id	sid	tid	token	lemma	pos
ejpam-4015	1	1	european	european	PROPN
ejpam-4015	1	2	journal	journal	PROPN
ejpam-4015	1	3	of	of	ADP
ejpam-4015	1	4	pure	pure	ADJ
ejpam-4015	1	5	and	and	CCONJ
ejpam-4015	1	6	applied	apply	VERB
ejpam-4015	1	7	mathematics	mathematic	NOUN
ejpam-4015	1	8	vol	vol	NOUN
ejpam-4015	1	9	.	.	PUNCT
ejpam-4015	2	1	14	14	NUM
ejpam-4015	2	2	,	,	PUNCT
ejpam-4015	2	3	no	no	INTJ
ejpam-4015	2	4	.	.	NOUN
ejpam-4015	2	5	3	3	NUM
ejpam-4015	2	6	,	,	PUNCT
ejpam-4015	2	7	2021	2021	NUM
ejpam-4015	2	8	,	,	PUNCT
ejpam-4015	2	9	863	863	NUM
ejpam-4015	2	10	-	-	SYM
ejpam-4015	2	11	880	880	NUM
ejpam-4015	2	12	issn	issn	PROPN
ejpam-4015	2	13	1307	1307	NUM
ejpam-4015	2	14	-	-	SYM
ejpam-4015	2	15	5543	5543	NUM
ejpam-4015	2	16	–	–	PUNCT
ejpam-4015	2	17	ejpam.com	ejpam.com	X
ejpam-4015	2	18	published	publish	VERB
ejpam-4015	2	19	by	by	ADP
ejpam-4015	2	20	new	new	PROPN
ejpam-4015	2	21	york	york	PROPN
ejpam-4015	2	22	business	business	PROPN
ejpam-4015	2	23	global	global	ADJ
ejpam-4015	2	24	new	new	ADJ
ejpam-4015	2	25	generalized	generalize	VERB
ejpam-4015	2	26	hermite−hadamard	hermite−hadamard	ADJ
ejpam-4015	2	27	type	type	NOUN
ejpam-4015	2	28	inequalities	inequality	NOUN
ejpam-4015	2	29	for	for	ADP
ejpam-4015	2	30	p−convex	p−convex	NOUN
ejpam-4015	2	31	functions	function	NOUN
ejpam-4015	2	32	in	in	ADP
ejpam-4015	2	33	the	the	DET
ejpam-4015	2	34	mixed	mixed	ADJ
ejpam-4015	2	35	kind	kind	NOUN
ejpam-4015	2	36	muhammad	muhammad	PROPN
ejpam-4015	2	37	bilal1,∗	bilal1,∗	NOUN
ejpam-4015	2	38	,	,	PUNCT
ejpam-4015	2	39	asif	asif	PROPN
ejpam-4015	2	40	r.	r.	PROPN
ejpam-4015	2	41	khan1	khan1	PROPN
ejpam-4015	3	1	1	1	NUM
ejpam-4015	3	2	department	department	NOUN
ejpam-4015	3	3	of	of	ADP
ejpam-4015	3	4	mathematics	mathematic	NOUN
ejpam-4015	3	5	,	,	PUNCT
ejpam-4015	3	6	university	university	PROPN
ejpam-4015	3	7	of	of	ADP
ejpam-4015	3	8	karachi	karachi	PROPN
ejpam-4015	3	9	,	,	PUNCT
ejpam-4015	3	10	university	university	NOUN
ejpam-4015	3	11	road	road	NOUN
ejpam-4015	3	12	,	,	PUNCT
ejpam-4015	3	13	karachi-75270	karachi-75270	INTJ
ejpam-4015	3	14	,	,	PUNCT
ejpam-4015	3	15	pakistan	pakistan	PROPN
ejpam-4015	3	16	abstract	abstract	NOUN
ejpam-4015	3	17	.	.	PUNCT
ejpam-4015	4	1	in	in	ADP
ejpam-4015	4	2	this	this	DET
ejpam-4015	4	3	article	article	NOUN
ejpam-4015	4	4	,	,	PUNCT
ejpam-4015	4	5	we	we	PRON
ejpam-4015	4	6	would	would	AUX
ejpam-4015	4	7	like	like	VERB
ejpam-4015	4	8	to	to	PART
ejpam-4015	4	9	state	state	VERB
ejpam-4015	4	10	generalized	generalize	VERB
ejpam-4015	4	11	results	result	NOUN
ejpam-4015	4	12	related	relate	VERB
ejpam-4015	4	13	to	to	ADP
ejpam-4015	4	14	well	well	ADV
ejpam-4015	4	15	-	-	PUNCT
ejpam-4015	4	16	known	know	VERB
ejpam-4015	4	17	hermite	hermite	ADJ
ejpam-4015	4	18	−	−	PROPN
ejpam-4015	4	19	hadamard	hadamard	ADJ
ejpam-4015	4	20	dual	dual	ADJ
ejpam-4015	4	21	inequality	inequality	NOUN
ejpam-4015	4	22	for	for	ADP
ejpam-4015	4	23	p−convex	p−convex	NOUN
ejpam-4015	4	24	functions	function	NOUN
ejpam-4015	4	25	using	use	VERB
ejpam-4015	4	26	the	the	DET
ejpam-4015	4	27	newly	newly	ADV
ejpam-4015	4	28	introduced	introduce	VERB
ejpam-4015	4	29	notion	notion	NOUN
ejpam-4015	4	30	of	of	ADP
ejpam-4015	4	31	(	(	PUNCT
ejpam-4015	4	32	s	s	X
ejpam-4015	4	33	,	,	PUNCT
ejpam-4015	4	34	r)−	r)−	PROPN
ejpam-4015	4	35	convexity	convexity	NOUN
ejpam-4015	4	36	(	(	PUNCT
ejpam-4015	4	37	s−convex	s−convex	X
ejpam-4015	4	38	function	function	NOUN
ejpam-4015	4	39	in	in	ADP
ejpam-4015	4	40	mixed	mixed	ADJ
ejpam-4015	4	41	kind	kind	NOUN
ejpam-4015	4	42	)	)	PUNCT
ejpam-4015	4	43	with	with	ADP
ejpam-4015	4	44	different	different	ADJ
ejpam-4015	4	45	techniques	technique	NOUN
ejpam-4015	4	46	.	.	PUNCT
ejpam-4015	5	1	hence	hence	ADV
ejpam-4015	5	2	various	various	ADJ
ejpam-4015	5	3	established	establish	VERB
ejpam-4015	5	4	and	and	CCONJ
ejpam-4015	5	5	new	new	ADJ
ejpam-4015	5	6	results	result	NOUN
ejpam-4015	5	7	would	would	AUX
ejpam-4015	5	8	be	be	AUX
ejpam-4015	5	9	captured	capture	VERB
ejpam-4015	5	10	as	as	ADP
ejpam-4015	5	11	special	special	ADJ
ejpam-4015	5	12	case	case	NOUN
ejpam-4015	5	13	.	.	PUNCT
ejpam-4015	6	1	2020	2020	NUM
ejpam-4015	6	2	mathematics	mathematic	NOUN
ejpam-4015	6	3	subject	subject	NOUN
ejpam-4015	6	4	classifications	classification	NOUN
ejpam-4015	6	5	:	:	PUNCT
ejpam-4015	6	6	26a46	26a46	NUM
ejpam-4015	6	7	,	,	PUNCT
ejpam-4015	6	8	26a51	26a51	NUM
ejpam-4015	6	9	,	,	PUNCT
ejpam-4015	6	10	26d07	26d07	NUM
ejpam-4015	6	11	,	,	PUNCT
ejpam-4015	6	12	26d99	26d99	NUM
ejpam-4015	6	13	key	key	ADJ
ejpam-4015	6	14	words	word	NOUN
ejpam-4015	6	15	and	and	CCONJ
ejpam-4015	6	16	phrases	phrase	NOUN
ejpam-4015	6	17	:	:	PUNCT
ejpam-4015	6	18	hermite−hadamard	hermite−hadamard	NUM
ejpam-4015	6	19	inequities	inequity	NOUN
ejpam-4015	6	20	,	,	PUNCT
ejpam-4015	6	21	p−convexity	p−convexity	NOUN
ejpam-4015	6	22	,	,	PUNCT
ejpam-4015	6	23	s−convexity	s−convexity	NOUN
ejpam-4015	6	24	in	in	ADP
ejpam-4015	6	25	the	the	DET
ejpam-4015	6	26	first	first	ADJ
ejpam-4015	6	27	kind	kind	NOUN
ejpam-4015	6	28	,	,	PUNCT
ejpam-4015	6	29	s−convexity	s−convexity	NOUN
ejpam-4015	6	30	in	in	ADP
ejpam-4015	6	31	the	the	DET
ejpam-4015	6	32	second	second	ADJ
ejpam-4015	6	33	kind	kind	NOUN
ejpam-4015	6	34	,	,	PUNCT
ejpam-4015	6	35	s−convexity	s−convexity	NOUN
ejpam-4015	6	36	in	in	ADP
ejpam-4015	6	37	the	the	DET
ejpam-4015	6	38	mixed	mixed	ADJ
ejpam-4015	6	39	kind	kind	NOUN
ejpam-4015	6	40	1	1	NUM
ejpam-4015	6	41	.	.	PUNCT
ejpam-4015	6	42	introduction	introduction	NOUN
ejpam-4015	6	43	and	and	CCONJ
ejpam-4015	6	44	preliminaries	preliminary	NOUN
ejpam-4015	6	45	the	the	DET
ejpam-4015	6	46	field	field	NOUN
ejpam-4015	6	47	of	of	ADP
ejpam-4015	6	48	mathematical	mathematical	ADJ
ejpam-4015	6	49	inequality	inequality	NOUN
ejpam-4015	6	50	is	be	AUX
ejpam-4015	6	51	very	very	ADV
ejpam-4015	6	52	conspicuous	conspicuous	ADJ
ejpam-4015	6	53	and	and	CCONJ
ejpam-4015	6	54	lucid	lucid	ADJ
ejpam-4015	6	55	for	for	ADP
ejpam-4015	6	56	researchers	researcher	NOUN
ejpam-4015	6	57	.	.	PUNCT
ejpam-4015	7	1	the	the	DET
ejpam-4015	7	2	basic	basic	ADJ
ejpam-4015	7	3	theory	theory	NOUN
ejpam-4015	7	4	of	of	ADP
ejpam-4015	7	5	convex	convex	PROPN
ejpam-4015	7	6	function	function	NOUN
ejpam-4015	7	7	holds	hold	VERB
ejpam-4015	7	8	a	a	DET
ejpam-4015	7	9	very	very	ADV
ejpam-4015	7	10	powerful	powerful	ADJ
ejpam-4015	7	11	solution	solution	NOUN
ejpam-4015	7	12	to	to	ADP
ejpam-4015	7	13	the	the	DET
ejpam-4015	7	14	problems	problem	NOUN
ejpam-4015	7	15	faced	face	VERB
ejpam-4015	7	16	by	by	ADP
ejpam-4015	7	17	researchers	researcher	NOUN
ejpam-4015	7	18	during	during	ADP
ejpam-4015	7	19	a	a	DET
ejpam-4015	7	20	detailed	detailed	ADJ
ejpam-4015	7	21	analysis	analysis	NOUN
ejpam-4015	7	22	.	.	PUNCT
ejpam-4015	8	1	this	this	DET
ejpam-4015	8	2	field	field	NOUN
ejpam-4015	8	3	of	of	ADP
ejpam-4015	8	4	mathematical	mathematical	ADJ
ejpam-4015	8	5	research	research	NOUN
ejpam-4015	8	6	provides	provide	VERB
ejpam-4015	8	7	an	an	DET
ejpam-4015	8	8	important	important	ADJ
ejpam-4015	8	9	contrivance	contrivance	NOUN
ejpam-4015	8	10	in	in	ADP
ejpam-4015	8	11	growth	growth	NOUN
ejpam-4015	8	12	of	of	ADP
ejpam-4015	8	13	various	various	ADJ
ejpam-4015	8	14	branches	branch	NOUN
ejpam-4015	8	15	of	of	ADP
ejpam-4015	8	16	research	research	NOUN
ejpam-4015	8	17	and	and	CCONJ
ejpam-4015	8	18	is	be	AUX
ejpam-4015	8	19	given	give	VERB
ejpam-4015	8	20	considerable	considerable	ADJ
ejpam-4015	8	21	attention	attention	NOUN
ejpam-4015	8	22	in	in	ADP
ejpam-4015	8	23	literature	literature	NOUN
ejpam-4015	8	24	.	.	PUNCT
ejpam-4015	9	1	convexity	convexity	NOUN
ejpam-4015	9	2	has	have	VERB
ejpam-4015	9	3	its	its	PRON
ejpam-4015	9	4	applications	application	NOUN
ejpam-4015	9	5	in	in	ADP
ejpam-4015	9	6	various	various	ADJ
ejpam-4015	9	7	fields	field	NOUN
ejpam-4015	9	8	of	of	ADP
ejpam-4015	9	9	professional	professional	ADJ
ejpam-4015	9	10	and	and	CCONJ
ejpam-4015	9	11	daily	daily	ADJ
ejpam-4015	9	12	life	life	NOUN
ejpam-4015	9	13	like	like	ADP
ejpam-4015	9	14	management	management	NOUN
ejpam-4015	9	15	sciences	science	NOUN
ejpam-4015	9	16	,	,	PUNCT
ejpam-4015	9	17	architecture	architecture	NOUN
ejpam-4015	9	18	,	,	PUNCT
ejpam-4015	9	19	arts	art	NOUN
ejpam-4015	9	20	,	,	PUNCT
ejpam-4015	9	21	industrial	industrial	ADJ
ejpam-4015	9	22	and	and	CCONJ
ejpam-4015	9	23	pharmaceutical	pharmaceutical	NOUN
ejpam-4015	9	24	research	research	NOUN
ejpam-4015	9	25	and	and	CCONJ
ejpam-4015	9	26	many	many	ADJ
ejpam-4015	9	27	more	more	ADJ
ejpam-4015	9	28	.	.	PUNCT
ejpam-4015	10	1	the	the	DET
ejpam-4015	10	2	hermite−hadamard	hermite−hadamard	ADJ
ejpam-4015	10	3	dual	dual	ADJ
ejpam-4015	10	4	inequalities	inequality	NOUN
ejpam-4015	10	5	have	have	VERB
ejpam-4015	10	6	a	a	DET
ejpam-4015	10	7	number	number	NOUN
ejpam-4015	10	8	of	of	ADP
ejpam-4015	10	9	different	different	ADJ
ejpam-4015	10	10	applications	application	NOUN
ejpam-4015	10	11	,	,	PUNCT
ejpam-4015	10	12	due	due	ADP
ejpam-4015	10	13	to	to	ADP
ejpam-4015	10	14	which	which	PRON
ejpam-4015	10	15	it	it	PRON
ejpam-4015	10	16	is	be	AUX
ejpam-4015	10	17	a	a	DET
ejpam-4015	10	18	general	general	ADJ
ejpam-4015	10	19	need	need	NOUN
ejpam-4015	10	20	that	that	SCONJ
ejpam-4015	10	21	one	one	PRON
ejpam-4015	10	22	should	should	AUX
ejpam-4015	10	23	study	study	VERB
ejpam-4015	10	24	them	they	PRON
ejpam-4015	10	25	,	,	PUNCT
ejpam-4015	10	26	specially	specially	ADV
ejpam-4015	10	27	those	those	PRON
ejpam-4015	10	28	involving	involve	VERB
ejpam-4015	10	29	p−convex	p−convex	NOUN
ejpam-4015	10	30	functions	function	NOUN
ejpam-4015	10	31	.	.	PUNCT
ejpam-4015	11	1	for	for	ADP
ejpam-4015	11	2	further	further	ADJ
ejpam-4015	11	3	study	study	NOUN
ejpam-4015	11	4	related	relate	VERB
ejpam-4015	11	5	to	to	ADP
ejpam-4015	11	6	the	the	DET
ejpam-4015	11	7	topic	topic	NOUN
ejpam-4015	11	8	we	we	PRON
ejpam-4015	11	9	refer	refer	VERB
ejpam-4015	11	10	the	the	DET
ejpam-4015	11	11	reader	reader	NOUN
ejpam-4015	11	12	following	follow	VERB
ejpam-4015	11	13	articles	article	NOUN
ejpam-4015	11	14	[	[	X
ejpam-4015	11	15	2	2	NUM
ejpam-4015	11	16	]	]	PUNCT
ejpam-4015	11	17	,	,	PUNCT
ejpam-4015	11	18	[	[	X
ejpam-4015	11	19	3	3	NUM
ejpam-4015	11	20	]	]	PUNCT
ejpam-4015	11	21	–	–	PUNCT
ejpam-4015	11	22	[	[	X
ejpam-4015	11	23	6	6	NUM
ejpam-4015	11	24	]	]	PUNCT
ejpam-4015	11	25	,	,	PUNCT
ejpam-4015	11	26	[	[	X
ejpam-4015	11	27	17	17	NUM
ejpam-4015	11	28	]	]	PUNCT
ejpam-4015	11	29	and	and	CCONJ
ejpam-4015	11	30	[	[	X
ejpam-4015	11	31	21	21	NUM
ejpam-4015	11	32	]	]	PUNCT
ejpam-4015	11	33	–	–	PUNCT
ejpam-4015	12	1	[	[	X
ejpam-4015	12	2	22	22	NUM
ejpam-4015	12	3	]	]	PUNCT
ejpam-4015	12	4	.	.	PUNCT
ejpam-4015	13	1	before	before	SCONJ
ejpam-4015	13	2	we	we	PRON
ejpam-4015	13	3	proceed	proceed	VERB
ejpam-4015	13	4	further	far	ADV
ejpam-4015	13	5	it	it	PRON
ejpam-4015	13	6	is	be	AUX
ejpam-4015	13	7	worth	worth	ADJ
ejpam-4015	13	8	mentioning	mention	VERB
ejpam-4015	13	9	here	here	ADV
ejpam-4015	13	10	,	,	PUNCT
ejpam-4015	13	11	we	we	PRON
ejpam-4015	13	12	introduce	introduce	VERB
ejpam-4015	13	13	some	some	DET
ejpam-4015	13	14	notation	notation	NOUN
ejpam-4015	13	15	which	which	PRON
ejpam-4015	13	16	we	we	PRON
ejpam-4015	13	17	would	would	AUX
ejpam-4015	13	18	use	use	VERB
ejpam-4015	13	19	in	in	ADP
ejpam-4015	13	20	this	this	DET
ejpam-4015	13	21	article	article	NOUN
ejpam-4015	13	22	:	:	PUNCT
ejpam-4015	13	23	i	i	PRON
ejpam-4015	13	24	is	be	AUX
ejpam-4015	13	25	a	a	DET
ejpam-4015	13	26	real	real	ADJ
ejpam-4015	13	27	interval	interval	NOUN
ejpam-4015	13	28	,	,	PUNCT
ejpam-4015	13	29	i	i	PRON
ejpam-4015	13	30	◦	◦	NOUN
ejpam-4015	13	31	is	be	AUX
ejpam-4015	13	32	interior	interior	ADJ
ejpam-4015	13	33	of	of	ADP
ejpam-4015	13	34	interval	interval	NOUN
ejpam-4015	13	35	i	i	PRON
ejpam-4015	13	36	,	,	PUNCT
ejpam-4015	13	37	mp	mp	PROPN
ejpam-4015	13	38	=	=	SYM
ejpam-4015	13	39	bp	bp	PROPN
ejpam-4015	14	1	−	−	PROPN
ejpam-4015	14	2	ap	ap	PROPN
ejpam-4015	14	3	p	p	PROPN
ejpam-4015	14	4	and	and	CCONJ
ejpam-4015	14	5	βr(a	βr(a	NUM
ejpam-4015	14	6	,	,	PUNCT
ejpam-4015	14	7	b	b	X
ejpam-4015	14	8	)	)	PUNCT
ejpam-4015	14	9	=	=	SYM
ejpam-4015	14	10	r∫	r∫	PROPN
ejpam-4015	14	11	0	0	NUM
ejpam-4015	14	12	ta−1(1	ta−1(1	NOUN
ejpam-4015	14	13	−	−	PROPN
ejpam-4015	14	14	t)b−1dt	t)b−1dt	PROPN
ejpam-4015	14	15	,	,	PUNCT
ejpam-4015	14	16	a	a	DET
ejpam-4015	14	17	,	,	PUNCT
ejpam-4015	14	18	b	b	X
ejpam-4015	14	19	>	>	X
ejpam-4015	14	20	0	0	NUM
ejpam-4015	14	21	is	be	AUX
ejpam-4015	14	22	incomplete	incomplete	ADJ
ejpam-4015	14	23	beta	beta	NOUN
ejpam-4015	14	24	function	function	NOUN
ejpam-4015	14	25	.	.	PUNCT
ejpam-4015	15	1	it	it	PRON
ejpam-4015	15	2	is	be	AUX
ejpam-4015	15	3	worth	worth	ADJ
ejpam-4015	15	4	mentioning	mention	VERB
ejpam-4015	15	5	that	that	SCONJ
ejpam-4015	15	6	throughout	throughout	ADP
