id	sid	tid	token	lemma	pos
ejpam-3728	1	1	european	european	PROPN
ejpam-3728	1	2	journal	journal	PROPN
ejpam-3728	1	3	of	of	ADP
ejpam-3728	1	4	pure	pure	ADJ
ejpam-3728	1	5	and	and	CCONJ
ejpam-3728	1	6	applied	apply	VERB
ejpam-3728	1	7	mathematics	mathematic	NOUN
ejpam-3728	1	8	vol	vol	NOUN
ejpam-3728	1	9	.	.	PROPN
ejpam-3728	2	1	13	13	NUM
ejpam-3728	2	2	,	,	PUNCT
ejpam-3728	2	3	no	no	INTJ
ejpam-3728	2	4	.	.	NOUN
ejpam-3728	2	5	5	5	NUM
ejpam-3728	2	6	,	,	PUNCT
ejpam-3728	2	7	2020	2020	NUM
ejpam-3728	2	8	,	,	PUNCT
ejpam-3728	2	9	1306	1306	NUM
ejpam-3728	2	10	-	-	SYM
ejpam-3728	2	11	1324	1324	NUM
ejpam-3728	2	12	issn	issn	VERB
ejpam-3728	2	13	1307	1307	NUM
ejpam-3728	2	14	-	-	SYM
ejpam-3728	2	15	5543	5543	NUM
ejpam-3728	2	16	–	–	PUNCT
ejpam-3728	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3728	2	18	published	publish	VERB
ejpam-3728	2	19	by	by	ADP
ejpam-3728	2	20	new	new	PROPN
ejpam-3728	2	21	york	york	PROPN
ejpam-3728	2	22	business	business	PROPN
ejpam-3728	2	23	global	global	ADJ
ejpam-3728	2	24	special	special	ADJ
ejpam-3728	2	25	issue	issue	NOUN
ejpam-3728	2	26	dedicated	dedicate	VERB
ejpam-3728	2	27	to	to	ADP
ejpam-3728	2	28	professor	professor	NOUN
ejpam-3728	2	29	hari	hari	PROPN
ejpam-3728	2	30	m.	m.	PROPN
ejpam-3728	2	31	srivastava	srivastava	PROPN
ejpam-3728	2	32	on	on	ADP
ejpam-3728	2	33	the	the	DET
ejpam-3728	2	34	occasion	occasion	NOUN
ejpam-3728	2	35	of	of	ADP
ejpam-3728	2	36	his	his	PRON
ejpam-3728	2	37	80th	80th	ADJ
ejpam-3728	2	38	birthday	birthday	NOUN
ejpam-3728	2	39	further	further	ADJ
ejpam-3728	2	40	approximations	approximation	NOUN
ejpam-3728	2	41	on	on	ADP
ejpam-3728	2	42	durrmeyer	durrmeyer	NOUN
ejpam-3728	2	43	modification	modification	NOUN
ejpam-3728	2	44	of	of	ADP
ejpam-3728	2	45	szász	szász	NOUN
ejpam-3728	2	46	-	-	PUNCT
ejpam-3728	2	47	mirakjan	mirakjan	NOUN
ejpam-3728	2	48	operators	operators	PROPN
ejpam-3728	2	49	rishikesh	rishikesh	PROPN
ejpam-3728	2	50	yadav1,∗	yadav1,∗	PROPN
ejpam-3728	2	51	,	,	PUNCT
ejpam-3728	2	52	ramakanta	ramakanta	ADJ
ejpam-3728	2	53	meher1	meher1	PROPN
ejpam-3728	2	54	,	,	PUNCT
ejpam-3728	2	55	vishnu	vishnu	ADJ
ejpam-3728	2	56	narayan	narayan	PROPN
ejpam-3728	2	57	mishra2	mishra2	PROPN
ejpam-3728	2	58	1	1	NUM
ejpam-3728	2	59	applied	apply	VERB
ejpam-3728	2	60	mathematics	mathematic	NOUN
ejpam-3728	2	61	and	and	CCONJ
ejpam-3728	2	62	humanities	humanities	PROPN
ejpam-3728	2	63	department	department	PROPN
ejpam-3728	2	64	,	,	PUNCT
ejpam-3728	2	65	sardar	sardar	PROPN
ejpam-3728	2	66	vallabhbhai	vallabhbhai	PROPN
ejpam-3728	2	67	national	national	PROPN
ejpam-3728	2	68	institute	institute	PROPN
ejpam-3728	2	69	of	of	ADP
ejpam-3728	2	70	technology	technology	PROPN
ejpam-3728	2	71	surat	surat	PROPN
ejpam-3728	2	72	,	,	PUNCT
ejpam-3728	2	73	surat-395	surat-395	ADJ
ejpam-3728	2	74	007	007	NUM
ejpam-3728	2	75	(	(	PUNCT
ejpam-3728	2	76	gujarat	gujarat	NOUN
ejpam-3728	2	77	)	)	PUNCT
ejpam-3728	2	78	,	,	PUNCT
ejpam-3728	2	79	india	india	PROPN
ejpam-3728	2	80	2	2	NUM
ejpam-3728	2	81	department	department	NOUN
ejpam-3728	2	82	of	of	ADP
ejpam-3728	2	83	mathematics	mathematic	NOUN
ejpam-3728	2	84	,	,	PUNCT
ejpam-3728	2	85	indira	indira	PROPN
ejpam-3728	2	86	gandhi	gandhi	PROPN
ejpam-3728	2	87	national	national	PROPN
ejpam-3728	2	88	tribal	tribal	PROPN
ejpam-3728	2	89	university	university	PROPN
ejpam-3728	2	90	,	,	PUNCT
ejpam-3728	2	91	lalpur	lalpur	PROPN
ejpam-3728	2	92	,	,	PUNCT
ejpam-3728	2	93	amarkantak-484	amarkantak-484	VERB
ejpam-3728	2	94	887	887	NUM
ejpam-3728	2	95	,	,	PUNCT
ejpam-3728	2	96	anuppur	anuppur	NOUN
ejpam-3728	2	97	,	,	PUNCT
ejpam-3728	2	98	madhya	madhya	PROPN
ejpam-3728	2	99	pradesh	pradesh	PROPN
ejpam-3728	2	100	,	,	PUNCT
ejpam-3728	2	101	india	india	PROPN
ejpam-3728	2	102	abstract	abstract	PROPN
ejpam-3728	2	103	.	.	PUNCT
ejpam-3728	3	1	the	the	DET
ejpam-3728	3	2	main	main	ADJ
ejpam-3728	3	3	purpose	purpose	NOUN
ejpam-3728	3	4	of	of	ADP
ejpam-3728	3	5	this	this	DET
ejpam-3728	3	6	paper	paper	NOUN
ejpam-3728	3	7	is	be	AUX
ejpam-3728	3	8	to	to	PART
ejpam-3728	3	9	determine	determine	VERB
ejpam-3728	3	10	the	the	DET
ejpam-3728	3	11	approximations	approximation	NOUN
ejpam-3728	3	12	of	of	ADP
ejpam-3728	3	13	durrmeyer	durrmeyer	NOUN
ejpam-3728	3	14	modification	modification	NOUN
ejpam-3728	3	15	of	of	ADP
ejpam-3728	3	16	szász	szász	NOUN
ejpam-3728	3	17	-	-	PUNCT
ejpam-3728	3	18	mirakjan	mirakjan	NOUN
ejpam-3728	3	19	operators	operator	NOUN
ejpam-3728	3	20	,	,	PUNCT
ejpam-3728	3	21	defined	define	VERB
ejpam-3728	3	22	by	by	ADP
ejpam-3728	3	23	mishra	mishra	PROPN
ejpam-3728	3	24	et	et	PROPN
ejpam-3728	3	25	al	al	PROPN
ejpam-3728	3	26	.	.	PUNCT
ejpam-3728	4	1	(	(	PUNCT
ejpam-3728	4	2	boll	boll	NOUN
ejpam-3728	4	3	.	.	PUNCT
ejpam-3728	5	1	unione	unione	PROPN
ejpam-3728	5	2	mat	mat	PROPN
ejpam-3728	5	3	.	.	PUNCT
ejpam-3728	5	4	ital	ital	PROPN
ejpam-3728	5	5	.	.	PUNCT
ejpam-3728	6	1	(	(	PUNCT
ejpam-3728	6	2	2016	2016	NUM
ejpam-3728	6	3	)	)	PUNCT
ejpam-3728	6	4	8(4):297	8(4):297	NUM
ejpam-3728	6	5	-	-	SYM
ejpam-3728	6	6	305	305	NUM
ejpam-3728	6	7	)	)	PUNCT
ejpam-3728	6	8	.	.	PUNCT
ejpam-3728	7	1	we	we	PRON
ejpam-3728	7	2	estimate	estimate	VERB
ejpam-3728	7	3	the	the	DET
ejpam-3728	7	4	order	order	NOUN
ejpam-3728	7	5	of	of	ADP
ejpam-3728	7	6	approximation	approximation	NOUN
ejpam-3728	7	7	of	of	ADP
ejpam-3728	7	8	the	the	DET
ejpam-3728	7	9	operators	operator	NOUN
ejpam-3728	7	10	for	for	ADP
ejpam-3728	7	11	the	the	DET
ejpam-3728	7	12	functions	function	NOUN
ejpam-3728	7	13	belonging	belong	VERB
ejpam-3728	7	14	to	to	ADP
ejpam-3728	7	15	the	the	DET
ejpam-3728	7	16	different	different	ADJ
ejpam-3728	7	17	spaces	space	NOUN
ejpam-3728	7	18	.	.	PUNCT
ejpam-3728	8	1	here	here	ADV
ejpam-3728	8	2	,	,	PUNCT
ejpam-3728	8	3	the	the	DET
ejpam-3728	8	4	rate	rate	NOUN
ejpam-3728	8	5	of	of	ADP
ejpam-3728	8	6	convergence	convergence	NOUN
ejpam-3728	8	7	of	of	ADP
ejpam-3728	8	8	the	the	DET
ejpam-3728	8	9	said	say	VERB
ejpam-3728	8	10	operators	operator	NOUN
ejpam-3728	8	11	is	be	AUX
ejpam-3728	8	12	established	establish	VERB
ejpam-3728	8	13	by	by	ADP
ejpam-3728	8	14	means	mean	NOUN
ejpam-3728	8	15	of	of	ADP
ejpam-3728	8	16	the	the	DET
ejpam-3728	8	17	function	function	NOUN
ejpam-3728	8	18	with	with	ADP
ejpam-3728	8	19	derivative	derivative	NOUN
ejpam-3728	8	20	of	of	ADP
ejpam-3728	8	21	the	the	DET
ejpam-3728	8	22	bounded	bounded	ADJ
ejpam-3728	8	23	variation	variation	NOUN
ejpam-3728	8	24	.	.	PUNCT
ejpam-3728	9	1	at	at	ADP
ejpam-3728	9	2	last	last	ADJ
ejpam-3728	9	3	,	,	PUNCT
ejpam-3728	9	4	the	the	DET
ejpam-3728	9	5	graphical	graphical	ADJ
ejpam-3728	9	6	analysis	analysis	NOUN
ejpam-3728	9	7	is	be	AUX
ejpam-3728	9	8	discussed	discuss	VERB
ejpam-3728	9	9	to	to	PART
ejpam-3728	9	10	support	support	VERB
ejpam-3728	9	11	the	the	DET
ejpam-3728	9	12	approximation	approximation	NOUN
ejpam-3728	9	13	results	result	NOUN
ejpam-3728	9	14	of	of	ADP
ejpam-3728	9	15	the	the	DET
ejpam-3728	9	16	operators	operator	NOUN
ejpam-3728	9	17	.	.	PUNCT
ejpam-3728	10	1	2020	2020	NUM
ejpam-3728	10	2	mathematics	mathematic	NOUN
ejpam-3728	10	3	subject	subject	NOUN
ejpam-3728	10	4	classifications	classification	NOUN
ejpam-3728	10	5	:	:	PUNCT
ejpam-3728	10	6	41a25	41a25	NUM
ejpam-3728	10	7	,	,	PUNCT
ejpam-3728	10	8	41a35	41a35	NUM
ejpam-3728	10	9	,	,	PUNCT
ejpam-3728	10	10	41a36	41a36	NUM
ejpam-3728	10	11	.	.	PUNCT
ejpam-3728	11	1	key	key	ADJ
ejpam-3728	11	2	words	word	NOUN
ejpam-3728	11	3	and	and	CCONJ
ejpam-3728	11	4	phrases	phrase	NOUN
ejpam-3728	11	5	:	:	PUNCT
ejpam-3728	11	6	szász	szász	NUM
ejpam-3728	11	7	-	-	PUNCT
ejpam-3728	11	8	mirakjan	mirakjan	NOUN
ejpam-3728	11	9	operators	operator	NOUN
ejpam-3728	11	10	,	,	PUNCT
ejpam-3728	11	11	rate	rate	NOUN
ejpam-3728	11	12	of	of	ADP
ejpam-3728	11	13	convergence	convergence	NOUN
ejpam-3728	11	14	,	,	PUNCT
ejpam-3728	11	15	peetres	peetre	VERB
ejpam-3728	11	16	k	k	ADJ
ejpam-3728	11	17	-	-	ADJ
ejpam-3728	11	18	functional	functional	ADJ
ejpam-3728	11	19	,	,	PUNCT
ejpam-3728	11	20	function	function	NOUN
ejpam-3728	11	21	of	of	ADP
ejpam-3728	11	22	bounded	bounded	ADJ
ejpam-3728	11	23	variation	variation	NOUN
ejpam-3728	11	24	.	.	PUNCT
ejpam-3728	12	1	1	1	X
ejpam-3728	12	2	.	.	X
ejpam-3728	12	3	introduction	introduction	NOUN
ejpam-3728	12	4	in	in	ADP
ejpam-3728	12	5	1944	1944	NUM
ejpam-3728	12	6	,	,	PUNCT
ejpam-3728	12	7	mirakjan	mirakjan	NOUN
ejpam-3728	12	8	[	[	X
ejpam-3728	12	9	8	8	NUM
ejpam-3728	12	10	]	]	PUNCT
ejpam-3728	12	11	and	and	CCONJ
ejpam-3728	12	12	1950	1950	NUM
ejpam-3728	12	13	,	,	PUNCT
ejpam-3728	12	14	szász	szász	PUNCT
ejpam-3728	13	1	[	[	X
ejpam-3728	13	2	16	16	NUM
ejpam-3728	13	3	]	]	PUNCT
ejpam-3728	13	4	introduced	introduce	VERB
ejpam-3728	13	5	operators	operator	NOUN
ejpam-3728	13	6	on	on	ADP
ejpam-3728	13	7	unbounded	unbounded	ADJ
ejpam-3728	13	8	interval	interval	NOUN
ejpam-3728	13	9	[	[	X
ejpam-3728	13	10	0,∞	0,∞	NOUN
ejpam-3728	13	11	)	)	PUNCT
ejpam-3728	13	12	,	,	PUNCT
ejpam-3728	13	13	known	know	VERB
ejpam-3728	13	14	as	as	ADP
ejpam-3728	13	15	szász	szász	NOUN
ejpam-3728	13	16	-	-	PUNCT
ejpam-3728	13	17	mirakjan	mirakjan	NOUN
ejpam-3728	13	18	operators	operator	NOUN
ejpam-3728	13	19	defined	define	VERB
ejpam-3728	13	20	by	by	ADP
ejpam-3728	13	21	sn(g;x	sn(g;x	ADJ
ejpam-3728	13	22	)	)	PUNCT
ejpam-3728	14	1	=	=	PUNCT
ejpam-3728	15	1	∞∑	∞∑	NUM
ejpam-3728	15	2	j=0	j=0	PROPN
ejpam-3728	15	3	sn	sn	PROPN
ejpam-3728	15	4	,	,	PUNCT
ejpam-3728	15	5	j(x)g	j(x)g	PROPN
ejpam-3728	15	6	(	(	PUNCT
ejpam-3728	15	7	j	j	PROPN
ejpam-3728	15	8	n	n	CCONJ
ejpam-3728	15	9	)	)	PUNCT
ejpam-3728	15	10	,	,	PUNCT
ejpam-3728	15	11	(	(	PUNCT
ejpam-3728	15	12	1	1	X
ejpam-3728	15	13	)	)	PUNCT
ejpam-3728	15	14	∗corresponding	∗corresponde	VERB
ejpam-3728	15	15	author	author	NOUN
ejpam-3728	15	16	.	.	PUNCT
ejpam-3728	16	1	doi	doi	NOUN
ejpam-3728	16	2	:	:	PUNCT
ejpam-3728	16	3	https://doi.org/10.29020/nybg.ejpam.v13i5.3728	https://doi.org/10.29020/nybg.ejpam.v13i5.3728	NOUN
ejpam-3728	16	4	email	email	NOUN
ejpam-3728	16	5	addresses	address	NOUN
ejpam-3728	16	6	:	:	PUNCT
ejpam-3728	16	7	rishikesh2506@gmail.com	rishikesh2506@gmail.com	X
ejpam-3728	16	8	(	(	PUNCT
ejpam-3728	16	9	r.	r.	PROPN
ejpam-3728	16	10	yadav	yadav	PROPN
ejpam-3728	16	11	)	)	PUNCT
ejpam-3728	16	12	,	,	PUNCT
ejpam-3728	16	13	meher	meher	PROPN
ejpam-3728	16	14	ramakanta@yahoo.com	ramakanta@yahoo.com	PROPN
ejpam-3728	16	15	(	(	PUNCT
ejpam-3728	16	16	r.	r.	PROPN
ejpam-3728	16	17	meher	meher	PROPN
ejpam-3728	16	18	)	)	PUNCT
ejpam-3728	16	19	,	,	PUNCT
ejpam-3728	16	20	vishnunarayanmishra@gmail.com	vishnunarayanmishra@gmail.com	X
ejpam-3728	16	21	(	(	PUNCT
ejpam-3728	16	22	v.	v.	ADP
ejpam-3728	16	23	n.	n.	PROPN
ejpam-3728	16	24	mishra	mishra	PROPN
ejpam-3728	16	25	)	)	PUNCT
ejpam-3728	16	26	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-3728	16	27	1306	1306	NUM
ejpam-3728	17	1	c	c	X
ejpam-3728	17	2	©	©	NOUN
ejpam-3728	17	3	2020	2020	NUM
ejpam-3728	17	4	ejpam	ejpam	VERB
ejpam-3728	17	5	all	all	DET
ejpam-3728	17	6	rights	right	NOUN
ejpam-3728	17	7	reserved	reserve	VERB
ejpam-3728	17	8	.	.	PUNCT
ejpam-3728	18	1	r.	r.	PROPN
ejpam-3728	18	2	yadav	yadav	PROPN
ejpam-3728	18	3	,	,	PUNCT
ejpam-3728	18	4	r.	r.	PROPN
ejpam-3728	18	5	meher	meher	PROPN
ejpam-3728	18	6	,	,	PUNCT
ejpam-3728	18	7	v.	v.	ADP
ejpam-3728	18	8	n.	n.	PROPN
ejpam-3728	18	9	mishra	mishra	PROPN
ejpam-3728	18	10	/	/	SYM
ejpam-3728	18	11	eur	eur	PROPN
ejpam-3728	18	12	.	.	PUNCT
ejpam-3728	19	1	j.	j.	PROPN
ejpam-3728	19	2	pure	pure	PROPN
ejpam-3728	19	3	appl	appl	PROPN
ejpam-3728	19	4	.	.	PROPN
ejpam-3728	19	5	math	math	PROPN
ejpam-3728	19	6	,	,	PUNCT
ejpam-3728	19	7	13	13	NUM
ejpam-3728	19	8	(	(	PUNCT
ejpam-3728	19	9	5	5	NUM
ejpam-3728	19	10	)	)	PUNCT
ejpam-3728	19	11	(	(	PUNCT
ejpam-3728	19	12	2020	2020	NUM
ejpam-3728	19	13	)	)	PUNCT
ejpam-3728	19	14	,	,	PUNCT
ejpam-3728	19	15	1306	1306	NUM
ejpam-3728	19	16	-	-	SYM
ejpam-3728	19	17	1324	1324	NUM
ejpam-3728	19	18	1307	1307	NUM
ejpam-3728	19	19	where	where	SCONJ
ejpam-3728	19	20	sn	sn	PROPN
ejpam-3728	19	21	,	,	PUNCT
ejpam-3728	19	22	j	j	PROPN
ejpam-3728	20	1	=	=	SYM
ejpam-3728	20	2	e−nx	e−nx	PROPN
ejpam-3728	20	3	(	(	PUNCT
ejpam-3728	20	4	nx)j	nx)j	PROPN
ejpam-3728	20	5	j	j	PROPN
ejpam-3728	20	6	!	!	PROPN
ejpam-3728	20	7	,	,	PUNCT
ejpam-3728	20	8	g	g	PROPN
ejpam-3728	20	9	∈	∈	PROPN
ejpam-3728	20	10	c2[0,∞	c2[0,∞	PROPN
ejpam-3728	20	11	)	)	PUNCT
ejpam-3728	20	12	=	=	PRON
ejpam-3728	20	13	{	{	PUNCT
ejpam-3728	20	14	g	g	PROPN
ejpam-3728	20	15	∈	∈	PROPN
ejpam-3728	20	16	c[0,∞	c[0,∞	NUM
ejpam-3728	20	17	)	)	PUNCT
ejpam-3728	20	18	:	:	PUNCT
ejpam-3728	21	1	lim	lim	PROPN
ejpam-3728	21	2	x→∞	x→∞	NUM
ejpam-3728	21	3	f(x	f(x	PROPN
ejpam-3728	21	4	)	)	PUNCT
ejpam-3728	21	5	1+x2	1+x2	NUM
ejpam-3728	21	6	exists	exist	VERB
ejpam-3728	21	7	and	and	CCONJ
ejpam-3728	21	8	finite	finite	ADJ
ejpam-3728	21	9	}	}	PUNCT
ejpam-3728	21	10	,	,	PUNCT
ejpam-3728	21	11	x	x	X
ejpam-3728	21	12	≥	≥	NOUN
ejpam-3728	21	13	0	0	NUM
ejpam-3728	21	14	and	and	CCONJ
ejpam-3728	21	15	for	for	ADP
ejpam-3728	21	16	all	all	DET
ejpam-3728	21	17	n	n	PRON
ejpam-3728	21	18	∈	∈	PROPN
ejpam-3728	21	19	n.	n.	NOUN
ejpam-3728	21	20	an	an	DET
ejpam-3728	21	21	integral	integral	ADJ
ejpam-3728	21	22	modification	modification	NOUN
ejpam-3728	21	23	of	of	ADP
ejpam-3728	21	24	the	the	DET
ejpam-3728	21	25	above	above	ADJ
ejpam-3728	21	26	operators	operator	NOUN
ejpam-3728	21	27	(	(	PUNCT
ejpam-3728	21	28	1	1	X
ejpam-3728	21	29	)	)	PUNCT
ejpam-3728	21	30	can	can	AUX
ejpam-3728	21	31	be	be	AUX
ejpam-3728	21	32	seen	see	VERB
ejpam-3728	21	33	in	in	ADP
ejpam-3728	21	34	[	[	X
ejpam-3728	21	35	2	2	NUM
ejpam-3728	21	36	]	]	PUNCT
ejpam-3728	21	37	to	to	PART
ejpam-3728	21	38	estimate	estimate	VERB
ejpam-3728	21	39	the	the	DET
ejpam-3728	21	40	approximation	approximation	NOUN
ejpam-3728	21	41	results	result	NOUN
ejpam-3728	21	42	for	for	ADP
ejpam-3728	21	43	the	the	DET
ejpam-3728	21	44	integrable	integrable	ADJ
ejpam-3728	21	45	function	function	NOUN
ejpam-3728	21	46	.	.	PUNCT
ejpam-3728	22	1	the	the	DET
ejpam-3728	22	2	important	important	ADJ
ejpam-3728	22	3	properties	property	NOUN
ejpam-3728	22	4	including	include	VERB
ejpam-3728	22	5	global	global	ADJ
ejpam-3728	22	6	results	result	NOUN
ejpam-3728	22	7	,	,	PUNCT
ejpam-3728	22	8	local	local	ADJ
ejpam-3728	22	9	results	result	NOUN
ejpam-3728	22	10	,	,	PUNCT
ejpam-3728	22	11	simultaneous	simultaneous	ADJ
ejpam-3728	22	12	approximation	approximation	NOUN
ejpam-3728	22	13	,	,	PUNCT
ejpam-3728	22	14	convergence	convergence	NOUN
ejpam-3728	22	15	properties	property	NOUN
ejpam-3728	22	16	,	,	PUNCT
ejpam-3728	22	17	etc	etc	X
ejpam-3728	22	18	.	.	X
ejpam-3728	22	19	have	have	AUX
ejpam-3728	22	20	been	be	AUX
ejpam-3728	22	21	studied	study	VERB
ejpam-3728	22	22	with	with	ADP
ejpam-3728	22	23	the	the	DET
ejpam-3728	22	24	above	above	ADJ
ejpam-3728	22	25	operators	operator	NOUN
ejpam-3728	22	26	and	and	CCONJ
ejpam-3728	22	27	their	their	PRON
ejpam-3728	22	28	modifications	modification	NOUN
ejpam-3728	22	29	in	in	ADP
ejpam-3728	22	30	various	various	ADJ
ejpam-3728	22	31	studies	study	NOUN
ejpam-3728	22	32	(	(	PUNCT
ejpam-3728	22	33	see	see	VERB
ejpam-3728	22	34	[	[	X
ejpam-3728	22	35	1	1	NUM
ejpam-3728	22	36	,	,	PUNCT
ejpam-3728	22	37	3	3	NUM
ejpam-3728	22	38	,	,	PUNCT
ejpam-3728	22	39	11–13	11–13	NUM
ejpam-3728	22	40	]	]	NUM
ejpam-3728	22	41	)	)	PUNCT
ejpam-3728	22	42	.	.	PUNCT
ejpam-3728	23	1	one	one	NUM
ejpam-3728	23	2	of	of	ADP
ejpam-3728	23	3	them	they	PRON
ejpam-3728	23	4	,	,	PUNCT
ejpam-3728	23	5	an	an	DET
ejpam-3728	23	6	interesting	interesting	ADJ
ejpam-3728	23	7	modification	modification	NOUN
ejpam-3728	23	8	was	be	AUX
ejpam-3728	23	9	the	the	DET
ejpam-3728	23	10	durrmeyer	durrmeyer	NOUN
ejpam-3728	23	11	modification	modification	NOUN
ejpam-3728	23	12	of	of	ADP
ejpam-3728	23	13	the	the	DET
ejpam-3728	23	14	szász	szász	NUM
ejpam-3728	23	15	-	-	PUNCT
ejpam-3728	23	16	mirakjan	mirakjan	NOUN
ejpam-3728	23	17	operators	operator	NOUN
ejpam-3728	23	18	and	and	CCONJ
ejpam-3728	23	19	is	be	AUX
ejpam-3728	23	20	written	write	VERB
ejpam-3728	23	21	as	as	ADP
ejpam-3728	23	22	:	:	PUNCT
ejpam-3728	23	23	dn(g;x	dn(g;x	PROPN
ejpam-3728	23	24	)	)	PUNCT
ejpam-3728	24	1	=	=	PUNCT
ejpam-3728	25	1	∞∑	∞∑	NUM
ejpam-3728	25	2	j=0	j=0	PROPN
ejpam-3728	25	3	sn	sn	PROPN
ejpam-3728	25	4	,	,	PUNCT
ejpam-3728	25	5	j(x	j(x	PROPN
ejpam-3728	25	6	)	)	PUNCT
ejpam-3728	25	7	∞∫	∞∫	PROPN
ejpam-3728	25	8	0	0	NUM
ejpam-3728	25	9	sn	sn	PROPN
ejpam-3728	25	10	,	,	PUNCT
ejpam-3728	25	11	j(t)g(t)dt	j(t)g(t)dt	PROPN
ejpam-3728	25	12	,	,	PUNCT
ejpam-3728	25	13	(	(	PUNCT
ejpam-3728	25	14	2	2	X
ejpam-3728	25	15	)	)	PUNCT
ejpam-3728	25	16	seen	see	VERB
ejpam-3728	25	17	in	in	ADP
ejpam-3728	25	18	[	[	X
ejpam-3728	25	19	7	7	NUM
ejpam-3728	25	20	]	]	PUNCT
ejpam-3728	25	21	.	.	PUNCT
ejpam-3728	26	1	also	also	ADV
ejpam-3728	26	2	,	,	PUNCT
ejpam-3728	26	3	another	another	DET
ejpam-3728	26	4	modification	modification	NOUN
ejpam-3728	26	5	into	into	ADP
ejpam-3728	26	6	stancu	stancu	ADJ
ejpam-3728	26	7	variant	variant	NOUN
ejpam-3728	26	8	appeared	appear	VERB
ejpam-3728	26	9	in	in	ADP
ejpam-3728	26	10	[	[	X
ejpam-3728	26	11	9	9	NUM
ejpam-3728	26	12	]	]	PUNCT
ejpam-3728	26	13	of	of	ADP
ejpam-3728	26	14	the	the	DET
ejpam-3728	26	15	above	above	ADJ
ejpam-3728	26	16	operators	operator	NOUN
ejpam-3728	26	17	(	(	PUNCT
ejpam-3728	26	18	2	2	NUM
ejpam-3728	26	19	)	)	PUNCT
ejpam-3728	26	20	and	and	CCONJ
ejpam-3728	26	21	related	related	ADJ
ejpam-3728	26	22	properties	property	NOUN
ejpam-3728	26	23	like	like	ADP
ejpam-3728	26	24	density	density	NOUN
ejpam-3728	26	25	,	,	PUNCT
ejpam-3728	26	26	direct	direct	ADJ
ejpam-3728	26	27	results	result	NOUN
ejpam-3728	26	28	as	as	ADV
ejpam-3728	26	29	well	well	ADV
ejpam-3728	26	30	as	as	ADP
ejpam-3728	26	31	voronovskaya	voronovskaya	NOUN
ejpam-3728	26	32	type	type	NOUN
ejpam-3728	26	33	theorem	theorem	NOUN
ejpam-3728	26	34	are	be	AUX
ejpam-3728	26	35	studied	study	VERB
ejpam-3728	26	36	.	.	PUNCT
ejpam-3728	27	1	many	many	ADJ
ejpam-3728	27	2	approximation	approximation	NOUN
ejpam-3728	27	3	results	result	NOUN
ejpam-3728	27	4	are	be	AUX
ejpam-3728	27	5	also	also	ADV
ejpam-3728	27	6	discussed	discuss	VERB
ejpam-3728	27	7	in	in	ADP
ejpam-3728	27	8	[	[	X
ejpam-3728	27	9	14	14	NUM
ejpam-3728	27	10	,	,	PUNCT
ejpam-3728	27	11	20	20	NUM
ejpam-3728	27	12	]	]	PUNCT
ejpam-3728	27	13	.	.	PUNCT
ejpam-3728	28	1	a	a	DET
ejpam-3728	28	2	natural	natural	ADJ
ejpam-3728	28	3	generalization	generalization	NOUN
ejpam-3728	28	4	is	be	AUX
ejpam-3728	28	5	carried	carry	VERB
ejpam-3728	28	6	out	out	ADP
ejpam-3728	28	7	for	for	ADP
ejpam-3728	28	8	the	the	DET
ejpam-3728	28	9	above	above	ADJ
ejpam-3728	28	10	operators	operator	NOUN
ejpam-3728	28	11	(	(	PUNCT
ejpam-3728	28	12	2	2	NUM
ejpam-3728	28	13	)	)	PUNCT
ejpam-3728	28	14	in	in	ADP
ejpam-3728	28	15	[	[	X
ejpam-3728	28	16	10	10	NUM
ejpam-3728	28	17	]	]	PUNCT
ejpam-3728	28	18	by	by	ADP
ejpam-3728	28	19	mishra	mishra	PROPN
ejpam-3728	28	20	et	et	PROPN
ejpam-3728	28	21	al	al	PROPN
ejpam-3728	28	22	.	.	PROPN
ejpam-3728	29	1	for	for	ADP
ejpam-3728	29	2	the	the	DET
ejpam-3728	29	3	study	study	NOUN
ejpam-3728	29	4	of	of	ADP
ejpam-3728	29	5	simultaneous	simultaneous	ADJ
ejpam-3728	29	6	approximation	approximation	NOUN
ejpam-3728	29	7	,	,	PUNCT
ejpam-3728	29	8	like	like	ADP
ejpam-3728	29	9	b∗n(g;x	b∗n(g;x	NOUN
ejpam-3728	29	10	)	)	PUNCT
ejpam-3728	29	11	=	=	PRON
ejpam-3728	29	12	un	un	PROPN
ejpam-3728	29	13	∞∑	∞∑	NUM
ejpam-3728	29	14	j=0	j=0	PROPN
ejpam-3728	29	15	sun	sun	PROPN
ejpam-3728	29	16	,	,	PUNCT
ejpam-3728	29	17	j(x	j(x	PROPN
ejpam-3728	29	18	)	)	PUNCT
ejpam-3728	29	19	∞∫	∞∫	PROPN
ejpam-3728	29	20	0	0	NUM
ejpam-3728	29	21	sun	sun	PROPN
ejpam-3728	29	22	,	,	PUNCT
ejpam-3728	29	23	j(t)g(t)dt	j(t)g(t)dt	PROPN
ejpam-3728	29	24	,	,	PUNCT
ejpam-3728	29	25	(	(	PUNCT
ejpam-3728	29	26	3	3	X
ejpam-3728	29	27	)	)	PUNCT
ejpam-3728	29	28	where	where	SCONJ
ejpam-3728	29	29	sun	sun	NOUN
ejpam-3728	29	30	,	,	PUNCT
ejpam-3728	29	31	j(x	j(x	PROPN
ejpam-3728	29	32	)	)	PUNCT
ejpam-3728	29	33	=	=	PUNCT
ejpam-3728	29	34	e−unx	e−unx	NOUN
ejpam-3728	29	35	(	(	PUNCT
ejpam-3728	29	36	unx)j	unx)j	PROPN
ejpam-3728	29	37	j	j	PROPN
ejpam-3728	29	38	!	!	PUNCT
ejpam-3728	29	39	by	by	ADP
ejpam-3728	29	40	considering	consider	VERB
ejpam-3728	29	41	the	the	DET
ejpam-3728	29	42	sequence	sequence	NOUN
ejpam-3728	29	43	un	un	PROPN
ejpam-3728	29	44	is	be	AUX
ejpam-3728	29	45	strictly	strictly	ADV
ejpam-3728	29	46	increasing	increase	VERB
ejpam-3728	29	47	of	of	ADP
ejpam-3728	29	48	positive	positive	ADJ
ejpam-3728	29	49	real	real	ADJ
ejpam-3728	29	50	number	number	NOUN
ejpam-3728	29	51	as	as	ADV
ejpam-3728	29	52	well	well	ADV
ejpam-3728	29	53	as	as	ADP
ejpam-3728	29	54	un	un	PROPN
ejpam-3728	29	55	→∞	→∞	PROPN
ejpam-3728	29	56	as	as	ADP
ejpam-3728	29	57	n→∞	n→∞	NUM
ejpam-3728	29	58	with	with	ADP
ejpam-3728	29	59	u1	u1	NOUN
ejpam-3728	29	60	=	=	SYM
ejpam-3728	29	61	1	1	X
ejpam-3728	29	62	.	.	PUNCT
ejpam-3728	30	1	our	our	PRON
ejpam-3728	30	2	main	main	ADJ
ejpam-3728	30	3	motive	motive	NOUN
ejpam-3728	30	4	is	be	AUX
ejpam-3728	30	5	to	to	PART
ejpam-3728	30	6	study	study	VERB
ejpam-3728	30	7	the	the	DET
ejpam-3728	30	8	approximation	approximation	NOUN
ejpam-3728	30	9	properties	property	NOUN
ejpam-3728	30	10	of	of	ADP
ejpam-3728	30	11	the	the	DET
ejpam-3728	30	12	proposed	propose	VERB
ejpam-3728	30	13	operators	operator	NOUN
ejpam-3728	30	14	(	(	PUNCT
ejpam-3728	30	15	3	3	X
ejpam-3728	30	16	)	)	PUNCT
ejpam-3728	30	17	for	for	ADP
ejpam-3728	30	18	the	the	DET
ejpam-3728	30	19	functions	function	NOUN
ejpam-3728	30	20	from	from	ADP
ejpam-3728	30	21	different	different	ADJ
ejpam-3728	30	22	spaces	space	NOUN
ejpam-3728	30	23	.	.	PUNCT
ejpam-3728	31	1	the	the	DET
ejpam-3728	31	2	important	important	ADJ
ejpam-3728	31	3	properties	property	NOUN
ejpam-3728	31	4	of	of	ADP
ejpam-3728	31	5	the	the	DET
ejpam-3728	31	6	above	above	ADJ
ejpam-3728	31	7	proposed	propose	VERB
ejpam-3728	31	8	operators	operator	NOUN
ejpam-3728	31	9	(	(	PUNCT
ejpam-3728	31	10	3	3	X
ejpam-3728	31	11	)	)	PUNCT
ejpam-3728	31	12	are	be	AUX
ejpam-3728	31	13	studied	study	VERB
ejpam-3728	31	14	by	by	ADP
ejpam-3728	31	15	authors	author	NOUN
ejpam-3728	31	16	which	which	PRON
ejpam-3728	31	17	can	can	AUX
ejpam-3728	31	18	also	also	ADV
ejpam-3728	31	19	be	be	AUX
ejpam-3728	31	20	applied	apply	VERB
ejpam-3728	31	21	to	to	ADP
ejpam-3728	31	22	the	the	DET
ejpam-3728	31	23	operators	operator	NOUN
ejpam-3728	31	24	defined	define	VERB
ejpam-3728	31	25	by	by	ADP
ejpam-3728	31	26	(	(	PUNCT
ejpam-3728	31	27	2	2	NUM
ejpam-3728	31	28	)	)	PUNCT
ejpam-3728	31	29	.	.	PUNCT
ejpam-3728	32	1	in	in	ADP
ejpam-3728	32	2	order	order	NOUN
ejpam-3728	32	3	to	to	PART
ejpam-3728	32	4	study	study	VERB
ejpam-3728	32	5	the	the	DET
ejpam-3728	32	6	operators	operator	NOUN
ejpam-3728	32	7	(	(	PUNCT
ejpam-3728	32	8	3	3	NUM
ejpam-3728	32	9	)	)	PUNCT
ejpam-3728	32	10	,	,	PUNCT
ejpam-3728	32	11	we	we	PRON
ejpam-3728	32	12	divide	divide	VERB
ejpam-3728	32	13	the	the	DET
ejpam-3728	32	14	paper	paper	NOUN
ejpam-3728	32	15	into	into	ADP
ejpam-3728	32	16	sections	section	NOUN
ejpam-3728	32	17	.	.	PUNCT
ejpam-3728	33	1	section	section	NOUN
ejpam-3728	33	2	second	second	NOUN
ejpam-3728	33	3	contains	contain	VERB
ejpam-3728	33	4	preliminary	preliminary	ADJ
ejpam-3728	33	5	results	result	NOUN
ejpam-3728	33	6	,	,	PUNCT
ejpam-3728	33	7	which	which	PRON
ejpam-3728	33	8	are	be	AUX
ejpam-3728	33	9	used	use	VERB
ejpam-3728	33	10	to	to	PART
ejpam-3728	33	11	prove	prove	VERB
ejpam-3728	33	12	the	the	DET
ejpam-3728	33	13	main	main	ADJ
ejpam-3728	33	14	theorems	theorem	NOUN
ejpam-3728	33	15	.	.	PUNCT
ejpam-3728	34	1	section	section	NOUN
ejpam-3728	34	2	third	third	ADJ
ejpam-3728	34	3	deals	deal	NOUN
ejpam-3728	34	4	with	with	ADP
ejpam-3728	34	5	the	the	DET
ejpam-3728	34	6	approximation	approximation	NOUN
ejpam-3728	34	7	properties	property	NOUN
ejpam-3728	34	8	of	of	ADP
ejpam-3728	34	9	the	the	DET
ejpam-3728	34	10	operators	operator	NOUN
ejpam-3728	34	11	for	for	ADP
ejpam-3728	34	12	the	the	DET
ejpam-3728	34	13	function	function	NOUN
ejpam-3728	34	14	belongs	belong	VERB
ejpam-3728	34	15	to	to	ADP
ejpam-3728	34	16	the	the	DET
ejpam-3728	34	17	different	different	ADJ
ejpam-3728	34	18	spaces	space	NOUN
ejpam-3728	34	19	of	of	ADP
ejpam-3728	34	20	functions	function	NOUN
ejpam-3728	34	21	classes	class	NOUN
ejpam-3728	34	22	.	.	PUNCT
ejpam-3728	35	1	in	in	ADP
ejpam-3728	35	2	section	section	NOUN
ejpam-3728	35	3	fourth	fourth	ADJ
ejpam-3728	35	4	,	,	PUNCT
ejpam-3728	35	5	the	the	DET
ejpam-3728	35	6	rate	rate	NOUN
ejpam-3728	35	7	of	of	ADP
ejpam-3728	35	8	convergence	convergence	NOUN
ejpam-3728	35	9	of	of	ADP
ejpam-3728	35	10	the	the	DET
ejpam-3728	35	11	operators	operator	NOUN
ejpam-3728	35	12	is	be	AUX
