id	sid	tid	token	lemma	pos
ejpam-5816	1	1	european	european	PROPN
ejpam-5816	1	2	journal	journal	PROPN
ejpam-5816	1	3	of	of	ADP
ejpam-5816	1	4	pure	pure	ADJ
ejpam-5816	1	5	and	and	CCONJ
ejpam-5816	1	6	applied	applied	ADJ
ejpam-5816	1	7	mathematics	mathematic	NOUN
ejpam-5816	1	8	2025	2025	NUM
ejpam-5816	1	9	,	,	PUNCT
ejpam-5816	1	10	vol	vol	NOUN
ejpam-5816	1	11	.	.	PROPN
ejpam-5816	1	12	18	18	NUM
ejpam-5816	1	13	,	,	PUNCT
ejpam-5816	1	14	issue	issue	NOUN
ejpam-5816	1	15	2	2	NUM
ejpam-5816	1	16	,	,	PUNCT
ejpam-5816	1	17	article	article	NOUN
ejpam-5816	1	18	number	number	NOUN
ejpam-5816	1	19	5816	5816	NUM
ejpam-5816	1	20	issn	issn	PROPN
ejpam-5816	1	21	1307	1307	NUM
ejpam-5816	1	22	-	-	SYM
ejpam-5816	1	23	5543	5543	NUM
ejpam-5816	1	24	–	–	PUNCT
ejpam-5816	2	1	ejpam.com	ejpam.com	X
ejpam-5816	2	2	published	publish	VERB
ejpam-5816	2	3	by	by	ADP
ejpam-5816	2	4	new	new	PROPN
ejpam-5816	2	5	york	york	PROPN
ejpam-5816	2	6	business	business	PROPN
ejpam-5816	2	7	global	global	ADJ
ejpam-5816	2	8	advancements	advancement	NOUN
ejpam-5816	2	9	in	in	ADP
ejpam-5816	2	10	ostrowski	ostrowski	ADJ
ejpam-5816	2	11	type	type	NOUN
ejpam-5816	2	12	fractional	fractional	ADJ
ejpam-5816	2	13	integral	integral	ADJ
ejpam-5816	2	14	inequalities	inequality	NOUN
ejpam-5816	2	15	via	via	ADP
ejpam-5816	2	16	applications	application	NOUN
ejpam-5816	2	17	of	of	ADP
ejpam-5816	2	18	jensen	jensen	PROPN
ejpam-5816	2	19	’s	’s	PART
ejpam-5816	2	20	and	and	CCONJ
ejpam-5816	2	21	young	young	PROPN
ejpam-5816	2	22	’s	’s	PART
ejpam-5816	2	23	inequalities	inequality	NOUN
ejpam-5816	2	24	gauhar	gauhar	PROPN
ejpam-5816	2	25	rahman1,∗	rahman1,∗	PROPN
ejpam-5816	2	26	,	,	PUNCT
ejpam-5816	2	27	muhammad	muhammad	PROPN
ejpam-5816	2	28	samraiz2	samraiz2	PROPN
ejpam-5816	2	29	,	,	PUNCT
ejpam-5816	2	30	çetin	çetin	PROPN
ejpam-5816	2	31	yıldız3,∗	yıldız3,∗	PROPN
ejpam-5816	2	32	,	,	PUNCT
ejpam-5816	2	33	maryam	maryam	PROPN
ejpam-5816	2	34	ali	ali	PROPN
ejpam-5816	2	35	alghafli4	alghafli4	PROPN
ejpam-5816	2	36	,	,	PUNCT
ejpam-5816	2	37	nabil	nabil	PROPN
ejpam-5816	2	38	mlaiki4	mlaiki4	PROPN
ejpam-5816	2	39	1	1	NUM
ejpam-5816	2	40	department	department	NOUN
ejpam-5816	2	41	of	of	ADP
ejpam-5816	2	42	mathematics	mathematic	NOUN
ejpam-5816	2	43	and	and	CCONJ
ejpam-5816	2	44	statistics	statistic	NOUN
ejpam-5816	2	45	,	,	PUNCT
ejpam-5816	2	46	hazara	hazara	PROPN
ejpam-5816	2	47	university	university	PROPN
ejpam-5816	2	48	,	,	PUNCT
ejpam-5816	2	49	mansehra	mansehra	PROPN
ejpam-5816	2	50	21300	21300	NUM
ejpam-5816	2	51	,	,	PUNCT
ejpam-5816	2	52	pakistan	pakistan	PROPN
ejpam-5816	2	53	2	2	NUM
ejpam-5816	2	54	department	department	NOUN
ejpam-5816	2	55	of	of	ADP
ejpam-5816	2	56	mathematics	mathematics	PROPN
ejpam-5816	2	57	,	,	PUNCT
ejpam-5816	2	58	university	university	PROPN
ejpam-5816	2	59	of	of	ADP
ejpam-5816	2	60	sargodha	sargodha	PROPN
ejpam-5816	2	61	p.o	p.o	PROPN
ejpam-5816	2	62	.	.	PROPN
ejpam-5816	2	63	box	box	PROPN
ejpam-5816	2	64	40100	40100	PROPN
ejpam-5816	2	65	,	,	PUNCT
ejpam-5816	2	66	sargodha	sargodha	PROPN
ejpam-5816	2	67	,	,	PUNCT
ejpam-5816	2	68	pakistan	pakistan	PROPN
ejpam-5816	2	69	3	3	NUM
ejpam-5816	2	70	deparment	deparment	NOUN
ejpam-5816	2	71	of	of	ADP
ejpam-5816	2	72	mathematics	mathematics	PROPN
ejpam-5816	2	73	,	,	PUNCT
ejpam-5816	2	74	k.k	k.k	PROPN
ejpam-5816	2	75	.	.	PROPN
ejpam-5816	2	76	education	education	PROPN
ejpam-5816	2	77	faculty	faculty	NOUN
ejpam-5816	2	78	,	,	PUNCT
ejpam-5816	2	79	atatürk	atatürk	PROPN
ejpam-5816	2	80	university	university	NOUN
ejpam-5816	2	81	,	,	PUNCT
ejpam-5816	2	82	25240	25240	NUM
ejpam-5816	2	83	erzurum	erzurum	PROPN
ejpam-5816	2	84	,	,	PUNCT
ejpam-5816	2	85	turkey	turkey	PROPN
ejpam-5816	2	86	4	4	NUM
ejpam-5816	2	87	department	department	NOUN
ejpam-5816	2	88	of	of	ADP
ejpam-5816	2	89	mathematics	mathematic	NOUN
ejpam-5816	2	90	and	and	CCONJ
ejpam-5816	2	91	sciences	science	NOUN
ejpam-5816	2	92	,	,	PUNCT
ejpam-5816	2	93	prince	prince	PROPN
ejpam-5816	2	94	sultan	sultan	PROPN
ejpam-5816	2	95	university	university	PROPN
ejpam-5816	2	96	,	,	PUNCT
ejpam-5816	2	97	riyadh	riyadh	NOUN
ejpam-5816	2	98	,	,	PUNCT
ejpam-5816	2	99	11586	11586	NUM
ejpam-5816	2	100	,	,	PUNCT
ejpam-5816	2	101	saudi	saudi	PROPN
ejpam-5816	2	102	arabia	arabia	PROPN
ejpam-5816	2	103	abstract	abstract	NOUN
ejpam-5816	2	104	.	.	PUNCT
ejpam-5816	3	1	fractional	fractional	ADJ
ejpam-5816	3	2	integral	integral	ADJ
ejpam-5816	3	3	operators	operator	NOUN
ejpam-5816	3	4	and	and	CCONJ
ejpam-5816	3	5	convexity	convexity	NOUN
ejpam-5816	3	6	have	have	VERB
ejpam-5816	3	7	a	a	DET
ejpam-5816	3	8	close	close	ADJ
ejpam-5816	3	9	link	link	NOUN
ejpam-5816	3	10	due	due	ADP
ejpam-5816	3	11	to	to	ADP
ejpam-5816	3	12	their	their	PRON
ejpam-5816	3	13	fascinating	fascinating	ADJ
ejpam-5816	3	14	properties	property	NOUN
ejpam-5816	3	15	in	in	ADP
ejpam-5816	3	16	the	the	DET
ejpam-5816	3	17	mathematical	mathematical	ADJ
ejpam-5816	3	18	sciences	science	NOUN
ejpam-5816	3	19	.	.	PUNCT
ejpam-5816	4	1	in	in	ADP
ejpam-5816	4	2	this	this	DET
ejpam-5816	4	3	paper	paper	NOUN
ejpam-5816	4	4	,	,	PUNCT
ejpam-5816	4	5	we	we	PRON
ejpam-5816	4	6	first	first	ADV
ejpam-5816	4	7	establish	establish	VERB
ejpam-5816	4	8	an	an	DET
ejpam-5816	4	9	integral	integral	ADJ
ejpam-5816	4	10	identity	identity	NOUN
ejpam-5816	4	11	involving	involve	VERB
ejpam-5816	4	12	the	the	DET
ejpam-5816	4	13	generalized	generalized	ADJ
ejpam-5816	4	14	hattaf	hattaf	NOUN
ejpam-5816	4	15	-	-	PUNCT
ejpam-5816	4	16	fractional	fractional	ADJ
ejpam-5816	4	17	integral	integral	ADJ
ejpam-5816	4	18	operators	operator	NOUN
ejpam-5816	4	19	.	.	PUNCT
ejpam-5816	5	1	by	by	ADP
ejpam-5816	5	2	using	use	VERB
ejpam-5816	5	3	the	the	DET
ejpam-5816	5	4	jensen	jensen	PROPN
ejpam-5816	5	5	integral	integral	ADJ
ejpam-5816	5	6	inequality	inequality	NOUN
ejpam-5816	5	7	,	,	PUNCT
ejpam-5816	5	8	young	young	PROPN
ejpam-5816	5	9	’s	’s	PART
ejpam-5816	5	10	inequality	inequality	NOUN
ejpam-5816	5	11	,	,	PUNCT
ejpam-5816	5	12	power	power	NOUN
ejpam-5816	5	13	-	-	PUNCT
ejpam-5816	5	14	mean	mean	NOUN
ejpam-5816	5	15	inequality	inequality	NOUN
ejpam-5816	5	16	,	,	PUNCT
ejpam-5816	5	17	and	and	CCONJ
ejpam-5816	5	18	hölder	hölder	NOUN
ejpam-5816	5	19	inequality	inequality	NOUN
ejpam-5816	5	20	,	,	PUNCT
ejpam-5816	5	21	we	we	PRON
ejpam-5816	5	22	then	then	ADV
ejpam-5816	5	23	apply	apply	VERB
ejpam-5816	5	24	this	this	DET
ejpam-5816	5	25	identity	identity	NOUN
ejpam-5816	5	26	to	to	PART
ejpam-5816	5	27	provide	provide	VERB
ejpam-5816	5	28	some	some	DET
ejpam-5816	5	29	new	new	ADJ
ejpam-5816	5	30	generalizations	generalization	NOUN
ejpam-5816	5	31	of	of	ADP
ejpam-5816	5	32	ostrowski	ostrowski	ADJ
ejpam-5816	5	33	type	type	NOUN
ejpam-5816	5	34	inequality	inequality	NOUN
ejpam-5816	5	35	for	for	ADP
ejpam-5816	5	36	the	the	DET
ejpam-5816	5	37	convexity	convexity	NOUN
ejpam-5816	5	38	of	of	ADP
ejpam-5816	5	39	|ℵ|	|ℵ|	PROPN
ejpam-5816	5	40	.	.	PUNCT
ejpam-5816	6	1	furthermore	furthermore	ADV
ejpam-5816	6	2	,	,	PUNCT
ejpam-5816	6	3	we	we	PRON
ejpam-5816	6	4	deduce	deduce	VERB
ejpam-5816	6	5	several	several	ADJ
ejpam-5816	6	6	special	special	ADJ
ejpam-5816	6	7	cases	case	NOUN
ejpam-5816	6	8	from	from	ADP
ejpam-5816	6	9	the	the	DET
ejpam-5816	6	10	main	main	ADJ
ejpam-5816	6	11	results	result	NOUN
ejpam-5816	6	12	.	.	PUNCT
ejpam-5816	7	1	the	the	DET
ejpam-5816	7	2	results	result	NOUN
ejpam-5816	7	3	of	of	ADP
ejpam-5816	7	4	this	this	DET
ejpam-5816	7	5	novel	novel	ADJ
ejpam-5816	7	6	investigation	investigation	NOUN
ejpam-5816	7	7	should	should	AUX
ejpam-5816	7	8	lead	lead	VERB
ejpam-5816	7	9	to	to	ADP
ejpam-5816	7	10	new	new	ADJ
ejpam-5816	7	11	discoveries	discovery	NOUN
ejpam-5816	7	12	in	in	ADP
ejpam-5816	7	13	the	the	DET
ejpam-5816	7	14	area	area	NOUN
ejpam-5816	7	15	of	of	ADP
ejpam-5816	7	16	fractional	fractional	ADJ
ejpam-5816	7	17	calculus	calculus	NOUN
ejpam-5816	7	18	and	and	CCONJ
ejpam-5816	7	19	inequalities	inequality	NOUN
ejpam-5816	7	20	.	.	PUNCT
ejpam-5816	8	1	2020	2020	NUM
ejpam-5816	8	2	mathematics	mathematic	NOUN
ejpam-5816	8	3	subject	subject	NOUN
ejpam-5816	8	4	classifications	classification	NOUN
ejpam-5816	8	5	:	:	PUNCT
ejpam-5816	8	6	26a33	26a33	NUM
ejpam-5816	8	7	,	,	PUNCT
ejpam-5816	8	8	26a51	26a51	NUM
ejpam-5816	8	9	,	,	PUNCT
ejpam-5816	8	10	26d10	26d10	NUM
ejpam-5816	8	11	key	key	ADJ
ejpam-5816	8	12	words	word	NOUN
ejpam-5816	8	13	and	and	CCONJ
ejpam-5816	8	14	phrases	phrase	NOUN
ejpam-5816	8	15	:	:	PUNCT
ejpam-5816	8	16	young	young	ADJ
ejpam-5816	8	17	inequality	inequality	NOUN
ejpam-5816	8	18	,	,	PUNCT
ejpam-5816	8	19	convex	convex	NOUN
ejpam-5816	8	20	function	function	NOUN
ejpam-5816	8	21	,	,	PUNCT
ejpam-5816	8	22	power	power	NOUN
ejpam-5816	8	23	mean	mean	NOUN
ejpam-5816	8	24	inequality	inequality	NOUN
ejpam-5816	8	25	,	,	PUNCT
ejpam-5816	8	26	fractional	fractional	ADJ
ejpam-5816	8	27	operators	operator	NOUN
ejpam-5816	8	28	1	1	NUM
ejpam-5816	8	29	.	.	PUNCT
ejpam-5816	9	1	introduction	introduction	NOUN
ejpam-5816	9	2	fractional	fractional	ADJ
ejpam-5816	9	3	integrals	integral	NOUN
ejpam-5816	9	4	and	and	CCONJ
ejpam-5816	9	5	derivatives	derivative	NOUN
ejpam-5816	9	6	have	have	AUX
ejpam-5816	9	7	attracted	attract	VERB
ejpam-5816	9	8	a	a	DET
ejpam-5816	9	9	lot	lot	NOUN
ejpam-5816	9	10	of	of	ADP
ejpam-5816	9	11	attention	attention	NOUN
ejpam-5816	9	12	from	from	ADP
ejpam-5816	9	13	researchers	researcher	NOUN
ejpam-5816	9	14	nowadays	nowadays	ADV
ejpam-5816	9	15	.	.	PUNCT
ejpam-5816	10	1	in	in	ADP
ejpam-5816	10	2	many	many	ADJ
ejpam-5816	10	3	cases	case	NOUN
ejpam-5816	10	4	,	,	PUNCT
ejpam-5816	10	5	fractional	fractional	ADJ
ejpam-5816	10	6	derivatives	derivative	NOUN
ejpam-5816	10	7	and	and	CCONJ
ejpam-5816	10	8	fractional	fractional	ADJ
ejpam-5816	10	9	integrals	integral	NOUN
ejpam-5816	10	10	provide	provide	VERB
ejpam-5816	10	11	more	more	ADV
ejpam-5816	10	12	accurate	accurate	ADJ
ejpam-5816	10	13	representations	representation	NOUN
ejpam-5816	10	14	of	of	ADP
ejpam-5816	10	15	the	the	DET
ejpam-5816	10	16	frameworks	framework	NOUN
ejpam-5816	10	17	than	than	ADP
ejpam-5816	10	18	ordinary	ordinary	ADJ
ejpam-5816	10	19	derivatives	derivative	NOUN
ejpam-5816	10	20	and	and	CCONJ
ejpam-5816	10	21	integrals	integral	NOUN
ejpam-5816	10	22	.	.	PUNCT
ejpam-5816	11	1	the	the	DET
ejpam-5816	11	2	fractional	fractional	ADJ
ejpam-5816	11	3	calculus	calculus	NOUN
ejpam-5816	11	4	is	be	AUX
ejpam-5816	11	5	currently	currently	ADV
ejpam-5816	11	6	widely	widely	ADV
ejpam-5816	11	7	employed	employ	VERB
ejpam-5816	11	8	in	in	ADP
ejpam-5816	11	9	many	many	ADJ
ejpam-5816	11	10	scientific	scientific	ADJ
ejpam-5816	11	11	domains	domain	NOUN
ejpam-5816	11	12	due	due	ADP
ejpam-5816	11	13	to	to	ADP
ejpam-5816	11	14	its	its	PRON
ejpam-5816	11	15	numerous	numerous	ADJ
ejpam-5816	11	16	applications	application	NOUN
ejpam-5816	11	17	.	.	PUNCT
ejpam-5816	12	1	the	the	DET
ejpam-5816	12	2	interest	interest	NOUN
ejpam-5816	12	3	of	of	ADP
ejpam-5816	12	4	researchers	researcher	NOUN
ejpam-5816	12	5	in	in	ADP
ejpam-5816	12	6	fractional	fractional	ADJ
ejpam-5816	12	7	derivative	derivative	ADJ
ejpam-5816	12	8	and	and	CCONJ
ejpam-5816	12	9	fractional	fractional	ADJ
ejpam-5816	12	10	∗corresponding	∗corresponding	NOUN
ejpam-5816	12	11	author	author	NOUN
ejpam-5816	12	12	.	.	PUNCT
ejpam-5816	13	1	∗corresponding	∗corresponde	VERB
ejpam-5816	13	2	author	author	NOUN
ejpam-5816	13	3	.	.	PUNCT
ejpam-5816	14	1	doi	doi	NOUN
ejpam-5816	14	2	:	:	PUNCT
ejpam-5816	14	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5816	https://doi.org/10.29020/nybg.ejpam.v18i2.5816	PROPN
ejpam-5816	14	4	email	email	NOUN
ejpam-5816	14	5	addresses	address	VERB
ejpam-5816	14	6	:	:	PUNCT
ejpam-5816	14	7	gauhar55uom@gmail.com	gauhar55uom@gmail.com	X
ejpam-5816	14	8	,	,	PUNCT
ejpam-5816	14	9	drgauhar.rahman@hu.edu.pk	drgauhar.rahman@hu.edu.pk	INTJ
ejpam-5816	14	10	(	(	PUNCT
ejpam-5816	14	11	g.	g.	PROPN
ejpam-5816	14	12	rahman	rahman	PROPN
ejpam-5816	14	13	)	)	PUNCT
ejpam-5816	14	14	,	,	PUNCT
ejpam-5816	14	15	muhammad.samraiz@uos.edu.pk;msamraizuos@gmail.com	muhammad.samraiz@uos.edu.pk;msamraizuos@gmail.com	PROPN
ejpam-5816	14	16	(	(	PUNCT
ejpam-5816	14	17	m.	m.	NOUN
ejpam-5816	14	18	samraiz	samraiz	PROPN
ejpam-5816	14	19	)	)	PUNCT
ejpam-5816	14	20	,	,	PUNCT
ejpam-5816	14	21	cetin@atauni.edu.tr	cetin@atauni.edu.tr	NOUN
ejpam-5816	14	22	(	(	PUNCT
ejpam-5816	14	23	ç.	ç.	ADP
ejpam-5816	14	24	yıldız	yıldız	PROPN
ejpam-5816	14	25	)	)	PUNCT
ejpam-5816	14	26	,	,	PUNCT
ejpam-5816	14	27	mghafli@psu.edu.sa	mghafli@psu.edu.sa	PROPN
ejpam-5816	14	28	(	(	PUNCT
ejpam-5816	14	29	m.	m.	NOUN
ejpam-5816	14	30	a.	a.	NOUN
ejpam-5816	14	31	alghafli	alghafli	PROPN
ejpam-5816	14	32	)	)	PUNCT
ejpam-5816	14	33	,	,	PUNCT
ejpam-5816	14	34	nmlaiki@psu.edu.sa	nmlaiki@psu.edu.sa	NOUN
ejpam-5816	14	35	;	;	PUNCT
ejpam-5816	14	36	nmlaiki2012@gmail.com	nmlaiki2012@gmail.com	X
ejpam-5816	15	1	(	(	PUNCT
ejpam-5816	15	2	n.	n.	PROPN
ejpam-5816	15	3	mlaiki	mlaiki	PROPN
ejpam-5816	15	4	)	)	PUNCT
ejpam-5816	15	5	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5816	16	1	1	1	NUM
ejpam-5816	16	2	copyright	copyright	NOUN
ejpam-5816	16	3	:	:	PUNCT
ejpam-5816	16	4	©	©	PROPN
ejpam-5816	16	5	2025	2025	NUM
ejpam-5816	16	6	the	the	DET
ejpam-5816	16	7	author(s	author(s	NOUN
ejpam-5816	16	8	)	)	PUNCT
ejpam-5816	16	9	.	.	PUNCT
ejpam-5816	17	1	(	(	PUNCT
ejpam-5816	17	2	cc	cc	NOUN
ejpam-5816	17	3	by	by	ADP
ejpam-5816	17	4	-	-	PUNCT
ejpam-5816	17	5	nc	nc	PROPN
ejpam-5816	17	6	4.0	4.0	NUM
ejpam-5816	17	7	)	)	PUNCT
ejpam-5816	17	8	g.	g.	PROPN
ejpam-5816	17	9	rahman	rahman	PROPN
ejpam-5816	17	10	et	et	PROPN
ejpam-5816	17	11	al	al	PROPN
ejpam-5816	17	12	.	.	PUNCT
ejpam-5816	17	13	/	/	SYM
ejpam-5816	17	14	eur	eur	PROPN
ejpam-5816	17	15	.	.	PUNCT
ejpam-5816	18	1	j.	j.	PROPN
ejpam-5816	18	2	pure	pure	PROPN
ejpam-5816	18	3	appl	appl	PROPN
ejpam-5816	18	4	.	.	PROPN
ejpam-5816	18	5	math	math	PROPN
ejpam-5816	18	6	,	,	PUNCT
ejpam-5816	18	7	18	18	NUM
ejpam-5816	18	8	(	(	PUNCT
ejpam-5816	18	9	2	2	NUM
ejpam-5816	18	10	)	)	PUNCT
ejpam-5816	18	11	(	(	PUNCT
ejpam-5816	18	12	2025	2025	NUM
ejpam-5816	18	13	)	)	PUNCT
ejpam-5816	18	14	,	,	PUNCT
ejpam-5816	18	15	5816	5816	NUM
ejpam-5816	18	16	2	2	NUM
ejpam-5816	18	17	of	of	ADP
ejpam-5816	18	18	18	18	NUM
ejpam-5816	18	19	integration	integration	NOUN
ejpam-5816	18	20	has	have	AUX
ejpam-5816	18	21	grown	grow	VERB
ejpam-5816	18	22	recently	recently	ADV
ejpam-5816	18	23	due	due	ADP
ejpam-5816	18	24	to	to	ADP
ejpam-5816	18	25	their	their	PRON
ejpam-5816	18	26	wide	wide	ADJ
ejpam-5816	18	27	applications	application	NOUN
ejpam-5816	18	28	in	in	ADP
ejpam-5816	18	29	diverse	diverse	ADJ
ejpam-5816	18	30	domain	domain	NOUN
ejpam-5816	18	31	,	,	PUNCT
ejpam-5816	18	32	for	for	ADP
ejpam-5816	18	33	example	example	NOUN
ejpam-5816	18	34	(	(	PUNCT
ejpam-5816	18	35	see	see	VERB
ejpam-5816	18	36	,	,	PUNCT
ejpam-5816	18	37	[	[	X
ejpam-5816	18	38	1–5	1–5	X
ejpam-5816	18	39	]	]	X
ejpam-5816	18	40	)	)	PUNCT
ejpam-5816	18	41	.	.	PUNCT
ejpam-5816	19	1	dumitru	dumitru	NOUN
ejpam-5816	19	2	and	and	CCONJ
ejpam-5816	19	3	arran	arran	NOUN
ejpam-5816	19	4	[	[	X
ejpam-5816	19	5	6	6	NUM
ejpam-5816	19	6	]	]	PUNCT
ejpam-5816	19	7	have	have	AUX
ejpam-5816	19	8	given	give	VERB
ejpam-5816	19	9	a	a	DET
ejpam-5816	19	10	new	new	ADJ
ejpam-5816	19	11	formula	formula	NOUN
ejpam-5816	19	12	for	for	ADP
ejpam-5816	19	13	fractional	fractional	ADJ
ejpam-5816	19	14	derivatives	derivative	NOUN
ejpam-5816	19	15	and	and	CCONJ
ejpam-5816	19	16	integrals	integral	NOUN
ejpam-5816	19	17	using	use	VERB
ejpam-5816	19	18	the	the	DET
ejpam-5816	19	19	mittag	mittag	ADJ
ejpam-5816	19	20	-	-	PUNCT
ejpam-5816	19	21	leffler	leffler	NOUN
ejpam-5816	19	22	kernel	kernel	NOUN
ejpam-5816	19	23	.	.	PUNCT
ejpam-5816	20	1	while	while	SCONJ
ejpam-5816	20	2	more	more	ADJ
ejpam-5816	20	3	theoretical	theoretical	ADJ
ejpam-5816	20	4	ideas	idea	NOUN
ejpam-5816	20	5	about	about	ADP
ejpam-5816	20	6	fractional	fractional	ADJ
ejpam-5816	20	7	operators	operator	NOUN
ejpam-5816	20	8	with	with	ADP
ejpam-5816	20	9	mittag	mittag	ADJ
ejpam-5816	20	10	-	-	PUNCT
ejpam-5816	20	11	leffler	leffler	NOUN
ejpam-5816	20	12	kernels	kernel	NOUN
ejpam-5816	20	13	(	(	PUNCT
ejpam-5816	20	14	atangana	atangana	NOUN
ejpam-5816	20	15	-	-	PUNCT
ejpam-5816	20	16	baleanu	baleanu	PROPN
ejpam-5816	20	17	operators	operator	NOUN
ejpam-5816	20	18	)	)	PUNCT
ejpam-5816	20	19	and	and	CCONJ
ejpam-5816	20	20	the	the	DET
ejpam-5816	20	21	higher	high	ADJ
ejpam-5816	20	22	-	-	PUNCT
ejpam-5816	20	23	order	order	NOUN
ejpam-5816	20	24	case	case	NOUN
ejpam-5816	20	25	have	have	AUX
ejpam-5816	20	26	been	be	AUX
ejpam-5816	20	27	discussed	discuss	VERB
ejpam-5816	20	28	in	in	ADP
ejpam-5816	20	29	[	[	X
ejpam-5816	20	30	7–9	7–9	NOUN
ejpam-5816	20	31	]	]	X
ejpam-5816	20	32	,	,	PUNCT
ejpam-5816	20	33	the	the	DET
ejpam-5816	20	34	generalization	generalization	NOUN
ejpam-5816	20	35	to	to	ADP
ejpam-5816	20	36	the	the	DET
ejpam-5816	20	37	generalized	generalized	ADJ
ejpam-5816	20	38	mittag	mittag	ADJ
ejpam-5816	20	39	-	-	PUNCT
ejpam-5816	20	40	leffler	leffler	NOUN
ejpam-5816	20	41	kernels	kernel	NOUN
ejpam-5816	20	42	to	to	PART
ejpam-5816	20	43	gain	gain	VERB
ejpam-5816	20	44	a	a	DET
ejpam-5816	20	45	semigroup	semigroup	ADJ
ejpam-5816	20	46	property	property	NOUN
ejpam-5816	20	47	has	have	AUX
ejpam-5816	20	48	recently	recently	ADV
ejpam-5816	20	49	been	be	AUX
ejpam-5816	20	50	developed	develop	VERB
ejpam-5816	20	51	in	in	ADP
ejpam-5816	20	52	[	[	X
ejpam-5816	20	53	10	10	NUM
ejpam-5816	20	54	,	,	PUNCT
ejpam-5816	20	55	11	11	NUM
ejpam-5816	20	56	]	]	PUNCT
ejpam-5816	20	57	.	.	PUNCT
ejpam-5816	21	1	in	in	ADP
ejpam-5816	21	2	the	the	DET
ejpam-5816	21	3	beginning	beginning	NOUN
ejpam-5816	21	4	,	,	PUNCT
ejpam-5816	21	5	many	many	ADJ
ejpam-5816	21	6	scientists	scientist	NOUN
ejpam-5816	21	7	working	work	VERB
ejpam-5816	21	8	in	in	ADP
ejpam-5816	21	9	different	different	ADJ
ejpam-5816	21	10	areas	area	NOUN
ejpam-5816	21	11	of	of	ADP
ejpam-5816	21	12	theory	theory	NOUN
ejpam-5816	21	13	of	of	ADP
ejpam-5816	21	14	inequalities	inequality	NOUN
ejpam-5816	21	15	employed	employ	VERB
ejpam-5816	21	16	fractional	fractional	ADJ
ejpam-5816	21	17	calculus	calculus	NOUN
ejpam-5816	21	18	as	as	ADP
ejpam-5816	21	19	an	an	DET
ejpam-5816	21	20	essential	essential	ADJ
ejpam-5816	21	21	tool	tool	NOUN
ejpam-5816	21	22	,	,	PUNCT
ejpam-5816	21	23	for	for	ADP
ejpam-5816	21	24	example	example	NOUN
ejpam-5816	21	25	,	,	PUNCT
ejpam-5816	21	26	[	[	X
ejpam-5816	21	27	12–16	12–16	NOUN
ejpam-5816	21	28	]	]	PUNCT
ejpam-5816	21	29	.	.	PUNCT
ejpam-5816	22	1	shuang	shuang	PROPN
ejpam-5816	22	2	and	and	CCONJ
ejpam-5816	22	3	qi	qi	PROPN
ejpam-5816	23	1	[	[	X
ejpam-5816	23	2	17	17	NUM
ejpam-5816	23	3	]	]	PUNCT
ejpam-5816	23	4	proved	prove	VERB
ejpam-5816	23	5	a	a	DET
ejpam-5816	23	6	number	number	NOUN
ejpam-5816	23	7	of	of	ADP
ejpam-5816	23	8	hermite	hermite	ADJ
ejpam-5816	23	9	-	-	PUNCT
ejpam-5816	23	10	hadamard	hadamard	ADJ
ejpam-5816	23	11	-	-	PUNCT
ejpam-5816	23	12	type	type	NOUN
ejpam-5816	23	13	inequalities	inequality	NOUN
ejpam-5816	23	14	and	and	CCONJ
ejpam-5816	23	15	examined	examine	VERB
ejpam-5816	23	16	specific	specific	ADJ
ejpam-5816	23	17	methods	method	NOUN
ejpam-5816	23	18	for	for	ADP
ejpam-5816	23	19	a	a	DET
ejpam-5816	23	20	class	class	NOUN
ejpam-5816	23	21	of	of	ADP
ejpam-5816	23	22	s	s	NOUN
ejpam-5816	23	23	-	-	PUNCT
ejpam-5816	23	24	convex	convex	NOUN
ejpam-5816	23	25	functions	function	NOUN
ejpam-5816	23	26	.	.	PUNCT
ejpam-5816	24	1	mehrez	mehrez	PROPN
ejpam-5816	24	2	and	and	CCONJ
ejpam-5816	24	3	agarwal	agarwal	PROPN
ejpam-5816	25	1	[	[	X
ejpam-5816	25	2	18	18	NUM
ejpam-5816	25	3	]	]	PUNCT
ejpam-5816	25	4	proved	prove	VERB
ejpam-5816	25	5	new	new	ADJ
ejpam-5816	25	6	integral	integral	ADJ
ejpam-5816	25	7	inequalities	inequality	NOUN
ejpam-5816	25	8	and	and	CCONJ
ejpam-5816	25	9	looked	look	VERB
ejpam-5816	25	10	at	at	ADP
ejpam-5816	25	11	specific	specific	ADJ
ejpam-5816	25	12	cases	case	NOUN
ejpam-5816	25	13	of	of	ADP
ejpam-5816	25	14	their	their	PRON
ejpam-5816	25	15	discoveries	discovery	NOUN
ejpam-5816	25	16	with	with	ADP
ejpam-5816	25	17	application	application	NOUN
ejpam-5816	25	18	to	to	ADP
ejpam-5816	25	19	special	special	ADJ
ejpam-5816	25	20	means	mean	NOUN
ejpam-5816	25	21	by	by	ADP
ejpam-5816	25	22	employing	employ	VERB
ejpam-5816	25	23	the	the	DET
ejpam-5816	25	24	conventional	conventional	ADJ
ejpam-5816	25	25	hermite	hermite	ADJ
ejpam-5816	25	26	-	-	PUNCT
ejpam-5816	25	27	hadamard	hadamard	ADJ
ejpam-5816	25	28	inequalities	inequality	NOUN
ejpam-5816	25	29	.	.	PUNCT
ejpam-5816	26	1	park	park	NOUN
ejpam-5816	26	2	et	et	PROPN
ejpam-5816	26	3	al	al	PROPN
ejpam-5816	26	4	.	.	PUNCT
ejpam-5816	27	1	[	[	X
ejpam-5816	27	2	19	19	NUM
ejpam-5816	27	3	]	]	PUNCT
ejpam-5816	27	4	researched	research	VERB
ejpam-5816	27	5	and	and	CCONJ
ejpam-5816	27	6	used	use	VERB
ejpam-5816	27	7	new	new	ADJ
ejpam-5816	27	8	generalized	generalized	ADJ
ejpam-5816	27	9	inequalities	inequality	NOUN
ejpam-5816	27	10	to	to	PART
ejpam-5816	27	11	stability	stability	VERB
ejpam-5816	27	12	analysis	analysis	NOUN
ejpam-5816	27	13	.	.	PUNCT
ejpam-5816	28	1	by	by	ADP
ejpam-5816	28	2	utilizing	utilize	VERB
ejpam-5816	28	3	the	the	DET
ejpam-5816	28	4	local	local	ADJ
ejpam-5816	28	5	fractional	fractional	ADJ
ejpam-5816	28	6	approach	approach	NOUN
ejpam-5816	28	7	,	,	PUNCT
ejpam-5816	28	8	fractional	fractional	ADJ
ejpam-5816	28	9	integral	integral	ADJ
ejpam-5816	28	10	inequalities	inequality	NOUN
ejpam-5816	28	11	were	be	AUX
ejpam-5816	28	12	generated	generate	VERB
ejpam-5816	28	13	by	by	ADP
ejpam-5816	28	14	sarikaya	sarikaya	PROPN
ejpam-5816	28	15	et	et	PROPN
ejpam-5816	28	16	al	al	PROPN
ejpam-5816	28	17	.	.	PUNCT
ejpam-5816	29	1	[	[	X
ejpam-5816	29	2	20	20	NUM
ejpam-5816	29	3	]	]	PUNCT
ejpam-5816	29	4	,	,	PUNCT
ejpam-5816	29	5	expanding	expand	VERB
ejpam-5816	29	6	upon	upon	SCONJ
ejpam-5816	29	7	the	the	DET
ejpam-5816	29	8	findings	finding	NOUN
ejpam-5816	29	9	found	find	VERB
ejpam-5816	29	10	in	in	ADP
ejpam-5816	29	11	the	the	DET
ejpam-5816	29	12	classical	classical	ADJ
ejpam-5816	29	13	literature	literature	NOUN
ejpam-5816	29	14	.	.	PUNCT
ejpam-5816	30	1	in	in	ADP
ejpam-5816	30	2	[	[	X
ejpam-5816	30	3	21	21	NUM
ejpam-5816	30	4	]	]	PUNCT
ejpam-5816	30	5	,	,	PUNCT
ejpam-5816	30	6	set	set	VERB
ejpam-5816	30	7	et	et	PROPN
ejpam-5816	30	8	al	al	PROPN
ejpam-5816	30	9	.	.	PROPN
ejpam-5816	30	10	presented	present	VERB
ejpam-5816	30	11	integral	integral	ADJ
ejpam-5816	30	12	inequalities	inequality	NOUN
ejpam-5816	30	13	for	for	ADP
ejpam-5816	30	14	differentiable	differentiable	ADJ
ejpam-5816	30	15	convex	convex	NOUN
ejpam-5816	30	16	functions	function	NOUN
ejpam-5816	30	17	via	via	ADP
ejpam-5816	30	18	atangana	atangana	PROPN
ejpam-5816	30	19	-	-	PUNCT
ejpam-5816	30	20	baleanu	baleanu	ADJ
ejpam-5816	30	21	fractional	fractional	ADJ
ejpam-5816	30	22	integral	integral	ADJ
ejpam-5816	30	23	operators	operator	NOUN
ejpam-5816	30	24	.	.	PUNCT
ejpam-5816	31	1	the	the	DET
ejpam-5816	31	2	various	various	ADJ
ejpam-5816	31	3	researchers	researcher	NOUN
ejpam-5816	31	4	examined	examine	VERB
ejpam-5816	31	5	a	a	DET
ejpam-5816	31	6	few	few	ADJ
ejpam-5816	31	7	noteworthy	noteworthy	ADJ
ejpam-5816	31	8	integral	integral	ADJ
ejpam-5816	31	9	inequalities	inequality	NOUN
ejpam-5816	31	10	using	use	VERB
ejpam-5816	31	11	various	various	ADJ
ejpam-5816	31	12	fractional	fractional	ADJ
ejpam-5816	31	13	methods	method	NOUN
ejpam-5816	31	14	.	.	PUNCT
ejpam-5816	32	1	we	we	PRON
ejpam-5816	32	2	refer	refer	VERB
ejpam-5816	32	3	the	the	DET
ejpam-5816	32	4	readers	reader	NOUN
ejpam-5816	32	5	to	to	ADP
ejpam-5816	32	6	the	the	DET
ejpam-5816	32	7	research	research	NOUN
ejpam-5816	32	8	conducted	conduct	VERB
ejpam-5816	32	9	by	by	ADP
ejpam-5816	32	10	[	[	X
ejpam-5816	32	11	22–25	22–25	NUM
ejpam-5816	32	12	]	]	PUNCT
ejpam-5816	32	13	.	.	PUNCT
ejpam-5816	33	1	2	2	X
ejpam-5816	33	2	.	.	X
ejpam-5816	33	3	preliminaries	preliminary	NOUN
ejpam-5816	33	4	it	it	PRON
ejpam-5816	33	5	is	be	AUX
ejpam-5816	33	6	clear	clear	ADJ
ejpam-5816	33	7	that	that	SCONJ
ejpam-5816	33	8	the	the	DET
ejpam-5816	33	9	convex	convex	NOUN
ejpam-5816	33	10	function	function	NOUN
ejpam-5816	33	11	is	be	AUX
ejpam-5816	33	12	essential	essential	ADJ
ejpam-5816	33	13	for	for	ADP
ejpam-5816	33	14	the	the	DET
ejpam-5816	33	15	study	study	NOUN
ejpam-5816	33	16	of	of	ADP
ejpam-5816	33	17	mathematical	mathematical	ADJ
ejpam-5816	33	18	inequalities	inequality	NOUN
ejpam-5816	33	19	since	since	SCONJ
ejpam-5816	33	20	it	it	PRON
ejpam-5816	33	21	has	have	VERB
ejpam-5816	33	22	several	several	ADJ
ejpam-5816	33	23	applications	application	NOUN
ejpam-5816	33	24	in	in	ADP
ejpam-5816	33	25	the	the	DET
ejpam-5816	33	26	fields	field	NOUN
ejpam-5816	33	27	of	of	ADP
ejpam-5816	33	28	pure	pure	ADJ
ejpam-5816	33	29	and	and	CCONJ
ejpam-5816	33	30	practical	practical	ADJ
ejpam-5816	33	31	mathematics	mathematic	NOUN
ejpam-5816	33	32	,	,	PUNCT
ejpam-5816	33	33	mechanics	mechanic	NOUN
ejpam-5816	33	34	,	,	PUNCT
ejpam-5816	33	35	probability	probability	NOUN
ejpam-5816	33	36	and	and	CCONJ
ejpam-5816	33	37	statistics	statistic	NOUN
ejpam-5816	33	38	theory	theory	NOUN
ejpam-5816	33	39	,	,	PUNCT
ejpam-5816	33	40	economics	economic	NOUN
ejpam-5816	33	41	,	,	PUNCT
ejpam-5816	33	42	engineering	engineering	NOUN
ejpam-5816	33	43	,	,	PUNCT
ejpam-5816	33	44	and	and	CCONJ
ejpam-5816	33	45	optimization	optimization	NOUN
ejpam-5816	33	46	theory	theory	NOUN
ejpam-5816	33	47	.	.	PUNCT
ejpam-5816	34	1	recently	recently	ADV
ejpam-5816	34	2	,	,	PUNCT
ejpam-5816	34	3	there	there	PRON
ejpam-5816	34	4	have	have	AUX
ejpam-5816	34	5	been	be	AUX
ejpam-5816	34	6	several	several	ADJ
ejpam-5816	34	7	mathematicians	mathematician	NOUN
ejpam-5816	34	8	working	work	VERB
ejpam-5816	34	9	on	on	ADP
ejpam-5816	34	10	convexity	convexity	NOUN
ejpam-5816	34	11	’s	’s	PART
ejpam-5816	34	12	theories	theory	NOUN
ejpam-5816	34	13	,	,	PUNCT
ejpam-5816	34	14	variations	variation	NOUN
ejpam-5816	34	15	,	,	PUNCT
ejpam-5816	34	16	augmentations	augmentation	NOUN
ejpam-5816	34	17	,	,	PUNCT
ejpam-5816	34	18	generalizations	generalization	NOUN
ejpam-5816	34	19	,	,	PUNCT
ejpam-5816	34	20	and	and	CCONJ
ejpam-5816	34	21	refinements	refinement	NOUN
ejpam-5816	34	22	.	.	PUNCT
ejpam-5816	35	1	for	for	ADP
ejpam-5816	35	2	example	example	NOUN
ejpam-5816	35	3	,	,	PUNCT
ejpam-5816	35	4	in	in	ADP
ejpam-5816	35	5	a	a	DET
ejpam-5816	35	6	number	number	NOUN
ejpam-5816	35	7	of	of	ADP
ejpam-5816	35	8	scientific	scientific	ADJ
ejpam-5816	35	9	and	and	CCONJ
ejpam-5816	35	10	mathematical	mathematical	ADJ
ejpam-5816	35	11	domains	domain	NOUN
ejpam-5816	35	12	,	,	PUNCT
ejpam-5816	35	13	it	it	PRON
ejpam-5816	35	14	is	be	AUX
ejpam-5816	35	15	a	a	DET
ejpam-5816	35	16	useful	useful	ADJ
ejpam-5816	35	17	tool	tool	NOUN
ejpam-5816	35	18	for	for	ADP
ejpam-5816	35	19	presenting	present	VERB
ejpam-5816	35	20	a	a	DET
ejpam-5816	35	21	variety	variety	NOUN
ejpam-5816	35	22	of	of	ADP
ejpam-5816	35	23	challenges	challenge	NOUN
ejpam-5816	35	24	and	and	CCONJ
ejpam-5816	35	25	demonstrating	demonstrate	VERB
ejpam-5816	35	26	awareness	awareness	NOUN
ejpam-5816	35	27	[	[	X
ejpam-5816	35	28	26–29	26–29	NOUN
ejpam-5816	35	29	]	]	X
ejpam-5816	35	30	.	.	PUNCT
ejpam-5816	36	1	the	the	DET
ejpam-5816	36	2	convexity	convexity	NOUN
ejpam-5816	36	3	property	property	NOUN
ejpam-5816	36	4	can	can	AUX
ejpam-5816	36	5	be	be	AUX
ejpam-5816	36	6	used	use	VERB
ejpam-5816	36	7	to	to	PART
ejpam-5816	36	8	generalize	generalize	VERB
ejpam-5816	36	9	a	a	DET
ejpam-5816	36	10	number	number	NOUN
ejpam-5816	36	11	of	of	ADP
ejpam-5816	36	12	well	well	ADV
ejpam-5816	36	13	-	-	PUNCT
ejpam-5816	36	14	known	know	VERB
ejpam-5816	36	15	inequalities	inequality	NOUN
ejpam-5816	36	16	,	,	PUNCT
ejpam-5816	36	17	such	such	ADJ
ejpam-5816	36	18	as	as	ADP
ejpam-5816	36	19	the	the	DET
ejpam-5816	36	20	opial	opial	ADJ
ejpam-5816	36	21	type	type	NOUN
ejpam-5816	36	22	inequality	inequality	NOUN
ejpam-5816	36	23	,	,	PUNCT
ejpam-5816	36	24	the	the	DET
ejpam-5816	36	25	hermite	hermite	ADJ
ejpam-5816	36	26	–	–	PUNCT
ejpam-5816	36	27	hadamard	hadamard	ADJ
ejpam-5816	36	28	inequality	inequality	NOUN
ejpam-5816	36	29	,	,	PUNCT
ejpam-5816	36	30	the	the	DET
ejpam-5816	36	31	ostrowski	ostrowski	ADJ
ejpam-5816	36	32	inequality	inequality	NOUN
ejpam-5816	36	33	,	,	PUNCT
ejpam-5816	36	34	the	the	DET
ejpam-5816	36	35	simpson	simpson	PROPN
ejpam-5816	36	36	inequality	inequality	PROPN
ejpam-5816	36	37	,	,	PUNCT
ejpam-5816	36	38	the	the	DET
ejpam-5816	36	39	bullen	bullen	PROPN
ejpam-5816	36	40	type	type	NOUN
ejpam-5816	36	41	inequality	inequality	NOUN
ejpam-5816	36	42	,	,	PUNCT
ejpam-5816	36	43	and	and	CCONJ
ejpam-5816	36	44	many	many	ADJ
ejpam-5816	36	45	more	more	ADJ
ejpam-5816	36	46	.	.	PUNCT
ejpam-5816	37	1	the	the	DET
ejpam-5816	37	2	ostrowski	ostrowski	ADJ
ejpam-5816	37	3	type	type	NOUN
ejpam-5816	37	4	inequality	inequality	NOUN
ejpam-5816	37	5	is	be	AUX
ejpam-5816	37	6	one	one	NUM
ejpam-5816	37	7	of	of	ADP
ejpam-5816	37	8	the	the	DET
ejpam-5816	37	9	most	most	ADV
ejpam-5816	37	10	extensively	extensively	ADV
ejpam-5816	37	11	studied	study	VERB
ejpam-5816	37	12	conclusions	conclusion	NOUN
ejpam-5816	37	13	involving	involve	VERB
ejpam-5816	37	14	several	several	ADJ
ejpam-5816	37	15	kinds	kind	NOUN
ejpam-5816	37	16	of	of	ADP
ejpam-5816	37	17	convexities	convexity	NOUN
ejpam-5816	37	18	.	.	PUNCT
ejpam-5816	38	1	definition	definition	NOUN
ejpam-5816	38	2	1	1	NUM
ejpam-5816	38	3	.	.	PUNCT
ejpam-5816	39	1	[	[	X
ejpam-5816	39	2	30	30	NUM
ejpam-5816	39	3	]	]	PUNCT
ejpam-5816	39	4	let	let	VERB
ejpam-5816	39	5	ℵ	ℵ	NOUN
ejpam-5816	39	6	:	:	PUNCT
ejpam-5816	39	7	i	i	PRON
ejpam-5816	39	8	⊆	⊆	NUM
ejpam-5816	39	9	r	r	NOUN
ejpam-5816	39	10	→	→	SYM
ejpam-5816	39	11	r	r	NOUN
ejpam-5816	39	12	be	be	AUX
ejpam-5816	39	13	a	a	DET
ejpam-5816	39	14	differentiable	differentiable	ADJ
ejpam-5816	39	15	function	function	NOUN
ejpam-5816	39	16	ℵ	ℵ	PROPN
ejpam-5816	39	17	∈	∈	PROPN
ejpam-5816	39	18	l1[r	l1[r	PROPN
ejpam-5816	39	19	,	,	PUNCT
ejpam-5816	39	20	s	s	AUX
ejpam-5816	39	21	]	]	X
ejpam-5816	39	22	with	with	ADP
ejpam-5816	39	23	r	r	NOUN
ejpam-5816	39	24	<	<	X
ejpam-5816	39	25	s	s	X
ejpam-5816	39	26	∈	∈	PROPN
ejpam-5816	39	27	i.	i.	NOUN
ejpam-5816	39	28	if	if	SCONJ
ejpam-5816	39	29	|ℵ′(t)|	|ℵ′(t)|	NOUN
ejpam-5816	39	30	≤	≤	ADV
ejpam-5816	40	1	k	k	NOUN
ejpam-5816	40	2	,	,	PUNCT
ejpam-5816	40	3	for	for	ADP
ejpam-5816	40	4	t	t	PROPN
ejpam-5816	40	5	∈	∈	PROPN
ejpam-5816	41	1	[	[	X
ejpam-5816	41	2	r	r	X
ejpam-5816	41	3	,	,	PUNCT
ejpam-5816	41	4	s	s	PART
ejpam-5816	41	5	]	]	X
ejpam-5816	41	6	,	,	PUNCT
ejpam-5816	41	7	then	then	ADV
ejpam-5816	41	8	the	the	DET
ejpam-5816	41	9	ostrowski	ostrowski	ADJ
ejpam-5816	41	10	type	type	NOUN
ejpam-5816	41	11	integral	integral	ADJ
ejpam-5816	41	12	inequality	inequality	NOUN
ejpam-5816	41	13	is	be	AUX
ejpam-5816	41	14	given	give	VERB
ejpam-5816	41	15	by	by	ADP
ejpam-5816	41	16	|	|	ADV
ejpam-5816	41	17	ℵ(t)−	ℵ(t)−	PROPN
ejpam-5816	41	18	1	1	NUM
ejpam-5816	41	19	s−	s−	PROPN
ejpam-5816	41	20	r	r	NOUN
ejpam-5816	41	21	∫	∫	PROPN
ejpam-5816	41	22	s	s	PART
ejpam-5816	41	23	r	r	NOUN
ejpam-5816	41	24	ℵ(t)dt	ℵ(t)dt	NUM
ejpam-5816	41	25	|≤	|≤	PROPN
ejpam-5816	41	26	k(s−	k(s−	PROPN
ejpam-5816	41	27	r	r	PROPN
ejpam-5816	41	28	)	)	PUNCT
ejpam-5816	41	29	[	[	PUNCT
ejpam-5816	41	30	1	1	NUM
ejpam-5816	41	31	4	4	NUM
ejpam-5816	41	32	+	+	CCONJ
ejpam-5816	41	33	(	(	PUNCT
ejpam-5816	41	34	t−	t−	PROPN
ejpam-5816	41	35	r+s	r+s	PROPN
ejpam-5816	41	36	2	2	NUM
ejpam-5816	41	37	)	)	PUNCT
ejpam-5816	41	38	(	(	PUNCT
ejpam-5816	41	39	r	r	NOUN
ejpam-5816	41	40	+	+	X
ejpam-5816	41	41	s)2	s)2	NOUN
ejpam-5816	41	42	]	]	PUNCT
ejpam-5816	41	43	,	,	PUNCT
ejpam-5816	41	44	where	where	SCONJ
ejpam-5816	41	45	1	1	NUM
ejpam-5816	41	46	4	4	NUM
ejpam-5816	41	47	is	be	AUX
ejpam-5816	41	48	the	the	DET
ejpam-5816	41	49	least	least	ADJ
ejpam-5816	41	50	possible	possible	ADJ
ejpam-5816	41	51	value	value	NOUN
ejpam-5816	41	52	.	.	PUNCT
ejpam-5816	42	1	mathematicians	mathematician	NOUN
ejpam-5816	42	2	and	and	CCONJ
ejpam-5816	42	3	scholars	scholar	NOUN
ejpam-5816	42	4	have	have	AUX
ejpam-5816	42	5	been	be	AUX
ejpam-5816	42	6	studying	study	VERB
ejpam-5816	42	7	this	this	DET
ejpam-5816	42	8	inequality	inequality	NOUN
ejpam-5816	42	9	with	with	ADP
ejpam-5816	42	10	significant	significant	ADJ
ejpam-5816	42	11	attention	attention	NOUN
ejpam-5816	42	12	and	and	CCONJ
ejpam-5816	42	13	effort	effort	NOUN
ejpam-5816	42	14	in	in	ADP
ejpam-5816	42	15	recent	recent	ADJ
ejpam-5816	42	16	years	year	NOUN
ejpam-5816	42	17	.	.	PUNCT
ejpam-5816	43	1	this	this	DET
ejpam-5816	43	2	inequality	inequality	NOUN
ejpam-5816	43	3	was	be	AUX
ejpam-5816	43	4	studied	study	VERB
ejpam-5816	43	5	in	in	ADP
ejpam-5816	43	6	1997	1997	NUM
ejpam-5816	43	7	by	by	ADP
ejpam-5816	43	8	dragomir	dragomir	NOUN
ejpam-5816	43	9	and	and	CCONJ
ejpam-5816	43	10	g.	g.	PROPN
ejpam-5816	43	11	rahman	rahman	PROPN
ejpam-5816	43	12	et	et	PROPN
ejpam-5816	43	13	al	al	PROPN
ejpam-5816	43	14	.	.	PUNCT
ejpam-5816	43	15	/	/	SYM
ejpam-5816	43	16	eur	eur	PROPN
ejpam-5816	43	17	.	.	PUNCT
ejpam-5816	44	1	j.	j.	PROPN
ejpam-5816	44	2	pure	pure	PROPN
ejpam-5816	44	3	appl	appl	PROPN
ejpam-5816	44	4	.	.	PROPN
ejpam-5816	44	5	math	math	PROPN
ejpam-5816	44	6	,	,	PUNCT
ejpam-5816	44	7	18	18	NUM
ejpam-5816	44	8	(	(	PUNCT
ejpam-5816	44	9	2	2	NUM
ejpam-5816	44	10	)	)	PUNCT
ejpam-5816	44	11	(	(	PUNCT
ejpam-5816	44	12	2025	2025	NUM
ejpam-5816	44	13	)	)	PUNCT
ejpam-5816	44	14	,	,	PUNCT
ejpam-5816	44	15	5816	5816	NUM
ejpam-5816	44	16	3	3	NUM
ejpam-5816	44	17	of	of	ADP
ejpam-5816	44	18	18	18	NUM
ejpam-5816	44	19	wang	wang	PROPN
ejpam-5816	45	1	[	[	X
ejpam-5816	45	2	31	31	NUM
ejpam-5816	45	3	,	,	PUNCT
ejpam-5816	45	4	32	32	NUM
ejpam-5816	45	5	]	]	PUNCT
ejpam-5816	45	6	with	with	ADP
ejpam-5816	45	7	relation	relation	NOUN
ejpam-5816	45	8	to	to	ADP
ejpam-5816	45	9	the	the	DET
ejpam-5816	45	10	lower	low	ADJ
ejpam-5816	45	11	and	and	CCONJ