ejpam-4015	15	7	this	this	DET
ejpam-4015	15	8	article	article	NOUN
ejpam-4015	15	9	we	we	PRON
ejpam-4015	15	10	used	use	VERB
ejpam-4015	15	11	the	the	DET
ejpam-4015	15	12	convention	convention	NOUN
ejpam-4015	15	13	that	that	PRON
ejpam-4015	15	14	00	00	PUNCT
ejpam-4015	16	1	=	=	SYM
ejpam-4015	16	2	1	1	X
ejpam-4015	16	3	.	.	PUNCT
ejpam-4015	17	1	we	we	PRON
ejpam-4015	17	2	shall	shall	AUX
ejpam-4015	17	3	start	start	VERB
ejpam-4015	17	4	with	with	ADP
ejpam-4015	17	5	some	some	DET
ejpam-4015	17	6	useful	useful	ADJ
ejpam-4015	17	7	definitions	definition	NOUN
ejpam-4015	17	8	and	and	CCONJ
ejpam-4015	17	9	results	result	NOUN
ejpam-4015	17	10	:	:	PUNCT
ejpam-4015	17	11	∗corresponding	∗corresponde	VERB
ejpam-4015	17	12	author	author	NOUN
ejpam-4015	17	13	.	.	PUNCT
ejpam-4015	18	1	doi	doi	NOUN
ejpam-4015	18	2	:	:	PUNCT
ejpam-4015	18	3	https://doi.org/10.29020/nybg.ejpam.v14i3.4015	https://doi.org/10.29020/nybg.ejpam.v14i3.4015	X
ejpam-4015	18	4	email	email	NOUN
ejpam-4015	18	5	addresses	address	NOUN
ejpam-4015	18	6	:	:	PUNCT
ejpam-4015	19	1	mbilalfawad@gmail.com	mbilalfawad@gmail.com	X
ejpam-4015	19	2	(	(	PUNCT
ejpam-4015	19	3	m.	m.	NOUN
ejpam-4015	19	4	bilal	bilal	PROPN
ejpam-4015	19	5	)	)	PUNCT
ejpam-4015	19	6	,	,	PUNCT
ejpam-4015	19	7	asifrk@uok.edu.pk	asifrk@uok.edu.pk	NOUN
ejpam-4015	19	8	(	(	PUNCT
ejpam-4015	19	9	a.	a.	PROPN
ejpam-4015	19	10	r.	r.	PROPN
ejpam-4015	19	11	khan	khan	PROPN
ejpam-4015	19	12	)	)	PUNCT
ejpam-4015	19	13	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4015	20	1	863	863	NUM
ejpam-4015	21	1	©	©	ADP
ejpam-4015	21	2	2021	2021	NUM
ejpam-4015	21	3	ejpam	ejpam	VERB
ejpam-4015	21	4	all	all	DET
ejpam-4015	21	5	rights	right	NOUN
ejpam-4015	21	6	reserved	reserve	VERB
ejpam-4015	21	7	.	.	PUNCT
ejpam-4015	22	1	muhammad	muhammad	PROPN
ejpam-4015	22	2	bilal	bilal	PROPN
ejpam-4015	22	3	,	,	PUNCT
ejpam-4015	22	4	asif	asif	PROPN
ejpam-4015	22	5	r.	r.	PROPN
ejpam-4015	22	6	khan	khan	PROPN
ejpam-4015	22	7	/	/	SYM
ejpam-4015	22	8	eur	eur	PROPN
ejpam-4015	22	9	.	.	PUNCT
ejpam-4015	23	1	j.	j.	PROPN
ejpam-4015	23	2	pure	pure	PROPN
ejpam-4015	23	3	appl	appl	PROPN
ejpam-4015	23	4	.	.	PROPN
ejpam-4015	23	5	math	math	PROPN
ejpam-4015	23	6	,	,	PUNCT
ejpam-4015	23	7	14	14	NUM
ejpam-4015	23	8	(	(	PUNCT
ejpam-4015	23	9	3	3	NUM
ejpam-4015	23	10	)	)	PUNCT
ejpam-4015	23	11	(	(	PUNCT
ejpam-4015	23	12	2021	2021	NUM
ejpam-4015	23	13	)	)	PUNCT
ejpam-4015	23	14	,	,	PUNCT
ejpam-4015	23	15	863	863	NUM
ejpam-4015	23	16	-	-	SYM
ejpam-4015	23	17	880	880	NUM
ejpam-4015	23	18	864	864	NUM
ejpam-4015	23	19	theorem	theorem	NOUN
ejpam-4015	23	20	1	1	NUM
ejpam-4015	23	21	.	.	PUNCT
ejpam-4015	24	1	[	[	X
ejpam-4015	24	2	10	10	NUM
ejpam-4015	24	3	]	]	PUNCT
ejpam-4015	24	4	let	let	VERB
ejpam-4015	24	5	f	f	NOUN
ejpam-4015	24	6	:	:	PUNCT
ejpam-4015	24	7	i	i	PRON
ejpam-4015	24	8	→	→	PUNCT
ejpam-4015	24	9	r	r	NOUN
ejpam-4015	24	10	be	be	AUX
ejpam-4015	24	11	a	a	DET
ejpam-4015	24	12	convex	convex	NOUN
ejpam-4015	24	13	function	function	NOUN
ejpam-4015	24	14	.	.	PUNCT
ejpam-4015	25	1	then	then	ADV
ejpam-4015	25	2	f	f	X
ejpam-4015	25	3	(	(	PUNCT
ejpam-4015	25	4	a+	a+	PROPN
ejpam-4015	25	5	b	b	PROPN
ejpam-4015	25	6	2	2	X
ejpam-4015	25	7	)	)	PUNCT
ejpam-4015	25	8	≤	≤	NOUN
ejpam-4015	25	9	1	1	NUM
ejpam-4015	25	10	b−	b−	PROPN
ejpam-4015	25	11	a	a	DET
ejpam-4015	25	12	b∫	b∫	PROPN
ejpam-4015	25	13	a	a	DET
ejpam-4015	25	14	f(y)dy	f(y)dy	ADV
ejpam-4015	25	15	≤	≤	NUM
ejpam-4015	25	16	f(a	f(a	NOUN
ejpam-4015	25	17	)	)	PUNCT
ejpam-4015	25	18	+	+	CCONJ
ejpam-4015	25	19	f(b	f(b	X
ejpam-4015	25	20	)	)	PUNCT
ejpam-4015	25	21	2	2	NUM
ejpam-4015	25	22	(	(	PUNCT
ejpam-4015	25	23	1	1	NUM
ejpam-4015	25	24	)	)	PUNCT
ejpam-4015	25	25	this	this	DET
ejpam-4015	25	26	result	result	NOUN
ejpam-4015	25	27	is	be	AUX
ejpam-4015	25	28	known	know	VERB
ejpam-4015	25	29	as	as	ADP
ejpam-4015	25	30	hermite−hadamard	hermite−hadamard	ADV
ejpam-4015	25	31	dual	dual	ADJ
ejpam-4015	25	32	inequality	inequality	NOUN
ejpam-4015	25	33	for	for	ADP
ejpam-4015	25	34	convex	convex	ADJ
ejpam-4015	25	35	function	function	NOUN
ejpam-4015	25	36	.	.	PUNCT
ejpam-4015	26	1	for	for	ADP
ejpam-4015	26	2	concave	concave	PROPN
ejpam-4015	26	3	function	function	PROPN
ejpam-4015	26	4	f	f	PROPN
ejpam-4015	26	5	,	,	PUNCT
ejpam-4015	26	6	both	both	DET
ejpam-4015	26	7	inequalities	inequality	NOUN
ejpam-4015	26	8	would	would	AUX
ejpam-4015	26	9	be	be	AUX
ejpam-4015	26	10	in	in	ADP
ejpam-4015	26	11	reverse	reverse	ADJ
ejpam-4015	26	12	order	order	NOUN
ejpam-4015	26	13	.	.	PUNCT
ejpam-4015	27	1	it	it	PRON
ejpam-4015	27	2	is	be	AUX
ejpam-4015	27	3	to	to	PART
ejpam-4015	27	4	be	be	AUX
ejpam-4015	27	5	noted	note	VERB
ejpam-4015	27	6	that	that	SCONJ
ejpam-4015	27	7	hadamard	hadamard	PROPN
ejpam-4015	27	8	’s	’s	PART
ejpam-4015	27	9	inequality	inequality	NOUN
ejpam-4015	27	10	may	may	AUX
ejpam-4015	27	11	be	be	AUX
ejpam-4015	27	12	regarded	regard	VERB
ejpam-4015	27	13	as	as	ADP
ejpam-4015	27	14	a	a	DET
ejpam-4015	27	15	refinement	refinement	NOUN
ejpam-4015	27	16	and	and	CCONJ
ejpam-4015	27	17	it	it	PRON
ejpam-4015	27	18	follows	follow	VERB
ejpam-4015	27	19	easily	easily	ADV
ejpam-4015	27	20	from	from	ADP
ejpam-4015	27	21	jensen	jensen	PROPN
ejpam-4015	27	22	’s	’s	PART
ejpam-4015	27	23	inequality	inequality	NOUN
ejpam-4015	27	24	.	.	PUNCT
ejpam-4015	28	1	hadamard	hadamard	PROPN
ejpam-4015	28	2	’s	’s	PART
ejpam-4015	28	3	inequality	inequality	NOUN
ejpam-4015	28	4	for	for	ADP
ejpam-4015	28	5	convex	convex	NOUN
ejpam-4015	28	6	function	function	NOUN
ejpam-4015	28	7	has	have	AUX
ejpam-4015	28	8	been	be	AUX
ejpam-4015	28	9	given	give	VERB
ejpam-4015	28	10	an	an	DET
ejpam-4015	28	11	illustrious	illustrious	ADJ
ejpam-4015	28	12	attention	attention	NOUN
ejpam-4015	28	13	in	in	ADP
ejpam-4015	28	14	recent	recent	ADJ
ejpam-4015	28	15	years	year	NOUN
ejpam-4015	28	16	and	and	CCONJ
ejpam-4015	28	17	a	a	DET
ejpam-4015	28	18	considerable	considerable	ADJ
ejpam-4015	28	19	variety	variety	NOUN
ejpam-4015	28	20	of	of	ADP
ejpam-4015	28	21	refinements	refinement	NOUN
ejpam-4015	28	22	(	(	PUNCT
ejpam-4015	28	23	see	see	VERB
ejpam-4015	28	24	[	[	X
ejpam-4015	28	25	1	1	NUM
ejpam-4015	28	26	]	]	PUNCT
ejpam-4015	28	27	–	–	PUNCT
ejpam-4015	29	1	[	[	X
ejpam-4015	29	2	5	5	NUM
ejpam-4015	29	3	]	]	PUNCT
ejpam-4015	29	4	,	,	PUNCT
ejpam-4015	29	5	[	[	X
ejpam-4015	29	6	9	9	NUM
ejpam-4015	29	7	]	]	PUNCT
ejpam-4015	29	8	and	and	CCONJ
ejpam-4015	30	1	[	[	X
ejpam-4015	30	2	11	11	NUM
ejpam-4015	30	3	]	]	PUNCT
ejpam-4015	30	4	–	–	PUNCT
ejpam-4015	30	5	[	[	X
ejpam-4015	30	6	16	16	NUM
ejpam-4015	30	7	]	]	PUNCT
ejpam-4015	30	8	)	)	PUNCT
ejpam-4015	30	9	.	.	PUNCT
ejpam-4015	31	1	we	we	PRON
ejpam-4015	31	2	recall	recall	VERB
ejpam-4015	31	3	here	here	ADV
ejpam-4015	31	4	definition	definition	NOUN
ejpam-4015	31	5	of	of	ADP
ejpam-4015	31	6	p−convex	p−convex	NOUN
ejpam-4015	31	7	function	function	NOUN
ejpam-4015	31	8	from	from	ADP
ejpam-4015	31	9	[	[	X
ejpam-4015	31	10	13	13	NUM
ejpam-4015	31	11	]	]	NUM
ejpam-4015	31	12	:	:	PUNCT
ejpam-4015	31	13	definition	definition	NOUN
ejpam-4015	31	14	1	1	NUM
ejpam-4015	31	15	.	.	PUNCT
ejpam-4015	32	1	a	a	DET
ejpam-4015	32	2	function	function	NOUN
ejpam-4015	32	3	f	f	NOUN
ejpam-4015	32	4	:	:	PUNCT
ejpam-4015	32	5	i	i	PRON
ejpam-4015	32	6	⊂	⊂	PROPN
ejpam-4015	32	7	(	(	PUNCT
ejpam-4015	32	8	0,∞)→	0,∞)→	NOUN
ejpam-4015	32	9	r	r	NOUN
ejpam-4015	32	10	is	be	AUX
ejpam-4015	32	11	said	say	VERB
ejpam-4015	32	12	to	to	PART
ejpam-4015	32	13	be	be	AUX
ejpam-4015	32	14	p−convex	p−convex	NOUN
ejpam-4015	32	15	,	,	PUNCT
ejpam-4015	32	16	if	if	SCONJ
ejpam-4015	32	17	f	f	PROPN
ejpam-4015	32	18	(	(	PUNCT
ejpam-4015	32	19	[	[	X
ejpam-4015	32	20	txp	txp	X
ejpam-4015	32	21	+	+	CCONJ
ejpam-4015	32	22	(	(	PUNCT
ejpam-4015	32	23	1−	1−	NUM
ejpam-4015	32	24	t)yp	t)yp	NOUN
ejpam-4015	32	25	]	]	X
ejpam-4015	32	26	1	1	NUM
ejpam-4015	32	27	p	p	NOUN
ejpam-4015	32	28	)	)	PUNCT
ejpam-4015	32	29	≤	≤	NOUN
ejpam-4015	32	30	tf(x	tf(x	NUM
ejpam-4015	32	31	)	)	PUNCT
ejpam-4015	33	1	+	+	CCONJ
ejpam-4015	33	2	(	(	PUNCT
ejpam-4015	33	3	1−	1−	NUM
ejpam-4015	33	4	t)f(y	t)f(y	NOUN
ejpam-4015	33	5	)	)	PUNCT
ejpam-4015	33	6	,	,	PUNCT
ejpam-4015	33	7	for	for	ADP
ejpam-4015	33	8	all	all	DET
ejpam-4015	33	9	x	x	NOUN
ejpam-4015	33	10	,	,	PUNCT
ejpam-4015	33	11	y	y	PROPN
ejpam-4015	33	12	∈	∈	PROPN
ejpam-4015	34	1	i	i	PRON
ejpam-4015	34	2	and	and	CCONJ
ejpam-4015	34	3	t	t	PROPN
ejpam-4015	34	4	∈	∈	PROPN
ejpam-4015	35	1	[	[	X
ejpam-4015	35	2	0	0	NUM
ejpam-4015	35	3	,	,	PUNCT
ejpam-4015	35	4	1	1	NUM
ejpam-4015	35	5	]	]	PUNCT
ejpam-4015	35	6	.	.	PUNCT
ejpam-4015	36	1	remark	remark	PROPN
ejpam-4015	36	2	1	1	NUM
ejpam-4015	36	3	.	.	PUNCT
ejpam-4015	37	1	if	if	SCONJ
ejpam-4015	37	2	we	we	PRON
ejpam-4015	37	3	choose	choose	VERB
ejpam-4015	37	4	p	p	NOUN
ejpam-4015	37	5	=	=	NOUN
ejpam-4015	37	6	1	1	NUM
ejpam-4015	37	7	and	and	CCONJ
ejpam-4015	37	8	p	p	NOUN
ejpam-4015	37	9	=	=	NOUN
ejpam-4015	37	10	−1	−1	NOUN
ejpam-4015	37	11	in	in	ADP
ejpam-4015	37	12	definition	definition	NOUN
ejpam-4015	37	13	1	1	NUM
ejpam-4015	37	14	,	,	PUNCT
ejpam-4015	37	15	we	we	PRON
ejpam-4015	37	16	get	get	VERB
ejpam-4015	37	17	the	the	DET
ejpam-4015	37	18	ordinary	ordinary	ADJ
ejpam-4015	37	19	convex	convex	NOUN
ejpam-4015	37	20	function	function	NOUN
ejpam-4015	37	21	[	[	X
ejpam-4015	37	22	4	4	NUM
ejpam-4015	37	23	]	]	PUNCT
ejpam-4015	37	24	and	and	CCONJ
ejpam-4015	37	25	harmonically	harmonically	ADV
ejpam-4015	37	26	convex	convex	VERB
ejpam-4015	37	27	function	function	NOUN
ejpam-4015	37	28	[	[	X
ejpam-4015	37	29	11	11	NUM
ejpam-4015	37	30	]	]	PUNCT
ejpam-4015	37	31	.	.	PUNCT
ejpam-4015	38	1	here	here	ADV
ejpam-4015	38	2	,	,	PUNCT
ejpam-4015	38	3	we	we	PRON
ejpam-4015	38	4	are	be	AUX
ejpam-4015	38	5	going	go	VERB
ejpam-4015	38	6	to	to	PART
ejpam-4015	38	7	introduce	introduce	VERB
ejpam-4015	38	8	some	some	DET
ejpam-4015	38	9	new	new	ADJ
ejpam-4015	38	10	types	type	NOUN
ejpam-4015	38	11	of	of	ADP
ejpam-4015	38	12	p−convex	p−convex	NOUN
ejpam-4015	38	13	function	function	NOUN
ejpam-4015	38	14	,	,	PUNCT
ejpam-4015	38	15	which	which	PRON
ejpam-4015	38	16	we	we	PRON
ejpam-4015	38	17	call	call	VERB
ejpam-4015	38	18	as	as	ADP
ejpam-4015	38	19	quasi	quasi	ADJ
ejpam-4015	38	20	p−convex	p−convex	NOUN
ejpam-4015	38	21	function	function	NOUN
ejpam-4015	38	22	and	and	CCONJ
ejpam-4015	38	23	p	p	NOUN
ejpam-4015	38	24	−	−	PROPN
ejpam-4015	38	25	p−convex	p−convex	NOUN
ejpam-4015	38	26	function	function	VERB
ejpam-4015	38	27	respectively	respectively	ADV
ejpam-4015	38	28	.	.	PUNCT
ejpam-4015	39	1	definition	definition	NOUN
ejpam-4015	39	2	2	2	NUM
ejpam-4015	39	3	.	.	PUNCT
ejpam-4015	40	1	let	let	VERB
ejpam-4015	40	2	p	p	PRON
ejpam-4015	40	3	∈	∈	PROPN
ejpam-4015	40	4	r	r	NOUN
ejpam-4015	40	5	\	\	PUNCT
ejpam-4015	40	6	{	{	PUNCT
ejpam-4015	40	7	0	0	NUM
ejpam-4015	40	8	}	}	PUNCT
ejpam-4015	40	9	.	.	PUNCT
ejpam-4015	41	1	a	a	DET
ejpam-4015	41	2	function	function	NOUN
ejpam-4015	41	3	f	f	NOUN
ejpam-4015	41	4	:	:	PUNCT
ejpam-4015	41	5	i	i	PRON
ejpam-4015	41	6	⊂	⊂	PROPN
ejpam-4015	41	7	(	(	PUNCT
ejpam-4015	41	8	0,∞	0,∞	NUM
ejpam-4015	41	9	)	)	PUNCT
ejpam-4015	41	10	→	→	PUNCT
ejpam-4015	42	1	[	[	X
ejpam-4015	42	2	0,∞	0,∞	NOUN
ejpam-4015	42	3	)	)	PUNCT
ejpam-4015	42	4	is	be	AUX
ejpam-4015	42	5	known	know	VERB
ejpam-4015	42	6	as	as	ADP
ejpam-4015	42	7	quasi	quasi	NOUN
ejpam-4015	42	8	p−convex	p−convex	NOUN
ejpam-4015	42	9	,	,	PUNCT
ejpam-4015	42	10	if	if	SCONJ
ejpam-4015	42	11	f	f	PROPN
ejpam-4015	42	12	(	(	PUNCT
ejpam-4015	42	13	[	[	X
ejpam-4015	42	14	txp	txp	X
ejpam-4015	42	15	+	+	CCONJ
ejpam-4015	42	16	(	(	PUNCT
ejpam-4015	42	17	1−	1−	NUM
ejpam-4015	42	18	t)yp	t)yp	NOUN
ejpam-4015	42	19	]	]	X
ejpam-4015	42	20	1	1	NUM
ejpam-4015	42	21	p	p	NOUN
ejpam-4015	42	22	)	)	PUNCT
ejpam-4015	42	23	≤	≤	NUM
ejpam-4015	42	24	max{f(x	max{f(x	PROPN
ejpam-4015	42	25	)	)	PUNCT
ejpam-4015	42	26	,	,	PUNCT
ejpam-4015	42	27	f(y	f(y	NOUN
ejpam-4015	42	28	)	)	PUNCT
ejpam-4015	42	29	}	}	PUNCT
ejpam-4015	42	30	for	for	ADP
ejpam-4015	42	31	all	all	DET
ejpam-4015	42	32	x	x	NOUN
ejpam-4015	42	33	,	,	PUNCT
ejpam-4015	42	34	y	y	PROPN
ejpam-4015	42	35	∈	∈	PROPN
ejpam-4015	43	1	i	i	PRON
ejpam-4015	43	2	and	and	CCONJ
ejpam-4015	43	3	t	t	PROPN
ejpam-4015	43	4	∈	∈	PROPN
ejpam-4015	44	1	[	[	X
ejpam-4015	44	2	0	0	NUM
ejpam-4015	44	3	,	,	PUNCT
ejpam-4015	44	4	1	1	NUM
ejpam-4015	44	5	]	]	PUNCT
ejpam-4015	44	6	.	.	PUNCT
ejpam-4015	45	1	remark	remark	PROPN
ejpam-4015	45	2	2	2	NUM
ejpam-4015	45	3	.	.	PUNCT
ejpam-4015	46	1	if	if	SCONJ
ejpam-4015	46	2	we	we	PRON
ejpam-4015	46	3	choose	choose	VERB
ejpam-4015	46	4	p	p	NOUN
ejpam-4015	46	5	=	=	NOUN
ejpam-4015	46	6	1	1	NUM
ejpam-4015	46	7	in	in	ADP
ejpam-4015	46	8	definition	definition	NOUN
ejpam-4015	46	9	2	2	NUM
ejpam-4015	46	10	,	,	PUNCT
