id	sid	tid	token	lemma	pos
ejpam-5834	1	1	european	european	PROPN
ejpam-5834	1	2	journal	journal	PROPN
ejpam-5834	1	3	of	of	ADP
ejpam-5834	1	4	pure	pure	ADJ
ejpam-5834	1	5	and	and	CCONJ
ejpam-5834	1	6	applied	applied	ADJ
ejpam-5834	1	7	mathematics	mathematic	NOUN
ejpam-5834	1	8	2025	2025	NUM
ejpam-5834	1	9	,	,	PUNCT
ejpam-5834	1	10	vol	vol	NOUN
ejpam-5834	1	11	.	.	PROPN
ejpam-5834	1	12	18	18	NUM
ejpam-5834	1	13	,	,	PUNCT
ejpam-5834	1	14	issue	issue	NOUN
ejpam-5834	1	15	1	1	NUM
ejpam-5834	1	16	,	,	PUNCT
ejpam-5834	1	17	article	article	NOUN
ejpam-5834	1	18	number	number	NOUN
ejpam-5834	1	19	5834	5834	NUM
ejpam-5834	1	20	issn	issn	VERB
ejpam-5834	1	21	1307	1307	NUM
ejpam-5834	1	22	-	-	SYM
ejpam-5834	1	23	5543	5543	NUM
ejpam-5834	1	24	–	–	PUNCT
ejpam-5834	1	25	ejpam.com	ejpam.com	X
ejpam-5834	1	26	published	publish	VERB
ejpam-5834	1	27	by	by	ADP
ejpam-5834	1	28	new	new	PROPN
ejpam-5834	1	29	york	york	PROPN
ejpam-5834	1	30	business	business	PROPN
ejpam-5834	1	31	global	global	ADJ
ejpam-5834	1	32	new	new	ADJ
ejpam-5834	1	33	inequalities	inequality	NOUN
ejpam-5834	1	34	for	for	ADP
ejpam-5834	1	35	differentiable	differentiable	ADJ
ejpam-5834	1	36	mappings	mapping	NOUN
ejpam-5834	1	37	via	via	ADP
ejpam-5834	1	38	fractional	fractional	ADJ
ejpam-5834	1	39	integral	integral	ADJ
ejpam-5834	1	40	operators	operator	NOUN
ejpam-5834	1	41	ohud	ohud	ADV
ejpam-5834	1	42	bulayhan	bulayhan	PROPN
ejpam-5834	1	43	almutairi	almutairi	PROPN
ejpam-5834	1	44	department	department	PROPN
ejpam-5834	1	45	of	of	ADP
ejpam-5834	1	46	mathematics	mathematics	PROPN
ejpam-5834	1	47	,	,	PUNCT
ejpam-5834	1	48	university	university	NOUN
ejpam-5834	1	49	of	of	ADP
ejpam-5834	1	50	hafr	hafr	PROPN
ejpam-5834	1	51	al	al	PROPN
ejpam-5834	1	52	batin	batin	PROPN
ejpam-5834	1	53	,	,	PUNCT
ejpam-5834	1	54	hafr	hafr	PROPN
ejpam-5834	1	55	al	al	PROPN
ejpam-5834	1	56	batin	batin	PROPN
ejpam-5834	1	57	31991	31991	NUM
ejpam-5834	1	58	,	,	PUNCT
ejpam-5834	1	59	saudi	saudi	PROPN
ejpam-5834	1	60	arabia	arabia	PROPN
ejpam-5834	1	61	abstract	abstract	NOUN
ejpam-5834	1	62	.	.	PUNCT
ejpam-5834	2	1	in	in	ADP
ejpam-5834	2	2	this	this	DET
ejpam-5834	2	3	study	study	NOUN
ejpam-5834	2	4	,	,	PUNCT
ejpam-5834	2	5	explicit	explicit	ADJ
ejpam-5834	2	6	bounds	bound	NOUN
ejpam-5834	2	7	for	for	ADP
ejpam-5834	2	8	the	the	DET
ejpam-5834	2	9	midpoint	midpoint	NOUN
ejpam-5834	2	10	type	type	NOUN
ejpam-5834	2	11	inequalities	inequality	NOUN
ejpam-5834	2	12	for	for	ADP
ejpam-5834	2	13	functions	function	NOUN
ejpam-5834	2	14	whose	whose	DET
ejpam-5834	2	15	twice	twice	ADV
ejpam-5834	2	16	differentiable	differentiable	ADJ
ejpam-5834	2	17	in	in	ADP
ejpam-5834	2	18	absolute	absolute	ADJ
ejpam-5834	2	19	value	value	NOUN
ejpam-5834	2	20	raised	raise	VERB
ejpam-5834	2	21	to	to	ADP
ejpam-5834	2	22	positive	positive	ADJ
ejpam-5834	2	23	real	real	ADJ
ejpam-5834	2	24	powers	power	NOUN
ejpam-5834	2	25	are	be	AUX
ejpam-5834	2	26	(	(	PUNCT
ejpam-5834	2	27	ρ	ρ	PROPN
ejpam-5834	2	28	,	,	PUNCT
ejpam-5834	2	29	s	s	PART
ejpam-5834	2	30	)	)	PUNCT
ejpam-5834	2	31	and	and	CCONJ
ejpam-5834	2	32	(	(	PUNCT
ejpam-5834	2	33	ρ	ρ	PROPN
ejpam-5834	2	34	,	,	PUNCT
ejpam-5834	2	35	s	s	PART
ejpam-5834	2	36	,	,	PUNCT
ejpam-5834	2	37	m)convexities	m)convexitie	NOUN
ejpam-5834	2	38	are	be	AUX
ejpam-5834	2	39	explored	explore	VERB
ejpam-5834	2	40	through	through	ADP
ejpam-5834	2	41	the	the	DET
ejpam-5834	2	42	integral	integral	ADJ
ejpam-5834	2	43	fractional	fractional	ADJ
ejpam-5834	2	44	operator	operator	NOUN
ejpam-5834	2	45	.	.	PUNCT
ejpam-5834	3	1	several	several	ADJ
ejpam-5834	3	2	estimate	estimate	NOUN
ejpam-5834	3	3	for	for	ADP
ejpam-5834	3	4	special	special	ADJ
ejpam-5834	3	5	functions	function	NOUN
ejpam-5834	3	6	including	include	VERB
ejpam-5834	3	7	euler	euler	PROPN
ejpam-5834	3	8	gamma	gamma	PROPN
ejpam-5834	3	9	,	,	PUNCT
ejpam-5834	3	10	incomplete	incomplete	ADJ
ejpam-5834	3	11	beta	beta	NOUN
ejpam-5834	3	12	and	and	CCONJ
ejpam-5834	3	13	hypergeometric	hypergeometric	ADJ
ejpam-5834	3	14	functions	function	NOUN
ejpam-5834	3	15	are	be	AUX
ejpam-5834	3	16	presented	present	VERB
ejpam-5834	3	17	in	in	ADP
ejpam-5834	3	18	the	the	DET
ejpam-5834	3	19	study	study	NOUN
ejpam-5834	3	20	.	.	PUNCT
ejpam-5834	4	1	2020	2020	NUM
ejpam-5834	4	2	mathematics	mathematic	NOUN
ejpam-5834	4	3	subject	subject	NOUN
ejpam-5834	4	4	classifications	classification	NOUN
ejpam-5834	4	5	:	:	PUNCT
ejpam-5834	4	6	26d10	26d10	NUM
ejpam-5834	4	7	,	,	PUNCT
ejpam-5834	4	8	26a33	26a33	NUM
ejpam-5834	4	9	,	,	PUNCT
ejpam-5834	4	10	33b15	33b15	NOUN
ejpam-5834	4	11	key	key	ADJ
ejpam-5834	4	12	words	word	NOUN
ejpam-5834	4	13	and	and	CCONJ
ejpam-5834	4	14	phrases	phrase	NOUN
ejpam-5834	4	15	:	:	PUNCT
ejpam-5834	4	16	riemann	riemann	PROPN
ejpam-5834	4	17	-	-	PUNCT
ejpam-5834	4	18	liouville	liouville	NOUN
ejpam-5834	4	19	integrals	integral	NOUN
ejpam-5834	4	20	,	,	PUNCT
ejpam-5834	4	21	hölder	hölder	PROPN
ejpam-5834	4	22	’s	’s	PART
ejpam-5834	4	23	inequality	inequality	NOUN
ejpam-5834	4	24	,	,	PUNCT
ejpam-5834	4	25	integral	integral	ADJ
ejpam-5834	4	26	inequality	inequality	NOUN
ejpam-5834	4	27	,	,	PUNCT
ejpam-5834	4	28	(	(	PUNCT
ejpam-5834	4	29	ρ	ρ	PROPN
ejpam-5834	4	30	,	,	PUNCT
ejpam-5834	4	31	s	s	PROPN
ejpam-5834	4	32	,	,	PUNCT
ejpam-5834	4	33	m)-convex	m)-convex	PUNCT
ejpam-5834	4	34	functions	function	NOUN
ejpam-5834	4	35	1	1	NUM
ejpam-5834	4	36	.	.	PUNCT
ejpam-5834	4	37	introduction	introduction	NOUN
ejpam-5834	4	38	fractional	fractional	ADJ
ejpam-5834	4	39	calculus	calculus	NOUN
ejpam-5834	4	40	–	–	PUNCT
ejpam-5834	4	41	whose	whose	DET
ejpam-5834	4	42	impact	impact	NOUN
ejpam-5834	4	43	on	on	ADP
ejpam-5834	4	44	both	both	CCONJ
ejpam-5834	4	45	pure	pure	ADJ
ejpam-5834	4	46	and	and	CCONJ
ejpam-5834	4	47	applied	applied	ADJ
ejpam-5834	4	48	sciences	science	NOUN
ejpam-5834	4	49	substantially	substantially	ADV
ejpam-5834	4	50	increased	increase	VERB
ejpam-5834	4	51	in	in	ADP
ejpam-5834	4	52	the	the	DET
ejpam-5834	4	53	last	last	ADJ
ejpam-5834	4	54	two	two	NUM
ejpam-5834	4	55	decades	decade	NOUN
ejpam-5834	4	56	–	–	PUNCT
ejpam-5834	4	57	captures	capture	VERB
ejpam-5834	4	58	the	the	DET
ejpam-5834	4	59	attention	attention	NOUN
ejpam-5834	4	60	of	of	ADP
ejpam-5834	4	61	many	many	ADJ
ejpam-5834	4	62	researchers	researcher	NOUN
ejpam-5834	4	63	.	.	PUNCT
ejpam-5834	5	1	in	in	ADP
ejpam-5834	5	2	addition	addition	NOUN
ejpam-5834	5	3	,	,	PUNCT
ejpam-5834	5	4	this	this	DET
ejpam-5834	5	5	area	area	NOUN
ejpam-5834	5	6	of	of	ADP
ejpam-5834	5	7	interest	interest	NOUN
ejpam-5834	5	8	invariably	invariably	ADV
ejpam-5834	5	9	remains	remain	VERB
ejpam-5834	5	10	one	one	NUM
ejpam-5834	5	11	of	of	ADP
ejpam-5834	5	12	the	the	DET
ejpam-5834	5	13	few	few	ADJ
ejpam-5834	5	14	disciplines	discipline	NOUN
ejpam-5834	5	15	that	that	PRON
ejpam-5834	5	16	immensely	immensely	ADV
ejpam-5834	5	17	contribute	contribute	VERB
ejpam-5834	5	18	to	to	ADP
ejpam-5834	5	19	not	not	PART
ejpam-5834	5	20	only	only	ADV
ejpam-5834	5	21	different	different	ADJ
ejpam-5834	5	22	areas	area	NOUN
ejpam-5834	5	23	of	of	ADP
ejpam-5834	5	24	mathematics	mathematic	NOUN
ejpam-5834	5	25	,	,	PUNCT
ejpam-5834	5	26	but	but	CCONJ
ejpam-5834	5	27	also	also	ADV
ejpam-5834	5	28	to	to	ADP
ejpam-5834	5	29	other	other	ADJ
ejpam-5834	5	30	natural	natural	ADJ
ejpam-5834	5	31	sciences	science	NOUN
ejpam-5834	5	32	.	.	PUNCT
ejpam-5834	6	1	one	one	NUM
ejpam-5834	6	2	of	of	ADP
ejpam-5834	6	3	such	such	ADJ
ejpam-5834	6	4	examples	example	NOUN
ejpam-5834	6	5	is	be	AUX
ejpam-5834	6	6	associated	associate	VERB
ejpam-5834	6	7	to	to	ADP
ejpam-5834	6	8	the	the	DET
ejpam-5834	6	9	existence	existence	NOUN
ejpam-5834	6	10	of	of	ADP
ejpam-5834	6	11	many	many	ADJ
ejpam-5834	6	12	fractional	fractional	ADJ
ejpam-5834	6	13	operators	operator	NOUN
ejpam-5834	6	14	in	in	ADP
ejpam-5834	6	15	those	those	DET
ejpam-5834	6	16	disciplines	discipline	NOUN
ejpam-5834	6	17	,	,	PUNCT
ejpam-5834	6	18	most	most	ADJ
ejpam-5834	6	19	of	of	ADP
ejpam-5834	6	20	which	which	PRON
ejpam-5834	6	21	occur	occur	VERB
ejpam-5834	6	22	through	through	ADP
ejpam-5834	6	23	different	different	ADJ
ejpam-5834	6	24	formulations	formulation	NOUN
ejpam-5834	6	25	differential	differential	NOUN
ejpam-5834	6	26	equations	equation	NOUN
ejpam-5834	6	27	.	.	PUNCT
ejpam-5834	7	1	this	this	DET
ejpam-5834	7	2	area	area	NOUN
ejpam-5834	7	3	has	have	AUX
ejpam-5834	7	4	been	be	AUX
ejpam-5834	7	5	developed	develop	VERB
ejpam-5834	7	6	through	through	ADP
ejpam-5834	7	7	the	the	DET
ejpam-5834	7	8	contributions	contribution	NOUN
ejpam-5834	7	9	of	of	ADP
ejpam-5834	7	10	many	many	ADJ
ejpam-5834	7	11	researchers	researcher	NOUN
ejpam-5834	7	12	;	;	PUNCT
ejpam-5834	7	13	for	for	ADP
ejpam-5834	7	14	example	example	NOUN
ejpam-5834	7	15	,	,	PUNCT
ejpam-5834	7	16	kilbas	kilbas	PROPN
ejpam-5834	7	17	et	et	PROPN
ejpam-5834	7	18	al	al	PROPN
ejpam-5834	7	19	.	.	PUNCT
ejpam-5834	8	1	[	[	X
ejpam-5834	8	2	9	9	NUM
ejpam-5834	8	3	]	]	PUNCT
ejpam-5834	8	4	gave	give	VERB
ejpam-5834	8	5	the	the	DET
ejpam-5834	8	6	background	background	NOUN
ejpam-5834	8	7	of	of	ADP
ejpam-5834	8	8	fractional	fractional	ADJ
ejpam-5834	8	9	differential	differential	ADJ
ejpam-5834	8	10	equations	equation	NOUN
ejpam-5834	8	11	,	,	PUNCT
ejpam-5834	8	12	xing	xing	PROPN
ejpam-5834	8	13	et	et	PROPN
ejpam-5834	8	14	al	al	PROPN
ejpam-5834	8	15	.	.	PUNCT
ejpam-5834	9	1	[	[	X
ejpam-5834	9	2	22	22	NUM
ejpam-5834	9	3	]	]	PUNCT
ejpam-5834	9	4	extended	extended	ADJ
ejpam-5834	9	5	hermite	hermite	PROPN
ejpam-5834	9	6	-	-	PUNCT
ejpam-5834	9	7	hadamard	hadamard	ADJ
ejpam-5834	9	8	inequalities	inequality	NOUN
ejpam-5834	9	9	using	use	VERB
ejpam-5834	9	10	fractional	fractional	ADJ
ejpam-5834	9	11	integrals	integral	NOUN
ejpam-5834	9	12	,	,	PUNCT
ejpam-5834	9	13	zhang	zhang	PROPN
ejpam-5834	9	14	et	et	PROPN
ejpam-5834	9	15	al.[7	al.[7	PROPN
ejpam-5834	9	16	]	]	PUNCT
ejpam-5834	9	17	generalized	generalize	VERB
ejpam-5834	9	18	the	the	DET
ejpam-5834	9	19	inequalities	inequality	NOUN
ejpam-5834	9	20	for	for	ADP
ejpam-5834	9	21	strongly	strongly	ADV
ejpam-5834	9	22	(	(	PUNCT
ejpam-5834	9	23	s	s	NOUN
ejpam-5834	9	24	,	,	PUNCT
ejpam-5834	9	25	m)-convexities	m)-convexitie	NOUN
ejpam-5834	9	26	,	,	PUNCT
ejpam-5834	9	27	and	and	CCONJ
ejpam-5834	9	28	noor	noor	PROPN
ejpam-5834	9	29	and	and	CCONJ
ejpam-5834	9	30	awan	awan	PROPN
ejpam-5834	10	1	[	[	X
ejpam-5834	10	2	11	11	NUM
ejpam-5834	10	3	]	]	PUNCT
ejpam-5834	10	4	established	establish	VERB
ejpam-5834	10	5	the	the	DET
ejpam-5834	10	6	inequalities	inequality	NOUN
ejpam-5834	10	7	with	with	ADP
ejpam-5834	10	8	two	two	NUM
ejpam-5834	10	9	different	different	ADJ
ejpam-5834	10	10	convexities	convexity	NOUN
ejpam-5834	10	11	.	.	PUNCT
ejpam-5834	11	1	these	these	DET
ejpam-5834	11	2	operators	operator	NOUN
ejpam-5834	11	3	have	have	AUX
ejpam-5834	11	4	been	be	AUX
ejpam-5834	11	5	used	use	VERB
ejpam-5834	11	6	to	to	PART
ejpam-5834	11	7	understand	understand	VERB
ejpam-5834	11	8	many	many	ADJ
ejpam-5834	11	9	problems	problem	NOUN
ejpam-5834	11	10	,	,	PUNCT
ejpam-5834	11	11	such	such	ADJ
ejpam-5834	11	12	as	as	ADP
ejpam-5834	11	13	the	the	DET
ejpam-5834	11	14	propagation	propagation	NOUN
ejpam-5834	11	15	of	of	ADP
ejpam-5834	11	16	sound	sound	NOUN
ejpam-5834	11	17	,	,	PUNCT
ejpam-5834	11	18	vibrations	vibration	NOUN
ejpam-5834	11	19	of	of	ADP
ejpam-5834	11	20	strings	string	NOUN
ejpam-5834	11	21	and	and	CCONJ
ejpam-5834	11	22	waves	wave	NOUN
ejpam-5834	11	23	in	in	ADP
ejpam-5834	11	24	liquids	liquid	NOUN
ejpam-5834	11	25	.	.	PUNCT
ejpam-5834	12	1	this	this	PRON
ejpam-5834	12	2	leads	lead	VERB
ejpam-5834	12	3	to	to	ADP
ejpam-5834	12	4	the	the	DET
ejpam-5834	12	5	establishment	establishment	NOUN
ejpam-5834	12	6	of	of	ADP
ejpam-5834	12	7	numerous	numerous	ADJ
ejpam-5834	12	8	fractional	fractional	ADJ
ejpam-5834	12	9	operators	operator	NOUN
ejpam-5834	12	10	–	–	PUNCT
ejpam-5834	12	11	including	include	VERB
ejpam-5834	12	12	riemann	riemann	PROPN
ejpam-5834	12	13	liouville	liouville	PROPN
ejpam-5834	12	14	,	,	PUNCT
ejpam-5834	12	15	caputo	caputo	PROPN
ejpam-5834	12	16	and	and	CCONJ
ejpam-5834	12	17	atangana	atangana	PROPN
ejpam-5834	12	18	baleanu	baleanu	PROPN
ejpam-5834	12	19	caputo	caputo	PROPN
ejpam-5834	12	20	–	–	PUNCT
ejpam-5834	12	21	as	as	ADV
ejpam-5834	12	22	well	well	ADV
ejpam-5834	12	23	as	as	ADP
ejpam-5834	12	24	studying	study	VERB
ejpam-5834	12	25	many	many	ADJ
ejpam-5834	12	26	vital	vital	ADJ
ejpam-5834	12	27	concepts	concept	NOUN
ejpam-5834	12	28	for	for	ADP
ejpam-5834	12	29	investigating	investigate	VERB
ejpam-5834	12	30	these	these	DET
ejpam-5834	12	31	operators	operator	NOUN
ejpam-5834	12	32	.	.	PUNCT
ejpam-5834	13	1	for	for	ADP
ejpam-5834	13	2	example	example	NOUN
ejpam-5834	13	3	,	,	PUNCT
ejpam-5834	13	4	the	the	DET
ejpam-5834	13	5	existence	existence	NOUN
ejpam-5834	13	6	of	of	ADP
ejpam-5834	13	7	unique	unique	ADJ
ejpam-5834	13	8	solution	solution	NOUN
ejpam-5834	13	9	of	of	ADP
ejpam-5834	13	10	many	many	ADJ
ejpam-5834	13	11	fractional	fractional	ADJ
ejpam-5834	13	12	differential	differential	NOUN
ejpam-5834	13	13	and	and	CCONJ
ejpam-5834	13	14	integral	integral	ADJ
ejpam-5834	13	15	equations	equation	NOUN
ejpam-5834	13	16	–	–	PUNCT
ejpam-5834	13	17	doi	doi	NOUN
ejpam-5834	13	18	:	:	PUNCT
ejpam-5834	13	19	https://doi.org/10.29020/nybg.ejpam.v18i1.5834	https://doi.org/10.29020/nybg.ejpam.v18i1.5834	PROPN
ejpam-5834	13	20	email	email	NOUN
ejpam-5834	13	21	addresses	address	VERB
ejpam-5834	13	22	:	:	PUNCT
ejpam-5834	13	23	ohoudbalmutairi@gmail.com	ohoudbalmutairi@gmail.com	X
ejpam-5834	13	24	,	,	PUNCT
ejpam-5834	13	25	dr.ohudalmutairi@uhb.edu.sa	dr.ohudalmutairi@uhb.edu.sa	PROPN
ejpam-5834	13	26	(	(	PUNCT
ejpam-5834	13	27	o.	o.	PROPN
ejpam-5834	13	28	b.	b.	PROPN
ejpam-5834	13	29	almutairi	almutairi	PROPN
ejpam-5834	13	30	)	)	PUNCT
ejpam-5834	13	31	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5834	14	1	1	1	NUM
ejpam-5834	14	2	copyright	copyright	NOUN
ejpam-5834	14	3	:	:	PUNCT
ejpam-5834	14	4	©	©	PROPN
ejpam-5834	14	5	2025	2025	NUM
ejpam-5834	14	6	the	the	DET
ejpam-5834	14	7	author(s	author(s	NOUN
ejpam-5834	14	8	)	)	PUNCT
ejpam-5834	14	9	.	.	PUNCT
ejpam-5834	15	1	(	(	PUNCT
ejpam-5834	15	2	cc	cc	NOUN
ejpam-5834	15	3	by	by	ADP
ejpam-5834	15	4	-	-	PUNCT
ejpam-5834	15	5	nc	nc	PROPN
ejpam-5834	15	6	4.0	4.0	NUM
ejpam-5834	15	7	)	)	PUNCT
ejpam-5834	15	8	o.	o.	PROPN
ejpam-5834	15	9	b.	b.	PROPN
ejpam-5834	15	10	almutairi	almutairi	PROPN
ejpam-5834	15	11	/	/	SYM
ejpam-5834	15	12	eur	eur	PROPN
ejpam-5834	15	13	.	.	PUNCT
ejpam-5834	16	1	j.	j.	PROPN
ejpam-5834	16	2	pure	pure	PROPN
ejpam-5834	16	3	appl	appl	PROPN
ejpam-5834	16	4	.	.	PROPN
ejpam-5834	16	5	math	math	PROPN
ejpam-5834	16	6	,	,	PUNCT
ejpam-5834	16	7	18	18	NUM
ejpam-5834	16	8	(	(	PUNCT
ejpam-5834	16	9	1	1	NUM
ejpam-5834	16	10	)	)	PUNCT
ejpam-5834	16	11	(	(	PUNCT
ejpam-5834	16	12	2025	2025	NUM
ejpam-5834	16	13	)	)	PUNCT
ejpam-5834	16	14	,	,	PUNCT
ejpam-5834	16	15	5834	5834	NUM
ejpam-5834	16	16	2	2	NUM
ejpam-5834	16	17	of	of	ADP
ejpam-5834	16	18	12	12	NUM
ejpam-5834	16	19	for	for	ADP
ejpam-5834	16	20	initial	initial	ADJ
ejpam-5834	16	21	and	and	CCONJ
ejpam-5834	16	22	boundary	boundary	ADJ
ejpam-5834	16	23	value	value	NOUN
ejpam-5834	16	24	problems	problem	NOUN
ejpam-5834	16	25	–	–	PUNCT
ejpam-5834	16	26	have	have	AUX
ejpam-5834	16	27	been	be	AUX
ejpam-5834	16	28	reported	report	VERB
ejpam-5834	16	29	through	through	ADP
ejpam-5834	16	30	these	these	DET
ejpam-5834	16	31	fractional	fractional	ADJ
ejpam-5834	16	32	operators	operator	NOUN
ejpam-5834	16	33	.	.	PUNCT
ejpam-5834	17	1	for	for	ADP
ejpam-5834	17	2	further	further	ADJ
ejpam-5834	17	3	studies	study	NOUN
ejpam-5834	17	4	,	,	PUNCT
ejpam-5834	17	5	see	see	VERB
ejpam-5834	17	6	[	[	X
ejpam-5834	17	7	10	10	NUM
ejpam-5834	17	8	,	,	PUNCT
ejpam-5834	17	9	13–15	13–15	NUM
ejpam-5834	17	10	,	,	PUNCT
ejpam-5834	17	11	17	17	NUM
ejpam-5834	17	12	]	]	PUNCT
ejpam-5834	17	13	.	.	PUNCT
ejpam-5834	18	1	fractional	fractional	ADJ
ejpam-5834	18	2	calculus	calculus	NOUN
ejpam-5834	18	3	,	,	PUNCT
ejpam-5834	18	4	whose	whose	DET
ejpam-5834	18	5	broad	broad	ADJ
ejpam-5834	18	6	contents	content	NOUN
ejpam-5834	18	7	have	have	AUX
ejpam-5834	18	8	been	be	AUX
ejpam-5834	18	9	rapidly	rapidly	ADV
ejpam-5834	18	10	developing	develop	VERB
ejpam-5834	18	11	in	in	ADP
ejpam-5834	18	12	mathematical	mathematical	ADJ
ejpam-5834	18	13	analysis	analysis	NOUN
ejpam-5834	18	14	,	,	PUNCT
ejpam-5834	18	15	plays	play	VERB
ejpam-5834	18	16	a	a	DET
ejpam-5834	18	17	vital	vital	ADJ
ejpam-5834	18	18	role	role	NOUN
ejpam-5834	18	19	in	in	ADP
ejpam-5834	18	20	approximation	approximation	NOUN
ejpam-5834	18	21	theory	theory	NOUN
ejpam-5834	18	22	.	.	PUNCT
ejpam-5834	19	1	one	one	NUM
ejpam-5834	19	2	example	example	NOUN
ejpam-5834	19	3	of	of	ADP
ejpam-5834	19	4	this	this	PRON
ejpam-5834	19	5	is	be	AUX
ejpam-5834	19	6	the	the	DET
ejpam-5834	19	7	frequent	frequent	ADJ
ejpam-5834	19	8	use	use	NOUN
ejpam-5834	19	9	of	of	ADP
ejpam-5834	19	10	integral	integral	ADJ
ejpam-5834	19	11	operators	operator	NOUN
ejpam-5834	19	12	in	in	ADP
ejpam-5834	19	13	the	the	DET
ejpam-5834	19	14	study	study	NOUN
ejpam-5834	19	15	of	of	ADP
ejpam-5834	19	16	inequalities	inequality	NOUN
ejpam-5834	19	17	.	.	PUNCT
ejpam-5834	20	1	consider	consider	VERB
ejpam-5834	20	2	an	an	DET
ejpam-5834	20	3	integrable	integrable	ADJ
ejpam-5834	20	4	function	function	NOUN
ejpam-5834	20	5	η	η	PROPN
ejpam-5834	20	6	:	:	PUNCT
ejpam-5834	21	1	[	[	X
ejpam-5834	21	2	k1	k1	X
ejpam-5834	21	3	,	,	PUNCT
ejpam-5834	21	4	k2	k2	NOUN
ejpam-5834	21	5	]	]	PUNCT
ejpam-5834	21	6	→	→	PUNCT
ejpam-5834	21	7	r	r	NOUN
ejpam-5834	21	8	over	over	ADP
ejpam-5834	21	9	[	[	X
ejpam-5834	21	10	k1	k1	NOUN
ejpam-5834	21	11	,	,	PUNCT
ejpam-5834	21	12	k2	k2	NOUN
ejpam-5834	21	13	]	]	PUNCT
ejpam-5834	21	14	.	.	PUNCT
ejpam-5834	22	1	this	this	DET
ejpam-5834	22	2	function	function	NOUN
ejpam-5834	22	3	is	be	AUX
ejpam-5834	22	4	belonging	belong	VERB
ejpam-5834	22	5	to	to	ADP
ejpam-5834	22	6	a	a	DET
ejpam-5834	22	7	space	space	NOUN
ejpam-5834	22	8	l1	l1	PROPN
ejpam-5834	22	9	[	[	X
ejpam-5834	22	10	k1	k1	PROPN
ejpam-5834	22	11	,	,	PUNCT
ejpam-5834	22	12	k2	k2	NOUN
ejpam-5834	22	13	]	]	PUNCT
ejpam-5834	22	14	representing	represent	VERB
ejpam-5834	22	15	the	the	DET
ejpam-5834	22	16	set	set	NOUN
ejpam-5834	22	17	of	of	ADP
ejpam-5834	22	18	lebesgue	lebesgue	NOUN
ejpam-5834	22	19	integrable	integrable	ADJ
ejpam-5834	22	20	over	over	ADP
ejpam-5834	22	21	the	the	DET
ejpam-5834	22	22	same	same	ADJ
ejpam-5834	22	23	interval	interval	NOUN
ejpam-5834	22	24	.	.	PUNCT
ejpam-5834	23	1	using	use	VERB
ejpam-5834	23	2	riemann	riemann	PROPN
ejpam-5834	23	3	-	-	PUNCT
ejpam-5834	23	4	liouville	liouville	VERB
ejpam-5834	23	5	fractional	fractional	ADJ
ejpam-5834	23	6	integrals	integral	NOUN
ejpam-5834	23	7	,	,	PUNCT
ejpam-5834	23	8	sarikaya	sarikaya	PROPN
ejpam-5834	23	9	et	et	PROPN
ejpam-5834	23	10	al	al	PROPN
ejpam-5834	23	11	.	.	PUNCT
ejpam-5834	24	1	[	[	X
ejpam-5834	24	2	19	19	NUM
ejpam-5834	24	3	]	]	PUNCT
ejpam-5834	24	4	studied	study	VERB
ejpam-5834	24	5	the	the	DET
ejpam-5834	24	6	following	follow	VERB
ejpam-5834	24	7	new	new	ADJ
ejpam-5834	24	8	integral	integral	ADJ
ejpam-5834	24	9	inequalities	inequality	NOUN
ejpam-5834	24	10	.	.	PUNCT
ejpam-5834	25	1	theorem	theorem	NOUN
ejpam-5834	25	2	1	1	NUM
ejpam-5834	25	3	.	.	PUNCT
ejpam-5834	26	1	[	[	X
ejpam-5834	26	2	19	19	NUM
ejpam-5834	26	3	]	]	PUNCT
ejpam-5834	26	4	let	let	VERB
ejpam-5834	26	5	η	η	PROPN
ejpam-5834	26	6	:	:	PUNCT
ejpam-5834	26	7	[	[	X
ejpam-5834	26	8	k1	k1	X
ejpam-5834	26	9	,	,	PUNCT
ejpam-5834	26	10	k2	k2	NOUN
ejpam-5834	26	11	]	]	PUNCT
ejpam-5834	26	12	→	→	PUNCT
ejpam-5834	26	13	r	r	NOUN
ejpam-5834	26	14	be	be	AUX
ejpam-5834	26	15	a	a	DET
ejpam-5834	26	16	positive	positive	ADJ
ejpam-5834	26	17	function	function	NOUN
ejpam-5834	26	18	with	with	ADP
ejpam-5834	26	19	0	0	NUM
ejpam-5834	26	20	≤	≤	NUM
ejpam-5834	26	21	k1	k1	NOUN
ejpam-5834	26	22	<	<	X
ejpam-5834	26	23	k2	k2	PROPN
ejpam-5834	26	24	and	and	CCONJ
ejpam-5834	26	25	η	η	PROPN
ejpam-5834	26	26	∈	∈	PROPN
ejpam-5834	26	27	l1[k1	l1[k1	PROPN
ejpam-5834	26	28	,	,	PUNCT
ejpam-5834	26	29	k2	k2	NOUN
ejpam-5834	26	30	]	]	PUNCT
ejpam-5834	26	31	.	.	PUNCT
ejpam-5834	27	1	if	if	SCONJ
ejpam-5834	27	2	η	η	PROPN
ejpam-5834	27	3	is	be	AUX
ejpam-5834	27	4	a	a	DET
ejpam-5834	27	5	convex	convex	ADJ
ejpam-5834	27	6	function	function	NOUN
ejpam-5834	27	7	on	on	ADP
ejpam-5834	27	8	[	[	X
ejpam-5834	27	9	k1	k1	NOUN
ejpam-5834	27	10	,	,	PUNCT
ejpam-5834	27	11	k2	k2	NOUN
ejpam-5834	27	12	]	]	PUNCT
ejpam-5834	27	13	,	,	PUNCT
ejpam-5834	27	14	then	then	ADV
ejpam-5834	27	15	the	the	DET
ejpam-5834	27	16	following	follow	VERB
ejpam-5834	27	17	inequalities	inequality	NOUN
ejpam-5834	27	18	for	for	ADP
ejpam-5834	27	19	fractional	fractional	ADJ
ejpam-5834	27	20	integrals	integral	NOUN
ejpam-5834	27	21	hold	hold	VERB
ejpam-5834	27	22	:	:	PUNCT
ejpam-5834	27	23	η	η	PROPN
ejpam-5834	27	24	(	(	PUNCT
ejpam-5834	27	25	k1	k1	X
ejpam-5834	27	26	+	+	CCONJ
ejpam-5834	27	27	k2	k2	ADJ
ejpam-5834	27	28	2	2	NUM
ejpam-5834	27	29	)	)	PUNCT
ejpam-5834	27	30	≤	≤	NOUN
ejpam-5834	27	31	γ(ρ+	γ(ρ+	ADP
ejpam-5834	28	1	1	1	NUM
ejpam-5834	28	2	)	)	PUNCT
ejpam-5834	28	3	2(k2	2(k2	NUM
ejpam-5834	28	4	−	−	PROPN
ejpam-5834	28	5	k1)ρ	k1)ρ	NOUN
ejpam-5834	28	6	[	[	PUNCT
ejpam-5834	28	7	jρ	jρ	NOUN
ejpam-5834	28	8	k+1	k+1	X
ejpam-5834	28	9	η(k2	η(k2	NOUN
ejpam-5834	28	10	)	)	PUNCT
ejpam-5834	29	1	+	+	CCONJ
ejpam-5834	29	2	jρ	jρ	PROPN
ejpam-5834	29	3	k−2	k−2	PROPN
ejpam-5834	29	4	η(k1	η(k1	PROPN
ejpam-5834	29	5	)	)	PUNCT
ejpam-5834	29	6	]	]	PUNCT
ejpam-5834	29	7	≤	≤	NUM
ejpam-5834	29	8	η(k1	η(k1	NOUN
ejpam-5834	29	9	)	)	PUNCT
ejpam-5834	29	10	+	+	NUM
ejpam-5834	29	11	η(k2	η(k2	NOUN
ejpam-5834	29	12	)	)	PUNCT
ejpam-5834	29	13	2	2	NUM
ejpam-5834	29	14	,	,	PUNCT
ejpam-5834	29	15	ρ	ρ	PROPN
ejpam-5834	29	16	>	>	X
ejpam-5834	29	17	0	0	NUM
ejpam-5834	29	18	.	.	PUNCT
ejpam-5834	30	1	(	(	PUNCT
ejpam-5834	30	2	1	1	X
ejpam-5834	30	3	)	)	PUNCT
ejpam-5834	30	4	due	due	ADP
ejpam-5834	30	5	to	to	ADP
ejpam-5834	30	6	vital	vital	ADJ
ejpam-5834	30	7	roles	role	NOUN
ejpam-5834	30	8	played	play	VERB
ejpam-5834	30	9	by	by	ADP
ejpam-5834	30	10	this	this	DET
ejpam-5834	30	11	inequality	inequality	NOUN
ejpam-5834	30	12	in	in	ADP
ejpam-5834	30	13	both	both	CCONJ
ejpam-5834	30	14	science	science	NOUN
ejpam-5834	30	15	and	and	CCONJ
ejpam-5834	30	16	engineering	engineering	NOUN
ejpam-5834	30	17	[	[	X
ejpam-5834	30	18	2	2	NUM
ejpam-5834	30	19	,	,	PUNCT
ejpam-5834	30	20	4	4	NUM
ejpam-5834	30	21	]	]	PUNCT
ejpam-5834	30	22	,	,	PUNCT
ejpam-5834	30	23	many	many	ADJ
ejpam-5834	30	24	authors	author	NOUN
ejpam-5834	30	25	improve	improve	VERB
ejpam-5834	30	26	,	,	PUNCT
ejpam-5834	30	27	extend	extend	VERB
ejpam-5834	30	28	and	and	CCONJ
ejpam-5834	30	29	generalize	generalize	VERB
ejpam-5834	30	30	inequality	inequality	NOUN
ejpam-5834	30	31	(	(	PUNCT
ejpam-5834	30	32	1	1	NUM
ejpam-5834	30	33	)	)	PUNCT
ejpam-5834	30	34	through	through	ADP
ejpam-5834	30	35	various	various	ADJ
ejpam-5834	30	36	types	type	NOUN
ejpam-5834	30	37	of	of	ADP
ejpam-5834	30	38	convexities	convexity	NOUN
ejpam-5834	30	39	and	and	CCONJ
ejpam-5834	30	40	fractional	fractional	ADJ
ejpam-5834	30	41	integrals	integral	NOUN
ejpam-5834	30	42	.	.	PUNCT
ejpam-5834	31	1	for	for	ADP
ejpam-5834	31	2	example	example	NOUN
ejpam-5834	31	3	,	,	PUNCT
ejpam-5834	31	4	agarwal	agarwal	PROPN
ejpam-5834	31	5	et	et	PROPN
ejpam-5834	31	6	al	al	PROPN
ejpam-5834	31	7	.	.	PUNCT
ejpam-5834	32	1	[	[	X
ejpam-5834	32	2	1	1	X
ejpam-5834	32	3	]	]	PUNCT
ejpam-5834	32	4	established	establish	VERB
ejpam-5834	32	5	new	new	ADJ
ejpam-5834	32	6	hermite	hermite	ADJ
ejpam-5834	32	7	-	-	PUNCT
ejpam-5834	32	8	hadamard	hadamard	ADJ
ejpam-5834	32	9	type	type	NOUN
ejpam-5834	32	10	inequalities	inequality	NOUN
ejpam-5834	32	11	via	via	ADP
ejpam-5834	32	12	generalized	generalized	ADJ
ejpam-5834	32	13	k	k	ADJ
ejpam-5834	32	14	-	-	PUNCT
ejpam-5834	32	15	fractional	fractional	ADJ
ejpam-5834	32	16	integrals	integral	NOUN
ejpam-5834	32	17	;	;	PUNCT
ejpam-5834	32	18	almutairi	almutairi	NOUN
ejpam-5834	32	19	[	[	X
ejpam-5834	32	20	3	3	NUM
ejpam-5834	32	21	]	]	PUNCT