ejpam-5816	45	12	upper	upper	ADJ
ejpam-5816	45	13	bounds	bound	NOUN
ejpam-5816	45	14	of	of	ADP
ejpam-5816	45	15	the	the	DET
ejpam-5816	45	16	first	first	ADJ
ejpam-5816	45	17	derivative	derivative	NOUN
ejpam-5816	45	18	.	.	PUNCT
ejpam-5816	46	1	it	it	PRON
ejpam-5816	46	2	was	be	AUX
ejpam-5816	46	3	investigated	investigate	VERB
ejpam-5816	46	4	by	by	ADP
ejpam-5816	46	5	barnett	barnett	PROPN
ejpam-5816	46	6	et	et	PROPN
ejpam-5816	46	7	al	al	PROPN
ejpam-5816	46	8	.	.	PROPN
ejpam-5816	46	9	and	and	CCONJ
ejpam-5816	46	10	cerone	cerone	VERB
ejpam-5816	46	11	et	et	PROPN
ejpam-5816	46	12	al	al	PROPN
ejpam-5816	46	13	.	.	PUNCT
ejpam-5816	47	1	[	[	X
ejpam-5816	47	2	33	33	NUM
ejpam-5816	47	3	,	,	PUNCT
ejpam-5816	47	4	34	34	NUM
ejpam-5816	47	5	]	]	PUNCT
ejpam-5816	48	1	that	that	SCONJ
ejpam-5816	48	2	this	this	DET
ejpam-5816	48	3	inequality	inequality	NOUN
ejpam-5816	48	4	involving	involve	VERB
ejpam-5816	48	5	twice	twice	ADV
ejpam-5816	48	6	differentiable	differentiable	ADJ
ejpam-5816	48	7	convex	convex	NOUN
ejpam-5816	48	8	functions	function	NOUN
ejpam-5816	48	9	involved	involve	VERB
ejpam-5816	48	10	.	.	PUNCT
ejpam-5816	49	1	definition	definition	NOUN
ejpam-5816	49	2	2	2	NUM
ejpam-5816	49	3	.	.	PUNCT
ejpam-5816	50	1	[	[	X
ejpam-5816	50	2	35	35	NUM
ejpam-5816	50	3	]	]	PUNCT
ejpam-5816	50	4	a	a	DET
ejpam-5816	50	5	function	function	NOUN
ejpam-5816	50	6	ℵ	ℵ	NOUN
ejpam-5816	50	7	:	:	PUNCT
ejpam-5816	50	8	[	[	X
ejpam-5816	50	9	r	r	X
ejpam-5816	50	10	,	,	PUNCT
ejpam-5816	50	11	s	s	PART
ejpam-5816	50	12	]	]	PUNCT
ejpam-5816	50	13	⊆	⊆	NUM
ejpam-5816	50	14	r	r	NOUN
ejpam-5816	50	15	→	→	SYM
ejpam-5816	50	16	r	r	NOUN
ejpam-5816	50	17	is	be	AUX
ejpam-5816	50	18	said	say	VERB
ejpam-5816	50	19	to	to	PART
ejpam-5816	50	20	be	be	AUX
ejpam-5816	50	21	convex	convex	ADJ
ejpam-5816	50	22	if	if	SCONJ
ejpam-5816	50	23	ℵ	ℵ	X
ejpam-5816	50	24	(	(	PUNCT
ejpam-5816	50	25	ρu+	ρu+	X
ejpam-5816	50	26	(	(	PUNCT
ejpam-5816	50	27	1−	1−	NUM
ejpam-5816	50	28	ρ)v	ρ)v	NOUN
ejpam-5816	50	29	)	)	PUNCT
ejpam-5816	50	30	≤	≤	NOUN
ejpam-5816	50	31	ρℵ(u	ρℵ(u	NUM
ejpam-5816	50	32	)	)	PUNCT
ejpam-5816	51	1	+	+	CCONJ
ejpam-5816	51	2	(	(	PUNCT
ejpam-5816	51	3	1−	1−	NUM
ejpam-5816	51	4	ρ)ℵ(v	ρ)ℵ(v	NUM
ejpam-5816	51	5	)	)	PUNCT
ejpam-5816	51	6	,	,	PUNCT
ejpam-5816	51	7	for	for	ADP
ejpam-5816	51	8	all	all	DET
ejpam-5816	51	9	u	u	NOUN
ejpam-5816	51	10	,	,	PUNCT
ejpam-5816	51	11	v	v	NOUN
ejpam-5816	51	12	∈	∈	PROPN
ejpam-5816	52	1	[	[	X
ejpam-5816	52	2	r	r	X
ejpam-5816	52	3	,	,	PUNCT
ejpam-5816	52	4	s	s	X
ejpam-5816	52	5	]	]	PUNCT
ejpam-5816	52	6	and	and	CCONJ
ejpam-5816	52	7	ρ	ρ	NUM
ejpam-5816	52	8	∈	∈	PROPN
ejpam-5816	53	1	[	[	X
ejpam-5816	53	2	0	0	NUM
ejpam-5816	53	3	,	,	PUNCT
ejpam-5816	53	4	1	1	NUM
ejpam-5816	53	5	]	]	PUNCT
ejpam-5816	53	6	.	.	PUNCT
ejpam-5816	54	1	convex	convex	NOUN
ejpam-5816	54	2	functions	function	NOUN
ejpam-5816	54	3	are	be	AUX
ejpam-5816	54	4	a	a	DET
ejpam-5816	54	5	concept	concept	NOUN
ejpam-5816	54	6	that	that	PRON
ejpam-5816	54	7	is	be	AUX
ejpam-5816	54	8	frequently	frequently	ADV
ejpam-5816	54	9	utilized	utilize	VERB
ejpam-5816	54	10	in	in	ADP
ejpam-5816	54	11	inequality	inequality	NOUN
ejpam-5816	54	12	theory	theory	NOUN
ejpam-5816	54	13	.	.	PUNCT
ejpam-5816	55	1	the	the	DET
ejpam-5816	55	2	hermite	hermite	PROPN
ejpam-5816	55	3	-	-	PUNCT
ejpam-5816	55	4	hadamard	hadamard	ADJ
ejpam-5816	55	5	inequality	inequality	NOUN
ejpam-5816	55	6	,	,	PUNCT
ejpam-5816	55	7	which	which	PRON
ejpam-5816	55	8	derives	derive	VERB
ejpam-5816	55	9	upper	upper	ADJ
ejpam-5816	55	10	and	and	CCONJ
ejpam-5816	55	11	lower	low	ADJ
ejpam-5816	55	12	bounds	bound	NOUN
ejpam-5816	55	13	from	from	ADP
ejpam-5816	55	14	averages	average	NOUN
ejpam-5816	55	15	of	of	ADP
ejpam-5816	55	16	the	the	DET
ejpam-5816	55	17	mean	mean	ADJ
ejpam-5816	55	18	value	value	NOUN
ejpam-5816	55	19	of	of	ADP
ejpam-5816	55	20	a	a	DET
ejpam-5816	55	21	convex	convex	NOUN
ejpam-5816	55	22	function	function	NOUN
ejpam-5816	55	23	,	,	PUNCT
ejpam-5816	55	24	is	be	AUX
ejpam-5816	55	25	as	as	SCONJ
ejpam-5816	55	26	follows	follow	VERB
ejpam-5816	55	27	:	:	PUNCT
ejpam-5816	55	28	definition	definition	NOUN
ejpam-5816	55	29	3	3	NUM
ejpam-5816	55	30	.	.	PUNCT
ejpam-5816	55	31	given	give	VERB
ejpam-5816	55	32	a	a	DET
ejpam-5816	55	33	convex	convex	NOUN
ejpam-5816	55	34	mapping	mapping	NOUN
ejpam-5816	55	35	ℵ	ℵ	NOUN
ejpam-5816	55	36	:	:	PUNCT
ejpam-5816	55	37	i	i	PRON
ejpam-5816	56	1	⊆	⊆	NUM
ejpam-5816	56	2	r	r	NOUN
ejpam-5816	56	3	→	→	SYM
ejpam-5816	56	4	r	r	NOUN
ejpam-5816	56	5	,	,	PUNCT
ejpam-5816	56	6	let	let	VERB
ejpam-5816	56	7	r	r	PRON
ejpam-5816	56	8	<	<	X
ejpam-5816	56	9	s	s	X
ejpam-5816	56	10	be	be	AUX
ejpam-5816	56	11	on	on	ADP
ejpam-5816	56	12	the	the	DET
ejpam-5816	56	13	interval	interval	NOUN
ejpam-5816	56	14	i	i	PRON
ejpam-5816	56	15	of	of	ADP
ejpam-5816	56	16	r.	r.	PROPN
ejpam-5816	56	17	then	then	ADV
ejpam-5816	56	18	the	the	DET
ejpam-5816	56	19	hermite	hermite	PROPN
ejpam-5816	56	20	-	-	PUNCT
ejpam-5816	56	21	hadamard	hadamard	ADJ
ejpam-5816	56	22	inequality	inequality	NOUN
ejpam-5816	56	23	is	be	AUX
ejpam-5816	56	24	defined	define	VERB
ejpam-5816	56	25	by	by	ADP
ejpam-5816	56	26	ℵ	ℵ	PROPN
ejpam-5816	56	27	(	(	PUNCT
ejpam-5816	56	28	r	r	NOUN
ejpam-5816	56	29	+	+	SYM
ejpam-5816	56	30	s	s	NOUN
ejpam-5816	56	31	2	2	NUM
ejpam-5816	56	32	)	)	PUNCT
ejpam-5816	56	33	≤	≤	NOUN
ejpam-5816	56	34	1	1	NUM
ejpam-5816	56	35	s−	s−	PROPN
ejpam-5816	56	36	r	r	NOUN
ejpam-5816	56	37	∫	∫	PROPN
ejpam-5816	56	38	s	s	PART
ejpam-5816	56	39	r	r	NOUN
ejpam-5816	56	40	ℵ(x)dx	ℵ(x)dx	PUNCT
ejpam-5816	56	41	≤	≤	NUM
ejpam-5816	56	42	ℵ(r	ℵ(r	PROPN
ejpam-5816	56	43	)	)	PUNCT
ejpam-5816	56	44	+	+	NUM
ejpam-5816	56	45	ℵ(s	ℵ(	NOUN
ejpam-5816	56	46	)	)	PUNCT
ejpam-5816	56	47	2	2	NUM
ejpam-5816	56	48	.	.	PUNCT
ejpam-5816	57	1	definition	definition	NOUN
ejpam-5816	57	2	4	4	NUM
ejpam-5816	57	3	.	.	PUNCT
ejpam-5816	58	1	[	[	X
ejpam-5816	58	2	36	36	NUM
ejpam-5816	58	3	]	]	PUNCT
ejpam-5816	58	4	the	the	DET
ejpam-5816	58	5	abc	abc	PROPN
ejpam-5816	58	6	-	-	PUNCT
ejpam-5816	58	7	fractional	fractional	ADJ
ejpam-5816	58	8	derivative	derivative	NOUN
ejpam-5816	58	9	is	be	AUX
ejpam-5816	58	10	defined	define	VERB
ejpam-5816	58	11	by	by	ADP
ejpam-5816	58	12	abcdκ	abcdκ	PROPN
ejpam-5816	58	13	r	r	NOUN
ejpam-5816	58	14	,	,	PUNCT
ejpam-5816	58	15	ξℵ(ξ	ξℵ(ξ	ADJ
ejpam-5816	58	16	)	)	PUNCT
ejpam-5816	59	1	=	=	SYM
ejpam-5816	59	2	m(κ	m(κ	PROPN
ejpam-5816	59	3	)	)	PUNCT
ejpam-5816	59	4	1−	1−	NUM
ejpam-5816	59	5	κ	κ	NOUN
ejpam-5816	59	6	∫	∫	PROPN
ejpam-5816	60	1	ξ	ξ	X
ejpam-5816	60	2	r	r	NOUN
ejpam-5816	60	3	ℵ′(η)eκ	ℵ′(η)eκ	PROPN
ejpam-5816	60	4	(	(	PUNCT
ejpam-5816	60	5	−κ(ξ	−κ(ξ	VERB
ejpam-5816	60	6	−	−	PROPN
ejpam-5816	60	7	η)κ	η)κ	X
ejpam-5816	60	8	1−	1−	NUM
ejpam-5816	60	9	κ	κ	NOUN
ejpam-5816	60	10	)	)	PUNCT
ejpam-5816	60	11	dη	dη	NOUN
ejpam-5816	60	12	,	,	PUNCT
ejpam-5816	60	13	where	where	SCONJ
ejpam-5816	60	14	0	0	PUNCT
ejpam-5816	60	15	<	<	X
ejpam-5816	60	16	κ	κ	X
ejpam-5816	60	17	<	<	X
ejpam-5816	60	18	1	1	NUM
ejpam-5816	60	19	,	,	PUNCT
ejpam-5816	60	20	ℵ′	ℵ′	CCONJ
ejpam-5816	60	21	∈	∈	PROPN
ejpam-5816	60	22	l1(r	l1(r	PROPN
ejpam-5816	60	23	,	,	PUNCT
ejpam-5816	60	24	t	t	X
ejpam-5816	60	25	]	]	PUNCT
ejpam-5816	60	26	and	and	CCONJ
ejpam-5816	60	27	m(κ	m(κ	NOUN
ejpam-5816	60	28	)	)	PUNCT
ejpam-5816	60	29	is	be	AUX
ejpam-5816	60	30	normalization	normalization	NOUN
ejpam-5816	60	31	function	function	NOUN
ejpam-5816	60	32	which	which	PRON
ejpam-5816	60	33	satisfies	satisfy	VERB
ejpam-5816	60	34	the	the	DET
ejpam-5816	60	35	condition	condition	NOUN
ejpam-5816	60	36	m(0	m(0	NOUN
ejpam-5816	60	37	)	)	PUNCT
ejpam-5816	60	38	=	=	SYM
ejpam-5816	60	39	m(1	m(1	NOUN
ejpam-5816	60	40	)	)	PUNCT
ejpam-5816	60	41	=	=	SYM
ejpam-5816	60	42	1	1	X
ejpam-5816	60	43	.	.	X
ejpam-5816	60	44	definition	definition	NOUN
ejpam-5816	60	45	5	5	NUM
ejpam-5816	60	46	.	.	PUNCT
ejpam-5816	61	1	[	[	X
ejpam-5816	61	2	37	37	NUM
ejpam-5816	61	3	,	,	PUNCT
ejpam-5816	61	4	38	38	NUM
ejpam-5816	61	5	]	]	PUNCT
ejpam-5816	61	6	the	the	DET
ejpam-5816	61	7	ab	ab	ADJ
ejpam-5816	61	8	-	-	PUNCT
ejpam-5816	61	9	fractional	fractional	ADJ
ejpam-5816	61	10	operator	operator	NOUN
ejpam-5816	61	11	for	for	ADP
ejpam-5816	61	12	ℵ	ℵ	NOUN
ejpam-5816	61	13	∈	∈	PROPN
ejpam-5816	61	14	l1(r	l1(r	PROPN
ejpam-5816	61	15	,	,	PUNCT
ejpam-5816	61	16	t	t	X
ejpam-5816	61	17	]	]	PUNCT
ejpam-5816	61	18	and	and	CCONJ
ejpam-5816	61	19	0	0	NUM
ejpam-5816	61	20	<	<	X
ejpam-5816	61	21	κ	κ	X
ejpam-5816	61	22	<	<	X
ejpam-5816	61	23	1	1	NUM
ejpam-5816	61	24	is	be	AUX
ejpam-5816	61	25	defined	define	VERB
ejpam-5816	61	26	by	by	ADP
ejpam-5816	61	27	abiκ	abiκ	PROPN
ejpam-5816	61	28	r	r	PROPN
ejpam-5816	61	29	,	,	PUNCT
ejpam-5816	61	30	ξℵ(ξ	ξℵ(ξ	ADJ
ejpam-5816	61	31	)	)	PUNCT
ejpam-5816	61	32	=	=	SYM
ejpam-5816	62	1	1−	1−	NUM
ejpam-5816	62	2	κ	κ	X
ejpam-5816	62	3	m(κ	m(κ	PROPN
ejpam-5816	62	4	)	)	PUNCT
ejpam-5816	62	5	ℵ(ξ	ℵ(ξ	NOUN
ejpam-5816	62	6	)	)	PUNCT
ejpam-5816	63	1	+	+	CCONJ
ejpam-5816	63	2	κ	κ	X
ejpam-5816	63	3	m(κ)γ(κ	m(κ)γ(κ	NOUN
ejpam-5816	63	4	)	)	PUNCT
ejpam-5816	63	5	∫	∫	PROPN
ejpam-5816	64	1	ξ	ξ	X
ejpam-5816	64	2	r	r	X
ejpam-5816	64	3	(	(	PUNCT
ejpam-5816	64	4	ξ	ξ	PROPN
ejpam-5816	64	5	−	−	PROPN
ejpam-5816	64	6	η)κ−1	η)κ−1	PROPN
ejpam-5816	64	7	ℵ(η)dη	ℵ(η)dη	PROPN
ejpam-5816	64	8	.	.	PUNCT
ejpam-5816	64	9	(	(	PUNCT
ejpam-5816	64	10	1	1	X
ejpam-5816	64	11	)	)	PUNCT
ejpam-5816	64	12	definition	definition	NOUN
ejpam-5816	64	13	6	6	NUM
ejpam-5816	64	14	.	.	PUNCT
ejpam-5816	65	1	[	[	X
ejpam-5816	65	2	39	39	NUM
ejpam-5816	65	3	]	]	PUNCT
ejpam-5816	65	4	the	the	DET
ejpam-5816	65	5	hattaf	hattaf	NOUN
ejpam-5816	65	6	fractional	fractional	ADJ
ejpam-5816	65	7	derivative	derivative	NOUN
ejpam-5816	65	8	is	be	AUX
ejpam-5816	65	9	defined	define	VERB
ejpam-5816	65	10	by	by	ADP
ejpam-5816	65	11	dκ	dκ	PROPN
ejpam-5816	65	12	,	,	PUNCT
ejpam-5816	65	13	σ	σ	PROPN
ejpam-5816	65	14	,	,	PUNCT
ejpam-5816	65	15	δ	δ	PROPN
ejpam-5816	65	16	r	r	PROPN
ejpam-5816	65	17	,	,	PUNCT
ejpam-5816	65	18	ξ	ξ	PROPN
ejpam-5816	65	19	,	,	PUNCT
ejpam-5816	65	20	ωℵ(ξ	ωℵ(ξ	NUM
ejpam-5816	65	21	)	)	PUNCT
ejpam-5816	66	1	=	=	SYM
ejpam-5816	66	2	m(κ	m(κ	PROPN
ejpam-5816	66	3	)	)	PUNCT
ejpam-5816	66	4	1−	1−	NUM
ejpam-5816	66	5	κ	κ	NOUN
ejpam-5816	66	6	1	1	NUM
ejpam-5816	66	7	ω(ξ	ω(ξ	NUM
ejpam-5816	66	8	)	)	PUNCT
ejpam-5816	66	9	∫	∫	NOUN
ejpam-5816	67	1	ξ	ξ	PRON
ejpam-5816	67	2	r	r	NOUN
ejpam-5816	67	3	eσ	eσ	NOUN
ejpam-5816	67	4	(	(	PUNCT
ejpam-5816	67	5	−κ(ξ	−κ(ξ	VERB
ejpam-5816	67	6	−	−	PROPN
ejpam-5816	67	7	η)δ	η)δ	NOUN
ejpam-5816	67	8	1−	1−	NUM
ejpam-5816	67	9	κ	κ	NOUN
ejpam-5816	67	10	)	)	PUNCT
ejpam-5816	67	11	d	d	NOUN
ejpam-5816	67	12	dt	dt	X
ejpam-5816	67	13	(	(	PUNCT
ejpam-5816	67	14	ωℵ)(η)dη	ωℵ)(η)dη	PROPN
ejpam-5816	67	15	,	,	PUNCT
ejpam-5816	67	16	where	where	SCONJ
ejpam-5816	67	17	0	0	NUM
ejpam-5816	67	18	<	<	X
ejpam-5816	67	19	κ	κ	X
ejpam-5816	67	20	<	<	X
ejpam-5816	67	21	1	1	NUM
ejpam-5816	67	22	,	,	PUNCT
ejpam-5816	67	23	ℵ′	ℵ′	CCONJ
ejpam-5816	67	24	∈	∈	PROPN
ejpam-5816	67	25	l1(r	l1(r	PROPN
ejpam-5816	67	26	,	,	PUNCT
ejpam-5816	67	27	t	t	X
ejpam-5816	67	28	]	]	PUNCT
ejpam-5816	67	29	ω	ω	X
ejpam-5816	67	30	∈	∈	PROPN
ejpam-5816	67	31	c1(a	c1(a	PROPN
ejpam-5816	67	32	,	,	PUNCT
ejpam-5816	67	33	b	b	NOUN
ejpam-5816	67	34	)	)	PUNCT
ejpam-5816	67	35	,	,	PUNCT
ejpam-5816	67	36	ω	ω	PROPN
ejpam-5816	67	37	,	,	PUNCT
ejpam-5816	67	38	ω′	ω′	X
ejpam-5816	67	39	>	>	X
ejpam-5816	67	40	0	0	PUNCT
ejpam-5816	68	1	on	on	ADP
ejpam-5816	68	2	[	[	X
ejpam-5816	68	3	a	a	X
ejpam-5816	68	4	,	,	PUNCT
ejpam-5816	68	5	b	b	NOUN
ejpam-5816	68	6	]	]	PUNCT
ejpam-5816	68	7	.	.	PUNCT
ejpam-5816	69	1	definition	definition	NOUN
ejpam-5816	69	2	7	7	NUM
ejpam-5816	69	3	.	.	PUNCT
ejpam-5816	70	1	[	[	X
ejpam-5816	70	2	39	39	NUM
ejpam-5816	70	3	]	]	PUNCT
ejpam-5816	70	4	the	the	DET
ejpam-5816	70	5	left	left	ADJ
ejpam-5816	70	6	sided	side	VERB
ejpam-5816	70	7	hattaf	hattaf	NOUN
ejpam-5816	70	8	fractional	fractional	ADJ
ejpam-5816	70	9	operator	operator	NOUN
ejpam-5816	70	10	for	for	ADP
ejpam-5816	70	11	ℵ	ℵ	NOUN
ejpam-5816	70	12	∈	∈	PROPN
ejpam-5816	70	13	l1(r	l1(r	PROPN
ejpam-5816	70	14	,	,	PUNCT
ejpam-5816	70	15	t	t	X
ejpam-5816	70	16	]	]	PUNCT
ejpam-5816	70	17	and	and	CCONJ
ejpam-5816	70	18	0	0	NUM
ejpam-5816	70	19	<	<	X
ejpam-5816	70	20	κ	κ	X
ejpam-5816	70	21	<	<	X
ejpam-5816	70	22	1	1	NUM
ejpam-5816	70	23	is	be	AUX
ejpam-5816	70	24	defined	define	VERB
ejpam-5816	70	25	by	by	ADP
ejpam-5816	70	26	iκ	iκ	PROPN
ejpam-5816	70	27	,	,	PUNCT
ejpam-5816	70	28	σ	σ	PROPN
ejpam-5816	70	29	,	,	PUNCT
ejpam-5816	70	30	ω	ω	PROPN
ejpam-5816	70	31	r	r	NOUN
ejpam-5816	70	32	,	,	PUNCT
ejpam-5816	70	33	ξ	ξ	NOUN
ejpam-5816	70	34	ℵ(ξ	ℵ(ξ	NOUN
ejpam-5816	70	35	)	)	PUNCT
ejpam-5816	70	36	=	=	SYM
ejpam-5816	70	37	1−	1−	NUM
ejpam-5816	70	38	κ	κ	X
ejpam-5816	70	39	m(κ	m(κ	PROPN
ejpam-5816	70	40	)	)	PUNCT
ejpam-5816	70	41	ℵ(ξ	ℵ(ξ	NOUN
ejpam-5816	70	42	)	)	PUNCT
ejpam-5816	71	1	+	+	SYM
ejpam-5816	71	2	κ	κ	PROPN
ejpam-5816	71	3	m(κ)γ(σ)ω(ξ	m(κ)γ(σ)ω(ξ	NUM
ejpam-5816	71	4	)	)	PUNCT
ejpam-5816	71	5	∫	∫	PROPN
ejpam-5816	72	1	ξ	ξ	X
ejpam-5816	72	2	r	r	X
ejpam-5816	72	3	(	(	PUNCT
ejpam-5816	72	4	ξ	ξ	PROPN
ejpam-5816	72	5	−	−	PROPN
ejpam-5816	72	6	η)σ−1	η)σ−1	PROPN
ejpam-5816	72	7	ω(η)ℵ(η)dη	ω(η)ℵ(η)dη	X
ejpam-5816	72	8	.	.	PUNCT
ejpam-5816	73	1	(	(	PUNCT
ejpam-5816	73	2	2	2	X
ejpam-5816	73	3	)	)	PUNCT
ejpam-5816	73	4	g.	g.	PROPN
ejpam-5816	73	5	rahman	rahman	PROPN
ejpam-5816	73	6	et	et	PROPN
ejpam-5816	73	7	al	al	PROPN
ejpam-5816	73	8	.	.	PUNCT
ejpam-5816	73	9	/	/	SYM
ejpam-5816	73	10	eur	eur	PROPN
ejpam-5816	73	11	.	.	PUNCT
ejpam-5816	74	1	j.	j.	PROPN
ejpam-5816	74	2	pure	pure	PROPN
ejpam-5816	74	3	appl	appl	PROPN
ejpam-5816	74	4	.	.	PROPN
ejpam-5816	74	5	math	math	PROPN
ejpam-5816	74	6	,	,	PUNCT
ejpam-5816	74	7	18	18	NUM
ejpam-5816	74	8	(	(	PUNCT
ejpam-5816	74	9	2	2	NUM
ejpam-5816	74	10	)	)	PUNCT
ejpam-5816	74	11	(	(	PUNCT
ejpam-5816	74	12	2025	2025	NUM
ejpam-5816	74	13	)	)	PUNCT
ejpam-5816	74	14	,	,	PUNCT
ejpam-5816	74	15	5816	5816	NUM
ejpam-5816	74	16	4	4	NUM
ejpam-5816	74	17	of	of	ADP
ejpam-5816	74	18	18	18	NUM
ejpam-5816	74	19	definition	definition	NOUN
ejpam-5816	74	20	8	8	NUM
ejpam-5816	74	21	.	.	PUNCT
ejpam-5816	75	1	the	the	DET
ejpam-5816	75	2	right	right	PROPN
ejpam-5816	75	3	sided	side	VERB
ejpam-5816	75	4	hattaf	hattaf	NOUN
ejpam-5816	75	5	fractional	fractional	ADJ
ejpam-5816	75	6	operator	operator	NOUN
ejpam-5816	75	7	for	for	ADP
ejpam-5816	75	8	ℵ	ℵ	NOUN
ejpam-5816	75	9	∈	∈	PROPN
ejpam-5816	75	10	l1(r	l1(r	PROPN
ejpam-5816	75	11	,	,	PUNCT
ejpam-5816	75	12	s	s	X
ejpam-5816	75	13	)	)	PUNCT
ejpam-5816	75	14	and	and	CCONJ
ejpam-5816	75	15	0	0	NUM
ejpam-5816	75	16	<	<	X
ejpam-5816	75	17	κ	κ	X
ejpam-5816	75	18	<	<	X
ejpam-5816	75	19	1	1	NUM
ejpam-5816	75	20	is	be	AUX
ejpam-5816	75	21	defined	define	VERB
ejpam-5816	75	22	by	by	ADP
ejpam-5816	75	23	iκ	iκ	PROPN
ejpam-5816	75	24	,	,	PUNCT
ejpam-5816	75	25	σ	σ	PROPN
ejpam-5816	75	26	,	,	PUNCT
ejpam-5816	75	27	ω	ω	PROPN
ejpam-5816	75	28	s	s	PROPN
ejpam-5816	75	29	,	,	PUNCT
ejpam-5816	75	30	ξ	ξ	PRON
ejpam-5816	75	31	ℵ(ξ	ℵ(ξ	NOUN
ejpam-5816	75	32	)	)	PUNCT
ejpam-5816	75	33	=	=	SYM
ejpam-5816	75	34	1−	1−	NUM
ejpam-5816	75	35	κ	κ	X
ejpam-5816	75	36	m(κ	m(κ	PROPN
ejpam-5816	75	37	)	)	PUNCT
ejpam-5816	75	38	ℵ(ξ	ℵ(ξ	NOUN
ejpam-5816	75	39	)	)	PUNCT
ejpam-5816	76	1	+	+	SYM
ejpam-5816	76	2	κ	κ	PROPN
ejpam-5816	76	3	m(κ)γ(σ)ω(ξ	m(κ)γ(σ)ω(ξ	NUM
ejpam-5816	76	4	)	)	PUNCT
ejpam-5816	76	5	∫	∫	PROPN
ejpam-5816	76	6	s	s	PROPN
ejpam-5816	77	1	ξ	ξ	PROPN
ejpam-5816	77	2	(	(	PUNCT
ejpam-5816	77	3	η	η	PROPN
ejpam-5816	77	4	−	−	PROPN
ejpam-5816	77	5	ξ)σ−1	ξ)σ−1	PROPN
ejpam-5816	77	6	ω(η)ℵ(η)dη	ω(η)ℵ(η)dη	PROPN
ejpam-5816	77	7	.	.	PUNCT
ejpam-5816	78	1	(	(	PUNCT
ejpam-5816	78	2	3	3	X
ejpam-5816	78	3	)	)	PUNCT
ejpam-5816	78	4	remark	remark	NOUN
ejpam-5816	78	5	1	1	NUM
ejpam-5816	78	6	.	.	PUNCT
ejpam-5816	78	7	i.	i.	PROPN
ejpam-5816	78	8	if	if	SCONJ
ejpam-5816	78	9	we	we	PRON
ejpam-5816	78	10	consider	consider	VERB
ejpam-5816	78	11	σ	σ	NOUN
ejpam-5816	78	12	=	=	PUNCT
ejpam-5816	78	13	κ	κ	NOUN
ejpam-5816	78	14	in	in	ADP
ejpam-5816	78	15	(	(	PUNCT
ejpam-5816	78	16	2	2	NUM
ejpam-5816	78	17	)	)	PUNCT
ejpam-5816	78	18	and	and	CCONJ
ejpam-5816	78	19	(	(	PUNCT
ejpam-5816	78	20	3	3	NUM
ejpam-5816	78	21	)	)	PUNCT
ejpam-5816	78	22	,	,	PUNCT
ejpam-5816	78	23	then	then	ADV
ejpam-5816	78	24	we	we	PRON
ejpam-5816	78	25	get	get	VERB
ejpam-5816	78	26	ab	ab	NOUN
ejpam-5816	78	27	-	-	NOUN
ejpam-5816	78	28	operator	operator	NOUN
ejpam-5816	78	29	defined	define	VERB
ejpam-5816	78	30	in	in	ADP
ejpam-5816	78	31	(	(	PUNCT
ejpam-5816	78	32	1	1	NUM
ejpam-5816	78	33	)	)	PUNCT
ejpam-5816	78	34	.	.	PUNCT
ejpam-5816	79	1	ii	ii	PROPN
ejpam-5816	79	2	.	.	PUNCT
ejpam-5816	80	1	if	if	SCONJ
ejpam-5816	80	2	we	we	PRON
ejpam-5816	80	3	consider	consider	VERB
ejpam-5816	80	4	σ	σ	NOUN
ejpam-5816	80	5	=	=	SYM
ejpam-5816	80	6	κ	κ	PROPN
ejpam-5816	80	7	and	and	CCONJ
ejpam-5816	80	8	ω	ω	NUM
ejpam-5816	80	9	=	=	SYM
ejpam-5816	80	10	1	1	NUM
ejpam-5816	80	11	in	in	ADP
ejpam-5816	80	12	(	(	PUNCT
ejpam-5816	80	13	2	2	NUM
ejpam-5816	80	14	)	)	PUNCT
ejpam-5816	80	15	and	and	CCONJ
ejpam-5816	80	16	(	(	PUNCT
ejpam-5816	80	17	3	3	NUM
ejpam-5816	80	18	)	)	PUNCT
ejpam-5816	80	19	,	,	PUNCT
ejpam-5816	80	20	then	then	ADV
ejpam-5816	80	21	we	we	PRON
ejpam-5816	80	22	get	get	VERB
ejpam-5816	80	23	ab	ab	NOUN
ejpam-5816	80	24	-	-	NOUN
ejpam-5816	80	25	operator	operator	NOUN
ejpam-5816	80	26	defined	define	VERB
ejpam-5816	80	27	in	in	ADP
ejpam-5816	80	28	(	(	PUNCT
ejpam-5816	80	29	1	1	NUM
ejpam-5816	80	30	)	)	PUNCT
ejpam-5816	80	31	.	.	PUNCT
ejpam-5816	81	1	definition	definition	NOUN
ejpam-5816	81	2	9	9	NUM
ejpam-5816	81	3	.	.	PUNCT
ejpam-5816	82	1	the	the	DET
ejpam-5816	82	2	left	left	ADJ
ejpam-5816	82	3	sided	side	VERB
ejpam-5816	82	4	hattaf	hattaf	NOUN
ejpam-5816	82	5	fractional	fractional	ADJ
ejpam-5816	82	6	operator	operator	NOUN
ejpam-5816	82	7	for	for	ADP
ejpam-5816	82	8	ω	ω	PROPN
ejpam-5816	82	9	=	=	SYM
ejpam-5816	82	10	1	1	NUM
ejpam-5816	82	11	,	,	PUNCT
ejpam-5816	82	12	ℵ	ℵ	NOUN
ejpam-5816	82	13	∈	∈	PROPN
ejpam-5816	82	14	l1(r	l1(r	PROPN
ejpam-5816	82	15	,	,	PUNCT
ejpam-5816	82	16	t	t	X
ejpam-5816	82	17	]	]	PUNCT
ejpam-5816	82	18	and	and	CCONJ
ejpam-5816	82	19	0	0	NUM
ejpam-5816	82	20	<	<	X
ejpam-5816	82	21	κ	κ	X
ejpam-5816	82	22	<	<	X
ejpam-5816	82	23	1	1	NUM
ejpam-5816	82	24	is	be	AUX
ejpam-5816	82	25	defined	define	VERB
ejpam-5816	82	26	by	by	ADP
ejpam-5816	82	27	iκ	iκ	PROPN
ejpam-5816	82	28	,	,	PUNCT
ejpam-5816	82	29	σ	σ	PROPN
ejpam-5816	82	30	r	r	PROPN
ejpam-5816	82	31	,	,	PUNCT
ejpam-5816	82	32	ξ	ξ	NOUN
ejpam-5816	82	33	ℵ(ξ	ℵ(ξ	NOUN
ejpam-5816	82	34	)	)	PUNCT
ejpam-5816	82	35	=	=	SYM
ejpam-5816	82	36	1−	1−	NUM
ejpam-5816	82	37	κ	κ	X
ejpam-5816	82	38	m(κ	m(κ	PROPN
ejpam-5816	82	39	)	)	PUNCT
ejpam-5816	82	40	ℵ(ξ	ℵ(ξ	NOUN
ejpam-5816	82	41	)	)	PUNCT
ejpam-5816	83	1	+	+	CCONJ
ejpam-5816	83	2	κ	κ	ADP
ejpam-5816	83	3	m(κ)γ(σ	m(κ)γ(σ	ADJ
ejpam-5816	83	4	∫	∫	PROPN
ejpam-5816	83	5	ξ	ξ	X
ejpam-5816	83	6	r	r	X
ejpam-5816	83	7	(	(	PUNCT
ejpam-5816	83	8	ξ	ξ	PROPN
ejpam-5816	83	9	−	−	PROPN
ejpam-5816	83	10	η)σ−1	η)σ−1	PROPN
ejpam-5816	83	11	ℵ(η)dη	ℵ(η)dη	X
ejpam-5816	83	12	.	.	PUNCT
ejpam-5816	84	1	(	(	PUNCT
ejpam-5816	84	2	4	4	X
ejpam-5816	84	3	)	)	PUNCT
ejpam-5816	84	4	definition	definition	NOUN
ejpam-5816	84	5	10	10	NUM
ejpam-5816	84	6	.	.	PUNCT
ejpam-5816	85	1	the	the	DET
ejpam-5816	85	2	right	right	PROPN
ejpam-5816	85	3	sided	side	VERB
ejpam-5816	85	4	hattaf	hattaf	NOUN
ejpam-5816	85	5	fractional	fractional	ADJ
ejpam-5816	85	6	operator	operator	NOUN
ejpam-5816	85	7	for	for	ADP
ejpam-5816	85	8	ω	ω	PROPN
ejpam-5816	85	9	=	=	SYM
ejpam-5816	85	10	1	1	NUM
ejpam-5816	85	11	,	,	PUNCT
ejpam-5816	85	12	ℵ	ℵ	NOUN
ejpam-5816	85	13	∈	∈	PROPN
ejpam-5816	85	14	l1(r	l1(r	PROPN
ejpam-5816	85	15	,	,	PUNCT
ejpam-5816	85	16	s	s	X
ejpam-5816	85	17	)	)	PUNCT
ejpam-5816	85	18	and	and	CCONJ
ejpam-5816	85	19	0	0	NUM
ejpam-5816	85	20	<	<	X
ejpam-5816	85	21	κ	κ	X
ejpam-5816	85	22	<	<	X
ejpam-5816	85	23	1	1	NUM
ejpam-5816	85	24	is	be	AUX
ejpam-5816	85	25	defined	define	VERB
ejpam-5816	85	26	by	by	ADP
ejpam-5816	85	27	iκ	iκ	PROPN
ejpam-5816	85	28	,	,	PUNCT
ejpam-5816	85	29	σ	σ	PROPN
ejpam-5816	85	30	s	s	PROPN
ejpam-5816	85	31	,	,	PUNCT
ejpam-5816	85	32	ξ	ξ	PRON
ejpam-5816	85	33	ℵ(ξ	ℵ(ξ	NOUN
ejpam-5816	85	34	)	)	PUNCT
ejpam-5816	85	35	=	=	SYM
ejpam-5816	85	36	1−	1−	NUM
ejpam-5816	85	37	κ	κ	X
ejpam-5816	85	38	m(κ	m(κ	PROPN
ejpam-5816	85	39	)	)	PUNCT
ejpam-5816	85	40	ℵ(ξ	ℵ(ξ	NOUN
ejpam-5816	85	41	)	)	PUNCT
ejpam-5816	85	42	+	+	CCONJ
ejpam-5816	85	43	κ	κ	X
ejpam-5816	85	44	m(κ)γ(σ	m(κ)γ(σ	X
ejpam-5816	85	45	)	)	PUNCT
ejpam-5816	85	46	∫	∫	PROPN
ejpam-5816	85	47	s	s	PROPN
ejpam-5816	85	48	ξ	ξ	PROPN
ejpam-5816	85	49	(	(	PUNCT
ejpam-5816	85	50	η	η	PROPN
ejpam-5816	85	51	−	−	PROPN
ejpam-5816	85	52	ξ)σ−1	ξ)σ−1	PROPN
ejpam-5816	85	53	ℵ(η)dη	ℵ(η)dη	PROPN
ejpam-5816	85	54	.	.	PUNCT
ejpam-5816	86	1	(	(	PUNCT
ejpam-5816	86	2	5	5	X
ejpam-5816	86	3	)	)	PUNCT
ejpam-5816	86	4	this	this	DET
ejpam-5816	86	5	paper	paper	NOUN
ejpam-5816	86	6	aims	aim	VERB
ejpam-5816	86	7	to	to	PART
ejpam-5816	86	8	derive	derive	VERB
ejpam-5816	86	9	an	an	DET
ejpam-5816	86	10	integral	integral	ADJ
ejpam-5816	86	11	identity	identity	NOUN
ejpam-5816	86	12	by	by	ADP
ejpam-5816	86	13	incorporating	incorporate	VERB
ejpam-5816	86	14	the	the	DET
ejpam-5816	86	15	hattaf	hattaf	NOUN
ejpam-5816	86	16	fractional	fractional	ADJ
ejpam-5816	86	17	integral	integral	ADJ
ejpam-5816	86	18	operators	operator	NOUN
ejpam-5816	86	19	(	(	PUNCT
ejpam-5816	86	20	4	4	NUM
ejpam-5816	86	21	)	)	PUNCT
ejpam-5816	86	22	and	and	CCONJ
ejpam-5816	86	23	(	(	PUNCT
ejpam-5816	86	24	5	5	NUM
ejpam-5816	86	25	)	)	PUNCT
ejpam-5816	86	26	and	and	CCONJ
ejpam-5816	86	27	uses	use	VERB
ejpam-5816	86	28	them	they	PRON
ejpam-5816	86	29	to	to	PART
ejpam-5816	86	30	prove	prove	VERB
ejpam-5816	86	31	the	the	DET
ejpam-5816	86	32	refinement	refinement	NOUN
ejpam-5816	86	33	of	of	ADP
ejpam-5816	86	34	ostrowski	ostrowski	ADJ
ejpam-5816	86	35	type	type	NOUN
ejpam-5816	86	36	integral	integral	ADJ
ejpam-5816	86	37	inequalities	inequality	NOUN
ejpam-5816	86	38	for	for	ADP
ejpam-5816	86	39	differentiable	differentiable	ADJ
ejpam-5816	86	40	convex	convex	NOUN
ejpam-5816	86	41	functions	function	NOUN
ejpam-5816	86	42	.	.	PUNCT
ejpam-5816	87	1	3	3	X
ejpam-5816	87	2	.	.	X
ejpam-5816	87	3	main	main	ADJ
ejpam-5816	87	4	result	result	NOUN
ejpam-5816	87	5	in	in	ADP
ejpam-5816	87	6	this	this	DET
ejpam-5816	87	7	section	section	NOUN
ejpam-5816	87	8	,	,	PUNCT
ejpam-5816	87	9	we	we	PRON
ejpam-5816	87	10	first	first	ADV
ejpam-5816	87	11	prove	prove	VERB
ejpam-5816	87	12	the	the	DET
ejpam-5816	87	13	following	follow	VERB
ejpam-5816	87	14	fractional	fractional	ADJ
ejpam-5816	87	15	integral	integral	ADJ
ejpam-5816	87	16	identity	identity	NOUN
ejpam-5816	87	17	which	which	PRON
ejpam-5816	87	18	will	will	AUX
ejpam-5816	87	19	be	be	AUX
ejpam-5816	87	20	used	use	VERB
ejpam-5816	87	21	in	in	ADP
ejpam-5816	87	22	our	our	PRON
ejpam-5816	87	23	main	main	ADJ
ejpam-5816	87	24	findings	finding	NOUN
ejpam-5816	87	25	.	.	PUNCT
ejpam-5816	88	1	lemma	lemma	PROPN
ejpam-5816	88	2	1	1	X
ejpam-5816	88	3	.	.	PUNCT
ejpam-5816	88	4	assume	assume	VERB
ejpam-5816	88	5	that	that	SCONJ
ejpam-5816	88	6	ℵ	ℵ	X
ejpam-5816	88	7	:	:	PUNCT
ejpam-5816	88	8	[	[	X
ejpam-5816	88	9	r	r	X
ejpam-5816	88	10	,	,	PUNCT
ejpam-5816	88	11	s	s	PART
ejpam-5816	88	12	]	]	X
ejpam-5816	88	13	→	→	PUNCT
ejpam-5816	88	14	r	r	NOUN
ejpam-5816	88	15	represents	represent	VERB
ejpam-5816	88	16	a	a	DET
ejpam-5816	88	17	differentiable	differentiable	ADJ
ejpam-5816	88	18	function	function	NOUN
ejpam-5816	88	19	on	on	ADP
ejpam-5816	88	20	(	(	PUNCT
ejpam-5816	88	21	r	r	NOUN
ejpam-5816	88	22	,	,	PUNCT
ejpam-5816	88	23	s	s	PART
ejpam-5816	88	24	)	)	PUNCT
ejpam-5816	88	25	,	,	PUNCT
ejpam-5816	88	26	where	where	SCONJ
ejpam-5816	88	27	ℵ′	ℵ′	ADP
ejpam-5816	88	28	∈	∈	PROPN
ejpam-5816	88	29	l1[r	l1[r	PROPN
ejpam-5816	88	30	,	,	PUNCT
ejpam-5816	88	31	s	s	X
ejpam-5816	88	32	]	]	PUNCT
ejpam-5816	88	33	and	and	CCONJ
ejpam-5816	88	34	r	r	X
ejpam-5816	88	35	<	<	X
ejpam-5816	88	36	s.	s.	PROPN
ejpam-5816	88	37	next	next	ADV
ejpam-5816	88	38	,	,	PUNCT
ejpam-5816	88	39	for	for	ADP
ejpam-5816	88	40	modified	modified	ADJ
ejpam-5816	88	41	hattaf	hattaf	NOUN
ejpam-5816	88	42	-	-	PUNCT
ejpam-5816	88	43	fractional	fractional	ADJ
ejpam-5816	88	44	integral	integral	ADJ
ejpam-5816	88	45	operators	operator	NOUN
ejpam-5816	88	46	,	,	PUNCT
ejpam-5816	88	47	we	we	PRON
ejpam-5816	88	48	have	have	VERB
ejpam-5816	88	49	the	the	DET
ejpam-5816	88	50	identity	identity	NOUN
ejpam-5816	88	51	given	give	VERB
ejpam-5816	88	52	below	below	ADP
ejpam-5816	88	53	:	:	PUNCT
ejpam-5816	88	54	[	[	PUNCT
ejpam-5816	88	55	(	(	PUNCT
ejpam-5816	88	56	t−	t−	ADJ
ejpam-5816	88	57	r)σ	r)σ	NOUN
ejpam-5816	88	58	+	+	CCONJ
ejpam-5816	88	59	(	(	PUNCT
ejpam-5816	88	60	s−	s−	PROPN
ejpam-5816	88	61	t)σ	t)σ	PUNCT
ejpam-5816	88	62	s−	s−	PROPN
ejpam-5816	88	63	r	r	NOUN
ejpam-5816	88	64	]	]	PUNCT
ejpam-5816	88	65	ℵ	ℵ	X
ejpam-5816	88	66	(	(	PUNCT
ejpam-5816	88	67	t	t	PROPN
ejpam-5816	88	68	)	)	PUNCT
ejpam-5816	89	1	+	+	NUM
ejpam-5816	89	2	σ(1−	σ(1−	PROPN
ejpam-5816	89	3	κ	κ	PART
ejpam-5816	89	4	)	)	PUNCT
ejpam-5816	89	5	κ(s−	κ(s−	PROPN
ejpam-5816	89	6	r	r	NOUN
ejpam-5816	89	7	)	)	PUNCT
ejpam-5816	89	8	γ(σ	γ(σ	PROPN
ejpam-5816	89	9	)	)	PUNCT
ejpam-5816	90	1	[	[	X
ejpam-5816	90	2	ℵ	ℵ	X
ejpam-5816	90	3	(	(	PUNCT
ejpam-5816	90	4	r	r	NOUN
ejpam-5816	90	5	)	)	PUNCT
ejpam-5816	90	6	+	+	NOUN
ejpam-5816	90	7	ℵ	ℵ	X
ejpam-5816	90	8	(	(	PUNCT
ejpam-5816	90	9	s	s	NOUN
ejpam-5816	90	10	)	)	PUNCT
ejpam-5816	90	11	]	]	PUNCT
ejpam-5816	91	1	−σm(κ)γ(σ	−σm(κ)γ(σ	ADJ
ejpam-5816	91	2	)	)	PUNCT
ejpam-5816	91	3	κ(s−	κ(s−	PROPN
ejpam-5816	91	4	r	r	NOUN
ejpam-5816	91	5	)	)	PUNCT
ejpam-5816	91	6	[	[	PUNCT
ejpam-5816	91	7	iκ	iκ	NOUN
ejpam-5816	91	8	,	,	PUNCT
ejpam-5816	91	9	σ	σ	PROPN
ejpam-5816	91	10	r	r	PROPN
ejpam-5816	91	11	,	,	PUNCT
ejpam-5816	91	12	t	t	PROPN
ejpam-5816	91	13	ℵ(r	ℵ(r	PROPN
ejpam-5816	91	14	)	)	PUNCT
ejpam-5816	92	1	+	+	NUM
ejpam-5816	92	2	iκ	iκ	X
ejpam-5816	92	3	,	,	PUNCT
ejpam-5816	92	4	σ	σ	PROPN
ejpam-5816	92	5	s	s	PROPN
ejpam-5816	92	6	,	,	PUNCT
ejpam-5816	92	7	t	t	PROPN
ejpam-5816	92	8	ℵ(s	ℵ(s	PROPN
ejpam-5816	92	9	)	)	PUNCT
ejpam-5816	92	10	]	]	PUNCT
ejpam-5816	93	1	=	=	PUNCT
ejpam-5816	93	2	(	(	PUNCT
ejpam-5816	93	3	t−	t−	X
ejpam-5816	93	4	r)σ+1	r)σ+1	PROPN
ejpam-5816	93	5	s−	s−	PROPN
ejpam-5816	94	1	r	r	NOUN
ejpam-5816	94	2	∫	∫	PROPN
ejpam-5816	94	3	1	1	NUM
ejpam-5816	94	4	0	0	NUM
ejpam-5816	94	5	ρσℵ′(ρt+	ρσℵ′(ρt+	PROPN
ejpam-5816	94	6	(	(	PUNCT
ejpam-5816	94	7	1−	1−	NUM
ejpam-5816	94	8	ρ)r)dρ−	ρ)r)dρ−	NUM
ejpam-5816	94	9	(	(	PUNCT
ejpam-5816	94	10	s−	s−	PROPN
ejpam-5816	94	11	t)σ+1	t)σ+1	PROPN
ejpam-5816	95	1	s−	s−	PROPN
ejpam-5816	95	2	r	r	NOUN
ejpam-5816	95	3	∫	∫	PROPN
ejpam-5816	95	4	1	1	NUM
ejpam-5816	95	5	0	0	NUM
ejpam-5816	95	6	ρϱℵ′(ρt+	ρϱℵ′(ρt+	PROPN
ejpam-5816	95	7	(	(	PUNCT
ejpam-5816	95	8	1−	1−	NUM
ejpam-5816	95	9	ρ)s)dρ	ρ)s)dρ	NOUN
ejpam-5816	95	10	,	,	PUNCT
ejpam-5816	95	11	where	where	SCONJ
ejpam-5816	95	12	κ	κ	PROPN
ejpam-5816	95	13	∈	∈	PROPN
ejpam-5816	95	14	(	(	PUNCT
ejpam-5816	95	15	0	0	NUM
ejpam-5816	95	16	,	,	PUNCT
ejpam-5816	95	17	1	1	NUM
ejpam-5816	95	18	]	]	PUNCT
ejpam-5816	95	19	,	,	PUNCT
ejpam-5816	95	20	t	t	PROPN
ejpam-5816	95	21	∈	∈	PROPN
ejpam-5816	96	1	[	[	X
ejpam-5816	96	2	r	r	X
ejpam-5816	96	3	,	,	PUNCT
ejpam-5816	96	4	s	s	PART
ejpam-5816	96	5	]	]	PUNCT
ejpam-5816	96	6	.	.	PUNCT
ejpam-5816	97	1	g.	g.	PROPN
ejpam-5816	97	2	rahman	rahman	PROPN
ejpam-5816	97	3	et	et	PROPN
ejpam-5816	97	4	al	al	PROPN
ejpam-5816	97	5	.	.	PUNCT
ejpam-5816	97	6	/	/	SYM
ejpam-5816	97	7	eur	eur	PROPN
ejpam-5816	97	8	.	.	PUNCT
ejpam-5816	98	1	j.	j.	PROPN
ejpam-5816	98	2	pure	pure	PROPN
ejpam-5816	98	3	appl	appl	PROPN
ejpam-5816	98	4	.	.	PROPN
ejpam-5816	98	5	math	math	PROPN
ejpam-5816	98	6	,	,	PUNCT
ejpam-5816	98	7	18	18	NUM
ejpam-5816	98	8	(	(	PUNCT
ejpam-5816	98	9	2	2	NUM
ejpam-5816	98	10	)	)	PUNCT
ejpam-5816	98	11	(	(	PUNCT
ejpam-5816	98	12	2025	2025	NUM
ejpam-5816	98	13	)	)	PUNCT
ejpam-5816	98	14	,	,	PUNCT
ejpam-5816	98	15	5816	5816	NUM
ejpam-5816	98	16	5	5	NUM
ejpam-5816	98	17	of	of	ADP
ejpam-5816	98	18	18	18	NUM
ejpam-5816	98	19	proof	proof	NOUN
ejpam-5816	98	20	.	.	PUNCT
ejpam-5816	99	1	for	for	ADP
ejpam-5816	99	2	simplicity	simplicity	NOUN
ejpam-5816	99	3	,	,	PUNCT
ejpam-5816	99	4	let	let	VERB
ejpam-5816	99	5	us	we	PRON
ejpam-5816	99	6	consider	consider	VERB
ejpam-5816	99	7	i	i	PRON
ejpam-5816	99	8	=	=	PUNCT
ejpam-5816	99	9	(	(	PUNCT
ejpam-5816	100	1	t−	t−	X
ejpam-5816	100	2	r)σ+1	r)σ+1	PROPN
ejpam-5816	100	3	s−	s−	PROPN
ejpam-5816	100	4	r	r	NOUN
ejpam-5816	100	5	∫	∫	PROPN
ejpam-5816	100	6	1	1	NUM
ejpam-5816	100	7	0	0	NUM
ejpam-5816	100	8	ρσℵ′(ρt+	ρσℵ′(ρt+	PROPN
ejpam-5816	100	9	(	(	PUNCT
ejpam-5816	100	10	1−	1−	NUM
ejpam-5816	100	11	ρ)r)dρ−	ρ)r)dρ−	NUM
ejpam-5816	100	12	(	(	PUNCT
ejpam-5816	100	13	s−	s−	PROPN
ejpam-5816	100	14	t)σ+1	t)σ+1	PROPN
ejpam-5816	101	1	s−	s−	PROPN
ejpam-5816	101	2	r	r	NOUN
ejpam-5816	101	3	∫	∫	PROPN
ejpam-5816	101	4	1	1	NUM
ejpam-5816	101	5	0	0	NUM
ejpam-5816	101	6	ρσℵ′(ρt+	ρσℵ′(ρt+	PROPN
ejpam-5816	101	7	(	(	PUNCT
ejpam-5816	101	8	1−	1−	NUM
ejpam-5816	101	9	ρ)s)dρ	ρ)s)dρ	X
ejpam-5816	101	10	=	=	PUNCT
ejpam-5816	101	11	(	(	PUNCT
ejpam-5816	101	12	t−	t−	X
ejpam-5816	101	13	r)σ+1	r)σ+1	PROPN
ejpam-5816	101	14	s−	s−	PROPN
ejpam-5816	101	15	r	r	PROPN
ejpam-5816	101	16	i1	i1	PROPN
ejpam-5816	101	17	−	−	PROPN
ejpam-5816	102	1	(	(	PUNCT
ejpam-5816	102	2	s−	s−	PROPN
ejpam-5816	102	3	t)σ+1	t)σ+1	PROPN
ejpam-5816	102	4	s−	s−	PROPN
ejpam-5816	102	5	r	r	NOUN
ejpam-5816	102	6	i2	i2	PROPN
ejpam-5816	102	7	,	,	PUNCT
ejpam-5816	102	8	(	(	PUNCT
ejpam-5816	102	9	6	6	NUM
ejpam-5816	102	10	)	)	PUNCT
ejpam-5816	102	11	where	where	SCONJ
ejpam-5816	102	12	i1	i1	PROPN
ejpam-5816	102	13	=	=	PUNCT
ejpam-5816	102	14	∫	∫	PROPN
ejpam-5816	102	15	1	1	NUM
ejpam-5816	102	16	0	0	NUM
ejpam-5816	102	17	ρσℵ′(ρt+	ρσℵ′(ρt+	PROPN
ejpam-5816	102	18	(	(	PUNCT
ejpam-5816	102	19	1−	1−	NUM
ejpam-5816	102	20	ρ)r)dρ	ρ)r)dρ	NOUN
ejpam-5816	102	21	=	=	PROPN
ejpam-5816	102	22	ρσℵ(ρt+	ρσℵ(ρt+	PROPN
ejpam-5816	102	23	(	(	PUNCT
ejpam-5816	102	24	1−	1−	NUM
ejpam-5816	102	25	ρ)r	ρ)r	NOUN
ejpam-5816	102	26	)	)	PUNCT
ejpam-5816	103	1	t−	t−	ADP
ejpam-5816	103	2	r	r	NOUN
ejpam-5816	103	3	|10	|10	NOUN
ejpam-5816	103	4	+	+	CCONJ
ejpam-5816	103	5	σ	σ	NOUN
ejpam-5816	103	6	t−	t−	PROPN
ejpam-5816	103	7	r	r	NOUN
ejpam-5816	103	8	∫	∫	PROPN
ejpam-5816	103	9	1	1	NUM
ejpam-5816	103	10	0	0	NUM
ejpam-5816	103	11	ρσ−1ℵ(ρt+	ρσ−1ℵ(ρt+	NOUN
ejpam-5816	103	12	(	(	PUNCT
ejpam-5816	103	13	1−	1−	NUM
ejpam-5816	103	14	ρ)r)dρ	ρ)r)dρ	NOUN
ejpam-5816	103	15	by	by	ADP
ejpam-5816	103	16	substituting	substitute	VERB
ejpam-5816	103	17	ρ	ρ	NOUN
ejpam-5816	103	18	=	=	SYM
ejpam-5816	103	19	u−r	u−r	ADJ
ejpam-5816	103	20	t−r	t−r	NOUN
ejpam-5816	103	21	in	in	ADP
ejpam-5816	103	22	the	the	DET
ejpam-5816	103	23	integral	integral	ADJ
ejpam-5816	103	24	part	part	NOUN
ejpam-5816	103	25	,	,	PUNCT
ejpam-5816	103	26	we	we	PRON
ejpam-5816	103	27	get	get	VERB
ejpam-5816	103	28	i1	i1	NOUN
ejpam-5816	103	29	=	=	PUNCT
ejpam-5816	103	30	ℵ(t	ℵ(t	PROPN
ejpam-5816	103	31	)	)	PUNCT
ejpam-5816	104	1	t−	t−	PROPN
ejpam-5816	104	2	r	r	NOUN
ejpam-5816	104	3	+	+	PROPN
ejpam-5816	104	4	σ	σ	NOUN
ejpam-5816	104	5	(	(	PUNCT
ejpam-5816	104	6	t−	t−	PROPN
ejpam-5816	104	7	r)σ+1	r)σ+1	PROPN
ejpam-5816	104	8	∫	∫	PROPN
ejpam-5816	104	9	t	t	PROPN
ejpam-5816	104	10	r	r	PROPN
ejpam-5816	104	11	(	(	PUNCT
ejpam-5816	104	12	u−	u−	PROPN
ejpam-5816	104	13	r)σ−1ℵ	r)σ−1ℵ	X
ejpam-5816	104	14	(	(	PUNCT
ejpam-5816	104	15	u	u	NOUN
ejpam-5816	104	16	)	)	PUNCT
ejpam-5816	104	17	du	du	PROPN
ejpam-5816	104	18	.	.	X
ejpam-5816	104	19	(	(	PUNCT
ejpam-5816	104	20	7	7	X
ejpam-5816	104	21	)	)	PUNCT
ejpam-5816	104	22	similarly	similarly	ADV
ejpam-5816	104	23	,	,	PUNCT
ejpam-5816	104	24	one	one	PRON
ejpam-5816	104	25	can	can	AUX
ejpam-5816	104	26	get	get	VERB
ejpam-5816	104	27	i2	i2	PROPN
ejpam-5816	104	28	=	=	PUNCT
ejpam-5816	104	29	−	−	PROPN
ejpam-5816	104	30	ℵ(t	ℵ(t	PROPN
ejpam-5816	104	31	)	)	PUNCT
ejpam-5816	104	32	s−	s−	PROPN
ejpam-5816	104	33	t	t	PROPN
ejpam-5816	104	34	+	+	CCONJ
ejpam-5816	104	35	σ	σ	PROPN
ejpam-5816	104	36	(	(	PUNCT
ejpam-5816	105	1	s−	s−	PROPN
ejpam-5816	105	2	t)σ+1	t)σ+1	PROPN
ejpam-5816	105	3	∫	∫	PROPN
ejpam-5816	105	4	s	s	PART
ejpam-5816	105	5	t	t	PROPN
ejpam-5816	105	6	(	(	PUNCT
ejpam-5816	105	7	s−	s−	PROPN
ejpam-5816	105	8	u)σ−1ℵ	u)σ−1ℵ	PROPN
ejpam-5816	105	9	(	(	PUNCT
ejpam-5816	105	10	u	u	NOUN
ejpam-5816	105	11	)	)	PUNCT
ejpam-5816	105	12	du	du	PROPN
ejpam-5816	105	13	.	.	X
ejpam-5816	106	1	(	(	PUNCT
ejpam-5816	106	2	8)	8)	NUM
ejpam-5816	106	3	by	by	ADP
ejpam-5816	106	4	substituting	substitute	VERB
ejpam-5816	106	5	(	(	PUNCT
ejpam-5816	106	6	7	7	NUM
ejpam-5816	106	7	)	)	PUNCT
ejpam-5816	106	8	and	and	CCONJ
ejpam-5816	106	9	(	(	PUNCT
ejpam-5816	106	10	8)	8)	NUM
ejpam-5816	106	11	in	in	ADP
ejpam-5816	106	12	(	(	PUNCT
ejpam-5816	106	13	6	6	NUM
ejpam-5816	106	14	)	)	PUNCT
ejpam-5816	106	15	and	and	CCONJ
ejpam-5816	106	16	then	then	ADV
ejpam-5816	106	17	after	after	ADP
ejpam-5816	106	18	a	a	DET
ejpam-5816	106	19	simple	simple	ADJ
ejpam-5816	106	20	computation	computation	NOUN
ejpam-5816	106	21	,	,	PUNCT
ejpam-5816	106	22	we	we	PRON
ejpam-5816	106	23	get	get	VERB
ejpam-5816	106	24	the	the	DET
ejpam-5816	106	25	desired	desire	VERB
ejpam-5816	106	26	lemma	lemma	PROPN
ejpam-5816	106	27	1	1	X
ejpam-5816	106	28	.	.	PUNCT
ejpam-5816	106	29	remark	remark	PROPN
ejpam-5816	106	30	2	2	NUM
ejpam-5816	106	31	.	.	PUNCT
ejpam-5816	106	32	applying	apply	VERB
ejpam-5816	106	33	lemma	lemma	PROPN
ejpam-5816	106	34	1	1	NUM
ejpam-5816	106	35	for	for	ADP
ejpam-5816	106	36	σ	σ	NOUN
ejpam-5816	106	37	=	=	SYM
ejpam-5816	106	38	κ	κ	NOUN
ejpam-5816	106	39	,	,	PUNCT
ejpam-5816	106	40	we	we	PRON
ejpam-5816	106	41	get	get	VERB
ejpam-5816	106	42	the	the	DET