ejpam-4015	46	11	we	we	PRON
ejpam-4015	46	12	get	get	VERB
ejpam-4015	46	13	the	the	DET
ejpam-4015	46	14	quasi	quasi	ADJ
ejpam-4015	46	15	convex	convex	NOUN
ejpam-4015	46	16	function	function	NOUN
ejpam-4015	46	17	[	[	X
ejpam-4015	46	18	14	14	NUM
ejpam-4015	46	19	]	]	PUNCT
ejpam-4015	46	20	.	.	PUNCT
ejpam-4015	47	1	definition	definition	NOUN
ejpam-4015	47	2	3	3	X
ejpam-4015	47	3	.	.	PUNCT
ejpam-4015	48	1	let	let	VERB
ejpam-4015	48	2	p	p	PRON
ejpam-4015	48	3	∈	∈	PROPN
ejpam-4015	48	4	r	r	NOUN
ejpam-4015	48	5	\	\	PUNCT
ejpam-4015	48	6	{	{	PUNCT
ejpam-4015	48	7	0	0	NUM
ejpam-4015	48	8	}	}	PUNCT
ejpam-4015	48	9	.	.	PUNCT
ejpam-4015	49	1	we	we	PRON
ejpam-4015	49	2	say	say	VERB
ejpam-4015	49	3	that	that	SCONJ
ejpam-4015	49	4	f	f	X
ejpam-4015	49	5	:	:	PUNCT
ejpam-4015	50	1	i	i	PRON
ejpam-4015	50	2	⊂	⊂	PROPN
ejpam-4015	50	3	(	(	PUNCT
ejpam-4015	50	4	0,∞	0,∞	NUM
ejpam-4015	50	5	)	)	PUNCT
ejpam-4015	50	6	→	→	PUNCT
ejpam-4015	51	1	[	[	X
ejpam-4015	51	2	0,∞	0,∞	NUM
ejpam-4015	51	3	)	)	PUNCT
ejpam-4015	51	4	is	be	AUX
ejpam-4015	51	5	a	a	DET
ejpam-4015	51	6	p	p	NOUN
ejpam-4015	51	7	−	−	NOUN
ejpam-4015	51	8	p−convex	p−convex	NOUN
ejpam-4015	51	9	function	function	NOUN
ejpam-4015	51	10	,	,	PUNCT
ejpam-4015	51	11	if	if	SCONJ
ejpam-4015	51	12	f	f	PROPN
ejpam-4015	51	13	is	be	AUX
ejpam-4015	51	14	a	a	DET
ejpam-4015	51	15	non	non	ADJ
ejpam-4015	51	16	-	-	ADJ
ejpam-4015	51	17	negative	negative	ADJ
ejpam-4015	51	18	and	and	CCONJ
ejpam-4015	51	19	for	for	ADP
ejpam-4015	51	20	all	all	DET
ejpam-4015	51	21	x	x	NOUN
ejpam-4015	51	22	,	,	PUNCT
ejpam-4015	51	23	y	y	PROPN
ejpam-4015	51	24	∈	∈	PROPN
ejpam-4015	52	1	i	i	PRON
ejpam-4015	52	2	and	and	CCONJ
ejpam-4015	52	3	t	t	PROPN
ejpam-4015	52	4	∈	∈	PROPN
ejpam-4015	53	1	[	[	X
ejpam-4015	53	2	0	0	NUM
ejpam-4015	53	3	,	,	PUNCT
ejpam-4015	53	4	1	1	NUM
ejpam-4015	53	5	]	]	PUNCT
ejpam-4015	53	6	,	,	PUNCT
ejpam-4015	53	7	we	we	PRON
ejpam-4015	53	8	have	have	VERB
ejpam-4015	53	9	f	f	X
ejpam-4015	53	10	(	(	PUNCT
ejpam-4015	53	11	[	[	X
ejpam-4015	53	12	txp	txp	X
ejpam-4015	53	13	+	+	CCONJ
ejpam-4015	53	14	(	(	PUNCT
ejpam-4015	53	15	1−	1−	NUM
ejpam-4015	53	16	t)yp	t)yp	NOUN
ejpam-4015	53	17	]	]	X
ejpam-4015	53	18	1	1	NUM
ejpam-4015	53	19	p	p	NOUN
ejpam-4015	53	20	)	)	PUNCT
ejpam-4015	53	21	≤	≤	NOUN
ejpam-4015	53	22	f(x	f(x	PROPN
ejpam-4015	53	23	)	)	PUNCT
ejpam-4015	54	1	+	+	SYM
ejpam-4015	54	2	f(y	f(y	NOUN
ejpam-4015	54	3	)	)	PUNCT
ejpam-4015	54	4	.	.	PUNCT
ejpam-4015	55	1	remark	remark	PROPN
ejpam-4015	55	2	3	3	NUM
ejpam-4015	55	3	.	.	PUNCT
ejpam-4015	56	1	if	if	SCONJ
ejpam-4015	56	2	we	we	PRON
ejpam-4015	56	3	choose	choose	VERB
ejpam-4015	56	4	p	p	NOUN
ejpam-4015	56	5	=	=	NOUN
ejpam-4015	56	6	1	1	NUM
ejpam-4015	56	7	in	in	ADP
ejpam-4015	56	8	definition	definition	NOUN
ejpam-4015	56	9	3	3	NUM
ejpam-4015	56	10	,	,	PUNCT
ejpam-4015	56	11	we	we	PRON
ejpam-4015	56	12	get	get	VERB
ejpam-4015	56	13	the	the	DET
ejpam-4015	56	14	p−convex	p−convex	NOUN
ejpam-4015	56	15	function	function	NOUN
ejpam-4015	56	16	[	[	X
ejpam-4015	56	17	8	8	NUM
ejpam-4015	56	18	]	]	PUNCT
ejpam-4015	56	19	.	.	PUNCT
ejpam-4015	57	1	now	now	ADV
ejpam-4015	57	2	,	,	PUNCT
ejpam-4015	57	3	we	we	PRON
ejpam-4015	57	4	are	be	AUX
ejpam-4015	57	5	going	go	VERB
ejpam-4015	57	6	to	to	PART
ejpam-4015	57	7	present	present	VERB
ejpam-4015	57	8	the	the	DET
ejpam-4015	57	9	definitions	definition	NOUN
ejpam-4015	57	10	of	of	ADP
ejpam-4015	57	11	s	s	PRON
ejpam-4015	57	12	−	−	PROPN
ejpam-4015	57	13	p−	p−	NOUN
ejpam-4015	57	14	convex	convex	NOUN
ejpam-4015	57	15	functions	function	NOUN
ejpam-4015	57	16	of	of	ADP
ejpam-4015	57	17	first	first	ADJ
ejpam-4015	57	18	and	and	CCONJ
ejpam-4015	57	19	second	second	ADJ
ejpam-4015	57	20	kind	kind	NOUN
ejpam-4015	57	21	extracted	extract	VERB
ejpam-4015	57	22	from	from	ADP
ejpam-4015	57	23	[	[	X
ejpam-4015	57	24	1	1	NUM
ejpam-4015	57	25	]	]	PUNCT
ejpam-4015	57	26	,	,	PUNCT
ejpam-4015	57	27	which	which	PRON
ejpam-4015	57	28	can	can	AUX
ejpam-4015	57	29	be	be	AUX
ejpam-4015	57	30	used	use	VERB
ejpam-4015	57	31	to	to	PART
ejpam-4015	57	32	generalize	generalize	VERB
ejpam-4015	57	33	the	the	DET
ejpam-4015	57	34	results	result	NOUN
ejpam-4015	57	35	for	for	ADP
ejpam-4015	57	36	hermite−hadamard	hermite−hadamard	ADJ
ejpam-4015	57	37	type	type	NOUN
ejpam-4015	57	38	inequality	inequality	NOUN
ejpam-4015	57	39	given	give	VERB
ejpam-4015	57	40	in	in	ADP
ejpam-4015	57	41	[	[	X
ejpam-4015	57	42	16	16	NUM
ejpam-4015	57	43	]	]	PUNCT
ejpam-4015	57	44	.	.	PUNCT
ejpam-4015	58	1	muhammad	muhammad	PROPN
ejpam-4015	58	2	bilal	bilal	PROPN
ejpam-4015	58	3	,	,	PUNCT
ejpam-4015	58	4	asif	asif	PROPN
ejpam-4015	58	5	r.	r.	PROPN
ejpam-4015	58	6	khan	khan	PROPN
ejpam-4015	58	7	/	/	SYM
ejpam-4015	58	8	eur	eur	PROPN
ejpam-4015	58	9	.	.	PUNCT
ejpam-4015	59	1	j.	j.	PROPN
ejpam-4015	59	2	pure	pure	PROPN
ejpam-4015	59	3	appl	appl	PROPN
ejpam-4015	59	4	.	.	PROPN
ejpam-4015	59	5	math	math	PROPN
ejpam-4015	59	6	,	,	PUNCT
ejpam-4015	59	7	14	14	NUM
ejpam-4015	59	8	(	(	PUNCT
ejpam-4015	59	9	3	3	NUM
ejpam-4015	59	10	)	)	PUNCT
ejpam-4015	59	11	(	(	PUNCT
ejpam-4015	59	12	2021	2021	NUM
ejpam-4015	59	13	)	)	PUNCT
ejpam-4015	59	14	,	,	PUNCT
ejpam-4015	59	15	863	863	NUM
ejpam-4015	59	16	-	-	SYM
ejpam-4015	59	17	880	880	NUM
ejpam-4015	59	18	865	865	NUM
ejpam-4015	59	19	definition	definition	NOUN
ejpam-4015	59	20	4	4	NUM
ejpam-4015	59	21	.	.	PUNCT
ejpam-4015	60	1	[	[	X
ejpam-4015	60	2	1	1	X
ejpam-4015	60	3	]	]	PUNCT
ejpam-4015	60	4	let	let	VERB
ejpam-4015	60	5	s	s	PRON
ejpam-4015	60	6	∈	∈	NOUN
ejpam-4015	61	1	[	[	X
ejpam-4015	61	2	0	0	NUM
ejpam-4015	61	3	,	,	PUNCT
ejpam-4015	61	4	1	1	NUM
ejpam-4015	61	5	]	]	PUNCT
ejpam-4015	61	6	,	,	PUNCT
ejpam-4015	61	7	p	p	PROPN
ejpam-4015	61	8	∈	∈	PROPN
ejpam-4015	61	9	r	r	NOUN
ejpam-4015	61	10	\	\	PUNCT
ejpam-4015	61	11	{	{	PUNCT
ejpam-4015	61	12	0	0	NUM
ejpam-4015	61	13	}	}	PUNCT
ejpam-4015	61	14	.	.	PUNCT
ejpam-4015	62	1	a	a	DET
ejpam-4015	62	2	function	function	NOUN
ejpam-4015	62	3	f	f	NOUN
ejpam-4015	62	4	:	:	PUNCT
ejpam-4015	62	5	i	i	PRON
ejpam-4015	62	6	⊂	⊂	X
ejpam-4015	62	7	(	(	PUNCT
ejpam-4015	62	8	0,∞)→	0,∞)→	NOUN
ejpam-4015	63	1	[	[	X
ejpam-4015	63	2	0,∞	0,∞	NOUN
ejpam-4015	63	3	)	)	PUNCT
ejpam-4015	63	4	is	be	AUX
ejpam-4015	63	5	said	say	VERB
ejpam-4015	63	6	to	to	PART
ejpam-4015	63	7	be	be	AUX
ejpam-4015	63	8	the	the	DET
ejpam-4015	63	9	s−	s−	PROPN
ejpam-4015	63	10	p−convex	p−convex	NOUN
ejpam-4015	63	11	function	function	NOUN
ejpam-4015	63	12	in	in	ADP
ejpam-4015	63	13	1st	1st	ADJ
ejpam-4015	63	14	kind	kind	NOUN
ejpam-4015	63	15	,	,	PUNCT
ejpam-4015	63	16	if	if	SCONJ
ejpam-4015	63	17	f	f	PROPN
ejpam-4015	63	18	(	(	PUNCT
ejpam-4015	63	19	[	[	X
ejpam-4015	63	20	txp	txp	X
ejpam-4015	63	21	+	+	CCONJ
ejpam-4015	63	22	(	(	PUNCT
ejpam-4015	63	23	1−	1−	NUM
ejpam-4015	63	24	t)yp	t)yp	NOUN
ejpam-4015	63	25	]	]	X
ejpam-4015	63	26	1	1	NUM
ejpam-4015	63	27	p	p	NOUN
ejpam-4015	63	28	)	)	PUNCT
ejpam-4015	63	29	≤	≤	NOUN
ejpam-4015	63	30	tsf(x	tsf(x	ADP
ejpam-4015	63	31	)	)	PUNCT
ejpam-4015	63	32	+	+	CCONJ
ejpam-4015	63	33	(	(	PUNCT
ejpam-4015	63	34	1−	1−	NUM
ejpam-4015	63	35	ts)f(y	ts)f(y	NUM
ejpam-4015	63	36	)	)	PUNCT
ejpam-4015	63	37	,	,	PUNCT
ejpam-4015	63	38	for	for	ADP
ejpam-4015	63	39	all	all	DET
ejpam-4015	63	40	x	x	NOUN
ejpam-4015	63	41	,	,	PUNCT
ejpam-4015	63	42	y	y	PROPN
ejpam-4015	63	43	∈	∈	PROPN
ejpam-4015	63	44	i	i	PRON
ejpam-4015	63	45	and	and	CCONJ
ejpam-4015	63	46	t	t	PROPN
ejpam-4015	63	47	∈	∈	PROPN
ejpam-4015	64	1	[	[	X
ejpam-4015	64	2	0	0	NUM
ejpam-4015	64	3	,	,	PUNCT
ejpam-4015	64	4	1	1	NUM
ejpam-4015	64	5	]	]	PUNCT
ejpam-4015	64	6	.	.	PUNCT
ejpam-4015	65	1	remark	remark	PROPN
ejpam-4015	65	2	4	4	NUM
ejpam-4015	65	3	.	.	PUNCT
ejpam-4015	66	1	following	follow	VERB
ejpam-4015	66	2	result	result	NOUN
ejpam-4015	66	3	will	will	AUX
ejpam-4015	66	4	be	be	AUX
ejpam-4015	66	5	obtained	obtain	VERB
ejpam-4015	66	6	by	by	ADP
ejpam-4015	66	7	replacing	replace	VERB
ejpam-4015	66	8	different	different	ADJ
ejpam-4015	66	9	values	value	NOUN
ejpam-4015	66	10	of	of	ADP
ejpam-4015	66	11	s	s	PRON
ejpam-4015	66	12	and	and	CCONJ
ejpam-4015	66	13	p	p	X
ejpam-4015	66	14	:	:	PUNCT
ejpam-4015	66	15	(	(	PUNCT
ejpam-4015	66	16	i	i	NOUN
ejpam-4015	66	17	)	)	PUNCT
ejpam-4015	66	18	note	note	VERB
ejpam-4015	66	19	that	that	SCONJ
ejpam-4015	66	20	in	in	ADP
ejpam-4015	66	21	the	the	DET
ejpam-4015	66	22	above	above	ADJ
ejpam-4015	66	23	definition	definition	NOUN
ejpam-4015	66	24	we	we	PRON
ejpam-4015	66	25	also	also	ADV
ejpam-4015	66	26	include	include	VERB
ejpam-4015	66	27	s	s	NOUN
ejpam-4015	66	28	=	=	SYM
ejpam-4015	66	29	0	0	NUM
ejpam-4015	66	30	.	.	PUNCT
ejpam-4015	67	1	further	far	ADV
ejpam-4015	67	2	,	,	PUNCT
ejpam-4015	67	3	if	if	SCONJ
ejpam-4015	67	4	we	we	PRON
ejpam-4015	67	5	put	put	VERB
ejpam-4015	67	6	s	s	NOUN
ejpam-4015	67	7	=	=	NOUN
ejpam-4015	67	8	0	0	NUM
ejpam-4015	67	9	,	,	PUNCT
ejpam-4015	67	10	we	we	PRON
ejpam-4015	67	11	easily	easily	ADV
ejpam-4015	67	12	get	get	VERB
ejpam-4015	67	13	the	the	DET
ejpam-4015	67	14	refinement	refinement	NOUN
ejpam-4015	67	15	of	of	ADP
ejpam-4015	67	16	definition	definition	NOUN
ejpam-4015	67	17	2	2	NUM
ejpam-4015	67	18	,	,	PUNCT
ejpam-4015	67	19	i.e.	i.e.	X
ejpam-4015	67	20	,	,	PUNCT
ejpam-4015	67	21	f	f	PROPN
ejpam-4015	67	22	(	(	PUNCT
ejpam-4015	67	23	[	[	X
ejpam-4015	67	24	txp	txp	X
ejpam-4015	67	25	+	+	CCONJ
ejpam-4015	67	26	(	(	PUNCT
ejpam-4015	67	27	1−	1−	NUM
ejpam-4015	67	28	t)yp	t)yp	NOUN
ejpam-4015	67	29	]	]	X
ejpam-4015	67	30	1	1	NUM
ejpam-4015	67	31	p	p	NOUN
ejpam-4015	67	32	)	)	PUNCT
ejpam-4015	67	33	≤	≤	NOUN
ejpam-4015	67	34	f(x	f(x	PROPN
ejpam-4015	67	35	)	)	PUNCT
ejpam-4015	67	36	≤	≤	NUM
ejpam-4015	67	37	max{f(x	max{f(x	PROPN
ejpam-4015	67	38	)	)	PUNCT
ejpam-4015	67	39	,	,	PUNCT
ejpam-4015	67	40	f(y	f(y	NOUN
ejpam-4015	67	41	)	)	PUNCT
ejpam-4015	67	42	}	}	PUNCT
ejpam-4015	67	43	(	(	PUNCT
ejpam-4015	67	44	ii	ii	NOUN
ejpam-4015	67	45	)	)	PUNCT
ejpam-4015	67	46	if	if	SCONJ
ejpam-4015	67	47	we	we	PRON
ejpam-4015	67	48	choose	choose	VERB
ejpam-4015	67	49	p	p	NOUN
ejpam-4015	67	50	=	=	NOUN
ejpam-4015	67	51	1	1	NUM
ejpam-4015	67	52	in	in	ADP
ejpam-4015	67	53	definition	definition	NOUN
ejpam-4015	67	54	4	4	NUM
ejpam-4015	67	55	,	,	PUNCT
ejpam-4015	67	56	we	we	PRON
ejpam-4015	67	57	get	get	VERB
ejpam-4015	67	58	the	the	DET
ejpam-4015	67	59	s−convex	s−convex	NOUN
ejpam-4015	67	60	function	function	NOUN
ejpam-4015	67	61	in	in	ADP
ejpam-4015	67	62	1st	1st	ADJ
ejpam-4015	67	63	kind	kind	NOUN
ejpam-4015	68	1	[	[	X
ejpam-4015	68	2	19	19	NUM
ejpam-4015	68	3	]	]	PUNCT
ejpam-4015	68	4	.	.	PUNCT
ejpam-4015	69	1	definition	definition	NOUN
ejpam-4015	69	2	5	5	NUM
ejpam-4015	69	3	.	.	PUNCT
ejpam-4015	70	1	[	[	X
ejpam-4015	70	2	1	1	X
ejpam-4015	70	3	]	]	PUNCT
ejpam-4015	70	4	let	let	VERB
ejpam-4015	70	5	s	s	PRON
ejpam-4015	70	6	∈	∈	NOUN
ejpam-4015	71	1	[	[	X
ejpam-4015	71	2	0	0	NUM
ejpam-4015	71	3	,	,	PUNCT
ejpam-4015	71	4	1	1	NUM
ejpam-4015	71	5	]	]	PUNCT
ejpam-4015	71	6	and	and	CCONJ
ejpam-4015	71	7	p	p	NOUN
ejpam-4015	71	8	∈	∈	PROPN
ejpam-4015	71	9	r	r	NOUN
ejpam-4015	71	10	\	\	PUNCT
ejpam-4015	71	11	{	{	PUNCT
ejpam-4015	71	12	0	0	NUM
ejpam-4015	71	13	}	}	PUNCT
ejpam-4015	71	14	.	.	PUNCT
ejpam-4015	72	1	a	a	DET
ejpam-4015	72	2	function	function	NOUN
ejpam-4015	72	3	f	f	NOUN
ejpam-4015	72	4	:	:	PUNCT
ejpam-4015	72	5	i	i	PRON
ejpam-4015	72	6	⊂	⊂	PROPN
ejpam-4015	72	7	(	(	PUNCT
ejpam-4015	72	8	0,∞	0,∞	NUM
ejpam-4015	72	9	)	)	PUNCT
ejpam-4015	72	10	→	→	PUNCT
ejpam-4015	73	1	[	[	X
ejpam-4015	73	2	0,∞	0,∞	NOUN
ejpam-4015	73	3	)	)	PUNCT
ejpam-4015	73	4	is	be	AUX
ejpam-4015	73	5	said	say	VERB
ejpam-4015	73	6	to	to	PART
ejpam-4015	73	7	be	be	AUX
ejpam-4015	73	8	the	the	DET
ejpam-4015	73	9	s−	s−	PROPN
ejpam-4015	73	10	p−convex	p−convex	NOUN
ejpam-4015	73	11	function	function	NOUN
ejpam-4015	73	12	in	in	ADP
ejpam-4015	73	13	2nd	2nd	ADJ
ejpam-4015	73	14	kind	kind	NOUN
ejpam-4015	73	15	,	,	PUNCT
ejpam-4015	73	16	if	if	SCONJ
ejpam-4015	73	17	f	f	PROPN
ejpam-4015	73	18	(	(	PUNCT
ejpam-4015	73	19	[	[	X
ejpam-4015	73	20	txp	txp	X
ejpam-4015	73	21	+	+	CCONJ
ejpam-4015	73	22	(	(	PUNCT
ejpam-4015	73	23	1−	1−	NUM
ejpam-4015	73	24	t)yp	t)yp	NOUN
ejpam-4015	73	25	]	]	X
ejpam-4015	73	26	1	1	NUM
ejpam-4015	73	27	p	p	NOUN
ejpam-4015	73	28	)	)	PUNCT
ejpam-4015	73	29	≤	≤	NOUN
ejpam-4015	73	30	tsf(x	tsf(x	ADP
ejpam-4015	73	31	)	)	PUNCT
ejpam-4015	73	32	+	+	CCONJ
ejpam-4015	73	33	(	(	PUNCT
ejpam-4015	73	34	1−	1−	NUM
ejpam-4015	73	35	t)sf(y	t)sf(y	ADP
ejpam-4015	73	36	)	)	PUNCT
ejpam-4015	73	37	,	,	PUNCT
ejpam-4015	73	38	for	for	ADP
ejpam-4015	73	39	all	all	DET
ejpam-4015	73	40	x	x	NOUN
ejpam-4015	73	41	,	,	PUNCT
ejpam-4015	73	42	y	y	PROPN
ejpam-4015	73	43	∈	∈	PROPN
ejpam-4015	74	1	i	i	PRON
ejpam-4015	74	2	and	and	CCONJ
ejpam-4015	74	3	t	t	PROPN
ejpam-4015	74	4	∈	∈	PROPN