ejpam-5834	32	22	explored	explore	VERB
ejpam-5834	32	23	fractional	fractional	ADJ
ejpam-5834	32	24	inequalities	inequality	NOUN
ejpam-5834	32	25	using	use	VERB
ejpam-5834	32	26	euler	euler	PROPN
ejpam-5834	32	27	’s	’s	PART
ejpam-5834	32	28	beta	beta	NOUN
ejpam-5834	32	29	function	function	NOUN
ejpam-5834	32	30	;	;	PUNCT
ejpam-5834	32	31	budak	budak	PROPN
ejpam-5834	32	32	et	et	PROPN
ejpam-5834	32	33	al	al	PROPN
ejpam-5834	32	34	.	.	PUNCT
ejpam-5834	33	1	[	[	X
ejpam-5834	33	2	5	5	NUM
ejpam-5834	33	3	]	]	PUNCT
ejpam-5834	33	4	developed	develop	VERB
ejpam-5834	33	5	hermite	hermite	PROPN
ejpam-5834	33	6	-	-	PUNCT
ejpam-5834	33	7	hadamard	hadamard	ADJ
ejpam-5834	33	8	-	-	PUNCT
ejpam-5834	33	9	type	type	NOUN
ejpam-5834	33	10	inequalities	inequality	NOUN
ejpam-5834	33	11	for	for	ADP
ejpam-5834	33	12	interval	interval	NOUN
ejpam-5834	33	13	-	-	PUNCT
ejpam-5834	33	14	valued	value	VERB
ejpam-5834	33	15	functions	function	NOUN
ejpam-5834	33	16	;	;	PUNCT
ejpam-5834	33	17	du	du	PROPN
ejpam-5834	33	18	and	and	CCONJ
ejpam-5834	33	19	peng	peng	PROPN
ejpam-5834	34	1	[	[	X
ejpam-5834	34	2	6	6	NUM
ejpam-5834	34	3	]	]	PUNCT
ejpam-5834	34	4	extended	extend	VERB
ejpam-5834	34	5	the	the	DET
ejpam-5834	34	6	idea	idea	NOUN
ejpam-5834	34	7	to	to	PART
ejpam-5834	34	8	report	report	VERB
ejpam-5834	34	9	hermite	hermite	ADJ
ejpam-5834	34	10	-	-	PUNCT
ejpam-5834	34	11	hadamard	hadamard	ADJ
ejpam-5834	34	12	type	type	NOUN
ejpam-5834	34	13	inequalities	inequality	NOUN
ejpam-5834	34	14	involving	involve	VERB
ejpam-5834	34	15	multiplicative	multiplicative	ADJ
ejpam-5834	34	16	riemann	riemann	PROPN
ejpam-5834	34	17	-	-	PUNCT
ejpam-5834	34	18	liouville	liouville	VERB
ejpam-5834	34	19	fractional	fractional	ADJ
ejpam-5834	34	20	integrals	integral	NOUN
ejpam-5834	34	21	.	.	PUNCT
ejpam-5834	35	1	noor	noor	PROPN
ejpam-5834	35	2	and	and	CCONJ
ejpam-5834	35	3	awan	awan	PROPN
ejpam-5834	36	1	[	[	X
ejpam-5834	36	2	11	11	NUM
ejpam-5834	36	3	]	]	PUNCT
ejpam-5834	36	4	established	establish	VERB
ejpam-5834	36	5	new	new	ADJ
ejpam-5834	36	6	results	result	NOUN
ejpam-5834	36	7	related	relate	VERB
ejpam-5834	36	8	to	to	ADP
ejpam-5834	36	9	the	the	DET
ejpam-5834	36	10	left	left	ADJ
ejpam-5834	36	11	hand	hand	NOUN
ejpam-5834	36	12	side	side	NOUN
ejpam-5834	36	13	of	of	ADP
ejpam-5834	36	14	(	(	PUNCT
ejpam-5834	36	15	1	1	NUM
ejpam-5834	36	16	)	)	PUNCT
ejpam-5834	36	17	for	for	ADP
ejpam-5834	36	18	twice	twice	ADJ
ejpam-5834	36	19	differentiable	differentiable	ADJ
ejpam-5834	36	20	s	s	NOUN
ejpam-5834	36	21	-	-	ADJ
ejpam-5834	36	22	convex	convex	NOUN
ejpam-5834	36	23	functions	function	NOUN
ejpam-5834	36	24	using	use	VERB
ejpam-5834	36	25	the	the	DET
ejpam-5834	36	26	following	follow	VERB
ejpam-5834	36	27	lemma	lemma	PROPN
ejpam-5834	36	28	.	.	PUNCT
ejpam-5834	37	1	lemma	lemma	PROPN
ejpam-5834	37	2	1	1	X
ejpam-5834	37	3	.	.	PUNCT
ejpam-5834	38	1	let	let	VERB
ejpam-5834	38	2	η	η	PROPN
ejpam-5834	38	3	:	:	PUNCT
ejpam-5834	38	4	[	[	X
ejpam-5834	38	5	k1	k1	X
ejpam-5834	38	6	,	,	PUNCT
ejpam-5834	38	7	k2	k2	NOUN
ejpam-5834	38	8	]	]	PUNCT
ejpam-5834	38	9	→	→	PUNCT
ejpam-5834	38	10	r	r	NOUN
ejpam-5834	38	11	be	be	AUX
ejpam-5834	38	12	a	a	DET
ejpam-5834	38	13	twice	twice	ADV
ejpam-5834	38	14	differentiable	differentiable	ADJ
ejpam-5834	38	15	function	function	NOUN
ejpam-5834	38	16	on	on	ADP
ejpam-5834	38	17	(	(	PUNCT
ejpam-5834	38	18	k1	k1	NOUN
ejpam-5834	38	19	,	,	PUNCT
ejpam-5834	38	20	k2	k2	NOUN
ejpam-5834	38	21	)	)	PUNCT
ejpam-5834	38	22	with	with	ADP
ejpam-5834	38	23	k1	k1	PROPN
ejpam-5834	38	24	<	<	X
ejpam-5834	38	25	k2	k2	PROPN
ejpam-5834	38	26	.	.	PUNCT
ejpam-5834	39	1	also	also	ADV
ejpam-5834	39	2	,	,	PUNCT
ejpam-5834	39	3	let	let	VERB
ejpam-5834	39	4	η′′	η′′	PROPN
ejpam-5834	39	5	∈	∈	PROPN
ejpam-5834	39	6	l[k1	l[k1	NOUN
ejpam-5834	39	7	,	,	PUNCT
ejpam-5834	39	8	k2	k2	NOUN
ejpam-5834	39	9	]	]	PUNCT
ejpam-5834	39	10	.	.	PUNCT
ejpam-5834	40	1	then	then	ADV
ejpam-5834	40	2	the	the	DET
ejpam-5834	40	3	following	follow	VERB
ejpam-5834	40	4	identity	identity	NOUN
ejpam-5834	40	5	holds	hold	VERB
ejpam-5834	40	6	true	true	ADJ
ejpam-5834	40	7	:	:	PUNCT
ejpam-5834	40	8	2ρ−1γ(ρ+	2ρ−1γ(ρ+	NUM
ejpam-5834	40	9	1	1	NUM
ejpam-5834	40	10	)	)	PUNCT
ejpam-5834	40	11	(	(	PUNCT
ejpam-5834	40	12	k2	k2	PROPN
ejpam-5834	40	13	−	−	PROPN
ejpam-5834	40	14	k1)ρ	k1)ρ	NOUN
ejpam-5834	40	15	[	[	PUNCT
ejpam-5834	40	16	jρ	jρ	PROPN
ejpam-5834	40	17	(	(	PUNCT
ejpam-5834	40	18	k1+k2	k1+k2	PROPN
ejpam-5834	40	19	2	2	NUM
ejpam-5834	40	20	)	)	PUNCT
ejpam-5834	40	21	−η(k1	−η(k1	PROPN
ejpam-5834	40	22	)	)	PUNCT
ejpam-5834	41	1	+	+	CCONJ
ejpam-5834	42	1	jρ	jρ	PROPN
ejpam-5834	42	2	(	(	PUNCT
ejpam-5834	42	3	k1+k2	k1+k2	PROPN
ejpam-5834	42	4	2	2	NUM
ejpam-5834	42	5	)	)	PUNCT
ejpam-5834	42	6	+	+	NOUN
ejpam-5834	42	7	η(k2	η(k2	NOUN
ejpam-5834	42	8	)	)	PUNCT
ejpam-5834	42	9	]	]	PUNCT
ejpam-5834	43	1	−	−	PROPN
ejpam-5834	43	2	η	η	X
ejpam-5834	43	3	(	(	PUNCT
ejpam-5834	43	4	k1	k1	X
ejpam-5834	43	5	+	+	CCONJ
ejpam-5834	43	6	k2	k2	ADJ
ejpam-5834	43	7	2	2	NUM
ejpam-5834	43	8	)	)	PUNCT
ejpam-5834	43	9	=	=	SYM
ejpam-5834	43	10	(	(	PUNCT
ejpam-5834	43	11	k2	k2	PROPN
ejpam-5834	43	12	−	−	PROPN
ejpam-5834	43	13	k1	k1	PROPN
ejpam-5834	43	14	)	)	PUNCT
ejpam-5834	43	15	2	2	NUM
ejpam-5834	43	16	8(ρ+	8(ρ+	NUM
ejpam-5834	43	17	1	1	NUM
ejpam-5834	43	18	)	)	PUNCT
ejpam-5834	43	19	∫	∫	PROPN
ejpam-5834	43	20	1	1	NUM
ejpam-5834	43	21	0	0	NUM
ejpam-5834	43	22	(	(	PUNCT
ejpam-5834	43	23	1−ϖ)ρ+1	1−ϖ)ρ+1	NUM
ejpam-5834	43	24	[	[	PUNCT
ejpam-5834	43	25	η′′	η′′	PROPN
ejpam-5834	43	26	(	(	PUNCT
ejpam-5834	43	27	1	1	NUM
ejpam-5834	43	28	+	+	NOUN
ejpam-5834	43	29	ϖ	ϖ	PROPN
ejpam-5834	43	30	2	2	NUM
ejpam-5834	43	31	k1	k1	NOUN
ejpam-5834	43	32	+	+	CCONJ
ejpam-5834	43	33	1−ϖ	1−ϖ	NUM
ejpam-5834	43	34	2	2	NUM
ejpam-5834	43	35	k2	k2	NOUN
ejpam-5834	43	36	)	)	PUNCT
ejpam-5834	43	37	+	+	CCONJ
ejpam-5834	43	38	η′′	η′′	NOUN
ejpam-5834	43	39	(	(	PUNCT
ejpam-5834	43	40	1	1	NUM
ejpam-5834	43	41	+	+	ADJ
ejpam-5834	43	42	ϖ	ϖ	PROPN
ejpam-5834	43	43	2	2	NUM
ejpam-5834	43	44	k2	k2	NOUN
ejpam-5834	43	45	+	+	CCONJ
ejpam-5834	43	46	1−ϖ	1−ϖ	NUM
ejpam-5834	43	47	2	2	NUM
ejpam-5834	43	48	k1	k1	NOUN
ejpam-5834	43	49	)	)	PUNCT
ejpam-5834	43	50	]	]	PUNCT
ejpam-5834	44	1	dϖ	dϖ	X
ejpam-5834	44	2	(	(	PUNCT
ejpam-5834	44	3	2	2	NUM
ejpam-5834	44	4	)	)	PUNCT
ejpam-5834	44	5	even	even	ADV
ejpam-5834	44	6	though	though	SCONJ
ejpam-5834	44	7	a	a	DET
ejpam-5834	44	8	classical	classical	ADJ
ejpam-5834	44	9	convexity	convexity	NOUN
ejpam-5834	44	10	which	which	PRON
ejpam-5834	44	11	was	be	AUX
ejpam-5834	44	12	later	later	ADV
ejpam-5834	44	13	replaced	replace	VERB
ejpam-5834	44	14	by	by	ADP
ejpam-5834	44	15	s	s	NOUN
ejpam-5834	44	16	-	-	NOUN
ejpam-5834	44	17	convexity	convexity	NOUN
ejpam-5834	44	18	[	[	X
ejpam-5834	44	19	11	11	NUM
ejpam-5834	44	20	]	]	PUNCT
ejpam-5834	44	21	has	have	AUX
ejpam-5834	44	22	been	be	AUX
ejpam-5834	44	23	previously	previously	ADV
ejpam-5834	44	24	used	use	VERB
ejpam-5834	44	25	to	to	PART
ejpam-5834	44	26	establish	establish	VERB
ejpam-5834	44	27	integral	integral	ADJ
ejpam-5834	44	28	inequalities	inequality	NOUN
ejpam-5834	44	29	[	[	X
ejpam-5834	44	30	19	19	NUM
ejpam-5834	44	31	]	]	PUNCT
ejpam-5834	44	32	,	,	PUNCT
ejpam-5834	44	33	the	the	DET
ejpam-5834	44	34	central	central	ADJ
ejpam-5834	44	35	idea	idea	NOUN
ejpam-5834	44	36	of	of	ADP
ejpam-5834	44	37	our	our	PRON
ejpam-5834	44	38	study	study	NOUN
ejpam-5834	44	39	lies	lie	VERB
ejpam-5834	44	40	in	in	ADP
ejpam-5834	44	41	establishing	establish	VERB
ejpam-5834	44	42	more	more	ADV
ejpam-5834	44	43	generalized	generalized	ADJ
ejpam-5834	44	44	integral	integral	ADJ
ejpam-5834	44	45	inequalities	inequality	NOUN
ejpam-5834	44	46	through	through	ADP
ejpam-5834	44	47	two	two	NUM
ejpam-5834	44	48	different	different	ADJ
ejpam-5834	44	49	classes	class	NOUN
ejpam-5834	44	50	of	of	ADP
ejpam-5834	44	51	convexities	convexity	NOUN
ejpam-5834	44	52	.	.	PUNCT
ejpam-5834	45	1	motivated	motivate	VERB
ejpam-5834	45	2	by	by	ADP
ejpam-5834	45	3	these	these	DET
ejpam-5834	45	4	two	two	NUM
ejpam-5834	45	5	mentioned	mention	VERB
ejpam-5834	45	6	independent	independent	ADJ
ejpam-5834	45	7	studies	study	NOUN
ejpam-5834	45	8	,	,	PUNCT
ejpam-5834	45	9	we	we	PRON
ejpam-5834	45	10	opt	opt	VERB
ejpam-5834	45	11	to	to	PART
ejpam-5834	45	12	obtain	obtain	VERB
ejpam-5834	45	13	new	new	ADJ
ejpam-5834	45	14	bounds	bound	NOUN
ejpam-5834	45	15	for	for	ADP
ejpam-5834	45	16	the	the	DET
ejpam-5834	45	17	midpoint	midpoint	NOUN
ejpam-5834	45	18	inequalities	inequality	NOUN
ejpam-5834	45	19	via	via	ADP
ejpam-5834	45	20	fractional	fractional	ADJ
ejpam-5834	45	21	integral	integral	ADJ
ejpam-5834	45	22	operator	operator	NOUN
ejpam-5834	45	23	.	.	PUNCT
ejpam-5834	46	1	two	two	NUM
ejpam-5834	46	2	generalized	generalized	ADJ
ejpam-5834	46	3	convexities	convexity	NOUN
ejpam-5834	46	4	(	(	PUNCT
ejpam-5834	46	5	ρ	ρ	PROPN
ejpam-5834	46	6	,	,	PUNCT
ejpam-5834	46	7	s	s	PART
ejpam-5834	46	8	)	)	PUNCT
ejpam-5834	46	9	and	and	CCONJ
ejpam-5834	46	10	(	(	PUNCT
ejpam-5834	46	11	ρ	ρ	PROPN
ejpam-5834	46	12	,	,	PUNCT
ejpam-5834	46	13	s	s	PART
ejpam-5834	46	14	,	,	PUNCT
ejpam-5834	46	15	m)-convexity	m)-convexity	NOUN
ejpam-5834	46	16	are	be	AUX
ejpam-5834	46	17	used	use	VERB
ejpam-5834	46	18	to	to	PART
ejpam-5834	46	19	establish	establish	VERB
ejpam-5834	46	20	the	the	DET
ejpam-5834	46	21	new	new	ADJ
ejpam-5834	46	22	bounds	bound	NOUN
ejpam-5834	46	23	.	.	PUNCT
ejpam-5834	47	1	some	some	PRON
ejpam-5834	47	2	of	of	ADP
ejpam-5834	47	3	our	our	PRON
ejpam-5834	47	4	findings	finding	NOUN
ejpam-5834	47	5	which	which	PRON
ejpam-5834	47	6	can	can	AUX
ejpam-5834	47	7	be	be	AUX
ejpam-5834	47	8	reduced	reduce	VERB
ejpam-5834	47	9	to	to	ADP
ejpam-5834	47	10	different	different	ADJ
ejpam-5834	47	11	inequalities	inequality	NOUN
ejpam-5834	47	12	through	through	ADP
ejpam-5834	47	13	various	various	ADJ
ejpam-5834	47	14	convexities	convexity	NOUN
ejpam-5834	47	15	are	be	AUX
ejpam-5834	47	16	obtained	obtain	VERB
ejpam-5834	47	17	.	.	PUNCT
ejpam-5834	48	1	the	the	DET
ejpam-5834	48	2	other	other	ADJ
ejpam-5834	48	3	parts	part	NOUN
ejpam-5834	48	4	of	of	ADP
ejpam-5834	48	5	this	this	DET
ejpam-5834	48	6	paper	paper	NOUN
ejpam-5834	48	7	are	be	AUX
ejpam-5834	48	8	organized	organize	VERB
ejpam-5834	48	9	as	as	SCONJ
ejpam-5834	48	10	follows	follow	VERB
ejpam-5834	48	11	.	.	PUNCT
ejpam-5834	49	1	preliminary	preliminary	ADJ
ejpam-5834	49	2	studies	study	NOUN
ejpam-5834	49	3	are	be	AUX
ejpam-5834	49	4	presented	present	VERB
ejpam-5834	49	5	in	in	ADP
ejpam-5834	49	6	section	section	NOUN
ejpam-5834	49	7	2	2	NUM
ejpam-5834	49	8	.	.	PUNCT
ejpam-5834	49	9	section	section	NOUN
ejpam-5834	49	10	3	3	NUM
ejpam-5834	49	11	presents	present	VERB
ejpam-5834	49	12	integral	integral	ADJ
ejpam-5834	49	13	inequalities	inequality	NOUN
ejpam-5834	49	14	involving	involve	VERB
ejpam-5834	49	15	(	(	PUNCT
ejpam-5834	49	16	ρ	ρ	PROPN
ejpam-5834	49	17	,	,	PUNCT
ejpam-5834	49	18	s	s	PART
ejpam-5834	49	19	)	)	PUNCT
ejpam-5834	49	20	and	and	CCONJ
ejpam-5834	49	21	(	(	PUNCT
ejpam-5834	49	22	ρ	ρ	PROPN
ejpam-5834	49	23	,	,	PUNCT
ejpam-5834	49	24	s	s	PROPN
ejpam-5834	49	25	,	,	PUNCT
ejpam-5834	49	26	m	m	NOUN
ejpam-5834	49	27	)	)	PUNCT
ejpam-5834	49	28	convex	convex	NOUN
ejpam-5834	49	29	functions	function	NOUN
ejpam-5834	49	30	via	via	ADP
ejpam-5834	49	31	fractional	fractional	ADJ
ejpam-5834	49	32	integral	integral	ADJ
ejpam-5834	49	33	operators	operator	NOUN
ejpam-5834	49	34	.	.	PUNCT
ejpam-5834	50	1	section	section	NOUN
ejpam-5834	50	2	4	4	NUM
ejpam-5834	50	3	concludes	conclude	VERB
ejpam-5834	50	4	the	the	DET
ejpam-5834	50	5	study	study	NOUN
ejpam-5834	50	6	.	.	PUNCT
ejpam-5834	51	1	o.	o.	PROPN
ejpam-5834	51	2	b.	b.	PROPN
ejpam-5834	51	3	almutairi	almutairi	PROPN
ejpam-5834	51	4	/	/	SYM
ejpam-5834	51	5	eur	eur	PROPN
ejpam-5834	51	6	.	.	PUNCT
ejpam-5834	52	1	j.	j.	PROPN
ejpam-5834	52	2	pure	pure	PROPN
ejpam-5834	52	3	appl	appl	PROPN
ejpam-5834	52	4	.	.	PROPN
ejpam-5834	52	5	math	math	PROPN
ejpam-5834	52	6	,	,	PUNCT
ejpam-5834	52	7	18	18	NUM
ejpam-5834	52	8	(	(	PUNCT
ejpam-5834	52	9	1	1	NUM
ejpam-5834	52	10	)	)	PUNCT
ejpam-5834	52	11	(	(	PUNCT
ejpam-5834	52	12	2025	2025	NUM
ejpam-5834	52	13	)	)	PUNCT
ejpam-5834	52	14	,	,	PUNCT
ejpam-5834	52	15	5834	5834	NUM
ejpam-5834	52	16	3	3	NUM
ejpam-5834	52	17	of	of	ADP
ejpam-5834	52	18	12	12	NUM
ejpam-5834	52	19	2	2	NUM
ejpam-5834	52	20	.	.	PUNCT
ejpam-5834	52	21	preliminaries	preliminary	NOUN
ejpam-5834	52	22	some	some	DET
ejpam-5834	52	23	basic	basic	ADJ
ejpam-5834	52	24	results	result	NOUN
ejpam-5834	52	25	of	of	ADP
ejpam-5834	52	26	different	different	ADJ
ejpam-5834	52	27	classes	class	NOUN
ejpam-5834	52	28	of	of	ADP
ejpam-5834	52	29	convex	convex	NOUN
ejpam-5834	52	30	functions	function	NOUN
ejpam-5834	52	31	,	,	PUNCT
ejpam-5834	52	32	riemann	riemann	PROPN
ejpam-5834	52	33	liouville	liouville	VERB
ejpam-5834	52	34	fractional	fractional	ADJ
ejpam-5834	52	35	integral	integral	ADJ
ejpam-5834	52	36	operator	operator	NOUN
ejpam-5834	52	37	and	and	CCONJ
ejpam-5834	52	38	special	special	ADJ
ejpam-5834	52	39	functions	function	NOUN
ejpam-5834	52	40	are	be	AUX
ejpam-5834	52	41	presented	present	VERB
ejpam-5834	52	42	in	in	ADP
ejpam-5834	52	43	this	this	DET
ejpam-5834	52	44	section	section	NOUN
ejpam-5834	52	45	.	.	PUNCT
ejpam-5834	53	1	these	these	DET
ejpam-5834	53	2	preliminary	preliminary	ADJ
ejpam-5834	53	3	results	result	NOUN
ejpam-5834	53	4	and	and	CCONJ
ejpam-5834	53	5	definitions	definition	NOUN
ejpam-5834	53	6	can	can	AUX
ejpam-5834	53	7	be	be	AUX
ejpam-5834	53	8	later	later	ADV
ejpam-5834	53	9	used	use	VERB
ejpam-5834	53	10	to	to	PART
ejpam-5834	53	11	establish	establish	VERB
ejpam-5834	53	12	our	our	PRON
ejpam-5834	53	13	main	main	ADJ
ejpam-5834	53	14	results	result	NOUN
ejpam-5834	53	15	.	.	PUNCT
ejpam-5834	54	1	therefore	therefore	ADV
ejpam-5834	54	2	,	,	PUNCT
ejpam-5834	54	3	the	the	DET
ejpam-5834	54	4	definitions	definition	NOUN
ejpam-5834	54	5	of	of	ADP
ejpam-5834	54	6	some	some	DET
ejpam-5834	54	7	types	type	NOUN
ejpam-5834	54	8	of	of	ADP
ejpam-5834	54	9	convexities	convexity	NOUN
ejpam-5834	54	10	are	be	AUX
ejpam-5834	54	11	given	give	VERB
ejpam-5834	54	12	as	as	SCONJ
ejpam-5834	54	13	follows	follow	VERB
ejpam-5834	54	14	.	.	PUNCT
ejpam-5834	55	1	definition	definition	NOUN
ejpam-5834	55	2	1	1	NUM
ejpam-5834	55	3	.	.	PUNCT
ejpam-5834	56	1	[	[	X
ejpam-5834	56	2	20	20	NUM
ejpam-5834	56	3	]	]	PUNCT
ejpam-5834	56	4	a	a	DET
ejpam-5834	56	5	function	function	NOUN
ejpam-5834	56	6	η	η	NOUN
ejpam-5834	56	7	:	:	PUNCT
ejpam-5834	57	1	[	[	X
ejpam-5834	57	2	0	0	NUM
ejpam-5834	57	3	,	,	PUNCT
ejpam-5834	57	4	d	d	X
ejpam-5834	57	5	]	]	X
ejpam-5834	57	6	→	→	PUNCT
ejpam-5834	57	7	r0	r0	NOUN
ejpam-5834	57	8	=	=	PUNCT
ejpam-5834	58	1	[	[	X
ejpam-5834	58	2	0,∞	0,∞	NOUN
ejpam-5834	58	3	)	)	PUNCT
ejpam-5834	58	4	is	be	AUX
ejpam-5834	58	5	said	say	VERB
ejpam-5834	58	6	to	to	PART
ejpam-5834	58	7	be	be	AUX
ejpam-5834	58	8	m	m	NOUN
ejpam-5834	58	9	-	-	NOUN
ejpam-5834	58	10	convex	convex	ADJ
ejpam-5834	58	11	on	on	ADP
ejpam-5834	58	12	[	[	X
ejpam-5834	58	13	0	0	NUM
ejpam-5834	58	14	,	,	PUNCT
ejpam-5834	58	15	d	d	X
ejpam-5834	58	16	]	]	X
ejpam-5834	58	17	for	for	ADP
ejpam-5834	58	18	some	some	DET
ejpam-5834	58	19	m	m	NOUN
ejpam-5834	58	20	∈	∈	NOUN
ejpam-5834	58	21	(	(	PUNCT
ejpam-5834	58	22	0	0	NUM
ejpam-5834	58	23	,	,	PUNCT
ejpam-5834	58	24	1	1	NUM
ejpam-5834	58	25	]	]	PUNCT
ejpam-5834	58	26	,	,	PUNCT
ejpam-5834	58	27	if	if	SCONJ
ejpam-5834	58	28	η(ϖk1	η(ϖk1	PROPN
ejpam-5834	58	29	+	+	PROPN
ejpam-5834	58	30	m(1−ϖ)k2	m(1−ϖ)k2	NOUN
ejpam-5834	58	31	)	)	PUNCT
ejpam-5834	58	32	≤	≤	NOUN
ejpam-5834	58	33	ϖη(k1	ϖη(k1	NOUN
ejpam-5834	58	34	)	)	PUNCT
ejpam-5834	58	35	+	+	NOUN
ejpam-5834	58	36	m(1−ϖ)η(k2	m(1−ϖ)η(k2	NOUN
ejpam-5834	58	37	)	)	PUNCT
ejpam-5834	58	38	,	,	PUNCT
ejpam-5834	58	39	for	for	ADP
ejpam-5834	58	40	all	all	DET
ejpam-5834	58	41	k1	k1	NOUN
ejpam-5834	58	42	,	,	PUNCT
ejpam-5834	58	43	k2	k2	PROPN
ejpam-5834	58	44	∈	∈	PROPN
ejpam-5834	59	1	[	[	X
ejpam-5834	59	2	0	0	NUM
ejpam-5834	59	3	,	,	PUNCT
ejpam-5834	59	4	d	d	X
ejpam-5834	59	5	]	]	X
ejpam-5834	59	6	and	and	CCONJ
ejpam-5834	59	7	ϖ	ϖ	PRON
ejpam-5834	59	8	∈	∈	PROPN
ejpam-5834	60	1	[	[	X
ejpam-5834	60	2	0	0	NUM
ejpam-5834	60	3	,	,	PUNCT
ejpam-5834	60	4	1	1	NUM
ejpam-5834	60	5	]	]	PUNCT
ejpam-5834	60	6	.	.	PUNCT
ejpam-5834	61	1	definition	definition	NOUN
ejpam-5834	61	2	2	2	NUM
ejpam-5834	61	3	.	.	PUNCT
ejpam-5834	62	1	[	[	X
ejpam-5834	62	2	8	8	NUM
ejpam-5834	62	3	]	]	PUNCT
ejpam-5834	62	4	a	a	DET
ejpam-5834	62	5	function	function	NOUN
ejpam-5834	62	6	η	η	NOUN
ejpam-5834	62	7	:	:	PUNCT
ejpam-5834	62	8	[	[	X
ejpam-5834	62	9	k1	k1	X
ejpam-5834	62	10	,	,	PUNCT
ejpam-5834	62	11	k2	k2	NOUN
ejpam-5834	62	12	]	]	PUNCT
ejpam-5834	62	13	⊂	⊂	PROPN
ejpam-5834	62	14	r	r	NOUN
ejpam-5834	62	15	→	→	SYM
ejpam-5834	62	16	r	r	NOUN
ejpam-5834	62	17	is	be	AUX
ejpam-5834	62	18	said	say	VERB
ejpam-5834	62	19	to	to	PART
ejpam-5834	62	20	be	be	AUX
ejpam-5834	62	21	s	s	NOUN
ejpam-5834	62	22	-	-	ADJ
ejpam-5834	62	23	convex	convex	ADJ
ejpam-5834	62	24	function	function	NOUN
ejpam-5834	62	25	of	of	ADP
ejpam-5834	62	26	the	the	DET
ejpam-5834	62	27	second	second	ADJ
ejpam-5834	62	28	kind	kind	NOUN
ejpam-5834	62	29	if	if	SCONJ
ejpam-5834	62	30	η((1−ϖ)k1	η((1−ϖ)k1	VERB
ejpam-5834	62	31	+	+	NOUN
ejpam-5834	62	32	ϖk2	ϖk2	NOUN
ejpam-5834	62	33	)	)	PUNCT
ejpam-5834	62	34	≤	≤	NOUN
ejpam-5834	62	35	(	(	PUNCT
ejpam-5834	62	36	1−ϖ)sη(k1	1−ϖ)sη(k1	NUM
ejpam-5834	62	37	)	)	PUNCT
ejpam-5834	63	1	+	+	NOUN
ejpam-5834	63	2	ϖsη(k2	ϖsη(k2	NOUN
ejpam-5834	63	3	)	)	PUNCT
ejpam-5834	63	4	,	,	PUNCT
ejpam-5834	63	5	for	for	ADP
ejpam-5834	63	6	all	all	DET
ejpam-5834	63	7	k1	k1	NOUN
ejpam-5834	63	8	,	,	PUNCT
ejpam-5834	63	9	k2	k2	PROPN
ejpam-5834	63	10	∈	∈	PROPN
ejpam-5834	63	11	(	(	PUNCT
ejpam-5834	63	12	0,∞	0,∞	NOUN
ejpam-5834	63	13	]	]	PUNCT
ejpam-5834	63	14	,	,	PUNCT
ejpam-5834	63	15	ϖ	ϖ	PROPN
ejpam-5834	63	16	∈	∈	PROPN
ejpam-5834	64	1	[	[	X
ejpam-5834	64	2	0	0	NUM
ejpam-5834	64	3	,	,	PUNCT
ejpam-5834	64	4	1	1	NUM
ejpam-5834	64	5	]	]	PUNCT
ejpam-5834	64	6	and	and	CCONJ
ejpam-5834	64	7	s	s	PROPN
ejpam-5834	64	8	∈	∈	PROPN
ejpam-5834	64	9	(	(	PUNCT
ejpam-5834	64	10	0	0	NUM
ejpam-5834	64	11	,	,	PUNCT
ejpam-5834	64	12	1	1	NUM
ejpam-5834	64	13	]	]	PUNCT
ejpam-5834	64	14	.	.	PUNCT
ejpam-5834	65	1	definition	definition	NOUN
ejpam-5834	65	2	3	3	NUM
ejpam-5834	65	3	.	.	PUNCT
ejpam-5834	66	1	[	[	X
ejpam-5834	66	2	21	21	NUM
ejpam-5834	66	3	]	]	PUNCT
ejpam-5834	66	4	for	for	ADP
ejpam-5834	66	5	some	some	DET
ejpam-5834	66	6	s	s	PART
ejpam-5834	66	7	∈	∈	PROPN
ejpam-5834	66	8	[	[	X
ejpam-5834	66	9	−1	−1	NOUN
ejpam-5834	66	10	,	,	PUNCT
ejpam-5834	66	11	1	1	NUM
ejpam-5834	66	12	]	]	PUNCT
ejpam-5834	66	13	and	and	CCONJ
ejpam-5834	66	14	ρ	ρ	PROPN
ejpam-5834	66	15	∈	∈	PROPN
ejpam-5834	66	16	(	(	PUNCT
ejpam-5834	66	17	0	0	NUM
ejpam-5834	66	18	,	,	PUNCT
ejpam-5834	66	19	1	1	NUM
ejpam-5834	66	20	]	]	PUNCT
ejpam-5834	66	21	,	,	PUNCT
ejpam-5834	66	22	a	a	DET
ejpam-5834	66	23	function	function	NOUN
ejpam-5834	66	24	η	η	NOUN
ejpam-5834	66	25	:	:	PUNCT
ejpam-5834	66	26	i	i	PRON
ejpam-5834	66	27	⊆	⊆	NUM
ejpam-5834	66	28	r	r	NOUN
ejpam-5834	66	29	→	→	SYM
ejpam-5834	66	30	r	r	NOUN
ejpam-5834	66	31	is	be	AUX
ejpam-5834	66	32	said	say	VERB
ejpam-5834	66	33	to	to	PART
ejpam-5834	66	34	be	be	AUX
ejpam-5834	66	35	(	(	PUNCT
ejpam-5834	66	36	ρ	ρ	NOUN
ejpam-5834	66	37	,	,	PUNCT
ejpam-5834	66	38	s)-convex	s)-convex	ADP
ejpam-5834	66	39	if	if	SCONJ
ejpam-5834	66	40	η(ϖk1	η(ϖk1	PROPN
ejpam-5834	66	41	+	+	CCONJ
ejpam-5834	66	42	(	(	PUNCT
ejpam-5834	66	43	1−ϖ)k2	1−ϖ)k2	X
ejpam-5834	66	44	)	)	PUNCT
ejpam-5834	66	45	≤	≤	NUM
ejpam-5834	66	46	ϖρsη(k1	ϖρsη(k1	NOUN
ejpam-5834	66	47	)	)	PUNCT
ejpam-5834	67	1	+	+	CCONJ
ejpam-5834	67	2	(	(	PUNCT
ejpam-5834	67	3	1−ϖρ)s	1−ϖρ)s	NUM
ejpam-5834	67	4	η(k2	η(k2	NOUN
ejpam-5834	67	5	)	)	PUNCT
ejpam-5834	67	6	,	,	PUNCT
ejpam-5834	67	7	for	for	ADP
ejpam-5834	67	8	all	all	DET
ejpam-5834	67	9	k1	k1	NOUN
ejpam-5834	67	10	,	,	PUNCT
ejpam-5834	67	11	k2	k2	PROPN
ejpam-5834	67	12	∈	∈	PROPN
ejpam-5834	68	1	i	i	PRON
ejpam-5834	68	2	and	and	CCONJ
ejpam-5834	68	3	ϖ	ϖ	PRON
ejpam-5834	68	4	∈	∈	PROPN
ejpam-5834	68	5	(	(	PUNCT
ejpam-5834	68	6	0	0	NUM
ejpam-5834	68	7	,	,	PUNCT
ejpam-5834	68	8	1	1	NUM
ejpam-5834	68	9	)	)	PUNCT
ejpam-5834	68	10	.	.	PUNCT
ejpam-5834	69	1	definition	definition	NOUN
ejpam-5834	69	2	4	4	NUM
ejpam-5834	69	3	.	.	PUNCT
ejpam-5834	70	1	[	[	X
ejpam-5834	70	2	21	21	NUM
ejpam-5834	70	3	]	]	PUNCT
ejpam-5834	70	4	the	the	DET
ejpam-5834	70	5	function	function	NOUN
ejpam-5834	70	6	η	η	PROPN
ejpam-5834	70	7	:	:	PUNCT
ejpam-5834	71	1	[	[	X
ejpam-5834	71	2	0	0	NUM
ejpam-5834	71	3	,	,	PUNCT
ejpam-5834	71	4	d	d	X
ejpam-5834	71	5	]	]	X
ejpam-5834	71	6	→	→	PUNCT
ejpam-5834	71	7	r	r	NOUN
ejpam-5834	71	8	is	be	AUX
ejpam-5834	71	9	said	say	VERB
ejpam-5834	71	10	to	to	PART
ejpam-5834	71	11	be	be	AUX
ejpam-5834	71	12	(	(	PUNCT
ejpam-5834	71	13	ρ	ρ	PROPN
ejpam-5834	71	14	,	,	PUNCT
ejpam-5834	71	15	s	s	NOUN
ejpam-5834	71	16	,	,	PUNCT
ejpam-5834	71	17	m)-convex	m)-convex	PUNCT
ejpam-5834	71	18	,	,	PUNCT
ejpam-5834	71	19	if	if	SCONJ
ejpam-5834	71	20	we	we	PRON
ejpam-5834	71	21	have	have	VERB
ejpam-5834	71	22	η(ϖk1	η(ϖk1	PROPN
ejpam-5834	71	23	+	+	NOUN
ejpam-5834	71	24	m(1−ϖ)k2	m(1−ϖ)k2	NOUN
ejpam-5834	71	25	)	)	PUNCT
ejpam-5834	71	26	≤	≤	NUM
ejpam-5834	71	27	ϖρsη(k1	ϖρsη(k1	NOUN
ejpam-5834	71	28	)	)	PUNCT
ejpam-5834	72	1	+	+	NOUN
ejpam-5834	72	2	m	m	PROPN
ejpam-5834	72	3	(	(	PUNCT
ejpam-5834	72	4	1−ϖρ)s	1−ϖρ)s	NOUN
ejpam-5834	72	5	η(k2	η(k2	NOUN
ejpam-5834	72	6	)	)	PUNCT
ejpam-5834	72	7	,	,	PUNCT
ejpam-5834	72	8	where	where	SCONJ
ejpam-5834	72	9	k1	k1	NOUN
ejpam-5834	72	10	,	,	PUNCT
ejpam-5834	72	11	k2	k2	PROPN
ejpam-5834	72	12	∈	∈	PROPN
ejpam-5834	73	1	[	[	X
ejpam-5834	73	2	0	0	NUM
ejpam-5834	73	3	,	,	PUNCT
ejpam-5834	73	4	d	d	X
ejpam-5834	73	5	]	]	X
ejpam-5834	73	6	,	,	PUNCT
ejpam-5834	73	7	ϖ	ϖ	PROPN
ejpam-5834	73	8	∈	∈	PROPN
ejpam-5834	73	9	(	(	PUNCT
ejpam-5834	73	10	0	0	NUM
ejpam-5834	73	11	,	,	PUNCT
ejpam-5834	73	12	1	1	NUM
ejpam-5834	73	13	)	)	PUNCT
ejpam-5834	73	14	and	and	CCONJ
ejpam-5834	73	15	for	for	ADP
ejpam-5834	73	16	some	some	DET
ejpam-5834	73	17	s	s	X
ejpam-5834	73	18	∈	∈	PROPN
ejpam-5834	73	19	[	[	X
ejpam-5834	73	20	−1	−1	NOUN
ejpam-5834	73	21	,	,	PUNCT
ejpam-5834	73	22	1	1	NUM
ejpam-5834	73	23	]	]	PUNCT
ejpam-5834	73	24	,	,	PUNCT
ejpam-5834	73	25	(	(	PUNCT
ejpam-5834	73	26	ρ	ρ	NOUN
ejpam-5834	73	27	,	,	PUNCT
ejpam-5834	73	28	m	m	NOUN
ejpam-5834	73	29	)	)	PUNCT
ejpam-5834	73	30	∈	∈	PROPN
ejpam-5834	73	31	(	(	PUNCT
ejpam-5834	73	32	0	0	NUM
ejpam-5834	73	33	,	,	PUNCT
ejpam-5834	73	34	1]2	1]2	NUM
ejpam-5834	73	35	.	.	PUNCT
ejpam-5834	74	1	different	different	ADJ
ejpam-5834	74	2	special	special	ADJ
ejpam-5834	74	3	cases	case	NOUN
ejpam-5834	74	4	are	be	AUX
ejpam-5834	74	5	considered	consider	VERB
ejpam-5834	74	6	in	in	ADP
ejpam-5834	74	7	the	the	DET
ejpam-5834	74	8	following	follow	VERB
ejpam-5834	74	9	remark	remark	NOUN
ejpam-5834	74	10	.	.	PUNCT
ejpam-5834	75	1	remark	remark	PROPN
ejpam-5834	75	2	1	1	NUM
ejpam-5834	75	3	.	.	PUNCT
ejpam-5834	76	1	definition	definition	NOUN
ejpam-5834	76	2	4	4	NUM
ejpam-5834	76	3	produces	produce	VERB
ejpam-5834	76	4	the	the	DET
ejpam-5834	76	5	following	following	NOUN
ejpam-5834	76	6	:	:	PUNCT
ejpam-5834	76	7	i.	i.	NOUN
ejpam-5834	76	8	if	if	SCONJ
ejpam-5834	76	9	s	s	VERB
ejpam-5834	76	10	=	=	NOUN
ejpam-5834	76	11	1	1	NUM
ejpam-5834	76	12	in	in	ADP
ejpam-5834	76	13	definition	definition	NOUN
ejpam-5834	76	14	4	4	NUM
ejpam-5834	76	15	,	,	PUNCT
ejpam-5834	76	16	then	then	ADV
ejpam-5834	76	17	we	we	PRON
ejpam-5834	76	18	get	get	VERB
ejpam-5834	76	19	the	the	DET
ejpam-5834	76	20	class	class	NOUN
ejpam-5834	76	21	of	of	ADP
ejpam-5834	76	22	(	(	PUNCT
ejpam-5834	76	23	ρ	ρ	PROPN
ejpam-5834	76	24	,	,	PUNCT
ejpam-5834	76	25	m)-convex	m)-convex	PUNCT
ejpam-5834	76	26	function	function	NOUN
ejpam-5834	76	27	.	.	PUNCT
ejpam-5834	77	1	ii	ii	PROPN
ejpam-5834	77	2	.	.	PUNCT
ejpam-5834	78	1	if	if	SCONJ
ejpam-5834	78	2	ρ	ρ	PROPN
ejpam-5834	78	3	=	=	SYM
ejpam-5834	78	4	1	1	NUM
ejpam-5834	78	5	,	,	PUNCT
