.	.	PUNCT
ejpam-3305	289	48	(	(	PUNCT
ejpam-3305	289	49	18	18	NUM
ejpam-3305	289	50	)	)	PUNCT
ejpam-3305	289	51	then	then	ADV
ejpam-3305	289	52	for	for	ADP
ejpam-3305	289	53	every	every	DET
ejpam-3305	289	54	f	f	PROPN
ejpam-3305	289	55	∈	∈	PROPN
ejpam-3305	289	56	lp	lp	PROPN
ejpam-3305	289	57	,	,	PUNCT
ejpam-3305	289	58	w[0,∞	w[0,∞	NUM
ejpam-3305	289	59	)	)	PUNCT
ejpam-3305	290	1	lim	lim	PROPN
ejpam-3305	290	2	n→∞	n→∞	PRON
ejpam-3305	291	1	‖	‖	PROPN
ejpam-3305	291	2	ln(f)−	ln(f)−	PROPN
ejpam-3305	291	3	f	f	PROPN
ejpam-3305	291	4	‖p	‖p	PROPN
ejpam-3305	291	5	,	,	PUNCT
ejpam-3305	291	6	w=	w=	NOUN
ejpam-3305	291	7	0	0	NUM
ejpam-3305	291	8	.	.	PUNCT
ejpam-3305	291	9	a.	a.	PROPN
ejpam-3305	291	10	kumar	kumar	PROPN
ejpam-3305	291	11	,	,	PUNCT
ejpam-3305	291	12	d.	d.	PROPN
ejpam-3305	291	13	tapiawala	tapiawala	PROPN
ejpam-3305	291	14	,	,	PUNCT
ejpam-3305	291	15	l.	l.	PROPN
ejpam-3305	291	16	n.	n.	PROPN
ejpam-3305	291	17	mishra	mishra	PROPN
ejpam-3305	291	18	/	/	SYM
ejpam-3305	291	19	eur	eur	PROPN
ejpam-3305	291	20	.	.	PUNCT
ejpam-3305	292	1	j.	j.	PROPN
ejpam-3305	292	2	pure	pure	PROPN
ejpam-3305	292	3	appl	appl	PROPN
ejpam-3305	292	4	.	.	PROPN
ejpam-3305	292	5	math	math	PROPN
ejpam-3305	292	6	,	,	PUNCT
ejpam-3305	292	7	11	11	NUM
ejpam-3305	292	8	(	(	PUNCT
ejpam-3305	292	9	4	4	NUM
ejpam-3305	292	10	)	)	PUNCT
ejpam-3305	292	11	(	(	PUNCT
ejpam-3305	292	12	2018	2018	NUM
ejpam-3305	292	13	)	)	PUNCT
ejpam-3305	292	14	,	,	PUNCT
ejpam-3305	292	15	958	958	NUM
ejpam-3305	292	16	-	-	SYM
ejpam-3305	292	17	975	975	NUM
ejpam-3305	292	18	970	970	NUM
ejpam-3305	292	19	now	now	ADV
ejpam-3305	292	20	we	we	PRON
ejpam-3305	292	21	choose	choose	VERB
ejpam-3305	292	22	w(x	w(x	NOUN
ejpam-3305	292	23	)	)	PUNCT
ejpam-3305	292	24	=	=	SYM
ejpam-3305	293	1	1	1	NUM
ejpam-3305	293	2	(	(	PUNCT
ejpam-3305	293	3	1+x2r)p	1+x2r)p	NUM
ejpam-3305	293	4	,	,	PUNCT
ejpam-3305	293	5	1	1	NUM
ejpam-3305	293	6	≤	≤	NOUN
ejpam-3305	293	7	p	p	X
ejpam-3305	293	8	<	<	X
ejpam-3305	293	9	∞	∞	PROPN
ejpam-3305	293	10	and	and	CCONJ
ejpam-3305	293	11	consider	consider	VERB
ejpam-3305	293	12	analogue	analogue	NOUN
ejpam-3305	293	13	weighted	weight	VERB
ejpam-3305	293	14	lp	lp	ADJ
ejpam-3305	293	15	-	-	PUNCT
ejpam-3305	293	16	space	space	NOUN
ejpam-3305	293	17	[	[	X
ejpam-3305	293	18	5	5	NUM
ejpam-3305	293	19	]	]	PUNCT
ejpam-3305	293	20	:	:	PUNCT
ejpam-3305	293	21	lp,2r[0,∞	lp,2r[0,∞	NUM
ejpam-3305	293	22	)	)	PUNCT
ejpam-3305	293	23	=	=	PRON
ejpam-3305	293	24	{	{	PUNCT
ejpam-3305	293	25	f	f	X
ejpam-3305	293	26	:	:	PUNCT
ejpam-3305	294	1	[	[	X
ejpam-3305	294	2	0,∞)→	0,∞)→	NOUN
ejpam-3305	294	3	r	r	NOUN
ejpam-3305	294	4	,	,	PUNCT
ejpam-3305	294	5	‖f‖p,2r	‖f‖p,2r	NOUN
ejpam-3305	294	6	=	=	SYM
ejpam-3305	294	7	(	(	PUNCT
ejpam-3305	294	8	∫	∫	PROPN
ejpam-3305	294	9	∞	∞	PROPN
ejpam-3305	294	10	0	0	NUM
ejpam-3305	294	11	∣∣∣∣	∣∣∣∣	PROPN
ejpam-3305	294	12	f(x	f(x	PROPN
ejpam-3305	294	13	)	)	PUNCT
ejpam-3305	294	14	1	1	NUM
ejpam-3305	295	1	+	+	CCONJ
ejpam-3305	295	2	x2r	x2r	PROPN
ejpam-3305	295	3	∣∣∣∣p	∣∣∣∣p	X
ejpam-3305	295	4	dx	dx	PROPN
ejpam-3305	295	5	)	)	PUNCT
ejpam-3305	295	6	1	1	NUM
ejpam-3305	296	1	p	p	NOUN
ejpam-3305	296	2	<	<	X
ejpam-3305	296	3	∞	∞	NUM
ejpam-3305	296	4	}	}	PUNCT
ejpam-3305	296	5	.	.	PUNCT
ejpam-3305	297	1	theorem	theorem	VERB
ejpam-3305	297	2	9	9	NUM
ejpam-3305	297	3	.	.	PUNCT
ejpam-3305	298	1	for	for	ADP
ejpam-3305	298	2	every	every	DET
ejpam-3305	298	3	f	f	PROPN
ejpam-3305	298	4	∈	∈	PROPN
ejpam-3305	298	5	lp,2r[0,∞	lp,2r[0,∞	NUM
ejpam-3305	298	6	)	)	PUNCT
ejpam-3305	298	7	,	,	PUNCT
ejpam-3305	298	8	r	r	NOUN
ejpam-3305	298	9	>	>	X
ejpam-3305	298	10	1	1	NUM
ejpam-3305	298	11	,	,	PUNCT
ejpam-3305	298	12	we	we	PRON
ejpam-3305	298	13	have	have	VERB
ejpam-3305	298	14	lim	lim	PROPN
ejpam-3305	298	15	n→∞	n→∞	PRON
ejpam-3305	298	16	‖m	‖m	NOUN
ejpam-3305	298	17	(	(	PUNCT
ejpam-3305	298	18	β	β	X
ejpam-3305	298	19	,	,	PUNCT
ejpam-3305	298	20	γ	γ	NOUN
ejpam-3305	298	21	)	)	PUNCT
ejpam-3305	298	22	n	n	CCONJ
ejpam-3305	298	23	,	,	PUNCT
ejpam-3305	298	24	α	α	PROPN
ejpam-3305	298	25	(	(	PUNCT
ejpam-3305	298	26	f)−	f)−	PROPN
ejpam-3305	298	27	f	f	PROPN
ejpam-3305	298	28	‖p,2r=	‖p,2r=	PROPN
ejpam-3305	298	29	0	0	X
ejpam-3305	298	30	.	.	PUNCT
ejpam-3305	299	1	proof	proof	NOUN
ejpam-3305	299	2	.	.	PUNCT
ejpam-3305	300	1	using	use	VERB
ejpam-3305	300	2	the	the	DET
ejpam-3305	300	3	theorem	theorem	NOUN
ejpam-3305	300	4	8	8	NUM
ejpam-3305	300	5	,	,	PUNCT
ejpam-3305	300	6	we	we	PRON
ejpam-3305	300	7	see	see	VERB
ejpam-3305	300	8	that	that	SCONJ
ejpam-3305	300	9	it	it	PRON
ejpam-3305	300	10	is	be	AUX
ejpam-3305	300	11	sufficient	sufficient	ADJ
ejpam-3305	300	12	to	to	PART
ejpam-3305	300	13	verify	verify	VERB
ejpam-3305	300	14	the	the	DET
ejpam-3305	300	15	three	three	NUM
ejpam-3305	300	16	conditions	condition	NOUN
ejpam-3305	300	17	(	(	PUNCT
ejpam-3305	300	18	18	18	NUM
ejpam-3305	300	19	)	)	PUNCT
ejpam-3305	300	20	.	.	PUNCT
ejpam-3305	301	1	since	since	SCONJ
ejpam-3305	301	2	m	m	PROPN
ejpam-3305	301	3	(	(	PUNCT
ejpam-3305	301	4	β	β	X
ejpam-3305	301	5	,	,	PUNCT
ejpam-3305	301	6	γ	γ	NOUN
ejpam-3305	301	7	)	)	PUNCT
ejpam-3305	301	8	n	n	CCONJ
ejpam-3305	301	9	,	,	PUNCT
ejpam-3305	301	10	α	α	PROPN
ejpam-3305	301	11	(	(	PUNCT
ejpam-3305	301	12	1;x	1;x	NUM
ejpam-3305	301	13	)	)	PUNCT
ejpam-3305	301	14	=	=	SYM
ejpam-3305	301	15	1	1	NUM
ejpam-3305	301	16	,	,	PUNCT
ejpam-3305	301	17	the	the	DET
ejpam-3305	301	18	first	first	ADJ
ejpam-3305	301	19	condition	condition	NOUN
ejpam-3305	301	20	is	be	AUX
ejpam-3305	301	21	obvious	obvious	ADJ
ejpam-3305	301	22	for	for	ADP
ejpam-3305	301	23	k	k	PROPN
ejpam-3305	301	24	=	=	SYM
ejpam-3305	301	25	0	0	PROPN
ejpam-3305	301	26	.	.	PUNCT
ejpam-3305	302	1	by	by	ADP
ejpam-3305	302	2	lemma	lemma	PROPN
ejpam-3305	302	3	2	2	NUM
ejpam-3305	302	4	,	,	PUNCT
ejpam-3305	302	5	for	for	ADP
ejpam-3305	302	6	k	k	PROPN
ejpam-3305	302	7	=	=	SYM
ejpam-3305	302	8	1	1	NUM
ejpam-3305	302	9	,	,	PUNCT
ejpam-3305	302	10	we	we	PRON
ejpam-3305	302	11	have(∫	have(∫	VERB
ejpam-3305	302	12	∞	∞	NUM
ejpam-3305	302	13	0	0	PUNCT
ejpam-3305	302	14	∣∣∣∣∣m	∣∣∣∣∣m	PROPN
ejpam-3305	302	15	(	(	PUNCT
ejpam-3305	302	16	β	β	X
ejpam-3305	302	17	,	,	PUNCT
ejpam-3305	302	18	γ	γ	NOUN
ejpam-3305	302	19	)	)	PUNCT
ejpam-3305	302	20	n	n	CCONJ
ejpam-3305	302	21	,	,	PUNCT
ejpam-3305	302	22	α	α	PROPN
ejpam-3305	302	23	(	(	PUNCT
ejpam-3305	302	24	t;x)−	t;x)−	NOUN
ejpam-3305	302	25	x	x	SYM
ejpam-3305	302	26	1	1	NUM
ejpam-3305	302	27	+	+	CCONJ
ejpam-3305	302	28	x2r	x2r	PROPN
ejpam-3305	303	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-3305	303	2	p	p	PROPN
ejpam-3305	303	3	dx	dx	PROPN
ejpam-3305	303	4	)	)	PUNCT
ejpam-3305	303	5	1	1	NUM
ejpam-3305	303	6	p	p	NOUN
ejpam-3305	303	7	≤	≤	NUM
ejpam-3305	303	8	γ	γ	X
ejpam-3305	303	9	n+	n+	PUNCT
ejpam-3305	303	10	γ	γ	X
ejpam-3305	303	11	(	(	PUNCT
ejpam-3305	303	12	∫	∫	PROPN
ejpam-3305	303	13	∞	∞	PROPN
ejpam-3305	303	14	0	0	NUM
ejpam-3305	303	15	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3305	303	16	x	x	SYM
ejpam-3305	303	17	1	1	NUM
ejpam-3305	303	18	+	+	CCONJ
ejpam-3305	303	19	x2r	x2r	PROPN
ejpam-3305	303	20	∣∣∣∣p	∣∣∣∣p	X
ejpam-3305	303	21	dx	dx	PROPN
ejpam-3305	303	22	)	)	PUNCT
ejpam-3305	303	23	1	1	NUM
ejpam-3305	304	1	p	p	NOUN
ejpam-3305	304	2	+	+	X
ejpam-3305	304	3	β	β	X
ejpam-3305	304	4	n+	n+	X
ejpam-3305	304	5	γ	γ	X
ejpam-3305	304	6	(	(	PUNCT
ejpam-3305	304	7	∫	∫	PROPN
ejpam-3305	304	8	∞	∞	PROPN
ejpam-3305	304	9	0	0	NUM
ejpam-3305	304	10	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3305	304	11	1	1	NUM
ejpam-3305	304	12	1	1	NUM
ejpam-3305	304	13	+	+	CCONJ
ejpam-3305	304	14	x2r	x2r	PROPN
ejpam-3305	304	15	∣∣∣∣p	∣∣∣∣p	X
ejpam-3305	304	16	dx	dx	PROPN
ejpam-3305	304	17	)	)	PUNCT
ejpam-3305	304	18	1	1	NUM
ejpam-3305	304	19	p	p	NOUN
ejpam-3305	304	20	which	which	PRON
ejpam-3305	304	21	implies	imply	VERB
ejpam-3305	304	22	that	that	SCONJ
ejpam-3305	304	23	lim	lim	PROPN
ejpam-3305	304	24	n→∞	n→∞	PRON
ejpam-3305	304	25	‖m	‖m	NOUN
ejpam-3305	304	26	(	(	PUNCT
ejpam-3305	304	27	β	β	X
ejpam-3305	304	28	,	,	PUNCT
ejpam-3305	304	29	γ	γ	NOUN
ejpam-3305	304	30	)	)	PUNCT
ejpam-3305	304	31	n	n	CCONJ
ejpam-3305	304	32	,	,	PUNCT
ejpam-3305	304	33	α	α	PROPN
ejpam-3305	304	34	(	(	PUNCT
ejpam-3305	304	35	t)−	t)−	PROPN
ejpam-3305	304	36	x	x	PUNCT
ejpam-3305	304	37	‖p,2r=	‖p,2r=	PROPN
ejpam-3305	304	38	0	0	NUM
ejpam-3305	304	39	.	.	PUNCT
ejpam-3305	305	1	for	for	ADP
ejpam-3305	305	2	k	k	PROPN
ejpam-3305	305	3	=	=	SYM
ejpam-3305	305	4	2	2	NUM
ejpam-3305	305	5	,	,	PUNCT
ejpam-3305	305	6	we	we	PRON
ejpam-3305	305	7	can	can	AUX
ejpam-3305	305	8	write(∫	write(∫	VERB
ejpam-3305	305	9	∞	∞	NUM
ejpam-3305	305	10	0	0	PUNCT
ejpam-3305	306	1	∣∣∣∣∣m	∣∣∣∣∣m	PROPN
ejpam-3305	306	2	(	(	PUNCT
ejpam-3305	306	3	β	β	X
ejpam-3305	306	4	,	,	PUNCT
ejpam-3305	306	5	γ	γ	NOUN
ejpam-3305	306	6	)	)	PUNCT
ejpam-3305	306	7	n	n	CCONJ
ejpam-3305	306	8	,	,	PUNCT
ejpam-3305	306	9	α	α	PROPN
ejpam-3305	306	10	(	(	PUNCT
ejpam-3305	306	11	t2;x)−	t2;x)−	NOUN
ejpam-3305	306	12	x2	x2	NOUN
ejpam-3305	306	13	1	1	NUM
ejpam-3305	306	14	+	+	CCONJ
ejpam-3305	306	15	x2r	x2r	PROPN
ejpam-3305	306	16	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-3305	306	17	p	p	PROPN
ejpam-3305	306	18	dx	dx	PROPN
ejpam-3305	306	19	)	)	PUNCT
ejpam-3305	306	20	1	1	NUM
ejpam-3305	306	21	p	p	NOUN
ejpam-3305	306	22	≤	≤	NOUN
ejpam-3305	306	23	(	(	PUNCT
ejpam-3305	306	24	n3(α+	n3(α+	PROPN
ejpam-3305	306	25	1	1	NUM
ejpam-3305	306	26	)	)	PUNCT
ejpam-3305	306	27	α(n−	α(n−	NUM
ejpam-3305	306	28	1)(n+	1)(n+	NUM
ejpam-3305	306	29	γ)2	γ)2	NOUN
ejpam-3305	306	30	−	−	NOUN
ejpam-3305	306	31	1	1	NUM
ejpam-3305	306	32	)	)	PUNCT
ejpam-3305	306	33	(	(	PUNCT
ejpam-3305	306	34	∫	∫	PROPN
ejpam-3305	306	35	∞	∞	PROPN
ejpam-3305	306	36	0	0	NUM
ejpam-3305	306	37	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3305	306	38	x2	x2	NOUN
ejpam-3305	306	39	1	1	NUM
ejpam-3305	306	40	+	+	CCONJ
ejpam-3305	306	41	x2r	x2r	PROPN
ejpam-3305	306	42	∣∣∣∣p	∣∣∣∣p	X
ejpam-3305	306	43	dx	dx	PROPN
ejpam-3305	306	44	)	)	PUNCT
ejpam-3305	306	45	1	1	NUM
ejpam-3305	306	46	p	p	NOUN
ejpam-3305	306	47	+	+	NOUN
ejpam-3305	306	48	2n2	2n2	NUM
ejpam-3305	306	49	+	+	CCONJ
ejpam-3305	306	50	2nβ(n−	2nβ(n−	NUM
ejpam-3305	306	51	1	1	NUM
ejpam-3305	306	52	)	)	PUNCT
ejpam-3305	306	53	(	(	PUNCT
ejpam-3305	306	54	n−	n−	NOUN
ejpam-3305	306	55	1)(n+	1)(n+	NUM
ejpam-3305	306	56	γ)2	γ)2	NOUN
ejpam-3305	306	57	(	(	PUNCT
ejpam-3305	306	58	∫	∫	PROPN
ejpam-3305	306	59	∞	∞	PROPN
ejpam-3305	306	60	0	0	NUM
ejpam-3305	307	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3305	307	2	x	x	SYM
ejpam-3305	307	3	1	1	NUM
ejpam-3305	307	4	+	+	CCONJ
ejpam-3305	307	5	x2r	x2r	PROPN
ejpam-3305	307	6	∣∣∣∣p	∣∣∣∣p	X
ejpam-3305	307	7	dx	dx	PROPN
ejpam-3305	307	8	)	)	PUNCT
ejpam-3305	307	9	1	1	NUM
ejpam-3305	308	1	p	p	NOUN
ejpam-3305	308	2	+	+	NUM
ejpam-3305	308	3	β2	β2	NOUN
ejpam-3305	308	4	(	(	PUNCT
ejpam-3305	308	5	n+	n+	X
ejpam-3305	308	6	γ)2	γ)2	NOUN
ejpam-3305	308	7	(	(	PUNCT
ejpam-3305	308	8	∫	∫	PROPN
ejpam-3305	308	9	∞	∞	PROPN
ejpam-3305	308	10	0	0	NUM
ejpam-3305	308	11	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3305	308	12	1	1	NUM
ejpam-3305	308	13	1	1	NUM
ejpam-3305	308	14	+	+	CCONJ
ejpam-3305	308	15	x2r	x2r	PROPN
ejpam-3305	308	16	∣∣∣∣p	∣∣∣∣p	X
ejpam-3305	308	17	dx	dx	PROPN
ejpam-3305	308	18	)	)	PUNCT
ejpam-3305	308	19	1	1	NUM
ejpam-3305	308	20	p	p	NOUN
ejpam-3305	308	21	which	which	PRON
ejpam-3305	308	22	implies	imply	VERB
ejpam-3305	308	23	that	that	SCONJ
ejpam-3305	308	24	lim	lim	PROPN
ejpam-3305	308	25	n→∞	n→∞	PRON
ejpam-3305	308	26	‖m	‖m	NOUN
ejpam-3305	308	27	(	(	PUNCT
ejpam-3305	308	28	β	β	X
ejpam-3305	308	29	,	,	PUNCT
ejpam-3305	308	30	γ	γ	NOUN
ejpam-3305	308	31	)	)	PUNCT
ejpam-3305	308	32	n	n	CCONJ
ejpam-3305	308	33	,	,	PUNCT
ejpam-3305	308	34	α	α	X
ejpam-3305	308	35	(	(	PUNCT
ejpam-3305	308	36	t2)−	t2)−	VERB
ejpam-3305	308	37	x2	x2	PROPN
ejpam-3305	308	38	‖p,2r=	‖p,2r=	PROPN
ejpam-3305	308	39	0	0	X
ejpam-3305	308	40	.	.	PUNCT
ejpam-3305	309	1	this	this	PRON
ejpam-3305	309	2	completes	complete	VERB
ejpam-3305	309	3	the	the	DET
ejpam-3305	309	4	proof	proof	NOUN
ejpam-3305	309	5	of	of	ADP
ejpam-3305	309	6	theorem	theorem	PROPN
ejpam-3305	309	7	.	.	PROPN
ejpam-3305	309	8	4	4	X
ejpam-3305	309	9	.	.	X
ejpam-3305	309	10	king	king	NOUN