ejpam-5816	106	43	lemma	lemma	PROPN
ejpam-5816	106	44	1	1	NUM
ejpam-5816	106	45	given	give	VERB
ejpam-5816	106	46	in	in	ADP
ejpam-5816	106	47	[	[	X
ejpam-5816	106	48	40	40	NUM
ejpam-5816	106	49	]	]	PUNCT
ejpam-5816	106	50	.	.	PUNCT
ejpam-5816	107	1	theorem	theorem	NOUN
ejpam-5816	107	2	1	1	NUM
ejpam-5816	107	3	.	.	PUNCT
ejpam-5816	107	4	assume	assume	VERB
ejpam-5816	107	5	that	that	SCONJ
ejpam-5816	107	6	ℵ	ℵ	X
ejpam-5816	107	7	:	:	PUNCT
ejpam-5816	107	8	[	[	X
ejpam-5816	107	9	r	r	X
ejpam-5816	107	10	,	,	PUNCT
ejpam-5816	107	11	s	s	PART
ejpam-5816	107	12	]	]	X
ejpam-5816	107	13	→	→	PUNCT
ejpam-5816	107	14	r	r	NOUN
ejpam-5816	107	15	be	be	AUX
ejpam-5816	107	16	a	a	DET
ejpam-5816	107	17	differentiable	differentiable	ADJ
ejpam-5816	107	18	function	function	NOUN
ejpam-5816	107	19	on	on	ADP
ejpam-5816	107	20	(	(	PUNCT
ejpam-5816	107	21	r	r	NOUN
ejpam-5816	107	22	,	,	PUNCT
ejpam-5816	107	23	s	s	PART
ejpam-5816	107	24	)	)	PUNCT
ejpam-5816	107	25	,	,	PUNCT
ejpam-5816	107	26	with	with	ADP
ejpam-5816	107	27	ℵ′	ℵ′	PUNCT
ejpam-5816	107	28	∈	∈	PROPN
ejpam-5816	107	29	l1[r	l1[r	PROPN
ejpam-5816	107	30	,	,	PUNCT
ejpam-5816	107	31	s	s	X
ejpam-5816	107	32	]	]	PUNCT
ejpam-5816	107	33	and	and	CCONJ
ejpam-5816	107	34	r	r	X
ejpam-5816	107	35	<	<	X
ejpam-5816	107	36	s.	s.	PROPN
ejpam-5816	107	37	then	then	ADV
ejpam-5816	107	38	,	,	PUNCT
ejpam-5816	107	39	the	the	DET
ejpam-5816	107	40	following	follow	VERB
ejpam-5816	107	41	inequality	inequality	NOUN
ejpam-5816	107	42	holds	hold	VERB
ejpam-5816	107	43	for	for	ADP
ejpam-5816	107	44	hattaf	hattaf	NOUN
ejpam-5816	107	45	-	-	PUNCT
ejpam-5816	107	46	fractional	fractional	ADJ
ejpam-5816	107	47	integral	integral	ADJ
ejpam-5816	107	48	operators	operator	NOUN
ejpam-5816	107	49	(	(	PUNCT
ejpam-5816	107	50	4	4	NUM
ejpam-5816	107	51	)	)	PUNCT
ejpam-5816	107	52	and	and	CCONJ
ejpam-5816	107	53	(	(	PUNCT
ejpam-5816	107	54	5	5	X
ejpam-5816	107	55	)	)	PUNCT
ejpam-5816	107	56	if	if	SCONJ
ejpam-5816	107	57	|ℵ′|	|ℵ′|	PROPN
ejpam-5816	107	58	is	be	AUX
ejpam-5816	107	59	a	a	DET
ejpam-5816	107	60	convex	convex	NOUN
ejpam-5816	107	61	function∣∣∣	function∣∣∣	NOUN
ejpam-5816	108	1	[	[	X
ejpam-5816	108	2	(	(	PUNCT
ejpam-5816	108	3	t−	t−	ADJ
ejpam-5816	108	4	r)σ	r)σ	NOUN
ejpam-5816	108	5	+	+	CCONJ
ejpam-5816	108	6	(	(	PUNCT
ejpam-5816	108	7	s−	s−	PROPN
ejpam-5816	108	8	t)σ	t)σ	PUNCT
ejpam-5816	108	9	s−	s−	PROPN
ejpam-5816	108	10	r	r	NOUN
ejpam-5816	108	11	]	]	PUNCT
ejpam-5816	108	12	ℵ	ℵ	X
ejpam-5816	108	13	(	(	PUNCT
ejpam-5816	108	14	t	t	PROPN
ejpam-5816	108	15	)	)	PUNCT
ejpam-5816	108	16	+	+	NUM
ejpam-5816	108	17	σ(1−	σ(1−	PROPN
ejpam-5816	108	18	κ	κ	PART
ejpam-5816	108	19	)	)	PUNCT
ejpam-5816	108	20	κ(s−	κ(s−	PROPN
ejpam-5816	108	21	r	r	NOUN
ejpam-5816	108	22	)	)	PUNCT
ejpam-5816	108	23	γ(σ	γ(σ	PROPN
ejpam-5816	108	24	)	)	PUNCT
ejpam-5816	109	1	[	[	X
ejpam-5816	109	2	ℵ	ℵ	X
ejpam-5816	109	3	(	(	PUNCT
ejpam-5816	109	4	r	r	NOUN
ejpam-5816	109	5	)	)	PUNCT
ejpam-5816	109	6	+	+	NOUN
ejpam-5816	109	7	ℵ	ℵ	X
ejpam-5816	109	8	(	(	PUNCT
ejpam-5816	109	9	s	s	NOUN
ejpam-5816	109	10	)	)	PUNCT
ejpam-5816	109	11	]	]	PUNCT
ejpam-5816	110	1	−σm(κ)γ(σ	−σm(κ)γ(σ	ADJ
ejpam-5816	110	2	)	)	PUNCT
ejpam-5816	110	3	κ(s−	κ(s−	PROPN
ejpam-5816	110	4	r	r	NOUN
ejpam-5816	110	5	)	)	PUNCT
ejpam-5816	110	6	[	[	PUNCT
ejpam-5816	110	7	iκ	iκ	NOUN
ejpam-5816	110	8	,	,	PUNCT
ejpam-5816	110	9	σ	σ	PROPN
ejpam-5816	110	10	r	r	PROPN
ejpam-5816	110	11	,	,	PUNCT
ejpam-5816	110	12	t	t	PROPN
ejpam-5816	110	13	ℵ(r	ℵ(r	PROPN
ejpam-5816	110	14	)	)	PUNCT
ejpam-5816	111	1	+	+	NUM
ejpam-5816	111	2	iκ	iκ	X
ejpam-5816	111	3	,	,	PUNCT
ejpam-5816	111	4	σ	σ	PROPN
ejpam-5816	111	5	s	s	PROPN
ejpam-5816	111	6	,	,	PUNCT
ejpam-5816	111	7	t	t	PROPN
ejpam-5816	111	8	ℵ(s	ℵ(s	PROPN
ejpam-5816	111	9	)	)	PUNCT
ejpam-5816	111	10	]	]	PUNCT
ejpam-5816	111	11	∣∣∣	∣∣∣	NOUN
ejpam-5816	111	12	≤(t−	≤(t−	NOUN
ejpam-5816	111	13	r)σ+1	r)σ+1	PROPN
ejpam-5816	111	14	s−	s−	PROPN
ejpam-5816	111	15	r	r	NOUN
ejpam-5816	111	16	{	{	PUNCT
ejpam-5816	111	17	ℵ′	ℵ′	X
ejpam-5816	111	18	(	(	PUNCT
ejpam-5816	111	19	t	t	NOUN
ejpam-5816	111	20	)	)	PUNCT
ejpam-5816	111	21	σ	σ	NOUN
ejpam-5816	112	1	+	+	NUM
ejpam-5816	112	2	2	2	NUM
ejpam-5816	112	3	+	+	NUM
ejpam-5816	112	4	ℵ′	ℵ′	ADP
ejpam-5816	112	5	(	(	PUNCT
ejpam-5816	112	6	r	r	NOUN
ejpam-5816	112	7	)	)	PUNCT
ejpam-5816	112	8	(	(	PUNCT
ejpam-5816	112	9	σ	σ	NOUN
ejpam-5816	112	10	+	+	NOUN
ejpam-5816	112	11	1)(σ	1)(σ	NUM
ejpam-5816	112	12	+	+	CCONJ
ejpam-5816	112	13	2	2	NUM
ejpam-5816	112	14	)	)	PUNCT
ejpam-5816	112	15	}	}	PUNCT
ejpam-5816	112	16	+	+	CCONJ
ejpam-5816	112	17	(	(	PUNCT
ejpam-5816	112	18	s−	s−	PROPN
ejpam-5816	112	19	t)σ+1	t)σ+1	PROPN
ejpam-5816	112	20	s−	s−	PROPN
ejpam-5816	112	21	r	r	NOUN
ejpam-5816	112	22	{	{	PUNCT
ejpam-5816	112	23	ℵ′	ℵ′	X
ejpam-5816	112	24	(	(	PUNCT
ejpam-5816	112	25	t	t	NOUN
ejpam-5816	112	26	)	)	PUNCT
ejpam-5816	112	27	σ	σ	NOUN
ejpam-5816	112	28	+	+	NUM
ejpam-5816	112	29	2	2	NUM
ejpam-5816	112	30	+	+	NUM
ejpam-5816	112	31	ℵ′	ℵ′	ADP
ejpam-5816	112	32	(	(	PUNCT
ejpam-5816	112	33	s	s	X
ejpam-5816	112	34	)	)	PUNCT
ejpam-5816	112	35	(	(	PUNCT
ejpam-5816	112	36	σ	σ	NOUN
ejpam-5816	112	37	+	+	NUM
ejpam-5816	112	38	1)(σ	1)(σ	NUM
ejpam-5816	112	39	+	+	CCONJ
ejpam-5816	112	40	2	2	NUM
ejpam-5816	112	41	)	)	PUNCT
ejpam-5816	112	42	}	}	PUNCT
ejpam-5816	112	43	,	,	PUNCT
ejpam-5816	112	44	where	where	SCONJ
ejpam-5816	112	45	t	t	PROPN
ejpam-5816	112	46	∈	∈	PROPN
ejpam-5816	112	47	[	[	X
ejpam-5816	112	48	r	r	X
ejpam-5816	112	49	,	,	PUNCT
ejpam-5816	112	50	s	s	PART
ejpam-5816	112	51	]	]	X
ejpam-5816	112	52	,	,	PUNCT
ejpam-5816	112	53	κ	κ	PROPN
ejpam-5816	112	54	∈	∈	PROPN
ejpam-5816	112	55	(	(	PUNCT
ejpam-5816	112	56	0	0	NUM
ejpam-5816	112	57	,	,	PUNCT
ejpam-5816	112	58	1	1	NUM
ejpam-5816	112	59	]	]	PUNCT
ejpam-5816	112	60	.	.	PUNCT
ejpam-5816	113	1	proof	proof	NOUN
ejpam-5816	113	2	.	.	PUNCT
ejpam-5816	114	1	by	by	ADP
ejpam-5816	114	2	using	use	VERB
ejpam-5816	114	3	lemma	lemma	PROPN
ejpam-5816	114	4	1	1	NUM
ejpam-5816	114	5	,	,	PUNCT
ejpam-5816	114	6	we	we	PRON
ejpam-5816	114	7	have∣∣∣	have∣∣∣	PUNCT
ejpam-5816	115	1	[	[	X
ejpam-5816	115	2	(	(	PUNCT
ejpam-5816	115	3	t−	t−	ADJ
ejpam-5816	115	4	r)σ	r)σ	NOUN
ejpam-5816	115	5	+	+	CCONJ
ejpam-5816	115	6	(	(	PUNCT
ejpam-5816	115	7	s−	s−	PROPN
ejpam-5816	115	8	t)σ	t)σ	PUNCT
ejpam-5816	115	9	s−	s−	PROPN
ejpam-5816	115	10	r	r	NOUN
ejpam-5816	115	11	]	]	PUNCT
ejpam-5816	115	12	ℵ	ℵ	X
ejpam-5816	115	13	(	(	PUNCT
ejpam-5816	115	14	t	t	PROPN
ejpam-5816	115	15	)	)	PUNCT
ejpam-5816	115	16	+	+	NUM
ejpam-5816	115	17	σ(1−	σ(1−	PROPN
ejpam-5816	115	18	κ	κ	PART
ejpam-5816	115	19	)	)	PUNCT
ejpam-5816	115	20	κ(s−	κ(s−	PROPN
ejpam-5816	115	21	r	r	NOUN
ejpam-5816	115	22	)	)	PUNCT
ejpam-5816	115	23	γ(σ	γ(σ	PROPN
ejpam-5816	115	24	)	)	PUNCT
ejpam-5816	116	1	[	[	X
ejpam-5816	116	2	ℵ	ℵ	X
ejpam-5816	116	3	(	(	PUNCT
ejpam-5816	116	4	r	r	NOUN
ejpam-5816	116	5	)	)	PUNCT
ejpam-5816	116	6	+	+	NOUN
ejpam-5816	116	7	ℵ	ℵ	X
ejpam-5816	116	8	(	(	PUNCT
ejpam-5816	116	9	s	s	NOUN
ejpam-5816	116	10	)	)	PUNCT
ejpam-5816	116	11	]	]	PUNCT
ejpam-5816	117	1	g.	g.	PROPN
ejpam-5816	117	2	rahman	rahman	PROPN
ejpam-5816	117	3	et	et	PROPN
ejpam-5816	117	4	al	al	PROPN
ejpam-5816	117	5	.	.	PUNCT
ejpam-5816	117	6	/	/	SYM
ejpam-5816	117	7	eur	eur	PROPN
ejpam-5816	117	8	.	.	PUNCT
ejpam-5816	118	1	j.	j.	PROPN
ejpam-5816	118	2	pure	pure	PROPN
ejpam-5816	118	3	appl	appl	PROPN
ejpam-5816	118	4	.	.	PROPN
ejpam-5816	118	5	math	math	PROPN
ejpam-5816	118	6	,	,	PUNCT
ejpam-5816	118	7	18	18	NUM
ejpam-5816	118	8	(	(	PUNCT
ejpam-5816	118	9	2	2	NUM
ejpam-5816	118	10	)	)	PUNCT
ejpam-5816	118	11	(	(	PUNCT
ejpam-5816	118	12	2025	2025	NUM
ejpam-5816	118	13	)	)	PUNCT
ejpam-5816	118	14	,	,	PUNCT
ejpam-5816	118	15	5816	5816	NUM
ejpam-5816	118	16	6	6	NUM
ejpam-5816	118	17	of	of	ADP
ejpam-5816	118	18	18	18	NUM
ejpam-5816	118	19	−σm(κ)γ(σ	−σm(κ)γ(σ	ADJ
ejpam-5816	118	20	)	)	PUNCT
ejpam-5816	118	21	κ(s−	κ(s−	PROPN
ejpam-5816	118	22	r	r	NOUN
ejpam-5816	118	23	)	)	PUNCT
ejpam-5816	118	24	[	[	PUNCT
ejpam-5816	118	25	iκ	iκ	NOUN
ejpam-5816	118	26	,	,	PUNCT
ejpam-5816	118	27	σ	σ	PROPN
ejpam-5816	118	28	r	r	PROPN
ejpam-5816	118	29	,	,	PUNCT
ejpam-5816	118	30	t	t	PROPN
ejpam-5816	118	31	ℵ(r	ℵ(r	PROPN
ejpam-5816	118	32	)	)	PUNCT
ejpam-5816	118	33	+	+	NUM
ejpam-5816	118	34	iκ	iκ	X
ejpam-5816	118	35	,	,	PUNCT
ejpam-5816	118	36	σ	σ	PROPN
ejpam-5816	118	37	s	s	PROPN
ejpam-5816	118	38	,	,	PUNCT
ejpam-5816	118	39	t	t	PROPN
ejpam-5816	118	40	ℵ(s	ℵ(s	PROPN
ejpam-5816	118	41	)	)	PUNCT
ejpam-5816	118	42	]	]	PUNCT
ejpam-5816	118	43	∣∣∣	∣∣∣	NOUN
ejpam-5816	118	44	≤(t−	≤(t−	NOUN
ejpam-5816	118	45	r)σ+1	r)σ+1	PROPN
ejpam-5816	118	46	s−	s−	PROPN
ejpam-5816	118	47	r	r	NOUN
ejpam-5816	118	48	∫	∫	PROPN
ejpam-5816	118	49	1	1	NUM
ejpam-5816	118	50	0	0	NUM
ejpam-5816	118	51	ρσ|ℵ′(ρt+	ρσ|ℵ′(ρt+	NOUN
ejpam-5816	118	52	(	(	PUNCT
ejpam-5816	118	53	1−	1−	NUM
ejpam-5816	118	54	ρ)r)|dρ−	ρ)r)|dρ−	NUM
ejpam-5816	118	55	(	(	PUNCT
ejpam-5816	118	56	s−	s−	PROPN
ejpam-5816	118	57	t)σ+1	t)σ+1	PROPN
ejpam-5816	119	1	s−	s−	PROPN
ejpam-5816	119	2	r	r	NOUN
ejpam-5816	119	3	∫	∫	PROPN
ejpam-5816	119	4	1	1	NUM
ejpam-5816	119	5	0	0	NUM
ejpam-5816	119	6	ρσ|ℵ′(ρt+	ρσ|ℵ′(ρt+	NOUN
ejpam-5816	119	7	(	(	PUNCT
ejpam-5816	119	8	1−	1−	NUM
ejpam-5816	119	9	ρ)s)|dρ	ρ)s)|dρ	NOUN
ejpam-5816	119	10	.	.	PUNCT
ejpam-5816	120	1	by	by	ADP
ejpam-5816	120	2	applying	apply	VERB
ejpam-5816	120	3	the	the	DET
ejpam-5816	120	4	convexity	convexity	NOUN
ejpam-5816	120	5	of	of	ADP
ejpam-5816	120	6	|ℵ′|	|ℵ′|	PROPN
ejpam-5816	120	7	,	,	PUNCT
ejpam-5816	120	8	we	we	PRON
ejpam-5816	120	9	get∣∣∣	get∣∣∣	VERB
ejpam-5816	121	1	[	[	X
ejpam-5816	121	2	(	(	PUNCT
ejpam-5816	121	3	t−	t−	ADJ
ejpam-5816	121	4	r)σ	r)σ	NOUN
ejpam-5816	121	5	+	+	CCONJ
ejpam-5816	121	6	(	(	PUNCT
ejpam-5816	121	7	s−	s−	PROPN
ejpam-5816	121	8	t)σ	t)σ	PUNCT
ejpam-5816	121	9	s−	s−	PROPN
ejpam-5816	121	10	r	r	NOUN
ejpam-5816	121	11	]	]	PUNCT
ejpam-5816	121	12	ℵ	ℵ	X
ejpam-5816	121	13	(	(	PUNCT
ejpam-5816	121	14	t	t	PROPN
ejpam-5816	121	15	)	)	PUNCT
ejpam-5816	121	16	+	+	NUM
ejpam-5816	121	17	σ(1−	σ(1−	PROPN
ejpam-5816	121	18	κ	κ	PART
ejpam-5816	121	19	)	)	PUNCT
ejpam-5816	121	20	κ(s−	κ(s−	PROPN
ejpam-5816	121	21	r	r	NOUN
ejpam-5816	121	22	)	)	PUNCT
ejpam-5816	121	23	γ(σ	γ(σ	PROPN
ejpam-5816	121	24	)	)	PUNCT
ejpam-5816	122	1	[	[	X
ejpam-5816	122	2	ℵ	ℵ	X
ejpam-5816	122	3	(	(	PUNCT
ejpam-5816	122	4	r	r	NOUN
ejpam-5816	122	5	)	)	PUNCT
ejpam-5816	122	6	+	+	NOUN
ejpam-5816	122	7	ℵ	ℵ	X
ejpam-5816	122	8	(	(	PUNCT
ejpam-5816	122	9	s	s	NOUN
ejpam-5816	122	10	)	)	PUNCT
ejpam-5816	122	11	]	]	PUNCT
ejpam-5816	123	1	−σm(κ)γ(σ	−σm(κ)γ(σ	ADJ
ejpam-5816	123	2	)	)	PUNCT
ejpam-5816	123	3	κ(s−	κ(s−	PROPN
ejpam-5816	123	4	r	r	NOUN
ejpam-5816	123	5	)	)	PUNCT
ejpam-5816	123	6	[	[	PUNCT
ejpam-5816	123	7	iκ	iκ	NOUN
ejpam-5816	123	8	,	,	PUNCT
ejpam-5816	123	9	σ	σ	PROPN
ejpam-5816	123	10	r	r	PROPN
ejpam-5816	123	11	,	,	PUNCT
ejpam-5816	123	12	t	t	PROPN
ejpam-5816	123	13	ℵ(r	ℵ(r	PROPN
ejpam-5816	123	14	)	)	PUNCT
ejpam-5816	124	1	+	+	NUM
ejpam-5816	124	2	iκ	iκ	X
ejpam-5816	124	3	,	,	PUNCT
ejpam-5816	124	4	σ	σ	PROPN
ejpam-5816	124	5	s	s	PROPN
ejpam-5816	124	6	,	,	PUNCT
ejpam-5816	124	7	t	t	PROPN
ejpam-5816	124	8	ℵ(s	ℵ(s	PROPN
ejpam-5816	124	9	)	)	PUNCT
ejpam-5816	124	10	]	]	PUNCT
ejpam-5816	124	11	∣∣∣	∣∣∣	NOUN
ejpam-5816	124	12	≤(t−	≤(t−	NOUN
ejpam-5816	124	13	r)σ+1	r)σ+1	PROPN
ejpam-5816	124	14	s−	s−	PROPN
ejpam-5816	124	15	r	r	NOUN
ejpam-5816	124	16	∫	∫	PROPN
ejpam-5816	124	17	1	1	NUM
ejpam-5816	124	18	0	0	NUM
ejpam-5816	124	19	ρσ[ρ	ρσ[ρ	PROPN
ejpam-5816	124	20	∣∣ℵ′(t	∣∣ℵ′(t	NOUN
ejpam-5816	124	21	)	)	PUNCT
ejpam-5816	124	22	∣∣+	∣∣+	X
ejpam-5816	124	23	(	(	PUNCT
ejpam-5816	124	24	1−	1−	NUM
ejpam-5816	124	25	ρ	ρ	NOUN
ejpam-5816	124	26	)	)	PUNCT
ejpam-5816	124	27	∣∣ℵ′(r	∣∣ℵ′(r	NOUN
ejpam-5816	124	28	)	)	PUNCT
ejpam-5816	124	29	∣∣]dρ	∣∣]dρ	NOUN
ejpam-5816	125	1	+	+	CCONJ
ejpam-5816	125	2	(	(	PUNCT
ejpam-5816	125	3	s−	s−	PROPN
ejpam-5816	125	4	t)σ+1	t)σ+1	PROPN
ejpam-5816	125	5	s−	s−	PROPN
ejpam-5816	126	1	r	r	NOUN
ejpam-5816	126	2	∫	∫	PROPN
ejpam-5816	126	3	1	1	NUM
ejpam-5816	126	4	0	0	NUM
ejpam-5816	126	5	ρσ[ρ	ρσ[ρ	PROPN
ejpam-5816	126	6	∣∣ℵ′(s	∣∣ℵ′(s	NOUN
ejpam-5816	126	7	)	)	PUNCT
ejpam-5816	126	8	∣∣+	∣∣+	PUNCT
ejpam-5816	126	9	(	(	PUNCT
ejpam-5816	126	10	1−	1−	NUM
ejpam-5816	126	11	ρ	ρ	NUM
ejpam-5816	126	12	)	)	PUNCT
ejpam-5816	126	13	∣∣ℵ′(t	∣∣ℵ′(t	NOUN
ejpam-5816	126	14	)	)	PUNCT
ejpam-5816	126	15	∣∣]dρ	∣∣]dρ	NOUN
ejpam-5816	126	16	.	.	PUNCT
ejpam-5816	127	1	after	after	ADP
ejpam-5816	127	2	solving	solve	VERB
ejpam-5816	127	3	the	the	DET
ejpam-5816	127	4	above	above	ADJ
ejpam-5816	127	5	integrals	integral	NOUN
ejpam-5816	127	6	,	,	PUNCT
ejpam-5816	127	7	we	we	PRON
ejpam-5816	127	8	get∣∣∣	get∣∣∣	VERB
ejpam-5816	128	1	[	[	X
ejpam-5816	128	2	(	(	PUNCT
ejpam-5816	128	3	t−	t−	ADJ
ejpam-5816	128	4	r)σ	r)σ	NOUN
ejpam-5816	128	5	+	+	CCONJ
ejpam-5816	128	6	(	(	PUNCT
ejpam-5816	128	7	s−	s−	PROPN
ejpam-5816	128	8	t)σ	t)σ	PUNCT
ejpam-5816	128	9	s−	s−	PROPN
ejpam-5816	128	10	r	r	NOUN
ejpam-5816	128	11	]	]	PUNCT
ejpam-5816	128	12	ℵ	ℵ	X
ejpam-5816	128	13	(	(	PUNCT
ejpam-5816	128	14	t	t	PROPN
ejpam-5816	128	15	)	)	PUNCT
ejpam-5816	128	16	+	+	NUM
ejpam-5816	128	17	σ(1−	σ(1−	PROPN
ejpam-5816	128	18	κ	κ	PART
ejpam-5816	128	19	)	)	PUNCT
ejpam-5816	128	20	κ(s−	κ(s−	PROPN
ejpam-5816	128	21	r	r	NOUN
ejpam-5816	128	22	)	)	PUNCT
ejpam-5816	128	23	γ(σ	γ(σ	PROPN
ejpam-5816	128	24	)	)	PUNCT
ejpam-5816	129	1	[	[	X
ejpam-5816	129	2	ℵ	ℵ	X
ejpam-5816	129	3	(	(	PUNCT
ejpam-5816	129	4	r	r	NOUN
ejpam-5816	129	5	)	)	PUNCT
ejpam-5816	129	6	+	+	NOUN
ejpam-5816	129	7	ℵ	ℵ	X
ejpam-5816	129	8	(	(	PUNCT
ejpam-5816	129	9	s	s	NOUN
ejpam-5816	129	10	)	)	PUNCT
ejpam-5816	129	11	]	]	PUNCT
ejpam-5816	130	1	−σm(κ)γ(σ	−σm(κ)γ(σ	ADJ
ejpam-5816	130	2	)	)	PUNCT
ejpam-5816	130	3	κ(s−	κ(s−	PROPN
ejpam-5816	130	4	r	r	NOUN
ejpam-5816	130	5	)	)	PUNCT
ejpam-5816	130	6	[	[	PUNCT
ejpam-5816	130	7	iκ	iκ	NOUN
ejpam-5816	130	8	,	,	PUNCT
ejpam-5816	130	9	σ	σ	PROPN
ejpam-5816	130	10	r	r	PROPN
ejpam-5816	130	11	,	,	PUNCT
ejpam-5816	130	12	t	t	PROPN
ejpam-5816	130	13	ℵ(r	ℵ(r	PROPN
ejpam-5816	130	14	)	)	PUNCT
ejpam-5816	131	1	+	+	NUM
ejpam-5816	131	2	iκ	iκ	X
ejpam-5816	131	3	,	,	PUNCT
ejpam-5816	131	4	σ	σ	PROPN
ejpam-5816	131	5	s	s	PROPN
ejpam-5816	131	6	,	,	PUNCT
ejpam-5816	131	7	t	t	PROPN
ejpam-5816	131	8	ℵ(s	ℵ(s	PROPN
ejpam-5816	131	9	)	)	PUNCT
ejpam-5816	131	10	]	]	PUNCT
ejpam-5816	131	11	∣∣∣	∣∣∣	NOUN
ejpam-5816	131	12	≤(t−	≤(t−	NOUN
ejpam-5816	131	13	r)σ+1	r)σ+1	PROPN
ejpam-5816	131	14	s−	s−	PROPN
ejpam-5816	131	15	r	r	NOUN
ejpam-5816	131	16	{	{	PUNCT
ejpam-5816	131	17	1	1	NUM
ejpam-5816	131	18	(	(	PUNCT
ejpam-5816	131	19	σ	σ	NOUN
ejpam-5816	131	20	+	+	NOUN
ejpam-5816	131	21	2	2	X
ejpam-5816	131	22	)	)	PUNCT
ejpam-5816	131	23	|ℵ′(t)|+	|ℵ′(t)|+	NOUN
ejpam-5816	131	24	1	1	NUM
ejpam-5816	131	25	(	(	PUNCT
ejpam-5816	131	26	σ	σ	NOUN
ejpam-5816	131	27	+	+	NUM
ejpam-5816	131	28	1)(σ	1)(σ	NUM
ejpam-5816	131	29	+	+	CCONJ
ejpam-5816	131	30	2	2	NUM
ejpam-5816	131	31	)	)	PUNCT
ejpam-5816	131	32	|ℵ′(r)|	|ℵ′(r)|	NOUN
ejpam-5816	131	33	}	}	PUNCT
ejpam-5816	132	1	+	+	CCONJ
ejpam-5816	132	2	(	(	PUNCT
ejpam-5816	132	3	s−	s−	PROPN
ejpam-5816	132	4	t)σ+1	t)σ+1	PROPN
ejpam-5816	132	5	s−	s−	PROPN
ejpam-5816	132	6	r	r	NOUN
ejpam-5816	132	7	{	{	PUNCT
ejpam-5816	132	8	1	1	NUM
ejpam-5816	132	9	(	(	PUNCT
ejpam-5816	132	10	σ	σ	NOUN
ejpam-5816	132	11	+	+	NOUN
ejpam-5816	132	12	2	2	X
ejpam-5816	132	13	)	)	PUNCT
ejpam-5816	132	14	|ℵ′(t)|+	|ℵ′(t)|+	NOUN
ejpam-5816	132	15	1	1	NUM
ejpam-5816	132	16	(	(	PUNCT
ejpam-5816	132	17	σ	σ	NOUN
ejpam-5816	132	18	+	+	NUM
ejpam-5816	132	19	1)(σ	1)(σ	NUM
ejpam-5816	132	20	+	+	CCONJ
ejpam-5816	132	21	2	2	NUM
ejpam-5816	132	22	)	)	PUNCT
ejpam-5816	132	23	|ℵ′(s)|	|ℵ′(s)|	NUM
ejpam-5816	132	24	}	}	PUNCT
ejpam-5816	132	25	,	,	PUNCT
ejpam-5816	132	26	which	which	PRON
ejpam-5816	132	27	complete	complete	VERB
ejpam-5816	132	28	the	the	DET
ejpam-5816	132	29	desired	desire	VERB
ejpam-5816	132	30	proof	proof	NOUN
ejpam-5816	132	31	.	.	PUNCT
ejpam-5816	133	1	corollary	corollary	ADJ
ejpam-5816	133	2	1	1	NUM
ejpam-5816	133	3	.	.	PUNCT
ejpam-5816	133	4	applying	apply	VERB
ejpam-5816	133	5	theorem	theorem	NOUN
ejpam-5816	133	6	1	1	NUM
ejpam-5816	133	7	for	for	ADP
ejpam-5816	133	8	|ℵ′|	|ℵ′|	PROPN
ejpam-5816	133	9	≤	≤	NOUN
ejpam-5816	134	1	k	k	NOUN
ejpam-5816	134	2	where	where	SCONJ
ejpam-5816	134	3	k	k	PROPN
ejpam-5816	134	4	>	>	X
ejpam-5816	134	5	0	0	PUNCT
ejpam-5816	134	6	,	,	PUNCT
ejpam-5816	134	7	we	we	PRON
ejpam-5816	134	8	get	get	VERB
ejpam-5816	134	9	the	the	DET
ejpam-5816	134	10	following	follow	VERB
ejpam-5816	134	11	inequality	inequality	NOUN
ejpam-5816	134	12	∣∣∣	∣∣∣	NOUN
ejpam-5816	135	1	[	[	X
ejpam-5816	135	2	(	(	PUNCT
ejpam-5816	135	3	t−	t−	ADJ
ejpam-5816	135	4	r)σ	r)σ	NOUN
ejpam-5816	135	5	+	+	CCONJ
ejpam-5816	135	6	(	(	PUNCT
ejpam-5816	135	7	s−	s−	PROPN
ejpam-5816	135	8	t)σ	t)σ	PUNCT
ejpam-5816	135	9	s−	s−	PROPN
ejpam-5816	135	10	r	r	NOUN
ejpam-5816	135	11	]	]	PUNCT
ejpam-5816	135	12	ℵ	ℵ	X
ejpam-5816	135	13	(	(	PUNCT
ejpam-5816	135	14	t	t	PROPN
ejpam-5816	135	15	)	)	PUNCT
ejpam-5816	135	16	+	+	NUM
ejpam-5816	135	17	σ(1−	σ(1−	PROPN
ejpam-5816	135	18	κ	κ	PART
ejpam-5816	135	19	)	)	PUNCT
ejpam-5816	135	20	κ(s−	κ(s−	PROPN
ejpam-5816	135	21	r	r	NOUN
ejpam-5816	135	22	)	)	PUNCT
ejpam-5816	135	23	γ(σ	γ(σ	PROPN
ejpam-5816	135	24	)	)	PUNCT
ejpam-5816	136	1	[	[	X
ejpam-5816	136	2	ℵ	ℵ	X
ejpam-5816	136	3	(	(	PUNCT
ejpam-5816	136	4	r	r	NOUN
ejpam-5816	136	5	)	)	PUNCT
ejpam-5816	136	6	+	+	NOUN
ejpam-5816	136	7	ℵ	ℵ	X
ejpam-5816	136	8	(	(	PUNCT
ejpam-5816	136	9	s	s	NOUN
ejpam-5816	136	10	)	)	PUNCT
ejpam-5816	136	11	]	]	PUNCT
ejpam-5816	137	1	−σm(κ)γ(σ	−σm(κ)γ(σ	ADJ
ejpam-5816	137	2	)	)	PUNCT
ejpam-5816	137	3	κ(s−	κ(s−	PROPN
ejpam-5816	137	4	r	r	NOUN
ejpam-5816	137	5	)	)	PUNCT
ejpam-5816	137	6	[	[	PUNCT
ejpam-5816	137	7	iκ	iκ	NOUN
ejpam-5816	137	8	,	,	PUNCT
ejpam-5816	137	9	σ	σ	PROPN
ejpam-5816	137	10	r	r	PROPN
ejpam-5816	137	11	,	,	PUNCT
ejpam-5816	137	12	t	t	PROPN
ejpam-5816	137	13	ℵ(r	ℵ(r	PROPN
ejpam-5816	137	14	)	)	PUNCT
ejpam-5816	138	1	+	+	NUM
ejpam-5816	138	2	iκ	iκ	X
ejpam-5816	138	3	,	,	PUNCT
ejpam-5816	138	4	σ	σ	PROPN
ejpam-5816	138	5	s	s	PROPN
ejpam-5816	138	6	,	,	PUNCT
ejpam-5816	138	7	t	t	PROPN
ejpam-5816	138	8	ℵ(s	ℵ(s	PROPN
ejpam-5816	138	9	)	)	PUNCT
ejpam-5816	138	10	]	]	PUNCT
ejpam-5816	138	11	∣∣∣	∣∣∣	X
ejpam-5816	138	12	≤	≤	X
ejpam-5816	138	13	k	k	NOUN
ejpam-5816	138	14	s−	s−	PROPN
ejpam-5816	138	15	r	r	NOUN
ejpam-5816	138	16	(	(	PUNCT
ejpam-5816	138	17	1	1	NUM
ejpam-5816	138	18	σ	σ	NOUN
ejpam-5816	138	19	+	+	CCONJ
ejpam-5816	138	20	2	2	NUM
ejpam-5816	138	21	+	+	SYM
ejpam-5816	138	22	1	1	NUM
ejpam-5816	138	23	(	(	PUNCT
ejpam-5816	138	24	σ	σ	NOUN
ejpam-5816	138	25	+	+	NUM
ejpam-5816	138	26	1)(σ	1)(σ	NUM
ejpam-5816	138	27	+	+	CCONJ
ejpam-5816	138	28	2	2	NUM
ejpam-5816	138	29	)	)	PUNCT
ejpam-5816	138	30	)	)	PUNCT
ejpam-5816	138	31	{	{	PUNCT
ejpam-5816	138	32	(	(	PUNCT
ejpam-5816	138	33	t−	t−	X
ejpam-5816	138	34	r)σ+1	r)σ+1	PROPN
ejpam-5816	138	35	+	+	CCONJ
ejpam-5816	138	36	(	(	PUNCT
ejpam-5816	138	37	s−	s−	PROPN
ejpam-5816	138	38	t)σ+1	t)σ+1	PROPN
ejpam-5816	138	39	}	}	PUNCT
ejpam-5816	138	40	.	.	PUNCT
ejpam-5816	139	1	corollary	corollary	ADJ
ejpam-5816	139	2	2	2	NUM
ejpam-5816	139	3	.	.	PUNCT
ejpam-5816	139	4	applying	apply	VERB
ejpam-5816	139	5	corollary	corollary	ADJ
ejpam-5816	139	6	1	1	NUM
ejpam-5816	139	7	for	for	ADP
ejpam-5816	139	8	t	t	NOUN
ejpam-5816	139	9	=	=	SYM
ejpam-5816	139	10	r+s	r+s	PROPN
ejpam-5816	139	11	2	2	NUM
ejpam-5816	139	12	,	,	PUNCT
ejpam-5816	139	13	we	we	PRON
ejpam-5816	139	14	get	get	VERB
ejpam-5816	139	15	the	the	DET
ejpam-5816	139	16	following	follow	VERB
ejpam-5816	139	17	inequality	inequality	NOUN
ejpam-5816	139	18	∣∣∣(s−	∣∣∣(s−	PROPN
ejpam-5816	139	19	r)σ−1	r)σ−1	NOUN
ejpam-5816	139	20	2σ−1	2σ−1	NUM
ejpam-5816	139	21	ℵ	ℵ	NOUN
ejpam-5816	139	22	(	(	PUNCT
ejpam-5816	139	23	r	r	NOUN
ejpam-5816	139	24	+	+	SYM
ejpam-5816	139	25	s	s	NOUN
ejpam-5816	139	26	2	2	NUM
ejpam-5816	139	27	)	)	PUNCT
ejpam-5816	140	1	+	+	NUM
ejpam-5816	140	2	σ(1−	σ(1−	PROPN
ejpam-5816	140	3	κ	κ	PART
ejpam-5816	140	4	)	)	PUNCT
ejpam-5816	140	5	κ(s−	κ(s−	PROPN
ejpam-5816	140	6	r	r	NOUN
ejpam-5816	140	7	)	)	PUNCT
ejpam-5816	141	1	γ(σ	γ(σ	PROPN
ejpam-5816	141	2	)	)	PUNCT
ejpam-5816	142	1	[	[	X
ejpam-5816	142	2	ℵ	ℵ	X
ejpam-5816	142	3	(	(	PUNCT
ejpam-5816	142	4	r	r	NOUN
ejpam-5816	142	5	)	)	PUNCT
ejpam-5816	142	6	+	+	NOUN
ejpam-5816	142	7	ℵ	ℵ	X
ejpam-5816	142	8	(	(	PUNCT
ejpam-5816	142	9	s	s	NOUN
ejpam-5816	142	10	)	)	PUNCT
ejpam-5816	142	11	]	]	PUNCT
ejpam-5816	143	1	g.	g.	PROPN
ejpam-5816	143	2	rahman	rahman	PROPN
ejpam-5816	143	3	et	et	PROPN
ejpam-5816	143	4	al	al	PROPN
ejpam-5816	143	5	.	.	PUNCT
ejpam-5816	143	6	/	/	SYM
ejpam-5816	143	7	eur	eur	PROPN
ejpam-5816	143	8	.	.	PUNCT
ejpam-5816	144	1	j.	j.	PROPN
ejpam-5816	144	2	pure	pure	PROPN
ejpam-5816	144	3	appl	appl	PROPN
ejpam-5816	144	4	.	.	PROPN
ejpam-5816	144	5	math	math	PROPN
ejpam-5816	144	6	,	,	PUNCT
ejpam-5816	144	7	18	18	NUM
ejpam-5816	144	8	(	(	PUNCT
ejpam-5816	144	9	2	2	NUM
ejpam-5816	144	10	)	)	PUNCT
ejpam-5816	144	11	(	(	PUNCT
ejpam-5816	144	12	2025	2025	NUM
ejpam-5816	144	13	)	)	PUNCT
ejpam-5816	144	14	,	,	PUNCT
ejpam-5816	144	15	5816	5816	NUM
ejpam-5816	144	16	7	7	NUM
ejpam-5816	144	17	of	of	ADP
ejpam-5816	144	18	18	18	NUM
ejpam-5816	144	19	−σm(κ)γ(σ	−σm(κ)γ(σ	ADJ
ejpam-5816	144	20	)	)	PUNCT
ejpam-5816	144	21	κ(s−	κ(s−	PROPN
ejpam-5816	144	22	r	r	NOUN
ejpam-5816	144	23	)	)	PUNCT
ejpam-5816	144	24	[	[	PUNCT
ejpam-5816	144	25	iκ	iκ	NOUN
ejpam-5816	144	26	,	,	PUNCT
ejpam-5816	144	27	σ	σ	NOUN
ejpam-5816	144	28	r	r	PROPN
ejpam-5816	144	29	,	,	PUNCT
ejpam-5816	144	30	r+s	r+s	NUM
ejpam-5816	144	31	2	2	NUM
ejpam-5816	144	32	ℵ(r	ℵ(r	NOUN
ejpam-5816	144	33	)	)	PUNCT
ejpam-5816	145	1	+	+	NUM
ejpam-5816	145	2	iκ	iκ	X
ejpam-5816	145	3	,	,	PUNCT
ejpam-5816	145	4	σ	σ	PROPN
ejpam-5816	145	5	s	s	PROPN
ejpam-5816	145	6	,	,	PUNCT
ejpam-5816	145	7	r+s	r+s	NUM
ejpam-5816	145	8	2	2	NUM
ejpam-5816	145	9	ℵ(s	ℵ(s	NOUN
ejpam-5816	145	10	)	)	PUNCT
ejpam-5816	145	11	]	]	PUNCT
ejpam-5816	145	12	∣∣∣	∣∣∣	X
ejpam-5816	145	13	≤k	≤k	PROPN
ejpam-5816	145	14	(	(	PUNCT
ejpam-5816	145	15	1	1	NUM
ejpam-5816	145	16	σ	σ	NOUN
ejpam-5816	145	17	+	+	NOUN
ejpam-5816	145	18	1	1	NUM
ejpam-5816	145	19	)	)	PUNCT
ejpam-5816	145	20	(	(	PUNCT
ejpam-5816	145	21	s−	s−	PROPN
ejpam-5816	145	22	r)σ	r)σ	VERB
ejpam-5816	145	23	2σ	2σ	NUM
ejpam-5816	145	24	.	.	PUNCT
ejpam-5816	146	1	remark	remark	VERB
ejpam-5816	146	2	3	3	NUM
ejpam-5816	146	3	.	.	PUNCT
ejpam-5816	146	4	applying	apply	VERB
ejpam-5816	146	5	theorem	theorem	NOUN
ejpam-5816	146	6	1	1	NUM
ejpam-5816	146	7	for	for	ADP
ejpam-5816	146	8	σ	σ	NOUN
ejpam-5816	146	9	=	=	SYM
ejpam-5816	146	10	κ	κ	NOUN
ejpam-5816	146	11	,	,	PUNCT
ejpam-5816	146	12	we	we	PRON
ejpam-5816	146	13	get	get	AUX
ejpam-5816	146	14	theorem	theorem	ADJ
ejpam-5816	146	15	1	1	NUM
ejpam-5816	146	16	proved	prove	VERB
ejpam-5816	146	17	by	by	ADP
ejpam-5816	146	18	ahmad	ahmad	PROPN
ejpam-5816	146	19	et	et	PROPN
ejpam-5816	146	20	al	al	PROPN
ejpam-5816	146	21	.	.	PUNCT
ejpam-5816	147	1	[	[	X
ejpam-5816	147	2	40	40	NUM
ejpam-5816	147	3	]	]	PUNCT
ejpam-5816	147	4	.	.	PUNCT
ejpam-5816	148	1	remark	remark	PROPN
ejpam-5816	148	2	4	4	NUM
ejpam-5816	148	3	.	.	PUNCT
ejpam-5816	148	4	applying	apply	VERB
ejpam-5816	148	5	corollary	corollary	ADJ
ejpam-5816	148	6	2	2	NUM
ejpam-5816	148	7	for	for	ADP
ejpam-5816	148	8	σ	σ	NOUN
ejpam-5816	148	9	=	=	SYM
ejpam-5816	148	10	κ	κ	NOUN
ejpam-5816	148	11	,	,	PUNCT
ejpam-5816	148	12	we	we	PRON
ejpam-5816	148	13	get	get	VERB
ejpam-5816	148	14	corollary	corollary	ADJ
ejpam-5816	148	15	2	2	NUM
ejpam-5816	148	16	proved	prove	VERB
ejpam-5816	148	17	earlier	early	ADV
ejpam-5816	148	18	by	by	ADP
ejpam-5816	148	19	ahmad	ahmad	PROPN
ejpam-5816	148	20	et	et	PROPN
ejpam-5816	148	21	al	al	PROPN
ejpam-5816	148	22	.	.	PUNCT
ejpam-5816	149	1	[	[	X
ejpam-5816	149	2	40	40	NUM
ejpam-5816	149	3	]	]	PUNCT
ejpam-5816	149	4	.	.	PUNCT
ejpam-5816	150	1	theorem	theorem	NOUN
ejpam-5816	150	2	2	2	NUM
ejpam-5816	150	3	.	.	PUNCT
ejpam-5816	151	1	let	let	VERB
ejpam-5816	151	2	ℵ	ℵ	NOUN
ejpam-5816	151	3	:	:	PUNCT
ejpam-5816	151	4	[	[	X
ejpam-5816	151	5	r	r	X
ejpam-5816	151	6	,	,	PUNCT
ejpam-5816	151	7	s	s	PART
ejpam-5816	151	8	]	]	X
ejpam-5816	151	9	→	→	PUNCT
ejpam-5816	151	10	r	r	NOUN
ejpam-5816	151	11	be	be	AUX
ejpam-5816	151	12	a	a	DET
ejpam-5816	151	13	differentiable	differentiable	ADJ
ejpam-5816	151	14	function	function	NOUN
ejpam-5816	151	15	on	on	ADP
ejpam-5816	151	16	(	(	PUNCT
ejpam-5816	151	17	r	r	NOUN
ejpam-5816	151	18	,	,	PUNCT
ejpam-5816	151	19	s	s	PART
ejpam-5816	151	20	)	)	PUNCT
ejpam-5816	151	21	with	with	ADP
ejpam-5816	151	22	r	r	NOUN
ejpam-5816	151	23	<	<	X
ejpam-5816	151	24	s	s	NOUN
ejpam-5816	151	25	and	and	CCONJ
ejpam-5816	151	26	ℵ′	ℵ′	PRON
ejpam-5816	151	27	∈	∈	PROPN
ejpam-5816	151	28	l1[r	l1[r	PROPN
ejpam-5816	151	29	,	,	PUNCT
ejpam-5816	151	30	s	s	PROPN
ejpam-5816	151	31	]	]	X
ejpam-5816	151	32	.	.	PUNCT
ejpam-5816	152	1	for	for	ADP
ejpam-5816	152	2	hattaf	hattaf	NOUN
ejpam-5816	152	3	-	-	PUNCT
ejpam-5816	152	4	fractional	fractional	ADJ
ejpam-5816	152	5	integral	integral	ADJ
ejpam-5816	152	6	operators	operator	NOUN
ejpam-5816	152	7	,	,	PUNCT
ejpam-5816	152	8	we	we	PRON
ejpam-5816	152	9	have	have	VERB
ejpam-5816	152	10	the	the	DET
ejpam-5816	152	11	following	follow	VERB
ejpam-5816	152	12	inequality	inequality	NOUN
ejpam-5816	152	13	if	if	SCONJ
ejpam-5816	152	14	|ℵ′|q	|ℵ′|q	NUM
ejpam-5816	152	15	is	be	AUX
ejpam-5816	152	16	a	a	DET
ejpam-5816	152	17	convex	convex	NOUN
ejpam-5816	152	18	function.∣∣∣	function.∣∣∣	ADP
ejpam-5816	152	19	[	[	X
ejpam-5816	152	20	(	(	PUNCT
ejpam-5816	152	21	t−	t−	ADJ
ejpam-5816	152	22	r)σ	r)σ	NOUN
ejpam-5816	152	23	+	+	CCONJ
ejpam-5816	152	24	(	(	PUNCT
ejpam-5816	152	25	s−	s−	PROPN
ejpam-5816	152	26	t)σ	t)σ	PUNCT
ejpam-5816	152	27	s−	s−	PROPN
ejpam-5816	152	28	r	r	NOUN
ejpam-5816	152	29	]	]	PUNCT
ejpam-5816	152	30	ℵ	ℵ	X
ejpam-5816	152	31	(	(	PUNCT
ejpam-5816	152	32	t	t	PROPN
ejpam-5816	152	33	)	)	PUNCT
ejpam-5816	153	1	+	+	NUM
ejpam-5816	153	2	σ(1−	σ(1−	PROPN
ejpam-5816	153	3	κ	κ	PART
ejpam-5816	153	4	)	)	PUNCT
ejpam-5816	153	5	κ(s−	κ(s−	PROPN
ejpam-5816	153	6	r	r	NOUN
ejpam-5816	153	7	)	)	PUNCT
ejpam-5816	153	8	γ(σ	γ(σ	PROPN
ejpam-5816	153	9	)	)	PUNCT
ejpam-5816	154	1	[	[	X
ejpam-5816	154	2	ℵ	ℵ	X
ejpam-5816	154	3	(	(	PUNCT
ejpam-5816	154	4	r	r	NOUN
ejpam-5816	154	5	)	)	PUNCT
ejpam-5816	154	6	+	+	NOUN
ejpam-5816	154	7	ℵ	ℵ	X
ejpam-5816	154	8	(	(	PUNCT
ejpam-5816	154	9	s	s	NOUN
ejpam-5816	154	10	)	)	PUNCT
ejpam-5816	154	11	]	]	PUNCT
ejpam-5816	155	1	−σm(κ)γ(σ	−σm(κ)γ(σ	ADJ
ejpam-5816	155	2	)	)	PUNCT
ejpam-5816	155	3	κ(s−	κ(s−	PROPN
ejpam-5816	155	4	r	r	NOUN
ejpam-5816	155	5	)	)	PUNCT
ejpam-5816	155	6	[	[	PUNCT
ejpam-5816	155	7	iκ	iκ	NOUN
ejpam-5816	155	8	,	,	PUNCT
ejpam-5816	155	9	σ	σ	PROPN
ejpam-5816	155	10	r	r	PROPN
ejpam-5816	155	11	,	,	PUNCT
ejpam-5816	155	12	t	t	PROPN
ejpam-5816	155	13	ℵ(r	ℵ(r	PROPN
ejpam-5816	155	14	)	)	PUNCT
ejpam-5816	156	1	+	+	NUM
ejpam-5816	156	2	iκ	iκ	X
ejpam-5816	156	3	,	,	PUNCT
ejpam-5816	156	4	σ	σ	PROPN
ejpam-5816	156	5	s	s	PROPN
ejpam-5816	156	6	,	,	PUNCT
ejpam-5816	156	7	t	t	PROPN
ejpam-5816	156	8	ℵ(s	ℵ(s	PROPN
ejpam-5816	156	9	)	)	PUNCT
ejpam-5816	156	10	]	]	PUNCT
ejpam-5816	156	11	∣∣∣	∣∣∣	NOUN
ejpam-5816	156	12	≤(t−	≤(t−	NOUN
ejpam-5816	157	1	r)σ+1	r)σ+1	PROPN
ejpam-5816	157	2	s−	s−	PROPN
ejpam-5816	157	3	r	r	NOUN
ejpam-5816	157	4	(	(	PUNCT
ejpam-5816	157	5	1	1	NUM
ejpam-5816	157	6	σp+	σp+	NOUN
ejpam-5816	157	7	1	1	NUM
ejpam-5816	157	8	)	)	PUNCT
ejpam-5816	157	9	1	1	NUM
ejpam-5816	158	1	p	p	NOUN
ejpam-5816	159	1	[	[	PUNCT
ejpam-5816	160	1	|	|	NOUN
ejpam-5816	160	2	ℵ′(t	ℵ′(t	NOUN
ejpam-5816	160	3	)	)	PUNCT
ejpam-5816	160	4	|q	|q	NOUN
ejpam-5816	161	1	+	+	CCONJ
ejpam-5816	161	2	|	|	ADV
ejpam-5816	161	3	ℵ′(r	ℵ′(r	NUM
ejpam-5816	161	4	)	)	PUNCT
ejpam-5816	161	5	|q	|q	NOUN
ejpam-5816	161	6	2	2	NUM
ejpam-5816	161	7	]	]	SYM
ejpam-5816	161	8	1	1	NUM
ejpam-5816	161	9	q	q	NOUN
ejpam-5816	161	10	+	+	CCONJ
ejpam-5816	161	11	(	(	PUNCT
ejpam-5816	161	12	s−	s−	PROPN
ejpam-5816	161	13	t)σ+1	t)σ+1	PROPN
ejpam-5816	161	14	s−	s−	PROPN
ejpam-5816	161	15	r	r	NOUN
ejpam-5816	161	16	(	(	PUNCT
ejpam-5816	161	17	1	1	NUM
ejpam-5816	161	18	σp+	σp+	NOUN
ejpam-5816	161	19	1	1	NUM
ejpam-5816	161	20	)	)	PUNCT
ejpam-5816	161	21	1	1	NUM
ejpam-5816	162	1	p	p	NOUN
ejpam-5816	162	2	[	[	PUNCT
ejpam-5816	162	3	|	|	NOUN
ejpam-5816	162	4	ℵ′(s	ℵ′(s	NUM
ejpam-5816	162	5	)	)	PUNCT
ejpam-5816	162	6	|q	|q	NOUN
ejpam-5816	163	1	+	+	CCONJ
ejpam-5816	163	2	|	|	CCONJ
ejpam-5816	163	3	ℵ′(t	ℵ′(t	PROPN
ejpam-5816	163	4	)	)	PUNCT
ejpam-5816	163	5	|q	|q	NOUN
ejpam-5816	163	6	2	2	NUM
ejpam-5816	163	7	]	]	SYM
ejpam-5816	163	8	1	1	NUM
ejpam-5816	163	9	q	q	NOUN
ejpam-5816	163	10	,	,	PUNCT
ejpam-5816	163	11	where	where	SCONJ
ejpam-5816	163	12	1	1	NUM
ejpam-5816	163	13	p	p	NOUN
ejpam-5816	164	1	+	+	NOUN
ejpam-5816	164	2	1	1	NUM
ejpam-5816	164	3	q	q	NOUN
ejpam-5816	164	4	=	=	SYM
ejpam-5816	164	5	1	1	NUM
ejpam-5816	164	6	,	,	PUNCT
ejpam-5816	164	7	t	t	PROPN
ejpam-5816	164	8	∈	∈	PROPN
ejpam-5816	165	1	[	[	X
ejpam-5816	165	2	r	r	X
ejpam-5816	165	3	,	,	PUNCT
ejpam-5816	165	4	s	s	PART
ejpam-5816	165	5	]	]	X
ejpam-5816	165	6	,	,	PUNCT
ejpam-5816	165	7	κ	κ	PROPN
ejpam-5816	165	8	∈	∈	PROPN
ejpam-5816	165	9	(	(	PUNCT
ejpam-5816	165	10	0	0	NUM
ejpam-5816	165	11	,	,	PUNCT
ejpam-5816	165	12	1	1	NUM
ejpam-5816	165	13	]	]	PUNCT
ejpam-5816	165	14	and	and	CCONJ
ejpam-5816	165	15	m(κ	m(κ	NUM
ejpam-5816	165	16	)	)	PUNCT
ejpam-5816	165	17	>	>	X
ejpam-5816	165	18	0	0	X
ejpam-5816	165	19	.	.	PUNCT
ejpam-5816	165	20	proof	proof	NOUN
ejpam-5816	165	21	.	.	PUNCT
ejpam-5816	166	1	by	by	ADP
ejpam-5816	166	2	applying	apply	VERB
ejpam-5816	166	3	lemma	lemma	PROPN
ejpam-5816	166	4	1	1	NUM
ejpam-5816	166	5	,	,	PUNCT
ejpam-5816	166	6	we	we	PRON
ejpam-5816	166	7	have∣∣∣	have∣∣∣	PUNCT
ejpam-5816	167	1	[	[	X
ejpam-5816	167	2	(	(	PUNCT
ejpam-5816	167	3	t−	t−	ADJ
ejpam-5816	167	4	r)σ	r)σ	NOUN
ejpam-5816	167	5	+	+	CCONJ
ejpam-5816	167	6	(	(	PUNCT
ejpam-5816	167	7	s−	s−	PROPN
ejpam-5816	167	8	t)σ	t)σ	PUNCT
ejpam-5816	167	9	s−	s−	PROPN
ejpam-5816	167	10	r	r	NOUN
ejpam-5816	167	11	]	]	PUNCT
ejpam-5816	167	12	ℵ	ℵ	X
ejpam-5816	167	13	(	(	PUNCT
ejpam-5816	167	14	t	t	PROPN
ejpam-5816	167	15	)	)	PUNCT
ejpam-5816	167	16	+	+	NUM
ejpam-5816	167	17	σ(1−	σ(1−	PROPN
ejpam-5816	167	18	κ	κ	PART
ejpam-5816	167	19	)	)	PUNCT
ejpam-5816	167	20	κ(s−	κ(s−	PROPN
ejpam-5816	167	21	r	r	NOUN
ejpam-5816	167	22	)	)	PUNCT
ejpam-5816	167	23	γ(σ	γ(σ	PROPN
ejpam-5816	167	24	)	)	PUNCT
ejpam-5816	168	1	[	[	X
ejpam-5816	168	2	ℵ	ℵ	X
ejpam-5816	168	3	(	(	PUNCT
ejpam-5816	168	4	r	r	NOUN
ejpam-5816	168	5	)	)	PUNCT
ejpam-5816	168	6	+	+	NOUN
ejpam-5816	168	7	ℵ	ℵ	X
ejpam-5816	168	8	(	(	PUNCT
ejpam-5816	168	9	s	s	NOUN
ejpam-5816	168	10	)	)	PUNCT
ejpam-5816	168	11	]	]	PUNCT
ejpam-5816	169	1	−σm(κ)γ(σ	−σm(κ)γ(σ	ADJ
ejpam-5816	169	2	)	)	PUNCT
ejpam-5816	169	3	κ(s−	κ(s−	PROPN
ejpam-5816	169	4	r	r	NOUN
ejpam-5816	169	5	)	)	PUNCT
ejpam-5816	169	6	[	[	PUNCT
ejpam-5816	169	7	iκ	iκ	NOUN
ejpam-5816	169	8	,	,	PUNCT
ejpam-5816	169	9	σ	σ	PROPN
ejpam-5816	169	10	r	r	PROPN
ejpam-5816	169	11	,	,	PUNCT
ejpam-5816	169	12	t	t	PROPN
ejpam-5816	169	13	ℵ(r	ℵ(r	PROPN
ejpam-5816	169	14	)	)	PUNCT
ejpam-5816	170	1	+	+	NUM
ejpam-5816	170	2	iκ	iκ	X
ejpam-5816	170	3	,	,	PUNCT
ejpam-5816	170	4	σ	σ	PROPN
ejpam-5816	170	5	s	s	PROPN
ejpam-5816	170	6	,	,	PUNCT
ejpam-5816	170	7	t	t	PROPN
ejpam-5816	170	8	ℵ(s	ℵ(s	PROPN
ejpam-5816	170	9	)	)	PUNCT
ejpam-5816	170	10	]	]	PUNCT
ejpam-5816	170	11	∣∣∣	∣∣∣	NOUN
ejpam-5816	170	12	≤(t−	≤(t−	PROPN
ejpam-5816	170	13	r)σ+1	r)σ+1	PROPN
ejpam-5816	170	14	s−	s−	PROPN
ejpam-5816	171	1	t	t	PROPN
ejpam-5816	171	2	∫	∫	PROPN
ejpam-5816	171	3	1	1	NUM
ejpam-5816	171	4	0	0	NUM
ejpam-5816	171	5	ρσ	ρσ	ADP
ejpam-5816	171	6	|	|	ADV
ejpam-5816	171	7	ℵ′(ρt+	ℵ′(ρt+	NOUN
ejpam-5816	171	8	(	(	PUNCT
ejpam-5816	171	9	1−	1−	NUM
ejpam-5816	171	10	ρ)r	ρ)r	X
ejpam-5816	171	11	)	)	PUNCT
ejpam-5816	172	1	|	|	ADV
ejpam-5816	172	2	dρ	dρ	INTJ
ejpam-5816	173	1	+	+	CCONJ
ejpam-5816	173	2	(	(	PUNCT
ejpam-5816	173	3	s−	s−	PROPN
ejpam-5816	173	4	t)σ+1	t)σ+1	PROPN
ejpam-5816	173	5	s−	s−	PROPN
ejpam-5816	173	6	t	t	PROPN
ejpam-5816	173	7	∫	∫	PROPN
ejpam-5816	173	8	1	1	NUM
ejpam-5816	173	9	0	0	NUM
ejpam-5816	173	10	ρσ	ρσ	ADP
ejpam-5816	173	11	|	|	ADV
ejpam-5816	173	12	ℵ′(ρt+	ℵ′(ρt+	NOUN
ejpam-5816	173	13	(	(	PUNCT
ejpam-5816	173	14	1−	1−	NUM
ejpam-5816	173	15	ρ)s	ρ)s	NOUN
ejpam-5816	173	16	)	)	PUNCT
ejpam-5816	174	1	|	|	ADV
ejpam-5816	174	2	dρ	dρ	INTJ
ejpam-5816	174	3	.	.	PUNCT
ejpam-5816	175	1	by	by	ADP
ejpam-5816	175	2	employing	employ	VERB
ejpam-5816	175	3	hölder	hölder	NOUN
ejpam-5816	175	4	inequality	inequality	NOUN
ejpam-5816	175	5	,	,	PUNCT
ejpam-5816	175	6	we	we	PRON
ejpam-5816	175	7	obtain∣∣∣	obtain∣∣∣	VERB
ejpam-5816	176	1	[	[	X
ejpam-5816	176	2	(	(	PUNCT
ejpam-5816	176	3	t−	t−	ADJ
ejpam-5816	176	4	r)σ	r)σ	NOUN
ejpam-5816	176	5	+	+	CCONJ
ejpam-5816	176	6	(	(	PUNCT
ejpam-5816	176	7	s−	s−	PROPN
ejpam-5816	176	8	t)σ	t)σ	PUNCT
ejpam-5816	176	9	s−	s−	PROPN
ejpam-5816	176	10	r	r	NOUN
ejpam-5816	176	11	]	]	PUNCT
ejpam-5816	176	12	ℵ	ℵ	X
ejpam-5816	176	13	(	(	PUNCT
ejpam-5816	176	14	t	t	PROPN
ejpam-5816	176	15	)	)	PUNCT
ejpam-5816	176	16	+	+	NUM
ejpam-5816	176	17	σ(1−	σ(1−	PROPN
ejpam-5816	176	18	κ	κ	PART
ejpam-5816	176	19	)	)	PUNCT
ejpam-5816	176	20	κ(s−	κ(s−	PROPN
ejpam-5816	176	21	r	r	NOUN
ejpam-5816	176	22	)	)	PUNCT
ejpam-5816	176	23	γ(σ	γ(σ	PROPN
ejpam-5816	176	24	)	)	PUNCT
ejpam-5816	177	1	[	[	X
ejpam-5816	177	2	ℵ	ℵ	X
ejpam-5816	177	3	(	(	PUNCT
ejpam-5816	177	4	r	r	NOUN
ejpam-5816	177	5	)	)	PUNCT
ejpam-5816	177	6	+	+	NOUN
ejpam-5816	177	7	ℵ	ℵ	X
ejpam-5816	177	8	(	(	PUNCT
ejpam-5816	177	9	s	s	NOUN
ejpam-5816	177	10	)	)	PUNCT
ejpam-5816	177	11	]	]	PUNCT
ejpam-5816	177	12	(	(	PUNCT
ejpam-5816	177	13	9	9	X
ejpam-5816	177	14	)	)	PUNCT
ejpam-5816	177	15	−σm(κ)γ(σ	−σm(κ)γ(σ	ADJ
ejpam-5816	177	16	)	)	PUNCT