ejpam-5834	78	6	then	then	ADV
ejpam-5834	78	7	definition	definition	NOUN
ejpam-5834	78	8	4	4	NUM
ejpam-5834	78	9	reduces	reduce	VERB
ejpam-5834	78	10	to	to	ADP
ejpam-5834	78	11	the	the	DET
ejpam-5834	78	12	definition	definition	NOUN
ejpam-5834	78	13	for	for	ADP
ejpam-5834	78	14	(	(	PUNCT
ejpam-5834	78	15	s	s	X
ejpam-5834	78	16	,	,	PUNCT
ejpam-5834	78	17	m)-convex	m)-convex	PUNCT
ejpam-5834	78	18	function	function	NOUN
ejpam-5834	78	19	.	.	PUNCT
ejpam-5834	79	1	iii	iii	X
ejpam-5834	79	2	.	.	PUNCT
ejpam-5834	80	1	if	if	SCONJ
ejpam-5834	80	2	ρ	ρ	PROPN
ejpam-5834	80	3	=	=	SYM
ejpam-5834	80	4	m	m	NOUN
ejpam-5834	80	5	=	=	NOUN
ejpam-5834	80	6	1	1	NUM
ejpam-5834	80	7	in	in	ADP
ejpam-5834	80	8	definition	definition	NOUN
ejpam-5834	80	9	4	4	NUM
ejpam-5834	80	10	,	,	PUNCT
ejpam-5834	80	11	then	then	ADV
ejpam-5834	80	12	we	we	PRON
ejpam-5834	80	13	have	have	VERB
ejpam-5834	80	14	the	the	DET
ejpam-5834	80	15	class	class	NOUN
ejpam-5834	80	16	of	of	ADP
ejpam-5834	80	17	extended	extended	ADJ
ejpam-5834	80	18	s	s	NOUN
ejpam-5834	80	19	-	-	ADJ
ejpam-5834	80	20	convex	convex	ADJ
ejpam-5834	80	21	function	function	NOUN
ejpam-5834	80	22	.	.	PUNCT
ejpam-5834	81	1	iv	iv	X
ejpam-5834	81	2	.	.	PUNCT
ejpam-5834	82	1	if	if	SCONJ
ejpam-5834	82	2	ρ	ρ	PROPN
ejpam-5834	82	3	=	=	SYM
ejpam-5834	82	4	s	s	PART
ejpam-5834	82	5	=	=	PUNCT
ejpam-5834	82	6	m	m	NOUN
ejpam-5834	82	7	=	=	NOUN
ejpam-5834	82	8	1	1	NUM
ejpam-5834	82	9	in	in	ADP
ejpam-5834	82	10	definition	definition	NOUN
ejpam-5834	82	11	4	4	NUM
ejpam-5834	82	12	,	,	PUNCT
ejpam-5834	82	13	then	then	ADV
ejpam-5834	82	14	we	we	PRON
ejpam-5834	82	15	obtain	obtain	VERB
ejpam-5834	82	16	the	the	DET
ejpam-5834	82	17	classical	classical	ADJ
ejpam-5834	82	18	convex	convex	NOUN
ejpam-5834	82	19	function	function	NOUN
ejpam-5834	82	20	.	.	PUNCT
ejpam-5834	83	1	we	we	PRON
ejpam-5834	83	2	know	know	VERB
ejpam-5834	83	3	present	present	ADJ
ejpam-5834	83	4	the	the	DET
ejpam-5834	83	5	defintions	defintion	NOUN
ejpam-5834	83	6	of	of	ADP
ejpam-5834	83	7	riemann	riemann	PROPN
ejpam-5834	83	8	-	-	PUNCT
ejpam-5834	83	9	liouville	liouville	NOUN
ejpam-5834	83	10	integrals	integral	NOUN
ejpam-5834	83	11	as	as	SCONJ
ejpam-5834	83	12	follows	follow	VERB
ejpam-5834	83	13	.	.	PUNCT
ejpam-5834	84	1	definition	definition	NOUN
ejpam-5834	84	2	5	5	NUM
ejpam-5834	84	3	.	.	PUNCT
ejpam-5834	85	1	[	[	X
ejpam-5834	85	2	18	18	NUM
ejpam-5834	85	3	]	]	PUNCT
ejpam-5834	85	4	let	let	VERB
ejpam-5834	85	5	η	η	PROPN
ejpam-5834	85	6	∈	∈	PROPN
ejpam-5834	85	7	l1[k1	l1[k1	PROPN
ejpam-5834	85	8	,	,	PUNCT
ejpam-5834	85	9	k2	k2	NOUN
ejpam-5834	85	10	]	]	PUNCT
ejpam-5834	85	11	.	.	PUNCT
ejpam-5834	86	1	the	the	DET
ejpam-5834	86	2	riemann	riemann	PROPN
ejpam-5834	86	3	-	-	PUNCT
ejpam-5834	86	4	liouville	liouville	VERB
ejpam-5834	86	5	fractional	fractional	ADJ
ejpam-5834	86	6	integrals	integral	NOUN
ejpam-5834	86	7	jα	jα	PROPN
ejpam-5834	86	8	k1	k1	PROPN
ejpam-5834	86	9	+	+	CCONJ
ejpam-5834	86	10	η	η	PROPN
ejpam-5834	86	11	and	and	CCONJ
ejpam-5834	86	12	jα	jα	PROPN
ejpam-5834	86	13	k2−η	k2−η	PROPN
ejpam-5834	86	14	of	of	ADP
ejpam-5834	86	15	order	order	NOUN
ejpam-5834	86	16	ρ	ρ	PROPN
ejpam-5834	86	17	>	>	X
ejpam-5834	86	18	0	0	PUNCT
ejpam-5834	86	19	with	with	SCONJ
ejpam-5834	86	20	k1	k1	PROPN
ejpam-5834	86	21	≥	≥	X
ejpam-5834	86	22	0	0	NUM
ejpam-5834	86	23	are	be	AUX
ejpam-5834	86	24	defined	define	VERB
ejpam-5834	86	25	by	by	ADP
ejpam-5834	86	26	jρ	jρ	ADV
ejpam-5834	86	27	k+1	k+1	PRON
ejpam-5834	86	28	η(x	η(x	X
ejpam-5834	86	29	)	)	PUNCT
ejpam-5834	86	30	=	=	SYM
ejpam-5834	86	31	1	1	NUM
ejpam-5834	86	32	γ(ρ	γ(ρ	PROPN
ejpam-5834	86	33	)	)	PUNCT
ejpam-5834	86	34	∫	∫	PROPN
ejpam-5834	87	1	x	x	X
ejpam-5834	87	2	k1	k1	PROPN
ejpam-5834	87	3	(	(	PUNCT
ejpam-5834	87	4	x−ϖ)ρ−1η(ϖ)dϖ	x−ϖ)ρ−1η(ϖ)dϖ	PROPN
ejpam-5834	87	5	,	,	PUNCT
ejpam-5834	87	6	x	x	X
ejpam-5834	87	7	>	>	X
ejpam-5834	87	8	k1	k1	PROPN
ejpam-5834	87	9	o.	o.	PROPN
ejpam-5834	87	10	b.	b.	PROPN
ejpam-5834	87	11	almutairi	almutairi	PROPN
ejpam-5834	87	12	/	/	SYM
ejpam-5834	87	13	eur	eur	PROPN
ejpam-5834	87	14	.	.	PUNCT
ejpam-5834	88	1	j.	j.	PROPN
ejpam-5834	88	2	pure	pure	PROPN
ejpam-5834	88	3	appl	appl	PROPN
ejpam-5834	88	4	.	.	PROPN
ejpam-5834	88	5	math	math	PROPN
ejpam-5834	88	6	,	,	PUNCT
ejpam-5834	88	7	18	18	NUM
ejpam-5834	88	8	(	(	PUNCT
ejpam-5834	88	9	1	1	NUM
ejpam-5834	88	10	)	)	PUNCT
ejpam-5834	88	11	(	(	PUNCT
ejpam-5834	88	12	2025	2025	NUM
ejpam-5834	88	13	)	)	PUNCT
ejpam-5834	88	14	,	,	PUNCT
ejpam-5834	88	15	5834	5834	NUM
ejpam-5834	88	16	4	4	NUM
ejpam-5834	88	17	of	of	ADP
ejpam-5834	88	18	12	12	NUM
ejpam-5834	88	19	and	and	CCONJ
ejpam-5834	88	20	jρ	jρ	PROPN
ejpam-5834	88	21	k−2	k−2	PROPN
ejpam-5834	88	22	η(x	η(x	PROPN
ejpam-5834	88	23	)	)	PUNCT
ejpam-5834	88	24	=	=	SYM
ejpam-5834	88	25	1	1	NUM
ejpam-5834	88	26	γ(ρ	γ(ρ	PROPN
ejpam-5834	88	27	)	)	PUNCT
ejpam-5834	88	28	∫	∫	PROPN
ejpam-5834	89	1	k2	k2	PROPN
ejpam-5834	89	2	x	x	PROPN
ejpam-5834	89	3	(	(	PUNCT
ejpam-5834	89	4	ϖ	ϖ	NOUN
ejpam-5834	89	5	−	−	NOUN
ejpam-5834	89	6	x)ρ−1η(ϖ)dϖ	x)ρ−1η(ϖ)dϖ	PROPN
ejpam-5834	89	7	,	,	PUNCT
ejpam-5834	89	8	x	x	X
ejpam-5834	89	9	<	<	X
ejpam-5834	89	10	k2	k2	PROPN
ejpam-5834	89	11	respectively	respectively	ADV
ejpam-5834	89	12	.	.	PUNCT
ejpam-5834	90	1	here	here	ADV
ejpam-5834	90	2	,	,	PUNCT
ejpam-5834	90	3	γ(ρ	γ(ρ	PROPN
ejpam-5834	90	4	)	)	PUNCT
ejpam-5834	90	5	is	be	AUX
ejpam-5834	90	6	the	the	DET
ejpam-5834	90	7	gamma	gamma	NOUN
ejpam-5834	90	8	function	function	NOUN
ejpam-5834	90	9	and	and	CCONJ
ejpam-5834	90	10	j0	j0	PROPN
ejpam-5834	90	11	k1	k1	PROPN
ejpam-5834	90	12	+	+	CCONJ
ejpam-5834	90	13	η(x	η(x	NOUN
ejpam-5834	90	14	)	)	PUNCT
ejpam-5834	90	15	=	=	SYM
ejpam-5834	90	16	j0	j0	PROPN
ejpam-5834	90	17	k2−η(x	k2−η(x	PROPN
ejpam-5834	90	18	)	)	PUNCT
ejpam-5834	90	19	=	=	SYM
ejpam-5834	90	20	η(x	η(x	NOUN
ejpam-5834	90	21	)	)	PUNCT
ejpam-5834	90	22	.	.	PUNCT
ejpam-5834	91	1	we	we	PRON
ejpam-5834	91	2	further	far	ADV
ejpam-5834	91	3	,	,	PUNCT
ejpam-5834	91	4	present	present	VERB
ejpam-5834	91	5	the	the	DET
ejpam-5834	91	6	definitions	definition	NOUN
ejpam-5834	91	7	of	of	ADP
ejpam-5834	91	8	some	some	DET
ejpam-5834	91	9	special	special	ADJ
ejpam-5834	91	10	functions	function	NOUN
ejpam-5834	91	11	as	as	SCONJ
ejpam-5834	91	12	follows	follow	VERB
ejpam-5834	91	13	.	.	PUNCT
ejpam-5834	92	1	definition	definition	NOUN
ejpam-5834	92	2	6	6	NUM
ejpam-5834	92	3	.	.	PUNCT
ejpam-5834	93	1	[	[	X
ejpam-5834	93	2	9	9	NUM
ejpam-5834	93	3	]	]	PUNCT
ejpam-5834	93	4	for	for	ADP
ejpam-5834	93	5	any	any	DET
ejpam-5834	93	6	complex	complex	ADJ
ejpam-5834	93	7	numbers	number	NOUN
ejpam-5834	93	8	and	and	CCONJ
ejpam-5834	93	9	nonpositive	nonpositive	ADJ
ejpam-5834	93	10	integers	integer	NOUN
ejpam-5834	93	11	k1	k1	PROPN
ejpam-5834	93	12	,	,	PUNCT
ejpam-5834	93	13	k2	k2	NOUN
ejpam-5834	93	14	such	such	ADJ
ejpam-5834	93	15	that	that	PRON
ejpam-5834	93	16	re(k1	re(k1	NOUN
ejpam-5834	93	17	)	)	PUNCT
ejpam-5834	93	18	>	>	X
ejpam-5834	93	19	0	0	NUM
ejpam-5834	93	20	and	and	CCONJ
ejpam-5834	93	21	re(k2	re(k2	NOUN
ejpam-5834	93	22	)	)	PUNCT
ejpam-5834	93	23	>	>	X
ejpam-5834	94	1	0	0	X
ejpam-5834	94	2	.	.	PUNCT
ejpam-5834	95	1	the	the	DET
ejpam-5834	95	2	beta	beta	ADJ
ejpam-5834	95	3	function	function	NOUN
ejpam-5834	95	4	is	be	AUX
ejpam-5834	95	5	defined	define	VERB
ejpam-5834	95	6	by	by	ADP
ejpam-5834	95	7	b(k1	b(k1	PROPN
ejpam-5834	95	8	,	,	PUNCT
ejpam-5834	95	9	k2	k2	NOUN
ejpam-5834	95	10	)	)	PUNCT
ejpam-5834	96	1	=	=	SYM
ejpam-5834	96	2	∫	∫	PROPN
ejpam-5834	96	3	1	1	NUM
ejpam-5834	96	4	0	0	NUM
ejpam-5834	96	5	ϖk1−1(1−ϖ)k2−1dϖ	ϖk1−1(1−ϖ)k2−1dϖ	X
ejpam-5834	96	6	=	=	SYM
ejpam-5834	96	7	γ(k1)γ(k2	γ(k1)γ(k2	PROPN
ejpam-5834	96	8	)	)	PUNCT
ejpam-5834	96	9	γ(k1	γ(k1	NOUN
ejpam-5834	97	1	+	+	X
ejpam-5834	97	2	k2	k2	ADJ
ejpam-5834	97	3	)	)	PUNCT
ejpam-5834	97	4	,	,	PUNCT
ejpam-5834	97	5	where	where	SCONJ
ejpam-5834	97	6	γ	γ	PROPN
ejpam-5834	97	7	is	be	AUX
ejpam-5834	97	8	the	the	DET
ejpam-5834	97	9	gamma	gamma	PROPN
ejpam-5834	97	10	function	function	NOUN
ejpam-5834	97	11	.	.	PUNCT
ejpam-5834	98	1	definition	definition	NOUN
ejpam-5834	98	2	7	7	NUM
ejpam-5834	98	3	.	.	PUNCT
ejpam-5834	99	1	[	[	X
ejpam-5834	99	2	12	12	NUM
ejpam-5834	99	3	]	]	PUNCT
ejpam-5834	99	4	for	for	ADP
ejpam-5834	99	5	any	any	DET
ejpam-5834	99	6	complex	complex	ADJ
ejpam-5834	99	7	numbers	number	NOUN
ejpam-5834	99	8	k1	k1	NOUN
ejpam-5834	99	9	,	,	PUNCT
ejpam-5834	99	10	k2	k2	PROPN
ejpam-5834	99	11	with	with	ADP
ejpam-5834	99	12	re	re	PROPN
ejpam-5834	99	13	(	(	PUNCT
ejpam-5834	99	14	k1	k1	NOUN
ejpam-5834	99	15	)	)	PUNCT
ejpam-5834	99	16	,	,	PUNCT
ejpam-5834	99	17	re	re	X
ejpam-5834	99	18	(	(	PUNCT
ejpam-5834	99	19	k2	k2	NOUN
ejpam-5834	99	20	)	)	PUNCT
ejpam-5834	99	21	>	>	X
ejpam-5834	99	22	0	0	NUM
ejpam-5834	99	23	,	,	PUNCT
ejpam-5834	99	24	the	the	DET
ejpam-5834	99	25	incomplete	incomplete	ADJ
ejpam-5834	99	26	beta	beta	NOUN
ejpam-5834	99	27	function	function	NOUN
ejpam-5834	99	28	is	be	AUX
ejpam-5834	99	29	defined	define	VERB
ejpam-5834	99	30	as	as	ADP
ejpam-5834	99	31	ba(k1	ba(k1	PROPN
ejpam-5834	99	32	,	,	PUNCT
ejpam-5834	99	33	k2	k2	NOUN
ejpam-5834	99	34	)	)	PUNCT
ejpam-5834	100	1	=	=	SYM
ejpam-5834	100	2	∫	∫	PROPN
ejpam-5834	100	3	a	a	DET
ejpam-5834	100	4	0	0	PUNCT
ejpam-5834	100	5	ϖk1−1(1−ϖ)k2−1dϖ	ϖk1−1(1−ϖ)k2−1dϖ	NOUN
ejpam-5834	100	6	,	,	PUNCT
ejpam-5834	100	7	0	0	PUNCT
ejpam-5834	100	8	<	<	X
ejpam-5834	100	9	a	a	PRON
ejpam-5834	100	10	<	<	X
ejpam-5834	100	11	1	1	NUM
ejpam-5834	100	12	.	.	PUNCT
ejpam-5834	100	13	definition	definition	NOUN
ejpam-5834	100	14	8	8	NUM
ejpam-5834	100	15	.	.	PUNCT
ejpam-5834	101	1	[	[	X
ejpam-5834	101	2	9	9	NUM
ejpam-5834	101	3	]	]	X
ejpam-5834	101	4	the	the	DET
ejpam-5834	101	5	integral	integral	ADJ
ejpam-5834	101	6	representation	representation	NOUN
ejpam-5834	101	7	of	of	ADP
ejpam-5834	101	8	the	the	DET
ejpam-5834	101	9	hypergeometric	hypergeometric	ADJ
ejpam-5834	101	10	function	function	NOUN
ejpam-5834	101	11	is	be	AUX
ejpam-5834	101	12	defined	define	VERB
ejpam-5834	101	13	for	for	ADP
ejpam-5834	101	14	k1	k1	NOUN
ejpam-5834	101	15	,	,	PUNCT
ejpam-5834	101	16	k2	k2	PROPN
ejpam-5834	101	17	∈	∈	PROPN
ejpam-5834	101	18	c	c	PROPN
ejpam-5834	101	19	and	and	CCONJ
ejpam-5834	101	20	k3	k3	PROPN
ejpam-5834	101	21	∈	∈	PROPN
ejpam-5834	101	22	c\z−	c\z−	NOUN
ejpam-5834	101	23	0	0	NUM
ejpam-5834	101	24	,	,	PUNCT
ejpam-5834	101	25	re(k3	re(k3	X
ejpam-5834	101	26	)	)	PUNCT
ejpam-5834	101	27	>	>	X
ejpam-5834	101	28	re(k2	re(k2	PROPN
ejpam-5834	101	29	)	)	PUNCT
ejpam-5834	101	30	>	>	X
ejpam-5834	101	31	0	0	NUM
ejpam-5834	101	32	,	,	PUNCT
ejpam-5834	101	33	and	and	CCONJ
ejpam-5834	101	34	|k4|	|k4|	NOUN
ejpam-5834	101	35	<	<	X
ejpam-5834	101	36	1	1	NUM
ejpam-5834	101	37	,	,	PUNCT
ejpam-5834	101	38	as	as	SCONJ
ejpam-5834	101	39	follows	follow	VERB
ejpam-5834	101	40	2f1(k1	2f1(k1	NUM
ejpam-5834	101	41	,	,	PUNCT
ejpam-5834	101	42	k2	k2	PROPN
ejpam-5834	101	43	,	,	PUNCT
ejpam-5834	101	44	k3	k3	PROPN
ejpam-5834	101	45	;	;	PUNCT
ejpam-5834	101	46	k4	k4	ADJ
ejpam-5834	101	47	)	)	PUNCT
ejpam-5834	101	48	=	=	SYM
ejpam-5834	101	49	1	1	NUM
ejpam-5834	101	50	b(k2	b(k2	NOUN
ejpam-5834	101	51	,	,	PUNCT
ejpam-5834	101	52	k3	k3	VERB
ejpam-5834	101	53	−	−	PROPN
ejpam-5834	101	54	k2	k2	PROPN
ejpam-5834	101	55	)	)	PUNCT
ejpam-5834	101	56	∫	∫	PROPN
ejpam-5834	102	1	1	1	NUM
ejpam-5834	102	2	0	0	NUM
ejpam-5834	102	3	ϖk2−1(1−ϖ)k3−k2−1(1−	ϖk2−1(1−ϖ)k3−k2−1(1−	PROPN
ejpam-5834	102	4	k4ϖ)−k1dϖ	k4ϖ)−k1dϖ	PROPN
ejpam-5834	102	5	,	,	PUNCT
ejpam-5834	102	6	where	where	SCONJ
ejpam-5834	102	7	b	b	X
ejpam-5834	102	8	(	(	PUNCT
ejpam-5834	102	9	.	.	PUNCT
ejpam-5834	102	10	,	,	PUNCT
ejpam-5834	102	11	.	.	PUNCT
ejpam-5834	102	12	)	)	PUNCT
ejpam-5834	102	13	is	be	AUX
ejpam-5834	102	14	the	the	DET
ejpam-5834	102	15	beta	beta	ADJ
ejpam-5834	102	16	function	function	NOUN
ejpam-5834	102	17	.	.	PUNCT
ejpam-5834	103	1	3	3	X
ejpam-5834	103	2	.	.	X
ejpam-5834	103	3	main	main	ADJ
ejpam-5834	103	4	result	result	NOUN
ejpam-5834	103	5	in	in	ADP
ejpam-5834	103	6	this	this	DET
ejpam-5834	103	7	section	section	NOUN
ejpam-5834	103	8	,	,	PUNCT
ejpam-5834	103	9	we	we	PRON
ejpam-5834	103	10	first	first	ADV
ejpam-5834	103	11	present	present	VERB
ejpam-5834	103	12	some	some	DET
ejpam-5834	103	13	generalized	generalized	ADJ
ejpam-5834	103	14	midpoint	midpoint	NOUN
ejpam-5834	103	15	type	type	NOUN
ejpam-5834	103	16	inequalities	inequality	NOUN
ejpam-5834	103	17	for	for	ADP
ejpam-5834	103	18	(	(	PUNCT
ejpam-5834	103	19	ρ	ρ	NOUN
ejpam-5834	103	20	,	,	PUNCT
ejpam-5834	103	21	s)convex	s)convex	NOUN
ejpam-5834	103	22	functions	function	NOUN
ejpam-5834	103	23	.	.	PUNCT
ejpam-5834	104	1	theorem	theorem	NOUN
ejpam-5834	104	2	2	2	NUM
ejpam-5834	104	3	.	.	PUNCT
ejpam-5834	104	4	suppose	suppose	VERB
ejpam-5834	104	5	that	that	SCONJ
ejpam-5834	104	6	η	η	PROPN
ejpam-5834	104	7	:	:	PUNCT
ejpam-5834	104	8	[	[	X
ejpam-5834	104	9	k1	k1	X
ejpam-5834	104	10	,	,	PUNCT
ejpam-5834	104	11	k2	k2	NOUN
ejpam-5834	104	12	]	]	PUNCT
ejpam-5834	104	13	→	→	PUNCT
ejpam-5834	104	14	r	r	NOUN
ejpam-5834	104	15	is	be	AUX
ejpam-5834	104	16	a	a	DET
ejpam-5834	104	17	twice	twice	ADV
ejpam-5834	104	18	differentiable	differentiable	ADJ
ejpam-5834	104	19	function	function	NOUN
ejpam-5834	104	20	on	on	ADP
ejpam-5834	104	21	(	(	PUNCT
ejpam-5834	104	22	k1	k1	NOUN
ejpam-5834	104	23	,	,	PUNCT
ejpam-5834	104	24	k2	k2	NOUN
ejpam-5834	104	25	)	)	PUNCT
ejpam-5834	104	26	with	with	ADP
ejpam-5834	104	27	k1	k1	PROPN
ejpam-5834	104	28	<	<	X
ejpam-5834	104	29	k2	k2	PROPN
ejpam-5834	104	30	.	.	PUNCT
ejpam-5834	105	1	if	if	SCONJ
ejpam-5834	105	2	|η′′|	|η′′|	PROPN
ejpam-5834	105	3	is	be	AUX
ejpam-5834	105	4	(	(	PUNCT
ejpam-5834	105	5	ρ	ρ	PROPN
ejpam-5834	105	6	,	,	PUNCT
ejpam-5834	105	7	s	s	PART
ejpam-5834	105	8	)	)	PUNCT
ejpam-5834	105	9	convex	convex	NOUN
ejpam-5834	105	10	function	function	NOUN
ejpam-5834	105	11	,	,	PUNCT
ejpam-5834	105	12	where	where	SCONJ
ejpam-5834	105	13	(	(	PUNCT
ejpam-5834	105	14	ρ	ρ	PROPN
ejpam-5834	105	15	,	,	PUNCT
ejpam-5834	105	16	s	s	PART
ejpam-5834	105	17	)	)	PUNCT
ejpam-5834	105	18	∈	∈	PROPN
ejpam-5834	105	19	(	(	PUNCT
ejpam-5834	105	20	0	0	NUM
ejpam-5834	105	21	,	,	PUNCT
ejpam-5834	105	22	1]2	1]2	NUM
ejpam-5834	105	23	and	and	CCONJ
ejpam-5834	105	24	η′′	η′′	PROPN
ejpam-5834	105	25	∈	∈	PROPN
ejpam-5834	105	26	l[k1	l[k1	NOUN
ejpam-5834	105	27	,	,	PUNCT
ejpam-5834	105	28	k2	k2	NOUN
ejpam-5834	105	29	]	]	PUNCT
ejpam-5834	105	30	,	,	PUNCT
ejpam-5834	105	31	then	then	ADV
ejpam-5834	105	32	the	the	DET
ejpam-5834	105	33	following∣∣∣∣∣2ρ−1γ(ρ+	following∣∣∣∣∣2ρ−1γ(ρ+	NOUN
ejpam-5834	105	34	1	1	NUM
ejpam-5834	105	35	)	)	PUNCT
ejpam-5834	105	36	(	(	PUNCT
ejpam-5834	105	37	k2	k2	PROPN
ejpam-5834	105	38	−	−	PROPN
ejpam-5834	105	39	k1)ρ	k1)ρ	NOUN
ejpam-5834	105	40	[	[	PUNCT
ejpam-5834	105	41	jρ	jρ	PROPN
ejpam-5834	105	42	(	(	PUNCT
ejpam-5834	105	43	k1+k2	k1+k2	PROPN
ejpam-5834	105	44	2	2	NUM
ejpam-5834	105	45	)	)	PUNCT
ejpam-5834	105	46	−η(k1	−η(k1	PROPN
ejpam-5834	105	47	)	)	PUNCT
ejpam-5834	106	1	+	+	CCONJ
ejpam-5834	106	2	jα	jα	NOUN
ejpam-5834	106	3	(	(	PUNCT
ejpam-5834	106	4	k1+k2	k1+k2	PROPN
ejpam-5834	106	5	2	2	NUM
ejpam-5834	106	6	)	)	PUNCT
ejpam-5834	106	7	+	+	NOUN
ejpam-5834	106	8	η(k2	η(k2	NOUN
ejpam-5834	106	9	)	)	PUNCT
ejpam-5834	106	10	]	]	PUNCT
ejpam-5834	106	11	−	−	PROPN
ejpam-5834	106	12	η	η	X
ejpam-5834	106	13	(	(	PUNCT
ejpam-5834	106	14	k1	k1	X
ejpam-5834	106	15	+	+	CCONJ
ejpam-5834	106	16	k2	k2	ADJ
ejpam-5834	106	17	2	2	NUM
ejpam-5834	106	18	)	)	PUNCT
ejpam-5834	106	19	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5834	106	20	≤	≤	PROPN
ejpam-5834	106	21	(	(	PUNCT
ejpam-5834	106	22	k2	k2	ADJ
ejpam-5834	106	23	−	−	PROPN
ejpam-5834	106	24	k1	k1	NOUN
ejpam-5834	106	25	)	)	PUNCT
ejpam-5834	106	26	2	2	NUM
ejpam-5834	106	27	2ρs+3(ρ+	2ρs+3(ρ+	NUM
ejpam-5834	106	28	1	1	NUM
ejpam-5834	106	29	)	)	PUNCT
ejpam-5834	106	30	[	[	X
ejpam-5834	106	31	∣∣η′′(k1)∣∣	∣∣η′′(k1)∣∣	NOUN
ejpam-5834	106	32	2f1(1,−ρs	2f1(1,−ρ	NOUN
ejpam-5834	106	33	;	;	PUNCT
ejpam-5834	106	34	3	3	NUM
ejpam-5834	106	35	+	+	CCONJ
ejpam-5834	106	36	k1;−1	k1;−1	NOUN
ejpam-5834	106	37	)	)	PUNCT
ejpam-5834	106	38	k1	k1	NOUN
ejpam-5834	106	39	+	+	CCONJ
ejpam-5834	106	40	2	2	NUM
ejpam-5834	106	41	+	+	CCONJ
ejpam-5834	106	42	∣∣η′′(k2)∣∣ω(ρ	∣∣η′′(k2)∣∣ω(ρ	NOUN
ejpam-5834	106	43	,	,	PUNCT
ejpam-5834	106	44	s,ϖ	s,ϖ	NOUN
ejpam-5834	106	45	)	)	PUNCT
ejpam-5834	106	46	+	+	CCONJ
ejpam-5834	106	47	∣∣η′′(k1)∣∣	∣∣η′′(k1)∣∣	PROPN
ejpam-5834	106	48	γ(ρs+	γ(ρs+	NOUN
ejpam-5834	106	49	ρ+	ρ+	NUM
ejpam-5834	106	50	2	2	NUM
ejpam-5834	106	51	)	)	PUNCT
ejpam-5834	106	52	γ(ρs+	γ(ρs+	NOUN
ejpam-5834	106	53	ρ+	ρ+	NUM
ejpam-5834	106	54	3	3	NUM
ejpam-5834	106	55	)	)	PUNCT
ejpam-5834	106	56	+	+	NUM
ejpam-5834	106	57	∣∣η′′(k2)∣∣ω(ρ	∣∣η′′(k2)∣∣ω(ρ	NOUN
ejpam-5834	106	58	,	,	PUNCT
ejpam-5834	106	59	s,ϖ	s,ϖ	NOUN
ejpam-5834	106	60	)	)	PUNCT
ejpam-5834	106	61	]	]	PUNCT
ejpam-5834	106	62	.	.	PUNCT
ejpam-5834	107	1	where	where	SCONJ
ejpam-5834	107	2	ω(ρ	ω(ρ	NOUN
ejpam-5834	107	3	,	,	PUNCT
ejpam-5834	107	4	s,ϖ	s,ϖ	NOUN
ejpam-5834	107	5	)	)	PUNCT
ejpam-5834	107	6	=	=	SYM
ejpam-5834	107	7	∫	∫	PROPN
ejpam-5834	107	8	1	1	NUM
ejpam-5834	107	9	0	0	NUM
ejpam-5834	107	10	(	(	PUNCT
ejpam-5834	107	11	1−ϖ)ρ+1(2ρ	1−ϖ)ρ+1(2ρ	NUM
ejpam-5834	107	12	−	−	NOUN
ejpam-5834	107	13	(	(	PUNCT
ejpam-5834	107	14	1	1	NUM
ejpam-5834	107	15	+	+	NOUN
ejpam-5834	107	16	ϖ)ρ)sdϖ	ϖ)ρ)sdϖ	NOUN
ejpam-5834	107	17	holds	hold	NOUN
ejpam-5834	107	18	.	.	PUNCT
ejpam-5834	108	1	o.	o.	PROPN
ejpam-5834	108	2	b.	b.	PROPN
ejpam-5834	108	3	almutairi	almutairi	PROPN
ejpam-5834	108	4	/	/	SYM
ejpam-5834	108	5	eur	eur	PROPN
ejpam-5834	108	6	.	.	PUNCT
ejpam-5834	109	1	j.	j.	PROPN
ejpam-5834	109	2	pure	pure	PROPN
ejpam-5834	109	3	appl	appl	PROPN
ejpam-5834	109	4	.	.	PROPN
ejpam-5834	109	5	math	math	PROPN
ejpam-5834	109	6	,	,	PUNCT
ejpam-5834	109	7	18	18	NUM
ejpam-5834	109	8	(	(	PUNCT
ejpam-5834	109	9	1	1	NUM
ejpam-5834	109	10	)	)	PUNCT
ejpam-5834	109	11	(	(	PUNCT
ejpam-5834	109	12	2025	2025	NUM
ejpam-5834	109	13	)	)	PUNCT
ejpam-5834	109	14	,	,	PUNCT
ejpam-5834	109	15	5834	5834	NUM
ejpam-5834	109	16	5	5	NUM
ejpam-5834	109	17	of	of	ADP
ejpam-5834	109	18	12	12	NUM
ejpam-5834	109	19	proof	proof	NOUN
ejpam-5834	109	20	.	.	PUNCT
ejpam-5834	110	1	we	we	PRON
ejpam-5834	110	2	now	now	ADV
ejpam-5834	110	3	use	use	VERB
ejpam-5834	110	4	identity	identity	NOUN
ejpam-5834	110	5	(	(	PUNCT
ejpam-5834	110	6	2	2	NUM
ejpam-5834	110	7	)	)	PUNCT
ejpam-5834	110	8	and	and	CCONJ
ejpam-5834	110	9	(	(	PUNCT
ejpam-5834	110	10	ρ	ρ	PROPN
ejpam-5834	110	11	,	,	PUNCT
ejpam-5834	110	12	s)-convexity	s)-convexity	NOUN
ejpam-5834	110	13	of	of	ADP
ejpam-5834	110	14	|η′′|	|η′′|	PROPN
ejpam-5834	110	15	to	to	PART
ejpam-5834	110	16	obtain	obtain	VERB
ejpam-5834	110	17	the	the	DET
ejpam-5834	110	18	following∣∣∣∣∣2ρ−1γ(ρ+	following∣∣∣∣∣2ρ−1γ(ρ+	NOUN
ejpam-5834	110	19	1	1	NUM
ejpam-5834	110	20	)	)	PUNCT
ejpam-5834	110	21	(	(	PUNCT
ejpam-5834	110	22	k2	k2	PROPN
ejpam-5834	110	23	−	−	PROPN
ejpam-5834	110	24	k1)ρ	k1)ρ	NOUN
ejpam-5834	110	25	[	[	PUNCT
ejpam-5834	110	26	jρ	jρ	PROPN
ejpam-5834	110	27	(	(	PUNCT
ejpam-5834	110	28	k1+k2	k1+k2	PROPN
ejpam-5834	110	29	2	2	NUM
ejpam-5834	110	30	)	)	PUNCT
ejpam-5834	110	31	−η(k1	−η(k1	PROPN
ejpam-5834	110	32	)	)	PUNCT
ejpam-5834	111	1	+	+	CCONJ
ejpam-5834	112	1	jρ	jρ	PROPN
ejpam-5834	112	2	(	(	PUNCT
ejpam-5834	112	3	k1+k2	k1+k2	PROPN
ejpam-5834	112	4	2	2	NUM
ejpam-5834	112	5	)	)	PUNCT
ejpam-5834	112	6	+	+	NOUN
ejpam-5834	112	7	η(k2	η(k2	NOUN
ejpam-5834	112	8	)	)	PUNCT
ejpam-5834	112	9	]	]	PUNCT
ejpam-5834	113	1	−	−	PROPN
ejpam-5834	113	2	η	η	X
ejpam-5834	113	3	(	(	PUNCT
ejpam-5834	113	4	k1	k1	X
ejpam-5834	113	5	+	+	CCONJ
ejpam-5834	113	6	k2	k2	ADJ
ejpam-5834	113	7	2	2	NUM
ejpam-5834	113	8	)	)	PUNCT
ejpam-5834	113	9	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5834	113	10	=	=	PUNCT
ejpam-5834	113	11	∣∣∣∣(k2	∣∣∣∣(k2	VERB
ejpam-5834	113	12	−	−	PROPN
ejpam-5834	113	13	k1	k1	NOUN
ejpam-5834	113	14	)	)	PUNCT
ejpam-5834	113	15	2	2	NUM
ejpam-5834	113	16	8(ρ+	8(ρ+	NUM
ejpam-5834	113	17	1	1	NUM
ejpam-5834	113	18	)	)	PUNCT
ejpam-5834	113	19	∫	∫	PROPN
ejpam-5834	113	20	1	1	NUM
ejpam-5834	113	21	0	0	NUM
ejpam-5834	113	22	(	(	PUNCT
ejpam-5834	113	23	1−ϖ)ρ+1	1−ϖ)ρ+1	NUM
ejpam-5834	113	24	[	[	PUNCT
ejpam-5834	113	25	η′′	η′′	PROPN
ejpam-5834	113	26	(	(	PUNCT
ejpam-5834	113	27	1	1	NUM
ejpam-5834	113	28	+	+	NOUN
ejpam-5834	113	29	ϖ	ϖ	PROPN
ejpam-5834	113	30	2	2	NUM
ejpam-5834	113	31	k1	k1	NOUN
ejpam-5834	113	32	+	+	CCONJ
ejpam-5834	113	33	1−ϖ	1−ϖ	NUM
ejpam-5834	113	34	2	2	NUM
ejpam-5834	113	35	k2	k2	NOUN
ejpam-5834	113	36	)	)	PUNCT
ejpam-5834	113	37	+	+	CCONJ
ejpam-5834	113	38	η′′	η′′	PROPN
ejpam-5834	113	39	(	(	PUNCT
ejpam-5834	113	40	1−ϖ	1−ϖ	NUM
ejpam-5834	113	41	2	2	NUM
ejpam-5834	113	42	k1	k1	NOUN
ejpam-5834	113	43	+	+	CCONJ
ejpam-5834	113	44	1	1	NUM
ejpam-5834	113	45	+	+	ADJ
ejpam-5834	113	46	ϖ	ϖ	PROPN
ejpam-5834	113	47	2	2	NUM
ejpam-5834	113	48	k2	k2	NOUN
ejpam-5834	113	49	)	)	PUNCT
ejpam-5834	113	50	]	]	PUNCT
ejpam-5834	114	1	dϖ	dϖ	ADP
ejpam-5834	114	2	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5834	114	3	≤	≤	PROPN
ejpam-5834	114	4	∣∣∣∣(k2	∣∣∣∣(k2	VERB
ejpam-5834	114	5	−	−	PROPN
ejpam-5834	114	6	k1	k1	NOUN
ejpam-5834	114	7	)	)	PUNCT
ejpam-5834	114	8	2	2	NUM
ejpam-5834	114	9	8(ρ+	8(ρ+	NUM
ejpam-5834	114	10	1	1	NUM
ejpam-5834	114	11	)	)	PUNCT
ejpam-5834	114	12	∫	∫	PROPN
ejpam-5834	114	13	1	1	NUM
ejpam-5834	114	14	0	0	NUM
ejpam-5834	114	15	(	(	PUNCT
ejpam-5834	114	16	1−ϖ)ρ+1η′′	1−ϖ)ρ+1η′′	NUM
ejpam-5834	114	17	(	(	PUNCT
ejpam-5834	114	18	1	1	NUM
ejpam-5834	114	19	+	+	NOUN
ejpam-5834	114	20	ϖ	ϖ	PROPN
ejpam-5834	114	21	2	2	NUM
ejpam-5834	114	22	k1	k1	NOUN
ejpam-5834	114	23	+	+	CCONJ
ejpam-5834	114	24	1−ϖ	1−ϖ	NUM
ejpam-5834	114	25	2	2	NUM
ejpam-5834	114	26	k2	k2	NOUN
ejpam-5834	114	27	)	)	PUNCT
ejpam-5834	114	28	dϖ	dϖ	ADP
ejpam-5834	114	29	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5834	114	30	+	+	NUM
ejpam-5834	114	31	∣∣∣∣(k2	∣∣∣∣(k2	VERB
ejpam-5834	114	32	−	−	PROPN
ejpam-5834	114	33	k1	k1	NOUN
ejpam-5834	114	34	)	)	PUNCT
ejpam-5834	114	35	2	2	NUM
ejpam-5834	114	36	8(ρ+	8(ρ+	NUM
ejpam-5834	114	37	1	1	NUM
ejpam-5834	114	38	)	)	PUNCT
ejpam-5834	114	39	∫	∫	PROPN
ejpam-5834	114	40	1	1	NUM
ejpam-5834	114	41	0	0	NUM
ejpam-5834	114	42	(	(	PUNCT
ejpam-5834	114	43	1−ϖ)ρ+1η′′	1−ϖ)ρ+1η′′	NUM
ejpam-5834	114	44	(	(	PUNCT
ejpam-5834	114	45	1−ϖ	1−ϖ	NUM
ejpam-5834	114	46	2	2	NUM
ejpam-5834	114	47	k1	k1	NOUN
ejpam-5834	114	48	+	+	CCONJ
ejpam-5834	114	49	1	1	NUM
ejpam-5834	114	50	+	+	ADJ
ejpam-5834	114	51	ϖ	ϖ	PROPN
ejpam-5834	114	52	2	2	NUM
ejpam-5834	114	53	k2	k2	NOUN
ejpam-5834	114	54	)	)	PUNCT
ejpam-5834	114	55	dϖ	dϖ	ADP
ejpam-5834	114	56	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5834	114	57	≤	≤	NOUN
ejpam-5834	114	58	(	(	PUNCT
ejpam-5834	114	59	k2	k2	NOUN
ejpam-5834	114	60	−	−	PROPN
ejpam-5834	114	61	k1	k1	PROPN
ejpam-5834	114	62	)	)	PUNCT
ejpam-5834	114	63	2	2	NUM
ejpam-5834	114	64	8(ρ+	8(ρ+	NUM
ejpam-5834	114	65	1	1	NUM
ejpam-5834	114	66	)	)	PUNCT
ejpam-5834	114	67	∫	∫	PROPN
ejpam-5834	114	68	1	1	NUM
ejpam-5834	114	69	0	0	NUM
ejpam-5834	114	70	(	(	PUNCT
ejpam-5834	114	71	1−ϖ)ρ+1	1−ϖ)ρ+1	NUM
ejpam-5834	114	72	∣∣∣∣η′′(1	∣∣∣∣η′′(1	VERB
ejpam-5834	114	73	+	+	NOUN
ejpam-5834	114	74	ϖ	ϖ	PROPN
ejpam-5834	114	75	2	2	NUM
ejpam-5834	114	76	k1	k1	NOUN
ejpam-5834	114	77	+	+	CCONJ
ejpam-5834	114	78	1−ϖ	1−ϖ	NUM
ejpam-5834	114	79	2	2	NUM
ejpam-5834	114	80	k2	k2	NOUN
ejpam-5834	114	81	)	)	PUNCT
ejpam-5834	114	82	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5834	114	83	dϖ	dϖ	NOUN
ejpam-5834	114	84	+	+	CCONJ
ejpam-5834	114	85	(	(	PUNCT
ejpam-5834	114	86	k2	k2	PROPN
ejpam-5834	114	87	−	−	PROPN
ejpam-5834	114	88	k1	k1	PROPN
ejpam-5834	114	89	)	)	PUNCT
ejpam-5834	114	90	2	2	NUM
ejpam-5834	114	91	8(ρ+	8(ρ+	NUM
ejpam-5834	114	92	1	1	NUM
ejpam-5834	114	93	)	)	PUNCT
ejpam-5834	114	94	∫	∫	PROPN
ejpam-5834	114	95	1	1	NUM
ejpam-5834	114	96	0	0	NUM
ejpam-5834	114	97	(	(	PUNCT
ejpam-5834	114	98	1−ϖ)ρ+1	1−ϖ)ρ+1	NUM
ejpam-5834	114	99	∣∣∣∣η′′(1−ϖ	∣∣∣∣η′′(1−ϖ	ADJ
ejpam-5834	114	100	2	2	NUM
ejpam-5834	114	101	k1	k1	NOUN
ejpam-5834	114	102	+	+	CCONJ
ejpam-5834	114	103	1	1	NUM