ejpam-3305	309	11	type	type	NOUN
ejpam-3305	309	12	modification	modification	NOUN
ejpam-3305	309	13	in	in	ADP
ejpam-3305	309	14	this	this	DET
ejpam-3305	309	15	section	section	NOUN
ejpam-3305	309	16	,	,	PUNCT
ejpam-3305	309	17	we	we	PRON
ejpam-3305	309	18	discuss	discuss	VERB
ejpam-3305	309	19	better	well	ADJ
ejpam-3305	309	20	convergence	convergence	NOUN
ejpam-3305	309	21	rates	rate	NOUN
ejpam-3305	309	22	by	by	ADP
ejpam-3305	309	23	king	king	NOUN
ejpam-3305	309	24	type	type	NOUN
ejpam-3305	309	25	operators	operator	NOUN
ejpam-3305	309	26	.	.	PUNCT
ejpam-3305	310	1	to	to	PART
ejpam-3305	310	2	make	make	VERB
ejpam-3305	310	3	the	the	DET
ejpam-3305	310	4	convergence	convergence	NOUN
ejpam-3305	310	5	faster	fast	ADV
ejpam-3305	310	6	,	,	PUNCT
ejpam-3305	310	7	king	king	NOUN
ejpam-3305	310	8	[	[	X
ejpam-3305	310	9	26	26	NUM
ejpam-3305	310	10	]	]	PUNCT
ejpam-3305	310	11	proposed	propose	VERB
ejpam-3305	310	12	an	an	DET
ejpam-3305	310	13	approach	approach	NOUN
ejpam-3305	310	14	to	to	PART
ejpam-3305	310	15	modify	modify	VERB
ejpam-3305	310	16	the	the	DET
ejpam-3305	310	17	classical	classical	ADJ
ejpam-3305	310	18	bernstein	bernstein	PROPN
ejpam-3305	310	19	polynomial	polynomial	PROPN
ejpam-3305	310	20	,	,	PUNCT
ejpam-3305	310	21	so	so	SCONJ
ejpam-3305	310	22	that	that	SCONJ
ejpam-3305	310	23	the	the	DET
ejpam-3305	310	24	sequence	sequence	NOUN
ejpam-3305	310	25	preserve	preserve	VERB
ejpam-3305	310	26	test	test	NOUN
ejpam-3305	310	27	functions	function	NOUN
ejpam-3305	310	28	e0	e0	PROPN
ejpam-3305	310	29	and	and	CCONJ
ejpam-3305	310	30	e2	e2	PROPN
ejpam-3305	310	31	,	,	PUNCT
ejpam-3305	310	32	where	where	SCONJ
ejpam-3305	310	33	ei(t	ei(t	NUM
ejpam-3305	310	34	)	)	PUNCT
ejpam-3305	311	1	=	=	SYM
ejpam-3305	311	2	ti	ti	X
ejpam-3305	311	3	,	,	PUNCT
ejpam-3305	311	4	i	i	NOUN
ejpam-3305	311	5	=	=	NOUN
ejpam-3305	311	6	0	0	NUM
ejpam-3305	311	7	,	,	PUNCT
ejpam-3305	311	8	1	1	NUM
ejpam-3305	311	9	,	,	PUNCT
ejpam-3305	311	10	2	2	NUM
ejpam-3305	311	11	.	.	PUNCT
ejpam-3305	312	1	after	after	ADP
ejpam-3305	312	2	this	this	DET
ejpam-3305	312	3	approach	approach	NOUN
ejpam-3305	312	4	many	many	ADJ
ejpam-3305	312	5	researcher	researcher	NOUN
ejpam-3305	312	6	contributed	contribute	VERB
ejpam-3305	312	7	in	in	ADP
ejpam-3305	312	8	this	this	DET
ejpam-3305	312	9	direction	direction	NOUN
ejpam-3305	312	10	.	.	PUNCT
ejpam-3305	313	1	as	as	ADP
ejpam-3305	313	2	the	the	DET
ejpam-3305	313	3	operator	operator	NOUN
ejpam-3305	313	4	m	m	PROPN
ejpam-3305	313	5	(	(	PUNCT
ejpam-3305	313	6	β	β	X
ejpam-3305	313	7	,	,	PUNCT
ejpam-3305	313	8	γ	γ	NOUN
ejpam-3305	313	9	)	)	PUNCT
ejpam-3305	313	10	n	n	CCONJ
ejpam-3305	313	11	,	,	PUNCT
ejpam-3305	313	12	α	α	PROPN
ejpam-3305	313	13	(	(	PUNCT
ejpam-3305	313	14	f	f	NOUN
ejpam-3305	313	15	;	;	PUNCT
ejpam-3305	313	16	x	x	X
ejpam-3305	313	17	)	)	PUNCT
ejpam-3305	313	18	defined	define	VERB
ejpam-3305	313	19	in	in	ADP
ejpam-3305	313	20	(	(	PUNCT
ejpam-3305	313	21	3	3	X
ejpam-3305	313	22	)	)	PUNCT
ejpam-3305	313	23	preserve	preserve	VERB
ejpam-3305	313	24	only	only	ADV
ejpam-3305	313	25	the	the	DET
ejpam-3305	313	26	constant	constant	ADJ
ejpam-3305	313	27	functions	function	NOUN
ejpam-3305	313	28	so	so	ADV
ejpam-3305	313	29	further	further	ADJ
ejpam-3305	313	30	modification	modification	NOUN
ejpam-3305	313	31	of	of	ADP
ejpam-3305	313	32	these	these	DET
ejpam-3305	313	33	operators	operator	NOUN
ejpam-3305	313	34	is	be	AUX
ejpam-3305	313	35	proposed	propose	VERB
ejpam-3305	313	36	to	to	PART
ejpam-3305	313	37	be	be	AUX
ejpam-3305	313	38	made	make	VERB
ejpam-3305	313	39	so	so	SCONJ
ejpam-3305	313	40	that	that	SCONJ
ejpam-3305	313	41	the	the	DET
ejpam-3305	313	42	modified	modify	VERB
ejpam-3305	313	43	operators	operator	NOUN
ejpam-3305	313	44	a.	a.	PROPN
ejpam-3305	313	45	kumar	kumar	PROPN
ejpam-3305	313	46	,	,	PUNCT
ejpam-3305	313	47	d.	d.	PROPN
ejpam-3305	313	48	tapiawala	tapiawala	PROPN
ejpam-3305	313	49	,	,	PUNCT
ejpam-3305	313	50	l.	l.	PROPN
ejpam-3305	313	51	n.	n.	PROPN
ejpam-3305	313	52	mishra	mishra	PROPN
ejpam-3305	313	53	/	/	SYM
ejpam-3305	313	54	eur	eur	PROPN
ejpam-3305	313	55	.	.	PUNCT
ejpam-3305	314	1	j.	j.	PROPN
ejpam-3305	314	2	pure	pure	PROPN
ejpam-3305	314	3	appl	appl	PROPN
ejpam-3305	314	4	.	.	PROPN
ejpam-3305	314	5	math	math	PROPN
ejpam-3305	314	6	,	,	PUNCT
ejpam-3305	314	7	11	11	NUM
ejpam-3305	314	8	(	(	PUNCT
ejpam-3305	314	9	4	4	NUM
ejpam-3305	314	10	)	)	PUNCT
ejpam-3305	314	11	(	(	PUNCT
ejpam-3305	314	12	2018	2018	NUM
ejpam-3305	314	13	)	)	PUNCT
ejpam-3305	314	14	,	,	PUNCT
ejpam-3305	314	15	958	958	NUM
ejpam-3305	314	16	-	-	SYM
ejpam-3305	314	17	975	975	NUM
ejpam-3305	314	18	971	971	NUM
ejpam-3305	314	19	preserve	preserve	VERB
ejpam-3305	314	20	the	the	DET
ejpam-3305	314	21	constant	constant	ADJ
ejpam-3305	314	22	as	as	ADV
ejpam-3305	314	23	well	well	ADV
ejpam-3305	314	24	as	as	ADP
ejpam-3305	314	25	linear	linear	ADJ
ejpam-3305	314	26	functions	function	NOUN
ejpam-3305	314	27	.	.	PUNCT
ejpam-3305	315	1	for	for	ADP
ejpam-3305	315	2	this	this	DET
ejpam-3305	315	3	purpose	purpose	NOUN
ejpam-3305	315	4	the	the	DET
ejpam-3305	315	5	modification	modification	NOUN
ejpam-3305	315	6	of	of	ADP
ejpam-3305	315	7	(	(	PUNCT
ejpam-3305	315	8	3	3	NUM
ejpam-3305	315	9	)	)	PUNCT
ejpam-3305	315	10	is	be	AUX
ejpam-3305	315	11	defined	define	VERB
ejpam-3305	315	12	as	as	ADP
ejpam-3305	315	13	m̂	m̂	PROPN
ejpam-3305	315	14	(	(	PUNCT
ejpam-3305	315	15	β	β	X
ejpam-3305	315	16	,	,	PUNCT
ejpam-3305	315	17	γ	γ	NOUN
ejpam-3305	315	18	)	)	PUNCT
ejpam-3305	315	19	n	n	CCONJ
ejpam-3305	315	20	,	,	PUNCT
ejpam-3305	315	21	α	α	PROPN
ejpam-3305	315	22	(	(	PUNCT
ejpam-3305	315	23	f	f	NOUN
ejpam-3305	315	24	;	;	PUNCT
ejpam-3305	315	25	x	x	X
ejpam-3305	315	26	)	)	PUNCT
ejpam-3305	315	27	=	=	PUNCT
ejpam-3305	316	1	∞∑	∞∑	NUM
ejpam-3305	316	2	k=1	k=1	PUNCT
ejpam-3305	316	3	m	m	VERB
ejpam-3305	316	4	(	(	PUNCT
ejpam-3305	316	5	α	α	NOUN
ejpam-3305	316	6	)	)	PUNCT
ejpam-3305	316	7	n	n	CCONJ
ejpam-3305	316	8	,	,	PUNCT
ejpam-3305	316	9	k(rn(x	k(rn(x	PROPN
ejpam-3305	316	10	)	)	PUNCT
ejpam-3305	316	11	)	)	PUNCT
ejpam-3305	317	1	∫	∫	PROPN
ejpam-3305	318	1	∞	∞	PROPN
ejpam-3305	318	2	0	0	NUM
ejpam-3305	318	3	bn	bn	PROPN
ejpam-3305	318	4	,	,	PUNCT
ejpam-3305	318	5	k(t)f	k(t)f	PROPN
ejpam-3305	318	6	(	(	PUNCT
ejpam-3305	318	7	nt+	nt+	NOUN
ejpam-3305	318	8	β	β	X
ejpam-3305	318	9	n+	n+	X
ejpam-3305	318	10	γ	γ	X
ejpam-3305	318	11	)	)	PUNCT
ejpam-3305	318	12	dt	dt	PROPN
ejpam-3305	319	1	+	+	CCONJ
ejpam-3305	319	2	(	(	PUNCT
ejpam-3305	319	3	α	α	X
ejpam-3305	319	4	α+	α+	X
ejpam-3305	319	5	nrn(x	nrn(x	NOUN
ejpam-3305	319	6	)	)	PUNCT
ejpam-3305	319	7	)	)	PUNCT
ejpam-3305	320	1	α	α	PRON
ejpam-3305	320	2	f	f	X
ejpam-3305	320	3	(	(	PUNCT
ejpam-3305	320	4	β	β	X
ejpam-3305	320	5	n+	n+	X
ejpam-3305	320	6	γ	γ	X
ejpam-3305	320	7	)	)	PUNCT
ejpam-3305	320	8	(	(	PUNCT
ejpam-3305	320	9	19	19	NUM
ejpam-3305	320	10	)	)	PUNCT
ejpam-3305	320	11	where	where	SCONJ
ejpam-3305	320	12	rn(x	rn(x	X
ejpam-3305	320	13	)	)	PUNCT
ejpam-3305	320	14	=	=	SYM
ejpam-3305	320	15	(	(	PUNCT
ejpam-3305	320	16	n+γ)x−β	n+γ)x−β	NUM
ejpam-3305	320	17	n	n	NOUN
ejpam-3305	320	18	and	and	CCONJ
ejpam-3305	320	19	x	x	PUNCT
ejpam-3305	320	20	∈	∈	NOUN
ejpam-3305	320	21	in	in	ADP
ejpam-3305	320	22	=	=	PUNCT
ejpam-3305	320	23	[	[	PUNCT
ejpam-3305	320	24	β	β	X
ejpam-3305	320	25	n+γ	n+γ	NUM
ejpam-3305	320	26	,	,	PUNCT
ejpam-3305	320	27	∞	∞	PROPN
ejpam-3305	320	28	)	)	PUNCT
ejpam-3305	320	29	.	.	PUNCT
ejpam-3305	321	1	lemma	lemma	PROPN
ejpam-3305	321	2	4	4	NUM
ejpam-3305	321	3	.	.	PUNCT
ejpam-3305	322	1	for	for	ADP
ejpam-3305	322	2	every	every	DET
ejpam-3305	322	3	x	x	SYM
ejpam-3305	322	4	∈	∈	PROPN
ejpam-3305	322	5	in	in	ADV
ejpam-3305	322	6	,	,	PUNCT
ejpam-3305	322	7	we	we	PRON
ejpam-3305	322	8	have	have	VERB
ejpam-3305	322	9	(	(	PUNCT
ejpam-3305	322	10	i	i	NOUN
ejpam-3305	322	11	)	)	PUNCT
ejpam-3305	322	12	m̂	m̂	PROPN
ejpam-3305	323	1	(	(	PUNCT
ejpam-3305	323	2	β	β	X
ejpam-3305	323	3	,	,	PUNCT
ejpam-3305	323	4	γ	γ	NOUN
ejpam-3305	323	5	)	)	PUNCT
ejpam-3305	323	6	n	n	CCONJ
ejpam-3305	323	7	,	,	PUNCT
ejpam-3305	323	8	α	α	PROPN
ejpam-3305	323	9	(	(	PUNCT
ejpam-3305	323	10	1;x	1;x	NUM
ejpam-3305	323	11	)	)	PUNCT
ejpam-3305	323	12	=	=	SYM
ejpam-3305	323	13	1	1	NUM
ejpam-3305	323	14	,	,	PUNCT
ejpam-3305	323	15	(	(	PUNCT
ejpam-3305	323	16	ii	ii	NOUN
ejpam-3305	323	17	)	)	PUNCT
ejpam-3305	323	18	m̂	m̂	PROPN
ejpam-3305	323	19	(	(	PUNCT
ejpam-3305	323	20	β	β	X
ejpam-3305	323	21	,	,	PUNCT
ejpam-3305	323	22	γ	γ	NOUN
ejpam-3305	323	23	)	)	PUNCT
ejpam-3305	323	24	n	n	CCONJ
ejpam-3305	323	25	,	,	PUNCT
ejpam-3305	323	26	α	α	PROPN
ejpam-3305	323	27	(	(	PUNCT
ejpam-3305	323	28	t;x	t;x	NUM
ejpam-3305	323	29	)	)	PUNCT
ejpam-3305	323	30	=	=	SYM
ejpam-3305	324	1	x	x	X
ejpam-3305	324	2	,	,	PUNCT
ejpam-3305	324	3	(	(	PUNCT
ejpam-3305	324	4	iii	iii	NOUN
ejpam-3305	324	5	)	)	PUNCT
ejpam-3305	324	6	m̂	m̂	NOUN
ejpam-3305	324	7	(	(	PUNCT
ejpam-3305	324	8	β	β	X
ejpam-3305	324	9	,	,	PUNCT
ejpam-3305	324	10	γ	γ	NOUN
ejpam-3305	324	11	)	)	PUNCT
ejpam-3305	324	12	n	n	CCONJ
ejpam-3305	324	13	,	,	PUNCT
ejpam-3305	324	14	α	α	PROPN
ejpam-3305	324	15	(	(	PUNCT
ejpam-3305	324	16	t2;x	t2;x	PROPN
ejpam-3305	324	17	)	)	PUNCT
ejpam-3305	324	18	=	=	PUNCT
ejpam-3305	325	1	n(α+	n(α+	NUM
ejpam-3305	325	2	1)x2	1)x2	NOUN
ejpam-3305	325	3	α(n−	α(n−	NUM
ejpam-3305	325	4	1	1	NUM
ejpam-3305	325	5	)	)	PUNCT
ejpam-3305	325	6	+	+	CCONJ
ejpam-3305	325	7	(	(	PUNCT
ejpam-3305	325	8	2nα−	2nα−	NUM
ejpam-3305	325	9	2αβ	2αβ	NOUN
ejpam-3305	325	10	−	−	PROPN
ejpam-3305	325	11	2nβ)x	2nβ)x	NOUN
ejpam-3305	325	12	α(n−	α(n−	VERB
ejpam-3305	325	13	1)(n+	1)(n+	NUM
ejpam-3305	325	14	γ	γ	NOUN
ejpam-3305	325	15	)	)	PUNCT
ejpam-3305	326	1	+	+	NUM
ejpam-3305	326	2	nβ2	nβ2	PROPN
ejpam-3305	327	1	+	+	CCONJ
ejpam-3305	327	2	αβ2	αβ2	ADJ
ejpam-3305	327	3	−	−	PROPN
ejpam-3305	328	1	2nαβ	2nαβ	NUM
ejpam-3305	328	2	α(n−	α(n−	NUM
ejpam-3305	328	3	1)(n+	1)(n+	NUM
ejpam-3305	328	4	γ)2	γ)2	NOUN
ejpam-3305	328	5	.	.	PUNCT
ejpam-3305	329	1	consequently	consequently	ADV
ejpam-3305	329	2	,	,	PUNCT
ejpam-3305	329	3	for	for	ADP
ejpam-3305	329	4	each	each	DET
ejpam-3305	329	5	x	x	SYM
ejpam-3305	329	6	∈	∈	PROPN
ejpam-3305	329	7	in	in	ADV
ejpam-3305	329	8	,	,	PUNCT
ejpam-3305	329	9	we	we	PRON
ejpam-3305	329	10	have	have	VERB
ejpam-3305	329	11	the	the	DET
ejpam-3305	329	12	following	follow	VERB
ejpam-3305	329	13	equalities	equality	NOUN
ejpam-3305	329	14	m̂	m̂	PROPN
ejpam-3305	329	15	(	(	PUNCT
ejpam-3305	329	16	β	β	X
ejpam-3305	329	17	,	,	PUNCT
ejpam-3305	329	18	γ	γ	NOUN
ejpam-3305	329	19	)	)	PUNCT
ejpam-3305	329	20	n	n	CCONJ
ejpam-3305	329	21	,	,	PUNCT
ejpam-3305	329	22	α	α	X
ejpam-3305	329	23	(	(	PUNCT
ejpam-3305	329	24	(	(	PUNCT
ejpam-3305	329	25	t−	t−	PROPN
ejpam-3305	329	26	x);x	x);x	PROPN
ejpam-3305	329	27	)	)	PUNCT
ejpam-3305	329	28	=	=	PUNCT
ejpam-3305	329	29	0	0	NUM
ejpam-3305	329	30	m̂	m̂	PROPN
ejpam-3305	329	31	(	(	PUNCT
ejpam-3305	329	32	β	β	X
ejpam-3305	329	33	,	,	PUNCT
ejpam-3305	329	34	γ	γ	NOUN
ejpam-3305	329	35	)	)	PUNCT
ejpam-3305	329	36	n	n	CCONJ
ejpam-3305	329	37	,	,	PUNCT
ejpam-3305	329	38	α	α	X
ejpam-3305	329	39	(	(	PUNCT
ejpam-3305	329	40	(	(	PUNCT
ejpam-3305	329	41	t−	t−	PROPN
ejpam-3305	329	42	x)2;x	x)2;x	NUM
ejpam-3305	329	43	)	)	PUNCT
ejpam-3305	329	44	=	=	SYM
ejpam-3305	330	1	(	(	PUNCT
ejpam-3305	330	2	n+	n+	NUM
ejpam-3305	330	3	α)x2	α)x2	NOUN
ejpam-3305	330	4	α(n−	α(n−	NUM
ejpam-3305	330	5	1	1	NUM
ejpam-3305	330	6	)	)	PUNCT
ejpam-3305	330	7	+	+	CCONJ
ejpam-3305	330	8	(	(	PUNCT
ejpam-3305	330	9	2nα−	2nα−	NUM
ejpam-3305	330	10	2αβ	2αβ	NOUN
ejpam-3305	330	11	−	−	PROPN
ejpam-3305	330	12	2nβ)x	2nβ)x	NOUN
ejpam-3305	330	13	α(n−	α(n−	VERB
ejpam-3305	330	14	1)(n+	1)(n+	NUM
ejpam-3305	330	15	γ	γ	NOUN
ejpam-3305	330	16	)	)	PUNCT
ejpam-3305	331	1	+	+	NUM
ejpam-3305	331	2	nβ2	nβ2	PROPN
ejpam-3305	332	1	+	+	CCONJ
ejpam-3305	332	2	αβ2	αβ2	ADJ
ejpam-3305	332	3	−	−	PROPN
ejpam-3305	333	1	2nαβ	2nαβ	NUM
ejpam-3305	333	2	α(n−	α(n−	NUM
ejpam-3305	333	3	1)(n+	1)(n+	NUM
ejpam-3305	333	4	γ)2	γ)2	NOUN
ejpam-3305	333	5	=	=	SYM
ejpam-3305	333	6	λ(β	λ(β	PROPN
ejpam-3305	333	7	,	,	PUNCT
ejpam-3305	333	8	γ)n	γ)n	X
ejpam-3305	333	9	,	,	PUNCT
ejpam-3305	333	10	α	α	PROPN
ejpam-3305	333	11	(	(	PUNCT
ejpam-3305	333	12	x	x	NOUN
ejpam-3305	333	13	)	)	PUNCT
ejpam-3305	333	14	.	.	PUNCT