ejpam-5816	177	17	κ(s−	κ(s−	PROPN
ejpam-5816	177	18	r	r	NOUN
ejpam-5816	177	19	)	)	PUNCT
ejpam-5816	177	20	[	[	PUNCT
ejpam-5816	177	21	iκ	iκ	NOUN
ejpam-5816	177	22	,	,	PUNCT
ejpam-5816	177	23	σ	σ	PROPN
ejpam-5816	177	24	r	r	PROPN
ejpam-5816	177	25	,	,	PUNCT
ejpam-5816	177	26	t	t	PROPN
ejpam-5816	177	27	ℵ(r	ℵ(r	PROPN
ejpam-5816	177	28	)	)	PUNCT
ejpam-5816	178	1	+	+	NUM
ejpam-5816	178	2	iκ	iκ	X
ejpam-5816	178	3	,	,	PUNCT
ejpam-5816	178	4	σ	σ	PROPN
ejpam-5816	178	5	s	s	PROPN
ejpam-5816	178	6	,	,	PUNCT
ejpam-5816	178	7	t	t	PROPN
ejpam-5816	178	8	ℵ(s	ℵ(s	PROPN
ejpam-5816	178	9	)	)	PUNCT
ejpam-5816	178	10	]	]	PUNCT
ejpam-5816	178	11	∣∣∣	∣∣∣	X
ejpam-5816	179	1	g.	g.	PROPN
ejpam-5816	179	2	rahman	rahman	PROPN
ejpam-5816	179	3	et	et	PROPN
ejpam-5816	179	4	al	al	PROPN
ejpam-5816	179	5	.	.	PUNCT
ejpam-5816	179	6	/	/	SYM
ejpam-5816	179	7	eur	eur	PROPN
ejpam-5816	179	8	.	.	PUNCT
ejpam-5816	180	1	j.	j.	PROPN
ejpam-5816	180	2	pure	pure	PROPN
ejpam-5816	180	3	appl	appl	PROPN
ejpam-5816	180	4	.	.	PROPN
ejpam-5816	180	5	math	math	PROPN
ejpam-5816	180	6	,	,	PUNCT
ejpam-5816	180	7	18	18	NUM
ejpam-5816	180	8	(	(	PUNCT
ejpam-5816	180	9	2	2	NUM
ejpam-5816	180	10	)	)	PUNCT
ejpam-5816	180	11	(	(	PUNCT
ejpam-5816	180	12	2025	2025	NUM
ejpam-5816	180	13	)	)	PUNCT
ejpam-5816	180	14	,	,	PUNCT
ejpam-5816	180	15	5816	5816	NUM
ejpam-5816	180	16	8	8	NUM
ejpam-5816	180	17	of	of	ADP
ejpam-5816	180	18	18	18	NUM
ejpam-5816	180	19	≤(t−	≤(t−	NOUN
ejpam-5816	180	20	r)σ+1	r)σ+1	PROPN
ejpam-5816	180	21	s−	s−	PROPN
ejpam-5816	180	22	t	t	PROPN
ejpam-5816	181	1	[	[	X
ejpam-5816	181	2	(	(	PUNCT
ejpam-5816	181	3	∫	∫	PROPN
ejpam-5816	181	4	1	1	NUM
ejpam-5816	181	5	0	0	NUM
ejpam-5816	181	6	ρϱpdρ	ρϱpdρ	NOUN
ejpam-5816	181	7	)	)	PUNCT
ejpam-5816	181	8	1	1	NUM
ejpam-5816	181	9	p	p	NOUN
ejpam-5816	181	10	(	(	PUNCT
ejpam-5816	181	11	∫	∫	PROPN
ejpam-5816	181	12	1	1	NUM
ejpam-5816	181	13	0	0	NUM
ejpam-5816	182	1	|	|	ADV
ejpam-5816	182	2	ℵ′(ρt+	ℵ′(ρt+	NOUN
ejpam-5816	182	3	(	(	PUNCT
ejpam-5816	182	4	1−	1−	NUM
ejpam-5816	182	5	ρ)r	ρ)r	X
ejpam-5816	182	6	)	)	PUNCT
ejpam-5816	182	7	|q	|q	NOUN
ejpam-5816	182	8	dρ	dρ	NOUN
ejpam-5816	182	9	)	)	PUNCT
ejpam-5816	182	10	1	1	NUM
ejpam-5816	182	11	q	q	NOUN
ejpam-5816	182	12	]	]	PUNCT
ejpam-5816	183	1	+	+	CCONJ
ejpam-5816	183	2	(	(	PUNCT
ejpam-5816	183	3	s−	s−	PROPN
ejpam-5816	183	4	t)ϱ+1	t)ϱ+1	ADV
ejpam-5816	183	5	s−	s−	PROPN
ejpam-5816	183	6	t	t	PROPN
ejpam-5816	183	7	[	[	X
ejpam-5816	183	8	(	(	PUNCT
ejpam-5816	183	9	∫	∫	PROPN
ejpam-5816	183	10	1	1	NUM
ejpam-5816	183	11	0	0	NUM
ejpam-5816	183	12	ρσpdρ	ρσpdρ	NOUN
ejpam-5816	183	13	)	)	PUNCT
ejpam-5816	183	14	1	1	NUM
ejpam-5816	183	15	p	p	NOUN
ejpam-5816	183	16	(	(	PUNCT
ejpam-5816	183	17	∫	∫	PROPN
ejpam-5816	183	18	1	1	NUM
ejpam-5816	183	19	0	0	NUM
ejpam-5816	184	1	|	|	ADV
ejpam-5816	184	2	ℵ′(ρt+	ℵ′(ρt+	NOUN
ejpam-5816	184	3	(	(	PUNCT
ejpam-5816	184	4	1−	1−	NUM
ejpam-5816	184	5	ρ)s	ρ)s	NOUN
ejpam-5816	184	6	)	)	PUNCT
ejpam-5816	184	7	|q	|q	NOUN
ejpam-5816	184	8	dρ	dρ	NOUN
ejpam-5816	184	9	)	)	PUNCT
ejpam-5816	184	10	1	1	NUM
ejpam-5816	184	11	q	q	NOUN
ejpam-5816	184	12	]	]	PUNCT
ejpam-5816	184	13	.	.	PUNCT
ejpam-5816	185	1	(	(	PUNCT
ejpam-5816	185	2	10	10	NUM
ejpam-5816	185	3	)	)	PUNCT
ejpam-5816	185	4	by	by	ADP
ejpam-5816	185	5	employing	employ	VERB
ejpam-5816	185	6	the	the	DET
ejpam-5816	185	7	convexity	convexity	NOUN
ejpam-5816	185	8	of	of	ADP
ejpam-5816	185	9	|	|	ADV
ejpam-5816	185	10	ℵ′	ℵ′	ADV
ejpam-5816	185	11	|q	|q	NOUN
ejpam-5816	185	12	,	,	PUNCT
ejpam-5816	185	13	we	we	PRON
ejpam-5816	185	14	have∫	have∫	VERB
ejpam-5816	185	15	1	1	NUM
ejpam-5816	185	16	0	0	NUM
ejpam-5816	186	1	|	|	ADV
ejpam-5816	186	2	ℵ′(ρt+	ℵ′(ρt+	NOUN
ejpam-5816	186	3	(	(	PUNCT
ejpam-5816	186	4	1−	1−	NUM
ejpam-5816	186	5	ρ)r	ρ)r	X
ejpam-5816	186	6	)	)	PUNCT
ejpam-5816	186	7	|q	|q	NOUN
ejpam-5816	186	8	dρ	dρ	PROPN
ejpam-5816	187	1	≤	≤	NUM
ejpam-5816	187	2	∫	∫	PROPN
ejpam-5816	188	1	1	1	NUM
ejpam-5816	188	2	0	0	NUM
ejpam-5816	189	1	[	[	X
ejpam-5816	189	2	ρ	ρ	NUM
ejpam-5816	189	3	|	|	NOUN
ejpam-5816	189	4	ℵ′(t	ℵ′(t	PROPN
ejpam-5816	189	5	)	)	PUNCT
ejpam-5816	189	6	|q	|q	NOUN
ejpam-5816	190	1	+	+	PROPN
ejpam-5816	190	2	(	(	PUNCT
ejpam-5816	190	3	1−	1−	NUM
ejpam-5816	190	4	ρ	ρ	NOUN
ejpam-5816	190	5	)	)	PUNCT
ejpam-5816	190	6	|	|	ADV
ejpam-5816	190	7	ℵ′(r	ℵ′(r	CCONJ
ejpam-5816	190	8	)	)	PUNCT
ejpam-5816	190	9	|q]dρ	|q]dρ	X
ejpam-5816	190	10	=	=	SYM
ejpam-5816	190	11	|	|	CCONJ
ejpam-5816	190	12	ℵ′(t	ℵ′(t	NOUN
ejpam-5816	190	13	)	)	PUNCT
ejpam-5816	190	14	|q	|q	NOUN
ejpam-5816	191	1	+	+	CCONJ
ejpam-5816	191	2	|	|	ADV
ejpam-5816	191	3	ℵ′(r	ℵ′(r	NUM
ejpam-5816	191	4	)	)	PUNCT
ejpam-5816	191	5	|q	|q	NOUN
ejpam-5816	191	6	2	2	NUM
ejpam-5816	191	7	(	(	PUNCT
ejpam-5816	191	8	11	11	NUM
ejpam-5816	191	9	)	)	PUNCT
ejpam-5816	191	10	and	and	CCONJ
ejpam-5816	191	11	∫	∫	PROPN
ejpam-5816	191	12	1	1	NUM
ejpam-5816	191	13	0	0	NUM
ejpam-5816	192	1	|	|	ADV
ejpam-5816	192	2	ℵ′(ρt+	ℵ′(ρt+	NOUN
ejpam-5816	192	3	(	(	PUNCT
ejpam-5816	192	4	1−	1−	NUM
ejpam-5816	192	5	ρ)s	ρ)s	NOUN
ejpam-5816	192	6	)	)	PUNCT
ejpam-5816	192	7	|q	|q	NOUN
ejpam-5816	192	8	dρ	dρ	PROPN
ejpam-5816	193	1	≤	≤	NUM
ejpam-5816	193	2	∫	∫	PROPN
ejpam-5816	194	1	1	1	NUM
ejpam-5816	194	2	0	0	NUM
ejpam-5816	195	1	[	[	X
ejpam-5816	195	2	ρ	ρ	NUM
ejpam-5816	195	3	|	|	NOUN
ejpam-5816	195	4	ℵ′(t	ℵ′(t	PROPN
ejpam-5816	195	5	)	)	PUNCT
ejpam-5816	195	6	|q	|q	NOUN
ejpam-5816	196	1	+	+	PROPN
ejpam-5816	196	2	(	(	PUNCT
ejpam-5816	196	3	1−	1−	NUM
ejpam-5816	196	4	ρ	ρ	NOUN
ejpam-5816	196	5	)	)	PUNCT
ejpam-5816	196	6	|	|	ADV
ejpam-5816	196	7	ℵ′(s	ℵ′(s	PUNCT
ejpam-5816	196	8	)	)	PUNCT
ejpam-5816	196	9	|q]dρ	|q]dρ	X
ejpam-5816	196	10	=	=	SYM
ejpam-5816	196	11	|	|	CCONJ
ejpam-5816	196	12	ℵ′(t	ℵ′(t	NOUN
ejpam-5816	196	13	)	)	PUNCT
ejpam-5816	196	14	|q	|q	NOUN
ejpam-5816	196	15	+	+	CCONJ
ejpam-5816	196	16	|	|	ADV
ejpam-5816	196	17	ℵ′(s	ℵ′(s	PRON
ejpam-5816	196	18	)	)	PUNCT
ejpam-5816	196	19	|q	|q	NOUN
ejpam-5816	196	20	2	2	NUM
ejpam-5816	196	21	.	.	PUNCT
ejpam-5816	197	1	(	(	PUNCT
ejpam-5816	197	2	12	12	NUM
ejpam-5816	197	3	)	)	PUNCT
ejpam-5816	197	4	substituting	substitute	VERB
ejpam-5816	197	5	(	(	PUNCT
ejpam-5816	197	6	11	11	NUM
ejpam-5816	197	7	)	)	PUNCT
ejpam-5816	197	8	and	and	CCONJ
ejpam-5816	197	9	(	(	PUNCT
ejpam-5816	197	10	12	12	NUM
ejpam-5816	197	11	)	)	PUNCT
ejpam-5816	197	12	in	in	ADP
ejpam-5816	197	13	(	(	PUNCT
ejpam-5816	197	14	9	9	NUM
ejpam-5816	197	15	)	)	PUNCT
ejpam-5816	197	16	and	and	CCONJ
ejpam-5816	197	17	then	then	ADV
ejpam-5816	197	18	solving	solve	VERB
ejpam-5816	197	19	the	the	DET
ejpam-5816	197	20	integrals	integral	NOUN
ejpam-5816	197	21	,	,	PUNCT
ejpam-5816	197	22	we	we	PRON
ejpam-5816	197	23	get	get	VERB
ejpam-5816	197	24	the	the	DET
ejpam-5816	197	25	required	required	ADJ
ejpam-5816	197	26	inequality	inequality	NOUN
ejpam-5816	197	27	.	.	PUNCT
ejpam-5816	198	1	corollary	corollary	ADJ
ejpam-5816	198	2	3	3	NUM
ejpam-5816	198	3	.	.	PUNCT
ejpam-5816	198	4	applying	apply	VERB
ejpam-5816	198	5	theorem	theorem	NOUN
ejpam-5816	198	6	2	2	NUM
ejpam-5816	198	7	for	for	ADP
ejpam-5816	198	8	|ℵ′|	|ℵ′|	PROPN
ejpam-5816	198	9	≤	≤	PROPN
ejpam-5816	199	1	k	k	NOUN
ejpam-5816	199	2	where	where	SCONJ
ejpam-5816	199	3	k	k	PROPN
ejpam-5816	199	4	>	>	X
ejpam-5816	199	5	0	0	PUNCT
ejpam-5816	199	6	,	,	PUNCT
ejpam-5816	199	7	we	we	PRON
ejpam-5816	199	8	get	get	VERB
ejpam-5816	199	9	the	the	DET
ejpam-5816	199	10	following	follow	VERB
ejpam-5816	199	11	inequality	inequality	NOUN
ejpam-5816	199	12	∣∣∣	∣∣∣	NOUN
ejpam-5816	200	1	[	[	X
ejpam-5816	200	2	(	(	PUNCT
ejpam-5816	200	3	t−	t−	ADJ
ejpam-5816	200	4	r)σ	r)σ	NOUN
ejpam-5816	200	5	+	+	CCONJ
ejpam-5816	200	6	(	(	PUNCT
ejpam-5816	200	7	s−	s−	PROPN
ejpam-5816	200	8	t)σ	t)σ	PUNCT
ejpam-5816	200	9	s−	s−	PROPN
ejpam-5816	200	10	r	r	NOUN
ejpam-5816	200	11	]	]	PUNCT
ejpam-5816	200	12	ℵ	ℵ	X
ejpam-5816	200	13	(	(	PUNCT
ejpam-5816	200	14	t	t	PROPN
ejpam-5816	200	15	)	)	PUNCT
ejpam-5816	200	16	+	+	NUM
ejpam-5816	200	17	σ(1−	σ(1−	PROPN
ejpam-5816	200	18	κ	κ	PART
ejpam-5816	200	19	)	)	PUNCT
ejpam-5816	200	20	κ(s−	κ(s−	PROPN
ejpam-5816	200	21	r	r	NOUN
ejpam-5816	200	22	)	)	PUNCT
ejpam-5816	200	23	γ(σ	γ(σ	PROPN
ejpam-5816	200	24	)	)	PUNCT
ejpam-5816	201	1	[	[	X
ejpam-5816	201	2	ℵ	ℵ	X
ejpam-5816	201	3	(	(	PUNCT
ejpam-5816	201	4	r	r	NOUN
ejpam-5816	201	5	)	)	PUNCT
ejpam-5816	201	6	+	+	NOUN
ejpam-5816	201	7	ℵ	ℵ	X
ejpam-5816	201	8	(	(	PUNCT
ejpam-5816	201	9	s	s	NOUN
ejpam-5816	201	10	)	)	PUNCT
ejpam-5816	201	11	]	]	PUNCT
ejpam-5816	202	1	−σm(κ)γ(σ	−σm(κ)γ(σ	ADJ
ejpam-5816	202	2	)	)	PUNCT
ejpam-5816	202	3	κ(s−	κ(s−	PROPN
ejpam-5816	202	4	r	r	NOUN
ejpam-5816	202	5	)	)	PUNCT
ejpam-5816	202	6	[	[	PUNCT
ejpam-5816	202	7	iκ	iκ	NOUN
ejpam-5816	202	8	,	,	PUNCT
ejpam-5816	202	9	σ	σ	PROPN
ejpam-5816	202	10	r	r	PROPN
ejpam-5816	202	11	,	,	PUNCT
ejpam-5816	202	12	t	t	PROPN
ejpam-5816	202	13	ℵ(r	ℵ(r	PROPN
ejpam-5816	202	14	)	)	PUNCT
ejpam-5816	203	1	+	+	NUM
ejpam-5816	203	2	iκ	iκ	X
ejpam-5816	203	3	,	,	PUNCT
ejpam-5816	203	4	σ	σ	PROPN
ejpam-5816	203	5	s	s	PROPN
ejpam-5816	203	6	,	,	PUNCT
ejpam-5816	203	7	t	t	PROPN
ejpam-5816	203	8	ℵ(s	ℵ(s	PROPN
ejpam-5816	203	9	)	)	PUNCT
ejpam-5816	203	10	]	]	PUNCT
ejpam-5816	203	11	∣∣∣	∣∣∣	X
ejpam-5816	203	12	≤	≤	X
ejpam-5816	203	13	k	k	NOUN
ejpam-5816	203	14	s−	s−	PROPN
ejpam-5816	203	15	r	r	NOUN
ejpam-5816	203	16	(	(	PUNCT
ejpam-5816	203	17	1	1	NUM
ejpam-5816	203	18	σp+	σp+	NOUN
ejpam-5816	203	19	1	1	NUM
ejpam-5816	203	20	)	)	PUNCT
ejpam-5816	203	21	1	1	NUM
ejpam-5816	203	22	p	p	NOUN
ejpam-5816	203	23	{	{	PUNCT
ejpam-5816	203	24	(	(	PUNCT
ejpam-5816	203	25	t−	t−	X
ejpam-5816	203	26	r)σ+1	r)σ+1	PROPN
ejpam-5816	203	27	+	+	CCONJ
ejpam-5816	203	28	(	(	PUNCT
ejpam-5816	203	29	s−	s−	PROPN
ejpam-5816	203	30	t)σ+1	t)σ+1	PROPN
ejpam-5816	203	31	}	}	PUNCT
ejpam-5816	203	32	.	.	PUNCT
ejpam-5816	204	1	corollary	corollary	ADJ
ejpam-5816	204	2	4	4	NUM
ejpam-5816	204	3	.	.	PUNCT
ejpam-5816	204	4	applying	apply	VERB
ejpam-5816	204	5	corollary	corollary	ADJ
ejpam-5816	204	6	3	3	NUM
ejpam-5816	204	7	for	for	ADP
ejpam-5816	204	8	t	t	NOUN
ejpam-5816	204	9	=	=	SYM
ejpam-5816	204	10	r+s	r+s	PROPN
ejpam-5816	204	11	2	2	NUM
ejpam-5816	204	12	,	,	PUNCT
ejpam-5816	204	13	we	we	PRON
ejpam-5816	204	14	get	get	VERB
ejpam-5816	204	15	the	the	DET
ejpam-5816	204	16	following	follow	VERB
ejpam-5816	204	17	inequality∣∣∣(s−	inequality∣∣∣(s−	PROPN
ejpam-5816	204	18	r)σ−1	r)σ−1	NOUN
ejpam-5816	204	19	2σ−1	2σ−1	NUM
ejpam-5816	204	20	ℵ	ℵ	NOUN
ejpam-5816	204	21	(	(	PUNCT
ejpam-5816	204	22	r	r	NOUN
ejpam-5816	204	23	+	+	SYM
ejpam-5816	204	24	s	s	NOUN
ejpam-5816	204	25	2	2	NUM
ejpam-5816	204	26	)	)	PUNCT
ejpam-5816	205	1	+	+	NUM
ejpam-5816	205	2	σ(1−	σ(1−	PROPN
ejpam-5816	205	3	κ	κ	PART
ejpam-5816	205	4	)	)	PUNCT
ejpam-5816	205	5	κ(s−	κ(s−	PROPN
ejpam-5816	205	6	r	r	NOUN
ejpam-5816	205	7	)	)	PUNCT
ejpam-5816	206	1	γ(σ	γ(σ	PROPN
ejpam-5816	206	2	)	)	PUNCT
ejpam-5816	207	1	[	[	X
ejpam-5816	207	2	ℵ	ℵ	X
ejpam-5816	207	3	(	(	PUNCT
ejpam-5816	207	4	r	r	NOUN
ejpam-5816	207	5	)	)	PUNCT
ejpam-5816	207	6	+	+	NOUN
ejpam-5816	207	7	ℵ	ℵ	X
ejpam-5816	207	8	(	(	PUNCT
ejpam-5816	207	9	s	s	NOUN
ejpam-5816	207	10	)	)	PUNCT
ejpam-5816	207	11	]	]	PUNCT
ejpam-5816	207	12	−σm(κ)γ(σ	−σm(κ)γ(σ	ADJ
ejpam-5816	207	13	)	)	PUNCT
ejpam-5816	207	14	κ(s−	κ(s−	PROPN
ejpam-5816	207	15	r	r	NOUN
ejpam-5816	207	16	)	)	PUNCT
ejpam-5816	207	17	[	[	PUNCT
ejpam-5816	207	18	iκ	iκ	NOUN
ejpam-5816	207	19	,	,	PUNCT
ejpam-5816	207	20	σ	σ	NOUN
ejpam-5816	207	21	r	r	PROPN
ejpam-5816	207	22	,	,	PUNCT
ejpam-5816	207	23	r+s	r+s	NUM
ejpam-5816	207	24	2	2	NUM
ejpam-5816	207	25	ℵ(r	ℵ(r	NOUN
ejpam-5816	207	26	)	)	PUNCT
ejpam-5816	208	1	+	+	NUM
ejpam-5816	208	2	iκ	iκ	X
ejpam-5816	208	3	,	,	PUNCT
ejpam-5816	208	4	σ	σ	PROPN
ejpam-5816	208	5	s	s	PROPN
ejpam-5816	208	6	,	,	PUNCT
ejpam-5816	208	7	r+s	r+s	NUM
ejpam-5816	208	8	2	2	NUM
ejpam-5816	208	9	ℵ(s	ℵ(s	NOUN
ejpam-5816	208	10	)	)	PUNCT
ejpam-5816	208	11	]	]	PUNCT
ejpam-5816	208	12	∣∣∣	∣∣∣	X
ejpam-5816	208	13	≤k	≤k	PROPN
ejpam-5816	208	14	(	(	PUNCT
ejpam-5816	208	15	1	1	NUM
ejpam-5816	208	16	σp+	σp+	NOUN
ejpam-5816	208	17	1	1	NUM
ejpam-5816	208	18	)	)	PUNCT
ejpam-5816	208	19	1	1	NUM
ejpam-5816	208	20	p	p	NOUN
ejpam-5816	208	21	(	(	PUNCT
ejpam-5816	208	22	s−	s−	PROPN
ejpam-5816	208	23	r)σ	r)σ	VERB
ejpam-5816	209	1	2σ	2σ	NUM
ejpam-5816	209	2	.	.	PUNCT
ejpam-5816	210	1	remark	remark	VERB
ejpam-5816	210	2	5	5	NUM
ejpam-5816	210	3	.	.	PUNCT
ejpam-5816	210	4	applying	apply	VERB
ejpam-5816	210	5	theorem	theorem	NOUN
ejpam-5816	210	6	2	2	NUM
ejpam-5816	210	7	for	for	ADP
ejpam-5816	210	8	σ	σ	NOUN
ejpam-5816	210	9	=	=	SYM
ejpam-5816	210	10	κ	κ	NOUN
ejpam-5816	210	11	,	,	PUNCT
ejpam-5816	210	12	we	we	PRON
ejpam-5816	210	13	get	get	AUX
ejpam-5816	210	14	theorem	theorem	ADJ
ejpam-5816	210	15	2	2	NUM
ejpam-5816	210	16	proved	prove	VERB
ejpam-5816	210	17	by	by	ADP
ejpam-5816	210	18	ahmad	ahmad	PROPN
ejpam-5816	210	19	et	et	PROPN
ejpam-5816	210	20	al	al	PROPN
ejpam-5816	210	21	.	.	PUNCT
ejpam-5816	211	1	[	[	X
ejpam-5816	211	2	40	40	NUM
ejpam-5816	211	3	]	]	PUNCT
ejpam-5816	211	4	.	.	PUNCT
ejpam-5816	212	1	g.	g.	PROPN
ejpam-5816	212	2	rahman	rahman	PROPN
ejpam-5816	212	3	et	et	PROPN
ejpam-5816	212	4	al	al	PROPN
ejpam-5816	212	5	.	.	PUNCT
ejpam-5816	212	6	/	/	SYM
ejpam-5816	212	7	eur	eur	PROPN
ejpam-5816	212	8	.	.	PUNCT
ejpam-5816	213	1	j.	j.	PROPN
ejpam-5816	213	2	pure	pure	PROPN
ejpam-5816	213	3	appl	appl	PROPN
ejpam-5816	213	4	.	.	PROPN
ejpam-5816	213	5	math	math	PROPN
ejpam-5816	213	6	,	,	PUNCT
ejpam-5816	213	7	18	18	NUM
ejpam-5816	213	8	(	(	PUNCT
ejpam-5816	213	9	2	2	NUM
ejpam-5816	213	10	)	)	PUNCT
ejpam-5816	213	11	(	(	PUNCT
ejpam-5816	213	12	2025	2025	NUM
ejpam-5816	213	13	)	)	PUNCT
ejpam-5816	213	14	,	,	PUNCT
ejpam-5816	213	15	5816	5816	NUM
ejpam-5816	213	16	9	9	NUM
ejpam-5816	213	17	of	of	ADP
ejpam-5816	213	18	18	18	NUM
ejpam-5816	213	19	remark	remark	NOUN
ejpam-5816	213	20	6	6	NUM
ejpam-5816	213	21	.	.	PUNCT
ejpam-5816	213	22	applying	apply	VERB
ejpam-5816	213	23	corollary	corollary	ADJ
ejpam-5816	213	24	4	4	NUM
ejpam-5816	213	25	for	for	ADP
ejpam-5816	213	26	σ	σ	NOUN
ejpam-5816	213	27	=	=	SYM
ejpam-5816	213	28	κ	κ	NOUN
ejpam-5816	213	29	,	,	PUNCT
ejpam-5816	213	30	we	we	PRON
ejpam-5816	213	31	get	get	VERB
ejpam-5816	213	32	corollary	corollary	ADJ
ejpam-5816	213	33	4	4	NUM
ejpam-5816	213	34	proved	prove	VERB
ejpam-5816	213	35	earlier	early	ADV
ejpam-5816	213	36	by	by	ADP
ejpam-5816	213	37	ahmad	ahmad	PROPN
ejpam-5816	213	38	et	et	PROPN
ejpam-5816	213	39	al	al	PROPN
ejpam-5816	213	40	.	.	PUNCT
ejpam-5816	214	1	[	[	X
ejpam-5816	214	2	40	40	NUM
ejpam-5816	214	3	]	]	PUNCT
ejpam-5816	214	4	.	.	PUNCT
ejpam-5816	215	1	theorem	theorem	NOUN
ejpam-5816	215	2	3	3	X
ejpam-5816	215	3	.	.	PUNCT
ejpam-5816	216	1	let	let	VERB
ejpam-5816	216	2	ℵ	ℵ	NOUN
ejpam-5816	216	3	:	:	PUNCT
ejpam-5816	216	4	[	[	X
ejpam-5816	216	5	r	r	X
ejpam-5816	216	6	,	,	PUNCT
ejpam-5816	216	7	s	s	PART
ejpam-5816	216	8	]	]	X
ejpam-5816	216	9	→	→	PUNCT
ejpam-5816	216	10	r	r	NOUN
ejpam-5816	216	11	be	be	AUX
ejpam-5816	216	12	a	a	DET
ejpam-5816	216	13	differentiable	differentiable	ADJ
ejpam-5816	216	14	function	function	NOUN
ejpam-5816	216	15	on	on	ADP
ejpam-5816	216	16	(	(	PUNCT
ejpam-5816	216	17	r	r	NOUN
ejpam-5816	216	18	,	,	PUNCT
ejpam-5816	216	19	s	s	PART
ejpam-5816	216	20	)	)	PUNCT
ejpam-5816	216	21	,	,	PUNCT
ejpam-5816	216	22	where	where	SCONJ
ejpam-5816	216	23	ℵ′	ℵ′	ADP
ejpam-5816	216	24	∈	∈	PROPN
ejpam-5816	216	25	l1[r	l1[r	PROPN
ejpam-5816	216	26	,	,	PUNCT
ejpam-5816	216	27	s	s	X
ejpam-5816	216	28	]	]	PUNCT
ejpam-5816	216	29	and	and	CCONJ
ejpam-5816	216	30	r	r	X
ejpam-5816	216	31	<	<	X
ejpam-5816	216	32	s.	s.	PROPN
ejpam-5816	216	33	the	the	DET
ejpam-5816	216	34	following	follow	VERB
ejpam-5816	216	35	inequality	inequality	NOUN
ejpam-5816	216	36	holds	hold	VERB
ejpam-5816	216	37	for	for	ADP
ejpam-5816	216	38	hattaf	hattaf	NOUN
ejpam-5816	216	39	-	-	PUNCT
ejpam-5816	216	40	fractional	fractional	ADJ
ejpam-5816	216	41	integral	integral	ADJ
ejpam-5816	216	42	operators	operator	NOUN
ejpam-5816	216	43	(	(	PUNCT
ejpam-5816	216	44	4	4	NUM
ejpam-5816	216	45	)	)	PUNCT
ejpam-5816	216	46	and	and	CCONJ
ejpam-5816	216	47	(	(	PUNCT
ejpam-5816	216	48	5	5	X
ejpam-5816	216	49	)	)	PUNCT
ejpam-5816	216	50	if	if	SCONJ
ejpam-5816	216	51	|ℵ′|q	|ℵ′|q	NUM
ejpam-5816	216	52	is	be	AUX
ejpam-5816	216	53	a	a	DET
ejpam-5816	216	54	convex	convex	NOUN
ejpam-5816	216	55	function.∣∣∣	function.∣∣∣	ADP
ejpam-5816	216	56	[	[	X
ejpam-5816	216	57	(	(	PUNCT
ejpam-5816	216	58	t−	t−	ADJ
ejpam-5816	216	59	r)σ	r)σ	NOUN
ejpam-5816	216	60	+	+	CCONJ
ejpam-5816	216	61	(	(	PUNCT
ejpam-5816	216	62	s−	s−	PROPN
ejpam-5816	216	63	t)σ	t)σ	PUNCT
ejpam-5816	216	64	s−	s−	PROPN
ejpam-5816	216	65	r	r	NOUN
ejpam-5816	216	66	]	]	PUNCT
ejpam-5816	216	67	ℵ	ℵ	X
ejpam-5816	216	68	(	(	PUNCT
ejpam-5816	216	69	t	t	PROPN
ejpam-5816	216	70	)	)	PUNCT
ejpam-5816	217	1	+	+	NUM
ejpam-5816	217	2	σ(1−	σ(1−	PROPN
ejpam-5816	217	3	κ	κ	PART
ejpam-5816	217	4	)	)	PUNCT
ejpam-5816	217	5	κ(s−	κ(s−	PROPN
ejpam-5816	217	6	r	r	NOUN
ejpam-5816	217	7	)	)	PUNCT
ejpam-5816	217	8	γ(σ	γ(σ	PROPN
ejpam-5816	217	9	)	)	PUNCT
ejpam-5816	218	1	[	[	X
ejpam-5816	218	2	ℵ	ℵ	X
ejpam-5816	218	3	(	(	PUNCT
ejpam-5816	218	4	r	r	NOUN
ejpam-5816	218	5	)	)	PUNCT
ejpam-5816	218	6	+	+	NOUN
ejpam-5816	218	7	ℵ	ℵ	X
ejpam-5816	218	8	(	(	PUNCT
ejpam-5816	218	9	s	s	NOUN
ejpam-5816	218	10	)	)	PUNCT
ejpam-5816	218	11	]	]	PUNCT
ejpam-5816	219	1	−σm(κ)γ(σ	−σm(κ)γ(σ	ADJ
ejpam-5816	219	2	)	)	PUNCT
ejpam-5816	219	3	κ(s−	κ(s−	PROPN
ejpam-5816	219	4	r	r	NOUN
ejpam-5816	219	5	)	)	PUNCT
ejpam-5816	219	6	[	[	PUNCT
ejpam-5816	219	7	iκ	iκ	NOUN
ejpam-5816	219	8	,	,	PUNCT
ejpam-5816	219	9	σ	σ	PROPN
ejpam-5816	219	10	r	r	PROPN
ejpam-5816	219	11	,	,	PUNCT
ejpam-5816	219	12	t	t	PROPN
ejpam-5816	219	13	ℵ(r	ℵ(r	PROPN
ejpam-5816	219	14	)	)	PUNCT
ejpam-5816	220	1	+	+	NUM
ejpam-5816	220	2	iκ	iκ	X
ejpam-5816	220	3	,	,	PUNCT
ejpam-5816	220	4	σ	σ	PROPN
ejpam-5816	220	5	s	s	PROPN
ejpam-5816	220	6	,	,	PUNCT
ejpam-5816	220	7	t	t	PROPN
ejpam-5816	220	8	ℵ(s	ℵ(s	PROPN
ejpam-5816	220	9	)	)	PUNCT
ejpam-5816	220	10	]	]	PUNCT
ejpam-5816	220	11	∣∣∣	∣∣∣	NOUN
ejpam-5816	220	12	≤(t−	≤(t−	NOUN
ejpam-5816	220	13	r)σ+1	r)σ+1	PROPN
ejpam-5816	220	14	s−	s−	PROPN
ejpam-5816	220	15	r	r	NOUN
ejpam-5816	220	16	(	(	PUNCT
ejpam-5816	220	17	1	1	NUM
ejpam-5816	220	18	p(σp+	p(σp+	NOUN
ejpam-5816	220	19	1	1	NUM
ejpam-5816	220	20	)	)	PUNCT
ejpam-5816	220	21	+	+	CCONJ
ejpam-5816	220	22	|	|	ADV
ejpam-5816	220	23	ℵ′(t	ℵ′(t	PROPN
ejpam-5816	220	24	)	)	PUNCT
ejpam-5816	220	25	|q	|q	NOUN
ejpam-5816	220	26	+	+	CCONJ
ejpam-5816	220	27	|	|	ADV
ejpam-5816	220	28	ℵ′(r	ℵ′(r	NUM
ejpam-5816	220	29	)	)	PUNCT
ejpam-5816	220	30	|q	|q	NOUN
ejpam-5816	220	31	2q	2q	NOUN
ejpam-5816	220	32	)	)	PUNCT
ejpam-5816	221	1	+	+	CCONJ
ejpam-5816	221	2	(	(	PUNCT
ejpam-5816	221	3	s−	s−	PROPN
ejpam-5816	221	4	t)σ+1	t)σ+1	PROPN
ejpam-5816	221	5	s−	s−	PROPN
ejpam-5816	221	6	t	t	PROPN
ejpam-5816	221	7	(	(	PUNCT
ejpam-5816	221	8	1	1	NUM
ejpam-5816	221	9	p(σp+	p(σp+	NOUN
ejpam-5816	221	10	1	1	NUM
ejpam-5816	221	11	)	)	PUNCT
ejpam-5816	221	12	+	+	CCONJ
ejpam-5816	221	13	|	|	ADV
ejpam-5816	221	14	ℵ′(s	ℵ′(s	PRON
ejpam-5816	221	15	)	)	PUNCT
ejpam-5816	221	16	|q	|q	NOUN
ejpam-5816	221	17	+	+	CCONJ
ejpam-5816	221	18	|	|	CCONJ
ejpam-5816	221	19	ℵ′(t	ℵ′(t	PROPN
ejpam-5816	221	20	)	)	PUNCT
ejpam-5816	221	21	|q	|q	NOUN
ejpam-5816	221	22	2q	2q	NUM
ejpam-5816	221	23	)	)	PUNCT
ejpam-5816	221	24	,	,	PUNCT
ejpam-5816	221	25	where	where	SCONJ
ejpam-5816	221	26	1	1	NUM
ejpam-5816	221	27	p	p	NOUN
ejpam-5816	221	28	+	+	NOUN
ejpam-5816	221	29	1	1	NUM
ejpam-5816	221	30	q	q	NOUN
ejpam-5816	221	31	=	=	SYM
ejpam-5816	221	32	1	1	NUM
ejpam-5816	221	33	,	,	PUNCT
ejpam-5816	221	34	t	t	PROPN
ejpam-5816	221	35	∈	∈	PROPN
ejpam-5816	222	1	[	[	X
ejpam-5816	222	2	r	r	X
ejpam-5816	222	3	,	,	PUNCT
ejpam-5816	222	4	s	s	PART
ejpam-5816	222	5	]	]	X
ejpam-5816	222	6	,	,	PUNCT
ejpam-5816	222	7	κ	κ	PROPN
ejpam-5816	222	8	∈	∈	PROPN
ejpam-5816	222	9	(	(	PUNCT
ejpam-5816	222	10	0	0	NUM
ejpam-5816	222	11	,	,	PUNCT
ejpam-5816	222	12	1	1	NUM
ejpam-5816	222	13	]	]	PUNCT
ejpam-5816	222	14	and	and	CCONJ
ejpam-5816	222	15	m(κ	m(κ	NUM
ejpam-5816	222	16	)	)	PUNCT
ejpam-5816	222	17	>	>	X
ejpam-5816	222	18	0	0	X
ejpam-5816	222	19	.	.	PUNCT
ejpam-5816	222	20	proof	proof	NOUN
ejpam-5816	222	21	.	.	PUNCT
ejpam-5816	223	1	by	by	ADP
ejpam-5816	223	2	utilizing	utilize	VERB
ejpam-5816	223	3	lemma	lemma	PROPN
ejpam-5816	223	4	1	1	NUM
ejpam-5816	223	5	,	,	PUNCT
ejpam-5816	223	6	we	we	PRON
ejpam-5816	223	7	have∣∣∣	have∣∣∣	PUNCT
ejpam-5816	224	1	[	[	X
ejpam-5816	224	2	(	(	PUNCT
ejpam-5816	224	3	t−	t−	ADJ
ejpam-5816	224	4	r)σ	r)σ	NOUN
ejpam-5816	224	5	+	+	CCONJ
ejpam-5816	224	6	(	(	PUNCT
ejpam-5816	224	7	s−	s−	PROPN
ejpam-5816	224	8	t)σ	t)σ	PUNCT
ejpam-5816	224	9	s−	s−	PROPN
ejpam-5816	224	10	r	r	NOUN
ejpam-5816	224	11	]	]	PUNCT
ejpam-5816	224	12	ℵ	ℵ	X
ejpam-5816	224	13	(	(	PUNCT
ejpam-5816	224	14	t	t	PROPN
ejpam-5816	224	15	)	)	PUNCT
ejpam-5816	224	16	+	+	NUM
ejpam-5816	224	17	σ(1−	σ(1−	PROPN
ejpam-5816	224	18	κ	κ	PART
ejpam-5816	224	19	)	)	PUNCT
ejpam-5816	224	20	κ(s−	κ(s−	PROPN
ejpam-5816	224	21	r	r	NOUN
ejpam-5816	224	22	)	)	PUNCT
ejpam-5816	224	23	γ(σ	γ(σ	PROPN
ejpam-5816	224	24	)	)	PUNCT
ejpam-5816	225	1	[	[	X
ejpam-5816	225	2	ℵ	ℵ	X
ejpam-5816	225	3	(	(	PUNCT
ejpam-5816	225	4	r	r	NOUN
ejpam-5816	225	5	)	)	PUNCT
ejpam-5816	225	6	+	+	NOUN
ejpam-5816	225	7	ℵ	ℵ	X
ejpam-5816	225	8	(	(	PUNCT
ejpam-5816	225	9	s	s	NOUN
ejpam-5816	225	10	)	)	PUNCT
ejpam-5816	225	11	]	]	PUNCT
ejpam-5816	226	1	−σm(κ)γ(σ	−σm(κ)γ(σ	ADJ
ejpam-5816	226	2	)	)	PUNCT
ejpam-5816	226	3	κ(s−	κ(s−	PROPN
ejpam-5816	226	4	r	r	NOUN
ejpam-5816	226	5	)	)	PUNCT
ejpam-5816	226	6	[	[	PUNCT
ejpam-5816	226	7	iκ	iκ	NOUN
ejpam-5816	226	8	,	,	PUNCT
ejpam-5816	226	9	σ	σ	PROPN
ejpam-5816	226	10	r	r	PROPN
ejpam-5816	226	11	,	,	PUNCT
ejpam-5816	226	12	t	t	PROPN
ejpam-5816	226	13	ℵ(r	ℵ(r	PROPN
ejpam-5816	226	14	)	)	PUNCT
ejpam-5816	227	1	+	+	NUM
ejpam-5816	227	2	iκ	iκ	X
ejpam-5816	227	3	,	,	PUNCT
ejpam-5816	227	4	σ	σ	PROPN
ejpam-5816	227	5	s	s	PROPN
ejpam-5816	227	6	,	,	PUNCT
ejpam-5816	227	7	t	t	PROPN
ejpam-5816	227	8	ℵ(s	ℵ(s	PROPN
ejpam-5816	227	9	)	)	PUNCT
ejpam-5816	227	10	]	]	PUNCT
ejpam-5816	227	11	∣∣∣	∣∣∣	NOUN
ejpam-5816	227	12	≤(t−	≤(t−	NOUN
ejpam-5816	228	1	r)σ+1	r)σ+1	PROPN
ejpam-5816	228	2	s−	s−	PROPN
ejpam-5816	228	3	r	r	NOUN
ejpam-5816	228	4	∫	∫	PROPN
ejpam-5816	228	5	1	1	NUM
ejpam-5816	228	6	0	0	NUM
ejpam-5816	228	7	ρσ	ρσ	ADP
ejpam-5816	228	8	|	|	ADV
ejpam-5816	228	9	ℵ′(ρt+	ℵ′(ρt+	NOUN
ejpam-5816	228	10	(	(	PUNCT
ejpam-5816	228	11	1−	1−	NUM
ejpam-5816	228	12	ρ)r	ρ)r	X
ejpam-5816	228	13	)	)	PUNCT
ejpam-5816	229	1	|	|	ADV
ejpam-5816	229	2	dρ	dρ	INTJ
ejpam-5816	230	1	+	+	CCONJ
ejpam-5816	230	2	(	(	PUNCT
ejpam-5816	230	3	s−	s−	PROPN
ejpam-5816	230	4	t)σ+1	t)σ+1	PROPN
ejpam-5816	230	5	s−	s−	PROPN
ejpam-5816	230	6	r	r	NOUN
ejpam-5816	230	7	∫	∫	PROPN
ejpam-5816	230	8	1	1	NUM
ejpam-5816	230	9	0	0	NUM
ejpam-5816	230	10	ρσ	ρσ	ADP
ejpam-5816	230	11	|	|	ADV
ejpam-5816	230	12	ℵ′(ρt+	ℵ′(ρt+	NOUN
ejpam-5816	230	13	(	(	PUNCT
ejpam-5816	230	14	1−	1−	NUM
ejpam-5816	230	15	ρ)s	ρ)s	NOUN
ejpam-5816	230	16	)	)	PUNCT
ejpam-5816	231	1	|	|	ADV
ejpam-5816	231	2	dρ	dρ	INTJ
ejpam-5816	231	3	.	.	PUNCT
ejpam-5816	232	1	by	by	ADP
ejpam-5816	232	2	employing	employ	VERB
ejpam-5816	232	3	young	young	ADJ
ejpam-5816	232	4	inequality	inequality	NOUN
ejpam-5816	232	5	as	as	ADP
ejpam-5816	232	6	uv	uv	NOUN
ejpam-5816	232	7	≤	≤	PROPN
ejpam-5816	232	8	up	up	ADP
ejpam-5816	232	9	p	p	NOUN
ejpam-5816	232	10	+	+	PROPN
ejpam-5816	232	11	vq	vq	PROPN
ejpam-5816	232	12	q	q	NOUN
ejpam-5816	232	13	in	in	ADP
ejpam-5816	232	14	above	above	ADV
ejpam-5816	232	15	,	,	PUNCT
ejpam-5816	232	16	we	we	PRON
ejpam-5816	232	17	have∣∣∣	have∣∣∣	PUNCT
ejpam-5816	233	1	[	[	X
ejpam-5816	233	2	(	(	PUNCT
ejpam-5816	233	3	t−	t−	ADJ
ejpam-5816	233	4	r)σ	r)σ	NOUN
ejpam-5816	233	5	+	+	CCONJ
ejpam-5816	233	6	(	(	PUNCT
ejpam-5816	233	7	s−	s−	PROPN
ejpam-5816	233	8	t)σ	t)σ	PUNCT
ejpam-5816	233	9	s−	s−	PROPN
ejpam-5816	233	10	r	r	NOUN
ejpam-5816	233	11	]	]	PUNCT
ejpam-5816	233	12	ℵ	ℵ	X
ejpam-5816	233	13	(	(	PUNCT
ejpam-5816	233	14	t	t	PROPN
ejpam-5816	233	15	)	)	PUNCT
ejpam-5816	233	16	+	+	NUM
ejpam-5816	233	17	σ(1−	σ(1−	PROPN
ejpam-5816	233	18	κ	κ	PART
ejpam-5816	233	19	)	)	PUNCT
ejpam-5816	233	20	κ(s−	κ(s−	PROPN
ejpam-5816	233	21	r	r	NOUN
ejpam-5816	233	22	)	)	PUNCT
ejpam-5816	233	23	γ(σ	γ(σ	PROPN
ejpam-5816	233	24	)	)	PUNCT
ejpam-5816	234	1	[	[	X
ejpam-5816	234	2	ℵ	ℵ	X
ejpam-5816	234	3	(	(	PUNCT
ejpam-5816	234	4	r	r	NOUN
ejpam-5816	234	5	)	)	PUNCT
ejpam-5816	234	6	+	+	NOUN
ejpam-5816	234	7	ℵ	ℵ	X
ejpam-5816	234	8	(	(	PUNCT
ejpam-5816	234	9	s	s	NOUN
ejpam-5816	234	10	)	)	PUNCT
ejpam-5816	234	11	]	]	X
ejpam-5816	234	12	(	(	PUNCT
ejpam-5816	234	13	13	13	NUM
ejpam-5816	234	14	)	)	PUNCT
ejpam-5816	234	15	−σm(κ)γ(σ	−σm(κ)γ(σ	ADJ
ejpam-5816	234	16	)	)	PUNCT
ejpam-5816	234	17	κ(s−	κ(s−	PROPN
ejpam-5816	234	18	r	r	NOUN
ejpam-5816	234	19	)	)	PUNCT
ejpam-5816	234	20	[	[	PUNCT
ejpam-5816	234	21	iκ	iκ	NOUN
ejpam-5816	234	22	,	,	PUNCT
ejpam-5816	234	23	σ	σ	PROPN
ejpam-5816	234	24	r	r	PROPN
ejpam-5816	234	25	,	,	PUNCT
ejpam-5816	234	26	t	t	PROPN
ejpam-5816	234	27	ℵ(r	ℵ(r	PROPN
ejpam-5816	234	28	)	)	PUNCT
ejpam-5816	235	1	+	+	NUM
ejpam-5816	235	2	iκ	iκ	X
ejpam-5816	235	3	,	,	PUNCT
ejpam-5816	235	4	σ	σ	PROPN
ejpam-5816	235	5	s	s	PROPN
ejpam-5816	235	6	,	,	PUNCT
ejpam-5816	235	7	t	t	PROPN
ejpam-5816	235	8	ℵ(s	ℵ(s	PROPN
ejpam-5816	235	9	)	)	PUNCT
ejpam-5816	235	10	]	]	PUNCT
ejpam-5816	235	11	∣∣∣	∣∣∣	NOUN
ejpam-5816	235	12	≤(t−	≤(t−	NOUN
ejpam-5816	236	1	r)σ+1	r)σ+1	PROPN
ejpam-5816	236	2	s−	s−	PROPN
ejpam-5816	236	3	r	r	NOUN
ejpam-5816	237	1	[	[	PUNCT
ejpam-5816	237	2	1	1	NUM
ejpam-5816	237	3	p	p	NOUN
ejpam-5816	237	4	∫	∫	PROPN
ejpam-5816	237	5	1	1	NUM
ejpam-5816	237	6	0	0	NUM
ejpam-5816	237	7	ρσpdρ+	ρσpdρ+	ADP
ejpam-5816	237	8	1	1	NUM
ejpam-5816	237	9	q	q	NOUN
ejpam-5816	237	10	∫	∫	PROPN
ejpam-5816	237	11	1	1	NUM
ejpam-5816	237	12	0	0	NUM
ejpam-5816	238	1	|	|	ADV
ejpam-5816	238	2	ℵ′(ρt+	ℵ′(ρt+	NOUN
ejpam-5816	238	3	(	(	PUNCT
ejpam-5816	238	4	1−	1−	NUM
ejpam-5816	238	5	ρ)r	ρ)r	X
ejpam-5816	238	6	)	)	PUNCT
ejpam-5816	238	7	|q	|q	NOUN
ejpam-5816	238	8	dρ	dρ	X
ejpam-5816	238	9	]	]	PUNCT
ejpam-5816	239	1	+	+	CCONJ
ejpam-5816	239	2	(	(	PUNCT
ejpam-5816	239	3	s−	s−	PROPN
ejpam-5816	239	4	t)σ+1	t)σ+1	PROPN
ejpam-5816	239	5	s−	s−	PROPN
ejpam-5816	239	6	r	r	NOUN
ejpam-5816	239	7	[	[	PUNCT
ejpam-5816	239	8	1	1	NUM
ejpam-5816	239	9	p	p	NOUN
ejpam-5816	239	10	∫	∫	PROPN
ejpam-5816	239	11	1	1	NUM
ejpam-5816	239	12	0	0	NUM
ejpam-5816	239	13	ρσpdρ+	ρσpdρ+	ADP
ejpam-5816	239	14	1	1	NUM
ejpam-5816	239	15	q	q	NOUN
ejpam-5816	239	16	∫	∫	PROPN
ejpam-5816	239	17	1	1	NUM
ejpam-5816	239	18	0	0	NUM
ejpam-5816	240	1	|	|	ADV
ejpam-5816	240	2	ℵ′(ρt+	ℵ′(ρt+	NOUN
ejpam-5816	240	3	(	(	PUNCT
ejpam-5816	240	4	1−	1−	NUM
ejpam-5816	240	5	ρ)s	ρ)s	NOUN
ejpam-5816	240	6	)	)	PUNCT
ejpam-5816	240	7	|q	|q	NOUN
ejpam-5816	240	8	dρ	dρ	X
ejpam-5816	240	9	]	]	PUNCT
ejpam-5816	240	10	.	.	PUNCT
ejpam-5816	241	1	(	(	PUNCT
ejpam-5816	241	2	14	14	NUM
ejpam-5816	241	3	)	)	PUNCT
ejpam-5816	241	4	since	since	SCONJ
ejpam-5816	241	5	|	|	ADV
ejpam-5816	241	6	ℵ′	ℵ′	CCONJ
ejpam-5816	241	7	|q	|q	NOUN
ejpam-5816	241	8	is	be	AUX
ejpam-5816	241	9	convex	convex	ADJ
ejpam-5816	241	10	,	,	PUNCT
ejpam-5816	241	11	so	so	ADV
ejpam-5816	241	12	therefore	therefore	ADV
ejpam-5816	241	13	we	we	PRON
ejpam-5816	241	14	have∫	have∫	VERB
ejpam-5816	241	15	1	1	NUM
ejpam-5816	241	16	0	0	NUM
ejpam-5816	242	1	|	|	ADV
ejpam-5816	242	2	ℵ′(ρt+	ℵ′(ρt+	NOUN
ejpam-5816	242	3	(	(	PUNCT
ejpam-5816	242	4	1−	1−	NUM
ejpam-5816	242	5	ρ)r	ρ)r	X
ejpam-5816	242	6	)	)	PUNCT
ejpam-5816	242	7	|q	|q	NOUN
ejpam-5816	242	8	dρ	dρ	PROPN
ejpam-5816	243	1	≤	≤	NUM
ejpam-5816	243	2	∫	∫	PROPN
ejpam-5816	244	1	1	1	NUM
ejpam-5816	244	2	0	0	NUM
ejpam-5816	245	1	[	[	X
ejpam-5816	245	2	ρ	ρ	NUM
ejpam-5816	245	3	|	|	NOUN
ejpam-5816	245	4	ℵ′(t	ℵ′(t	PROPN
ejpam-5816	245	5	)	)	PUNCT
ejpam-5816	245	6	|q	|q	NOUN
ejpam-5816	246	1	+	+	PROPN
ejpam-5816	246	2	(	(	PUNCT
ejpam-5816	246	3	1−	1−	NUM
ejpam-5816	246	4	ρ	ρ	NOUN
ejpam-5816	246	5	)	)	PUNCT
ejpam-5816	246	6	|	|	ADV
ejpam-5816	246	7	ℵ′(r	ℵ′(r	CCONJ
ejpam-5816	246	8	)	)	PUNCT
ejpam-5816	246	9	|q]dρ	|q]dρ	PROPN
ejpam-5816	247	1	g.	g.	PROPN
ejpam-5816	247	2	rahman	rahman	PROPN
ejpam-5816	247	3	et	et	PROPN
ejpam-5816	247	4	al	al	PROPN
ejpam-5816	247	5	.	.	PUNCT
ejpam-5816	247	6	/	/	SYM
ejpam-5816	247	7	eur	eur	PROPN
ejpam-5816	247	8	.	.	PUNCT
ejpam-5816	248	1	j.	j.	PROPN
ejpam-5816	248	2	pure	pure	PROPN
ejpam-5816	248	3	appl	appl	PROPN
ejpam-5816	248	4	.	.	PROPN
ejpam-5816	248	5	math	math	PROPN
ejpam-5816	248	6	,	,	PUNCT
ejpam-5816	248	7	18	18	NUM
ejpam-5816	248	8	(	(	PUNCT
ejpam-5816	248	9	2	2	NUM
ejpam-5816	248	10	)	)	PUNCT
ejpam-5816	248	11	(	(	PUNCT
ejpam-5816	248	12	2025	2025	NUM
ejpam-5816	248	13	)	)	PUNCT
ejpam-5816	248	14	,	,	PUNCT
ejpam-5816	248	15	5816	5816	NUM
ejpam-5816	248	16	10	10	NUM
ejpam-5816	248	17	of	of	ADP
ejpam-5816	248	18	18	18	NUM
ejpam-5816	248	19	=	=	SYM
ejpam-5816	248	20	|	|	NOUN
ejpam-5816	248	21	ℵ′(t	ℵ′(t	NOUN
ejpam-5816	248	22	)	)	PUNCT
ejpam-5816	248	23	|q	|q	NOUN
ejpam-5816	249	1	+	+	CCONJ
ejpam-5816	249	2	|	|	ADV
ejpam-5816	249	3	ℵ′(r	ℵ′(r	NUM
ejpam-5816	249	4	)	)	PUNCT
ejpam-5816	249	5	|q	|q	NOUN
ejpam-5816	249	6	2	2	NUM
ejpam-5816	249	7	(	(	PUNCT
ejpam-5816	249	8	15	15	NUM
ejpam-5816	249	9	)	)	PUNCT
ejpam-5816	249	10	and	and	CCONJ
ejpam-5816	249	11	∫	∫	PROPN
ejpam-5816	249	12	1	1	NUM
ejpam-5816	249	13	0	0	NUM
ejpam-5816	250	1	|	|	ADV
ejpam-5816	250	2	ℵ′(ρt+	ℵ′(ρt+	NOUN
ejpam-5816	250	3	(	(	PUNCT
ejpam-5816	250	4	1−	1−	NUM
ejpam-5816	250	5	ρ)s	ρ)s	NOUN
ejpam-5816	250	6	)	)	PUNCT
ejpam-5816	250	7	|q	|q	NOUN
ejpam-5816	250	8	dρ	dρ	PROPN
ejpam-5816	251	1	≤	≤	NUM
ejpam-5816	251	2	∫	∫	PROPN
ejpam-5816	252	1	1	1	NUM
ejpam-5816	252	2	0	0	NUM
ejpam-5816	253	1	[	[	X
ejpam-5816	253	2	ρ	ρ	NUM
ejpam-5816	253	3	|	|	NOUN
ejpam-5816	253	4	ℵ′(t	ℵ′(t	PROPN
ejpam-5816	253	5	)	)	PUNCT
ejpam-5816	253	6	|q	|q	NOUN
ejpam-5816	254	1	+	+	PROPN
ejpam-5816	254	2	(	(	PUNCT
ejpam-5816	254	3	1−	1−	NUM
ejpam-5816	254	4	ρ	ρ	NOUN
ejpam-5816	254	5	)	)	PUNCT
ejpam-5816	254	6	|	|	ADV
ejpam-5816	254	7	ℵ′(s	ℵ′(s	PUNCT
ejpam-5816	254	8	)	)	PUNCT
ejpam-5816	254	9	|q]dρ	|q]dρ	X
ejpam-5816	254	10	=	=	SYM
ejpam-5816	254	11	|	|	CCONJ
ejpam-5816	254	12	ℵ′(t	ℵ′(t	NOUN
ejpam-5816	254	13	)	)	PUNCT
ejpam-5816	254	14	|q	|q	NOUN
ejpam-5816	254	15	+	+	CCONJ
ejpam-5816	254	16	|	|	ADV
ejpam-5816	254	17	ℵ′(s	ℵ′(s	PRON
ejpam-5816	254	18	)	)	PUNCT
ejpam-5816	254	19	|q	|q	NOUN
ejpam-5816	254	20	2	2	NUM
ejpam-5816	254	21	.	.	PUNCT
ejpam-5816	255	1	(	(	PUNCT
ejpam-5816	255	2	16	16	NUM
ejpam-5816	255	3	)	)	PUNCT
ejpam-5816	255	4	substituting	substitute	VERB
ejpam-5816	255	5	(	(	PUNCT
ejpam-5816	255	6	15	15	NUM
ejpam-5816	255	7	)	)	PUNCT
ejpam-5816	255	8	and	and	CCONJ
ejpam-5816	255	9	(	(	PUNCT
ejpam-5816	255	10	16	16	NUM
ejpam-5816	255	11	)	)	PUNCT
ejpam-5816	255	12	in	in	ADP
ejpam-5816	255	13	(	(	PUNCT
ejpam-5816	255	14	13	13	NUM
ejpam-5816	255	15	)	)	PUNCT
ejpam-5816	255	16	and	and	CCONJ
ejpam-5816	255	17	then	then	ADV
ejpam-5816	255	18	by	by	ADP
ejpam-5816	255	19	solving	solve	VERB
ejpam-5816	255	20	the	the	DET
ejpam-5816	255	21	integrals	integral	NOUN
ejpam-5816	255	22	,	,	PUNCT
ejpam-5816	255	23	we	we	PRON
ejpam-5816	255	24	get	get	VERB
ejpam-5816	255	25	the	the	DET
ejpam-5816	255	26	desired	desire	VERB
ejpam-5816	255	27	proof	proof	NOUN
ejpam-5816	255	28	.	.	PUNCT
ejpam-5816	256	1	corollary	corollary	ADJ
ejpam-5816	256	2	5	5	NUM
ejpam-5816	256	3	.	.	PUNCT
ejpam-5816	256	4	applying	apply	VERB
ejpam-5816	256	5	theorem	theorem	NOUN
ejpam-5816	256	6	3	3	NUM
ejpam-5816	256	7	for	for	ADP
ejpam-5816	256	8	|ℵ′|	|ℵ′|	PROPN
ejpam-5816	256	9	≤	≤	PROPN
ejpam-5816	257	1	k	k	NOUN
ejpam-5816	257	2	where	where	SCONJ
ejpam-5816	257	3	k	k	PROPN
ejpam-5816	257	4	>	>	X
ejpam-5816	257	5	0	0	PUNCT
ejpam-5816	257	6	,	,	PUNCT
ejpam-5816	257	7	we	we	PRON
ejpam-5816	257	8	get	get	VERB
ejpam-5816	257	9	the	the	DET
ejpam-5816	257	10	following	follow	VERB
ejpam-5816	257	11	inequality	inequality	NOUN
ejpam-5816	257	12	∣∣∣	∣∣∣	NOUN
ejpam-5816	258	1	[	[	X
ejpam-5816	258	2	(	(	PUNCT
ejpam-5816	258	3	t−	t−	ADJ
ejpam-5816	258	4	r)σ	r)σ	NOUN
ejpam-5816	258	5	+	+	CCONJ
ejpam-5816	258	6	(	(	PUNCT
ejpam-5816	258	7	s−	s−	PROPN
ejpam-5816	258	8	t)σ	t)σ	PUNCT
ejpam-5816	258	9	s−	s−	PROPN
ejpam-5816	258	10	r	r	NOUN
ejpam-5816	258	11	]	]	PUNCT
ejpam-5816	258	12	ℵ	ℵ	X
ejpam-5816	258	13	(	(	PUNCT
ejpam-5816	258	14	t	t	PROPN
ejpam-5816	258	15	)	)	PUNCT
ejpam-5816	258	16	+	+	NUM
ejpam-5816	258	17	σ(1−	σ(1−	PROPN
ejpam-5816	258	18	κ	κ	PART
ejpam-5816	258	19	)	)	PUNCT
ejpam-5816	258	20	κ(s−	κ(s−	PROPN
ejpam-5816	258	21	r	r	NOUN
ejpam-5816	258	22	)	)	PUNCT
ejpam-5816	258	23	γ(σ	γ(σ	PROPN
ejpam-5816	258	24	)	)	PUNCT
ejpam-5816	259	1	[	[	X
ejpam-5816	259	2	ℵ	ℵ	X
ejpam-5816	259	3	(	(	PUNCT
ejpam-5816	259	4	r	r	NOUN
ejpam-5816	259	5	)	)	PUNCT
ejpam-5816	259	6	+	+	NOUN
ejpam-5816	259	7	ℵ	ℵ	X
ejpam-5816	259	8	(	(	PUNCT
ejpam-5816	259	9	s	s	NOUN
ejpam-5816	259	10	)	)	PUNCT
ejpam-5816	259	11	]	]	PUNCT
ejpam-5816	260	1	−σm(κ)γ(σ	−σm(κ)γ(σ	ADJ
ejpam-5816	260	2	)	)	PUNCT
ejpam-5816	260	3	κ(s−	κ(s−	PROPN
ejpam-5816	260	4	r	r	NOUN
ejpam-5816	260	5	)	)	PUNCT
ejpam-5816	260	6	[	[	PUNCT
ejpam-5816	260	7	iκ	iκ	NOUN
ejpam-5816	260	8	,	,	PUNCT
ejpam-5816	260	9	σ	σ	PROPN
ejpam-5816	260	10	r	r	PROPN
ejpam-5816	260	11	,	,	PUNCT
ejpam-5816	260	12	t	t	PROPN
ejpam-5816	260	13	ℵ(r	ℵ(r	PROPN
ejpam-5816	260	14	)	)	PUNCT
ejpam-5816	261	1	+	+	NUM
ejpam-5816	261	2	iκ	iκ	X
ejpam-5816	261	3	,	,	PUNCT
ejpam-5816	261	4	σ	σ	PROPN
ejpam-5816	261	5	s	s	PROPN
ejpam-5816	261	6	,	,	PUNCT
ejpam-5816	261	7	t	t	PROPN
ejpam-5816	261	8	ℵ(s	ℵ(s	PROPN
ejpam-5816	261	9	)	)	PUNCT
ejpam-5816	261	10	]	]	PUNCT
ejpam-5816	261	11	∣∣∣	∣∣∣	X
ejpam-5816	261	12	≤	≤	X
ejpam-5816	261	13	(	(	PUNCT
ejpam-5816	261	14	1	1	NUM
ejpam-5816	261	15	p(σp+	p(σp+	NOUN