ejpam-4015	75	1	[	[	X
ejpam-4015	75	2	0	0	NUM
ejpam-4015	75	3	,	,	PUNCT
ejpam-4015	75	4	1	1	NUM
ejpam-4015	75	5	]	]	PUNCT
ejpam-4015	75	6	.	.	PUNCT
ejpam-4015	76	1	remark	remark	PROPN
ejpam-4015	76	2	5	5	NUM
ejpam-4015	76	3	.	.	PUNCT
ejpam-4015	77	1	following	follow	VERB
ejpam-4015	77	2	result	result	NOUN
ejpam-4015	77	3	will	will	AUX
ejpam-4015	77	4	be	be	AUX
ejpam-4015	77	5	obtained	obtain	VERB
ejpam-4015	77	6	by	by	ADP
ejpam-4015	77	7	replacing	replace	VERB
ejpam-4015	77	8	different	different	ADJ
ejpam-4015	77	9	values	value	NOUN
ejpam-4015	77	10	of	of	ADP
ejpam-4015	77	11	s	s	PRON
ejpam-4015	77	12	and	and	CCONJ
ejpam-4015	77	13	p	p	X
ejpam-4015	77	14	:	:	PUNCT
ejpam-4015	77	15	(	(	PUNCT
ejpam-4015	77	16	i	i	NOUN
ejpam-4015	77	17	)	)	PUNCT
ejpam-4015	77	18	in	in	ADP
ejpam-4015	77	19	the	the	DET
ejpam-4015	77	20	similar	similar	ADJ
ejpam-4015	77	21	manner	manner	NOUN
ejpam-4015	77	22	,	,	PUNCT
ejpam-4015	77	23	we	we	PRON
ejpam-4015	77	24	have	have	AUX
ejpam-4015	77	25	slightly	slightly	ADV
ejpam-4015	77	26	improved	improve	VERB
ejpam-4015	77	27	the	the	DET
ejpam-4015	77	28	above	above	ADJ
ejpam-4015	77	29	definition	definition	NOUN
ejpam-4015	77	30	by	by	ADP
ejpam-4015	77	31	including	include	VERB
ejpam-4015	77	32	s	s	NOUN
ejpam-4015	77	33	=	=	SYM
ejpam-4015	77	34	0	0	NUM
ejpam-4015	77	35	.	.	PUNCT
ejpam-4015	78	1	further	far	ADV
ejpam-4015	78	2	,	,	PUNCT
ejpam-4015	78	3	if	if	SCONJ
ejpam-4015	78	4	we	we	PRON
ejpam-4015	78	5	put	put	VERB
ejpam-4015	78	6	s	s	NOUN
ejpam-4015	78	7	=	=	NOUN
ejpam-4015	78	8	0	0	NUM
ejpam-4015	78	9	,	,	PUNCT
ejpam-4015	78	10	we	we	PRON
ejpam-4015	78	11	easily	easily	ADV
ejpam-4015	78	12	get	get	VERB
ejpam-4015	78	13	the	the	DET
ejpam-4015	78	14	definition	definition	NOUN
ejpam-4015	78	15	3	3	NUM
ejpam-4015	78	16	.	.	PUNCT
ejpam-4015	78	17	(	(	PUNCT
ejpam-4015	78	18	ii	ii	NOUN
ejpam-4015	78	19	)	)	PUNCT
ejpam-4015	78	20	if	if	SCONJ
ejpam-4015	78	21	we	we	PRON
ejpam-4015	78	22	choose	choose	VERB
ejpam-4015	78	23	p	p	NOUN
ejpam-4015	78	24	=	=	NOUN
ejpam-4015	78	25	1	1	NUM
ejpam-4015	78	26	in	in	ADP
ejpam-4015	78	27	definition	definition	NOUN
ejpam-4015	78	28	5	5	NUM
ejpam-4015	78	29	,	,	PUNCT
ejpam-4015	78	30	we	we	PRON
ejpam-4015	78	31	get	get	VERB
ejpam-4015	78	32	the	the	DET
ejpam-4015	78	33	s−convex	s−convex	NOUN
ejpam-4015	78	34	function	function	NOUN
ejpam-4015	78	35	in	in	ADP
ejpam-4015	78	36	2nd	2nd	ADJ
ejpam-4015	78	37	kind	kind	NOUN
ejpam-4015	79	1	[	[	X
ejpam-4015	79	2	7	7	NUM
ejpam-4015	79	3	]	]	PUNCT
ejpam-4015	79	4	.	.	PUNCT
ejpam-4015	80	1	now	now	ADV
ejpam-4015	80	2	,	,	PUNCT
ejpam-4015	80	3	we	we	PRON
ejpam-4015	80	4	are	be	AUX
ejpam-4015	80	5	going	go	VERB
ejpam-4015	80	6	to	to	PART
ejpam-4015	80	7	give	give	VERB
ejpam-4015	80	8	the	the	DET
ejpam-4015	80	9	definition	definition	NOUN
ejpam-4015	80	10	of	of	ADP
ejpam-4015	80	11	s	s	PRON
ejpam-4015	80	12	−	−	NOUN
ejpam-4015	80	13	p−convex	p−convex	NOUN
ejpam-4015	80	14	function	function	NOUN
ejpam-4015	80	15	in	in	ADP
ejpam-4015	80	16	mixed	mixed	ADJ
ejpam-4015	80	17	kind	kind	NOUN
ejpam-4015	80	18	(	(	PUNCT
ejpam-4015	80	19	or	or	CCONJ
ejpam-4015	80	20	(	(	PUNCT
ejpam-4015	80	21	s	s	NOUN
ejpam-4015	80	22	,	,	PUNCT
ejpam-4015	80	23	r)−p−convex	r)−p−convex	NOUN
ejpam-4015	80	24	function	function	NOUN
ejpam-4015	80	25	)	)	PUNCT
ejpam-4015	80	26	by	by	ADP
ejpam-4015	80	27	further	far	ADV
ejpam-4015	80	28	generalizing	generalize	VERB
ejpam-4015	80	29	the	the	DET
ejpam-4015	80	30	definitions	definition	NOUN
ejpam-4015	80	31	4	4	NUM
ejpam-4015	80	32	and	and	CCONJ
ejpam-4015	80	33	5	5	NUM
ejpam-4015	80	34	such	such	ADJ
ejpam-4015	80	35	that	that	SCONJ
ejpam-4015	80	36	we	we	PRON
ejpam-4015	80	37	can	can	AUX
ejpam-4015	80	38	easily	easily	ADV
ejpam-4015	80	39	obtained	obtain	VERB
ejpam-4015	80	40	both	both	DET
ejpam-4015	80	41	the	the	DET
ejpam-4015	80	42	definitions	definition	NOUN
ejpam-4015	80	43	by	by	ADP
ejpam-4015	80	44	imposing	impose	VERB
ejpam-4015	80	45	certain	certain	ADJ
ejpam-4015	80	46	restrictions	restriction	NOUN
ejpam-4015	80	47	on	on	ADP
ejpam-4015	80	48	r	r	NOUN
ejpam-4015	80	49	and	and	CCONJ
ejpam-4015	80	50	s.	s.	PROPN
ejpam-4015	80	51	definition	definition	NOUN
ejpam-4015	80	52	6	6	NUM
ejpam-4015	80	53	.	.	PUNCT
ejpam-4015	81	1	let	let	VERB
ejpam-4015	81	2	(	(	PUNCT
ejpam-4015	81	3	s	s	X
ejpam-4015	81	4	,	,	PUNCT
ejpam-4015	81	5	r	r	NOUN
ejpam-4015	81	6	)	)	PUNCT
ejpam-4015	81	7	∈	∈	NOUN
ejpam-4015	82	1	[	[	X
ejpam-4015	82	2	0	0	NUM
ejpam-4015	82	3	,	,	PUNCT
ejpam-4015	82	4	1]2	1]2	NUM
ejpam-4015	82	5	,	,	PUNCT
ejpam-4015	82	6	p	p	PROPN
ejpam-4015	82	7	∈	∈	PROPN
ejpam-4015	82	8	r	r	NOUN
ejpam-4015	82	9	\	\	PUNCT
ejpam-4015	82	10	{	{	PUNCT
ejpam-4015	82	11	0	0	NUM
ejpam-4015	82	12	}	}	PUNCT
ejpam-4015	82	13	.	.	PUNCT
ejpam-4015	83	1	a	a	DET
ejpam-4015	83	2	function	function	NOUN
ejpam-4015	83	3	f	f	NOUN
ejpam-4015	83	4	:	:	PUNCT
ejpam-4015	83	5	i	i	PRON
ejpam-4015	83	6	⊂	⊂	PROPN
ejpam-4015	83	7	(	(	PUNCT
ejpam-4015	83	8	0,∞	0,∞	NUM
ejpam-4015	83	9	)	)	PUNCT
ejpam-4015	83	10	→	→	PUNCT
ejpam-4015	84	1	[	[	X
ejpam-4015	84	2	0,∞	0,∞	NOUN
ejpam-4015	84	3	)	)	PUNCT
ejpam-4015	84	4	is	be	AUX
ejpam-4015	84	5	said	say	VERB
ejpam-4015	84	6	to	to	PART
ejpam-4015	84	7	be	be	AUX
ejpam-4015	84	8	the	the	DET
ejpam-4015	84	9	(	(	PUNCT
ejpam-4015	84	10	s	s	X
ejpam-4015	84	11	,	,	PUNCT
ejpam-4015	84	12	r)−	r)−	PROPN
ejpam-4015	84	13	p−convex	p−convex	NOUN
ejpam-4015	84	14	function	function	NOUN
ejpam-4015	84	15	(	(	PUNCT
ejpam-4015	84	16	or	or	CCONJ
ejpam-4015	84	17	s−	s−	PROPN
ejpam-4015	84	18	p−convex	p−convex	NOUN
ejpam-4015	84	19	function	function	NOUN
ejpam-4015	84	20	in	in	ADP
ejpam-4015	84	21	mixed	mixed	ADJ
ejpam-4015	84	22	kind	kind	NOUN
ejpam-4015	84	23	)	)	PUNCT
ejpam-4015	84	24	,	,	PUNCT
ejpam-4015	84	25	if	if	SCONJ
ejpam-4015	84	26	f	f	PROPN
ejpam-4015	84	27	(	(	PUNCT
ejpam-4015	84	28	[	[	X
ejpam-4015	84	29	txp	txp	X
ejpam-4015	84	30	+	+	CCONJ
ejpam-4015	84	31	(	(	PUNCT
ejpam-4015	84	32	1−	1−	NUM
ejpam-4015	84	33	t)yp	t)yp	NOUN
ejpam-4015	84	34	]	]	X
ejpam-4015	84	35	1	1	NUM
ejpam-4015	84	36	p	p	NOUN
ejpam-4015	84	37	)	)	PUNCT
ejpam-4015	84	38	≤	≤	PROPN
ejpam-4015	84	39	trsf(x	trsf(x	PROPN
ejpam-4015	84	40	)	)	PUNCT
ejpam-4015	84	41	+	+	CCONJ
ejpam-4015	84	42	(	(	PUNCT
ejpam-4015	84	43	1−	1−	NUM
ejpam-4015	84	44	tr)sf(y	tr)sf(y	NOUN
ejpam-4015	84	45	)	)	PUNCT
ejpam-4015	84	46	,	,	PUNCT
ejpam-4015	84	47	(	(	PUNCT
ejpam-4015	84	48	2	2	X
ejpam-4015	84	49	)	)	PUNCT
ejpam-4015	84	50	for	for	ADP
ejpam-4015	84	51	all	all	DET
ejpam-4015	84	52	x	x	NOUN
ejpam-4015	84	53	,	,	PUNCT
ejpam-4015	84	54	y	y	PROPN
ejpam-4015	84	55	∈	∈	PROPN
ejpam-4015	84	56	i	i	PRON
ejpam-4015	84	57	and	and	CCONJ
ejpam-4015	84	58	t	t	PROPN
ejpam-4015	84	59	∈	∈	PROPN
ejpam-4015	85	1	[	[	X
ejpam-4015	85	2	0	0	NUM
ejpam-4015	85	3	,	,	PUNCT
ejpam-4015	85	4	1	1	NUM
ejpam-4015	85	5	]	]	PUNCT
ejpam-4015	85	6	.	.	PUNCT
ejpam-4015	86	1	remark	remark	PROPN
ejpam-4015	86	2	6	6	NUM
ejpam-4015	86	3	.	.	PUNCT
ejpam-4015	87	1	following	follow	VERB
ejpam-4015	87	2	well	well	ADV
ejpam-4015	87	3	known	know	VERB
ejpam-4015	87	4	results	result	NOUN
ejpam-4015	87	5	will	will	AUX
ejpam-4015	87	6	be	be	AUX
ejpam-4015	87	7	obtained	obtain	VERB
ejpam-4015	87	8	by	by	ADP
ejpam-4015	87	9	taking	take	VERB
ejpam-4015	87	10	the	the	DET
ejpam-4015	87	11	different	different	ADJ
ejpam-4015	87	12	combinations	combination	NOUN
ejpam-4015	87	13	of	of	ADP
ejpam-4015	87	14	values	value	NOUN
ejpam-4015	87	15	of	of	ADP
ejpam-4015	87	16	r	r	NOUN
ejpam-4015	87	17	,	,	PUNCT
ejpam-4015	87	18	s	s	PART
ejpam-4015	87	19	and	and	CCONJ
ejpam-4015	87	20	p.	p.	NOUN
ejpam-4015	87	21	(	(	PUNCT
ejpam-4015	87	22	i	i	NOUN
ejpam-4015	87	23	)	)	PUNCT
ejpam-4015	87	24	if	if	SCONJ
ejpam-4015	87	25	we	we	PRON
ejpam-4015	87	26	choose	choose	VERB
ejpam-4015	87	27	s	s	NOUN
ejpam-4015	87	28	=	=	SYM
ejpam-4015	87	29	1	1	NUM
ejpam-4015	87	30	in	in	ADP
ejpam-4015	87	31	(	(	PUNCT
ejpam-4015	87	32	2	2	NUM
ejpam-4015	87	33	)	)	PUNCT
ejpam-4015	87	34	,	,	PUNCT
ejpam-4015	87	35	we	we	PRON
ejpam-4015	87	36	get	get	VERB
ejpam-4015	87	37	s−	s−	PROPN
ejpam-4015	87	38	p−convex	p−convex	NOUN
ejpam-4015	87	39	function	function	NOUN
ejpam-4015	87	40	in	in	ADP
ejpam-4015	87	41	1st	1st	ADJ
ejpam-4015	87	42	kind	kind	NOUN
ejpam-4015	87	43	.	.	PUNCT
ejpam-4015	88	1	(	(	PUNCT
ejpam-4015	88	2	ii	ii	NOUN
ejpam-4015	88	3	)	)	PUNCT
ejpam-4015	88	4	if	if	SCONJ
ejpam-4015	88	5	we	we	PRON
ejpam-4015	88	6	choose	choose	VERB
ejpam-4015	88	7	r	r	NOUN
ejpam-4015	88	8	=	=	SYM
ejpam-4015	88	9	1	1	NUM
ejpam-4015	88	10	in	in	ADP
ejpam-4015	88	11	(	(	PUNCT
ejpam-4015	88	12	2	2	NUM
ejpam-4015	88	13	)	)	PUNCT
ejpam-4015	88	14	,	,	PUNCT
ejpam-4015	88	15	we	we	PRON
ejpam-4015	88	16	get	get	VERB
ejpam-4015	88	17	s−	s−	PROPN
ejpam-4015	88	18	p−convex	p−convex	NOUN
ejpam-4015	88	19	function	function	NOUN
ejpam-4015	88	20	in	in	ADP
ejpam-4015	88	21	2st	2st	ADJ
ejpam-4015	88	22	kind	kind	NOUN
ejpam-4015	88	23	.	.	PUNCT
ejpam-4015	89	1	muhammad	muhammad	PROPN
ejpam-4015	89	2	bilal	bilal	PROPN
ejpam-4015	89	3	,	,	PUNCT
ejpam-4015	89	4	asif	asif	PROPN
ejpam-4015	89	5	r.	r.	PROPN
ejpam-4015	89	6	khan	khan	PROPN
ejpam-4015	89	7	/	/	SYM
ejpam-4015	89	8	eur	eur	PROPN
ejpam-4015	89	9	.	.	PUNCT
ejpam-4015	90	1	j.	j.	PROPN
ejpam-4015	90	2	pure	pure	PROPN
ejpam-4015	90	3	appl	appl	PROPN
ejpam-4015	90	4	.	.	PROPN
ejpam-4015	90	5	math	math	PROPN
ejpam-4015	90	6	,	,	PUNCT
ejpam-4015	90	7	14	14	NUM
ejpam-4015	90	8	(	(	PUNCT
ejpam-4015	90	9	3	3	NUM
ejpam-4015	90	10	)	)	PUNCT
ejpam-4015	90	11	(	(	PUNCT
ejpam-4015	90	12	2021	2021	NUM
ejpam-4015	90	13	)	)	PUNCT
ejpam-4015	90	14	,	,	PUNCT
ejpam-4015	90	15	863	863	NUM
ejpam-4015	90	16	-	-	SYM
ejpam-4015	90	17	880	880	NUM
ejpam-4015	90	18	866	866	NUM
ejpam-4015	90	19	(	(	PUNCT
ejpam-4015	90	20	iii	iii	X
ejpam-4015	90	21	)	)	PUNCT
ejpam-4015	90	22	if	if	SCONJ
ejpam-4015	90	23	we	we	PRON
ejpam-4015	90	24	choose	choose	VERB
ejpam-4015	90	25	r	r	NOUN
ejpam-4015	90	26	=	=	SYM
ejpam-4015	90	27	s	s	NOUN
ejpam-4015	90	28	=	=	SYM
ejpam-4015	90	29	1	1	NUM
ejpam-4015	90	30	in	in	ADP
ejpam-4015	90	31	(	(	PUNCT
ejpam-4015	90	32	2	2	NUM
ejpam-4015	90	33	)	)	PUNCT
ejpam-4015	90	34	,	,	PUNCT
ejpam-4015	90	35	we	we	PRON
ejpam-4015	90	36	get	get	VERB
ejpam-4015	90	37	p−convex	p−convex	NOUN
ejpam-4015	90	38	function	function	NOUN
ejpam-4015	90	39	.	.	PUNCT
ejpam-4015	91	1	(	(	PUNCT
ejpam-4015	91	2	iv	iv	X
ejpam-4015	91	3	)	)	PUNCT
ejpam-4015	91	4	if	if	SCONJ
ejpam-4015	91	5	we	we	PRON
ejpam-4015	91	6	choose	choose	VERB
ejpam-4015	91	7	r	r	NOUN
ejpam-4015	91	8	=	=	SYM
ejpam-4015	91	9	0	0	NUM
ejpam-4015	91	10	in	in	ADP
ejpam-4015	91	11	(	(	PUNCT
ejpam-4015	91	12	2	2	NUM
ejpam-4015	91	13	)	)	PUNCT
ejpam-4015	91	14	,	,	PUNCT
ejpam-4015	91	15	we	we	PRON
ejpam-4015	91	16	get	get	VERB
ejpam-4015	91	17	refinement	refinement	NOUN
ejpam-4015	91	18	of	of	ADP
ejpam-4015	91	19	quasi	quasi	ADJ
ejpam-4015	91	20	p−convex	p−convex	NOUN
ejpam-4015	91	21	function	function	NOUN
ejpam-4015	91	22	.	.	PUNCT
ejpam-4015	92	1	(	(	PUNCT
ejpam-4015	92	2	v	v	NOUN
ejpam-4015	92	3	)	)	PUNCT
ejpam-4015	92	4	if	if	SCONJ
ejpam-4015	92	5	we	we	PRON
ejpam-4015	92	6	choose	choose	VERB
ejpam-4015	92	7	r	r	NOUN
ejpam-4015	92	8	=	=	SYM
ejpam-4015	92	9	1	1	NUM
ejpam-4015	92	10	and	and	CCONJ
ejpam-4015	92	11	s	s	X
ejpam-4015	92	12	=	=	SYM
ejpam-4015	92	13	0	0	NUM
ejpam-4015	92	14	in	in	ADP
ejpam-4015	92	15	(	(	PUNCT
ejpam-4015	92	16	2	2	NUM
ejpam-4015	92	17	)	)	PUNCT
ejpam-4015	92	18	,	,	PUNCT
ejpam-4015	92	19	we	we	PRON
ejpam-4015	92	20	get	get	VERB
ejpam-4015	92	21	p	p	NOUN
ejpam-4015	92	22	−	−	NOUN
ejpam-4015	92	23	p−convex	p−convex	NOUN
ejpam-4015	92	24	function	function	NOUN
ejpam-4015	92	25	.	.	PUNCT
ejpam-4015	93	1	(	(	PUNCT
ejpam-4015	93	2	vi	vi	X
ejpam-4015	93	3	)	)	PUNCT
ejpam-4015	93	4	if	if	SCONJ
ejpam-4015	93	5	we	we	PRON
ejpam-4015	93	6	choose	choose	VERB
ejpam-4015	93	7	p	p	NOUN
ejpam-4015	93	8	=	=	NOUN
ejpam-4015	93	9	1	1	NUM
ejpam-4015	93	10	in	in	ADP
ejpam-4015	93	11	(	(	PUNCT
ejpam-4015	93	12	2	2	NUM
ejpam-4015	93	13	)	)	PUNCT
ejpam-4015	93	14	,	,	PUNCT
ejpam-4015	93	15	we	we	PRON
ejpam-4015	93	16	get	get	VERB
ejpam-4015	93	17	(	(	PUNCT
ejpam-4015	93	18	s	s	X
ejpam-4015	93	19	,	,	PUNCT
ejpam-4015	93	20	r)−convex	r)−convex	PROPN
ejpam-4015	93	21	function	function	VERB
ejpam-4015	93	22	in	in	ADP
ejpam-4015	93	23	mixed	mixed	ADJ
ejpam-4015	93	24	kind	kind	NOUN
ejpam-4015	94	1	[	[	X
ejpam-4015	94	2	14	14	NUM
ejpam-4015	94	3	]	]	PUNCT
ejpam-4015	94	4	.	.	PUNCT
ejpam-4015	95	1	(	(	PUNCT
ejpam-4015	95	2	vii	vii	PROPN
ejpam-4015	95	3	)	)	PUNCT
ejpam-4015	95	4	if	if	SCONJ
ejpam-4015	95	5	we	we	PRON
ejpam-4015	95	6	choose	choose	VERB
ejpam-4015	95	7	p	p	X
ejpam-4015	95	8	=	=	PUNCT