ejpam-3305	334	1	(	(	PUNCT
ejpam-3305	334	2	20	20	NUM
ejpam-3305	334	3	)	)	PUNCT
ejpam-3305	334	4	theorem	theorem	VERB
ejpam-3305	334	5	10	10	NUM
ejpam-3305	334	6	.	.	PUNCT
ejpam-3305	335	1	for	for	ADP
ejpam-3305	335	2	f	f	PROPN
ejpam-3305	335	3	∈	∈	PROPN
ejpam-3305	335	4	cb(in	cb(in	PROPN
ejpam-3305	335	5	)	)	PUNCT
ejpam-3305	335	6	,	,	PUNCT
ejpam-3305	335	7	we	we	PRON
ejpam-3305	335	8	have	have	VERB
ejpam-3305	335	9	|m̂	|m̂	VERB
ejpam-3305	335	10	(	(	PUNCT
ejpam-3305	335	11	β	β	X
ejpam-3305	335	12	,	,	PUNCT
ejpam-3305	335	13	γ	γ	NOUN
ejpam-3305	335	14	)	)	PUNCT
ejpam-3305	335	15	n	n	CCONJ
ejpam-3305	335	16	,	,	PUNCT
ejpam-3305	335	17	α	α	PROPN
ejpam-3305	335	18	(	(	PUNCT
ejpam-3305	335	19	f	f	X
ejpam-3305	335	20	;	;	PUNCT
ejpam-3305	335	21	x)−	x)−	PROPN
ejpam-3305	335	22	f(x)|	f(x)|	VERB
ejpam-3305	335	23	≤m	≤m	PROPN
ejpam-3305	335	24	′ω2	′ω2	NUM
ejpam-3305	335	25	(	(	PUNCT
ejpam-3305	335	26	f	f	X
ejpam-3305	335	27	,	,	PUNCT
ejpam-3305	335	28	√	√	PROPN
ejpam-3305	335	29	λ	λ	PROPN
ejpam-3305	335	30	(	(	PUNCT
ejpam-3305	335	31	β	β	X
ejpam-3305	335	32	,	,	PUNCT
ejpam-3305	335	33	γ	γ	NOUN
ejpam-3305	335	34	)	)	PUNCT
ejpam-3305	335	35	n	n	CCONJ
ejpam-3305	335	36	,	,	PUNCT
ejpam-3305	335	37	α	α	PROPN
ejpam-3305	335	38	(	(	PUNCT
ejpam-3305	335	39	x	x	NOUN
ejpam-3305	335	40	)	)	PUNCT
ejpam-3305	335	41	)	)	PUNCT
ejpam-3305	335	42	,	,	PUNCT
ejpam-3305	335	43	where	where	SCONJ
ejpam-3305	335	44	λ	λ	X
ejpam-3305	335	45	(	(	PUNCT
ejpam-3305	335	46	β	β	X
ejpam-3305	335	47	,	,	PUNCT
ejpam-3305	335	48	γ	γ	NOUN
ejpam-3305	335	49	)	)	PUNCT
ejpam-3305	335	50	n	n	CCONJ
ejpam-3305	335	51	,	,	PUNCT
ejpam-3305	335	52	α	α	PROPN
ejpam-3305	335	53	(	(	PUNCT
ejpam-3305	335	54	x	x	NOUN
ejpam-3305	335	55	)	)	PUNCT
ejpam-3305	335	56	is	be	AUX
ejpam-3305	335	57	given	give	VERB
ejpam-3305	335	58	by	by	ADP
ejpam-3305	335	59	(	(	PUNCT
ejpam-3305	335	60	20	20	NUM
ejpam-3305	335	61	)	)	PUNCT
ejpam-3305	335	62	and	and	CCONJ
ejpam-3305	335	63	m	m	AUX
ejpam-3305	335	64	′	′	NUM
ejpam-3305	335	65	is	be	AUX
ejpam-3305	335	66	a	a	DET
ejpam-3305	335	67	positive	positive	ADJ
ejpam-3305	335	68	constant	constant	NOUN
ejpam-3305	335	69	.	.	PUNCT
ejpam-3305	336	1	proof	proof	NOUN
ejpam-3305	336	2	.	.	PUNCT
ejpam-3305	337	1	let	let	VERB
ejpam-3305	337	2	g	g	PROPN
ejpam-3305	337	3	∈w	∈w	NOUN
ejpam-3305	337	4	2	2	NUM
ejpam-3305	337	5	and	and	CCONJ
ejpam-3305	337	6	x	x	NOUN
ejpam-3305	337	7	,	,	PUNCT
ejpam-3305	337	8	t	t	PROPN
ejpam-3305	337	9	∈	∈	PROPN
ejpam-3305	337	10	in	in	ADP
ejpam-3305	337	11	.	.	PUNCT
ejpam-3305	338	1	using	use	VERB
ejpam-3305	338	2	the	the	DET
ejpam-3305	338	3	taylor	taylor	PROPN
ejpam-3305	338	4	’s	’s	PART
ejpam-3305	338	5	expansion	expansion	NOUN
ejpam-3305	338	6	we	we	PRON
ejpam-3305	338	7	have	have	VERB
ejpam-3305	338	8	g(t	g(t	PROPN
ejpam-3305	338	9	)	)	PUNCT
ejpam-3305	339	1	=	=	SYM
ejpam-3305	339	2	g(x	g(x	NOUN
ejpam-3305	339	3	)	)	PUNCT
ejpam-3305	340	1	+	+	CCONJ
ejpam-3305	340	2	(	(	PUNCT
ejpam-3305	340	3	t−	t−	PROPN
ejpam-3305	340	4	x)g′(x	x)g′(x	PROPN
ejpam-3305	340	5	)	)	PUNCT
ejpam-3305	341	1	+	+	NUM
ejpam-3305	341	2	∫	∫	PROPN
ejpam-3305	341	3	t	t	NOUN
ejpam-3305	341	4	x	x	X
ejpam-3305	341	5	(	(	PUNCT
ejpam-3305	341	6	t−	t−	PROPN
ejpam-3305	341	7	v)g′′(v)dv	v)g′′(v)dv	PROPN
ejpam-3305	341	8	.	.	PUNCT
ejpam-3305	342	1	applying	apply	VERB
ejpam-3305	342	2	m̂	m̂	PROPN
ejpam-3305	342	3	(	(	PUNCT
ejpam-3305	342	4	β	β	X
ejpam-3305	342	5	,	,	PUNCT
ejpam-3305	342	6	γ	γ	NOUN
ejpam-3305	342	7	)	)	PUNCT
ejpam-3305	342	8	n	n	CCONJ
ejpam-3305	342	9	,	,	PUNCT
ejpam-3305	342	10	α	α	NOUN
ejpam-3305	342	11	on	on	ADP
ejpam-3305	342	12	both	both	DET
ejpam-3305	342	13	sides	side	NOUN
ejpam-3305	342	14	and	and	CCONJ
ejpam-3305	342	15	using	use	VERB
ejpam-3305	342	16	lemma	lemma	PROPN
ejpam-3305	342	17	?	?	PUNCT
ejpam-3305	342	18	?	?	PUNCT
ejpam-3305	342	19	,	,	PUNCT
ejpam-3305	342	20	we	we	PRON
ejpam-3305	342	21	get	get	VERB
ejpam-3305	342	22	m̂	m̂	NOUN
ejpam-3305	342	23	(	(	PUNCT
ejpam-3305	342	24	β	β	X
ejpam-3305	342	25	,	,	PUNCT
ejpam-3305	342	26	γ	γ	NOUN
ejpam-3305	342	27	)	)	PUNCT
ejpam-3305	342	28	n	n	CCONJ
ejpam-3305	342	29	,	,	PUNCT
ejpam-3305	342	30	α	α	PROPN
ejpam-3305	342	31	(	(	PUNCT
ejpam-3305	342	32	g;x)−	g;x)−	PROPN
ejpam-3305	342	33	g(x	g(x	PROPN
ejpam-3305	342	34	)	)	PUNCT
ejpam-3305	343	1	=	=	SYM
ejpam-3305	343	2	m̂	m̂	PROPN
ejpam-3305	343	3	(	(	PUNCT
ejpam-3305	343	4	β	β	X
ejpam-3305	343	5	,	,	PUNCT
ejpam-3305	343	6	γ	γ	NOUN
ejpam-3305	343	7	)	)	PUNCT
ejpam-3305	343	8	n	n	CCONJ
ejpam-3305	343	9	,	,	PUNCT
ejpam-3305	343	10	α	α	PROPN
ejpam-3305	343	11	(	(	PUNCT
ejpam-3305	343	12	∫	∫	PROPN
ejpam-3305	343	13	t	t	PROPN
ejpam-3305	343	14	x	x	X
ejpam-3305	343	15	(	(	PUNCT
ejpam-3305	343	16	t−	t−	PROPN
ejpam-3305	343	17	v)g′′(v)dv	v)g′′(v)dv	PROPN
ejpam-3305	343	18	,	,	PUNCT
ejpam-3305	343	19	x	x	PROPN
ejpam-3305	343	20	)	)	PUNCT
ejpam-3305	343	21	.	.	PUNCT
ejpam-3305	344	1	references	reference	NOUN
ejpam-3305	344	2	972	972	NUM
ejpam-3305	344	3	obviously	obviously	ADV
ejpam-3305	344	4	,	,	PUNCT
ejpam-3305	344	5	we	we	PRON
ejpam-3305	344	6	have	have	VERB
ejpam-3305	344	7	∣∣∣∣∫	∣∣∣∣∫	DET
ejpam-3305	344	8	t	t	NOUN
ejpam-3305	344	9	x	x	SYM
ejpam-3305	344	10	(	(	PUNCT
ejpam-3305	344	11	t−	t−	PROPN
ejpam-3305	344	12	v)g′′(v)dv	v)g′′(v)dv	PROPN
ejpam-3305	344	13	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3305	344	14	≤	≤	NOUN
ejpam-3305	344	15	(	(	PUNCT
ejpam-3305	344	16	t−	t−	PROPN
ejpam-3305	344	17	x)2‖g′′‖.	x)2‖g′′‖.	PROPN
ejpam-3305	344	18	therefore	therefore	ADV
ejpam-3305	344	19	|	|	ADV
ejpam-3305	344	20	m̂	m̂	PROPN
ejpam-3305	344	21	(	(	PUNCT
ejpam-3305	344	22	β	β	X
ejpam-3305	344	23	,	,	PUNCT
ejpam-3305	344	24	γ	γ	NOUN
ejpam-3305	344	25	)	)	PUNCT
ejpam-3305	344	26	n	n	CCONJ
ejpam-3305	344	27	,	,	PUNCT
ejpam-3305	344	28	α	α	PROPN
ejpam-3305	344	29	(	(	PUNCT
ejpam-3305	344	30	g;x)−	g;x)−	PROPN
ejpam-3305	344	31	g(x	g(x	PROPN
ejpam-3305	344	32	)	)	PUNCT
ejpam-3305	344	33	|≤	|≤	PROPN
ejpam-3305	344	34	m̂	m̂	PROPN
ejpam-3305	344	35	(	(	PUNCT
ejpam-3305	344	36	β	β	X
ejpam-3305	344	37	,	,	PUNCT
ejpam-3305	344	38	γ	γ	NOUN
ejpam-3305	344	39	)	)	PUNCT
ejpam-3305	344	40	n	n	CCONJ
ejpam-3305	344	41	,	,	PUNCT
ejpam-3305	344	42	α	α	X
ejpam-3305	344	43	(	(	PUNCT
ejpam-3305	344	44	(	(	PUNCT
ejpam-3305	344	45	t−	t−	PROPN
ejpam-3305	344	46	x)2;x	x)2;x	NUM
ejpam-3305	344	47	)	)	PUNCT
ejpam-3305	345	1	‖	‖	PROPN
ejpam-3305	345	2	g′′	g′′	PROPN
ejpam-3305	345	3	‖=	‖=	PROPN
ejpam-3305	345	4	λ(β	λ(β	PROPN
ejpam-3305	345	5	,	,	PUNCT
ejpam-3305	345	6	γ)n	γ)n	ADJ
ejpam-3305	345	7	,	,	PUNCT
ejpam-3305	345	8	α	α	PROPN
ejpam-3305	345	9	(	(	PUNCT
ejpam-3305	345	10	x	x	NOUN
ejpam-3305	345	11	)	)	PUNCT
ejpam-3305	345	12	‖	‖	PROPN
ejpam-3305	345	13	g′′	g′′	PROPN
ejpam-3305	345	14	‖	‖	PROPN
ejpam-3305	345	15	.	.	PUNCT
ejpam-3305	346	1	since	since	SCONJ
ejpam-3305	346	2	|	|	PROPN
ejpam-3305	346	3	m̂	m̂	PROPN
ejpam-3305	346	4	(	(	PUNCT
ejpam-3305	346	5	β	β	X
ejpam-3305	346	6	,	,	PUNCT
ejpam-3305	346	7	γ	γ	NOUN
ejpam-3305	346	8	)	)	PUNCT
ejpam-3305	346	9	n	n	CCONJ
ejpam-3305	346	10	,	,	PUNCT
ejpam-3305	346	11	α	α	PROPN
ejpam-3305	346	12	(	(	PUNCT
ejpam-3305	346	13	f	f	NOUN
ejpam-3305	346	14	;	;	PUNCT
ejpam-3305	346	15	x	x	X
ejpam-3305	346	16	)	)	PUNCT
ejpam-3305	346	17	|≤	|≤	PROPN
ejpam-3305	346	18	‖f‖	‖f‖	PROPN
ejpam-3305	346	19	,	,	PUNCT
ejpam-3305	346	20	we	we	PRON
ejpam-3305	346	21	get	get	VERB
ejpam-3305	346	22	|	|	ADV
ejpam-3305	346	23	m̂	m̂	PROPN
ejpam-3305	346	24	(	(	PUNCT
ejpam-3305	346	25	β	β	X
ejpam-3305	346	26	,	,	PUNCT
ejpam-3305	346	27	γ	γ	NOUN
ejpam-3305	346	28	)	)	PUNCT
ejpam-3305	346	29	n	n	CCONJ
ejpam-3305	346	30	,	,	PUNCT
ejpam-3305	346	31	α	α	PROPN
ejpam-3305	346	32	(	(	PUNCT
ejpam-3305	346	33	f	f	PROPN
ejpam-3305	346	34	;	;	PUNCT
ejpam-3305	346	35	x)−	x)−	PROPN
ejpam-3305	346	36	f(x	f(x	PROPN
ejpam-3305	346	37	)	)	PUNCT
ejpam-3305	347	1	|	|	ADV
ejpam-3305	347	2	≤	≤	PUNCT
ejpam-3305	347	3	|	|	ADV
ejpam-3305	347	4	m̂	m̂	PROPN
ejpam-3305	347	5	(	(	PUNCT
ejpam-3305	347	6	β	β	X
ejpam-3305	347	7	,	,	PUNCT
ejpam-3305	347	8	γ	γ	NOUN
ejpam-3305	347	9	)	)	PUNCT
ejpam-3305	347	10	n	n	CCONJ
ejpam-3305	347	11	,	,	PUNCT
ejpam-3305	347	12	α	α	PROPN
ejpam-3305	347	13	(	(	PUNCT
ejpam-3305	347	14	f	f	PROPN
ejpam-3305	347	15	−	−	PROPN
ejpam-3305	347	16	g;x	g;x	PROPN
ejpam-3305	347	17	)	)	PUNCT
ejpam-3305	348	1	|	|	ADV
ejpam-3305	349	1	+	+	CCONJ
ejpam-3305	349	2	|	|	ADV
ejpam-3305	349	3	(	(	PUNCT
ejpam-3305	349	4	f	f	PROPN
ejpam-3305	349	5	−	−	PROPN
ejpam-3305	349	6	g)(x	g)(x	PROPN
ejpam-3305	349	7	)	)	PUNCT
ejpam-3305	350	1	|	|	ADV
ejpam-3305	351	1	+	+	CCONJ
ejpam-3305	351	2	|	|	ADV
ejpam-3305	351	3	m̂	m̂	X
ejpam-3305	351	4	(	(	PUNCT
ejpam-3305	351	5	β	β	X
ejpam-3305	351	6	,	,	PUNCT
ejpam-3305	351	7	γ	γ	NOUN
ejpam-3305	351	8	)	)	PUNCT
ejpam-3305	351	9	n	n	CCONJ
ejpam-3305	351	10	,	,	PUNCT
ejpam-3305	351	11	α	α	PROPN
ejpam-3305	351	12	(	(	PUNCT
ejpam-3305	351	13	g;x)−	g;x)−	PROPN
ejpam-3305	351	14	g(x	g(x	PROPN
ejpam-3305	351	15	)	)	PUNCT
ejpam-3305	352	1	|	|	ADV
ejpam-3305	352	2	≤	≤	NOUN
ejpam-3305	352	3	2‖f	2‖f	NUM
ejpam-3305	352	4	−	−	PROPN
ejpam-3305	352	5	g‖+	g‖+	PROPN
ejpam-3305	352	6	λ(β	λ(β	PROPN
ejpam-3305	352	7	,	,	PUNCT
ejpam-3305	352	8	γ)n	γ)n	X
ejpam-3305	352	9	,	,	PUNCT
ejpam-3305	352	10	α	α	PROPN
ejpam-3305	352	11	(	(	PUNCT
ejpam-3305	352	12	x)‖g′′‖.	x)‖g′′‖.	NOUN
ejpam-3305	352	13	finally	finally	ADV
ejpam-3305	352	14	,	,	PUNCT
ejpam-3305	352	15	taking	take	VERB
ejpam-3305	352	16	the	the	DET
ejpam-3305	352	17	infimum	infimum	NOUN
ejpam-3305	352	18	over	over	ADP
ejpam-3305	352	19	all	all	PRON
ejpam-3305	352	20	g	g	NOUN
ejpam-3305	352	21	∈w	∈w	NOUN
ejpam-3305	352	22	2	2	NUM
ejpam-3305	352	23	and	and	CCONJ
ejpam-3305	352	24	using	use	VERB
ejpam-3305	352	25	(	(	PUNCT
ejpam-3305	352	26	10	10	NUM
ejpam-3305	352	27	)	)	PUNCT
ejpam-3305	352	28	we	we	PRON
ejpam-3305	352	29	obtain	obtain	VERB
ejpam-3305	352	30	|	|	ADV
ejpam-3305	352	31	m̂	m̂	PROPN
ejpam-3305	352	32	(	(	PUNCT
ejpam-3305	352	33	β	β	X
ejpam-3305	352	34	,	,	PUNCT
ejpam-3305	352	35	γ	γ	NOUN
ejpam-3305	352	36	)	)	PUNCT
ejpam-3305	352	37	n	n	CCONJ
ejpam-3305	352	38	,	,	PUNCT
ejpam-3305	352	39	α	α	PROPN
ejpam-3305	352	40	(	(	PUNCT
ejpam-3305	352	41	f	f	PROPN
ejpam-3305	352	42	;	;	PUNCT
ejpam-3305	352	43	x)−	x)−	PROPN
ejpam-3305	352	44	f(x	f(x	PROPN
ejpam-3305	352	45	)	)	PUNCT
ejpam-3305	352	46	|≤m	|≤m	NUM
ejpam-3305	352	47	′ω2	′ω2	NUM
ejpam-3305	352	48	(	(	PUNCT
ejpam-3305	352	49	f	f	X
ejpam-3305	352	50	,	,	PUNCT
ejpam-3305	352	51	√	√	PROPN
ejpam-3305	352	52	λ	λ	PROPN
ejpam-3305	352	53	(	(	PUNCT
ejpam-3305	352	54	β	β	X
ejpam-3305	352	55	,	,	PUNCT
ejpam-3305	352	56	γ	γ	NOUN
ejpam-3305	352	57	)	)	PUNCT
ejpam-3305	352	58	n	n	CCONJ
ejpam-3305	352	59	,	,	PUNCT
ejpam-3305	352	60	α	α	PROPN
ejpam-3305	352	61	(	(	PUNCT
ejpam-3305	352	62	x	x	NOUN
ejpam-3305	352	63	)	)	PUNCT
ejpam-3305	352	64	)	)	PUNCT
ejpam-3305	352	65	,	,	PUNCT
ejpam-3305	352	66	which	which	PRON
ejpam-3305	352	67	proves	prove	VERB
ejpam-3305	352	68	the	the	DET
ejpam-3305	352	69	theorem	theorem	PROPN
ejpam-3305	352	70	.	.	PUNCT
ejpam-3305	352	71	theorem	theorem	NOUN
ejpam-3305	352	72	11	11	NUM
ejpam-3305	352	73	.	.	PUNCT
ejpam-3305	353	1	let	let	VERB
ejpam-3305	353	2	f	f	PROPN
ejpam-3305	353	3	∈	∈	PROPN
ejpam-3305	353	4	cb(in	cb(in	PROPN
ejpam-3305	353	5	)	)	PUNCT
ejpam-3305	353	6	.	.	PUNCT
ejpam-3305	354	1	if	if	SCONJ
ejpam-3305	354	2	f	f	PROPN
ejpam-3305	354	3	′	′	PROPN
ejpam-3305	354	4	,	,	PUNCT
ejpam-3305	354	5	f	f	PROPN
ejpam-3305	355	1	′′	′′	PROPN
ejpam-3305	355	2	exists	exist	VERB
ejpam-3305	355	3	at	at	ADP
ejpam-3305	355	4	a	a	DET
ejpam-3305	355	5	fixed	fixed	ADJ
ejpam-3305	355	6	point	point	NOUN
ejpam-3305	355	7	x	x	X
ejpam-3305	355	8	∈	∈	NOUN
ejpam-3305	355	9	in	in	ADP
ejpam-3305	355	10	,	,	PUNCT
ejpam-3305	355	11	then	then	ADV
ejpam-3305	355	12	we	we	PRON
ejpam-3305	355	13	have	have	VERB
ejpam-3305	355	14	lim	lim	PROPN
ejpam-3305	355	15	n→∞	n→∞	NUM
ejpam-3305	355	16	n	n	PROPN
ejpam-3305	355	17	(	(	PUNCT
ejpam-3305	355	18	m̂	m̂	X
ejpam-3305	355	19	(	(	PUNCT
ejpam-3305	355	20	β	β	X
ejpam-3305	355	21	,	,	PUNCT
ejpam-3305	355	22	γ	γ	NOUN
ejpam-3305	355	23	)	)	PUNCT
ejpam-3305	355	24	n	n	CCONJ
ejpam-3305	355	25	,	,	PUNCT
ejpam-3305	355	26	α	α	PROPN
ejpam-3305	355	27	(	(	PUNCT
ejpam-3305	355	28	f	f	PROPN