ejpam-5816	261	16	1	1	NUM
ejpam-5816	261	17	)	)	PUNCT
ejpam-5816	262	1	+	+	CCONJ
ejpam-5816	262	2	kq	kq	PROPN
ejpam-5816	262	3	q	q	PROPN
ejpam-5816	262	4	)	)	PUNCT
ejpam-5816	262	5	{	{	PUNCT
ejpam-5816	262	6	(	(	PUNCT
ejpam-5816	262	7	t−	t−	X
ejpam-5816	262	8	r)σ+1	r)σ+1	PROPN
ejpam-5816	262	9	s−	s−	PROPN
ejpam-5816	262	10	r	r	NOUN
ejpam-5816	262	11	+	+	CCONJ
ejpam-5816	262	12	(	(	PUNCT
ejpam-5816	262	13	s−	s−	PROPN
ejpam-5816	262	14	t)σ+1	t)σ+1	PROPN
ejpam-5816	262	15	s−	s−	PROPN
ejpam-5816	262	16	r	r	NOUN
ejpam-5816	262	17	}	}	PUNCT
ejpam-5816	262	18	.	.	PUNCT
ejpam-5816	263	1	corollary	corollary	ADJ
ejpam-5816	263	2	6	6	NUM
ejpam-5816	263	3	.	.	PUNCT
ejpam-5816	263	4	applying	apply	VERB
ejpam-5816	263	5	corollary	corollary	NOUN
ejpam-5816	263	6	5	5	NUM
ejpam-5816	263	7	for	for	ADP
ejpam-5816	263	8	t	t	NOUN
ejpam-5816	263	9	=	=	SYM
ejpam-5816	263	10	r+s	r+s	PROPN
ejpam-5816	263	11	2	2	NUM
ejpam-5816	263	12	,	,	PUNCT
ejpam-5816	263	13	we	we	PRON
ejpam-5816	263	14	get	get	VERB
ejpam-5816	263	15	the	the	DET
ejpam-5816	263	16	following	follow	VERB
ejpam-5816	263	17	inequality	inequality	NOUN
ejpam-5816	263	18	∣∣∣(s−	∣∣∣(s−	PROPN
ejpam-5816	263	19	r)σ−1	r)σ−1	NOUN
ejpam-5816	263	20	2σ−1	2σ−1	NUM
ejpam-5816	263	21	ℵ	ℵ	NOUN
ejpam-5816	263	22	(	(	PUNCT
ejpam-5816	263	23	r	r	NOUN
ejpam-5816	263	24	+	+	SYM
ejpam-5816	263	25	s	s	NOUN
ejpam-5816	263	26	2	2	NUM
ejpam-5816	263	27	)	)	PUNCT
ejpam-5816	264	1	+	+	NUM
ejpam-5816	264	2	σ(1−	σ(1−	PROPN
ejpam-5816	264	3	κ	κ	PART
ejpam-5816	264	4	)	)	PUNCT
ejpam-5816	264	5	κ(s−	κ(s−	PROPN
ejpam-5816	264	6	r	r	NOUN
ejpam-5816	264	7	)	)	PUNCT
ejpam-5816	265	1	γ(σ	γ(σ	PROPN
ejpam-5816	265	2	)	)	PUNCT
ejpam-5816	266	1	[	[	X
ejpam-5816	266	2	ℵ	ℵ	X
ejpam-5816	266	3	(	(	PUNCT
ejpam-5816	266	4	r	r	NOUN
ejpam-5816	266	5	)	)	PUNCT
ejpam-5816	266	6	+	+	NOUN
ejpam-5816	266	7	ℵ	ℵ	X
ejpam-5816	266	8	(	(	PUNCT
ejpam-5816	266	9	s	s	NOUN
ejpam-5816	266	10	)	)	PUNCT
ejpam-5816	266	11	]	]	PUNCT
ejpam-5816	266	12	−σm(κ)γ(σ	−σm(κ)γ(σ	ADJ
ejpam-5816	266	13	)	)	PUNCT
ejpam-5816	266	14	κ(s−	κ(s−	PROPN
ejpam-5816	266	15	r	r	NOUN
ejpam-5816	266	16	)	)	PUNCT
ejpam-5816	266	17	[	[	PUNCT
ejpam-5816	266	18	iκ	iκ	NOUN
ejpam-5816	266	19	,	,	PUNCT
ejpam-5816	266	20	σ	σ	NOUN
ejpam-5816	266	21	r	r	PROPN
ejpam-5816	266	22	,	,	PUNCT
ejpam-5816	266	23	r+s	r+s	NUM
ejpam-5816	266	24	2	2	NUM
ejpam-5816	266	25	ℵ(r	ℵ(r	NOUN
ejpam-5816	266	26	)	)	PUNCT
ejpam-5816	267	1	+	+	NUM
ejpam-5816	267	2	iκ	iκ	X
ejpam-5816	267	3	,	,	PUNCT
ejpam-5816	267	4	σ	σ	PROPN
ejpam-5816	267	5	s	s	PROPN
ejpam-5816	267	6	,	,	PUNCT
ejpam-5816	267	7	r+s	r+s	NUM
ejpam-5816	267	8	2	2	NUM
ejpam-5816	267	9	ℵ(s	ℵ(s	NOUN
ejpam-5816	267	10	)	)	PUNCT
ejpam-5816	267	11	]	]	PUNCT
ejpam-5816	267	12	∣∣∣	∣∣∣	X
ejpam-5816	267	13	≤	≤	X
ejpam-5816	267	14	(	(	PUNCT
ejpam-5816	267	15	1	1	NUM
ejpam-5816	267	16	p(σp+	p(σp+	NOUN
ejpam-5816	267	17	1	1	NUM
ejpam-5816	267	18	)	)	PUNCT
ejpam-5816	267	19	+	+	CCONJ
ejpam-5816	268	1	kq	kq	PROPN
ejpam-5816	268	2	q	q	PROPN
ejpam-5816	268	3	)	)	PUNCT
ejpam-5816	268	4	{	{	PUNCT
ejpam-5816	268	5	(	(	PUNCT
ejpam-5816	268	6	s−	s−	PROPN
ejpam-5816	268	7	r)σ	r)σ	VERB
ejpam-5816	268	8	2σ	2σ	NUM
ejpam-5816	268	9	}	}	PUNCT
ejpam-5816	268	10	.	.	PUNCT
ejpam-5816	269	1	remark	remark	NOUN
ejpam-5816	269	2	7	7	NUM
ejpam-5816	269	3	.	.	PUNCT
ejpam-5816	269	4	applying	apply	VERB
ejpam-5816	269	5	theorem	theorem	NOUN
ejpam-5816	269	6	3	3	NUM
ejpam-5816	269	7	for	for	ADP
ejpam-5816	269	8	σ	σ	NOUN
ejpam-5816	269	9	=	=	SYM
ejpam-5816	269	10	κ	κ	NOUN
ejpam-5816	269	11	,	,	PUNCT
ejpam-5816	269	12	we	we	PRON
ejpam-5816	269	13	get	get	AUX
ejpam-5816	269	14	theorem	theorem	ADJ
ejpam-5816	269	15	3	3	NUM
ejpam-5816	269	16	proved	prove	VERB
ejpam-5816	269	17	by	by	ADP
ejpam-5816	269	18	ahmad	ahmad	PROPN
ejpam-5816	269	19	et	et	PROPN
ejpam-5816	269	20	al	al	PROPN
ejpam-5816	269	21	.	.	PUNCT
ejpam-5816	270	1	[	[	X
ejpam-5816	270	2	40	40	NUM
ejpam-5816	270	3	]	]	PUNCT
ejpam-5816	270	4	.	.	PUNCT
ejpam-5816	271	1	remark	remark	PROPN
ejpam-5816	271	2	8	8	NUM
ejpam-5816	271	3	.	.	PUNCT
ejpam-5816	272	1	applying	apply	VERB
ejpam-5816	272	2	corollary	corollary	NOUN
ejpam-5816	272	3	6	6	NUM
ejpam-5816	272	4	for	for	ADP
ejpam-5816	272	5	σ	σ	NOUN
ejpam-5816	272	6	=	=	SYM
ejpam-5816	272	7	κ	κ	NOUN
ejpam-5816	272	8	,	,	PUNCT
ejpam-5816	272	9	we	we	PRON
ejpam-5816	272	10	get	get	VERB
ejpam-5816	272	11	corollary	corollary	ADJ
ejpam-5816	272	12	6	6	NUM
ejpam-5816	272	13	proved	prove	VERB
ejpam-5816	272	14	earlier	early	ADV
ejpam-5816	272	15	by	by	ADP
ejpam-5816	272	16	ahmad	ahmad	PROPN
ejpam-5816	272	17	et	et	PROPN
ejpam-5816	272	18	al	al	PROPN
ejpam-5816	272	19	.	.	PUNCT
ejpam-5816	273	1	[	[	X
ejpam-5816	273	2	40	40	NUM
ejpam-5816	273	3	]	]	PUNCT
ejpam-5816	273	4	.	.	PUNCT
ejpam-5816	274	1	theorem	theorem	ADJ
ejpam-5816	274	2	4	4	NUM
ejpam-5816	274	3	.	.	PUNCT
ejpam-5816	275	1	let	let	VERB
ejpam-5816	275	2	ℵ	ℵ	NOUN
ejpam-5816	275	3	:	:	PUNCT
ejpam-5816	275	4	[	[	X
ejpam-5816	275	5	r	r	X
ejpam-5816	275	6	,	,	PUNCT
ejpam-5816	275	7	s	s	PART
ejpam-5816	275	8	]	]	X
ejpam-5816	275	9	→	→	PUNCT
ejpam-5816	275	10	r	r	NOUN
ejpam-5816	275	11	be	be	AUX
ejpam-5816	275	12	a	a	DET
ejpam-5816	275	13	differentiable	differentiable	ADJ
ejpam-5816	275	14	function	function	NOUN
ejpam-5816	275	15	on	on	ADP
ejpam-5816	275	16	(	(	PUNCT
ejpam-5816	275	17	r	r	NOUN
ejpam-5816	275	18	,	,	PUNCT
ejpam-5816	275	19	s	s	PART
ejpam-5816	275	20	)	)	PUNCT
ejpam-5816	275	21	,	,	PUNCT
ejpam-5816	275	22	where	where	SCONJ
ejpam-5816	275	23	ℵ′	ℵ′	ADP
ejpam-5816	275	24	∈	∈	PROPN
ejpam-5816	275	25	l1[r	l1[r	PROPN
ejpam-5816	275	26	,	,	PUNCT
ejpam-5816	275	27	s	s	X
ejpam-5816	275	28	]	]	PUNCT
ejpam-5816	275	29	and	and	CCONJ
ejpam-5816	275	30	r	r	X
ejpam-5816	275	31	<	<	X
ejpam-5816	275	32	s.	s.	PROPN
ejpam-5816	275	33	the	the	DET
ejpam-5816	275	34	following	follow	VERB
ejpam-5816	275	35	inequality	inequality	NOUN
ejpam-5816	275	36	holds	hold	VERB
ejpam-5816	275	37	for	for	ADP
ejpam-5816	275	38	hattaf	hattaf	NOUN
ejpam-5816	275	39	-	-	PUNCT
ejpam-5816	275	40	fractional	fractional	ADJ
ejpam-5816	275	41	integral	integral	ADJ
ejpam-5816	275	42	operators	operator	NOUN
ejpam-5816	275	43	if	if	SCONJ
ejpam-5816	275	44	|ℵ′|q	|ℵ′|q	NUM
ejpam-5816	275	45	is	be	AUX
ejpam-5816	275	46	a	a	DET
ejpam-5816	275	47	convex	convex	NOUN
ejpam-5816	275	48	function	function	NOUN
ejpam-5816	275	49	∣∣∣	∣∣∣	NOUN
ejpam-5816	276	1	[	[	X
ejpam-5816	276	2	(	(	PUNCT
ejpam-5816	276	3	t−	t−	ADJ
ejpam-5816	276	4	r)σ	r)σ	NOUN
ejpam-5816	276	5	+	+	CCONJ
ejpam-5816	276	6	(	(	PUNCT
ejpam-5816	276	7	s−	s−	PROPN
ejpam-5816	276	8	t)σ	t)σ	PUNCT
ejpam-5816	276	9	s−	s−	PROPN
ejpam-5816	276	10	r	r	NOUN
ejpam-5816	276	11	]	]	PUNCT
ejpam-5816	276	12	ℵ	ℵ	X
ejpam-5816	276	13	(	(	PUNCT
ejpam-5816	276	14	t	t	PROPN
ejpam-5816	276	15	)	)	PUNCT
ejpam-5816	276	16	+	+	NUM
ejpam-5816	276	17	σ(1−	σ(1−	PROPN
ejpam-5816	276	18	κ	κ	PART
ejpam-5816	276	19	)	)	PUNCT
ejpam-5816	276	20	κ(s−	κ(s−	PROPN
ejpam-5816	276	21	r	r	NOUN
ejpam-5816	276	22	)	)	PUNCT
ejpam-5816	276	23	γ(σ	γ(σ	PROPN
ejpam-5816	276	24	)	)	PUNCT
ejpam-5816	277	1	[	[	X
ejpam-5816	277	2	ℵ	ℵ	X
ejpam-5816	277	3	(	(	PUNCT
ejpam-5816	277	4	r	r	NOUN
ejpam-5816	277	5	)	)	PUNCT
ejpam-5816	277	6	+	+	NOUN
ejpam-5816	277	7	ℵ	ℵ	X
ejpam-5816	277	8	(	(	PUNCT
ejpam-5816	277	9	s	s	NOUN
ejpam-5816	277	10	)	)	PUNCT
ejpam-5816	277	11	]	]	PUNCT
ejpam-5816	278	1	g.	g.	PROPN
ejpam-5816	278	2	rahman	rahman	PROPN
ejpam-5816	278	3	et	et	PROPN
ejpam-5816	278	4	al	al	PROPN
ejpam-5816	278	5	.	.	PUNCT
ejpam-5816	278	6	/	/	SYM
ejpam-5816	278	7	eur	eur	PROPN
ejpam-5816	278	8	.	.	PUNCT
ejpam-5816	279	1	j.	j.	PROPN
ejpam-5816	279	2	pure	pure	PROPN
ejpam-5816	279	3	appl	appl	PROPN
ejpam-5816	279	4	.	.	PROPN
ejpam-5816	279	5	math	math	PROPN
ejpam-5816	279	6	,	,	PUNCT
ejpam-5816	279	7	18	18	NUM
ejpam-5816	279	8	(	(	PUNCT
ejpam-5816	279	9	2	2	NUM
ejpam-5816	279	10	)	)	PUNCT
ejpam-5816	279	11	(	(	PUNCT
ejpam-5816	279	12	2025	2025	NUM
ejpam-5816	279	13	)	)	PUNCT
ejpam-5816	279	14	,	,	PUNCT
ejpam-5816	279	15	5816	5816	NUM
ejpam-5816	279	16	11	11	NUM
ejpam-5816	279	17	of	of	ADP
ejpam-5816	279	18	18	18	NUM
ejpam-5816	279	19	−σm(κ)γ(σ	−σm(κ)γ(σ	ADJ
ejpam-5816	279	20	)	)	PUNCT
ejpam-5816	279	21	κ(s−	κ(s−	PROPN
ejpam-5816	279	22	r	r	NOUN
ejpam-5816	279	23	)	)	PUNCT
ejpam-5816	279	24	[	[	PUNCT
ejpam-5816	279	25	iκ	iκ	NOUN
ejpam-5816	279	26	,	,	PUNCT
ejpam-5816	279	27	σ	σ	PROPN
ejpam-5816	279	28	r	r	PROPN
ejpam-5816	279	29	,	,	PUNCT
ejpam-5816	279	30	t	t	PROPN
ejpam-5816	279	31	ℵ(r	ℵ(r	PROPN
ejpam-5816	279	32	)	)	PUNCT
ejpam-5816	280	1	+	+	NUM
ejpam-5816	280	2	iκ	iκ	X
ejpam-5816	280	3	,	,	PUNCT
ejpam-5816	280	4	σ	σ	PROPN
ejpam-5816	280	5	s	s	PROPN
ejpam-5816	280	6	,	,	PUNCT
ejpam-5816	280	7	t	t	PROPN
ejpam-5816	280	8	ℵ(s	ℵ(s	PROPN
ejpam-5816	280	9	)	)	PUNCT
ejpam-5816	280	10	]	]	PUNCT
ejpam-5816	280	11	∣∣∣	∣∣∣	NOUN
ejpam-5816	280	12	≤(t−	≤(t−	NOUN
ejpam-5816	281	1	r)σ+1	r)σ+1	PROPN
ejpam-5816	281	2	s−	s−	PROPN
ejpam-5816	281	3	r	r	NOUN
ejpam-5816	281	4	(	(	PUNCT
ejpam-5816	281	5	1	1	NUM
ejpam-5816	281	6	σ	σ	NOUN
ejpam-5816	281	7	+	+	NOUN
ejpam-5816	281	8	1	1	NUM
ejpam-5816	281	9	)	)	PUNCT
ejpam-5816	281	10	1−	1−	NUM
ejpam-5816	281	11	1	1	NUM
ejpam-5816	281	12	q	q	NOUN
ejpam-5816	281	13	[	[	PUNCT
ejpam-5816	281	14	|	|	NOUN
ejpam-5816	281	15	ℵ′(t	ℵ′(t	NOUN
ejpam-5816	281	16	)	)	PUNCT
ejpam-5816	281	17	|q	|q	NOUN
ejpam-5816	281	18	(	(	PUNCT
ejpam-5816	281	19	σ	σ	NOUN
ejpam-5816	281	20	+	+	NOUN
ejpam-5816	281	21	2	2	NUM
ejpam-5816	281	22	)	)	PUNCT
ejpam-5816	281	23	+	+	CCONJ
ejpam-5816	281	24	|	|	ADV
ejpam-5816	281	25	ℵ′(r	ℵ′(r	NUM
ejpam-5816	281	26	)	)	PUNCT
ejpam-5816	281	27	|q	|q	NOUN
ejpam-5816	281	28	(	(	PUNCT
ejpam-5816	281	29	σ	σ	NOUN
ejpam-5816	281	30	+	+	NUM
ejpam-5816	281	31	1)(σ	1)(σ	NUM
ejpam-5816	281	32	+	+	CCONJ
ejpam-5816	281	33	2	2	NUM
ejpam-5816	281	34	)	)	PUNCT
ejpam-5816	281	35	]	]	PUNCT
ejpam-5816	281	36	1	1	NUM
ejpam-5816	281	37	q	q	NOUN
ejpam-5816	281	38	+	+	CCONJ
ejpam-5816	281	39	(	(	PUNCT
ejpam-5816	281	40	s−	s−	PROPN
ejpam-5816	281	41	t)σ+1	t)σ+1	PROPN
ejpam-5816	281	42	s−	s−	PROPN
ejpam-5816	281	43	r	r	NOUN
ejpam-5816	281	44	(	(	PUNCT
ejpam-5816	281	45	1	1	NUM
ejpam-5816	281	46	σ	σ	NOUN
ejpam-5816	281	47	+	+	NOUN
ejpam-5816	281	48	1	1	NUM
ejpam-5816	281	49	)	)	PUNCT
ejpam-5816	281	50	1−	1−	NUM
ejpam-5816	281	51	1	1	NUM
ejpam-5816	281	52	q	q	NOUN
ejpam-5816	281	53	[	[	PUNCT
ejpam-5816	281	54	|	|	NOUN
ejpam-5816	281	55	ℵ′(s	ℵ′(s	NUM
ejpam-5816	281	56	)	)	PUNCT
ejpam-5816	281	57	|q	|q	NOUN
ejpam-5816	281	58	(	(	PUNCT
ejpam-5816	281	59	σ	σ	NOUN
ejpam-5816	281	60	+	+	NUM
ejpam-5816	281	61	1)(σ	1)(σ	NUM
ejpam-5816	281	62	+	+	CCONJ
ejpam-5816	281	63	2	2	NUM
ejpam-5816	281	64	)	)	PUNCT
ejpam-5816	281	65	+	+	CCONJ
ejpam-5816	281	66	|	|	ADV
ejpam-5816	281	67	ℵ′(t	ℵ′(t	PROPN
ejpam-5816	281	68	)	)	PUNCT
ejpam-5816	281	69	|q	|q	NOUN
ejpam-5816	281	70	(	(	PUNCT
ejpam-5816	281	71	σ	σ	NOUN
ejpam-5816	281	72	+	+	PROPN
ejpam-5816	281	73	2	2	NUM
ejpam-5816	281	74	)	)	PUNCT
ejpam-5816	281	75	]	]	PUNCT
ejpam-5816	281	76	1	1	NUM
ejpam-5816	281	77	q	q	NOUN
ejpam-5816	281	78	,	,	PUNCT
ejpam-5816	281	79	where	where	SCONJ
ejpam-5816	281	80	q	q	PROPN
ejpam-5816	281	81	≥	≥	NUM
ejpam-5816	281	82	1	1	NUM
ejpam-5816	281	83	,	,	PUNCT
ejpam-5816	281	84	t	t	PROPN
ejpam-5816	281	85	∈	∈	PROPN
ejpam-5816	282	1	[	[	X
ejpam-5816	282	2	r	r	X
ejpam-5816	282	3	,	,	PUNCT
ejpam-5816	282	4	s	s	PART
ejpam-5816	282	5	]	]	X
ejpam-5816	282	6	,	,	PUNCT
ejpam-5816	282	7	κ	κ	PROPN
ejpam-5816	282	8	∈	∈	PROPN
ejpam-5816	282	9	(	(	PUNCT
ejpam-5816	282	10	0	0	NUM
ejpam-5816	282	11	,	,	PUNCT
ejpam-5816	282	12	1	1	NUM
ejpam-5816	282	13	]	]	PUNCT
ejpam-5816	282	14	and	and	CCONJ
ejpam-5816	282	15	m(κ	m(κ	NUM
ejpam-5816	282	16	)	)	PUNCT
ejpam-5816	282	17	>	>	X
ejpam-5816	282	18	0	0	X
ejpam-5816	282	19	.	.	PUNCT
ejpam-5816	282	20	proof	proof	NOUN
ejpam-5816	282	21	.	.	PUNCT
ejpam-5816	283	1	by	by	ADP
ejpam-5816	283	2	utilizing	utilize	VERB
ejpam-5816	283	3	lemma	lemma	PROPN
ejpam-5816	283	4	1	1	NUM
ejpam-5816	283	5	,	,	PUNCT
ejpam-5816	283	6	we	we	PRON
ejpam-5816	283	7	have∣∣∣	have∣∣∣	PUNCT
ejpam-5816	284	1	[	[	X
ejpam-5816	284	2	(	(	PUNCT
ejpam-5816	284	3	t−	t−	ADJ
ejpam-5816	284	4	r)σ	r)σ	NOUN
ejpam-5816	284	5	+	+	CCONJ
ejpam-5816	284	6	(	(	PUNCT
ejpam-5816	284	7	s−	s−	PROPN
ejpam-5816	284	8	t)σ	t)σ	PUNCT
ejpam-5816	284	9	s−	s−	PROPN
ejpam-5816	284	10	r	r	NOUN
ejpam-5816	284	11	]	]	PUNCT
ejpam-5816	284	12	ℵ	ℵ	X
ejpam-5816	284	13	(	(	PUNCT
ejpam-5816	284	14	t	t	PROPN
ejpam-5816	284	15	)	)	PUNCT
ejpam-5816	284	16	+	+	NUM
ejpam-5816	284	17	σ(1−	σ(1−	PROPN
ejpam-5816	284	18	κ	κ	PART
ejpam-5816	284	19	)	)	PUNCT
ejpam-5816	284	20	κ(s−	κ(s−	PROPN
ejpam-5816	284	21	r	r	NOUN
ejpam-5816	284	22	)	)	PUNCT
ejpam-5816	284	23	γ(σ	γ(σ	PROPN
ejpam-5816	284	24	)	)	PUNCT
ejpam-5816	285	1	[	[	X
ejpam-5816	285	2	ℵ	ℵ	X
ejpam-5816	285	3	(	(	PUNCT
ejpam-5816	285	4	r	r	NOUN
ejpam-5816	285	5	)	)	PUNCT
ejpam-5816	285	6	+	+	NOUN
ejpam-5816	285	7	ℵ	ℵ	X
ejpam-5816	285	8	(	(	PUNCT
ejpam-5816	285	9	s	s	NOUN
ejpam-5816	285	10	)	)	PUNCT
ejpam-5816	285	11	]	]	PUNCT
ejpam-5816	286	1	−σm(κ)γ(σ	−σm(κ)γ(σ	ADJ
ejpam-5816	286	2	)	)	PUNCT
ejpam-5816	286	3	κ(s−	κ(s−	PROPN
ejpam-5816	286	4	r	r	NOUN
ejpam-5816	286	5	)	)	PUNCT
ejpam-5816	286	6	[	[	PUNCT
ejpam-5816	286	7	iκ	iκ	NOUN
ejpam-5816	286	8	,	,	PUNCT
ejpam-5816	286	9	σ	σ	PROPN
ejpam-5816	286	10	r	r	PROPN
ejpam-5816	286	11	,	,	PUNCT
ejpam-5816	286	12	t	t	PROPN
ejpam-5816	286	13	ℵ(r	ℵ(r	PROPN
ejpam-5816	286	14	)	)	PUNCT
ejpam-5816	287	1	+	+	NUM
ejpam-5816	287	2	iκ	iκ	X
ejpam-5816	287	3	,	,	PUNCT
ejpam-5816	287	4	σ	σ	PROPN
ejpam-5816	287	5	s	s	PROPN
ejpam-5816	287	6	,	,	PUNCT
ejpam-5816	287	7	t	t	PROPN
ejpam-5816	287	8	ℵ(s	ℵ(s	PROPN
ejpam-5816	287	9	)	)	PUNCT
ejpam-5816	287	10	]	]	PUNCT
ejpam-5816	287	11	∣∣∣	∣∣∣	NOUN
ejpam-5816	287	12	≤(t−	≤(t−	NOUN
ejpam-5816	288	1	r)σ+1	r)σ+1	PROPN
ejpam-5816	288	2	s−	s−	PROPN
ejpam-5816	288	3	r	r	NOUN
ejpam-5816	288	4	∫	∫	PROPN
ejpam-5816	288	5	1	1	NUM
ejpam-5816	288	6	0	0	NUM
ejpam-5816	288	7	ρσ	ρσ	ADP
ejpam-5816	288	8	|	|	ADV
ejpam-5816	288	9	ℵ′(ρt+	ℵ′(ρt+	NOUN
ejpam-5816	288	10	(	(	PUNCT
ejpam-5816	288	11	1−	1−	NUM
ejpam-5816	288	12	ρ)r	ρ)r	X
ejpam-5816	288	13	)	)	PUNCT
ejpam-5816	289	1	|	|	ADV
ejpam-5816	289	2	dρ	dρ	INTJ
ejpam-5816	290	1	+	+	CCONJ
ejpam-5816	290	2	(	(	PUNCT
ejpam-5816	290	3	s−	s−	PROPN
ejpam-5816	290	4	t)σ+1	t)σ+1	PROPN
ejpam-5816	290	5	s−	s−	PROPN
ejpam-5816	290	6	r	r	NOUN
ejpam-5816	290	7	∫	∫	PROPN
ejpam-5816	290	8	1	1	NUM
ejpam-5816	290	9	0	0	NUM
ejpam-5816	290	10	ρσ	ρσ	ADP
ejpam-5816	290	11	|	|	ADV
ejpam-5816	290	12	ℵ′(ρt+	ℵ′(ρt+	NOUN
ejpam-5816	290	13	(	(	PUNCT
ejpam-5816	290	14	1−	1−	NUM
ejpam-5816	290	15	ρ)s	ρ)s	NOUN
ejpam-5816	290	16	)	)	PUNCT
ejpam-5816	291	1	|	|	ADV
ejpam-5816	291	2	dρ	dρ	INTJ
ejpam-5816	291	3	.	.	PUNCT
ejpam-5816	292	1	by	by	ADP
ejpam-5816	292	2	employing	employ	VERB
ejpam-5816	292	3	power	power	NOUN
ejpam-5816	292	4	mean	mean	NOUN
ejpam-5816	292	5	inequality	inequality	NOUN
ejpam-5816	292	6	,	,	PUNCT
ejpam-5816	292	7	we	we	PRON
ejpam-5816	292	8	obtain∣∣∣	obtain∣∣∣	VERB
ejpam-5816	293	1	[	[	X
ejpam-5816	293	2	(	(	PUNCT
ejpam-5816	293	3	t−	t−	ADJ
ejpam-5816	293	4	r)σ	r)σ	NOUN
ejpam-5816	293	5	+	+	CCONJ
ejpam-5816	293	6	(	(	PUNCT
ejpam-5816	293	7	s−	s−	PROPN
ejpam-5816	293	8	t)σ	t)σ	PUNCT
ejpam-5816	293	9	s−	s−	PROPN
ejpam-5816	293	10	r	r	NOUN
ejpam-5816	293	11	]	]	PUNCT
ejpam-5816	293	12	ℵ	ℵ	X
ejpam-5816	293	13	(	(	PUNCT
ejpam-5816	293	14	t	t	PROPN
ejpam-5816	293	15	)	)	PUNCT
ejpam-5816	293	16	+	+	NUM
ejpam-5816	293	17	σ(1−	σ(1−	PROPN
ejpam-5816	293	18	κ	κ	PART
ejpam-5816	293	19	)	)	PUNCT
ejpam-5816	293	20	κ(s−	κ(s−	PROPN
ejpam-5816	293	21	r	r	NOUN
ejpam-5816	293	22	)	)	PUNCT
ejpam-5816	293	23	γ(σ	γ(σ	PROPN
ejpam-5816	293	24	)	)	PUNCT
ejpam-5816	294	1	[	[	X
ejpam-5816	294	2	ℵ	ℵ	X
ejpam-5816	294	3	(	(	PUNCT
ejpam-5816	294	4	r	r	NOUN
ejpam-5816	294	5	)	)	PUNCT
ejpam-5816	294	6	+	+	NOUN
ejpam-5816	294	7	ℵ	ℵ	X
ejpam-5816	294	8	(	(	PUNCT
ejpam-5816	294	9	s	s	NOUN
ejpam-5816	294	10	)	)	PUNCT
ejpam-5816	294	11	]	]	PUNCT
ejpam-5816	295	1	−σm(κ)γ(σ	−σm(κ)γ(σ	ADJ
ejpam-5816	295	2	)	)	PUNCT
ejpam-5816	295	3	κ(s−	κ(s−	PROPN
ejpam-5816	295	4	r	r	NOUN
ejpam-5816	295	5	)	)	PUNCT
ejpam-5816	295	6	[	[	PUNCT
ejpam-5816	295	7	iκ	iκ	NOUN
ejpam-5816	295	8	,	,	PUNCT
ejpam-5816	295	9	σ	σ	PROPN
ejpam-5816	295	10	r	r	PROPN
ejpam-5816	295	11	,	,	PUNCT
ejpam-5816	295	12	t	t	PROPN
ejpam-5816	295	13	ℵ(r	ℵ(r	PROPN
ejpam-5816	295	14	)	)	PUNCT
ejpam-5816	296	1	+	+	NUM
ejpam-5816	296	2	iκ	iκ	X
ejpam-5816	296	3	,	,	PUNCT
ejpam-5816	296	4	σ	σ	PROPN
ejpam-5816	296	5	s	s	PROPN
ejpam-5816	296	6	,	,	PUNCT
ejpam-5816	296	7	t	t	PROPN
ejpam-5816	296	8	ℵ(s	ℵ(s	PROPN
ejpam-5816	296	9	)	)	PUNCT
ejpam-5816	296	10	]	]	PUNCT
ejpam-5816	296	11	∣∣∣	∣∣∣	NOUN
ejpam-5816	296	12	≤(t−	≤(t−	NOUN
ejpam-5816	297	1	r)σ+1	r)σ+1	PROPN
ejpam-5816	297	2	s−	s−	PROPN
ejpam-5816	297	3	r	r	PROPN
ejpam-5816	297	4	(	(	PUNCT
ejpam-5816	297	5	∫	∫	PROPN
ejpam-5816	297	6	1	1	NUM
ejpam-5816	297	7	0	0	NUM
ejpam-5816	297	8	ρσdρ	ρσdρ	NOUN
ejpam-5816	297	9	)	)	PUNCT
ejpam-5816	297	10	1−	1−	NUM
ejpam-5816	297	11	1	1	NUM
ejpam-5816	297	12	q	q	NOUN
ejpam-5816	297	13	(	(	PUNCT
ejpam-5816	297	14	∫	∫	PROPN
ejpam-5816	297	15	1	1	NUM
ejpam-5816	297	16	0	0	NUM
ejpam-5816	297	17	ρσ	ρσ	ADP
ejpam-5816	297	18	|	|	ADV
ejpam-5816	297	19	ℵ′(ρt+	ℵ′(ρt+	NOUN
ejpam-5816	297	20	(	(	PUNCT
ejpam-5816	297	21	1−	1−	NUM
ejpam-5816	297	22	ρ)r	ρ)r	X
ejpam-5816	297	23	)	)	PUNCT
ejpam-5816	297	24	|q	|q	NOUN
ejpam-5816	297	25	dρ	dρ	NOUN
ejpam-5816	297	26	)	)	PUNCT
ejpam-5816	297	27	1	1	NUM
ejpam-5816	297	28	q	q	NOUN
ejpam-5816	297	29	+	+	CCONJ
ejpam-5816	297	30	(	(	PUNCT
ejpam-5816	297	31	s−	s−	PROPN
ejpam-5816	297	32	t)σ+1	t)σ+1	PROPN
ejpam-5816	297	33	s−	s−	PROPN
ejpam-5816	297	34	r	r	PROPN
ejpam-5816	297	35	(	(	PUNCT
ejpam-5816	297	36	∫	∫	PROPN
ejpam-5816	297	37	1	1	NUM
ejpam-5816	297	38	0	0	NUM
ejpam-5816	297	39	ρσdρ	ρσdρ	NOUN
ejpam-5816	297	40	)	)	PUNCT
ejpam-5816	297	41	1−	1−	NUM
ejpam-5816	297	42	1	1	NUM
ejpam-5816	297	43	q	q	NOUN
ejpam-5816	297	44	(	(	PUNCT
ejpam-5816	297	45	∫	∫	PROPN
ejpam-5816	297	46	1	1	NUM
ejpam-5816	297	47	0	0	NUM
ejpam-5816	297	48	ρσ	ρσ	ADP
ejpam-5816	297	49	|	|	ADV
ejpam-5816	297	50	ℵ′(ρt+	ℵ′(ρt+	NOUN
ejpam-5816	297	51	(	(	PUNCT
ejpam-5816	297	52	1−	1−	NUM
ejpam-5816	297	53	ρ)s	ρ)s	NOUN
ejpam-5816	297	54	)	)	PUNCT
ejpam-5816	297	55	|q	|q	NOUN
ejpam-5816	297	56	dρ	dρ	NOUN
ejpam-5816	297	57	)	)	PUNCT
ejpam-5816	297	58	1	1	NUM
ejpam-5816	297	59	q	q	NOUN
ejpam-5816	297	60	.	.	PUNCT
ejpam-5816	298	1	now	now	ADV
ejpam-5816	298	2	,	,	PUNCT
ejpam-5816	298	3	by	by	ADP
ejpam-5816	298	4	utilizing	utilize	VERB
ejpam-5816	298	5	the	the	DET
ejpam-5816	298	6	convexity	convexity	NOUN
ejpam-5816	298	7	of	of	ADP
ejpam-5816	298	8	|	|	ADV
ejpam-5816	298	9	ℵ′	ℵ′	ADV
ejpam-5816	298	10	|q	|q	NOUN
ejpam-5816	298	11	,	,	PUNCT
ejpam-5816	298	12	we	we	PRON
ejpam-5816	298	13	get∣∣∣	get∣∣∣	VERB
ejpam-5816	298	14	[	[	X
ejpam-5816	298	15	(	(	PUNCT
ejpam-5816	298	16	t−	t−	ADJ
ejpam-5816	298	17	r)σ	r)σ	NOUN
ejpam-5816	298	18	+	+	CCONJ
ejpam-5816	298	19	(	(	PUNCT
ejpam-5816	298	20	s−	s−	PROPN
ejpam-5816	298	21	t)σ	t)σ	PUNCT
ejpam-5816	298	22	s−	s−	PROPN
ejpam-5816	298	23	r	r	NOUN
ejpam-5816	298	24	]	]	PUNCT
ejpam-5816	298	25	ℵ	ℵ	X
ejpam-5816	298	26	(	(	PUNCT
ejpam-5816	298	27	t	t	PROPN
ejpam-5816	298	28	)	)	PUNCT
ejpam-5816	298	29	+	+	NUM
ejpam-5816	298	30	σ(1−	σ(1−	PROPN
ejpam-5816	298	31	κ	κ	PART
ejpam-5816	298	32	)	)	PUNCT
ejpam-5816	298	33	κ(s−	κ(s−	PROPN
ejpam-5816	298	34	r	r	NOUN
ejpam-5816	298	35	)	)	PUNCT
ejpam-5816	298	36	γ(σ	γ(σ	PROPN
ejpam-5816	298	37	)	)	PUNCT
ejpam-5816	299	1	[	[	X
ejpam-5816	299	2	ℵ	ℵ	X
ejpam-5816	299	3	(	(	PUNCT
ejpam-5816	299	4	r	r	NOUN
ejpam-5816	299	5	)	)	PUNCT
ejpam-5816	299	6	+	+	NOUN
ejpam-5816	299	7	ℵ	ℵ	X
ejpam-5816	299	8	(	(	PUNCT
ejpam-5816	299	9	s	s	NOUN
ejpam-5816	299	10	)	)	PUNCT
ejpam-5816	299	11	]	]	PUNCT
ejpam-5816	300	1	−σm(κ)γ(σ	−σm(κ)γ(σ	ADJ
ejpam-5816	300	2	)	)	PUNCT
ejpam-5816	300	3	κ(s−	κ(s−	PROPN
ejpam-5816	300	4	r	r	NOUN
ejpam-5816	300	5	)	)	PUNCT
ejpam-5816	300	6	[	[	PUNCT
ejpam-5816	300	7	iκ	iκ	NOUN
ejpam-5816	300	8	,	,	PUNCT
ejpam-5816	300	9	σ	σ	PROPN
ejpam-5816	300	10	r	r	PROPN
ejpam-5816	300	11	,	,	PUNCT
ejpam-5816	300	12	t	t	PROPN
ejpam-5816	300	13	ℵ(r	ℵ(r	PROPN
ejpam-5816	300	14	)	)	PUNCT
ejpam-5816	301	1	+	+	NUM
ejpam-5816	301	2	iκ	iκ	X
ejpam-5816	301	3	,	,	PUNCT
ejpam-5816	301	4	σ	σ	PROPN
ejpam-5816	301	5	s	s	PROPN
ejpam-5816	301	6	,	,	PUNCT
ejpam-5816	301	7	t	t	PROPN
ejpam-5816	301	8	ℵ(s	ℵ(s	PROPN
ejpam-5816	301	9	)	)	PUNCT
ejpam-5816	301	10	]	]	PUNCT
ejpam-5816	301	11	∣∣∣	∣∣∣	NOUN
ejpam-5816	301	12	≤(t−	≤(t−	NOUN
ejpam-5816	302	1	r)σ+1	r)σ+1	PROPN
ejpam-5816	302	2	s−	s−	PROPN
ejpam-5816	302	3	r	r	PROPN
ejpam-5816	302	4	(	(	PUNCT
ejpam-5816	302	5	∫	∫	PROPN
ejpam-5816	302	6	1	1	NUM
ejpam-5816	302	7	0	0	NUM
ejpam-5816	302	8	ρσdρ	ρσdρ	NOUN
ejpam-5816	302	9	)	)	PUNCT
ejpam-5816	302	10	1−	1−	NUM
ejpam-5816	302	11	1	1	NUM
ejpam-5816	302	12	q	q	NOUN
ejpam-5816	302	13	(	(	PUNCT
ejpam-5816	302	14	∫	∫	PROPN
ejpam-5816	302	15	1	1	NUM
ejpam-5816	302	16	0	0	NUM
ejpam-5816	302	17	ρσ[ρ	ρσ[ρ	PROPN
ejpam-5816	302	18	|	|	CCONJ
ejpam-5816	302	19	ℵ′(t	ℵ′(t	PROPN
ejpam-5816	302	20	)	)	PUNCT
ejpam-5816	302	21	|q	|q	NOUN
ejpam-5816	303	1	+	+	PROPN
ejpam-5816	303	2	(	(	PUNCT
ejpam-5816	303	3	1−	1−	NUM
ejpam-5816	303	4	ρ	ρ	NOUN
ejpam-5816	303	5	)	)	PUNCT
ejpam-5816	303	6	|	|	ADV
ejpam-5816	303	7	ℵ′(r	ℵ′(r	CCONJ
ejpam-5816	303	8	)	)	PUNCT
ejpam-5816	303	9	|q]dρ	|q]dρ	X
ejpam-5816	303	10	)	)	PUNCT
ejpam-5816	303	11	1	1	NUM
ejpam-5816	303	12	q	q	NOUN
ejpam-5816	303	13	+	+	CCONJ
ejpam-5816	303	14	(	(	PUNCT
ejpam-5816	303	15	s−	s−	PROPN
ejpam-5816	303	16	t)σ+1	t)σ+1	PROPN
ejpam-5816	303	17	s−	s−	PROPN
ejpam-5816	303	18	r	r	PROPN
ejpam-5816	303	19	(	(	PUNCT
ejpam-5816	303	20	∫	∫	PROPN
ejpam-5816	303	21	1	1	NUM
ejpam-5816	303	22	0	0	NUM
ejpam-5816	303	23	ρσdρ	ρσdρ	NOUN
ejpam-5816	303	24	)	)	PUNCT
ejpam-5816	303	25	1−	1−	NUM
ejpam-5816	303	26	1	1	NUM
ejpam-5816	303	27	q	q	NOUN
ejpam-5816	303	28	(	(	PUNCT
ejpam-5816	303	29	∫	∫	PROPN
ejpam-5816	303	30	1	1	NUM
ejpam-5816	303	31	0	0	NUM
ejpam-5816	303	32	ρσ[ρ	ρσ[ρ	PROPN
ejpam-5816	303	33	|	|	CCONJ
ejpam-5816	303	34	ℵ′(t	ℵ′(t	PROPN
ejpam-5816	303	35	)	)	PUNCT
ejpam-5816	303	36	|q	|q	NOUN
ejpam-5816	304	1	+	+	PROPN
ejpam-5816	304	2	(	(	PUNCT
ejpam-5816	304	3	1−	1−	NUM
ejpam-5816	304	4	ρ	ρ	NOUN
ejpam-5816	304	5	)	)	PUNCT
ejpam-5816	304	6	|	|	ADV
ejpam-5816	304	7	ℵ′(s	ℵ′(s	PUNCT
ejpam-5816	304	8	)	)	PUNCT
ejpam-5816	304	9	|q]dρ	|q]dρ	X
ejpam-5816	304	10	)	)	PUNCT
ejpam-5816	304	11	1	1	NUM
ejpam-5816	304	12	q	q	PROPN
ejpam-5816	304	13	g.	g.	PROPN
ejpam-5816	304	14	rahman	rahman	PROPN
ejpam-5816	304	15	et	et	PROPN
ejpam-5816	304	16	al	al	PROPN
ejpam-5816	304	17	.	.	PUNCT
ejpam-5816	304	18	/	/	SYM
ejpam-5816	304	19	eur	eur	PROPN
ejpam-5816	304	20	.	.	PUNCT
ejpam-5816	305	1	j.	j.	PROPN
ejpam-5816	305	2	pure	pure	PROPN
ejpam-5816	305	3	appl	appl	PROPN
ejpam-5816	305	4	.	.	PROPN
ejpam-5816	305	5	math	math	PROPN
ejpam-5816	305	6	,	,	PUNCT
ejpam-5816	305	7	18	18	NUM
ejpam-5816	305	8	(	(	PUNCT
ejpam-5816	305	9	2	2	NUM
ejpam-5816	305	10	)	)	PUNCT
ejpam-5816	305	11	(	(	PUNCT
ejpam-5816	305	12	2025	2025	NUM
ejpam-5816	305	13	)	)	PUNCT
ejpam-5816	305	14	,	,	PUNCT
ejpam-5816	305	15	5816	5816	NUM
ejpam-5816	305	16	12	12	NUM
ejpam-5816	305	17	of	of	ADP
ejpam-5816	305	18	18	18	NUM
ejpam-5816	305	19	≤(t−	≤(t−	NOUN
ejpam-5816	305	20	r)σ+1	r)σ+1	PROPN
ejpam-5816	305	21	s−	s−	PROPN
ejpam-5816	305	22	r	r	NOUN
ejpam-5816	305	23	(	(	PUNCT
ejpam-5816	305	24	1	1	NUM
ejpam-5816	305	25	σ	σ	NOUN
ejpam-5816	305	26	+	+	NOUN
ejpam-5816	305	27	1	1	NUM
ejpam-5816	305	28	)	)	PUNCT
ejpam-5816	305	29	1−	1−	NUM
ejpam-5816	306	1	1	1	NUM
ejpam-5816	306	2	q	q	NOUN
ejpam-5816	307	1	[	[	PUNCT
ejpam-5816	307	2	|	|	NOUN
ejpam-5816	307	3	ℵ′(t	ℵ′(t	NOUN
ejpam-5816	307	4	)	)	PUNCT
ejpam-5816	307	5	|q	|q	NOUN
ejpam-5816	307	6	(	(	PUNCT
ejpam-5816	307	7	σ	σ	NOUN
ejpam-5816	307	8	+	+	NOUN
ejpam-5816	307	9	2	2	NUM
ejpam-5816	307	10	)	)	PUNCT
ejpam-5816	307	11	+	+	CCONJ
ejpam-5816	307	12	|	|	ADV
ejpam-5816	307	13	ℵ′(r	ℵ′(r	NUM
ejpam-5816	307	14	)	)	PUNCT
ejpam-5816	307	15	|q	|q	NOUN
ejpam-5816	307	16	(	(	PUNCT
ejpam-5816	307	17	σ	σ	NOUN
ejpam-5816	307	18	+	+	NUM
ejpam-5816	307	19	1)(σ	1)(σ	NUM
ejpam-5816	307	20	+	+	CCONJ
ejpam-5816	307	21	2	2	NUM
ejpam-5816	307	22	)	)	PUNCT
ejpam-5816	307	23	]	]	PUNCT
ejpam-5816	307	24	1	1	NUM
ejpam-5816	307	25	q	q	NOUN
ejpam-5816	307	26	+	+	CCONJ
ejpam-5816	307	27	(	(	PUNCT
ejpam-5816	307	28	s−	s−	PROPN
ejpam-5816	307	29	t)σ+1	t)σ+1	PROPN
ejpam-5816	307	30	s−	s−	PROPN
ejpam-5816	307	31	r	r	NOUN
ejpam-5816	307	32	(	(	PUNCT
ejpam-5816	307	33	1	1	NUM
ejpam-5816	307	34	σ	σ	NOUN
ejpam-5816	307	35	+	+	NOUN
ejpam-5816	307	36	1	1	NUM
ejpam-5816	307	37	)	)	PUNCT
ejpam-5816	307	38	1−	1−	NUM
ejpam-5816	307	39	1	1	NUM
ejpam-5816	307	40	q	q	NOUN
ejpam-5816	307	41	[	[	PUNCT
ejpam-5816	307	42	|	|	NOUN
ejpam-5816	307	43	ℵ′(t	ℵ′(t	NOUN
ejpam-5816	307	44	)	)	PUNCT
ejpam-5816	307	45	|q	|q	NOUN
ejpam-5816	307	46	(	(	PUNCT
ejpam-5816	307	47	σ	σ	NOUN
ejpam-5816	307	48	+	+	NOUN
ejpam-5816	307	49	2	2	NUM
ejpam-5816	307	50	)	)	PUNCT
ejpam-5816	307	51	+	+	CCONJ
ejpam-5816	307	52	|	|	ADV
ejpam-5816	307	53	ℵ′(s	ℵ′(s	PRON
ejpam-5816	307	54	)	)	PUNCT
ejpam-5816	307	55	|q	|q	NOUN
ejpam-5816	307	56	(	(	PUNCT
ejpam-5816	307	57	σ	σ	NOUN
ejpam-5816	307	58	+	+	NUM
ejpam-5816	307	59	1)(σ	1)(σ	NUM
ejpam-5816	307	60	+	+	CCONJ
ejpam-5816	307	61	2	2	NUM
ejpam-5816	307	62	)	)	PUNCT
ejpam-5816	307	63	]	]	PUNCT
ejpam-5816	307	64	1	1	NUM
ejpam-5816	307	65	q	q	NOUN
ejpam-5816	307	66	,	,	PUNCT
ejpam-5816	307	67	which	which	PRON
ejpam-5816	307	68	complete	complete	VERB
ejpam-5816	307	69	the	the	DET
ejpam-5816	307	70	proof	proof	NOUN
ejpam-5816	307	71	.	.	PUNCT
ejpam-5816	308	1	corollary	corollary	ADJ
ejpam-5816	308	2	7	7	NUM
ejpam-5816	308	3	.	.	PUNCT
ejpam-5816	308	4	applying	apply	VERB
ejpam-5816	308	5	theorem	theorem	NOUN
ejpam-5816	308	6	4	4	NUM
ejpam-5816	308	7	for	for	ADP
ejpam-5816	308	8	|ℵ′|	|ℵ′|	PROPN
ejpam-5816	308	9	≤	≤	PUNCT
ejpam-5816	309	1	k	k	NOUN
ejpam-5816	309	2	where	where	SCONJ
ejpam-5816	309	3	k	k	PROPN
ejpam-5816	309	4	>	>	X
ejpam-5816	309	5	0	0	PUNCT
ejpam-5816	309	6	,	,	PUNCT
ejpam-5816	309	7	we	we	PRON
ejpam-5816	309	8	get	get	VERB
ejpam-5816	309	9	the	the	DET
ejpam-5816	309	10	following	follow	VERB
ejpam-5816	309	11	inequality	inequality	NOUN
ejpam-5816	309	12	∣∣∣	∣∣∣	NOUN
ejpam-5816	310	1	[	[	X
ejpam-5816	310	2	(	(	PUNCT
ejpam-5816	310	3	t−	t−	ADJ
ejpam-5816	310	4	r)σ	r)σ	NOUN
ejpam-5816	310	5	+	+	CCONJ
ejpam-5816	310	6	(	(	PUNCT
ejpam-5816	310	7	s−	s−	PROPN
ejpam-5816	310	8	t)σ	t)σ	PUNCT
ejpam-5816	310	9	s−	s−	PROPN
ejpam-5816	310	10	r	r	NOUN
ejpam-5816	310	11	]	]	PUNCT
ejpam-5816	310	12	ℵ	ℵ	X
ejpam-5816	310	13	(	(	PUNCT
ejpam-5816	310	14	t	t	PROPN
ejpam-5816	310	15	)	)	PUNCT
ejpam-5816	310	16	+	+	NUM
ejpam-5816	310	17	σ(1−	σ(1−	PROPN
ejpam-5816	310	18	κ	κ	PART
ejpam-5816	310	19	)	)	PUNCT
ejpam-5816	310	20	κ(s−	κ(s−	PROPN
ejpam-5816	310	21	r	r	NOUN
ejpam-5816	310	22	)	)	PUNCT
ejpam-5816	310	23	γ(σ	γ(σ	PROPN
ejpam-5816	310	24	)	)	PUNCT
ejpam-5816	311	1	[	[	X
ejpam-5816	311	2	ℵ	ℵ	X
ejpam-5816	311	3	(	(	PUNCT
ejpam-5816	311	4	r	r	NOUN
ejpam-5816	311	5	)	)	PUNCT
ejpam-5816	311	6	+	+	NOUN
ejpam-5816	311	7	ℵ	ℵ	X
ejpam-5816	311	8	(	(	PUNCT
ejpam-5816	311	9	s	s	NOUN
ejpam-5816	311	10	)	)	PUNCT
ejpam-5816	311	11	]	]	PUNCT
ejpam-5816	312	1	−σm(κ)γ(σ	−σm(κ)γ(σ	ADJ
ejpam-5816	312	2	)	)	PUNCT
ejpam-5816	312	3	κ(s−	κ(s−	PROPN
ejpam-5816	312	4	r	r	NOUN
ejpam-5816	312	5	)	)	PUNCT
ejpam-5816	312	6	[	[	PUNCT
ejpam-5816	312	7	iκ	iκ	NOUN
ejpam-5816	312	8	,	,	PUNCT
ejpam-5816	312	9	σ	σ	PROPN
ejpam-5816	312	10	r	r	PROPN
ejpam-5816	312	11	,	,	PUNCT
ejpam-5816	312	12	t	t	PROPN
ejpam-5816	312	13	ℵ(r	ℵ(r	PROPN
ejpam-5816	312	14	)	)	PUNCT
ejpam-5816	313	1	+	+	NUM
ejpam-5816	313	2	iκ	iκ	X
ejpam-5816	313	3	,	,	PUNCT
ejpam-5816	313	4	σ	σ	PROPN
ejpam-5816	313	5	s	s	PROPN
ejpam-5816	313	6	,	,	PUNCT
ejpam-5816	313	7	t	t	PROPN
ejpam-5816	313	8	ℵ(s	ℵ(s	PROPN
ejpam-5816	313	9	)	)	PUNCT
ejpam-5816	313	10	]	]	PUNCT
ejpam-5816	313	11	∣∣∣	∣∣∣	X
ejpam-5816	313	12	≤	≤	X
ejpam-5816	313	13	k	k	NOUN
ejpam-5816	313	14	s−	s−	PROPN
ejpam-5816	313	15	r	r	NOUN
ejpam-5816	313	16	(	(	PUNCT
ejpam-5816	313	17	1	1	NUM
ejpam-5816	313	18	σ	σ	NOUN
ejpam-5816	313	19	+	+	NOUN
ejpam-5816	313	20	1	1	NUM
ejpam-5816	313	21	)	)	PUNCT
ejpam-5816	313	22	{	{	PUNCT
ejpam-5816	313	23	(	(	PUNCT
ejpam-5816	313	24	t−	t−	X
ejpam-5816	313	25	r)σ+1	r)σ+1	PROPN
ejpam-5816	313	26	+	+	CCONJ
ejpam-5816	313	27	(	(	PUNCT
ejpam-5816	313	28	s−	s−	PROPN
ejpam-5816	313	29	t)σ+1	t)σ+1	PROPN
ejpam-5816	313	30	}	}	PUNCT
ejpam-5816	313	31	.	.	PUNCT
ejpam-5816	314	1	corollary	corollary	ADJ
ejpam-5816	314	2	8	8	NUM
ejpam-5816	314	3	.	.	PUNCT
ejpam-5816	315	1	applying	apply	VERB
ejpam-5816	315	2	corollary	corollary	NOUN
ejpam-5816	315	3	7	7	NUM
ejpam-5816	315	4	for	for	ADP
ejpam-5816	315	5	t	t	NOUN
ejpam-5816	315	6	=	=	SYM
ejpam-5816	315	7	r+s	r+s	PROPN
ejpam-5816	315	8	2	2	NUM
ejpam-5816	315	9	,	,	PUNCT
ejpam-5816	315	10	we	we	PRON
ejpam-5816	315	11	get	get	VERB
ejpam-5816	315	12	the	the	DET
ejpam-5816	315	13	following	follow	VERB
ejpam-5816	315	14	inequality	inequality	NOUN
ejpam-5816	315	15	∣∣∣	∣∣∣	NOUN
ejpam-5816	316	1	[	[	X
ejpam-5816	316	2	(	(	PUNCT
ejpam-5816	316	3	s−	s−	PROPN
ejpam-5816	316	4	r)σ−1	r)σ−1	VERB
ejpam-5816	316	5	2σ−2	2σ−2	NUM
ejpam-5816	316	6	]	]	PUNCT
ejpam-5816	316	7	ℵ	ℵ	X
ejpam-5816	316	8	(	(	PUNCT
ejpam-5816	316	9	r	r	NOUN
ejpam-5816	316	10	+	+	SYM
ejpam-5816	316	11	s	s	NOUN
ejpam-5816	316	12	2	2	NUM
ejpam-5816	316	13	)	)	PUNCT
ejpam-5816	316	14	+	+	NUM
ejpam-5816	316	15	σ(1−	σ(1−	PROPN
ejpam-5816	316	16	κ	κ	PART
ejpam-5816	316	17	)	)	PUNCT
ejpam-5816	316	18	κ(s−	κ(s−	PROPN
ejpam-5816	316	19	r	r	NOUN
ejpam-5816	316	20	)	)	PUNCT
ejpam-5816	316	21	γ(σ	γ(σ	PROPN
ejpam-5816	316	22	)	)	PUNCT
ejpam-5816	317	1	[	[	X
ejpam-5816	317	2	ℵ	ℵ	X
ejpam-5816	317	3	(	(	PUNCT
ejpam-5816	317	4	r	r	NOUN
ejpam-5816	317	5	)	)	PUNCT
ejpam-5816	317	6	+	+	NOUN
ejpam-5816	317	7	ℵ	ℵ	X
ejpam-5816	317	8	(	(	PUNCT
ejpam-5816	317	9	s	s	NOUN
ejpam-5816	317	10	)	)	PUNCT
ejpam-5816	317	11	]	]	PUNCT
ejpam-5816	317	12	−σm(κ)γ(σ	−σm(κ)γ(σ	ADJ
ejpam-5816	317	13	)	)	PUNCT
ejpam-5816	317	14	κ(s−	κ(s−	PROPN
ejpam-5816	317	15	r	r	NOUN
ejpam-5816	317	16	)	)	PUNCT
ejpam-5816	317	17	[	[	PUNCT
ejpam-5816	317	18	iκ	iκ	NOUN
ejpam-5816	317	19	,	,	PUNCT
ejpam-5816	317	20	σ	σ	NOUN
ejpam-5816	317	21	r	r	PROPN
ejpam-5816	317	22	,	,	PUNCT
ejpam-5816	317	23	r+s	r+s	NUM
ejpam-5816	317	24	2	2	NUM
ejpam-5816	317	25	ℵ(r	ℵ(r	NOUN
ejpam-5816	317	26	)	)	PUNCT
ejpam-5816	318	1	+	+	NUM
ejpam-5816	318	2	iκ	iκ	X
ejpam-5816	318	3	,	,	PUNCT
ejpam-5816	318	4	σ	σ	PROPN
ejpam-5816	318	5	s	s	PROPN
ejpam-5816	318	6	,	,	PUNCT
ejpam-5816	318	7	r+s	r+s	NUM
ejpam-5816	318	8	2	2	NUM
ejpam-5816	318	9	ℵ(s	ℵ(s	NOUN
ejpam-5816	318	10	)	)	PUNCT
ejpam-5816	318	11	]	]	PUNCT
ejpam-5816	318	12	∣∣∣	∣∣∣	X
ejpam-5816	318	13	≤	≤	X
ejpam-5816	318	14	k	k	NOUN
ejpam-5816	318	15	s−	s−	PROPN
ejpam-5816	318	16	r	r	NOUN
ejpam-5816	318	17	(	(	PUNCT
ejpam-5816	318	18	1	1	NUM
ejpam-5816	318	19	σ	σ	NOUN
ejpam-5816	318	20	+	+	NOUN
ejpam-5816	318	21	1	1	NUM
ejpam-5816	318	22	)	)	PUNCT
ejpam-5816	318	23	(	(	PUNCT
ejpam-5816	318	24	s−	s−	PROPN
ejpam-5816	318	25	r)σ	r)σ	VERB
ejpam-5816	319	1	2σ	2σ	NUM
ejpam-5816	319	2	.	.	PUNCT
ejpam-5816	320	1	remark	remark	VERB
ejpam-5816	320	2	9	9	NUM
ejpam-5816	320	3	.	.	PUNCT
ejpam-5816	321	1	applying	apply	VERB
ejpam-5816	321	2	theorem	theorem	NOUN
ejpam-5816	321	3	4	4	NUM
ejpam-5816	321	4	for	for	ADP
ejpam-5816	321	5	σ	σ	NOUN
ejpam-5816	321	6	=	=	SYM
ejpam-5816	321	7	κ	κ	NOUN
ejpam-5816	321	8	,	,	PUNCT
ejpam-5816	321	9	we	we	PRON
ejpam-5816	321	10	get	get	AUX
ejpam-5816	321	11	theorem	theorem	ADJ
ejpam-5816	321	12	4	4	NUM
ejpam-5816	321	13	proved	prove	VERB
ejpam-5816	321	14	by	by	ADP
ejpam-5816	321	15	ahmad	ahmad	PROPN
ejpam-5816	321	16	et	et	PROPN
ejpam-5816	321	17	al	al	PROPN
ejpam-5816	321	18	.	.	PUNCT
ejpam-5816	322	1	[	[	X
ejpam-5816	322	2	40	40	NUM
ejpam-5816	322	3	]	]	PUNCT
ejpam-5816	322	4	.	.	PUNCT
ejpam-5816	323	1	remark	remark	PROPN
ejpam-5816	323	2	10	10	NUM
ejpam-5816	323	3	.	.	PUNCT
ejpam-5816	324	1	applying	apply	VERB
ejpam-5816	324	2	corollary	corollary	ADJ
ejpam-5816	324	3	8	8	NUM
ejpam-5816	324	4	for	for	ADP
ejpam-5816	324	5	σ	σ	NOUN
ejpam-5816	324	6	=	=	SYM
ejpam-5816	324	7	κ	κ	NOUN
ejpam-5816	324	8	,	,	PUNCT
ejpam-5816	324	9	we	we	PRON
ejpam-5816	324	10	get	get	VERB
ejpam-5816	324	11	corollary	corollary	ADJ
ejpam-5816	324	12	8	8	NUM
ejpam-5816	324	13	proved	prove	VERB
ejpam-5816	324	14	earlier	early	ADV
ejpam-5816	324	15	by	by	ADP
ejpam-5816	324	16	ahmad	ahmad	PROPN
ejpam-5816	324	17	et	et	PROPN
ejpam-5816	324	18	al	al	PROPN
ejpam-5816	324	19	.	.	PUNCT
ejpam-5816	325	1	[	[	X
ejpam-5816	325	2	40	40	NUM
ejpam-5816	325	3	]	]	PUNCT
ejpam-5816	325	4	.	.	PUNCT
ejpam-5816	326	1	theorem	theorem	NOUN
ejpam-5816	326	2	5	5	NUM
ejpam-5816	326	3	.	.	PUNCT
ejpam-5816	327	1	let	let	VERB
ejpam-5816	327	2	ℵ	ℵ	NOUN
ejpam-5816	327	3	:	:	PUNCT
ejpam-5816	327	4	[	[	X
ejpam-5816	327	5	r	r	X
ejpam-5816	327	6	,	,	PUNCT
ejpam-5816	327	7	s	s	PART
ejpam-5816	327	8	]	]	X
ejpam-5816	327	9	→	→	PUNCT
ejpam-5816	327	10	r	r	NOUN
ejpam-5816	327	11	be	be	AUX
ejpam-5816	327	12	a	a	DET
ejpam-5816	327	13	differentiable	differentiable	ADJ
ejpam-5816	327	14	function	function	NOUN
ejpam-5816	327	15	on	on	ADP
ejpam-5816	327	16	(	(	PUNCT
ejpam-5816	327	17	r	r	NOUN
ejpam-5816	327	18	,	,	PUNCT
ejpam-5816	327	19	s	s	PART
ejpam-5816	327	20	)	)	PUNCT
ejpam-5816	327	21	,	,	PUNCT
ejpam-5816	327	22	where	where	SCONJ
ejpam-5816	327	23	ℵ′	ℵ′	ADP
ejpam-5816	327	24	∈	∈	PROPN
ejpam-5816	327	25	l1[r	l1[r	PROPN
ejpam-5816	327	26	,	,	PUNCT
ejpam-5816	327	27	s	s	X
ejpam-5816	327	28	]	]	PUNCT
ejpam-5816	327	29	and	and	CCONJ
ejpam-5816	327	30	r	r	X
ejpam-5816	327	31	<	<	X