ejpam-5834	114	104	+	+	ADJ
ejpam-5834	114	105	ϖ	ϖ	PROPN
ejpam-5834	114	106	2	2	NUM
ejpam-5834	114	107	k2	k2	NOUN
ejpam-5834	114	108	)	)	PUNCT
ejpam-5834	114	109	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5834	114	110	dϖ	dϖ	ADP
ejpam-5834	114	111	≤	≤	PROPN
ejpam-5834	114	112	(	(	PUNCT
ejpam-5834	114	113	k2	k2	NOUN
ejpam-5834	114	114	−	−	PROPN
ejpam-5834	114	115	k1	k1	PROPN
ejpam-5834	114	116	)	)	PUNCT
ejpam-5834	114	117	2	2	NUM
ejpam-5834	114	118	8(ρ+	8(ρ+	NUM
ejpam-5834	114	119	1	1	NUM
ejpam-5834	114	120	)	)	PUNCT
ejpam-5834	115	1	[	[	X
ejpam-5834	115	2	∫	∫	X
ejpam-5834	115	3	1	1	NUM
ejpam-5834	115	4	0	0	NUM
ejpam-5834	115	5	(	(	PUNCT
ejpam-5834	115	6	1−ϖ)ρ+1	1−ϖ)ρ+1	NUM
ejpam-5834	115	7	[	[	X
ejpam-5834	115	8	(	(	PUNCT
ejpam-5834	115	9	1	1	NUM
ejpam-5834	115	10	+	+	NOUN
ejpam-5834	115	11	ϖ	ϖ	NOUN
ejpam-5834	115	12	2	2	NUM
ejpam-5834	115	13	)	)	PUNCT
ejpam-5834	115	14	ρs	ρs	ADV
ejpam-5834	116	1	∣∣η′′(k1)∣∣+	∣∣η′′(k1)∣∣+	PROPN
ejpam-5834	116	2	(	(	PUNCT
ejpam-5834	116	3	1−	1−	NUM
ejpam-5834	116	4	(	(	PUNCT
ejpam-5834	116	5	1−ϖ	1−ϖ	NUM
ejpam-5834	116	6	2	2	NUM
ejpam-5834	116	7	)	)	PUNCT
ejpam-5834	116	8	ρ)s	ρ)s	NOUN
ejpam-5834	116	9	∣∣η′′(k2)∣∣	∣∣η′′(k2)∣∣	NOUN
ejpam-5834	116	10	]	]	PUNCT
ejpam-5834	116	11	dϖ	dϖ	PROPN
ejpam-5834	116	12	+	+	CCONJ
ejpam-5834	116	13	∫	∫	PROPN
ejpam-5834	116	14	1	1	NUM
ejpam-5834	116	15	0	0	NUM
ejpam-5834	116	16	(	(	PUNCT
ejpam-5834	116	17	1−ϖ)ρ+1	1−ϖ)ρ+1	NUM
ejpam-5834	116	18	[	[	X
ejpam-5834	116	19	(	(	PUNCT
ejpam-5834	116	20	1−ϖ	1−ϖ	NUM
ejpam-5834	116	21	2	2	NUM
ejpam-5834	116	22	)	)	PUNCT
ejpam-5834	116	23	ρs	ρs	ADV
ejpam-5834	116	24	∣∣η′′(k1)∣∣+	∣∣η′′(k1)∣∣+	PROPN
ejpam-5834	116	25	(	(	PUNCT
ejpam-5834	116	26	1−	1−	NUM
ejpam-5834	116	27	(	(	PUNCT
ejpam-5834	116	28	1	1	NUM
ejpam-5834	116	29	+	+	NOUN
ejpam-5834	116	30	ϖ	ϖ	NOUN
ejpam-5834	116	31	2	2	NUM
ejpam-5834	116	32	)	)	PUNCT
ejpam-5834	116	33	ρ)s	ρ)s	NOUN
ejpam-5834	116	34	∣∣η′′(k2)∣∣	∣∣η′′(k2)∣∣	X
ejpam-5834	116	35	]	]	PUNCT
ejpam-5834	116	36	dϖ	dϖ	X
ejpam-5834	116	37	]	]	X
ejpam-5834	116	38	=	=	SYM
ejpam-5834	116	39	(	(	PUNCT
ejpam-5834	116	40	k2	k2	PROPN
ejpam-5834	116	41	−	−	PROPN
ejpam-5834	116	42	k1	k1	NOUN
ejpam-5834	116	43	)	)	PUNCT
ejpam-5834	116	44	2	2	NUM
ejpam-5834	116	45	2ρs+3(ρ+	2ρs+3(ρ+	NUM
ejpam-5834	116	46	1	1	NUM
ejpam-5834	116	47	)	)	PUNCT
ejpam-5834	117	1	[	[	X
ejpam-5834	117	2	∣∣η′′(k1)∣∣	∣∣η′′(k1)∣∣	PRON
ejpam-5834	117	3	∫	∫	PROPN
ejpam-5834	117	4	1	1	NUM
ejpam-5834	117	5	0	0	NUM
ejpam-5834	117	6	(	(	PUNCT
ejpam-5834	117	7	1−ϖ)ρ+1(1	1−ϖ)ρ+1(1	NUM
ejpam-5834	117	8	+	+	NOUN
ejpam-5834	117	9	ϖ)ρsdϖ	ϖ)ρsdϖ	NOUN
ejpam-5834	117	10	+	+	SYM
ejpam-5834	117	11	∣∣η′′(k2)∣∣	∣∣η′′(k2)∣∣	X
ejpam-5834	117	12	∫	∫	X
ejpam-5834	117	13	1	1	NUM
ejpam-5834	117	14	0	0	NUM
ejpam-5834	117	15	(	(	PUNCT
ejpam-5834	117	16	1−ϖ)ρ+1(2ρ	1−ϖ)ρ+1(2ρ	NUM
ejpam-5834	117	17	−	−	NOUN
ejpam-5834	117	18	(	(	PUNCT
ejpam-5834	117	19	1−ϖ)ρ)sdϖ	1−ϖ)ρ)sdϖ	NOUN
ejpam-5834	117	20	+	+	CCONJ
ejpam-5834	117	21	∣∣η′′(k1)∣∣	∣∣η′′(k1)∣∣	PROPN
ejpam-5834	117	22	∫	∫	PROPN
ejpam-5834	117	23	1	1	NUM
ejpam-5834	117	24	0	0	NUM
ejpam-5834	117	25	(	(	PUNCT
ejpam-5834	117	26	1−ϖ)ρ+1(1−ϖ)ρsdϖ	1−ϖ)ρ+1(1−ϖ)ρsdϖ	NUM
ejpam-5834	117	27	+	+	SYM
ejpam-5834	117	28	∣∣η′′(k2)∣∣	∣∣η′′(k2)∣∣	ADV
ejpam-5834	117	29	∫	∫	X
ejpam-5834	117	30	1	1	NUM
ejpam-5834	117	31	0	0	NUM
ejpam-5834	117	32	(	(	PUNCT
ejpam-5834	117	33	1−ϖ)ρ+1(2ρ	1−ϖ)ρ+1(2ρ	NUM
ejpam-5834	117	34	−	−	NOUN
ejpam-5834	117	35	(	(	PUNCT
ejpam-5834	117	36	1	1	NUM
ejpam-5834	117	37	+	+	NOUN
ejpam-5834	117	38	ϖ)ρ)sdϖ	ϖ)ρ)sdϖ	NOUN
ejpam-5834	117	39	]	]	X
ejpam-5834	117	40	=	=	SYM
ejpam-5834	117	41	(	(	PUNCT
ejpam-5834	117	42	k2	k2	PROPN
ejpam-5834	117	43	−	−	PROPN
ejpam-5834	117	44	k1	k1	NOUN
ejpam-5834	117	45	)	)	PUNCT
ejpam-5834	117	46	2	2	NUM
ejpam-5834	117	47	2ρs+3(ρ+	2ρs+3(ρ+	NUM
ejpam-5834	117	48	1	1	NUM
ejpam-5834	117	49	)	)	PUNCT
ejpam-5834	117	50	[	[	X
ejpam-5834	117	51	∣∣η′′(k1)∣∣	∣∣η′′(k1)∣∣	NOUN
ejpam-5834	117	52	2f1(1,−ρs	2f1(1,−ρ	NOUN
ejpam-5834	117	53	;	;	PUNCT
ejpam-5834	117	54	3	3	NUM
ejpam-5834	117	55	+	+	CCONJ
ejpam-5834	117	56	k1;−1	k1;−1	NOUN
ejpam-5834	117	57	)	)	PUNCT
ejpam-5834	117	58	k1	k1	NOUN
ejpam-5834	117	59	+	+	CCONJ
ejpam-5834	117	60	2	2	NUM
ejpam-5834	117	61	+	+	NUM
ejpam-5834	117	62	∣∣η′′(k2)∣∣	∣∣η′′(k2)∣∣	ADV
ejpam-5834	117	63	∫	∫	X
ejpam-5834	117	64	1	1	NUM
ejpam-5834	117	65	0	0	NUM
ejpam-5834	117	66	(	(	PUNCT
ejpam-5834	117	67	1−ϖ)ρ+1(2ρ	1−ϖ)ρ+1(2ρ	NUM
ejpam-5834	117	68	−	−	NOUN
ejpam-5834	117	69	(	(	PUNCT
ejpam-5834	117	70	1−ϖ)ρ)sdϖ	1−ϖ)ρ)sdϖ	NOUN
ejpam-5834	117	71	+	+	CCONJ
ejpam-5834	117	72	∣∣η′′(k1)∣∣	∣∣η′′(k1)∣∣	PROPN
ejpam-5834	117	73	γ(ρs+	γ(ρs+	NOUN
ejpam-5834	117	74	ρ+	ρ+	NUM
ejpam-5834	117	75	2	2	NUM
ejpam-5834	117	76	)	)	PUNCT
ejpam-5834	117	77	γ(ρs+	γ(ρs+	NOUN
ejpam-5834	117	78	ρ+	ρ+	NUM
ejpam-5834	117	79	3	3	NUM
ejpam-5834	117	80	)	)	PUNCT
ejpam-5834	117	81	+	+	NUM
ejpam-5834	117	82	∣∣η′′(k2)∣∣	∣∣η′′(k2)∣∣	X
ejpam-5834	117	83	∫	∫	X
ejpam-5834	117	84	1	1	NUM
ejpam-5834	117	85	0	0	NUM
ejpam-5834	117	86	(	(	PUNCT
ejpam-5834	117	87	1	1	NUM
ejpam-5834	117	88	+	+	ADJ
ejpam-5834	117	89	ϖ)ρ+1(2ρ	ϖ)ρ+1(2ρ	ADJ
ejpam-5834	117	90	−	−	PROPN
ejpam-5834	117	91	(	(	PUNCT
ejpam-5834	117	92	1	1	NUM
ejpam-5834	117	93	+	+	NOUN
ejpam-5834	117	94	ϖ)ρ)sdϖ	ϖ)ρ)sdϖ	NOUN
ejpam-5834	117	95	]	]	PUNCT
ejpam-5834	117	96	≤	≤	NUM
ejpam-5834	117	97	(	(	PUNCT
ejpam-5834	117	98	k2	k2	ADJ
ejpam-5834	117	99	−	−	PROPN
ejpam-5834	117	100	k1	k1	NOUN
ejpam-5834	117	101	)	)	PUNCT
ejpam-5834	117	102	2	2	NUM
ejpam-5834	117	103	2ρs+3(ρ+	2ρs+3(ρ+	NUM
ejpam-5834	117	104	1	1	NUM
ejpam-5834	117	105	)	)	PUNCT
ejpam-5834	118	1	[	[	X
ejpam-5834	118	2	∣∣η′′(k1)∣∣	∣∣η′′(k1)∣∣	NOUN
ejpam-5834	118	3	2f1(1,−ρs	2f1(1,−ρ	NOUN
ejpam-5834	118	4	;	;	PUNCT
ejpam-5834	118	5	3	3	NUM
ejpam-5834	118	6	+	+	CCONJ
ejpam-5834	118	7	k1;−1	k1;−1	NOUN
ejpam-5834	118	8	)	)	PUNCT
ejpam-5834	118	9	k1	k1	NOUN
ejpam-5834	118	10	+	+	CCONJ
ejpam-5834	118	11	2	2	NUM
ejpam-5834	118	12	+	+	CCONJ
ejpam-5834	118	13	∣∣η′′(k2)∣∣ω(ρ	∣∣η′′(k2)∣∣ω(ρ	NOUN
ejpam-5834	118	14	,	,	PUNCT
ejpam-5834	118	15	s,ϖ	s,ϖ	NOUN
ejpam-5834	118	16	)	)	PUNCT
ejpam-5834	118	17	+	+	CCONJ
ejpam-5834	118	18	∣∣η′′(k1)∣∣	∣∣η′′(k1)∣∣	PROPN
ejpam-5834	118	19	γ(ρs+	γ(ρs+	NOUN
ejpam-5834	118	20	ρ+	ρ+	NUM
ejpam-5834	118	21	2	2	NUM
ejpam-5834	118	22	)	)	PUNCT
ejpam-5834	118	23	γ(ρs+	γ(ρs+	NOUN
ejpam-5834	118	24	ρ+	ρ+	NUM
ejpam-5834	118	25	3	3	NUM
ejpam-5834	118	26	)	)	PUNCT
ejpam-5834	118	27	+	+	NUM
ejpam-5834	118	28	∣∣η′′(k2)∣∣ω(ρ	∣∣η′′(k2)∣∣ω(ρ	NOUN
ejpam-5834	118	29	,	,	PUNCT
ejpam-5834	118	30	s,ϖ	s,ϖ	NOUN
ejpam-5834	118	31	)	)	PUNCT
ejpam-5834	118	32	]	]	PUNCT
ejpam-5834	118	33	.	.	PUNCT
ejpam-5834	119	1	theorem	theorem	NOUN
ejpam-5834	119	2	3	3	X
ejpam-5834	119	3	.	.	PUNCT
ejpam-5834	120	1	let	let	VERB
ejpam-5834	120	2	η	η	PROPN
ejpam-5834	120	3	:	:	PUNCT
ejpam-5834	120	4	[	[	X
ejpam-5834	120	5	k1	k1	X
ejpam-5834	120	6	,	,	PUNCT
ejpam-5834	120	7	k2	k2	NOUN
ejpam-5834	120	8	]	]	PUNCT
ejpam-5834	120	9	→	→	PUNCT
ejpam-5834	120	10	r	r	NOUN
ejpam-5834	120	11	be	be	VERB
ejpam-5834	120	12	twice	twice	ADV
ejpam-5834	120	13	differentiable	differentiable	ADJ
ejpam-5834	120	14	function	function	NOUN
ejpam-5834	120	15	on	on	ADP
ejpam-5834	120	16	(	(	PUNCT
ejpam-5834	120	17	k1	k1	NOUN
ejpam-5834	120	18	,	,	PUNCT
ejpam-5834	120	19	k2	k2	NOUN
ejpam-5834	120	20	)	)	PUNCT
ejpam-5834	120	21	with	with	ADP
ejpam-5834	120	22	k1	k1	PROPN
ejpam-5834	120	23	<	<	X
ejpam-5834	120	24	k2	k2	PROPN
ejpam-5834	120	25	.	.	PUNCT
ejpam-5834	121	1	if	if	SCONJ
ejpam-5834	121	2	η′′	η′′	PROPN
ejpam-5834	121	3	∈	∈	PROPN
ejpam-5834	121	4	l[k1	l[k1	NOUN
ejpam-5834	121	5	,	,	PUNCT
ejpam-5834	121	6	k2	k2	NOUN
ejpam-5834	121	7	]	]	PUNCT
ejpam-5834	121	8	and	and	CCONJ
ejpam-5834	121	9	|η′′|q	|η′′|q	NOUN
ejpam-5834	121	10	is	be	AUX
ejpam-5834	121	11	(	(	PUNCT
ejpam-5834	121	12	ρ	ρ	NOUN
ejpam-5834	121	13	,	,	PUNCT
ejpam-5834	121	14	s)-convex	s)-convex	PUNCT
ejpam-5834	121	15	function	function	NOUN
ejpam-5834	121	16	of	of	ADP
ejpam-5834	121	17	second	second	ADJ
ejpam-5834	121	18	kind	kind	NOUN
ejpam-5834	121	19	,	,	PUNCT
ejpam-5834	121	20	then	then	ADV
ejpam-5834	121	21	,	,	PUNCT
ejpam-5834	121	22	we	we	PRON
ejpam-5834	121	23	have	have	VERB
ejpam-5834	121	24	the	the	DET
ejpam-5834	121	25	following	follow	VERB
ejpam-5834	121	26	inequality	inequality	NOUN
ejpam-5834	121	27	for	for	ADP
ejpam-5834	121	28	fractional	fractional	ADJ
ejpam-5834	121	29	integrals:∣∣∣∣∣2ρ−1γ(ρ+	integrals:∣∣∣∣∣2ρ−1γ(ρ+	PROPN
ejpam-5834	121	30	1	1	NUM
ejpam-5834	121	31	)	)	PUNCT
ejpam-5834	121	32	(	(	PUNCT
ejpam-5834	121	33	k2	k2	PROPN
ejpam-5834	121	34	−	−	PROPN
ejpam-5834	121	35	k1)ρ	k1)ρ	NOUN
ejpam-5834	121	36	[	[	PUNCT
ejpam-5834	121	37	jρ	jρ	PROPN
ejpam-5834	121	38	(	(	PUNCT
ejpam-5834	121	39	k1+k2	k1+k2	PROPN
ejpam-5834	121	40	2	2	NUM
ejpam-5834	121	41	)	)	PUNCT
ejpam-5834	121	42	−η(k1	−η(k1	PROPN
ejpam-5834	121	43	)	)	PUNCT
ejpam-5834	122	1	+	+	CCONJ
ejpam-5834	123	1	jρ	jρ	PROPN
ejpam-5834	123	2	(	(	PUNCT
ejpam-5834	123	3	k1+k2	k1+k2	PROPN
ejpam-5834	123	4	2	2	NUM
ejpam-5834	123	5	)	)	PUNCT
ejpam-5834	123	6	+	+	NOUN
ejpam-5834	123	7	η(k2	η(k2	NOUN
ejpam-5834	123	8	)	)	PUNCT
ejpam-5834	123	9	]	]	PUNCT
ejpam-5834	124	1	−	−	PROPN
ejpam-5834	124	2	η	η	X
ejpam-5834	124	3	(	(	PUNCT
ejpam-5834	124	4	k1	k1	X
ejpam-5834	124	5	+	+	CCONJ
ejpam-5834	124	6	k2	k2	ADJ
ejpam-5834	124	7	2	2	NUM
ejpam-5834	124	8	)	)	PUNCT
ejpam-5834	124	9	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5834	124	10	≤	≤	PROPN
ejpam-5834	124	11	(	(	PUNCT
ejpam-5834	124	12	k2	k2	ADJ
ejpam-5834	124	13	−	−	PROPN
ejpam-5834	124	14	k1	k1	PROPN
ejpam-5834	124	15	)	)	PUNCT
ejpam-5834	124	16	2	2	NUM
ejpam-5834	124	17	23(ρ+	23(ρ+	NUM
ejpam-5834	124	18	1	1	NUM
ejpam-5834	124	19	)	)	PUNCT
ejpam-5834	124	20	(	(	PUNCT
ejpam-5834	124	21	1	1	NUM
ejpam-5834	124	22	p(ρ+	p(ρ+	NOUN
ejpam-5834	124	23	1	1	NUM
ejpam-5834	124	24	)	)	PUNCT
ejpam-5834	124	25	+	+	CCONJ
ejpam-5834	124	26	1	1	X
ejpam-5834	124	27	)	)	PUNCT
ejpam-5834	124	28	1	1	NUM
ejpam-5834	124	29	p	p	NOUN
ejpam-5834	124	30	(	(	PUNCT
ejpam-5834	124	31	(	(	PUNCT
ejpam-5834	124	32	2−	2−	NUM
ejpam-5834	124	33	2−ρs	2−ρs	NUM
ejpam-5834	124	34	ρs+	ρs+	NOUN
ejpam-5834	124	35	1	1	NUM
ejpam-5834	124	36	)	)	PUNCT
ejpam-5834	124	37	+	+	CCONJ
ejpam-5834	124	38	(	(	PUNCT
ejpam-5834	124	39	2−ρs	2−ρs	NUM
ejpam-5834	124	40	ρs+	ρs+	NOUN
ejpam-5834	124	41	1	1	NUM
ejpam-5834	124	42	)	)	PUNCT
ejpam-5834	124	43	)	)	PUNCT
ejpam-5834	124	44	1	1	NUM
ejpam-5834	124	45	q	q	NOUN
ejpam-5834	124	46	[	[	PUNCT
ejpam-5834	124	47	∣∣η′′(k1)∣∣q	∣∣η′′(k1)∣∣q	X
ejpam-5834	124	48	+	+	CCONJ
ejpam-5834	124	49	∣∣η′′(k2)∣∣q	∣∣η′′(k2)∣∣q	PROPN
ejpam-5834	124	50	]	]	X
ejpam-5834	124	51	1q	1q	PROPN
ejpam-5834	124	52	o.	o.	PROPN
ejpam-5834	124	53	b.	b.	PROPN
ejpam-5834	124	54	almutairi	almutairi	PROPN
ejpam-5834	124	55	/	/	SYM
ejpam-5834	124	56	eur	eur	PROPN
ejpam-5834	124	57	.	.	PUNCT
ejpam-5834	125	1	j.	j.	PROPN
ejpam-5834	125	2	pure	pure	PROPN
ejpam-5834	125	3	appl	appl	PROPN
ejpam-5834	125	4	.	.	PROPN
ejpam-5834	125	5	math	math	PROPN
ejpam-5834	125	6	,	,	PUNCT
ejpam-5834	125	7	18	18	NUM
ejpam-5834	125	8	(	(	PUNCT
ejpam-5834	125	9	1	1	NUM
ejpam-5834	125	10	)	)	PUNCT
ejpam-5834	125	11	(	(	PUNCT
ejpam-5834	125	12	2025	2025	NUM
ejpam-5834	125	13	)	)	PUNCT
ejpam-5834	125	14	,	,	PUNCT
ejpam-5834	125	15	5834	5834	NUM
ejpam-5834	125	16	6	6	NUM
ejpam-5834	125	17	of	of	ADP
ejpam-5834	125	18	12	12	NUM
ejpam-5834	125	19	proof	proof	NOUN
ejpam-5834	125	20	.	.	PUNCT
ejpam-5834	126	1	applying	apply	VERB
ejpam-5834	126	2	hölder	hölder	NOUN
ejpam-5834	126	3	’s	’s	PART
ejpam-5834	126	4	inequality	inequality	NOUN
ejpam-5834	126	5	,	,	PUNCT
ejpam-5834	126	6	(	(	PUNCT
ejpam-5834	126	7	ρ	ρ	NOUN
ejpam-5834	126	8	,	,	PUNCT
ejpam-5834	126	9	s)-convex	s)-convex	NOUN
ejpam-5834	126	10	of	of	ADP
ejpam-5834	126	11	|η′′|q	|η′′|q	NOUN
ejpam-5834	126	12	and	and	CCONJ
ejpam-5834	126	13	lemma1	lemma1	PROPN
ejpam-5834	126	14	,	,	PUNCT
ejpam-5834	126	15	we	we	PRON
ejpam-5834	126	16	get∣∣∣∣∣2ρ−1γ(ρ+	get∣∣∣∣∣2ρ−1γ(ρ+	VERB
ejpam-5834	126	17	1	1	NUM
ejpam-5834	126	18	)	)	PUNCT
ejpam-5834	126	19	(	(	PUNCT
ejpam-5834	126	20	k2	k2	PROPN
ejpam-5834	126	21	−	−	PROPN
ejpam-5834	126	22	k1)α	k1)α	NOUN
ejpam-5834	126	23	[	[	PUNCT
ejpam-5834	126	24	jρ	jρ	PROPN
ejpam-5834	126	25	(	(	PUNCT
ejpam-5834	126	26	k1+k2	k1+k2	PROPN
ejpam-5834	126	27	2	2	NUM
ejpam-5834	126	28	)	)	PUNCT
ejpam-5834	126	29	−η(k1	−η(k1	PROPN
ejpam-5834	126	30	)	)	PUNCT
ejpam-5834	127	1	+	+	CCONJ
ejpam-5834	127	2	jα	jα	NOUN
ejpam-5834	127	3	(	(	PUNCT
ejpam-5834	127	4	k1+k2	k1+k2	PROPN
ejpam-5834	127	5	2	2	NUM
ejpam-5834	127	6	)	)	PUNCT
ejpam-5834	127	7	+	+	NOUN
ejpam-5834	127	8	η(k2	η(k2	NOUN
ejpam-5834	127	9	)	)	PUNCT
ejpam-5834	127	10	]	]	PUNCT
ejpam-5834	127	11	−	−	PROPN
ejpam-5834	127	12	η	η	X
ejpam-5834	127	13	(	(	PUNCT
ejpam-5834	127	14	k1	k1	X
ejpam-5834	127	15	+	+	CCONJ
ejpam-5834	127	16	k2	k2	ADJ
ejpam-5834	127	17	2	2	NUM
ejpam-5834	127	18	)	)	PUNCT
ejpam-5834	127	19	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5834	127	20	=	=	PUNCT
ejpam-5834	127	21	∣∣∣∣(k2	∣∣∣∣(k2	VERB
ejpam-5834	127	22	−	−	PROPN
ejpam-5834	127	23	k1	k1	NOUN
ejpam-5834	127	24	)	)	PUNCT
ejpam-5834	127	25	2	2	NUM
ejpam-5834	127	26	8(α+	8(α+	NUM
ejpam-5834	127	27	1	1	NUM
ejpam-5834	127	28	)	)	PUNCT
ejpam-5834	127	29	∫	∫	PROPN
ejpam-5834	128	1	1	1	NUM
ejpam-5834	128	2	0	0	NUM
ejpam-5834	128	3	(	(	PUNCT
ejpam-5834	128	4	1−ϖ)α+1	1−ϖ)α+1	NUM
ejpam-5834	128	5	[	[	PUNCT
ejpam-5834	128	6	η′′	η′′	PROPN
ejpam-5834	128	7	(	(	PUNCT
ejpam-5834	128	8	1	1	NUM
ejpam-5834	128	9	+	+	NOUN
ejpam-5834	128	10	ϖ	ϖ	PROPN
ejpam-5834	128	11	2	2	NUM
ejpam-5834	128	12	k1	k1	NOUN
ejpam-5834	128	13	+	+	CCONJ
ejpam-5834	128	14	1−ϖ	1−ϖ	NUM
ejpam-5834	128	15	2	2	NUM
ejpam-5834	128	16	k2	k2	NOUN
ejpam-5834	128	17	)	)	PUNCT
ejpam-5834	129	1	+	+	CCONJ
ejpam-5834	129	2	η′	η′	NOUN
ejpam-5834	129	3	(	(	PUNCT
ejpam-5834	129	4	1−ϖ	1−ϖ	NUM
ejpam-5834	129	5	2	2	NUM
ejpam-5834	129	6	k1	k1	NOUN
ejpam-5834	129	7	+	+	CCONJ
ejpam-5834	129	8	1	1	NUM
ejpam-5834	129	9	+	+	ADJ
ejpam-5834	129	10	ϖ	ϖ	PROPN
ejpam-5834	129	11	2	2	NUM
ejpam-5834	129	12	k2	k2	NOUN
ejpam-5834	129	13	)	)	PUNCT
ejpam-5834	129	14	]	]	PUNCT
ejpam-5834	130	1	dϖ	dϖ	ADP
ejpam-5834	130	2	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5834	130	3	≤	≤	PROPN
ejpam-5834	130	4	∣∣∣∣(k2	∣∣∣∣(k2	VERB
ejpam-5834	130	5	−	−	PROPN
ejpam-5834	130	6	k1	k1	NOUN
ejpam-5834	130	7	)	)	PUNCT
ejpam-5834	130	8	2	2	NUM
ejpam-5834	130	9	8(ρ+	8(ρ+	NUM
ejpam-5834	130	10	1	1	NUM
ejpam-5834	130	11	)	)	PUNCT
ejpam-5834	130	12	∫	∫	PROPN
ejpam-5834	130	13	1	1	NUM
ejpam-5834	130	14	0	0	NUM
ejpam-5834	130	15	(	(	PUNCT
ejpam-5834	130	16	1−ϖ)ρ+1η′′	1−ϖ)ρ+1η′′	NUM
ejpam-5834	130	17	(	(	PUNCT
ejpam-5834	130	18	1	1	NUM
ejpam-5834	130	19	+	+	NOUN
ejpam-5834	130	20	ϖ	ϖ	PROPN
ejpam-5834	130	21	2	2	NUM
ejpam-5834	130	22	k1	k1	NOUN
ejpam-5834	130	23	+	+	CCONJ
ejpam-5834	130	24	1−ϖ	1−ϖ	NUM
ejpam-5834	130	25	2	2	NUM
ejpam-5834	130	26	k2	k2	NOUN
ejpam-5834	130	27	)	)	PUNCT
ejpam-5834	130	28	dϖ	dϖ	ADP
ejpam-5834	130	29	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5834	130	30	+	+	NUM
ejpam-5834	130	31	∣∣∣∣k2	∣∣∣∣k2	NUM
ejpam-5834	130	32	−	−	NOUN
ejpam-5834	130	33	k1	k1	PROPN
ejpam-5834	130	34	4	4	NUM
ejpam-5834	130	35	∫	∫	NOUN
ejpam-5834	130	36	1	1	NUM
ejpam-5834	130	37	0	0	NUM
ejpam-5834	130	38	(	(	PUNCT
ejpam-5834	130	39	1−ϖ)ρ+1η′′	1−ϖ)ρ+1η′′	NUM
ejpam-5834	130	40	(	(	PUNCT
ejpam-5834	130	41	1−ϖ	1−ϖ	NUM
ejpam-5834	130	42	2	2	NUM
ejpam-5834	130	43	k1	k1	NOUN
ejpam-5834	130	44	+	+	CCONJ
ejpam-5834	130	45	1	1	NUM
ejpam-5834	130	46	+	+	ADJ
ejpam-5834	130	47	ϖ	ϖ	PROPN
ejpam-5834	130	48	2	2	NUM
ejpam-5834	130	49	k2	k2	NOUN
ejpam-5834	130	50	)	)	PUNCT
ejpam-5834	130	51	dϖ	dϖ	ADP
ejpam-5834	130	52	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5834	130	53	≤	≤	NOUN
ejpam-5834	130	54	(	(	PUNCT
ejpam-5834	130	55	k2	k2	NOUN
ejpam-5834	130	56	−	−	PROPN
ejpam-5834	130	57	k1	k1	PROPN
ejpam-5834	130	58	)	)	PUNCT
ejpam-5834	130	59	2	2	NUM
ejpam-5834	130	60	8(ρ+	8(ρ+	NUM
ejpam-5834	130	61	1	1	NUM
ejpam-5834	130	62	)	)	PUNCT
ejpam-5834	130	63	{	{	PUNCT
ejpam-5834	130	64	(	(	PUNCT
ejpam-5834	130	65	∫	∫	PROPN
ejpam-5834	130	66	1	1	NUM
ejpam-5834	130	67	0	0	NUM
ejpam-5834	130	68	(	(	PUNCT
ejpam-5834	130	69	1−ϖ)p(ρ+1)dϖ	1−ϖ)p(ρ+1)dϖ	PROPN
ejpam-5834	130	70	)	)	PUNCT
ejpam-5834	130	71	1	1	NUM
ejpam-5834	130	72	p	p	NOUN
ejpam-5834	130	73	(	(	PUNCT
ejpam-5834	130	74	∫	∫	PROPN
ejpam-5834	130	75	1	1	NUM
ejpam-5834	130	76	0	0	NUM
ejpam-5834	130	77	∣∣∣∣η′′(1	∣∣∣∣η′′(1	VERB
ejpam-5834	130	78	+	+	NOUN
ejpam-5834	130	79	ϖ	ϖ	PROPN
ejpam-5834	130	80	2	2	NUM
ejpam-5834	130	81	k1	k1	NOUN
ejpam-5834	130	82	+	+	CCONJ
ejpam-5834	130	83	1−ϖ	1−ϖ	NUM
ejpam-5834	130	84	2	2	NUM
ejpam-5834	130	85	k2	k2	NOUN
ejpam-5834	130	86	)	)	PUNCT
ejpam-5834	130	87	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5834	131	1	dϖ	dϖ	PROPN
ejpam-5834	131	2	)	)	PUNCT
ejpam-5834	131	3	1	1	NUM
ejpam-5834	131	4	q	q	NOUN
ejpam-5834	131	5	+	+	CCONJ
ejpam-5834	131	6	(	(	PUNCT
ejpam-5834	131	7	∫	∫	PROPN
ejpam-5834	131	8	1	1	NUM
ejpam-5834	131	9	0	0	NUM
ejpam-5834	131	10	(	(	PUNCT
ejpam-5834	131	11	1−ϖ)p(ρ+1)dϖ	1−ϖ)p(ρ+1)dϖ	PROPN
ejpam-5834	131	12	)	)	PUNCT
ejpam-5834	131	13	1	1	NUM
ejpam-5834	131	14	p	p	NOUN
ejpam-5834	131	15	(	(	PUNCT
ejpam-5834	131	16	∫	∫	PROPN
ejpam-5834	131	17	1	1	NUM
ejpam-5834	131	18	0	0	NUM
ejpam-5834	131	19	∣∣∣∣η′′(1−ϖ	∣∣∣∣η′′(1−ϖ	ADJ
ejpam-5834	131	20	2	2	NUM
ejpam-5834	131	21	k1	k1	NOUN
ejpam-5834	131	22	+	+	CCONJ
ejpam-5834	131	23	1	1	NUM
ejpam-5834	131	24	+	+	ADJ
ejpam-5834	131	25	ϖ	ϖ	PROPN
ejpam-5834	131	26	2	2	NUM
ejpam-5834	131	27	k2	k2	NOUN
ejpam-5834	131	28	)	)	PUNCT
ejpam-5834	131	29	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5834	132	1	dϖ	dϖ	PROPN
ejpam-5834	132	2	)	)	PUNCT
ejpam-5834	132	3	1	1	NUM
ejpam-5834	132	4	q	q	NOUN
ejpam-5834	132	5	}	}	PUNCT
ejpam-5834	132	6	≤	≤	PROPN
ejpam-5834	132	7	(	(	PUNCT
ejpam-5834	132	8	k2	k2	ADJ
ejpam-5834	132	9	−	−	PROPN
ejpam-5834	132	10	k1	k1	PROPN
ejpam-5834	132	11	)	)	PUNCT
ejpam-5834	132	12	2	2	NUM
ejpam-5834	132	13	8(ρ+	8(ρ+	NUM
ejpam-5834	132	14	1	1	NUM
ejpam-5834	132	15	)	)	PUNCT
ejpam-5834	132	16	(	(	PUNCT
ejpam-5834	132	17	1	1	NUM
ejpam-5834	132	18	p(ρ+	p(ρ+	NOUN
ejpam-5834	132	19	1	1	NUM
ejpam-5834	132	20	)	)	PUNCT
ejpam-5834	132	21	+	+	CCONJ
ejpam-5834	132	22	1	1	X
ejpam-5834	132	23	)	)	PUNCT
ejpam-5834	132	24	1	1	NUM
ejpam-5834	132	25	p	p	NOUN
ejpam-5834	132	26	{	{	PUNCT
ejpam-5834	132	27	(	(	PUNCT
ejpam-5834	132	28	∣∣η′′(k1)∣∣q	∣∣η′′(k1)∣∣q	NOUN
ejpam-5834	132	29	∫	∫	PROPN
ejpam-5834	132	30	1	1	NUM
ejpam-5834	132	31	0	0	NUM
ejpam-5834	132	32	(	(	PUNCT
ejpam-5834	132	33	1	1	NUM
ejpam-5834	132	34	+	+	NOUN
ejpam-5834	132	35	ϖ	ϖ	NOUN
ejpam-5834	132	36	2	2	NUM
ejpam-5834	132	37	)	)	PUNCT
ejpam-5834	132	38	ρs	ρs	ADP
ejpam-5834	132	39	dϖ	dϖ	ADP
ejpam-5834	132	40	+	+	CCONJ
ejpam-5834	132	41	∣∣η′′(k2)∣∣q	∣∣η′′(k2)∣∣q	X
ejpam-5834	132	42	∫	∫	PROPN
ejpam-5834	132	43	1	1	NUM
ejpam-5834	132	44	0	0	NUM
ejpam-5834	132	45	(	(	PUNCT
ejpam-5834	132	46	1−	1−	NUM
ejpam-5834	132	47	(	(	PUNCT
ejpam-5834	132	48	1−ϖ	1−ϖ	NUM
ejpam-5834	132	49	2	2	NUM
ejpam-5834	132	50	)	)	PUNCT
ejpam-5834	132	51	ρ)s	ρ)s	NOUN
ejpam-5834	132	52	dϖ	dϖ	X
ejpam-5834	132	53	)	)	PUNCT
ejpam-5834	132	54	1	1	NUM
ejpam-5834	132	55	q	q	NOUN
ejpam-5834	133	1	+	+	CCONJ
ejpam-5834	133	2	(	(	PUNCT
ejpam-5834	133	3	∣∣η′′(k1)∣∣q	∣∣η′′(k1)∣∣q	NOUN
ejpam-5834	133	4	∫	∫	PROPN
ejpam-5834	133	5	1	1	NUM
ejpam-5834	133	6	0	0	NUM
ejpam-5834	133	7	(	(	PUNCT
ejpam-5834	133	8	1−ϖ	1−ϖ	NUM
ejpam-5834	133	9	2	2	NUM
ejpam-5834	133	10	)	)	PUNCT
ejpam-5834	133	11	ρs	ρs	ADP
ejpam-5834	133	12	dϖ	dϖ	ADP
ejpam-5834	133	13	+	+	CCONJ
ejpam-5834	133	14	∣∣η′′(k2)∣∣q	∣∣η′′(k2)∣∣q	X
ejpam-5834	133	15	∫	∫	PROPN
ejpam-5834	133	16	1	1	NUM
ejpam-5834	133	17	0	0	NUM
ejpam-5834	133	18	(	(	PUNCT
ejpam-5834	133	19	1−	1−	NUM
ejpam-5834	133	20	(	(	PUNCT
ejpam-5834	133	21	1	1	NUM
ejpam-5834	133	22	+	+	NOUN
ejpam-5834	133	23	ϖ	ϖ	NOUN
ejpam-5834	133	24	2	2	NUM
ejpam-5834	133	25	)	)	PUNCT
ejpam-5834	133	26	ρ)s	ρ)s	NOUN
ejpam-5834	133	27	dϖ	dϖ	X
ejpam-5834	133	28	)	)	PUNCT
ejpam-5834	133	29	1	1	NUM
ejpam-5834	133	30	q	q	NOUN
ejpam-5834	133	31	}	}	PUNCT
ejpam-5834	133	32	≤	≤	PROPN
ejpam-5834	133	33	(	(	PUNCT
ejpam-5834	133	34	k2	k2	ADJ
ejpam-5834	133	35	−	−	PROPN
ejpam-5834	133	36	k1	k1	PROPN
ejpam-5834	133	37	)	)	PUNCT
ejpam-5834	133	38	2	2	NUM
ejpam-5834	133	39	8(ρ+	8(ρ+	NUM
ejpam-5834	133	40	1	1	NUM
ejpam-5834	133	41	)	)	PUNCT
ejpam-5834	133	42	(	(	PUNCT
ejpam-5834	133	43	1	1	NUM
ejpam-5834	133	44	p(ρ+	p(ρ+	NOUN
ejpam-5834	133	45	1	1	NUM
ejpam-5834	133	46	)	)	PUNCT
ejpam-5834	133	47	+	+	CCONJ
ejpam-5834	133	48	1	1	X
ejpam-5834	133	49	)	)	PUNCT
ejpam-5834	133	50	1	1	NUM
ejpam-5834	134	1	p	p	NOUN
ejpam-5834	134	2	[	[	X
ejpam-5834	134	3	{	{	PUNCT
ejpam-5834	134	4	∣∣η′′(k1)∣∣q	∣∣η′′(k1)∣∣q	X
ejpam-5834	134	5	(	(	PUNCT
ejpam-5834	134	6	2−	2−	NUM
ejpam-5834	134	7	2−ρs	2−ρs	NUM
ejpam-5834	134	8	ρs+	ρs+	NOUN
ejpam-5834	134	9	1	1	NUM
ejpam-5834	134	10	)	)	PUNCT
ejpam-5834	134	11	+	+	CCONJ
ejpam-5834	134	12	∣∣η′′(k2)∣∣q	∣∣η′′(k2)∣∣q	X
ejpam-5834	134	13	(	(	PUNCT
ejpam-5834	134	14	2−	2−	NUM
ejpam-5834	134	15	2−ρs	2−ρs	NUM
ejpam-5834	134	16	ρs+	ρs+	NOUN
ejpam-5834	134	17	1	1	NUM
ejpam-5834	134	18	)	)	PUNCT
ejpam-5834	134	19	}	}	PUNCT
ejpam-5834	134	20	1	1	NUM
ejpam-5834	134	21	q	q	NOUN
ejpam-5834	134	22	+	+	NUM
ejpam-5834	134	23	{	{	PUNCT
ejpam-5834	134	24	∣∣η′′(k1)∣∣q	∣∣η′′(k1)∣∣q	X
ejpam-5834	134	25	(	(	PUNCT
ejpam-5834	134	26	2−ρs	2−ρs	NUM
ejpam-5834	134	27	ρs+	ρs+	NOUN
ejpam-5834	134	28	1	1	NUM
ejpam-5834	134	29	)	)	PUNCT
ejpam-5834	134	30	+	+	CCONJ
ejpam-5834	134	31	∣∣η′′(k2)∣∣q	∣∣η′′(k2)∣∣q	X
ejpam-5834	134	32	(	(	PUNCT
ejpam-5834	134	33	2−ρs	2−ρs	NUM
ejpam-5834	134	34	ρs+	ρs+	NOUN
ejpam-5834	134	35	1	1	NUM
ejpam-5834	134	36	)	)	PUNCT
ejpam-5834	134	37	}	}	PUNCT
ejpam-5834	134	38	1	1	NUM
ejpam-5834	134	39	q	q	NOUN
ejpam-5834	134	40	]	]	PUNCT
ejpam-5834	134	41	≤	≤	X
ejpam-5834	134	42	(	(	PUNCT
ejpam-5834	134	43	k2	k2	ADJ
ejpam-5834	134	44	−	−	PROPN
ejpam-5834	134	45	k1	k1	PROPN
ejpam-5834	134	46	)	)	PUNCT
ejpam-5834	134	47	2	2	NUM
ejpam-5834	134	48	23(ρ+	23(ρ+	NUM
ejpam-5834	134	49	1	1	NUM
ejpam-5834	134	50	)	)	PUNCT
ejpam-5834	134	51	(	(	PUNCT
ejpam-5834	134	52	1	1	NUM
ejpam-5834	134	53	p(ρ+	p(ρ+	NOUN
ejpam-5834	134	54	1	1	NUM
ejpam-5834	134	55	)	)	PUNCT
ejpam-5834	134	56	+	+	CCONJ
ejpam-5834	134	57	1	1	X
ejpam-5834	134	58	)	)	PUNCT
ejpam-5834	134	59	1	1	NUM
ejpam-5834	134	60	p	p	NOUN
ejpam-5834	134	61	(	(	PUNCT
ejpam-5834	134	62	(	(	PUNCT
ejpam-5834	134	63	2−	2−	NUM
ejpam-5834	134	64	2−ρs	2−ρs	NUM
ejpam-5834	134	65	ρs+	ρs+	NOUN
ejpam-5834	134	66	1	1	NUM
ejpam-5834	134	67	)	)	PUNCT
ejpam-5834	134	68	+	+	CCONJ
ejpam-5834	134	69	(	(	PUNCT
ejpam-5834	134	70	2−ρs	2−ρs	NUM
ejpam-5834	134	71	ρs+	ρs+	NOUN
ejpam-5834	134	72	1	1	NUM
ejpam-5834	134	73	)	)	PUNCT
ejpam-5834	134	74	)	)	PUNCT
ejpam-5834	134	75	1	1	NUM
ejpam-5834	134	76	q	q	NOUN
ejpam-5834	134	77	[	[	PUNCT
ejpam-5834	134	78	∣∣η′′(k1)∣∣q	∣∣η′′(k1)∣∣q	X
ejpam-5834	134	79	+	+	CCONJ
ejpam-5834	134	80	∣∣η′′(k2)∣∣q	∣∣η′′(k2)∣∣q	NOUN
ejpam-5834	134	81	]	]	X
ejpam-5834	134	82	1q	1q	X
ejpam-5834	134	83	using	use	VERB
ejpam-5834	134	84	power	power	NOUN
ejpam-5834	134	85	-	-	PUNCT
ejpam-5834	134	86	mean	mean	NOUN
ejpam-5834	134	87	inequality	inequality	NOUN
ejpam-5834	134	88	,	,	PUNCT
ejpam-5834	134	89	we	we	PRON
ejpam-5834	134	90	obtain	obtain	VERB
ejpam-5834	134	91	the	the	DET
ejpam-5834	134	92	following	follow	VERB
ejpam-5834	134	93	integral	integral	ADJ
ejpam-5834	134	94	inequalities	inequality	NOUN
ejpam-5834	134	95	.	.	PUNCT
ejpam-5834	135	1	theorem	theorem	NOUN
ejpam-5834	135	2	4	4	NUM
ejpam-5834	135	3	.	.	PUNCT
ejpam-5834	136	1	let	let	VERB
ejpam-5834	136	2	η	η	PROPN
ejpam-5834	136	3	:	:	PUNCT
ejpam-5834	136	4	[	[	X
ejpam-5834	136	5	k1	k1	X
ejpam-5834	136	6	,	,	PUNCT
ejpam-5834	136	7	k2	k2	NOUN
ejpam-5834	136	8	]	]	PUNCT
ejpam-5834	136	9	→	→	PUNCT
ejpam-5834	136	10	r	r	NOUN
ejpam-5834	136	11	be	be	VERB
ejpam-5834	136	12	twice	twice	ADV
ejpam-5834	136	13	differentiable	differentiable	ADJ
ejpam-5834	136	14	function	function	NOUN
ejpam-5834	136	15	on	on	ADP