ejpam-4015	95	9	s	s	PART
ejpam-4015	95	10	=	=	SYM
ejpam-4015	95	11	1	1	NUM
ejpam-4015	95	12	in	in	ADP
ejpam-4015	95	13	(	(	PUNCT
ejpam-4015	95	14	2	2	NUM
ejpam-4015	95	15	)	)	PUNCT
ejpam-4015	95	16	,	,	PUNCT
ejpam-4015	95	17	we	we	PRON
ejpam-4015	95	18	get	get	VERB
ejpam-4015	95	19	s−convex	s−convex	PRON
ejpam-4015	95	20	function	function	NOUN
ejpam-4015	95	21	in	in	ADP
ejpam-4015	95	22	1st	1st	ADJ
ejpam-4015	95	23	kind	kind	NOUN
ejpam-4015	95	24	.	.	PUNCT
ejpam-4015	96	1	(	(	PUNCT
ejpam-4015	96	2	viii	viii	NOUN
ejpam-4015	96	3	)	)	PUNCT
ejpam-4015	96	4	if	if	SCONJ
ejpam-4015	96	5	we	we	PRON
ejpam-4015	96	6	choose	choose	VERB
ejpam-4015	96	7	p	p	NOUN
ejpam-4015	96	8	=	=	PUNCT
ejpam-4015	96	9	r	r	NOUN
ejpam-4015	96	10	=	=	SYM
ejpam-4015	96	11	1	1	NUM
ejpam-4015	96	12	in	in	ADP
ejpam-4015	96	13	(	(	PUNCT
ejpam-4015	96	14	2	2	NUM
ejpam-4015	96	15	)	)	PUNCT
ejpam-4015	96	16	,	,	PUNCT
ejpam-4015	96	17	we	we	PRON
ejpam-4015	96	18	get	get	VERB
ejpam-4015	96	19	s−convex	s−convex	PRON
ejpam-4015	96	20	function	function	NOUN
ejpam-4015	96	21	in	in	ADP
ejpam-4015	96	22	2st	2st	ADJ
ejpam-4015	96	23	kind	kind	NOUN
ejpam-4015	96	24	.	.	PUNCT
ejpam-4015	97	1	(	(	PUNCT
ejpam-4015	97	2	ix	ix	ADP
ejpam-4015	97	3	)	)	PUNCT
ejpam-4015	97	4	if	if	SCONJ
ejpam-4015	97	5	we	we	PRON
ejpam-4015	97	6	choose	choose	VERB
ejpam-4015	97	7	p	p	NOUN
ejpam-4015	97	8	=	=	PUNCT
ejpam-4015	97	9	r	r	NOUN
ejpam-4015	97	10	=	=	SYM
ejpam-4015	97	11	s	s	NOUN
ejpam-4015	97	12	=	=	SYM
ejpam-4015	97	13	1	1	NUM
ejpam-4015	97	14	in	in	ADP
ejpam-4015	97	15	(	(	PUNCT
ejpam-4015	97	16	2	2	NUM
ejpam-4015	97	17	)	)	PUNCT
ejpam-4015	97	18	,	,	PUNCT
ejpam-4015	97	19	we	we	PRON
ejpam-4015	97	20	get	get	VERB
ejpam-4015	97	21	ordinary	ordinary	ADJ
ejpam-4015	97	22	convex	convex	NOUN
ejpam-4015	97	23	function	function	NOUN
ejpam-4015	97	24	.	.	PUNCT
ejpam-4015	98	1	(	(	PUNCT
ejpam-4015	98	2	x	x	X
ejpam-4015	98	3	)	)	PUNCT
ejpam-4015	98	4	if	if	SCONJ
ejpam-4015	98	5	we	we	PRON
ejpam-4015	98	6	choose	choose	VERB
ejpam-4015	98	7	p	p	NOUN
ejpam-4015	98	8	=	=	NOUN
ejpam-4015	98	9	1	1	NUM
ejpam-4015	98	10	and	and	CCONJ
ejpam-4015	98	11	r	r	NOUN
ejpam-4015	98	12	=	=	SYM
ejpam-4015	98	13	0	0	NUM
ejpam-4015	98	14	in	in	ADP
ejpam-4015	98	15	(	(	PUNCT
ejpam-4015	98	16	2	2	NUM
ejpam-4015	98	17	)	)	PUNCT
ejpam-4015	98	18	,	,	PUNCT
ejpam-4015	98	19	we	we	PRON
ejpam-4015	98	20	get	get	VERB
ejpam-4015	98	21	refinement	refinement	NOUN
ejpam-4015	98	22	of	of	ADP
ejpam-4015	98	23	quasi	quasi	ADJ
ejpam-4015	98	24	convex	convex	PROPN
ejpam-4015	98	25	function	function	NOUN
ejpam-4015	98	26	.	.	PUNCT
ejpam-4015	99	1	(	(	PUNCT
ejpam-4015	99	2	xi	xi	X
ejpam-4015	99	3	)	)	PUNCT
ejpam-4015	99	4	if	if	SCONJ
ejpam-4015	99	5	we	we	PRON
ejpam-4015	99	6	choose	choose	VERB
ejpam-4015	99	7	p	p	NOUN
ejpam-4015	99	8	=	=	PUNCT
ejpam-4015	99	9	r	r	NOUN
ejpam-4015	99	10	=	=	SYM
ejpam-4015	99	11	1	1	NUM
ejpam-4015	99	12	and	and	CCONJ
ejpam-4015	99	13	s	s	X
ejpam-4015	99	14	=	=	SYM
ejpam-4015	99	15	0	0	NUM
ejpam-4015	99	16	in	in	ADP
ejpam-4015	99	17	(	(	PUNCT
ejpam-4015	99	18	2	2	NUM
ejpam-4015	99	19	)	)	PUNCT
ejpam-4015	99	20	,	,	PUNCT
ejpam-4015	99	21	we	we	PRON
ejpam-4015	99	22	get	get	VERB
ejpam-4015	99	23	p−convex	p−convex	NOUN
ejpam-4015	99	24	function	function	NOUN
ejpam-4015	99	25	.	.	PUNCT
ejpam-4015	100	1	renowned	renowned	ADJ
ejpam-4015	100	2	hölder	hölder	PROPN
ejpam-4015	100	3	’s	’s	PART
ejpam-4015	100	4	inequality	inequality	NOUN
ejpam-4015	100	5	in	in	ADP
ejpam-4015	100	6	its	its	PRON
ejpam-4015	100	7	general	general	ADJ
ejpam-4015	100	8	integral	integral	ADJ
ejpam-4015	100	9	form	form	NOUN
ejpam-4015	100	10	is	be	AUX
ejpam-4015	100	11	given	give	VERB
ejpam-4015	100	12	as	as	SCONJ
ejpam-4015	100	13	follows	follow	VERB
ejpam-4015	100	14	[	[	X
ejpam-4015	100	15	18	18	NUM
ejpam-4015	100	16	]	]	NUM
ejpam-4015	100	17	:	:	PUNCT
ejpam-4015	100	18	theorem	theorem	NOUN
ejpam-4015	100	19	2	2	X
ejpam-4015	100	20	.	.	PUNCT
ejpam-4015	101	1	let	let	VERB
ejpam-4015	101	2	1	1	NUM
ejpam-4015	101	3	≤	≤	NOUN
ejpam-4015	101	4	p	p	X
ejpam-4015	101	5	,	,	PUNCT
ejpam-4015	101	6	q	q	PROPN
ejpam-4015	101	7	≤	≤	NOUN
ejpam-4015	101	8	∞	∞	NUM
ejpam-4015	101	9	with	with	ADP
ejpam-4015	101	10	1	1	NUM
ejpam-4015	101	11	p	p	NOUN
ejpam-4015	101	12	+	+	NOUN
ejpam-4015	102	1	1	1	NUM
ejpam-4015	102	2	q	q	NOUN
ejpam-4015	102	3	=	=	NOUN
ejpam-4015	102	4	1	1	X
ejpam-4015	102	5	.	.	PUNCT
ejpam-4015	103	1	if	if	SCONJ
ejpam-4015	103	2	f	f	PROPN
ejpam-4015	103	3	∈	∈	PROPN
ejpam-4015	103	4	lp	lp	PROPN
ejpam-4015	103	5	and	and	CCONJ
ejpam-4015	103	6	φ	φ	NUM
ejpam-4015	103	7	∈	∈	PROPN
ejpam-4015	103	8	lq	lq	NOUN
ejpam-4015	103	9	,	,	PUNCT
ejpam-4015	103	10	then	then	ADV
ejpam-4015	103	11	fφ	fφ	PROPN
ejpam-4015	103	12	∈	∈	PROPN
ejpam-4015	103	13	l1	l1	PROPN
ejpam-4015	103	14	and∫	and∫	PROPN
ejpam-4015	103	15	|f(u)φ(u)|du	|f(u)φ(u)|du	VERB
ejpam-4015	103	16	≤	≤	ADJ
ejpam-4015	103	17	‖f‖p‖φ‖q	‖f‖p‖φ‖q	NOUN
ejpam-4015	103	18	(	(	PUNCT
ejpam-4015	103	19	3	3	X
ejpam-4015	103	20	)	)	PUNCT
ejpam-4015	104	1	where	where	SCONJ
ejpam-4015	104	2	f	f	PROPN
ejpam-4015	104	3	∈	∈	PROPN
ejpam-4015	104	4	lp	lp	NOUN
ejpam-4015	104	5	if	if	SCONJ
ejpam-4015	104	6	‖f‖p	‖f‖p	NOUN
ejpam-4015	104	7	=	=	SYM
ejpam-4015	104	8	(	(	PUNCT
ejpam-4015	104	9	∫	∫	PROPN
ejpam-4015	104	10	|f(u)|pdu	|f(u)|pdu	NUM
ejpam-4015	104	11	)	)	PUNCT
ejpam-4015	104	12	1	1	NUM
ejpam-4015	104	13	p	p	NOUN
ejpam-4015	104	14	<	<	X
ejpam-4015	104	15	∞.	∞.	PROPN
ejpam-4015	104	16	note	note	VERB
ejpam-4015	104	17	that	that	SCONJ
ejpam-4015	104	18	if	if	SCONJ
ejpam-4015	104	19	we	we	PRON
ejpam-4015	104	20	put	put	VERB
ejpam-4015	104	21	p	p	NOUN
ejpam-4015	104	22	=	=	NOUN
ejpam-4015	104	23	q	q	NOUN
ejpam-4015	104	24	=	=	SYM
ejpam-4015	104	25	2	2	NUM
ejpam-4015	104	26	,	,	PUNCT
ejpam-4015	104	27	the	the	DET
ejpam-4015	104	28	above	above	ADJ
ejpam-4015	104	29	inequality	inequality	NOUN
ejpam-4015	104	30	becomes	become	VERB
ejpam-4015	104	31	cauchy	cauchy	NOUN
ejpam-4015	104	32	–	–	PUNCT
ejpam-4015	104	33	schwarz	schwarz	PROPN
ejpam-4015	104	34	inequality	inequality	NOUN
ejpam-4015	104	35	.	.	PUNCT
ejpam-4015	105	1	also	also	ADV
ejpam-4015	105	2	,	,	PUNCT
ejpam-4015	105	3	if	if	SCONJ
ejpam-4015	105	4	we	we	PRON
ejpam-4015	105	5	put	put	VERB
ejpam-4015	105	6	q	q	NOUN
ejpam-4015	105	7	=	=	NOUN
ejpam-4015	105	8	1	1	NUM
ejpam-4015	105	9	and	and	CCONJ
ejpam-4015	105	10	let	let	VERB
ejpam-4015	105	11	p	p	NOUN
ejpam-4015	105	12	→	→	SYM
ejpam-4015	105	13	∞	∞	PROPN
ejpam-4015	105	14	,	,	PUNCT
ejpam-4015	105	15	then	then	ADV
ejpam-4015	105	16	we	we	PRON
ejpam-4015	105	17	get,∫	get,∫	PUNCT
ejpam-4015	105	18	|f(u)φ(u)|du	|f(u)φ(u)|du	VERB
ejpam-4015	105	19	≤	≤	NUM
ejpam-4015	105	20	||f	||f	NOUN
ejpam-4015	105	21	||∞||φ||1	||∞||φ||1	NOUN
ejpam-4015	105	22	where	where	SCONJ
ejpam-4015	105	23	||f	||f	PROPN
ejpam-4015	105	24	||∞	||∞	PROPN
ejpam-4015	105	25	stands	stand	VERB
ejpam-4015	105	26	for	for	ADP
ejpam-4015	105	27	the	the	DET
ejpam-4015	105	28	essential	essential	ADJ
ejpam-4015	105	29	supremum	supremum	NOUN
ejpam-4015	105	30	of	of	ADP
ejpam-4015	105	31	|f	|f	PROPN
ejpam-4015	105	32	|	|	ADV
ejpam-4015	105	33	,	,	PUNCT
ejpam-4015	105	34	i.e.	i.e.	X
ejpam-4015	105	35	,	,	PUNCT
ejpam-4015	105	36	||f	||f	PROPN
ejpam-4015	105	37	||∞	||∞	PROPN
ejpam-4015	105	38	=	=	SYM
ejpam-4015	105	39	ess	ess	PROPN
ejpam-4015	105	40	sup	sup	PROPN
ejpam-4015	105	41	∀u	∀u	PROPN
ejpam-4015	105	42	|f(u)|	|f(u)|	NOUN
ejpam-4015	105	43	.	.	PUNCT
ejpam-4015	105	44	definition	definition	NOUN
ejpam-4015	105	45	7	7	NUM
ejpam-4015	105	46	.	.	PUNCT
ejpam-4015	106	1	let	let	VERB
ejpam-4015	106	2	f	f	PROPN
ejpam-4015	106	3	,	,	PUNCT
ejpam-4015	106	4	φ	φ	PROPN
ejpam-4015	106	5	are	be	AUX
ejpam-4015	106	6	real	real	ADV
ejpam-4015	106	7	valued	value	VERB
ejpam-4015	106	8	functions	function	NOUN
ejpam-4015	106	9	defined	define	VERB
ejpam-4015	106	10	on	on	ADP
ejpam-4015	106	11	[	[	X
ejpam-4015	106	12	a	a	X
ejpam-4015	106	13	,	,	PUNCT
ejpam-4015	106	14	b	b	NOUN
ejpam-4015	106	15	]	]	PUNCT
ejpam-4015	106	16	and	and	CCONJ
ejpam-4015	106	17	if	if	SCONJ
ejpam-4015	106	18	|f	|f	PROPN
ejpam-4015	107	1	|	|	ADV
ejpam-4015	107	2	and	and	CCONJ
ejpam-4015	107	3	|f	|f	PRON
ejpam-4015	107	4	||φ|q	||φ|q	ADV
ejpam-4015	107	5	are	be	AUX
ejpam-4015	107	6	integrable	integrable	ADJ
ejpam-4015	107	7	on	on	ADP
ejpam-4015	107	8	[	[	X
ejpam-4015	107	9	a	a	X
ejpam-4015	107	10	,	,	PUNCT
ejpam-4015	107	11	b	b	NOUN
ejpam-4015	107	12	]	]	X
ejpam-4015	107	13	,	,	PUNCT
ejpam-4015	107	14	then	then	ADV
ejpam-4015	107	15	for	for	ADP
ejpam-4015	107	16	q	q	PROPN
ejpam-4015	107	17	≥	≥	NUM
ejpam-4015	107	18	1	1	NUM
ejpam-4015	107	19	we	we	PRON
ejpam-4015	107	20	have	have	AUX
ejpam-4015	107	21	:	:	PUNCT
ejpam-4015	107	22	b∫	b∫	NOUN
ejpam-4015	107	23	a	a	DET
ejpam-4015	107	24	|f(u)||φ(u)|du	|f(u)||φ(u)|du	NOUN
ejpam-4015	107	25	≤	≤	PUNCT
ejpam-4015	107	26			PROPN
ejpam-4015	107	27	b∫	b∫	PROPN
ejpam-4015	107	28	a	a	DET
ejpam-4015	107	29	|f(u)|du	|f(u)|du	NOUN
ejpam-4015	107	30	1−	1−	NOUN
ejpam-4015	107	31	1	1	NUM
ejpam-4015	107	32	q	q	NOUN
ejpam-4015	107	33			PROPN
ejpam-4015	107	34	b∫	b∫	PROPN
ejpam-4015	107	35	a	a	DET
ejpam-4015	107	36	|f(u)||φ(u)|qdu	|f(u)||φ(u)|qdu	NOUN
ejpam-4015	107	37			PROPN
ejpam-4015	107	38	1	1	NUM
ejpam-4015	107	39	q	q	NOUN
ejpam-4015	107	40	.	.	PUNCT
ejpam-4015	108	1	the	the	DET
ejpam-4015	108	2	above	above	ADJ
ejpam-4015	108	3	inequality	inequality	NOUN
ejpam-4015	108	4	is	be	AUX
ejpam-4015	108	5	known	know	VERB
ejpam-4015	108	6	as	as	ADP
ejpam-4015	108	7	power	power	NOUN
ejpam-4015	108	8	mean	mean	NOUN
ejpam-4015	108	9	inequality	inequality	NOUN
ejpam-4015	108	10	(	(	PUNCT
ejpam-4015	108	11	see	see	VERB
ejpam-4015	108	12	[	[	X
ejpam-4015	108	13	21	21	NUM
ejpam-4015	108	14	]	]	PUNCT
ejpam-4015	108	15	)	)	PUNCT
ejpam-4015	108	16	.	.	PUNCT
ejpam-4015	109	1	in	in	ADP
ejpam-4015	109	2	[	[	X
ejpam-4015	109	3	12	12	NUM
ejpam-4015	109	4	]	]	PUNCT
ejpam-4015	109	5	,	,	PUNCT
ejpam-4015	109	6	i̇.	i̇.	PROPN
ejpam-4015	109	7	işcan	işcan	AUX
ejpam-4015	109	8	stated	state	VERB
ejpam-4015	109	9	and	and	CCONJ
ejpam-4015	109	10	proved	prove	VERB
ejpam-4015	109	11	a	a	DET
ejpam-4015	109	12	result	result	NOUN
ejpam-4015	109	13	related	relate	VERB
ejpam-4015	109	14	to	to	ADP
ejpam-4015	109	15	hermite−hadamard	hermite−hadamard	ADV
ejpam-4015	109	16	dual	dual	ADJ
ejpam-4015	109	17	inequality	inequality	NOUN
ejpam-4015	109	18	for	for	ADP
ejpam-4015	109	19	p−convex	p−convex	NOUN
ejpam-4015	109	20	functions	function	NOUN
ejpam-4015	109	21	which	which	PRON
ejpam-4015	109	22	we	we	PRON
ejpam-4015	109	23	recall	recall	VERB
ejpam-4015	109	24	here	here	ADV
ejpam-4015	109	25	:	:	PUNCT
ejpam-4015	109	26	muhammad	muhammad	PROPN
ejpam-4015	109	27	bilal	bilal	PROPN
ejpam-4015	109	28	,	,	PUNCT
ejpam-4015	109	29	asif	asif	PROPN
ejpam-4015	109	30	r.	r.	PROPN
ejpam-4015	109	31	khan	khan	PROPN
ejpam-4015	109	32	/	/	SYM
ejpam-4015	109	33	eur	eur	PROPN
ejpam-4015	109	34	.	.	PUNCT
ejpam-4015	110	1	j.	j.	PROPN
ejpam-4015	110	2	pure	pure	PROPN
ejpam-4015	110	3	appl	appl	PROPN
ejpam-4015	110	4	.	.	PROPN
ejpam-4015	110	5	math	math	PROPN
ejpam-4015	110	6	,	,	PUNCT
ejpam-4015	110	7	14	14	NUM
ejpam-4015	110	8	(	(	PUNCT
ejpam-4015	110	9	3	3	NUM
ejpam-4015	110	10	)	)	PUNCT
ejpam-4015	110	11	(	(	PUNCT
ejpam-4015	110	12	2021	2021	NUM
ejpam-4015	110	13	)	)	PUNCT
ejpam-4015	110	14	,	,	PUNCT
ejpam-4015	110	15	863	863	NUM
ejpam-4015	110	16	-	-	SYM
ejpam-4015	110	17	880	880	NUM
ejpam-4015	110	18	867	867	NUM
ejpam-4015	110	19	theorem	theorem	NOUN
ejpam-4015	110	20	3	3	X
ejpam-4015	110	21	.	.	PUNCT
ejpam-4015	111	1	let	let	VERB
ejpam-4015	111	2	f	f	NOUN
ejpam-4015	111	3	:	:	PUNCT
ejpam-4015	112	1	i	i	PRON
ejpam-4015	112	2	⊂	⊂	PROPN
ejpam-4015	112	3	(	(	PUNCT
ejpam-4015	112	4	0,∞	0,∞	NUM
ejpam-4015	112	5	)	)	PUNCT
ejpam-4015	112	6	→	→	PUNCT
ejpam-4015	112	7	r	r	NOUN
ejpam-4015	112	8	be	be	AUX
ejpam-4015	112	9	a	a	DET
ejpam-4015	112	10	p−convex	p−convex	NOUN
ejpam-4015	112	11	function	function	NOUN
ejpam-4015	112	12	,	,	PUNCT
ejpam-4015	112	13	p	p	NOUN
ejpam-4015	112	14	∈	∈	PROPN
ejpam-4015	112	15	r	r	NOUN
ejpam-4015	112	16	\	\	PUNCT
ejpam-4015	112	17	{	{	PUNCT
ejpam-4015	112	18	0	0	NUM
ejpam-4015	112	19	}	}	PUNCT
ejpam-4015	112	20	and	and	CCONJ
ejpam-4015	112	21	a	a	DET
ejpam-4015	112	22	,	,	PUNCT
ejpam-4015	112	23	b	b	X
ejpam-4015	112	24	∈	∈	NOUN
ejpam-4015	112	25	i	i	PRON
ejpam-4015	112	26	with	with	ADP
ejpam-4015	112	27	a	a	DET
ejpam-4015	112	28	<	<	X
ejpam-4015	112	29	b.	b.	NOUN
ejpam-4015	112	30	if	if	SCONJ
ejpam-4015	112	31	f	f	PROPN
ejpam-4015	112	32	∈	∈	PROPN
ejpam-4015	112	33	l[a	l[a	NOUN
ejpam-4015	112	34	,	,	PUNCT
ejpam-4015	112	35	b	b	NOUN
ejpam-4015	112	36	]	]	X
ejpam-4015	112	37	,	,	PUNCT
ejpam-4015	112	38	then	then	ADV