ejpam-3728	35	13	estimated	estimate	VERB
ejpam-3728	35	14	for	for	ADP
ejpam-3728	35	15	the	the	DET
ejpam-3728	35	16	functions	function	NOUN
ejpam-3728	35	17	with	with	ADP
ejpam-3728	35	18	derivative	derivative	NOUN
ejpam-3728	35	19	of	of	ADP
ejpam-3728	35	20	bounded	bounded	ADJ
ejpam-3728	35	21	variation	variation	NOUN
ejpam-3728	35	22	.	.	PUNCT
ejpam-3728	36	1	at	at	ADP
ejpam-3728	36	2	last	last	ADV
ejpam-3728	36	3	,	,	PUNCT
ejpam-3728	36	4	we	we	PRON
ejpam-3728	36	5	present	present	VERB
ejpam-3728	36	6	the	the	DET
ejpam-3728	36	7	graphical	graphical	ADJ
ejpam-3728	36	8	and	and	CCONJ
ejpam-3728	36	9	numerical	numerical	ADJ
ejpam-3728	36	10	representation	representation	NOUN
ejpam-3728	36	11	for	for	ADP
ejpam-3728	36	12	the	the	DET
ejpam-3728	36	13	operators	operator	NOUN
ejpam-3728	36	14	in	in	ADP
ejpam-3728	36	15	order	order	NOUN
ejpam-3728	36	16	to	to	PART
ejpam-3728	36	17	show	show	VERB
ejpam-3728	36	18	the	the	DET
ejpam-3728	36	19	convergence	convergence	NOUN
ejpam-3728	36	20	of	of	ADP
ejpam-3728	36	21	the	the	DET
ejpam-3728	36	22	operators	operator	NOUN
ejpam-3728	36	23	.	.	PUNCT
ejpam-3728	37	1	2	2	X
ejpam-3728	37	2	.	.	X
ejpam-3728	37	3	preliminary	preliminary	ADJ
ejpam-3728	37	4	this	this	DET
ejpam-3728	37	5	section	section	NOUN
ejpam-3728	37	6	contains	contain	VERB
ejpam-3728	37	7	the	the	DET
ejpam-3728	37	8	basic	basic	ADJ
ejpam-3728	37	9	properties	property	NOUN
ejpam-3728	37	10	of	of	ADP
ejpam-3728	37	11	the	the	DET
ejpam-3728	37	12	defined	define	VERB
ejpam-3728	37	13	operators	operator	NOUN
ejpam-3728	37	14	(	(	PUNCT
ejpam-3728	37	15	3	3	NUM
ejpam-3728	37	16	)	)	PUNCT
ejpam-3728	37	17	.	.	PUNCT
ejpam-3728	38	1	in	in	ADP
ejpam-3728	38	2	order	order	NOUN
ejpam-3728	38	3	to	to	PART
ejpam-3728	38	4	prove	prove	VERB
ejpam-3728	38	5	approximations	approximation	NOUN
ejpam-3728	38	6	properties	property	NOUN
ejpam-3728	38	7	,	,	PUNCT
ejpam-3728	38	8	we	we	PRON
ejpam-3728	38	9	need	need	VERB
ejpam-3728	38	10	basic	basic	ADJ
ejpam-3728	38	11	lemmas	lemma	NOUN
ejpam-3728	38	12	.	.	PUNCT
ejpam-3728	39	1	lemma	lemma	PROPN
ejpam-3728	39	2	1	1	NUM
ejpam-3728	39	3	.	.	PUNCT
ejpam-3728	40	1	for	for	ADP
ejpam-3728	40	2	all	all	DET
ejpam-3728	40	3	x	x	PRON
ejpam-3728	40	4	≥	≥	NUM
ejpam-3728	40	5	0	0	NUM
ejpam-3728	40	6	and	and	CCONJ
ejpam-3728	40	7	n	n	PRON
ejpam-3728	40	8	∈	∈	PROPN
ejpam-3728	40	9	n	n	CCONJ
ejpam-3728	40	10	,	,	PUNCT
ejpam-3728	40	11	we	we	PRON
ejpam-3728	40	12	have	have	VERB
ejpam-3728	40	13	b∗n(1;x	b∗n(1;x	X
ejpam-3728	40	14	)	)	PUNCT
ejpam-3728	41	1	=	=	SYM
ejpam-3728	41	2	1	1	NUM
ejpam-3728	41	3	r.	r.	PROPN
ejpam-3728	41	4	yadav	yadav	PROPN
ejpam-3728	41	5	,	,	PUNCT
ejpam-3728	41	6	r.	r.	PROPN
ejpam-3728	41	7	meher	meher	PROPN
ejpam-3728	41	8	,	,	PUNCT
ejpam-3728	41	9	v.	v.	ADP
ejpam-3728	41	10	n.	n.	PROPN
ejpam-3728	41	11	mishra	mishra	PROPN
ejpam-3728	41	12	/	/	SYM
ejpam-3728	41	13	eur	eur	PROPN
ejpam-3728	41	14	.	.	PUNCT
ejpam-3728	42	1	j.	j.	PROPN
ejpam-3728	42	2	pure	pure	PROPN
ejpam-3728	42	3	appl	appl	PROPN
ejpam-3728	42	4	.	.	PROPN
ejpam-3728	42	5	math	math	PROPN
ejpam-3728	42	6	,	,	PUNCT
ejpam-3728	42	7	13	13	NUM
ejpam-3728	42	8	(	(	PUNCT
ejpam-3728	42	9	5	5	NUM
ejpam-3728	42	10	)	)	PUNCT
ejpam-3728	42	11	(	(	PUNCT
ejpam-3728	42	12	2020	2020	NUM
ejpam-3728	42	13	)	)	PUNCT
ejpam-3728	42	14	,	,	PUNCT
ejpam-3728	42	15	1306	1306	NUM
ejpam-3728	42	16	-	-	SYM
ejpam-3728	42	17	1324	1324	NUM
ejpam-3728	42	18	1308	1308	NUM
ejpam-3728	42	19	b∗n(t;x	b∗n(t;x	PROPN
ejpam-3728	42	20	)	)	PUNCT
ejpam-3728	42	21	=	=	SYM
ejpam-3728	42	22	1	1	NUM
ejpam-3728	42	23	un	un	NOUN
ejpam-3728	42	24	+	+	CCONJ
ejpam-3728	42	25	x	x	SYM
ejpam-3728	42	26	b∗n(t2;x	b∗n(t2;x	PROPN
ejpam-3728	42	27	)	)	PUNCT
ejpam-3728	42	28	=	=	SYM
ejpam-3728	42	29	2	2	NUM
ejpam-3728	43	1	+	+	NUM
ejpam-3728	43	2	4xun	4xun	NUM
ejpam-3728	43	3	+	+	NOUN
ejpam-3728	43	4	x2u2n	x2u2n	PUNCT
ejpam-3728	43	5	u2n	u2n	PROPN
ejpam-3728	43	6	b∗n(t3;x	b∗n(t3;x	PROPN
ejpam-3728	43	7	)	)	PUNCT
ejpam-3728	43	8	=	=	SYM
ejpam-3728	43	9	6	6	NUM
ejpam-3728	43	10	+	+	NUM
ejpam-3728	43	11	18xun	18xun	NOUN
ejpam-3728	44	1	+	+	CCONJ
ejpam-3728	44	2	9x2u2n	9x2u2n	NUM
ejpam-3728	45	1	+	+	NUM
ejpam-3728	45	2	x3u3n	x3u3n	PUNCT
ejpam-3728	45	3	u3n	u3n	PROPN
ejpam-3728	45	4	.	.	PUNCT
ejpam-3728	46	1	proof	proof	NOUN
ejpam-3728	46	2	.	.	PUNCT
ejpam-3728	47	1	we	we	PRON
ejpam-3728	47	2	can	can	AUX
ejpam-3728	47	3	easily	easily	ADV
ejpam-3728	47	4	proof	proof	VERB
ejpam-3728	47	5	the	the	DET
ejpam-3728	47	6	above	above	ADJ
ejpam-3728	47	7	parts	part	NOUN
ejpam-3728	47	8	of	of	ADP
ejpam-3728	47	9	the	the	DET
ejpam-3728	47	10	lemma	lemma	PROPN
ejpam-3728	47	11	,	,	PUNCT
ejpam-3728	47	12	so	so	SCONJ
ejpam-3728	47	13	we	we	PRON
ejpam-3728	47	14	omit	omit	VERB
ejpam-3728	47	15	the	the	DET
ejpam-3728	47	16	proof	proof	NOUN
ejpam-3728	47	17	.	.	PUNCT
ejpam-3728	48	1	lemma	lemma	PROPN
ejpam-3728	48	2	2	2	X
ejpam-3728	48	3	.	.	PUNCT
ejpam-3728	48	4	consider	consider	VERB
ejpam-3728	48	5	the	the	DET
ejpam-3728	48	6	function	function	NOUN
ejpam-3728	48	7	g	g	NOUN
ejpam-3728	48	8	is	be	AUX
ejpam-3728	48	9	integrable	integrable	ADJ
ejpam-3728	48	10	,	,	PUNCT
ejpam-3728	48	11	continuous	continuous	ADJ
ejpam-3728	48	12	,	,	PUNCT
ejpam-3728	48	13	bounded	bound	VERB
ejpam-3728	48	14	on	on	ADP
ejpam-3728	48	15	given	give	VERB
ejpam-3728	48	16	interval	interval	NOUN
ejpam-3728	48	17	[	[	X
ejpam-3728	48	18	0,∞	0,∞	NOUN
ejpam-3728	48	19	)	)	PUNCT
ejpam-3728	48	20	,	,	PUNCT
ejpam-3728	48	21	then	then	ADV
ejpam-3728	48	22	the	the	DET
ejpam-3728	48	23	central	central	ADJ
ejpam-3728	48	24	moments	moment	NOUN
ejpam-3728	48	25	can	can	AUX
ejpam-3728	48	26	be	be	AUX
ejpam-3728	48	27	obtained	obtain	VERB
ejpam-3728	48	28	as	as	ADP
ejpam-3728	48	29	:	:	PUNCT
ejpam-3728	48	30	ωn	ωn	NUM
ejpam-3728	48	31	,	,	PUNCT
ejpam-3728	48	32	m	m	VERB
ejpam-3728	48	33	=	=	SYM
ejpam-3728	48	34	un	un	PROPN
ejpam-3728	48	35	∞∑	∞∑	NUM
ejpam-3728	48	36	j=0	j=0	PROPN
ejpam-3728	48	37	sun	sun	PROPN
ejpam-3728	48	38	,	,	PUNCT
ejpam-3728	48	39	j(x	j(x	PROPN
ejpam-3728	48	40	)	)	PUNCT
ejpam-3728	48	41	∞∫	∞∫	PROPN
ejpam-3728	48	42	0	0	NUM
ejpam-3728	48	43	sun	sun	PROPN
ejpam-3728	48	44	,	,	PUNCT
ejpam-3728	48	45	j(t)(t−	j(t)(t−	PROPN
ejpam-3728	48	46	x)mdt	x)mdt	PROPN
ejpam-3728	48	47	,	,	PUNCT
ejpam-3728	48	48	(	(	PUNCT
ejpam-3728	48	49	4	4	X
ejpam-3728	48	50	)	)	PUNCT
ejpam-3728	48	51	where	where	SCONJ
ejpam-3728	48	52	m	m	VERB
ejpam-3728	48	53	=	=	SYM
ejpam-3728	48	54	0	0	NUM
ejpam-3728	48	55	,	,	PUNCT
ejpam-3728	48	56	1	1	NUM
ejpam-3728	48	57	,	,	PUNCT
ejpam-3728	48	58	2	2	NUM
ejpam-3728	48	59	,	,	PUNCT
ejpam-3728	48	60	.	.	PUNCT
ejpam-3728	48	61	.	.	PUNCT
ejpam-3728	49	1	..	..	PUNCT
ejpam-3728	50	1	so	so	ADV
ejpam-3728	50	2	for	for	ADP
ejpam-3728	50	3	m	m	PROPN
ejpam-3728	50	4	=	=	SYM
ejpam-3728	50	5	0	0	NUM
ejpam-3728	50	6	,	,	PUNCT
ejpam-3728	50	7	1	1	NUM
ejpam-3728	50	8	,	,	PUNCT
ejpam-3728	50	9	we	we	PRON
ejpam-3728	50	10	get	get	VERB
ejpam-3728	50	11	the	the	DET
ejpam-3728	50	12	the	the	DET
ejpam-3728	50	13	central	central	ADJ
ejpam-3728	50	14	moments	moment	NOUN
ejpam-3728	50	15	as	as	SCONJ
ejpam-3728	50	16	follows	follow	VERB
ejpam-3728	50	17	:	:	PUNCT
ejpam-3728	50	18	ωn,0	ωn,0	PROPN
ejpam-3728	50	19	=	=	SYM
ejpam-3728	50	20	1,ωn,1	1,ωn,1	NUM
ejpam-3728	50	21	=	=	SYM
ejpam-3728	50	22	1	1	NUM
ejpam-3728	50	23	un	un	NOUN
ejpam-3728	50	24	,	,	PUNCT
ejpam-3728	50	25	(	(	PUNCT
ejpam-3728	50	26	5	5	NUM
ejpam-3728	50	27	)	)	PUNCT
ejpam-3728	50	28	in	in	ADP
ejpam-3728	50	29	general	general	ADJ
ejpam-3728	50	30	,	,	PUNCT
ejpam-3728	50	31	we	we	PRON
ejpam-3728	50	32	have	have	AUX
ejpam-3728	50	33	unωn	unωn	VERB
ejpam-3728	50	34	,	,	PUNCT
ejpam-3728	50	35	m+1	m+1	PROPN
ejpam-3728	50	36	=	=	SYM
ejpam-3728	50	37	x	x	X
ejpam-3728	50	38	(	(	PUNCT
ejpam-3728	50	39	ω′n	ω′n	PROPN
ejpam-3728	50	40	,	,	PUNCT
ejpam-3728	50	41	m	m	VERB
ejpam-3728	50	42	+	+	ADJ
ejpam-3728	50	43	2mωn	2mωn	NOUN
ejpam-3728	50	44	,	,	PUNCT
ejpam-3728	50	45	m−1	m−1	PROPN
ejpam-3728	50	46	+	+	CCONJ
ejpam-3728	50	47	(	(	PUNCT
ejpam-3728	50	48	1	1	NUM
ejpam-3728	50	49	+	+	ADJ
ejpam-3728	50	50	m)ωn	m)ωn	PROPN
ejpam-3728	50	51	,	,	PUNCT
ejpam-3728	50	52	m	m	PROPN
ejpam-3728	50	53	)	)	PUNCT
ejpam-3728	50	54	,	,	PUNCT
ejpam-3728	50	55	(	(	PUNCT
ejpam-3728	50	56	6	6	X
ejpam-3728	50	57	)	)	PUNCT
ejpam-3728	50	58	this	this	PRON
ejpam-3728	50	59	lead	lead	VERB
ejpam-3728	50	60	us	we	PRON
ejpam-3728	50	61	to	to	ADP
ejpam-3728	50	62	ωn	ωn	PROPN
ejpam-3728	50	63	,	,	PUNCT
ejpam-3728	50	64	m	m	VERB
ejpam-3728	50	65	=	=	ADJ
ejpam-3728	50	66	o	o	X
ejpam-3728	50	67	(	(	PUNCT
ejpam-3728	50	68	u	u	NOUN
ejpam-3728	50	69	−[m+1	−[m+1	PRON
ejpam-3728	50	70	2	2	NUM
ejpam-3728	50	71	]	]	PUNCT
ejpam-3728	50	72	n	n	CCONJ
ejpam-3728	50	73	)	)	PUNCT
ejpam-3728	50	74	.	.	PUNCT
ejpam-3728	51	1	(	(	PUNCT
ejpam-3728	51	2	7	7	X
ejpam-3728	51	3	)	)	PUNCT
ejpam-3728	51	4	lemma	lemma	PROPN
ejpam-3728	51	5	3	3	X
ejpam-3728	51	6	.	.	PUNCT
ejpam-3728	52	1	let	let	VERB
ejpam-3728	52	2	the	the	DET
ejpam-3728	52	3	function	function	NOUN
ejpam-3728	52	4	g	g	NOUN
ejpam-3728	52	5	be	be	AUX
ejpam-3728	52	6	the	the	DET
ejpam-3728	52	7	continuous	continuous	ADJ
ejpam-3728	52	8	and	and	CCONJ
ejpam-3728	52	9	bounded	bound	VERB
ejpam-3728	52	10	on	on	ADP
ejpam-3728	52	11	[	[	X
ejpam-3728	52	12	0,∞	0,∞	NOUN
ejpam-3728	52	13	)	)	PUNCT
ejpam-3728	52	14	endowed	endow	VERB
ejpam-3728	52	15	with	with	ADP
ejpam-3728	52	16	supremum	supremum	ADJ
ejpam-3728	52	17	norm	norm	NOUN
ejpam-3728	52	18	‖g(x)‖	‖g(x)‖	PUNCT
ejpam-3728	52	19	=	=	SYM
ejpam-3728	52	20	sup	sup	NOUN
ejpam-3728	52	21	x≥0	x≥0	PROPN
ejpam-3728	52	22	|g|	|g|	PROPN
ejpam-3728	52	23	then	then	ADV
ejpam-3728	52	24	,	,	PUNCT
ejpam-3728	52	25	we	we	PRON
ejpam-3728	52	26	have	have	AUX
ejpam-3728	52	27	|b∗n(g;x)|	|b∗n(g;x)|	NOUN
ejpam-3728	52	28	≤	≤	ADJ
ejpam-3728	52	29	‖g‖.	‖g‖.	NOUN
ejpam-3728	52	30	(	(	PUNCT
ejpam-3728	52	31	8)	8)	NUM
ejpam-3728	52	32	remark	remark	NOUN
ejpam-3728	52	33	1	1	NUM
ejpam-3728	52	34	.	.	PUNCT
ejpam-3728	53	1	for	for	ADP
ejpam-3728	53	2	second	second	ADJ
ejpam-3728	53	3	order	order	NOUN
ejpam-3728	53	4	central	central	ADJ
ejpam-3728	53	5	moment	moment	NOUN
ejpam-3728	53	6	,	,	PUNCT
ejpam-3728	53	7	it	it	PRON
ejpam-3728	53	8	can	can	AUX
ejpam-3728	53	9	be	be	AUX
ejpam-3728	53	10	written	write	VERB
ejpam-3728	53	11	as	as	ADP
ejpam-3728	53	12	ωn,2	ωn,2	PROPN
ejpam-3728	53	13	=	=	SYM
ejpam-3728	53	14	2(1	2(1	NUM
ejpam-3728	53	15	+	+	CCONJ
ejpam-3728	53	16	unx	unx	ADJ
ejpam-3728	53	17	)	)	PUNCT
ejpam-3728	53	18	u2n	u2n	PROPN
ejpam-3728	53	19	=	=	SYM
ejpam-3728	53	20	2	2	NUM
ejpam-3728	53	21	un	un	PROPN
ejpam-3728	53	22	(	(	PUNCT
ejpam-3728	53	23	x+	x+	PROPN
ejpam-3728	53	24	1	1	NUM
ejpam-3728	53	25	un	un	PROPN
ejpam-3728	53	26	)	)	PUNCT
ejpam-3728	54	1	=	=	SYM
ejpam-3728	54	2	2	2	NUM
ejpam-3728	54	3	un	un	PROPN
ejpam-3728	54	4	ζ2n(x	ζ2n(x	PROPN
ejpam-3728	54	5	)	)	PUNCT
ejpam-3728	54	6	,	,	PUNCT
ejpam-3728	54	7	(	(	PUNCT
ejpam-3728	54	8	9	9	X
ejpam-3728	54	9	)	)	PUNCT
ejpam-3728	54	10	where	where	SCONJ
ejpam-3728	54	11	ζ2n(x	ζ2n(x	NOUN
ejpam-3728	54	12	)	)	PUNCT
ejpam-3728	54	13	=	=	SYM
ejpam-3728	54	14	(	(	PUNCT
ejpam-3728	54	15	x+	x+	PROPN
ejpam-3728	54	16	1	1	NUM
ejpam-3728	54	17	un	un	PROPN
ejpam-3728	54	18	)	)	PUNCT
ejpam-3728	54	19	.	.	PUNCT
ejpam-3728	55	1	r.	r.	PROPN
ejpam-3728	55	2	yadav	yadav	PROPN
ejpam-3728	55	3	,	,	PUNCT
ejpam-3728	55	4	r.	r.	PROPN
ejpam-3728	55	5	meher	meher	PROPN
ejpam-3728	55	6	,	,	PUNCT
ejpam-3728	55	7	v.	v.	ADP
ejpam-3728	55	8	n.	n.	PROPN
ejpam-3728	55	9	mishra	mishra	PROPN
ejpam-3728	55	10	/	/	SYM
ejpam-3728	55	11	eur	eur	PROPN
ejpam-3728	55	12	.	.	PUNCT
ejpam-3728	56	1	j.	j.	PROPN
ejpam-3728	56	2	pure	pure	PROPN
ejpam-3728	56	3	appl	appl	PROPN
ejpam-3728	56	4	.	.	PROPN
ejpam-3728	56	5	math	math	PROPN
ejpam-3728	56	6	,	,	PUNCT
ejpam-3728	56	7	13	13	NUM
ejpam-3728	56	8	(	(	PUNCT
ejpam-3728	56	9	5	5	NUM
ejpam-3728	56	10	)	)	PUNCT
ejpam-3728	56	11	(	(	PUNCT
ejpam-3728	56	12	2020	2020	NUM
ejpam-3728	56	13	)	)	PUNCT
ejpam-3728	56	14	,	,	PUNCT
ejpam-3728	56	15	1306	1306	NUM
ejpam-3728	56	16	-	-	SYM
ejpam-3728	56	17	1324	1324	NUM
ejpam-3728	56	18	1309	1309	NUM
ejpam-3728	56	19	3	3	NUM
ejpam-3728	56	20	.	.	PUNCT
ejpam-3728	56	21	approximation	approximation	NOUN
ejpam-3728	56	22	properties	property	NOUN
ejpam-3728	56	23	consider	consider	VERB
ejpam-3728	56	24	cb[0,∞	cb[0,∞	PROPN
ejpam-3728	56	25	)	)	PUNCT
ejpam-3728	56	26	be	be	AUX
ejpam-3728	56	27	the	the	DET
ejpam-3728	56	28	space	space	NOUN
ejpam-3728	56	29	of	of	ADP
ejpam-3728	56	30	all	all	DET
ejpam-3728	56	31	continuous	continuous	ADJ
ejpam-3728	56	32	and	and	CCONJ
ejpam-3728	56	33	bounded	bounded	ADJ
ejpam-3728	56	34	function	function	NOUN
ejpam-3728	56	35	defined	define	VERB
ejpam-3728	56	36	on	on	ADP
ejpam-3728	56	37	[	[	X
ejpam-3728	56	38	0,∞	0,∞	NOUN
ejpam-3728	56	39	)	)	PUNCT
ejpam-3728	56	40	,	,	PUNCT
ejpam-3728	56	41	endowed	endow	VERB
ejpam-3728	56	42	with	with	ADP
ejpam-3728	56	43	supremum	supremum	ADJ
ejpam-3728	56	44	norm	norm	NOUN
ejpam-3728	56	45	‖g‖	‖g‖	X
ejpam-3728	56	46	=	=	SYM
ejpam-3728	56	47	sup	sup	NOUN
ejpam-3728	56	48	x≥0	x≥0	PROPN
ejpam-3728	56	49	|g(x)|	|g(x)|	PROPN
ejpam-3728	56	50	,	,	PUNCT
ejpam-3728	56	51	also	also	ADV
ejpam-3728	56	52	let	let	VERB
ejpam-3728	56	53	for	for	ADP
ejpam-3728	56	54	any	any	DET
ejpam-3728	56	55	δ	δ	PROPN
ejpam-3728	56	56	>	>	X
ejpam-3728	56	57	0	0	PUNCT
ejpam-3728	57	1	k2(g	k2(g	PROPN
ejpam-3728	57	2	;	;	PUNCT
ejpam-3728	57	3	δ	δ	X
ejpam-3728	57	4	)	)	PUNCT
ejpam-3728	57	5	=	=	SYM
ejpam-3728	58	1	inf	inf	PROPN
ejpam-3728	58	2	f∈e	f∈e	PROPN
ejpam-3728	58	3	{	{	PUNCT
ejpam-3728	58	4	‖g	‖g	PROPN
ejpam-3728	58	5	−	−	PROPN
ejpam-3728	58	6	f‖+	f‖+	PROPN
ejpam-3728	58	7	δ‖f	δ‖f	PROPN
ejpam-3728	58	8	′′‖	′′‖	PROPN
ejpam-3728	58	9	}	}	PUNCT
ejpam-3728	58	10	(	(	PUNCT
ejpam-3728	58	11	10	10	NUM
ejpam-3728	58	12	)	)	PUNCT
ejpam-3728	58	13	be	be	VERB
ejpam-3728	58	14	the	the	DET
ejpam-3728	58	15	peetre	peetre	NOUN
ejpam-3728	58	16	’s	’s	PART
ejpam-3728	58	17	k	k	NOUN
ejpam-3728	58	18	-	-	ADJ
ejpam-3728	58	19	functional	functional	ADJ
ejpam-3728	58	20	,	,	PUNCT
ejpam-3728	58	21	where	where	SCONJ
ejpam-3728	58	22	e	e	NOUN
ejpam-3728	58	23	=	=	PRON
ejpam-3728	58	24	{	{	PUNCT
ejpam-3728	58	25	f	f	PROPN
ejpam-3728	58	26	∈	∈	PROPN
ejpam-3728	58	27	cb[0,∞	cb[0,∞	PROPN
ejpam-3728	58	28	)	)	PUNCT
ejpam-3728	58	29	:	:	PUNCT
ejpam-3728	59	1	f	f	PROPN
ejpam-3728	59	2	′	′	PROPN
ejpam-3728	59	3	,	,	PUNCT
ejpam-3728	59	4	f	f	PROPN
ejpam-3728	60	1	′′	′′	PROPN
ejpam-3728	60	2	∈	∈	PROPN
ejpam-3728	60	3	cb[0,∞	cb[0,∞	PROPN
ejpam-3728	60	4	)	)	PUNCT
ejpam-3728	60	5	}	}	PUNCT
ejpam-3728	60	6	.	.	PUNCT
ejpam-3728	61	1	also	also	ADV
ejpam-3728	61	2	a	a	DET
ejpam-3728	61	3	relation	relation	NOUN
ejpam-3728	61	4	can	can	AUX
ejpam-3728	61	5	be	be	AUX
ejpam-3728	61	6	seen	see	VERB
ejpam-3728	61	7	for	for	ADP
ejpam-3728	61	8	which	which	PRON
ejpam-3728	61	9	there	there	PRON
ejpam-3728	61	10	exists	exist	VERB
ejpam-3728	61	11	a	a	DET
ejpam-3728	61	12	positive	positive	ADJ
ejpam-3728	61	13	constant	constant	ADJ
ejpam-3728	61	14	m	m	NOUN
ejpam-3728	61	15	such	such	ADJ
ejpam-3728	61	16	that	that	SCONJ
ejpam-3728	61	17	:	:	PUNCT
ejpam-3728	61	18	k2(g	k2(g	PROPN
ejpam-3728	61	19	;	;	PUNCT
ejpam-3728	61	20	δ	δ	PROPN
ejpam-3728	61	21	)	)	PUNCT
ejpam-3728	61	22	≤mω2(g	≤mω2(g	VERB
ejpam-3728	61	23	,	,	PUNCT
ejpam-3728	61	24	√	√	PROPN
ejpam-3728	61	25	δ	δ	PROPN
ejpam-3728	61	26	)	)	PUNCT
ejpam-3728	61	27	,	,	PUNCT
ejpam-3728	61	28	δ	δ	PROPN
ejpam-3728	61	29	>	>	X
ejpam-3728	61	30	0	0	NUM
ejpam-3728	61	31	,	,	PUNCT
ejpam-3728	61	32	(	(	PUNCT
ejpam-3728	61	33	11	11	NUM
ejpam-3728	61	34	)	)	PUNCT
ejpam-3728	61	35	where	where	SCONJ
ejpam-3728	61	36	ω2(g	ω2(g	NUM
ejpam-3728	61	37	,	,	PUNCT
ejpam-3728	61	38	√	√	NUM
ejpam-3728	61	39	δ	δ	NOUN
ejpam-3728	61	40	)	)	PUNCT
ejpam-3728	61	41	is	be	AUX
ejpam-3728	61	42	second	second	ADJ
ejpam-3728	61	43	order	order	NOUN
ejpam-3728	61	44	modulus	modulus	NOUN
ejpam-3728	61	45	of	of	ADP
ejpam-3728	61	46	smoothness	smoothness	NOUN
ejpam-3728	61	47	for	for	ADP
ejpam-3728	61	48	the	the	DET
ejpam-3728	61	49	function	function	NOUN
ejpam-3728	61	50	g	g	PROPN
ejpam-3728	61	51	∈	∈	PROPN
ejpam-3728	61	52	cb[0,∞	cb[0,∞	PROPN
ejpam-3728	61	53	)	)	PUNCT
ejpam-3728	61	54	,	,	PUNCT
ejpam-3728	61	55	which	which	PRON
ejpam-3728	61	56	is	be	AUX
ejpam-3728	61	57	defined	define	VERB
ejpam-3728	61	58	by	by	ADP
ejpam-3728	61	59	:	:	PUNCT
ejpam-3728	61	60	ω2(g	ω2(g	NUM
ejpam-3728	61	61	,	,	PUNCT
ejpam-3728	61	62	δ	δ	X
ejpam-3728	61	63	)	)	PUNCT
ejpam-3728	62	1	=	=	PUNCT
ejpam-3728	62	2	sup{g(x+	sup{g(x+	PROPN
ejpam-3728	62	3	h)−	h)−	PROPN
ejpam-3728	62	4	2g(x	2g(x	NUM
ejpam-3728	62	5	)	)	PUNCT
ejpam-3728	63	1	+	+	CCONJ
ejpam-3728	63	2	g(x−	g(x−	NOUN
ejpam-3728	63	3	h	h	NOUN
ejpam-3728	63	4	)	)	PUNCT
ejpam-3728	63	5	:	:	PUNCT
ejpam-3728	64	1	x	x	X
ejpam-3728	64	2	,	,	PUNCT
ejpam-3728	64	3	x±	x±	PROPN
ejpam-3728	64	4	h	h	PROPN
ejpam-3728	64	5	∈	∈	PROPN
ejpam-3728	65	1	[	[	X
ejpam-3728	65	2	0,∞	0,∞	NOUN
ejpam-3728	65	3	)	)	PUNCT
ejpam-3728	65	4	,	,	PUNCT
ejpam-3728	65	5	0	0	NUM
ejpam-3728	65	6	≤	≤	NUM
ejpam-3728	65	7	h	h	NOUN
ejpam-3728	65	8	≤	≤	NUM
ejpam-3728	65	9	δ	δ	X
ejpam-3728	65	10	}	}	PUNCT
ejpam-3728	65	11	,	,	PUNCT
ejpam-3728	65	12	(	(	PUNCT
ejpam-3728	65	13	12	12	NUM
ejpam-3728	65	14	)	)	PUNCT
ejpam-3728	65	15	also	also	ADV
ejpam-3728	65	16	usual	usual	ADJ
ejpam-3728	65	17	modulus	modulus	NOUN
ejpam-3728	65	18	of	of	ADP
ejpam-3728	65	19	continuity	continuity	NOUN
ejpam-3728	65	20	can	can	AUX
ejpam-3728	65	21	be	be	AUX
ejpam-3728	65	22	defined	define	VERB
ejpam-3728	65	23	for	for	ADP
ejpam-3728	65	24	the	the	DET
ejpam-3728	65	25	function	function	NOUN
ejpam-3728	65	26	g	g	PROPN
ejpam-3728	65	27	∈	∈	PROPN
ejpam-3728	65	28	cb[0,∞	cb[0,∞	PROPN
ejpam-3728	65	29	)	)	PUNCT
ejpam-3728	65	30	as	as	SCONJ
ejpam-3728	65	31	follows	follow	VERB
ejpam-3728	65	32	:	:	PUNCT
ejpam-3728	65	33	ω(g	ω(g	NOUN
ejpam-3728	65	34	,	,	PUNCT
ejpam-3728	65	35	δ	δ	PROPN
ejpam-3728	65	36	)	)	PUNCT
ejpam-3728	66	1	=	=	PRON
ejpam-3728	66	2	{	{	PUNCT
ejpam-3728	66	3	g(y)−	g(y)−	INTJ
ejpam-3728	66	4	g(x	g(x	NOUN
ejpam-3728	66	5	)	)	PUNCT
ejpam-3728	66	6	:	:	PUNCT
ejpam-3728	67	1	x	x	X
ejpam-3728	67	2	,	,	PUNCT
ejpam-3728	67	3	y	y	PROPN
ejpam-3728	67	4	∈	∈	PROPN
ejpam-3728	68	1	[	[	X
ejpam-3728	68	2	0,∞	0,∞	NOUN
ejpam-3728	68	3	)	)	PUNCT
ejpam-3728	68	4	,	,	PUNCT
ejpam-3728	68	5	|y	|y	NOUN
ejpam-3728	68	6	−	−	PROPN
ejpam-3728	68	7	x|	x|	PROPN
ejpam-3728	68	8	≤	≤	PROPN
ejpam-3728	68	9	δ	δ	PROPN
ejpam-3728	68	10	,	,	PUNCT
ejpam-3728	68	11	δ	δ	PROPN
ejpam-3728	68	12	>	>	X
ejpam-3728	68	13	0	0	NUM
ejpam-3728	68	14	}	}	PUNCT
ejpam-3728	68	15	.	.	PUNCT
ejpam-3728	69	1	(	(	PUNCT
ejpam-3728	69	2	13	13	NUM
ejpam-3728	69	3	)	)	PUNCT
ejpam-3728	69	4	theorem	theorem	NOUN
ejpam-3728	69	5	1	1	NUM
ejpam-3728	69	6	.	.	X
ejpam-3728	70	1	consider	consider	VERB
ejpam-3728	70	2	g	g	PROPN
ejpam-3728	70	3	∈	∈	PROPN
ejpam-3728	70	4	cb[0,∞	cb[0,∞	PROPN
ejpam-3728	70	5	)	)	PUNCT
ejpam-3728	70	6	and	and	CCONJ
ejpam-3728	70	7	for	for	ADP
ejpam-3728	70	8	all	all	DET
ejpam-3728	70	9	x	x	PRON
ejpam-3728	70	10	≥	≥	NOUN
ejpam-3728	70	11	0	0	NUM
ejpam-3728	71	1	then	then	ADV
ejpam-3728	71	2	there	there	PRON
ejpam-3728	71	3	exists	exist	VERB
ejpam-3728	71	4	a	a	DET
ejpam-3728	71	5	positive	positive	ADJ
ejpam-3728	71	6	constant	constant	ADJ
ejpam-3728	71	7	c	c	NOUN
ejpam-3728	71	8	such	such	ADJ
ejpam-3728	71	9	that	that	SCONJ
ejpam-3728	71	10	|b∗n(g;x)−	|b∗n(g;x)−	PROPN
ejpam-3728	71	11	g(x)|	g(x)|	VERB
ejpam-3728	71	12	≤	≤	NUM
ejpam-3728	71	13	cω2	cω2	NOUN
ejpam-3728	71	14	(	(	PUNCT
ejpam-3728	71	15	g	g	NOUN
ejpam-3728	71	16	,	,	PUNCT
ejpam-3728	71	17	√	√	PROPN
ejpam-3728	71	18	δn	δn	NOUN
ejpam-3728	71	19	2	2	NUM
ejpam-3728	71	20	)	)	PUNCT
ejpam-3728	72	1	+	+	CCONJ
ejpam-3728	72	2	ω	ω	NUM
ejpam-3728	72	3	(	(	PUNCT
ejpam-3728	72	4	g	g	NOUN
ejpam-3728	72	5	,	,	PUNCT
ejpam-3728	72	6	γn	γn	NUM
ejpam-3728	72	7	)	)	PUNCT
ejpam-3728	72	8	,	,	PUNCT
ejpam-3728	72	9	(	(	PUNCT
ejpam-3728	72	10	14	14	NUM
ejpam-3728	72	11	)	)	PUNCT
ejpam-3728	72	12	where	where	SCONJ
ejpam-3728	72	13	δn	δn	NOUN
ejpam-3728	72	14	=	=	SYM
ejpam-3728	72	15	b̃∗n((t−	b̃∗n((t−	NOUN
ejpam-3728	72	16	x)2;x	x)2;x	NUM
ejpam-3728	72	17	)	)	PUNCT
ejpam-3728	73	1	+	+	CCONJ
ejpam-3728	73	2	1	1	NUM
ejpam-3728	73	3	u2n	u2n	NOUN
ejpam-3728	73	4	and	and	CCONJ
ejpam-3728	73	5	γn	γn	NOUN
ejpam-3728	73	6	=	=	PUNCT
ejpam-3728	73	7	b̃∗n((t−	b̃∗n((t−	PROPN
ejpam-3728	73	8	x);x	x);x	PROPN
ejpam-3728	73	9	)	)	PUNCT
ejpam-3728	73	10	.	.	PUNCT
ejpam-3728	74	1	proof	proof	NOUN
ejpam-3728	74	2	.	.	PUNCT
ejpam-3728	75	1	here	here	ADV
ejpam-3728	75	2	,	,	PUNCT
ejpam-3728	75	3	we	we	PRON
ejpam-3728	75	4	consider	consider	VERB
ejpam-3728	75	5	the	the	DET
ejpam-3728	75	6	auxiliary	auxiliary	ADJ
ejpam-3728	75	7	operators	operator	NOUN
ejpam-3728	75	8	as	as	SCONJ
ejpam-3728	75	9	follows	follow	VERB
ejpam-3728	75	10	:	:	PUNCT
ejpam-3728	75	11	s̃∗n(g;x	s̃∗n(g;x	ADJ
ejpam-3728	75	12	)	)	PUNCT
ejpam-3728	76	1	=	=	SYM
ejpam-3728	76	2	b∗n(g;x)−	b∗n(g;x)−	PROPN
ejpam-3728	76	3	g	g	PROPN
ejpam-3728	76	4	(	(	PUNCT
ejpam-3728	76	5	1	1	NUM
ejpam-3728	76	6	un	un	PROPN
ejpam-3728	76	7	+	+	NOUN
ejpam-3728	76	8	x	x	X
ejpam-3728	76	9	)	)	PUNCT
ejpam-3728	77	1	+	+	CCONJ
ejpam-3728	77	2	g(x	g(x	NOUN
ejpam-3728	77	3	)	)	PUNCT
ejpam-3728	77	4	.	.	PUNCT
ejpam-3728	78	1	(	(	PUNCT
ejpam-3728	78	2	15	15	X
ejpam-3728	78	3	)	)	PUNCT
ejpam-3728	78	4	let	let	VERB
ejpam-3728	78	5	f	f	PROPN
ejpam-3728	78	6	∈	∈	PROPN
ejpam-3728	78	7	e	e	PROPN
ejpam-3728	78	8	,	,	PUNCT
ejpam-3728	78	9	x	x	X
ejpam-3728	78	10	≥	≥	NOUN
ejpam-3728	78	11	0	0	NUM
ejpam-3728	78	12	then	then	ADV
ejpam-3728	78	13	using	use	VERB
ejpam-3728	78	14	taylor	taylor	PROPN
ejpam-3728	78	15	’s	’s	PART
ejpam-3728	78	16	formula	formula	NOUN
ejpam-3728	78	17	,	,	PUNCT
ejpam-3728	78	18	we	we	PRON
ejpam-3728	78	19	get	get	VERB
ejpam-3728	78	20	f(t)−	f(t)−	PROPN
ejpam-3728	78	21	f(x	f(x	PROPN
ejpam-3728	78	22	)	)	PUNCT
ejpam-3728	79	1	=	=	PUNCT
ejpam-3728	79	2	(	(	PUNCT
ejpam-3728	79	3	t−	t−	PROPN
ejpam-3728	79	4	x)f	x)f	X
ejpam-3728	79	5	′(x	′(x	NOUN
ejpam-3728	79	6	)	)	PUNCT
ejpam-3728	80	1	+	+	CCONJ
ejpam-3728	81	1	t∫	t∫	NOUN
ejpam-3728	81	2	0	0	NUM
ejpam-3728	81	3	(	(	PUNCT
ejpam-3728	81	4	t−	t−	X
ejpam-3728	81	5	v)f	v)f	NOUN
ejpam-3728	81	6	′′(v)dv	′′(v)dv	PROPN
ejpam-3728	81	7	.	.	PUNCT
ejpam-3728	82	1	(	(	PUNCT
ejpam-3728	82	2	16	16	NUM
ejpam-3728	82	3	)	)	PUNCT
ejpam-3728	82	4	applying	apply	VERB
ejpam-3728	82	5	the	the	DET
ejpam-3728	82	6	operators	operator	NOUN
ejpam-3728	82	7	b̃∗n	b̃∗n	NUM
ejpam-3728	82	8	on	on	ADP
ejpam-3728	82	9	the	the	DET
ejpam-3728	82	10	both	both	DET
ejpam-3728	82	11	sides	side	NOUN
ejpam-3728	82	12	to	to	ADP
ejpam-3728	82	13	the	the	DET
ejpam-3728	82	14	above	above	ADJ
ejpam-3728	82	15	expression	expression	NOUN
ejpam-3728	82	16	,	,	PUNCT
ejpam-3728	82	17	it	it	PRON
ejpam-3728	82	18	yields	yield	VERB
ejpam-3728	82	19	:	:	PUNCT
ejpam-3728	82	20	b̃∗n(f	b̃∗n(f	VERB
ejpam-3728	82	21	;	;	PUNCT
ejpam-3728	82	22	x)−	x)−	PROPN
ejpam-3728	82	23	f(x	f(x	PROPN
ejpam-3728	82	24	)	)	PUNCT
ejpam-3728	83	1	=	=	PUNCT
ejpam-3728	83	2	f	f	PROPN
ejpam-3728	83	3	′(x)b̃∗n(t−	′(x)b̃∗n(t−	PROPN
ejpam-3728	83	4	x;x	x;x	NUM
ejpam-3728	83	5	)	)	PUNCT
ejpam-3728	84	1	+	+	CCONJ
ejpam-3728	84	2	b̃∗n	b̃∗n	NUM
ejpam-3728	84	3			PROPN
ejpam-3728	84	4	t∫	t∫	PROPN
ejpam-3728	84	5	x	x	SYM
ejpam-3728	84	6	(	(	PUNCT
ejpam-3728	84	7	t−	t−	X
ejpam-3728	84	8	v)f	v)f	NOUN
ejpam-3728	84	9	′′(v)dv	′′(v)dv	PROPN
ejpam-3728	84	10			PROPN
ejpam-3728	84	11	r.	r.	PROPN
ejpam-3728	84	12	yadav	yadav	PROPN
ejpam-3728	84	13	,	,	PUNCT
ejpam-3728	84	14	r.	r.	PROPN
ejpam-3728	84	15	meher	meher	PROPN
ejpam-3728	84	16	,	,	PUNCT
ejpam-3728	84	17	v.	v.	ADP
ejpam-3728	84	18	n.	n.	PROPN
ejpam-3728	84	19	mishra	mishra	PROPN
ejpam-3728	84	20	/	/	SYM
ejpam-3728	84	21	eur	eur	PROPN
ejpam-3728	84	22	.	.	PUNCT
ejpam-3728	85	1	j.	j.	PROPN
ejpam-3728	85	2	pure	pure	PROPN
ejpam-3728	85	3	appl	appl	PROPN
ejpam-3728	85	4	.	.	PROPN
ejpam-3728	85	5	math	math	PROPN
ejpam-3728	85	6	,	,	PUNCT
ejpam-3728	85	7	13	13	NUM
ejpam-3728	85	8	(	(	PUNCT
ejpam-3728	85	9	5	5	NUM
ejpam-3728	85	10	)	)	PUNCT
ejpam-3728	85	11	(	(	PUNCT
ejpam-3728	85	12	2020	2020	NUM
ejpam-3728	85	13	)	)	PUNCT
ejpam-3728	85	14	,	,	PUNCT
ejpam-3728	85	15	1306	1306	NUM
ejpam-3728	85	16	-	-	SYM
ejpam-3728	85	17	1324	1324	NUM
ejpam-3728	85	18	1310	1310	NUM
ejpam-3728	85	19	=	=	SYM
ejpam-3728	85	20	b̃∗n	b̃∗n	NUM
ejpam-3728	85	21			PROPN
ejpam-3728	85	22	t∫	t∫	PROPN
ejpam-3728	85	23	x	x	SYM
ejpam-3728	85	24	(	(	PUNCT
ejpam-3728	85	25	t−	t−	X
ejpam-3728	85	26	v)f	v)f	NOUN
ejpam-3728	85	27	′′(v)dv	′′(v)dv	X
ejpam-3728	85	28			PROPN
ejpam-3728	85	29	=	=	SYM
ejpam-3728	85	30	s∗n	s∗n	PROPN