ejpam-3305	355	29	;	;	PUNCT
ejpam-3305	355	30	x)−	x)−	PROPN
ejpam-3305	355	31	f(x	f(x	PROPN
ejpam-3305	355	32	)	)	PUNCT
ejpam-3305	355	33	)	)	PUNCT
ejpam-3305	356	1	=	=	PUNCT
ejpam-3305	356	2	x	x	SYM
ejpam-3305	356	3	2	2	NUM
ejpam-3305	356	4	(	(	PUNCT
ejpam-3305	356	5	2	2	NUM
ejpam-3305	356	6	+	+	CCONJ
ejpam-3305	356	7	(	(	PUNCT
ejpam-3305	356	8	l	l	NOUN
ejpam-3305	356	9	+	+	NUM
ejpam-3305	356	10	1)x	1)x	NUM
ejpam-3305	356	11	)	)	PUNCT
ejpam-3305	356	12	f	f	PROPN
ejpam-3305	356	13	′′(x	′′(x	PROPN
ejpam-3305	356	14	)	)	PUNCT
ejpam-3305	356	15	.	.	PUNCT
ejpam-3305	357	1	the	the	DET
ejpam-3305	357	2	proof	proof	NOUN
ejpam-3305	357	3	follows	follow	VERB
ejpam-3305	357	4	along	along	ADP
ejpam-3305	357	5	the	the	DET
ejpam-3305	357	6	lines	line	NOUN
ejpam-3305	357	7	of	of	ADP
ejpam-3305	357	8	theorem	theorem	ADJ
ejpam-3305	357	9	2	2	NUM
ejpam-3305	357	10	.	.	PUNCT
ejpam-3305	357	11	acknowledgements	acknowledgement	NOUN
ejpam-3305	357	12	the	the	DET
ejpam-3305	357	13	authors	author	NOUN
ejpam-3305	357	14	would	would	AUX
ejpam-3305	357	15	like	like	VERB
ejpam-3305	357	16	to	to	PART
ejpam-3305	357	17	express	express	VERB
ejpam-3305	357	18	their	their	PRON
ejpam-3305	357	19	deep	deep	ADJ
ejpam-3305	357	20	gratitude	gratitude	NOUN
ejpam-3305	357	21	to	to	ADP
ejpam-3305	357	22	the	the	DET
ejpam-3305	357	23	anonymous	anonymous	PROPN
ejpam-3305	357	24	learned	learn	VERB
ejpam-3305	357	25	referee(s	referee(s	PROPN
ejpam-3305	357	26	)	)	PUNCT
ejpam-3305	357	27	and	and	CCONJ
ejpam-3305	357	28	the	the	DET
ejpam-3305	357	29	editor	editor	NOUN
ejpam-3305	357	30	for	for	ADP
ejpam-3305	357	31	their	their	PRON
ejpam-3305	357	32	valuable	valuable	ADJ
ejpam-3305	357	33	suggestions	suggestion	NOUN
ejpam-3305	357	34	and	and	CCONJ
ejpam-3305	357	35	constructive	constructive	ADJ
ejpam-3305	357	36	comments	comment	NOUN
ejpam-3305	357	37	,	,	PUNCT
ejpam-3305	357	38	which	which	PRON
ejpam-3305	357	39	resulted	result	VERB
ejpam-3305	357	40	in	in	ADP
ejpam-3305	357	41	the	the	DET
ejpam-3305	357	42	subsequent	subsequent	ADJ
ejpam-3305	357	43	improvement	improvement	NOUN
ejpam-3305	357	44	of	of	ADP
ejpam-3305	357	45	this	this	DET
ejpam-3305	357	46	research	research	NOUN
ejpam-3305	357	47	article	article	NOUN
ejpam-3305	357	48	.	.	PUNCT
ejpam-3305	358	1	the	the	DET
ejpam-3305	358	2	third	third	ADJ
ejpam-3305	358	3	author	author	NOUN
ejpam-3305	358	4	lakshmi	lakshmi	PROPN
ejpam-3305	358	5	narayan	narayan	PROPN
ejpam-3305	358	6	mishra	mishra	PROPN
ejpam-3305	358	7	is	be	AUX
ejpam-3305	358	8	much	much	ADV
ejpam-3305	358	9	thankful	thankful	ADJ
ejpam-3305	358	10	to	to	ADP
ejpam-3305	358	11	the	the	DET
ejpam-3305	358	12	department	department	NOUN
ejpam-3305	358	13	of	of	ADP
ejpam-3305	358	14	mathematics	mathematic	NOUN
ejpam-3305	358	15	,	,	PUNCT
ejpam-3305	358	16	school	school	NOUN
ejpam-3305	358	17	of	of	ADP
ejpam-3305	358	18	advanced	advanced	ADJ
ejpam-3305	358	19	sciences	science	NOUN
ejpam-3305	358	20	(	(	PUNCT
ejpam-3305	358	21	sas	sas	PROPN
ejpam-3305	358	22	)	)	PUNCT
ejpam-3305	358	23	,	,	PUNCT
ejpam-3305	358	24	vellore	vellore	PROPN
ejpam-3305	358	25	institute	institute	PROPN
ejpam-3305	358	26	of	of	ADP
ejpam-3305	358	27	technology	technology	PROPN
ejpam-3305	358	28	(	(	PUNCT
ejpam-3305	358	29	vit	vit	NOUN
ejpam-3305	358	30	)	)	PUNCT
ejpam-3305	358	31	university	university	NOUN
ejpam-3305	358	32	,	,	PUNCT
ejpam-3305	358	33	vellore	vellore	NOUN
ejpam-3305	358	34	,	,	PUNCT
ejpam-3305	358	35	tamil	tamil	PROPN
ejpam-3305	358	36	nadu	nadu	NOUN
ejpam-3305	358	37	for	for	ADP
ejpam-3305	358	38	supporting	support	VERB
ejpam-3305	358	39	this	this	DET
ejpam-3305	358	40	research	research	NOUN
ejpam-3305	358	41	article	article	NOUN
ejpam-3305	358	42	.	.	PUNCT
ejpam-3305	359	1	references	reference	NOUN
ejpam-3305	359	2	[	[	X
ejpam-3305	359	3	1	1	X
ejpam-3305	359	4	]	]	PUNCT
ejpam-3305	359	5	t.	t.	NOUN
ejpam-3305	359	6	acar	acar	NOUN
ejpam-3305	359	7	,	,	PUNCT
ejpam-3305	359	8	l.n	l.n	PROPN
ejpam-3305	359	9	.	.	PROPN
ejpam-3305	359	10	mishra	mishra	PROPN
ejpam-3305	359	11	,	,	PUNCT
ejpam-3305	359	12	v.n	v.n	PROPN
ejpam-3305	359	13	.	.	PROPN
ejpam-3305	359	14	mishra	mishra	PROPN
ejpam-3305	359	15	,	,	PUNCT
ejpam-3305	359	16	simultaneous	simultaneous	ADJ
ejpam-3305	359	17	approximation	approximation	NOUN
ejpam-3305	359	18	for	for	ADP
ejpam-3305	359	19	generalized	generalized	ADJ
ejpam-3305	359	20	srivastava	srivastava	PROPN
ejpam-3305	359	21	-	-	PUNCT
ejpam-3305	359	22	gupta	gupta	PROPN
ejpam-3305	359	23	operators	operator	NOUN
ejpam-3305	359	24	,	,	PUNCT
ejpam-3305	359	25	journal	journal	NOUN
ejpam-3305	359	26	of	of	ADP
ejpam-3305	359	27	function	function	NOUN
ejpam-3305	359	28	spaces	space	NOUN
ejpam-3305	359	29	volume	volume	NOUN
ejpam-3305	359	30	2015	2015	NUM
ejpam-3305	359	31	,	,	PUNCT
ejpam-3305	359	32	article	article	NOUN
ejpam-3305	359	33	i	i	PROPN
ejpam-3305	359	34	d	d	PROPN
ejpam-3305	359	35	936308	936308	NUM
ejpam-3305	359	36	,	,	PUNCT
ejpam-3305	359	37	11	11	NUM
ejpam-3305	359	38	pages	page	NOUN
ejpam-3305	359	39	.	.	PUNCT
ejpam-3305	360	1	[	[	X
ejpam-3305	360	2	2	2	NUM
ejpam-3305	360	3	]	]	X
ejpam-3305	360	4	r.a	r.a	PROPN
ejpam-3305	360	5	.	.	PROPN
ejpam-3305	360	6	devore	devore	PROPN
ejpam-3305	360	7	,	,	PUNCT
ejpam-3305	360	8	g.g	g.g	PROPN
ejpam-3305	360	9	.	.	PROPN
ejpam-3305	360	10	lorentz	lorentz	PROPN
ejpam-3305	360	11	,	,	PUNCT
ejpam-3305	360	12	constructive	constructive	ADJ
ejpam-3305	360	13	approximation	approximation	NOUN
ejpam-3305	360	14	,	,	PUNCT
ejpam-3305	360	15	springer	springer	NOUN
ejpam-3305	360	16	,	,	PUNCT
ejpam-3305	360	17	berlin	berlin	PROPN
ejpam-3305	360	18	(	(	PUNCT
ejpam-3305	360	19	1993	1993	NUM
ejpam-3305	360	20	)	)	PUNCT
ejpam-3305	360	21	.	.	PUNCT
ejpam-3305	361	1	[	[	X
ejpam-3305	361	2	3	3	X
ejpam-3305	361	3	]	]	PUNCT
ejpam-3305	361	4	z.	z.	PROPN
ejpam-3305	361	5	ditzian	ditzian	PROPN
ejpam-3305	361	6	,	,	PUNCT
ejpam-3305	361	7	v.	v.	ADP
ejpam-3305	361	8	totik	totik	PROPN
ejpam-3305	361	9	,	,	PUNCT
ejpam-3305	361	10	moduli	modulus	NOUN
ejpam-3305	361	11	of	of	ADP
ejpam-3305	361	12	smoothness	smoothness	NOUN
ejpam-3305	361	13	,	,	PUNCT
ejpam-3305	361	14	springer	springer	NOUN
ejpam-3305	361	15	-	-	PUNCT
ejpam-3305	361	16	verlag	verlag	PROPN
ejpam-3305	361	17	,	,	PUNCT
ejpam-3305	361	18	new	new	PROPN
ejpam-3305	361	19	york	york	PROPN
ejpam-3305	361	20	,	,	PUNCT
ejpam-3305	361	21	1987	1987	NUM
ejpam-3305	361	22	.	.	PUNCT
ejpam-3305	362	1	references	reference	NOUN
ejpam-3305	362	2	973	973	NUM
ejpam-3305	363	1	[	[	X
ejpam-3305	363	2	4	4	NUM
ejpam-3305	363	3	]	]	X
ejpam-3305	363	4	a.r	a.r	PROPN
ejpam-3305	363	5	.	.	PROPN
ejpam-3305	363	6	devdhara	devdhara	PROPN
ejpam-3305	363	7	,	,	PUNCT
ejpam-3305	363	8	v.n	v.n	PROPN
ejpam-3305	363	9	.	.	PROPN
ejpam-3305	363	10	mishra	mishra	PROPN
ejpam-3305	363	11	,	,	PUNCT
ejpam-3305	363	12	local	local	ADJ
ejpam-3305	363	13	approximation	approximation	NOUN
ejpam-3305	363	14	results	result	NOUN
ejpam-3305	363	15	for	for	ADP
ejpam-3305	363	16	stancu	stancu	ADJ
ejpam-3305	363	17	variant	variant	NOUN
ejpam-3305	363	18	of	of	ADP
ejpam-3305	363	19	modified	modify	VERB
ejpam-3305	363	20	szasz	szasz	NOUN
ejpam-3305	363	21	-	-	PUNCT
ejpam-3305	363	22	mirakjan	mirakjan	NOUN
ejpam-3305	363	23	operators	operator	NOUN
ejpam-3305	363	24	,	,	PUNCT
ejpam-3305	363	25	eur	eur	PROPN
ejpam-3305	363	26	.	.	PUNCT
ejpam-3305	364	1	j.	j.	PROPN
ejpam-3305	364	2	pure	pure	PROPN
ejpam-3305	364	3	appl	appl	PROPN
ejpam-3305	364	4	.	.	PUNCT
ejpam-3305	364	5	math	math	PROPN
ejpam-3305	364	6	.	.	PUNCT
ejpam-3305	365	1	,	,	PUNCT
ejpam-3305	365	2	vol	vol	NOUN
ejpam-3305	365	3	.	.	PROPN
ejpam-3305	366	1	11	11	NUM
ejpam-3305	366	2	,	,	PUNCT
ejpam-3305	366	3	no	no	INTJ
ejpam-3305	366	4	.	.	NOUN
ejpam-3305	366	5	2	2	NUM
ejpam-3305	366	6	(	(	PUNCT
ejpam-3305	366	7	2018	2018	NUM
ejpam-3305	366	8	)	)	PUNCT
ejpam-3305	366	9	,	,	PUNCT
ejpam-3305	366	10	400	400	NUM
ejpam-3305	366	11	-	-	SYM
ejpam-3305	366	12	409	409	NUM
ejpam-3305	366	13	.	.	PUNCT
ejpam-3305	367	1	[	[	X
ejpam-3305	367	2	5	5	X
ejpam-3305	367	3	]	]	PUNCT
ejpam-3305	367	4	e.	e.	PROPN
ejpam-3305	367	5	deniz	deniz	PROPN
ejpam-3305	367	6	,	,	PUNCT
ejpam-3305	367	7	a.	a.	PROPN
ejpam-3305	367	8	aral	aral	PROPN
ejpam-3305	367	9	,	,	PUNCT
ejpam-3305	367	10	g.	g.	PROPN
ejpam-3305	367	11	ulusoy	ulusoy	PROPN
ejpam-3305	367	12	,	,	PUNCT
ejpam-3305	367	13	new	new	ADJ
ejpam-3305	367	14	integral	integral	ADJ
ejpam-3305	367	15	type	type	NOUN
ejpam-3305	367	16	operators	operator	NOUN
ejpam-3305	367	17	,	,	PUNCT
ejpam-3305	367	18	filomat	filomat	NOUN
ejpam-3305	367	19	,	,	PUNCT
ejpam-3305	367	20	31:9	31:9	NUM
ejpam-3305	367	21	(	(	PUNCT
ejpam-3305	367	22	2017	2017	NUM
ejpam-3305	367	23	)	)	PUNCT
ejpam-3305	367	24	,	,	PUNCT
ejpam-3305	367	25	2851	2851	NUM
ejpam-3305	367	26	-	-	SYM
ejpam-3305	367	27	2865	2865	NUM
ejpam-3305	367	28	.	.	PUNCT
ejpam-3305	368	1	[	[	X
ejpam-3305	368	2	6	6	NUM
ejpam-3305	368	3	]	]	X
ejpam-3305	368	4	a.d	a.d	PROPN
ejpam-3305	368	5	.	.	PROPN
ejpam-3305	368	6	gadjiev	gadjiev	PROPN
ejpam-3305	368	7	,	,	PUNCT
ejpam-3305	368	8	theorems	theorem	NOUN
ejpam-3305	368	9	of	of	ADP
ejpam-3305	368	10	the	the	DET
ejpam-3305	368	11	type	type	NOUN
ejpam-3305	368	12	of	of	ADP
ejpam-3305	368	13	p.p	p.p	PROPN
ejpam-3305	368	14	.	.	PROPN
ejpam-3305	368	15	korovkin	korovkin	PROPN
ejpam-3305	368	16	’s	’s	PART
ejpam-3305	368	17	theorems	theorem	NOUN
ejpam-3305	368	18	,	,	PUNCT
ejpam-3305	368	19	matematicheskie	matematicheskie	NOUN
ejpam-3305	368	20	zametki	zametki	NOUN
ejpam-3305	368	21	,	,	PUNCT
ejpam-3305	368	22	20(5	20(5	NUM
ejpam-3305	368	23	)	)	PUNCT
ejpam-3305	368	24	(	(	PUNCT
ejpam-3305	368	25	1976	1976	NUM
ejpam-3305	368	26	)	)	PUNCT
ejpam-3305	368	27	,	,	PUNCT
ejpam-3305	368	28	781	781	NUM
ejpam-3305	368	29	-	-	SYM
ejpam-3305	368	30	786	786	NUM
ejpam-3305	368	31	.	.	PUNCT
ejpam-3305	369	1	[	[	X
ejpam-3305	369	2	7	7	X
ejpam-3305	369	3	]	]	X
ejpam-3305	369	4	a.d	a.d	PROPN
ejpam-3305	369	5	.	.	PROPN
ejpam-3305	369	6	gadjiev	gadjiev	PROPN
ejpam-3305	369	7	,	,	PUNCT
ejpam-3305	369	8	the	the	DET
ejpam-3305	369	9	convergence	convergence	NOUN
ejpam-3305	369	10	problem	problem	NOUN
ejpam-3305	369	11	for	for	ADP
ejpam-3305	369	12	a	a	DET
ejpam-3305	369	13	sequence	sequence	NOUN
ejpam-3305	369	14	of	of	ADP
ejpam-3305	369	15	positive	positive	ADJ
ejpam-3305	369	16	linear	linear	PROPN
ejpam-3305	369	17	operators	operator	NOUN
ejpam-3305	369	18	on	on	ADP
ejpam-3305	369	19	bounded	bounded	ADJ
ejpam-3305	369	20	sets	set	NOUN
ejpam-3305	369	21	and	and	CCONJ
ejpam-3305	369	22	theorems	theorem	NOUN
ejpam-3305	369	23	analogous	analogous	ADJ
ejpam-3305	369	24	to	to	ADP
ejpam-3305	369	25	that	that	PRON
ejpam-3305	369	26	of	of	ADP
ejpam-3305	369	27	p.p	p.p	PROPN
ejpam-3305	369	28	.	.	PROPN
ejpam-3305	369	29	korovkin	korovkin	PROPN
ejpam-3305	369	30	,	,	PUNCT
ejpam-3305	369	31	dokl	dokl	NOUN
ejpam-3305	369	32	.	.	PUNCT
ejpam-3305	370	1	akad	akad	PROPN
ejpam-3305	370	2	.	.	PUNCT
ejpam-3305	371	1	nauk	nauk	PROPN
ejpam-3305	371	2	sssr	sssr	NOUN
ejpam-3305	371	3	218(5	218(5	NUM
ejpam-3305	371	4	)	)	PUNCT
ejpam-3305	371	5	(	(	PUNCT
ejpam-3305	371	6	1974	1974	NUM
ejpam-3305	371	7	)	)	PUNCT
ejpam-3305	371	8	;	;	PUNCT
ejpam-3305	371	9	transl	transl	PROPN
ejpam-3305	371	10	.	.	PUNCT
ejpam-3305	372	1	in	in	ADP
ejpam-3305	372	2	soviet	soviet	ADJ
ejpam-3305	372	3	math	math	NOUN
ejpam-3305	372	4	.	.	PUNCT
ejpam-3305	373	1	dokl	dokl	NOUN
ejpam-3305	373	2	.	.	PUNCT
ejpam-3305	374	1	15(5	15(5	NUM
ejpam-3305	374	2	)	)	PUNCT
ejpam-3305	374	3	(	(	PUNCT
ejpam-3305	374	4	1974	1974	NUM
ejpam-3305	374	5	)	)	PUNCT
ejpam-3305	374	6	,	,	PUNCT
ejpam-3305	374	7	1433	1433	NUM
ejpam-3305	374	8	-	-	SYM
ejpam-3305	374	9	1436	1436	NUM
ejpam-3305	374	10	.	.	PUNCT
ejpam-3305	375	1	[	[	X
ejpam-3305	375	2	8	8	NUM
ejpam-3305	375	3	]	]	X
ejpam-3305	375	4	a.d	a.d	PROPN
ejpam-3305	375	5	.	.	PROPN
ejpam-3305	375	6	gadjiev	gadjiev	PROPN
ejpam-3305	375	7	,	,	PUNCT
ejpam-3305	375	8	a.	a.	PROPN
ejpam-3305	375	9	aral	aral	PROPN
ejpam-3305	375	10	,	,	PUNCT
ejpam-3305	375	11	the	the	DET
ejpam-3305	375	12	weighted	weighted	ADJ
ejpam-3305	375	13	lp	lp	NOUN
ejpam-3305	375	14	-	-	NOUN
ejpam-3305	375	15	approximation	approximation	NOUN
ejpam-3305	375	16	with	with	ADP
ejpam-3305	375	17	positive	positive	ADJ