ejpam-4015	112	39	the	the	DET
ejpam-4015	112	40	following	follow	VERB
ejpam-4015	112	41	inequalities	inequality	NOUN
ejpam-4015	112	42	holds	hold	VERB
ejpam-4015	112	43	:	:	PUNCT
ejpam-4015	112	44	f	f	PROPN
ejpam-4015	112	45	(	(	PUNCT
ejpam-4015	112	46	[	[	PUNCT
ejpam-4015	112	47	ap	ap	PROPN
ejpam-4015	113	1	+	+	NUM
ejpam-4015	113	2	bp	bp	PROPN
ejpam-4015	113	3	2	2	NUM
ejpam-4015	113	4	]	]	PUNCT
ejpam-4015	113	5	1	1	NUM
ejpam-4015	113	6	p	p	NOUN
ejpam-4015	113	7	)	)	PUNCT
ejpam-4015	113	8	≤	≤	NUM
ejpam-4015	113	9	1	1	NUM
ejpam-4015	113	10	mp	mp	PROPN
ejpam-4015	113	11	∫	∫	PROPN
ejpam-4015	113	12	b	b	PROPN
ejpam-4015	113	13	a	a	DET
ejpam-4015	113	14	f(x	f(x	PROPN
ejpam-4015	113	15	)	)	PUNCT
ejpam-4015	114	1	x1−p	x1−p	PROPN
ejpam-4015	114	2	dx	dx	PROPN
ejpam-4015	114	3	≤	≤	NUM
ejpam-4015	114	4	f(a	f(a	NOUN
ejpam-4015	114	5	)	)	PUNCT
ejpam-4015	115	1	+	+	CCONJ
ejpam-4015	115	2	f(b	f(b	X
ejpam-4015	115	3	)	)	PUNCT
ejpam-4015	115	4	2	2	NUM
ejpam-4015	115	5	.	.	PUNCT
ejpam-4015	116	1	(	(	PUNCT
ejpam-4015	116	2	4	4	X
ejpam-4015	116	3	)	)	PUNCT
ejpam-4015	116	4	remark	remark	NOUN
ejpam-4015	116	5	7	7	NUM
ejpam-4015	116	6	.	.	PUNCT
ejpam-4015	116	7	by	by	ADP
ejpam-4015	116	8	taking	take	VERB
ejpam-4015	116	9	different	different	ADJ
ejpam-4015	116	10	values	value	NOUN
ejpam-4015	116	11	of	of	ADP
ejpam-4015	116	12	p	p	X
ejpam-4015	116	13	,	,	PUNCT
ejpam-4015	116	14	we	we	PRON
ejpam-4015	116	15	easily	easily	ADV
ejpam-4015	116	16	obtain	obtain	VERB
ejpam-4015	116	17	following	follow	VERB
ejpam-4015	116	18	results	result	NOUN
ejpam-4015	116	19	:	:	PUNCT
ejpam-4015	116	20	(	(	PUNCT
ejpam-4015	116	21	i	i	NOUN
ejpam-4015	116	22	)	)	PUNCT
ejpam-4015	116	23	it	it	PRON
ejpam-4015	116	24	can	can	AUX
ejpam-4015	116	25	be	be	AUX
ejpam-4015	116	26	verified	verify	VERB
ejpam-4015	116	27	that	that	SCONJ
ejpam-4015	116	28	theorem	theorem	NOUN
ejpam-4015	116	29	1	1	NUM
ejpam-4015	116	30	is	be	AUX
ejpam-4015	116	31	obtained	obtain	VERB
ejpam-4015	116	32	by	by	ADP
ejpam-4015	116	33	taking	take	VERB
ejpam-4015	116	34	p	p	NOUN
ejpam-4015	116	35	=	=	NOUN
ejpam-4015	116	36	1	1	NUM
ejpam-4015	116	37	in	in	ADP
ejpam-4015	116	38	the	the	DET
ejpam-4015	116	39	above	above	ADJ
ejpam-4015	116	40	result	result	NOUN
ejpam-4015	116	41	.	.	PUNCT
ejpam-4015	117	1	(	(	PUNCT
ejpam-4015	117	2	ii	ii	X
ejpam-4015	117	3	)	)	PUNCT
ejpam-4015	117	4	it	it	PRON
ejpam-4015	117	5	can	can	AUX
ejpam-4015	117	6	be	be	AUX
ejpam-4015	117	7	verified	verify	VERB
ejpam-4015	117	8	that	that	SCONJ
ejpam-4015	117	9	theorem	theorem	VERB
ejpam-4015	117	10	3	3	NUM
ejpam-4015	117	11	of	of	ADP
ejpam-4015	117	12	[	[	X
ejpam-4015	117	13	11	11	NUM
ejpam-4015	117	14	]	]	PUNCT
ejpam-4015	117	15	is	be	AUX
ejpam-4015	117	16	obtained	obtain	VERB
ejpam-4015	117	17	by	by	ADP
ejpam-4015	117	18	taking	take	VERB
ejpam-4015	117	19	p	p	NOUN
ejpam-4015	117	20	=	=	NOUN
ejpam-4015	117	21	−1	−1	NOUN
ejpam-4015	117	22	in	in	ADP
ejpam-4015	117	23	the	the	DET
ejpam-4015	117	24	above	above	ADJ
ejpam-4015	117	25	result	result	NOUN
ejpam-4015	117	26	.	.	PUNCT
ejpam-4015	118	1	now	now	ADV
ejpam-4015	118	2	we	we	PRON
ejpam-4015	118	3	state	state	VERB
ejpam-4015	118	4	the	the	DET
ejpam-4015	118	5	following	follow	VERB
ejpam-4015	118	6	identity	identity	NOUN
ejpam-4015	118	7	which	which	PRON
ejpam-4015	118	8	will	will	AUX
ejpam-4015	118	9	be	be	AUX
ejpam-4015	118	10	used	use	VERB
ejpam-4015	118	11	to	to	PART
ejpam-4015	118	12	derive	derive	VERB
ejpam-4015	118	13	the	the	DET
ejpam-4015	118	14	main	main	ADJ
ejpam-4015	118	15	results	result	NOUN
ejpam-4015	118	16	of	of	ADP
ejpam-4015	118	17	this	this	DET
ejpam-4015	118	18	article	article	NOUN
ejpam-4015	118	19	.	.	PUNCT
ejpam-4015	119	1	lemma	lemma	PROPN
ejpam-4015	119	2	1	1	NUM
ejpam-4015	119	3	.	.	PUNCT
ejpam-4015	120	1	[	[	X
ejpam-4015	120	2	20	20	NUM
ejpam-4015	120	3	]	]	PUNCT
ejpam-4015	120	4	let	let	VERB
ejpam-4015	120	5	f	f	NOUN
ejpam-4015	120	6	:	:	PUNCT
ejpam-4015	120	7	i	i	PRON
ejpam-4015	120	8	⊂	⊂	PROPN
ejpam-4015	120	9	(	(	PUNCT
ejpam-4015	120	10	0,∞	0,∞	NUM
ejpam-4015	120	11	)	)	PUNCT
ejpam-4015	121	1	→	→	PUNCT
ejpam-4015	121	2	r	r	NOUN
ejpam-4015	121	3	be	be	AUX
ejpam-4015	121	4	a	a	DET
ejpam-4015	121	5	differentiable	differentiable	ADJ
ejpam-4015	121	6	mapping	mapping	NOUN
ejpam-4015	121	7	on	on	ADP
ejpam-4015	121	8	i	i	PRON
ejpam-4015	121	9	◦	◦	NOUN
ejpam-4015	121	10	and	and	CCONJ
ejpam-4015	121	11	a	a	DET
ejpam-4015	121	12	,	,	PUNCT
ejpam-4015	121	13	b	b	X
ejpam-4015	121	14	∈	∈	PROPN
ejpam-4015	121	15	i	i	PRON
ejpam-4015	121	16	◦	◦	VERB
ejpam-4015	121	17	with	with	ADP
ejpam-4015	121	18	a	a	DET
ejpam-4015	121	19	<	<	X
ejpam-4015	121	20	b	b	NOUN
ejpam-4015	121	21	,	,	PUNCT
ejpam-4015	121	22	p	p	NOUN
ejpam-4015	121	23	∈	∈	PROPN
ejpam-4015	121	24	r	r	NOUN
ejpam-4015	121	25	\	\	PUNCT
ejpam-4015	121	26	{	{	PUNCT
ejpam-4015	121	27	0	0	NUM
ejpam-4015	121	28	}	}	PUNCT
ejpam-4015	121	29	.	.	PUNCT
ejpam-4015	122	1	if	if	SCONJ
ejpam-4015	122	2	f	f	PROPN
ejpam-4015	122	3	′	′	NUM
ejpam-4015	122	4	∈	∈	PROPN
ejpam-4015	122	5	l[a	l[a	NOUN
ejpam-4015	122	6	,	,	PUNCT
ejpam-4015	122	7	b	b	NOUN
ejpam-4015	122	8	]	]	X
ejpam-4015	122	9	then	then	ADV
ejpam-4015	122	10	the	the	DET
ejpam-4015	122	11	following	follow	VERB
ejpam-4015	122	12	identity	identity	NOUN
ejpam-4015	122	13	holds	hold	VERB
ejpam-4015	122	14	:	:	PUNCT
ejpam-4015	122	15	b∫	b∫	PROPN
ejpam-4015	122	16	a	a	DET
ejpam-4015	122	17	f(x	f(x	PROPN
ejpam-4015	122	18	)	)	PUNCT
ejpam-4015	123	1	x1−p	x1−p	PROPN
ejpam-4015	124	1	dx−mpf	dx−mpf	NOUN
ejpam-4015	124	2	(	(	PUNCT
ejpam-4015	124	3	[	[	PUNCT
ejpam-4015	124	4	ap	ap	PROPN
ejpam-4015	124	5	+	+	NUM
ejpam-4015	124	6	bp	bp	PROPN
ejpam-4015	124	7	2	2	NUM
ejpam-4015	124	8	]	]	PUNCT
ejpam-4015	124	9	1	1	NUM
ejpam-4015	124	10	p	p	NOUN
ejpam-4015	124	11	)	)	PUNCT
ejpam-4015	124	12	=	=	SYM
ejpam-4015	125	1	m2	m2	PROPN
ejpam-4015	125	2	p	p	PROPN
ejpam-4015	125	3	1∫	1∫	NUM
ejpam-4015	125	4	0	0	NUM
ejpam-4015	125	5	k(t	k(t	NOUN
ejpam-4015	125	6	)	)	PUNCT
ejpam-4015	126	1	[	[	X
ejpam-4015	126	2	tap	tap	NOUN
ejpam-4015	126	3	+	+	CCONJ
ejpam-4015	126	4	(	(	PUNCT
ejpam-4015	126	5	1−	1−	NUM
ejpam-4015	126	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	126	7	1	1	NUM
ejpam-4015	126	8	p	p	NOUN
ejpam-4015	126	9	f	f	NOUN
ejpam-4015	126	10	′	′	NUM
ejpam-4015	127	1	(	(	PUNCT
ejpam-4015	127	2	[	[	X
ejpam-4015	127	3	tap	tap	NOUN
ejpam-4015	127	4	+	+	CCONJ
ejpam-4015	127	5	(	(	PUNCT
ejpam-4015	127	6	1−	1−	NUM
ejpam-4015	127	7	t)bp	t)bp	PROPN
ejpam-4015	127	8	]	]	X
ejpam-4015	127	9	1	1	NUM
ejpam-4015	127	10	p	p	NOUN
ejpam-4015	127	11	)	)	PUNCT
ejpam-4015	127	12	dt	dt	PROPN
ejpam-4015	127	13	.	.	PUNCT
ejpam-4015	128	1	where	where	SCONJ
ejpam-4015	128	2	k(t	k(t	NOUN
ejpam-4015	128	3	)	)	PUNCT
ejpam-4015	128	4	=	=	SYM
ejpam-4015	128	5			PROPN
ejpam-4015	128	6	t	t	PROPN
ejpam-4015	128	7	,	,	PUNCT
ejpam-4015	128	8	t	t	PROPN
ejpam-4015	128	9	∈	∈	PROPN
ejpam-4015	129	1	[	[	X
ejpam-4015	129	2	0	0	NUM
ejpam-4015	129	3	,	,	PUNCT
ejpam-4015	129	4	12	12	NUM
ejpam-4015	129	5	)	)	PUNCT
ejpam-4015	129	6	,	,	PUNCT
ejpam-4015	129	7	t−	t−	PROPN
ejpam-4015	129	8	1	1	NUM
ejpam-4015	129	9	,	,	PUNCT
ejpam-4015	129	10	t	t	PROPN
ejpam-4015	129	11	∈	∈	PROPN
ejpam-4015	129	12	[	[	PUNCT
ejpam-4015	129	13	1	1	NUM
ejpam-4015	129	14	2	2	NUM
ejpam-4015	129	15	,	,	PUNCT
ejpam-4015	129	16	1	1	NUM
ejpam-4015	129	17	]	]	PUNCT
ejpam-4015	129	18	,	,	PUNCT
ejpam-4015	129	19	this	this	DET
ejpam-4015	129	20	article	article	NOUN
ejpam-4015	129	21	is	be	AUX
ejpam-4015	129	22	organized	organize	VERB
ejpam-4015	129	23	as	as	ADP
ejpam-4015	129	24	:	:	PUNCT
ejpam-4015	129	25	in	in	ADP
ejpam-4015	129	26	the	the	DET
ejpam-4015	129	27	next	next	ADJ
ejpam-4015	129	28	section	section	NOUN
ejpam-4015	129	29	,	,	PUNCT
ejpam-4015	129	30	we	we	PRON
ejpam-4015	129	31	are	be	AUX
ejpam-4015	129	32	going	go	VERB
ejpam-4015	129	33	to	to	PART
ejpam-4015	129	34	estimate	estimate	VERB
ejpam-4015	129	35	the	the	DET
ejpam-4015	129	36	bounds	bound	NOUN
ejpam-4015	129	37	of	of	ADP
ejpam-4015	129	38	one	one	NUM
ejpam-4015	129	39	of	of	ADP
ejpam-4015	129	40	the	the	DET
ejpam-4015	129	41	hermite−hadamard	hermite−hadamard	ADJ
ejpam-4015	129	42	inequalities	inequality	NOUN
ejpam-4015	129	43	(	(	PUNCT
ejpam-4015	129	44	by	by	ADP
ejpam-4015	129	45	taking	take	VERB
ejpam-4015	129	46	absolute	absolute	ADJ
ejpam-4015	129	47	difference	difference	NOUN
ejpam-4015	129	48	of	of	ADP
ejpam-4015	129	49	first	first	ADJ
ejpam-4015	129	50	term	term	NOUN
ejpam-4015	129	51	and	and	CCONJ
ejpam-4015	129	52	middle	middle	ADJ
ejpam-4015	129	53	term	term	NOUN
ejpam-4015	129	54	of	of	ADP
ejpam-4015	129	55	(	(	PUNCT
ejpam-4015	129	56	4	4	NUM
ejpam-4015	129	57	)	)	PUNCT
ejpam-4015	129	58	)	)	PUNCT
ejpam-4015	129	59	by	by	ADP
ejpam-4015	129	60	using	use	VERB
ejpam-4015	129	61	first	first	ADJ
ejpam-4015	129	62	differentiable	differentiable	ADJ
ejpam-4015	129	63	p−convex	p−convex	NOUN
ejpam-4015	129	64	functions	function	NOUN
ejpam-4015	129	65	in	in	ADP
ejpam-4015	129	66	mixed	mixed	ADJ
ejpam-4015	129	67	kind	kind	NOUN
ejpam-4015	129	68	.	.	PUNCT
ejpam-4015	130	1	these	these	DET
ejpam-4015	130	2	results	result	NOUN
ejpam-4015	130	3	would	would	AUX
ejpam-4015	130	4	capture	capture	VERB
ejpam-4015	130	5	various	various	ADJ
ejpam-4015	130	6	results	result	NOUN
ejpam-4015	130	7	stated	state	VERB
ejpam-4015	130	8	in	in	ADP
ejpam-4015	130	9	[	[	X
ejpam-4015	130	10	15	15	NUM
ejpam-4015	130	11	]	]	PUNCT
ejpam-4015	130	12	,	,	PUNCT
ejpam-4015	130	13	[	[	X
ejpam-4015	130	14	16	16	NUM
ejpam-4015	130	15	]	]	PUNCT
ejpam-4015	130	16	and	and	CCONJ
ejpam-4015	130	17	[	[	X
ejpam-4015	130	18	20	20	NUM
ejpam-4015	130	19	]	]	PUNCT
ejpam-4015	130	20	as	as	ADP
ejpam-4015	130	21	special	special	ADJ
ejpam-4015	130	22	cases	case	NOUN
ejpam-4015	130	23	and	and	CCONJ
ejpam-4015	130	24	the	the	DET
ejpam-4015	130	25	last	last	ADJ
ejpam-4015	130	26	section	section	NOUN
ejpam-4015	130	27	gives	give	VERB
ejpam-4015	130	28	us	we	PRON
ejpam-4015	130	29	conclusion	conclusion	NOUN
ejpam-4015	130	30	with	with	ADP
ejpam-4015	130	31	some	some	DET
ejpam-4015	130	32	remarks	remark	NOUN
ejpam-4015	130	33	and	and	CCONJ
ejpam-4015	130	34	future	future	ADJ
ejpam-4015	130	35	ideas	idea	NOUN
ejpam-4015	130	36	.	.	PUNCT
ejpam-4015	131	1	2	2	X
ejpam-4015	131	2	.	.	X
ejpam-4015	131	3	estimations	estimation	NOUN
ejpam-4015	131	4	of	of	ADP
ejpam-4015	131	5	bound	bind	VERB
ejpam-4015	131	6	of	of	ADP
ejpam-4015	131	7	hermite−hadamard	hermite−hadamard	PROPN
ejpam-4015	131	8	(	(	PUNCT
ejpam-4015	131	9	left	left	ADJ
ejpam-4015	131	10	)	)	PUNCT
ejpam-4015	131	11	inequality	inequality	NOUN
ejpam-4015	131	12	for	for	ADP
ejpam-4015	131	13	mixed	mixed	ADJ
ejpam-4015	131	14	kind	kind	NOUN
ejpam-4015	131	15	s−convex	s−convex	AUX
ejpam-4015	131	16	function	function	VERB
ejpam-4015	131	17	now	now	ADV
ejpam-4015	131	18	we	we	PRON
ejpam-4015	131	19	are	be	AUX
ejpam-4015	131	20	going	go	VERB
ejpam-4015	131	21	to	to	PART
ejpam-4015	131	22	state	state	VERB
ejpam-4015	131	23	and	and	CCONJ
ejpam-4015	131	24	prove	prove	VERB
ejpam-4015	131	25	three	three	NUM
ejpam-4015	131	26	generalized	generalized	ADJ
ejpam-4015	131	27	results	result	NOUN
ejpam-4015	131	28	related	relate	VERB
ejpam-4015	131	29	to	to	ADP
ejpam-4015	131	30	hermite	hermite	PROPN
ejpam-4015	131	31	−hadamard	−hadamard	ADV
ejpam-4015	131	32	type	type	NOUN
ejpam-4015	131	33	inequalities	inequality	NOUN
ejpam-4015	131	34	for	for	ADP
ejpam-4015	131	35	p−	p−	NOUN
ejpam-4015	131	36	convex	convex	NOUN
ejpam-4015	131	37	function	function	NOUN
ejpam-4015	131	38	in	in	ADP
ejpam-4015	131	39	mixed	mixed	ADJ
ejpam-4015	131	40	kind	kind	NOUN
ejpam-4015	131	41	using	use	VERB
ejpam-4015	131	42	definition	definition	NOUN
ejpam-4015	131	43	6	6	NUM
ejpam-4015	131	44	,	,	PUNCT
ejpam-4015	131	45	definition	definition	NOUN
ejpam-4015	131	46	7	7	NUM
ejpam-4015	131	47	and	and	CCONJ
ejpam-4015	131	48	theorem	theorem	VERB
ejpam-4015	131	49	2	2	NUM
ejpam-4015	131	50	.	.	PUNCT
ejpam-4015	131	51	muhammad	muhammad	PROPN
ejpam-4015	131	52	bilal	bilal	PROPN
ejpam-4015	131	53	,	,	PUNCT
ejpam-4015	131	54	asif	asif	PROPN
ejpam-4015	131	55	r.	r.	PROPN
ejpam-4015	131	56	khan	khan	PROPN
ejpam-4015	131	57	/	/	SYM
ejpam-4015	131	58	eur	eur	PROPN
ejpam-4015	131	59	.	.	PUNCT
ejpam-4015	132	1	j.	j.	PROPN
ejpam-4015	132	2	pure	pure	PROPN
ejpam-4015	132	3	appl	appl	PROPN
ejpam-4015	132	4	.	.	PROPN
ejpam-4015	132	5	math	math	PROPN
ejpam-4015	132	6	,	,	PUNCT
ejpam-4015	132	7	14	14	NUM
ejpam-4015	132	8	(	(	PUNCT
ejpam-4015	132	9	3	3	NUM
ejpam-4015	132	10	)	)	PUNCT
ejpam-4015	132	11	(	(	PUNCT
ejpam-4015	132	12	2021	2021	NUM
ejpam-4015	132	13	)	)	PUNCT
ejpam-4015	132	14	,	,	PUNCT
ejpam-4015	132	15	863	863	NUM
ejpam-4015	132	16	-	-	SYM
ejpam-4015	132	17	880	880	NUM