ejpam-3728	85	31			PROPN
ejpam-3728	85	32	t∫	t∫	PROPN
ejpam-3728	85	33	x	x	SYM
ejpam-3728	85	34	(	(	PUNCT
ejpam-3728	85	35	t−	t−	X
ejpam-3728	85	36	v)f	v)f	NOUN
ejpam-3728	86	1	′′(v)dv	′′(v)dv	NOUN
ejpam-3728	86	2	−	−	ADJ
ejpam-3728	87	1			PROPN
ejpam-3728	88	1	(	(	PUNCT
ejpam-3728	88	2	1	1	NUM
ejpam-3728	88	3	un	un	NOUN
ejpam-3728	88	4	+	+	NOUN
ejpam-3728	88	5	x	x	NOUN
ejpam-3728	88	6	)	)	PUNCT
ejpam-3728	88	7	∫	∫	PROPN
ejpam-3728	88	8	x	x	PROPN
ejpam-3728	88	9	(	(	PUNCT
ejpam-3728	88	10	1	1	NUM
ejpam-3728	88	11	un	un	PROPN
ejpam-3728	88	12	+	+	PROPN
ejpam-3728	88	13	x−	x−	PROPN
ejpam-3728	88	14	v	v	X
ejpam-3728	88	15	)	)	PUNCT
ejpam-3728	89	1	f	f	PROPN
ejpam-3728	89	2	′′(v)dv	′′(v)dv	PROPN
ejpam-3728	89	3			PROPN
ejpam-3728	89	4	.(17	.(17	PUNCT
ejpam-3728	89	5	)	)	PUNCT
ejpam-3728	90	1	here	here	ADV
ejpam-3728	90	2	,	,	PUNCT
ejpam-3728	90	3	the	the	DET
ejpam-3728	90	4	following	follow	VERB
ejpam-3728	90	5	inequalities	inequality	NOUN
ejpam-3728	90	6	are	be	AUX
ejpam-3728	90	7	as:∣∣∣∣∣∣	as:∣∣∣∣∣∣	ADJ
ejpam-3728	90	8	t∫	t∫	PROPN
ejpam-3728	90	9	x	x	SYM
ejpam-3728	90	10	(	(	PUNCT
ejpam-3728	90	11	t−	t−	X
ejpam-3728	90	12	v)f	v)f	NOUN
ejpam-3728	90	13	′′(v)dv	′′(v)dv	NOUN
ejpam-3728	90	14	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-3728	90	15	≤	≤	NOUN
ejpam-3728	90	16	(	(	PUNCT
ejpam-3728	90	17	t−	t−	PROPN
ejpam-3728	90	18	x)2‖f	x)2‖f	PROPN
ejpam-3728	90	19	′′‖	′′‖	PROPN
ejpam-3728	90	20	(	(	PUNCT
ejpam-3728	90	21	18	18	NUM
ejpam-3728	90	22	)	)	PUNCT
ejpam-3728	90	23	and	and	CCONJ
ejpam-3728	90	24	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-3728	90	25	(	(	PUNCT
ejpam-3728	90	26	1	1	NUM
ejpam-3728	90	27	un	un	NOUN
ejpam-3728	90	28	+	+	NOUN
ejpam-3728	90	29	x	x	NOUN
ejpam-3728	90	30	)	)	PUNCT
ejpam-3728	90	31	∫	∫	PROPN
ejpam-3728	91	1	x	x	PROPN
ejpam-3728	91	2	(	(	PUNCT
ejpam-3728	91	3	1	1	NUM
ejpam-3728	91	4	un	un	PROPN
ejpam-3728	91	5	+	+	PROPN
ejpam-3728	91	6	x−	x−	PROPN
ejpam-3728	91	7	v	v	PROPN
ejpam-3728	91	8	)	)	PUNCT
ejpam-3728	91	9	f	f	PROPN
ejpam-3728	91	10	′′(v)dv	′′(v)dv	PROPN
ejpam-3728	91	11	∣∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣∣	PROPN
ejpam-3728	91	12	≤	≤	PROPN
ejpam-3728	91	13	1	1	NUM
ejpam-3728	91	14	u2n	u2n	NOUN
ejpam-3728	91	15	‖f	‖f	ADP
ejpam-3728	91	16	′′‖.	′′‖.	NOUN
ejpam-3728	91	17	(	(	PUNCT
ejpam-3728	91	18	19	19	NUM
ejpam-3728	91	19	)	)	PUNCT
ejpam-3728	91	20	by	by	ADP
ejpam-3728	91	21	considering	consider	VERB
ejpam-3728	91	22	the	the	DET
ejpam-3728	91	23	above	above	ADJ
ejpam-3728	91	24	inequalities	inequality	NOUN
ejpam-3728	91	25	(	(	PUNCT
ejpam-3728	91	26	18	18	NUM
ejpam-3728	91	27	,	,	PUNCT
ejpam-3728	91	28	19	19	NUM
ejpam-3728	91	29	)	)	PUNCT
ejpam-3728	91	30	and	and	CCONJ
ejpam-3728	91	31	with	with	ADP
ejpam-3728	91	32	the	the	DET
ejpam-3728	91	33	help	help	NOUN
ejpam-3728	91	34	of	of	ADP
ejpam-3728	91	35	(	(	PUNCT
ejpam-3728	91	36	17	17	NUM
ejpam-3728	91	37	)	)	PUNCT
ejpam-3728	91	38	,	,	PUNCT
ejpam-3728	91	39	we	we	PRON
ejpam-3728	91	40	obtain	obtain	VERB
ejpam-3728	91	41	b̃∗n(f	b̃∗n(f	ADP
ejpam-3728	91	42	;	;	PUNCT
ejpam-3728	91	43	x)−	x)−	PROPN
ejpam-3728	91	44	f(x	f(x	PROPN
ejpam-3728	91	45	)	)	PUNCT
ejpam-3728	92	1	=	=	PRON
ejpam-3728	92	2	{	{	PUNCT
ejpam-3728	92	3	b̃∗n((t−	b̃∗n((t−	NOUN
ejpam-3728	92	4	x)2;x	x)2;x	NUM
ejpam-3728	92	5	)	)	PUNCT
ejpam-3728	93	1	+	+	CCONJ
ejpam-3728	93	2	1	1	NUM
ejpam-3728	93	3	u2n	u2n	NOUN
ejpam-3728	93	4	}	}	PUNCT
ejpam-3728	93	5	‖f	‖f	ADP
ejpam-3728	93	6	′′‖	′′‖	NOUN
ejpam-3728	93	7	(	(	PUNCT
ejpam-3728	93	8	20	20	NUM
ejpam-3728	93	9	)	)	PUNCT
ejpam-3728	93	10	=	=	SYM
ejpam-3728	93	11	δn‖f	δn‖f	NOUN
ejpam-3728	93	12	′′‖.	′′‖.	NOUN
ejpam-3728	93	13	(	(	PUNCT
ejpam-3728	93	14	21	21	NUM
ejpam-3728	93	15	)	)	PUNCT
ejpam-3728	93	16	also	also	ADV
ejpam-3728	93	17	,	,	PUNCT
ejpam-3728	93	18	|s∗n(g;x)|	|s∗n(g;x)|	ADJ
ejpam-3728	93	19	≤	≤	NOUN
ejpam-3728	93	20	‖g‖.	‖g‖.	NOUN
ejpam-3728	93	21	using	use	VERB
ejpam-3728	93	22	this	this	DET
ejpam-3728	93	23	property	property	NOUN
ejpam-3728	93	24	,	,	PUNCT
ejpam-3728	93	25	we	we	PRON
ejpam-3728	93	26	get	get	VERB
ejpam-3728	93	27	|s∗n(g;x))−	|s∗n(g;x))−	ADV
ejpam-3728	93	28	g(x)|	g(x)|	NOUN
ejpam-3728	93	29	≤	≤	NOUN
ejpam-3728	93	30	|b̃∗n(g	|b̃∗n(g	ADJ
ejpam-3728	93	31	−	−	PROPN
ejpam-3728	93	32	f	f	X
ejpam-3728	93	33	;	;	PUNCT
ejpam-3728	93	34	x)−	x)−	PROPN
ejpam-3728	93	35	(	(	PUNCT
ejpam-3728	93	36	g	g	PROPN
ejpam-3728	93	37	−	−	PROPN
ejpam-3728	93	38	f)(x)|+	f)(x)|+	PROPN
ejpam-3728	93	39	|b̃∗n(f	|b̃∗n(f	NOUN
ejpam-3728	93	40	;	;	PUNCT
ejpam-3728	93	41	x)−	x)−	PROPN
ejpam-3728	93	42	f(x)|	f(x)|	VERB
ejpam-3728	93	43	+	+	NUM
ejpam-3728	93	44	∣∣∣∣g	∣∣∣∣g	NOUN
ejpam-3728	93	45	(	(	PUNCT
ejpam-3728	93	46	1	1	NUM
ejpam-3728	93	47	un	un	NOUN
ejpam-3728	93	48	+	+	NOUN
ejpam-3728	93	49	x	x	X
ejpam-3728	93	50	)	)	PUNCT
ejpam-3728	93	51	−	−	ADP
ejpam-3728	93	52	g(x	g(x	NOUN
ejpam-3728	93	53	)	)	PUNCT
ejpam-3728	94	1	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3728	94	2	≤	≤	NUM
ejpam-3728	94	3	4‖g	4‖g	NUM
ejpam-3728	94	4	−	−	PROPN
ejpam-3728	94	5	f‖+	f‖+	PROPN
ejpam-3728	94	6	|b̃∗n(f	|b̃∗n(f	NOUN
ejpam-3728	94	7	;	;	PUNCT
ejpam-3728	94	8	x)−	x)−	PROPN
ejpam-3728	94	9	f(x)|+	f(x)|+	PROPN
ejpam-3728	94	10	∣∣∣∣g	∣∣∣∣g	NOUN
ejpam-3728	94	11	(	(	PUNCT
ejpam-3728	94	12	1	1	NUM
ejpam-3728	94	13	un	un	NOUN
ejpam-3728	94	14	+	+	NOUN
ejpam-3728	94	15	x	x	X
ejpam-3728	94	16	)	)	PUNCT
ejpam-3728	94	17	−	−	ADP
ejpam-3728	94	18	g(x	g(x	NOUN
ejpam-3728	94	19	)	)	PUNCT
ejpam-3728	94	20	∣∣∣∣	∣∣∣∣	NOUN
ejpam-3728	94	21	,	,	PUNCT
ejpam-3728	94	22	using	use	VERB
ejpam-3728	94	23	(	(	PUNCT
ejpam-3728	94	24	20	20	NUM
ejpam-3728	94	25	)	)	PUNCT
ejpam-3728	94	26	and	and	CCONJ
ejpam-3728	94	27	with	with	ADP
ejpam-3728	94	28	the	the	DET
ejpam-3728	94	29	help	help	NOUN
ejpam-3728	94	30	of	of	ADP
ejpam-3728	94	31	modulus	modulus	NOUN
ejpam-3728	94	32	of	of	ADP
ejpam-3728	94	33	continuity	continuity	NOUN
ejpam-3728	94	34	,	,	PUNCT
ejpam-3728	94	35	we	we	PRON
ejpam-3728	94	36	obtain	obtain	VERB
ejpam-3728	94	37	|s∗n(g;x)−	|s∗n(g;x)−	PROPN
ejpam-3728	94	38	g(x)|	g(x)|	NOUN
ejpam-3728	94	39	≤	≤	NUM
ejpam-3728	94	40	4‖g	4‖g	NUM
ejpam-3728	94	41	−	−	PROPN
ejpam-3728	94	42	f‖+	f‖+	NOUN
ejpam-3728	94	43	δn‖f	δn‖f	NOUN
ejpam-3728	94	44	′′‖+	′′‖+	PROPN
ejpam-3728	94	45	ω	ω	X
ejpam-3728	94	46	(	(	PUNCT
ejpam-3728	94	47	g	g	NOUN
ejpam-3728	94	48	,	,	PUNCT
ejpam-3728	94	49	γn	γn	NOUN
ejpam-3728	94	50	)	)	PUNCT
ejpam-3728	94	51	.	.	PUNCT
ejpam-3728	95	1	taking	take	VERB
ejpam-3728	95	2	the	the	DET
ejpam-3728	95	3	infimum	infimum	NOUN
ejpam-3728	95	4	for	for	ADP
ejpam-3728	95	5	all	all	DET
ejpam-3728	95	6	f	f	PROPN
ejpam-3728	95	7	∈	∈	PROPN
ejpam-3728	95	8	e	e	NOUN
ejpam-3728	95	9	on	on	ADP
ejpam-3728	95	10	the	the	DET
ejpam-3728	95	11	right	right	ADJ
ejpam-3728	95	12	hand	hand	NOUN
ejpam-3728	95	13	side	side	NOUN
ejpam-3728	95	14	and	and	CCONJ
ejpam-3728	95	15	by	by	ADP
ejpam-3728	95	16	relation	relation	NOUN
ejpam-3728	95	17	(	(	PUNCT
ejpam-3728	95	18	11	11	NUM
ejpam-3728	95	19	)	)	PUNCT
ejpam-3728	95	20	,	,	PUNCT
ejpam-3728	95	21	we	we	PRON
ejpam-3728	95	22	get	get	VERB
ejpam-3728	95	23	|s∗n(g;x)−	|s∗n(g;x)−	NUM
ejpam-3728	95	24	g(x)|	g(x)|	NOUN
ejpam-3728	95	25	≤	≤	NUM
ejpam-3728	95	26	4k2	4k2	NUM
ejpam-3728	96	1	(	(	PUNCT
ejpam-3728	96	2	g	g	NOUN
ejpam-3728	96	3	;	;	PUNCT
ejpam-3728	96	4	1	1	NUM
ejpam-3728	96	5	4	4	NUM
ejpam-3728	96	6	δn	δn	NOUN
ejpam-3728	96	7	)	)	PUNCT
ejpam-3728	97	1	+	+	CCONJ
ejpam-3728	97	2	ω	ω	NUM
ejpam-3728	97	3	(	(	PUNCT
ejpam-3728	97	4	g	g	NOUN
ejpam-3728	97	5	,	,	PUNCT
ejpam-3728	97	6	γn	γn	NOUN
ejpam-3728	97	7	)	)	PUNCT
ejpam-3728	97	8	≤	≤	NUM
ejpam-3728	97	9	cω2	cω2	NOUN
ejpam-3728	97	10	(	(	PUNCT
ejpam-3728	97	11	g	g	NOUN
ejpam-3728	97	12	,	,	PUNCT
ejpam-3728	97	13	√	√	PROPN
ejpam-3728	97	14	δn	δn	NOUN
ejpam-3728	97	15	2	2	NUM
ejpam-3728	97	16	)	)	PUNCT
ejpam-3728	97	17	+	+	CCONJ
ejpam-3728	98	1	ω	ω	NUM
ejpam-3728	98	2	(	(	PUNCT
ejpam-3728	98	3	g	g	NOUN
ejpam-3728	98	4	,	,	PUNCT
ejpam-3728	98	5	γn	γn	NOUN
ejpam-3728	98	6	)	)	PUNCT
ejpam-3728	98	7	.	.	PUNCT
ejpam-3728	99	1	r.	r.	PROPN
ejpam-3728	99	2	yadav	yadav	PROPN
ejpam-3728	99	3	,	,	PUNCT
ejpam-3728	99	4	r.	r.	PROPN
ejpam-3728	99	5	meher	meher	PROPN
ejpam-3728	99	6	,	,	PUNCT
ejpam-3728	99	7	v.	v.	ADP
ejpam-3728	99	8	n.	n.	PROPN
ejpam-3728	99	9	mishra	mishra	PROPN
ejpam-3728	99	10	/	/	SYM
ejpam-3728	99	11	eur	eur	PROPN
ejpam-3728	99	12	.	.	PUNCT
ejpam-3728	100	1	j.	j.	PROPN
ejpam-3728	100	2	pure	pure	PROPN
ejpam-3728	100	3	appl	appl	PROPN
ejpam-3728	100	4	.	.	PROPN
ejpam-3728	100	5	math	math	PROPN
ejpam-3728	100	6	,	,	PUNCT
ejpam-3728	100	7	13	13	NUM
ejpam-3728	100	8	(	(	PUNCT
ejpam-3728	100	9	5	5	NUM
ejpam-3728	100	10	)	)	PUNCT
ejpam-3728	100	11	(	(	PUNCT
ejpam-3728	100	12	2020	2020	NUM
ejpam-3728	100	13	)	)	PUNCT
ejpam-3728	100	14	,	,	PUNCT
ejpam-3728	100	15	1306	1306	NUM
ejpam-3728	100	16	-	-	SYM
ejpam-3728	100	17	1324	1324	NUM
ejpam-3728	100	18	1311	1311	NUM
ejpam-3728	100	19	thus	thus	ADV
ejpam-3728	100	20	,	,	PUNCT
ejpam-3728	100	21	the	the	DET
ejpam-3728	100	22	proof	proof	NOUN
ejpam-3728	100	23	is	be	AUX
ejpam-3728	100	24	completed	complete	VERB
ejpam-3728	100	25	.	.	PUNCT
ejpam-3728	101	1	now	now	ADV
ejpam-3728	101	2	,	,	PUNCT
ejpam-3728	101	3	we	we	PRON
ejpam-3728	101	4	estimate	estimate	VERB
ejpam-3728	101	5	the	the	DET
ejpam-3728	101	6	approximation	approximation	NOUN
ejpam-3728	101	7	of	of	ADP
ejpam-3728	101	8	the	the	DET
ejpam-3728	101	9	defined	define	VERB
ejpam-3728	101	10	operators	operator	NOUN
ejpam-3728	101	11	(	(	PUNCT
ejpam-3728	101	12	3	3	NUM
ejpam-3728	101	13	)	)	PUNCT
ejpam-3728	101	14	,	,	PUNCT
ejpam-3728	101	15	by	by	ADP
ejpam-3728	101	16	new	new	ADJ
ejpam-3728	101	17	type	type	NOUN
ejpam-3728	101	18	of	of	ADP
ejpam-3728	101	19	lipschitz	lipschitz	NOUN
ejpam-3728	101	20	maximal	maximal	ADJ
ejpam-3728	101	21	function	function	NOUN
ejpam-3728	101	22	with	with	ADP
ejpam-3728	101	23	order	order	NOUN
ejpam-3728	101	24	s	s	X
ejpam-3728	101	25	∈	∈	NOUN
ejpam-3728	101	26	(	(	PUNCT
ejpam-3728	101	27	0	0	NUM
ejpam-3728	101	28	,	,	PUNCT
ejpam-3728	101	29	1	1	NUM
ejpam-3728	101	30	]	]	PUNCT
ejpam-3728	101	31	,	,	PUNCT
ejpam-3728	101	32	defined	define	VERB
ejpam-3728	101	33	by	by	ADP
ejpam-3728	101	34	lenze	lenze	PROPN
ejpam-3728	102	1	[	[	X
ejpam-3728	102	2	6	6	NUM
ejpam-3728	102	3	]	]	PUNCT
ejpam-3728	102	4	as	as	ADP
ejpam-3728	102	5	τs(g	τs(g	X
ejpam-3728	102	6	,	,	PUNCT
ejpam-3728	102	7	x	x	X
ejpam-3728	102	8	)	)	PUNCT
ejpam-3728	102	9	=	=	SYM
ejpam-3728	102	10	sup	sup	NOUN
ejpam-3728	102	11	x	x	NOUN
ejpam-3728	102	12	,	,	PUNCT
ejpam-3728	102	13	t≥0	t≥0	PROPN
ejpam-3728	102	14	|g(t)−	|g(t)−	PROPN
ejpam-3728	102	15	g(x)|	g(x)|	VERB
ejpam-3728	102	16	|t−	|t−	PROPN
ejpam-3728	102	17	x|s	x|s	PROPN
ejpam-3728	102	18	,	,	PUNCT
ejpam-3728	102	19	t	t	PROPN
ejpam-3728	102	20	6=	6=	PROPN
ejpam-3728	102	21	x.	x.	PROPN
ejpam-3728	102	22	(	(	PUNCT
ejpam-3728	102	23	22	22	NUM
ejpam-3728	102	24	)	)	PUNCT
ejpam-3728	102	25	using	use	VERB
ejpam-3728	102	26	definition	definition	NOUN
ejpam-3728	102	27	of	of	ADP
ejpam-3728	102	28	lipschitz	lipschitz	VERB
ejpam-3728	102	29	maximal	maximal	ADJ
ejpam-3728	102	30	function	function	NOUN
ejpam-3728	102	31	,	,	PUNCT
ejpam-3728	102	32	we	we	PRON
ejpam-3728	102	33	have	have	VERB
ejpam-3728	102	34	a	a	DET
ejpam-3728	102	35	theorem	theorem	VERB
ejpam-3728	102	36	.	.	PUNCT
ejpam-3728	103	1	theorem	theorem	NOUN
ejpam-3728	103	2	2	2	NUM
ejpam-3728	103	3	.	.	X
ejpam-3728	104	1	for	for	ADP
ejpam-3728	104	2	any	any	DET
ejpam-3728	104	3	g	g	PROPN
ejpam-3728	104	4	∈	∈	PROPN
ejpam-3728	104	5	cb[0,∞	cb[0,∞	PROPN
ejpam-3728	104	6	)	)	PUNCT
ejpam-3728	104	7	with	with	ADP
ejpam-3728	104	8	s	s	X
ejpam-3728	104	9	∈	∈	PROPN
ejpam-3728	104	10	(	(	PUNCT
ejpam-3728	104	11	0	0	NUM
ejpam-3728	104	12	,	,	PUNCT
ejpam-3728	104	13	1	1	NUM
ejpam-3728	104	14	]	]	PUNCT
ejpam-3728	104	15	then	then	ADV
ejpam-3728	104	16	one	one	PRON
ejpam-3728	104	17	can	can	AUX
ejpam-3728	104	18	obtain	obtain	VERB
ejpam-3728	104	19	|b∗n(g;x)−	|b∗n(g;x)−	PROPN
ejpam-3728	104	20	g(x)|	g(x)|	VERB
ejpam-3728	104	21	≤	≤	NOUN
ejpam-3728	104	22	τs(g	τs(g	PUNCT
ejpam-3728	104	23	,	,	PUNCT
ejpam-3728	104	24	x	x	X
ejpam-3728	104	25	)	)	PUNCT
ejpam-3728	104	26	(	(	PUNCT
ejpam-3728	104	27	ωn,2	ωn,2	PROPN
ejpam-3728	104	28	)	)	PUNCT
ejpam-3728	104	29	s	s	PART
ejpam-3728	104	30	2	2	NUM
ejpam-3728	104	31	.	.	PUNCT
ejpam-3728	105	1	proof	proof	NOUN
ejpam-3728	105	2	.	.	PUNCT
ejpam-3728	106	1	by	by	ADP
ejpam-3728	106	2	equation	equation	NOUN
ejpam-3728	106	3	(	(	PUNCT
ejpam-3728	106	4	22	22	NUM
ejpam-3728	106	5	)	)	PUNCT
ejpam-3728	106	6	,	,	PUNCT
ejpam-3728	106	7	we	we	PRON
ejpam-3728	106	8	can	can	AUX
ejpam-3728	106	9	write	write	VERB
ejpam-3728	106	10	|b∗n(g;x)−	|b∗n(g;x)−	PROPN
ejpam-3728	106	11	g(x)|	g(x)|	VERB
ejpam-3728	106	12	≤	≤	NOUN
ejpam-3728	106	13	τs(g	τs(g	PUNCT
ejpam-3728	106	14	,	,	PUNCT
ejpam-3728	106	15	x)b∗n(|t−	x)b∗n(|t−	PROPN
ejpam-3728	106	16	x|s;x	x|s;x	PROPN
ejpam-3728	106	17	)	)	PUNCT
ejpam-3728	106	18	.	.	PUNCT
ejpam-3728	107	1	using	use	VERB
ejpam-3728	107	2	,	,	PUNCT
ejpam-3728	107	3	hölder	hölder	PROPN
ejpam-3728	107	4	’s	’s	PART
ejpam-3728	107	5	inequality	inequality	NOUN
ejpam-3728	107	6	with	with	ADP
ejpam-3728	107	7	j	j	PROPN
ejpam-3728	107	8	=	=	SYM
ejpam-3728	107	9	2	2	NUM
ejpam-3728	107	10	s	s	NOUN
ejpam-3728	107	11	,	,	PUNCT
ejpam-3728	107	12	l	l	NOUN
ejpam-3728	107	13	=	=	SYM
ejpam-3728	107	14	2	2	NUM
ejpam-3728	107	15	2−s	2−s	NUM
ejpam-3728	107	16	,	,	PUNCT
ejpam-3728	107	17	one	one	PRON
ejpam-3728	107	18	can	can	AUX
ejpam-3728	107	19	get	get	VERB
ejpam-3728	107	20	|b∗n(g;x)−	|b∗n(g;x)−	PROPN
ejpam-3728	107	21	g(x)|	g(x)|	VERB
ejpam-3728	107	22	≤	≤	NOUN
ejpam-3728	107	23	τs(g	τs(g	PUNCT
ejpam-3728	107	24	,	,	PUNCT
ejpam-3728	107	25	x	x	PRON
ejpam-3728	107	26	)	)	PUNCT
ejpam-3728	107	27	(	(	PUNCT
ejpam-3728	107	28	b∗n(g;x)((t−	b∗n(g;x)((t−	PROPN
ejpam-3728	107	29	x)2;x	x)2;x	NUM
ejpam-3728	107	30	)	)	PUNCT
ejpam-3728	107	31	)	)	PUNCT
ejpam-3728	108	1	s	s	PART
ejpam-3728	108	2	2	2	NUM
ejpam-3728	108	3	=	=	SYM
ejpam-3728	108	4	τs(f	τs(f	NUM
ejpam-3728	108	5	,	,	PUNCT
ejpam-3728	108	6	x	x	X
ejpam-3728	108	7	)	)	PUNCT
ejpam-3728	108	8	(	(	PUNCT
ejpam-3728	108	9	ωn,2	ωn,2	PROPN
ejpam-3728	108	10	)	)	PUNCT
ejpam-3728	108	11	s	s	PART
ejpam-3728	108	12	2	2	NUM
ejpam-3728	108	13	.	.	PUNCT
ejpam-3728	109	1	next	next	ADJ
ejpam-3728	109	2	theorem	theorem	NOUN
ejpam-3728	109	3	is	be	AUX
ejpam-3728	109	4	based	base	VERB
ejpam-3728	109	5	on	on	ADP
ejpam-3728	109	6	modified	modify	VERB
ejpam-3728	109	7	lipschitz	lipschitz	NOUN
ejpam-3728	109	8	type	type	NOUN
ejpam-3728	109	9	spaces	space	NOUN
ejpam-3728	109	10	[	[	X
ejpam-3728	109	11	15	15	NUM
ejpam-3728	109	12	]	]	PUNCT
ejpam-3728	109	13	and	and	CCONJ
ejpam-3728	109	14	this	this	DET
ejpam-3728	109	15	spaces	space	NOUN
ejpam-3728	109	16	is	be	AUX
ejpam-3728	109	17	defined	define	VERB
ejpam-3728	109	18	by	by	ADP
ejpam-3728	109	19	lipm1,m2	lipm1,m2	PROPN
ejpam-3728	109	20	m	m	PROPN
ejpam-3728	109	21	(	(	PUNCT
ejpam-3728	109	22	s	s	X
ejpam-3728	109	23	)	)	PUNCT
ejpam-3728	110	1	=	=	SYM
ejpam-3728	110	2	{	{	PUNCT
ejpam-3728	110	3	g	g	PROPN
ejpam-3728	110	4	∈	∈	PROPN
ejpam-3728	110	5	cb[0,∞	cb[0,∞	PROPN
ejpam-3728	110	6	)	)	PUNCT
ejpam-3728	110	7	:	:	PUNCT
ejpam-3728	110	8	|g(l1)−	|g(l1)−	PROPN
ejpam-3728	110	9	g(l2)|	g(l2)|	PROPN
ejpam-3728	110	10	≤m	≤m	PROPN
ejpam-3728	110	11	|l1	|l1	NOUN
ejpam-3728	110	12	−	−	PUNCT
ejpam-3728	111	1	l2|s	l2|s	PROPN
ejpam-3728	111	2	(	(	PUNCT
ejpam-3728	111	3	l1	l1	PROPN
ejpam-3728	111	4	+	+	CCONJ
ejpam-3728	111	5	l22m1	l22m1	NOUN
ejpam-3728	111	6	+	+	CCONJ
ejpam-3728	111	7	l2m2	l2m2	X
ejpam-3728	111	8	)	)	PUNCT
ejpam-3728	111	9	s	s	NOUN
ejpam-3728	111	10	2	2	NUM
ejpam-3728	111	11	,	,	PUNCT
ejpam-3728	111	12	where	where	SCONJ
ejpam-3728	111	13	l1	l1	PROPN
ejpam-3728	111	14	,	,	PUNCT
ejpam-3728	111	15	l2	l2	VERB
ejpam-3728	111	16	≥	≥	NOUN
ejpam-3728	111	17	0	0	NUM
ejpam-3728	111	18	are	be	AUX
ejpam-3728	111	19	variables	variable	NOUN
ejpam-3728	111	20	,	,	PUNCT
ejpam-3728	111	21	s	s	NOUN
ejpam-3728	111	22	∈	∈	PROPN
ejpam-3728	111	23	(	(	PUNCT
ejpam-3728	111	24	0	0	NUM
ejpam-3728	111	25	,	,	PUNCT
ejpam-3728	111	26	1	1	NUM
ejpam-3728	111	27	]	]	PUNCT
ejpam-3728	111	28	}	}	PUNCT
ejpam-3728	111	29	and	and	CCONJ
ejpam-3728	111	30	m1,m2	m1,m2	PROPN
ejpam-3728	111	31	are	be	AUX
ejpam-3728	111	32	the	the	DET
ejpam-3728	111	33	fixed	fix	VERB
ejpam-3728	111	34	numbers	number	NOUN
ejpam-3728	111	35	and	and	CCONJ
ejpam-3728	111	36	m	m	VERB
ejpam-3728	111	37	>	>	X
ejpam-3728	111	38	0	0	PUNCT
ejpam-3728	112	1	is	be	AUX
ejpam-3728	112	2	a	a	DET
ejpam-3728	112	3	constant	constant	ADJ
ejpam-3728	112	4	.	.	PUNCT
ejpam-3728	113	1	theorem	theorem	NOUN
ejpam-3728	113	2	3	3	NUM
ejpam-3728	113	3	.	.	X
ejpam-3728	114	1	for	for	ADP
ejpam-3728	114	2	g	g	PROPN
ejpam-3728	114	3	∈	∈	PROPN
ejpam-3728	114	4	lipm1,m2	lipm1,m2	PROPN
ejpam-3728	114	5	m	m	PROPN
ejpam-3728	114	6	(	(	PUNCT
ejpam-3728	114	7	s	s	NOUN
ejpam-3728	114	8	)	)	PUNCT
ejpam-3728	114	9	and	and	CCONJ
ejpam-3728	114	10	0	0	NUM
ejpam-3728	114	11	<	<	X
ejpam-3728	114	12	s	s	X
ejpam-3728	114	13	≤	≤	NUM
ejpam-3728	114	14	1	1	NUM
ejpam-3728	114	15	,	,	PUNCT
ejpam-3728	114	16	an	an	DET
ejpam-3728	114	17	inequality	inequality	NOUN
ejpam-3728	114	18	holds	hold	VERB
ejpam-3728	114	19	:	:	PUNCT
ejpam-3728	114	20	|b∗n(g;x)−	|b∗n(g;x)−	PROPN
ejpam-3728	114	21	g(x)|	g(x)|	VERB
ejpam-3728	114	22	≤	≤	NUM
ejpam-3728	114	23	m	m	VERB
ejpam-3728	114	24	(	(	PUNCT
ejpam-3728	114	25	ωn,2	ωn,2	PROPN
ejpam-3728	114	26	x(xm1	x(xm1	PROPN
ejpam-3728	114	27	+	+	SYM
ejpam-3728	114	28	m2	m2	PROPN
ejpam-3728	114	29	)	)	PUNCT
ejpam-3728	114	30	)	)	PUNCT
ejpam-3728	115	1	s	s	PART
ejpam-3728	115	2	2	2	NUM
ejpam-3728	115	3	,	,	PUNCT
ejpam-3728	115	4	m	m	VERB
ejpam-3728	115	5	>	>	X
ejpam-3728	115	6	0	0	NUM
ejpam-3728	115	7	,	,	PUNCT
ejpam-3728	115	8	x	x	X
ejpam-3728	115	9	∈	∈	PROPN
ejpam-3728	116	1	[	[	X
ejpam-3728	116	2	0,∞	0,∞	NOUN
ejpam-3728	116	3	)	)	PUNCT
ejpam-3728	116	4	.	.	PUNCT
ejpam-3728	117	1	proof	proof	NOUN
ejpam-3728	117	2	.	.	PUNCT
ejpam-3728	118	1	we	we	PRON
ejpam-3728	118	2	have	have	VERB
ejpam-3728	118	3	s	s	X
ejpam-3728	118	4	∈	∈	NOUN
ejpam-3728	118	5	(	(	PUNCT
ejpam-3728	118	6	0	0	NUM
ejpam-3728	118	7	,	,	PUNCT
ejpam-3728	118	8	1	1	NUM
ejpam-3728	118	9	]	]	PUNCT
ejpam-3728	118	10	and	and	CCONJ
ejpam-3728	118	11	in	in	ADP
ejpam-3728	118	12	order	order	NOUN
ejpam-3728	118	13	to	to	PART
ejpam-3728	118	14	prove	prove	VERB
ejpam-3728	118	15	the	the	DET
ejpam-3728	118	16	above	above	ADJ
ejpam-3728	118	17	theorem	theorem	NOUN
ejpam-3728	118	18	,	,	PUNCT
ejpam-3728	118	19	we	we	PRON
ejpam-3728	118	20	discuss	discuss	VERB
ejpam-3728	118	21	the	the	DET
ejpam-3728	118	22	cases	case	NOUN
ejpam-3728	118	23	on	on	ADP
ejpam-3728	118	24	s.	s.	PROPN
ejpam-3728	118	25	case	case	PROPN
ejpam-3728	118	26	1	1	X
ejpam-3728	118	27	.	.	PUNCT
ejpam-3728	119	1	if	if	SCONJ
ejpam-3728	119	2	we	we	PRON
ejpam-3728	119	3	consider	consider	VERB
ejpam-3728	119	4	s	s	PRON
ejpam-3728	119	5	=	=	NOUN
ejpam-3728	119	6	1	1	NUM
ejpam-3728	119	7	then	then	ADV
ejpam-3728	119	8	for	for	ADP
ejpam-3728	119	9	all	all	DET
ejpam-3728	119	10	t	t	PROPN
ejpam-3728	119	11	,	,	PUNCT
ejpam-3728	119	12	x	x	X
ejpam-3728	119	13	≥	≥	NOUN
ejpam-3728	119	14	0	0	NUM
ejpam-3728	119	15	,	,	PUNCT
ejpam-3728	119	16	we	we	PRON
ejpam-3728	119	17	can	can	AUX
ejpam-3728	119	18	observe	observe	VERB
ejpam-3728	119	19	that	that	SCONJ
ejpam-3728	119	20	1	1	NUM
ejpam-3728	119	21	t+x2m1+xm2	t+x2m1+xm2	NUM
ejpam-3728	119	22	)	)	PUNCT
ejpam-3728	119	23	≤	≤	NUM
ejpam-3728	119	24	1	1	NUM
ejpam-3728	119	25	x(xm1+m2	x(xm1+m2	NOUN
ejpam-3728	119	26	)	)	PUNCT
ejpam-3728	119	27	then	then	ADV
ejpam-3728	119	28	|b∗n(g;x)−	|b∗n(g;x)−	PROPN
ejpam-3728	119	29	g(x)|	g(x)|	VERB
ejpam-3728	119	30	≤	≤	NUM
ejpam-3728	119	31	b∗n(|g(t)−	b∗n(|g(t)−	PROPN
ejpam-3728	119	32	g(x)|;x	g(x)|;x	PROPN
ejpam-3728	119	33	)	)	PUNCT
ejpam-3728	119	34	r.	r.	PROPN
ejpam-3728	119	35	yadav	yadav	PROPN
ejpam-3728	119	36	,	,	PUNCT
ejpam-3728	119	37	r.	r.	PROPN
ejpam-3728	119	38	meher	meher	PROPN
ejpam-3728	119	39	,	,	PUNCT
ejpam-3728	119	40	v.	v.	ADP
ejpam-3728	119	41	n.	n.	PROPN
ejpam-3728	119	42	mishra	mishra	PROPN
ejpam-3728	119	43	/	/	SYM
ejpam-3728	119	44	eur	eur	PROPN
ejpam-3728	119	45	.	.	PUNCT
ejpam-3728	120	1	j.	j.	PROPN
ejpam-3728	120	2	pure	pure	PROPN
ejpam-3728	120	3	appl	appl	PROPN
ejpam-3728	120	4	.	.	PROPN
ejpam-3728	120	5	math	math	PROPN
ejpam-3728	120	6	,	,	PUNCT
ejpam-3728	120	7	13	13	NUM
ejpam-3728	120	8	(	(	PUNCT
ejpam-3728	120	9	5	5	NUM
ejpam-3728	120	10	)	)	PUNCT
ejpam-3728	120	11	(	(	PUNCT
ejpam-3728	120	12	2020	2020	NUM
ejpam-3728	120	13	)	)	PUNCT
ejpam-3728	120	14	,	,	PUNCT
ejpam-3728	120	15	1306	1306	NUM
ejpam-3728	120	16	-	-	SYM
ejpam-3728	120	17	1324	1324	NUM
ejpam-3728	120	18	1312	1312	NUM
ejpam-3728	120	19	≤	≤	NOUN
ejpam-3728	120	20	mb∗n	mb∗n	NOUN
ejpam-3728	120	21	(	(	PUNCT
ejpam-3728	120	22	|t−	|t−	PROPN
ejpam-3728	120	23	x|	x|	PROPN
ejpam-3728	120	24	(	(	PUNCT
ejpam-3728	120	25	t+	t+	NOUN
ejpam-3728	120	26	x2m1	x2m1	X
ejpam-3728	120	27	+	+	NUM
ejpam-3728	120	28	xm2	xm2	NOUN
ejpam-3728	120	29	)	)	PUNCT
ejpam-3728	120	30	1	1	NUM
ejpam-3728	120	31	2	2	NUM
ejpam-3728	120	32	;	;	PUNCT
ejpam-3728	120	33	x	x	X
ejpam-3728	120	34	)	)	PUNCT
ejpam-3728	120	35	≤	≤	NUM
ejpam-3728	120	36	m	m	VERB
ejpam-3728	120	37	(	(	PUNCT
ejpam-3728	120	38	x(xm1	x(xm1	PROPN
ejpam-3728	120	39	+	+	NOUN
ejpam-3728	120	40	m2	m2	PROPN
ejpam-3728	120	41	)	)	PUNCT
ejpam-3728	120	42	)	)	PUNCT
ejpam-3728	120	43	1	1	NUM
ejpam-3728	120	44	2	2	NUM
ejpam-3728	120	45	b∗n(|t−	b∗n(|t−	PROPN
ejpam-3728	120	46	x|;x	x|;x	PROPN
ejpam-3728	120	47	)	)	PUNCT
ejpam-3728	121	1	≤	≤	NUM
ejpam-3728	121	2	m	m	VERB
ejpam-3728	121	3	(	(	PUNCT
ejpam-3728	121	4	x(xa1	x(xa1	PROPN
ejpam-3728	121	5	+	+	NUM
ejpam-3728	121	6	a2	a2	PROPN
ejpam-3728	121	7	)	)	PUNCT
ejpam-3728	121	8	)	)	PUNCT
ejpam-3728	121	9	1	1	NUM
ejpam-3728	121	10	2	2	NUM
ejpam-3728	121	11	(	(	PUNCT
ejpam-3728	121	12	ωn,2	ωn,2	PROPN
ejpam-3728	121	13	)	)	PUNCT
ejpam-3728	121	14	1	1	NUM
ejpam-3728	121	15	2	2	NUM
ejpam-3728	121	16	≤	≤	NUM
ejpam-3728	121	17	m	m	VERB
ejpam-3728	121	18	(	(	PUNCT
ejpam-3728	121	19	ωn,2	ωn,2	PROPN
ejpam-3728	121	20	x(xm1	x(xm1	PROPN
ejpam-3728	121	21	+	+	SYM
ejpam-3728	121	22	m2	m2	PROPN
ejpam-3728	121	23	)	)	PUNCT
ejpam-3728	121	24	)	)	PUNCT
ejpam-3728	121	25	1	1	NUM
ejpam-3728	121	26	2	2	NUM
ejpam-3728	121	27	.	.	PUNCT
ejpam-3728	122	1	case	case	NOUN
ejpam-3728	122	2	2	2	NUM
ejpam-3728	122	3	.	.	X
ejpam-3728	123	1	for	for	ADP
ejpam-3728	123	2	s	s	PROPN
ejpam-3728	123	3	∈	∈	PROPN
ejpam-3728	123	4	(	(	PUNCT
ejpam-3728	123	5	0	0	NUM
ejpam-3728	123	6	,	,	PUNCT
ejpam-3728	123	7	1	1	NUM
ejpam-3728	123	8	)	)	PUNCT
ejpam-3728	123	9	then	then	ADV
ejpam-3728	123	10	using	use	VERB
ejpam-3728	123	11	hölder	hölder	NOUN
ejpam-3728	123	12	inequality	inequality	NOUN
ejpam-3728	123	13	with	with	ADP
ejpam-3728	123	14	p	p	NOUN
ejpam-3728	123	15	=	=	SYM
ejpam-3728	123	16	2	2	NUM
ejpam-3728	123	17	s	s	NOUN
ejpam-3728	123	18	,	,	PUNCT
ejpam-3728	123	19	q	q	NOUN
ejpam-3728	123	20	=	=	PUNCT
ejpam-3728	123	21	2	2	NUM
ejpam-3728	123	22	2−s	2−s	NUM
ejpam-3728	123	23	,	,	PUNCT
ejpam-3728	123	24	we	we	PRON
ejpam-3728	123	25	get	get	VERB
ejpam-3728	123	26	|b∗n(g;x)−	|b∗n(g;x)−	PROPN
ejpam-3728	123	27	g(x)|	g(x)|	NOUN
ejpam-3728	123	28	≤	≤	NUM
ejpam-3728	123	29	(	(	PUNCT
ejpam-3728	123	30	b∗n(|g(t)−	b∗n(|g(t)−	PROPN
ejpam-3728	123	31	g(x)|	g(x)|	NOUN
ejpam-3728	123	32	2	2	NUM
ejpam-3728	123	33	s	s	NOUN
ejpam-3728	123	34	;	;	PUNCT
ejpam-3728	123	35	x	x	X
ejpam-3728	123	36	)	)	PUNCT
ejpam-3728	123	37	)	)	PUNCT
ejpam-3728	124	1	s	s	PART
ejpam-3728	124	2	2	2	NUM
ejpam-3728	124	3	≤mb∗n	≤mb∗n	NOUN
ejpam-3728	124	4	(	(	PUNCT
ejpam-3728	124	5	|t−	|t−	PROPN
ejpam-3728	124	6	x|2	x|2	PROPN
ejpam-3728	124	7	(	(	PUNCT
ejpam-3728	124	8	t+	t+	NOUN
ejpam-3728	124	9	x2m1	x2m1	X
ejpam-3728	124	10	+	+	NUM
ejpam-3728	124	11	xm2	xm2	PROPN
ejpam-3728	124	12	)	)	PUNCT
ejpam-3728	124	13	;	;	PUNCT
ejpam-3728	124	14	x	x	X
ejpam-3728	124	15	)	)	PUNCT
ejpam-3728	124	16	s	s	PART
ejpam-3728	124	17	2	2	NUM
ejpam-3728	124	18	≤	≤	NOUN
ejpam-3728	124	19	mb∗n	mb∗n	NOUN
ejpam-3728	124	20	(	(	PUNCT
ejpam-3728	124	21	|t−	|t−	PROPN
ejpam-3728	124	22	x|2	x|2	PROPN
ejpam-3728	124	23	(	(	PUNCT
ejpam-3728	124	24	x(xm1	x(xm1	PROPN
ejpam-3728	124	25	+	+	PROPN
ejpam-3728	124	26	m2	m2	PROPN
ejpam-3728	124	27	)	)	PUNCT
ejpam-3728	124	28	)	)	PUNCT
ejpam-3728	124	29	;	;	PUNCT
ejpam-3728	124	30	x	x	X
ejpam-3728	124	31	)	)	PUNCT
ejpam-3728	124	32	s	s	PART
ejpam-3728	124	33	2	2	NUM
ejpam-3728	124	34	≤	≤	NUM
ejpam-3728	124	35	m	m	VERB
ejpam-3728	124	36	(	(	PUNCT
ejpam-3728	124	37	ωn,2	ωn,2	PROPN
ejpam-3728	124	38	x(xm1	x(xm1	PROPN