ejpam-5834	136	16	(	(	PUNCT
ejpam-5834	136	17	k1	k1	NOUN
ejpam-5834	136	18	,	,	PUNCT
ejpam-5834	136	19	k2	k2	NOUN
ejpam-5834	136	20	)	)	PUNCT
ejpam-5834	136	21	with	with	ADP
ejpam-5834	136	22	k1	k1	PROPN
ejpam-5834	136	23	<	<	X
ejpam-5834	136	24	k2	k2	PROPN
ejpam-5834	136	25	.	.	PUNCT
ejpam-5834	137	1	if	if	SCONJ
ejpam-5834	137	2	η′′	η′′	PROPN
ejpam-5834	137	3	∈	∈	PROPN
ejpam-5834	137	4	l[k1	l[k1	NOUN
ejpam-5834	137	5	,	,	PUNCT
ejpam-5834	137	6	k2	k2	NOUN
ejpam-5834	137	7	]	]	PUNCT
ejpam-5834	137	8	and	and	CCONJ
ejpam-5834	137	9	|η′′|q	|η′′|q	NOUN
ejpam-5834	137	10	is	be	AUX
ejpam-5834	137	11	(	(	PUNCT
ejpam-5834	137	12	ρ	ρ	NOUN
ejpam-5834	137	13	,	,	PUNCT
ejpam-5834	137	14	s)-convex	s)-convex	PUNCT
ejpam-5834	137	15	function	function	NOUN
ejpam-5834	137	16	of	of	ADP
ejpam-5834	137	17	second	second	ADJ
ejpam-5834	137	18	kind	kind	NOUN
ejpam-5834	137	19	,	,	PUNCT
ejpam-5834	137	20	then	then	ADV
ejpam-5834	137	21	,	,	PUNCT
ejpam-5834	137	22	we	we	PRON
ejpam-5834	137	23	have	have	VERB
ejpam-5834	137	24	the	the	DET
ejpam-5834	137	25	following	follow	VERB
ejpam-5834	137	26	inequality	inequality	NOUN
ejpam-5834	137	27	for	for	ADP
ejpam-5834	137	28	fractional	fractional	ADJ
ejpam-5834	137	29	integrals:∣∣∣∣∣2ρ−1γ(ρ+1	integrals:∣∣∣∣∣2ρ−1γ(ρ+1	NOUN
ejpam-5834	137	30	)	)	PUNCT
ejpam-5834	137	31	(	(	PUNCT
ejpam-5834	137	32	k2−k1)α	k2−k1)α	NOUN
ejpam-5834	137	33	[	[	PUNCT
ejpam-5834	137	34	jρ	jρ	PROPN
ejpam-5834	137	35	(	(	PUNCT
ejpam-5834	137	36	k1+k2	k1+k2	PROPN
ejpam-5834	137	37	2	2	NUM
ejpam-5834	137	38	)	)	PUNCT
ejpam-5834	137	39	−η(k1	−η(k1	PROPN
ejpam-5834	137	40	)	)	PUNCT
ejpam-5834	138	1	+	+	CCONJ
ejpam-5834	139	1	jρ	jρ	PROPN
ejpam-5834	139	2	(	(	PUNCT
ejpam-5834	139	3	k1+k2b	k1+k2b	PROPN
ejpam-5834	139	4	2	2	NUM
ejpam-5834	139	5	)	)	PUNCT
ejpam-5834	139	6	+	+	NOUN
ejpam-5834	139	7	η(k2	η(k2	NOUN
ejpam-5834	139	8	)	)	PUNCT
ejpam-5834	139	9	]	]	PUNCT
ejpam-5834	140	1	−	−	PROPN
ejpam-5834	140	2	η	η	PROPN
ejpam-5834	140	3	(	(	PUNCT
ejpam-5834	140	4	k1+k2	k1+k2	PROPN
ejpam-5834	140	5	2	2	NUM
ejpam-5834	140	6	)	)	PUNCT
ejpam-5834	140	7	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5834	140	8	≤	≤	NOUN
ejpam-5834	140	9	(	(	PUNCT
ejpam-5834	140	10	k2−k1)2	k2−k1)2	PROPN
ejpam-5834	140	11	23(ρ+1	23(ρ+1	NUM
ejpam-5834	140	12	)	)	PUNCT
ejpam-5834	140	13	(	(	PUNCT
ejpam-5834	140	14	1	1	NUM
ejpam-5834	140	15	ρ+2	ρ+2	NUM
ejpam-5834	140	16	)	)	PUNCT
ejpam-5834	140	17	1−	1−	NUM
ejpam-5834	140	18	1	1	NUM
ejpam-5834	140	19	q	q	NOUN
ejpam-5834	140	20	{	{	PUNCT
ejpam-5834	140	21	(	(	PUNCT
ejpam-5834	140	22	|η′′(k1)|q	|η′′(k1)|q	NOUN
ejpam-5834	140	23	2f1(1,−ρs;3+k1;−1	2f1(1,−ρs;3+k1;−1	NOUN
ejpam-5834	140	24	)	)	PUNCT
ejpam-5834	140	25	k1	k1	NOUN
ejpam-5834	140	26	+	+	PROPN
ejpam-5834	140	27	2	2	NUM
ejpam-5834	140	28	+	+	NUM
ejpam-5834	140	29	|η′′(k2)|q	|η′′(k2)|q	NOUN
ejpam-5834	140	30	ω(ρ	ω(ρ	NUM
ejpam-5834	140	31	,	,	PUNCT
ejpam-5834	140	32	s,ϖ	s,ϖ	NOUN
ejpam-5834	140	33	)	)	PUNCT
ejpam-5834	140	34	)	)	PUNCT
ejpam-5834	140	35	1	1	NUM
ejpam-5834	140	36	q	q	NOUN
ejpam-5834	140	37	+	+	NUM
ejpam-5834	140	38	(	(	PUNCT
ejpam-5834	140	39	|η′′(k1)|q	|η′′(k1)|q	PROPN
ejpam-5834	140	40	(	(	PUNCT
ejpam-5834	140	41	γ(ρs+ρ+2	γ(ρs+ρ+2	PROPN
ejpam-5834	140	42	)	)	PUNCT
ejpam-5834	140	43	γ(ρs+ρ+3	γ(ρs+ρ+3	NOUN
ejpam-5834	140	44	)	)	PUNCT
ejpam-5834	140	45	)	)	PUNCT
ejpam-5834	141	1	+	+	CCONJ
ejpam-5834	141	2	|η′′(k2)|q	|η′′(k2)|q	NOUN
ejpam-5834	141	3	ω(ρ	ω(ρ	NUM
ejpam-5834	141	4	,	,	PUNCT
ejpam-5834	141	5	s,ϖ	s,ϖ	NOUN
ejpam-5834	141	6	)	)	PUNCT
ejpam-5834	141	7	)	)	PUNCT
ejpam-5834	141	8	1	1	NUM
ejpam-5834	141	9	q	q	NOUN
ejpam-5834	141	10	}	}	PUNCT
ejpam-5834	141	11	o.	o.	PROPN
ejpam-5834	141	12	b.	b.	PROPN
ejpam-5834	141	13	almutairi	almutairi	PROPN
ejpam-5834	141	14	/	/	SYM
ejpam-5834	141	15	eur	eur	PROPN
ejpam-5834	141	16	.	.	PUNCT
ejpam-5834	142	1	j.	j.	PROPN
ejpam-5834	142	2	pure	pure	PROPN
ejpam-5834	142	3	appl	appl	PROPN
ejpam-5834	142	4	.	.	PROPN
ejpam-5834	142	5	math	math	PROPN
ejpam-5834	142	6	,	,	PUNCT
ejpam-5834	142	7	18	18	NUM
ejpam-5834	142	8	(	(	PUNCT
ejpam-5834	142	9	1	1	NUM
ejpam-5834	142	10	)	)	PUNCT
ejpam-5834	142	11	(	(	PUNCT
ejpam-5834	142	12	2025	2025	NUM
ejpam-5834	142	13	)	)	PUNCT
ejpam-5834	142	14	,	,	PUNCT
ejpam-5834	142	15	5834	5834	NUM
ejpam-5834	142	16	7	7	NUM
ejpam-5834	142	17	of	of	ADP
ejpam-5834	142	18	12	12	NUM
ejpam-5834	142	19	proof	proof	NOUN
ejpam-5834	142	20	.	.	PUNCT
ejpam-5834	143	1	applying	apply	VERB
ejpam-5834	143	2	lemma	lemma	PROPN
ejpam-5834	143	3	1	1	NUM
ejpam-5834	143	4	,	,	PUNCT
ejpam-5834	143	5	power	power	NOUN
ejpam-5834	143	6	-	-	PUNCT
ejpam-5834	143	7	mean	mean	NOUN
ejpam-5834	143	8	inequality	inequality	NOUN
ejpam-5834	143	9	and	and	CCONJ
ejpam-5834	143	10	the	the	DET
ejpam-5834	143	11	fact	fact	NOUN
ejpam-5834	143	12	that	that	SCONJ
ejpam-5834	143	13	|η′′|q	|η′′|q	NOUN
ejpam-5834	143	14	is	be	AUX
ejpam-5834	143	15	(	(	PUNCT
ejpam-5834	143	16	ρ	ρ	NOUN
ejpam-5834	143	17	,	,	PUNCT
ejpam-5834	143	18	s)convex	s)convex	NUM
ejpam-5834	143	19	function	function	NOUN
ejpam-5834	143	20	,	,	PUNCT
ejpam-5834	143	21	we	we	PRON
ejpam-5834	143	22	have∣∣∣∣∣2ρ−1γ(ρ+	have∣∣∣∣∣2ρ−1γ(ρ+	VERB
ejpam-5834	143	23	1	1	NUM
ejpam-5834	143	24	)	)	PUNCT
ejpam-5834	143	25	(	(	PUNCT
ejpam-5834	143	26	k2	k2	PROPN
ejpam-5834	143	27	−	−	PROPN
ejpam-5834	143	28	k1)ρ	k1)ρ	NOUN
ejpam-5834	143	29	[	[	PUNCT
ejpam-5834	143	30	jρ	jρ	PROPN
ejpam-5834	143	31	(	(	PUNCT
ejpam-5834	143	32	k1+k2	k1+k2	PROPN
ejpam-5834	143	33	2	2	NUM
ejpam-5834	143	34	)	)	PUNCT
ejpam-5834	143	35	−η(k1	−η(k1	PROPN
ejpam-5834	143	36	)	)	PUNCT
ejpam-5834	144	1	+	+	CCONJ
ejpam-5834	144	2	jα	jα	NOUN
ejpam-5834	144	3	(	(	PUNCT
ejpam-5834	144	4	k1+k2	k1+k2	PROPN
ejpam-5834	144	5	2	2	NUM
ejpam-5834	144	6	)	)	PUNCT
ejpam-5834	144	7	+	+	NOUN
ejpam-5834	144	8	η(k2	η(k2	NOUN
ejpam-5834	144	9	)	)	PUNCT
ejpam-5834	144	10	]	]	PUNCT
ejpam-5834	144	11	−	−	PROPN
ejpam-5834	144	12	η	η	X
ejpam-5834	144	13	(	(	PUNCT
ejpam-5834	144	14	k1	k1	X
ejpam-5834	144	15	+	+	CCONJ
ejpam-5834	144	16	k2	k2	ADJ
ejpam-5834	144	17	2	2	NUM
ejpam-5834	144	18	)	)	PUNCT
ejpam-5834	144	19	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5834	144	20	=	=	PUNCT
ejpam-5834	144	21	∣∣∣∣(k2	∣∣∣∣(k2	VERB
ejpam-5834	144	22	−	−	PROPN
ejpam-5834	144	23	k1	k1	NOUN
ejpam-5834	144	24	)	)	PUNCT
ejpam-5834	144	25	2	2	NUM
ejpam-5834	144	26	8(ρ+	8(ρ+	NUM
ejpam-5834	144	27	1	1	NUM
ejpam-5834	144	28	)	)	PUNCT
ejpam-5834	144	29	∫	∫	PROPN
ejpam-5834	145	1	1	1	NUM
ejpam-5834	145	2	0	0	NUM
ejpam-5834	145	3	(	(	PUNCT
ejpam-5834	145	4	1−ϖ)ρ+1	1−ϖ)ρ+1	NUM
ejpam-5834	145	5	[	[	PUNCT
ejpam-5834	145	6	η′′	η′′	PROPN
ejpam-5834	145	7	(	(	PUNCT
ejpam-5834	145	8	1	1	NUM
ejpam-5834	145	9	+	+	NOUN
ejpam-5834	145	10	ϖ	ϖ	PROPN
ejpam-5834	145	11	2	2	NUM
ejpam-5834	145	12	k1	k1	NOUN
ejpam-5834	145	13	+	+	CCONJ
ejpam-5834	145	14	1−ϖ	1−ϖ	NUM
ejpam-5834	145	15	2	2	NUM
ejpam-5834	145	16	k2	k2	NOUN
ejpam-5834	145	17	)	)	PUNCT
ejpam-5834	146	1	+	+	CCONJ
ejpam-5834	146	2	η′	η′	NOUN
ejpam-5834	146	3	(	(	PUNCT
ejpam-5834	146	4	1−ϖ	1−ϖ	NUM
ejpam-5834	146	5	2	2	NUM
ejpam-5834	146	6	k1	k1	NOUN
ejpam-5834	146	7	+	+	CCONJ
ejpam-5834	146	8	1	1	NUM
ejpam-5834	146	9	+	+	ADJ
ejpam-5834	146	10	ϖ	ϖ	PROPN
ejpam-5834	146	11	2	2	NUM
ejpam-5834	146	12	k2	k2	NOUN
ejpam-5834	146	13	)	)	PUNCT
ejpam-5834	146	14	]	]	PUNCT
ejpam-5834	147	1	dϖ	dϖ	ADP
ejpam-5834	147	2	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5834	147	3	≤	≤	PROPN
ejpam-5834	147	4	∣∣∣∣(k2	∣∣∣∣(k2	VERB
ejpam-5834	147	5	−	−	PROPN
ejpam-5834	147	6	k1	k1	NOUN
ejpam-5834	147	7	)	)	PUNCT
ejpam-5834	147	8	2	2	NUM
ejpam-5834	147	9	8(ρ+	8(ρ+	NUM
ejpam-5834	147	10	1	1	NUM
ejpam-5834	147	11	)	)	PUNCT
ejpam-5834	147	12	∫	∫	PROPN
ejpam-5834	147	13	1	1	NUM
ejpam-5834	147	14	0	0	NUM
ejpam-5834	147	15	(	(	PUNCT
ejpam-5834	147	16	1−ϖ)ρ+1η′′	1−ϖ)ρ+1η′′	NUM
ejpam-5834	147	17	(	(	PUNCT
ejpam-5834	147	18	1	1	NUM
ejpam-5834	147	19	+	+	NOUN
ejpam-5834	147	20	ϖ	ϖ	PROPN
ejpam-5834	147	21	2	2	NUM
ejpam-5834	147	22	k1	k1	NOUN
ejpam-5834	147	23	+	+	CCONJ
ejpam-5834	147	24	1−ϖ	1−ϖ	NUM
ejpam-5834	147	25	2	2	NUM
ejpam-5834	147	26	k2	k2	NOUN
ejpam-5834	147	27	)	)	PUNCT
ejpam-5834	147	28	dϖ	dϖ	ADP
ejpam-5834	147	29	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5834	147	30	+	+	NUM
ejpam-5834	147	31	∣∣∣∣k2	∣∣∣∣k2	NUM
ejpam-5834	147	32	−	−	NOUN
ejpam-5834	147	33	k1	k1	PROPN
ejpam-5834	147	34	4	4	NUM
ejpam-5834	147	35	∫	∫	NOUN
ejpam-5834	147	36	1	1	NUM
ejpam-5834	147	37	0	0	NUM
ejpam-5834	147	38	(	(	PUNCT
ejpam-5834	147	39	1−ϖ)ρ+1η′′	1−ϖ)ρ+1η′′	NUM
ejpam-5834	147	40	(	(	PUNCT
ejpam-5834	147	41	1−ϖ	1−ϖ	NUM
ejpam-5834	147	42	2	2	NUM
ejpam-5834	147	43	k1	k1	NOUN
ejpam-5834	147	44	+	+	CCONJ
ejpam-5834	147	45	1	1	NUM
ejpam-5834	147	46	+	+	ADJ
ejpam-5834	147	47	ϖ	ϖ	PROPN
ejpam-5834	147	48	2	2	NUM
ejpam-5834	147	49	k2	k2	NOUN
ejpam-5834	147	50	)	)	PUNCT
ejpam-5834	147	51	dϖ	dϖ	ADP
ejpam-5834	147	52	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5834	147	53	≤	≤	NOUN
ejpam-5834	147	54	(	(	PUNCT
ejpam-5834	147	55	k2	k2	NOUN
ejpam-5834	147	56	−	−	PROPN
ejpam-5834	147	57	k1	k1	PROPN
ejpam-5834	147	58	)	)	PUNCT
ejpam-5834	147	59	2	2	NUM
ejpam-5834	147	60	8(ρ+	8(ρ+	NUM
ejpam-5834	147	61	1	1	NUM
ejpam-5834	147	62	)	)	PUNCT
ejpam-5834	147	63	{	{	PUNCT
ejpam-5834	147	64	(	(	PUNCT
ejpam-5834	147	65	∫	∫	PROPN
ejpam-5834	147	66	1	1	NUM
ejpam-5834	147	67	0	0	NUM
ejpam-5834	147	68	(	(	PUNCT
ejpam-5834	147	69	1−ϖ)(ρ+1)dϖ	1−ϖ)(ρ+1)dϖ	NUM
ejpam-5834	147	70	)	)	PUNCT
ejpam-5834	147	71	1−	1−	PROPN
ejpam-5834	147	72	1	1	NUM
ejpam-5834	147	73	q	q	NOUN
ejpam-5834	147	74	(	(	PUNCT
ejpam-5834	147	75	∫	∫	PROPN
ejpam-5834	147	76	1	1	NUM
ejpam-5834	147	77	0	0	NUM
ejpam-5834	147	78	(	(	PUNCT
ejpam-5834	147	79	1−ϖ)(ρ+1	1−ϖ)(ρ+1	NUM
ejpam-5834	147	80	)	)	PUNCT
ejpam-5834	147	81	∣∣∣∣η′′(1	∣∣∣∣η′′(1	VERB
ejpam-5834	147	82	+	+	ADV
ejpam-5834	147	83	ϖ	ϖ	PROPN
ejpam-5834	147	84	2	2	NUM
ejpam-5834	147	85	k1	k1	NOUN
ejpam-5834	147	86	+	+	CCONJ
ejpam-5834	147	87	1−ϖ	1−ϖ	NUM
ejpam-5834	147	88	2	2	NUM
ejpam-5834	147	89	k2	k2	NOUN
ejpam-5834	147	90	)	)	PUNCT
ejpam-5834	147	91	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5834	148	1	dϖ	dϖ	PROPN
ejpam-5834	148	2	)	)	PUNCT
ejpam-5834	148	3	1	1	NUM
ejpam-5834	148	4	q	q	NOUN
ejpam-5834	149	1	+	+	CCONJ
ejpam-5834	149	2	(	(	PUNCT
ejpam-5834	149	3	∫	∫	PROPN
ejpam-5834	149	4	1	1	NUM
ejpam-5834	149	5	0	0	NUM
ejpam-5834	149	6	(	(	PUNCT
ejpam-5834	149	7	1−ϖ)(ρ+1)dϖ	1−ϖ)(ρ+1)dϖ	NUM
ejpam-5834	149	8	)	)	PUNCT
ejpam-5834	149	9	1−	1−	PROPN
ejpam-5834	149	10	1	1	NUM
ejpam-5834	149	11	q	q	NOUN
ejpam-5834	149	12	(	(	PUNCT
ejpam-5834	149	13	∫	∫	PROPN
ejpam-5834	149	14	1	1	NUM
ejpam-5834	149	15	0	0	NUM
ejpam-5834	149	16	(	(	PUNCT
ejpam-5834	149	17	1−ϖ)(ρ+1	1−ϖ)(ρ+1	NUM
ejpam-5834	149	18	)	)	PUNCT
ejpam-5834	149	19	∣∣∣∣η′′(1−ϖ	∣∣∣∣η′′(1−ϖ	ADJ
ejpam-5834	149	20	2	2	NUM
ejpam-5834	149	21	k1	k1	NOUN
ejpam-5834	149	22	+	+	CCONJ
ejpam-5834	149	23	1	1	NUM
ejpam-5834	149	24	+	+	ADJ
ejpam-5834	149	25	ϖ	ϖ	PROPN
ejpam-5834	149	26	2	2	NUM
ejpam-5834	149	27	k2	k2	NOUN
ejpam-5834	149	28	)	)	PUNCT
ejpam-5834	149	29	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5834	150	1	dϖ	dϖ	PROPN
ejpam-5834	150	2	)	)	PUNCT
ejpam-5834	150	3	1	1	NUM
ejpam-5834	150	4	q	q	NOUN
ejpam-5834	150	5	}	}	PUNCT
ejpam-5834	150	6	≤	≤	PROPN
ejpam-5834	150	7	(	(	PUNCT
ejpam-5834	150	8	k2	k2	ADJ
ejpam-5834	150	9	−	−	PROPN
ejpam-5834	150	10	k1	k1	PROPN
ejpam-5834	150	11	)	)	PUNCT
ejpam-5834	150	12	2	2	NUM
ejpam-5834	150	13	23(ρ+	23(ρ+	NUM
ejpam-5834	150	14	1	1	NUM
ejpam-5834	150	15	)	)	PUNCT
ejpam-5834	150	16	(	(	PUNCT
ejpam-5834	150	17	1	1	NUM
ejpam-5834	150	18	ρ+	ρ+	NUM
ejpam-5834	150	19	2	2	NUM
ejpam-5834	150	20	)	)	PUNCT
ejpam-5834	150	21	1−	1−	NUM
ejpam-5834	150	22	1	1	NUM
ejpam-5834	150	23	q	q	NOUN
ejpam-5834	150	24	{	{	PUNCT
ejpam-5834	150	25	(	(	PUNCT
ejpam-5834	150	26	∣∣η′′(k1)∣∣q	∣∣η′′(k1)∣∣q	NOUN
ejpam-5834	150	27	2f1(1,−ρs	2f1(1,−ρs	NUM
ejpam-5834	150	28	;	;	PUNCT
ejpam-5834	150	29	3	3	NUM
ejpam-5834	150	30	+	+	CCONJ
ejpam-5834	150	31	k2;−1	k2;−1	NOUN
ejpam-5834	150	32	)	)	PUNCT
ejpam-5834	150	33	k1	k1	NOUN
ejpam-5834	150	34	+	+	CCONJ
ejpam-5834	150	35	2	2	NUM
ejpam-5834	150	36	+	+	CCONJ
ejpam-5834	150	37	∣∣η′′(k2)∣∣q	∣∣η′′(k2)∣∣q	PROPN
ejpam-5834	150	38	ω(ρ	ω(ρ	NUM
ejpam-5834	150	39	,	,	PUNCT
ejpam-5834	150	40	s,ϖ	s,ϖ	NOUN
ejpam-5834	150	41	)	)	PUNCT
ejpam-5834	150	42	)	)	PUNCT
ejpam-5834	150	43	1	1	NUM
ejpam-5834	150	44	q	q	NOUN
ejpam-5834	150	45	+	+	CCONJ
ejpam-5834	150	46	(	(	PUNCT
ejpam-5834	150	47	∣∣η′′(k1)∣∣q	∣∣η′′(k1)∣∣q	PROPN
ejpam-5834	150	48	(	(	PUNCT
ejpam-5834	150	49	γ(ρs+	γ(ρs+	PROPN
ejpam-5834	150	50	ρ+	ρ+	NUM
ejpam-5834	150	51	2	2	NUM
ejpam-5834	150	52	)	)	PUNCT
ejpam-5834	150	53	γ(ρs+	γ(ρs+	NOUN
ejpam-5834	150	54	α+	α+	PRON
ejpam-5834	150	55	3	3	NUM
ejpam-5834	150	56	)	)	PUNCT
ejpam-5834	150	57	)	)	PUNCT
ejpam-5834	151	1	+	+	CCONJ
ejpam-5834	151	2	∣∣η′′(k2)∣∣q	∣∣η′′(k2)∣∣q	PROPN
ejpam-5834	151	3	ω(ρ	ω(ρ	NUM
ejpam-5834	151	4	,	,	PUNCT
ejpam-5834	151	5	s,ϖ	s,ϖ	NOUN
ejpam-5834	151	6	)	)	PUNCT
ejpam-5834	151	7	)	)	PUNCT
ejpam-5834	151	8	1	1	NUM
ejpam-5834	151	9	q	q	NOUN
ejpam-5834	151	10	}	}	PUNCT
ejpam-5834	151	11	now	now	ADV
ejpam-5834	151	12	,	,	PUNCT
ejpam-5834	151	13	we	we	PRON
ejpam-5834	151	14	present	present	VERB
ejpam-5834	151	15	generalized	generalized	ADJ
ejpam-5834	151	16	integral	integral	ADJ
ejpam-5834	151	17	inequalities	inequality	NOUN
ejpam-5834	151	18	via	via	ADP
ejpam-5834	151	19	riemann	riemann	PROPN
ejpam-5834	151	20	-	-	PUNCT
ejpam-5834	151	21	liouville	liouville	VERB
ejpam-5834	151	22	operators	operator	NOUN
ejpam-5834	151	23	for	for	ADP
ejpam-5834	151	24	mappings	mapping	NOUN
ejpam-5834	151	25	whose	whose	DET
ejpam-5834	151	26	twice	twice	ADV
ejpam-5834	151	27	differentiable	differentiable	ADJ
ejpam-5834	151	28	are	be	AUX
ejpam-5834	151	29	(	(	PUNCT
ejpam-5834	151	30	ρ	ρ	PROPN
ejpam-5834	151	31	,	,	PUNCT
ejpam-5834	151	32	s	s	PROPN
ejpam-5834	151	33	,	,	PUNCT
ejpam-5834	151	34	m	m	NOUN
ejpam-5834	151	35	)	)	PUNCT
ejpam-5834	151	36	.	.	PUNCT
ejpam-5834	152	1	theorem	theorem	NOUN
ejpam-5834	152	2	5	5	NUM
ejpam-5834	152	3	.	.	PUNCT
ejpam-5834	153	1	let	let	VERB
ejpam-5834	153	2	η	η	PROPN
ejpam-5834	153	3	:	:	PUNCT
ejpam-5834	153	4	[	[	X
ejpam-5834	153	5	k1	k1	X
ejpam-5834	153	6	,	,	PUNCT
ejpam-5834	153	7	k2	k2	NOUN
ejpam-5834	153	8	]	]	PUNCT
ejpam-5834	153	9	→	→	PUNCT
ejpam-5834	153	10	r	r	NOUN
ejpam-5834	153	11	be	be	VERB
ejpam-5834	153	12	twice	twice	ADV
ejpam-5834	153	13	differentiable	differentiable	ADJ
ejpam-5834	153	14	function	function	NOUN
ejpam-5834	153	15	on	on	ADP
ejpam-5834	153	16	(	(	PUNCT
ejpam-5834	153	17	k1	k1	NOUN
ejpam-5834	153	18	,	,	PUNCT
ejpam-5834	153	19	k2	k2	NOUN
ejpam-5834	153	20	)	)	PUNCT
ejpam-5834	153	21	with	with	ADP
ejpam-5834	153	22	k1	k1	PROPN
ejpam-5834	153	23	<	<	X
ejpam-5834	153	24	k2	k2	PROPN
ejpam-5834	153	25	.	.	PUNCT
ejpam-5834	154	1	if	if	SCONJ
ejpam-5834	154	2	η′′	η′′	PROPN
ejpam-5834	154	3	∈	∈	PROPN
ejpam-5834	154	4	l[k1	l[k1	NOUN
ejpam-5834	154	5	,	,	PUNCT
ejpam-5834	154	6	k2	k2	NOUN
ejpam-5834	154	7	]	]	PUNCT
ejpam-5834	154	8	and	and	CCONJ
ejpam-5834	154	9	|η′′|	|η′′|	PROPN
ejpam-5834	154	10	is	be	AUX
ejpam-5834	154	11	(	(	PUNCT
ejpam-5834	154	12	ρ	ρ	PROPN
ejpam-5834	154	13	,	,	PUNCT
ejpam-5834	154	14	s	s	PROPN
ejpam-5834	154	15	,	,	PUNCT
ejpam-5834	154	16	m	m	NOUN
ejpam-5834	154	17	)	)	PUNCT
ejpam-5834	154	18	convex	convex	NOUN
ejpam-5834	154	19	function	function	NOUN
ejpam-5834	154	20	,	,	PUNCT
ejpam-5834	154	21	where	where	SCONJ
ejpam-5834	154	22	(	(	PUNCT
ejpam-5834	154	23	ρ	ρ	NOUN
ejpam-5834	154	24	,	,	PUNCT
ejpam-5834	154	25	m	m	NOUN
ejpam-5834	154	26	)	)	PUNCT
ejpam-5834	154	27	∈	∈	PROPN
ejpam-5834	154	28	(	(	PUNCT
ejpam-5834	154	29	0	0	NUM
ejpam-5834	154	30	,	,	PUNCT
ejpam-5834	154	31	1]2	1]2	NUM
ejpam-5834	154	32	,	,	PUNCT
ejpam-5834	154	33	s	s	PROPN
ejpam-5834	154	34	∈	∈	PROPN
ejpam-5834	154	35	(	(	PUNCT
ejpam-5834	154	36	−1	−1	NOUN
ejpam-5834	154	37	,	,	PUNCT
ejpam-5834	154	38	1	1	NUM
ejpam-5834	154	39	]	]	PUNCT
ejpam-5834	154	40	then	then	ADV
ejpam-5834	154	41	,	,	PUNCT
ejpam-5834	154	42	we	we	PRON
ejpam-5834	154	43	have	have	VERB
ejpam-5834	154	44	the	the	DET
ejpam-5834	154	45	following	follow	VERB
ejpam-5834	154	46	inequality	inequality	NOUN
ejpam-5834	154	47	for	for	ADP
ejpam-5834	154	48	fractional	fractional	ADJ
ejpam-5834	154	49	integrals:∣∣∣∣∣2ρ−1γ(ρ+	integrals:∣∣∣∣∣2ρ−1γ(ρ+	PROPN
ejpam-5834	154	50	1	1	NUM
ejpam-5834	154	51	)	)	PUNCT
ejpam-5834	154	52	(	(	PUNCT
ejpam-5834	154	53	k2	k2	PROPN
ejpam-5834	154	54	−	−	PROPN
ejpam-5834	154	55	k1)ρ	k1)ρ	NOUN
ejpam-5834	154	56	[	[	PUNCT
ejpam-5834	154	57	jρ	jρ	PROPN
ejpam-5834	154	58	(	(	PUNCT
ejpam-5834	154	59	k1+k2	k1+k2	PROPN
ejpam-5834	154	60	2	2	NUM
ejpam-5834	154	61	)	)	PUNCT
ejpam-5834	154	62	−η(k1	−η(k1	PROPN
ejpam-5834	154	63	)	)	PUNCT
ejpam-5834	155	1	+	+	CCONJ
ejpam-5834	156	1	jρ	jρ	PROPN
ejpam-5834	156	2	(	(	PUNCT
ejpam-5834	156	3	k1+k2	k1+k2	PROPN
ejpam-5834	156	4	2	2	NUM
ejpam-5834	156	5	)	)	PUNCT
ejpam-5834	156	6	+	+	NOUN
ejpam-5834	156	7	η(k2	η(k2	NOUN
ejpam-5834	156	8	)	)	PUNCT
ejpam-5834	156	9	]	]	PUNCT
ejpam-5834	157	1	−	−	PROPN
ejpam-5834	157	2	η	η	X
ejpam-5834	157	3	(	(	PUNCT
ejpam-5834	157	4	k1	k1	X
ejpam-5834	157	5	+	+	CCONJ
ejpam-5834	157	6	k2	k2	ADJ
ejpam-5834	157	7	2	2	NUM
ejpam-5834	157	8	)	)	PUNCT
ejpam-5834	157	9	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5834	157	10	≤	≤	PROPN
ejpam-5834	157	11	(	(	PUNCT
ejpam-5834	157	12	k2	k2	ADJ
ejpam-5834	157	13	−	−	PROPN
ejpam-5834	157	14	k1	k1	NOUN
ejpam-5834	157	15	)	)	PUNCT
ejpam-5834	157	16	2	2	NUM
ejpam-5834	157	17	2ρs+3(ρ+	2ρs+3(ρ+	NUM
ejpam-5834	157	18	1	1	NUM
ejpam-5834	157	19	)	)	PUNCT
ejpam-5834	157	20	[	[	X
ejpam-5834	157	21	∣∣η′′(k1)∣∣	∣∣η′′(k1)∣∣	NOUN
ejpam-5834	157	22	2f1(1,−ρs	2f1(1,−ρ	NOUN
ejpam-5834	157	23	;	;	PUNCT
ejpam-5834	157	24	3	3	NUM
ejpam-5834	157	25	+	+	CCONJ
ejpam-5834	157	26	k1;−1	k1;−1	NOUN
ejpam-5834	157	27	)	)	PUNCT
ejpam-5834	157	28	k1	k1	NOUN
ejpam-5834	157	29	+	+	CCONJ
ejpam-5834	157	30	2	2	NUM
ejpam-5834	157	31	+	+	NOUN
ejpam-5834	157	32	m	m	PROPN
ejpam-5834	157	33	∣∣∣∣η′′(k2	∣∣∣∣η′′(k2	PROPN
ejpam-5834	157	34	m	m	PROPN
ejpam-5834	157	35	)	)	PUNCT
ejpam-5834	157	36	∣∣∣∣ω(ρ	∣∣∣∣ω(ρ	PROPN
ejpam-5834	157	37	,	,	PUNCT
ejpam-5834	157	38	s,ϖ	s,ϖ	NOUN
ejpam-5834	157	39	)	)	PUNCT
ejpam-5834	157	40	+	+	CCONJ
ejpam-5834	157	41	∣∣η′′(k1)∣∣	∣∣η′′(k1)∣∣	PROPN
ejpam-5834	157	42	γ(ρs+	γ(ρs+	NOUN
ejpam-5834	157	43	ρ+	ρ+	NUM
ejpam-5834	157	44	2	2	NUM
ejpam-5834	157	45	)	)	PUNCT
ejpam-5834	157	46	γ(ρs+	γ(ρs+	NOUN
ejpam-5834	157	47	ρ+	ρ+	NUM
ejpam-5834	157	48	3	3	X
ejpam-5834	157	49	)	)	PUNCT
ejpam-5834	157	50	+	+	NOUN
ejpam-5834	157	51	m	m	PROPN
ejpam-5834	157	52	∣∣∣∣η′′(k2	∣∣∣∣η′′(k2	PROPN
ejpam-5834	157	53	m	m	PROPN
ejpam-5834	157	54	)	)	PUNCT
ejpam-5834	157	55	∣∣∣∣ω(ρ	∣∣∣∣ω(ρ	PROPN
ejpam-5834	157	56	,	,	PUNCT
ejpam-5834	157	57	s,ϖ	s,ϖ	NOUN
ejpam-5834	157	58	)	)	PUNCT
ejpam-5834	157	59	]	]	PUNCT
ejpam-5834	157	60	,	,	PUNCT
ejpam-5834	157	61	where	where	SCONJ
ejpam-5834	157	62	ω(ρ	ω(ρ	NOUN
ejpam-5834	157	63	,	,	PUNCT
ejpam-5834	157	64	s,ϖ	s,ϖ	NOUN
ejpam-5834	157	65	)	)	PUNCT
ejpam-5834	157	66	=	=	SYM
ejpam-5834	157	67	∫	∫	PROPN
ejpam-5834	157	68	1	1	NUM
ejpam-5834	157	69	0	0	NUM
ejpam-5834	157	70	(	(	PUNCT
ejpam-5834	157	71	1−ϖ)ρ+1(2ρ	1−ϖ)ρ+1(2ρ	NUM
ejpam-5834	157	72	−	−	NOUN
ejpam-5834	157	73	(	(	PUNCT
ejpam-5834	157	74	1	1	NUM
ejpam-5834	157	75	+	+	NOUN
ejpam-5834	157	76	ϖ)ρ)sdϖ.	ϖ)ρ)sdϖ.	NOUN
ejpam-5834	157	77	proof	proof	NOUN
ejpam-5834	157	78	.	.	PUNCT
ejpam-5834	158	1	using	use	VERB
ejpam-5834	158	2	lemma	lemma	PROPN
ejpam-5834	158	3	1	1	NUM
ejpam-5834	158	4	and	and	CCONJ
ejpam-5834	158	5	the	the	DET
ejpam-5834	158	6	fact	fact	NOUN
ejpam-5834	158	7	that	that	SCONJ
ejpam-5834	158	8	|η′′|	|η′′|	PROPN
ejpam-5834	158	9	is	be	AUX
ejpam-5834	158	10	(	(	PUNCT
ejpam-5834	158	11	ρ	ρ	PROPN
ejpam-5834	158	12	,	,	PUNCT
ejpam-5834	158	13	s	s	NOUN
ejpam-5834	158	14	,	,	PUNCT
ejpam-5834	158	15	m)-convexity	m)-convexity	NOUN
ejpam-5834	158	16	,	,	PUNCT
ejpam-5834	158	17	we	we	PRON
ejpam-5834	158	18	get	get	VERB
ejpam-5834	158	19	the	the	DET
ejpam-5834	158	20	folo	folo	NOUN
ejpam-5834	158	21	.	.	PUNCT
ejpam-5834	159	1	b.	b.	PROPN
ejpam-5834	159	2	almutairi	almutairi	PROPN
ejpam-5834	159	3	/	/	SYM
ejpam-5834	159	4	eur	eur	PROPN
ejpam-5834	159	5	.	.	PUNCT
ejpam-5834	160	1	j.	j.	PROPN
ejpam-5834	160	2	pure	pure	PROPN
ejpam-5834	160	3	appl	appl	PROPN
ejpam-5834	160	4	.	.	PROPN
ejpam-5834	160	5	math	math	PROPN
ejpam-5834	160	6	,	,	PUNCT
ejpam-5834	160	7	18	18	NUM
ejpam-5834	160	8	(	(	PUNCT
ejpam-5834	160	9	1	1	NUM
ejpam-5834	160	10	)	)	PUNCT
ejpam-5834	160	11	(	(	PUNCT
ejpam-5834	160	12	2025	2025	NUM
ejpam-5834	160	13	)	)	PUNCT
ejpam-5834	160	14	,	,	PUNCT
ejpam-5834	160	15	5834	5834	NUM
ejpam-5834	160	16	8	8	NUM
ejpam-5834	160	17	of	of	ADP
ejpam-5834	160	18	12	12	NUM
ejpam-5834	160	19	lowing∣∣∣∣∣2ρ−1γ(ρ+	lowing∣∣∣∣∣2ρ−1γ(ρ+	ADJ
ejpam-5834	160	20	1	1	NUM
ejpam-5834	160	21	)	)	PUNCT
ejpam-5834	160	22	(	(	PUNCT
ejpam-5834	160	23	k2	k2	PROPN
ejpam-5834	160	24	−	−	PROPN
ejpam-5834	160	25	k1)ρ	k1)ρ	NOUN
ejpam-5834	160	26	[	[	PUNCT
ejpam-5834	160	27	jρ	jρ	PROPN
ejpam-5834	160	28	(	(	PUNCT
ejpam-5834	160	29	k1+k2	k1+k2	PROPN
ejpam-5834	160	30	2	2	NUM
ejpam-5834	160	31	)	)	PUNCT
ejpam-5834	160	32	−η(k1	−η(k1	PROPN
ejpam-5834	160	33	)	)	PUNCT
ejpam-5834	161	1	+	+	CCONJ
ejpam-5834	162	1	jρ	jρ	PROPN
ejpam-5834	162	2	(	(	PUNCT
ejpam-5834	162	3	k1+k2	k1+k2	PROPN
ejpam-5834	162	4	2	2	NUM
ejpam-5834	162	5	)	)	PUNCT
ejpam-5834	162	6	+	+	NOUN
ejpam-5834	162	7	η(k2	η(k2	NOUN
ejpam-5834	162	8	)	)	PUNCT
ejpam-5834	162	9	]	]	PUNCT
ejpam-5834	163	1	−	−	PROPN
ejpam-5834	163	2	η	η	X
ejpam-5834	163	3	(	(	PUNCT
ejpam-5834	163	4	k1	k1	X
ejpam-5834	163	5	+	+	CCONJ
ejpam-5834	163	6	k2	k2	ADJ
ejpam-5834	163	7	2	2	NUM
ejpam-5834	163	8	)	)	PUNCT
ejpam-5834	163	9	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5834	163	10	=	=	PUNCT
ejpam-5834	163	11	∣∣∣∣(k2	∣∣∣∣(k2	VERB
ejpam-5834	163	12	−	−	PROPN
ejpam-5834	163	13	k1	k1	NOUN
ejpam-5834	163	14	)	)	PUNCT
ejpam-5834	163	15	2	2	NUM
ejpam-5834	163	16	8(ρ+	8(ρ+	NUM
ejpam-5834	163	17	1	1	NUM
ejpam-5834	163	18	)	)	PUNCT
ejpam-5834	163	19	∫	∫	PROPN
ejpam-5834	163	20	1	1	NUM
ejpam-5834	163	21	0	0	NUM
ejpam-5834	163	22	(	(	PUNCT
ejpam-5834	163	23	1−ϖ)ρ+1	1−ϖ)ρ+1	NUM
ejpam-5834	163	24	[	[	PUNCT
ejpam-5834	163	25	η′′	η′′	PROPN
ejpam-5834	163	26	(	(	PUNCT
ejpam-5834	163	27	1	1	NUM
ejpam-5834	163	28	+	+	NOUN
ejpam-5834	163	29	ϖ	ϖ	PROPN
ejpam-5834	163	30	2	2	NUM
ejpam-5834	163	31	k1	k1	NOUN
ejpam-5834	163	32	+	+	CCONJ
ejpam-5834	163	33	1−ϖ	1−ϖ	NUM
ejpam-5834	163	34	2	2	NUM
ejpam-5834	163	35	k2	k2	NOUN
ejpam-5834	163	36	)	)	PUNCT
ejpam-5834	163	37	+	+	CCONJ
ejpam-5834	163	38	η′′	η′′	PROPN
ejpam-5834	163	39	(	(	PUNCT
ejpam-5834	163	40	1−ϖ	1−ϖ	NUM
ejpam-5834	163	41	2	2	NUM
ejpam-5834	163	42	k1	k1	NOUN
ejpam-5834	163	43	+	+	CCONJ
ejpam-5834	163	44	1	1	NUM
ejpam-5834	163	45	+	+	ADJ
ejpam-5834	163	46	ϖ	ϖ	PROPN
ejpam-5834	163	47	2	2	NUM
ejpam-5834	163	48	k2	k2	NOUN
ejpam-5834	163	49	)	)	PUNCT
ejpam-5834	163	50	]	]	PUNCT
ejpam-5834	164	1	dϖ	dϖ	ADP
ejpam-5834	164	2	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5834	164	3	≤	≤	PROPN
ejpam-5834	164	4	∣∣∣∣(k2	∣∣∣∣(k2	VERB
ejpam-5834	164	5	−	−	PROPN
ejpam-5834	164	6	k1	k1	NOUN
ejpam-5834	164	7	)	)	PUNCT
ejpam-5834	164	8	2	2	NUM
ejpam-5834	164	9	8(ρ+	8(ρ+	NUM
ejpam-5834	164	10	1	1	NUM
ejpam-5834	164	11	)	)	PUNCT
ejpam-5834	164	12	∫	∫	PROPN
ejpam-5834	164	13	1	1	NUM
ejpam-5834	164	14	0	0	NUM
ejpam-5834	164	15	(	(	PUNCT
ejpam-5834	164	16	1−ϖ)ρ+1η′′	1−ϖ)ρ+1η′′	NUM
ejpam-5834	164	17	(	(	PUNCT
ejpam-5834	164	18	1	1	NUM
ejpam-5834	164	19	+	+	NOUN
ejpam-5834	164	20	ϖ	ϖ	PROPN
ejpam-5834	164	21	2	2	NUM
ejpam-5834	164	22	k1	k1	NOUN
ejpam-5834	164	23	+	+	CCONJ
ejpam-5834	164	24	1−ϖ	1−ϖ	NUM
ejpam-5834	164	25	2	2	NUM
ejpam-5834	164	26	k2	k2	NOUN
ejpam-5834	164	27	)	)	PUNCT
ejpam-5834	164	28	dϖ	dϖ	ADP
ejpam-5834	164	29	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5834	164	30	+	+	NUM
ejpam-5834	164	31	∣∣∣∣(k2	∣∣∣∣(k2	VERB
ejpam-5834	164	32	−	−	PROPN
ejpam-5834	164	33	k1	k1	NOUN
ejpam-5834	164	34	)	)	PUNCT