ejpam-3305	375	18	linear	linear	PROPN
ejpam-3305	375	19	operators	operator	NOUN
ejpam-3305	375	20	on	on	ADP
ejpam-3305	375	21	unbounded	unbounded	ADJ
ejpam-3305	375	22	sets	set	NOUN
ejpam-3305	375	23	,	,	PUNCT
ejpam-3305	375	24	appl	appl	PROPN
ejpam-3305	375	25	.	.	PROPN
ejpam-3305	375	26	math	math	NOUN
ejpam-3305	375	27	.	.	PUNCT
ejpam-3305	376	1	letters	letter	NOUN
ejpam-3305	376	2	,	,	PUNCT
ejpam-3305	376	3	20	20	NUM
ejpam-3305	376	4	(	(	PUNCT
ejpam-3305	376	5	2007	2007	NUM
ejpam-3305	376	6	)	)	PUNCT
ejpam-3305	376	7	,	,	PUNCT
ejpam-3305	376	8	1046	1046	NUM
ejpam-3305	376	9	-	-	SYM
ejpam-3305	376	10	1051	1051	NUM
ejpam-3305	376	11	.	.	PUNCT
ejpam-3305	377	1	[	[	X
ejpam-3305	377	2	9	9	NUM
ejpam-3305	377	3	]	]	X
ejpam-3305	377	4	a.r	a.r	PROPN
ejpam-3305	377	5	.	.	PROPN
ejpam-3305	377	6	gairola	gairola	PROPN
ejpam-3305	377	7	,	,	PUNCT
ejpam-3305	377	8	deepmala	deepmala	PROPN
ejpam-3305	377	9	,	,	PUNCT
ejpam-3305	377	10	l.n	l.n	PROPN
ejpam-3305	377	11	.	.	PROPN
ejpam-3305	377	12	mishra	mishra	PROPN
ejpam-3305	377	13	,	,	PUNCT
ejpam-3305	377	14	on	on	ADP
ejpam-3305	377	15	the	the	DET
ejpam-3305	377	16	q	q	NOUN
ejpam-3305	377	17	-	-	PUNCT
ejpam-3305	377	18	derivatives	derivative	NOUN
ejpam-3305	377	19	of	of	ADP
ejpam-3305	377	20	a	a	DET
ejpam-3305	377	21	certain	certain	ADJ
ejpam-3305	377	22	linear	linear	ADJ
ejpam-3305	377	23	positive	positive	ADJ
ejpam-3305	377	24	operators	operator	NOUN
ejpam-3305	377	25	,	,	PUNCT
ejpam-3305	377	26	iranian	iranian	ADJ
ejpam-3305	377	27	journal	journal	PROPN
ejpam-3305	377	28	of	of	ADP
ejpam-3305	377	29	science	science	NOUN
ejpam-3305	377	30	and	and	CCONJ
ejpam-3305	377	31	technology	technology	NOUN
ejpam-3305	377	32	,	,	PUNCT
ejpam-3305	377	33	transactions	transaction	VERB
ejpam-3305	377	34	a	a	DET
ejpam-3305	377	35	:	:	PUNCT
ejpam-3305	377	36	science	science	NOUN
ejpam-3305	377	37	,	,	PUNCT
ejpam-3305	377	38	vol	vol	NOUN
ejpam-3305	377	39	.	.	PROPN
ejpam-3305	378	1	42	42	NUM
ejpam-3305	378	2	,	,	PUNCT
ejpam-3305	378	3	no	no	INTJ
ejpam-3305	378	4	.	.	NOUN
ejpam-3305	378	5	3	3	NUM
ejpam-3305	378	6	,	,	PUNCT
ejpam-3305	378	7	(	(	PUNCT
ejpam-3305	378	8	2018	2018	NUM
ejpam-3305	378	9	)	)	PUNCT
ejpam-3305	378	10	,	,	PUNCT
ejpam-3305	379	1	pp	pp	ADJ
ejpam-3305	379	2	.	.	PUNCT
ejpam-3305	380	1	1409	1409	NUM
ejpam-3305	380	2	-	-	SYM
ejpam-3305	380	3	1417	1417	NUM
ejpam-3305	380	4	.	.	PUNCT
ejpam-3305	381	1	doi	doi	NOUN
ejpam-3305	381	2	10.1007	10.1007	NUM
ejpam-3305	381	3	/	/	SYM
ejpam-3305	381	4	s40995	s40995	VERB
ejpam-3305	381	5	-	-	PUNCT
ejpam-3305	381	6	017	017	NUM
ejpam-3305	381	7	-	-	PUNCT
ejpam-3305	381	8	0227	0227	NUM
ejpam-3305	381	9	-	-	SYM
ejpam-3305	381	10	8	8	NUM
ejpam-3305	381	11	.	.	PUNCT
ejpam-3305	382	1	[	[	X
ejpam-3305	382	2	10	10	NUM
ejpam-3305	382	3	]	]	X
ejpam-3305	382	4	a.r	a.r	PROPN
ejpam-3305	382	5	.	.	PROPN
ejpam-3305	382	6	gairola	gairola	PROPN
ejpam-3305	382	7	,	,	PUNCT
ejpam-3305	382	8	deepmala	deepmala	PROPN
ejpam-3305	382	9	,	,	PUNCT
ejpam-3305	382	10	l.n	l.n	PROPN
ejpam-3305	382	11	.	.	PROPN
ejpam-3305	382	12	mishra	mishra	PROPN
ejpam-3305	382	13	,	,	PUNCT
ejpam-3305	382	14	rate	rate	NOUN
ejpam-3305	382	15	of	of	ADP
ejpam-3305	382	16	approximation	approximation	NOUN
ejpam-3305	382	17	by	by	ADP
ejpam-3305	382	18	finite	finite	ADJ
ejpam-3305	382	19	iterates	iterate	NOUN
ejpam-3305	382	20	of	of	ADP
ejpam-3305	382	21	q	q	NOUN
ejpam-3305	382	22	-	-	PUNCT
ejpam-3305	382	23	durrmeyer	durrmeyer	NOUN
ejpam-3305	382	24	operators	operator	NOUN
ejpam-3305	382	25	,	,	PUNCT
ejpam-3305	382	26	proc	proc	PROPN
ejpam-3305	382	27	.	.	PUNCT
ejpam-3305	383	1	natl	natl	PROPN
ejpam-3305	383	2	.	.	PUNCT
ejpam-3305	384	1	acad	acad	PROPN
ejpam-3305	384	2	.	.	PUNCT
ejpam-3305	385	1	sci	sci	PROPN
ejpam-3305	385	2	.	.	PROPN
ejpam-3305	385	3	,	,	PUNCT
ejpam-3305	385	4	india	india	PROPN
ejpam-3305	385	5	,	,	PUNCT
ejpam-3305	385	6	sect	sect	NOUN
ejpam-3305	385	7	.	.	PUNCT
ejpam-3305	386	1	a	a	DET
ejpam-3305	386	2	phys	phy	NOUN
ejpam-3305	386	3	.	.	PUNCT
ejpam-3305	387	1	sci	sci	PROPN
ejpam-3305	387	2	.	.	PUNCT
ejpam-3305	387	3	(	(	PUNCT
ejpam-3305	387	4	april	april	PROPN
ejpam-3305	387	5	-	-	PUNCT
ejpam-3305	387	6	june	june	PROPN
ejpam-3305	387	7	2016	2016	NUM
ejpam-3305	387	8	)	)	PUNCT
ejpam-3305	387	9	86(2):229	86(2):229	NUM
ejpam-3305	387	10	-	-	SYM
ejpam-3305	387	11	234	234	NUM
ejpam-3305	387	12	(	(	PUNCT
ejpam-3305	387	13	2016	2016	NUM
ejpam-3305	387	14	)	)	PUNCT
ejpam-3305	387	15	.	.	PUNCT
ejpam-3305	388	1	doi	doi	NOUN
ejpam-3305	388	2	:	:	PUNCT
ejpam-3305	388	3	10.1007	10.1007	NUM
ejpam-3305	388	4	/	/	SYM
ejpam-3305	388	5	s40010	s40010	NOUN
ejpam-3305	388	6	-	-	PUNCT
ejpam-3305	388	7	016	016	NUM
ejpam-3305	388	8	-	-	PUNCT
ejpam-3305	388	9	0267	0267	NUM
ejpam-3305	388	10	-	-	PUNCT
ejpam-3305	388	11	z	z	NOUN
ejpam-3305	389	1	[	[	X
ejpam-3305	389	2	11	11	NUM
ejpam-3305	389	3	]	]	X
ejpam-3305	389	4	v.	v.	CCONJ
ejpam-3305	389	5	gupta	gupta	PROPN
ejpam-3305	389	6	,	,	PUNCT
ejpam-3305	389	7	d.	d.	PROPN
ejpam-3305	389	8	agrawal	agrawal	PROPN
ejpam-3305	389	9	,	,	PUNCT
ejpam-3305	389	10	approximation	approximation	NOUN
ejpam-3305	389	11	results	result	NOUN
ejpam-3305	389	12	by	by	ADP
ejpam-3305	389	13	certain	certain	ADJ
ejpam-3305	389	14	genuine	genuine	ADJ
ejpam-3305	389	15	operators	operator	NOUN
ejpam-3305	389	16	of	of	ADP
ejpam-3305	389	17	integral	integral	ADJ
ejpam-3305	389	18	type	type	NOUN
ejpam-3305	389	19	,	,	PUNCT
ejpam-3305	389	20	kragujevac	kragujevac	PROPN
ejpam-3305	389	21	journal	journal	NOUN
ejpam-3305	389	22	of	of	ADP
ejpam-3305	389	23	mathematics	mathematic	NOUN
ejpam-3305	389	24	,	,	PUNCT
ejpam-3305	389	25	42	42	NUM
ejpam-3305	389	26	(	(	PUNCT
ejpam-3305	389	27	3	3	NUM
ejpam-3305	389	28	)	)	PUNCT
ejpam-3305	389	29	(	(	PUNCT
ejpam-3305	389	30	2018	2018	NUM
ejpam-3305	389	31	)	)	PUNCT
ejpam-3305	389	32	,	,	PUNCT
ejpam-3305	389	33	335	335	NUM
ejpam-3305	389	34	-	-	SYM
ejpam-3305	389	35	348	348	NUM
ejpam-3305	389	36	.	.	PUNCT
ejpam-3305	390	1	[	[	X
ejpam-3305	390	2	12	12	NUM
ejpam-3305	390	3	]	]	X
ejpam-3305	390	4	r.b	r.b	PROPN
ejpam-3305	390	5	.	.	PROPN
ejpam-3305	390	6	gandhi	gandhi	PROPN
ejpam-3305	390	7	,	,	PUNCT
ejpam-3305	390	8	deepmala	deepmala	PROPN
ejpam-3305	390	9	,	,	PUNCT
ejpam-3305	390	10	v.n	v.n	PROPN
ejpam-3305	390	11	.	.	PROPN
ejpam-3305	390	12	mishra	mishra	PROPN
ejpam-3305	390	13	,	,	PUNCT
ejpam-3305	390	14	local	local	ADJ
ejpam-3305	390	15	and	and	CCONJ
ejpam-3305	390	16	global	global	ADJ
ejpam-3305	390	17	results	result	NOUN
ejpam-3305	390	18	for	for	ADP
ejpam-3305	390	19	modified	modify	VERB
ejpam-3305	390	20	szászmirakjan	szászmirakjan	PROPN
ejpam-3305	390	21	operators	operator	NOUN
ejpam-3305	390	22	,	,	PUNCT
ejpam-3305	390	23	math	math	NOUN
ejpam-3305	390	24	.	.	PUNCT
ejpam-3305	390	25	method	method	PROPN
ejpam-3305	390	26	.	.	PUNCT
ejpam-3305	391	1	appl	appl	PROPN
ejpam-3305	391	2	.	.	PUNCT
ejpam-3305	392	1	sci	sci	PROPN
ejpam-3305	392	2	.	.	PROPN
ejpam-3305	392	3	,	,	PUNCT
ejpam-3305	392	4	vol	vol	NOUN
ejpam-3305	392	5	.	.	PROPN
ejpam-3305	392	6	40	40	NUM
ejpam-3305	392	7	,	,	PUNCT
ejpam-3305	392	8	issue	issue	NOUN
ejpam-3305	392	9	7	7	NUM
ejpam-3305	392	10	,	,	PUNCT
ejpam-3305	392	11	(	(	PUNCT
ejpam-3305	392	12	2017	2017	NUM
ejpam-3305	392	13	)	)	PUNCT
ejpam-3305	392	14	,	,	PUNCT
ejpam-3305	392	15	pp	pp	ADJ
ejpam-3305	392	16	.	.	PUNCT
ejpam-3305	392	17	2491	2491	NUM
ejpam-3305	392	18	-	-	SYM
ejpam-3305	392	19	2504	2504	NUM
ejpam-3305	392	20	.	.	PUNCT
ejpam-3305	393	1	doi	doi	NOUN
ejpam-3305	393	2	:	:	PUNCT
ejpam-3305	393	3	10.1002	10.1002	NUM
ejpam-3305	393	4	/	/	SYM
ejpam-3305	393	5	mma.4171	mma.4171	NOUN
ejpam-3305	393	6	.	.	PUNCT
ejpam-3305	394	1	[	[	X
ejpam-3305	394	2	13	13	NUM
ejpam-3305	394	3	]	]	X
ejpam-3305	394	4	g.c	g.c	PROPN
ejpam-3305	394	5	.	.	PROPN
ejpam-3305	394	6	jain	jain	PROPN
ejpam-3305	394	7	,	,	PUNCT
ejpam-3305	394	8	approximation	approximation	NOUN
ejpam-3305	394	9	of	of	ADP
ejpam-3305	394	10	functions	function	NOUN
ejpam-3305	394	11	by	by	ADP
ejpam-3305	394	12	a	a	DET
ejpam-3305	394	13	new	new	ADJ
ejpam-3305	394	14	class	class	NOUN
ejpam-3305	394	15	of	of	ADP
ejpam-3305	394	16	linear	linear	PROPN
ejpam-3305	394	17	operators	operator	NOUN
ejpam-3305	394	18	,	,	PUNCT
ejpam-3305	394	19	j.	j.	PROPN
ejpam-3305	394	20	aust	aust	PROPN
ejpam-3305	394	21	.	.	PUNCT
ejpam-3305	395	1	math	math	PROPN
ejpam-3305	395	2	.	.	PUNCT
ejpam-3305	396	1	soc	soc	PROPN
ejpam-3305	396	2	.	.	PUNCT
ejpam-3305	396	3	,	,	PUNCT
ejpam-3305	396	4	13:3	13:3	NUM
ejpam-3305	396	5	(	(	PUNCT
ejpam-3305	396	6	1972	1972	NUM
ejpam-3305	396	7	)	)	PUNCT
ejpam-3305	396	8	,	,	PUNCT
ejpam-3305	396	9	271	271	NUM
ejpam-3305	396	10	-	-	SYM
ejpam-3305	396	11	276	276	NUM
ejpam-3305	396	12	.	.	PUNCT
ejpam-3305	397	1	[	[	X
ejpam-3305	397	2	14	14	NUM
ejpam-3305	397	3	]	]	PUNCT
ejpam-3305	397	4	a.	a.	PROPN
ejpam-3305	397	5	kajla	kajla	PROPN
ejpam-3305	397	6	,	,	PUNCT
ejpam-3305	397	7	direct	direct	ADJ
ejpam-3305	397	8	estimates	estimate	NOUN
ejpam-3305	397	9	of	of	ADP
ejpam-3305	397	10	certain	certain	ADJ
ejpam-3305	397	11	mihes.an	mihes.an	PROPN
ejpam-3305	397	12	-	-	PUNCT
ejpam-3305	397	13	durrmeyer	durrmeyer	NOUN
ejpam-3305	397	14	type	type	NOUN
ejpam-3305	397	15	operators	operator	NOUN
ejpam-3305	397	16	,	,	PUNCT
ejpam-3305	397	17	adv	adv	PROPN
ejpam-3305	397	18	.	.	PUNCT
ejpam-3305	397	19	oper	oper	PROPN
ejpam-3305	397	20	.	.	PROPN
ejpam-3305	397	21	theory	theory	NOUN
ejpam-3305	397	22	2	2	NUM
ejpam-3305	397	23	(	(	PUNCT
ejpam-3305	397	24	2017	2017	NUM
ejpam-3305	397	25	)	)	PUNCT
ejpam-3305	397	26	,	,	PUNCT
ejpam-3305	397	27	no	no	INTJ
ejpam-3305	397	28	.	.	NOUN
ejpam-3305	397	29	2	2	NUM
ejpam-3305	397	30	,	,	PUNCT
ejpam-3305	397	31	16217178	16217178	NUM
ejpam-3305	397	32	.	.	PUNCT
ejpam-3305	398	1	http://doi.org/10.22034/aot.1612-1079	http://doi.org/10.22034/aot.1612-1079	PROPN
ejpam-3305	399	1	[	[	X
ejpam-3305	399	2	15	15	NUM
ejpam-3305	399	3	]	]	X
ejpam-3305	399	4	a.	a.	NOUN
ejpam-3305	399	5	kajla	kajla	PROPN
ejpam-3305	399	6	,	,	PUNCT
ejpam-3305	399	7	approximation	approximation	NOUN
ejpam-3305	399	8	for	for	ADP
ejpam-3305	399	9	a	a	DET
ejpam-3305	399	10	summation	summation	NOUN
ejpam-3305	399	11	-	-	PUNCT
ejpam-3305	399	12	integral	integral	ADJ
ejpam-3305	399	13	type	type	NOUN
ejpam-3305	399	14	link	link	NOUN
ejpam-3305	399	15	operators	operator	NOUN
ejpam-3305	399	16	,	,	PUNCT
ejpam-3305	399	17	khayyam	khayyam	PROPN
ejpam-3305	399	18	.	.	PUNCT
ejpam-3305	400	1	j.	j.	PROPN
ejpam-3305	400	2	math	math	PROPN
ejpam-3305	400	3	.	.	PUNCT
ejpam-3305	401	1	3	3	NUM
ejpam-3305	401	2	(	(	PUNCT
ejpam-3305	401	3	2017	2017	NUM
ejpam-3305	401	4	)	)	PUNCT
ejpam-3305	401	5	,	,	PUNCT
ejpam-3305	401	6	no	no	INTJ
ejpam-3305	401	7	.	.	NOUN
ejpam-3305	401	8	1	1	NUM
ejpam-3305	401	9	,	,	PUNCT
ejpam-3305	401	10	441760	441760	NUM
ejpam-3305	401	11	.	.	PUNCT
ejpam-3305	402	1	doi	doi	NOUN
ejpam-3305	402	2	:	:	PUNCT
ejpam-3305	402	3	10.22034	10.22034	NUM
ejpam-3305	402	4	/	/	SYM
ejpam-3305	402	5	kjm.2017.45322	kjm.2017.45322	PROPN
ejpam-3305	402	6	[	[	X
ejpam-3305	402	7	16	16	NUM
ejpam-3305	402	8	]	]	PUNCT
ejpam-3305	402	9	a.	a.	NOUN
ejpam-3305	402	10	kumar	kumar	PROPN
ejpam-3305	402	11	,	,	PUNCT
ejpam-3305	402	12	approximation	approximation	NOUN
ejpam-3305	402	13	by	by	ADP
ejpam-3305	402	14	stancu	stancu	PROPN
ejpam-3305	402	15	type	type	NOUN
ejpam-3305	402	16	generalized	generalize	VERB
ejpam-3305	402	17	srivastava	srivastava	PROPN
ejpam-3305	402	18	-	-	PUNCT
ejpam-3305	402	19	gupta	gupta	PROPN
ejpam-3305	402	20	operators	operator	NOUN
ejpam-3305	402	21	based	base	VERB
ejpam-3305	402	22	on	on	ADP
ejpam-3305	402	23	certain	certain	ADJ
ejpam-3305	402	24	parameter	parameter	NOUN
ejpam-3305	402	25	,	,	PUNCT
ejpam-3305	402	26	khayyam	khayyam	PROPN
ejpam-3305	402	27	j.	j.	PROPN
ejpam-3305	402	28	math	math	PROPN
ejpam-3305	402	29	.	.	PUNCT
ejpam-3305	402	30	,	,	PUNCT
ejpam-3305	402	31	vol	vol	NOUN
ejpam-3305	402	32	.	.	PROPN
ejpam-3305	403	1	3	3	NUM
ejpam-3305	403	2	,	,	PUNCT
ejpam-3305	403	3	no	no	INTJ
ejpam-3305	403	4	.	.	NOUN
ejpam-3305	403	5	2	2	NUM
ejpam-3305	403	6	(	(	PUNCT
ejpam-3305	403	7	2017	2017	NUM
ejpam-3305	403	8	)	)	PUNCT
ejpam-3305	403	9	,	,	PUNCT
ejpam-3305	403	10	pp	pp	ADP
ejpam-3305	403	11	.	.	PUNCT
ejpam-3305	404	1	147	147	NUM