ejpam-3728	124	39	+	+	SYM
ejpam-3728	124	40	m2	m2	PROPN
ejpam-3728	124	41	)	)	PUNCT
ejpam-3728	124	42	)	)	PUNCT
ejpam-3728	124	43	s	s	VERB
ejpam-3728	124	44	2	2	NUM
ejpam-3728	124	45	.	.	PUNCT
ejpam-3728	125	1	this	this	PRON
ejpam-3728	125	2	complete	complete	ADJ
ejpam-3728	125	3	the	the	DET
ejpam-3728	125	4	proof	proof	NOUN
ejpam-3728	125	5	.	.	PUNCT
ejpam-3728	126	1	theorem	theorem	ADJ
ejpam-3728	126	2	4	4	NUM
ejpam-3728	126	3	.	.	X
ejpam-3728	126	4	for	for	ADP
ejpam-3728	126	5	the	the	DET
ejpam-3728	126	6	function	function	NOUN
ejpam-3728	126	7	g	g	NOUN
ejpam-3728	126	8	which	which	PRON
ejpam-3728	126	9	is	be	AUX
ejpam-3728	126	10	continuous	continuous	ADJ
ejpam-3728	126	11	and	and	CCONJ
ejpam-3728	126	12	bounded	bound	VERB
ejpam-3728	126	13	on	on	ADP
ejpam-3728	126	14	[	[	X
ejpam-3728	126	15	0,∞	0,∞	NOUN
ejpam-3728	126	16	)	)	PUNCT
ejpam-3728	126	17	,	,	PUNCT
ejpam-3728	126	18	the	the	DET
ejpam-3728	126	19	convergence	convergence	NOUN
ejpam-3728	126	20	of	of	ADP
ejpam-3728	126	21	the	the	DET
ejpam-3728	126	22	operators	operator	NOUN
ejpam-3728	126	23	can	can	AUX
ejpam-3728	126	24	be	be	AUX
ejpam-3728	126	25	obtained	obtain	VERB
ejpam-3728	126	26	as	as	ADP
ejpam-3728	126	27	:	:	PUNCT
ejpam-3728	126	28	lim	lim	PROPN
ejpam-3728	126	29	n→∞	n→∞	NUM
ejpam-3728	126	30	b∗n(g;x	b∗n(g;x	PROPN
ejpam-3728	126	31	)	)	PUNCT
ejpam-3728	126	32	=	=	SYM
ejpam-3728	126	33	g(x	g(x	NOUN
ejpam-3728	126	34	)	)	PUNCT
ejpam-3728	126	35	,	,	PUNCT
ejpam-3728	126	36	(	(	PUNCT
ejpam-3728	126	37	23	23	NUM
ejpam-3728	126	38	)	)	PUNCT
ejpam-3728	126	39	uniformly	uniformly	ADV
ejpam-3728	126	40	on	on	ADP
ejpam-3728	126	41	any	any	DET
ejpam-3728	126	42	compact	compact	ADJ
ejpam-3728	126	43	interval	interval	NOUN
ejpam-3728	126	44	of	of	ADP
ejpam-3728	126	45	[	[	X
ejpam-3728	126	46	0,∞	0,∞	NUM
ejpam-3728	126	47	)	)	PUNCT
ejpam-3728	126	48	.	.	PUNCT
ejpam-3728	127	1	proof	proof	NOUN
ejpam-3728	127	2	.	.	PUNCT
ejpam-3728	128	1	using	use	VERB
ejpam-3728	128	2	bohman	bohman	NOUN
ejpam-3728	128	3	-	-	PUNCT
ejpam-3728	128	4	korovkin	korovkin	NOUN
ejpam-3728	128	5	theorem	theorem	PROPN
ejpam-3728	128	6	,	,	PUNCT
ejpam-3728	128	7	we	we	PRON
ejpam-3728	128	8	can	can	AUX
ejpam-3728	128	9	get	get	VERB
ejpam-3728	128	10	our	our	PRON
ejpam-3728	128	11	required	require	VERB
ejpam-3728	128	12	result	result	NOUN
ejpam-3728	128	13	.	.	PUNCT
ejpam-3728	129	1	since	since	SCONJ
ejpam-3728	129	2	lim	lim	PROPN
ejpam-3728	129	3	n→∞	n→∞	NUM
ejpam-3728	129	4	b∗n(1;x	b∗n(1;x	PROPN
ejpam-3728	129	5	)	)	PUNCT
ejpam-3728	129	6	→	→	SYM
ejpam-3728	129	7	1	1	NUM
ejpam-3728	129	8	,	,	PUNCT
ejpam-3728	129	9	lim	lim	PROPN
ejpam-3728	129	10	n→∞	n→∞	X
ejpam-3728	129	11	b∗n(t;x	b∗n(t;x	PROPN
ejpam-3728	129	12	)	)	PUNCT
ejpam-3728	129	13	→	→	SYM
ejpam-3728	129	14	x	x	X
ejpam-3728	129	15	,	,	PUNCT
ejpam-3728	129	16	lim	lim	PROPN
ejpam-3728	129	17	n→∞	n→∞	NUM
ejpam-3728	129	18	b∗n(t2;x	b∗n(t2;x	PROPN
ejpam-3728	129	19	)	)	PUNCT
ejpam-3728	129	20	→	→	SYM
ejpam-3728	129	21	x2	x2	NOUN
ejpam-3728	129	22	and	and	CCONJ
ejpam-3728	129	23	hence	hence	ADV
ejpam-3728	129	24	the	the	DET
ejpam-3728	129	25	proposed	propose	VERB
ejpam-3728	129	26	operators	operator	NOUN
ejpam-3728	129	27	b∗n(g;x	b∗n(g;x	NOUN
ejpam-3728	129	28	)	)	PUNCT
ejpam-3728	129	29	converge	converge	VERB
ejpam-3728	129	30	uniformly	uniformly	ADV
ejpam-3728	129	31	to	to	ADP
ejpam-3728	129	32	the	the	DET
ejpam-3728	129	33	function	function	NOUN
ejpam-3728	129	34	g(x	g(x	NOUN
ejpam-3728	129	35	)	)	PUNCT
ejpam-3728	129	36	on	on	ADP
ejpam-3728	129	37	any	any	DET
ejpam-3728	129	38	compact	compact	ADJ
ejpam-3728	129	39	interval	interval	NOUN
ejpam-3728	129	40	of	of	ADP
ejpam-3728	129	41	[	[	X
ejpam-3728	129	42	0,∞	0,∞	NOUN
ejpam-3728	129	43	)	)	PUNCT
ejpam-3728	129	44	.	.	PUNCT
ejpam-3728	130	1	4	4	X
ejpam-3728	130	2	.	.	X
ejpam-3728	130	3	rate	rate	NOUN
ejpam-3728	130	4	of	of	ADP
ejpam-3728	130	5	convergence	convergence	NOUN
ejpam-3728	130	6	by	by	ADP
ejpam-3728	130	7	means	mean	NOUN
ejpam-3728	130	8	of	of	ADP
ejpam-3728	130	9	the	the	DET
ejpam-3728	130	10	function	function	NOUN
ejpam-3728	130	11	with	with	ADP
ejpam-3728	130	12	derivative	derivative	NOUN
ejpam-3728	130	13	of	of	ADP
ejpam-3728	130	14	bounded	bounded	ADJ
ejpam-3728	130	15	variation	variation	NOUN
ejpam-3728	130	16	this	this	DET
ejpam-3728	130	17	section	section	NOUN
ejpam-3728	130	18	consists	consist	VERB
ejpam-3728	130	19	the	the	DET
ejpam-3728	130	20	rate	rate	NOUN
ejpam-3728	130	21	of	of	ADP
ejpam-3728	130	22	convergence	convergence	NOUN
ejpam-3728	130	23	by	by	ADP
ejpam-3728	130	24	means	mean	NOUN
ejpam-3728	130	25	of	of	ADP
ejpam-3728	130	26	the	the	DET
ejpam-3728	130	27	function	function	NOUN
ejpam-3728	130	28	with	with	ADP
ejpam-3728	130	29	derivative	derivative	NOUN
ejpam-3728	130	30	of	of	ADP
ejpam-3728	130	31	bounded	bounded	ADJ
ejpam-3728	130	32	variation	variation	NOUN
ejpam-3728	130	33	.	.	PUNCT
ejpam-3728	131	1	let	let	AUX
ejpam-3728	131	2	dbv	dbv	PROPN
ejpam-3728	131	3	[	[	X
ejpam-3728	131	4	0,∞	0,∞	NOUN
ejpam-3728	131	5	)	)	PUNCT
ejpam-3728	131	6	be	be	VERB
ejpam-3728	131	7	the	the	DET
ejpam-3728	131	8	set	set	NOUN
ejpam-3728	131	9	of	of	ADP
ejpam-3728	131	10	all	all	DET
ejpam-3728	131	11	class	class	NOUN
ejpam-3728	131	12	of	of	ADP
ejpam-3728	131	13	function	function	NOUN
ejpam-3728	131	14	having	have	VERB
ejpam-3728	131	15	derivative	derivative	NOUN
ejpam-3728	131	16	of	of	ADP
ejpam-3728	131	17	bounded	bounded	ADJ
ejpam-3728	131	18	variation	variation	NOUN
ejpam-3728	131	19	on	on	ADP
ejpam-3728	131	20	every	every	DET
ejpam-3728	131	21	compact	compact	ADJ
ejpam-3728	131	22	interval	interval	NOUN
ejpam-3728	131	23	of	of	ADP
ejpam-3728	131	24	[	[	X
ejpam-3728	131	25	0,∞	0,∞	NOUN
ejpam-3728	131	26	)	)	PUNCT
ejpam-3728	131	27	.	.	PUNCT
ejpam-3728	132	1	the	the	DET
ejpam-3728	132	2	following	follow	VERB
ejpam-3728	132	3	representation	representation	NOUN
ejpam-3728	132	4	for	for	ADP
ejpam-3728	132	5	the	the	DET
ejpam-3728	132	6	function	function	NOUN
ejpam-3728	132	7	g	g	PROPN
ejpam-3728	132	8	∈	∈	PROPN
ejpam-3728	132	9	dbv	dbv	PROPN
ejpam-3728	133	1	[	[	X
ejpam-3728	133	2	0,∞	0,∞	NUM
ejpam-3728	133	3	)	)	PUNCT
ejpam-3728	133	4	,	,	PUNCT
ejpam-3728	133	5	is	be	AUX
ejpam-3728	133	6	as	as	SCONJ
ejpam-3728	133	7	follows	follow	VERB
ejpam-3728	133	8	:	:	PUNCT
ejpam-3728	133	9	g(x	g(x	NOUN
ejpam-3728	133	10	)	)	PUNCT
ejpam-3728	134	1	=	=	PUNCT
ejpam-3728	135	1	x∫	x∫	ADJ
ejpam-3728	135	2	0	0	NUM
ejpam-3728	135	3	h(t)dt+	h(t)dt+	NOUN
ejpam-3728	135	4	g(0	g(0	NOUN
ejpam-3728	135	5	)	)	PUNCT
ejpam-3728	135	6	,	,	PUNCT
ejpam-3728	135	7	(	(	PUNCT
ejpam-3728	135	8	24	24	NUM
ejpam-3728	135	9	)	)	PUNCT
ejpam-3728	135	10	r.	r.	PROPN
ejpam-3728	135	11	yadav	yadav	PROPN
ejpam-3728	135	12	,	,	PUNCT
ejpam-3728	135	13	r.	r.	PROPN
ejpam-3728	135	14	meher	meher	PROPN
ejpam-3728	135	15	,	,	PUNCT
ejpam-3728	135	16	v.	v.	ADP
ejpam-3728	135	17	n.	n.	PROPN
ejpam-3728	135	18	mishra	mishra	PROPN
ejpam-3728	135	19	/	/	SYM
ejpam-3728	135	20	eur	eur	PROPN
ejpam-3728	135	21	.	.	PUNCT
ejpam-3728	136	1	j.	j.	PROPN
ejpam-3728	136	2	pure	pure	PROPN
ejpam-3728	136	3	appl	appl	PROPN
ejpam-3728	136	4	.	.	PROPN
ejpam-3728	136	5	math	math	PROPN
ejpam-3728	136	6	,	,	PUNCT
ejpam-3728	136	7	13	13	NUM
ejpam-3728	136	8	(	(	PUNCT
ejpam-3728	136	9	5	5	NUM
ejpam-3728	136	10	)	)	PUNCT
ejpam-3728	136	11	(	(	PUNCT
ejpam-3728	136	12	2020	2020	NUM
ejpam-3728	136	13	)	)	PUNCT
ejpam-3728	136	14	,	,	PUNCT
ejpam-3728	136	15	1306	1306	NUM
ejpam-3728	136	16	-	-	SYM
ejpam-3728	136	17	1324	1324	NUM
ejpam-3728	136	18	1313	1313	NUM
ejpam-3728	136	19	where	where	SCONJ
ejpam-3728	136	20	h(t	h(t	PROPN
ejpam-3728	136	21	)	)	PUNCT
ejpam-3728	136	22	is	be	AUX
ejpam-3728	136	23	a	a	DET
ejpam-3728	136	24	function	function	NOUN
ejpam-3728	136	25	with	with	ADP
ejpam-3728	136	26	derivative	derivative	NOUN
ejpam-3728	136	27	of	of	ADP
ejpam-3728	136	28	bounded	bounded	ADJ
ejpam-3728	136	29	variation	variation	NOUN
ejpam-3728	136	30	on	on	ADP
ejpam-3728	136	31	any	any	DET
ejpam-3728	136	32	compact	compact	ADJ
ejpam-3728	136	33	interval	interval	NOUN
ejpam-3728	136	34	of	of	ADP
ejpam-3728	136	35	[	[	X
ejpam-3728	136	36	0,∞	0,∞	NOUN
ejpam-3728	136	37	)	)	PUNCT
ejpam-3728	136	38	.	.	PUNCT
ejpam-3728	137	1	for	for	ADP
ejpam-3728	137	2	investigation	investigation	NOUN
ejpam-3728	137	3	of	of	ADP
ejpam-3728	137	4	the	the	DET
ejpam-3728	137	5	convergence	convergence	NOUN
ejpam-3728	137	6	of	of	ADP
ejpam-3728	137	7	the	the	DET
ejpam-3728	137	8	above	above	ADJ
ejpam-3728	137	9	operators	operator	NOUN
ejpam-3728	137	10	(	(	PUNCT
ejpam-3728	137	11	3	3	X
ejpam-3728	137	12	)	)	PUNCT
ejpam-3728	137	13	to	to	ADP
ejpam-3728	137	14	the	the	DET
ejpam-3728	137	15	function	function	NOUN
ejpam-3728	137	16	with	with	ADP
ejpam-3728	137	17	derivative	derivative	NOUN
ejpam-3728	137	18	of	of	ADP
ejpam-3728	137	19	bounded	bounded	ADJ
ejpam-3728	137	20	variation	variation	NOUN
ejpam-3728	137	21	,	,	PUNCT
ejpam-3728	137	22	we	we	PRON
ejpam-3728	137	23	rewrite	rewrite	VERB
ejpam-3728	137	24	(	(	PUNCT
ejpam-3728	137	25	3	3	NUM
ejpam-3728	137	26	)	)	PUNCT
ejpam-3728	137	27	as	as	SCONJ
ejpam-3728	137	28	follows	follow	VERB
ejpam-3728	137	29	:	:	PUNCT
ejpam-3728	137	30	b∗n(g;x	b∗n(g;x	X
ejpam-3728	137	31	)	)	PUNCT
ejpam-3728	137	32	=	=	SYM
ejpam-3728	138	1	∫	∫	PROPN
ejpam-3728	138	2	∞	∞	NUM
ejpam-3728	138	3	0	0	NUM
ejpam-3728	138	4	yn(x	yn(x	PROPN
ejpam-3728	138	5	,	,	PUNCT
ejpam-3728	138	6	t)g(t)dt	t)g(t)dt	NOUN
ejpam-3728	138	7	,	,	PUNCT
ejpam-3728	138	8	(	(	PUNCT
ejpam-3728	138	9	25	25	NUM
ejpam-3728	138	10	)	)	PUNCT
ejpam-3728	138	11	where	where	SCONJ
ejpam-3728	138	12	yn(x	yn(x	X
ejpam-3728	138	13	,	,	PUNCT
ejpam-3728	138	14	t	t	PROPN
ejpam-3728	138	15	)	)	PUNCT
ejpam-3728	138	16	=	=	PRON
ejpam-3728	138	17	un	un	PROPN
ejpam-3728	138	18	∞∑	∞∑	NUM
ejpam-3728	138	19	j=0	j=0	PROPN
ejpam-3728	138	20	sun	sun	PROPN
ejpam-3728	138	21	,	,	PUNCT
ejpam-3728	138	22	j(x	j(x	PROPN
ejpam-3728	138	23	)	)	PUNCT
ejpam-3728	138	24	sun	sun	NOUN
ejpam-3728	138	25	,	,	PUNCT
ejpam-3728	138	26	j(t	j(t	PROPN
ejpam-3728	138	27	)	)	PUNCT
ejpam-3728	138	28	.	.	PUNCT
ejpam-3728	139	1	such	such	ADJ
ejpam-3728	139	2	type	type	NOUN
ejpam-3728	139	3	of	of	ADP
ejpam-3728	139	4	properties	property	NOUN
ejpam-3728	139	5	have	have	AUX
ejpam-3728	139	6	been	be	AUX
ejpam-3728	139	7	studied	study	VERB
ejpam-3728	139	8	by	by	ADP
ejpam-3728	139	9	researchers	researcher	NOUN
ejpam-3728	139	10	using	use	VERB
ejpam-3728	139	11	various	various	ADJ
ejpam-3728	139	12	operators	operator	NOUN
ejpam-3728	139	13	(	(	PUNCT
ejpam-3728	139	14	see	see	VERB
ejpam-3728	139	15	[	[	X
ejpam-3728	139	16	4	4	NUM
ejpam-3728	139	17	,	,	PUNCT
ejpam-3728	139	18	5	5	NUM
ejpam-3728	139	19	,	,	PUNCT
ejpam-3728	139	20	17–19	17–19	NUM
ejpam-3728	139	21	]	]	PUNCT
ejpam-3728	139	22	)	)	PUNCT
ejpam-3728	139	23	.	.	PUNCT
ejpam-3728	140	1	lemma	lemma	PROPN
ejpam-3728	140	2	4	4	NUM
ejpam-3728	140	3	.	.	PUNCT
ejpam-3728	140	4	for	for	ADP
ejpam-3728	140	5	sufficiently	sufficiently	ADV
ejpam-3728	140	6	large	large	ADJ
ejpam-3728	140	7	value	value	NOUN
ejpam-3728	140	8	of	of	ADP
ejpam-3728	140	9	n	n	PRON
ejpam-3728	140	10	and	and	CCONJ
ejpam-3728	140	11	for	for	ADP
ejpam-3728	140	12	all	all	DET
ejpam-3728	140	13	x	x	PRON
ejpam-3728	140	14	≥	≥	NOUN
ejpam-3728	140	15	0	0	NUM
ejpam-3728	140	16	,	,	PUNCT
ejpam-3728	140	17	we	we	PRON
ejpam-3728	140	18	have	have	VERB
ejpam-3728	140	19	(	(	PUNCT
ejpam-3728	140	20	i	i	NOUN
ejpam-3728	140	21	)	)	PUNCT
ejpam-3728	140	22	in(x	in(x	X
ejpam-3728	140	23	,	,	PUNCT
ejpam-3728	140	24	t	t	X
ejpam-3728	140	25	)	)	PUNCT
ejpam-3728	141	1	=	=	PUNCT
ejpam-3728	141	2	y∫	y∫	NOUN
ejpam-3728	141	3	0	0	NUM
ejpam-3728	141	4	yn(x	yn(x	SYM
ejpam-3728	141	5	,	,	PUNCT
ejpam-3728	141	6	t)dt	t)dt	PROPN
ejpam-3728	141	7	≤	≤	ADJ
ejpam-3728	141	8	2	2	NUM
ejpam-3728	141	9	(	(	PUNCT
ejpam-3728	141	10	x−y)2un	x−y)2un	PROPN
ejpam-3728	141	11	ζ	ζ	PROPN
ejpam-3728	141	12	2	2	NUM
ejpam-3728	141	13	n(x	n(x	NOUN
ejpam-3728	141	14	)	)	PUNCT
ejpam-3728	141	15	,	,	PUNCT
ejpam-3728	141	16	0	0	NUM
ejpam-3728	141	17	≤	≤	NUM
ejpam-3728	142	1	y	y	NOUN
ejpam-3728	142	2	<	<	X
ejpam-3728	142	3	x	x	X
ejpam-3728	142	4	,	,	PUNCT
ejpam-3728	142	5	(	(	PUNCT
ejpam-3728	142	6	ii	ii	NOUN
ejpam-3728	142	7	)	)	PUNCT
ejpam-3728	142	8	1−	1−	NUM
ejpam-3728	142	9	in(x	in(x	X
ejpam-3728	142	10	,	,	PUNCT
ejpam-3728	142	11	t	t	PROPN
ejpam-3728	142	12	)	)	PUNCT
ejpam-3728	142	13	=	=	SYM
ejpam-3728	143	1	∞∫	∞∫	PROPN
ejpam-3728	143	2	z	z	PROPN
ejpam-3728	143	3	yn(x	yn(x	X
ejpam-3728	143	4	,	,	PUNCT
ejpam-3728	143	5	t)dt	t)dt	PROPN
ejpam-3728	143	6	≤	≤	ADJ
ejpam-3728	143	7	2	2	NUM
ejpam-3728	143	8	(	(	PUNCT
ejpam-3728	143	9	z−x)2un	z−x)2un	PROPN
ejpam-3728	143	10	ζ	ζ	PROPN
ejpam-3728	143	11	2	2	NUM
ejpam-3728	143	12	n(x	n(x	PROPN
ejpam-3728	143	13	)	)	PUNCT
ejpam-3728	143	14	,	,	PUNCT
ejpam-3728	143	15	x	x	SYM
ejpam-3728	143	16	≤	≤	X
ejpam-3728	143	17	z	z	NOUN
ejpam-3728	143	18	<	<	X
ejpam-3728	143	19	∞.	∞.	PROPN
ejpam-3728	143	20	proof	proof	NOUN
ejpam-3728	143	21	.	.	PUNCT
ejpam-3728	144	1	using	use	VERB
ejpam-3728	144	2	the	the	DET
ejpam-3728	144	3	lemma	lemma	PROPN
ejpam-3728	144	4	2	2	NUM
ejpam-3728	144	5	and	and	CCONJ
ejpam-3728	144	6	since	since	SCONJ
ejpam-3728	144	7	the	the	DET
ejpam-3728	144	8	value	value	NOUN
ejpam-3728	144	9	of	of	ADP
ejpam-3728	144	10	n	n	NUM
ejpam-3728	144	11	is	be	AUX
ejpam-3728	144	12	sufficiently	sufficiently	ADV
ejpam-3728	144	13	large	large	ADJ
ejpam-3728	144	14	,	,	PUNCT
ejpam-3728	144	15	so	so	ADV
ejpam-3728	144	16	we	we	PRON
ejpam-3728	144	17	have	have	VERB
ejpam-3728	144	18	in(x	in(x	NOUN
ejpam-3728	144	19	,	,	PUNCT
ejpam-3728	144	20	t	t	PROPN
ejpam-3728	144	21	)	)	PUNCT
ejpam-3728	144	22	=	=	PUNCT
ejpam-3728	145	1	y∫	y∫	NOUN
ejpam-3728	145	2	0	0	NUM
ejpam-3728	145	3	yn(x	yn(x	SYM
ejpam-3728	145	4	,	,	PUNCT
ejpam-3728	145	5	t)dt	t)dt	PROPN
ejpam-3728	145	6	≤	≤	PUNCT
ejpam-3728	146	1	y∫	y∫	NOUN
ejpam-3728	146	2	0	0	PUNCT
ejpam-3728	147	1	(	(	PUNCT
ejpam-3728	147	2	(	(	PUNCT
ejpam-3728	147	3	x−	x−	PROPN
ejpam-3728	147	4	t)2	t)2	PROPN
ejpam-3728	147	5	(	(	PUNCT
ejpam-3728	147	6	x−	x−	PROPN
ejpam-3728	147	7	y)2	y)2	NOUN
ejpam-3728	147	8	)	)	PUNCT
ejpam-3728	147	9	yn(x	yn(x	ADP
ejpam-3728	147	10	,	,	PUNCT
ejpam-3728	147	11	t)dt	t)dt	PROPN
ejpam-3728	147	12	=	=	SYM
ejpam-3728	147	13	2	2	NUM
ejpam-3728	147	14	(	(	PUNCT
ejpam-3728	147	15	x−	x−	PROPN
ejpam-3728	147	16	y)2un	y)2un	PROPN
ejpam-3728	147	17	ζ2n(x	ζ2n(x	PROPN
ejpam-3728	147	18	)	)	PUNCT
ejpam-3728	147	19	.	.	PUNCT
ejpam-3728	148	1	similarly	similarly	ADV
ejpam-3728	148	2	,	,	PUNCT
ejpam-3728	148	3	we	we	PRON
ejpam-3728	148	4	can	can	AUX
ejpam-3728	148	5	prove	prove	VERB
ejpam-3728	148	6	other	other	ADJ
ejpam-3728	148	7	inequality	inequality	NOUN
ejpam-3728	148	8	.	.	PUNCT
ejpam-3728	149	1	theorem	theorem	NOUN
ejpam-3728	149	2	5	5	NUM
ejpam-3728	149	3	.	.	PUNCT
ejpam-3728	150	1	let	let	VERB
ejpam-3728	150	2	g	g	PROPN
ejpam-3728	150	3	∈	∈	PROPN
ejpam-3728	150	4	dbv	dbv	PROPN
ejpam-3728	151	1	[	[	X
ejpam-3728	151	2	0,∞	0,∞	NUM
ejpam-3728	151	3	)	)	PUNCT
ejpam-3728	151	4	,	,	PUNCT
ejpam-3728	151	5	then	then	ADV
ejpam-3728	151	6	for	for	ADP
ejpam-3728	151	7	all	all	DET
ejpam-3728	151	8	x	x	PRON
ejpam-3728	151	9	≥	≥	NOUN
ejpam-3728	151	10	0	0	NUM
ejpam-3728	151	11	,	,	PUNCT
ejpam-3728	151	12	an	an	DET
ejpam-3728	151	13	upper	upper	ADJ
ejpam-3728	151	14	bound	bound	NOUN
ejpam-3728	151	15	of	of	ADP
ejpam-3728	151	16	the	the	DET
ejpam-3728	151	17	operators	operator	NOUN
ejpam-3728	151	18	to	to	ADP
ejpam-3728	151	19	the	the	DET
ejpam-3728	151	20	function	function	NOUN
ejpam-3728	151	21	can	can	AUX
ejpam-3728	151	22	be	be	AUX
ejpam-3728	151	23	as	as	SCONJ
ejpam-3728	151	24	:	:	PUNCT
ejpam-3728	151	25	|b∗n(g;x)−	|b∗n(g;x)−	NOUN
ejpam-3728	151	26	g(x)|	g(x)|	VERB
ejpam-3728	151	27	≤	≤	NUM
ejpam-3728	151	28	1	1	NUM
ejpam-3728	151	29	2un	2un	NOUN
ejpam-3728	151	30	|g′(x+	|g′(x+	NUM
ejpam-3728	151	31	)	)	PUNCT
ejpam-3728	152	1	+	+	CCONJ
ejpam-3728	152	2	g′(x−)|+	g′(x−)|+	INTJ
ejpam-3728	152	3	√	√	ADV
ejpam-3728	152	4	1	1	NUM
ejpam-3728	152	5	2un	2un	ADJ
ejpam-3728	152	6	|g′(x+)−	|g′(x+)−	NOUN
ejpam-3728	152	7	g′(x−)|ζn(x	g′(x−)|ζn(x	NOUN
ejpam-3728	152	8	)	)	PUNCT
ejpam-3728	153	1	+	+	CCONJ
ejpam-3728	153	2	2ζ2n(x	2ζ2n(x	NUM
ejpam-3728	153	3	)	)	PUNCT
ejpam-3728	153	4	xun	xun	PROPN
ejpam-3728	154	1	[	[	PUNCT
ejpam-3728	154	2	√	√	PROPN
ejpam-3728	154	3	un]∑	un]∑	PROPN
ejpam-3728	154	4	j=0	j=0	PROPN
ejpam-3728	154	5	(	(	PUNCT
ejpam-3728	154	6	v	v	ADP
ejpam-3728	154	7	t	t	NOUN
ejpam-3728	154	8	x−x	x−x	PROPN
ejpam-3728	154	9	j	j	PROPN
ejpam-3728	154	10	g′x	g′x	NOUN
ejpam-3728	154	11	)	)	PUNCT
ejpam-3728	155	1	+	+	CCONJ
ejpam-3728	155	2	x	x	SYM
ejpam-3728	155	3	√	√	NUM
ejpam-3728	155	4	un	un	PROPN
ejpam-3728	155	5	(	(	PUNCT
ejpam-3728	155	6	v	v	NOUN
ejpam-3728	155	7	x	x	X
ejpam-3728	155	8	x−	x−	PROPN
ejpam-3728	155	9	x√	x√	PROPN
ejpam-3728	155	10	un	un	PROPN
ejpam-3728	155	11	g′x	g′x	PROPN
ejpam-3728	155	12	)	)	PUNCT
ejpam-3728	156	1	+	+	CCONJ
ejpam-3728	156	2	x	x	PUNCT
ejpam-3728	156	3	√	√	NUM
ejpam-3728	156	4	un	un	PROPN
ejpam-3728	156	5	v	v	PROPN
ejpam-3728	156	6	x+	x+	PROPN
ejpam-3728	156	7	x√	x√	PROPN
ejpam-3728	156	8	un	un	PROPN
ejpam-3728	156	9	x	x	X
ejpam-3728	156	10	(	(	PUNCT
ejpam-3728	156	11	g′x	g′x	NOUN
ejpam-3728	156	12	)	)	PUNCT
ejpam-3728	156	13	+	+	CCONJ
ejpam-3728	156	14	2ζ2n(x	2ζ2n(x	NUM
ejpam-3728	156	15	)	)	PUNCT
ejpam-3728	156	16	xun	xun	PROPN
ejpam-3728	157	1	[	[	PUNCT
ejpam-3728	157	2	√	√	PROPN
ejpam-3728	157	3	un]∑	un]∑	PROPN
ejpam-3728	157	4	j=0	j=0	PROPN
ejpam-3728	157	5	v	v	ADP
ejpam-3728	157	6	x+x	x+x	PROPN
ejpam-3728	157	7	j	j	PROPN
ejpam-3728	157	8	x	x	SYM
ejpam-3728	157	9	(	(	PUNCT
ejpam-3728	157	10	g′x	g′x	NOUN
ejpam-3728	157	11	)	)	PUNCT
ejpam-3728	157	12	,	,	PUNCT
ejpam-3728	157	13	r.	r.	PROPN
ejpam-3728	157	14	yadav	yadav	PROPN
ejpam-3728	157	15	,	,	PUNCT
ejpam-3728	157	16	r.	r.	PROPN
ejpam-3728	157	17	meher	meher	PROPN
ejpam-3728	157	18	,	,	PUNCT
ejpam-3728	157	19	v.	v.	ADP
ejpam-3728	157	20	n.	n.	PROPN
ejpam-3728	157	21	mishra	mishra	PROPN
ejpam-3728	157	22	/	/	SYM
ejpam-3728	157	23	eur	eur	PROPN
ejpam-3728	157	24	.	.	PUNCT
ejpam-3728	158	1	j.	j.	PROPN
ejpam-3728	158	2	pure	pure	PROPN
ejpam-3728	158	3	appl	appl	PROPN
ejpam-3728	158	4	.	.	PROPN
ejpam-3728	158	5	math	math	PROPN
ejpam-3728	158	6	,	,	PUNCT
ejpam-3728	158	7	13	13	NUM
ejpam-3728	158	8	(	(	PUNCT
ejpam-3728	158	9	5	5	NUM
ejpam-3728	158	10	)	)	PUNCT
ejpam-3728	158	11	(	(	PUNCT
ejpam-3728	158	12	2020	2020	NUM
ejpam-3728	158	13	)	)	PUNCT
ejpam-3728	158	14	,	,	PUNCT
ejpam-3728	158	15	1306	1306	NUM
ejpam-3728	158	16	-	-	SYM
ejpam-3728	158	17	1324	1324	NUM
ejpam-3728	158	18	1314	1314	NUM
ejpam-3728	158	19	where	where	SCONJ
ejpam-3728	158	20	gx(t	gx(t	VERB
ejpam-3728	158	21	)	)	PUNCT
ejpam-3728	158	22	=	=	PUNCT
ejpam-3728	159	1			PROPN
ejpam-3728	159	2	g(t)−	g(t)−	PROPN
ejpam-3728	159	3	g(x−	g(x−	PROPN
ejpam-3728	159	4	)	)	PUNCT
ejpam-3728	159	5	,	,	PUNCT
ejpam-3728	159	6	0	0	NUM
ejpam-3728	159	7	≤	≤	NUM
ejpam-3728	159	8	t	t	X
ejpam-3728	159	9	<	<	X
ejpam-3728	159	10	x	x	X
ejpam-3728	159	11	,	,	PUNCT
ejpam-3728	159	12	0	0	NUM
ejpam-3728	159	13	,	,	PUNCT
ejpam-3728	159	14	t	t	NOUN
ejpam-3728	159	15	=	=	SYM
ejpam-3728	159	16	x	x	PROPN
ejpam-3728	159	17	,	,	PUNCT
ejpam-3728	159	18	g(t)−	g(t)−	PROPN
ejpam-3728	159	19	g(x+	g(x+	PROPN
ejpam-3728	159	20	)	)	PUNCT
ejpam-3728	159	21	,	,	PUNCT
ejpam-3728	159	22	x	x	X
ejpam-3728	159	23	<	<	X
ejpam-3728	159	24	t	t	X
ejpam-3728	159	25	<	<	X
ejpam-3728	159	26	∞	∞	PROPN
ejpam-3728	159	27	(	(	PUNCT
ejpam-3728	159	28	26	26	NUM
ejpam-3728	159	29	)	)	PUNCT
ejpam-3728	159	30	be	be	AUX
ejpam-3728	159	31	an	an	DET
ejpam-3728	159	32	auxiliary	auxiliary	ADJ
ejpam-3728	159	33	operator	operator	NOUN
ejpam-3728	159	34	and	and	CCONJ
ejpam-3728	159	35	v	v	ADP
ejpam-3728	159	36	b	b	PROPN
ejpam-3728	159	37	a	a	DET
ejpam-3728	159	38	g(x	g(x	NOUN
ejpam-3728	159	39	)	)	PUNCT
ejpam-3728	159	40	denotes	denote	VERB
ejpam-3728	159	41	the	the	DET
ejpam-3728	159	42	total	total	ADJ
ejpam-3728	159	43	variation	variation	NOUN
ejpam-3728	159	44	of	of	ADP
ejpam-3728	159	45	the	the	DET
ejpam-3728	159	46	function	function	NOUN
ejpam-3728	159	47	g(x	g(x	NOUN
ejpam-3728	159	48	)	)	PUNCT
ejpam-3728	159	49	on	on	ADP
ejpam-3728	159	50	[	[	X
ejpam-3728	159	51	a	a	X
ejpam-3728	159	52	,	,	PUNCT
ejpam-3728	159	53	b	b	NOUN
ejpam-3728	159	54	]	]	PUNCT
ejpam-3728	159	55	.	.	PUNCT
ejpam-3728	160	1	proof	proof	NOUN
ejpam-3728	160	2	.	.	PUNCT
ejpam-3728	161	1	since	since	SCONJ
ejpam-3728	161	2	,	,	PUNCT
ejpam-3728	161	3	b∗n(1;x	b∗n(1;x	PROPN
ejpam-3728	161	4	)	)	PUNCT
ejpam-3728	161	5	=	=	NOUN
ejpam-3728	161	6	1	1	NUM
ejpam-3728	161	7	and	and	CCONJ
ejpam-3728	161	8	hence	hence	ADV
ejpam-3728	161	9	,	,	PUNCT
ejpam-3728	161	10	one	one	PRON
ejpam-3728	161	11	can	can	AUX
ejpam-3728	161	12	write	write	VERB
ejpam-3728	161	13	b∗n(g;x)−	b∗n(g;x)−	PROPN
ejpam-3728	161	14	g(x	g(x	NOUN
ejpam-3728	161	15	)	)	PUNCT
ejpam-3728	162	1	=	=	SYM
ejpam-3728	163	1	∫	∫	PROPN
ejpam-3728	164	1	∞	∞	NUM
ejpam-3728	164	2	0	0	PUNCT
ejpam-3728	164	3	(	(	PUNCT
ejpam-3728	164	4	g(t)−	g(t)−	PROPN
ejpam-3728	164	5	g(x))yn(x	g(x))yn(x	PROPN
ejpam-3728	164	6	,	,	PUNCT
ejpam-3728	165	1	t)dt	t)dt	PROPN
ejpam-3728	165	2	=	=	SYM
ejpam-3728	165	3	∫	∫	PROPN
ejpam-3728	165	4	∞	∞	PROPN
ejpam-3728	165	5	0	0	NUM
ejpam-3728	165	6	yn(x	yn(x	SYM
ejpam-3728	165	7	,	,	PUNCT
ejpam-3728	165	8	t)dt	t)dt	PROPN
ejpam-3728	165	9	t∫	t∫	PROPN
ejpam-3728	165	10	x	x	SYM
ejpam-3728	165	11	g′(u)du	g′(u)du	PROPN
ejpam-3728	165	12	.	.	PUNCT
ejpam-3728	166	1	now	now	ADV
ejpam-3728	166	2	,	,	PUNCT
ejpam-3728	166	3	for	for	ADP
ejpam-3728	166	4	g	g	PROPN
ejpam-3728	166	5	∈	∈	PROPN
ejpam-3728	166	6	dbv	dbv	PROPN
ejpam-3728	167	1	[	[	X
ejpam-3728	167	2	0,∞	0,∞	NUM
ejpam-3728	167	3	)	)	PUNCT
ejpam-3728	167	4	,	,	PUNCT
ejpam-3728	167	5	we	we	PRON
ejpam-3728	167	6	can	can	AUX
ejpam-3728	167	7	write	write	VERB
ejpam-3728	167	8	as	as	ADP
ejpam-3728	167	9	:	:	PUNCT
ejpam-3728	167	10	g′(u	g′(u	PROPN
ejpam-3728	167	11	)	)	PUNCT
ejpam-3728	167	12	=	=	SYM
ejpam-3728	167	13	1	1	NUM
ejpam-3728	167	14	2	2	NUM
ejpam-3728	167	15	(	(	PUNCT
ejpam-3728	167	16	g′(x+	g′(x+	ADV
ejpam-3728	167	17	)	)	PUNCT
ejpam-3728	167	18	+	+	NUM
ejpam-3728	167	19	g′(x−	g′(x−	NOUN
ejpam-3728	167	20	)	)	PUNCT
ejpam-3728	167	21	)	)	PUNCT
ejpam-3728	168	1	+	+	CCONJ
ejpam-3728	168	2	g′x(u	g′x(u	NOUN
ejpam-3728	168	3	)	)	PUNCT
ejpam-3728	169	1	+	+	CCONJ
ejpam-3728	169	2	1	1	NUM
ejpam-3728	169	3	2	2	NUM
ejpam-3728	169	4	(	(	PUNCT
ejpam-3728	169	5	g′(x+	g′(x+	ADV
ejpam-3728	169	6	)	)	PUNCT
ejpam-3728	169	7	+	+	NUM
ejpam-3728	169	8	g′(x−	g′(x−	NOUN
ejpam-3728	169	9	)	)	PUNCT
ejpam-3728	169	10	)	)	PUNCT
ejpam-3728	170	1	(	(	PUNCT
ejpam-3728	170	2	sgn(u−	sgn(u−	X
ejpam-3728	170	3	x	x	X
ejpam-3728	170	4	)	)	PUNCT
ejpam-3728	170	5	)	)	PUNCT
ejpam-3728	171	1	+	+	NOUN
ejpam-3728	171	2	η(u	η(u	NOUN
ejpam-3728	171	3	)	)	PUNCT
ejpam-3728	171	4	(	(	PUNCT
ejpam-3728	171	5	g′(u)−	g′(u)−	NOUN
ejpam-3728	171	6	1	1	NUM
ejpam-3728	171	7	2	2	NUM
ejpam-3728	171	8	(	(	PUNCT
ejpam-3728	171	9	g′(x+	g′(x+	ADV
ejpam-3728	171	10	)	)	PUNCT
ejpam-3728	171	11	+	+	NUM
ejpam-3728	171	12	g′(x−	g′(x−	NOUN
ejpam-3728	171	13	)	)	PUNCT
ejpam-3728	171	14	)	)	PUNCT
ejpam-3728	171	15	)	)	PUNCT
ejpam-3728	171	16	,	,	PUNCT
ejpam-3728	171	17	where	where	SCONJ
ejpam-3728	171	18	η(u	η(u	NOUN
ejpam-3728	171	19	)	)	PUNCT
ejpam-3728	171	20	=	=	PRON
ejpam-3728	171	21	{	{	PUNCT
ejpam-3728	171	22	1	1	NUM
ejpam-3728	171	23	u	u	NOUN
ejpam-3728	171	24	=	=	NOUN
ejpam-3728	171	25	x	x	SYM
ejpam-3728	171	26	0	0	NUM
ejpam-3728	171	27	u	u	PROPN
ejpam-3728	171	28	6=	6=	PROPN
ejpam-3728	171	29	x.	x.	PROPN
ejpam-3728	171	30	(	(	PUNCT
ejpam-3728	171	31	27	27	NUM
ejpam-3728	171	32	)	)	PUNCT
ejpam-3728	171	33	and	and	CCONJ
ejpam-3728	171	34	then	then	ADV
ejpam-3728	171	35	,	,	PUNCT
ejpam-3728	171	36	one	one	PRON
ejpam-3728	171	37	can	can	AUX
ejpam-3728	171	38	show	show	VERB
ejpam-3728	171	39	∞∫	∞∫	PROPN
ejpam-3728	171	40	0	0	NUM
ejpam-3728	171	41	yn(x	yn(x	PROPN
ejpam-3728	171	42	,	,	PUNCT
ejpam-3728	171	43	t	t	PROPN
ejpam-3728	171	44	)	)	PUNCT
ejpam-3728	171	45	t∫	t∫	PROPN
ejpam-3728	171	46	x	x	SYM
ejpam-3728	171	47	(	(	PUNCT
ejpam-3728	171	48	η(u){g′(u)−	η(u){g′(u)−	NOUN
ejpam-3728	171	49	1	1	NUM
ejpam-3728	171	50	2	2	NUM
ejpam-3728	171	51	(	(	PUNCT
ejpam-3728	171	52	g′(x+	g′(x+	ADV
ejpam-3728	171	53	)	)	PUNCT
ejpam-3728	171	54	+	+	NUM
ejpam-3728	171	55	g′(x−))}du	g′(x−))}du	NOUN
ejpam-3728	171	56	)	)	PUNCT
ejpam-3728	171	57	dt	dt	NOUN
ejpam-3728	172	1	=	=	PUNCT
ejpam-3728	172	2	0	0	PROPN
ejpam-3728	172	3	.	.	PUNCT
ejpam-3728	173	1	(	(	PUNCT
ejpam-3728	173	2	28	28	NUM
ejpam-3728	173	3	)	)	PUNCT
ejpam-3728	173	4	using	use	VERB
ejpam-3728	173	5	(	(	PUNCT