ejpam-5834	164	35	2	2	NUM
ejpam-5834	164	36	8(ρ+	8(ρ+	NUM
ejpam-5834	164	37	1	1	NUM
ejpam-5834	164	38	)	)	PUNCT
ejpam-5834	164	39	∫	∫	PROPN
ejpam-5834	164	40	1	1	NUM
ejpam-5834	164	41	0	0	NUM
ejpam-5834	164	42	(	(	PUNCT
ejpam-5834	164	43	1−ϖ)ρ+1η′′	1−ϖ)ρ+1η′′	NUM
ejpam-5834	164	44	(	(	PUNCT
ejpam-5834	164	45	1−ϖ	1−ϖ	NUM
ejpam-5834	164	46	2	2	NUM
ejpam-5834	164	47	k1	k1	NOUN
ejpam-5834	164	48	+	+	CCONJ
ejpam-5834	164	49	1	1	NUM
ejpam-5834	164	50	+	+	ADJ
ejpam-5834	164	51	ϖ	ϖ	PROPN
ejpam-5834	164	52	2	2	NUM
ejpam-5834	164	53	k2	k2	NOUN
ejpam-5834	164	54	)	)	PUNCT
ejpam-5834	164	55	dϖ	dϖ	ADP
ejpam-5834	164	56	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5834	164	57	≤	≤	NOUN
ejpam-5834	164	58	(	(	PUNCT
ejpam-5834	164	59	k2	k2	NOUN
ejpam-5834	164	60	−	−	PROPN
ejpam-5834	164	61	k1	k1	PROPN
ejpam-5834	164	62	)	)	PUNCT
ejpam-5834	164	63	2	2	NUM
ejpam-5834	164	64	8(ρ+	8(ρ+	NUM
ejpam-5834	164	65	1	1	NUM
ejpam-5834	164	66	)	)	PUNCT
ejpam-5834	164	67	∫	∫	PROPN
ejpam-5834	164	68	1	1	NUM
ejpam-5834	164	69	0	0	NUM
ejpam-5834	164	70	(	(	PUNCT
ejpam-5834	164	71	1−ϖ)ρ+1	1−ϖ)ρ+1	NUM
ejpam-5834	164	72	∣∣∣∣η′′(1	∣∣∣∣η′′(1	VERB
ejpam-5834	164	73	+	+	NOUN
ejpam-5834	164	74	ϖ	ϖ	PROPN
ejpam-5834	164	75	2	2	NUM
ejpam-5834	164	76	k1	k1	NOUN
ejpam-5834	164	77	+	+	CCONJ
ejpam-5834	164	78	1−ϖ	1−ϖ	NUM
ejpam-5834	164	79	2	2	NUM
ejpam-5834	164	80	k2	k2	NOUN
ejpam-5834	164	81	)	)	PUNCT
ejpam-5834	164	82	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5834	164	83	dϖ	dϖ	NOUN
ejpam-5834	164	84	+	+	CCONJ
ejpam-5834	164	85	(	(	PUNCT
ejpam-5834	164	86	k2	k2	PROPN
ejpam-5834	164	87	−	−	PROPN
ejpam-5834	164	88	k1	k1	PROPN
ejpam-5834	164	89	)	)	PUNCT
ejpam-5834	164	90	2	2	NUM
ejpam-5834	164	91	8(ρ+	8(ρ+	NUM
ejpam-5834	164	92	1	1	NUM
ejpam-5834	164	93	)	)	PUNCT
ejpam-5834	164	94	∫	∫	PROPN
ejpam-5834	164	95	1	1	NUM
ejpam-5834	164	96	0	0	NUM
ejpam-5834	164	97	(	(	PUNCT
ejpam-5834	164	98	1−ϖ)ρ+1	1−ϖ)ρ+1	NUM
ejpam-5834	164	99	∣∣∣∣η′′(1−ϖ	∣∣∣∣η′′(1−ϖ	ADJ
ejpam-5834	164	100	2	2	NUM
ejpam-5834	164	101	k1	k1	NOUN
ejpam-5834	164	102	+	+	CCONJ
ejpam-5834	164	103	1	1	NUM
ejpam-5834	164	104	+	+	ADJ
ejpam-5834	164	105	ϖ	ϖ	PROPN
ejpam-5834	164	106	2	2	NUM
ejpam-5834	164	107	k2	k2	NOUN
ejpam-5834	164	108	)	)	PUNCT
ejpam-5834	164	109	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5834	164	110	dϖ	dϖ	ADP
ejpam-5834	164	111	≤	≤	PROPN
ejpam-5834	164	112	(	(	PUNCT
ejpam-5834	164	113	k2	k2	NOUN
ejpam-5834	164	114	−	−	PROPN
ejpam-5834	164	115	k1	k1	PROPN
ejpam-5834	164	116	)	)	PUNCT
ejpam-5834	164	117	2	2	NUM
ejpam-5834	164	118	8(ρ+	8(ρ+	NUM
ejpam-5834	164	119	1	1	NUM
ejpam-5834	164	120	)	)	PUNCT
ejpam-5834	165	1	[	[	X
ejpam-5834	165	2	∫	∫	X
ejpam-5834	165	3	1	1	NUM
ejpam-5834	165	4	0	0	NUM
ejpam-5834	165	5	(	(	PUNCT
ejpam-5834	165	6	1−ϖ)ρ+1	1−ϖ)ρ+1	NUM
ejpam-5834	165	7	[	[	X
ejpam-5834	165	8	(	(	PUNCT
ejpam-5834	165	9	1	1	NUM
ejpam-5834	165	10	+	+	NOUN
ejpam-5834	165	11	ϖ	ϖ	NOUN
ejpam-5834	165	12	2	2	NUM
ejpam-5834	165	13	)	)	PUNCT
ejpam-5834	165	14	ρs	ρs	ADV
ejpam-5834	165	15	∣∣η′′(k1)∣∣+	∣∣η′′(k1)∣∣+	PROPN
ejpam-5834	165	16	(	(	PUNCT
ejpam-5834	165	17	1−	1−	NUM
ejpam-5834	165	18	(	(	PUNCT
ejpam-5834	165	19	1−ϖ	1−ϖ	NUM
ejpam-5834	165	20	2	2	NUM
ejpam-5834	165	21	)	)	PUNCT
ejpam-5834	165	22	ρ)s	ρ)s	NOUN
ejpam-5834	165	23	m	m	VERB
ejpam-5834	165	24	∣∣∣∣η′′(k2	∣∣∣∣η′′(k2	PROPN
ejpam-5834	165	25	m	m	NOUN
ejpam-5834	165	26	)	)	PUNCT
ejpam-5834	165	27	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5834	165	28	]	]	PUNCT
ejpam-5834	165	29	dϖ	dϖ	X
ejpam-5834	165	30	+	+	CCONJ
ejpam-5834	165	31	∫	∫	PROPN
ejpam-5834	165	32	1	1	NUM
ejpam-5834	165	33	0	0	NUM
ejpam-5834	165	34	(	(	PUNCT
ejpam-5834	165	35	1−ϖ)ρ+1	1−ϖ)ρ+1	NUM
ejpam-5834	165	36	[	[	X
ejpam-5834	165	37	(	(	PUNCT
ejpam-5834	165	38	1−ϖ	1−ϖ	NUM
ejpam-5834	165	39	2	2	NUM
ejpam-5834	165	40	)	)	PUNCT
ejpam-5834	165	41	ρs	ρs	ADP
ejpam-5834	165	42	∣∣η′′(k1)∣∣+m	∣∣η′′(k1)∣∣+m	PROPN
ejpam-5834	165	43	(	(	PUNCT
ejpam-5834	165	44	1−	1−	NUM
ejpam-5834	165	45	(	(	PUNCT
ejpam-5834	165	46	1	1	NUM
ejpam-5834	165	47	+	+	NOUN
ejpam-5834	165	48	ϖ	ϖ	NOUN
ejpam-5834	165	49	2	2	NUM
ejpam-5834	165	50	)	)	PUNCT
ejpam-5834	165	51	ρ)s	ρ)s	NOUN
ejpam-5834	165	52	∣∣∣∣η′′(k2	∣∣∣∣η′′(k2	PROPN
ejpam-5834	165	53	m	m	NOUN
ejpam-5834	165	54	)	)	PUNCT
ejpam-5834	165	55	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5834	165	56	]	]	PUNCT
ejpam-5834	165	57	dϖ	dϖ	ADP
ejpam-5834	165	58	]	]	X
ejpam-5834	165	59	=	=	SYM
ejpam-5834	165	60	(	(	PUNCT
ejpam-5834	165	61	k2	k2	PROPN
ejpam-5834	165	62	−	−	PROPN
ejpam-5834	165	63	k1	k1	NOUN
ejpam-5834	165	64	)	)	PUNCT
ejpam-5834	165	65	2	2	NUM
ejpam-5834	165	66	2ρs+3(ρ+	2ρs+3(ρ+	NUM
ejpam-5834	165	67	1	1	NUM
ejpam-5834	165	68	)	)	PUNCT
ejpam-5834	166	1	[	[	X
ejpam-5834	166	2	∣∣η′′(k1)∣∣	∣∣η′′(k1)∣∣	PRON
ejpam-5834	166	3	∫	∫	PROPN
ejpam-5834	166	4	1	1	NUM
ejpam-5834	166	5	0	0	NUM
ejpam-5834	166	6	(	(	PUNCT
ejpam-5834	166	7	1−ϖ)ρ+1(1	1−ϖ)ρ+1(1	NUM
ejpam-5834	166	8	+	+	NOUN
ejpam-5834	166	9	ϖ)ρsdϖ	ϖ)ρsdϖ	NOUN
ejpam-5834	166	10	+	+	NOUN
ejpam-5834	166	11	m	m	PROPN
ejpam-5834	166	12	∣∣∣∣η′′(k2	∣∣∣∣η′′(k2	PROPN
ejpam-5834	166	13	m	m	NOUN
ejpam-5834	166	14	)	)	PUNCT
ejpam-5834	166	15	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5834	166	16	∫	∫	PROPN
ejpam-5834	166	17	1	1	NUM
ejpam-5834	166	18	0	0	NUM
ejpam-5834	166	19	(	(	PUNCT
ejpam-5834	166	20	1−ϖ)ρ+1(2ρ	1−ϖ)ρ+1(2ρ	NUM
ejpam-5834	166	21	−	−	NOUN
ejpam-5834	166	22	(	(	PUNCT
ejpam-5834	166	23	1−ϖ)ρ)sdϖ	1−ϖ)ρ)sdϖ	NOUN
ejpam-5834	166	24	+	+	CCONJ
ejpam-5834	166	25	∣∣η′′(k1)∣∣	∣∣η′′(k1)∣∣	PROPN
ejpam-5834	166	26	∫	∫	PROPN
ejpam-5834	166	27	1	1	NUM
ejpam-5834	166	28	0	0	NUM
ejpam-5834	166	29	(	(	PUNCT
ejpam-5834	166	30	1−ϖ)ρ+1(1−ϖ)ρsdϖ	1−ϖ)ρ+1(1−ϖ)ρsdϖ	NUM
ejpam-5834	166	31	+	+	NOUN
ejpam-5834	166	32	m	m	PROPN
ejpam-5834	166	33	∣∣∣∣η′′(k2	∣∣∣∣η′′(k2	PROPN
ejpam-5834	166	34	m	m	NOUN
ejpam-5834	166	35	)	)	PUNCT
ejpam-5834	166	36	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5834	166	37	∫	∫	PROPN
ejpam-5834	166	38	1	1	NUM
ejpam-5834	166	39	0	0	NUM
ejpam-5834	166	40	(	(	PUNCT
ejpam-5834	166	41	1−ϖ)ρ+1(2ρ	1−ϖ)ρ+1(2ρ	NUM
ejpam-5834	166	42	−	−	NOUN
ejpam-5834	166	43	(	(	PUNCT
ejpam-5834	166	44	1	1	NUM
ejpam-5834	166	45	+	+	NOUN
ejpam-5834	166	46	ϖ)ρ)sdϖ	ϖ)ρ)sdϖ	NOUN
ejpam-5834	166	47	]	]	X
ejpam-5834	166	48	=	=	SYM
ejpam-5834	166	49	(	(	PUNCT
ejpam-5834	166	50	k2	k2	PROPN
ejpam-5834	166	51	−	−	PROPN
ejpam-5834	166	52	k1	k1	NOUN
ejpam-5834	166	53	)	)	PUNCT
ejpam-5834	166	54	2	2	NUM
ejpam-5834	166	55	2ρs+3(ρ+	2ρs+3(ρ+	NUM
ejpam-5834	166	56	1	1	NUM
ejpam-5834	166	57	)	)	PUNCT
ejpam-5834	166	58	[	[	X
ejpam-5834	166	59	∣∣η′′(k1)∣∣	∣∣η′′(k1)∣∣	NOUN
ejpam-5834	166	60	2f1(1,−ρs	2f1(1,−ρ	NOUN
ejpam-5834	166	61	;	;	PUNCT
ejpam-5834	166	62	3	3	NUM
ejpam-5834	166	63	+	+	CCONJ
ejpam-5834	166	64	k1;−1	k1;−1	NOUN
ejpam-5834	166	65	)	)	PUNCT
ejpam-5834	166	66	k1	k1	NOUN
ejpam-5834	166	67	+	+	CCONJ
ejpam-5834	166	68	2	2	NUM
ejpam-5834	166	69	+	+	NOUN
ejpam-5834	166	70	m	m	PROPN
ejpam-5834	166	71	∣∣∣∣η′′(k2	∣∣∣∣η′′(k2	PROPN
ejpam-5834	166	72	m	m	NOUN
ejpam-5834	166	73	)	)	PUNCT
ejpam-5834	166	74	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5834	166	75	∫	∫	PROPN
ejpam-5834	166	76	1	1	NUM
ejpam-5834	166	77	0	0	NUM
ejpam-5834	166	78	(	(	PUNCT
ejpam-5834	166	79	1−ϖ)ρ+1(2ρ	1−ϖ)ρ+1(2ρ	NUM
ejpam-5834	166	80	−	−	NOUN
ejpam-5834	166	81	(	(	PUNCT
ejpam-5834	166	82	1−ϖ)ρ)sdϖ	1−ϖ)ρ)sdϖ	NOUN
ejpam-5834	166	83	+	+	CCONJ
ejpam-5834	166	84	∣∣η′′(k1)∣∣	∣∣η′′(k1)∣∣	PROPN
ejpam-5834	166	85	γ(ρs+	γ(ρs+	NOUN
ejpam-5834	166	86	ρ+	ρ+	NUM
ejpam-5834	166	87	2	2	NUM
ejpam-5834	166	88	)	)	PUNCT
ejpam-5834	166	89	γ(ρs+	γ(ρs+	NOUN
ejpam-5834	166	90	ρ+	ρ+	NUM
ejpam-5834	166	91	3	3	X
ejpam-5834	166	92	)	)	PUNCT
ejpam-5834	166	93	+	+	NOUN
ejpam-5834	166	94	m	m	PROPN
ejpam-5834	166	95	∣∣∣∣η′′(k2	∣∣∣∣η′′(k2	PROPN
ejpam-5834	166	96	m	m	NOUN
ejpam-5834	166	97	)	)	PUNCT
ejpam-5834	166	98	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5834	166	99	∫	∫	PROPN
ejpam-5834	166	100	1	1	NUM
ejpam-5834	166	101	0	0	NUM
ejpam-5834	166	102	(	(	PUNCT
ejpam-5834	166	103	1	1	NUM
ejpam-5834	166	104	+	+	ADJ
ejpam-5834	166	105	ϖ)ρ+1(2ρ	ϖ)ρ+1(2ρ	ADJ
ejpam-5834	166	106	−	−	PROPN
ejpam-5834	166	107	(	(	PUNCT
ejpam-5834	166	108	1	1	NUM
ejpam-5834	166	109	+	+	NOUN
ejpam-5834	166	110	ϖ)ρ)sdϖ	ϖ)ρ)sdϖ	NOUN
ejpam-5834	166	111	]	]	PUNCT
ejpam-5834	166	112	≤	≤	NUM
ejpam-5834	166	113	(	(	PUNCT
ejpam-5834	166	114	k2	k2	ADJ
ejpam-5834	166	115	−	−	PROPN
ejpam-5834	166	116	k1	k1	NOUN
ejpam-5834	166	117	)	)	PUNCT
ejpam-5834	166	118	2	2	NUM
ejpam-5834	166	119	2ρs+3(ρ+	2ρs+3(ρ+	NUM
ejpam-5834	166	120	1	1	NUM
ejpam-5834	166	121	)	)	PUNCT
ejpam-5834	166	122	[	[	X
ejpam-5834	166	123	∣∣η′′(k1)∣∣	∣∣η′′(k1)∣∣	NOUN
ejpam-5834	166	124	2f1(1,−ρs	2f1(1,−ρ	NOUN
ejpam-5834	166	125	;	;	PUNCT
ejpam-5834	166	126	3	3	NUM
ejpam-5834	166	127	+	+	CCONJ
ejpam-5834	166	128	k1;−1	k1;−1	NOUN
ejpam-5834	166	129	)	)	PUNCT
ejpam-5834	166	130	k1	k1	NOUN
ejpam-5834	166	131	+	+	CCONJ
ejpam-5834	166	132	2	2	NUM
ejpam-5834	166	133	+	+	NOUN
ejpam-5834	166	134	m	m	PROPN
ejpam-5834	166	135	∣∣∣∣η′′(k2	∣∣∣∣η′′(k2	PROPN
ejpam-5834	166	136	m	m	PROPN
ejpam-5834	166	137	)	)	PUNCT
ejpam-5834	166	138	∣∣∣∣ω(ρ	∣∣∣∣ω(ρ	PROPN
ejpam-5834	166	139	,	,	PUNCT
ejpam-5834	166	140	s,ϖ	s,ϖ	NOUN
ejpam-5834	166	141	)	)	PUNCT
ejpam-5834	166	142	+	+	CCONJ
ejpam-5834	166	143	∣∣η′′(k1)∣∣	∣∣η′′(k1)∣∣	PROPN
ejpam-5834	166	144	γ(ρs+	γ(ρs+	NOUN
ejpam-5834	166	145	ρ+	ρ+	NUM
ejpam-5834	166	146	2	2	NUM
ejpam-5834	166	147	)	)	PUNCT
ejpam-5834	166	148	γ(ρs+	γ(ρs+	NOUN
ejpam-5834	166	149	ρ+	ρ+	NUM
ejpam-5834	166	150	3	3	X
ejpam-5834	166	151	)	)	PUNCT
ejpam-5834	166	152	+	+	NOUN
ejpam-5834	166	153	m	m	PROPN
ejpam-5834	166	154	∣∣∣∣η′′(k2	∣∣∣∣η′′(k2	PROPN
ejpam-5834	166	155	m	m	PROPN
ejpam-5834	166	156	)	)	PUNCT
ejpam-5834	166	157	∣∣∣∣ω(ρ	∣∣∣∣ω(ρ	PROPN
ejpam-5834	166	158	,	,	PUNCT
ejpam-5834	166	159	s,ϖ	s,ϖ	NOUN
ejpam-5834	166	160	)	)	PUNCT
ejpam-5834	166	161	]	]	PUNCT
ejpam-5834	166	162	.	.	PUNCT
ejpam-5834	167	1	theorem	theorem	ADJ
ejpam-5834	167	2	6	6	NUM
ejpam-5834	167	3	.	.	PUNCT
ejpam-5834	168	1	let	let	VERB
ejpam-5834	168	2	η	η	PROPN
ejpam-5834	168	3	:	:	PUNCT
ejpam-5834	168	4	[	[	X
ejpam-5834	168	5	k1	k1	X
ejpam-5834	168	6	,	,	PUNCT
ejpam-5834	168	7	k2	k2	NOUN
ejpam-5834	168	8	]	]	PUNCT
ejpam-5834	168	9	→	→	PUNCT
ejpam-5834	168	10	r	r	NOUN
ejpam-5834	168	11	be	be	VERB
ejpam-5834	168	12	twice	twice	ADV
ejpam-5834	168	13	differentiable	differentiable	ADJ
ejpam-5834	168	14	function	function	NOUN
ejpam-5834	168	15	on	on	ADP
ejpam-5834	168	16	(	(	PUNCT
ejpam-5834	168	17	k1	k1	NOUN
ejpam-5834	168	18	,	,	PUNCT
ejpam-5834	168	19	k2	k2	NOUN
ejpam-5834	168	20	)	)	PUNCT
ejpam-5834	168	21	with	with	ADP
ejpam-5834	168	22	k1	k1	PROPN
ejpam-5834	168	23	<	<	X
ejpam-5834	168	24	k2	k2	PROPN
ejpam-5834	168	25	.	.	PUNCT
ejpam-5834	169	1	if	if	SCONJ
ejpam-5834	169	2	η′′	η′′	PROPN
ejpam-5834	169	3	∈	∈	PROPN
ejpam-5834	169	4	l[k1	l[k1	NOUN
ejpam-5834	169	5	,	,	PUNCT
ejpam-5834	169	6	k2	k2	NOUN
ejpam-5834	169	7	]	]	PUNCT
ejpam-5834	169	8	and	and	CCONJ
ejpam-5834	169	9	|η′′|q	|η′′|q	NOUN
ejpam-5834	169	10	is	be	AUX
ejpam-5834	169	11	(	(	PUNCT
ejpam-5834	169	12	ρ	ρ	PROPN
ejpam-5834	169	13	,	,	PUNCT
ejpam-5834	169	14	s	s	PROPN
ejpam-5834	169	15	,	,	PUNCT
ejpam-5834	169	16	m	m	VERB
ejpam-5834	169	17	)	)	PUNCT
ejpam-5834	169	18	is	be	AUX
ejpam-5834	169	19	convex	convex	ADJ
ejpam-5834	169	20	function	function	NOUN
ejpam-5834	169	21	,	,	PUNCT
ejpam-5834	169	22	where	where	SCONJ
ejpam-5834	169	23	(	(	PUNCT
ejpam-5834	169	24	ρ	ρ	NOUN
ejpam-5834	169	25	,	,	PUNCT
ejpam-5834	169	26	m	m	NOUN
ejpam-5834	169	27	)	)	PUNCT
ejpam-5834	169	28	∈	∈	PROPN
ejpam-5834	169	29	(	(	PUNCT
ejpam-5834	169	30	0	0	NUM
ejpam-5834	169	31	,	,	PUNCT
ejpam-5834	169	32	1]2	1]2	NUM
ejpam-5834	169	33	,	,	PUNCT
ejpam-5834	169	34	o.	o.	PROPN
ejpam-5834	169	35	b.	b.	PROPN
ejpam-5834	169	36	almutairi	almutairi	PROPN
ejpam-5834	169	37	/	/	SYM
ejpam-5834	169	38	eur	eur	PROPN
ejpam-5834	169	39	.	.	PUNCT
ejpam-5834	170	1	j.	j.	PROPN
ejpam-5834	170	2	pure	pure	PROPN
ejpam-5834	170	3	appl	appl	PROPN
ejpam-5834	170	4	.	.	PROPN
ejpam-5834	170	5	math	math	PROPN
ejpam-5834	170	6	,	,	PUNCT
ejpam-5834	170	7	18	18	NUM
ejpam-5834	170	8	(	(	PUNCT
ejpam-5834	170	9	1	1	NUM
ejpam-5834	170	10	)	)	PUNCT
ejpam-5834	170	11	(	(	PUNCT
ejpam-5834	170	12	2025	2025	NUM
ejpam-5834	170	13	)	)	PUNCT
ejpam-5834	170	14	,	,	PUNCT
ejpam-5834	170	15	5834	5834	NUM
ejpam-5834	170	16	9	9	NUM
ejpam-5834	170	17	of	of	ADP
ejpam-5834	170	18	12	12	NUM
ejpam-5834	170	19	s	s	NOUN
ejpam-5834	170	20	∈	∈	PROPN
ejpam-5834	170	21	(	(	PUNCT
ejpam-5834	170	22	−1	−1	NOUN
ejpam-5834	170	23	,	,	PUNCT
ejpam-5834	170	24	1	1	NUM
ejpam-5834	170	25	]	]	PUNCT
ejpam-5834	170	26	,	,	PUNCT
ejpam-5834	170	27	then	then	ADV
ejpam-5834	170	28	,	,	PUNCT
ejpam-5834	170	29	we	we	PRON
ejpam-5834	170	30	have	have	VERB
ejpam-5834	170	31	the	the	DET
ejpam-5834	170	32	following	follow	VERB
ejpam-5834	170	33	inequality	inequality	NOUN
ejpam-5834	170	34	for	for	ADP
ejpam-5834	170	35	fractional	fractional	ADJ
ejpam-5834	170	36	integrals:∣∣∣∣∣2ρ−1γ(ρ+	integrals:∣∣∣∣∣2ρ−1γ(ρ+	PROPN
ejpam-5834	170	37	1	1	NUM
ejpam-5834	170	38	)	)	PUNCT
ejpam-5834	170	39	(	(	PUNCT
ejpam-5834	170	40	k2	k2	PROPN
ejpam-5834	170	41	−	−	PROPN
ejpam-5834	170	42	k1)ρ	k1)ρ	NOUN
ejpam-5834	170	43	[	[	PUNCT
ejpam-5834	170	44	jρ	jρ	PROPN
ejpam-5834	170	45	(	(	PUNCT
ejpam-5834	170	46	k1+k2	k1+k2	PROPN
ejpam-5834	170	47	2	2	NUM
ejpam-5834	170	48	)	)	PUNCT
ejpam-5834	170	49	−η(k1	−η(k1	PROPN
ejpam-5834	170	50	)	)	PUNCT
ejpam-5834	171	1	+	+	CCONJ
ejpam-5834	172	1	jρ	jρ	PROPN
ejpam-5834	172	2	(	(	PUNCT
ejpam-5834	172	3	k1+k2	k1+k2	PROPN
ejpam-5834	172	4	2	2	NUM
ejpam-5834	172	5	)	)	PUNCT
ejpam-5834	172	6	+	+	NOUN
ejpam-5834	172	7	η(k2	η(k2	NOUN
ejpam-5834	172	8	)	)	PUNCT
ejpam-5834	172	9	]	]	PUNCT
ejpam-5834	173	1	−	−	PROPN
ejpam-5834	173	2	η	η	X
ejpam-5834	173	3	(	(	PUNCT
ejpam-5834	173	4	k1	k1	X
ejpam-5834	173	5	+	+	CCONJ
ejpam-5834	173	6	k2	k2	ADJ
ejpam-5834	173	7	2	2	NUM
ejpam-5834	173	8	)	)	PUNCT
ejpam-5834	173	9	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5834	173	10	≤	≤	PROPN
ejpam-5834	173	11	(	(	PUNCT
ejpam-5834	173	12	k2	k2	ADJ
ejpam-5834	173	13	−	−	PROPN
ejpam-5834	173	14	k1	k1	PROPN
ejpam-5834	173	15	)	)	PUNCT
ejpam-5834	173	16	2	2	NUM
ejpam-5834	173	17	8(ρ+	8(ρ+	NUM
ejpam-5834	173	18	1	1	NUM
ejpam-5834	173	19	)	)	PUNCT
ejpam-5834	173	20	(	(	PUNCT
ejpam-5834	173	21	1	1	NUM
ejpam-5834	173	22	p(ρ+	p(ρ+	NOUN
ejpam-5834	173	23	1	1	NUM
ejpam-5834	173	24	)	)	PUNCT
ejpam-5834	173	25	+	+	CCONJ
ejpam-5834	173	26	1	1	X
ejpam-5834	173	27	)	)	PUNCT
ejpam-5834	173	28	1	1	NUM
ejpam-5834	173	29	p	p	NOUN
ejpam-5834	173	30	[	[	X
ejpam-5834	173	31	{	{	PUNCT
ejpam-5834	173	32	∣∣η′′(k1)∣∣q	∣∣η′′(k1)∣∣q	X
ejpam-5834	173	33	(	(	PUNCT
ejpam-5834	173	34	2−	2−	NUM
ejpam-5834	173	35	2−ρs	2−ρs	NUM
ejpam-5834	173	36	ρs+	ρs+	NOUN
ejpam-5834	173	37	1	1	NUM
ejpam-5834	173	38	)	)	PUNCT
ejpam-5834	174	1	+	+	VERB
ejpam-5834	174	2	m	m	VERB
ejpam-5834	174	3	∣∣∣∣η′′(k2	∣∣∣∣η′′(k2	PROPN
ejpam-5834	174	4	m	m	NOUN
ejpam-5834	174	5	)	)	PUNCT
ejpam-5834	174	6	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5834	174	7	(	(	PUNCT
ejpam-5834	174	8	2−	2−	NUM
ejpam-5834	174	9	2−ρs	2−ρs	NUM
ejpam-5834	174	10	ρs+	ρs+	NOUN
ejpam-5834	174	11	1	1	NUM
ejpam-5834	174	12	)	)	PUNCT
ejpam-5834	174	13	}	}	PUNCT
ejpam-5834	174	14	1	1	NUM
ejpam-5834	174	15	q	q	NOUN
ejpam-5834	174	16	+	+	NUM
ejpam-5834	174	17	{	{	PUNCT
ejpam-5834	174	18	∣∣η′′(k1)∣∣q	∣∣η′′(k1)∣∣q	X
ejpam-5834	174	19	(	(	PUNCT
ejpam-5834	174	20	2−ρs	2−ρs	NUM
ejpam-5834	174	21	ρs+	ρs+	NOUN
ejpam-5834	174	22	1	1	NUM
ejpam-5834	174	23	)	)	PUNCT
ejpam-5834	175	1	+	+	VERB
ejpam-5834	175	2	m	m	VERB
ejpam-5834	175	3	∣∣∣∣η′′(k2	∣∣∣∣η′′(k2	PROPN
ejpam-5834	175	4	m	m	NOUN
ejpam-5834	175	5	)	)	PUNCT
ejpam-5834	175	6	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5834	176	1	(	(	PUNCT
ejpam-5834	176	2	2−ρs	2−ρs	NUM
ejpam-5834	176	3	ρs+	ρs+	NOUN
ejpam-5834	176	4	1	1	NUM
ejpam-5834	176	5	)	)	PUNCT
ejpam-5834	176	6	}	}	PUNCT
ejpam-5834	176	7	1	1	NUM
ejpam-5834	176	8	q	q	NOUN
ejpam-5834	176	9	]	]	PUNCT
ejpam-5834	176	10	proof	proof	NOUN
ejpam-5834	176	11	.	.	PUNCT
ejpam-5834	177	1	applying	apply	VERB
ejpam-5834	177	2	hölder	hölder	NOUN
ejpam-5834	177	3	’s	’s	PART
ejpam-5834	177	4	inequality	inequality	NOUN
ejpam-5834	177	5	,	,	PUNCT
ejpam-5834	177	6	lemma	lemma	PROPN
ejpam-5834	177	7	1	1	NUM
ejpam-5834	177	8	and	and	CCONJ
ejpam-5834	177	9	the	the	DET
ejpam-5834	177	10	fact	fact	NOUN
ejpam-5834	177	11	that	that	SCONJ
ejpam-5834	177	12	|η′′|q	|η′′|q	NOUN
ejpam-5834	177	13	is	be	AUX
ejpam-5834	177	14	(	(	PUNCT
ejpam-5834	177	15	ρ	ρ	PROPN
ejpam-5834	177	16	,	,	PUNCT
ejpam-5834	177	17	s	s	PART
ejpam-5834	177	18	,	,	PUNCT
ejpam-5834	177	19	m)convex	m)convex	PROPN
ejpam-5834	177	20	function	function	NOUN
ejpam-5834	177	21	,	,	PUNCT
ejpam-5834	177	22	we	we	PRON
ejpam-5834	177	23	have∣∣∣∣∣2ρ−1γ(ρ+	have∣∣∣∣∣2ρ−1γ(ρ+	VERB
ejpam-5834	177	24	1	1	NUM
ejpam-5834	177	25	)	)	PUNCT
ejpam-5834	177	26	(	(	PUNCT
ejpam-5834	177	27	k2	k2	PROPN
ejpam-5834	177	28	−	−	PROPN
ejpam-5834	177	29	k1)ρ	k1)ρ	NOUN
ejpam-5834	177	30	[	[	PUNCT
ejpam-5834	177	31	jρ	jρ	PROPN
ejpam-5834	177	32	(	(	PUNCT
ejpam-5834	177	33	k1+k2	k1+k2	PROPN
ejpam-5834	177	34	2	2	NUM
ejpam-5834	177	35	)	)	PUNCT
ejpam-5834	177	36	−η(k1	−η(k1	PROPN
ejpam-5834	177	37	)	)	PUNCT
ejpam-5834	178	1	+	+	CCONJ
ejpam-5834	179	1	jρ	jρ	PROPN
ejpam-5834	179	2	(	(	PUNCT
ejpam-5834	179	3	k1+k2	k1+k2	PROPN
ejpam-5834	179	4	2	2	NUM
ejpam-5834	179	5	)	)	PUNCT
ejpam-5834	179	6	+	+	NOUN
ejpam-5834	179	7	η(k2	η(k2	NOUN
ejpam-5834	179	8	)	)	PUNCT
ejpam-5834	179	9	]	]	PUNCT
ejpam-5834	180	1	−	−	PROPN
ejpam-5834	180	2	η	η	X
ejpam-5834	180	3	(	(	PUNCT
ejpam-5834	180	4	k1	k1	X
ejpam-5834	180	5	+	+	CCONJ
ejpam-5834	180	6	k2	k2	ADJ
ejpam-5834	180	7	2	2	NUM
ejpam-5834	180	8	)	)	PUNCT
ejpam-5834	180	9	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5834	180	10	=	=	PUNCT
ejpam-5834	180	11	∣∣∣∣(k2	∣∣∣∣(k2	VERB
ejpam-5834	180	12	−	−	PROPN
ejpam-5834	180	13	k1	k1	NOUN
ejpam-5834	180	14	)	)	PUNCT
ejpam-5834	180	15	2	2	NUM
ejpam-5834	180	16	8(ρ+	8(ρ+	NUM
ejpam-5834	180	17	1	1	NUM
ejpam-5834	180	18	)	)	PUNCT
ejpam-5834	180	19	∫	∫	PROPN
ejpam-5834	180	20	1	1	NUM
ejpam-5834	180	21	0	0	NUM
ejpam-5834	180	22	(	(	PUNCT
ejpam-5834	180	23	1−ϖ)ρ+1	1−ϖ)ρ+1	NUM
ejpam-5834	180	24	[	[	PUNCT
ejpam-5834	180	25	η′′	η′′	PROPN
ejpam-5834	180	26	(	(	PUNCT
ejpam-5834	180	27	1	1	NUM
ejpam-5834	180	28	+	+	NOUN
ejpam-5834	180	29	ϖ	ϖ	PROPN
ejpam-5834	180	30	2	2	NUM
ejpam-5834	180	31	k1	k1	NOUN
ejpam-5834	180	32	+	+	CCONJ
ejpam-5834	180	33	1−ϖ	1−ϖ	NUM
ejpam-5834	180	34	2	2	NUM
ejpam-5834	180	35	k2	k2	NOUN
ejpam-5834	180	36	)	)	PUNCT
ejpam-5834	181	1	+	+	CCONJ
ejpam-5834	181	2	η′	η′	NOUN
ejpam-5834	181	3	(	(	PUNCT
ejpam-5834	181	4	1−ϖ	1−ϖ	NUM
ejpam-5834	181	5	2	2	NUM
ejpam-5834	181	6	k1	k1	NOUN
ejpam-5834	181	7	+	+	CCONJ
ejpam-5834	181	8	1	1	NUM
ejpam-5834	181	9	+	+	ADJ
ejpam-5834	181	10	ϖ	ϖ	PROPN
ejpam-5834	181	11	2	2	NUM
ejpam-5834	181	12	k2	k2	NOUN
ejpam-5834	181	13	)	)	PUNCT
ejpam-5834	181	14	]	]	PUNCT
ejpam-5834	182	1	dϖ	dϖ	ADP
ejpam-5834	182	2	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5834	182	3	≤	≤	PROPN
ejpam-5834	182	4	∣∣∣∣(k2	∣∣∣∣(k2	VERB
ejpam-5834	182	5	−	−	PROPN
ejpam-5834	182	6	k1	k1	NOUN
ejpam-5834	182	7	)	)	PUNCT
ejpam-5834	182	8	2	2	NUM
ejpam-5834	182	9	8(ρ+	8(ρ+	NUM
ejpam-5834	182	10	1	1	NUM
ejpam-5834	182	11	)	)	PUNCT
ejpam-5834	182	12	∫	∫	PROPN
ejpam-5834	182	13	1	1	NUM
ejpam-5834	182	14	0	0	NUM
ejpam-5834	182	15	(	(	PUNCT
ejpam-5834	182	16	1−ϖ)ρ+1η′′	1−ϖ)ρ+1η′′	NUM
ejpam-5834	182	17	(	(	PUNCT
ejpam-5834	182	18	1	1	NUM
ejpam-5834	182	19	+	+	NOUN
ejpam-5834	182	20	ϖ	ϖ	PROPN
ejpam-5834	182	21	2	2	NUM
ejpam-5834	182	22	k1	k1	NOUN
ejpam-5834	182	23	+	+	CCONJ
ejpam-5834	182	24	1−ϖ	1−ϖ	NUM
ejpam-5834	182	25	2	2	NUM
ejpam-5834	182	26	k2	k2	NOUN
ejpam-5834	182	27	)	)	PUNCT
ejpam-5834	182	28	dϖ	dϖ	ADP
ejpam-5834	182	29	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5834	182	30	+	+	NUM
ejpam-5834	182	31	∣∣∣∣k2	∣∣∣∣k2	NUM
ejpam-5834	182	32	−	−	NOUN
ejpam-5834	182	33	k1	k1	PROPN
ejpam-5834	182	34	4	4	NUM
ejpam-5834	182	35	∫	∫	NOUN
ejpam-5834	182	36	1	1	NUM
ejpam-5834	182	37	0	0	NUM
ejpam-5834	182	38	(	(	PUNCT
ejpam-5834	182	39	1−ϖ)ρ+1η′′	1−ϖ)ρ+1η′′	NUM
ejpam-5834	182	40	(	(	PUNCT
ejpam-5834	182	41	1−ϖ	1−ϖ	NUM
ejpam-5834	182	42	2	2	NUM
ejpam-5834	182	43	k1	k1	NOUN
ejpam-5834	182	44	+	+	CCONJ
ejpam-5834	182	45	1	1	NUM
ejpam-5834	182	46	+	+	ADJ
ejpam-5834	182	47	ϖ	ϖ	PROPN
ejpam-5834	182	48	2	2	NUM
ejpam-5834	182	49	k2	k2	NOUN
ejpam-5834	182	50	)	)	PUNCT
ejpam-5834	182	51	dϖ	dϖ	ADP
ejpam-5834	182	52	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5834	182	53	≤	≤	NOUN
ejpam-5834	182	54	(	(	PUNCT
ejpam-5834	182	55	k2	k2	NOUN
ejpam-5834	182	56	−	−	PROPN
ejpam-5834	182	57	k1	k1	PROPN
ejpam-5834	182	58	)	)	PUNCT
ejpam-5834	182	59	2	2	NUM
ejpam-5834	182	60	8(ρ+	8(ρ+	NUM
ejpam-5834	182	61	1	1	NUM
ejpam-5834	182	62	)	)	PUNCT
ejpam-5834	182	63	{	{	PUNCT
ejpam-5834	182	64	(	(	PUNCT
ejpam-5834	182	65	∫	∫	PROPN
ejpam-5834	182	66	1	1	NUM
ejpam-5834	182	67	0	0	NUM
ejpam-5834	182	68	(	(	PUNCT
ejpam-5834	182	69	1−ϖ)p(ρ+1)dϖ	1−ϖ)p(ρ+1)dϖ	PROPN
ejpam-5834	182	70	)	)	PUNCT
ejpam-5834	182	71	1	1	NUM
ejpam-5834	182	72	p	p	NOUN
ejpam-5834	182	73	(	(	PUNCT
ejpam-5834	182	74	∫	∫	PROPN
ejpam-5834	182	75	1	1	NUM
ejpam-5834	182	76	0	0	NUM
ejpam-5834	182	77	∣∣∣∣η′′(1	∣∣∣∣η′′(1	VERB
ejpam-5834	182	78	+	+	NOUN
ejpam-5834	182	79	ϖ	ϖ	PROPN
ejpam-5834	182	80	2	2	NUM
ejpam-5834	182	81	k1	k1	NOUN
ejpam-5834	182	82	+	+	CCONJ
ejpam-5834	182	83	1−ϖ	1−ϖ	NUM
ejpam-5834	182	84	2	2	NUM
ejpam-5834	182	85	k2	k2	NOUN
ejpam-5834	182	86	)	)	PUNCT
ejpam-5834	182	87	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5834	183	1	dϖ	dϖ	PROPN
ejpam-5834	183	2	)	)	PUNCT
ejpam-5834	183	3	1	1	NUM
ejpam-5834	183	4	q	q	NOUN
ejpam-5834	183	5	+	+	CCONJ
ejpam-5834	183	6	(	(	PUNCT
ejpam-5834	183	7	∫	∫	PROPN
ejpam-5834	183	8	1	1	NUM
ejpam-5834	183	9	0	0	NUM
ejpam-5834	183	10	(	(	PUNCT
ejpam-5834	183	11	1−ϖ)p(ρ+1)dϖ	1−ϖ)p(ρ+1)dϖ	PROPN
ejpam-5834	183	12	)	)	PUNCT
ejpam-5834	183	13	1	1	NUM
ejpam-5834	183	14	p	p	NOUN
ejpam-5834	183	15	(	(	PUNCT
ejpam-5834	183	16	∫	∫	PROPN
ejpam-5834	183	17	1	1	NUM
ejpam-5834	183	18	0	0	NUM
ejpam-5834	183	19	∣∣∣∣η′′(1−ϖ	∣∣∣∣η′′(1−ϖ	ADJ
ejpam-5834	183	20	2	2	NUM
ejpam-5834	183	21	k1	k1	NOUN
ejpam-5834	183	22	+	+	CCONJ
ejpam-5834	183	23	1	1	NUM
ejpam-5834	183	24	+	+	ADJ
ejpam-5834	183	25	ϖ	ϖ	PROPN
ejpam-5834	183	26	2	2	NUM
ejpam-5834	183	27	k2	k2	NOUN
ejpam-5834	183	28	)	)	PUNCT
ejpam-5834	183	29	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5834	184	1	dϖ	dϖ	PROPN
ejpam-5834	184	2	)	)	PUNCT
ejpam-5834	184	3	1	1	NUM
ejpam-5834	184	4	q	q	NOUN
ejpam-5834	184	5	}	}	PUNCT
ejpam-5834	184	6	≤	≤	PROPN
ejpam-5834	184	7	(	(	PUNCT
ejpam-5834	184	8	k2	k2	ADJ
ejpam-5834	184	9	−	−	PROPN
ejpam-5834	184	10	k1	k1	PROPN
ejpam-5834	184	11	)	)	PUNCT
ejpam-5834	184	12	2	2	NUM
ejpam-5834	184	13	8(ρ+	8(ρ+	NUM
ejpam-5834	184	14	1	1	NUM
ejpam-5834	184	15	)	)	PUNCT
ejpam-5834	184	16	(	(	PUNCT
ejpam-5834	184	17	1	1	NUM
ejpam-5834	184	18	p(ρ+	p(ρ+	NOUN
ejpam-5834	184	19	1	1	NUM
ejpam-5834	184	20	)	)	PUNCT
ejpam-5834	184	21	+	+	CCONJ
ejpam-5834	184	22	1	1	X
ejpam-5834	184	23	)	)	PUNCT
ejpam-5834	184	24	1	1	NUM
ejpam-5834	184	25	p	p	NOUN
ejpam-5834	184	26	{	{	PUNCT
ejpam-5834	184	27	(	(	PUNCT
ejpam-5834	184	28	∣∣η′′(k1)∣∣q	∣∣η′′(k1)∣∣q	NOUN
ejpam-5834	184	29	∫	∫	PROPN
ejpam-5834	184	30	1	1	NUM
ejpam-5834	184	31	0	0	NUM
ejpam-5834	184	32	(	(	PUNCT
ejpam-5834	184	33	1	1	NUM
ejpam-5834	184	34	+	+	NOUN
ejpam-5834	184	35	ϖ	ϖ	NOUN
ejpam-5834	184	36	2	2	NUM
ejpam-5834	184	37	)	)	PUNCT
ejpam-5834	184	38	ρs	ρs	ADP
ejpam-5834	184	39	dϖ	dϖ	ADP
ejpam-5834	184	40	+	+	NOUN
ejpam-5834	184	41	m	m	PROPN
ejpam-5834	184	42	∣∣∣∣η′′(k2	∣∣∣∣η′′(k2	PROPN
ejpam-5834	184	43	m	m	NOUN
ejpam-5834	184	44	)	)	PUNCT
ejpam-5834	184	45	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5834	184	46	∫	∫	PROPN
ejpam-5834	185	1	1	1	NUM
ejpam-5834	185	2	0	0	NUM
ejpam-5834	185	3	(	(	PUNCT
ejpam-5834	185	4	1−	1−	NUM
ejpam-5834	185	5	(	(	PUNCT