ejpam-5816	327	32	s.	s.	PROPN
ejpam-5816	327	33	for	for	ADP
ejpam-5816	327	34	hattaf	hattaf	NOUN
ejpam-5816	327	35	-	-	PUNCT
ejpam-5816	327	36	fractional	fractional	ADJ
ejpam-5816	327	37	integral	integral	ADJ
ejpam-5816	327	38	operators	operator	NOUN
ejpam-5816	327	39	(	(	PUNCT
ejpam-5816	327	40	4	4	NUM
ejpam-5816	327	41	)	)	PUNCT
ejpam-5816	327	42	and	and	CCONJ
ejpam-5816	327	43	(	(	PUNCT
ejpam-5816	327	44	5	5	NUM
ejpam-5816	327	45	)	)	PUNCT
ejpam-5816	327	46	,	,	PUNCT
ejpam-5816	327	47	we	we	PRON
ejpam-5816	327	48	have	have	VERB
ejpam-5816	327	49	the	the	DET
ejpam-5816	327	50	following	follow	VERB
ejpam-5816	327	51	inequality	inequality	NOUN
ejpam-5816	327	52	if	if	SCONJ
ejpam-5816	327	53	|ℵ′|	|ℵ′|	PROPN
ejpam-5816	327	54	is	be	AUX
ejpam-5816	327	55	a	a	DET
ejpam-5816	327	56	concave	concave	NOUN
ejpam-5816	327	57	function∣∣∣	function∣∣∣	NOUN
ejpam-5816	328	1	[	[	X
ejpam-5816	328	2	(	(	PUNCT
ejpam-5816	328	3	t−	t−	ADJ
ejpam-5816	328	4	r)σ	r)σ	NOUN
ejpam-5816	328	5	+	+	CCONJ
ejpam-5816	328	6	(	(	PUNCT
ejpam-5816	328	7	s−	s−	PROPN
ejpam-5816	328	8	t)σ	t)σ	PUNCT
ejpam-5816	328	9	s−	s−	PROPN
ejpam-5816	328	10	r	r	NOUN
ejpam-5816	328	11	]	]	PUNCT
ejpam-5816	328	12	ℵ	ℵ	X
ejpam-5816	328	13	(	(	PUNCT
ejpam-5816	328	14	t	t	PROPN
ejpam-5816	328	15	)	)	PUNCT
ejpam-5816	328	16	+	+	NUM
ejpam-5816	328	17	σ(1−	σ(1−	PROPN
ejpam-5816	328	18	κ	κ	PART
ejpam-5816	328	19	)	)	PUNCT
ejpam-5816	328	20	κ(s−	κ(s−	PROPN
ejpam-5816	328	21	r	r	NOUN
ejpam-5816	328	22	)	)	PUNCT
ejpam-5816	328	23	γ(σ	γ(σ	PROPN
ejpam-5816	328	24	)	)	PUNCT
ejpam-5816	329	1	[	[	X
ejpam-5816	329	2	ℵ	ℵ	X
ejpam-5816	329	3	(	(	PUNCT
ejpam-5816	329	4	r	r	NOUN
ejpam-5816	329	5	)	)	PUNCT
ejpam-5816	329	6	+	+	NOUN
ejpam-5816	329	7	ℵ	ℵ	X
ejpam-5816	329	8	(	(	PUNCT
ejpam-5816	329	9	s	s	NOUN
ejpam-5816	329	10	)	)	PUNCT
ejpam-5816	329	11	]	]	PUNCT
ejpam-5816	330	1	−σm(κ)γ(σ	−σm(κ)γ(σ	ADJ
ejpam-5816	330	2	)	)	PUNCT
ejpam-5816	330	3	κ(s−	κ(s−	PROPN
ejpam-5816	330	4	r	r	NOUN
ejpam-5816	330	5	)	)	PUNCT
ejpam-5816	330	6	[	[	PUNCT
ejpam-5816	330	7	iκ	iκ	NOUN
ejpam-5816	330	8	,	,	PUNCT
ejpam-5816	330	9	σ	σ	PROPN
ejpam-5816	330	10	r	r	PROPN
ejpam-5816	330	11	,	,	PUNCT
ejpam-5816	330	12	t	t	PROPN
ejpam-5816	330	13	ℵ(r	ℵ(r	PROPN
ejpam-5816	330	14	)	)	PUNCT
ejpam-5816	331	1	+	+	NUM
ejpam-5816	331	2	iκ	iκ	X
ejpam-5816	331	3	,	,	PUNCT
ejpam-5816	331	4	σ	σ	PROPN
ejpam-5816	331	5	s	s	PROPN
ejpam-5816	331	6	,	,	PUNCT
ejpam-5816	331	7	t	t	PROPN
ejpam-5816	331	8	ℵ(s	ℵ(s	PROPN
ejpam-5816	331	9	)	)	PUNCT
ejpam-5816	331	10	]	]	PUNCT
ejpam-5816	331	11	∣∣∣	∣∣∣	NOUN
ejpam-5816	331	12	≤(t−	≤(t−	NOUN
ejpam-5816	332	1	r)σ+1	r)σ+1	PROPN
ejpam-5816	332	2	s−	s−	PROPN
ejpam-5816	332	3	r	r	NOUN
ejpam-5816	332	4	(	(	PUNCT
ejpam-5816	332	5	1	1	NUM
ejpam-5816	332	6	σ	σ	NOUN
ejpam-5816	332	7	+	+	NOUN
ejpam-5816	332	8	1	1	X
ejpam-5816	332	9	)	)	PUNCT
ejpam-5816	332	10	|	|	ADV
ejpam-5816	332	11	ℵ′	ℵ′	ADP
ejpam-5816	332	12	(	(	PUNCT
ejpam-5816	332	13	(	(	PUNCT
ejpam-5816	332	14	σ	σ	X
ejpam-5816	332	15	+	+	NOUN
ejpam-5816	332	16	1)t+	1)t+	NUM
ejpam-5816	332	17	r	r	NOUN
ejpam-5816	332	18	σ	σ	NOUN
ejpam-5816	332	19	+	+	CCONJ
ejpam-5816	332	20	2	2	X
ejpam-5816	332	21	)	)	PUNCT
ejpam-5816	332	22	|	|	ADV
ejpam-5816	333	1	+	+	PROPN
ejpam-5816	333	2	(	(	PUNCT
ejpam-5816	333	3	s−	s−	PROPN
ejpam-5816	333	4	t)σ+1	t)σ+1	PROPN
ejpam-5816	333	5	s−	s−	PROPN
ejpam-5816	333	6	r	r	NOUN
ejpam-5816	333	7	(	(	PUNCT
ejpam-5816	333	8	1	1	NUM
ejpam-5816	333	9	σ	σ	NOUN
ejpam-5816	333	10	+	+	NOUN
ejpam-5816	333	11	1	1	X
ejpam-5816	333	12	)	)	PUNCT
ejpam-5816	333	13	|	|	ADV
ejpam-5816	333	14	ℵ′	ℵ′	ADP
ejpam-5816	333	15	(	(	PUNCT
ejpam-5816	333	16	(	(	PUNCT
ejpam-5816	333	17	σ	σ	X
ejpam-5816	333	18	+	+	NOUN
ejpam-5816	333	19	1)t+	1)t+	NUM
ejpam-5816	333	20	s	s	NOUN
ejpam-5816	333	21	σ	σ	NOUN
ejpam-5816	333	22	+	+	CCONJ
ejpam-5816	333	23	2	2	X
ejpam-5816	333	24	)	)	PUNCT
ejpam-5816	333	25	|	|	ADV
ejpam-5816	333	26	,	,	PUNCT
ejpam-5816	333	27	where	where	SCONJ
ejpam-5816	333	28	κ	κ	PROPN
ejpam-5816	333	29	∈	∈	PROPN
ejpam-5816	333	30	(	(	PUNCT
ejpam-5816	333	31	0	0	NUM
ejpam-5816	333	32	,	,	PUNCT
ejpam-5816	333	33	1	1	NUM
ejpam-5816	333	34	]	]	PUNCT
ejpam-5816	333	35	and	and	CCONJ
ejpam-5816	333	36	m(κ	m(κ	NUM
ejpam-5816	333	37	)	)	PUNCT
ejpam-5816	333	38	>	>	X
ejpam-5816	333	39	0	0	X
ejpam-5816	333	40	.	.	PUNCT
ejpam-5816	334	1	g.	g.	PROPN
ejpam-5816	334	2	rahman	rahman	PROPN
ejpam-5816	334	3	et	et	PROPN
ejpam-5816	334	4	al	al	PROPN
ejpam-5816	334	5	.	.	PUNCT
ejpam-5816	334	6	/	/	SYM
ejpam-5816	334	7	eur	eur	PROPN
ejpam-5816	334	8	.	.	PUNCT
ejpam-5816	335	1	j.	j.	PROPN
ejpam-5816	335	2	pure	pure	PROPN
ejpam-5816	335	3	appl	appl	PROPN
ejpam-5816	335	4	.	.	PROPN
ejpam-5816	335	5	math	math	PROPN
ejpam-5816	335	6	,	,	PUNCT
ejpam-5816	335	7	18	18	NUM
ejpam-5816	335	8	(	(	PUNCT
ejpam-5816	335	9	2	2	NUM
ejpam-5816	335	10	)	)	PUNCT
ejpam-5816	335	11	(	(	PUNCT
ejpam-5816	335	12	2025	2025	NUM
ejpam-5816	335	13	)	)	PUNCT
ejpam-5816	335	14	,	,	PUNCT
ejpam-5816	335	15	5816	5816	NUM
ejpam-5816	335	16	13	13	NUM
ejpam-5816	335	17	of	of	ADP
ejpam-5816	335	18	18	18	NUM
ejpam-5816	335	19	proof	proof	NOUN
ejpam-5816	335	20	.	.	PUNCT
ejpam-5816	336	1	by	by	ADP
ejpam-5816	336	2	utilizing	utilize	VERB
ejpam-5816	336	3	lemma	lemma	PROPN
ejpam-5816	336	4	1	1	NUM
ejpam-5816	336	5	,	,	PUNCT
ejpam-5816	336	6	we	we	PRON
ejpam-5816	336	7	have∣∣∣	have∣∣∣	PUNCT
ejpam-5816	337	1	[	[	X
ejpam-5816	337	2	(	(	PUNCT
ejpam-5816	337	3	t−	t−	ADJ
ejpam-5816	337	4	r)σ	r)σ	NOUN
ejpam-5816	337	5	+	+	CCONJ
ejpam-5816	337	6	(	(	PUNCT
ejpam-5816	337	7	s−	s−	PROPN
ejpam-5816	337	8	t)σ	t)σ	PUNCT
ejpam-5816	337	9	s−	s−	PROPN
ejpam-5816	337	10	r	r	NOUN
ejpam-5816	337	11	]	]	PUNCT
ejpam-5816	337	12	ℵ	ℵ	X
ejpam-5816	337	13	(	(	PUNCT
ejpam-5816	337	14	t	t	PROPN
ejpam-5816	337	15	)	)	PUNCT
ejpam-5816	337	16	+	+	NUM
ejpam-5816	337	17	σ(1−	σ(1−	PROPN
ejpam-5816	337	18	κ	κ	PART
ejpam-5816	337	19	)	)	PUNCT
ejpam-5816	337	20	κ(s−	κ(s−	PROPN
ejpam-5816	337	21	r	r	NOUN
ejpam-5816	337	22	)	)	PUNCT
ejpam-5816	337	23	γ(σ	γ(σ	PROPN
ejpam-5816	337	24	)	)	PUNCT
ejpam-5816	338	1	[	[	X
ejpam-5816	338	2	ℵ	ℵ	X
ejpam-5816	338	3	(	(	PUNCT
ejpam-5816	338	4	r	r	NOUN
ejpam-5816	338	5	)	)	PUNCT
ejpam-5816	338	6	+	+	NOUN
ejpam-5816	338	7	ℵ	ℵ	X
ejpam-5816	338	8	(	(	PUNCT
ejpam-5816	338	9	s	s	NOUN
ejpam-5816	338	10	)	)	PUNCT
ejpam-5816	338	11	]	]	PUNCT
ejpam-5816	339	1	−σm(κ)γ(σ	−σm(κ)γ(σ	ADJ
ejpam-5816	339	2	)	)	PUNCT
ejpam-5816	339	3	κ(s−	κ(s−	PROPN
ejpam-5816	339	4	r	r	NOUN
ejpam-5816	339	5	)	)	PUNCT
ejpam-5816	339	6	[	[	PUNCT
ejpam-5816	339	7	iκ	iκ	NOUN
ejpam-5816	339	8	,	,	PUNCT
ejpam-5816	339	9	σ	σ	PROPN
ejpam-5816	339	10	r	r	PROPN
ejpam-5816	339	11	,	,	PUNCT
ejpam-5816	339	12	t	t	PROPN
ejpam-5816	339	13	ℵ(r	ℵ(r	PROPN
ejpam-5816	339	14	)	)	PUNCT
ejpam-5816	340	1	+	+	NUM
ejpam-5816	340	2	iκ	iκ	X
ejpam-5816	340	3	,	,	PUNCT
ejpam-5816	340	4	σ	σ	PROPN
ejpam-5816	340	5	s	s	PROPN
ejpam-5816	340	6	,	,	PUNCT
ejpam-5816	340	7	t	t	PROPN
ejpam-5816	340	8	ℵ(s	ℵ(s	PROPN
ejpam-5816	340	9	)	)	PUNCT
ejpam-5816	340	10	]	]	PUNCT
ejpam-5816	340	11	∣∣∣	∣∣∣	NOUN
ejpam-5816	340	12	≤(t−	≤(t−	NOUN
ejpam-5816	341	1	r)σ+1	r)σ+1	PROPN
ejpam-5816	341	2	s−	s−	PROPN
ejpam-5816	341	3	r	r	NOUN
ejpam-5816	341	4	∫	∫	PROPN
ejpam-5816	341	5	1	1	NUM
ejpam-5816	341	6	0	0	NUM
ejpam-5816	341	7	ρσ	ρσ	ADP
ejpam-5816	341	8	|	|	ADV
ejpam-5816	341	9	ℵ′(ρt+	ℵ′(ρt+	NOUN
ejpam-5816	341	10	(	(	PUNCT
ejpam-5816	341	11	1−	1−	NUM
ejpam-5816	341	12	ρ)r	ρ)r	X
ejpam-5816	341	13	)	)	PUNCT
ejpam-5816	342	1	|	|	ADV
ejpam-5816	342	2	dρ	dρ	INTJ
ejpam-5816	343	1	+	+	CCONJ
ejpam-5816	343	2	(	(	PUNCT
ejpam-5816	343	3	s−	s−	PROPN
ejpam-5816	343	4	t)σ+1	t)σ+1	PROPN
ejpam-5816	343	5	s−	s−	PROPN
ejpam-5816	343	6	r	r	NOUN
ejpam-5816	343	7	∫	∫	PROPN
ejpam-5816	343	8	1	1	NUM
ejpam-5816	343	9	0	0	NUM
ejpam-5816	343	10	ρσ	ρσ	ADP
ejpam-5816	343	11	|	|	ADV
ejpam-5816	343	12	ℵ′(ρt+	ℵ′(ρt+	NOUN
ejpam-5816	343	13	(	(	PUNCT
ejpam-5816	343	14	1−	1−	NUM
ejpam-5816	343	15	ρ)s	ρ)s	NOUN
ejpam-5816	343	16	)	)	PUNCT
ejpam-5816	344	1	|	|	ADV
ejpam-5816	344	2	dρ	dρ	INTJ
ejpam-5816	344	3	.	.	PUNCT
ejpam-5816	345	1	by	by	ADP
ejpam-5816	345	2	employing	employ	VERB
ejpam-5816	345	3	the	the	DET
ejpam-5816	345	4	jensen	jensen	PROPN
ejpam-5816	345	5	integral	integral	ADJ
ejpam-5816	345	6	inequality	inequality	NOUN
ejpam-5816	345	7	,	,	PUNCT
ejpam-5816	345	8	we	we	PRON
ejpam-5816	345	9	get∣∣∣	get∣∣∣	VERB
ejpam-5816	346	1	[	[	X
ejpam-5816	346	2	(	(	PUNCT
ejpam-5816	346	3	t−	t−	ADJ
ejpam-5816	346	4	r)σ	r)σ	NOUN
ejpam-5816	346	5	+	+	CCONJ
ejpam-5816	346	6	(	(	PUNCT
ejpam-5816	346	7	s−	s−	PROPN
ejpam-5816	346	8	t)σ	t)σ	PUNCT
ejpam-5816	346	9	s−	s−	PROPN
ejpam-5816	346	10	r	r	NOUN
ejpam-5816	346	11	]	]	PUNCT
ejpam-5816	346	12	ℵ	ℵ	X
ejpam-5816	346	13	(	(	PUNCT
ejpam-5816	346	14	t	t	PROPN
ejpam-5816	346	15	)	)	PUNCT
ejpam-5816	346	16	+	+	NUM
ejpam-5816	346	17	σ(1−	σ(1−	PROPN
ejpam-5816	346	18	κ	κ	PART
ejpam-5816	346	19	)	)	PUNCT
ejpam-5816	346	20	κ(s−	κ(s−	PROPN
ejpam-5816	346	21	r	r	NOUN
ejpam-5816	346	22	)	)	PUNCT
ejpam-5816	346	23	γ(σ	γ(σ	PROPN
ejpam-5816	346	24	)	)	PUNCT
ejpam-5816	347	1	[	[	X
ejpam-5816	347	2	ℵ	ℵ	X
ejpam-5816	347	3	(	(	PUNCT
ejpam-5816	347	4	r	r	NOUN
ejpam-5816	347	5	)	)	PUNCT
ejpam-5816	347	6	+	+	NOUN
ejpam-5816	347	7	ℵ	ℵ	X
ejpam-5816	347	8	(	(	PUNCT
ejpam-5816	347	9	s	s	NOUN
ejpam-5816	347	10	)	)	PUNCT
ejpam-5816	347	11	]	]	PUNCT
ejpam-5816	348	1	−σm(κ)γ(σ	−σm(κ)γ(σ	ADJ
ejpam-5816	348	2	)	)	PUNCT
ejpam-5816	348	3	κ(s−	κ(s−	PROPN
ejpam-5816	348	4	r	r	NOUN
ejpam-5816	348	5	)	)	PUNCT
ejpam-5816	348	6	[	[	PUNCT
ejpam-5816	348	7	iκ	iκ	NOUN
ejpam-5816	348	8	,	,	PUNCT
ejpam-5816	348	9	σ	σ	PROPN
ejpam-5816	348	10	r	r	PROPN
ejpam-5816	348	11	,	,	PUNCT
ejpam-5816	348	12	t	t	PROPN
ejpam-5816	348	13	ℵ(r	ℵ(r	PROPN
ejpam-5816	348	14	)	)	PUNCT
ejpam-5816	349	1	+	+	NUM
ejpam-5816	349	2	iκ	iκ	X
ejpam-5816	349	3	,	,	PUNCT
ejpam-5816	349	4	σ	σ	PROPN
ejpam-5816	349	5	s	s	PROPN
ejpam-5816	349	6	,	,	PUNCT
ejpam-5816	349	7	t	t	PROPN
ejpam-5816	349	8	ℵ(s	ℵ(s	PROPN
ejpam-5816	349	9	)	)	PUNCT
ejpam-5816	349	10	]	]	PUNCT
ejpam-5816	349	11	∣∣∣	∣∣∣	NOUN
ejpam-5816	349	12	≤(t−	≤(t−	NOUN
ejpam-5816	350	1	r)σ+1	r)σ+1	PROPN
ejpam-5816	350	2	s−	s−	PROPN
ejpam-5816	350	3	r	r	PROPN
ejpam-5816	350	4	(	(	PUNCT
ejpam-5816	350	5	∫	∫	PROPN
ejpam-5816	350	6	1	1	NUM
ejpam-5816	350	7	0	0	NUM
ejpam-5816	350	8	ρσdρ	ρσdρ	NOUN
ejpam-5816	350	9	)	)	PUNCT
ejpam-5816	351	1	|	|	ADV
ejpam-5816	351	2	ℵ′	ℵ′	ADV
ejpam-5816	351	3	(	(	PUNCT
ejpam-5816	351	4	∫	∫	PROPN
ejpam-5816	351	5	1	1	NUM
ejpam-5816	351	6	0	0	NUM
ejpam-5816	351	7	ρσ(ρt+	ρσ(ρt+	PROPN
ejpam-5816	351	8	(	(	PUNCT
ejpam-5816	351	9	1−	1−	NUM
ejpam-5816	351	10	ρ)r)dρ∫	ρ)r)dρ∫	NOUN
ejpam-5816	351	11	1	1	NUM
ejpam-5816	351	12	0	0	NUM
ejpam-5816	351	13	ρσdρ	ρσdρ	NOUN
ejpam-5816	351	14	)	)	PUNCT
ejpam-5816	352	1	|	|	ADV
ejpam-5816	353	1	+	+	CCONJ
ejpam-5816	353	2	(	(	PUNCT
ejpam-5816	353	3	s−	s−	PROPN
ejpam-5816	353	4	t)σ+1	t)σ+1	PROPN
ejpam-5816	353	5	s−	s−	PROPN
ejpam-5816	353	6	r	r	PROPN
ejpam-5816	353	7	(	(	PUNCT
ejpam-5816	353	8	∫	∫	PROPN
ejpam-5816	353	9	1	1	NUM
ejpam-5816	353	10	0	0	NUM
ejpam-5816	353	11	ρσdρ	ρσdρ	NOUN
ejpam-5816	353	12	)	)	PUNCT
ejpam-5816	354	1	|	|	ADV
ejpam-5816	354	2	ℵ′	ℵ′	ADV
ejpam-5816	354	3	(	(	PUNCT
ejpam-5816	354	4	∫	∫	PROPN
ejpam-5816	354	5	1	1	NUM
ejpam-5816	354	6	0	0	NUM
ejpam-5816	354	7	ρσ(ρt+	ρσ(ρt+	PROPN
ejpam-5816	354	8	(	(	PUNCT
ejpam-5816	354	9	1−	1−	NUM
ejpam-5816	354	10	ρ)s)dρ∫	ρ)s)dρ∫	SYM
ejpam-5816	354	11	1	1	NUM
ejpam-5816	354	12	0	0	NUM
ejpam-5816	354	13	ρσdρ	ρσdρ	NOUN
ejpam-5816	354	14	)	)	PUNCT
ejpam-5816	354	15	|	|	ADV
ejpam-5816	354	16	.	.	PUNCT
ejpam-5816	355	1	after	after	ADP
ejpam-5816	355	2	simple	simple	ADJ
ejpam-5816	355	3	calculation	calculation	NOUN
ejpam-5816	355	4	of	of	ADP
ejpam-5816	355	5	above	above	ADJ
ejpam-5816	355	6	integrals	integral	NOUN
ejpam-5816	355	7	,	,	PUNCT
ejpam-5816	355	8	we	we	PRON
ejpam-5816	355	9	get	get	VERB
ejpam-5816	355	10	the	the	DET
ejpam-5816	355	11	required	required	ADJ
ejpam-5816	355	12	inequality	inequality	NOUN
ejpam-5816	355	13	.	.	PUNCT
ejpam-5816	356	1	corollary	corollary	ADJ
ejpam-5816	356	2	9	9	NUM
ejpam-5816	356	3	.	.	PUNCT
ejpam-5816	357	1	applying	apply	VERB
ejpam-5816	357	2	theorem	theorem	NOUN
ejpam-5816	357	3	5	5	NUM
ejpam-5816	357	4	for	for	ADP
ejpam-5816	357	5	|ℵ′|	|ℵ′|	PROPN
ejpam-5816	357	6	≤	≤	PROPN
ejpam-5816	358	1	k	k	NOUN
ejpam-5816	358	2	where	where	SCONJ
ejpam-5816	358	3	k	k	PROPN
ejpam-5816	358	4	>	>	X
ejpam-5816	358	5	0	0	PUNCT
ejpam-5816	358	6	,	,	PUNCT
ejpam-5816	358	7	we	we	PRON
ejpam-5816	358	8	get	get	VERB
ejpam-5816	358	9	the	the	DET
ejpam-5816	358	10	following	follow	VERB
ejpam-5816	358	11	inequality	inequality	NOUN
ejpam-5816	358	12	∣∣∣	∣∣∣	NOUN
ejpam-5816	359	1	[	[	X
ejpam-5816	359	2	(	(	PUNCT
ejpam-5816	359	3	t−	t−	ADJ
ejpam-5816	359	4	r)σ	r)σ	NOUN
ejpam-5816	359	5	+	+	CCONJ
ejpam-5816	359	6	(	(	PUNCT
ejpam-5816	359	7	s−	s−	PROPN
ejpam-5816	359	8	t)σ	t)σ	PUNCT
ejpam-5816	359	9	s−	s−	PROPN
ejpam-5816	359	10	r	r	NOUN
ejpam-5816	359	11	]	]	PUNCT
ejpam-5816	359	12	ℵ	ℵ	X
ejpam-5816	359	13	(	(	PUNCT
ejpam-5816	359	14	t	t	PROPN
ejpam-5816	359	15	)	)	PUNCT
ejpam-5816	359	16	+	+	NUM
ejpam-5816	359	17	σ(1−	σ(1−	PROPN
ejpam-5816	359	18	κ	κ	PART
ejpam-5816	359	19	)	)	PUNCT
ejpam-5816	359	20	κ(s−	κ(s−	PROPN
ejpam-5816	359	21	r	r	NOUN
ejpam-5816	359	22	)	)	PUNCT
ejpam-5816	359	23	γ(σ	γ(σ	PROPN
ejpam-5816	359	24	)	)	PUNCT
ejpam-5816	360	1	[	[	X
ejpam-5816	360	2	ℵ	ℵ	X
ejpam-5816	360	3	(	(	PUNCT
ejpam-5816	360	4	r	r	NOUN
ejpam-5816	360	5	)	)	PUNCT
ejpam-5816	360	6	+	+	NOUN
ejpam-5816	360	7	ℵ	ℵ	X
ejpam-5816	360	8	(	(	PUNCT
ejpam-5816	360	9	s	s	NOUN
ejpam-5816	360	10	)	)	PUNCT
ejpam-5816	360	11	]	]	PUNCT
ejpam-5816	361	1	−σm(κ)γ(σ	−σm(κ)γ(σ	ADJ
ejpam-5816	361	2	)	)	PUNCT
ejpam-5816	361	3	κ(s−	κ(s−	PROPN
ejpam-5816	361	4	r	r	NOUN
ejpam-5816	361	5	)	)	PUNCT
ejpam-5816	361	6	[	[	PUNCT
ejpam-5816	361	7	iκ	iκ	NOUN
ejpam-5816	361	8	,	,	PUNCT
ejpam-5816	361	9	σ	σ	PROPN
ejpam-5816	361	10	r	r	PROPN
ejpam-5816	361	11	,	,	PUNCT
ejpam-5816	361	12	t	t	PROPN
ejpam-5816	361	13	ℵ(r	ℵ(r	PROPN
ejpam-5816	361	14	)	)	PUNCT
ejpam-5816	362	1	+	+	NUM
ejpam-5816	362	2	iκ	iκ	X
ejpam-5816	362	3	,	,	PUNCT
ejpam-5816	362	4	σ	σ	PROPN
ejpam-5816	362	5	s	s	PROPN
ejpam-5816	362	6	,	,	PUNCT
ejpam-5816	362	7	t	t	PROPN
ejpam-5816	362	8	ℵ(s	ℵ(s	PROPN
ejpam-5816	362	9	)	)	PUNCT
ejpam-5816	362	10	]	]	PUNCT
ejpam-5816	362	11	∣∣∣	∣∣∣	X
ejpam-5816	362	12	≤	≤	X
ejpam-5816	362	13	k	k	NOUN
ejpam-5816	362	14	s−	s−	PROPN
ejpam-5816	362	15	r	r	NOUN
ejpam-5816	362	16	(	(	PUNCT
ejpam-5816	362	17	1	1	NUM
ejpam-5816	362	18	σ	σ	NOUN
ejpam-5816	362	19	+	+	NOUN
ejpam-5816	362	20	1	1	NUM
ejpam-5816	362	21	)	)	PUNCT
ejpam-5816	362	22	{	{	PUNCT
ejpam-5816	362	23	(	(	PUNCT
ejpam-5816	362	24	t−	t−	X
ejpam-5816	362	25	r)σ+1	r)σ+1	PROPN
ejpam-5816	362	26	+	+	CCONJ
ejpam-5816	362	27	(	(	PUNCT
ejpam-5816	362	28	s−	s−	PROPN
ejpam-5816	362	29	t)σ+1	t)σ+1	PROPN
ejpam-5816	362	30	}	}	PUNCT
ejpam-5816	362	31	.	.	PUNCT
ejpam-5816	363	1	remark	remark	NOUN
ejpam-5816	363	2	11	11	NUM
ejpam-5816	363	3	.	.	PUNCT
ejpam-5816	364	1	applying	apply	VERB
ejpam-5816	364	2	theorem	theorem	NOUN
ejpam-5816	364	3	5	5	NUM
ejpam-5816	364	4	for	for	ADP
ejpam-5816	364	5	κ	κ	NOUN
ejpam-5816	364	6	=	=	SYM
ejpam-5816	364	7	σ	σ	PROPN
ejpam-5816	364	8	,	,	PUNCT
ejpam-5816	364	9	we	we	PRON
ejpam-5816	364	10	get	get	AUX
ejpam-5816	364	11	theorem	theorem	ADJ
ejpam-5816	364	12	5	5	NUM
ejpam-5816	364	13	proved	prove	VERB
ejpam-5816	364	14	by	by	ADP
ejpam-5816	364	15	ahmad	ahmad	PROPN
ejpam-5816	364	16	et	et	PROPN
ejpam-5816	364	17	al	al	PROPN
ejpam-5816	364	18	.	.	PUNCT
ejpam-5816	365	1	[	[	X
ejpam-5816	365	2	40	40	NUM
ejpam-5816	365	3	]	]	PUNCT
ejpam-5816	365	4	.	.	PUNCT
ejpam-5816	366	1	remark	remark	PROPN
ejpam-5816	366	2	12	12	NUM
ejpam-5816	366	3	.	.	PUNCT
ejpam-5816	367	1	applying	apply	VERB
ejpam-5816	367	2	corollary	corollary	ADJ
ejpam-5816	367	3	9	9	NUM
ejpam-5816	367	4	for	for	ADP
ejpam-5816	367	5	κ	κ	NOUN
ejpam-5816	367	6	=	=	SYM
ejpam-5816	367	7	σ	σ	PROPN
ejpam-5816	367	8	,	,	PUNCT
ejpam-5816	367	9	we	we	PRON
ejpam-5816	367	10	get	get	VERB
ejpam-5816	367	11	corollary	corollary	ADJ
ejpam-5816	367	12	9	9	NUM
ejpam-5816	367	13	proved	prove	VERB
ejpam-5816	367	14	earlier	early	ADV
ejpam-5816	367	15	by	by	ADP
ejpam-5816	367	16	ahmad	ahmad	PROPN
ejpam-5816	367	17	et	et	PROPN
ejpam-5816	367	18	al	al	PROPN
ejpam-5816	367	19	.	.	PUNCT
ejpam-5816	368	1	[	[	X
ejpam-5816	368	2	40	40	NUM
ejpam-5816	368	3	]	]	PUNCT
ejpam-5816	368	4	.	.	PUNCT
ejpam-5816	369	1	theorem	theorem	ADJ
ejpam-5816	369	2	6	6	NUM
ejpam-5816	369	3	.	.	PUNCT
ejpam-5816	370	1	assume	assume	VERB
ejpam-5816	370	2	that	that	SCONJ
ejpam-5816	370	3	the	the	DET
ejpam-5816	370	4	function	function	NOUN
ejpam-5816	370	5	ψ	ψ	X
ejpam-5816	370	6	:	:	PUNCT
ejpam-5816	371	1	[	[	X
ejpam-5816	371	2	r	r	X
ejpam-5816	371	3	,	,	PUNCT
ejpam-5816	371	4	s	s	PART
ejpam-5816	371	5	]	]	X
ejpam-5816	371	6	→	→	PUNCT
ejpam-5816	371	7	r	r	NOUN
ejpam-5816	371	8	has	have	VERB
ejpam-5816	371	9	a	a	DET
ejpam-5816	371	10	continuous	continuous	ADJ
ejpam-5816	371	11	derivative	derivative	NOUN
ejpam-5816	371	12	on	on	ADP
ejpam-5816	371	13	[	[	X
ejpam-5816	371	14	r	r	X
ejpam-5816	371	15	,	,	PUNCT
ejpam-5816	371	16	s	s	X
ejpam-5816	371	17	]	]	PUNCT
ejpam-5816	371	18	and	and	CCONJ
ejpam-5816	371	19	is	be	AUX
ejpam-5816	371	20	strictly	strictly	ADV
ejpam-5816	371	21	increasing	increase	VERB
ejpam-5816	371	22	and	and	CCONJ
ejpam-5816	371	23	positive	positive	ADJ
ejpam-5816	371	24	.	.	PUNCT
ejpam-5816	372	1	let	let	VERB
ejpam-5816	372	2	ℵ	ℵ	NOUN
ejpam-5816	372	3	:	:	PUNCT
ejpam-5816	372	4	[	[	X
ejpam-5816	372	5	r	r	X
ejpam-5816	372	6	,	,	PUNCT
ejpam-5816	372	7	s	s	PART
ejpam-5816	372	8	]	]	X
ejpam-5816	372	9	→	→	PUNCT
ejpam-5816	372	10	r	r	NOUN
ejpam-5816	372	11	be	be	AUX
ejpam-5816	372	12	a	a	DET
ejpam-5816	372	13	differentiable	differentiable	ADJ
ejpam-5816	372	14	function	function	NOUN
ejpam-5816	372	15	on	on	ADP
ejpam-5816	372	16	g.	g.	PROPN
ejpam-5816	372	17	rahman	rahman	PROPN
ejpam-5816	372	18	et	et	PROPN
ejpam-5816	372	19	al	al	PROPN
ejpam-5816	372	20	.	.	PUNCT
ejpam-5816	372	21	/	/	SYM
ejpam-5816	372	22	eur	eur	PROPN
ejpam-5816	372	23	.	.	PUNCT
ejpam-5816	373	1	j.	j.	PROPN
ejpam-5816	373	2	pure	pure	PROPN
ejpam-5816	373	3	appl	appl	PROPN
ejpam-5816	373	4	.	.	PROPN
ejpam-5816	373	5	math	math	PROPN
ejpam-5816	373	6	,	,	PUNCT
ejpam-5816	373	7	18	18	NUM
ejpam-5816	373	8	(	(	PUNCT
ejpam-5816	373	9	2	2	NUM
ejpam-5816	373	10	)	)	PUNCT
ejpam-5816	373	11	(	(	PUNCT
ejpam-5816	373	12	2025	2025	NUM
ejpam-5816	373	13	)	)	PUNCT
ejpam-5816	373	14	,	,	PUNCT
ejpam-5816	373	15	5816	5816	NUM
ejpam-5816	373	16	14	14	NUM
ejpam-5816	373	17	of	of	ADP
ejpam-5816	373	18	18	18	NUM
ejpam-5816	373	19	(	(	PUNCT
ejpam-5816	373	20	r	r	NOUN
ejpam-5816	373	21	,	,	PUNCT
ejpam-5816	373	22	s	s	PART
ejpam-5816	373	23	)	)	PUNCT
ejpam-5816	373	24	,	,	PUNCT
ejpam-5816	373	25	where	where	SCONJ
ejpam-5816	373	26	ℵ′	ℵ′	ADP
ejpam-5816	373	27	∈	∈	PROPN
ejpam-5816	373	28	l1[r	l1[r	PROPN
ejpam-5816	373	29	,	,	PUNCT
ejpam-5816	373	30	s	s	X
ejpam-5816	373	31	]	]	PUNCT
ejpam-5816	373	32	and	and	CCONJ
ejpam-5816	373	33	r	r	X
ejpam-5816	373	34	<	<	X
ejpam-5816	373	35	s.	s.	PROPN
ejpam-5816	373	36	for	for	ADP
ejpam-5816	373	37	hattaf	hattaf	NOUN
ejpam-5816	373	38	-	-	PUNCT
ejpam-5816	373	39	fractional	fractional	ADJ
ejpam-5816	373	40	integral	integral	ADJ
ejpam-5816	373	41	operators	operator	NOUN
ejpam-5816	373	42	,	,	PUNCT
ejpam-5816	373	43	we	we	PRON
ejpam-5816	373	44	have	have	VERB
ejpam-5816	373	45	the	the	DET
ejpam-5816	373	46	following	follow	VERB
ejpam-5816	373	47	inequality	inequality	NOUN
ejpam-5816	373	48	if	if	SCONJ
ejpam-5816	373	49	|ℵ′|q	|ℵ′|q	NUM
ejpam-5816	373	50	is	be	AUX
ejpam-5816	373	51	a	a	DET
ejpam-5816	373	52	concave	concave	NOUN
ejpam-5816	373	53	function∣∣∣	function∣∣∣	NOUN
ejpam-5816	374	1	[	[	X
ejpam-5816	374	2	(	(	PUNCT
ejpam-5816	374	3	t−	t−	ADJ
ejpam-5816	374	4	r)σ	r)σ	NOUN
ejpam-5816	374	5	+	+	CCONJ
ejpam-5816	374	6	(	(	PUNCT
ejpam-5816	374	7	s−	s−	PROPN
ejpam-5816	374	8	t)σ	t)σ	PUNCT
ejpam-5816	374	9	s−	s−	PROPN
ejpam-5816	374	10	r	r	NOUN
ejpam-5816	374	11	]	]	PUNCT
ejpam-5816	374	12	ℵ	ℵ	X
ejpam-5816	374	13	(	(	PUNCT
ejpam-5816	374	14	t	t	PROPN
ejpam-5816	374	15	)	)	PUNCT
ejpam-5816	374	16	+	+	NUM
ejpam-5816	374	17	σ(1−	σ(1−	PROPN
ejpam-5816	374	18	κ	κ	PART
ejpam-5816	374	19	)	)	PUNCT
ejpam-5816	374	20	κ(s−	κ(s−	PROPN
ejpam-5816	374	21	r	r	NOUN
ejpam-5816	374	22	)	)	PUNCT
ejpam-5816	374	23	γ(σ	γ(σ	PROPN
ejpam-5816	374	24	)	)	PUNCT
ejpam-5816	375	1	[	[	X
ejpam-5816	375	2	ℵ	ℵ	X
ejpam-5816	375	3	(	(	PUNCT
ejpam-5816	375	4	r	r	NOUN
ejpam-5816	375	5	)	)	PUNCT
ejpam-5816	375	6	+	+	NOUN
ejpam-5816	375	7	ℵ	ℵ	X
ejpam-5816	375	8	(	(	PUNCT
ejpam-5816	375	9	s	s	NOUN
ejpam-5816	375	10	)	)	PUNCT
ejpam-5816	375	11	]	]	PUNCT
ejpam-5816	376	1	−σm(κ)γ(σ	−σm(κ)γ(σ	ADJ
ejpam-5816	376	2	)	)	PUNCT
ejpam-5816	376	3	κ(s−	κ(s−	PROPN
ejpam-5816	376	4	r	r	NOUN
ejpam-5816	376	5	)	)	PUNCT
ejpam-5816	376	6	[	[	PUNCT
ejpam-5816	376	7	iκ	iκ	NOUN
ejpam-5816	376	8	,	,	PUNCT
ejpam-5816	376	9	σ	σ	PROPN
ejpam-5816	376	10	r	r	PROPN
ejpam-5816	376	11	,	,	PUNCT
ejpam-5816	376	12	t	t	PROPN
ejpam-5816	376	13	ℵ(r	ℵ(r	PROPN
ejpam-5816	376	14	)	)	PUNCT
ejpam-5816	377	1	+	+	NUM
ejpam-5816	377	2	iκ	iκ	X
ejpam-5816	377	3	,	,	PUNCT
ejpam-5816	377	4	σ	σ	PROPN
ejpam-5816	377	5	s	s	PROPN
ejpam-5816	377	6	,	,	PUNCT
ejpam-5816	377	7	t	t	PROPN
ejpam-5816	377	8	ℵ(s	ℵ(s	PROPN
ejpam-5816	377	9	)	)	PUNCT
ejpam-5816	377	10	]	]	PUNCT
ejpam-5816	377	11	∣∣∣	∣∣∣	NOUN
ejpam-5816	377	12	≤(t−	≤(t−	NOUN
ejpam-5816	378	1	r)σ+1	r)σ+1	PROPN
ejpam-5816	378	2	s−	s−	PROPN
ejpam-5816	378	3	r	r	NOUN
ejpam-5816	378	4	(	(	PUNCT
ejpam-5816	378	5	1	1	NUM
ejpam-5816	378	6	σp+	σp+	NOUN
ejpam-5816	378	7	1	1	NUM
ejpam-5816	378	8	)	)	PUNCT
ejpam-5816	378	9	1	1	NUM
ejpam-5816	378	10	p	p	NOUN
ejpam-5816	378	11	|	|	ADV
ejpam-5816	378	12	ℵ′	ℵ′	ADP
ejpam-5816	378	13	(	(	PUNCT
ejpam-5816	378	14	t+	t+	PUNCT
ejpam-5816	378	15	r	r	NOUN
ejpam-5816	378	16	2	2	NUM
ejpam-5816	378	17	)	)	PUNCT
ejpam-5816	378	18	|	|	ADV
ejpam-5816	379	1	+	+	PROPN
ejpam-5816	379	2	(	(	PUNCT
ejpam-5816	379	3	s−	s−	PROPN
ejpam-5816	379	4	t)σ+1	t)σ+1	PROPN
ejpam-5816	380	1	s−	s−	PROPN
ejpam-5816	380	2	r	r	NOUN
ejpam-5816	380	3	(	(	PUNCT
ejpam-5816	380	4	1	1	NUM
ejpam-5816	380	5	σp+	σp+	NOUN
ejpam-5816	380	6	1	1	NUM
ejpam-5816	380	7	)	)	PUNCT
ejpam-5816	380	8	1	1	NUM
ejpam-5816	380	9	p	p	NOUN
ejpam-5816	380	10	|	|	ADV
ejpam-5816	380	11	ℵ′	ℵ′	ADP
ejpam-5816	380	12	(	(	PUNCT
ejpam-5816	380	13	s+	s+	ADV
ejpam-5816	380	14	t	t	PROPN
ejpam-5816	380	15	2	2	NUM
ejpam-5816	380	16	)	)	PUNCT
ejpam-5816	380	17	|	|	ADV
ejpam-5816	380	18	,	,	PUNCT
ejpam-5816	380	19	where	where	SCONJ
ejpam-5816	380	20	1	1	NUM
ejpam-5816	380	21	p	p	NOUN
ejpam-5816	380	22	+	+	NOUN
ejpam-5816	380	23	1	1	NUM
ejpam-5816	380	24	q	q	NOUN
ejpam-5816	380	25	=	=	SYM
ejpam-5816	380	26	1	1	NUM
ejpam-5816	380	27	,	,	PUNCT
ejpam-5816	380	28	q	q	ADJ
ejpam-5816	380	29	>	>	X
ejpam-5816	380	30	1	1	NUM
ejpam-5816	380	31	,	,	PUNCT
ejpam-5816	380	32	t	t	PROPN
ejpam-5816	380	33	∈	∈	PROPN
ejpam-5816	381	1	[	[	X
ejpam-5816	381	2	r	r	X
ejpam-5816	381	3	,	,	PUNCT
ejpam-5816	381	4	s	s	PART
ejpam-5816	381	5	]	]	X
ejpam-5816	381	6	,	,	PUNCT
ejpam-5816	381	7	κ	κ	PROPN
ejpam-5816	381	8	∈	∈	PROPN
ejpam-5816	381	9	(	(	PUNCT
ejpam-5816	381	10	0	0	NUM
ejpam-5816	381	11	,	,	PUNCT
ejpam-5816	381	12	1	1	NUM
ejpam-5816	381	13	]	]	PUNCT
ejpam-5816	381	14	and	and	CCONJ
ejpam-5816	381	15	m(κ	m(κ	NUM
ejpam-5816	381	16	)	)	PUNCT
ejpam-5816	381	17	>	>	X
ejpam-5816	381	18	0	0	X
ejpam-5816	381	19	.	.	PUNCT
ejpam-5816	381	20	proof	proof	NOUN
ejpam-5816	381	21	.	.	PUNCT
ejpam-5816	382	1	by	by	ADP
ejpam-5816	382	2	utilizing	utilize	VERB
ejpam-5816	382	3	lemma	lemma	PROPN
ejpam-5816	382	4	1	1	NUM
ejpam-5816	382	5	,	,	PUNCT
ejpam-5816	382	6	we	we	PRON
ejpam-5816	382	7	have∣∣∣	have∣∣∣	PUNCT
ejpam-5816	383	1	[	[	X
ejpam-5816	383	2	(	(	PUNCT
ejpam-5816	383	3	t−	t−	ADJ
ejpam-5816	383	4	r)σ	r)σ	NOUN
ejpam-5816	383	5	+	+	CCONJ
ejpam-5816	383	6	(	(	PUNCT
ejpam-5816	383	7	s−	s−	PROPN
ejpam-5816	383	8	t)σ	t)σ	PUNCT
ejpam-5816	383	9	s−	s−	PROPN
ejpam-5816	383	10	r	r	NOUN
ejpam-5816	383	11	]	]	PUNCT
ejpam-5816	383	12	ℵ	ℵ	X
ejpam-5816	383	13	(	(	PUNCT
ejpam-5816	383	14	t	t	PROPN
ejpam-5816	383	15	)	)	PUNCT
ejpam-5816	383	16	+	+	NUM
ejpam-5816	383	17	σ(1−	σ(1−	PROPN
ejpam-5816	383	18	κ	κ	PART
ejpam-5816	383	19	)	)	PUNCT
ejpam-5816	383	20	κ(s−	κ(s−	PROPN
ejpam-5816	383	21	r	r	NOUN
ejpam-5816	383	22	)	)	PUNCT
ejpam-5816	383	23	γ(σ	γ(σ	PROPN
ejpam-5816	383	24	)	)	PUNCT
ejpam-5816	384	1	[	[	X
ejpam-5816	384	2	ℵ	ℵ	X
ejpam-5816	384	3	(	(	PUNCT
ejpam-5816	384	4	r	r	NOUN
ejpam-5816	384	5	)	)	PUNCT
ejpam-5816	384	6	+	+	NOUN
ejpam-5816	384	7	ℵ	ℵ	X
ejpam-5816	384	8	(	(	PUNCT
ejpam-5816	384	9	s	s	NOUN
ejpam-5816	384	10	)	)	PUNCT
ejpam-5816	384	11	]	]	PUNCT
ejpam-5816	385	1	−σm(κ)γ(σ	−σm(κ)γ(σ	ADJ
ejpam-5816	385	2	)	)	PUNCT
ejpam-5816	385	3	κ(s−	κ(s−	PROPN
ejpam-5816	385	4	r	r	NOUN
ejpam-5816	385	5	)	)	PUNCT
ejpam-5816	385	6	[	[	PUNCT
ejpam-5816	385	7	iκ	iκ	NOUN
ejpam-5816	385	8	,	,	PUNCT
ejpam-5816	385	9	σ	σ	PROPN
ejpam-5816	385	10	r	r	PROPN
ejpam-5816	385	11	,	,	PUNCT
ejpam-5816	385	12	t	t	PROPN
ejpam-5816	385	13	ℵ(r	ℵ(r	PROPN
ejpam-5816	385	14	)	)	PUNCT
ejpam-5816	386	1	+	+	NUM
ejpam-5816	386	2	iκ	iκ	X
ejpam-5816	386	3	,	,	PUNCT
ejpam-5816	386	4	σ	σ	PROPN
ejpam-5816	386	5	s	s	PROPN
ejpam-5816	386	6	,	,	PUNCT
ejpam-5816	386	7	t	t	PROPN
ejpam-5816	386	8	ℵ(s	ℵ(s	PROPN
ejpam-5816	386	9	)	)	PUNCT
ejpam-5816	386	10	]	]	PUNCT
ejpam-5816	386	11	∣∣∣	∣∣∣	NOUN
ejpam-5816	386	12	≤(t−	≤(t−	NOUN
ejpam-5816	387	1	r)σ+1	r)σ+1	PROPN
ejpam-5816	387	2	s−	s−	PROPN
ejpam-5816	387	3	r	r	NOUN
ejpam-5816	387	4	∫	∫	PROPN
ejpam-5816	387	5	1	1	NUM
ejpam-5816	387	6	0	0	NUM
ejpam-5816	387	7	ρσ	ρσ	ADP
ejpam-5816	387	8	|	|	ADV
ejpam-5816	387	9	ℵ′(ρt+	ℵ′(ρt+	NOUN
ejpam-5816	387	10	(	(	PUNCT
ejpam-5816	387	11	1−	1−	NUM
ejpam-5816	387	12	ρ)r	ρ)r	X
ejpam-5816	387	13	)	)	PUNCT
ejpam-5816	388	1	|	|	ADV
ejpam-5816	388	2	dρ	dρ	INTJ
ejpam-5816	389	1	+	+	CCONJ
ejpam-5816	389	2	(	(	PUNCT
ejpam-5816	389	3	s−	s−	PROPN
ejpam-5816	389	4	t)σ+1	t)σ+1	PROPN
ejpam-5816	389	5	s−	s−	PROPN
ejpam-5816	389	6	r	r	NOUN
ejpam-5816	389	7	∫	∫	PROPN
ejpam-5816	389	8	1	1	NUM
ejpam-5816	389	9	0	0	NUM
ejpam-5816	389	10	ρσ	ρσ	ADP
ejpam-5816	389	11	|	|	ADV
ejpam-5816	389	12	ℵ′(ρt+	ℵ′(ρt+	NOUN
ejpam-5816	389	13	(	(	PUNCT
ejpam-5816	389	14	1−	1−	NUM
ejpam-5816	389	15	ρ)s	ρ)s	NOUN
ejpam-5816	389	16	)	)	PUNCT
ejpam-5816	390	1	|	|	ADV
ejpam-5816	390	2	dρ	dρ	INTJ
ejpam-5816	390	3	.	.	PUNCT
ejpam-5816	391	1	by	by	ADP
ejpam-5816	391	2	employing	employ	VERB
ejpam-5816	391	3	the	the	DET
ejpam-5816	391	4	hölder	hölder	NOUN
ejpam-5816	391	5	integral	integral	ADJ
ejpam-5816	391	6	inequality	inequality	NOUN
ejpam-5816	391	7	,	,	PUNCT
ejpam-5816	391	8	we	we	PRON
ejpam-5816	391	9	obtain∣∣∣	obtain∣∣∣	VERB
ejpam-5816	392	1	[	[	X
ejpam-5816	392	2	(	(	PUNCT
ejpam-5816	392	3	t−	t−	ADJ
ejpam-5816	392	4	r)σ	r)σ	NOUN
ejpam-5816	392	5	+	+	CCONJ
ejpam-5816	392	6	(	(	PUNCT
ejpam-5816	392	7	s−	s−	PROPN
ejpam-5816	392	8	t)σ	t)σ	PUNCT
ejpam-5816	392	9	s−	s−	PROPN
ejpam-5816	392	10	r	r	NOUN
ejpam-5816	392	11	]	]	PUNCT
ejpam-5816	392	12	ℵ	ℵ	X
ejpam-5816	392	13	(	(	PUNCT
ejpam-5816	392	14	t	t	PROPN
ejpam-5816	392	15	)	)	PUNCT
ejpam-5816	392	16	+	+	NUM
ejpam-5816	392	17	σ(1−	σ(1−	PROPN
ejpam-5816	392	18	κ	κ	PART
ejpam-5816	392	19	)	)	PUNCT
ejpam-5816	392	20	κ(s−	κ(s−	PROPN
ejpam-5816	392	21	r	r	NOUN
ejpam-5816	392	22	)	)	PUNCT
ejpam-5816	392	23	γ(σ	γ(σ	PROPN
ejpam-5816	392	24	)	)	PUNCT
ejpam-5816	393	1	[	[	X
ejpam-5816	393	2	ℵ	ℵ	X
ejpam-5816	393	3	(	(	PUNCT
ejpam-5816	393	4	r	r	NOUN
ejpam-5816	393	5	)	)	PUNCT
ejpam-5816	393	6	+	+	NOUN
ejpam-5816	393	7	ℵ	ℵ	X
ejpam-5816	393	8	(	(	PUNCT
ejpam-5816	393	9	s	s	NOUN
ejpam-5816	393	10	)	)	PUNCT
ejpam-5816	393	11	]	]	PUNCT
ejpam-5816	394	1	−σm(κ)γ(σ	−σm(κ)γ(σ	ADJ
ejpam-5816	394	2	)	)	PUNCT
ejpam-5816	394	3	κ(s−	κ(s−	PROPN
ejpam-5816	394	4	r	r	NOUN
ejpam-5816	394	5	)	)	PUNCT
ejpam-5816	394	6	[	[	PUNCT
ejpam-5816	394	7	iκ	iκ	NOUN
ejpam-5816	394	8	,	,	PUNCT
ejpam-5816	394	9	σ	σ	PROPN
ejpam-5816	394	10	r	r	PROPN
ejpam-5816	394	11	,	,	PUNCT
ejpam-5816	394	12	t	t	PROPN
ejpam-5816	394	13	ℵ(r	ℵ(r	PROPN
ejpam-5816	394	14	)	)	PUNCT
ejpam-5816	395	1	+	+	NUM
ejpam-5816	395	2	iκ	iκ	X
ejpam-5816	395	3	,	,	PUNCT
ejpam-5816	395	4	σ	σ	PROPN
ejpam-5816	395	5	s	s	PROPN
ejpam-5816	395	6	,	,	PUNCT
ejpam-5816	395	7	t	t	PROPN
ejpam-5816	395	8	ℵ(s	ℵ(s	PROPN
ejpam-5816	395	9	)	)	PUNCT
ejpam-5816	395	10	]	]	PUNCT
ejpam-5816	395	11	∣∣∣	∣∣∣	NOUN
ejpam-5816	395	12	≤(t−	≤(t−	NOUN
ejpam-5816	396	1	r)σ+1	r)σ+1	PROPN
ejpam-5816	396	2	s−	s−	PROPN
ejpam-5816	396	3	r	r	PROPN
ejpam-5816	396	4	(	(	PUNCT
ejpam-5816	396	5	∫	∫	PROPN
ejpam-5816	396	6	1	1	NUM
ejpam-5816	396	7	0	0	NUM
ejpam-5816	396	8	ρσpdρ	ρσpdρ	NOUN
ejpam-5816	396	9	)	)	PUNCT
ejpam-5816	396	10	1	1	NUM
ejpam-5816	397	1	p	p	NOUN
ejpam-5816	397	2	(	(	PUNCT
ejpam-5816	397	3	∫	∫	PROPN
ejpam-5816	397	4	1	1	NUM
ejpam-5816	397	5	0	0	NUM
ejpam-5816	398	1	|	|	ADV
ejpam-5816	398	2	ℵ′(ρt+	ℵ′(ρt+	NOUN
ejpam-5816	398	3	(	(	PUNCT
ejpam-5816	398	4	1−	1−	NUM
ejpam-5816	398	5	ρ)r	ρ)r	X
ejpam-5816	398	6	)	)	PUNCT
ejpam-5816	398	7	|q	|q	NOUN
ejpam-5816	398	8	dρ	dρ	NOUN
ejpam-5816	398	9	)	)	PUNCT
ejpam-5816	398	10	1	1	NUM
ejpam-5816	398	11	q	q	NOUN
ejpam-5816	398	12	+	+	CCONJ
ejpam-5816	398	13	(	(	PUNCT
ejpam-5816	398	14	s−	s−	PROPN
ejpam-5816	398	15	t)σ+1	t)σ+1	PROPN
ejpam-5816	398	16	s−	s−	PROPN
ejpam-5816	398	17	r	r	PROPN
ejpam-5816	398	18	(	(	PUNCT
ejpam-5816	398	19	∫	∫	PROPN
ejpam-5816	398	20	1	1	NUM
ejpam-5816	398	21	0	0	NUM
ejpam-5816	398	22	ρσpdρ	ρσpdρ	NOUN
ejpam-5816	398	23	)	)	PUNCT
ejpam-5816	399	1	1	1	NUM
ejpam-5816	399	2	p	p	NOUN
ejpam-5816	399	3	(	(	PUNCT
ejpam-5816	399	4	∫	∫	PROPN
ejpam-5816	399	5	1	1	NUM
ejpam-5816	399	6	0	0	NUM
ejpam-5816	399	7	|	|	ADV
ejpam-5816	399	8	ℵ′(ρt+	ℵ′(ρt+	NOUN
ejpam-5816	399	9	(	(	PUNCT
ejpam-5816	399	10	1−	1−	NUM
ejpam-5816	399	11	ρ)s	ρ)s	NOUN
ejpam-5816	399	12	)	)	PUNCT
ejpam-5816	399	13	|q	|q	NOUN
ejpam-5816	399	14	dρ	dρ	NOUN
ejpam-5816	399	15	)	)	PUNCT
ejpam-5816	399	16	1	1	NUM
ejpam-5816	399	17	q	q	NOUN
ejpam-5816	399	18	.	.	PUNCT
ejpam-5816	400	1	now	now	ADV
ejpam-5816	400	2	,	,	PUNCT
ejpam-5816	400	3	by	by	ADP
ejpam-5816	400	4	employing	employ	VERB
ejpam-5816	400	5	the	the	DET
ejpam-5816	400	6	convexity	convexity	NOUN
ejpam-5816	400	7	of	of	ADP
ejpam-5816	400	8	|	|	ADV
ejpam-5816	400	9	ℵ′	ℵ′	CCONJ
ejpam-5816	400	10	|q	|q	NOUN
ejpam-5816	400	11	and	and	CCONJ
ejpam-5816	400	12	jensen	jensen	PROPN
ejpam-5816	400	13	integral	integral	ADJ
ejpam-5816	400	14	inequality	inequality	NOUN
ejpam-5816	400	15	,	,	PUNCT
ejpam-5816	400	16	we	we	PRON
ejpam-5816	400	17	obtain∣∣∣	obtain∣∣∣	VERB
ejpam-5816	401	1	[	[	X
ejpam-5816	401	2	(	(	PUNCT
ejpam-5816	401	3	t−	t−	ADJ
ejpam-5816	401	4	r)σ	r)σ	NOUN
ejpam-5816	401	5	+	+	CCONJ
ejpam-5816	401	6	(	(	PUNCT
ejpam-5816	401	7	s−	s−	PROPN
ejpam-5816	401	8	t)σ	t)σ	PUNCT
ejpam-5816	401	9	s−	s−	PROPN
ejpam-5816	401	10	r	r	NOUN
ejpam-5816	401	11	]	]	PUNCT
ejpam-5816	401	12	ℵ	ℵ	X
ejpam-5816	401	13	(	(	PUNCT
ejpam-5816	401	14	t	t	PROPN
ejpam-5816	401	15	)	)	PUNCT
ejpam-5816	401	16	+	+	NUM
ejpam-5816	401	17	σ(1−	σ(1−	PROPN
ejpam-5816	401	18	κ	κ	PART
ejpam-5816	401	19	)	)	PUNCT
ejpam-5816	401	20	κ(s−	κ(s−	PROPN
ejpam-5816	401	21	r	r	NOUN
ejpam-5816	401	22	)	)	PUNCT
ejpam-5816	401	23	γ(σ	γ(σ	PROPN
ejpam-5816	401	24	)	)	PUNCT
ejpam-5816	402	1	[	[	X
ejpam-5816	402	2	ℵ	ℵ	X
ejpam-5816	402	3	(	(	PUNCT
ejpam-5816	402	4	r	r	NOUN
ejpam-5816	402	5	)	)	PUNCT
ejpam-5816	402	6	+	+	NOUN
ejpam-5816	402	7	ℵ	ℵ	X
ejpam-5816	402	8	(	(	PUNCT
ejpam-5816	402	9	s	s	NOUN
ejpam-5816	402	10	)	)	PUNCT
ejpam-5816	402	11	]	]	X
ejpam-5816	402	12	(	(	PUNCT
ejpam-5816	402	13	17	17	NUM
ejpam-5816	402	14	)	)	PUNCT
ejpam-5816	402	15	−σm(κ)γ(σ	−σm(κ)γ(σ	ADJ
ejpam-5816	402	16	)	)	PUNCT
ejpam-5816	402	17	κ(s−	κ(s−	PROPN
ejpam-5816	402	18	r	r	NOUN
ejpam-5816	402	19	)	)	PUNCT
ejpam-5816	402	20	[	[	PUNCT
ejpam-5816	402	21	iκ	iκ	NOUN
ejpam-5816	402	22	,	,	PUNCT
ejpam-5816	402	23	σ	σ	PROPN
ejpam-5816	402	24	r	r	PROPN
ejpam-5816	402	25	,	,	PUNCT
ejpam-5816	402	26	t	t	PROPN
ejpam-5816	402	27	ℵ(r	ℵ(r	PROPN
ejpam-5816	402	28	)	)	PUNCT
ejpam-5816	403	1	+	+	NUM
ejpam-5816	403	2	iκ	iκ	X
ejpam-5816	403	3	,	,	PUNCT
ejpam-5816	403	4	σ	σ	PROPN
ejpam-5816	403	5	s	s	PROPN
ejpam-5816	403	6	,	,	PUNCT
ejpam-5816	403	7	t	t	PROPN
ejpam-5816	403	8	ℵ(s	ℵ(s	PROPN
ejpam-5816	403	9	)	)	PUNCT
ejpam-5816	403	10	]	]	PUNCT
ejpam-5816	403	11	∣∣∣	∣∣∣	NOUN
ejpam-5816	403	12	≤(t−	≤(t−	NOUN
ejpam-5816	404	1	r)σ+1	r)σ+1	PROPN
ejpam-5816	404	2	s−	s−	PROPN
ejpam-5816	404	3	r	r	PROPN
ejpam-5816	404	4	(	(	PUNCT
ejpam-5816	404	5	∫	∫	PROPN
ejpam-5816	404	6	1	1	NUM
ejpam-5816	404	7	0	0	NUM
ejpam-5816	404	8	ρσpdρ	ρσpdρ	NOUN
ejpam-5816	404	9	)	)	PUNCT
ejpam-5816	404	10	1	1	NUM
ejpam-5816	405	1	p	p	NOUN
ejpam-5816	405	2	(	(	PUNCT
ejpam-5816	405	3	∫	∫	PROPN
ejpam-5816	405	4	1	1	NUM
ejpam-5816	405	5	0	0	NUM
ejpam-5816	406	1	|	|	ADV
ejpam-5816	406	2	ℵ′(ρt+	ℵ′(ρt+	NOUN
ejpam-5816	406	3	(	(	PUNCT
ejpam-5816	406	4	1−	1−	NUM
ejpam-5816	406	5	ρ)r	ρ)r	X
ejpam-5816	406	6	)	)	PUNCT
ejpam-5816	406	7	|q	|q	NOUN
ejpam-5816	406	8	dρ	dρ	NOUN
ejpam-5816	406	9	)	)	PUNCT
ejpam-5816	406	10	1	1	NUM
ejpam-5816	406	11	q	q	PROPN
ejpam-5816	406	12	g.	g.	PROPN
ejpam-5816	407	1	rahman	rahman	PROPN
ejpam-5816	407	2	et	et	PROPN
ejpam-5816	407	3	al	al	PROPN
ejpam-5816	407	4	.	.	PUNCT
ejpam-5816	407	5	/	/	SYM
ejpam-5816	407	6	eur	eur	PROPN
ejpam-5816	407	7	.	.	PUNCT
ejpam-5816	408	1	j.	j.	PROPN
ejpam-5816	408	2	pure	pure	PROPN
ejpam-5816	408	3	appl	appl	PROPN
ejpam-5816	408	4	.	.	PROPN
ejpam-5816	408	5	math	math	PROPN
ejpam-5816	408	6	,	,	PUNCT
ejpam-5816	408	7	18	18	NUM
ejpam-5816	408	8	(	(	PUNCT
ejpam-5816	408	9	2	2	NUM
ejpam-5816	408	10	)	)	PUNCT
ejpam-5816	408	11	(	(	PUNCT
ejpam-5816	408	12	2025	2025	NUM