ejpam-4015	132	18	868	868	NUM
ejpam-4015	132	19	theorem	theorem	NOUN
ejpam-4015	132	20	4	4	NUM
ejpam-4015	132	21	.	.	PUNCT
ejpam-4015	133	1	let	let	VERB
ejpam-4015	133	2	f	f	NOUN
ejpam-4015	133	3	:	:	PUNCT
ejpam-4015	134	1	i	i	PRON
ejpam-4015	134	2	⊂	⊂	PROPN
ejpam-4015	134	3	(	(	PUNCT
ejpam-4015	134	4	0,∞	0,∞	NUM
ejpam-4015	134	5	)	)	PUNCT
ejpam-4015	134	6	→	→	PUNCT
ejpam-4015	134	7	r	r	NOUN
ejpam-4015	134	8	be	be	AUX
ejpam-4015	134	9	a	a	DET
ejpam-4015	134	10	differentiable	differentiable	ADJ
ejpam-4015	134	11	mapping	mapping	NOUN
ejpam-4015	134	12	on	on	ADP
ejpam-4015	134	13	i	i	PRON
ejpam-4015	134	14	◦	◦	VERB
ejpam-4015	134	15	such	such	ADJ
ejpam-4015	134	16	that	that	SCONJ
ejpam-4015	134	17	f	f	PROPN
ejpam-4015	134	18	′	′	NUM
ejpam-4015	134	19	∈	∈	PROPN
ejpam-4015	134	20	l[a	l[a	NOUN
ejpam-4015	134	21	,	,	PUNCT
ejpam-4015	134	22	b	b	NOUN
ejpam-4015	134	23	]	]	X
ejpam-4015	134	24	,	,	PUNCT
ejpam-4015	134	25	where	where	SCONJ
ejpam-4015	134	26	a	a	X
ejpam-4015	134	27	,	,	PUNCT
ejpam-4015	134	28	b	b	X
ejpam-4015	134	29	∈	∈	PROPN
ejpam-4015	134	30	i	i	PRON
ejpam-4015	134	31	◦	◦	NOUN
ejpam-4015	134	32	and	and	CCONJ
ejpam-4015	134	33	a	a	DET
ejpam-4015	134	34	<	<	X
ejpam-4015	134	35	b.	b.	NOUN
ejpam-4015	134	36	if	if	SCONJ
ejpam-4015	134	37	|f	|f	PROPN
ejpam-4015	134	38	′|	′|	NUM
ejpam-4015	134	39	is	be	AUX
ejpam-4015	134	40	s−	s−	PROPN
ejpam-4015	134	41	p−convex	p−convex	NOUN
ejpam-4015	134	42	in	in	ADP
ejpam-4015	134	43	the	the	DET
ejpam-4015	134	44	mixed	mixed	ADJ
ejpam-4015	134	45	kind	kind	NOUN
ejpam-4015	134	46	on	on	ADP
ejpam-4015	134	47	i	i	PRON
ejpam-4015	134	48	for	for	ADP
ejpam-4015	134	49	some	some	DET
ejpam-4015	134	50	fixed	fix	VERB
ejpam-4015	134	51	r	r	NOUN
ejpam-4015	134	52	,	,	PUNCT
ejpam-4015	134	53	s	s	NOUN
ejpam-4015	134	54	∈	∈	PROPN
ejpam-4015	135	1	[	[	X
ejpam-4015	135	2	0	0	NUM
ejpam-4015	135	3	,	,	PUNCT
ejpam-4015	135	4	1	1	NUM
ejpam-4015	135	5	]	]	PUNCT
ejpam-4015	135	6	on	on	ADP
ejpam-4015	135	7	[	[	X
ejpam-4015	135	8	a	a	DET
ejpam-4015	135	9	,	,	PUNCT
ejpam-4015	135	10	b	b	NOUN
ejpam-4015	135	11	]	]	X
ejpam-4015	135	12	for	for	ADP
ejpam-4015	135	13	p	p	PROPN
ejpam-4015	135	14	∈	∈	PROPN
ejpam-4015	135	15	r	r	NOUN
ejpam-4015	135	16	\	\	PUNCT
ejpam-4015	135	17	{	{	PUNCT
ejpam-4015	135	18	0	0	NUM
ejpam-4015	135	19	}	}	PUNCT
ejpam-4015	135	20	,	,	PUNCT
ejpam-4015	135	21	then	then	ADV
ejpam-4015	135	22	following	follow	VERB
ejpam-4015	135	23	inequality	inequality	NOUN
ejpam-4015	135	24	holds:∣∣∣∣∣∣	holds:∣∣∣∣∣∣	PROPN
ejpam-4015	135	25	b∫	b∫	PROPN
ejpam-4015	135	26	a	a	DET
ejpam-4015	135	27	f(x	f(x	PROPN
ejpam-4015	135	28	)	)	PUNCT
ejpam-4015	135	29	x1−p	x1−p	PROPN
ejpam-4015	136	1	dx−mpf	dx−mpf	NOUN
ejpam-4015	136	2	(	(	PUNCT
ejpam-4015	136	3	[	[	PUNCT
ejpam-4015	136	4	ap	ap	PROPN
ejpam-4015	136	5	+	+	NUM
ejpam-4015	136	6	bp	bp	PROPN
ejpam-4015	136	7	2	2	NUM
ejpam-4015	136	8	]	]	PUNCT
ejpam-4015	136	9	1	1	NUM
ejpam-4015	136	10	p	p	NOUN
ejpam-4015	136	11	)	)	PUNCT
ejpam-4015	136	12	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4015	136	13	≤m2	≤m2	ADP
ejpam-4015	136	14	p	p	PROPN
ejpam-4015	137	1	[	[	X
ejpam-4015	137	2	a(p)|f	a(p)|f	INTJ
ejpam-4015	137	3	′(a)|+b(p)|f	′(a)|+b(p)|f	NOUN
ejpam-4015	137	4	′(b)|	′(b)|	NOUN
ejpam-4015	137	5	]	]	PUNCT
ejpam-4015	137	6	.	.	PUNCT
ejpam-4015	138	1	where	where	SCONJ
ejpam-4015	138	2	a(p	a(p	NOUN
ejpam-4015	138	3	)	)	PUNCT
ejpam-4015	138	4	=	=	SYM
ejpam-4015	138	5			NUM
ejpam-4015	138	6	1/2∫	1/2∫	NUM
ejpam-4015	138	7	0	0	NUM
ejpam-4015	138	8	trs+1	trs+1	NOUN
ejpam-4015	138	9	[	[	X
ejpam-4015	138	10	tap	tap	NOUN
ejpam-4015	138	11	+	+	CCONJ
ejpam-4015	138	12	(	(	PUNCT
ejpam-4015	138	13	1−	1−	NUM
ejpam-4015	138	14	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	138	15	1	1	NUM
ejpam-4015	138	16	p	p	NOUN
ejpam-4015	138	17	dt+	dt+	NOUN
ejpam-4015	138	18	1∫	1∫	NUM
ejpam-4015	138	19	1/2	1/2	NUM
ejpam-4015	138	20	trs	trs	PROPN
ejpam-4015	138	21	−	−	PROPN
ejpam-4015	138	22	trs+1	trs+1	NOUN
ejpam-4015	139	1	[	[	X
ejpam-4015	139	2	tap	tap	NOUN
ejpam-4015	139	3	+	+	CCONJ
ejpam-4015	139	4	(	(	PUNCT
ejpam-4015	139	5	1−	1−	NUM
ejpam-4015	139	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	139	7	1	1	NUM
ejpam-4015	139	8	p	p	NOUN
ejpam-4015	139	9	dt	dt	X
ejpam-4015	139	10			NUM
ejpam-4015	139	11	b(p	b(p	NOUN
ejpam-4015	139	12	)	)	PUNCT
ejpam-4015	140	1	=	=	SYM
ejpam-4015	140	2			NUM
ejpam-4015	140	3	1/2∫	1/2∫	NUM
ejpam-4015	140	4	0	0	NUM
ejpam-4015	140	5	t(1−	t(1−	PROPN
ejpam-4015	140	6	tr)s	tr)s	PROPN
ejpam-4015	140	7	[	[	X
ejpam-4015	140	8	tap	tap	NOUN
ejpam-4015	140	9	+	+	CCONJ
ejpam-4015	140	10	(	(	PUNCT
ejpam-4015	140	11	1−	1−	NUM
ejpam-4015	140	12	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	140	13	1	1	NUM
ejpam-4015	140	14	p	p	NOUN
ejpam-4015	140	15	dt+	dt+	NOUN
ejpam-4015	140	16	1∫	1∫	NUM
ejpam-4015	140	17	1/2	1/2	NUM
ejpam-4015	140	18	(	(	PUNCT
ejpam-4015	140	19	1−	1−	NUM
ejpam-4015	140	20	t)(1−	t)(1−	NOUN
ejpam-4015	140	21	tr)s	tr)s	NUM
ejpam-4015	140	22	[	[	X
ejpam-4015	140	23	tap	tap	NOUN
ejpam-4015	140	24	+	+	CCONJ
ejpam-4015	140	25	(	(	PUNCT
ejpam-4015	140	26	1−	1−	NUM
ejpam-4015	140	27	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	140	28	1	1	NUM
ejpam-4015	140	29	p	p	NOUN
ejpam-4015	140	30	dt	dt	X
ejpam-4015	140	31			NUM
ejpam-4015	140	32	proof	proof	NOUN
ejpam-4015	140	33	.	.	PUNCT
ejpam-4015	141	1	by	by	ADP
ejpam-4015	141	2	using	use	VERB
ejpam-4015	141	3	lemma	lemma	PROPN
ejpam-4015	141	4	1	1	NUM
ejpam-4015	141	5	and	and	CCONJ
ejpam-4015	141	6	then	then	ADV
ejpam-4015	141	7	by	by	ADP
ejpam-4015	141	8	applying	apply	VERB
ejpam-4015	141	9	the	the	DET
ejpam-4015	141	10	definition	definition	NOUN
ejpam-4015	141	11	of	of	ADP
ejpam-4015	141	12	mixed	mixed	ADJ
ejpam-4015	141	13	kind	kind	NOUN
ejpam-4015	141	14	s	s	NOUN
ejpam-4015	141	15	−	−	PROPN
ejpam-4015	141	16	p−convexity	p−convexity	PROPN
ejpam-4015	141	17	of	of	ADP
ejpam-4015	141	18	|f	|f	PRON
ejpam-4015	141	19	′|	′|	NUM
ejpam-4015	141	20	on	on	ADP
ejpam-4015	141	21	i	i	PRON
ejpam-4015	141	22	,	,	PUNCT
ejpam-4015	141	23	we	we	PRON
ejpam-4015	141	24	have,∣∣∣∣∣∣	have,∣∣∣∣∣∣	VERB
ejpam-4015	141	25	b∫	b∫	PROPN
ejpam-4015	141	26	a	a	DET
ejpam-4015	141	27	f(x	f(x	PROPN
ejpam-4015	141	28	)	)	PUNCT
ejpam-4015	142	1	x1−p	x1−p	PROPN
ejpam-4015	143	1	dx−mpf	dx−mpf	NOUN
ejpam-4015	143	2	(	(	PUNCT
ejpam-4015	143	3	[	[	PUNCT
ejpam-4015	143	4	ap	ap	PROPN
ejpam-4015	143	5	+	+	NUM
ejpam-4015	143	6	bp	bp	PROPN
ejpam-4015	143	7	2	2	NUM
ejpam-4015	143	8	]	]	PUNCT
ejpam-4015	143	9	1	1	NUM
ejpam-4015	143	10	p	p	NOUN
ejpam-4015	143	11	)	)	PUNCT
ejpam-4015	143	12	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4015	143	13	≤	≤	PROPN
ejpam-4015	143	14	m2	m2	PROPN
ejpam-4015	143	15	p	p	PROPN
ejpam-4015	143	16			NUM
ejpam-4015	143	17	1/2∫	1/2∫	NUM
ejpam-4015	143	18	0	0	NUM
ejpam-4015	143	19	t	t	NOUN
ejpam-4015	143	20	[	[	X
ejpam-4015	143	21	tap	tap	NOUN
ejpam-4015	143	22	+	+	CCONJ
ejpam-4015	143	23	(	(	PUNCT
ejpam-4015	143	24	1−	1−	NUM
ejpam-4015	143	25	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	143	26	1	1	NUM
ejpam-4015	143	27	p	p	NOUN
ejpam-4015	143	28	∣∣∣f	∣∣∣f	NOUN
ejpam-4015	144	1	′	′	NUM
ejpam-4015	144	2	(	(	PUNCT
ejpam-4015	144	3	[	[	X
ejpam-4015	144	4	tap	tap	NOUN
ejpam-4015	144	5	+	+	CCONJ
ejpam-4015	144	6	(	(	PUNCT
ejpam-4015	144	7	1−	1−	NUM
ejpam-4015	144	8	t)bp	t)bp	PROPN
ejpam-4015	144	9	]	]	X
ejpam-4015	144	10	1	1	NUM
ejpam-4015	144	11	p	p	NOUN
ejpam-4015	144	12	)	)	PUNCT
ejpam-4015	144	13	∣∣∣	∣∣∣	NOUN
ejpam-4015	144	14	dt	dt	ADP
ejpam-4015	145	1	+	+	CCONJ
ejpam-4015	145	2	1∫	1∫	NUM
ejpam-4015	145	3	1/2	1/2	NUM
ejpam-4015	145	4	1−	1−	NUM
ejpam-4015	145	5	t	t	NOUN
ejpam-4015	145	6	[	[	X
ejpam-4015	145	7	tap	tap	NOUN
ejpam-4015	145	8	+	+	CCONJ
ejpam-4015	145	9	(	(	PUNCT
ejpam-4015	145	10	1−	1−	NUM
ejpam-4015	145	11	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	145	12	1	1	NUM
ejpam-4015	145	13	p	p	NOUN
ejpam-4015	145	14	∣∣∣f	∣∣∣f	NOUN
ejpam-4015	146	1	′	′	NUM
ejpam-4015	146	2	(	(	PUNCT
ejpam-4015	146	3	[	[	X
ejpam-4015	146	4	tap	tap	NOUN
ejpam-4015	146	5	+	+	CCONJ
ejpam-4015	146	6	(	(	PUNCT
ejpam-4015	146	7	1−	1−	NUM
ejpam-4015	146	8	t)bp	t)bp	PROPN
ejpam-4015	146	9	]	]	X
ejpam-4015	146	10	1	1	NUM
ejpam-4015	146	11	p	p	NOUN
ejpam-4015	146	12	)	)	PUNCT
ejpam-4015	146	13	∣∣∣	∣∣∣	ADJ
ejpam-4015	146	14	dt	dt	ADP
ejpam-4015	147	1			NUM
ejpam-4015	147	2	≤	≤	NOUN
ejpam-4015	147	3	m2	m2	PROPN
ejpam-4015	147	4	p	p	PROPN
ejpam-4015	147	5			NUM
ejpam-4015	147	6	1/2∫	1/2∫	NUM
ejpam-4015	147	7	0	0	NUM
ejpam-4015	147	8	t	t	NOUN
ejpam-4015	147	9	[	[	X
ejpam-4015	147	10	tap	tap	NOUN
ejpam-4015	147	11	+	+	CCONJ
ejpam-4015	147	12	(	(	PUNCT
ejpam-4015	147	13	1−	1−	NUM
ejpam-4015	147	14	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	147	15	1	1	NUM
ejpam-4015	147	16	p	p	NOUN
ejpam-4015	147	17	{	{	PUNCT
ejpam-4015	147	18	trs|f	trs|f	PROPN
ejpam-4015	147	19	′(a)|+	′(a)|+	PROPN
ejpam-4015	147	20	(	(	PUNCT
ejpam-4015	147	21	1−	1−	NUM
ejpam-4015	147	22	tr)s|f	tr)s|f	NOUN
ejpam-4015	147	23	′(b)|	′(b)|	VERB
ejpam-4015	147	24	}	}	PUNCT
ejpam-4015	147	25	dt	dt	PROPN
ejpam-4015	148	1	+	+	CCONJ
ejpam-4015	148	2	1∫	1∫	NUM
ejpam-4015	148	3	1/2	1/2	NUM
ejpam-4015	148	4	1−	1−	NUM
ejpam-4015	148	5	t	t	NOUN
ejpam-4015	148	6	[	[	X
ejpam-4015	148	7	tap	tap	NOUN
ejpam-4015	148	8	+	+	CCONJ
ejpam-4015	148	9	(	(	PUNCT
ejpam-4015	148	10	1−	1−	NUM
ejpam-4015	148	11	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	148	12	1	1	NUM
ejpam-4015	148	13	p	p	NOUN
ejpam-4015	148	14	{	{	PUNCT
ejpam-4015	148	15	trs|f	trs|f	PROPN
ejpam-4015	148	16	′(a)|+	′(a)|+	PROPN
ejpam-4015	148	17	(	(	PUNCT
ejpam-4015	148	18	1−	1−	NUM
ejpam-4015	148	19	tr)s|f	tr)s|f	NOUN
ejpam-4015	148	20	′(b)|	′(b)|	VERB
ejpam-4015	148	21	}	}	PUNCT
ejpam-4015	148	22	dt	dt	ADP
ejpam-4015	148	23			NUM
ejpam-4015	148	24	=	=	SYM
ejpam-4015	148	25	m2	m2	PROPN
ejpam-4015	148	26	p	p	PROPN
ejpam-4015	148	27			PRON
ejpam-4015	148	28			NOUN
ejpam-4015	148	29	1/2∫	1/2∫	NUM
ejpam-4015	148	30	0	0	NUM
ejpam-4015	148	31	trs+1	trs+1	NOUN
ejpam-4015	148	32	[	[	X
ejpam-4015	148	33	tap	tap	NOUN
ejpam-4015	148	34	+	+	CCONJ
ejpam-4015	148	35	(	(	PUNCT
ejpam-4015	148	36	1−	1−	NUM
ejpam-4015	148	37	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	148	38	1	1	NUM
ejpam-4015	148	39	p	p	NOUN
ejpam-4015	148	40	dt+	dt+	NOUN
ejpam-4015	148	41	1∫	1∫	NUM
ejpam-4015	148	42	1/2	1/2	NUM
ejpam-4015	148	43	trs	trs	PROPN
ejpam-4015	148	44	−	−	PROPN
ejpam-4015	148	45	trs+1	trs+1	NOUN
ejpam-4015	148	46	[	[	X
ejpam-4015	148	47	tap	tap	NOUN
ejpam-4015	148	48	+	+	CCONJ
ejpam-4015	148	49	(	(	PUNCT
ejpam-4015	148	50	1−	1−	NUM
ejpam-4015	148	51	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	148	52	1	1	NUM
ejpam-4015	149	1	p	p	NOUN
ejpam-4015	149	2	dt	dt	X
ejpam-4015	149	3			PROPN
ejpam-4015	149	4	|f	|f	PROPN
ejpam-4015	149	5	′(a)|	′(a)|	X
ejpam-4015	150	1	+	+	CCONJ
ejpam-4015	151	1			PRON
ejpam-4015	151	2	1/2∫	1/2∫	NUM
ejpam-4015	151	3	0	0	NUM
ejpam-4015	152	1	t(1−	t(1−	PROPN
ejpam-4015	152	2	tr)s	tr)s	PROPN
ejpam-4015	152	3	[	[	X
ejpam-4015	152	4	tap	tap	NOUN
ejpam-4015	152	5	+	+	CCONJ
ejpam-4015	152	6	(	(	PUNCT
ejpam-4015	152	7	1−	1−	NUM
ejpam-4015	152	8	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	152	9	1	1	NUM
ejpam-4015	152	10	p	p	NOUN
ejpam-4015	152	11	dt+	dt+	NOUN
ejpam-4015	152	12	1∫	1∫	NUM
ejpam-4015	152	13	1/2	1/2	NUM
ejpam-4015	152	14	(	(	PUNCT
ejpam-4015	152	15	1−	1−	NUM
ejpam-4015	152	16	t)(1−	t)(1−	NOUN
ejpam-4015	152	17	tr)s	tr)s	NUM
ejpam-4015	152	18	[	[	X
ejpam-4015	152	19	tap	tap	NOUN
ejpam-4015	152	20	+	+	CCONJ
ejpam-4015	152	21	(	(	PUNCT
ejpam-4015	152	22	1−	1−	NUM
ejpam-4015	152	23	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	152	24	1	1	NUM
ejpam-4015	152	25	p	p	NOUN
ejpam-4015	152	26	dt	dt	X
ejpam-4015	152	27			PROPN
ejpam-4015	152	28	|f	|f	PROPN
ejpam-4015	152	29	′(b)|	′(b)|	VERB
ejpam-4015	152	30			NUM
ejpam-4015	152	31	muhammad	muhammad	PROPN
ejpam-4015	152	32	bilal	bilal	PROPN
ejpam-4015	152	33	,	,	PUNCT
ejpam-4015	152	34	asif	asif	PROPN
ejpam-4015	152	35	r.	r.	PROPN
ejpam-4015	152	36	khan	khan	PROPN
ejpam-4015	152	37	/	/	SYM
ejpam-4015	152	38	eur	eur	PROPN
ejpam-4015	152	39	.	.	PUNCT
ejpam-4015	153	1	j.	j.	PROPN
ejpam-4015	153	2	pure	pure	PROPN
ejpam-4015	153	3	appl	appl	PROPN
ejpam-4015	153	4	.	.	PROPN
ejpam-4015	153	5	math	math	PROPN
ejpam-4015	153	6	,	,	PUNCT
ejpam-4015	153	7	14	14	NUM
ejpam-4015	153	8	(	(	PUNCT
ejpam-4015	153	9	3	3	NUM
ejpam-4015	153	10	)	)	PUNCT
ejpam-4015	153	11	(	(	PUNCT
ejpam-4015	153	12	2021	2021	NUM
ejpam-4015	153	13	)	)	PUNCT
ejpam-4015	153	14	,	,	PUNCT
ejpam-4015	153	15	863	863	NUM
ejpam-4015	153	16	-	-	SYM
ejpam-4015	153	17	880	880	NUM
ejpam-4015	153	18	869	869	NUM
ejpam-4015	153	19	which	which	PRON