ejpam-5834	185	6	1−ϖ	1−ϖ	NUM
ejpam-5834	185	7	2	2	NUM
ejpam-5834	185	8	)	)	PUNCT
ejpam-5834	185	9	ρ)s	ρ)s	NOUN
ejpam-5834	185	10	dϖ	dϖ	X
ejpam-5834	185	11	)	)	PUNCT
ejpam-5834	185	12	1	1	NUM
ejpam-5834	185	13	q	q	NOUN
ejpam-5834	185	14	+	+	CCONJ
ejpam-5834	185	15	(	(	PUNCT
ejpam-5834	185	16	∣∣η′′(k1)∣∣q	∣∣η′′(k1)∣∣q	NOUN
ejpam-5834	185	17	∫	∫	PROPN
ejpam-5834	185	18	1	1	NUM
ejpam-5834	185	19	0	0	NUM
ejpam-5834	185	20	(	(	PUNCT
ejpam-5834	185	21	1−ϖ	1−ϖ	NUM
ejpam-5834	185	22	2	2	NUM
ejpam-5834	185	23	)	)	PUNCT
ejpam-5834	185	24	ρs	ρs	ADP
ejpam-5834	185	25	dϖ	dϖ	ADP
ejpam-5834	185	26	+	+	NOUN
ejpam-5834	185	27	m	m	PROPN
ejpam-5834	185	28	∣∣∣∣η′′(k2	∣∣∣∣η′′(k2	PROPN
ejpam-5834	185	29	m	m	NOUN
ejpam-5834	185	30	)	)	PUNCT
ejpam-5834	185	31	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5834	186	1	∫	∫	PROPN
ejpam-5834	186	2	1	1	NUM
ejpam-5834	186	3	0	0	NUM
ejpam-5834	186	4	(	(	PUNCT
ejpam-5834	186	5	1−	1−	NUM
ejpam-5834	186	6	(	(	PUNCT
ejpam-5834	186	7	1	1	NUM
ejpam-5834	186	8	+	+	NOUN
ejpam-5834	186	9	ϖ	ϖ	NOUN
ejpam-5834	186	10	2	2	NUM
ejpam-5834	186	11	)	)	PUNCT
ejpam-5834	186	12	ρ)s	ρ)s	NOUN
ejpam-5834	186	13	dϖ	dϖ	X
ejpam-5834	186	14	)	)	PUNCT
ejpam-5834	186	15	1	1	NUM
ejpam-5834	186	16	q	q	NOUN
ejpam-5834	186	17	}	}	PUNCT
ejpam-5834	186	18	≤	≤	PROPN
ejpam-5834	186	19	(	(	PUNCT
ejpam-5834	186	20	k2	k2	ADJ
ejpam-5834	186	21	−	−	PROPN
ejpam-5834	186	22	k1	k1	PROPN
ejpam-5834	186	23	)	)	PUNCT
ejpam-5834	186	24	2	2	NUM
ejpam-5834	186	25	8(ρ+	8(ρ+	NUM
ejpam-5834	186	26	1	1	NUM
ejpam-5834	186	27	)	)	PUNCT
ejpam-5834	186	28	(	(	PUNCT
ejpam-5834	186	29	1	1	NUM
ejpam-5834	186	30	p(ρ+	p(ρ+	NOUN
ejpam-5834	186	31	1	1	NUM
ejpam-5834	186	32	)	)	PUNCT
ejpam-5834	186	33	+	+	CCONJ
ejpam-5834	186	34	1	1	X
ejpam-5834	186	35	)	)	PUNCT
ejpam-5834	186	36	1	1	NUM
ejpam-5834	187	1	p	p	NOUN
ejpam-5834	187	2	[	[	X
ejpam-5834	187	3	{	{	PUNCT
ejpam-5834	187	4	∣∣η′′(k1)∣∣q	∣∣η′′(k1)∣∣q	X
ejpam-5834	187	5	(	(	PUNCT
ejpam-5834	187	6	2−	2−	NUM
ejpam-5834	187	7	2−ρs	2−ρs	NUM
ejpam-5834	187	8	ρs+	ρs+	NOUN
ejpam-5834	187	9	1	1	NUM
ejpam-5834	187	10	)	)	PUNCT
ejpam-5834	188	1	+	+	VERB
ejpam-5834	188	2	m	m	VERB
ejpam-5834	188	3	∣∣∣∣η′′(k2	∣∣∣∣η′′(k2	PROPN
ejpam-5834	188	4	m	m	NOUN
ejpam-5834	188	5	)	)	PUNCT
ejpam-5834	188	6	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5834	188	7	(	(	PUNCT
ejpam-5834	188	8	2−	2−	NUM
ejpam-5834	188	9	2−ρs	2−ρs	NUM
ejpam-5834	188	10	ρs+	ρs+	NOUN
ejpam-5834	188	11	1	1	NUM
ejpam-5834	188	12	)	)	PUNCT
ejpam-5834	188	13	}	}	PUNCT
ejpam-5834	188	14	1	1	NUM
ejpam-5834	188	15	q	q	NOUN
ejpam-5834	188	16	+	+	NUM
ejpam-5834	188	17	{	{	PUNCT
ejpam-5834	188	18	∣∣η′′(k1)∣∣q	∣∣η′′(k1)∣∣q	X
ejpam-5834	188	19	(	(	PUNCT
ejpam-5834	188	20	2−ρs	2−ρs	NUM
ejpam-5834	188	21	ρs+	ρs+	NOUN
ejpam-5834	188	22	1	1	NUM
ejpam-5834	188	23	)	)	PUNCT
ejpam-5834	189	1	+	+	VERB
ejpam-5834	189	2	m	m	VERB
ejpam-5834	189	3	∣∣∣∣η′′(k2	∣∣∣∣η′′(k2	PROPN
ejpam-5834	189	4	m	m	NOUN
ejpam-5834	189	5	)	)	PUNCT
ejpam-5834	189	6	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5834	190	1	(	(	PUNCT
ejpam-5834	190	2	2−ρs	2−ρs	NUM
ejpam-5834	190	3	ρs+	ρs+	NOUN
ejpam-5834	190	4	1	1	NUM
ejpam-5834	190	5	)	)	PUNCT
ejpam-5834	190	6	}	}	PUNCT
ejpam-5834	190	7	1	1	NUM
ejpam-5834	190	8	q	q	NOUN
ejpam-5834	190	9	]	]	PUNCT
ejpam-5834	190	10	.	.	PUNCT
ejpam-5834	191	1	o.	o.	PROPN
ejpam-5834	191	2	b.	b.	PROPN
ejpam-5834	191	3	almutairi	almutairi	PROPN
ejpam-5834	191	4	/	/	SYM
ejpam-5834	191	5	eur	eur	PROPN
ejpam-5834	191	6	.	.	PUNCT
ejpam-5834	192	1	j.	j.	PROPN
ejpam-5834	192	2	pure	pure	PROPN
ejpam-5834	192	3	appl	appl	PROPN
ejpam-5834	192	4	.	.	PROPN
ejpam-5834	192	5	math	math	PROPN
ejpam-5834	192	6	,	,	PUNCT
ejpam-5834	192	7	18	18	NUM
ejpam-5834	192	8	(	(	PUNCT
ejpam-5834	192	9	1	1	NUM
ejpam-5834	192	10	)	)	PUNCT
ejpam-5834	192	11	(	(	PUNCT
ejpam-5834	192	12	2025	2025	NUM
ejpam-5834	192	13	)	)	PUNCT
ejpam-5834	192	14	,	,	PUNCT
ejpam-5834	192	15	5834	5834	NUM
ejpam-5834	192	16	10	10	NUM
ejpam-5834	192	17	of	of	ADP
ejpam-5834	192	18	12	12	NUM
ejpam-5834	192	19	∣∣∣∣∣2ρ−1γ(ρ+	∣∣∣∣∣2ρ−1γ(ρ+	NOUN
ejpam-5834	192	20	1	1	NUM
ejpam-5834	192	21	)	)	PUNCT
ejpam-5834	192	22	(	(	PUNCT
ejpam-5834	192	23	k2	k2	PROPN
ejpam-5834	192	24	−	−	PROPN
ejpam-5834	192	25	k1)ρ	k1)ρ	NOUN
ejpam-5834	192	26	[	[	PUNCT
ejpam-5834	192	27	jρ	jρ	PROPN
ejpam-5834	192	28	(	(	PUNCT
ejpam-5834	192	29	k1+k2	k1+k2	PROPN
ejpam-5834	192	30	2	2	NUM
ejpam-5834	192	31	)	)	PUNCT
ejpam-5834	192	32	−η(k1	−η(k1	PROPN
ejpam-5834	192	33	)	)	PUNCT
ejpam-5834	193	1	+	+	CCONJ
ejpam-5834	194	1	jρ	jρ	PROPN
ejpam-5834	194	2	(	(	PUNCT
ejpam-5834	194	3	k1+k2	k1+k2	PROPN
ejpam-5834	194	4	2	2	NUM
ejpam-5834	194	5	)	)	PUNCT
ejpam-5834	194	6	+	+	NOUN
ejpam-5834	194	7	η(k2	η(k2	NOUN
ejpam-5834	194	8	)	)	PUNCT
ejpam-5834	194	9	]	]	PUNCT
ejpam-5834	195	1	−	−	PROPN
ejpam-5834	195	2	η	η	X
ejpam-5834	195	3	(	(	PUNCT
ejpam-5834	195	4	k1	k1	X
ejpam-5834	195	5	+	+	CCONJ
ejpam-5834	195	6	k2	k2	ADJ
ejpam-5834	195	7	2	2	NUM
ejpam-5834	195	8	)	)	PUNCT
ejpam-5834	195	9	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5834	195	10	=	=	PUNCT
ejpam-5834	195	11	∣∣∣∣(k2	∣∣∣∣(k2	VERB
ejpam-5834	195	12	−	−	PROPN
ejpam-5834	195	13	k1	k1	NOUN
ejpam-5834	195	14	)	)	PUNCT
ejpam-5834	195	15	2	2	NUM
ejpam-5834	195	16	8(ρ+	8(ρ+	NUM
ejpam-5834	195	17	1	1	NUM
ejpam-5834	195	18	)	)	PUNCT
ejpam-5834	195	19	∫	∫	PROPN
ejpam-5834	195	20	1	1	NUM
ejpam-5834	195	21	0	0	NUM
ejpam-5834	195	22	(	(	PUNCT
ejpam-5834	195	23	1−ϖ)ρ+1	1−ϖ)ρ+1	NUM
ejpam-5834	195	24	[	[	PUNCT
ejpam-5834	195	25	η′′	η′′	PROPN
ejpam-5834	195	26	(	(	PUNCT
ejpam-5834	195	27	1	1	NUM
ejpam-5834	195	28	+	+	NOUN
ejpam-5834	195	29	ϖ	ϖ	PROPN
ejpam-5834	195	30	2	2	NUM
ejpam-5834	195	31	k1	k1	NOUN
ejpam-5834	195	32	+	+	CCONJ
ejpam-5834	195	33	1−ϖ	1−ϖ	NUM
ejpam-5834	195	34	2	2	NUM
ejpam-5834	195	35	k2	k2	NOUN
ejpam-5834	195	36	)	)	PUNCT
ejpam-5834	196	1	+	+	CCONJ
ejpam-5834	196	2	η′	η′	NOUN
ejpam-5834	196	3	(	(	PUNCT
ejpam-5834	196	4	1−ϖ	1−ϖ	NUM
ejpam-5834	196	5	2	2	NUM
ejpam-5834	196	6	k1	k1	NOUN
ejpam-5834	196	7	+	+	CCONJ
ejpam-5834	196	8	1	1	NUM
ejpam-5834	196	9	+	+	ADJ
ejpam-5834	196	10	ϖ	ϖ	PROPN
ejpam-5834	196	11	2	2	NUM
ejpam-5834	196	12	k2	k2	NOUN
ejpam-5834	196	13	)	)	PUNCT
ejpam-5834	196	14	]	]	PUNCT
ejpam-5834	197	1	dϖ	dϖ	ADP
ejpam-5834	197	2	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5834	197	3	≤	≤	NOUN
ejpam-5834	197	4	(	(	PUNCT
ejpam-5834	197	5	k2	k2	NOUN
ejpam-5834	197	6	−	−	PROPN
ejpam-5834	197	7	k1	k1	PROPN
ejpam-5834	197	8	)	)	PUNCT
ejpam-5834	197	9	2	2	NUM
ejpam-5834	197	10	8(ρ+	8(ρ+	NUM
ejpam-5834	197	11	1	1	NUM
ejpam-5834	197	12	)	)	PUNCT
ejpam-5834	198	1	[	[	X
ejpam-5834	198	2	∫	∫	X
ejpam-5834	198	3	1	1	NUM
ejpam-5834	198	4	0	0	NUM
ejpam-5834	198	5	(	(	PUNCT
ejpam-5834	198	6	1−ϖ)ρ+1	1−ϖ)ρ+1	NUM
ejpam-5834	198	7	∣∣∣∣η′′(1	∣∣∣∣η′′(1	VERB
ejpam-5834	198	8	+	+	NOUN
ejpam-5834	198	9	ϖ	ϖ	PROPN
ejpam-5834	198	10	2	2	NUM
ejpam-5834	198	11	k1	k1	NOUN
ejpam-5834	198	12	+	+	CCONJ
ejpam-5834	198	13	1−ϖ	1−ϖ	NUM
ejpam-5834	198	14	2	2	NUM
ejpam-5834	198	15	k2	k2	NOUN
ejpam-5834	198	16	)	)	PUNCT
ejpam-5834	198	17	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5834	198	18	dϖ	dϖ	NOUN
ejpam-5834	198	19	+	+	CCONJ
ejpam-5834	198	20	∫	∫	PROPN
ejpam-5834	198	21	1	1	NUM
ejpam-5834	198	22	0	0	NUM
ejpam-5834	198	23	(	(	PUNCT
ejpam-5834	198	24	1−ϖ)ρ+1	1−ϖ)ρ+1	NUM
ejpam-5834	198	25	∣∣∣∣η′′(1−ϖ	∣∣∣∣η′′(1−ϖ	ADJ
ejpam-5834	198	26	2	2	NUM
ejpam-5834	198	27	k1	k1	NOUN
ejpam-5834	198	28	+	+	CCONJ
ejpam-5834	198	29	1	1	NUM
ejpam-5834	198	30	+	+	ADJ
ejpam-5834	198	31	ϖ	ϖ	PROPN
ejpam-5834	198	32	2	2	NUM
ejpam-5834	198	33	k2	k2	NOUN
ejpam-5834	198	34	)	)	PUNCT
ejpam-5834	198	35	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5834	198	36	dϖ	dϖ	PROPN
ejpam-5834	198	37	]	]	X
ejpam-5834	198	38	≤	≤	PROPN
ejpam-5834	198	39	(	(	PUNCT
ejpam-5834	198	40	k2	k2	NOUN
ejpam-5834	198	41	−	−	PROPN
ejpam-5834	198	42	k1	k1	PROPN
ejpam-5834	198	43	)	)	PUNCT
ejpam-5834	198	44	2	2	NUM
ejpam-5834	198	45	8(ρ+	8(ρ+	NUM
ejpam-5834	198	46	1	1	NUM
ejpam-5834	198	47	)	)	PUNCT
ejpam-5834	198	48	(	(	PUNCT
ejpam-5834	198	49	1	1	NUM
ejpam-5834	198	50	p(ρ+	p(ρ+	NOUN
ejpam-5834	198	51	1	1	NUM
ejpam-5834	198	52	)	)	PUNCT
ejpam-5834	198	53	+	+	CCONJ
ejpam-5834	198	54	1	1	X
ejpam-5834	198	55	)	)	PUNCT
ejpam-5834	198	56	1	1	NUM
ejpam-5834	198	57	p	p	NOUN
ejpam-5834	198	58	{	{	PUNCT
ejpam-5834	198	59	[	[	X
ejpam-5834	198	60	(	(	PUNCT
ejpam-5834	198	61	∫	∫	PROPN
ejpam-5834	198	62	1	1	NUM
ejpam-5834	198	63	0	0	NUM
ejpam-5834	198	64	(	(	PUNCT
ejpam-5834	198	65	1−ϖ)p(ρ+1)dϖ	1−ϖ)p(ρ+1)dϖ	PROPN
ejpam-5834	198	66	)	)	PUNCT
ejpam-5834	198	67	1	1	NUM
ejpam-5834	198	68	p	p	NOUN
ejpam-5834	198	69	(	(	PUNCT
ejpam-5834	198	70	∫	∫	PROPN
ejpam-5834	198	71	1	1	NUM
ejpam-5834	198	72	0	0	NUM
ejpam-5834	198	73	∣∣∣∣η′′(1	∣∣∣∣η′′(1	VERB
ejpam-5834	199	1	+	+	NOUN
ejpam-5834	199	2	ϖ	ϖ	PROPN
ejpam-5834	199	3	2	2	NUM
ejpam-5834	199	4	k1	k1	NOUN
ejpam-5834	199	5	+	+	CCONJ
ejpam-5834	199	6	1−ϖ	1−ϖ	NUM
ejpam-5834	199	7	2	2	NUM
ejpam-5834	199	8	k2	k2	NOUN
ejpam-5834	199	9	)	)	PUNCT
ejpam-5834	199	10	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5834	200	1	dϖ	dϖ	PROPN
ejpam-5834	200	2	)	)	PUNCT
ejpam-5834	200	3	1	1	NUM
ejpam-5834	200	4	q	q	NOUN
ejpam-5834	200	5	]	]	PUNCT
ejpam-5834	201	1	+	+	CCONJ
ejpam-5834	201	2	[	[	X
ejpam-5834	201	3	(	(	PUNCT
ejpam-5834	201	4	∫	∫	PROPN
ejpam-5834	201	5	1	1	NUM
ejpam-5834	201	6	0	0	NUM
ejpam-5834	201	7	(	(	PUNCT
ejpam-5834	201	8	1−ϖ)p(ρ+1)dϖ	1−ϖ)p(ρ+1)dϖ	PROPN
ejpam-5834	201	9	)	)	PUNCT
ejpam-5834	201	10	1	1	NUM
ejpam-5834	201	11	p	p	NOUN
ejpam-5834	201	12	(	(	PUNCT
ejpam-5834	201	13	∫	∫	PROPN
ejpam-5834	201	14	1	1	NUM
ejpam-5834	201	15	0	0	NUM
ejpam-5834	201	16	∣∣∣∣η′′(1−ϖ	∣∣∣∣η′′(1−ϖ	ADJ
ejpam-5834	201	17	2	2	NUM
ejpam-5834	201	18	k1	k1	NOUN
ejpam-5834	201	19	+	+	CCONJ
ejpam-5834	201	20	1	1	NUM
ejpam-5834	201	21	+	+	ADJ
ejpam-5834	201	22	ϖ	ϖ	PROPN
ejpam-5834	201	23	2	2	NUM
ejpam-5834	201	24	k2	k2	NOUN
ejpam-5834	201	25	)	)	PUNCT
ejpam-5834	201	26	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5834	202	1	dϖ	dϖ	PROPN
ejpam-5834	202	2	)	)	PUNCT
ejpam-5834	202	3	1	1	NUM
ejpam-5834	202	4	q	q	NOUN
ejpam-5834	202	5	]	]	X
ejpam-5834	202	6	}	}	PUNCT
ejpam-5834	202	7	≤	≤	NUM
ejpam-5834	202	8	(	(	PUNCT
ejpam-5834	202	9	k2	k2	ADJ
ejpam-5834	202	10	−	−	PROPN
ejpam-5834	202	11	k1	k1	PROPN
ejpam-5834	202	12	)	)	PUNCT
ejpam-5834	202	13	2	2	NUM
ejpam-5834	202	14	8(ρ+	8(ρ+	NUM
ejpam-5834	202	15	1	1	NUM
ejpam-5834	202	16	)	)	PUNCT
ejpam-5834	202	17	(	(	PUNCT
ejpam-5834	202	18	1	1	NUM
ejpam-5834	202	19	p(ρ+	p(ρ+	NOUN
ejpam-5834	202	20	1	1	NUM
ejpam-5834	202	21	)	)	PUNCT
ejpam-5834	202	22	+	+	CCONJ
ejpam-5834	202	23	1	1	X
ejpam-5834	202	24	)	)	PUNCT
ejpam-5834	202	25	1	1	NUM
ejpam-5834	203	1	p	p	NOUN
ejpam-5834	203	2	[	[	X
ejpam-5834	203	3	{	{	PUNCT
ejpam-5834	203	4	∣∣η′′(k1)∣∣q	∣∣η′′(k1)∣∣q	X
ejpam-5834	203	5	(	(	PUNCT
ejpam-5834	203	6	2−	2−	NUM
ejpam-5834	203	7	2−ρs	2−ρs	NUM
ejpam-5834	203	8	ρs+	ρs+	NOUN
ejpam-5834	203	9	1	1	NUM
ejpam-5834	203	10	)	)	PUNCT
ejpam-5834	204	1	+	+	VERB
ejpam-5834	204	2	m	m	VERB
ejpam-5834	204	3	∣∣∣∣η′′(k2	∣∣∣∣η′′(k2	PROPN
ejpam-5834	204	4	m	m	NOUN
ejpam-5834	204	5	)	)	PUNCT
ejpam-5834	204	6	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5834	204	7	(	(	PUNCT
ejpam-5834	204	8	2−	2−	NUM
ejpam-5834	204	9	2−ρs	2−ρs	NUM
ejpam-5834	204	10	ρs+	ρs+	NOUN
ejpam-5834	204	11	1	1	NUM
ejpam-5834	204	12	)	)	PUNCT
ejpam-5834	204	13	}	}	PUNCT
ejpam-5834	204	14	1	1	NUM
ejpam-5834	204	15	q	q	NOUN
ejpam-5834	204	16	+	+	NUM
ejpam-5834	204	17	{	{	PUNCT
ejpam-5834	204	18	∣∣η′′(k1)∣∣q	∣∣η′′(k1)∣∣q	X
ejpam-5834	204	19	(	(	PUNCT
ejpam-5834	204	20	2−ρs	2−ρs	NUM
ejpam-5834	204	21	ρs+	ρs+	NOUN
ejpam-5834	204	22	1	1	NUM
ejpam-5834	204	23	)	)	PUNCT
ejpam-5834	205	1	+	+	VERB
ejpam-5834	205	2	m	m	VERB
ejpam-5834	205	3	∣∣∣∣η′′(k2	∣∣∣∣η′′(k2	PROPN
ejpam-5834	205	4	m	m	NOUN
ejpam-5834	205	5	)	)	PUNCT
ejpam-5834	205	6	∣∣∣∣q	∣∣∣∣q	PROPN
ejpam-5834	206	1	(	(	PUNCT
ejpam-5834	206	2	2−ρs	2−ρs	NUM
ejpam-5834	206	3	ρs+	ρs+	NOUN
ejpam-5834	206	4	1	1	NUM
ejpam-5834	206	5	)	)	PUNCT
ejpam-5834	206	6	}	}	PUNCT
ejpam-5834	206	7	1	1	NUM
ejpam-5834	206	8	q	q	NOUN
ejpam-5834	206	9	]	]	PUNCT
ejpam-5834	206	10	.	.	PUNCT
ejpam-5834	207	1	4	4	X
ejpam-5834	207	2	.	.	X
ejpam-5834	207	3	conclusion	conclusion	NOUN
ejpam-5834	207	4	fractional	fractional	PROPN
ejpam-5834	207	5	calculus	calculus	NOUN
ejpam-5834	207	6	plays	play	VERB
ejpam-5834	207	7	a	a	DET
ejpam-5834	207	8	vital	vital	ADJ
ejpam-5834	207	9	role	role	NOUN
ejpam-5834	207	10	in	in	ADP
ejpam-5834	207	11	understanding	understand	VERB
ejpam-5834	207	12	problems	problem	NOUN
ejpam-5834	207	13	in	in	ADP
ejpam-5834	207	14	pure	pure	ADJ
ejpam-5834	207	15	and	and	CCONJ
ejpam-5834	207	16	applied	apply	VERB
ejpam-5834	207	17	sciences	science	NOUN
ejpam-5834	207	18	due	due	ADP
ejpam-5834	207	19	to	to	ADP
ejpam-5834	207	20	its	its	PRON
ejpam-5834	207	21	possession	possession	NOUN
ejpam-5834	207	22	of	of	ADP
ejpam-5834	207	23	many	many	ADJ
ejpam-5834	207	24	interesting	interesting	ADJ
ejpam-5834	207	25	integral	integral	ADJ
ejpam-5834	207	26	and	and	CCONJ
ejpam-5834	207	27	differential	differential	ADJ
ejpam-5834	207	28	operators	operator	NOUN
ejpam-5834	207	29	.	.	PUNCT
ejpam-5834	208	1	in	in	ADP
ejpam-5834	208	2	this	this	DET
ejpam-5834	208	3	study	study	NOUN
ejpam-5834	208	4	,	,	PUNCT
ejpam-5834	208	5	therefore	therefore	ADV
ejpam-5834	208	6	,	,	PUNCT
ejpam-5834	208	7	we	we	PRON
ejpam-5834	208	8	employed	employ	VERB
ejpam-5834	208	9	a	a	DET
ejpam-5834	208	10	riemann	riemann	PROPN
ejpam-5834	208	11	-	-	PUNCT
ejpam-5834	208	12	liouville	liouville	NOUN
ejpam-5834	208	13	operator	operator	NOUN
ejpam-5834	208	14	to	to	PART
ejpam-5834	208	15	establish	establish	VERB
ejpam-5834	208	16	some	some	DET
ejpam-5834	208	17	new	new	ADJ
ejpam-5834	208	18	fractional	fractional	ADJ
ejpam-5834	208	19	integral	integral	ADJ
ejpam-5834	208	20	inequalities	inequality	NOUN
ejpam-5834	208	21	for	for	ADP
ejpam-5834	208	22	mappings	mapping	NOUN
ejpam-5834	208	23	whose	whose	DET
ejpam-5834	208	24	second	second	ADJ
ejpam-5834	208	25	derivatives	derivative	NOUN
ejpam-5834	208	26	,	,	PUNCT
ejpam-5834	208	27	raised	raise	VERB
ejpam-5834	208	28	to	to	ADP
ejpam-5834	208	29	positive	positive	ADJ
ejpam-5834	208	30	powers	power	NOUN
ejpam-5834	208	31	,	,	PUNCT
ejpam-5834	208	32	exhibit	exhibit	NOUN
ejpam-5834	208	33	(	(	PUNCT
ejpam-5834	208	34	ρ	ρ	NOUN
ejpam-5834	208	35	,	,	PUNCT
ejpam-5834	208	36	s)-convexity	s)-convexity	NOUN
ejpam-5834	208	37	and	and	CCONJ
ejpam-5834	208	38	(	(	PUNCT
ejpam-5834	208	39	ρ	ρ	PROPN
ejpam-5834	208	40	,	,	PUNCT
ejpam-5834	208	41	s	s	PROPN
ejpam-5834	208	42	,	,	PUNCT
ejpam-5834	208	43	m)-convexities	m)-convexitie	NOUN
ejpam-5834	208	44	.	.	PUNCT
ejpam-5834	209	1	our	our	PRON
ejpam-5834	209	2	study	study	NOUN
ejpam-5834	209	3	established	establish	VERB
ejpam-5834	209	4	new	new	ADJ
ejpam-5834	209	5	inequalities	inequality	NOUN
ejpam-5834	209	6	of	of	ADP
ejpam-5834	209	7	midpoint	midpoint	NOUN
ejpam-5834	209	8	type	type	NOUN
ejpam-5834	209	9	involving	involve	VERB
ejpam-5834	209	10	fractional	fractional	ADJ
ejpam-5834	209	11	operators	operator	NOUN
ejpam-5834	209	12	through	through	ADP
ejpam-5834	209	13	generalized	generalized	ADJ
ejpam-5834	209	14	classes	class	NOUN
ejpam-5834	209	15	of	of	ADP
ejpam-5834	209	16	convexities	convexity	NOUN
ejpam-5834	209	17	.	.	PUNCT
ejpam-5834	210	1	several	several	ADJ
ejpam-5834	210	2	estimates	estimate	NOUN
ejpam-5834	210	3	of	of	ADP
ejpam-5834	210	4	special	special	ADJ
ejpam-5834	210	5	functions	function	NOUN
ejpam-5834	210	6	including	include	VERB
ejpam-5834	210	7	incomplete	incomplete	ADJ
ejpam-5834	210	8	beta	beta	NOUN
ejpam-5834	210	9	,	,	PUNCT
ejpam-5834	210	10	euler	euler	NOUN
ejpam-5834	210	11	gamma	gamma	PROPN
ejpam-5834	210	12	and	and	CCONJ
ejpam-5834	210	13	hyperglycemic	hyperglycemic	ADJ
ejpam-5834	210	14	functions	function	NOUN
ejpam-5834	210	15	are	be	AUX
ejpam-5834	210	16	reported	report	VERB
ejpam-5834	210	17	in	in	ADP
ejpam-5834	210	18	this	this	DET
ejpam-5834	210	19	study	study	NOUN
ejpam-5834	210	20	.	.	PUNCT
ejpam-5834	211	1	our	our	PRON
ejpam-5834	211	2	findings	finding	NOUN
ejpam-5834	211	3	can	can	AUX
ejpam-5834	211	4	enhance	enhance	VERB
ejpam-5834	211	5	the	the	DET
ejpam-5834	211	6	techniques	technique	NOUN
ejpam-5834	211	7	by	by	ADP
ejpam-5834	211	8	which	which	PRON
ejpam-5834	211	9	the	the	DET
ejpam-5834	211	10	properties	property	NOUN
ejpam-5834	211	11	of	of	ADP
ejpam-5834	211	12	convexity	convexity	NOUN
ejpam-5834	211	13	along	along	ADP
ejpam-5834	211	14	with	with	ADP
ejpam-5834	211	15	their	their	PRON
ejpam-5834	211	16	generalizations	generalization	NOUN
ejpam-5834	211	17	can	can	AUX
ejpam-5834	211	18	be	be	AUX
ejpam-5834	211	19	thoroughly	thoroughly	ADV
ejpam-5834	211	20	studied	study	VERB
ejpam-5834	211	21	through	through	ADP
ejpam-5834	211	22	fractional	fractional	ADJ
ejpam-5834	211	23	calculus	calculus	NOUN
ejpam-5834	211	24	.	.	PUNCT
ejpam-5834	212	1	the	the	DET
ejpam-5834	212	2	findings	finding	NOUN
ejpam-5834	212	3	of	of	ADP
ejpam-5834	212	4	this	this	DET
ejpam-5834	212	5	study	study	NOUN
ejpam-5834	212	6	can	can	AUX
ejpam-5834	212	7	be	be	AUX
ejpam-5834	212	8	relevant	relevant	ADJ
ejpam-5834	212	9	in	in	ADP
ejpam-5834	212	10	different	different	ADJ
ejpam-5834	212	11	areas	area	NOUN
ejpam-5834	212	12	of	of	ADP
ejpam-5834	212	13	interest	interest	NOUN
ejpam-5834	212	14	where	where	SCONJ
ejpam-5834	212	15	the	the	DET
ejpam-5834	212	16	fractional	fractional	ADJ
ejpam-5834	212	17	calculus	calculus	NOUN
ejpam-5834	212	18	is	be	AUX
ejpam-5834	212	19	extensibility	extensibility	NOUN
ejpam-5834	212	20	used	use	VERB
ejpam-5834	212	21	.	.	PUNCT
ejpam-5834	213	1	our	our	PRON
ejpam-5834	213	2	inequalities	inequality	NOUN
ejpam-5834	213	3	can	can	AUX
ejpam-5834	213	4	be	be	AUX
ejpam-5834	213	5	specifically	specifically	ADV
ejpam-5834	213	6	used	use	VERB
ejpam-5834	213	7	to	to	PART
ejpam-5834	213	8	estimate	estimate	VERB
ejpam-5834	213	9	the	the	DET
ejpam-5834	213	10	error	error	NOUN
ejpam-5834	213	11	bounds	bound	NOUN
ejpam-5834	213	12	for	for	ADP
ejpam-5834	213	13	numerical	numerical	ADJ
ejpam-5834	213	14	integration	integration	NOUN
ejpam-5834	213	15	by	by	ADP
ejpam-5834	213	16	improving	improve	VERB
ejpam-5834	213	17	the	the	DET
ejpam-5834	213	18	accuracy	accuracy	NOUN
ejpam-5834	213	19	of	of	ADP
ejpam-5834	213	20	quadrature	quadrature	NOUN
ejpam-5834	213	21	methods	method	NOUN
ejpam-5834	213	22	.	.	PUNCT
ejpam-5834	214	1	future	future	ADJ
ejpam-5834	214	2	studies	study	NOUN
ejpam-5834	214	3	should	should	AUX
ejpam-5834	214	4	include	include	VERB
ejpam-5834	214	5	the	the	DET
ejpam-5834	214	6	use	use	NOUN
ejpam-5834	214	7	of	of	ADP
ejpam-5834	214	8	different	different	ADJ
ejpam-5834	214	9	fractional	fractional	ADJ
ejpam-5834	214	10	integral	integral	ADJ
ejpam-5834	214	11	operators	operator	NOUN
ejpam-5834	214	12	,	,	PUNCT
ejpam-5834	214	13	such	such	ADJ
ejpam-5834	214	14	as	as	ADP
ejpam-5834	214	15	the	the	DET
ejpam-5834	214	16	generalized	generalized	ADJ
ejpam-5834	214	17	fractional	fractional	ADJ
ejpam-5834	214	18	integral	integral	ADJ
ejpam-5834	214	19	operator	operator	NOUN
ejpam-5834	214	20	unifying	unify	VERB
ejpam-5834	214	21	two	two	NUM
ejpam-5834	214	22	existing	exist	VERB
ejpam-5834	214	23	fractional	fractional	ADJ
ejpam-5834	214	24	integral	integral	ADJ
ejpam-5834	214	25	operators	operator	NOUN
ejpam-5834	214	26	[	[	X
ejpam-5834	214	27	16	16	NUM
ejpam-5834	214	28	]	]	X
ejpam-5834	214	29	,	,	PUNCT
ejpam-5834	214	30	together	together	ADV
ejpam-5834	214	31	with	with	ADP
ejpam-5834	214	32	other	other	ADJ
ejpam-5834	214	33	classes	class	NOUN
ejpam-5834	214	34	of	of	ADP
ejpam-5834	214	35	convexities	convexity	NOUN
ejpam-5834	214	36	to	to	PART
ejpam-5834	214	37	establish	establish	VERB
ejpam-5834	214	38	different	different	ADJ
ejpam-5834	214	39	inequalities	inequality	NOUN
ejpam-5834	214	40	.	.	PUNCT
ejpam-5834	215	1	o.	o.	PROPN
ejpam-5834	215	2	b.	b.	PROPN
ejpam-5834	215	3	almutairi	almutairi	PROPN
ejpam-5834	215	4	/	/	SYM
ejpam-5834	215	5	eur	eur	PROPN
ejpam-5834	215	6	.	.	PUNCT
ejpam-5834	216	1	j.	j.	PROPN
ejpam-5834	216	2	pure	pure	PROPN
ejpam-5834	216	3	appl	appl	PROPN
ejpam-5834	216	4	.	.	PROPN
ejpam-5834	216	5	math	math	PROPN
ejpam-5834	216	6	,	,	PUNCT
ejpam-5834	216	7	18	18	NUM
ejpam-5834	216	8	(	(	PUNCT
ejpam-5834	216	9	1	1	NUM
ejpam-5834	216	10	)	)	PUNCT
ejpam-5834	216	11	(	(	PUNCT
ejpam-5834	216	12	2025	2025	NUM
ejpam-5834	216	13	)	)	PUNCT
ejpam-5834	216	14	,	,	PUNCT
ejpam-5834	216	15	5834	5834	NUM
ejpam-5834	216	16	11	11	NUM
ejpam-5834	216	17	of	of	ADP
ejpam-5834	216	18	12	12	NUM
ejpam-5834	216	19	references	reference	NOUN
ejpam-5834	216	20	[	[	X
ejpam-5834	216	21	1	1	NUM
ejpam-5834	216	22	]	]	X
ejpam-5834	216	23	praveen	praveen	PROPN
ejpam-5834	216	24	agarwal	agarwal	PROPN
ejpam-5834	216	25	,	,	PUNCT
ejpam-5834	216	26	mohamed	mohamed	PROPN
ejpam-5834	216	27	jleli	jleli	PROPN
ejpam-5834	216	28	,	,	PUNCT
ejpam-5834	216	29	and	and	CCONJ
ejpam-5834	216	30	muharrem	muharrem	ADJ
ejpam-5834	216	31	tomar	tomar	NOUN
ejpam-5834	216	32	.	.	PUNCT
ejpam-5834	217	1	certain	certain	ADJ
ejpam-5834	217	2	hermitehadamard	hermitehadamard	NOUN
ejpam-5834	217	3	type	type	NOUN
ejpam-5834	217	4	inequalities	inequality	NOUN
ejpam-5834	217	5	via	via	ADP
ejpam-5834	217	6	generalized	generalized	ADJ
ejpam-5834	217	7	k	k	ADJ
ejpam-5834	217	8	-	-	PUNCT
ejpam-5834	217	9	fractional	fractional	ADJ
ejpam-5834	217	10	integrals	integral	NOUN
ejpam-5834	217	11	.	.	PUNCT
ejpam-5834	218	1	journal	journal	NOUN
ejpam-5834	218	2	of	of	ADP
ejpam-5834	218	3	inequalities	inequality	NOUN
ejpam-5834	218	4	and	and	CCONJ
ejpam-5834	218	5	applications	application	NOUN
ejpam-5834	218	6	,	,	PUNCT
ejpam-5834	218	7	2017:1–10	2017:1–10	NUM
ejpam-5834	218	8	,	,	PUNCT
ejpam-5834	218	9	2017	2017	NUM
ejpam-5834	218	10	.	.	PUNCT
ejpam-5834	219	1	[	[	X
ejpam-5834	219	2	2	2	X
ejpam-5834	219	3	]	]	PUNCT
ejpam-5834	219	4	ravi	ravi	NOUN
ejpam-5834	219	5	p	p	PROPN
ejpam-5834	219	6	agarwal	agarwal	PROPN
ejpam-5834	219	7	.	.	PUNCT
ejpam-5834	220	1	inequalities	inequality	NOUN
ejpam-5834	220	2	and	and	CCONJ
ejpam-5834	220	3	applications	application	NOUN
ejpam-5834	220	4	,	,	PUNCT
ejpam-5834	220	5	volume	volume	NOUN
ejpam-5834	220	6	3	3	NUM
ejpam-5834	220	7	.	.	PUNCT
ejpam-5834	221	1	world	world	PROPN
ejpam-5834	221	2	scientific	scientific	ADJ
ejpam-5834	221	3	,	,	PUNCT
ejpam-5834	221	4	1994	1994	NUM
ejpam-5834	221	5	.	.	PUNCT
ejpam-5834	222	1	[	[	X
ejpam-5834	222	2	3	3	X
ejpam-5834	222	3	]	]	X
ejpam-5834	222	4	ohud	ohud	PROPN
ejpam-5834	222	5	bulayhan	bulayhan	PROPN
ejpam-5834	222	6	almutairi	almutairi	PROPN
ejpam-5834	222	7	.	.	PUNCT
ejpam-5834	223	1	new	new	ADJ
ejpam-5834	223	2	fractional	fractional	ADJ
ejpam-5834	223	3	integral	integral	ADJ
ejpam-5834	223	4	inequalities	inequality	NOUN
ejpam-5834	223	5	via	via	ADP
ejpam-5834	223	6	euler	euler	PROPN
ejpam-5834	223	7	’s	’s	PART
ejpam-5834	223	8	beta	beta	NOUN
ejpam-5834	223	9	function	function	NOUN
ejpam-5834	223	10	.	.	PUNCT
ejpam-5834	224	1	open	open	ADJ
ejpam-5834	224	2	mathematics	mathematic	NOUN
ejpam-5834	224	3	,	,	PUNCT
ejpam-5834	224	4	21(1):20230163	21(1):20230163	NUM
ejpam-5834	224	5	,	,	PUNCT
ejpam-5834	224	6	2023	2023	NUM
ejpam-5834	224	7	.	.	PUNCT
ejpam-5834	225	1	[	[	X
ejpam-5834	225	2	4	4	X
ejpam-5834	225	3	]	]	X
ejpam-5834	225	4	drumi	drumi	NOUN
ejpam-5834	225	5	d	d	PROPN
ejpam-5834	225	6	bainov	bainov	NOUN
ejpam-5834	225	7	and	and	CCONJ
ejpam-5834	225	8	pavel	pavel	PROPN
ejpam-5834	225	9	s	s	PART
ejpam-5834	225	10	simeonov	simeonov	NOUN
ejpam-5834	225	11	.	.	PUNCT
ejpam-5834	226	1	integral	integral	ADJ
ejpam-5834	226	2	inequalities	inequality	NOUN
ejpam-5834	226	3	and	and	CCONJ
ejpam-5834	226	4	applications	application	NOUN
ejpam-5834	226	5	,	,	PUNCT
ejpam-5834	226	6	volume	volume	NOUN
ejpam-5834	226	7	57	57	NUM
ejpam-5834	226	8	.	.	PUNCT
ejpam-5834	227	1	springer	springer	NOUN
ejpam-5834	227	2	science	science	PROPN
ejpam-5834	227	3	&	&	CCONJ
ejpam-5834	227	4	business	business	NOUN
ejpam-5834	227	5	media	medium	NOUN
ejpam-5834	227	6	,	,	PUNCT