ejpam-3728	173	6	25	25	NUM
ejpam-3728	173	7	)	)	PUNCT
ejpam-3728	173	8	,	,	PUNCT
ejpam-3728	173	9	we	we	PRON
ejpam-3728	173	10	can	can	AUX
ejpam-3728	173	11	get	get	VERB
ejpam-3728	173	12	∞∫	∞∫	PROPN
ejpam-3728	173	13	0	0	NUM
ejpam-3728	173	14	yn(x	yn(x	PROPN
ejpam-3728	173	15	,	,	PUNCT
ejpam-3728	173	16	t	t	PROPN
ejpam-3728	173	17	)	)	PUNCT
ejpam-3728	173	18			PROPN
ejpam-3728	173	19	s∫	s∫	NOUN
ejpam-3728	173	20	x	x	SYM
ejpam-3728	173	21	1	1	NUM
ejpam-3728	173	22	2	2	NUM
ejpam-3728	173	23	(	(	PUNCT
ejpam-3728	173	24	g′(x+	g′(x+	ADV
ejpam-3728	173	25	)	)	PUNCT
ejpam-3728	173	26	+	+	NUM
ejpam-3728	173	27	g′(x−	g′(x−	NOUN
ejpam-3728	173	28	)	)	PUNCT
ejpam-3728	173	29	)	)	PUNCT
ejpam-3728	174	1	du	du	PROPN
ejpam-3728	174	2			PROPN
ejpam-3728	174	3	dt	dt	NOUN
ejpam-3728	174	4	=	=	NOUN
ejpam-3728	174	5	1	1	NUM
ejpam-3728	174	6	2	2	NUM
ejpam-3728	174	7	(	(	PUNCT
ejpam-3728	174	8	g′(x+	g′(x+	ADV
ejpam-3728	174	9	)	)	PUNCT
ejpam-3728	174	10	+	+	NUM
ejpam-3728	174	11	g′(x−	g′(x−	NOUN
ejpam-3728	174	12	)	)	PUNCT
ejpam-3728	174	13	)	)	PUNCT
ejpam-3728	175	1	∞∫	∞∫	PROPN
ejpam-3728	175	2	0	0	NUM
ejpam-3728	175	3	yn(x	yn(x	PROPN
ejpam-3728	175	4	,	,	PUNCT
ejpam-3728	175	5	t)(t−	t)(t−	NOUN
ejpam-3728	175	6	x	x	X
ejpam-3728	175	7	)	)	PUNCT
ejpam-3728	175	8	dt	dt	NOUN
ejpam-3728	176	1	=	=	NOUN
ejpam-3728	176	2	1	1	NUM
ejpam-3728	176	3	2	2	NUM
ejpam-3728	176	4	(	(	PUNCT
ejpam-3728	176	5	g′(x+	g′(x+	ADV
ejpam-3728	176	6	)	)	PUNCT
ejpam-3728	177	1	+	+	SYM
ejpam-3728	177	2	g′(x−))ωn,1	g′(x−))ωn,1	X
ejpam-3728	177	3	.	.	PUNCT
ejpam-3728	178	1	(	(	PUNCT
ejpam-3728	178	2	29	29	NUM
ejpam-3728	178	3	)	)	PUNCT
ejpam-3728	178	4	and	and	CCONJ
ejpam-3728	178	5	r.	r.	PROPN
ejpam-3728	178	6	yadav	yadav	PROPN
ejpam-3728	178	7	,	,	PUNCT
ejpam-3728	178	8	r.	r.	PROPN
ejpam-3728	178	9	meher	meher	PROPN
ejpam-3728	178	10	,	,	PUNCT
ejpam-3728	178	11	v.	v.	ADP
ejpam-3728	178	12	n.	n.	PROPN
ejpam-3728	178	13	mishra	mishra	PROPN
ejpam-3728	178	14	/	/	SYM
ejpam-3728	178	15	eur	eur	PROPN
ejpam-3728	178	16	.	.	PUNCT
ejpam-3728	179	1	j.	j.	PROPN
ejpam-3728	179	2	pure	pure	PROPN
ejpam-3728	179	3	appl	appl	PROPN
ejpam-3728	179	4	.	.	PROPN
ejpam-3728	179	5	math	math	PROPN
ejpam-3728	179	6	,	,	PUNCT
ejpam-3728	179	7	13	13	NUM
ejpam-3728	179	8	(	(	PUNCT
ejpam-3728	179	9	5	5	NUM
ejpam-3728	179	10	)	)	PUNCT
ejpam-3728	179	11	(	(	PUNCT
ejpam-3728	179	12	2020	2020	NUM
ejpam-3728	179	13	)	)	PUNCT
ejpam-3728	179	14	,	,	PUNCT
ejpam-3728	179	15	1306	1306	NUM
ejpam-3728	179	16	-	-	SYM
ejpam-3728	179	17	1324	1324	NUM
ejpam-3728	179	18	1315	1315	NUM
ejpam-3728	179	19	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-3728	179	20	∞∫	∞∫	PROPN
ejpam-3728	179	21	0	0	NUM
ejpam-3728	180	1	yn(x	yn(x	PROPN
ejpam-3728	180	2	,	,	PUNCT
ejpam-3728	180	3	t	t	PROPN
ejpam-3728	180	4	)	)	PUNCT
ejpam-3728	180	5	1	1	PROPN
ejpam-3728	180	6	2	2	NUM
ejpam-3728	180	7	t∫	t∫	NOUN
ejpam-3728	180	8	x	x	SYM
ejpam-3728	180	9	(	(	PUNCT
ejpam-3728	180	10	g′(x+)−	g′(x+)−	NOUN
ejpam-3728	180	11	g′(x−))sgn(u−	g′(x−))sgn(u−	PROPN
ejpam-3728	180	12	x	x	SYM
ejpam-3728	180	13	)	)	PUNCT
ejpam-3728	180	14	du	du	PROPN
ejpam-3728	180	15			PROPN
ejpam-3728	180	16	dt	dt	X
ejpam-3728	180	17	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-3728	180	18	≤	≤	ADV
ejpam-3728	180	19	1	1	NUM
ejpam-3728	180	20	2	2	NUM
ejpam-3728	180	21	|(g′(x+)−	|(g′(x+)−	NOUN
ejpam-3728	180	22	g′(x−))|	g′(x−))|	PROPN
ejpam-3728	180	23	∞∫	∞∫	PROPN
ejpam-3728	180	24	0	0	NUM
ejpam-3728	180	25	yn(x	yn(x	NUM
ejpam-3728	180	26	,	,	PUNCT
ejpam-3728	180	27	t)|t−	t)|t−	ADJ
ejpam-3728	180	28	x|	x|	NOUN
ejpam-3728	180	29	dt	dt	NOUN
ejpam-3728	180	30	≤	≤	NUM
ejpam-3728	180	31	1	1	NUM
ejpam-3728	180	32	2	2	NUM
ejpam-3728	180	33	|(g′(x+)−	|(g′(x+)−	NOUN
ejpam-3728	180	34	g′(x−))|	g′(x−))|	PROPN
ejpam-3728	180	35	∞∫	∞∫	PROPN
ejpam-3728	180	36	0	0	NUM
ejpam-3728	180	37	|t−	|t−	PROPN
ejpam-3728	180	38	x|yn(x	x|yn(x	NUM
ejpam-3728	180	39	,	,	PUNCT
ejpam-3728	180	40	t)dt	t)dt	PROPN
ejpam-3728	180	41	≤	≤	ADJ
ejpam-3728	180	42	1	1	NUM
ejpam-3728	180	43	2	2	NUM
ejpam-3728	180	44	|(g′(x+)−	|(g′(x+)−	NOUN
ejpam-3728	180	45	g′(x−)|	g′(x−)|	PROPN
ejpam-3728	180	46	(	(	PUNCT
ejpam-3728	180	47	ωn,2	ωn,2	PROPN
ejpam-3728	180	48	)	)	PUNCT
ejpam-3728	180	49	1	1	NUM
ejpam-3728	180	50	2	2	NUM
ejpam-3728	180	51	.	.	PUNCT
ejpam-3728	181	1	(	(	PUNCT
ejpam-3728	181	2	30	30	NUM
ejpam-3728	181	3	)	)	PUNCT
ejpam-3728	181	4	using	use	VERB
ejpam-3728	181	5	(	(	PUNCT
ejpam-3728	181	6	9	9	NUM
ejpam-3728	181	7	)	)	PUNCT
ejpam-3728	181	8	,	,	PUNCT
ejpam-3728	181	9	we	we	PRON
ejpam-3728	181	10	get	get	VERB
ejpam-3728	181	11	:	:	PUNCT
ejpam-3728	181	12	|b∗n(g;x)−	|b∗n(g;x)−	NOUN
ejpam-3728	181	13	g(x)|	g(x)|	VERB
ejpam-3728	181	14	≤	≤	NUM
ejpam-3728	181	15	1	1	NUM
ejpam-3728	181	16	2	2	NUM
ejpam-3728	181	17	|g′(x+	|g′(x+	NUM
ejpam-3728	181	18	)	)	PUNCT
ejpam-3728	182	1	+	+	CCONJ
ejpam-3728	182	2	g′(x−)|ωn,1	g′(x−)|ωn,1	NOUN
ejpam-3728	182	3	+	+	CCONJ
ejpam-3728	182	4	1	1	NUM
ejpam-3728	182	5	2	2	NUM
ejpam-3728	182	6	|g′(x+)−	|g′(x+)−	NOUN
ejpam-3728	182	7	g′(x−)|	g′(x−)|	NOUN
ejpam-3728	182	8	√	√	PROPN
ejpam-3728	182	9	2	2	NUM
ejpam-3728	182	10	un	un	PROPN
ejpam-3728	182	11	ζn(x	ζn(x	X
ejpam-3728	182	12	)	)	PUNCT
ejpam-3728	183	1	+	+	CCONJ
ejpam-3728	183	2	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-3728	183	3	∞∫	∞∫	PROPN
ejpam-3728	183	4	0	0	NUM
ejpam-3728	183	5	yn(x	yn(x	PROPN
ejpam-3728	183	6	,	,	PUNCT
ejpam-3728	183	7	t	t	PROPN
ejpam-3728	183	8	)	)	PUNCT
ejpam-3728	183	9	1	1	PROPN
ejpam-3728	183	10	2	2	NUM
ejpam-3728	183	11	s∫	s∫	NOUN
ejpam-3728	183	12	x	x	SYM
ejpam-3728	183	13	(	(	PUNCT
ejpam-3728	183	14	g′x(u	g′x(u	PROPN
ejpam-3728	183	15	)	)	PUNCT
ejpam-3728	183	16	)	)	PUNCT
ejpam-3728	183	17	du	du	PROPN
ejpam-3728	183	18			PROPN
ejpam-3728	183	19	dt	dt	X
ejpam-3728	183	20	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-3728	183	21	.	.	PUNCT
ejpam-3728	184	1	(	(	PUNCT
ejpam-3728	184	2	31	31	NUM
ejpam-3728	184	3	)	)	PUNCT
ejpam-3728	184	4	here	here	ADV
ejpam-3728	184	5	,	,	PUNCT
ejpam-3728	184	6	∞∫	∞∫	PROPN
ejpam-3728	184	7	0	0	NUM
ejpam-3728	184	8	yn(x	yn(x	PROPN
ejpam-3728	184	9	,	,	PUNCT
ejpam-3728	184	10	t	t	PROPN
ejpam-3728	184	11	)	)	PUNCT
ejpam-3728	184	12			PROPN
ejpam-3728	184	13	s∫	s∫	NOUN
ejpam-3728	184	14	x	x	SYM
ejpam-3728	184	15	(	(	PUNCT
ejpam-3728	184	16	g′x(u	g′x(u	PROPN
ejpam-3728	184	17	)	)	PUNCT
ejpam-3728	184	18	)	)	PUNCT
ejpam-3728	184	19	du	du	PROPN
ejpam-3728	184	20			PROPN
ejpam-3728	184	21	dt	dt	NOUN
ejpam-3728	185	1	=	=	PUNCT
ejpam-3728	186	1	x∫	x∫	PROPN
ejpam-3728	186	2	0	0	NUM
ejpam-3728	186	3	yn(x	yn(x	NUM
ejpam-3728	186	4	,	,	PUNCT
ejpam-3728	186	5	t	t	PROPN
ejpam-3728	186	6	)	)	PUNCT
ejpam-3728	186	7			PROPN
ejpam-3728	186	8	s∫	s∫	NOUN
ejpam-3728	186	9	x	x	SYM
ejpam-3728	186	10	(	(	PUNCT
ejpam-3728	186	11	g′x(u	g′x(u	PROPN
ejpam-3728	186	12	)	)	PUNCT
ejpam-3728	186	13	)	)	PUNCT
ejpam-3728	186	14	du	du	PROPN
ejpam-3728	186	15			PROPN
ejpam-3728	186	16	dt+	dt+	NOUN
ejpam-3728	186	17	∞∫	∞∫	PROPN
ejpam-3728	186	18	x	x	SYM
ejpam-3728	186	19	yn(x	yn(x	PROPN
ejpam-3728	186	20	,	,	PUNCT
ejpam-3728	186	21	t)(x	t)(x	PROPN
ejpam-3728	186	22	,	,	PUNCT
ejpam-3728	186	23	t	t	NOUN
ejpam-3728	186	24	)	)	PUNCT
ejpam-3728	186	25			PROPN
ejpam-3728	186	26	t∫	t∫	PROPN
ejpam-3728	186	27	x	x	SYM
ejpam-3728	186	28	(	(	PUNCT
ejpam-3728	186	29	g′x(u	g′x(u	PROPN
ejpam-3728	186	30	)	)	PUNCT
ejpam-3728	186	31	)	)	PUNCT
ejpam-3728	186	32	du	du	PROPN
ejpam-3728	186	33			PROPN
ejpam-3728	186	34	dt	dt	NOUN
ejpam-3728	186	35	=	=	SYM
ejpam-3728	186	36	p1	p1	PROPN
ejpam-3728	186	37	+	+	CCONJ
ejpam-3728	186	38	p2	p2	NOUN
ejpam-3728	186	39	,	,	PUNCT
ejpam-3728	186	40	(	(	PUNCT
ejpam-3728	186	41	32	32	NUM
ejpam-3728	186	42	)	)	PUNCT
ejpam-3728	186	43	where	where	SCONJ
ejpam-3728	186	44	p1	p1	PROPN
ejpam-3728	186	45	=	=	PUNCT
ejpam-3728	187	1	x∫	x∫	PROPN
ejpam-3728	187	2	0	0	X
ejpam-3728	188	1			PROPN
ejpam-3728	188	2	t∫	t∫	PROPN
ejpam-3728	188	3	x	x	SYM
ejpam-3728	188	4	(	(	PUNCT
ejpam-3728	188	5	g′x(u	g′x(u	PROPN
ejpam-3728	188	6	)	)	PUNCT
ejpam-3728	188	7	)	)	PUNCT
ejpam-3728	188	8	du	du	PROPN
ejpam-3728	188	9			PROPN
ejpam-3728	188	10	∂	∂	X
ejpam-3728	188	11	∂t	∂t	PROPN
ejpam-3728	188	12	(	(	PUNCT
ejpam-3728	188	13	in(x	in(x	X
ejpam-3728	188	14	,	,	PUNCT
ejpam-3728	188	15	t))dt	t))dt	X
ejpam-3728	188	16	=	=	SYM
ejpam-3728	188	17	x∫	x∫	ADJ
ejpam-3728	188	18	0	0	NUM
ejpam-3728	188	19	g′x(t)in(x	g′x(t)in(x	NOUN
ejpam-3728	188	20	,	,	PUNCT
ejpam-3728	188	21	t)dt	t)dt	PROPN
ejpam-3728	188	22	=	=	PUNCT
ejpam-3728	188	23	y∫	y∫	PROPN
ejpam-3728	188	24	0	0	NUM
ejpam-3728	188	25	g′x(t)in(x	g′x(t)in(x	NOUN
ejpam-3728	188	26	,	,	PUNCT
ejpam-3728	188	27	t)dt+	t)dt+	PUNCT
ejpam-3728	188	28	x∫	x∫	PROPN
ejpam-3728	188	29	y	y	PROPN
ejpam-3728	188	30	g′x(t)in(x	g′x(t)in(x	PROPN
ejpam-3728	188	31	,	,	PUNCT
ejpam-3728	188	32	t)dt	t)dt	PROPN
ejpam-3728	188	33	.	.	PROPN
ejpam-3728	188	34	(	(	PUNCT
ejpam-3728	188	35	33	33	NUM
ejpam-3728	188	36	)	)	PUNCT
ejpam-3728	188	37	here	here	ADV
ejpam-3728	188	38	,	,	PUNCT
ejpam-3728	188	39	we	we	PRON
ejpam-3728	188	40	consider	consider	VERB
ejpam-3728	188	41	y	y	PROPN
ejpam-3728	188	42	=	=	SYM
ejpam-3728	188	43	x−	x−	PROPN
ejpam-3728	188	44	x√	x√	PROPN
ejpam-3728	188	45	un	un	PROPN
ejpam-3728	188	46	then	then	ADV
ejpam-3728	188	47	by	by	ADP
ejpam-3728	188	48	the	the	DET
ejpam-3728	188	49	above	above	ADJ
ejpam-3728	188	50	equality	equality	NOUN
ejpam-3728	188	51	,	,	PUNCT
ejpam-3728	188	52	one	one	PRON
ejpam-3728	188	53	can	can	AUX
ejpam-3728	188	54	write	write	VERB
ejpam-3728	188	55	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	PROPN
ejpam-3728	189	1	x∫	x∫	PROPN
ejpam-3728	189	2	x−	x−	PROPN
ejpam-3728	189	3	x√	x√	PROPN
ejpam-3728	189	4	un	un	PROPN
ejpam-3728	189	5	g′x(t)in(x	g′x(t)in(x	PROPN
ejpam-3728	189	6	,	,	PUNCT
ejpam-3728	189	7	t)dt	t)dt	PROPN
ejpam-3728	189	8	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	ADP
ejpam-3728	189	9	≤	≤	NOUN
ejpam-3728	190	1	x∫	x∫	PROPN
ejpam-3728	190	2	x−	x−	PROPN
ejpam-3728	190	3	x√	x√	PROPN
ejpam-3728	190	4	un	un	PROPN
ejpam-3728	190	5	|g′x(t)||in(x	|g′x(t)||in(x	PROPN
ejpam-3728	190	6	,	,	PUNCT
ejpam-3728	190	7	t)|dt	t)|dt	PROPN
ejpam-3728	190	8	r.	r.	PROPN
ejpam-3728	190	9	yadav	yadav	PROPN
ejpam-3728	190	10	,	,	PUNCT
ejpam-3728	190	11	r.	r.	PROPN
ejpam-3728	190	12	meher	meher	PROPN
ejpam-3728	190	13	,	,	PUNCT
ejpam-3728	190	14	v.	v.	ADP
ejpam-3728	190	15	n.	n.	PROPN
ejpam-3728	190	16	mishra	mishra	PROPN
ejpam-3728	190	17	/	/	SYM
ejpam-3728	190	18	eur	eur	PROPN
ejpam-3728	190	19	.	.	PUNCT
ejpam-3728	191	1	j.	j.	PROPN
ejpam-3728	191	2	pure	pure	PROPN
ejpam-3728	191	3	appl	appl	PROPN
ejpam-3728	191	4	.	.	PROPN
ejpam-3728	191	5	math	math	PROPN
ejpam-3728	191	6	,	,	PUNCT
ejpam-3728	191	7	13	13	NUM
ejpam-3728	191	8	(	(	PUNCT
ejpam-3728	191	9	5	5	NUM
ejpam-3728	191	10	)	)	PUNCT
ejpam-3728	191	11	(	(	PUNCT
ejpam-3728	191	12	2020	2020	NUM
ejpam-3728	191	13	)	)	PUNCT
ejpam-3728	191	14	,	,	PUNCT
ejpam-3728	191	15	1306	1306	NUM
ejpam-3728	191	16	-	-	SYM
ejpam-3728	191	17	1324	1324	NUM
ejpam-3728	191	18	1316	1316	NUM
ejpam-3728	191	19	≤	≤	NOUN
ejpam-3728	192	1	x∫	x∫	PROPN
ejpam-3728	192	2	x−	x−	PROPN
ejpam-3728	192	3	x√	x√	PROPN
ejpam-3728	192	4	un	un	PROPN
ejpam-3728	192	5	|g′x(t)−	|g′x(t)−	PROPN
ejpam-3728	192	6	g′x(x)|dt	g′x(x)|dt	PROPN
ejpam-3728	192	7	,	,	PUNCT
ejpam-3728	192	8	g′x(x	g′x(x	PROPN
ejpam-3728	192	9	)	)	PUNCT
ejpam-3728	192	10	=	=	SYM
ejpam-3728	192	11	0	0	NUM
ejpam-3728	192	12	,	,	PUNCT
ejpam-3728	192	13	(	(	PUNCT
ejpam-3728	192	14	where	where	SCONJ
ejpam-3728	192	15	|in(x	|in(x	X
ejpam-3728	192	16	,	,	PUNCT
ejpam-3728	192	17	t)|	t)|	ADJ
ejpam-3728	192	18	≤	≤	ADJ
ejpam-3728	192	19	1	1	NUM
ejpam-3728	192	20	)	)	PUNCT
ejpam-3728	192	21	≤	≤	NOUN
ejpam-3728	193	1	x∫	x∫	PROPN
ejpam-3728	193	2	x−	x−	PROPN
ejpam-3728	194	1	x√	x√	PROPN
ejpam-3728	194	2	un	un	PROPN
ejpam-3728	194	3	v	v	X
ejpam-3728	194	4	x	x	SYM
ejpam-3728	194	5	t	t	NOUN
ejpam-3728	194	6	g	g	NOUN
ejpam-3728	194	7	′	′	NUM
ejpam-3728	194	8	xdt	xdt	NOUN
ejpam-3728	194	9	≤	≤	NOUN
ejpam-3728	194	10	v	v	NUM
ejpam-3728	194	11	x	x	SYM
ejpam-3728	194	12	x−	x−	PROPN
ejpam-3728	194	13	x√	x√	PROPN
ejpam-3728	194	14	un	un	PROPN
ejpam-3728	194	15	g′x	g′x	PROPN
ejpam-3728	194	16	x∫	x∫	ADJ
ejpam-3728	194	17	x−	x−	PROPN
ejpam-3728	194	18	x√	x√	PROPN
ejpam-3728	194	19	un	un	PROPN
ejpam-3728	194	20	dt	dt	PROPN
ejpam-3728	195	1	=	=	PUNCT
ejpam-3728	195	2	x	x	SYM
ejpam-3728	195	3	√	√	PROPN
ejpam-3728	195	4	un	un	PROPN
ejpam-3728	195	5	(	(	PUNCT
ejpam-3728	195	6	v	v	NOUN
ejpam-3728	195	7	x	x	X
ejpam-3728	195	8	x−	x−	PROPN
ejpam-3728	195	9	x√	x√	PROPN
ejpam-3728	195	10	un	un	PROPN
ejpam-3728	195	11	g′x	g′x	PROPN
ejpam-3728	195	12	)	)	PUNCT
ejpam-3728	195	13	.	.	PUNCT
ejpam-3728	196	1	(	(	PUNCT
ejpam-3728	196	2	34	34	NUM
ejpam-3728	196	3	)	)	PUNCT
ejpam-3728	196	4	using	use	VERB
ejpam-3728	196	5	lemma	lemma	PROPN
ejpam-3728	196	6	4	4	NUM
ejpam-3728	196	7	for	for	ADP
ejpam-3728	196	8	solving	solve	VERB
ejpam-3728	196	9	second	second	ADJ
ejpam-3728	196	10	term	term	NOUN
ejpam-3728	196	11	by	by	ADP
ejpam-3728	196	12	substituting	substitute	VERB
ejpam-3728	196	13	t	t	PROPN
ejpam-3728	196	14	=	=	SYM
ejpam-3728	196	15	x−	x−	PROPN
ejpam-3728	196	16	x	x	SYM
ejpam-3728	196	17	u	u	PROPN
ejpam-3728	196	18	,	,	PUNCT
ejpam-3728	196	19	we	we	PRON
ejpam-3728	196	20	get	get	VERB
ejpam-3728	196	21	x−	x−	PROPN
ejpam-3728	196	22	x√	x√	PROPN
ejpam-3728	196	23	un∫	un∫	PROPN
ejpam-3728	196	24	x	x	SYM
ejpam-3728	196	25	|g′x(t)|in(x	|g′x(t)|in(x	ADJ
ejpam-3728	196	26	,	,	PUNCT
ejpam-3728	196	27	t)dt	t)dt	PROPN
ejpam-3728	196	28	≤	≤	ADJ
ejpam-3728	196	29	2ζ2n(x	2ζ2n(x	NUM
ejpam-3728	196	30	)	)	PUNCT
ejpam-3728	197	1	un	un	PROPN
ejpam-3728	197	2	x−	x−	PROPN
ejpam-3728	197	3	x√	x√	PROPN
ejpam-3728	197	4	un∫	un∫	PROPN
ejpam-3728	197	5	x	x	X
ejpam-3728	197	6	|g′x(t)|	|g′x(t)|	PRON
ejpam-3728	197	7	(	(	PUNCT
ejpam-3728	197	8	x−	x−	PROPN
ejpam-3728	197	9	t)2	t)2	PROPN
ejpam-3728	197	10	dt	dt	NOUN
ejpam-3728	197	11	≤	≤	ADJ
ejpam-3728	197	12	2ζ2n(x	2ζ2n(x	NUM
ejpam-3728	197	13	)	)	PUNCT
ejpam-3728	197	14	un	un	PROPN
ejpam-3728	197	15	x−	x−	PROPN
ejpam-3728	197	16	x√	x√	PROPN
ejpam-3728	197	17	un∫	un∫	PROPN
ejpam-3728	197	18	x	x	SYM
ejpam-3728	197	19	v	v	NOUN
ejpam-3728	197	20	x	x	SYM
ejpam-3728	197	21	t	t	NOUN
ejpam-3728	197	22	g	g	NOUN
ejpam-3728	197	23	′	′	NUM
ejpam-3728	197	24	x	x	SYM
ejpam-3728	197	25	1	1	NUM
ejpam-3728	197	26	(	(	PUNCT
ejpam-3728	197	27	x−	x−	PROPN
ejpam-3728	197	28	t)2	t)2	PROPN
ejpam-3728	197	29	dt	dt	NOUN
ejpam-3728	197	30	=	=	SYM
ejpam-3728	197	31	2ζ2n(x	2ζ2n(x	PROPN
ejpam-3728	197	32	)	)	PUNCT
ejpam-3728	197	33	xun	xun	PROPN
ejpam-3728	198	1	√	√	PROPN
ejpam-3728	199	1	un∫	un∫	NOUN
ejpam-3728	199	2	x	x	SYM
ejpam-3728	199	3	v	v	NOUN
ejpam-3728	199	4	s	s	NOUN
ejpam-3728	199	5	x−	x−	PROPN
ejpam-3728	199	6	x	x	SYM
ejpam-3728	199	7	u	u	NOUN
ejpam-3728	199	8	g′xdu	g′xdu	PROPN
ejpam-3728	199	9	≤	≤	NOUN
ejpam-3728	199	10	2ζ2n(x	2ζ2n(x	NUM
ejpam-3728	199	11	)	)	PUNCT
ejpam-3728	200	1	xun	xun	PROPN
ejpam-3728	201	1	[	[	PUNCT
ejpam-3728	201	2	√	√	PROPN
ejpam-3728	201	3	un]∑	un]∑	PROPN
ejpam-3728	201	4	j=0	j=0	PROPN
ejpam-3728	201	5	(	(	PUNCT
ejpam-3728	201	6	v	v	ADP
ejpam-3728	201	7	t	t	NOUN
ejpam-3728	201	8	x−x	x−x	PROPN
ejpam-3728	201	9	j	j	PROPN
ejpam-3728	201	10	g′x	g′x	PROPN
ejpam-3728	201	11	)	)	PUNCT
ejpam-3728	201	12	.	.	PUNCT
ejpam-3728	202	1	(	(	PUNCT
ejpam-3728	202	2	35	35	NUM
ejpam-3728	202	3	)	)	PUNCT
ejpam-3728	202	4	hence	hence	ADV
ejpam-3728	202	5	,	,	PUNCT
ejpam-3728	202	6	|p1|	|p1|	ADV
ejpam-3728	202	7	≤	≤	ADJ
ejpam-3728	202	8	2ζ2n(x	2ζ2n(x	NUM
ejpam-3728	202	9	)	)	PUNCT
ejpam-3728	202	10	xun	xun	PROPN
ejpam-3728	203	1	[	[	PUNCT
ejpam-3728	203	2	√	√	PROPN
ejpam-3728	203	3	un]∑	un]∑	PROPN
ejpam-3728	203	4	j=0	j=0	PROPN
ejpam-3728	203	5	(	(	PUNCT
ejpam-3728	203	6	v	v	ADP
ejpam-3728	203	7	t	t	NOUN
ejpam-3728	203	8	x−x	x−x	PROPN
ejpam-3728	203	9	j	j	PROPN
ejpam-3728	203	10	g′x	g′x	NOUN
ejpam-3728	203	11	)	)	PUNCT
ejpam-3728	204	1	+	+	CCONJ
ejpam-3728	204	2	x	x	SYM
ejpam-3728	204	3	√	√	NUM
ejpam-3728	204	4	un	un	PROPN
ejpam-3728	204	5	(	(	PUNCT
ejpam-3728	204	6	v	v	NOUN
ejpam-3728	204	7	x	x	X
ejpam-3728	204	8	x−	x−	PROPN
ejpam-3728	204	9	x√	x√	PROPN
ejpam-3728	204	10	un	un	PROPN
ejpam-3728	204	11	g′x	g′x	PROPN
ejpam-3728	204	12	)	)	PUNCT
ejpam-3728	204	13	.	.	PUNCT
ejpam-3728	205	1	(	(	PUNCT
ejpam-3728	205	2	36	36	NUM
ejpam-3728	205	3	)	)	PUNCT
ejpam-3728	205	4	to	to	PART
ejpam-3728	205	5	solve	solve	VERB
ejpam-3728	205	6	p2	p2	NOUN
ejpam-3728	205	7	,	,	PUNCT
ejpam-3728	205	8	we	we	PRON
ejpam-3728	205	9	reform	reform	VERB
ejpam-3728	205	10	p2	p2	NOUN
ejpam-3728	205	11	and	and	CCONJ
ejpam-3728	205	12	integrating	integrate	VERB
ejpam-3728	205	13	by	by	ADP
ejpam-3728	205	14	parts	part	NOUN
ejpam-3728	205	15	,	,	PUNCT
ejpam-3728	205	16	we	we	PRON
ejpam-3728	205	17	have	have	VERB
ejpam-3728	205	18	|p2|	|p2|	PROPN
ejpam-3728	205	19	=	=	SYM
ejpam-3728	206	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-3728	206	2	z∫	z∫	NOUN
ejpam-3728	206	3	x	x	PUNCT
ejpam-3728	206	4			PROPN
ejpam-3728	206	5	t∫	t∫	PROPN
ejpam-3728	206	6	x	x	X
ejpam-3728	206	7	g′x(u)du	g′x(u)du	PROPN
ejpam-3728	206	8			PROPN
ejpam-3728	206	9	∂	∂	X
ejpam-3728	206	10	∂t	∂t	PROPN
ejpam-3728	206	11	(	(	PUNCT
ejpam-3728	206	12	1−	1−	NUM
ejpam-3728	206	13	in(x	in(x	X
ejpam-3728	206	14	,	,	PUNCT
ejpam-3728	206	15	t))dt+	t))dt+	PROPN
ejpam-3728	206	16	∞∫	∞∫	PROPN
ejpam-3728	207	1	z	z	NOUN
ejpam-3728	208	1			PROPN
ejpam-3728	208	2	t∫	t∫	PROPN
ejpam-3728	208	3	x	x	X
ejpam-3728	208	4	g′x(u)du	g′x(u)du	PROPN
ejpam-3728	208	5			PROPN
ejpam-3728	208	6	∂	∂	X
ejpam-3728	208	7	∂t	∂t	PROPN
ejpam-3728	208	8	(	(	PUNCT
ejpam-3728	208	9	1−	1−	NUM
ejpam-3728	208	10	in(x	in(x	X
ejpam-3728	208	11	,	,	PUNCT
ejpam-3728	208	12	t))dt	t))dt	PROPN
ejpam-3728	208	13	∣∣∣∣∣	∣∣∣∣∣	PUNCT
ejpam-3728	208	14	≤	≤	NOUN
ejpam-3728	208	15	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-3728	208	16	z∫	z∫	NOUN
ejpam-3728	208	17	x	x	SYM
ejpam-3728	208	18			PROPN
ejpam-3728	208	19	t∫	t∫	PROPN
ejpam-3728	208	20	x	x	X
ejpam-3728	208	21	g′x(u)du	g′x(u)du	PROPN
ejpam-3728	208	22			PROPN
ejpam-3728	208	23	∂	∂	X
ejpam-3728	208	24	∂t	∂t	PROPN
ejpam-3728	208	25	(	(	PUNCT
ejpam-3728	208	26	1−	1−	NUM
ejpam-3728	208	27	in(x	in(x	X
ejpam-3728	208	28	,	,	PUNCT
ejpam-3728	208	29	t))dt	t))dt	PROPN
ejpam-3728	208	30	∣∣∣∣∣∣+	∣∣∣∣∣∣+	PROPN
ejpam-3728	208	31	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-3728	208	32	∞∫	∞∫	PROPN
ejpam-3728	208	33	z	z	PROPN
ejpam-3728	209	1			PROPN
ejpam-3728	209	2	t∫	t∫	PROPN
ejpam-3728	209	3	x	x	X
ejpam-3728	209	4	g′x(u)du	g′x(u)du	PROPN
ejpam-3728	209	5			PROPN
ejpam-3728	209	6	∂	∂	X
ejpam-3728	209	7	∂t	∂t	PROPN
ejpam-3728	209	8	(	(	PUNCT
ejpam-3728	209	9	1−	1−	NUM
ejpam-3728	209	10	in(x	in(x	X
ejpam-3728	209	11	,	,	PUNCT
ejpam-3728	209	12	t))dt	t))dt	PROPN
ejpam-3728	209	13	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-3728	209	14	r.	r.	PROPN
ejpam-3728	209	15	yadav	yadav	PROPN
ejpam-3728	209	16	,	,	PUNCT
ejpam-3728	209	17	r.	r.	PROPN
ejpam-3728	209	18	meher	meher	PROPN
ejpam-3728	209	19	,	,	PUNCT
ejpam-3728	209	20	v.	v.	ADP
ejpam-3728	209	21	n.	n.	PROPN
ejpam-3728	209	22	mishra	mishra	PROPN
ejpam-3728	209	23	/	/	SYM
ejpam-3728	209	24	eur	eur	PROPN
ejpam-3728	209	25	.	.	PUNCT
ejpam-3728	210	1	j.	j.	PROPN
ejpam-3728	210	2	pure	pure	PROPN
ejpam-3728	210	3	appl	appl	PROPN
ejpam-3728	210	4	.	.	PROPN
ejpam-3728	210	5	math	math	PROPN
ejpam-3728	210	6	,	,	PUNCT
ejpam-3728	210	7	13	13	NUM
ejpam-3728	210	8	(	(	PUNCT
ejpam-3728	210	9	5	5	NUM
ejpam-3728	210	10	)	)	PUNCT
ejpam-3728	210	11	(	(	PUNCT
ejpam-3728	210	12	2020	2020	NUM
ejpam-3728	210	13	)	)	PUNCT
ejpam-3728	210	14	,	,	PUNCT
ejpam-3728	210	15	1306	1306	NUM
ejpam-3728	210	16	-	-	SYM
ejpam-3728	210	17	1324	1324	NUM
ejpam-3728	210	18	1317	1317	NUM
ejpam-3728	210	19	=	=	PUNCT
ejpam-3728	211	1	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-3728	211	2			NOUN
ejpam-3728	211	3	t∫	t∫	PRON
ejpam-3728	211	4	x	x	SYM
ejpam-3728	211	5	g′x(u)du(1−	g′x(u)du(1−	PROPN
ejpam-3728	211	6	in(x	in(x	X
ejpam-3728	211	7	,	,	PUNCT
ejpam-3728	211	8	t	t	PROPN
ejpam-3728	211	9	)	)	PUNCT
ejpam-3728	211	10	)	)	PUNCT
ejpam-3728	212	1	z	z	NOUN
ejpam-3728	212	2	x	x	PUNCT
ejpam-3728	212	3	−	−	PROPN
ejpam-3728	212	4	z∫	z∫	NOUN
ejpam-3728	212	5	x	x	SYM
ejpam-3728	212	6	g′x(t)(1−	g′x(t)(1−	PROPN
ejpam-3728	212	7	in(x	in(x	X
ejpam-3728	212	8	,	,	PUNCT
ejpam-3728	212	9	t))dt	t))dt	PROPN
ejpam-3728	212	10	+	+	CCONJ
ejpam-3728	212	11			PUNCT
ejpam-3728	212	12	t∫	t∫	ADJ
ejpam-3728	212	13	x	x	SYM
ejpam-3728	212	14	g′x(u)du(1−	g′x(u)du(1−	PROPN
ejpam-3728	212	15	in(x	in(x	X
ejpam-3728	212	16	,	,	PUNCT
ejpam-3728	212	17	t	t	PROPN
ejpam-3728	212	18	)	)	PUNCT
ejpam-3728	212	19	)	)	PUNCT
ejpam-3728	212	20	∞	∞	NOUN
ejpam-3728	212	21	z	z	PROPN
ejpam-3728	213	1	−	−	PROPN
ejpam-3728	213	2	∞∫	∞∫	PROPN
ejpam-3728	213	3	z	z	PROPN
ejpam-3728	213	4	g′x(t)(1−	g′x(t)(1−	PROPN
ejpam-3728	213	5	in(x	in(x	X
ejpam-3728	213	6	,	,	PUNCT
ejpam-3728	213	7	t))dt	t))dt	X
ejpam-3728	213	8	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-3728	213	9	=	=	SYM
ejpam-3728	214	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-3728	214	2	z∫	z∫	NOUN
ejpam-3728	214	3	x	x	X
ejpam-3728	215	1	g′x(u)du(1−	g′x(u)du(1−	PROPN
ejpam-3728	215	2	in(x	in(x	X
ejpam-3728	215	3	,	,	PUNCT
ejpam-3728	215	4	z))−	z))−	NUM
ejpam-3728	215	5	z∫	z∫	NOUN
ejpam-3728	215	6	x	x	PUNCT
ejpam-3728	215	7	g′x(t)(1−	g′x(t)(1−	NOUN
ejpam-3728	215	8	in(x	in(x	X
ejpam-3728	215	9	,	,	PUNCT
ejpam-3728	215	10	t))dt	t))dt	PROPN
ejpam-3728	215	11	−	−	PROPN
ejpam-3728	215	12	z∫	z∫	NOUN
ejpam-3728	215	13	x	x	PUNCT
ejpam-3728	215	14	g′x(u)du(1−	g′x(u)du(1−	PROPN
ejpam-3728	215	15	in(x	in(x	X
ejpam-3728	215	16	,	,	PUNCT
ejpam-3728	215	17	z))−	z))−	NUM
ejpam-3728	215	18	∞∫	∞∫	PROPN
ejpam-3728	215	19	z	z	PROPN
ejpam-3728	215	20	g′x(t)(1−	g′x(t)(1−	PROPN
ejpam-3728	215	21	in(x	in(x	X
ejpam-3728	215	22	,	,	PUNCT
ejpam-3728	215	23	t))dt	t))dt	X
ejpam-3728	215	24	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-3728	215	25	=	=	SYM
ejpam-3728	215	26	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-3728	215	27	z∫	z∫	NOUN
ejpam-3728	215	28	x	x	PUNCT
ejpam-3728	215	29	g′x(t)(1−	g′x(t)(1−	NOUN
ejpam-3728	215	30	in(x	in(x	X
ejpam-3728	215	31	,	,	PUNCT
ejpam-3728	215	32	t))dt+	t))dt+	PROPN
ejpam-3728	215	33	∞∫	∞∫	PROPN
ejpam-3728	215	34	z	z	PROPN
ejpam-3728	215	35	g′x(t)(1−	g′x(t)(1−	PROPN
ejpam-3728	215	36	in(x	in(x	X
ejpam-3728	215	37	,	,	PUNCT
ejpam-3728	215	38	t))dt	t))dt	X
ejpam-3728	215	39	∣∣∣∣∣	∣∣∣∣∣	NOUN
ejpam-3728	215	40	≤	≤	PROPN
ejpam-3728	215	41	z∫	z∫	X
ejpam-3728	215	42	x	x	SYM
ejpam-3728	215	43	v	v	ADP
ejpam-3728	215	44	t	t	PROPN
ejpam-3728	215	45	x(g′x)dt+	x(g′x)dt+	PUNCT
ejpam-3728	215	46	2ζ2n(x	2ζ2n(x	NUM
ejpam-3728	215	47	)	)	PUNCT
ejpam-3728	215	48	un	un	PROPN
ejpam-3728	215	49	∞∫	∞∫	PROPN
ejpam-3728	215	50	z	z	PROPN
ejpam-3728	215	51	v	v	ADP
ejpam-3728	215	52	t	t	PROPN
ejpam-3728	215	53	x(g′x	x(g′x	PROPN
ejpam-3728	215	54	)	)	PUNCT
ejpam-3728	215	55	1	1	NUM
ejpam-3728	215	56	(	(	PUNCT
ejpam-3728	215	57	t−	t−	PROPN
ejpam-3728	215	58	x)2	x)2	PROPN
ejpam-3728	215	59	dt	dt	X
ejpam-3728	215	60	≤	≤	NUM
ejpam-3728	215	61	x	x	SYM
ejpam-3728	215	62	√	√	PROPN
ejpam-3728	215	63	un	un	PROPN
ejpam-3728	215	64	v	v	PROPN
ejpam-3728	215	65	x+	x+	PROPN
ejpam-3728	215	66	x√	x√	PROPN
ejpam-3728	215	67	un	un	PROPN
ejpam-3728	215	68	x	x	X
ejpam-3728	215	69	(	(	PUNCT
ejpam-3728	215	70	g′x	g′x	NOUN
ejpam-3728	215	71	)	)	PUNCT
ejpam-3728	215	72	+	+	CCONJ
ejpam-3728	215	73	2ζ2n(x	2ζ2n(x	NUM
ejpam-3728	215	74	)	)	PUNCT
ejpam-3728	215	75	un	un	PROPN
ejpam-3728	215	76	∞∫	∞∫	PROPN
ejpam-3728	215	77	x+	x+	NUM
ejpam-3728	215	78	x√	x√	PROPN
ejpam-3728	215	79	un	un	PROPN
ejpam-3728	215	80	v	v	PROPN
ejpam-3728	215	81	t	t	PROPN
ejpam-3728	215	82	x(g′x	x(g′x	PROPN
ejpam-3728	215	83	)	)	PUNCT
ejpam-3728	215	84	1	1	NUM
ejpam-3728	215	85	(	(	PUNCT
ejpam-3728	215	86	t−	t−	PROPN
ejpam-3728	215	87	x)2	x)2	PROPN
ejpam-3728	215	88	dt	dt	X
ejpam-3728	215	89	.	.	PUNCT
ejpam-3728	216	1	on	on	ADP
ejpam-3728	216	2	substituting	substitute	VERB
ejpam-3728	216	3	t	t	NOUN
ejpam-3728	216	4	=	=	PUNCT
ejpam-3728	216	5	x	x	SYM
ejpam-3728	216	6	(	(	PUNCT
ejpam-3728	216	7	1	1	NUM
ejpam-3728	216	8	+	+	SYM
ejpam-3728	216	9	1	1	NUM
ejpam-3728	216	10	β	β	NOUN
ejpam-3728	216	11	)	)	PUNCT
ejpam-3728	216	12	,	,	PUNCT
ejpam-3728	216	13	we	we	PRON
ejpam-3728	216	14	obtain	obtain	VERB
ejpam-3728	216	15	|p2|	|p2|	PROPN
ejpam-3728	216	16	≤	≤	NUM
ejpam-3728	216	17	x	x	PUNCT
ejpam-3728	216	18	√	√	PROPN
ejpam-3728	216	19	un	un	PROPN
ejpam-3728	216	20	v	v	PROPN
ejpam-3728	216	21	x+	x+	PROPN
ejpam-3728	216	22	x√	x√	PROPN
ejpam-3728	216	23	un	un	PROPN