ejpam-3305	404	2	-	-	SYM
ejpam-3305	404	3	159	159	NUM
ejpam-3305	404	4	.	.	PUNCT
ejpam-3305	405	1	doi	doi	NOUN
ejpam-3305	405	2	:	:	PUNCT
ejpam-3305	405	3	10.22034	10.22034	NUM
ejpam-3305	405	4	/	/	SYM
ejpam-3305	405	5	kjm.2017.49477	kjm.2017.49477	NOUN
ejpam-3305	406	1	[	[	X
ejpam-3305	406	2	17	17	NUM
ejpam-3305	406	3	]	]	PUNCT
ejpam-3305	406	4	a.	a.	NOUN
ejpam-3305	406	5	kumar	kumar	PROPN
ejpam-3305	406	6	,	,	PUNCT
ejpam-3305	406	7	general	general	ADJ
ejpam-3305	406	8	gamma	gamma	NOUN
ejpam-3305	406	9	type	type	NOUN
ejpam-3305	406	10	operators	operator	NOUN
ejpam-3305	406	11	in	in	ADP
ejpam-3305	406	12	lp	lp	ADJ
ejpam-3305	406	13	spaces	space	NOUN
ejpam-3305	406	14	,	,	PUNCT
ejpam-3305	406	15	palestine	palestine	PROPN
ejpam-3305	406	16	journal	journal	PROPN
ejpam-3305	406	17	of	of	ADP
ejpam-3305	406	18	mathematics	mathematic	NOUN
ejpam-3305	406	19	,	,	PUNCT
ejpam-3305	406	20	7	7	NUM
ejpam-3305	406	21	(	(	PUNCT
ejpam-3305	406	22	1	1	NUM
ejpam-3305	406	23	)	)	PUNCT
ejpam-3305	406	24	(	(	PUNCT
ejpam-3305	406	25	2018	2018	NUM
ejpam-3305	406	26	)	)	PUNCT
ejpam-3305	406	27	,	,	PUNCT
ejpam-3305	406	28	73	73	NUM
ejpam-3305	406	29	-	-	SYM
ejpam-3305	406	30	79	79	NUM
ejpam-3305	406	31	.	.	PUNCT
ejpam-3305	407	1	references	reference	NOUN
ejpam-3305	407	2	974	974	NUM
ejpam-3305	408	1	[	[	SYM
ejpam-3305	408	2	18	18	NUM
ejpam-3305	408	3	]	]	PUNCT
ejpam-3305	408	4	a.	a.	NOUN
ejpam-3305	408	5	kumar	kumar	PROPN
ejpam-3305	408	6	,	,	PUNCT
ejpam-3305	408	7	voronovskaja	voronovskaja	PROPN
ejpam-3305	408	8	type	type	VERB
ejpam-3305	408	9	asymptotic	asymptotic	ADJ
ejpam-3305	408	10	approximation	approximation	NOUN
ejpam-3305	408	11	by	by	ADP
ejpam-3305	408	12	general	general	ADJ
ejpam-3305	408	13	gamma	gamma	PROPN
ejpam-3305	408	14	type	type	NOUN
ejpam-3305	408	15	operators	operator	NOUN
ejpam-3305	408	16	,	,	PUNCT
ejpam-3305	408	17	int	int	NOUN
ejpam-3305	408	18	.	.	PUNCT
ejpam-3305	409	1	j.	j.	PROPN
ejpam-3305	409	2	of	of	ADP
ejpam-3305	409	3	mathematics	mathematics	PROPN
ejpam-3305	409	4	and	and	CCONJ
ejpam-3305	409	5	its	its	PRON
ejpam-3305	409	6	applications	application	NOUN
ejpam-3305	409	7	,	,	PUNCT
ejpam-3305	409	8	3(4	3(4	PROPN
ejpam-3305	409	9	-	-	SYM
ejpam-3305	409	10	b	b	NOUN
ejpam-3305	409	11	)	)	PUNCT
ejpam-3305	409	12	(	(	PUNCT
ejpam-3305	409	13	2015	2015	NUM
ejpam-3305	409	14	)	)	PUNCT
ejpam-3305	409	15	71	71	NUM
ejpam-3305	409	16	-	-	SYM
ejpam-3305	409	17	78	78	NUM
ejpam-3305	409	18	.	.	PUNCT
ejpam-3305	410	1	[	[	X
ejpam-3305	410	2	19	19	NUM
ejpam-3305	410	3	]	]	PUNCT
ejpam-3305	410	4	a.	a.	NOUN
ejpam-3305	410	5	kumar	kumar	PROPN
ejpam-3305	410	6	,	,	PUNCT
ejpam-3305	410	7	d.k	d.k	PROPN
ejpam-3305	410	8	.	.	PROPN
ejpam-3305	410	9	vishwakarma	vishwakarma	PROPN
ejpam-3305	410	10	,	,	PUNCT
ejpam-3305	410	11	global	global	ADJ
ejpam-3305	410	12	approximation	approximation	NOUN
ejpam-3305	410	13	theorems	theorem	NOUN
ejpam-3305	410	14	for	for	ADP
ejpam-3305	410	15	general	general	ADJ
ejpam-3305	410	16	gamma	gamma	NOUN
ejpam-3305	410	17	type	type	NOUN
ejpam-3305	410	18	operators	operator	NOUN
ejpam-3305	410	19	,	,	PUNCT
ejpam-3305	410	20	int	int	NOUN
ejpam-3305	410	21	.	.	PUNCT
ejpam-3305	411	1	j.	j.	PROPN
ejpam-3305	411	2	of	of	ADP
ejpam-3305	411	3	adv	adv	PROPN
ejpam-3305	411	4	.	.	PUNCT
ejpam-3305	412	1	in	in	ADP
ejpam-3305	412	2	appl	appl	PROPN
ejpam-3305	412	3	.	.	PUNCT
ejpam-3305	412	4	math	math	PROPN
ejpam-3305	412	5	.	.	PUNCT
ejpam-3305	413	1	and	and	CCONJ
ejpam-3305	413	2	mech	mech	NOUN
ejpam-3305	413	3	.	.	PUNCT
ejpam-3305	414	1	3(2	3(2	NUM
ejpam-3305	414	2	)	)	PUNCT
ejpam-3305	414	3	(	(	PUNCT
ejpam-3305	414	4	2015	2015	NUM
ejpam-3305	414	5	)	)	PUNCT
ejpam-3305	414	6	,	,	PUNCT
ejpam-3305	414	7	77	77	NUM
ejpam-3305	414	8	-	-	SYM
ejpam-3305	414	9	83	83	NUM
ejpam-3305	414	10	.	.	PUNCT
ejpam-3305	415	1	[	[	X
ejpam-3305	415	2	20	20	NUM
ejpam-3305	415	3	]	]	PUNCT
ejpam-3305	415	4	a.	a.	NOUN
ejpam-3305	415	5	kumar	kumar	PROPN
ejpam-3305	415	6	,	,	PUNCT
ejpam-3305	415	7	vandana	vandana	PROPN
ejpam-3305	415	8	,	,	PUNCT
ejpam-3305	415	9	approximation	approximation	NOUN
ejpam-3305	415	10	by	by	ADP
ejpam-3305	415	11	genuine	genuine	ADJ
ejpam-3305	415	12	lupaş-beta	lupaş-beta	PROPN
ejpam-3305	415	13	-	-	PUNCT
ejpam-3305	415	14	stancu	stancu	PROPN
ejpam-3305	415	15	operators	operator	NOUN
ejpam-3305	415	16	,	,	PUNCT
ejpam-3305	415	17	j.	j.	PROPN
ejpam-3305	415	18	appl	appl	PROPN
ejpam-3305	415	19	.	.	PROPN
ejpam-3305	415	20	math	math	PROPN
ejpam-3305	415	21	.	.	PUNCT
ejpam-3305	416	1	and	and	CCONJ
ejpam-3305	416	2	informatics	informatics	PROPN
ejpam-3305	416	3	,	,	PUNCT
ejpam-3305	416	4	vol	vol	NOUN
ejpam-3305	416	5	.	.	PROPN
ejpam-3305	416	6	36	36	NUM
ejpam-3305	416	7	(	(	PUNCT
ejpam-3305	416	8	2018	2018	NUM
ejpam-3305	416	9	)	)	PUNCT
ejpam-3305	416	10	,	,	PUNCT
ejpam-3305	416	11	no	no	INTJ
ejpam-3305	416	12	.	.	NOUN
ejpam-3305	416	13	1	1	NUM
ejpam-3305	416	14	-	-	SYM
ejpam-3305	416	15	2	2	NUM
ejpam-3305	416	16	,	,	PUNCT
ejpam-3305	416	17	pp	pp	ADJ
ejpam-3305	416	18	.	.	PUNCT
ejpam-3305	417	1	15	15	NUM
ejpam-3305	417	2	-	-	SYM
ejpam-3305	417	3	28	28	NUM
ejpam-3305	417	4	.	.	PUNCT
ejpam-3305	418	1	https://doi.org/10.14317/jami.2018.015	https://doi.org/10.14317/jami.2018.015	PROPN
ejpam-3305	418	2	[	[	X
ejpam-3305	418	3	21	21	NUM
ejpam-3305	418	4	]	]	PUNCT
ejpam-3305	418	5	a.	a.	NOUN
ejpam-3305	418	6	kumar	kumar	PROPN
ejpam-3305	418	7	,	,	PUNCT
ejpam-3305	418	8	vandana	vandana	PROPN
ejpam-3305	418	9	,	,	PUNCT
ejpam-3305	418	10	some	some	DET
ejpam-3305	418	11	approximation	approximation	NOUN
ejpam-3305	418	12	properties	property	NOUN
ejpam-3305	418	13	of	of	ADP
ejpam-3305	418	14	generalized	generalized	ADJ
ejpam-3305	418	15	integral	integral	ADJ
ejpam-3305	418	16	type	type	NOUN
ejpam-3305	418	17	operators	operator	NOUN
ejpam-3305	418	18	,	,	PUNCT
ejpam-3305	418	19	tbilisi	tbilisi	PROPN
ejpam-3305	418	20	mathematical	mathematical	PROPN
ejpam-3305	418	21	journal	journal	PROPN
ejpam-3305	418	22	,	,	PUNCT
ejpam-3305	418	23	11	11	NUM
ejpam-3305	418	24	(	(	PUNCT
ejpam-3305	418	25	1	1	NUM
ejpam-3305	418	26	)	)	PUNCT
ejpam-3305	418	27	(	(	PUNCT
ejpam-3305	418	28	2018	2018	NUM
ejpam-3305	418	29	)	)	PUNCT
ejpam-3305	418	30	,	,	PUNCT
ejpam-3305	418	31	pp	pp	PROPN
ejpam-3305	418	32	.	.	PUNCT
ejpam-3305	419	1	99	99	NUM
ejpam-3305	419	2	-	-	SYM
ejpam-3305	419	3	116	116	NUM
ejpam-3305	419	4	.	.	PUNCT
ejpam-3305	420	1	doi	doi	PROPN
ejpam-3305	420	2	10.2478	10.2478	NUM
ejpam-3305	420	3	/	/	SYM
ejpam-3305	420	4	tmj2018	tmj2018	NOUN
ejpam-3305	420	5	-	-	PUNCT
ejpam-3305	420	6	0007	0007	NUM
ejpam-3305	420	7	.	.	PUNCT
ejpam-3305	421	1	[	[	X
ejpam-3305	421	2	22	22	NUM
ejpam-3305	421	3	]	]	PUNCT
ejpam-3305	421	4	a.	a.	NOUN
ejpam-3305	421	5	kumar	kumar	PROPN
ejpam-3305	421	6	,	,	PUNCT
ejpam-3305	421	7	vandana	vandana	PROPN
ejpam-3305	421	8	,	,	PUNCT
ejpam-3305	421	9	approximation	approximation	NOUN
ejpam-3305	421	10	properties	property	NOUN
ejpam-3305	421	11	of	of	ADP
ejpam-3305	421	12	modified	modified	ADJ
ejpam-3305	421	13	srivastava	srivastava	PROPN
ejpam-3305	421	14	-	-	PUNCT
ejpam-3305	421	15	gupta	gupta	PROPN
ejpam-3305	421	16	operators	operator	NOUN
ejpam-3305	421	17	based	base	VERB
ejpam-3305	421	18	on	on	ADP
ejpam-3305	421	19	certain	certain	ADJ
ejpam-3305	421	20	parameter	parameter	NOUN
ejpam-3305	421	21	,	,	PUNCT
ejpam-3305	421	22	bol	bol	NOUN
ejpam-3305	421	23	.	.	PUNCT
ejpam-3305	421	24	soc	soc	PROPN
ejpam-3305	421	25	.	.	PUNCT
ejpam-3305	422	1	paran	paran	PROPN
ejpam-3305	422	2	.	.	PUNCT
ejpam-3305	423	1	mat	mat	PROPN
ejpam-3305	423	2	.	.	PROPN
ejpam-3305	423	3	,	,	PUNCT
ejpam-3305	423	4	v.	v.	ADP
ejpam-3305	423	5	38	38	NUM
ejpam-3305	423	6	(	(	PUNCT
ejpam-3305	423	7	1	1	NUM
ejpam-3305	423	8	)	)	PUNCT
ejpam-3305	423	9	(	(	PUNCT
ejpam-3305	423	10	2020	2020	NUM
ejpam-3305	423	11	)	)	PUNCT
ejpam-3305	423	12	,	,	PUNCT
ejpam-3305	423	13	41	41	NUM
ejpam-3305	423	14	-	-	SYM
ejpam-3305	423	15	53	53	NUM
ejpam-3305	423	16	.	.	PUNCT
ejpam-3305	423	17	doi:10.5269	doi:10.5269	ADJ
ejpam-3305	423	18	/	/	SYM
ejpam-3305	423	19	bspm.v38i1.36907	bspm.v38i1.36907	X
ejpam-3305	424	1	[	[	X
ejpam-3305	424	2	23	23	NUM
ejpam-3305	424	3	]	]	PUNCT
ejpam-3305	424	4	a.	a.	NOUN
ejpam-3305	424	5	kumar	kumar	PROPN
ejpam-3305	424	6	,	,	PUNCT
ejpam-3305	424	7	l.n	l.n	PROPN
ejpam-3305	424	8	.	.	PROPN
ejpam-3305	424	9	mishra	mishra	PROPN
ejpam-3305	424	10	,	,	PUNCT
ejpam-3305	424	11	approximation	approximation	NOUN
ejpam-3305	424	12	by	by	ADP
ejpam-3305	424	13	modified	modify	VERB
ejpam-3305	424	14	jain	jain	PROPN
ejpam-3305	424	15	-	-	PUNCT
ejpam-3305	424	16	baskakov	baskakov	PROPN
ejpam-3305	424	17	-	-	PUNCT
ejpam-3305	424	18	stancu	stancu	PROPN
ejpam-3305	424	19	operators	operator	NOUN
ejpam-3305	424	20	,	,	PUNCT
ejpam-3305	424	21	tbilisi	tbilisi	PROPN
ejpam-3305	424	22	mathematical	mathematical	PROPN
ejpam-3305	424	23	journal	journal	PROPN
ejpam-3305	424	24	,	,	PUNCT
ejpam-3305	424	25	10(2	10(2	NUM
ejpam-3305	424	26	)	)	PUNCT
ejpam-3305	424	27	(	(	PUNCT
ejpam-3305	424	28	2017	2017	NUM
ejpam-3305	424	29	)	)	PUNCT
ejpam-3305	424	30	,	,	PUNCT
ejpam-3305	424	31	pp	pp	ADP
ejpam-3305	424	32	.	.	PUNCT
ejpam-3305	425	1	185	185	NUM
ejpam-3305	425	2	-	-	SYM
ejpam-3305	425	3	199	199	NUM
ejpam-3305	425	4	.	.	PUNCT
ejpam-3305	426	1	[	[	X
ejpam-3305	426	2	24	24	NUM
ejpam-3305	426	3	]	]	PUNCT
ejpam-3305	426	4	a.	a.	NOUN
ejpam-3305	426	5	kumar	kumar	PROPN
ejpam-3305	426	6	,	,	PUNCT
ejpam-3305	426	7	v.n	v.n	PROPN
ejpam-3305	426	8	.	.	PROPN
ejpam-3305	426	9	mishra	mishra	PROPN
ejpam-3305	426	10	,	,	PUNCT
ejpam-3305	426	11	dipti	dipti	VERB
ejpam-3305	426	12	tapiawala	tapiawala	ADJ
ejpam-3305	426	13	,	,	PUNCT
ejpam-3305	426	14	stancu	stancu	ADJ
ejpam-3305	426	15	type	type	NOUN
ejpam-3305	426	16	generalization	generalization	NOUN
ejpam-3305	426	17	of	of	ADP
ejpam-3305	426	18	modified	modify	VERB
ejpam-3305	426	19	srivastava	srivastava	PROPN
ejpam-3305	426	20	-	-	PUNCT
ejpam-3305	426	21	gupta	gupta	PROPN
ejpam-3305	426	22	operators	operator	NOUN
ejpam-3305	426	23	,	,	PUNCT
ejpam-3305	426	24	eur	eur	PROPN
ejpam-3305	426	25	.	.	PUNCT
ejpam-3305	427	1	j.	j.	PROPN
ejpam-3305	427	2	pure	pure	PROPN
ejpam-3305	427	3	appl	appl	PROPN
ejpam-3305	427	4	.	.	PUNCT
ejpam-3305	427	5	math	math	PROPN
ejpam-3305	427	6	.	.	PUNCT
ejpam-3305	428	1	,	,	PUNCT
ejpam-3305	428	2	vol	vol	NOUN
ejpam-3305	428	3	.	.	PROPN
ejpam-3305	429	1	10	10	NUM
ejpam-3305	429	2	,	,	PUNCT
ejpam-3305	429	3	no	no	INTJ
ejpam-3305	429	4	.	.	NOUN
ejpam-3305	429	5	4	4	NUM
ejpam-3305	429	6	(	(	PUNCT
ejpam-3305	429	7	2017	2017	NUM
ejpam-3305	429	8	)	)	PUNCT
ejpam-3305	429	9	,	,	PUNCT
ejpam-3305	429	10	890907	890907	NUM
ejpam-3305	429	11	.	.	PUNCT
ejpam-3305	430	1	[	[	X
ejpam-3305	430	2	25	25	NUM
ejpam-3305	430	3	]	]	PUNCT
ejpam-3305	430	4	a.	a.	NOUN
ejpam-3305	430	5	sathish	sathish	PROPN
ejpam-3305	430	6	kumar	kumar	PROPN
ejpam-3305	430	7	,	,	PUNCT
ejpam-3305	430	8	t.	t.	NOUN
ejpam-3305	430	9	acar	acar	NOUN
ejpam-3305	430	10	,	,	PUNCT
ejpam-3305	430	11	approximation	approximation	NOUN
ejpam-3305	430	12	by	by	ADP
ejpam-3305	430	13	generalized	generalized	ADJ
ejpam-3305	430	14	baskakov	baskakov	PROPN
ejpam-3305	430	15	-	-	PUNCT
ejpam-3305	430	16	durrmeyerstancu	durrmeyerstancu	ADJ
ejpam-3305	430	17	type	type	NOUN
ejpam-3305	430	18	operators	operator	NOUN
ejpam-3305	430	19	,	,	PUNCT
ejpam-3305	430	20	rend.circ.mat	rend.circ.mat	NOUN
ejpam-3305	430	21	.	.	PUNCT
ejpam-3305	430	22	palermo	palermo	NOUN
ejpam-3305	430	23	,	,	PUNCT
ejpam-3305	430	24	65	65	NUM
ejpam-3305	430	25	(	(	PUNCT
ejpam-3305	430	26	3	3	NUM
ejpam-3305	430	27	)	)	PUNCT
ejpam-3305	430	28	(	(	PUNCT
ejpam-3305	430	29	2016	2016	NUM
ejpam-3305	430	30	)	)	PUNCT
ejpam-3305	430	31	.	.	PUNCT
ejpam-3305	431	1	doi	doi	X
ejpam-3305	431	2	10.1007	10.1007	NUM
ejpam-3305	431	3	/	/	SYM
ejpam-3305	431	4	s12215016	s12215016	PROPN
ejpam-3305	431	5	-	-	PUNCT
ejpam-3305	431	6	0242	0242	NUM
ejpam-3305	431	7	-	-	SYM
ejpam-3305	431	8	1	1	NUM
ejpam-3305	432	1	[	[	X
ejpam-3305	432	2	26	26	NUM
ejpam-3305	432	3	]	]	X
ejpam-3305	432	4	j.p	j.p	PROPN
ejpam-3305	432	5	.	.	PROPN
ejpam-3305	432	6	king	king	PROPN
ejpam-3305	432	7	,	,	PUNCT
ejpam-3305	432	8	positive	positive	ADJ
ejpam-3305	432	9	linear	linear	NOUN
ejpam-3305	432	10	operators	operator	NOUN
ejpam-3305	432	11	which	which	PRON