ejpam-5834	227	7	2013	2013	NUM
ejpam-5834	227	8	.	.	PUNCT
ejpam-5834	228	1	[	[	X
ejpam-5834	228	2	5	5	X
ejpam-5834	228	3	]	]	X
ejpam-5834	228	4	hüseyin	hüseyin	PROPN
ejpam-5834	228	5	budak	budak	PROPN
ejpam-5834	228	6	,	,	PUNCT
ejpam-5834	228	7	tuba	tuba	PROPN
ejpam-5834	228	8	tunç	tunç	NOUN
ejpam-5834	228	9	,	,	PUNCT
ejpam-5834	228	10	and	and	CCONJ
ejpam-5834	228	11	mehmet	mehmet	PROPN
ejpam-5834	228	12	sarikaya	sarikaya	PROPN
ejpam-5834	228	13	.	.	PUNCT
ejpam-5834	229	1	fractional	fractional	ADJ
ejpam-5834	229	2	hermite	hermite	ADJ
ejpam-5834	229	3	-	-	PUNCT
ejpam-5834	229	4	hadamardtype	hadamardtype	NOUN
ejpam-5834	229	5	inequalities	inequality	NOUN
ejpam-5834	229	6	for	for	ADP
ejpam-5834	229	7	interval	interval	NOUN
ejpam-5834	229	8	-	-	PUNCT
ejpam-5834	229	9	valued	value	VERB
ejpam-5834	229	10	functions	function	NOUN
ejpam-5834	229	11	.	.	PUNCT
ejpam-5834	230	1	proceedings	proceeding	NOUN
ejpam-5834	230	2	of	of	ADP
ejpam-5834	230	3	the	the	DET
ejpam-5834	230	4	american	american	PROPN
ejpam-5834	230	5	mathematical	mathematical	PROPN
ejpam-5834	230	6	society	society	NOUN
ejpam-5834	230	7	,	,	PUNCT
ejpam-5834	230	8	148(2):705–718	148(2):705–718	NUM
ejpam-5834	230	9	,	,	PUNCT
ejpam-5834	230	10	2020	2020	NUM
ejpam-5834	230	11	.	.	PUNCT
ejpam-5834	231	1	[	[	X
ejpam-5834	231	2	6	6	NUM
ejpam-5834	231	3	]	]	PUNCT
ejpam-5834	231	4	tingsong	tingsong	PROPN
ejpam-5834	231	5	du	du	PROPN
ejpam-5834	231	6	and	and	CCONJ
ejpam-5834	231	7	yu	yu	PROPN
ejpam-5834	231	8	peng	peng	PROPN
ejpam-5834	231	9	.	.	PUNCT
ejpam-5834	232	1	hermite	hermite	PROPN
ejpam-5834	232	2	–	–	PUNCT
ejpam-5834	232	3	hadamard	hadamard	ADJ
ejpam-5834	232	4	type	type	NOUN
ejpam-5834	232	5	inequalities	inequality	NOUN
ejpam-5834	232	6	for	for	ADP
ejpam-5834	232	7	multiplicative	multiplicative	ADJ
ejpam-5834	232	8	riemann	riemann	PROPN
ejpam-5834	232	9	–	–	PUNCT
ejpam-5834	232	10	liouville	liouville	VERB
ejpam-5834	232	11	fractional	fractional	ADJ
ejpam-5834	232	12	integrals	integral	NOUN
ejpam-5834	232	13	.	.	PUNCT
ejpam-5834	233	1	journal	journal	NOUN
ejpam-5834	233	2	of	of	ADP
ejpam-5834	233	3	computational	computational	ADJ
ejpam-5834	233	4	and	and	CCONJ
ejpam-5834	233	5	applied	applied	ADJ
ejpam-5834	233	6	mathematics	mathematic	NOUN
ejpam-5834	233	7	,	,	PUNCT
ejpam-5834	233	8	440:115582	440:115582	NUM
ejpam-5834	233	9	,	,	PUNCT
ejpam-5834	233	10	2024	2024	NUM
ejpam-5834	233	11	.	.	PUNCT
ejpam-5834	234	1	[	[	X
ejpam-5834	234	2	7	7	X
ejpam-5834	234	3	]	]	X
ejpam-5834	234	4	ghulam	ghulam	PROPN
ejpam-5834	234	5	farid	farid	PROPN
ejpam-5834	234	6	,	,	PUNCT
ejpam-5834	234	7	young	young	ADJ
ejpam-5834	234	8	chel	chel	PROPN
ejpam-5834	234	9	kwun	kwun	PROPN
ejpam-5834	234	10	,	,	PUNCT
ejpam-5834	234	11	hafsa	hafsa	PROPN
ejpam-5834	234	12	yasmeen	yasmeen	PROPN
ejpam-5834	234	13	,	,	PUNCT
ejpam-5834	234	14	abdullah	abdullah	PROPN
ejpam-5834	234	15	akkurt	akkurt	PROPN
ejpam-5834	234	16	,	,	PUNCT
ejpam-5834	234	17	and	and	CCONJ
ejpam-5834	234	18	shin	shin	PROPN
ejpam-5834	234	19	min	min	PROPN
ejpam-5834	234	20	kang	kang	PROPN
ejpam-5834	234	21	.	.	PROPN
ejpam-5834	234	22	inequalities	inequality	NOUN
ejpam-5834	234	23	for	for	ADP
ejpam-5834	234	24	generalized	generalized	ADJ
ejpam-5834	234	25	riemann	riemann	PROPN
ejpam-5834	234	26	–	–	PUNCT
ejpam-5834	234	27	liouville	liouville	VERB
ejpam-5834	234	28	fractional	fractional	ADJ
ejpam-5834	234	29	integrals	integral	NOUN
ejpam-5834	234	30	of	of	ADP
ejpam-5834	234	31	generalized	generalize	VERB
ejpam-5834	234	32	strongly	strongly	ADV
ejpam-5834	234	33	convex	convex	NOUN
ejpam-5834	234	34	functions	function	NOUN
ejpam-5834	234	35	.	.	PUNCT
ejpam-5834	235	1	advances	advance	NOUN
ejpam-5834	235	2	in	in	ADP
ejpam-5834	235	3	difference	difference	NOUN
ejpam-5834	235	4	equations	equation	NOUN
ejpam-5834	235	5	,	,	PUNCT
ejpam-5834	235	6	2021:1–25	2021:1–25	NUM
ejpam-5834	235	7	,	,	PUNCT
ejpam-5834	235	8	2021	2021	NUM
ejpam-5834	235	9	.	.	PUNCT
ejpam-5834	236	1	[	[	X
ejpam-5834	236	2	8	8	NUM
ejpam-5834	236	3	]	]	X
ejpam-5834	236	4	henryk	henryk	ADV
ejpam-5834	236	5	hudzik	hudzik	ADV
ejpam-5834	236	6	and	and	CCONJ
ejpam-5834	236	7	lech	lech	PROPN
ejpam-5834	236	8	maligranda	maligranda	PROPN
ejpam-5834	236	9	.	.	PUNCT
ejpam-5834	237	1	some	some	DET
ejpam-5834	237	2	remarks	remark	NOUN
ejpam-5834	237	3	on	on	ADP
ejpam-5834	237	4	s	s	NOUN
ejpam-5834	237	5	-	-	PUNCT
ejpam-5834	237	6	convex	convex	ADJ
ejpam-5834	237	7	functions	function	NOUN
ejpam-5834	237	8	.	.	PUNCT
ejpam-5834	238	1	aequationes	aequatione	NOUN
ejpam-5834	238	2	mathematicae	mathematicae	PROPN
ejpam-5834	238	3	,	,	PUNCT
ejpam-5834	238	4	48:100–111	48:100–111	PROPN
ejpam-5834	238	5	,	,	PUNCT
ejpam-5834	238	6	1994	1994	NUM
ejpam-5834	238	7	.	.	PUNCT
ejpam-5834	239	1	[	[	X
ejpam-5834	239	2	9	9	X
ejpam-5834	239	3	]	]	PUNCT
ejpam-5834	239	4	anatolĭı	anatolĭı	PROPN
ejpam-5834	239	5	aleksandrovich	aleksandrovich	PROPN
ejpam-5834	239	6	kilbas	kilbas	PROPN
ejpam-5834	239	7	,	,	PUNCT
ejpam-5834	239	8	hari	hari	PROPN
ejpam-5834	239	9	m	m	PROPN
ejpam-5834	239	10	srivastava	srivastava	PROPN
ejpam-5834	239	11	,	,	PUNCT
ejpam-5834	239	12	and	and	CCONJ
ejpam-5834	239	13	juan	juan	PROPN
ejpam-5834	239	14	j	j	PROPN
ejpam-5834	239	15	trujillo	trujillo	PROPN
ejpam-5834	239	16	.	.	PUNCT
ejpam-5834	239	17	theory	theory	NOUN
ejpam-5834	239	18	and	and	CCONJ
ejpam-5834	239	19	applications	application	NOUN
ejpam-5834	239	20	of	of	ADP
ejpam-5834	239	21	fractional	fractional	ADJ
ejpam-5834	239	22	differential	differential	ADJ
ejpam-5834	239	23	equations	equation	NOUN
ejpam-5834	239	24	,	,	PUNCT
ejpam-5834	239	25	volume	volume	NOUN
ejpam-5834	239	26	204	204	NUM
ejpam-5834	239	27	.	.	PUNCT
ejpam-5834	240	1	elsevier	elsevier	NOUN
ejpam-5834	240	2	,	,	PUNCT
ejpam-5834	240	3	2006	2006	NUM
ejpam-5834	240	4	.	.	PUNCT
ejpam-5834	241	1	[	[	X
ejpam-5834	241	2	10	10	NUM
ejpam-5834	241	3	]	]	X
ejpam-5834	241	4	mohamed	mohamed	PROPN
ejpam-5834	241	5	metwali	metwali	PROPN
ejpam-5834	241	6	and	and	CCONJ
ejpam-5834	241	7	vishnu	vishnu	PROPN
ejpam-5834	241	8	narayan	narayan	PROPN
ejpam-5834	241	9	mishra	mishra	PROPN
ejpam-5834	241	10	.	.	PROPN
ejpam-5834	242	1	on	on	ADP
ejpam-5834	242	2	the	the	DET
ejpam-5834	242	3	measure	measure	NOUN
ejpam-5834	242	4	of	of	ADP
ejpam-5834	242	5	noncompactness	noncompactness	ADJ
ejpam-5834	242	6	in	in	ADP
ejpam-5834	242	7	lp(r+	lp(r+	NOUN
ejpam-5834	242	8	)	)	PUNCT
ejpam-5834	242	9	and	and	CCONJ
ejpam-5834	242	10	applications	application	NOUN
ejpam-5834	242	11	to	to	ADP
ejpam-5834	242	12	a	a	DET
ejpam-5834	242	13	product	product	NOUN
ejpam-5834	242	14	of	of	ADP
ejpam-5834	242	15	n	n	CCONJ
ejpam-5834	242	16	-	-	PUNCT
ejpam-5834	242	17	integral	integral	ADJ
ejpam-5834	242	18	equations	equation	NOUN
ejpam-5834	242	19	.	.	PUNCT
ejpam-5834	243	1	turkish	turkish	ADJ
ejpam-5834	243	2	journal	journal	NOUN
ejpam-5834	243	3	of	of	ADP
ejpam-5834	243	4	mathematics	mathematic	NOUN
ejpam-5834	243	5	,	,	PUNCT
ejpam-5834	243	6	47(1):372–386	47(1):372–386	NUM
ejpam-5834	243	7	,	,	PUNCT
ejpam-5834	243	8	2023	2023	NUM
ejpam-5834	243	9	.	.	PUNCT
ejpam-5834	244	1	[	[	X
ejpam-5834	244	2	11	11	NUM
ejpam-5834	244	3	]	]	PUNCT
ejpam-5834	244	4	muhammad	muhammad	PROPN
ejpam-5834	244	5	aslam	aslam	PROPN
ejpam-5834	244	6	noor	noor	PROPN
ejpam-5834	244	7	and	and	CCONJ
ejpam-5834	244	8	muhammad	muhammad	PROPN
ejpam-5834	244	9	uzair	uzair	PROPN
ejpam-5834	244	10	awan	awan	PROPN
ejpam-5834	244	11	.	.	PUNCT
ejpam-5834	245	1	some	some	DET
ejpam-5834	245	2	integral	integral	ADJ
ejpam-5834	245	3	inequalities	inequality	NOUN
ejpam-5834	245	4	for	for	ADP
ejpam-5834	245	5	two	two	NUM
ejpam-5834	245	6	kinds	kind	NOUN
ejpam-5834	245	7	of	of	ADP
ejpam-5834	245	8	convexities	convexity	NOUN
ejpam-5834	245	9	via	via	ADP
ejpam-5834	245	10	fractional	fractional	ADJ
ejpam-5834	245	11	integrals	integral	NOUN
ejpam-5834	245	12	.	.	PUNCT
ejpam-5834	246	1	trans	trans	PROPN
ejpam-5834	246	2	.	.	PUNCT
ejpam-5834	247	1	j.	j.	PROPN
ejpam-5834	247	2	math	math	PROPN
ejpam-5834	247	3	.	.	PUNCT
ejpam-5834	248	1	mech	mech	PROPN
ejpam-5834	248	2	,	,	PUNCT
ejpam-5834	248	3	5(2):129	5(2):129	NUM
ejpam-5834	248	4	–	–	PUNCT
ejpam-5834	248	5	136	136	NUM
ejpam-5834	248	6	,	,	PUNCT
ejpam-5834	248	7	2013	2013	NUM
ejpam-5834	248	8	.	.	PUNCT
ejpam-5834	249	1	[	[	X
ejpam-5834	249	2	12	12	NUM
ejpam-5834	249	3	]	]	X
ejpam-5834	249	4	emin	emin	PROPN
ejpam-5834	249	5	özçaḡ	özçaḡ	PROPN
ejpam-5834	249	6	,	,	PUNCT
ejpam-5834	249	7	inci	inci	PROPN
ejpam-5834	249	8	ege	ege	PROPN
ejpam-5834	249	9	,	,	PUNCT
ejpam-5834	249	10	and	and	CCONJ
ejpam-5834	249	11	haşmet	haşmet	PROPN
ejpam-5834	249	12	gürçay	gürçay	NOUN
ejpam-5834	249	13	.	.	PUNCT
ejpam-5834	250	1	an	an	DET
ejpam-5834	250	2	extension	extension	NOUN
ejpam-5834	250	3	of	of	ADP
ejpam-5834	250	4	the	the	DET
ejpam-5834	250	5	incomplete	incomplete	ADJ
ejpam-5834	250	6	beta	beta	ADJ
ejpam-5834	250	7	function	function	NOUN
ejpam-5834	250	8	for	for	ADP
ejpam-5834	250	9	negative	negative	ADJ
ejpam-5834	250	10	integers	integer	NOUN
ejpam-5834	250	11	.	.	PUNCT
ejpam-5834	251	1	journal	journal	PROPN
ejpam-5834	251	2	of	of	ADP
ejpam-5834	251	3	mathematical	mathematical	ADJ
ejpam-5834	251	4	analysis	analysis	NOUN
ejpam-5834	251	5	and	and	CCONJ
ejpam-5834	251	6	applications	application	NOUN
ejpam-5834	251	7	,	,	PUNCT
ejpam-5834	251	8	338(2):984–992	338(2):984–992	NUM
ejpam-5834	251	9	,	,	PUNCT
ejpam-5834	251	10	2008	2008	NUM
ejpam-5834	251	11	.	.	PUNCT
ejpam-5834	252	1	[	[	X
ejpam-5834	252	2	13	13	NUM
ejpam-5834	252	3	]	]	X
ejpam-5834	252	4	vijai	vijai	PROPN
ejpam-5834	252	5	kumar	kumar	PROPN
ejpam-5834	252	6	pathak	pathak	PROPN
ejpam-5834	252	7	,	,	PUNCT
ejpam-5834	252	8	lakshmi	lakshmi	PROPN
ejpam-5834	252	9	narayan	narayan	PROPN
ejpam-5834	252	10	mishra	mishra	PROPN
ejpam-5834	252	11	,	,	PUNCT
ejpam-5834	252	12	and	and	CCONJ
ejpam-5834	252	13	vishnu	vishnu	PROPN
ejpam-5834	252	14	narayan	narayan	PROPN
ejpam-5834	252	15	mishra	mishra	PROPN
ejpam-5834	252	16	.	.	PROPN
ejpam-5834	253	1	on	on	ADP
ejpam-5834	253	2	the	the	DET
ejpam-5834	253	3	solvability	solvability	NOUN
ejpam-5834	253	4	of	of	ADP
ejpam-5834	253	5	a	a	DET
ejpam-5834	253	6	class	class	NOUN
ejpam-5834	253	7	of	of	ADP
ejpam-5834	253	8	nonlinear	nonlinear	ADJ
ejpam-5834	253	9	functional	functional	ADJ
ejpam-5834	253	10	integral	integral	ADJ
ejpam-5834	253	11	equations	equation	NOUN
ejpam-5834	253	12	involving	involve	VERB
ejpam-5834	253	13	erdélyi	erdélyi	PROPN
ejpam-5834	253	14	–	–	PUNCT
ejpam-5834	253	15	kober	kober	NOUN
ejpam-5834	253	16	fractional	fractional	ADJ
ejpam-5834	253	17	operator	operator	NOUN
ejpam-5834	253	18	.	.	PUNCT
ejpam-5834	254	1	mathematical	mathematical	ADJ
ejpam-5834	254	2	methods	method	NOUN
ejpam-5834	254	3	in	in	ADP
ejpam-5834	254	4	the	the	DET
ejpam-5834	254	5	applied	apply	VERB
ejpam-5834	254	6	sciences	science	NOUN
ejpam-5834	254	7	,	,	PUNCT
ejpam-5834	254	8	46(13):14340–14352	46(13):14340–14352	NUM
ejpam-5834	254	9	,	,	PUNCT
ejpam-5834	254	10	2023	2023	NUM
ejpam-5834	254	11	.	.	PUNCT
ejpam-5834	255	1	[	[	X
ejpam-5834	255	2	14	14	NUM
ejpam-5834	255	3	]	]	X
ejpam-5834	255	4	supriya	supriya	PROPN
ejpam-5834	255	5	kumar	kumar	PROPN
ejpam-5834	255	6	paul	paul	PROPN
ejpam-5834	255	7	and	and	CCONJ
ejpam-5834	255	8	lakshmi	lakshmi	PROPN
ejpam-5834	255	9	narayan	narayan	PROPN
ejpam-5834	255	10	mishra	mishra	PROPN
ejpam-5834	255	11	.	.	PROPN
ejpam-5834	255	12	approximation	approximation	NOUN
ejpam-5834	255	13	of	of	ADP
ejpam-5834	255	14	solutions	solution	NOUN
ejpam-5834	255	15	through	through	ADP
ejpam-5834	255	16	the	the	DET
ejpam-5834	255	17	fibonacci	fibonacci	NOUN
ejpam-5834	255	18	wavelets	wavelet	NOUN
ejpam-5834	255	19	and	and	CCONJ
ejpam-5834	255	20	measure	measure	NOUN
ejpam-5834	255	21	of	of	ADP
ejpam-5834	255	22	noncompactness	noncompactness	ADJ
ejpam-5834	255	23	to	to	AUX
ejpam-5834	255	24	nonlinear	nonlinear	PROPN
ejpam-5834	255	25	volterra	volterra	NOUN
ejpam-5834	255	26	-	-	PUNCT
ejpam-5834	255	27	fredholm	fredholm	NOUN
ejpam-5834	255	28	fractional	fractional	ADJ
ejpam-5834	255	29	integral	integral	ADJ
ejpam-5834	255	30	equations	equation	NOUN
ejpam-5834	255	31	.	.	PUNCT
ejpam-5834	256	1	korean	korean	ADJ
ejpam-5834	256	2	journal	journal	PROPN
ejpam-5834	256	3	of	of	ADP
ejpam-5834	256	4	mathematics	mathematic	NOUN
ejpam-5834	256	5	,	,	PUNCT
ejpam-5834	256	6	32(1):137–162	32(1):137–162	NUM
ejpam-5834	256	7	,	,	PUNCT
ejpam-5834	256	8	2024	2024	NUM
ejpam-5834	256	9	.	.	PUNCT
ejpam-5834	257	1	[	[	X
ejpam-5834	257	2	15	15	NUM
ejpam-5834	257	3	]	]	X
ejpam-5834	257	4	supriya	supriya	PROPN
ejpam-5834	257	5	kumar	kumar	PROPN
ejpam-5834	257	6	paul	paul	PROPN
ejpam-5834	257	7	,	,	PUNCT
ejpam-5834	257	8	lakshmi	lakshmi	PROPN
ejpam-5834	257	9	narayan	narayan	PROPN
ejpam-5834	257	10	mishra	mishra	PROPN
ejpam-5834	257	11	,	,	PUNCT
ejpam-5834	257	12	and	and	CCONJ
ejpam-5834	257	13	vishnu	vishnu	PROPN
ejpam-5834	257	14	narayan	narayan	PROPN
ejpam-5834	257	15	mishra	mishra	PROPN
ejpam-5834	257	16	.	.	PROPN
ejpam-5834	257	17	approximate	approximate	PROPN
ejpam-5834	257	18	numerical	numerical	PROPN
ejpam-5834	257	19	solutions	solution	NOUN
ejpam-5834	257	20	of	of	ADP
ejpam-5834	257	21	fractional	fractional	ADJ
ejpam-5834	257	22	integral	integral	ADJ
ejpam-5834	257	23	equations	equation	NOUN
ejpam-5834	257	24	using	use	VERB
ejpam-5834	257	25	laguerre	laguerre	NOUN
ejpam-5834	257	26	and	and	CCONJ
ejpam-5834	257	27	touchard	touchard	NOUN
ejpam-5834	257	28	polynomials	polynomial	NOUN
ejpam-5834	257	29	.	.	PUNCT
ejpam-5834	258	1	palestine	palestine	PROPN
ejpam-5834	258	2	journal	journal	PROPN
ejpam-5834	258	3	of	of	ADP
ejpam-5834	258	4	mathematics	mathematic	NOUN
ejpam-5834	258	5	,	,	PUNCT
ejpam-5834	258	6	12(3	12(3	NUM
ejpam-5834	258	7	)	)	PUNCT
ejpam-5834	258	8	,	,	PUNCT
ejpam-5834	258	9	2023	2023	NUM
ejpam-5834	258	10	.	.	PUNCT
ejpam-5834	259	1	[	[	X
ejpam-5834	259	2	16	16	NUM
ejpam-5834	259	3	]	]	X
ejpam-5834	259	4	supriya	supriya	PROPN
ejpam-5834	259	5	kumar	kumar	PROPN
ejpam-5834	259	6	paul	paul	PROPN
ejpam-5834	259	7	,	,	PUNCT
ejpam-5834	259	8	lakshmi	lakshmi	PROPN
ejpam-5834	259	9	narayan	narayan	PROPN
ejpam-5834	259	10	mishra	mishra	PROPN
ejpam-5834	259	11	,	,	PUNCT
ejpam-5834	259	12	and	and	CCONJ
ejpam-5834	259	13	vishnu	vishnu	PROPN
ejpam-5834	259	14	narayan	narayan	PROPN
ejpam-5834	259	15	mishra	mishra	PROPN
ejpam-5834	259	16	.	.	PROPN
ejpam-5834	259	17	reo	reo	PROPN
ejpam-5834	259	18	.	.	PUNCT
ejpam-5834	259	19	b.	b.	PROPN
ejpam-5834	259	20	almutairi	almutairi	PROPN
ejpam-5834	259	21	/	/	SYM
ejpam-5834	259	22	eur	eur	PROPN
ejpam-5834	259	23	.	.	PUNCT
ejpam-5834	260	1	j.	j.	PROPN
ejpam-5834	260	2	pure	pure	PROPN
ejpam-5834	260	3	appl	appl	PROPN
ejpam-5834	260	4	.	.	PROPN
ejpam-5834	260	5	math	math	PROPN
ejpam-5834	260	6	,	,	PUNCT
ejpam-5834	260	7	18	18	NUM
ejpam-5834	260	8	(	(	PUNCT
ejpam-5834	260	9	1	1	NUM
ejpam-5834	260	10	)	)	PUNCT
ejpam-5834	260	11	(	(	PUNCT
ejpam-5834	260	12	2025	2025	NUM
ejpam-5834	260	13	)	)	PUNCT
ejpam-5834	260	14	,	,	PUNCT
ejpam-5834	260	15	5834	5834	NUM
ejpam-5834	260	16	12	12	NUM
ejpam-5834	260	17	of	of	ADP
ejpam-5834	260	18	12	12	NUM
ejpam-5834	260	19	sults	sult	NOUN
ejpam-5834	260	20	on	on	ADP
ejpam-5834	260	21	integral	integral	ADJ
ejpam-5834	260	22	inequalities	inequality	NOUN
ejpam-5834	260	23	for	for	ADP
ejpam-5834	260	24	a	a	DET
ejpam-5834	260	25	generalized	generalized	ADJ
ejpam-5834	260	26	fractional	fractional	ADJ
ejpam-5834	260	27	integral	integral	ADJ
ejpam-5834	260	28	operator	operator	NOUN
ejpam-5834	260	29	unifying	unify	VERB
ejpam-5834	260	30	two	two	NUM
ejpam-5834	260	31	existing	exist	VERB
ejpam-5834	260	32	fractional	fractional	ADJ
ejpam-5834	260	33	integral	integral	ADJ
ejpam-5834	260	34	operators	operator	NOUN
ejpam-5834	260	35	.	.	PUNCT
ejpam-5834	261	1	nonlinear	nonlinear	ADJ
ejpam-5834	261	2	analysis	analysis	NOUN
ejpam-5834	261	3	:	:	PUNCT
ejpam-5834	261	4	modelling	modelling	NOUN
ejpam-5834	261	5	and	and	CCONJ
ejpam-5834	261	6	control	control	NOUN
ejpam-5834	261	7	,	,	PUNCT
ejpam-5834	261	8	29(6):1080–1105	29(6):1080–1105	PROPN
ejpam-5834	261	9	,	,	PUNCT
ejpam-5834	261	10	2024	2024	NUM
ejpam-5834	261	11	.	.	PUNCT
ejpam-5834	262	1	[	[	X
ejpam-5834	262	2	17	17	NUM
ejpam-5834	262	3	]	]	X
ejpam-5834	262	4	supriya	supriya	PROPN
ejpam-5834	262	5	kumar	kumar	PROPN
ejpam-5834	262	6	paul	paul	PROPN
ejpam-5834	262	7	,	,	PUNCT
ejpam-5834	262	8	lakshmi	lakshmi	PROPN
ejpam-5834	262	9	narayan	narayan	PROPN
ejpam-5834	262	10	mishra	mishra	PROPN
ejpam-5834	262	11	,	,	PUNCT
ejpam-5834	262	12	vishnu	vishnu	PROPN
ejpam-5834	262	13	narayan	narayan	PROPN
ejpam-5834	262	14	mishra	mishra	PROPN
ejpam-5834	262	15	,	,	PUNCT
ejpam-5834	262	16	and	and	CCONJ
ejpam-5834	262	17	dumitru	dumitru	PROPN
ejpam-5834	262	18	baleanu	baleanu	NOUN
ejpam-5834	262	19	.	.	PUNCT
ejpam-5834	263	1	analysis	analysis	NOUN
ejpam-5834	263	2	of	of	ADP
ejpam-5834	263	3	mixed	mixed	ADJ
ejpam-5834	263	4	type	type	NOUN
ejpam-5834	263	5	nonlinear	nonlinear	PROPN
ejpam-5834	263	6	volterra	volterra	PROPN
ejpam-5834	263	7	–	–	PUNCT
ejpam-5834	263	8	fredholm	fredholm	ADJ
ejpam-5834	263	9	integral	integral	ADJ
ejpam-5834	263	10	equations	equation	NOUN
ejpam-5834	263	11	involving	involve	VERB
ejpam-5834	263	12	the	the	DET
ejpam-5834	263	13	erdélyi	erdélyi	PROPN
ejpam-5834	263	14	–	–	PUNCT
ejpam-5834	263	15	kober	kober	NOUN
ejpam-5834	263	16	fractional	fractional	ADJ
ejpam-5834	263	17	operator	operator	NOUN
ejpam-5834	263	18	.	.	PUNCT
ejpam-5834	264	1	journal	journal	PROPN
ejpam-5834	264	2	of	of	ADP
ejpam-5834	264	3	king	king	PROPN
ejpam-5834	264	4	saud	saud	PROPN
ejpam-5834	264	5	university	university	PROPN
ejpam-5834	264	6	-	-	PUNCT
ejpam-5834	264	7	science	science	NOUN
ejpam-5834	264	8	,	,	PUNCT
ejpam-5834	264	9	35(10):102949	35(10):102949	NUM
ejpam-5834	264	10	,	,	PUNCT
ejpam-5834	264	11	2023	2023	NUM
ejpam-5834	264	12	.	.	PUNCT
ejpam-5834	265	1	[	[	X
ejpam-5834	265	2	18	18	NUM
ejpam-5834	265	3	]	]	X
ejpam-5834	265	4	stefan	stefan	PROPN
ejpam-5834	265	5	g	g	PROPN
ejpam-5834	265	6	samko	samko	PROPN
ejpam-5834	265	7	.	.	PUNCT
ejpam-5834	266	1	fractional	fractional	ADJ
ejpam-5834	266	2	integrals	integral	NOUN
ejpam-5834	266	3	and	and	CCONJ
ejpam-5834	266	4	derivatives	derivative	NOUN
ejpam-5834	266	5	.	.	PUNCT
ejpam-5834	267	1	theory	theory	NOUN
ejpam-5834	267	2	and	and	CCONJ
ejpam-5834	267	3	applications	application	NOUN
ejpam-5834	267	4	,	,	PUNCT
ejpam-5834	267	5	1993	1993	NUM
ejpam-5834	267	6	.	.	PUNCT
ejpam-5834	268	1	[	[	X
ejpam-5834	268	2	19	19	NUM
ejpam-5834	268	3	]	]	X
ejpam-5834	268	4	mehmet	mehmet	PROPN
ejpam-5834	268	5	zeki	zeki	PROPN
ejpam-5834	268	6	sarikaya	sarikaya	PROPN
ejpam-5834	268	7	,	,	PUNCT
ejpam-5834	268	8	erhan	erhan	SCONJ
ejpam-5834	268	9	set	set	VERB
ejpam-5834	268	10	,	,	PUNCT
ejpam-5834	268	11	hatice	hatice	NOUN
ejpam-5834	268	12	yaldiz	yaldiz	NOUN
ejpam-5834	268	13	,	,	PUNCT
ejpam-5834	268	14	and	and	CCONJ
ejpam-5834	268	15	nagihan	nagihan	ADP
ejpam-5834	268	16	başak	başak	PROPN
ejpam-5834	268	17	.	.	PUNCT
ejpam-5834	269	1	hermite	hermite	PROPN
ejpam-5834	269	2	–	–	PUNCT
ejpam-5834	269	3	hadamard	hadamard	NOUN
ejpam-5834	269	4	’s	’s	PART
ejpam-5834	269	5	inequalities	inequality	NOUN
ejpam-5834	269	6	for	for	ADP
ejpam-5834	269	7	fractional	fractional	ADJ
ejpam-5834	269	8	integrals	integral	NOUN
ejpam-5834	269	9	and	and	CCONJ
ejpam-5834	269	10	related	relate	VERB
ejpam-5834	269	11	fractional	fractional	ADJ
ejpam-5834	269	12	inequalities	inequality	NOUN
ejpam-5834	269	13	.	.	PUNCT
ejpam-5834	270	1	mathematical	mathematical	ADJ
ejpam-5834	270	2	and	and	CCONJ
ejpam-5834	270	3	computer	computer	NOUN
ejpam-5834	270	4	modelling	modelling	NOUN
ejpam-5834	270	5	,	,	PUNCT
ejpam-5834	270	6	57(9	57(9	NOUN
ejpam-5834	270	7	-	-	SYM
ejpam-5834	270	8	10):2403–2407	10):2403–2407	NOUN
ejpam-5834	270	9	,	,	PUNCT
ejpam-5834	270	10	2013	2013	NUM
ejpam-5834	270	11	.	.	PUNCT
ejpam-5834	271	1	[	[	X
ejpam-5834	271	2	20	20	NUM
ejpam-5834	271	3	]	]	X
ejpam-5834	271	4	gheorghe	gheorghe	NOUN
ejpam-5834	271	5	toader	toader	NOUN
ejpam-5834	271	6	.	.	PUNCT
ejpam-5834	272	1	some	some	DET
ejpam-5834	272	2	generalizations	generalization	NOUN
ejpam-5834	272	3	of	of	ADP
ejpam-5834	272	4	the	the	DET
ejpam-5834	272	5	convexity	convexity	NOUN
ejpam-5834	272	6	.	.	PUNCT
ejpam-5834	273	1	in	in	ADP
ejpam-5834	273	2	proceedings	proceeding	NOUN
ejpam-5834	273	3	of	of	ADP
ejpam-5834	273	4	the	the	DET
ejpam-5834	273	5	colloquium	colloquium	NOUN
ejpam-5834	273	6	on	on	ADP
ejpam-5834	273	7	approximation	approximation	NOUN
ejpam-5834	273	8	and	and	CCONJ
ejpam-5834	273	9	optimization	optimization	NOUN
ejpam-5834	273	10	,	,	PUNCT
ejpam-5834	273	11	volume	volume	NOUN
ejpam-5834	273	12	329	329	NUM
ejpam-5834	273	13	,	,	PUNCT
ejpam-5834	273	14	page	page	NOUN
ejpam-5834	273	15	338	338	NUM
ejpam-5834	273	16	.	.	PUNCT
ejpam-5834	274	1	university	university	NOUN
ejpam-5834	274	2	of	of	ADP
ejpam-5834	274	3	cluj	cluj	PROPN
ejpam-5834	274	4	-	-	PUNCT
ejpam-5834	274	5	napoca	napoca	NOUN
ejpam-5834	274	6	cluj	cluj	PROPN
ejpam-5834	274	7	-	-	PUNCT
ejpam-5834	274	8	napoca	napoca	PROPN
ejpam-5834	274	9	,	,	PUNCT
ejpam-5834	274	10	romania	romania	PROPN
ejpam-5834	274	11	,	,	PUNCT
ejpam-5834	274	12	1984	1984	NUM
ejpam-5834	274	13	.	.	PUNCT
ejpam-5834	275	1	[	[	X
ejpam-5834	275	2	21	21	NUM
ejpam-5834	275	3	]	]	X
ejpam-5834	275	4	bo	bo	PROPN
ejpam-5834	275	5	-	-	PUNCT
ejpam-5834	275	6	yan	yan	PROPN
ejpam-5834	275	7	xi	xi	PROPN
ejpam-5834	275	8	,	,	PUNCT
ejpam-5834	275	9	dan	dan	PROPN
ejpam-5834	275	10	-	-	PUNCT
ejpam-5834	275	11	dan	dan	PROPN
ejpam-5834	275	12	gao	gao	PROPN
ejpam-5834	275	13	,	,	PUNCT
ejpam-5834	275	14	and	and	CCONJ
ejpam-5834	275	15	feng	feng	PROPN
ejpam-5834	275	16	qi	qi	PROPN
ejpam-5834	275	17	.	.	PUNCT
ejpam-5834	275	18	integral	integral	ADJ
ejpam-5834	275	19	inequalities	inequality	NOUN
ejpam-5834	275	20	of	of	ADP
ejpam-5834	275	21	hermite	hermite	ADJ
ejpam-5834	275	22	–	–	PUNCT
ejpam-5834	275	23	hadamard	hadamard	ADJ
ejpam-5834	275	24	type	type	NOUN
ejpam-5834	275	25	for	for	ADP
ejpam-5834	275	26	(	(	PUNCT
ejpam-5834	275	27	α	α	NOUN
ejpam-5834	275	28	,	,	PUNCT
ejpam-5834	275	29	s)-convex	s)-convex	PUNCT
ejpam-5834	275	30	and	and	CCONJ
ejpam-5834	275	31	(	(	PUNCT
ejpam-5834	275	32	α	α	NOUN
ejpam-5834	275	33	,	,	PUNCT
ejpam-5834	275	34	s	s	PROPN
ejpam-5834	275	35	,	,	PUNCT
ejpam-5834	275	36	m)-convex	m)-convex	NOUN
ejpam-5834	275	37	functions	function	NOUN
ejpam-5834	275	38	.	.	PUNCT
ejpam-5834	276	1	italian	italian	ADJ
ejpam-5834	276	2	journal	journal	NOUN
ejpam-5834	276	3	of	of	ADP
ejpam-5834	276	4	pure	pure	ADJ
ejpam-5834	276	5	and	and	CCONJ
ejpam-5834	276	6	applied	applied	ADJ
ejpam-5834	276	7	mathematics	mathematic	NOUN
ejpam-5834	276	8	,	,	PUNCT
ejpam-5834	276	9	(	(	PUNCT
ejpam-5834	276	10	44):499–510	44):499–510	NUM
ejpam-5834	276	11	,	,	PUNCT
ejpam-5834	276	12	2020	2020	NUM
ejpam-5834	276	13	.	.	PUNCT
ejpam-5834	277	1	[	[	X
ejpam-5834	277	2	22	22	NUM
ejpam-5834	277	3	]	]	X
ejpam-5834	277	4	yi	yi	PROPN
ejpam-5834	277	5	xing	xing	PROPN
ejpam-5834	277	6	,	,	PUNCT
ejpam-5834	277	7	chaoqun	chaoqun	PROPN
ejpam-5834	277	8	jiang	jiang	PROPN
ejpam-5834	277	9	,	,	PUNCT
ejpam-5834	277	10	and	and	CCONJ
ejpam-5834	277	11	jianmiao	jianmiao	PROPN
ejpam-5834	277	12	ruan	ruan	PROPN
ejpam-5834	277	13	.	.	PUNCT
ejpam-5834	278	1	hermite	hermite	PROPN
ejpam-5834	278	2	-	-	PUNCT
ejpam-5834	278	3	hadamard	hadamard	ADJ
ejpam-5834	278	4	type	type	NOUN
ejpam-5834	278	5	inequalities	inequality	NOUN
ejpam-5834	278	6	for	for	ADP
ejpam-5834	278	7	riemann	riemann	PROPN
ejpam-5834	278	8	-	-	PUNCT
ejpam-5834	278	9	liouville	liouville	VERB
ejpam-5834	278	10	fractional	fractional	ADJ
ejpam-5834	278	11	integrals	integral	NOUN
ejpam-5834	278	12	via	via	ADP
ejpam-5834	278	13	strongly	strongly	ADV
ejpam-5834	278	14	h	h	ADJ
ejpam-5834	278	15	-	-	PUNCT
ejpam-5834	278	16	convex	convex	NOUN
ejpam-5834	278	17	functions	function	NOUN
ejpam-5834	278	18	.	.	PUNCT
ejpam-5834	279	1	authorea	authorea	PROPN
ejpam-5834	279	2	preprints	preprint	NOUN
ejpam-5834	279	3	,	,	PUNCT
ejpam-5834	279	4	2024	2024	NUM
ejpam-5834	279	5	.	.	PUNCT