ejpam-3728	216	24	x	x	X
ejpam-3728	216	25	(	(	PUNCT
ejpam-3728	216	26	g′x	g′x	NOUN
ejpam-3728	216	27	)	)	PUNCT
ejpam-3728	216	28	+	+	CCONJ
ejpam-3728	216	29	2ζ2n(x	2ζ2n(x	NUM
ejpam-3728	216	30	)	)	PUNCT
ejpam-3728	216	31	xun	xun	PROPN
ejpam-3728	217	1	√	√	PROPN
ejpam-3728	217	2	un∫	un∫	VERB
ejpam-3728	217	3	0	0	NUM
ejpam-3728	217	4	v	v	NOUN
ejpam-3728	217	5	x+	x+	PROPN
ejpam-3728	217	6	x	x	X
ejpam-3728	217	7	β	β	X
ejpam-3728	217	8	x	x	X
ejpam-3728	217	9	(	(	PUNCT
ejpam-3728	217	10	g′x)dβ	g′x)dβ	ADP
ejpam-3728	217	11	≤	≤	NUM
ejpam-3728	217	12	x	x	SYM
ejpam-3728	217	13	√	√	PROPN
ejpam-3728	217	14	un	un	PROPN
ejpam-3728	217	15	v	v	PROPN
ejpam-3728	217	16	x+	x+	PROPN
ejpam-3728	217	17	x√	x√	PROPN
ejpam-3728	217	18	un	un	PROPN
ejpam-3728	217	19	x	x	X
ejpam-3728	217	20	(	(	PUNCT
ejpam-3728	217	21	g′x	g′x	NOUN
ejpam-3728	217	22	)	)	PUNCT
ejpam-3728	217	23	+	+	CCONJ
ejpam-3728	217	24	2ζ2n(x	2ζ2n(x	NUM
ejpam-3728	217	25	)	)	PUNCT
ejpam-3728	217	26	xun	xun	PROPN
ejpam-3728	218	1	[	[	PUNCT
ejpam-3728	218	2	√	√	PROPN
ejpam-3728	218	3	un]∑	un]∑	PROPN
ejpam-3728	218	4	j=0	j=0	VERB
ejpam-3728	218	5	√	√	ADP
ejpam-3728	218	6	j+1∫	j+1∫	PROPN
ejpam-3728	218	7	j	j	PROPN
ejpam-3728	218	8	v	v	ADP
ejpam-3728	218	9	x+x	x+x	PROPN
ejpam-3728	218	10	j	j	PROPN
ejpam-3728	218	11	x	x	INTJ
ejpam-3728	218	12	(	(	PUNCT
ejpam-3728	218	13	g′x)dβ	g′x)dβ	ADP
ejpam-3728	218	14	=	=	PUNCT
ejpam-3728	218	15	x	x	SYM
ejpam-3728	218	16	√	√	PROPN
ejpam-3728	218	17	un	un	PROPN
ejpam-3728	218	18	v	v	PROPN
ejpam-3728	218	19	x+	x+	PROPN
ejpam-3728	218	20	x√	x√	PROPN
ejpam-3728	218	21	un	un	PROPN
ejpam-3728	218	22	x	x	X
ejpam-3728	218	23	(	(	PUNCT
ejpam-3728	218	24	g′x	g′x	NOUN
ejpam-3728	218	25	)	)	PUNCT
ejpam-3728	218	26	+	+	CCONJ
ejpam-3728	218	27	2ζ2n(x	2ζ2n(x	NUM
ejpam-3728	218	28	)	)	PUNCT
ejpam-3728	218	29	xun	xun	PROPN
ejpam-3728	219	1	[	[	PUNCT
ejpam-3728	219	2	√	√	PROPN
ejpam-3728	219	3	un]∑	un]∑	PROPN
ejpam-3728	219	4	j=0	j=0	PROPN
ejpam-3728	219	5	v	v	ADP
ejpam-3728	219	6	x+x	x+x	PROPN
ejpam-3728	219	7	j	j	PROPN
ejpam-3728	219	8	x	x	SYM
ejpam-3728	219	9	(	(	PUNCT
ejpam-3728	219	10	g′x	g′x	NOUN
ejpam-3728	219	11	)	)	PUNCT
ejpam-3728	219	12	.	.	PUNCT
ejpam-3728	220	1	using	use	VERB
ejpam-3728	220	2	the	the	DET
ejpam-3728	220	3	value	value	NOUN
ejpam-3728	220	4	of	of	ADP
ejpam-3728	220	5	p1	p1	NOUN
ejpam-3728	220	6	,	,	PUNCT
ejpam-3728	220	7	p2	p2	PROPN
ejpam-3728	220	8	in	in	ADP
ejpam-3728	220	9	(	(	PUNCT
ejpam-3728	220	10	32	32	NUM
ejpam-3728	220	11	)	)	PUNCT
ejpam-3728	220	12	,	,	PUNCT
ejpam-3728	220	13	we	we	PRON
ejpam-3728	220	14	obtain	obtain	VERB
ejpam-3728	220	15	∞∫	∞∫	PROPN
ejpam-3728	220	16	0	0	NUM
ejpam-3728	220	17	yn(x	yn(x	PROPN
ejpam-3728	220	18	,	,	PUNCT
ejpam-3728	220	19	t	t	PROPN
ejpam-3728	220	20	)	)	PUNCT
ejpam-3728	220	21			PROPN
ejpam-3728	220	22	s∫	s∫	NOUN
ejpam-3728	220	23	x	x	SYM
ejpam-3728	220	24	(	(	PUNCT
ejpam-3728	220	25	g′x(u	g′x(u	PROPN
ejpam-3728	220	26	)	)	PUNCT
ejpam-3728	220	27	)	)	PUNCT
ejpam-3728	220	28	du	du	PROPN
ejpam-3728	220	29			PROPN
ejpam-3728	220	30	dt	dt	NOUN
ejpam-3728	220	31	=	=	SYM
ejpam-3728	220	32	2ζ2n(x	2ζ2n(x	NUM
ejpam-3728	220	33	)	)	PUNCT
ejpam-3728	220	34	xun	xun	PROPN
ejpam-3728	221	1	[	[	PUNCT
ejpam-3728	221	2	√	√	PROPN
ejpam-3728	221	3	un]∑	un]∑	PROPN
ejpam-3728	221	4	j=0	j=0	PROPN
ejpam-3728	221	5	(	(	PUNCT
ejpam-3728	221	6	v	v	ADP
ejpam-3728	221	7	t	t	NOUN
ejpam-3728	221	8	x−x	x−x	PROPN
ejpam-3728	221	9	j	j	PROPN
ejpam-3728	221	10	g′x	g′x	NOUN
ejpam-3728	221	11	)	)	PUNCT
ejpam-3728	222	1	+	+	CCONJ
ejpam-3728	222	2	x	x	SYM
ejpam-3728	222	3	√	√	NUM
ejpam-3728	222	4	un	un	PROPN
ejpam-3728	222	5	(	(	PUNCT
ejpam-3728	222	6	v	v	NOUN
ejpam-3728	222	7	x	x	X
ejpam-3728	222	8	x−	x−	PROPN
ejpam-3728	222	9	x√	x√	PROPN
ejpam-3728	222	10	un	un	PROPN
ejpam-3728	222	11	g′x	g′x	PROPN
ejpam-3728	222	12	)	)	PUNCT
ejpam-3728	223	1	+	+	CCONJ
ejpam-3728	223	2	x	x	PUNCT
ejpam-3728	223	3	√	√	NUM
ejpam-3728	223	4	un	un	PROPN
ejpam-3728	223	5	v	v	PROPN
ejpam-3728	223	6	x+	x+	PROPN
ejpam-3728	223	7	x√	x√	PROPN
ejpam-3728	223	8	un	un	PROPN
ejpam-3728	223	9	x	x	X
ejpam-3728	223	10	(	(	PUNCT
ejpam-3728	223	11	g′x	g′x	NOUN
ejpam-3728	223	12	)	)	PUNCT
ejpam-3728	223	13	+	+	CCONJ
ejpam-3728	223	14	2ζ2n(x	2ζ2n(x	NUM
ejpam-3728	223	15	)	)	PUNCT
ejpam-3728	223	16	xun	xun	PROPN
ejpam-3728	224	1	[	[	PUNCT
ejpam-3728	224	2	√	√	PROPN
ejpam-3728	224	3	un]∑	un]∑	PROPN
ejpam-3728	224	4	j=0	j=0	PROPN
ejpam-3728	224	5	v	v	ADP
ejpam-3728	224	6	x+x	x+x	PROPN
ejpam-3728	224	7	j	j	PROPN
ejpam-3728	224	8	x	x	SYM
ejpam-3728	224	9	(	(	PUNCT
ejpam-3728	224	10	g′x	g′x	NOUN
ejpam-3728	224	11	)	)	PUNCT
ejpam-3728	224	12	.	.	PUNCT
ejpam-3728	225	1	(	(	PUNCT
ejpam-3728	225	2	37	37	NUM
ejpam-3728	225	3	)	)	PUNCT
ejpam-3728	225	4	r.	r.	PROPN
ejpam-3728	225	5	yadav	yadav	PROPN
ejpam-3728	225	6	,	,	PUNCT
ejpam-3728	225	7	r.	r.	PROPN
ejpam-3728	225	8	meher	meher	PROPN
ejpam-3728	225	9	,	,	PUNCT
ejpam-3728	225	10	v.	v.	ADP
ejpam-3728	225	11	n.	n.	PROPN
ejpam-3728	225	12	mishra	mishra	PROPN
ejpam-3728	225	13	/	/	SYM
ejpam-3728	225	14	eur	eur	PROPN
ejpam-3728	225	15	.	.	PUNCT
ejpam-3728	226	1	j.	j.	PROPN
ejpam-3728	226	2	pure	pure	PROPN
ejpam-3728	226	3	appl	appl	PROPN
ejpam-3728	226	4	.	.	PROPN
ejpam-3728	226	5	math	math	PROPN
ejpam-3728	226	6	,	,	PUNCT
ejpam-3728	226	7	13	13	NUM
ejpam-3728	226	8	(	(	PUNCT
ejpam-3728	226	9	5	5	NUM
ejpam-3728	226	10	)	)	PUNCT
ejpam-3728	226	11	(	(	PUNCT
ejpam-3728	226	12	2020	2020	NUM
ejpam-3728	226	13	)	)	PUNCT
ejpam-3728	226	14	,	,	PUNCT
ejpam-3728	226	15	1306	1306	NUM
ejpam-3728	226	16	-	-	SYM
ejpam-3728	226	17	1324	1324	NUM
ejpam-3728	226	18	1318	1318	NUM
ejpam-3728	226	19	put	put	VERB
ejpam-3728	226	20	the	the	DET
ejpam-3728	226	21	above	above	ADJ
ejpam-3728	226	22	value	value	NOUN
ejpam-3728	226	23	from	from	ADP
ejpam-3728	226	24	(	(	PUNCT
ejpam-3728	226	25	37	37	NUM
ejpam-3728	226	26	)	)	PUNCT
ejpam-3728	226	27	in	in	ADP
ejpam-3728	226	28	(	(	PUNCT
ejpam-3728	226	29	31	31	NUM
ejpam-3728	226	30	)	)	PUNCT
ejpam-3728	226	31	,	,	PUNCT
ejpam-3728	226	32	we	we	PRON
ejpam-3728	226	33	obtain	obtain	VERB
ejpam-3728	226	34	required	require	VERB
ejpam-3728	226	35	result	result	NOUN
ejpam-3728	226	36	|b∗n(g;x)−	|b∗n(g;x)−	PROPN
ejpam-3728	226	37	g(x)|	g(x)|	VERB
ejpam-3728	226	38	≤	≤	NUM
ejpam-3728	226	39	1	1	NUM
ejpam-3728	226	40	2un	2un	NOUN
ejpam-3728	226	41	|g′(x+	|g′(x+	NUM
ejpam-3728	226	42	)	)	PUNCT
ejpam-3728	227	1	+	+	CCONJ
ejpam-3728	227	2	g′(x−)|+	g′(x−)|+	INTJ
ejpam-3728	227	3	√	√	ADV
ejpam-3728	227	4	1	1	NUM
ejpam-3728	227	5	2un	2un	ADJ
ejpam-3728	227	6	|g′(x+)−	|g′(x+)−	NOUN
ejpam-3728	227	7	g′(x−)|ζn(x	g′(x−)|ζn(x	NOUN
ejpam-3728	227	8	)	)	PUNCT
ejpam-3728	228	1	+	+	CCONJ
ejpam-3728	228	2	2ζ2n(x	2ζ2n(x	NUM
ejpam-3728	228	3	)	)	PUNCT
ejpam-3728	228	4	xun	xun	PROPN
ejpam-3728	229	1	[	[	PUNCT
ejpam-3728	229	2	√	√	PROPN
ejpam-3728	229	3	un]∑	un]∑	PROPN
ejpam-3728	229	4	j=0	j=0	PROPN
ejpam-3728	229	5	(	(	PUNCT
ejpam-3728	229	6	v	v	ADP
ejpam-3728	229	7	t	t	NOUN
ejpam-3728	229	8	x−x	x−x	PROPN
ejpam-3728	229	9	j	j	PROPN
ejpam-3728	229	10	g′x	g′x	NOUN
ejpam-3728	229	11	)	)	PUNCT
ejpam-3728	230	1	+	+	CCONJ
ejpam-3728	230	2	x	x	SYM
ejpam-3728	230	3	√	√	NUM
ejpam-3728	230	4	un	un	PROPN
ejpam-3728	230	5	(	(	PUNCT
ejpam-3728	230	6	v	v	NOUN
ejpam-3728	230	7	x	x	X
ejpam-3728	230	8	x−	x−	PROPN
ejpam-3728	230	9	x√	x√	PROPN
ejpam-3728	230	10	un	un	PROPN
ejpam-3728	230	11	g′x	g′x	PROPN
ejpam-3728	230	12	)	)	PUNCT
ejpam-3728	231	1	+	+	CCONJ
ejpam-3728	231	2	x	x	PUNCT
ejpam-3728	231	3	√	√	NUM
ejpam-3728	231	4	un	un	PROPN
ejpam-3728	231	5	v	v	PROPN
ejpam-3728	231	6	x+	x+	PROPN
ejpam-3728	231	7	x√	x√	PROPN
ejpam-3728	231	8	un	un	PROPN
ejpam-3728	231	9	x	x	X
ejpam-3728	231	10	(	(	PUNCT
ejpam-3728	231	11	g′x	g′x	NOUN
ejpam-3728	231	12	)	)	PUNCT
ejpam-3728	231	13	+	+	CCONJ
ejpam-3728	231	14	2ζ2n(x	2ζ2n(x	NUM
ejpam-3728	231	15	)	)	PUNCT
ejpam-3728	231	16	xun	xun	PROPN
ejpam-3728	232	1	[	[	PUNCT
ejpam-3728	232	2	√	√	PROPN
ejpam-3728	232	3	un]∑	un]∑	PROPN
ejpam-3728	232	4	j=0	j=0	PROPN
ejpam-3728	232	5	v	v	ADP
ejpam-3728	232	6	x+x	x+x	PROPN
ejpam-3728	232	7	j	j	PROPN
ejpam-3728	232	8	x	x	SYM
ejpam-3728	232	9	(	(	PUNCT
ejpam-3728	232	10	g′x	g′x	NOUN
ejpam-3728	232	11	)	)	PUNCT
ejpam-3728	232	12	.	.	PUNCT
ejpam-3728	233	1	5	5	X
ejpam-3728	233	2	.	.	X
ejpam-3728	233	3	graphical	graphical	ADJ
ejpam-3728	233	4	and	and	CCONJ
ejpam-3728	233	5	numerical	numerical	ADJ
ejpam-3728	233	6	analysis	analysis	NOUN
ejpam-3728	233	7	of	of	ADP
ejpam-3728	233	8	the	the	DET
ejpam-3728	233	9	operators	operator	NOUN
ejpam-3728	233	10	in	in	ADP
ejpam-3728	233	11	this	this	DET
ejpam-3728	233	12	section	section	NOUN
ejpam-3728	233	13	,	,	PUNCT
ejpam-3728	233	14	we	we	PRON
ejpam-3728	233	15	study	study	VERB
ejpam-3728	233	16	the	the	DET
ejpam-3728	233	17	graphical	graphical	ADJ
ejpam-3728	233	18	representation	representation	NOUN
ejpam-3728	233	19	and	and	CCONJ
ejpam-3728	233	20	numerical	numerical	ADJ
ejpam-3728	233	21	analysis	analysis	NOUN
ejpam-3728	233	22	of	of	ADP
ejpam-3728	233	23	the	the	DET
ejpam-3728	233	24	operators	operator	NOUN
ejpam-3728	233	25	to	to	ADP
ejpam-3728	233	26	the	the	DET
ejpam-3728	233	27	function	function	NOUN
ejpam-3728	233	28	.	.	PUNCT
ejpam-3728	234	1	example	example	NOUN
ejpam-3728	235	1	1	1	NUM
ejpam-3728	235	2	.	.	PUNCT
ejpam-3728	235	3	let	let	VERB
ejpam-3728	235	4	the	the	DET
ejpam-3728	235	5	function	function	NOUN
ejpam-3728	235	6	g	g	NOUN
ejpam-3728	235	7	:	:	PUNCT
ejpam-3728	236	1	[	[	X
ejpam-3728	236	2	0	0	NUM
ejpam-3728	236	3	,	,	PUNCT
ejpam-3728	236	4	2.5	2.5	NUM
ejpam-3728	236	5	]	]	PUNCT
ejpam-3728	236	6	→	→	X
ejpam-3728	236	7	[	[	X
ejpam-3728	236	8	0,∞	0,∞	NUM
ejpam-3728	236	9	)	)	PUNCT
ejpam-3728	236	10	such	such	ADJ
ejpam-3728	236	11	that	that	SCONJ
ejpam-3728	236	12	g(x	g(x	NOUN
ejpam-3728	236	13	)	)	PUNCT
ejpam-3728	236	14	=	=	SYM
ejpam-3728	236	15	−x3e−5x(blue	−x3e−5x(blue	NOUN
ejpam-3728	236	16	)	)	PUNCT
ejpam-3728	236	17	for	for	ADP
ejpam-3728	236	18	all	all	DET
ejpam-3728	236	19	x	x	SYM
ejpam-3728	236	20	∈	∈	PROPN
ejpam-3728	237	1	[	[	X
ejpam-3728	237	2	0	0	NUM
ejpam-3728	237	3	,	,	PUNCT
ejpam-3728	237	4	2.5	2.5	NUM
ejpam-3728	237	5	]	]	PUNCT
ejpam-3728	237	6	.	.	PUNCT
ejpam-3728	238	1	choosing	choose	VERB
ejpam-3728	238	2	un	un	PROPN
ejpam-3728	238	3	=	=	PROPN
ejpam-3728	238	4	n	n	PROPN
ejpam-3728	238	5	=	=	SYM
ejpam-3728	238	6	15	15	NUM
ejpam-3728	238	7	,	,	PUNCT
ejpam-3728	238	8	35	35	NUM
ejpam-3728	238	9	,	,	PUNCT
ejpam-3728	238	10	50	50	NUM
ejpam-3728	238	11	and	and	CCONJ
ejpam-3728	238	12	then	then	ADV
ejpam-3728	238	13	corresponding	correspond	VERB
ejpam-3728	238	14	operators	operator	NOUN
ejpam-3728	238	15	are	be	AUX
ejpam-3728	238	16	s∗15(g;x	s∗15(g;x	PROPN
ejpam-3728	238	17	)	)	PUNCT
ejpam-3728	238	18	,	,	PUNCT
ejpam-3728	238	19	s∗35(g;x	s∗35(g;x	PROPN
ejpam-3728	238	20	)	)	PUNCT
ejpam-3728	238	21	,	,	PUNCT
ejpam-3728	238	22	s∗50(g;x	s∗50(g;x	PROPN
ejpam-3728	238	23	)	)	PUNCT
ejpam-3728	238	24	represent	represent	VERB
ejpam-3728	238	25	green	green	ADJ
ejpam-3728	238	26	,	,	PUNCT
ejpam-3728	238	27	red	red	ADJ
ejpam-3728	238	28	and	and	CCONJ
ejpam-3728	238	29	black	black	ADJ
ejpam-3728	238	30	colors	color	NOUN
ejpam-3728	238	31	respectively	respectively	ADV
ejpam-3728	238	32	in	in	ADP
ejpam-3728	238	33	the	the	DET
ejpam-3728	238	34	given	give	VERB
ejpam-3728	238	35	figure	figure	NOUN
ejpam-3728	238	36	1	1	NUM
ejpam-3728	238	37	.	.	PUNCT
ejpam-3728	239	1	one	one	PRON
ejpam-3728	239	2	can	can	AUX
ejpam-3728	239	3	observe	observe	VERB
ejpam-3728	239	4	that	that	SCONJ
ejpam-3728	239	5	as	as	SCONJ
ejpam-3728	239	6	the	the	DET
ejpam-3728	239	7	value	value	NOUN
ejpam-3728	239	8	of	of	ADP
ejpam-3728	239	9	n	n	NUM
ejpam-3728	239	10	is	be	AUX
ejpam-3728	239	11	increased	increase	VERB
ejpam-3728	239	12	,	,	PUNCT
ejpam-3728	239	13	the	the	DET
ejpam-3728	239	14	error	error	NOUN
ejpam-3728	239	15	of	of	ADP
ejpam-3728	239	16	the	the	DET
ejpam-3728	239	17	operators	operator	NOUN
ejpam-3728	239	18	to	to	ADP
ejpam-3728	239	19	the	the	DET
ejpam-3728	239	20	function	function	NOUN
ejpam-3728	239	21	is	be	AUX
ejpam-3728	239	22	going	go	VERB
ejpam-3728	239	23	to	to	PART
ejpam-3728	239	24	be	be	AUX
ejpam-3728	239	25	least	least	ADJ
ejpam-3728	239	26	.	.	PUNCT
ejpam-3728	240	1	we	we	PRON
ejpam-3728	240	2	can	can	AUX
ejpam-3728	240	3	say	say	VERB
ejpam-3728	240	4	that	that	SCONJ
ejpam-3728	240	5	the	the	DET
ejpam-3728	240	6	approach	approach	NOUN
ejpam-3728	240	7	of	of	ADP
ejpam-3728	240	8	the	the	DET
ejpam-3728	240	9	operators	operator	NOUN
ejpam-3728	240	10	to	to	ADP
ejpam-3728	240	11	the	the	DET
ejpam-3728	240	12	function	function	NOUN
ejpam-3728	240	13	is	be	AUX
ejpam-3728	240	14	good	good	ADJ
ejpam-3728	240	15	for	for	ADP
ejpam-3728	240	16	the	the	DET
ejpam-3728	240	17	large	large	ADJ
ejpam-3728	240	18	value	value	NOUN
ejpam-3728	240	19	of	of	ADP
ejpam-3728	240	20	n.	n.	NOUN
ejpam-3728	240	21	but	but	CCONJ
ejpam-3728	240	22	for	for	ADP
ejpam-3728	240	23	the	the	DET
ejpam-3728	240	24	same	same	ADJ
ejpam-3728	240	25	function	function	NOUN
ejpam-3728	240	26	,	,	PUNCT
ejpam-3728	240	27	if	if	SCONJ
ejpam-3728	240	28	we	we	PRON
ejpam-3728	240	29	move	move	VERB
ejpam-3728	240	30	towards	towards	ADP
ejpam-3728	240	31	the	the	DET
ejpam-3728	240	32	truncation	truncation	NOUN
ejpam-3728	240	33	type	type	NOUN
ejpam-3728	240	34	error	error	NOUN
ejpam-3728	240	35	,	,	PUNCT
ejpam-3728	240	36	we	we	PRON
ejpam-3728	240	37	can	can	AUX
ejpam-3728	240	38	observe	observe	VERB
ejpam-3728	240	39	by	by	ADP
ejpam-3728	240	40	figure	figure	NOUN
ejpam-3728	240	41	2	2	NUM
ejpam-3728	240	42	,	,	PUNCT
ejpam-3728	240	43	the	the	DET
ejpam-3728	240	44	approximation	approximation	NOUN
ejpam-3728	240	45	is	be	AUX
ejpam-3728	240	46	not	not	PART
ejpam-3728	240	47	better	well	ADJ
ejpam-3728	240	48	throughout	throughout	ADP
ejpam-3728	240	49	the	the	DET
ejpam-3728	240	50	interval	interval	NOUN
ejpam-3728	240	51	[	[	X
ejpam-3728	240	52	0	0	NUM
ejpam-3728	240	53	,	,	PUNCT
ejpam-3728	240	54	2.5	2.5	NUM
ejpam-3728	240	55	]	]	PUNCT
ejpam-3728	240	56	.	.	PUNCT
ejpam-3728	241	1	here	here	ADV
ejpam-3728	241	2	we	we	PRON
ejpam-3728	241	3	consider	consider	VERB
ejpam-3728	241	4	the	the	DET
ejpam-3728	241	5	un	un	PROPN
ejpam-3728	241	6	=	=	PROPN
ejpam-3728	241	7	n	n	PROPN
ejpam-3728	241	8	=	=	SYM
ejpam-3728	241	9	15	15	NUM
ejpam-3728	241	10	,	,	PUNCT
ejpam-3728	241	11	35	35	NUM
ejpam-3728	241	12	,	,	PUNCT
ejpam-3728	241	13	50	50	NUM
ejpam-3728	241	14	and	and	CCONJ
ejpam-3728	241	15	j	j	NOUN
ejpam-3728	241	16	=	=	SYM
ejpam-3728	241	17	15	15	NUM
ejpam-3728	241	18	,	,	PUNCT
ejpam-3728	241	19	35	35	NUM
ejpam-3728	241	20	,	,	PUNCT
ejpam-3728	241	21	50	50	NUM
ejpam-3728	241	22	,	,	PUNCT
ejpam-3728	241	23	using	use	VERB
ejpam-3728	241	24	these	these	DET
ejpam-3728	241	25	values	value	NOUN
ejpam-3728	241	26	,	,	PUNCT
ejpam-3728	241	27	the	the	DET
ejpam-3728	241	28	truncation	truncation	NOUN
ejpam-3728	241	29	is	be	AUX
ejpam-3728	241	30	determined	determine	VERB
ejpam-3728	241	31	.	.	PUNCT
ejpam-3728	242	1	so	so	ADV
ejpam-3728	242	2	one	one	PRON
ejpam-3728	242	3	can	can	AUX
ejpam-3728	242	4	observe	observe	VERB
ejpam-3728	242	5	that	that	SCONJ
ejpam-3728	242	6	at	at	ADP
ejpam-3728	242	7	a	a	DET
ejpam-3728	242	8	some	some	DET
ejpam-3728	242	9	stage	stage	NOUN
ejpam-3728	242	10	,	,	PUNCT
ejpam-3728	242	11	its	its	PRON
ejpam-3728	242	12	going	go	VERB
ejpam-3728	242	13	good	good	ADJ
ejpam-3728	242	14	but	but	CCONJ
ejpam-3728	242	15	not	not	PART
ejpam-3728	242	16	at	at	ADV
ejpam-3728	242	17	all	all	ADV
ejpam-3728	242	18	.	.	PUNCT
ejpam-3728	243	1	g	g	NOUN
ejpam-3728	243	2	15	15	NUM
ejpam-3728	243	3	35	35	NUM
ejpam-3728	243	4	50	50	NUM
ejpam-3728	243	5	0.0	0.0	NUM
ejpam-3728	243	6	0.5	0.5	NUM
ejpam-3728	243	7	1.0	1.0	NUM
ejpam-3728	243	8	1.5	1.5	NUM
ejpam-3728	243	9	2.0	2.0	NUM
ejpam-3728	243	10	2.5	2.5	NUM
ejpam-3728	243	11	-0.010	-0.010	X
ejpam-3728	243	12	-0.008	-0.008	X
ejpam-3728	243	13	-0.006	-0.006	X
ejpam-3728	243	14	-0.004	-0.004	PUNCT
ejpam-3728	243	15	-0.002	-0.002	PUNCT
ejpam-3728	243	16	0.000	0.000	NUM
ejpam-3728	243	17	figure	figure	NOUN
ejpam-3728	243	18	1	1	NUM
ejpam-3728	243	19	:	:	PUNCT
ejpam-3728	243	20	the	the	DET
ejpam-3728	243	21	convergence	convergence	NOUN
ejpam-3728	243	22	of	of	ADP
ejpam-3728	243	23	the	the	DET
ejpam-3728	243	24	operators	operator	NOUN
ejpam-3728	243	25	s∗n(g;x	s∗n(g;x	PART
ejpam-3728	243	26	)	)	PUNCT
ejpam-3728	243	27	to	to	ADP
ejpam-3728	243	28	the	the	DET
ejpam-3728	243	29	function	function	NOUN
ejpam-3728	243	30	g(x)(blue	g(x)(blue	NOUN
ejpam-3728	243	31	)	)	PUNCT
ejpam-3728	243	32	.	.	PUNCT
ejpam-3728	244	1	now	now	ADV
ejpam-3728	244	2	,	,	PUNCT
ejpam-3728	244	3	we	we	PRON
ejpam-3728	244	4	determine	determine	VERB
ejpam-3728	244	5	the	the	DET
ejpam-3728	244	6	convergence	convergence	NOUN
ejpam-3728	244	7	of	of	ADP
ejpam-3728	244	8	the	the	DET
ejpam-3728	244	9	operators	operator	NOUN
ejpam-3728	244	10	to	to	ADP
ejpam-3728	244	11	the	the	DET
ejpam-3728	244	12	function	function	NOUN
ejpam-3728	244	13	by	by	ADP
ejpam-3728	244	14	considering	consider	VERB
ejpam-3728	244	15	the	the	DET
ejpam-3728	244	16	different	different	ADJ
ejpam-3728	244	17	sequences	sequence	NOUN
ejpam-3728	244	18	for	for	ADP
ejpam-3728	244	19	the	the	DET
ejpam-3728	244	20	operators	operator	NOUN
ejpam-3728	244	21	and	and	CCONJ
ejpam-3728	244	22	then	then	ADV
ejpam-3728	244	23	we	we	PRON
ejpam-3728	244	24	see	see	VERB
ejpam-3728	244	25	that	that	SCONJ
ejpam-3728	244	26	the	the	DET
ejpam-3728	244	27	variation	variation	NOUN
ejpam-3728	244	28	of	of	ADP
ejpam-3728	244	29	the	the	DET
ejpam-3728	244	30	convergence	convergence	NOUN
ejpam-3728	244	31	to	to	ADP
ejpam-3728	244	32	the	the	DET
ejpam-3728	244	33	function	function	NOUN
ejpam-3728	244	34	is	be	AUX
ejpam-3728	244	35	changed	change	VERB
ejpam-3728	244	36	.	.	PUNCT
ejpam-3728	245	1	r.	r.	PROPN
ejpam-3728	245	2	yadav	yadav	PROPN
ejpam-3728	245	3	,	,	PUNCT
ejpam-3728	245	4	r.	r.	PROPN
ejpam-3728	245	5	meher	meher	PROPN
ejpam-3728	245	6	,	,	PUNCT
ejpam-3728	245	7	v.	v.	ADP
ejpam-3728	245	8	n.	n.	PROPN
ejpam-3728	245	9	mishra	mishra	PROPN
ejpam-3728	245	10	/	/	SYM
ejpam-3728	245	11	eur	eur	PROPN
ejpam-3728	245	12	.	.	PUNCT
ejpam-3728	246	1	j.	j.	PROPN
ejpam-3728	246	2	pure	pure	PROPN
ejpam-3728	246	3	appl	appl	PROPN
ejpam-3728	246	4	.	.	PROPN
ejpam-3728	246	5	math	math	PROPN
ejpam-3728	246	6	,	,	PUNCT
ejpam-3728	246	7	13	13	NUM
ejpam-3728	246	8	(	(	PUNCT
ejpam-3728	246	9	5	5	NUM
ejpam-3728	246	10	)	)	PUNCT
ejpam-3728	246	11	(	(	PUNCT
ejpam-3728	246	12	2020	2020	NUM
ejpam-3728	246	13	)	)	PUNCT
ejpam-3728	246	14	,	,	PUNCT
ejpam-3728	246	15	1306	1306	NUM
ejpam-3728	246	16	-	-	SYM
ejpam-3728	246	17	1324	1324	NUM
ejpam-3728	246	18	1319	1319	NUM
ejpam-3728	246	19	g	g	PROPN
ejpam-3728	246	20	15	15	NUM
ejpam-3728	246	21	35	35	NUM
ejpam-3728	246	22	50	50	NUM
ejpam-3728	246	23	0.0	0.0	NUM
ejpam-3728	246	24	0.5	0.5	NUM
ejpam-3728	246	25	1.0	1.0	NUM
ejpam-3728	246	26	1.5	1.5	NUM
ejpam-3728	246	27	2.0	2.0	NUM
ejpam-3728	246	28	2.5	2.5	NUM
ejpam-3728	246	29	-0.010	-0.010	X
ejpam-3728	246	30	-0.008	-0.008	X
ejpam-3728	246	31	-0.006	-0.006	X
ejpam-3728	246	32	-0.004	-0.004	PUNCT
ejpam-3728	246	33	-0.002	-0.002	PUNCT
ejpam-3728	246	34	0.000	0.000	NUM
ejpam-3728	246	35	figure	figure	NOUN
ejpam-3728	246	36	2	2	NUM
ejpam-3728	246	37	:	:	PUNCT
ejpam-3728	246	38	the	the	DET
ejpam-3728	246	39	convergence	convergence	NOUN
ejpam-3728	246	40	of	of	ADP
ejpam-3728	246	41	the	the	DET
ejpam-3728	246	42	operators	operator	NOUN
ejpam-3728	246	43	s∗n(g;x	s∗n(g;x	PART
ejpam-3728	246	44	)	)	PUNCT
ejpam-3728	246	45	to	to	ADP
ejpam-3728	246	46	the	the	DET
ejpam-3728	246	47	function	function	NOUN
ejpam-3728	246	48	g(x)(blue	g(x)(blue	NOUN
ejpam-3728	246	49	)	)	PUNCT
ejpam-3728	246	50	.	.	PUNCT
ejpam-3728	247	1	example	example	NOUN
ejpam-3728	248	1	2	2	NUM
ejpam-3728	248	2	.	.	PUNCT
ejpam-3728	248	3	let	let	VERB
ejpam-3728	248	4	the	the	DET
ejpam-3728	248	5	function	function	NOUN
ejpam-3728	248	6	g(x	g(x	NOUN
ejpam-3728	248	7	)	)	PUNCT
ejpam-3728	249	1	=	=	SYM
ejpam-3728	249	2	x2e2x(black	x2e2x(black	PROPN
ejpam-3728	249	3	)	)	PUNCT
ejpam-3728	249	4	,	,	PUNCT
ejpam-3728	249	5	for	for	SCONJ
ejpam-3728	249	6	all	all	PRON
ejpam-3728	249	7	0	0	NUM
ejpam-3728	249	8	≤	≤	NUM
ejpam-3728	249	9	x	x	SYM
ejpam-3728	249	10	≤	≤	NUM
ejpam-3728	249	11	2.5	2.5	NUM
ejpam-3728	249	12	.	.	PUNCT
ejpam-3728	250	1	here	here	ADV
ejpam-3728	250	2	,	,	PUNCT
ejpam-3728	250	3	we	we	PRON
ejpam-3728	250	4	consider	consider	VERB
ejpam-3728	250	5	un	un	PROPN
ejpam-3728	250	6	=	=	PROPN
ejpam-3728	250	7	n	n	PROPN
ejpam-3728	250	8	and	and	CCONJ
ejpam-3728	250	9	choosing	choose	VERB
ejpam-3728	250	10	the	the	DET
ejpam-3728	250	11	value	value	NOUN
ejpam-3728	250	12	of	of	ADP
ejpam-3728	250	13	n	n	NOUN
ejpam-3728	250	14	=	=	NUM
ejpam-3728	250	15	10	10	NUM
ejpam-3728	250	16	,	,	PUNCT
ejpam-3728	250	17	50	50	NUM
ejpam-3728	250	18	,	,	PUNCT
ejpam-3728	250	19	100	100	NUM
ejpam-3728	250	20	,	,	PUNCT
ejpam-3728	250	21	200	200	NUM
ejpam-3728	250	22	,	,	PUNCT
ejpam-3728	250	23	250	250	NUM
ejpam-3728	250	24	,	,	PUNCT
ejpam-3728	250	25	500	500	NUM
ejpam-3728	250	26	,	,	PUNCT
ejpam-3728	250	27	1000	1000	NUM
ejpam-3728	250	28	,	,	PUNCT
ejpam-3728	250	29	for	for	ADP
ejpam-3728	250	30	which	which	PRON
ejpam-3728	250	31	the	the	DET
ejpam-3728	250	32	operators	operator	NOUN
ejpam-3728	250	33	’s	’s	PART
ejpam-3728	250	34	curve	curve	NOUN
ejpam-3728	250	35	is	be	AUX
ejpam-3728	250	36	red	red	ADJ
ejpam-3728	250	37	for	for	ADP
ejpam-3728	250	38	the	the	DET
ejpam-3728	250	39	all	all	DET
ejpam-3728	250	40	values	value	NOUN
ejpam-3728	250	41	of	of	ADP
ejpam-3728	250	42	n.	n.	NOUN
ejpam-3728	250	43	then	then	ADV
ejpam-3728	250	44	,	,	PUNCT
ejpam-3728	250	45	we	we	PRON
ejpam-3728	250	46	can	can	AUX
ejpam-3728	250	47	observe	observe	VERB
ejpam-3728	250	48	the	the	DET
ejpam-3728	250	49	error	error	NOUN
ejpam-3728	250	50	estimations	estimation	NOUN
ejpam-3728	250	51	by	by	ADP
ejpam-3728	250	52	figure	figure	NOUN
ejpam-3728	250	53	3	3	NUM
ejpam-3728	250	54	as	as	ADP
ejpam-3728	250	55	well	well	ADV
ejpam-3728	250	56	table	table	NOUN
ejpam-3728	250	57	1	1	NUM
ejpam-3728	250	58	at	at	ADP
ejpam-3728	250	59	different	different	ADJ
ejpam-3728	250	60	points	point	NOUN
ejpam-3728	250	61	of	of	ADP
ejpam-3728	250	62	x	x	X
ejpam-3728	250	63	,	,	PUNCT
ejpam-3728	250	64	which	which	PRON
ejpam-3728	250	65	is	be	AUX
ejpam-3728	250	66	going	go	VERB
ejpam-3728	250	67	to	to	PART
ejpam-3728	250	68	be	be	AUX
ejpam-3728	250	69	better	well	ADJ
ejpam-3728	250	70	as	as	SCONJ
ejpam-3728	250	71	the	the	DET
ejpam-3728	250	72	value	value	NOUN
ejpam-3728	250	73	of	of	ADP
ejpam-3728	250	74	n	n	NUM
ejpam-3728	250	75	is	be	AUX
ejpam-3728	250	76	increased	increase	VERB
ejpam-3728	250	77	.	.	PUNCT
ejpam-3728	251	1	figure	figure	VERB
ejpam-3728	251	2	3	3	NUM
ejpam-3728	251	3	:	:	PUNCT
ejpam-3728	251	4	the	the	DET
ejpam-3728	251	5	convergence	convergence	NOUN
ejpam-3728	251	6	of	of	ADP
ejpam-3728	251	7	the	the	DET
ejpam-3728	251	8	operators	operator	NOUN
ejpam-3728	251	9	s∗n(g;x	s∗n(g;x	PART
ejpam-3728	251	10	)	)	PUNCT
ejpam-3728	251	11	to	to	ADP
ejpam-3728	251	12	the	the	DET
ejpam-3728	251	13	function	function	NOUN
ejpam-3728	251	14	g(x	g(x	NOUN
ejpam-3728	251	15	)	)	PUNCT
ejpam-3728	251	16	.	.	PUNCT
ejpam-3728	252	1	table	table	NOUN
ejpam-3728	252	2	1	1	NUM
ejpam-3728	252	3	:	:	PUNCT
ejpam-3728	252	4	convergence	convergence	NOUN
ejpam-3728	252	5	estimations	estimation	NOUN
ejpam-3728	252	6	of	of	ADP
ejpam-3728	252	7	the	the	DET
ejpam-3728	252	8	operators	operator	NOUN
ejpam-3728	252	9	b∗n(g;x	b∗n(g;x	PROPN
ejpam-3728	252	10	)	)	PUNCT
ejpam-3728	252	11	to	to	ADP
ejpam-3728	252	12	the	the	DET
ejpam-3728	252	13	function	function	NOUN
ejpam-3728	252	14	g(x	g(x	NOUN
ejpam-3728	252	15	)	)	PUNCT
ejpam-3728	253	1	x	x	SYM
ejpam-3728	253	2	↓	↓	PROPN
ejpam-3728	253	3	,	,	PUNCT
ejpam-3728	253	4	un	un	PROPN
ejpam-3728	253	5	=	=	PROPN
ejpam-3728	253	6	n→	n→	PROPN
ejpam-3728	253	7	at	at	ADP
ejpam-3728	253	8	n=10	n=10	PRON
ejpam-3728	253	9	at	at	ADP
ejpam-3728	253	10	n=50	n=50	ADJ
ejpam-3728	253	11	at	at	ADP
ejpam-3728	253	12	n=100	n=100	NUM
ejpam-3728	253	13	at	at	ADP
ejpam-3728	253	14	n=200	n=200	PROPN
ejpam-3728	253	15	at	at	ADP
ejpam-3728	253	16	n=250	n=250	PROPN
ejpam-3728	253	17	at	at	ADP
ejpam-3728	253	18	n=500	n=500	NUM
ejpam-3728	253	19	at	at	ADP
ejpam-3728	253	20	n=1000	n=1000	PROPN
ejpam-3728	253	21	0.1	0.1	NUM
ejpam-3728	253	22	0.202522	0.202522	NUM
ejpam-3728	253	23	0.0156053	0.0156053	NUM
ejpam-3728	253	24	0.0069326	0.0069326	NUM
ejpam-3728	254	1	0.00326665	0.00326665	NUM
ejpam-3728	254	2	0.00258244	0.00258244	NUM
ejpam-3728	254	3	0.00126086	0.00126086	NUM
ejpam-3728	254	4	0.000622967	0.000622967	NUM
ejpam-3728	254	5	0.5	0.5	NUM