ejpam-3305	432	12	preserve	preserve	VERB
ejpam-3305	432	13	x2	x2	PROPN
ejpam-3305	432	14	,	,	PUNCT
ejpam-3305	432	15	acta	acta	PROPN
ejpam-3305	432	16	math	math	PROPN
ejpam-3305	432	17	.	.	PUNCT
ejpam-3305	433	1	hungar	hungar	PROPN
ejpam-3305	433	2	.	.	PUNCT
ejpam-3305	433	3	,	,	PUNCT
ejpam-3305	433	4	99(3	99(3	NUM
ejpam-3305	433	5	)	)	PUNCT
ejpam-3305	433	6	(	(	PUNCT
ejpam-3305	433	7	2003	2003	NUM
ejpam-3305	433	8	)	)	PUNCT
ejpam-3305	433	9	,	,	PUNCT
ejpam-3305	433	10	203	203	NUM
ejpam-3305	433	11	-	-	SYM
ejpam-3305	433	12	208	208	NUM
ejpam-3305	433	13	.	.	PUNCT
ejpam-3305	434	1	[	[	X
ejpam-3305	434	2	27	27	NUM
ejpam-3305	434	3	]	]	X
ejpam-3305	434	4	kejal	kejal	PROPN
ejpam-3305	434	5	khatri	khatri	PROPN
ejpam-3305	434	6	,	,	PUNCT
ejpam-3305	434	7	v.n	v.n	PROPN
ejpam-3305	434	8	.	.	PROPN
ejpam-3305	434	9	mishra	mishra	PROPN
ejpam-3305	434	10	,	,	PUNCT
ejpam-3305	434	11	generalized	generalize	VERB
ejpam-3305	434	12	szasz	szasz	NOUN
ejpam-3305	434	13	-	-	PUNCT
ejpam-3305	434	14	mirakyan	mirakyan	ADJ
ejpam-3305	434	15	operators	operator	NOUN
ejpam-3305	434	16	involving	involve	VERB
ejpam-3305	434	17	brenke	brenke	ADJ
ejpam-3305	434	18	type	type	NOUN
ejpam-3305	434	19	polynomials	polynomial	NOUN
ejpam-3305	434	20	,	,	PUNCT
ejpam-3305	434	21	appl	appl	PROPN
ejpam-3305	434	22	.	.	PROPN
ejpam-3305	434	23	math	math	PROPN
ejpam-3305	434	24	.	.	PUNCT
ejpam-3305	435	1	comp	comp	PROPN
ejpam-3305	435	2	.	.	PUNCT
ejpam-3305	435	3	,	,	PUNCT
ejpam-3305	435	4	324	324	NUM
ejpam-3305	435	5	(	(	PUNCT
ejpam-3305	435	6	2018	2018	NUM
ejpam-3305	435	7	)	)	PUNCT
ejpam-3305	435	8	,	,	PUNCT
ejpam-3305	435	9	228	228	NUM
ejpam-3305	435	10	-	-	SYM
ejpam-3305	435	11	238	238	NUM
ejpam-3305	435	12	.	.	PUNCT
ejpam-3305	436	1	[	[	X
ejpam-3305	436	2	28	28	NUM
ejpam-3305	436	3	]	]	X
ejpam-3305	436	4	c.p	c.p	PROPN
ejpam-3305	436	5	.	.	PROPN
ejpam-3305	437	1	may	may	AUX
ejpam-3305	437	2	,	,	PUNCT
ejpam-3305	437	3	on	on	ADP
ejpam-3305	437	4	phillips	phillips	PROPN
ejpam-3305	437	5	operators	operators	PROPN
ejpam-3305	437	6	,	,	PUNCT
ejpam-3305	437	7	j.	j.	PROPN
ejpam-3305	437	8	approx	approx	PROPN
ejpam-3305	437	9	.	.	PUNCT
ejpam-3305	438	1	theory	theory	NOUN
ejpam-3305	438	2	,	,	PUNCT
ejpam-3305	438	3	20	20	NUM
ejpam-3305	438	4	(	(	PUNCT
ejpam-3305	438	5	1977	1977	NUM
ejpam-3305	438	6	)	)	PUNCT
ejpam-3305	438	7	,	,	PUNCT
ejpam-3305	438	8	315	315	NUM
ejpam-3305	438	9	-	-	SYM
ejpam-3305	438	10	332	332	NUM
ejpam-3305	438	11	.	.	PUNCT
ejpam-3305	439	1	[	[	X
ejpam-3305	439	2	29	29	NUM
ejpam-3305	439	3	]	]	X
ejpam-3305	439	4	m.	m.	NOUN
ejpam-3305	439	5	mursaleen	mursaleen	PROPN
ejpam-3305	439	6	,	,	PUNCT
ejpam-3305	439	7	t.	t.	PROPN
ejpam-3305	439	8	khan	khan	PROPN
ejpam-3305	439	9	,	,	PUNCT
ejpam-3305	439	10	on	on	ADP
ejpam-3305	439	11	approximation	approximation	NOUN
ejpam-3305	439	12	by	by	ADP
ejpam-3305	439	13	stancu	stancu	ADJ
ejpam-3305	439	14	type	type	NOUN
ejpam-3305	439	15	jakimovski	jakimovski	ADJ
ejpam-3305	439	16	-	-	PUNCT
ejpam-3305	439	17	leviatandurrmeyer	leviatandurrmeyer	NOUN
ejpam-3305	439	18	operators	operator	NOUN
ejpam-3305	439	19	,	,	PUNCT
ejpam-3305	439	20	azerbaijan	azerbaijan	PROPN
ejpam-3305	439	21	journal	journal	PROPN
ejpam-3305	439	22	of	of	ADP
ejpam-3305	439	23	mathematics	mathematic	NOUN
ejpam-3305	439	24	,	,	PUNCT
ejpam-3305	439	25	v.	v.	ADP
ejpam-3305	439	26	7	7	NUM
ejpam-3305	439	27	,	,	PUNCT
ejpam-3305	439	28	no	no	DET
ejpam-3305	439	29	1	1	NUM
ejpam-3305	439	30	(	(	PUNCT
ejpam-3305	439	31	2017	2017	NUM
ejpam-3305	439	32	)	)	PUNCT
ejpam-3305	439	33	,	,	PUNCT
ejpam-3305	439	34	16	16	NUM
ejpam-3305	439	35	-	-	SYM
ejpam-3305	439	36	26	26	NUM
ejpam-3305	439	37	.	.	PUNCT
ejpam-3305	440	1	[	[	X
ejpam-3305	440	2	30	30	NUM
ejpam-3305	440	3	]	]	X
ejpam-3305	440	4	v.n	v.n	PROPN
ejpam-3305	440	5	.	.	PROPN
ejpam-3305	440	6	mishra	mishra	PROPN
ejpam-3305	440	7	,	,	PUNCT
ejpam-3305	440	8	preeti	preeti	PROPN
ejpam-3305	440	9	sharma	sharma	PROPN
ejpam-3305	440	10	,	,	PUNCT
ejpam-3305	440	11	on	on	ADP
ejpam-3305	440	12	approximation	approximation	NOUN
ejpam-3305	440	13	properties	property	NOUN
ejpam-3305	440	14	of	of	ADP
ejpam-3305	440	15	baskakov	baskakov	PROPN
ejpam-3305	440	16	-	-	PUNCT
ejpam-3305	440	17	schurer	schurer	NOUN
ejpam-3305	440	18	-	-	PUNCT
ejpam-3305	440	19	sźasz	sźasz	NOUN
ejpam-3305	440	20	operators	operator	NOUN
ejpam-3305	440	21	,	,	PUNCT
ejpam-3305	440	22	arxiv:1508.05292v1	arxiv:1508.05292v1	PRON
ejpam-3305	441	1	[	[	X
ejpam-3305	441	2	math.fa	math.fa	X
ejpam-3305	441	3	]	]	X
ejpam-3305	441	4	21	21	NUM
ejpam-3305	441	5	aug	aug	PROPN
ejpam-3305	441	6	2015	2015	NUM
ejpam-3305	441	7	.	.	PUNCT
ejpam-3305	442	1	[	[	X
ejpam-3305	442	2	31	31	NUM
ejpam-3305	442	3	]	]	X
ejpam-3305	442	4	v.n	v.n	PROPN
ejpam-3305	442	5	.	.	PROPN
ejpam-3305	442	6	mishra	mishra	PROPN
ejpam-3305	442	7	,	,	PUNCT
ejpam-3305	442	8	k.	k.	PROPN
ejpam-3305	442	9	khatri	khatri	PROPN
ejpam-3305	442	10	,	,	PUNCT
ejpam-3305	442	11	l.n	l.n	PROPN
ejpam-3305	442	12	.	.	PROPN
ejpam-3305	442	13	mishra	mishra	PROPN
ejpam-3305	442	14	,	,	PUNCT
ejpam-3305	442	15	some	some	DET
ejpam-3305	442	16	approximation	approximation	NOUN
ejpam-3305	442	17	properties	property	NOUN
ejpam-3305	442	18	of	of	ADP
ejpam-3305	442	19	q	q	NOUN
ejpam-3305	442	20	-	-	PUNCT
ejpam-3305	442	21	baskakovbeta	baskakovbeta	NOUN
ejpam-3305	442	22	-	-	PUNCT
ejpam-3305	442	23	stancu	stancu	PROPN
ejpam-3305	442	24	type	type	NOUN
ejpam-3305	442	25	operators	operator	NOUN
ejpam-3305	442	26	,	,	PUNCT
ejpam-3305	442	27	journal	journal	NOUN
ejpam-3305	442	28	of	of	ADP
ejpam-3305	442	29	calculus	calculus	NOUN
ejpam-3305	442	30	of	of	ADP
ejpam-3305	442	31	variations	variation	NOUN
ejpam-3305	442	32	,	,	PUNCT
ejpam-3305	442	33	volume	volume	NOUN
ejpam-3305	442	34	2013	2013	NUM
ejpam-3305	442	35	,	,	PUNCT
ejpam-3305	442	36	article	article	NOUN
ejpam-3305	442	37	i	i	PROPN
ejpam-3305	442	38	d	d	PROPN
ejpam-3305	442	39	814824	814824	NUM
ejpam-3305	442	40	,	,	PUNCT
ejpam-3305	442	41	8	8	NUM
ejpam-3305	442	42	pages	page	NOUN
ejpam-3305	442	43	.	.	PUNCT
ejpam-3305	443	1	references	reference	NOUN
ejpam-3305	443	2	975	975	NUM
ejpam-3305	444	1	[	[	X
ejpam-3305	444	2	32	32	NUM
ejpam-3305	444	3	]	]	X
ejpam-3305	444	4	v.n	v.n	PROPN
ejpam-3305	444	5	.	.	PROPN
ejpam-3305	444	6	mishra	mishra	PROPN
ejpam-3305	444	7	,	,	PUNCT
ejpam-3305	444	8	k.	k.	PROPN
ejpam-3305	444	9	khatri	khatri	PROPN
ejpam-3305	444	10	,	,	PUNCT
ejpam-3305	444	11	l.n	l.n	PROPN
ejpam-3305	444	12	.	.	PROPN
ejpam-3305	444	13	mishra	mishra	PROPN
ejpam-3305	444	14	,	,	PUNCT
ejpam-3305	444	15	deepmala	deepmala	PROPN
ejpam-3305	444	16	,	,	PUNCT
ejpam-3305	444	17	inverse	inverse	NOUN
ejpam-3305	444	18	result	result	NOUN
ejpam-3305	444	19	in	in	ADP
ejpam-3305	444	20	simultaneous	simultaneous	ADJ
ejpam-3305	444	21	approximation	approximation	NOUN
ejpam-3305	444	22	by	by	ADP
ejpam-3305	444	23	baskakov	baskakov	PROPN
ejpam-3305	444	24	-	-	PUNCT
ejpam-3305	444	25	durrmeyer	durrmeyer	NOUN
ejpam-3305	444	26	-	-	PUNCT
ejpam-3305	444	27	stancu	stancu	PROPN
ejpam-3305	444	28	operators	operator	NOUN
ejpam-3305	444	29	,	,	PUNCT
ejpam-3305	444	30	journal	journal	NOUN
ejpam-3305	444	31	of	of	ADP
ejpam-3305	444	32	inequalities	inequality	NOUN
ejpam-3305	444	33	and	and	CCONJ
ejpam-3305	444	34	applications	application	NOUN
ejpam-3305	444	35	2013	2013	NUM
ejpam-3305	444	36	,	,	PUNCT
ejpam-3305	444	37	2013:586	2013:586	NUM
ejpam-3305	444	38	.	.	PUNCT
ejpam-3305	444	39	doi:10.1186/1029	doi:10.1186/1029	VERB
ejpam-3305	444	40	-	-	PROPN
ejpam-3305	444	41	242x-2013	242x-2013	NUM
ejpam-3305	444	42	-	-	PUNCT
ejpam-3305	444	43	586	586	NUM
ejpam-3305	444	44	.	.	PUNCT
ejpam-3305	445	1	[	[	X
ejpam-3305	445	2	33	33	NUM
ejpam-3305	445	3	]	]	X
ejpam-3305	445	4	v.n	v.n	PROPN
ejpam-3305	445	5	.	.	PROPN
ejpam-3305	445	6	mishra	mishra	PROPN
ejpam-3305	445	7	,	,	PUNCT
ejpam-3305	445	8	rajiv	rajiv	PROPN
ejpam-3305	445	9	b.	b.	PROPN
ejpam-3305	445	10	gandhi	gandhi	PROPN
ejpam-3305	445	11	,	,	PUNCT
ejpam-3305	445	12	ram	ram	NOUN
ejpam-3305	445	13	n.	n.	NOUN
ejpam-3305	445	14	mohapatraa	mohapatraa	NOUN
ejpam-3305	445	15	,	,	PUNCT
ejpam-3305	445	16	summation	summation	NOUN
ejpam-3305	445	17	-	-	PUNCT
ejpam-3305	445	18	integral	integral	ADJ
ejpam-3305	445	19	type	type	NOUN
ejpam-3305	445	20	modification	modification	NOUN
ejpam-3305	445	21	of	of	ADP
ejpam-3305	445	22	sźasz	sźasz	NOUN
ejpam-3305	445	23	-	-	PUNCT
ejpam-3305	445	24	mirakjan	mirakjan	NOUN
ejpam-3305	445	25	-	-	PUNCT
ejpam-3305	445	26	stancu	stancu	PROPN
ejpam-3305	445	27	operators	operator	NOUN
ejpam-3305	445	28	,	,	PUNCT
ejpam-3305	445	29	j.	j.	PROPN
ejpam-3305	445	30	numer	numer	PROPN
ejpam-3305	445	31	.	.	PUNCT
ejpam-3305	445	32	anal	anal	PROPN
ejpam-3305	445	33	.	.	PUNCT
ejpam-3305	446	1	approx	approx	PROPN
ejpam-3305	446	2	.	.	PUNCT
ejpam-3305	447	1	theory	theory	NOUN
ejpam-3305	447	2	,	,	PUNCT
ejpam-3305	447	3	vol	vol	NOUN
ejpam-3305	447	4	.	.	PROPN
ejpam-3305	447	5	45	45	NUM
ejpam-3305	447	6	,	,	PUNCT
ejpam-3305	447	7	no.1	no.1	NUM
ejpam-3305	447	8	(	(	PUNCT
ejpam-3305	447	9	2016	2016	NUM
ejpam-3305	447	10	)	)	PUNCT
ejpam-3305	447	11	,	,	PUNCT
ejpam-3305	447	12	pp	pp	PROPN
ejpam-3305	447	13	.	.	PUNCT
ejpam-3305	448	1	27	27	NUM
ejpam-3305	448	2	-	-	SYM
ejpam-3305	448	3	36	36	NUM
ejpam-3305	448	4	.	.	PUNCT
ejpam-3305	449	1	[	[	X
ejpam-3305	449	2	34	34	NUM
ejpam-3305	449	3	]	]	X
ejpam-3305	449	4	v.n	v.n	PROPN
ejpam-3305	449	5	.	.	PROPN
ejpam-3305	449	6	mishra	mishra	PROPN
ejpam-3305	449	7	,	,	PUNCT
ejpam-3305	449	8	a.r	a.r	PROPN
ejpam-3305	449	9	.	.	PROPN
ejpam-3305	449	10	devdhara	devdhara	PROPN
ejpam-3305	449	11	,	,	PUNCT
ejpam-3305	449	12	r.b	r.b	PROPN
ejpam-3305	449	13	.	.	PROPN
ejpam-3305	449	14	gandhi	gandhi	PROPN
ejpam-3305	449	15	,	,	PUNCT
ejpam-3305	449	16	global	global	ADJ
ejpam-3305	449	17	approximation	approximation	NOUN
ejpam-3305	449	18	theorems	theorem	NOUN
ejpam-3305	449	19	for	for	ADP
ejpam-3305	449	20	the	the	DET
ejpam-3305	449	21	generalized	generalize	VERB
ejpam-3305	449	22	szasz	szasz	NOUN
ejpam-3305	449	23	-	-	PUNCT
ejpam-3305	449	24	mirakjan	mirakjan	NOUN
ejpam-3305	449	25	type	type	NOUN
ejpam-3305	449	26	operators	operator	NOUN
ejpam-3305	449	27	in	in	ADP
ejpam-3305	449	28	exponential	exponential	ADJ
ejpam-3305	449	29	weight	weight	NOUN
ejpam-3305	449	30	spaces	space	NOUN
ejpam-3305	449	31	,	,	PUNCT
ejpam-3305	449	32	appl	appl	PROPN
ejpam-3305	449	33	.	.	PROPN
ejpam-3305	449	34	math	math	PROPN
ejpam-3305	449	35	.	.	PUNCT
ejpam-3305	450	1	comp	comp	PROPN
ejpam-3305	450	2	.	.	PUNCT
ejpam-3305	450	3	,	,	PUNCT
ejpam-3305	450	4	336	336	NUM
ejpam-3305	450	5	(	(	PUNCT
ejpam-3305	450	6	2018	2018	NUM
ejpam-3305	450	7	)	)	PUNCT
ejpam-3305	450	8	,	,	PUNCT
ejpam-3305	450	9	206	206	NUM
ejpam-3305	450	10	-	-	SYM
ejpam-3305	450	11	214	214	NUM
ejpam-3305	450	12	.	.	PUNCT
ejpam-3305	451	1	[	[	X
ejpam-3305	451	2	35	35	NUM
ejpam-3305	451	3	]	]	X
ejpam-3305	451	4	v.n	v.n	PROPN
ejpam-3305	451	5	.	.	PROPN
ejpam-3305	451	6	mishra	mishra	PROPN
ejpam-3305	451	7	,	,	PUNCT
ejpam-3305	451	8	h.h	h.h	PROPN
ejpam-3305	451	9	.	.	PROPN
ejpam-3305	451	10	khan	khan	PROPN
ejpam-3305	451	11	,	,	PUNCT
ejpam-3305	451	12	kejal	kejal	PROPN
ejpam-3305	451	13	khatri	khatri	PROPN
ejpam-3305	451	14	and	and	CCONJ
ejpam-3305	451	15	l.n	l.n	PROPN
ejpam-3305	451	16	.	.	PROPN
ejpam-3305	451	17	mishra	mishra	PROPN
ejpam-3305	451	18	,	,	PUNCT
ejpam-3305	451	19	hypergeometric	hypergeometric	ADJ
ejpam-3305	451	20	representation	representation	NOUN
ejpam-3305	451	21	for	for	ADP
ejpam-3305	451	22	baskakov	baskakov	PROPN
ejpam-3305	451	23	-	-	PUNCT
ejpam-3305	451	24	durrmeyer	durrmeyer	NOUN
ejpam-3305	451	25	-	-	PUNCT
ejpam-3305	451	26	stancu	stancu	NOUN
ejpam-3305	451	27	type	type	NOUN
ejpam-3305	451	28	operators	operator	NOUN
ejpam-3305	451	29	,	,	PUNCT
ejpam-3305	451	30	bulletin	bulletin	NOUN
ejpam-3305	451	31	of	of	ADP
ejpam-3305	451	32	mathematical	mathematical	ADJ
ejpam-3305	451	33	analysis	analysis	NOUN
ejpam-3305	451	34	and	and	CCONJ
ejpam-3305	451	35	applications	application	NOUN
ejpam-3305	451	36	,	,	PUNCT
ejpam-3305	451	37	issn	issn	PROPN
ejpam-3305	451	38	:	:	PUNCT
ejpam-3305	451	39	1821	1821	NUM
ejpam-3305	451	40	-	-	SYM
ejpam-3305	451	41	129	129	NUM
ejpam-3305	451	42	,	,	PUNCT
ejpam-3305	451	43	vol	vol	NOUN