ejpam-5816	408	13	)	)	PUNCT
ejpam-5816	408	14	,	,	PUNCT
ejpam-5816	408	15	5816	5816	NUM
ejpam-5816	408	16	15	15	NUM
ejpam-5816	408	17	of	of	ADP
ejpam-5816	408	18	18	18	NUM
ejpam-5816	408	19	+	+	CCONJ
ejpam-5816	408	20	(	(	PUNCT
ejpam-5816	408	21	s−	s−	PROPN
ejpam-5816	408	22	t)σ+1	t)σ+1	PROPN
ejpam-5816	409	1	s−	s−	PROPN
ejpam-5816	409	2	r	r	PROPN
ejpam-5816	409	3	(	(	PUNCT
ejpam-5816	409	4	∫	∫	PROPN
ejpam-5816	409	5	1	1	NUM
ejpam-5816	409	6	0	0	NUM
ejpam-5816	409	7	ρσpdρ	ρσpdρ	NOUN
ejpam-5816	409	8	)	)	PUNCT
ejpam-5816	409	9	1	1	NUM
ejpam-5816	409	10	p	p	NOUN
ejpam-5816	409	11	(	(	PUNCT
ejpam-5816	409	12	∫	∫	PROPN
ejpam-5816	409	13	1	1	NUM
ejpam-5816	409	14	0	0	NUM
ejpam-5816	410	1	|	|	ADV
ejpam-5816	410	2	ℵ′(ρt+	ℵ′(ρt+	NOUN
ejpam-5816	410	3	(	(	PUNCT
ejpam-5816	410	4	1−	1−	NUM
ejpam-5816	410	5	ρ)s	ρ)s	NOUN
ejpam-5816	410	6	)	)	PUNCT
ejpam-5816	410	7	|q	|q	NOUN
ejpam-5816	410	8	dρ	dρ	NOUN
ejpam-5816	410	9	)	)	PUNCT
ejpam-5816	410	10	1	1	NUM
ejpam-5816	410	11	q	q	NOUN
ejpam-5816	410	12	.	.	PUNCT
ejpam-5816	411	1	(	(	PUNCT
ejpam-5816	411	2	18	18	NUM
ejpam-5816	411	3	)	)	PUNCT
ejpam-5816	411	4	now	now	ADV
ejpam-5816	411	5	,	,	PUNCT
ejpam-5816	411	6	since∫	since∫	VERB
ejpam-5816	411	7	1	1	NUM
ejpam-5816	411	8	0	0	NUM
ejpam-5816	412	1	|	|	ADV
ejpam-5816	412	2	ℵ′(ρt+	ℵ′(ρt+	NOUN
ejpam-5816	412	3	(	(	PUNCT
ejpam-5816	412	4	1−	1−	NUM
ejpam-5816	412	5	ρ)r	ρ)r	X
ejpam-5816	412	6	)	)	PUNCT
ejpam-5816	412	7	|q	|q	NOUN
ejpam-5816	412	8	dρ	dρ	PROPN
ejpam-5816	413	1	≤	≤	NUM
ejpam-5816	413	2	∫	∫	PROPN
ejpam-5816	413	3	1	1	NUM
ejpam-5816	413	4	0	0	NUM
ejpam-5816	414	1	ρ0	ρ0	NOUN
ejpam-5816	415	1	|	|	ADV
ejpam-5816	415	2	ℵ′(ρt+	ℵ′(ρt+	NOUN
ejpam-5816	415	3	(	(	PUNCT
ejpam-5816	415	4	1−	1−	NUM
ejpam-5816	415	5	ρ)r	ρ)r	X
ejpam-5816	415	6	)	)	PUNCT
ejpam-5816	415	7	|q	|q	NOUN
ejpam-5816	415	8	dρ	dρ	ADJ
ejpam-5816	415	9	≤	≤	PROPN
ejpam-5816	415	10	(	(	PUNCT
ejpam-5816	415	11	∫	∫	PROPN
ejpam-5816	415	12	1	1	NUM
ejpam-5816	415	13	0	0	NUM
ejpam-5816	415	14	ρ0dρ	ρ0dρ	NUM
ejpam-5816	415	15	)	)	PUNCT
ejpam-5816	416	1	|	|	ADV
ejpam-5816	416	2	ℵ′	ℵ′	ADP
ejpam-5816	416	3	(	(	PUNCT
ejpam-5816	416	4	1∫	1∫	NUM
ejpam-5816	416	5	1	1	NUM
ejpam-5816	416	6	0	0	NUM
ejpam-5816	416	7	ρ0dρ	ρ0dρ	NUM
ejpam-5816	416	8	∫	∫	PROPN
ejpam-5816	416	9	1	1	NUM
ejpam-5816	416	10	0	0	NUM
ejpam-5816	416	11	(	(	PUNCT
ejpam-5816	416	12	ρt+	ρt+	NOUN
ejpam-5816	416	13	(	(	PUNCT
ejpam-5816	416	14	1−	1−	NUM
ejpam-5816	416	15	ρ)r)dρ	ρ)r)dρ	NOUN
ejpam-5816	416	16	)	)	PUNCT
ejpam-5816	416	17	|q	|q	NOUN
ejpam-5816	416	18	≤	≤	PUNCT
ejpam-5816	417	1	|	|	ADV
ejpam-5816	417	2	ℵ′	ℵ′	ADP
ejpam-5816	417	3	(	(	PUNCT
ejpam-5816	417	4	t+	t+	PUNCT
ejpam-5816	417	5	r	r	NOUN
ejpam-5816	417	6	2	2	NUM
ejpam-5816	417	7	)	)	PUNCT
ejpam-5816	417	8	|q	|q	NOUN
ejpam-5816	417	9	.	.	PUNCT
ejpam-5816	418	1	(	(	PUNCT
ejpam-5816	418	2	19	19	NUM
ejpam-5816	418	3	)	)	PUNCT
ejpam-5816	418	4	similarly	similarly	ADV
ejpam-5816	418	5	∫	∫	PROPN
ejpam-5816	418	6	1	1	NUM
ejpam-5816	418	7	0	0	NUM
ejpam-5816	419	1	|	|	ADV
ejpam-5816	419	2	ℵ′(ρt+	ℵ′(ρt+	NOUN
ejpam-5816	419	3	(	(	PUNCT
ejpam-5816	419	4	1−	1−	NUM
ejpam-5816	419	5	ρ)s	ρ)s	NOUN
ejpam-5816	419	6	)	)	PUNCT
ejpam-5816	419	7	|q	|q	NOUN
ejpam-5816	419	8	dρ	dρ	PROPN
ejpam-5816	419	9	≤|	≤|	NOUN
ejpam-5816	419	10	ℵ′	ℵ′	PRON
ejpam-5816	419	11	(	(	PUNCT
ejpam-5816	419	12	t+	t+	NOUN
ejpam-5816	419	13	s	s	NOUN
ejpam-5816	419	14	2	2	NUM
ejpam-5816	419	15	)	)	PUNCT
ejpam-5816	419	16	|q	|q	NOUN
ejpam-5816	419	17	.	.	PUNCT
ejpam-5816	420	1	(	(	PUNCT
ejpam-5816	420	2	20	20	NUM
ejpam-5816	420	3	)	)	PUNCT
ejpam-5816	420	4	by	by	ADP
ejpam-5816	420	5	substituting	substitute	VERB
ejpam-5816	420	6	(	(	PUNCT
ejpam-5816	420	7	20	20	NUM
ejpam-5816	420	8	)	)	PUNCT
ejpam-5816	420	9	and	and	CCONJ
ejpam-5816	420	10	(	(	PUNCT
ejpam-5816	420	11	19	19	NUM
ejpam-5816	420	12	)	)	PUNCT
ejpam-5816	420	13	in	in	ADP
ejpam-5816	420	14	(	(	PUNCT
ejpam-5816	420	15	17	17	NUM
ejpam-5816	420	16	)	)	PUNCT
ejpam-5816	420	17	and	and	CCONJ
ejpam-5816	420	18	then	then	ADV
ejpam-5816	420	19	solving	solve	VERB
ejpam-5816	420	20	the	the	DET
ejpam-5816	420	21	integrals	integral	NOUN
ejpam-5816	420	22	,	,	PUNCT
ejpam-5816	420	23	we	we	PRON
ejpam-5816	420	24	get	get	VERB
ejpam-5816	420	25	the	the	DET
ejpam-5816	420	26	desire	desire	NOUN
ejpam-5816	420	27	assertion	assertion	NOUN
ejpam-5816	420	28	.	.	PUNCT
ejpam-5816	421	1	corollary	corollary	ADJ
ejpam-5816	421	2	10	10	NUM
ejpam-5816	421	3	.	.	PUNCT
ejpam-5816	422	1	applying	apply	VERB
ejpam-5816	422	2	theorem	theorem	NOUN
ejpam-5816	422	3	6	6	NUM
ejpam-5816	422	4	for	for	ADP
ejpam-5816	422	5	t	t	NOUN
ejpam-5816	422	6	=	=	SYM
ejpam-5816	422	7	r+s	r+s	PROPN
ejpam-5816	422	8	2	2	NUM
ejpam-5816	422	9	,	,	PUNCT
ejpam-5816	422	10	we	we	PRON
ejpam-5816	422	11	get	get	VERB
ejpam-5816	422	12	the	the	DET
ejpam-5816	422	13	following	follow	VERB
ejpam-5816	422	14	inequality∣∣∣(s−	inequality∣∣∣(s−	PROPN
ejpam-5816	422	15	r)σ−1	r)σ−1	NOUN
ejpam-5816	422	16	2σ−1	2σ−1	NUM
ejpam-5816	422	17	ℵ	ℵ	NOUN
ejpam-5816	422	18	(	(	PUNCT
ejpam-5816	422	19	r	r	NOUN
ejpam-5816	422	20	+	+	SYM
ejpam-5816	422	21	s	s	NOUN
ejpam-5816	422	22	2	2	NUM
ejpam-5816	422	23	)	)	PUNCT
ejpam-5816	423	1	+	+	NUM
ejpam-5816	423	2	σ(1−	σ(1−	PROPN
ejpam-5816	423	3	κ	κ	PART
ejpam-5816	423	4	)	)	PUNCT
ejpam-5816	423	5	κ(s−	κ(s−	PROPN
ejpam-5816	423	6	r	r	NOUN
ejpam-5816	423	7	)	)	PUNCT
ejpam-5816	424	1	γ(σ	γ(σ	PROPN
ejpam-5816	424	2	)	)	PUNCT
ejpam-5816	425	1	[	[	X
ejpam-5816	425	2	ℵ	ℵ	X
ejpam-5816	425	3	(	(	PUNCT
ejpam-5816	425	4	r	r	NOUN
ejpam-5816	425	5	)	)	PUNCT
ejpam-5816	425	6	+	+	NOUN
ejpam-5816	425	7	ℵ	ℵ	X
ejpam-5816	425	8	(	(	PUNCT
ejpam-5816	425	9	s	s	NOUN
ejpam-5816	425	10	)	)	PUNCT
ejpam-5816	425	11	]	]	PUNCT
ejpam-5816	425	12	−σm(κ)γ(σ	−σm(κ)γ(σ	ADJ
ejpam-5816	425	13	)	)	PUNCT
ejpam-5816	425	14	κ(s−	κ(s−	PROPN
ejpam-5816	425	15	r	r	NOUN
ejpam-5816	425	16	)	)	PUNCT
ejpam-5816	425	17	[	[	PUNCT
ejpam-5816	425	18	iκ	iκ	NOUN
ejpam-5816	425	19	,	,	PUNCT
ejpam-5816	425	20	σ	σ	NOUN
ejpam-5816	425	21	r	r	PROPN
ejpam-5816	425	22	,	,	PUNCT
ejpam-5816	425	23	r+s	r+s	NUM
ejpam-5816	425	24	2	2	NUM
ejpam-5816	425	25	ℵ(r	ℵ(r	NOUN
ejpam-5816	425	26	)	)	PUNCT
ejpam-5816	426	1	+	+	NUM
ejpam-5816	426	2	iκ	iκ	X
ejpam-5816	426	3	,	,	PUNCT
ejpam-5816	426	4	σ	σ	PROPN
ejpam-5816	426	5	s	s	PROPN
ejpam-5816	426	6	,	,	PUNCT
ejpam-5816	426	7	r+s	r+s	NUM
ejpam-5816	426	8	2	2	NUM
ejpam-5816	426	9	ℵ(s	ℵ(s	NOUN
ejpam-5816	426	10	)	)	PUNCT
ejpam-5816	426	11	]	]	PUNCT
ejpam-5816	426	12	∣∣∣	∣∣∣	NOUN
ejpam-5816	426	13	≤	≤	X
ejpam-5816	426	14	(	(	PUNCT
ejpam-5816	426	15	1	1	NUM
ejpam-5816	426	16	σp+	σp+	NOUN
ejpam-5816	426	17	1	1	NUM
ejpam-5816	426	18	)	)	PUNCT
ejpam-5816	426	19	1	1	NUM
ejpam-5816	426	20	p	p	NOUN
ejpam-5816	426	21	1	1	NUM
ejpam-5816	426	22	s−	s−	NOUN
ejpam-5816	426	23	r	r	NOUN
ejpam-5816	426	24	{	{	PUNCT
ejpam-5816	426	25	(	(	PUNCT
ejpam-5816	426	26	s−	s−	PROPN
ejpam-5816	426	27	t)σ+1	t)σ+1	PROPN
ejpam-5816	427	1	|	|	ADV
ejpam-5816	427	2	ℵ′	ℵ′	ADP
ejpam-5816	427	3	(	(	PUNCT
ejpam-5816	427	4	3r	3r	NUM
ejpam-5816	427	5	+	+	SYM
ejpam-5816	427	6	s	s	NOUN
ejpam-5816	427	7	4	4	NUM
ejpam-5816	427	8	)	)	PUNCT
ejpam-5816	427	9	|	|	ADV
ejpam-5816	427	10	+	+	PROPN
ejpam-5816	427	11	(	(	PUNCT
ejpam-5816	427	12	s−	s−	PROPN
ejpam-5816	427	13	t)σ+1	t)σ+1	PROPN
ejpam-5816	427	14	|	|	ADV
ejpam-5816	427	15	ℵ′	ℵ′	ADP
ejpam-5816	427	16	(	(	PUNCT
ejpam-5816	427	17	r	r	NOUN
ejpam-5816	427	18	+	+	NOUN
ejpam-5816	427	19	3s	3s	NUM
ejpam-5816	427	20	4	4	NUM
ejpam-5816	427	21	)	)	PUNCT
ejpam-5816	427	22	|	|	ADV
ejpam-5816	427	23	}	}	PUNCT
ejpam-5816	427	24	.	.	PUNCT
ejpam-5816	428	1	remark	remark	NOUN
ejpam-5816	428	2	13	13	NUM
ejpam-5816	428	3	.	.	PUNCT
ejpam-5816	429	1	applying	apply	VERB
ejpam-5816	429	2	theorem	theorem	NOUN
ejpam-5816	429	3	6	6	NUM
ejpam-5816	429	4	for	for	ADP
ejpam-5816	429	5	σ	σ	NOUN
ejpam-5816	429	6	=	=	SYM
ejpam-5816	429	7	κ	κ	NOUN
ejpam-5816	429	8	,	,	PUNCT
ejpam-5816	429	9	we	we	PRON
ejpam-5816	429	10	get	get	AUX
ejpam-5816	429	11	theorem	theorem	VERB
ejpam-5816	429	12	6	6	NUM
ejpam-5816	429	13	proved	prove	VERB
ejpam-5816	429	14	by	by	ADP
ejpam-5816	429	15	ahmad	ahmad	PROPN
ejpam-5816	429	16	et	et	PROPN
ejpam-5816	429	17	al	al	PROPN
ejpam-5816	429	18	.	.	PUNCT
ejpam-5816	430	1	[	[	X
ejpam-5816	430	2	40	40	NUM
ejpam-5816	430	3	]	]	PUNCT
ejpam-5816	430	4	.	.	PUNCT
ejpam-5816	431	1	remark	remark	PROPN
ejpam-5816	431	2	14	14	NUM
ejpam-5816	431	3	.	.	PUNCT
ejpam-5816	432	1	applying	apply	VERB
ejpam-5816	432	2	corollary	corollary	NOUN
ejpam-5816	432	3	10	10	NUM
ejpam-5816	432	4	for	for	ADP
ejpam-5816	432	5	σ	σ	NOUN
ejpam-5816	432	6	=	=	SYM
ejpam-5816	432	7	κ	κ	NOUN
ejpam-5816	432	8	,	,	PUNCT
ejpam-5816	432	9	we	we	PRON
ejpam-5816	432	10	get	get	VERB
ejpam-5816	432	11	corollary	corollary	ADJ
ejpam-5816	432	12	10	10	NUM
ejpam-5816	432	13	proved	prove	VERB
ejpam-5816	432	14	earlier	early	ADV
ejpam-5816	432	15	by	by	ADP
ejpam-5816	432	16	ahmad	ahmad	PROPN
ejpam-5816	432	17	et	et	PROPN
ejpam-5816	432	18	al	al	PROPN
ejpam-5816	432	19	.	.	PUNCT
ejpam-5816	433	1	[	[	X
ejpam-5816	433	2	40	40	NUM
ejpam-5816	433	3	]	]	PUNCT
ejpam-5816	433	4	.	.	PUNCT
ejpam-5816	434	1	4	4	X
ejpam-5816	434	2	.	.	X
ejpam-5816	434	3	concluding	conclude	VERB
ejpam-5816	434	4	remarks	remark	NOUN
ejpam-5816	434	5	in	in	ADP
ejpam-5816	434	6	this	this	DET
ejpam-5816	434	7	paper	paper	NOUN
ejpam-5816	434	8	,	,	PUNCT
ejpam-5816	434	9	we	we	PRON
ejpam-5816	434	10	developed	develop	VERB
ejpam-5816	434	11	ostrowski	ostrowski	ADJ
ejpam-5816	434	12	-	-	PUNCT
ejpam-5816	434	13	type	type	NOUN
ejpam-5816	434	14	inequalities	inequality	NOUN
ejpam-5816	434	15	for	for	ADP
ejpam-5816	434	16	convex	convex	NOUN
ejpam-5816	434	17	functions	function	NOUN
ejpam-5816	434	18	containing	contain	VERB
ejpam-5816	434	19	the	the	DET
ejpam-5816	434	20	hattaf	hattaf	NOUN
ejpam-5816	434	21	fractional	fractional	ADJ
ejpam-5816	434	22	integral	integral	ADJ
ejpam-5816	434	23	operators	operator	NOUN
ejpam-5816	434	24	.	.	PUNCT
ejpam-5816	435	1	the	the	DET
ejpam-5816	435	2	results	result	NOUN
ejpam-5816	435	3	presented	present	VERB
ejpam-5816	435	4	in	in	ADP
ejpam-5816	435	5	this	this	DET
ejpam-5816	435	6	paper	paper	NOUN
ejpam-5816	435	7	are	be	AUX
ejpam-5816	435	8	original	original	ADJ
ejpam-5816	435	9	to	to	ADP
ejpam-5816	435	10	the	the	DET
ejpam-5816	435	11	best	good	ADJ
ejpam-5816	435	12	of	of	ADP
ejpam-5816	435	13	our	our	PRON
ejpam-5816	435	14	knowledge	knowledge	NOUN
ejpam-5816	435	15	.	.	PUNCT
ejpam-5816	436	1	given	give	VERB
ejpam-5816	436	2	the	the	DET
ejpam-5816	436	3	widespread	widespread	ADJ
ejpam-5816	436	4	applications	application	NOUN
ejpam-5816	436	5	of	of	ADP
ejpam-5816	436	6	convex	convex	NOUN
ejpam-5816	436	7	functions	function	NOUN
ejpam-5816	436	8	in	in	ADP
ejpam-5816	436	9	numerous	numerous	ADJ
ejpam-5816	436	10	scientific	scientific	ADJ
ejpam-5816	436	11	fields	field	NOUN
ejpam-5816	436	12	,	,	PUNCT
ejpam-5816	436	13	our	our	PRON
ejpam-5816	436	14	unique	unique	ADJ
ejpam-5816	436	15	advancements	advancement	NOUN
ejpam-5816	436	16	are	be	AUX
ejpam-5816	436	17	believed	believe	VERB
ejpam-5816	436	18	to	to	PART
ejpam-5816	436	19	be	be	AUX
ejpam-5816	436	20	applicable	applicable	ADJ
ejpam-5816	436	21	to	to	ADP
ejpam-5816	436	22	several	several	ADJ
ejpam-5816	436	23	special	special	ADJ
ejpam-5816	436	24	functions	function	NOUN
ejpam-5816	436	25	,	,	PUNCT
ejpam-5816	436	26	including	include	VERB
ejpam-5816	436	27	convexity	convexity	NOUN
ejpam-5816	436	28	,	,	PUNCT
ejpam-5816	436	29	interval	interval	NOUN
ejpam-5816	436	30	analysis	analysis	NOUN
ejpam-5816	436	31	,	,	PUNCT
ejpam-5816	436	32	quantum	quantum	NOUN
ejpam-5816	436	33	calculus	calculus	NOUN
ejpam-5816	436	34	,	,	PUNCT
ejpam-5816	436	35	fractional	fractional	ADJ
ejpam-5816	436	36	calculus	calculus	NOUN
ejpam-5816	436	37	,	,	PUNCT
ejpam-5816	436	38	and	and	CCONJ
ejpam-5816	436	39	coordinates	coordinate	NOUN
ejpam-5816	436	40	.	.	PUNCT
ejpam-5816	437	1	the	the	DET
ejpam-5816	437	2	inequalities	inequality	NOUN
ejpam-5816	437	3	in	in	ADP
ejpam-5816	437	4	term	term	NOUN
ejpam-5816	437	5	of	of	ADP
ejpam-5816	437	6	ab	ab	PROPN
ejpam-5816	437	7	operators	operator	NOUN
ejpam-5816	437	8	will	will	AUX
ejpam-5816	437	9	be	be	AUX
ejpam-5816	437	10	restored	restore	VERB
ejpam-5816	437	11	if	if	SCONJ
ejpam-5816	437	12	we	we	PRON
ejpam-5816	437	13	put	put	VERB
ejpam-5816	437	14	κ	κ	NOUN
ejpam-5816	437	15	=	=	SYM
ejpam-5816	437	16	σ	σ	PROPN
ejpam-5816	437	17	and	and	CCONJ
ejpam-5816	437	18	classical	classical	ADJ
ejpam-5816	437	19	inequalities	inequality	NOUN
ejpam-5816	437	20	if	if	SCONJ
ejpam-5816	437	21	we	we	PRON
ejpam-5816	437	22	put	put	VERB
ejpam-5816	438	1	κ	κ	NOUN
ejpam-5816	438	2	=	=	PUNCT
ejpam-5816	438	3	σ	σ	PROPN
ejpam-5816	438	4	=	=	SYM
ejpam-5816	438	5	1	1	X
ejpam-5816	438	6	.	.	X
ejpam-5816	438	7	one	one	PRON
ejpam-5816	438	8	can	can	AUX
ejpam-5816	438	9	obtain	obtain	VERB
ejpam-5816	438	10	grüss	grüss	PROPN
ejpam-5816	438	11	type	type	NOUN
ejpam-5816	438	12	inequalities	inequality	NOUN
ejpam-5816	438	13	,	,	PUNCT
ejpam-5816	438	14	chebyshev	chebyshev	NOUN
ejpam-5816	438	15	type	type	NOUN
ejpam-5816	438	16	inequalities	inequality	NOUN
ejpam-5816	438	17	,	,	PUNCT
ejpam-5816	438	18	reverse	reverse	VERB
ejpam-5816	438	19	minkowski	minkowski	PROPN
ejpam-5816	438	20	’s	’s	PART
ejpam-5816	438	21	type	type	NOUN
ejpam-5816	438	22	inequalities	inequality	NOUN
ejpam-5816	438	23	and	and	CCONJ
ejpam-5816	438	24	certain	certain	ADJ
ejpam-5816	438	25	other	other	ADJ
ejpam-5816	438	26	type	type	NOUN
ejpam-5816	438	27	inequalities	inequality	NOUN
ejpam-5816	438	28	by	by	ADP
ejpam-5816	438	29	using	use	VERB
ejpam-5816	438	30	hattaf	hattaf	NOUN
ejpam-5816	438	31	fractional	fractional	ADJ
ejpam-5816	438	32	integral	integral	ADJ
ejpam-5816	438	33	operators	operator	NOUN
ejpam-5816	438	34	.	.	PUNCT
ejpam-5816	439	1	g.	g.	PROPN
ejpam-5816	439	2	rahman	rahman	PROPN
ejpam-5816	439	3	et	et	PROPN
ejpam-5816	439	4	al	al	PROPN
ejpam-5816	439	5	.	.	PUNCT
ejpam-5816	439	6	/	/	SYM
ejpam-5816	439	7	eur	eur	PROPN
ejpam-5816	439	8	.	.	PUNCT
ejpam-5816	440	1	j.	j.	PROPN
ejpam-5816	440	2	pure	pure	PROPN
ejpam-5816	440	3	appl	appl	PROPN
ejpam-5816	440	4	.	.	PROPN
ejpam-5816	440	5	math	math	PROPN
ejpam-5816	440	6	,	,	PUNCT
ejpam-5816	440	7	18	18	NUM
ejpam-5816	440	8	(	(	PUNCT
ejpam-5816	440	9	2	2	NUM
ejpam-5816	440	10	)	)	PUNCT
ejpam-5816	440	11	(	(	PUNCT
ejpam-5816	440	12	2025	2025	NUM
ejpam-5816	440	13	)	)	PUNCT
ejpam-5816	440	14	,	,	PUNCT
ejpam-5816	440	15	5816	5816	NUM
ejpam-5816	440	16	16	16	NUM
ejpam-5816	440	17	of	of	ADP
ejpam-5816	440	18	18	18	NUM
ejpam-5816	440	19	acknowledgements	acknowledgement	NOUN
ejpam-5816	440	20	the	the	DET
ejpam-5816	440	21	authors	author	NOUN
ejpam-5816	440	22	m.	m.	NOUN
ejpam-5816	440	23	a.	a.	NOUN
ejpam-5816	440	24	alghafli	alghafli	PROPN
ejpam-5816	440	25	and	and	CCONJ
ejpam-5816	440	26	n.	n.	PROPN
ejpam-5816	440	27	mlaiki	mlaiki	PROPN
ejpam-5816	440	28	would	would	AUX
ejpam-5816	440	29	like	like	VERB
ejpam-5816	440	30	to	to	PART
ejpam-5816	440	31	thank	thank	VERB
ejpam-5816	440	32	prince	prince	PROPN
ejpam-5816	440	33	sultan	sultan	PROPN
ejpam-5816	440	34	university	university	PROPN
ejpam-5816	440	35	for	for	ADP
ejpam-5816	440	36	paying	pay	VERB
ejpam-5816	440	37	the	the	DET
ejpam-5816	440	38	publication	publication	NOUN
ejpam-5816	440	39	fees	fee	NOUN
ejpam-5816	440	40	for	for	ADP
ejpam-5816	440	41	this	this	DET
ejpam-5816	440	42	work	work	NOUN
ejpam-5816	440	43	through	through	ADP
ejpam-5816	440	44	tas	ta	NOUN
ejpam-5816	440	45	lab	lab	PROPN
ejpam-5816	440	46	.	.	PUNCT
ejpam-5816	441	1	declaration	declaration	NOUN
ejpam-5816	441	2	competing	compete	VERB
ejpam-5816	441	3	interests	interest	NOUN
ejpam-5816	441	4	all	all	DET
ejpam-5816	441	5	authors	author	NOUN
ejpam-5816	441	6	declare	declare	VERB
ejpam-5816	441	7	no	no	DET
ejpam-5816	441	8	conflict	conflict	NOUN
ejpam-5816	441	9	of	of	ADP
ejpam-5816	441	10	interest	interest	NOUN
ejpam-5816	441	11	.	.	PUNCT
ejpam-5816	442	1	author	author	NOUN
ejpam-5816	442	2	’s	’s	PART
ejpam-5816	442	3	contributions	contribution	NOUN
ejpam-5816	442	4	the	the	DET
ejpam-5816	442	5	authors	author	NOUN
ejpam-5816	442	6	have	have	AUX
ejpam-5816	442	7	worked	work	VERB
ejpam-5816	442	8	equally	equally	ADV
ejpam-5816	442	9	when	when	SCONJ
ejpam-5816	442	10	writing	write	VERB
ejpam-5816	442	11	this	this	DET
ejpam-5816	442	12	paper	paper	NOUN
ejpam-5816	442	13	.	.	PUNCT
ejpam-5816	443	1	all	all	DET
ejpam-5816	443	2	authors	author	NOUN
ejpam-5816	443	3	read	read	VERB
ejpam-5816	443	4	and	and	CCONJ
ejpam-5816	443	5	approved	approve	VERB
ejpam-5816	443	6	the	the	DET
ejpam-5816	443	7	final	final	ADJ
ejpam-5816	443	8	manuscript	manuscript	NOUN
ejpam-5816	443	9	.	.	PUNCT
ejpam-5816	444	1	references	reference	NOUN
ejpam-5816	444	2	[	[	X
ejpam-5816	444	3	1	1	NUM
ejpam-5816	444	4	]	]	PUNCT
ejpam-5816	444	5	m.	m.	NOUN
ejpam-5816	444	6	samraiz	samraiz	PROPN
ejpam-5816	444	7	,	,	PUNCT
ejpam-5816	444	8	z.	z.	PROPN
ejpam-5816	444	9	perveen	perveen	PROPN
ejpam-5816	444	10	,	,	PUNCT
ejpam-5816	444	11	t.	t.	PROPN
ejpam-5816	444	12	abdeljawad	abdeljawad	PROPN
ejpam-5816	444	13	,	,	PUNCT
ejpam-5816	444	14	s.	s.	PROPN
ejpam-5816	444	15	iqbal	iqbal	PROPN
ejpam-5816	444	16	,	,	PUNCT
ejpam-5816	444	17	and	and	CCONJ
ejpam-5816	444	18	s.	s.	PROPN
ejpam-5816	444	19	naheed	naheed	PROPN
ejpam-5816	444	20	.	.	PUNCT
ejpam-5816	445	1	on	on	ADP
ejpam-5816	445	2	certain	certain	ADJ
ejpam-5816	445	3	fractional	fractional	ADJ
ejpam-5816	445	4	calculus	calculus	NOUN
ejpam-5816	445	5	operators	operator	NOUN
ejpam-5816	445	6	and	and	CCONJ
ejpam-5816	445	7	their	their	PRON
ejpam-5816	445	8	applications	application	NOUN
ejpam-5816	445	9	in	in	ADP
ejpam-5816	445	10	mathematical	mathematical	ADJ
ejpam-5816	445	11	physics	physics	NOUN
ejpam-5816	445	12	.	.	PUNCT
ejpam-5816	446	1	physica	physica	PROPN
ejpam-5816	446	2	scripta	scripta	PROPN
ejpam-5816	446	3	,	,	PUNCT
ejpam-5816	446	4	95(11):115210	95(11):115210	NUM
ejpam-5816	446	5	,	,	PUNCT
ejpam-5816	446	6	2020	2020	NUM
ejpam-5816	446	7	.	.	PUNCT
ejpam-5816	447	1	[	[	X
ejpam-5816	447	2	2	2	NUM
ejpam-5816	447	3	]	]	PUNCT
ejpam-5816	447	4	m.	m.	NOUN
ejpam-5816	447	5	samraiz	samraiz	PROPN
ejpam-5816	447	6	,	,	PUNCT
ejpam-5816	447	7	z.	z.	PROPN
ejpam-5816	447	8	perveen	perveen	PROPN
ejpam-5816	447	9	,	,	PUNCT
ejpam-5816	447	10	g.	g.	PROPN
ejpam-5816	447	11	rahman	rahman	PROPN
ejpam-5816	447	12	,	,	PUNCT
ejpam-5816	447	13	k.	k.	PROPN
ejpam-5816	447	14	s.	s.	PROPN
ejpam-5816	447	15	nisar	nisar	PROPN
ejpam-5816	447	16	,	,	PUNCT
ejpam-5816	447	17	and	and	CCONJ
ejpam-5816	447	18	devendra	devendra	PROPN
ejpam-5816	447	19	kumar	kumar	PROPN
ejpam-5816	447	20	.	.	PUNCT
ejpam-5816	448	1	on	on	ADP
ejpam-5816	448	2	(	(	PUNCT
ejpam-5816	448	3	k	k	X
ejpam-5816	448	4	,	,	PUNCT
ejpam-5816	448	5	s)hilfer	s)hilfer	NOUN
ejpam-5816	448	6	prabhakar	prabhakar	NOUN
ejpam-5816	448	7	fractional	fractional	ADJ
ejpam-5816	448	8	derivative	derivative	NOUN
ejpam-5816	448	9	with	with	ADP
ejpam-5816	448	10	applications	application	NOUN
ejpam-5816	448	11	in	in	ADP
ejpam-5816	448	12	mathematical	mathematical	ADJ
ejpam-5816	448	13	physics	physic	NOUN
ejpam-5816	448	14	.	.	PUNCT
ejpam-5816	449	1	frontiers	frontier	NOUN
ejpam-5816	449	2	in	in	ADP
ejpam-5816	449	3	physics	physics	PROPN
ejpam-5816	449	4	,	,	PUNCT
ejpam-5816	449	5	8:1–9	8:1–9	NUM
ejpam-5816	449	6	,	,	PUNCT
ejpam-5816	449	7	2020	2020	NUM
ejpam-5816	449	8	.	.	PUNCT
ejpam-5816	450	1	[	[	X
ejpam-5816	450	2	3	3	NUM
ejpam-5816	450	3	]	]	X
ejpam-5816	450	4	a.	a.	NOUN
ejpam-5816	450	5	nazir	nazir	PROPN
ejpam-5816	450	6	,	,	PUNCT
ejpam-5816	450	7	g.	g.	PROPN
ejpam-5816	450	8	rahman	rahman	PROPN
ejpam-5816	450	9	,	,	PUNCT
ejpam-5816	450	10	a.	a.	PROPN
ejpam-5816	450	11	ali	ali	PROPN
ejpam-5816	450	12	,	,	PUNCT
ejpam-5816	450	13	s.	s.	PROPN
ejpam-5816	450	14	naheed	naheed	PROPN
ejpam-5816	450	15	,	,	PUNCT
ejpam-5816	450	16	k.	k.	PROPN
ejpam-5816	450	17	s.	s.	PROPN
ejpam-5816	450	18	nisar	nisar	PROPN
ejpam-5816	450	19	,	,	PUNCT
ejpam-5816	450	20	w.	w.	PROPN
ejpam-5816	450	21	albalawi	albalawi	PROPN
ejpam-5816	450	22	,	,	PUNCT
ejpam-5816	450	23	and	and	CCONJ
ejpam-5816	450	24	h.	h.	PROPN
ejpam-5816	450	25	y.	y.	PROPN
ejpam-5816	450	26	zahran	zahran	PROPN
ejpam-5816	450	27	.	.	PUNCT
ejpam-5816	451	1	on	on	ADP
ejpam-5816	451	2	generalized	generalized	ADJ
ejpam-5816	451	3	fractional	fractional	ADJ
ejpam-5816	451	4	integral	integral	ADJ
ejpam-5816	451	5	with	with	ADP
ejpam-5816	451	6	multivariate	multivariate	NOUN
ejpam-5816	451	7	mittag	mittag	ADJ
ejpam-5816	451	8	-	-	PUNCT
ejpam-5816	451	9	leffler	leffler	NOUN
ejpam-5816	451	10	function	function	NOUN
ejpam-5816	451	11	and	and	CCONJ
ejpam-5816	451	12	its	its	PRON
ejpam-5816	451	13	applications	application	NOUN
ejpam-5816	451	14	.	.	PUNCT
ejpam-5816	452	1	alexandria	alexandria	PROPN
ejpam-5816	452	2	engineering	engineering	PROPN
ejpam-5816	452	3	journal	journal	PROPN
ejpam-5816	452	4	,	,	PUNCT
ejpam-5816	452	5	61:9187–9201	61:9187–9201	PROPN
ejpam-5816	452	6	,	,	PUNCT
ejpam-5816	452	7	2022	2022	NUM
ejpam-5816	452	8	.	.	PUNCT
ejpam-5816	453	1	[	[	X
ejpam-5816	453	2	4	4	NUM
ejpam-5816	453	3	]	]	X
ejpam-5816	453	4	m.	m.	NOUN
ejpam-5816	453	5	samraiz	samraiz	PROPN
ejpam-5816	453	6	,	,	PUNCT
ejpam-5816	453	7	a.	a.	PROPN
ejpam-5816	453	8	mehmood	mehmood	PROPN
ejpam-5816	453	9	,	,	PUNCT
ejpam-5816	453	10	s.	s.	PROPN
ejpam-5816	453	11	naheed	naheed	PROPN
ejpam-5816	453	12	,	,	PUNCT
ejpam-5816	453	13	g.	g.	PROPN
ejpam-5816	453	14	rahman	rahman	PROPN
ejpam-5816	453	15	,	,	PUNCT
ejpam-5816	453	16	a.	a.	NOUN
ejpam-5816	453	17	kashuri	kashuri	PROPN
ejpam-5816	453	18	,	,	PUNCT
ejpam-5816	453	19	and	and	CCONJ
ejpam-5816	453	20	k.	k.	X
ejpam-5816	453	21	nonlaopon	nonlaopon	NOUN
ejpam-5816	453	22	.	.	PUNCT
ejpam-5816	454	1	on	on	ADP
ejpam-5816	454	2	novel	novel	ADJ
ejpam-5816	454	3	fractional	fractional	ADJ
ejpam-5816	454	4	operators	operator	NOUN
ejpam-5816	454	5	involving	involve	VERB
ejpam-5816	454	6	the	the	DET
ejpam-5816	454	7	multivariate	multivariate	NOUN
ejpam-5816	454	8	mittag	mittag	ADJ
ejpam-5816	454	9	–	–	PUNCT
ejpam-5816	454	10	leffler	leffler	NOUN
ejpam-5816	454	11	function	function	NOUN
ejpam-5816	454	12	.	.	PUNCT
ejpam-5816	455	1	mathematics	mathematic	NOUN
ejpam-5816	455	2	,	,	PUNCT
ejpam-5816	455	3	10(21):3991	10(21):3991	NUM
ejpam-5816	455	4	,	,	PUNCT
ejpam-5816	455	5	2022	2022	NUM
ejpam-5816	455	6	.	.	PUNCT
ejpam-5816	456	1	[	[	X
ejpam-5816	456	2	5	5	NUM
ejpam-5816	456	3	]	]	PUNCT
ejpam-5816	456	4	m.	m.	NOUN
ejpam-5816	456	5	samraiz	samraiz	PROPN
ejpam-5816	456	6	,	,	PUNCT
ejpam-5816	456	7	m.	m.	NOUN
ejpam-5816	456	8	umer	umer	PROPN
ejpam-5816	456	9	,	,	PUNCT
ejpam-5816	456	10	t.	t.	PROPN
ejpam-5816	456	11	abdeljawad	abdeljawad	PROPN
ejpam-5816	456	12	,	,	PUNCT
ejpam-5816	456	13	s.	s.	PROPN
ejpam-5816	456	14	naheed	naheed	PROPN
ejpam-5816	456	15	,	,	PUNCT
ejpam-5816	456	16	g.	g.	PROPN
ejpam-5816	456	17	rahman	rahman	PROPN
ejpam-5816	456	18	,	,	PUNCT
ejpam-5816	456	19	and	and	CCONJ
ejpam-5816	456	20	k.	k.	PROPN
ejpam-5816	456	21	shah	shah	PROPN
ejpam-5816	456	22	.	.	PUNCT
ejpam-5816	457	1	on	on	ADP
ejpam-5816	457	2	riemann	riemann	PROPN
ejpam-5816	457	3	-	-	PUNCT
ejpam-5816	457	4	type	type	NOUN
ejpam-5816	457	5	weighted	weight	VERB
ejpam-5816	457	6	fractional	fractional	ADJ
ejpam-5816	457	7	operators	operator	NOUN
ejpam-5816	457	8	and	and	CCONJ
ejpam-5816	457	9	solutions	solution	NOUN
ejpam-5816	457	10	to	to	ADP
ejpam-5816	457	11	cauchy	cauchy	NOUN
ejpam-5816	457	12	problems	problem	NOUN
ejpam-5816	457	13	.	.	PUNCT
ejpam-5816	458	1	computer	computer	NOUN
ejpam-5816	458	2	modeling	modeling	NOUN
ejpam-5816	458	3	in	in	ADP
ejpam-5816	458	4	engineering	engineering	NOUN
ejpam-5816	458	5	and	and	CCONJ
ejpam-5816	458	6	sciences	science	NOUN
ejpam-5816	458	7	,	,	PUNCT
ejpam-5816	458	8	36(1):901–918	36(1):901–918	NOUN
ejpam-5816	458	9	,	,	PUNCT
ejpam-5816	458	10	2023	2023	NUM
ejpam-5816	458	11	.	.	PUNCT
ejpam-5816	459	1	[	[	X
ejpam-5816	459	2	6	6	NUM
ejpam-5816	459	3	]	]	X
ejpam-5816	459	4	d.	d.	PROPN
ejpam-5816	459	5	baleanu	baleanu	PROPN
ejpam-5816	459	6	and	and	CCONJ
ejpam-5816	459	7	a.	a.	NOUN
ejpam-5816	459	8	fernandez	fernandez	PROPN
ejpam-5816	459	9	.	.	PUNCT
ejpam-5816	460	1	on	on	ADP
ejpam-5816	460	2	some	some	DET
ejpam-5816	460	3	new	new	ADJ
ejpam-5816	460	4	properties	property	NOUN
ejpam-5816	460	5	of	of	ADP
ejpam-5816	460	6	fractional	fractional	ADJ
ejpam-5816	460	7	derivatives	derivative	NOUN
ejpam-5816	460	8	with	with	ADP
ejpam-5816	460	9	mittag	mittag	ADJ
ejpam-5816	460	10	-	-	PUNCT
ejpam-5816	460	11	leffler	leffler	NOUN
ejpam-5816	460	12	kernel	kernel	NOUN
ejpam-5816	460	13	.	.	PUNCT
ejpam-5816	461	1	communications	communication	NOUN
ejpam-5816	461	2	in	in	ADP
ejpam-5816	461	3	nonlinear	nonlinear	ADJ
ejpam-5816	461	4	science	science	NOUN
ejpam-5816	461	5	and	and	CCONJ
ejpam-5816	461	6	numerical	numerical	PROPN
ejpam-5816	461	7	simulation	simulation	PROPN
ejpam-5816	461	8	,	,	PUNCT
ejpam-5816	461	9	59:444–462	59:444–462	PROPN
ejpam-5816	461	10	,	,	PUNCT
ejpam-5816	461	11	2018	2018	NUM
ejpam-5816	461	12	.	.	PUNCT
ejpam-5816	462	1	[	[	X
ejpam-5816	462	2	7	7	X
ejpam-5816	462	3	]	]	X
ejpam-5816	462	4	t.	t.	NOUN
ejpam-5816	462	5	abdeljawad	abdeljawad	PROPN
ejpam-5816	462	6	and	and	CCONJ
ejpam-5816	462	7	d.	d.	PROPN
ejpam-5816	462	8	baleanu	baleanu	PROPN
ejpam-5816	462	9	.	.	PUNCT
ejpam-5816	463	1	integration	integration	NOUN
ejpam-5816	463	2	by	by	ADP
ejpam-5816	463	3	parts	part	NOUN
ejpam-5816	463	4	and	and	CCONJ
ejpam-5816	463	5	its	its	PRON
ejpam-5816	463	6	applications	application	NOUN
ejpam-5816	463	7	of	of	ADP
ejpam-5816	463	8	a	a	DET
ejpam-5816	463	9	new	new	ADJ
ejpam-5816	463	10	nonlocal	nonlocal	ADJ
ejpam-5816	463	11	fractional	fractional	ADJ
ejpam-5816	463	12	derivative	derivative	NOUN
ejpam-5816	463	13	with	with	ADP
ejpam-5816	463	14	mittag	mittag	ADJ
ejpam-5816	463	15	-	-	PUNCT
ejpam-5816	463	16	leffler	leffler	NOUN
ejpam-5816	463	17	nonsingular	nonsingular	ADJ
ejpam-5816	463	18	kernel	kernel	PROPN
ejpam-5816	463	19	.	.	PUNCT
ejpam-5816	464	1	journal	journal	PROPN
ejpam-5816	464	2	of	of	ADP
ejpam-5816	464	3	nonlinear	nonlinear	PROPN
ejpam-5816	464	4	sciences	sciences	PROPN
ejpam-5816	464	5	and	and	CCONJ
ejpam-5816	464	6	applications	application	NOUN
ejpam-5816	464	7	,	,	PUNCT
ejpam-5816	464	8	10(3):1098–1107	10(3):1098–1107	NUM
ejpam-5816	464	9	,	,	PUNCT
ejpam-5816	464	10	2017	2017	NUM
ejpam-5816	464	11	.	.	PUNCT
ejpam-5816	465	1	[	[	X
ejpam-5816	465	2	8	8	X
ejpam-5816	465	3	]	]	PUNCT
ejpam-5816	465	4	t.	t.	NOUN
ejpam-5816	465	5	abdeljawad	abdeljawad	NOUN
ejpam-5816	465	6	.	.	PUNCT
ejpam-5816	466	1	a	a	DET
ejpam-5816	466	2	lyapunov	lyapunov	ADJ
ejpam-5816	466	3	type	type	NOUN
ejpam-5816	466	4	inequality	inequality	NOUN
ejpam-5816	466	5	for	for	ADP
ejpam-5816	466	6	fractional	fractional	ADJ
ejpam-5816	466	7	operators	operator	NOUN
ejpam-5816	466	8	with	with	ADP
ejpam-5816	466	9	nonsingular	nonsingular	ADJ
ejpam-5816	466	10	mittag	mittag	ADJ
ejpam-5816	466	11	-	-	PUNCT
ejpam-5816	466	12	leffler	leffler	NOUN
ejpam-5816	466	13	kernel	kernel	NOUN
ejpam-5816	466	14	.	.	PUNCT
ejpam-5816	467	1	journal	journal	PROPN
ejpam-5816	467	2	of	of	ADP
ejpam-5816	467	3	inequalities	inequality	NOUN
ejpam-5816	467	4	and	and	CCONJ
ejpam-5816	467	5	applications	application	NOUN
ejpam-5816	467	6	,	,	PUNCT
ejpam-5816	467	7	2017:130	2017:130	NOUN
ejpam-5816	467	8	,	,	PUNCT
ejpam-5816	467	9	2017	2017	NUM
ejpam-5816	467	10	.	.	PUNCT
ejpam-5816	468	1	[	[	X
ejpam-5816	468	2	9	9	NUM
ejpam-5816	468	3	]	]	PUNCT
ejpam-5816	468	4	w.	w.	PROPN
ejpam-5816	468	5	h.	h.	PROPN
ejpam-5816	468	6	huang	huang	PROPN
ejpam-5816	468	7	,	,	PUNCT
ejpam-5816	468	8	m.	m.	PROPN
ejpam-5816	468	9	samraiz	samraiz	PROPN
ejpam-5816	468	10	,	,	PUNCT
ejpam-5816	468	11	a.	a.	PROPN
ejpam-5816	468	12	mehmood	mehmood	PROPN
ejpam-5816	468	13	,	,	PUNCT
ejpam-5816	468	14	d.	d.	PROPN
ejpam-5816	468	15	baleanu	baleanu	PROPN
ejpam-5816	468	16	,	,	PUNCT
ejpam-5816	468	17	g.	g.	PROPN
ejpam-5816	468	18	rahman	rahman	PROPN
ejpam-5816	468	19	,	,	PUNCT
ejpam-5816	468	20	and	and	CCONJ
ejpam-5816	468	21	s.	s.	PROPN
ejpam-5816	468	22	naheed	naheed	PROPN
ejpam-5816	468	23	.	.	PUNCT
ejpam-5816	468	24	modified	modify	VERB
ejpam-5816	468	25	atangana	atangana	PROPN
ejpam-5816	468	26	-	-	PUNCT
ejpam-5816	468	27	baleanu	baleanu	ADJ
ejpam-5816	468	28	fractional	fractional	ADJ
ejpam-5816	468	29	operators	operator	NOUN
ejpam-5816	468	30	involving	involve	VERB
ejpam-5816	468	31	generalized	generalize	VERB
ejpam-5816	468	32	mittag	mittag	ADJ
ejpam-5816	468	33	-	-	PUNCT
ejpam-5816	468	34	leffler	leffler	NOUN
ejpam-5816	468	35	function	function	NOUN
ejpam-5816	468	36	.	.	PUNCT
ejpam-5816	469	1	alexandria	alexandria	PROPN
ejpam-5816	469	2	engineering	engineering	PROPN
ejpam-5816	469	3	journal	journal	PROPN
ejpam-5816	469	4	,	,	PUNCT
ejpam-5816	469	5	75:639–648	75:639–648	PROPN
ejpam-5816	469	6	,	,	PUNCT
ejpam-5816	469	7	2023	2023	NUM
ejpam-5816	469	8	.	.	PUNCT
ejpam-5816	470	1	g.	g.	PROPN
ejpam-5816	470	2	rahman	rahman	PROPN
ejpam-5816	470	3	et	et	PROPN
ejpam-5816	470	4	al	al	PROPN
ejpam-5816	470	5	.	.	PUNCT
ejpam-5816	470	6	/	/	SYM
ejpam-5816	470	7	eur	eur	PROPN
ejpam-5816	470	8	.	.	PUNCT
ejpam-5816	471	1	j.	j.	PROPN
ejpam-5816	471	2	pure	pure	PROPN
ejpam-5816	471	3	appl	appl	PROPN
ejpam-5816	471	4	.	.	PROPN
ejpam-5816	471	5	math	math	PROPN
ejpam-5816	471	6	,	,	PUNCT
ejpam-5816	471	7	18	18	NUM
ejpam-5816	471	8	(	(	PUNCT
ejpam-5816	471	9	2	2	NUM
ejpam-5816	471	10	)	)	PUNCT
ejpam-5816	471	11	(	(	PUNCT
ejpam-5816	471	12	2025	2025	NUM
ejpam-5816	471	13	)	)	PUNCT
ejpam-5816	471	14	,	,	PUNCT
ejpam-5816	471	15	5816	5816	NUM
ejpam-5816	471	16	17	17	NUM
ejpam-5816	471	17	of	of	ADP
ejpam-5816	471	18	18	18	NUM
ejpam-5816	472	1	[	[	SYM
ejpam-5816	472	2	10	10	NUM
ejpam-5816	472	3	]	]	PUNCT
ejpam-5816	472	4	t.	t.	NOUN
ejpam-5816	472	5	abdeljawad	abdeljawad	PROPN
ejpam-5816	472	6	and	and	CCONJ
ejpam-5816	472	7	d.	d.	PROPN
ejpam-5816	472	8	baleanu	baleanu	PROPN
ejpam-5816	472	9	.	.	PUNCT
ejpam-5816	473	1	on	on	ADP
ejpam-5816	473	2	fractional	fractional	ADJ
ejpam-5816	473	3	derivatives	derivative	NOUN
ejpam-5816	473	4	with	with	ADP
ejpam-5816	473	5	generalized	generalized	ADJ
ejpam-5816	473	6	mittagleffler	mittagleffler	NOUN
ejpam-5816	473	7	kernels	kernel	NOUN
ejpam-5816	473	8	.	.	PUNCT
ejpam-5816	474	1	advances	advance	NOUN
ejpam-5816	474	2	in	in	ADP
ejpam-5816	474	3	difference	difference	NOUN
ejpam-5816	474	4	equations	equation	NOUN
ejpam-5816	474	5	,	,	PUNCT
ejpam-5816	474	6	2018:468	2018:468	NUM
ejpam-5816	474	7	,	,	PUNCT
ejpam-5816	474	8	2018	2018	NUM
ejpam-5816	474	9	.	.	PUNCT
ejpam-5816	475	1	[	[	X
ejpam-5816	475	2	11	11	NUM
ejpam-5816	475	3	]	]	PUNCT
ejpam-5816	475	4	t.	t.	PROPN
ejpam-5816	475	5	abdeljawad	abdeljawad	NOUN
ejpam-5816	475	6	.	.	PUNCT
ejpam-5816	476	1	fractional	fractional	ADJ
ejpam-5816	476	2	operators	operator	NOUN
ejpam-5816	476	3	with	with	ADP
ejpam-5816	476	4	generalized	generalized	ADJ
ejpam-5816	476	5	mittag	mittag	ADJ
ejpam-5816	476	6	-	-	PUNCT
ejpam-5816	476	7	leffler	leffler	NOUN
ejpam-5816	476	8	kernels	kernel	NOUN
ejpam-5816	476	9	and	and	CCONJ
ejpam-5816	476	10	their	their	PRON
ejpam-5816	476	11	iterated	iterated	ADJ
ejpam-5816	476	12	differintegrals	differintegral	NOUN
ejpam-5816	476	13	.	.	PUNCT
ejpam-5816	477	1	chaos	chaos	NOUN
ejpam-5816	477	2	:	:	PUNCT
ejpam-5816	477	3	an	an	DET
ejpam-5816	477	4	interdisciplinary	interdisciplinary	ADJ
ejpam-5816	477	5	journal	journal	NOUN
ejpam-5816	477	6	of	of	ADP
ejpam-5816	477	7	nonlinear	nonlinear	ADJ
ejpam-5816	477	8	science	science	NOUN
ejpam-5816	477	9	,	,	PUNCT
ejpam-5816	477	10	29:2	29:2	NUM
ejpam-5816	477	11	,	,	PUNCT
ejpam-5816	477	12	2019	2019	NUM
ejpam-5816	477	13	.	.	PUNCT
ejpam-5816	478	1	[	[	X
ejpam-5816	478	2	12	12	NUM
ejpam-5816	478	3	]	]	PUNCT
ejpam-5816	478	4	s.	s.	PROPN
ejpam-5816	478	5	s.	s.	PROPN
ejpam-5816	478	6	dragomir	dragomir	PROPN
ejpam-5816	478	7	.	.	PROPN
ejpam-5816	478	8	ostrowski	ostrowski	ADJ
ejpam-5816	478	9	type	type	NOUN
ejpam-5816	478	10	inequalities	inequality	NOUN
ejpam-5816	478	11	for	for	ADP
ejpam-5816	478	12	riemann	riemann	PROPN
ejpam-5816	478	13	–	–	PUNCT
ejpam-5816	478	14	liouville	liouville	VERB
ejpam-5816	478	15	fractional	fractional	ADJ
ejpam-5816	478	16	integrals	integral	NOUN
ejpam-5816	478	17	of	of	ADP
ejpam-5816	478	18	absolutely	absolutely	ADV
ejpam-5816	478	19	continuous	continuous	ADJ
ejpam-5816	478	20	functions	function	NOUN
ejpam-5816	478	21	in	in	ADP
ejpam-5816	478	22	terms	term	NOUN
ejpam-5816	478	23	of	of	ADP
ejpam-5816	478	24	norms	norm	NOUN
ejpam-5816	478	25	.	.	PUNCT
ejpam-5816	479	1	rgmia	rgmia	NOUN
ejpam-5816	479	2	research	research	NOUN
ejpam-5816	479	3	report	report	NOUN
ejpam-5816	479	4	collection	collection	NOUN
ejpam-5816	479	5	,	,	PUNCT
ejpam-5816	479	6	20:49	20:49	NUM
ejpam-5816	479	7	,	,	PUNCT
ejpam-5816	479	8	2017	2017	NUM
ejpam-5816	479	9	.	.	PUNCT
ejpam-5816	480	1	[	[	X
ejpam-5816	480	2	13	13	NUM
ejpam-5816	480	3	]	]	PUNCT
ejpam-5816	480	4	m.	m.	NOUN
ejpam-5816	480	5	z.	z.	PROPN
ejpam-5816	480	6	sarikaya	sarikaya	PROPN
ejpam-5816	480	7	,	,	PUNCT
ejpam-5816	480	8	e.	e.	PROPN
ejpam-5816	480	9	set	set	PROPN
ejpam-5816	480	10	,	,	PUNCT
ejpam-5816	480	11	h.	h.	PROPN
ejpam-5816	480	12	yaldiz	yaldiz	PROPN
ejpam-5816	480	13	,	,	PUNCT
ejpam-5816	480	14	and	and	CCONJ
ejpam-5816	480	15	n.	n.	PROPN
ejpam-5816	480	16	başak	başak	PROPN
ejpam-5816	480	17	.	.	PUNCT
ejpam-5816	481	1	hermite	hermite	PROPN
ejpam-5816	481	2	–	–	PUNCT
ejpam-5816	481	3	hadamard	hadamard	ADJ
ejpam-5816	481	4	inequalities	inequality	NOUN
ejpam-5816	481	5	for	for	ADP
ejpam-5816	481	6	fractional	fractional	ADJ
ejpam-5816	481	7	integrals	integral	NOUN
ejpam-5816	481	8	and	and	CCONJ
ejpam-5816	481	9	related	relate	VERB
ejpam-5816	481	10	fractional	fractional	ADJ
ejpam-5816	481	11	inequalities	inequality	NOUN
ejpam-5816	481	12	.	.	PUNCT