ejpam-3728	254	6	3.82396	3.82396	NUM
ejpam-3728	254	7	0.325365	0.325365	NUM
ejpam-3728	254	8	0.148479	0.148479	NUM
ejpam-3728	254	9	0.0710035	0.0710035	NUM
ejpam-3728	254	10	0.0563036	0.0563036	NUM
ejpam-3728	254	11	0.0276615	0.0276615	NUM
ejpam-3728	254	12	0.0137104	0.0137104	NUM
ejpam-3728	254	13	0.9	0.9	NUM
ejpam-3728	254	14	27.2622	27.2622	NUM
ejpam-3728	254	15	2.13631	2.13631	NUM
ejpam-3728	254	16	0.969982	0.969982	NUM
ejpam-3728	254	17	0.462837	0.462837	NUM
ejpam-3728	255	1	0.366865	0.366865	NUM
ejpam-3728	255	2	0.180094	0.180094	NUM
ejpam-3728	255	3	0.0892291	0.0892291	NUM
ejpam-3728	255	4	1.0	1.0	NUM
ejpam-3728	255	5	42.1618	42.1618	NUM
ejpam-3728	255	6	3.22439	3.22439	NUM
ejpam-3728	255	7	1.46137	1.46137	NUM
ejpam-3728	255	8	0.696735	0.696735	NUM
ejpam-3728	255	9	0.552174	0.552174	NUM
ejpam-3728	255	10	0.270979	0.270979	NUM
ejpam-3728	255	11	0.134238	0.134238	NUM
ejpam-3728	255	12	1.5	1.5	NUM
ejpam-3728	255	13	310.724	310.724	NUM
ejpam-3728	255	14	20.8491	20.8491	NUM
ejpam-3728	255	15	9.3538	9.3538	NUM
ejpam-3728	255	16	4.43876	4.43876	NUM
ejpam-3728	255	17	3.51461	3.51461	NUM
ejpam-3728	255	18	1.72172	1.72172	NUM
ejpam-3728	255	19	0.852162	0.852162	NUM
ejpam-3728	255	20	2.0	2.0	NUM
ejpam-3728	255	21	1888.96	1888.96	NUM
ejpam-3728	255	22	110.236	110.236	NUM
ejpam-3728	255	23	48.9145	48.9145	NUM
ejpam-3728	255	24	23.0939	23.0939	NUM
ejpam-3728	255	25	18.2677	18.2677	NUM
ejpam-3728	255	26	8.93151	8.93151	NUM
ejpam-3728	255	27	4.4164	4.4164	NUM
ejpam-3728	255	28	2.5	2.5	NUM
ejpam-3728	255	29	10237.6	10237.6	NUM
ejpam-3728	255	30	516.742	516.742	NUM
ejpam-3728	255	31	226.689	226.689	NUM
ejpam-3728	255	32	106.464	106.464	NUM
ejpam-3728	255	33	84.1292	84.1292	NUM
ejpam-3728	255	34	41.0503	41.0503	NUM
ejpam-3728	255	35	20.2783	20.2783	NUM
ejpam-3728	255	36	r.	r.	PROPN
ejpam-3728	255	37	yadav	yadav	PROPN
ejpam-3728	255	38	,	,	PUNCT
ejpam-3728	255	39	r.	r.	PROPN
ejpam-3728	255	40	meher	meher	PROPN
ejpam-3728	255	41	,	,	PUNCT
ejpam-3728	255	42	v.	v.	ADP
ejpam-3728	255	43	n.	n.	PROPN
ejpam-3728	255	44	mishra	mishra	PROPN
ejpam-3728	255	45	/	/	SYM
ejpam-3728	255	46	eur	eur	PROPN
ejpam-3728	255	47	.	.	PUNCT
ejpam-3728	256	1	j.	j.	PROPN
ejpam-3728	256	2	pure	pure	PROPN
ejpam-3728	256	3	appl	appl	PROPN
ejpam-3728	256	4	.	.	PROPN
ejpam-3728	256	5	math	math	PROPN
ejpam-3728	256	6	,	,	PUNCT
ejpam-3728	256	7	13	13	NUM
ejpam-3728	256	8	(	(	PUNCT
ejpam-3728	256	9	5	5	NUM
ejpam-3728	256	10	)	)	PUNCT
ejpam-3728	256	11	(	(	PUNCT
ejpam-3728	256	12	2020	2020	NUM
ejpam-3728	256	13	)	)	PUNCT
ejpam-3728	256	14	,	,	PUNCT
ejpam-3728	256	15	1306	1306	NUM
ejpam-3728	256	16	-	-	SYM
ejpam-3728	256	17	1324	1324	NUM
ejpam-3728	256	18	1320	1320	NUM
ejpam-3728	256	19	example	example	NOUN
ejpam-3728	256	20	3	3	X
ejpam-3728	256	21	.	.	X
ejpam-3728	257	1	let	let	VERB
ejpam-3728	257	2	for	for	ADP
ejpam-3728	257	3	the	the	DET
ejpam-3728	257	4	same	same	ADJ
ejpam-3728	257	5	function	function	NOUN
ejpam-3728	257	6	g(x	g(x	NOUN
ejpam-3728	257	7	)	)	PUNCT
ejpam-3728	258	1	=	=	SYM
ejpam-3728	258	2	x2e2x(black	x2e2x(black	PROPN
ejpam-3728	258	3	)	)	PUNCT
ejpam-3728	258	4	,	,	PUNCT
ejpam-3728	258	5	for	for	SCONJ
ejpam-3728	258	6	all	all	PRON
ejpam-3728	258	7	0	0	NUM
ejpam-3728	258	8	≤	≤	NUM
ejpam-3728	258	9	x	x	SYM
ejpam-3728	258	10	≤	≤	NUM
ejpam-3728	258	11	2.5	2.5	NUM
ejpam-3728	258	12	.	.	PUNCT
ejpam-3728	259	1	here	here	ADV
ejpam-3728	259	2	,	,	PUNCT
ejpam-3728	259	3	we	we	PRON
ejpam-3728	259	4	consider	consider	VERB
ejpam-3728	259	5	un	un	PROPN
ejpam-3728	259	6	=	=	PROPN
ejpam-3728	259	7	n	n	PROPN
ejpam-3728	259	8	3	3	NUM
ejpam-3728	259	9	2	2	NUM
ejpam-3728	259	10	and	and	CCONJ
ejpam-3728	259	11	choosing	choose	VERB
ejpam-3728	259	12	the	the	DET
ejpam-3728	259	13	value	value	NOUN
ejpam-3728	259	14	of	of	ADP
ejpam-3728	259	15	n	n	NOUN
ejpam-3728	259	16	=	=	NUM
ejpam-3728	259	17	10	10	NUM
ejpam-3728	259	18	,	,	PUNCT
ejpam-3728	259	19	50	50	NUM
ejpam-3728	259	20	,	,	PUNCT
ejpam-3728	259	21	100	100	NUM
ejpam-3728	259	22	,	,	PUNCT
ejpam-3728	259	23	200	200	NUM
ejpam-3728	259	24	,	,	PUNCT
ejpam-3728	259	25	250	250	NUM
ejpam-3728	259	26	,	,	PUNCT
ejpam-3728	259	27	500	500	NUM
ejpam-3728	259	28	,	,	PUNCT
ejpam-3728	259	29	1000	1000	NUM
ejpam-3728	259	30	,	,	PUNCT
ejpam-3728	259	31	the	the	DET
ejpam-3728	259	32	curves	curve	NOUN
ejpam-3728	259	33	of	of	ADP
ejpam-3728	259	34	the	the	DET
ejpam-3728	259	35	operators	operator	NOUN
ejpam-3728	259	36	(	(	PUNCT
ejpam-3728	259	37	3	3	X
ejpam-3728	259	38	)	)	PUNCT
ejpam-3728	259	39	represent	represent	VERB
ejpam-3728	259	40	green	green	ADJ
ejpam-3728	259	41	color	color	NOUN
ejpam-3728	259	42	for	for	ADP
ejpam-3728	259	43	all	all	DET
ejpam-3728	259	44	values	value	NOUN
ejpam-3728	259	45	of	of	ADP
ejpam-3728	259	46	n	n	DET
ejpam-3728	259	47	3	3	NUM
ejpam-3728	259	48	2	2	NUM
ejpam-3728	259	49	for	for	ADP
ejpam-3728	259	50	the	the	DET
ejpam-3728	259	51	operators	operator	NOUN
ejpam-3728	259	52	(	(	PUNCT
ejpam-3728	259	53	3	3	NUM
ejpam-3728	259	54	)	)	PUNCT
ejpam-3728	259	55	.	.	PUNCT
ejpam-3728	260	1	hence	hence	ADV
ejpam-3728	260	2	,	,	PUNCT
ejpam-3728	260	3	we	we	PRON
ejpam-3728	260	4	can	can	AUX
ejpam-3728	260	5	observe	observe	VERB
ejpam-3728	260	6	the	the	DET
ejpam-3728	260	7	error	error	NOUN
ejpam-3728	260	8	estimations	estimation	NOUN
ejpam-3728	260	9	by	by	ADP
ejpam-3728	260	10	figure	figure	NOUN
ejpam-3728	260	11	4	4	NUM
ejpam-3728	260	12	as	as	ADV
ejpam-3728	260	13	well	well	ADV
ejpam-3728	260	14	table	table	NOUN
ejpam-3728	260	15	2	2	NUM
ejpam-3728	260	16	at	at	ADP
ejpam-3728	260	17	the	the	DET
ejpam-3728	260	18	different	different	ADJ
ejpam-3728	260	19	points	point	NOUN
ejpam-3728	260	20	of	of	ADP
ejpam-3728	260	21	x.	x.	NOUN
ejpam-3728	260	22	figure	figure	NOUN
ejpam-3728	260	23	4	4	NUM
ejpam-3728	260	24	:	:	PUNCT
ejpam-3728	260	25	the	the	DET
ejpam-3728	260	26	convergence	convergence	NOUN
ejpam-3728	260	27	of	of	ADP
ejpam-3728	260	28	the	the	DET
ejpam-3728	260	29	operators	operator	NOUN
ejpam-3728	260	30	s∗n(g;x	s∗n(g;x	PART
ejpam-3728	260	31	)	)	PUNCT
ejpam-3728	260	32	to	to	ADP
ejpam-3728	260	33	the	the	DET
ejpam-3728	260	34	function	function	NOUN
ejpam-3728	260	35	g(x	g(x	NOUN
ejpam-3728	260	36	)	)	PUNCT
ejpam-3728	260	37	.	.	PUNCT
ejpam-3728	261	1	table	table	NOUN
ejpam-3728	261	2	2	2	NUM
ejpam-3728	261	3	:	:	PUNCT
ejpam-3728	262	1	convergence	convergence	NOUN
ejpam-3728	262	2	estimations	estimation	NOUN
ejpam-3728	262	3	of	of	ADP
ejpam-3728	262	4	the	the	DET
ejpam-3728	262	5	operators	operator	NOUN
ejpam-3728	262	6	b∗n(g;x	b∗n(g;x	PROPN
ejpam-3728	262	7	)	)	PUNCT
ejpam-3728	262	8	to	to	ADP
ejpam-3728	262	9	the	the	DET
ejpam-3728	262	10	function	function	NOUN
ejpam-3728	262	11	g(x	g(x	NOUN
ejpam-3728	262	12	)	)	PUNCT
ejpam-3728	262	13	.	.	PUNCT
ejpam-3728	263	1	x	x	PUNCT
ejpam-3728	263	2	↓	↓	PROPN
ejpam-3728	263	3	,	,	PUNCT
ejpam-3728	263	4	un	un	PROPN
ejpam-3728	263	5	=	=	PROPN
ejpam-3728	263	6	n	n	PROPN
ejpam-3728	263	7	3	3	NUM
ejpam-3728	263	8	2	2	NUM
ejpam-3728	263	9	→	→	PUNCT
ejpam-3728	263	10	at	at	ADP
ejpam-3728	263	11	n=10	n=10	NOUN
ejpam-3728	263	12	at	at	ADP
ejpam-3728	263	13	n=50	n=50	ADJ
ejpam-3728	263	14	at	at	ADP
ejpam-3728	263	15	n=100	n=100	NUM
ejpam-3728	263	16	at	at	ADP
ejpam-3728	263	17	n=200	n=200	PROPN
ejpam-3728	263	18	at	at	ADP
ejpam-3728	263	19	n=250	n=250	PROPN
ejpam-3728	263	20	at	at	ADP
ejpam-3728	263	21	n=500	n=500	NUM
ejpam-3728	263	22	0.1	0.1	NUM
ejpam-3728	263	23	0.0282979	0.0282979	NUM
ejpam-3728	263	24	0.0018008	0.0018008	NUM
ejpam-3728	263	25	0.000622967	0.000622967	NUM
ejpam-3728	263	26	0.000218562	0.000218562	NUM
ejpam-3728	263	27	0.000156203	0.000156203	NUM
ejpam-3728	263	28	0.0000551185	0.0000551185	NUM
ejpam-3728	263	29	0.5	0.5	NUM
ejpam-3728	263	30	0.574288	0.574288	NUM
ejpam-3728	263	31	0.0394044	0.0394044	NUM
ejpam-3728	263	32	0.0137104	0.0137104	NUM
ejpam-3728	263	33	0.0048201	0.0048201	NUM
ejpam-3728	263	34	0.00344596	0.00344596	NUM
ejpam-3728	263	35	0.0012166	0.0012166	NUM
ejpam-3728	263	36	0.9	0.9	NUM
ejpam-3728	263	37	3.79761	3.79761	NUM
ejpam-3728	263	38	0.256632	0.256632	NUM
ejpam-3728	263	39	0.0892291	0.0892291	NUM
ejpam-3728	263	40	0.0313623	0.0313623	NUM
ejpam-3728	263	41	0.0224205	0.0224205	NUM
ejpam-3728	263	42	0.00791509	0.00791509	NUM
ejpam-3728	263	43	1.0	1.0	NUM
ejpam-3728	263	44	5.74555	5.74555	NUM
ejpam-3728	263	45	0.386191	0.386191	NUM
ejpam-3728	263	46	0.134238	0.134238	NUM
ejpam-3728	263	47	0.0471774	0.0471774	NUM
ejpam-3728	263	48	0.033726	0.033726	NUM
ejpam-3728	263	49	0.011906	0.011906	NUM
ejpam-3728	263	50	1.5	1.5	NUM
ejpam-3728	263	51	37.6466	37.6466	NUM
ejpam-3728	263	52	2.45554	2.45554	NUM
ejpam-3728	263	53	0.852162	0.852162	NUM
ejpam-3728	263	54	0.299321	0.299321	NUM
ejpam-3728	263	55	0.213959	0.213959	NUM
ejpam-3728	263	56	0.0755213	0.0755213	NUM
ejpam-3728	263	57	2.0	2.0	NUM
ejpam-3728	263	58	201.92	201.92	NUM
ejpam-3728	263	59	12.7484	12.7484	NUM
ejpam-3728	263	60	4.4164	4.4164	NUM
ejpam-3728	263	61	1.55031	1.55031	NUM
ejpam-3728	263	62	1.10808	1.10808	NUM
ejpam-3728	263	63	0.391058	0.391058	NUM
ejpam-3728	263	64	2.5	2.5	NUM
ejpam-3728	263	65	960.667	960.667	NUM
ejpam-3728	263	66	58.6418	58.6418	NUM
ejpam-3728	263	67	20.2783	20.2783	NUM
ejpam-3728	264	1	7.11386	7.11386	NUM
ejpam-3728	264	2	5.08411	5.08411	NUM
ejpam-3728	264	3	1.79398	1.79398	NUM
ejpam-3728	264	4	x	x	SYM
ejpam-3728	264	5	↓	↓	PROPN
ejpam-3728	264	6	,	,	PUNCT
ejpam-3728	264	7	un	un	PROPN
ejpam-3728	264	8	=	=	PROPN
ejpam-3728	264	9	n	n	PROPN
ejpam-3728	264	10	3	3	NUM
ejpam-3728	264	11	2	2	NUM
ejpam-3728	264	12	→	→	PUNCT
ejpam-3728	264	13	at	at	ADP
ejpam-3728	264	14	n=1000	n=1000	PROPN
ejpam-3728	264	15	0.1	0.1	NUM
ejpam-3728	264	16	0.0000194739	0.0000194739	NUM
ejpam-3728	264	17	0.5	0.5	NUM
ejpam-3728	264	18	0.000429916	0.000429916	NUM
ejpam-3728	264	19	0.9	0.9	NUM
ejpam-3728	264	20	0.00279694	0.00279694	NUM
ejpam-3728	264	21	1.0	1.0	NUM
ejpam-3728	264	22	0.00420715	0.00420715	NUM
ejpam-3728	264	23	1.5	1.5	NUM
ejpam-3728	264	24	0.0266852	0.0266852	NUM
ejpam-3728	264	25	2.0	2.0	NUM
ejpam-3728	264	26	0.138172	0.138172	NUM
ejpam-3728	264	27	2.5	2.5	NUM
ejpam-3728	264	28	0.633827	0.633827	NUM
ejpam-3728	264	29	example	example	NOUN
ejpam-3728	264	30	4	4	X
ejpam-3728	264	31	.	.	PUNCT
ejpam-3728	264	32	further	far	ADV
ejpam-3728	264	33	for	for	ADP
ejpam-3728	264	34	the	the	DET
ejpam-3728	264	35	function	function	NOUN
ejpam-3728	264	36	g(x	g(x	NOUN
ejpam-3728	264	37	)	)	PUNCT
ejpam-3728	264	38	=	=	SYM
ejpam-3728	264	39	x2e2x(black	x2e2x(black	PROPN
ejpam-3728	264	40	)	)	PUNCT
ejpam-3728	264	41	,	,	PUNCT
ejpam-3728	264	42	for	for	ADP
ejpam-3728	264	43	all	all	PRON
ejpam-3728	264	44	0	0	NUM
ejpam-3728	264	45	≤	≤	NUM
ejpam-3728	264	46	x	x	SYM
ejpam-3728	264	47	≤	≤	NUM
ejpam-3728	264	48	2.5	2.5	NUM
ejpam-3728	264	49	,	,	PUNCT
ejpam-3728	264	50	one	one	PRON
ejpam-3728	264	51	can	can	AUX
ejpam-3728	264	52	see	see	VERB
ejpam-3728	264	53	the	the	DET
ejpam-3728	264	54	error	error	NOUN
ejpam-3728	264	55	estimations	estimation	NOUN
ejpam-3728	264	56	of	of	ADP
ejpam-3728	264	57	the	the	DET
ejpam-3728	264	58	operators	operator	NOUN
ejpam-3728	264	59	(	(	PUNCT
ejpam-3728	264	60	3	3	NUM
ejpam-3728	264	61	)	)	PUNCT
ejpam-3728	264	62	.	.	PUNCT
ejpam-3728	265	1	here	here	ADV
ejpam-3728	265	2	,	,	PUNCT
ejpam-3728	265	3	we	we	PRON
ejpam-3728	265	4	consider	consider	VERB
ejpam-3728	265	5	un	un	PROPN
ejpam-3728	265	6	=	=	PROPN
ejpam-3728	265	7	n2	n2	PROPN
ejpam-3728	265	8	and	and	CCONJ
ejpam-3728	265	9	choosing	choose	VERB
ejpam-3728	265	10	the	the	DET
ejpam-3728	265	11	value	value	NOUN
ejpam-3728	265	12	of	of	ADP
ejpam-3728	265	13	n	n	NOUN
ejpam-3728	265	14	=	=	NUM
ejpam-3728	265	15	10	10	NUM
ejpam-3728	265	16	,	,	PUNCT
ejpam-3728	265	17	50	50	NUM
ejpam-3728	265	18	,	,	PUNCT
ejpam-3728	265	19	100	100	NUM
ejpam-3728	265	20	,	,	PUNCT
ejpam-3728	265	21	200	200	NUM
ejpam-3728	265	22	,	,	PUNCT
ejpam-3728	265	23	250	250	NUM
ejpam-3728	265	24	,	,	PUNCT
ejpam-3728	265	25	500	500	NUM
ejpam-3728	265	26	,	,	PUNCT
ejpam-3728	265	27	1000	1000	NUM
ejpam-3728	265	28	,	,	PUNCT
ejpam-3728	265	29	the	the	DET
ejpam-3728	265	30	curves	curve	NOUN
ejpam-3728	265	31	of	of	ADP
ejpam-3728	265	32	the	the	DET
ejpam-3728	265	33	operators	operator	NOUN
ejpam-3728	265	34	(	(	PUNCT
ejpam-3728	265	35	3	3	X
ejpam-3728	265	36	)	)	PUNCT
ejpam-3728	265	37	represent	represent	VERB
ejpam-3728	265	38	magenta	magenta	NOUN
ejpam-3728	265	39	color	color	NOUN
ejpam-3728	265	40	for	for	ADP
ejpam-3728	265	41	all	all	DET
ejpam-3728	265	42	values	value	NOUN
ejpam-3728	265	43	of	of	ADP
ejpam-3728	265	44	n2	n2	NOUN
ejpam-3728	265	45	of	of	ADP
ejpam-3728	265	46	the	the	DET
ejpam-3728	265	47	operators	operator	NOUN
ejpam-3728	265	48	.	.	PUNCT
ejpam-3728	266	1	hence	hence	ADV
ejpam-3728	266	2	,	,	PUNCT
ejpam-3728	266	3	we	we	PRON
ejpam-3728	266	4	can	can	AUX
ejpam-3728	266	5	observe	observe	VERB
ejpam-3728	266	6	the	the	DET
ejpam-3728	266	7	error	error	NOUN
ejpam-3728	266	8	estimations	estimation	NOUN
ejpam-3728	266	9	by	by	ADP
ejpam-3728	266	10	figure	figure	NOUN
ejpam-3728	266	11	5	5	NUM
ejpam-3728	266	12	as	as	ADP
ejpam-3728	266	13	well	well	ADV
ejpam-3728	266	14	table	table	NOUN
ejpam-3728	266	15	3	3	NUM
ejpam-3728	266	16	at	at	ADP
ejpam-3728	266	17	different	different	ADJ
ejpam-3728	266	18	points	point	NOUN
ejpam-3728	266	19	of	of	ADP
ejpam-3728	266	20	x.	x.	NOUN
ejpam-3728	266	21	by	by	ADP
ejpam-3728	266	22	observing	observe	VERB
ejpam-3728	266	23	,	,	PUNCT
ejpam-3728	266	24	we	we	PRON
ejpam-3728	266	25	can	can	AUX
ejpam-3728	266	26	see	see	VERB
ejpam-3728	266	27	,	,	PUNCT
ejpam-3728	266	28	the	the	DET
ejpam-3728	266	29	function	function	NOUN
ejpam-3728	266	30	’s	’s	PART
ejpam-3728	266	31	curve	curve	NOUN
ejpam-3728	266	32	almost	almost	ADV
ejpam-3728	266	33	overlapped	overlap	VERB
ejpam-3728	266	34	by	by	ADP
ejpam-3728	266	35	the	the	DET
ejpam-3728	266	36	curves	curve	NOUN
ejpam-3728	266	37	of	of	ADP
ejpam-3728	266	38	the	the	DET
ejpam-3728	266	39	operators	operator	NOUN
ejpam-3728	266	40	.	.	PUNCT
ejpam-3728	267	1	r.	r.	PROPN
ejpam-3728	267	2	yadav	yadav	PROPN
ejpam-3728	267	3	,	,	PUNCT
ejpam-3728	267	4	r.	r.	PROPN
ejpam-3728	267	5	meher	meher	PROPN
ejpam-3728	267	6	,	,	PUNCT
ejpam-3728	267	7	v.	v.	ADP
ejpam-3728	267	8	n.	n.	PROPN
ejpam-3728	267	9	mishra	mishra	PROPN
ejpam-3728	267	10	/	/	SYM
ejpam-3728	267	11	eur	eur	PROPN
ejpam-3728	267	12	.	.	PUNCT
ejpam-3728	268	1	j.	j.	PROPN
ejpam-3728	268	2	pure	pure	PROPN
ejpam-3728	268	3	appl	appl	PROPN
ejpam-3728	268	4	.	.	PROPN
ejpam-3728	268	5	math	math	PROPN
ejpam-3728	268	6	,	,	PUNCT
ejpam-3728	268	7	13	13	NUM
ejpam-3728	268	8	(	(	PUNCT
ejpam-3728	268	9	5	5	NUM
ejpam-3728	268	10	)	)	PUNCT
ejpam-3728	268	11	(	(	PUNCT
ejpam-3728	268	12	2020	2020	NUM
ejpam-3728	268	13	)	)	PUNCT
ejpam-3728	268	14	,	,	PUNCT
ejpam-3728	268	15	1306	1306	NUM
ejpam-3728	268	16	-	-	SYM
ejpam-3728	268	17	1324	1324	NUM
ejpam-3728	268	18	1321	1321	NUM
ejpam-3728	268	19	figure	figure	NOUN
ejpam-3728	268	20	5	5	NUM
ejpam-3728	268	21	:	:	PUNCT
ejpam-3728	268	22	the	the	DET
ejpam-3728	268	23	convergence	convergence	NOUN
ejpam-3728	268	24	of	of	ADP
ejpam-3728	268	25	the	the	DET
ejpam-3728	268	26	operators	operator	NOUN
ejpam-3728	268	27	s∗n(g;x	s∗n(g;x	PART
ejpam-3728	268	28	)	)	PUNCT
ejpam-3728	268	29	to	to	ADP
ejpam-3728	268	30	the	the	DET
ejpam-3728	268	31	function	function	NOUN
ejpam-3728	268	32	g(x	g(x	NOUN
ejpam-3728	268	33	)	)	PUNCT
ejpam-3728	268	34	.	.	PUNCT
ejpam-3728	269	1	table	table	NOUN
ejpam-3728	269	2	3	3	NUM
ejpam-3728	269	3	:	:	PUNCT
ejpam-3728	270	1	convergence	convergence	NOUN
ejpam-3728	270	2	estimations	estimation	NOUN
ejpam-3728	270	3	of	of	ADP
ejpam-3728	270	4	the	the	DET
ejpam-3728	270	5	operators	operator	NOUN
ejpam-3728	270	6	b∗n(g;x	b∗n(g;x	PROPN
ejpam-3728	270	7	)	)	PUNCT
ejpam-3728	270	8	to	to	ADP
ejpam-3728	270	9	the	the	DET
ejpam-3728	270	10	function	function	NOUN
ejpam-3728	270	11	g(x	g(x	NOUN
ejpam-3728	270	12	)	)	PUNCT
ejpam-3728	270	13	un	un	PROPN
ejpam-3728	270	14	=	=	PROPN
ejpam-3728	270	15	n2	n2	PROPN
ejpam-3728	270	16	→	→	PUNCT
ejpam-3728	270	17	at	at	ADP
ejpam-3728	270	18	n=10	n=10	NOUN
ejpam-3728	270	19	at	at	ADP
ejpam-3728	270	20	n=50	n=50	ADJ
ejpam-3728	270	21	at	at	ADP
ejpam-3728	270	22	n=100	n=100	NUM
ejpam-3728	270	23	at	at	ADP
ejpam-3728	270	24	n=200	n=200	PROPN
ejpam-3728	270	25	at	at	ADP
ejpam-3728	270	26	n=250	n=250	PROPN
ejpam-3728	270	27	at	at	ADP
ejpam-3728	270	28	n=500	n=500	NUM
ejpam-3728	270	29	x=0.1	x=0.1	NOUN
ejpam-3728	270	30	0.0069326	0.0069326	NUM
ejpam-3728	271	1	0.000247412	0.000247412	NUM
ejpam-3728	271	2	0.0000616321	0.0000616321	NUM
ejpam-3728	271	3	0.0000153943	0.0000153943	NUM
ejpam-3728	271	4	9.85127×10−6	9.85127×10−6	NUM
ejpam-3728	271	5	2.462477×10−6	2.462477×10−6	NUM
ejpam-3728	271	6	x=0.5	x=0.5	NOUN
ejpam-3728	271	7	0.148479	0.148479	NUM
ejpam-3728	271	8	0.00545553	0.00545553	NUM
ejpam-3728	271	9	0.00136032	0.00136032	NUM
ejpam-3728	271	10	0.000339859	0.000339859	NUM
ejpam-3728	271	11	0.000217493	0.000217493	NUM
ejpam-3728	271	12	0.0000543675	0.0000543675	NUM
ejpam-3728	271	13	x=0.9	x=0.9	NOUN
ejpam-3728	272	1	0.969982	0.969982	NUM
ejpam-3728	272	2	0.0354973	0.0354973	NUM
ejpam-3728	272	3	0.00885019	0.00885019	NUM
ejpam-3728	272	4	0.00221104	0.00221104	NUM
ejpam-3728	272	5	0.00141495	0.00141495	NUM
ejpam-3728	272	6	0.000353699	0.000353699	NUM
ejpam-3728	272	7	x=1.0	x=1.0	PROPN
ejpam-3728	272	8	1.46137	1.46137	NUM
ejpam-3728	272	9	0.053398	0.053398	NUM
ejpam-3728	272	10	0.0133126	0.0133126	NOUN
ejpam-3728	272	11	0.00332584	0.00332584	NUM
ejpam-3728	272	12	0.00212836	0.00212836	NUM
ejpam-3728	272	13	0.000532032	0.000532032	NUM
ejpam-3728	272	14	x=1.5	x=1.5	NOUN
ejpam-3728	272	15	9.3538	9.3538	NUM
ejpam-3728	272	16	0.338802	0.338802	NUM
ejpam-3728	272	17	0.0844444	0.0844444	NUM
ejpam-3728	272	18	0.0210951	0.0210951	NUM
ejpam-3728	272	19	0.0134997	0.0134997	NUM
ejpam-3728	272	20	0.00337451	0.00337451	NUM
ejpam-3728	272	21	x=2.0	x=2.0	X
ejpam-3728	272	22	48.9145	48.9145	NUM
ejpam-3728	273	1	1.75487	1.75487	NUM
ejpam-3728	273	2	0.437267	0.437267	NUM
ejpam-3728	273	3	0.109226	0.109226	NUM
ejpam-3728	273	4	0.069898	0.069898	NUM
ejpam-3728	273	5	0.0174722	0.0174722	NUM
ejpam-3728	273	6	x=2.5	x=2.5	NUM
ejpam-3728	273	7	226.689	226.689	NUM
ejpam-3728	273	8	8.0529	8.0529	NUM
ejpam-3728	273	9	2.00598	2.00598	NUM
ejpam-3728	273	10	0.501045	0.501045	NUM
ejpam-3728	273	11	0.320634	0.320634	NUM
ejpam-3728	273	12	0.080147	0.080147	NUM
ejpam-3728	273	13	un	un	PROPN
ejpam-3728	273	14	=	=	PROPN
ejpam-3728	273	15	n2	n2	PROPN
ejpam-3728	273	16	→	→	PUNCT
ejpam-3728	273	17	at	at	ADP
ejpam-3728	273	18	n=1000	n=1000	PROPN
ejpam-3728	273	19	x=0.1	x=0.1	NOUN
ejpam-3728	273	20	6.15594×10−7	6.15594×10−7	NUM
ejpam-3728	273	21	x=0.5	x=0.5	NOUN
ejpam-3728	273	22	0.0000135915	0.0000135915	NUM
ejpam-3728	273	23	x=0.9	x=0.9	NOUN
ejpam-3728	273	24	0.0000884224	0.0000884224	NUM
ejpam-3728	273	25	x=1.0	x=1.0	SYM
ejpam-3728	273	26	0.000133004	0.000133004	NUM
ejpam-3728	273	27	x=1.5	x=1.5	NOUN
ejpam-3728	273	28	0.000843601	0.000843601	NUM
ejpam-3728	273	29	x=2.0	x=2.0	NOUN
ejpam-3728	273	30	0.0043679	0.0043679	NUM
ejpam-3728	273	31	x=2.5	x=2.5	NOUN
ejpam-3728	273	32	0.020036	0.020036	NUM
ejpam-3728	273	33	references	reference	NOUN
ejpam-3728	273	34	1322	1322	NUM
ejpam-3728	273	35	example	example	NOUN
ejpam-3728	273	36	5	5	NUM
ejpam-3728	273	37	.	.	PUNCT
ejpam-3728	274	1	at	at	ADP
ejpam-3728	274	2	the	the	DET
ejpam-3728	274	3	same	same	ADJ
ejpam-3728	274	4	time	time	NOUN
ejpam-3728	274	5	for	for	ADP
ejpam-3728	274	6	the	the	DET
ejpam-3728	274	7	same	same	ADJ
ejpam-3728	274	8	function	function	NOUN
ejpam-3728	274	9	g(x	g(x	NOUN
ejpam-3728	274	10	)	)	PUNCT
ejpam-3728	274	11	=	=	PUNCT
ejpam-3728	274	12	x2e2x	x2e2x	X
ejpam-3728	274	13	,	,	PUNCT
ejpam-3728	274	14	0	0	NUM
ejpam-3728	274	15	≤	≤	NUM
ejpam-3728	274	16	x	x	SYM
ejpam-3728	274	17	≤	≤	NUM
ejpam-3728	274	18	2.5	2.5	NUM
ejpam-3728	274	19	,	,	PUNCT
ejpam-3728	274	20	we	we	PRON
ejpam-3728	274	21	can	can	AUX
ejpam-3728	274	22	observe	observe	VERB
ejpam-3728	274	23	by	by	ADP
ejpam-3728	274	24	the	the	DET
ejpam-3728	274	25	given	give	VERB
ejpam-3728	274	26	figure	figure	NOUN
ejpam-3728	274	27	6	6	NUM
ejpam-3728	274	28	that	that	SCONJ
ejpam-3728	274	29	the	the	DET
ejpam-3728	274	30	accuracy	accuracy	NOUN
ejpam-3728	274	31	of	of	ADP
ejpam-3728	274	32	the	the	DET
ejpam-3728	274	33	convergence	convergence	NOUN
ejpam-3728	274	34	for	for	ADP
ejpam-3728	274	35	the	the	DET
ejpam-3728	274	36	operators	operator	NOUN
ejpam-3728	274	37	(	(	PUNCT
ejpam-3728	274	38	3	3	X
ejpam-3728	274	39	)	)	PUNCT
ejpam-3728	274	40	is	be	AUX
ejpam-3728	274	41	better	well	ADJ
ejpam-3728	274	42	when	when	SCONJ
ejpam-3728	274	43	un	un	PROPN
ejpam-3728	274	44	=	=	PROPN
ejpam-3728	274	45	n2	n2	PROPN
ejpam-3728	274	46	is	be	AUX
ejpam-3728	274	47	taken	take	VERB
ejpam-3728	274	48	rather	rather	ADV
ejpam-3728	274	49	than	than	ADP
ejpam-3728	274	50	when	when	SCONJ
ejpam-3728	274	51	we	we	PRON
ejpam-3728	274	52	choose	choose	VERB
ejpam-3728	274	53	the	the	DET
ejpam-3728	274	54	sequences	sequence	NOUN
ejpam-3728	274	55	un	un	PROPN
ejpam-3728	274	56	=	=	PROPN
ejpam-3728	274	57	n	n	PROPN
ejpam-3728	274	58	and	and	CCONJ
ejpam-3728	274	59	un	un	PROPN
ejpam-3728	274	60	=	=	PROPN
ejpam-3728	275	1	n	n	PROPN
ejpam-3728	275	2	3	3	NUM
ejpam-3728	275	3	2	2	NUM
ejpam-3728	275	4	for	for	ADP
ejpam-3728	275	5	the	the	DET
ejpam-3728	275	6	same	same	ADJ
ejpam-3728	275	7	operators	operator	NOUN
ejpam-3728	275	8	(	(	PUNCT
ejpam-3728	275	9	3	3	NUM
ejpam-3728	275	10	)	)	PUNCT
ejpam-3728	275	11	.	.	PUNCT
ejpam-3728	276	1	figure	figure	VERB
ejpam-3728	276	2	6	6	NUM
ejpam-3728	276	3	:	:	PUNCT
ejpam-3728	276	4	the	the	DET
ejpam-3728	276	5	convergence	convergence	NOUN
ejpam-3728	276	6	of	of	ADP
ejpam-3728	276	7	the	the	DET
ejpam-3728	276	8	operators	operator	NOUN
ejpam-3728	276	9	s∗n(g;x	s∗n(g;x	PART
ejpam-3728	276	10	)	)	PUNCT
ejpam-3728	276	11	to	to	ADP
ejpam-3728	276	12	the	the	DET
ejpam-3728	276	13	function	function	NOUN
ejpam-3728	276	14	g(x	g(x	NOUN
ejpam-3728	276	15	)	)	PUNCT
ejpam-3728	276	16	.	.	PUNCT
ejpam-3728	277	1	remark	remark	NOUN
ejpam-3728	277	2	:	:	PUNCT
ejpam-3728	277	3	after	after	ADP
ejpam-3728	277	4	observing	observe	VERB
ejpam-3728	277	5	by	by	ADP
ejpam-3728	277	6	all	all	DET
ejpam-3728	277	7	the	the	DET
ejpam-3728	277	8	figures	figure	NOUN
ejpam-3728	277	9	(	(	PUNCT
ejpam-3728	277	10	1)-(6	1)-(6	NUM
ejpam-3728	277	11	)	)	PUNCT
ejpam-3728	277	12	and	and	CCONJ
ejpam-3728	277	13	tables	table	NOUN
ejpam-3728	277	14	(	(	PUNCT
ejpam-3728	277	15	1)-(3	1)-(3	NUM
ejpam-3728	277	16	)	)	PUNCT
ejpam-3728	277	17	,	,	PUNCT
ejpam-3728	277	18	we	we	PRON
ejpam-3728	277	19	can	can	AUX
ejpam-3728	277	20	conclude	conclude	VERB
ejpam-3728	277	21	that	that	SCONJ
ejpam-3728	277	22	the	the	DET
ejpam-3728	277	23	better	well	ADJ
ejpam-3728	277	24	approximation	approximation	NOUN
ejpam-3728	277	25	can	can	AUX
ejpam-3728	277	26	be	be	AUX
ejpam-3728	277	27	obtained	obtain	VERB
ejpam-3728	277	28	by	by	ADP
ejpam-3728	277	29	choosing	choose	VERB
ejpam-3728	277	30	the	the	DET
ejpam-3728	277	31	appropriate	appropriate	ADJ
ejpam-3728	277	32	sequence	sequence	NOUN
ejpam-3728	277	33	for	for	ADP
ejpam-3728	277	34	the	the	DET
ejpam-3728	277	35	operators	operator	NOUN
ejpam-3728	277	36	(	(	PUNCT
ejpam-3728	277	37	3	3	NUM
ejpam-3728	277	38	)	)	PUNCT
ejpam-3728	277	39	and	and	CCONJ
ejpam-3728	277	40	in	in	ADP
ejpam-3728	277	41	addition	addition	NOUN
ejpam-3728	277	42	,	,	PUNCT
ejpam-3728	277	43	will	will	AUX
ejpam-3728	277	44	get	get	VERB
ejpam-3728	277	45	good	good	ADJ
ejpam-3728	277	46	approximation	approximation	NOUN
ejpam-3728	277	47	by	by	ADP
ejpam-3728	277	48	the	the	DET
ejpam-3728	277	49	operators	operator	NOUN
ejpam-3728	277	50	(	(	PUNCT
ejpam-3728	277	51	3	3	X
ejpam-3728	277	52	)	)	PUNCT
ejpam-3728	277	53	for	for	ADP
ejpam-3728	277	54	the	the	DET
ejpam-3728	277	55	large	large	ADJ
ejpam-3728	277	56	value	value	NOUN
ejpam-3728	277	57	of	of	ADP
ejpam-3728	277	58	n	n	PROPN
ejpam-3728	277	59	of	of	ADP
ejpam-3728	277	60	the	the	DET
ejpam-3728	277	61	positive	positive	ADJ
ejpam-3728	277	62	and	and	CCONJ
ejpam-3728	277	63	real	real	ADJ
ejpam-3728	277	64	sequence	sequence	NOUN
ejpam-3728	277	65	.	.	PUNCT
ejpam-3728	278	1	conclusion	conclusion	NOUN
ejpam-3728	278	2	:	:	PUNCT
ejpam-3728	278	3	the	the	DET
ejpam-3728	278	4	approximation	approximation	NOUN
ejpam-3728	278	5	properties	property	NOUN
ejpam-3728	278	6	have	have	AUX
ejpam-3728	278	7	been	be	AUX
ejpam-3728	278	8	determined	determine	VERB
ejpam-3728	278	9	for	for	ADP
ejpam-3728	278	10	the	the	DET
ejpam-3728	278	11	functions	function	NOUN
ejpam-3728	278	12	belonging	belong	VERB
ejpam-3728	278	13	to	to	ADP
ejpam-3728	278	14	different	different	ADJ