ejpam-3305	451	44	.	.	PROPN
ejpam-3305	451	45	5	5	NUM
ejpam-3305	451	46	,	,	PUNCT
ejpam-3305	451	47	issue	issue	NOUN
ejpam-3305	451	48	3	3	NUM
ejpam-3305	451	49	,	,	PUNCT
ejpam-3305	451	50	(	(	PUNCT
ejpam-3305	451	51	2013	2013	NUM
ejpam-3305	451	52	)	)	PUNCT
ejpam-3305	451	53	,	,	PUNCT
ejpam-3305	451	54	18	18	NUM
ejpam-3305	451	55	-	-	SYM
ejpam-3305	451	56	26	26	NUM
ejpam-3305	451	57	.	.	PUNCT
ejpam-3305	452	1	[	[	X
ejpam-3305	452	2	36	36	NUM
ejpam-3305	452	3	]	]	X
ejpam-3305	452	4	v.n	v.n	PROPN
ejpam-3305	452	5	.	.	PROPN
ejpam-3305	452	6	mishra	mishra	PROPN
ejpam-3305	452	7	,	,	PUNCT
ejpam-3305	452	8	kejal	kejal	PROPN
ejpam-3305	452	9	khatri	khatri	PROPN
ejpam-3305	452	10	and	and	CCONJ
ejpam-3305	452	11	l.n	l.n	PROPN
ejpam-3305	452	12	.	.	PROPN
ejpam-3305	452	13	mishra	mishra	PROPN
ejpam-3305	452	14	,	,	PUNCT
ejpam-3305	452	15	statistical	statistical	ADJ
ejpam-3305	452	16	approximation	approximation	NOUN
ejpam-3305	452	17	by	by	ADP
ejpam-3305	452	18	kantorovich	kantorovich	PROPN
ejpam-3305	452	19	type	type	NOUN
ejpam-3305	452	20	discrete	discrete	ADJ
ejpam-3305	452	21	q	q	ADJ
ejpam-3305	452	22	-	-	PUNCT
ejpam-3305	452	23	beta	beta	ADJ
ejpam-3305	452	24	operators	operator	NOUN
ejpam-3305	452	25	,	,	PUNCT
ejpam-3305	452	26	advances	advance	NOUN
ejpam-3305	452	27	in	in	ADP
ejpam-3305	452	28	difference	difference	NOUN
ejpam-3305	452	29	equations	equation	NOUN
ejpam-3305	452	30	,	,	PUNCT
ejpam-3305	452	31	2013	2013	NUM
ejpam-3305	452	32	,	,	PUNCT
ejpam-3305	452	33	2013:345	2013:345	NUM
ejpam-3305	452	34	,	,	PUNCT
ejpam-3305	452	35	doi	doi	NOUN
ejpam-3305	452	36	:	:	PUNCT
ejpam-3305	452	37	10.1186/10.1186/1687	10.1186/10.1186/1687	NUM
ejpam-3305	452	38	-	-	PUNCT
ejpam-3305	452	39	1847	1847	NUM
ejpam-3305	452	40	-	-	PUNCT
ejpam-3305	452	41	2013	2013	NUM
ejpam-3305	452	42	-	-	SYM
ejpam-3305	452	43	345	345	NUM
ejpam-3305	452	44	.	.	PUNCT
ejpam-3305	453	1	[	[	X
ejpam-3305	453	2	37	37	NUM
ejpam-3305	453	3	]	]	X
ejpam-3305	453	4	v.n	v.n	PROPN
ejpam-3305	453	5	.	.	PROPN
ejpam-3305	453	6	mishra	mishra	PROPN
ejpam-3305	453	7	,	,	PUNCT
ejpam-3305	453	8	kejal	kejal	PROPN
ejpam-3305	453	9	khatri	khatri	PROPN
ejpam-3305	453	10	and	and	CCONJ
ejpam-3305	453	11	l.n	l.n	PROPN
ejpam-3305	453	12	.	.	PROPN
ejpam-3305	453	13	mishra	mishra	PROPN
ejpam-3305	453	14	,	,	PUNCT
ejpam-3305	453	15	on	on	ADP
ejpam-3305	453	16	simultaneous	simultaneous	ADJ
ejpam-3305	453	17	approximation	approximation	NOUN
ejpam-3305	453	18	for	for	ADP
ejpam-3305	453	19	baskakov	baskakov	PROPN
ejpam-3305	453	20	-	-	PUNCT
ejpam-3305	453	21	durrmeyer	durrmeyer	NOUN
ejpam-3305	453	22	-	-	PUNCT
ejpam-3305	453	23	stancu	stancu	NOUN
ejpam-3305	453	24	type	type	NOUN
ejpam-3305	453	25	operators	operator	NOUN
ejpam-3305	453	26	,	,	PUNCT
ejpam-3305	453	27	journal	journal	NOUN
ejpam-3305	453	28	of	of	ADP
ejpam-3305	453	29	ultra	ultra	ADJ
ejpam-3305	453	30	scientist	scientist	NOUN
ejpam-3305	453	31	of	of	ADP
ejpam-3305	453	32	physical	physical	ADJ
ejpam-3305	453	33	sciences	science	NOUN
ejpam-3305	453	34	,	,	PUNCT
ejpam-3305	453	35	vol	vol	NOUN
ejpam-3305	453	36	.	.	PROPN
ejpam-3305	453	37	24	24	NUM
ejpam-3305	453	38	,	,	PUNCT
ejpam-3305	453	39	no	no	INTJ
ejpam-3305	453	40	.	.	PUNCT
ejpam-3305	454	1	(	(	PUNCT
ejpam-3305	454	2	3)a	3)a	PROPN
ejpam-3305	454	3	,	,	PUNCT
ejpam-3305	454	4	2012	2012	NUM
ejpam-3305	454	5	,	,	PUNCT
ejpam-3305	454	6	pp	pp	ADJ
ejpam-3305	454	7	.	.	PUNCT
ejpam-3305	455	1	567	567	NUM
ejpam-3305	455	2	-	-	SYM
ejpam-3305	455	3	577	577	NUM
ejpam-3305	455	4	.	.	PUNCT
ejpam-3305	456	1	[	[	X
ejpam-3305	456	2	38	38	NUM
ejpam-3305	456	3	]	]	PUNCT
ejpam-3305	456	4	v.	v.	ADP
ejpam-3305	456	5	mihesan	mihesan	ADJ
ejpam-3305	456	6	,	,	PUNCT
ejpam-3305	456	7	gamma	gamma	NOUN
ejpam-3305	456	8	approximating	approximate	VERB
ejpam-3305	456	9	operators	operator	NOUN
ejpam-3305	456	10	,	,	PUNCT
ejpam-3305	456	11	creat	creat	PROPN
ejpam-3305	456	12	.	.	PUNCT
ejpam-3305	456	13	math	math	PROPN
ejpam-3305	456	14	.	.	PUNCT
ejpam-3305	457	1	inform	inform	NOUN
ejpam-3305	457	2	.	.	PUNCT
ejpam-3305	458	1	,	,	PUNCT
ejpam-3305	458	2	17	17	NUM
ejpam-3305	458	3	(	(	PUNCT
ejpam-3305	458	4	3	3	NUM
ejpam-3305	458	5	)	)	PUNCT
ejpam-3305	458	6	(	(	PUNCT
ejpam-3305	458	7	2008	2008	NUM
ejpam-3305	458	8	)	)	PUNCT
ejpam-3305	458	9	,	,	PUNCT
ejpam-3305	458	10	466	466	NUM
ejpam-3305	458	11	-	-	SYM
ejpam-3305	458	12	472	472	NUM
ejpam-3305	458	13	.	.	PUNCT
ejpam-3305	459	1	[	[	X
ejpam-3305	459	2	39	39	NUM
ejpam-3305	459	3	]	]	X
ejpam-3305	459	4	m.a	m.a	PROPN
ejpam-3305	459	5	.	.	PROPN
ejpam-3305	459	6	özarslan	özarslan	PROPN
ejpam-3305	459	7	,	,	PUNCT
ejpam-3305	459	8	h.	h.	PROPN
ejpam-3305	459	9	aktuğlu	aktuğlu	PROPN
ejpam-3305	459	10	,	,	PUNCT
ejpam-3305	459	11	local	local	ADJ
ejpam-3305	459	12	approximation	approximation	NOUN
ejpam-3305	459	13	for	for	ADP
ejpam-3305	459	14	certain	certain	ADJ
ejpam-3305	459	15	king	king	NOUN
ejpam-3305	459	16	type	type	NOUN
ejpam-3305	459	17	operators	operator	NOUN
ejpam-3305	459	18	,	,	PUNCT
ejpam-3305	459	19	filomat	filomat	PROPN
ejpam-3305	459	20	,	,	PUNCT
ejpam-3305	459	21	27:1	27:1	NUM
ejpam-3305	459	22	(	(	PUNCT
ejpam-3305	459	23	2013	2013	NUM
ejpam-3305	459	24	)	)	PUNCT
ejpam-3305	459	25	,	,	PUNCT
ejpam-3305	459	26	173	173	NUM
ejpam-3305	459	27	-	-	SYM
ejpam-3305	459	28	181	181	NUM
ejpam-3305	459	29	.	.	PUNCT
ejpam-3305	460	1	[	[	X
ejpam-3305	460	2	40	40	NUM
ejpam-3305	460	3	]	]	X
ejpam-3305	460	4	r.s	r.s	PROPN
ejpam-3305	460	5	.	.	PROPN
ejpam-3305	460	6	phillips	phillips	PROPN
ejpam-3305	460	7	,	,	PUNCT
ejpam-3305	460	8	an	an	DET
ejpam-3305	460	9	inversion	inversion	NOUN
ejpam-3305	460	10	formula	formula	NOUN
ejpam-3305	460	11	for	for	ADP
ejpam-3305	460	12	laplace	laplace	NOUN
ejpam-3305	460	13	transforms	transform	VERB
ejpam-3305	460	14	semi	semi	NOUN
ejpam-3305	460	15	-	-	NOUN
ejpam-3305	460	16	groups	group	NOUN
ejpam-3305	460	17	of	of	ADP
ejpam-3305	460	18	linear	linear	PROPN
ejpam-3305	460	19	operators	operator	NOUN
ejpam-3305	460	20	,	,	PUNCT
ejpam-3305	460	21	ann	ann	PROPN
ejpam-3305	460	22	.	.	PROPN
ejpam-3305	460	23	math	math	PROPN
ejpam-3305	460	24	.	.	PUNCT
ejpam-3305	461	1	,	,	PUNCT
ejpam-3305	461	2	59	59	NUM
ejpam-3305	461	3	(	(	PUNCT
ejpam-3305	461	4	1954	1954	NUM
ejpam-3305	461	5	)	)	PUNCT
ejpam-3305	461	6	,	,	PUNCT
ejpam-3305	461	7	325	325	NUM
ejpam-3305	461	8	-	-	SYM
ejpam-3305	461	9	356	356	NUM
ejpam-3305	461	10	.	.	PUNCT
ejpam-3305	462	1	[	[	X
ejpam-3305	462	2	41	41	NUM
ejpam-3305	462	3	]	]	PUNCT
ejpam-3305	462	4	p.	p.	NOUN
ejpam-3305	462	5	patel	patel	PROPN
ejpam-3305	462	6	,	,	PUNCT
ejpam-3305	462	7	v.n	v.n	PROPN
ejpam-3305	462	8	.	.	PROPN
ejpam-3305	462	9	mishra	mishra	PROPN
ejpam-3305	462	10	,	,	PUNCT
ejpam-3305	462	11	approximation	approximation	NOUN
ejpam-3305	462	12	properties	property	NOUN
ejpam-3305	462	13	of	of	ADP
ejpam-3305	462	14	certain	certain	ADJ
ejpam-3305	462	15	summation	summation	NOUN
ejpam-3305	462	16	integral	integral	ADJ
ejpam-3305	462	17	type	type	NOUN
ejpam-3305	462	18	operators	operator	NOUN
ejpam-3305	462	19	,	,	PUNCT
ejpam-3305	462	20	demonstratio	demonstratio	PROPN
ejpam-3305	462	21	mathematica	mathematica	PROPN
ejpam-3305	462	22	,	,	PUNCT
ejpam-3305	462	23	vol	vol	NOUN
ejpam-3305	462	24	.	.	PUNCT
ejpam-3305	462	25	xlviii	xlviii	PROPN
ejpam-3305	463	1	no	no	INTJ
ejpam-3305	463	2	.	.	PROPN
ejpam-3305	463	3	1	1	NUM
ejpam-3305	463	4	,	,	PUNCT
ejpam-3305	463	5	2015	2015	NUM
ejpam-3305	463	6	.	.	PUNCT
ejpam-3305	464	1	[	[	X
ejpam-3305	464	2	42	42	NUM
ejpam-3305	464	3	]	]	X
ejpam-3305	464	4	d.d	d.d	PROPN
ejpam-3305	464	5	.	.	PROPN
ejpam-3305	464	6	stancu	stancu	PROPN
ejpam-3305	464	7	,	,	PUNCT
ejpam-3305	464	8	approximation	approximation	NOUN
ejpam-3305	464	9	of	of	ADP
ejpam-3305	464	10	functions	function	NOUN
ejpam-3305	464	11	by	by	ADP
ejpam-3305	464	12	a	a	DET
ejpam-3305	464	13	new	new	ADJ
ejpam-3305	464	14	class	class	NOUN
ejpam-3305	464	15	of	of	ADP
ejpam-3305	464	16	linear	linear	ADJ
ejpam-3305	464	17	polynomial	polynomial	ADJ
ejpam-3305	464	18	operators	operator	NOUN
ejpam-3305	464	19	,	,	PUNCT
ejpam-3305	464	20	rev	rev	PROPN
ejpam-3305	464	21	.	.	PROPN
ejpam-3305	464	22	roum	roum	PROPN
ejpam-3305	464	23	.	.	PUNCT
ejpam-3305	465	1	math	math	NOUN
ejpam-3305	465	2	.	.	PUNCT
ejpam-3305	466	1	pures	pure	NOUN
ejpam-3305	466	2	appl	appl	PROPN
ejpam-3305	466	3	.	.	PROPN
ejpam-3305	466	4	,	,	PUNCT
ejpam-3305	466	5	13	13	NUM
ejpam-3305	466	6	(	(	PUNCT
ejpam-3305	466	7	8)	8)	NUM
ejpam-3305	466	8	(	(	PUNCT
ejpam-3305	466	9	1968	1968	NUM
ejpam-3305	466	10	)	)	PUNCT
ejpam-3305	466	11	,	,	PUNCT
ejpam-3305	466	12	1173	1173	NUM
ejpam-3305	466	13	-	-	SYM
ejpam-3305	466	14	1194	1194	NUM
ejpam-3305	466	15	.	.	PUNCT
ejpam-3305	467	1	[	[	X
ejpam-3305	467	2	43	43	NUM
ejpam-3305	467	3	]	]	X
ejpam-3305	467	4	o.	o.	PROPN
ejpam-3305	467	5	szász	szász	PROPN
ejpam-3305	467	6	,	,	PUNCT
ejpam-3305	467	7	generalization	generalization	NOUN
ejpam-3305	467	8	of	of	ADP
ejpam-3305	467	9	s.	s.	PROPN
ejpam-3305	467	10	bernstein	bernstein	PROPN
ejpam-3305	467	11	’s	’s	PART
ejpam-3305	467	12	polynomials	polynomial	NOUN
ejpam-3305	467	13	to	to	ADP
ejpam-3305	467	14	the	the	DET
ejpam-3305	467	15	infinite	infinite	ADJ
ejpam-3305	467	16	interval	interval	NOUN
ejpam-3305	467	17	,	,	PUNCT
ejpam-3305	467	18	j.	j.	PROPN
ejpam-3305	467	19	res	res	PROPN
ejpam-3305	467	20	.	.	PUNCT
ejpam-3305	468	1	nat	nat	PROPN
ejpam-3305	468	2	.	.	PUNCT
ejpam-3305	469	1	bur	bur	PROPN
ejpam-3305	469	2	.	.	PUNCT
ejpam-3305	470	1	stand	stand	VERB
ejpam-3305	470	2	.	.	PUNCT
ejpam-3305	471	1	,	,	PUNCT
ejpam-3305	471	2	45	45	NUM
ejpam-3305	471	3	(	(	PUNCT
ejpam-3305	471	4	1950	1950	NUM
ejpam-3305	471	5	)	)	PUNCT
ejpam-3305	471	6	,	,	PUNCT
ejpam-3305	471	7	239	239	NUM
ejpam-3305	471	8	-	-	SYM
ejpam-3305	471	9	245	245	NUM
ejpam-3305	471	10	.	.	PUNCT
ejpam-3305	472	1	[	[	X
ejpam-3305	472	2	44	44	NUM
ejpam-3305	472	3	]	]	X
ejpam-3305	472	4	d.k	d.k	PROPN
ejpam-3305	472	5	.	.	PROPN
ejpam-3305	472	6	verma	verma	PROPN
ejpam-3305	472	7	,	,	PUNCT
ejpam-3305	472	8	v.	v.	PROPN
ejpam-3305	472	9	gupta	gupta	PROPN
ejpam-3305	472	10	,	,	PUNCT
ejpam-3305	472	11	p.n	p.n	PROPN
ejpam-3305	472	12	.	.	PROPN
ejpam-3305	472	13	agrawal	agrawal	PROPN
ejpam-3305	472	14	,	,	PUNCT
ejpam-3305	472	15	some	some	DET
ejpam-3305	472	16	approximation	approximation	NOUN
ejpam-3305	472	17	properties	property	NOUN
ejpam-3305	472	18	of	of	ADP
ejpam-3305	472	19	baskakovdurrmeyer	baskakovdurrmeyer	NOUN
ejpam-3305	472	20	-	-	PUNCT
ejpam-3305	472	21	stancu	stancu	PROPN
ejpam-3305	472	22	operators	operator	NOUN
ejpam-3305	472	23	,	,	PUNCT
ejpam-3305	472	24	appl	appl	PROPN
ejpam-3305	472	25	.	.	PROPN
ejpam-3305	472	26	math	math	PROPN
ejpam-3305	472	27	.	.	PUNCT
ejpam-3305	473	1	comput	comput	NOUN
ejpam-3305	473	2	.	.	PUNCT
ejpam-3305	474	1	,	,	PUNCT
ejpam-3305	474	2	218	218	NUM
ejpam-3305	474	3	(	(	PUNCT
ejpam-3305	474	4	11	11	NUM
ejpam-3305	474	5	)	)	PUNCT
ejpam-3305	474	6	(	(	PUNCT
ejpam-3305	474	7	2012	2012	NUM
ejpam-3305	474	8	)	)	PUNCT
ejpam-3305	474	9	,	,	PUNCT
ejpam-3305	474	10	6549	6549	NUM
ejpam-3305	474	11	-	-	SYM
ejpam-3305	474	12	6556	6556	NUM
ejpam-3305	474	13	.	.	PUNCT
ejpam-3305	475	1	[	[	X
ejpam-3305	475	2	45	45	NUM
ejpam-3305	475	3	]	]	PUNCT
ejpam-3305	475	4	i.	i.	NOUN
ejpam-3305	475	5	yüksel	yüksel	PROPN
ejpam-3305	475	6	,	,	PUNCT
ejpam-3305	475	7	n.	n.	NOUN
ejpam-3305	475	8	ispir	ispir	PROPN
ejpam-3305	475	9	,	,	PUNCT
ejpam-3305	475	10	weighted	weight	VERB
ejpam-3305	475	11	approximation	approximation	NOUN
ejpam-3305	475	12	by	by	ADP
ejpam-3305	475	13	a	a	DET
ejpam-3305	475	14	certain	certain	ADJ
ejpam-3305	475	15	family	family	NOUN
ejpam-3305	475	16	of	of	ADP
ejpam-3305	475	17	summation	summation	NOUN
ejpam-3305	475	18	integral	integral	ADJ
ejpam-3305	475	19	type	type	NOUN
ejpam-3305	475	20	operators	operator	NOUN
ejpam-3305	475	21	,	,	PUNCT
ejpam-3305	475	22	comput	comput	NOUN
ejpam-3305	475	23	.	.	PUNCT
ejpam-3305	476	1	math	math	NOUN
ejpam-3305	476	2	.	.	PUNCT
ejpam-3305	477	1	appl	appl	PROPN
ejpam-3305	477	2	.	.	PROPN
ejpam-3305	478	1	,	,	PUNCT
ejpam-3305	478	2	52	52	NUM
ejpam-3305	478	3	(	(	PUNCT
ejpam-3305	478	4	2006	2006	NUM
ejpam-3305	478	5	)	)	PUNCT
ejpam-3305	478	6	,	,	PUNCT
ejpam-3305	478	7	1463171470	1463171470	NUM
ejpam-3305	478	8	.	.	PUNCT