ejpam-5816	482	1	mathematical	mathematical	ADJ
ejpam-5816	482	2	and	and	CCONJ
ejpam-5816	482	3	computer	computer	NOUN
ejpam-5816	482	4	modelling	modelling	NOUN
ejpam-5816	482	5	,	,	PUNCT
ejpam-5816	482	6	57:2403–2407	57:2403–2407	NUM
ejpam-5816	482	7	,	,	PUNCT
ejpam-5816	482	8	2013	2013	NUM
ejpam-5816	482	9	.	.	PUNCT
ejpam-5816	483	1	[	[	X
ejpam-5816	483	2	14	14	NUM
ejpam-5816	483	3	]	]	PUNCT
ejpam-5816	483	4	m.	m.	NOUN
ejpam-5816	483	5	z.	z.	PROPN
ejpam-5816	483	6	sarikaya	sarikaya	PROPN
ejpam-5816	483	7	and	and	CCONJ
ejpam-5816	483	8	h.	h.	PROPN
ejpam-5816	483	9	yildirim	yildirim	PROPN
ejpam-5816	483	10	.	.	PUNCT
ejpam-5816	484	1	on	on	ADP
ejpam-5816	484	2	hermite	hermite	ADJ
ejpam-5816	484	3	–	–	PUNCT
ejpam-5816	484	4	hadamard	hadamard	ADJ
ejpam-5816	484	5	type	type	NOUN
ejpam-5816	484	6	inequalities	inequality	NOUN
ejpam-5816	484	7	for	for	ADP
ejpam-5816	484	8	riemann	riemann	PROPN
ejpam-5816	484	9	-	-	PUNCT
ejpam-5816	484	10	liouville	liouville	VERB
ejpam-5816	484	11	fractional	fractional	ADJ
ejpam-5816	484	12	integrals	integral	NOUN
ejpam-5816	484	13	.	.	PUNCT
ejpam-5816	485	1	miskolc	miskolc	ADJ
ejpam-5816	485	2	mathematical	mathematical	ADJ
ejpam-5816	485	3	notes	note	NOUN
ejpam-5816	485	4	,	,	PUNCT
ejpam-5816	485	5	17:1049–1059	17:1049–1059	NUM
ejpam-5816	485	6	,	,	PUNCT
ejpam-5816	485	7	2017	2017	NUM
ejpam-5816	485	8	.	.	PUNCT
ejpam-5816	486	1	[	[	X
ejpam-5816	486	2	15	15	NUM
ejpam-5816	486	3	]	]	X
ejpam-5816	486	4	h.	h.	PROPN
ejpam-5816	486	5	m.	m.	PROPN
ejpam-5816	486	6	srivastava	srivastava	PROPN
ejpam-5816	486	7	,	,	PUNCT
ejpam-5816	486	8	z.	z.	PROPN
ejpam-5816	486	9	h.	h.	PROPN
ejpam-5816	486	10	zhang	zhang	PROPN
ejpam-5816	486	11	,	,	PUNCT
ejpam-5816	486	12	and	and	CCONJ
ejpam-5816	486	13	y.	y.	PROPN
ejpam-5816	486	14	d.	d.	PROPN
ejpam-5816	486	15	wu	wu	PROPN
ejpam-5816	486	16	.	.	PUNCT
ejpam-5816	487	1	some	some	DET
ejpam-5816	487	2	further	further	ADJ
ejpam-5816	487	3	refinements	refinement	NOUN
ejpam-5816	487	4	and	and	CCONJ
ejpam-5816	487	5	extensions	extension	NOUN
ejpam-5816	487	6	of	of	ADP
ejpam-5816	487	7	the	the	DET
ejpam-5816	487	8	hermite	hermite	ADJ
ejpam-5816	487	9	–	–	PUNCT
ejpam-5816	487	10	hadamard	hadamard	ADJ
ejpam-5816	487	11	and	and	CCONJ
ejpam-5816	487	12	jensen	jensen	PROPN
ejpam-5816	487	13	inequalities	inequality	NOUN
ejpam-5816	487	14	in	in	ADP
ejpam-5816	487	15	several	several	ADJ
ejpam-5816	487	16	variables	variable	NOUN
ejpam-5816	487	17	.	.	PUNCT
ejpam-5816	488	1	mathematical	mathematical	ADJ
ejpam-5816	488	2	and	and	CCONJ
ejpam-5816	488	3	computer	computer	NOUN
ejpam-5816	488	4	modelling	modelling	NOUN
ejpam-5816	488	5	,	,	PUNCT
ejpam-5816	488	6	54:2709–2717	54:2709–2717	NUM
ejpam-5816	488	7	,	,	PUNCT
ejpam-5816	488	8	2011	2011	NUM
ejpam-5816	488	9	.	.	PUNCT
ejpam-5816	489	1	[	[	X
ejpam-5816	489	2	16	16	NUM
ejpam-5816	489	3	]	]	PUNCT
ejpam-5816	489	4	a.	a.	NOUN
ejpam-5816	489	5	rafiq	rafiq	PROPN
ejpam-5816	489	6	,	,	PUNCT
ejpam-5816	489	7	n.	n.	PROPN
ejpam-5816	489	8	a.	a.	PROPN
ejpam-5816	489	9	mir	mir	PROPN
ejpam-5816	489	10	,	,	PUNCT
ejpam-5816	489	11	and	and	CCONJ
ejpam-5816	489	12	f.	f.	PROPN
ejpam-5816	489	13	ahmad	ahmad	PROPN
ejpam-5816	489	14	.	.	PROPN
ejpam-5816	490	1	weighted	weight	VERB
ejpam-5816	490	2	chebyshev	chebyshev	PROPN
ejpam-5816	490	3	–	–	PUNCT
ejpam-5816	490	4	ostrowski	ostrowski	ADJ
ejpam-5816	490	5	type	type	NOUN
ejpam-5816	490	6	inequalities	inequality	NOUN
ejpam-5816	490	7	.	.	PUNCT
ejpam-5816	491	1	applied	apply	VERB
ejpam-5816	491	2	mathematics	mathematic	NOUN
ejpam-5816	491	3	and	and	CCONJ
ejpam-5816	491	4	mechanics	mechanic	NOUN
ejpam-5816	491	5	,	,	PUNCT
ejpam-5816	491	6	28:901–906	28:901–906	NUM
ejpam-5816	491	7	,	,	PUNCT
ejpam-5816	491	8	2007	2007	NUM
ejpam-5816	491	9	.	.	PUNCT
ejpam-5816	492	1	[	[	X
ejpam-5816	492	2	17	17	NUM
ejpam-5816	492	3	]	]	X
ejpam-5816	492	4	y.	y.	PROPN
ejpam-5816	492	5	shuang	shuang	PROPN
ejpam-5816	492	6	and	and	CCONJ
ejpam-5816	492	7	f.	f.	PROPN
ejpam-5816	492	8	qi	qi	PROPN
ejpam-5816	492	9	.	.	PUNCT
ejpam-5816	492	10	integral	integral	ADJ
ejpam-5816	492	11	inequalities	inequality	NOUN
ejpam-5816	492	12	of	of	ADP
ejpam-5816	492	13	hermite	hermite	ADJ
ejpam-5816	492	14	–	–	PUNCT
ejpam-5816	492	15	hadamard	hadamard	ADJ
ejpam-5816	492	16	type	type	NOUN
ejpam-5816	492	17	for	for	ADP
ejpam-5816	492	18	extended	extended	ADJ
ejpam-5816	492	19	s	s	NOUN
ejpam-5816	492	20	-	-	PUNCT
ejpam-5816	492	21	convex	convex	ADJ
ejpam-5816	492	22	functions	function	NOUN
ejpam-5816	492	23	and	and	CCONJ
ejpam-5816	492	24	applications	application	NOUN
ejpam-5816	492	25	.	.	PUNCT
ejpam-5816	493	1	mathematics	mathematic	NOUN
ejpam-5816	493	2	,	,	PUNCT
ejpam-5816	493	3	6(11):223	6(11):223	NUM
ejpam-5816	493	4	,	,	PUNCT
ejpam-5816	493	5	2018	2018	NUM
ejpam-5816	493	6	.	.	PUNCT
ejpam-5816	494	1	[	[	X
ejpam-5816	494	2	18	18	NUM
ejpam-5816	494	3	]	]	PUNCT
ejpam-5816	494	4	k.	k.	PROPN
ejpam-5816	494	5	mehrez	mehrez	PROPN
ejpam-5816	494	6	and	and	CCONJ
ejpam-5816	494	7	p.	p.	PROPN
ejpam-5816	494	8	agarwal	agarwal	PROPN
ejpam-5816	494	9	.	.	PUNCT
ejpam-5816	495	1	new	new	ADJ
ejpam-5816	495	2	hermite	hermite	ADJ
ejpam-5816	495	3	–	–	PUNCT
ejpam-5816	495	4	hadamard	hadamard	ADJ
ejpam-5816	495	5	type	type	NOUN
ejpam-5816	495	6	integral	integral	ADJ
ejpam-5816	495	7	inequalities	inequality	NOUN
ejpam-5816	495	8	for	for	ADP
ejpam-5816	495	9	convex	convex	NOUN
ejpam-5816	495	10	functions	function	NOUN
ejpam-5816	495	11	and	and	CCONJ
ejpam-5816	495	12	their	their	PRON
ejpam-5816	495	13	applications	application	NOUN
ejpam-5816	495	14	.	.	PUNCT
ejpam-5816	496	1	journal	journal	NOUN
ejpam-5816	496	2	of	of	ADP
ejpam-5816	496	3	computational	computational	ADJ
ejpam-5816	496	4	and	and	CCONJ
ejpam-5816	496	5	applied	applied	ADJ
ejpam-5816	496	6	mathematics	mathematic	NOUN
ejpam-5816	496	7	,	,	PUNCT
ejpam-5816	496	8	350:274–285	350:274–285	NUM
ejpam-5816	496	9	,	,	PUNCT
ejpam-5816	496	10	2019	2019	NUM
ejpam-5816	496	11	.	.	PUNCT
ejpam-5816	497	1	[	[	X
ejpam-5816	497	2	19	19	NUM
ejpam-5816	497	3	]	]	PUNCT
ejpam-5816	497	4	m.	m.	NOUN
ejpam-5816	497	5	j.	j.	PROPN
ejpam-5816	497	6	park	park	PROPN
ejpam-5816	497	7	,	,	PUNCT
ejpam-5816	497	8	o.	o.	PROPN
ejpam-5816	497	9	m.	m.	PROPN
ejpam-5816	497	10	kwon	kwon	PROPN
ejpam-5816	497	11	,	,	PUNCT
ejpam-5816	497	12	and	and	CCONJ
ejpam-5816	497	13	j.	j.	PROPN
ejpam-5816	497	14	h.	h.	PROPN
ejpam-5816	497	15	ryu	ryu	PROPN
ejpam-5816	497	16	.	.	PUNCT
ejpam-5816	498	1	generalized	generalized	ADJ
ejpam-5816	498	2	integral	integral	ADJ
ejpam-5816	498	3	inequality	inequality	NOUN
ejpam-5816	498	4	:	:	PUNCT
ejpam-5816	498	5	application	application	NOUN
ejpam-5816	498	6	to	to	ADP
ejpam-5816	498	7	time	time	NOUN
ejpam-5816	498	8	-	-	PUNCT
ejpam-5816	498	9	delay	delay	NOUN
ejpam-5816	498	10	systems	system	NOUN
ejpam-5816	498	11	.	.	PUNCT
ejpam-5816	499	1	applied	apply	VERB
ejpam-5816	499	2	mathematics	mathematics	NOUN
ejpam-5816	499	3	letters	letter	NOUN
ejpam-5816	499	4	,	,	PUNCT
ejpam-5816	499	5	77:6–12	77:6–12	NUM
ejpam-5816	499	6	,	,	PUNCT
ejpam-5816	499	7	2018	2018	NUM
ejpam-5816	499	8	.	.	PUNCT
ejpam-5816	500	1	[	[	X
ejpam-5816	500	2	20	20	NUM
ejpam-5816	500	3	]	]	PUNCT
ejpam-5816	500	4	m.	m.	NOUN
ejpam-5816	500	5	z.	z.	PROPN
ejpam-5816	500	6	sarikaya	sarikaya	PROPN
ejpam-5816	500	7	,	,	PUNCT
ejpam-5816	500	8	t.	t.	NOUN
ejpam-5816	500	9	tunc	tunc	NOUN
ejpam-5816	500	10	,	,	PUNCT
ejpam-5816	500	11	and	and	CCONJ
ejpam-5816	500	12	h.	h.	PROPN
ejpam-5816	500	13	budak	budak	PROPN
ejpam-5816	500	14	.	.	PUNCT
ejpam-5816	501	1	on	on	ADP
ejpam-5816	501	2	generalized	generalize	VERB
ejpam-5816	501	3	some	some	DET
ejpam-5816	501	4	integral	integral	ADJ
ejpam-5816	501	5	inequalities	inequality	NOUN
ejpam-5816	501	6	for	for	ADP
ejpam-5816	501	7	local	local	ADJ
ejpam-5816	501	8	fractional	fractional	ADJ
ejpam-5816	501	9	integrals	integral	NOUN
ejpam-5816	501	10	.	.	PUNCT
ejpam-5816	502	1	applied	apply	VERB
ejpam-5816	502	2	mathematics	mathematic	NOUN
ejpam-5816	502	3	and	and	CCONJ
ejpam-5816	502	4	computation	computation	NOUN
ejpam-5816	502	5	,	,	PUNCT
ejpam-5816	502	6	276:316–323	276:316–323	NUM
ejpam-5816	502	7	,	,	PUNCT
ejpam-5816	502	8	2016	2016	NUM
ejpam-5816	502	9	.	.	PUNCT
ejpam-5816	503	1	[	[	X
ejpam-5816	503	2	21	21	NUM
ejpam-5816	503	3	]	]	X
ejpam-5816	503	4	e.	e.	PROPN
ejpam-5816	503	5	set	set	PROPN
ejpam-5816	503	6	,	,	PUNCT
ejpam-5816	503	7	s.	s.	PROPN
ejpam-5816	503	8	i.	i.	PROPN
ejpam-5816	503	9	butt	butt	PROPN
ejpam-5816	503	10	,	,	PUNCT
ejpam-5816	503	11	a.	a.	PROPN
ejpam-5816	503	12	o.	o.	PROPN
ejpam-5816	503	13	akdemir	akdemir	PROPN
ejpam-5816	503	14	,	,	PUNCT
ejpam-5816	503	15	a.	a.	PROPN
ejpam-5816	503	16	karaoğlan	karaoğlan	PROPN
ejpam-5816	503	17	,	,	PUNCT
ejpam-5816	503	18	and	and	CCONJ
ejpam-5816	503	19	t.	t.	PROPN
ejpam-5816	503	20	abdeljawad	abdeljawad	NOUN
ejpam-5816	503	21	.	.	PUNCT
ejpam-5816	504	1	new	new	ADJ
ejpam-5816	504	2	integral	integral	ADJ
ejpam-5816	504	3	inequalities	inequality	NOUN
ejpam-5816	504	4	for	for	ADP
ejpam-5816	504	5	differentiable	differentiable	ADJ
ejpam-5816	504	6	convex	convex	NOUN
ejpam-5816	504	7	functions	function	NOUN
ejpam-5816	504	8	via	via	ADP
ejpam-5816	504	9	atangana	atangana	PROPN
ejpam-5816	504	10	-	-	PUNCT
ejpam-5816	504	11	baleanu	baleanu	ADJ
ejpam-5816	504	12	fractional	fractional	ADJ
ejpam-5816	504	13	integral	integral	ADJ
ejpam-5816	504	14	operators	operator	NOUN
ejpam-5816	504	15	.	.	PUNCT
ejpam-5816	505	1	chaos	chaos	NOUN
ejpam-5816	505	2	,	,	PUNCT
ejpam-5816	505	3	solitons	soliton	NOUN
ejpam-5816	505	4	and	and	CCONJ
ejpam-5816	505	5	fractals	fractal	NOUN
ejpam-5816	505	6	,	,	PUNCT
ejpam-5816	505	7	143:110554	143:110554	NUM
ejpam-5816	505	8	,	,	PUNCT
ejpam-5816	505	9	2021	2021	NUM
ejpam-5816	505	10	.	.	PUNCT
ejpam-5816	506	1	[	[	X
ejpam-5816	506	2	22	22	NUM
ejpam-5816	506	3	]	]	X
ejpam-5816	506	4	g.	g.	PROPN
ejpam-5816	506	5	rahman	rahman	PROPN
ejpam-5816	506	6	,	,	PUNCT
ejpam-5816	506	7	k.	k.	PROPN
ejpam-5816	506	8	s.	s.	PROPN
ejpam-5816	506	9	nisar	nisar	PROPN
ejpam-5816	506	10	,	,	PUNCT
ejpam-5816	506	11	and	and	CCONJ
ejpam-5816	506	12	f.	f.	PROPN
ejpam-5816	506	13	qi	qi	PROPN
ejpam-5816	506	14	.	.	PUNCT
ejpam-5816	507	1	some	some	DET
ejpam-5816	507	2	new	new	ADJ
ejpam-5816	507	3	inequalities	inequality	NOUN
ejpam-5816	507	4	of	of	ADP
ejpam-5816	507	5	the	the	DET
ejpam-5816	507	6	grüss	grüss	PROPN
ejpam-5816	507	7	type	type	NOUN
ejpam-5816	507	8	for	for	ADP
ejpam-5816	507	9	conformable	conformable	ADJ
ejpam-5816	507	10	fractional	fractional	ADJ
ejpam-5816	507	11	integrals	integral	NOUN
ejpam-5816	507	12	.	.	PUNCT
ejpam-5816	508	1	aims	aim	VERB
ejpam-5816	508	2	mathematics	mathematic	NOUN
ejpam-5816	508	3	,	,	PUNCT
ejpam-5816	508	4	3(4):575–583	3(4):575–583	NOUN
ejpam-5816	508	5	,	,	PUNCT
ejpam-5816	508	6	2018	2018	NUM
ejpam-5816	508	7	.	.	PUNCT
ejpam-5816	509	1	[	[	X
ejpam-5816	509	2	23	23	NUM
ejpam-5816	509	3	]	]	X
ejpam-5816	509	4	g.	g.	PROPN
ejpam-5816	509	5	rahman	rahman	PROPN
ejpam-5816	509	6	,	,	PUNCT
ejpam-5816	509	7	k.	k.	PROPN
ejpam-5816	509	8	s.	s.	PROPN
ejpam-5816	509	9	nisar	nisar	PROPN
ejpam-5816	509	10	,	,	PUNCT
ejpam-5816	509	11	a.	a.	NOUN
ejpam-5816	509	12	ghaffar	ghaffar	NOUN
ejpam-5816	509	13	,	,	PUNCT
ejpam-5816	509	14	and	and	CCONJ
ejpam-5816	509	15	f.	f.	PROPN
ejpam-5816	509	16	qi	qi	PROPN
ejpam-5816	509	17	.	.	PUNCT
ejpam-5816	510	1	some	some	DET
ejpam-5816	510	2	inequalities	inequality	NOUN
ejpam-5816	510	3	of	of	ADP
ejpam-5816	510	4	the	the	DET
ejpam-5816	510	5	grüss	grüss	PROPN
ejpam-5816	510	6	type	type	NOUN
ejpam-5816	510	7	for	for	ADP
ejpam-5816	510	8	conformable	conformable	ADJ
ejpam-5816	510	9	k	k	ADJ
ejpam-5816	510	10	-	-	ADJ
ejpam-5816	510	11	fractional	fractional	ADJ
ejpam-5816	510	12	integral	integral	ADJ
ejpam-5816	510	13	operators	operator	NOUN
ejpam-5816	510	14	.	.	PUNCT
ejpam-5816	511	1	revista	revista	PROPN
ejpam-5816	511	2	de	de	X
ejpam-5816	511	3	la	la	PROPN
ejpam-5816	511	4	real	real	PROPN
ejpam-5816	511	5	academia	academia	PROPN
ejpam-5816	511	6	de	de	PROPN
ejpam-5816	511	7	ciencias	ciencias	PROPN
ejpam-5816	511	8	exactas	exacta	NOUN
ejpam-5816	511	9	,	,	PUNCT
ejpam-5816	511	10	f́ısicas	f́ısicas	PROPN
ejpam-5816	511	11	y	y	PROPN
ejpam-5816	511	12	naturales	naturale	NOUN
ejpam-5816	511	13	.	.	PUNCT
ejpam-5816	512	1	serie	serie	PROPN
ejpam-5816	512	2	a.	a.	PROPN
ejpam-5816	512	3	matemáticas	matemáticas	PROPN
ejpam-5816	512	4	,	,	PUNCT
ejpam-5816	512	5	114:9	114:9	NUM
ejpam-5816	512	6	,	,	PUNCT
ejpam-5816	512	7	2020	2020	NUM
ejpam-5816	512	8	.	.	PUNCT
ejpam-5816	513	1	[	[	X
ejpam-5816	513	2	24	24	NUM
ejpam-5816	513	3	]	]	X
ejpam-5816	513	4	g.	g.	PROPN
ejpam-5816	513	5	rahman	rahman	PROPN
ejpam-5816	513	6	,	,	PUNCT
ejpam-5816	513	7	z.	z.	PROPN
ejpam-5816	513	8	ullah	ullah	PROPN
ejpam-5816	513	9	,	,	PUNCT
ejpam-5816	513	10	a.	a.	PROPN
ejpam-5816	513	11	khan	khan	PROPN
ejpam-5816	513	12	,	,	PUNCT
ejpam-5816	513	13	e.	e.	PROPN
ejpam-5816	513	14	set	set	PROPN
ejpam-5816	513	15	,	,	PUNCT
ejpam-5816	513	16	and	and	CCONJ
ejpam-5816	513	17	k.	k.	PROPN
ejpam-5816	513	18	s.	s.	PROPN
ejpam-5816	513	19	nisar	nisar	PROPN
ejpam-5816	513	20	.	.	PUNCT
ejpam-5816	514	1	certain	certain	ADJ
ejpam-5816	514	2	chebyshev	chebyshev	NOUN
ejpam-5816	514	3	type	type	NOUN
ejpam-5816	514	4	inequalities	inequality	NOUN
ejpam-5816	514	5	involving	involve	VERB
ejpam-5816	514	6	fractional	fractional	ADJ
ejpam-5816	514	7	conformable	conformable	ADJ
ejpam-5816	514	8	integral	integral	ADJ
ejpam-5816	514	9	operators	operator	NOUN
ejpam-5816	514	10	.	.	PUNCT
ejpam-5816	515	1	mathematics	mathematic	NOUN
ejpam-5816	515	2	,	,	PUNCT
ejpam-5816	515	3	7:364	7:364	NUM
ejpam-5816	515	4	,	,	PUNCT
ejpam-5816	515	5	2019	2019	NUM
ejpam-5816	515	6	.	.	PUNCT
ejpam-5816	516	1	[	[	X
ejpam-5816	516	2	25	25	NUM
ejpam-5816	516	3	]	]	X
ejpam-5816	516	4	g.	g.	PROPN
ejpam-5816	516	5	rahman	rahman	PROPN
ejpam-5816	516	6	,	,	PUNCT
ejpam-5816	516	7	t.	t.	PROPN
ejpam-5816	516	8	abdeljawad	abdeljawad	PROPN
ejpam-5816	516	9	,	,	PUNCT
ejpam-5816	516	10	f.	f.	PROPN
ejpam-5816	516	11	jarad	jarad	PROPN
ejpam-5816	516	12	,	,	PUNCT
ejpam-5816	516	13	and	and	CCONJ
ejpam-5816	516	14	k.	k.	PROPN
ejpam-5816	516	15	s.	s.	PROPN
ejpam-5816	516	16	nisar	nisar	PROPN
ejpam-5816	516	17	.	.	PUNCT
ejpam-5816	517	1	bounds	bound	NOUN
ejpam-5816	517	2	of	of	ADP
ejpam-5816	517	3	generalized	generalized	ADJ
ejpam-5816	517	4	proportional	proportional	ADJ
ejpam-5816	517	5	fractional	fractional	ADJ
ejpam-5816	517	6	integrals	integral	NOUN
ejpam-5816	517	7	in	in	ADP
ejpam-5816	517	8	general	general	ADJ
ejpam-5816	517	9	form	form	NOUN
ejpam-5816	517	10	via	via	ADP
ejpam-5816	517	11	convex	convex	NOUN
ejpam-5816	517	12	functions	function	NOUN
ejpam-5816	517	13	and	and	CCONJ
ejpam-5816	517	14	their	their	PRON
ejpam-5816	517	15	applications	application	NOUN
ejpam-5816	517	16	.	.	PUNCT
ejpam-5816	518	1	mathematics	mathematic	NOUN
ejpam-5816	518	2	,	,	PUNCT
ejpam-5816	518	3	8:113	8:113	NUM
ejpam-5816	518	4	,	,	PUNCT
ejpam-5816	518	5	2020	2020	NUM
ejpam-5816	518	6	.	.	PUNCT
ejpam-5816	519	1	[	[	X
ejpam-5816	519	2	26	26	NUM
ejpam-5816	519	3	]	]	PUNCT
ejpam-5816	519	4	t.	t.	NOUN
ejpam-5816	519	5	toplu	toplu	PROPN
ejpam-5816	519	6	,	,	PUNCT
ejpam-5816	519	7	m.	m.	NOUN
ejpam-5816	519	8	kadkal	kadkal	PROPN
ejpam-5816	519	9	,	,	PUNCT
ejpam-5816	519	10	and	and	CCONJ
ejpam-5816	519	11	i̇.	i̇.	VERB
ejpam-5816	519	12	i̇şcan	i̇şcan	PROPN
ejpam-5816	519	13	.	.	PUNCT
ejpam-5816	520	1	on	on	ADP
ejpam-5816	520	2	n	n	CCONJ
ejpam-5816	520	3	-	-	PUNCT
ejpam-5816	520	4	polynomial	polynomial	ADJ
ejpam-5816	520	5	convexity	convexity	NOUN
ejpam-5816	520	6	and	and	CCONJ
ejpam-5816	521	1	some	some	DET
ejpam-5816	521	2	related	related	ADJ
ejpam-5816	521	3	g.	g.	PROPN
ejpam-5816	521	4	rahman	rahman	PROPN
ejpam-5816	521	5	et	et	PROPN
ejpam-5816	521	6	al	al	PROPN
ejpam-5816	521	7	.	.	PUNCT
ejpam-5816	521	8	/	/	SYM
ejpam-5816	521	9	eur	eur	PROPN
ejpam-5816	521	10	.	.	PUNCT
ejpam-5816	522	1	j.	j.	PROPN
ejpam-5816	522	2	pure	pure	PROPN
ejpam-5816	522	3	appl	appl	PROPN
ejpam-5816	522	4	.	.	PROPN
ejpam-5816	522	5	math	math	PROPN
ejpam-5816	522	6	,	,	PUNCT
ejpam-5816	522	7	18	18	NUM
ejpam-5816	522	8	(	(	PUNCT
ejpam-5816	522	9	2	2	NUM
ejpam-5816	522	10	)	)	PUNCT
ejpam-5816	522	11	(	(	PUNCT
ejpam-5816	522	12	2025	2025	NUM
ejpam-5816	522	13	)	)	PUNCT
ejpam-5816	522	14	,	,	PUNCT
ejpam-5816	522	15	5816	5816	NUM
ejpam-5816	522	16	18	18	NUM
ejpam-5816	522	17	of	of	ADP
ejpam-5816	522	18	18	18	NUM
ejpam-5816	522	19	inequalities	inequality	NOUN
ejpam-5816	522	20	.	.	PUNCT
ejpam-5816	523	1	aims	aim	VERB
ejpam-5816	523	2	mathematics	mathematic	NOUN
ejpam-5816	523	3	,	,	PUNCT
ejpam-5816	523	4	5:1304–1318	5:1304–1318	NUM
ejpam-5816	523	5	,	,	PUNCT
ejpam-5816	523	6	2020	2020	NUM
ejpam-5816	523	7	.	.	PUNCT
ejpam-5816	524	1	[	[	X
ejpam-5816	524	2	27	27	NUM
ejpam-5816	524	3	]	]	PUNCT
ejpam-5816	524	4	m.	m.	NOUN
ejpam-5816	524	5	kadkal	kadkal	NOUN
ejpam-5816	524	6	and	and	CCONJ
ejpam-5816	524	7	i̇.	i̇.	ADJ
ejpam-5816	524	8	i̇şcan	i̇şcan	PROPN
ejpam-5816	524	9	.	.	PUNCT
ejpam-5816	525	1	exponential	exponential	ADJ
ejpam-5816	525	2	type	type	NOUN
ejpam-5816	525	3	convexity	convexity	NOUN
ejpam-5816	525	4	and	and	CCONJ
ejpam-5816	525	5	some	some	DET
ejpam-5816	525	6	related	related	ADJ
ejpam-5816	525	7	inequalities	inequality	NOUN
ejpam-5816	525	8	.	.	PUNCT
ejpam-5816	526	1	journal	journal	PROPN
ejpam-5816	526	2	of	of	ADP
ejpam-5816	526	3	inequalities	inequality	NOUN
ejpam-5816	526	4	and	and	CCONJ
ejpam-5816	526	5	applications	application	NOUN
ejpam-5816	526	6	,	,	PUNCT
ejpam-5816	526	7	2009:82	2009:82	NUM
ejpam-5816	526	8	,	,	PUNCT
ejpam-5816	526	9	2020	2020	NUM
ejpam-5816	526	10	.	.	PUNCT
ejpam-5816	527	1	[	[	X
ejpam-5816	527	2	28	28	NUM
ejpam-5816	527	3	]	]	X
ejpam-5816	527	4	s.	s.	PROPN
ejpam-5816	527	5	i.	i.	PROPN
ejpam-5816	527	6	butt	butt	PROPN
ejpam-5816	527	7	,	,	PUNCT
ejpam-5816	527	8	m.	m.	NOUN
ejpam-5816	527	9	tariq	tariq	PROPN
ejpam-5816	527	10	,	,	PUNCT
ejpam-5816	527	11	a.	a.	PROPN
ejpam-5816	527	12	aslam	aslam	PROPN
ejpam-5816	527	13	,	,	PUNCT
ejpam-5816	527	14	h.	h.	PROPN
ejpam-5816	527	15	ahmad	ahmad	PROPN
ejpam-5816	527	16	,	,	PUNCT
ejpam-5816	527	17	and	and	CCONJ
ejpam-5816	527	18	t.	t.	PROPN
ejpam-5816	527	19	a.	a.	PROPN
ejpam-5816	527	20	nofel	nofel	PROPN
ejpam-5816	527	21	.	.	PUNCT
ejpam-5816	528	1	hermite	hermite	PROPN
ejpam-5816	528	2	–	–	PUNCT
ejpam-5816	528	3	hadamard	hadamard	ADJ
ejpam-5816	528	4	type	type	NOUN
ejpam-5816	528	5	inequalities	inequality	NOUN
ejpam-5816	528	6	via	via	ADP
ejpam-5816	528	7	generalized	generalized	ADJ
ejpam-5816	528	8	harmonic	harmonic	ADJ
ejpam-5816	528	9	exponential	exponential	ADJ
ejpam-5816	528	10	convexity	convexity	NOUN
ejpam-5816	528	11	.	.	PUNCT
ejpam-5816	529	1	journal	journal	NOUN
ejpam-5816	529	2	of	of	ADP
ejpam-5816	529	3	function	function	NOUN
ejpam-5816	529	4	spaces	space	NOUN
ejpam-5816	529	5	,	,	PUNCT
ejpam-5816	529	6	2021:5533491	2021:5533491	NUM
ejpam-5816	529	7	,	,	PUNCT
ejpam-5816	529	8	2021	2021	NUM
ejpam-5816	529	9	.	.	PUNCT
ejpam-5816	530	1	[	[	X
ejpam-5816	530	2	29	29	NUM
ejpam-5816	530	3	]	]	PUNCT
ejpam-5816	530	4	m.	m.	NOUN
ejpam-5816	530	5	tariq	tariq	PROPN
ejpam-5816	530	6	.	.	PUNCT
ejpam-5816	531	1	new	new	ADJ
ejpam-5816	531	2	hermite	hermite	ADJ
ejpam-5816	531	3	–	–	PUNCT
ejpam-5816	531	4	hadamard	hadamard	ADJ
ejpam-5816	531	5	type	type	NOUN
ejpam-5816	531	6	inequalities	inequality	NOUN
ejpam-5816	531	7	via	via	ADP
ejpam-5816	531	8	p	p	ADJ
ejpam-5816	531	9	-	-	PUNCT
ejpam-5816	531	10	harmonic	harmonic	ADJ
ejpam-5816	531	11	exponential	exponential	ADJ
ejpam-5816	531	12	type	type	NOUN
ejpam-5816	531	13	convexity	convexity	NOUN
ejpam-5816	531	14	and	and	CCONJ
ejpam-5816	531	15	applications	application	NOUN
ejpam-5816	531	16	.	.	PUNCT
ejpam-5816	532	1	universal	universal	ADJ
ejpam-5816	532	2	journal	journal	PROPN
ejpam-5816	532	3	of	of	ADP
ejpam-5816	532	4	mathematics	mathematic	NOUN
ejpam-5816	532	5	and	and	CCONJ
ejpam-5816	532	6	applications	application	NOUN
ejpam-5816	532	7	,	,	PUNCT
ejpam-5816	532	8	4:59	4:59	NUM
ejpam-5816	532	9	–	–	PUNCT
ejpam-5816	532	10	69	69	NUM
ejpam-5816	532	11	,	,	PUNCT
ejpam-5816	532	12	2021	2021	NUM
ejpam-5816	532	13	.	.	PUNCT
ejpam-5816	533	1	[	[	X
ejpam-5816	533	2	30	30	NUM
ejpam-5816	533	3	]	]	X
ejpam-5816	533	4	d.	d.	PROPN
ejpam-5816	533	5	s.	s.	PROPN
ejpam-5816	533	6	mitrinović	mitrinović	PROPN
ejpam-5816	533	7	,	,	PUNCT
ejpam-5816	533	8	j.	j.	PROPN
ejpam-5816	533	9	pečarić	pečarić	PROPN
ejpam-5816	533	10	,	,	PUNCT
ejpam-5816	533	11	and	and	CCONJ
ejpam-5816	533	12	a.	a.	NOUN
ejpam-5816	533	13	m.	m.	NOUN
ejpam-5816	533	14	fink	fink	PROPN
ejpam-5816	533	15	.	.	PUNCT
ejpam-5816	534	1	inequalities	inequality	NOUN
ejpam-5816	534	2	involving	involve	VERB
ejpam-5816	534	3	functions	function	NOUN
ejpam-5816	534	4	and	and	CCONJ
ejpam-5816	534	5	their	their	PRON
ejpam-5816	534	6	integrals	integral	NOUN
ejpam-5816	534	7	and	and	CCONJ
ejpam-5816	534	8	derivatives	derivative	NOUN
ejpam-5816	534	9	,	,	PUNCT
ejpam-5816	534	10	volume	volume	NOUN
ejpam-5816	534	11	53	53	NUM
ejpam-5816	534	12	.	.	PUNCT
ejpam-5816	535	1	springer	springer	NOUN
ejpam-5816	535	2	science	science	NOUN
ejpam-5816	535	3	and	and	CCONJ
ejpam-5816	535	4	business	business	NOUN
ejpam-5816	535	5	media	medium	NOUN
ejpam-5816	535	6	,	,	PUNCT
ejpam-5816	535	7	dordrecht	dordrecht	PROPN
ejpam-5816	535	8	,	,	PUNCT
ejpam-5816	535	9	the	the	DET
ejpam-5816	535	10	netherlands	netherlands	PROPN
ejpam-5816	535	11	,	,	PUNCT
ejpam-5816	535	12	2012	2012	NUM
ejpam-5816	535	13	.	.	PUNCT
ejpam-5816	536	1	[	[	X
ejpam-5816	536	2	31	31	NUM
ejpam-5816	536	3	]	]	PUNCT
ejpam-5816	536	4	s.	s.	PROPN
ejpam-5816	536	5	s.	s.	PROPN
ejpam-5816	536	6	dragomir	dragomir	PROPN
ejpam-5816	536	7	and	and	CCONJ
ejpam-5816	536	8	s.	s.	PROPN
ejpam-5816	536	9	wang	wang	PROPN
ejpam-5816	536	10	.	.	PUNCT
ejpam-5816	537	1	a	a	DET
ejpam-5816	537	2	new	new	ADJ
ejpam-5816	537	3	inequality	inequality	NOUN
ejpam-5816	537	4	of	of	ADP
ejpam-5816	537	5	ostrowski	ostrowski	ADJ
ejpam-5816	537	6	type	type	NOUN
ejpam-5816	537	7	in	in	ADP
ejpam-5816	537	8	l1	l1	PROPN
ejpam-5816	537	9	norm	norm	NOUN
ejpam-5816	537	10	and	and	CCONJ
ejpam-5816	537	11	applications	application	NOUN
ejpam-5816	537	12	to	to	ADP
ejpam-5816	537	13	some	some	DET
ejpam-5816	537	14	special	special	ADJ
ejpam-5816	537	15	means	mean	NOUN
ejpam-5816	537	16	and	and	CCONJ
ejpam-5816	537	17	to	to	ADP
ejpam-5816	537	18	some	some	DET
ejpam-5816	537	19	numerical	numerical	ADJ
ejpam-5816	537	20	quadrature	quadrature	NOUN
ejpam-5816	537	21	rules	rule	NOUN
ejpam-5816	537	22	.	.	PUNCT
ejpam-5816	538	1	tamkang	tamkang	PROPN
ejpam-5816	538	2	journal	journal	PROPN
ejpam-5816	538	3	of	of	ADP
ejpam-5816	538	4	mathematics	mathematics	PROPN
ejpam-5816	538	5	,	,	PUNCT
ejpam-5816	538	6	28:239–244	28:239–244	NUM
ejpam-5816	538	7	,	,	PUNCT
ejpam-5816	538	8	1997	1997	NUM
ejpam-5816	538	9	.	.	PUNCT
ejpam-5816	539	1	[	[	X
ejpam-5816	539	2	32	32	NUM
ejpam-5816	539	3	]	]	PUNCT
ejpam-5816	539	4	s.	s.	PROPN
ejpam-5816	539	5	s.	s.	PROPN
ejpam-5816	539	6	dragomir	dragomir	PROPN
ejpam-5816	539	7	and	and	CCONJ
ejpam-5816	539	8	s.	s.	PROPN
ejpam-5816	539	9	wang	wang	PROPN
ejpam-5816	539	10	.	.	PUNCT
ejpam-5816	540	1	applications	application	NOUN
ejpam-5816	540	2	of	of	ADP
ejpam-5816	540	3	ostrowski	ostrowski	NOUN
ejpam-5816	540	4	’s	’s	PART
ejpam-5816	540	5	inequality	inequality	NOUN
ejpam-5816	540	6	to	to	ADP
ejpam-5816	540	7	the	the	DET
ejpam-5816	540	8	estimation	estimation	NOUN
ejpam-5816	540	9	of	of	ADP
ejpam-5816	540	10	error	error	NOUN
ejpam-5816	540	11	bounds	bound	NOUN
ejpam-5816	540	12	for	for	ADP
ejpam-5816	540	13	some	some	DET
ejpam-5816	540	14	special	special	ADJ
ejpam-5816	540	15	means	mean	NOUN
ejpam-5816	540	16	and	and	CCONJ
ejpam-5816	540	17	for	for	ADP
ejpam-5816	540	18	some	some	DET
ejpam-5816	540	19	numerical	numerical	ADJ
ejpam-5816	540	20	quadrature	quadrature	NOUN
ejpam-5816	540	21	rules	rule	NOUN
ejpam-5816	540	22	.	.	PUNCT
ejpam-5816	541	1	applied	apply	VERB
ejpam-5816	541	2	mathematics	mathematics	NOUN
ejpam-5816	541	3	letters	letter	NOUN
ejpam-5816	541	4	,	,	PUNCT
ejpam-5816	541	5	11:105–109	11:105–109	NUM
ejpam-5816	541	6	,	,	PUNCT
ejpam-5816	541	7	1998	1998	NUM
ejpam-5816	541	8	.	.	PUNCT
ejpam-5816	542	1	[	[	X
ejpam-5816	542	2	33	33	NUM
ejpam-5816	542	3	]	]	X
ejpam-5816	542	4	n.	n.	PROPN
ejpam-5816	542	5	s.	s.	PROPN
ejpam-5816	542	6	barnett	barnett	PROPN
ejpam-5816	542	7	and	and	CCONJ
ejpam-5816	542	8	s.	s.	PROPN
ejpam-5816	542	9	s.	s.	PROPN
ejpam-5816	542	10	dragomir	dragomir	PROPN
ejpam-5816	542	11	.	.	PUNCT
ejpam-5816	543	1	an	an	DET
ejpam-5816	543	2	ostrowski	ostrowski	ADJ
ejpam-5816	543	3	type	type	NOUN
ejpam-5816	543	4	inequality	inequality	NOUN
ejpam-5816	543	5	for	for	ADP
ejpam-5816	543	6	double	double	ADJ
ejpam-5816	543	7	integrals	integral	NOUN
ejpam-5816	543	8	and	and	CCONJ
ejpam-5816	543	9	applications	application	NOUN
ejpam-5816	543	10	for	for	ADP
ejpam-5816	543	11	cubature	cubature	ADJ
ejpam-5816	543	12	formulae	formulae	NOUN
ejpam-5816	543	13	.	.	PUNCT
ejpam-5816	544	1	soochow	soochow	PROPN
ejpam-5816	544	2	journal	journal	PROPN
ejpam-5816	544	3	of	of	ADP
ejpam-5816	544	4	mathematics	mathematic	NOUN
ejpam-5816	544	5	,	,	PUNCT
ejpam-5816	544	6	27:109–114	27:109–114	NUM
ejpam-5816	544	7	,	,	PUNCT
ejpam-5816	544	8	2001	2001	NUM
ejpam-5816	544	9	.	.	PUNCT
ejpam-5816	545	1	[	[	X
ejpam-5816	545	2	34	34	NUM
ejpam-5816	545	3	]	]	PUNCT
ejpam-5816	545	4	p.	p.	NOUN
ejpam-5816	545	5	cerone	cerone	NOUN
ejpam-5816	545	6	,	,	PUNCT
ejpam-5816	545	7	s.	s.	PROPN
ejpam-5816	545	8	s.	s.	PROPN
ejpam-5816	545	9	dragomir	dragomir	PROPN
ejpam-5816	545	10	,	,	PUNCT
ejpam-5816	545	11	and	and	CCONJ
ejpam-5816	545	12	j.	j.	PROPN
ejpam-5816	545	13	roumeliotis	roumeliotis	PROPN
ejpam-5816	545	14	.	.	PUNCT
ejpam-5816	546	1	an	an	DET
ejpam-5816	546	2	inequality	inequality	NOUN
ejpam-5816	546	3	of	of	ADP
ejpam-5816	546	4	ostrowski	ostrowski	ADJ
ejpam-5816	546	5	type	type	NOUN
ejpam-5816	546	6	for	for	ADP
ejpam-5816	546	7	mappings	mapping	NOUN
ejpam-5816	546	8	whose	whose	DET
ejpam-5816	546	9	second	second	ADJ
ejpam-5816	546	10	derivatives	derivative	NOUN
ejpam-5816	546	11	are	be	AUX
ejpam-5816	546	12	bounded	bound	VERB
ejpam-5816	546	13	and	and	CCONJ
ejpam-5816	546	14	applications	application	NOUN
ejpam-5816	546	15	.	.	PUNCT
ejpam-5816	547	1	east	east	PROPN
ejpam-5816	547	2	asian	asian	PROPN
ejpam-5816	547	3	mathematical	mathematical	ADJ
ejpam-5816	547	4	journal	journal	NOUN
ejpam-5816	547	5	,	,	PUNCT
ejpam-5816	547	6	15:1–9	15:1–9	NUM
ejpam-5816	547	7	,	,	PUNCT
ejpam-5816	547	8	1999	1999	NUM
ejpam-5816	547	9	.	.	PUNCT
ejpam-5816	548	1	[	[	X
ejpam-5816	548	2	35	35	NUM
ejpam-5816	548	3	]	]	PUNCT
ejpam-5816	548	4	z.	z.	PROPN
ejpam-5816	548	5	retkes	retkes	PROPN
ejpam-5816	548	6	.	.	PUNCT
ejpam-5816	549	1	an	an	DET
ejpam-5816	549	2	extension	extension	NOUN
ejpam-5816	549	3	of	of	ADP
ejpam-5816	549	4	the	the	DET
ejpam-5816	549	5	hermite	hermite	ADJ
ejpam-5816	549	6	–	–	PUNCT
ejpam-5816	549	7	hadamard	hadamard	ADJ
ejpam-5816	549	8	inequality	inequality	NOUN
ejpam-5816	549	9	.	.	PUNCT
ejpam-5816	550	1	acta	acta	PROPN
ejpam-5816	550	2	scientiarum	scientiarum	PROPN
ejpam-5816	550	3	mathematicarum	mathematicarum	PROPN
ejpam-5816	550	4	(	(	PUNCT
ejpam-5816	550	5	szeged	szeged	PROPN
ejpam-5816	550	6	)	)	PUNCT
ejpam-5816	550	7	,	,	PUNCT
ejpam-5816	550	8	74(1):95–106	74(1):95–106	NUM
ejpam-5816	550	9	,	,	PUNCT
ejpam-5816	550	10	2008	2008	NUM
ejpam-5816	550	11	.	.	PUNCT
ejpam-5816	551	1	[	[	X
ejpam-5816	551	2	36	36	NUM
ejpam-5816	551	3	]	]	PUNCT
ejpam-5816	551	4	k.	k.	PROPN
ejpam-5816	551	5	m.	m.	NOUN
ejpam-5816	551	6	owolabi	owolabi	NOUN
ejpam-5816	551	7	.	.	PUNCT
ejpam-5816	552	1	modelling	modelling	NOUN
ejpam-5816	552	2	and	and	CCONJ
ejpam-5816	552	3	simulation	simulation	NOUN
ejpam-5816	552	4	of	of	ADP
ejpam-5816	552	5	a	a	DET
ejpam-5816	552	6	dynamical	dynamical	ADJ
ejpam-5816	552	7	system	system	NOUN
ejpam-5816	552	8	with	with	ADP
ejpam-5816	552	9	the	the	DET
ejpam-5816	552	10	atangana	atangana	PROPN
ejpam-5816	552	11	–	–	PUNCT
ejpam-5816	552	12	baleanu	baleanu	ADJ
ejpam-5816	552	13	fractional	fractional	ADJ
ejpam-5816	552	14	derivative	derivative	NOUN
ejpam-5816	552	15	.	.	PUNCT
ejpam-5816	553	1	european	european	PROPN
ejpam-5816	553	2	physical	physical	PROPN
ejpam-5816	553	3	journal	journal	PROPN
ejpam-5816	553	4	plus	plus	CCONJ
ejpam-5816	553	5	,	,	PUNCT
ejpam-5816	553	6	133(1):15	133(1):15	NUM
ejpam-5816	553	7	,	,	PUNCT
ejpam-5816	553	8	2018	2018	NUM
ejpam-5816	553	9	.	.	PUNCT
ejpam-5816	554	1	[	[	X
ejpam-5816	554	2	37	37	NUM
ejpam-5816	554	3	]	]	X
ejpam-5816	554	4	d.	d.	PROPN
ejpam-5816	554	5	kumar	kumar	PROPN
ejpam-5816	554	6	,	,	PUNCT
ejpam-5816	554	7	j.	j.	PROPN
ejpam-5816	554	8	singh	singh	PROPN
ejpam-5816	554	9	,	,	PUNCT
ejpam-5816	554	10	and	and	CCONJ
ejpam-5816	554	11	d.	d.	PROPN
ejpam-5816	554	12	baleanu	baleanu	PROPN
ejpam-5816	554	13	.	.	PUNCT
ejpam-5816	555	1	analysis	analysis	NOUN
ejpam-5816	555	2	of	of	ADP
ejpam-5816	555	3	regularized	regularize	VERB
ejpam-5816	555	4	long	long	ADJ
ejpam-5816	555	5	-	-	PUNCT
ejpam-5816	555	6	wave	wave	NOUN
ejpam-5816	555	7	equation	equation	NOUN
ejpam-5816	555	8	associated	associate	VERB
ejpam-5816	555	9	with	with	ADP
ejpam-5816	555	10	a	a	DET
ejpam-5816	555	11	new	new	ADJ
ejpam-5816	555	12	fractional	fractional	ADJ
ejpam-5816	555	13	operator	operator	NOUN
ejpam-5816	555	14	with	with	ADP
ejpam-5816	555	15	mittag	mittag	ADJ
ejpam-5816	555	16	-	-	PUNCT
ejpam-5816	555	17	leffler	leffler	NOUN
ejpam-5816	555	18	type	type	NOUN
ejpam-5816	555	19	kernel	kernel	NOUN
ejpam-5816	555	20	.	.	PUNCT
ejpam-5816	556	1	physica	physica	PROPN
ejpam-5816	556	2	a	a	DET
ejpam-5816	556	3	:	:	PUNCT
ejpam-5816	556	4	statistical	statistical	ADJ
ejpam-5816	556	5	mechanics	mechanic	NOUN
ejpam-5816	556	6	and	and	CCONJ
ejpam-5816	556	7	its	its	PRON
ejpam-5816	556	8	applications	application	NOUN
ejpam-5816	556	9	,	,	PUNCT
ejpam-5816	556	10	492:155–167	492:155–167	NUM
ejpam-5816	556	11	,	,	PUNCT
ejpam-5816	556	12	2018	2018	NUM
ejpam-5816	556	13	.	.	PUNCT
ejpam-5816	557	1	[	[	X
ejpam-5816	557	2	38	38	NUM
ejpam-5816	557	3	]	]	PUNCT
ejpam-5816	557	4	z.	z.	PROPN
ejpam-5816	557	5	jianke	jianke	PROPN
ejpam-5816	557	6	,	,	PUNCT
ejpam-5816	557	7	w.	w.	PROPN
ejpam-5816	557	8	gaofeng	gaofeng	PROPN
ejpam-5816	557	9	,	,	PUNCT
ejpam-5816	557	10	z.	z.	PROPN
ejpam-5816	557	11	xiaobin	xiaobin	PROPN
ejpam-5816	557	12	,	,	PUNCT
ejpam-5816	557	13	and	and	CCONJ
ejpam-5816	557	14	z.	z.	PROPN
ejpam-5816	557	15	chang	chang	PROPN
ejpam-5816	557	16	.	.	PUNCT
ejpam-5816	558	1	generalized	generalize	VERB
ejpam-5816	558	2	euler	euler	PROPN
ejpam-5816	558	3	–	–	PUNCT
ejpam-5816	558	4	lagrange	lagrange	NOUN
ejpam-5816	558	5	equations	equation	NOUN
ejpam-5816	558	6	for	for	ADP
ejpam-5816	558	7	fuzzy	fuzzy	ADJ
ejpam-5816	558	8	fractional	fractional	ADJ
ejpam-5816	558	9	variational	variational	ADJ
ejpam-5816	558	10	problems	problem	NOUN
ejpam-5816	558	11	under	under	ADP
ejpam-5816	558	12	gh	gh	PROPN
ejpam-5816	558	13	-	-	PUNCT
ejpam-5816	558	14	atangana	atangana	PROPN
ejpam-5816	558	15	–	–	PUNCT
ejpam-5816	558	16	baleanu	baleanu	PROPN
ejpam-5816	558	17	differentiability	differentiability	PROPN
ejpam-5816	558	18	.	.	PUNCT
ejpam-5816	558	19	journal	journal	PROPN
ejpam-5816	558	20	of	of	ADP
ejpam-5816	558	21	function	function	NOUN
ejpam-5816	558	22	spaces	space	NOUN
ejpam-5816	558	23	,	,	PUNCT
ejpam-5816	558	24	2018:2740678	2018:2740678	NUM
ejpam-5816	558	25	,	,	PUNCT
ejpam-5816	558	26	2018	2018	NUM
ejpam-5816	558	27	.	.	PUNCT
ejpam-5816	559	1	[	[	X
ejpam-5816	559	2	39	39	NUM
ejpam-5816	559	3	]	]	PUNCT
ejpam-5816	559	4	k.	k.	PROPN
ejpam-5816	559	5	hattaf	hattaf	PROPN
ejpam-5816	559	6	.	.	PUNCT
ejpam-5816	560	1	a	a	DET
ejpam-5816	560	2	new	new	ADJ
ejpam-5816	560	3	generalized	generalized	ADJ
ejpam-5816	560	4	definition	definition	NOUN
ejpam-5816	560	5	of	of	ADP
ejpam-5816	560	6	fractional	fractional	ADJ
ejpam-5816	560	7	derivative	derivative	NOUN
ejpam-5816	560	8	with	with	ADP
ejpam-5816	560	9	non	non	ADJ
ejpam-5816	560	10	-	-	ADJ
ejpam-5816	560	11	singular	singular	ADJ
ejpam-5816	560	12	kernel	kernel	NOUN
ejpam-5816	560	13	.	.	PUNCT
ejpam-5816	561	1	computation	computation	NOUN
ejpam-5816	561	2	,	,	PUNCT
ejpam-5816	561	3	8:49	8:49	NUM
ejpam-5816	561	4	,	,	PUNCT
ejpam-5816	561	5	2020	2020	NUM
ejpam-5816	561	6	.	.	PUNCT
ejpam-5816	562	1	[	[	X
ejpam-5816	562	2	40	40	NUM
ejpam-5816	562	3	]	]	PUNCT
ejpam-5816	562	4	h.	h.	PROPN
ejpam-5816	562	5	ahmad	ahmad	PROPN
ejpam-5816	562	6	,	,	PUNCT
ejpam-5816	562	7	m.	m.	NOUN
ejpam-5816	562	8	tariq	tariq	PROPN
ejpam-5816	562	9	,	,	PUNCT
ejpam-5816	562	10	s.	s.	PROPN
ejpam-5816	562	11	k.	k.	PROPN
ejpam-5816	562	12	sahoo	sahoo	PROPN
ejpam-5816	562	13	,	,	PUNCT
ejpam-5816	562	14	s.	s.	PROPN
ejpam-5816	562	15	askar	askar	PROPN
ejpam-5816	562	16	,	,	PUNCT
ejpam-5816	562	17	a.	a.	PROPN
ejpam-5816	562	18	e.	e.	PROPN
ejpam-5816	562	19	abouelregal	abouelregal	PROPN
ejpam-5816	562	20	,	,	PUNCT
ejpam-5816	562	21	and	and	CCONJ
ejpam-5816	562	22	k.	k.	PROPN
ejpam-5816	562	23	m.	m.	PROPN
ejpam-5816	562	24	khedher	khedher	PROPN
ejpam-5816	562	25	.	.	PUNCT
ejpam-5816	563	1	refinements	refinement	NOUN
ejpam-5816	563	2	of	of	ADP
ejpam-5816	563	3	ostrowski	ostrowski	ADJ
ejpam-5816	563	4	type	type	NOUN
ejpam-5816	563	5	integral	integral	ADJ
ejpam-5816	563	6	inequalities	inequality	NOUN
ejpam-5816	563	7	involving	involve	VERB
ejpam-5816	563	8	atangana	atangana	PROPN
ejpam-5816	563	9	–	–	PUNCT
ejpam-5816	563	10	baleanu	baleanu	ADJ
ejpam-5816	563	11	fractional	fractional	ADJ
ejpam-5816	563	12	integral	integral	ADJ
ejpam-5816	563	13	operator	operator	NOUN
ejpam-5816	563	14	.	.	PUNCT
ejpam-5816	563	15	symmetry	symmetry	PROPN
ejpam-5816	563	16	,	,	PUNCT
ejpam-5816	563	17	13:2059	13:2059	NUM
ejpam-5816	563	18	,	,	PUNCT
ejpam-5816	563	19	2021	2021	NUM
ejpam-5816	563	20	.	.	PUNCT