ejpam-3728	278	15	spaces	space	NOUN
ejpam-3728	278	16	and	and	CCONJ
ejpam-3728	278	17	moreover	moreover	ADV
ejpam-3728	278	18	the	the	DET
ejpam-3728	278	19	rate	rate	NOUN
ejpam-3728	278	20	of	of	ADP
ejpam-3728	278	21	the	the	DET
ejpam-3728	278	22	convergence	convergence	NOUN
ejpam-3728	278	23	of	of	ADP
ejpam-3728	278	24	the	the	DET
ejpam-3728	278	25	operators	operator	NOUN
ejpam-3728	278	26	has	have	AUX
ejpam-3728	278	27	been	be	AUX
ejpam-3728	278	28	discussed	discuss	VERB
ejpam-3728	278	29	.	.	PUNCT
ejpam-3728	279	1	to	to	PART
ejpam-3728	279	2	validate	validate	VERB
ejpam-3728	279	3	the	the	DET
ejpam-3728	279	4	approximation	approximation	NOUN
ejpam-3728	279	5	results	result	NOUN
ejpam-3728	279	6	,	,	PUNCT
ejpam-3728	279	7	the	the	DET
ejpam-3728	279	8	graphical	graphical	ADJ
ejpam-3728	279	9	representation	representation	NOUN
ejpam-3728	279	10	and	and	CCONJ
ejpam-3728	279	11	numerical	numerical	ADJ
ejpam-3728	279	12	analysis	analysis	NOUN
ejpam-3728	279	13	have	have	AUX
ejpam-3728	279	14	been	be	AUX
ejpam-3728	279	15	studied	study	VERB
ejpam-3728	279	16	.	.	PUNCT
ejpam-3728	280	1	acknowledgements	acknowledgement	NOUN
ejpam-3728	280	2	the	the	DET
ejpam-3728	280	3	authors	author	NOUN
ejpam-3728	280	4	would	would	AUX
ejpam-3728	280	5	like	like	VERB
ejpam-3728	280	6	to	to	PART
ejpam-3728	280	7	express	express	VERB
ejpam-3728	280	8	their	their	PRON
ejpam-3728	280	9	deep	deep	ADJ
ejpam-3728	280	10	gratitude	gratitude	NOUN
ejpam-3728	280	11	to	to	ADP
ejpam-3728	280	12	the	the	DET
ejpam-3728	280	13	anonymous	anonymous	ADJ
ejpam-3728	280	14	learned	learn	VERB
ejpam-3728	280	15	referees	referee	NOUN
ejpam-3728	280	16	for	for	ADP
ejpam-3728	280	17	their	their	PRON
ejpam-3728	280	18	keen	keen	ADJ
ejpam-3728	280	19	reading	reading	NOUN
ejpam-3728	280	20	,	,	PUNCT
ejpam-3728	280	21	valuable	valuable	ADJ
ejpam-3728	280	22	suggestions	suggestion	NOUN
ejpam-3728	280	23	,	,	PUNCT
ejpam-3728	280	24	and	and	CCONJ
ejpam-3728	280	25	constructive	constructive	ADJ
ejpam-3728	280	26	comments	comment	NOUN
ejpam-3728	280	27	,	,	PUNCT
ejpam-3728	280	28	which	which	PRON
ejpam-3728	280	29	resulted	result	VERB
ejpam-3728	280	30	in	in	ADP
ejpam-3728	280	31	the	the	DET
ejpam-3728	280	32	subsequent	subsequent	ADJ
ejpam-3728	280	33	improvement	improvement	NOUN
ejpam-3728	280	34	of	of	ADP
ejpam-3728	280	35	this	this	DET
ejpam-3728	280	36	research	research	NOUN
ejpam-3728	280	37	article	article	NOUN
ejpam-3728	280	38	.	.	PUNCT
ejpam-3728	281	1	all	all	DET
ejpam-3728	281	2	the	the	DET
ejpam-3728	281	3	authors	author	NOUN
ejpam-3728	281	4	read	read	VERB
ejpam-3728	281	5	and	and	CCONJ
ejpam-3728	281	6	approved	approve	VERB
ejpam-3728	281	7	the	the	DET
ejpam-3728	281	8	final	final	ADJ
ejpam-3728	281	9	version	version	NOUN
ejpam-3728	281	10	of	of	ADP
ejpam-3728	281	11	the	the	DET
ejpam-3728	281	12	manuscript	manuscript	NOUN
ejpam-3728	281	13	.	.	PUNCT
ejpam-3728	282	1	the	the	DET
ejpam-3728	282	2	authors	author	NOUN
ejpam-3728	282	3	declare	declare	VERB
ejpam-3728	282	4	that	that	SCONJ
ejpam-3728	282	5	there	there	PRON
ejpam-3728	282	6	are	be	VERB
ejpam-3728	282	7	no	no	DET
ejpam-3728	282	8	conflicts	conflict	NOUN
ejpam-3728	282	9	of	of	ADP
ejpam-3728	282	10	interest	interest	NOUN
ejpam-3728	282	11	to	to	ADP
ejpam-3728	282	12	this	this	DET
ejpam-3728	282	13	work	work	NOUN
ejpam-3728	282	14	.	.	PUNCT
ejpam-3728	283	1	references	reference	NOUN
ejpam-3728	283	2	[	[	X
ejpam-3728	283	3	1	1	NUM
ejpam-3728	283	4	]	]	PUNCT
ejpam-3728	283	5	t	t	NOUN
ejpam-3728	283	6	acar	acar	VERB
ejpam-3728	283	7	and	and	CCONJ
ejpam-3728	283	8	g	g	NOUN
ejpam-3728	283	9	ulusoy	ulusoy	NOUN
ejpam-3728	283	10	.	.	PUNCT
ejpam-3728	284	1	approximation	approximation	NOUN
ejpam-3728	284	2	by	by	ADP
ejpam-3728	284	3	modified	modify	VERB
ejpam-3728	284	4	szász	szász	NOUN
ejpam-3728	284	5	-	-	PUNCT
ejpam-3728	284	6	durrmeyer	durrmeyer	NOUN
ejpam-3728	284	7	operators	operator	NOUN
ejpam-3728	284	8	.	.	PUNCT
ejpam-3728	285	1	periodica	periodica	PROPN
ejpam-3728	285	2	mathematica	mathematica	PROPN
ejpam-3728	285	3	hungarica	hungarica	PROPN
ejpam-3728	285	4	,	,	PUNCT
ejpam-3728	285	5	72(1):64–75	72(1):64–75	NUM
ejpam-3728	285	6	,	,	PUNCT
ejpam-3728	285	7	2016	2016	NUM
ejpam-3728	285	8	.	.	PUNCT
ejpam-3728	286	1	[	[	X
ejpam-3728	286	2	2	2	X
ejpam-3728	286	3	]	]	PUNCT
ejpam-3728	286	4	pl	pl	X
ejpam-3728	286	5	butzer	butzer	NOUN
ejpam-3728	286	6	.	.	PUNCT
ejpam-3728	287	1	on	on	ADP
ejpam-3728	287	2	the	the	DET
ejpam-3728	287	3	extensions	extension	NOUN
ejpam-3728	287	4	of	of	ADP
ejpam-3728	287	5	bernstein	bernstein	PROPN
ejpam-3728	287	6	polynomials	polynomial	NOUN
ejpam-3728	287	7	to	to	ADP
ejpam-3728	287	8	the	the	DET
ejpam-3728	287	9	infinite	infinite	ADJ
ejpam-3728	287	10	interval	interval	NOUN
ejpam-3728	287	11	.	.	PUNCT
ejpam-3728	288	1	proceedings	proceeding	NOUN
ejpam-3728	288	2	of	of	ADP
ejpam-3728	288	3	the	the	DET
ejpam-3728	288	4	american	american	PROPN
ejpam-3728	288	5	mathematical	mathematical	PROPN
ejpam-3728	288	6	society	society	NOUN
ejpam-3728	288	7	,	,	PUNCT
ejpam-3728	288	8	5(4):547–553	5(4):547–553	NUM
ejpam-3728	288	9	,	,	PUNCT
ejpam-3728	288	10	1954	1954	NUM
ejpam-3728	288	11	.	.	PUNCT
ejpam-3728	289	1	[	[	X
ejpam-3728	289	2	3	3	NUM
ejpam-3728	289	3	]	]	PUNCT
ejpam-3728	289	4	ar	ar	PROPN
ejpam-3728	289	5	gairola	gairola	PROPN
ejpam-3728	289	6	,	,	PUNCT
ejpam-3728	289	7	deepmala	deepmala	PROPN
ejpam-3728	289	8	,	,	PUNCT
ejpam-3728	289	9	and	and	CCONJ
ejpam-3728	289	10	ln	ln	PROPN
ejpam-3728	289	11	mishra	mishra	PROPN
ejpam-3728	289	12	.	.	PROPN
ejpam-3728	289	13	rate	rate	PROPN
ejpam-3728	289	14	of	of	ADP
ejpam-3728	289	15	approximation	approximation	NOUN
ejpam-3728	289	16	by	by	ADP
ejpam-3728	289	17	finite	finite	ADJ
ejpam-3728	289	18	iterates	iterate	NOUN
ejpam-3728	289	19	of	of	ADP
ejpam-3728	289	20	q	q	NOUN
ejpam-3728	289	21	-	-	PUNCT
ejpam-3728	289	22	durrmeyer	durrmeyer	NOUN
ejpam-3728	289	23	operators	operator	NOUN
ejpam-3728	289	24	.	.	PUNCT
ejpam-3728	290	1	proceedings	proceeding	NOUN
ejpam-3728	290	2	of	of	ADP
ejpam-3728	290	3	the	the	DET
ejpam-3728	290	4	national	national	PROPN
ejpam-3728	290	5	academy	academy	PROPN
ejpam-3728	290	6	of	of	ADP
ejpam-3728	290	7	sciences	sciences	PROPN
ejpam-3728	290	8	,	,	PUNCT
ejpam-3728	290	9	india	india	PROPN
ejpam-3728	290	10	section	section	PROPN
ejpam-3728	290	11	a	a	DET
ejpam-3728	290	12	:	:	PUNCT
ejpam-3728	290	13	physical	physical	ADJ
ejpam-3728	290	14	sciences	science	NOUN
ejpam-3728	290	15	,	,	PUNCT
ejpam-3728	290	16	86(2):229–234	86(2):229–234	NUM
ejpam-3728	290	17	,	,	PUNCT
ejpam-3728	290	18	2016	2016	NUM
ejpam-3728	290	19	.	.	PUNCT
ejpam-3728	291	1	references	reference	NOUN
ejpam-3728	291	2	1323	1323	NUM
ejpam-3728	291	3	[	[	X
ejpam-3728	291	4	4	4	NUM
ejpam-3728	291	5	]	]	PUNCT
ejpam-3728	291	6	n	n	PRON
ejpam-3728	291	7	ispir	ispir	NOUN
ejpam-3728	291	8	.	.	PUNCT
ejpam-3728	292	1	rate	rate	NOUN
ejpam-3728	292	2	of	of	ADP
ejpam-3728	292	3	convergence	convergence	NOUN
ejpam-3728	292	4	of	of	ADP
ejpam-3728	292	5	generalized	generalized	ADJ
ejpam-3728	292	6	rational	rational	ADJ
ejpam-3728	292	7	type	type	NOUN
ejpam-3728	292	8	baskakov	baskakov	PROPN
ejpam-3728	292	9	operators	operator	NOUN
ejpam-3728	292	10	.	.	PUNCT
ejpam-3728	293	1	mathematical	mathematical	ADJ
ejpam-3728	293	2	and	and	CCONJ
ejpam-3728	293	3	computer	computer	NOUN
ejpam-3728	293	4	modelling	modelling	NOUN
ejpam-3728	293	5	,	,	PUNCT
ejpam-3728	293	6	46(5	46(5	PROPN
ejpam-3728	293	7	-	-	PROPN
ejpam-3728	293	8	6):625–631	6):625–631	NUM
ejpam-3728	293	9	,	,	PUNCT
ejpam-3728	293	10	2007	2007	NUM
ejpam-3728	293	11	.	.	PUNCT
ejpam-3728	294	1	[	[	X
ejpam-3728	294	2	5	5	NUM
ejpam-3728	294	3	]	]	SYM
ejpam-3728	294	4	h	h	NOUN
ejpam-3728	294	5	karsli	karsli	ADJ
ejpam-3728	294	6	.	.	PUNCT
ejpam-3728	295	1	rate	rate	NOUN
ejpam-3728	295	2	of	of	ADP
ejpam-3728	295	3	convergence	convergence	NOUN
ejpam-3728	295	4	of	of	ADP
ejpam-3728	295	5	new	new	ADJ
ejpam-3728	295	6	gamma	gamma	NOUN
ejpam-3728	295	7	type	type	NOUN
ejpam-3728	295	8	operators	operator	NOUN
ejpam-3728	295	9	for	for	ADP
ejpam-3728	295	10	functions	function	NOUN
ejpam-3728	295	11	with	with	ADP
ejpam-3728	295	12	derivatives	derivative	NOUN
ejpam-3728	295	13	of	of	ADP
ejpam-3728	295	14	bounded	bounded	ADJ
ejpam-3728	295	15	variation	variation	NOUN
ejpam-3728	295	16	.	.	PUNCT
ejpam-3728	296	1	mathematical	mathematical	ADJ
ejpam-3728	296	2	and	and	CCONJ
ejpam-3728	296	3	computer	computer	NOUN
ejpam-3728	296	4	modelling	modelling	NOUN
ejpam-3728	296	5	,	,	PUNCT
ejpam-3728	296	6	45(5	45(5	PROPN
ejpam-3728	296	7	-	-	PUNCT
ejpam-3728	296	8	6):617	6):617	NUM
ejpam-3728	296	9	–	–	PUNCT
ejpam-3728	296	10	624	624	NUM
ejpam-3728	296	11	,	,	PUNCT
ejpam-3728	296	12	2007	2007	NUM
ejpam-3728	296	13	.	.	PUNCT
ejpam-3728	297	1	[	[	X
ejpam-3728	297	2	6	6	NUM
ejpam-3728	297	3	]	]	SYM
ejpam-3728	297	4	b	b	NOUN
ejpam-3728	297	5	lenze	lenze	NOUN
ejpam-3728	297	6	.	.	PUNCT
ejpam-3728	298	1	on	on	ADP
ejpam-3728	298	2	lipschitz	lipschitz	NOUN
ejpam-3728	298	3	-	-	PUNCT
ejpam-3728	298	4	type	type	NOUN
ejpam-3728	298	5	maximal	maximal	ADJ
ejpam-3728	298	6	functions	function	NOUN
ejpam-3728	298	7	and	and	CCONJ
ejpam-3728	298	8	their	their	PRON
ejpam-3728	298	9	smoothness	smoothness	ADJ
ejpam-3728	298	10	spaces	space	NOUN
ejpam-3728	298	11	.	.	PUNCT
ejpam-3728	299	1	in	in	ADP
ejpam-3728	299	2	indagationes	indagatione	NOUN
ejpam-3728	299	3	mathematicae	mathematicae	NOUN
ejpam-3728	299	4	(	(	PUNCT
ejpam-3728	299	5	proceedings	proceeding	NOUN
ejpam-3728	299	6	)	)	PUNCT
ejpam-3728	299	7	,	,	PUNCT
ejpam-3728	299	8	volume	volume	NOUN
ejpam-3728	299	9	91	91	NUM
ejpam-3728	299	10	,	,	PUNCT
ejpam-3728	299	11	pages	page	NOUN
ejpam-3728	299	12	53–63	53–63	NUM
ejpam-3728	299	13	.	.	PUNCT
ejpam-3728	300	1	elsevier	elsevier	NOUN
ejpam-3728	300	2	,	,	PUNCT
ejpam-3728	300	3	1988	1988	NUM
ejpam-3728	300	4	.	.	PUNCT
ejpam-3728	301	1	[	[	X
ejpam-3728	301	2	7	7	X
ejpam-3728	301	3	]	]	X
ejpam-3728	301	4	sm	sm	NOUN
ejpam-3728	301	5	mazhar	mazhar	NOUN
ejpam-3728	301	6	and	and	CCONJ
ejpam-3728	301	7	v	v	ADP
ejpam-3728	301	8	totik	totik	NOUN
ejpam-3728	301	9	.	.	PUNCT
ejpam-3728	302	1	approximation	approximation	NOUN
ejpam-3728	302	2	by	by	ADP
ejpam-3728	302	3	modified	modify	VERB
ejpam-3728	302	4	szász	szász	NOUN
ejpam-3728	302	5	-	-	NOUN
ejpam-3728	302	6	operators	operator	NOUN
ejpam-3728	302	7	.	.	PUNCT
ejpam-3728	303	1	acta	acta	PROPN
ejpam-3728	303	2	scientiarum	scientiarum	PROPN
ejpam-3728	303	3	mathematicarum	mathematicarum	PROPN
ejpam-3728	303	4	,	,	PUNCT
ejpam-3728	303	5	49(1	49(1	PROPN
ejpam-3728	303	6	-	-	SYM
ejpam-3728	303	7	4):257–269	4):257–269	NUM
ejpam-3728	303	8	,	,	PUNCT
ejpam-3728	303	9	1985	1985	NUM
ejpam-3728	303	10	.	.	PUNCT
ejpam-3728	304	1	[	[	X
ejpam-3728	304	2	8	8	NUM
ejpam-3728	304	3	]	]	X
ejpam-3728	304	4	gm	gm	PROPN
ejpam-3728	304	5	mirakjan	mirakjan	PROPN
ejpam-3728	304	6	.	.	PUNCT
ejpam-3728	305	1	approximation	approximation	NOUN
ejpam-3728	305	2	of	of	ADP
ejpam-3728	305	3	continuous	continuous	ADJ
ejpam-3728	305	4	functions	function	NOUN
ejpam-3728	305	5	with	with	ADP
ejpam-3728	305	6	the	the	DET
ejpam-3728	305	7	aid	aid	NOUN
ejpam-3728	305	8	of	of	ADP
ejpam-3728	305	9	polynomials	polynomial	NOUN
ejpam-3728	305	10	.	.	PUNCT
ejpam-3728	306	1	in	in	ADP
ejpam-3728	306	2	dokl	dokl	NOUN
ejpam-3728	306	3	.	.	PUNCT
ejpam-3728	307	1	acad	acad	PROPN
ejpam-3728	307	2	.	.	PUNCT
ejpam-3728	308	1	nauk	nauk	PROPN
ejpam-3728	308	2	sssr	sssr	PROPN
ejpam-3728	308	3	,	,	PUNCT
ejpam-3728	308	4	volume	volume	NOUN
ejpam-3728	308	5	31	31	NUM
ejpam-3728	308	6	,	,	PUNCT
ejpam-3728	308	7	pages	page	NOUN
ejpam-3728	308	8	201–205	201–205	NUM
ejpam-3728	308	9	,	,	PUNCT
ejpam-3728	308	10	1941	1941	NUM
ejpam-3728	308	11	.	.	PUNCT
ejpam-3728	309	1	[	[	X
ejpam-3728	309	2	9	9	NUM
ejpam-3728	309	3	]	]	PUNCT
ejpam-3728	309	4	vn	vn	PROPN
ejpam-3728	309	5	mishra	mishra	PROPN
ejpam-3728	309	6	and	and	CCONJ
ejpam-3728	309	7	rb	rb	PROPN
ejpam-3728	309	8	gandhi	gandhi	PROPN
ejpam-3728	309	9	.	.	PUNCT
ejpam-3728	310	1	simultaneous	simultaneous	ADJ
ejpam-3728	310	2	approximation	approximation	NOUN
ejpam-3728	310	3	by	by	ADP
ejpam-3728	310	4	szász	szász	NUM
ejpam-3728	310	5	–	–	PUNCT
ejpam-3728	310	6	mirakjan	mirakjan	ADJ
ejpam-3728	310	7	–	–	PUNCT
ejpam-3728	310	8	stancu	stancu	ADJ
ejpam-3728	310	9	–	–	PUNCT
ejpam-3728	310	10	durrmeyer	durrmeyer	NOUN
ejpam-3728	310	11	type	type	NOUN
ejpam-3728	310	12	operators	operator	NOUN
ejpam-3728	310	13	.	.	PUNCT
ejpam-3728	311	1	periodica	periodica	PROPN
ejpam-3728	311	2	mathematica	mathematica	PROPN
ejpam-3728	311	3	hungarica	hungarica	PROPN
ejpam-3728	311	4	,	,	PUNCT
ejpam-3728	311	5	74(1):118–127	74(1):118–127	PROPN
ejpam-3728	311	6	,	,	PUNCT
ejpam-3728	311	7	2017	2017	NUM
ejpam-3728	311	8	.	.	PUNCT
ejpam-3728	312	1	[	[	X
ejpam-3728	312	2	10	10	NUM
ejpam-3728	312	3	]	]	PUNCT
ejpam-3728	312	4	vn	vn	PROPN
ejpam-3728	312	5	mishra	mishra	PROPN
ejpam-3728	312	6	,	,	PUNCT
ejpam-3728	312	7	rb	rb	PROPN
ejpam-3728	312	8	gandhi	gandhi	PROPN
ejpam-3728	312	9	,	,	PUNCT
ejpam-3728	312	10	and	and	CCONJ
ejpam-3728	312	11	fa	fa	PROPN
ejpam-3728	312	12	nasaireh	nasaireh	NOUN
ejpam-3728	312	13	.	.	PUNCT
ejpam-3728	313	1	simultaneous	simultaneous	ADJ
ejpam-3728	313	2	approximation	approximation	NOUN
ejpam-3728	313	3	by	by	ADP
ejpam-3728	313	4	szász	szász	NUM
ejpam-3728	313	5	–	–	PUNCT
ejpam-3728	313	6	mirakjan	mirakjan	ADJ
ejpam-3728	313	7	–	–	PUNCT
ejpam-3728	313	8	durrmeyer	durrmeyer	NOUN
ejpam-3728	313	9	-	-	PUNCT
ejpam-3728	313	10	type	type	NOUN
ejpam-3728	313	11	operators	operator	NOUN
ejpam-3728	313	12	.	.	PUNCT
ejpam-3728	314	1	bollettino	bollettino	PROPN
ejpam-3728	314	2	dell’unione	dell’unione	PROPN
ejpam-3728	314	3	matematica	matematica	PROPN
ejpam-3728	314	4	italiana	italiana	PROPN
ejpam-3728	314	5	,	,	PUNCT
ejpam-3728	314	6	8(4):297–305	8(4):297–305	NOUN
ejpam-3728	314	7	,	,	PUNCT
ejpam-3728	314	8	2016	2016	NUM
ejpam-3728	314	9	.	.	PUNCT
ejpam-3728	315	1	[	[	X
ejpam-3728	315	2	11	11	NUM
ejpam-3728	315	3	]	]	PUNCT
ejpam-3728	315	4	vn	vn	PROPN
ejpam-3728	315	5	mishra	mishra	PROPN
ejpam-3728	315	6	,	,	PUNCT
ejpam-3728	315	7	hh	hh	PROPN
ejpam-3728	315	8	khan	khan	PROPN
ejpam-3728	315	9	,	,	PUNCT
ejpam-3728	315	10	k	k	PROPN
ejpam-3728	315	11	khatri	khatri	PROPN
ejpam-3728	315	12	,	,	PUNCT
ejpam-3728	315	13	and	and	CCONJ
ejpam-3728	315	14	ln	ln	PROPN
ejpam-3728	315	15	mishra	mishra	PROPN
ejpam-3728	315	16	.	.	PROPN
ejpam-3728	315	17	hypergeometric	hypergeometric	ADJ
ejpam-3728	315	18	representation	representation	NOUN
ejpam-3728	315	19	for	for	ADP
ejpam-3728	315	20	baskakov	baskakov	PROPN
ejpam-3728	315	21	-	-	PUNCT
ejpam-3728	315	22	durrmeyer	durrmeyer	NOUN
ejpam-3728	315	23	-	-	PUNCT
ejpam-3728	315	24	stancu	stancu	NOUN
ejpam-3728	315	25	type	type	NOUN
ejpam-3728	315	26	operators	operator	NOUN
ejpam-3728	315	27	.	.	PUNCT
ejpam-3728	316	1	bulletin	bulletin	NOUN
ejpam-3728	316	2	of	of	ADP
ejpam-3728	316	3	mathematical	mathematical	ADJ
ejpam-3728	316	4	analysis	analysis	NOUN
ejpam-3728	316	5	&	&	CCONJ
ejpam-3728	316	6	applications	application	NOUN
ejpam-3728	316	7	,	,	PUNCT
ejpam-3728	316	8	5(3	5(3	NUM
ejpam-3728	316	9	)	)	PUNCT
ejpam-3728	316	10	,	,	PUNCT
ejpam-3728	316	11	2013	2013	NUM
ejpam-3728	316	12	.	.	PUNCT
ejpam-3728	317	1	[	[	X
ejpam-3728	317	2	12	12	NUM
ejpam-3728	317	3	]	]	PUNCT
ejpam-3728	317	4	vn	vn	PROPN
ejpam-3728	317	5	mishra	mishra	PROPN
ejpam-3728	317	6	,	,	PUNCT
ejpam-3728	317	7	k	k	PROPN
ejpam-3728	317	8	khatri	khatri	PROPN
ejpam-3728	317	9	,	,	PUNCT
ejpam-3728	317	10	and	and	CCONJ
ejpam-3728	317	11	ln	ln	PROPN
ejpam-3728	317	12	mishra	mishra	PROPN
ejpam-3728	317	13	.	.	PROPN
ejpam-3728	317	14	on	on	ADP
ejpam-3728	317	15	simultaneous	simultaneous	ADJ
ejpam-3728	317	16	approximation	approximation	NOUN
ejpam-3728	317	17	for	for	ADP
ejpam-3728	317	18	baskakovdurrmeyer	baskakovdurrmeyer	NOUN
ejpam-3728	317	19	-	-	PUNCT
ejpam-3728	317	20	stancu	stancu	PROPN
ejpam-3728	317	21	type	type	NOUN
ejpam-3728	317	22	operators	operator	NOUN
ejpam-3728	317	23	.	.	PUNCT
ejpam-3728	318	1	journal	journal	NOUN
ejpam-3728	318	2	of	of	ADP
ejpam-3728	318	3	ultra	ultra	ADJ
ejpam-3728	318	4	scientist	scientist	NOUN
ejpam-3728	318	5	of	of	ADP
ejpam-3728	318	6	physical	physical	ADJ
ejpam-3728	318	7	sciences	science	NOUN
ejpam-3728	318	8	,	,	PUNCT
ejpam-3728	318	9	24(3):567–577	24(3):567–577	NUM
ejpam-3728	318	10	,	,	PUNCT
ejpam-3728	318	11	2012	2012	NUM
ejpam-3728	318	12	.	.	PUNCT
ejpam-3728	319	1	[	[	X
ejpam-3728	319	2	13	13	NUM
ejpam-3728	319	3	]	]	PUNCT
ejpam-3728	319	4	vn	vn	PROPN
ejpam-3728	319	5	mishra	mishra	PROPN
ejpam-3728	319	6	,	,	PUNCT
ejpam-3728	319	7	k	k	PROPN
ejpam-3728	319	8	khatri	khatri	PROPN
ejpam-3728	319	9	,	,	PUNCT
ejpam-3728	319	10	ln	ln	PROPN
ejpam-3728	319	11	mishra	mishra	PROPN
ejpam-3728	319	12	,	,	PUNCT
ejpam-3728	319	13	and	and	CCONJ
ejpam-3728	319	14	deepmala	deepmala	PROPN
ejpam-3728	319	15	.	.	PUNCT
ejpam-3728	319	16	inverse	inverse	NOUN
ejpam-3728	319	17	result	result	NOUN
ejpam-3728	319	18	in	in	ADP
ejpam-3728	319	19	simultaneous	simultaneous	ADJ
ejpam-3728	319	20	approximation	approximation	NOUN
ejpam-3728	319	21	by	by	ADP
ejpam-3728	319	22	baskakov	baskakov	PROPN
ejpam-3728	319	23	-	-	PUNCT
ejpam-3728	319	24	durrmeyer	durrmeyer	NOUN
ejpam-3728	319	25	-	-	PUNCT
ejpam-3728	319	26	stancu	stancu	PROPN
ejpam-3728	319	27	operators	operator	NOUN
ejpam-3728	319	28	.	.	PUNCT
ejpam-3728	320	1	journal	journal	PROPN
ejpam-3728	320	2	of	of	ADP
ejpam-3728	320	3	inequalities	inequality	NOUN
ejpam-3728	320	4	and	and	CCONJ
ejpam-3728	320	5	applications	application	NOUN
ejpam-3728	320	6	,	,	PUNCT
ejpam-3728	320	7	2013(1):586	2013(1):586	NUM
ejpam-3728	320	8	,	,	PUNCT
ejpam-3728	320	9	2013	2013	NUM
ejpam-3728	320	10	.	.	PUNCT
ejpam-3728	321	1	[	[	X
ejpam-3728	321	2	14	14	NUM
ejpam-3728	321	3	]	]	X
ejpam-3728	321	4	vn	vn	PROPN
ejpam-3728	321	5	mishra	mishra	PROPN
ejpam-3728	321	6	and	and	CCONJ
ejpam-3728	321	7	r	r	PROPN
ejpam-3728	321	8	yadav	yadav	NOUN
ejpam-3728	321	9	.	.	PUNCT
ejpam-3728	322	1	some	some	DET
ejpam-3728	322	2	estimations	estimation	NOUN
ejpam-3728	322	3	of	of	ADP
ejpam-3728	322	4	summation	summation	NOUN
ejpam-3728	322	5	-	-	PUNCT
ejpam-3728	322	6	integral	integral	ADJ
ejpam-3728	322	7	-	-	PUNCT
ejpam-3728	322	8	type	type	NOUN
ejpam-3728	322	9	operators	operator	NOUN
ejpam-3728	322	10	.	.	PUNCT
ejpam-3728	323	1	tbilisi	tbilisi	PROPN
ejpam-3728	323	2	mathematical	mathematical	PROPN
ejpam-3728	323	3	journal	journal	PROPN
ejpam-3728	323	4	,	,	PUNCT
ejpam-3728	323	5	11(3):175–191	11(3):175–191	PROPN
ejpam-3728	323	6	,	,	PUNCT
ejpam-3728	323	7	2018	2018	NUM
ejpam-3728	323	8	.	.	PUNCT
ejpam-3728	324	1	[	[	X
ejpam-3728	324	2	15	15	NUM
ejpam-3728	324	3	]	]	X
ejpam-3728	324	4	ma	ma	PROPN
ejpam-3728	324	5	özarslan	özarslan	PROPN
ejpam-3728	324	6	and	and	CCONJ
ejpam-3728	324	7	h	h	PROPN
ejpam-3728	324	8	aktuğlu	aktuğlu	PROPN
ejpam-3728	324	9	.	.	PUNCT
ejpam-3728	325	1	local	local	ADJ
ejpam-3728	325	2	approximation	approximation	NOUN
ejpam-3728	325	3	properties	property	NOUN
ejpam-3728	325	4	for	for	ADP
ejpam-3728	325	5	certain	certain	ADJ
ejpam-3728	325	6	king	king	NOUN
ejpam-3728	325	7	type	type	NOUN
ejpam-3728	325	8	operators	operator	NOUN
ejpam-3728	325	9	.	.	PUNCT
ejpam-3728	326	1	filomat	filomat	NOUN
ejpam-3728	326	2	,	,	PUNCT
ejpam-3728	326	3	27(1):173–181	27(1):173–181	NUM
ejpam-3728	326	4	,	,	PUNCT
ejpam-3728	326	5	2013	2013	NUM
ejpam-3728	326	6	.	.	PUNCT
ejpam-3728	327	1	[	[	X
ejpam-3728	327	2	16	16	NUM
ejpam-3728	327	3	]	]	X
ejpam-3728	327	4	o	o	X
ejpam-3728	327	5	szász	szász	NUM
ejpam-3728	327	6	.	.	PUNCT
ejpam-3728	327	7	generalization	generalization	NOUN
ejpam-3728	327	8	of	of	ADP
ejpam-3728	327	9	s.	s.	PROPN
ejpam-3728	327	10	bernstein	bernstein	PROPN
ejpam-3728	327	11	’s	’s	PART
ejpam-3728	327	12	polynomials	polynomial	NOUN
ejpam-3728	327	13	to	to	ADP
ejpam-3728	327	14	the	the	DET
ejpam-3728	327	15	infinite	infinite	ADJ
ejpam-3728	327	16	interval	interval	NOUN
ejpam-3728	327	17	.	.	PUNCT
ejpam-3728	328	1	j.	j.	PROPN
ejpam-3728	328	2	res	res	PROPN
ejpam-3728	328	3	.	.	PUNCT
ejpam-3728	329	1	nat	nat	PROPN
ejpam-3728	329	2	.	.	PUNCT
ejpam-3728	330	1	bur	bur	PROPN
ejpam-3728	330	2	.	.	PROPN
ejpam-3728	330	3	standards	standard	NOUN
ejpam-3728	330	4	,	,	PUNCT
ejpam-3728	330	5	45:239–245	45:239–245	PROPN
ejpam-3728	330	6	,	,	PUNCT
ejpam-3728	330	7	1950	1950	NUM
ejpam-3728	330	8	.	.	PUNCT
ejpam-3728	331	1	[	[	X
ejpam-3728	331	2	17	17	NUM
ejpam-3728	331	3	]	]	X
ejpam-3728	331	4	r	r	NOUN
ejpam-3728	331	5	yadav	yadav	NOUN
ejpam-3728	331	6	,	,	PUNCT
ejpam-3728	331	7	r	r	NOUN
ejpam-3728	331	8	meher	meher	NOUN
ejpam-3728	331	9	,	,	PUNCT
ejpam-3728	331	10	and	and	CCONJ
ejpam-3728	331	11	vn	vn	PROPN
ejpam-3728	331	12	mishra	mishra	PROPN
ejpam-3728	331	13	.	.	PROPN
ejpam-3728	331	14	approximation	approximation	NOUN
ejpam-3728	331	15	on	on	ADP
ejpam-3728	331	16	durrmeyer	durrmeyer	PROPN
ejpam-3728	331	17	modification	modification	NOUN
ejpam-3728	331	18	of	of	ADP
ejpam-3728	331	19	generalized	generalized	ADJ
ejpam-3728	331	20	szász	szász	NUM
ejpam-3728	331	21	-	-	PUNCT
ejpam-3728	331	22	mirakjan	mirakjan	NOUN
ejpam-3728	331	23	operators	operator	NOUN
ejpam-3728	331	24	.	.	PUNCT
ejpam-3728	332	1	arxiv	arxiv	PROPN
ejpam-3728	332	2	preprint	preprint	PROPN
ejpam-3728	332	3	arxiv:1911.12972	arxiv:1911.12972	PROPN
ejpam-3728	332	4	,	,	PUNCT
ejpam-3728	332	5	2019	2019	NUM
ejpam-3728	332	6	.	.	PUNCT
ejpam-3728	333	1	references	reference	NOUN
ejpam-3728	333	2	1324	1324	NUM
ejpam-3728	333	3	[	[	X
ejpam-3728	333	4	18	18	NUM
ejpam-3728	333	5	]	]	X
ejpam-3728	333	6	r	r	NOUN
ejpam-3728	333	7	yadav	yadav	NOUN
ejpam-3728	333	8	,	,	PUNCT
ejpam-3728	333	9	r	r	NOUN
ejpam-3728	333	10	meher	meher	NOUN
ejpam-3728	333	11	,	,	PUNCT
ejpam-3728	333	12	and	and	CCONJ
ejpam-3728	333	13	vn	vn	PROPN
ejpam-3728	333	14	mishra	mishra	PROPN
ejpam-3728	333	15	.	.	PROPN
ejpam-3728	334	1	approximation	approximation	NOUN
ejpam-3728	334	2	properties	property	NOUN
ejpam-3728	334	3	by	by	ADP
ejpam-3728	334	4	some	some	DET
ejpam-3728	334	5	modified	modify	VERB
ejpam-3728	334	6	szász	szász	NUM
ejpam-3728	334	7	-	-	PUNCT
ejpam-3728	334	8	mirakjan	mirakjan	ADJ
ejpam-3728	334	9	-	-	PUNCT
ejpam-3728	334	10	kantorovich	kantorovich	NOUN
ejpam-3728	334	11	operators	operator	NOUN
ejpam-3728	334	12	.	.	PUNCT
ejpam-3728	335	1	arxiv	arxiv	PROPN
ejpam-3728	335	2	preprint	preprint	NOUN
ejpam-3728	335	3	arxiv:1912.04537	arxiv:1912.04537	NOUN
ejpam-3728	335	4	,	,	PUNCT
ejpam-3728	335	5	2019	2019	NUM
ejpam-3728	335	6	.	.	PUNCT
ejpam-3728	336	1	[	[	X
ejpam-3728	336	2	19	19	NUM
ejpam-3728	336	3	]	]	X
ejpam-3728	336	4	r	r	NOUN
ejpam-3728	336	5	yadav	yadav	NOUN
ejpam-3728	336	6	,	,	PUNCT
ejpam-3728	336	7	r	r	NOUN
ejpam-3728	336	8	meher	meher	NOUN
ejpam-3728	336	9	,	,	PUNCT
ejpam-3728	336	10	and	and	CCONJ
ejpam-3728	336	11	vn	vn	PROPN
ejpam-3728	336	12	mishra	mishra	PROPN
ejpam-3728	336	13	.	.	PROPN
ejpam-3728	336	14	approximations	approximation	NOUN
ejpam-3728	336	15	on	on	ADP
ejpam-3728	336	16	stancu	stancu	ADJ
ejpam-3728	336	17	variant	variant	NOUN
ejpam-3728	336	18	of	of	ADP
ejpam-3728	336	19	szászmirakjan	szászmirakjan	PROPN
ejpam-3728	336	20	-	-	PUNCT
ejpam-3728	336	21	kantorovich	kantorovich	NOUN
ejpam-3728	336	22	type	type	NOUN
ejpam-3728	336	23	operators	operator	NOUN
ejpam-3728	336	24	.	.	PUNCT
ejpam-3728	337	1	arxiv	arxiv	PROPN
ejpam-3728	337	2	preprint	preprint	PROPN
ejpam-3728	337	3	arxiv:1911.11479	arxiv:1911.11479	PROPN
ejpam-3728	337	4	,	,	PUNCT
ejpam-3728	337	5	2019	2019	NUM
ejpam-3728	337	6	.	.	PUNCT
ejpam-3728	338	1	[	[	X
ejpam-3728	338	2	20	20	NUM
ejpam-3728	338	3	]	]	X
ejpam-3728	338	4	r	r	NOUN
ejpam-3728	338	5	yadav	yadav	NOUN
ejpam-3728	338	6	,	,	PUNCT
ejpam-3728	338	7	r	r	NOUN
ejpam-3728	338	8	meher	meher	NOUN
ejpam-3728	338	9	,	,	PUNCT
ejpam-3728	338	10	and	and	CCONJ
ejpam-3728	338	11	vn	vn	PROPN
ejpam-3728	338	12	mishra	mishra	PROPN
ejpam-3728	338	13	.	.	PROPN
ejpam-3728	339	1	quantitative	quantitative	ADJ
ejpam-3728	339	2	estimations	estimation	NOUN
ejpam-3728	339	3	of	of	ADP
ejpam-3728	339	4	bivariate	bivariate	ADJ
ejpam-3728	339	5	summationintegral	summationintegral	ADJ
ejpam-3728	339	6	–	–	PUNCT
ejpam-3728	339	7	type	type	NOUN
ejpam-3728	339	8	operators	operator	NOUN
ejpam-3728	339	9	.	.	PUNCT
ejpam-3728	340	1	mathematical	mathematical	ADJ
ejpam-3728	340	2	methods	method	NOUN
ejpam-3728	340	3	in	in	ADP
ejpam-3728	340	4	the	the	DET
ejpam-3728	340	5	applied	apply	VERB
ejpam-3728	340	6	sciences	science	NOUN
ejpam-3728	340	7	,	,	PUNCT
ejpam-3728	340	8	42(18):7172	42(18):7172	NUM
ejpam-3728	340	9	–	–	PUNCT
ejpam-3728	340	10	7191	7191	NUM
ejpam-3728	340	11	,	,	PUNCT
ejpam-3728	340	12	2019	2019	NUM
ejpam-3728	340	13	.	.	PUNCT