ejpam-4015	153	20	completes	complete	VERB
ejpam-4015	153	21	the	the	DET
ejpam-4015	153	22	proof	proof	NOUN
ejpam-4015	153	23	.	.	PUNCT
ejpam-4015	154	1	remark	remark	VERB
ejpam-4015	154	2	8	8	NUM
ejpam-4015	154	3	.	.	PUNCT
ejpam-4015	155	1	in	in	ADP
ejpam-4015	155	2	theorem	theorem	NOUN
ejpam-4015	155	3	4	4	NUM
ejpam-4015	155	4	,	,	PUNCT
ejpam-4015	155	5	we	we	PRON
ejpam-4015	155	6	can	can	AUX
ejpam-4015	155	7	get	get	VERB
ejpam-4015	155	8	the	the	DET
ejpam-4015	155	9	following	follow	VERB
ejpam-4015	155	10	results	result	NOUN
ejpam-4015	155	11	:	:	PUNCT
ejpam-4015	155	12	(	(	PUNCT
ejpam-4015	155	13	i	i	NOUN
ejpam-4015	155	14	)	)	PUNCT
ejpam-4015	155	15	if	if	SCONJ
ejpam-4015	155	16	one	one	PRON
ejpam-4015	155	17	takes	take	VERB
ejpam-4015	155	18	r	r	NOUN
ejpam-4015	155	19	=	=	SYM
ejpam-4015	155	20	s	s	NOUN
ejpam-4015	155	21	=	=	SYM
ejpam-4015	155	22	1	1	NUM
ejpam-4015	155	23	,	,	PUNCT
ejpam-4015	155	24	then	then	ADV
ejpam-4015	155	25	one	one	PRON
ejpam-4015	155	26	has	have	AUX
ejpam-4015	155	27	theorem	theorem	VERB
ejpam-4015	155	28	3.3	3.3	NUM
ejpam-4015	155	29	of	of	ADP
ejpam-4015	155	30	[	[	X
ejpam-4015	155	31	20	20	NUM
ejpam-4015	155	32	]	]	PUNCT
ejpam-4015	155	33	.	.	PUNCT
ejpam-4015	156	1	(	(	PUNCT
ejpam-4015	156	2	ii	ii	NOUN
ejpam-4015	156	3	)	)	PUNCT
ejpam-4015	156	4	if	if	SCONJ
ejpam-4015	156	5	one	one	PRON
ejpam-4015	156	6	takes	take	VERB
ejpam-4015	156	7	p	p	NOUN
ejpam-4015	156	8	=	=	NOUN
ejpam-4015	156	9	r	r	NOUN
ejpam-4015	156	10	=	=	SYM
ejpam-4015	156	11	s	s	NOUN
ejpam-4015	156	12	=	=	SYM
ejpam-4015	156	13	1	1	NUM
ejpam-4015	156	14	,	,	PUNCT
ejpam-4015	156	15	then	then	ADV
ejpam-4015	156	16	one	one	PRON
ejpam-4015	156	17	has	have	VERB
ejpam-4015	156	18	the	the	DET
ejpam-4015	156	19	theorem	theorem	ADJ
ejpam-4015	156	20	2.2	2.2	NUM
ejpam-4015	156	21	of	of	ADP
ejpam-4015	156	22	[	[	X
ejpam-4015	156	23	15	15	NUM
ejpam-4015	156	24	]	]	PUNCT
ejpam-4015	156	25	.	.	PUNCT
ejpam-4015	157	1	corollary	corollary	ADJ
ejpam-4015	157	2	1	1	NUM
ejpam-4015	157	3	.	.	PUNCT
ejpam-4015	158	1	in	in	ADP
ejpam-4015	158	2	theorem	theorem	NOUN
ejpam-4015	158	3	4	4	NUM
ejpam-4015	158	4	,	,	PUNCT
ejpam-4015	158	5	one	one	PRON
ejpam-4015	158	6	can	can	AUX
ejpam-4015	158	7	see	see	VERB
ejpam-4015	158	8	the	the	DET
ejpam-4015	158	9	following	following	NOUN
ejpam-4015	158	10	:	:	PUNCT
ejpam-4015	158	11	(	(	PUNCT
ejpam-4015	158	12	i	i	NOUN
ejpam-4015	158	13	)	)	PUNCT
ejpam-4015	158	14	if	if	SCONJ
ejpam-4015	158	15	one	one	PRON
ejpam-4015	158	16	takes	take	VERB
ejpam-4015	158	17	s	s	NOUN
ejpam-4015	158	18	=	=	NOUN
ejpam-4015	158	19	1	1	NUM
ejpam-4015	158	20	then	then	ADV
ejpam-4015	158	21	one	one	NUM
ejpam-4015	158	22	has	have	VERB
ejpam-4015	158	23	the	the	DET
ejpam-4015	158	24	following	follow	VERB
ejpam-4015	158	25	hermite	hermite	ADJ
ejpam-4015	158	26	–	–	PUNCT
ejpam-4015	158	27	hadamard	hadamard	ADJ
ejpam-4015	158	28	type	type	NOUN
ejpam-4015	158	29	inequality	inequality	NOUN
ejpam-4015	158	30	for	for	ADP
ejpam-4015	158	31	s−	s−	PROPN
ejpam-4015	158	32	p−convex	p−convex	NOUN
ejpam-4015	158	33	functions	function	NOUN
ejpam-4015	158	34	in	in	ADP
ejpam-4015	158	35	1st	1st	ADJ
ejpam-4015	158	36	kind:∣∣∣∣∣∣	kind:∣∣∣∣∣∣	PROPN
ejpam-4015	158	37	b∫	b∫	PROPN
ejpam-4015	158	38	a	a	DET
ejpam-4015	158	39	f(x	f(x	PROPN
ejpam-4015	158	40	)	)	PUNCT
ejpam-4015	159	1	x1−p	x1−p	PROPN
ejpam-4015	160	1	dx−mpf	dx−mpf	NOUN
ejpam-4015	160	2	(	(	PUNCT
ejpam-4015	160	3	[	[	PUNCT
ejpam-4015	160	4	ap	ap	PROPN
ejpam-4015	160	5	+	+	NUM
ejpam-4015	160	6	bp	bp	PROPN
ejpam-4015	160	7	2	2	NUM
ejpam-4015	160	8	]	]	PUNCT
ejpam-4015	160	9	1	1	NUM
ejpam-4015	160	10	p	p	NOUN
ejpam-4015	160	11	)	)	PUNCT
ejpam-4015	160	12	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4015	160	13	≤	≤	ADJ
ejpam-4015	160	14	m2	m2	PROPN
ejpam-4015	160	15	p	p	PROPN
ejpam-4015	160	16			PRON
ejpam-4015	160	17			NOUN
ejpam-4015	160	18	1/2∫	1/2∫	NUM
ejpam-4015	160	19	0	0	NUM
ejpam-4015	160	20	ts+1	ts+1	PROPN
ejpam-4015	161	1	[	[	X
ejpam-4015	161	2	tap	tap	NOUN
ejpam-4015	161	3	+	+	CCONJ
ejpam-4015	161	4	(	(	PUNCT
ejpam-4015	161	5	1−	1−	NUM
ejpam-4015	161	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	161	7	1	1	NUM
ejpam-4015	161	8	p	p	NOUN
ejpam-4015	161	9	dt+	dt+	NOUN
ejpam-4015	161	10	1∫	1∫	NUM
ejpam-4015	161	11	1/2	1/2	NUM
ejpam-4015	161	12	ts	ts	ADP
ejpam-4015	161	13	−	−	PROPN
ejpam-4015	161	14	ts+1	ts+1	PROPN
ejpam-4015	162	1	[	[	X
ejpam-4015	162	2	tap	tap	NOUN
ejpam-4015	162	3	+	+	CCONJ
ejpam-4015	162	4	(	(	PUNCT
ejpam-4015	162	5	1−	1−	NUM
ejpam-4015	162	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	162	7	1	1	NUM
ejpam-4015	162	8	p	p	NOUN
ejpam-4015	162	9	dt	dt	X
ejpam-4015	162	10			PROPN
ejpam-4015	162	11	|f	|f	PROPN
ejpam-4015	162	12	′(a)|	′(a)|	X
ejpam-4015	163	1	+	+	CCONJ
ejpam-4015	163	2			PRON
ejpam-4015	163	3	1/2∫	1/2∫	NOUN
ejpam-4015	163	4	0	0	NUM
ejpam-4015	164	1	t−	t−	PROPN
ejpam-4015	164	2	ts+1	ts+1	PROPN
ejpam-4015	165	1	[	[	X
ejpam-4015	165	2	tap	tap	NOUN
ejpam-4015	165	3	+	+	CCONJ
ejpam-4015	165	4	(	(	PUNCT
ejpam-4015	165	5	1−	1−	NUM
ejpam-4015	165	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	165	7	1	1	NUM
ejpam-4015	165	8	p	p	NOUN
ejpam-4015	165	9	dt+	dt+	NOUN
ejpam-4015	165	10	1∫	1∫	NUM
ejpam-4015	165	11	1/2	1/2	NUM
ejpam-4015	165	12	1−	1−	NUM
ejpam-4015	166	1	t−	t−	PROPN
ejpam-4015	166	2	ts	ts	ADP
ejpam-4015	166	3	+	+	NUM
ejpam-4015	166	4	ts+1	ts+1	X
ejpam-4015	166	5	[	[	X
ejpam-4015	166	6	tap	tap	NOUN
ejpam-4015	166	7	+	+	CCONJ
ejpam-4015	166	8	(	(	PUNCT
ejpam-4015	166	9	1−	1−	NUM
ejpam-4015	166	10	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	166	11	1	1	NUM
ejpam-4015	166	12	p	p	NOUN
ejpam-4015	166	13	dt	dt	X
ejpam-4015	166	14			PROPN
ejpam-4015	166	15	|f	|f	PROPN
ejpam-4015	167	1	′(b)|	′(b)|	VERB
ejpam-4015	167	2			PRON
ejpam-4015	167	3	.	.	PUNCT
ejpam-4015	168	1	(	(	PUNCT
ejpam-4015	168	2	ii	ii	NOUN
ejpam-4015	168	3	)	)	PUNCT
ejpam-4015	168	4	if	if	SCONJ
ejpam-4015	168	5	one	one	PRON
ejpam-4015	168	6	takes	take	VERB
ejpam-4015	168	7	r	r	NOUN
ejpam-4015	168	8	=	=	SYM
ejpam-4015	168	9	1	1	NUM
ejpam-4015	168	10	,	,	PUNCT
ejpam-4015	168	11	then	then	ADV
ejpam-4015	168	12	one	one	PRON
ejpam-4015	168	13	has	have	VERB
ejpam-4015	168	14	the	the	DET
ejpam-4015	168	15	following	follow	VERB
ejpam-4015	168	16	hermite	hermite	ADJ
ejpam-4015	168	17	–	–	PUNCT
ejpam-4015	168	18	hadamard	hadamard	ADJ
ejpam-4015	168	19	type	type	NOUN
ejpam-4015	168	20	inequality	inequality	NOUN
ejpam-4015	168	21	for	for	ADP
ejpam-4015	168	22	s−	s−	PROPN
ejpam-4015	168	23	p−convex	p−convex	NOUN
ejpam-4015	168	24	functions	function	NOUN
ejpam-4015	168	25	in	in	ADP
ejpam-4015	168	26	2nd	2nd	ADJ
ejpam-4015	168	27	kind:∣∣∣∣∣∣	kind:∣∣∣∣∣∣	PROPN
ejpam-4015	168	28	b∫	b∫	PROPN
ejpam-4015	168	29	a	a	DET
ejpam-4015	168	30	f(x	f(x	PROPN
ejpam-4015	168	31	)	)	PUNCT
ejpam-4015	169	1	x1−p	x1−p	PROPN
ejpam-4015	170	1	dx−mpf	dx−mpf	NOUN
ejpam-4015	170	2	(	(	PUNCT
ejpam-4015	170	3	[	[	PUNCT
ejpam-4015	170	4	ap	ap	PROPN
ejpam-4015	170	5	+	+	NUM
ejpam-4015	170	6	bp	bp	PROPN
ejpam-4015	170	7	2	2	NUM
ejpam-4015	170	8	]	]	PUNCT
ejpam-4015	170	9	1	1	NUM
ejpam-4015	170	10	p	p	NOUN
ejpam-4015	170	11	)	)	PUNCT
ejpam-4015	170	12	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4015	170	13	≤	≤	ADJ
ejpam-4015	170	14	m2	m2	PROPN
ejpam-4015	170	15	p	p	PROPN
ejpam-4015	170	16			PRON
ejpam-4015	170	17			NOUN
ejpam-4015	170	18	1/2∫	1/2∫	NUM
ejpam-4015	170	19	0	0	NUM
ejpam-4015	170	20	ts+1	ts+1	PROPN
ejpam-4015	171	1	[	[	X
ejpam-4015	171	2	tap	tap	NOUN
ejpam-4015	171	3	+	+	CCONJ
ejpam-4015	171	4	(	(	PUNCT
ejpam-4015	171	5	1−	1−	NUM
ejpam-4015	171	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	171	7	1	1	NUM
ejpam-4015	171	8	p	p	NOUN
ejpam-4015	171	9	dt+	dt+	NOUN
ejpam-4015	171	10	1∫	1∫	NUM
ejpam-4015	171	11	1/2	1/2	NUM
ejpam-4015	171	12	ts	ts	ADP
ejpam-4015	171	13	−	−	PROPN
ejpam-4015	171	14	ts+1	ts+1	PROPN
ejpam-4015	172	1	[	[	X
ejpam-4015	172	2	tap	tap	NOUN
ejpam-4015	172	3	+	+	CCONJ
ejpam-4015	172	4	(	(	PUNCT
ejpam-4015	172	5	1−	1−	NUM
ejpam-4015	172	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	172	7	1	1	NUM
ejpam-4015	172	8	p	p	NOUN
ejpam-4015	172	9	dt	dt	X
ejpam-4015	172	10			PROPN
ejpam-4015	172	11	|f	|f	PROPN
ejpam-4015	172	12	′(a)|	′(a)|	X
ejpam-4015	173	1	+	+	CCONJ
ejpam-4015	173	2			PROPN
ejpam-4015	173	3	1/2∫	1/2∫	NUM
ejpam-4015	173	4	0	0	NUM
ejpam-4015	173	5	t(1−	t(1−	ADJ
ejpam-4015	173	6	t)s	t)s	PROPN
ejpam-4015	174	1	[	[	X
ejpam-4015	174	2	tap	tap	NOUN
ejpam-4015	174	3	+	+	CCONJ
ejpam-4015	174	4	(	(	PUNCT
ejpam-4015	174	5	1−	1−	NUM
ejpam-4015	174	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	174	7	1	1	NUM
ejpam-4015	174	8	p	p	NOUN
ejpam-4015	174	9	dt+	dt+	NOUN
ejpam-4015	174	10	1∫	1∫	NUM
ejpam-4015	174	11	1/2	1/2	NUM
ejpam-4015	174	12	(	(	PUNCT
ejpam-4015	174	13	1−	1−	NUM
ejpam-4015	174	14	t)s+1	t)s+1	NOUN
ejpam-4015	174	15	[	[	X
ejpam-4015	174	16	tap	tap	NOUN
ejpam-4015	174	17	+	+	CCONJ
ejpam-4015	174	18	(	(	PUNCT
ejpam-4015	174	19	1−	1−	NUM
ejpam-4015	174	20	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	174	21	1	1	NUM
ejpam-4015	174	22	p	p	NOUN
ejpam-4015	174	23	dt	dt	X
ejpam-4015	174	24			PROPN
ejpam-4015	174	25	|f	|f	PROPN
ejpam-4015	174	26	′(b)|	′(b)|	VERB
ejpam-4015	174	27			PRON
ejpam-4015	174	28	.	.	PUNCT
ejpam-4015	175	1	(	(	PUNCT
ejpam-4015	175	2	iii	iii	X
ejpam-4015	175	3	)	)	PUNCT
ejpam-4015	175	4	if	if	SCONJ
ejpam-4015	175	5	one	one	PRON
ejpam-4015	175	6	takes	take	VERB
ejpam-4015	175	7	p	p	NOUN
ejpam-4015	175	8	=	=	NOUN
ejpam-4015	175	9	1	1	NUM
ejpam-4015	175	10	,	,	PUNCT
ejpam-4015	175	11	then	then	ADV
ejpam-4015	175	12	one	one	PRON
ejpam-4015	175	13	has	have	VERB
ejpam-4015	175	14	the	the	DET
ejpam-4015	175	15	following	follow	VERB
ejpam-4015	175	16	hermite	hermite	ADJ
ejpam-4015	175	17	–	–	PUNCT
ejpam-4015	175	18	hadamard	hadamard	ADJ
ejpam-4015	175	19	type	type	NOUN
ejpam-4015	175	20	inequality	inequality	NOUN
ejpam-4015	175	21	for	for	ADP
ejpam-4015	175	22	(	(	PUNCT
ejpam-4015	175	23	s	s	X
ejpam-4015	175	24	,	,	PUNCT
ejpam-4015	175	25	r)−convex	r)−convex	PROPN
ejpam-4015	175	26	functions	function	NOUN
ejpam-4015	175	27	in	in	ADP
ejpam-4015	175	28	mixed	mixed	ADJ
ejpam-4015	175	29	kind:∣∣∣∣∣∣	kind:∣∣∣∣∣∣	NOUN
ejpam-4015	175	30	b∫	b∫	PROPN
ejpam-4015	175	31	a	a	DET
ejpam-4015	175	32	f(x)dx−m1f	f(x)dx−m1f	NOUN
ejpam-4015	175	33	(	(	PUNCT
ejpam-4015	175	34	a+	a+	NOUN
ejpam-4015	175	35	b	b	NOUN
ejpam-4015	175	36	2	2	NUM
ejpam-4015	175	37	)	)	PUNCT
ejpam-4015	175	38	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-4015	175	39	muhammad	muhammad	PROPN
ejpam-4015	175	40	bilal	bilal	PROPN
ejpam-4015	175	41	,	,	PUNCT
ejpam-4015	175	42	asif	asif	PROPN
ejpam-4015	175	43	r.	r.	PROPN
ejpam-4015	175	44	khan	khan	PROPN
ejpam-4015	175	45	/	/	SYM
ejpam-4015	175	46	eur	eur	PROPN
ejpam-4015	175	47	.	.	PUNCT
ejpam-4015	176	1	j.	j.	PROPN
ejpam-4015	176	2	pure	pure	PROPN
ejpam-4015	176	3	appl	appl	PROPN
ejpam-4015	176	4	.	.	PROPN
ejpam-4015	176	5	math	math	PROPN
ejpam-4015	176	6	,	,	PUNCT
ejpam-4015	176	7	14	14	NUM
ejpam-4015	176	8	(	(	PUNCT
ejpam-4015	176	9	3	3	NUM
ejpam-4015	176	10	)	)	PUNCT
ejpam-4015	176	11	(	(	PUNCT
ejpam-4015	176	12	2021	2021	NUM
ejpam-4015	176	13	)	)	PUNCT
ejpam-4015	176	14	,	,	PUNCT
ejpam-4015	176	15	863	863	NUM
ejpam-4015	176	16	-	-	SYM
ejpam-4015	176	17	880	880	NUM
ejpam-4015	176	18	870	870	NUM
ejpam-4015	176	19	≤	≤	NOUN
ejpam-4015	176	20	m2	m2	PROPN
ejpam-4015	176	21	1	1	NUM
ejpam-4015	177	1	[	[	X
ejpam-4015	177	2	{	{	PUNCT
ejpam-4015	177	3	β1/2r	β1/2r	ADJ
ejpam-4015	177	4	(	(	PUNCT
ejpam-4015	177	5	2	2	NUM
ejpam-4015	177	6	r	r	NOUN
ejpam-4015	177	7	,	,	PUNCT
ejpam-4015	177	8	s+	s+	X
ejpam-4015	177	9	1	1	X
ejpam-4015	177	10	)	)	PUNCT
ejpam-4015	178	1	+	+	NUM
ejpam-4015	178	2	β1−1/2r	β1−1/2r	NOUN
ejpam-4015	178	3	(	(	PUNCT
ejpam-4015	178	4	s+	s+	NUM
ejpam-4015	178	5	1	1	NUM
ejpam-4015	178	6	,	,	PUNCT
ejpam-4015	178	7	1	1	NUM
ejpam-4015	178	8	r	r	NOUN
ejpam-4015	178	9	)	)	PUNCT
ejpam-4015	178	10	−	−	NOUN
ejpam-4015	178	11	β1−1/2r	β1−1/2r	NOUN
ejpam-4015	178	12	(	(	PUNCT
ejpam-4015	178	13	s+	s+	NUM
ejpam-4015	178	14	1	1	NUM
ejpam-4015	178	15	,	,	PUNCT
ejpam-4015	178	16	2	2	NUM
ejpam-4015	178	17	r	r	NOUN
ejpam-4015	178	18	)	)	PUNCT
ejpam-4015	178	19	}	}	PUNCT
ejpam-4015	178	20	|f	|f	PROPN
ejpam-4015	179	1	′(b)|	′(b)|	VERB
ejpam-4015	179	2	r	r	NOUN
ejpam-4015	179	3	+	+	CCONJ
ejpam-4015	179	4	(	(	PUNCT
ejpam-4015	179	5	2rs+1	2rs+1	NUM
ejpam-4015	179	6	−	−	NOUN
ejpam-4015	179	7	1	1	NUM
ejpam-4015	179	8	)	)	PUNCT
ejpam-4015	179	9	2rs+1(rs+	2rs+1(rs+	NOUN
ejpam-4015	179	10	1)(rs+	1)(rs+	NUM
ejpam-4015	179	11	2	2	NUM
ejpam-4015	179	12	)	)	PUNCT
ejpam-4015	179	13	|f	|f	PROPN
ejpam-4015	179	14	′(a)|	′(a)|	X
ejpam-4015	179	15	]	]	PUNCT
ejpam-4015	179	16	.	.	PUNCT
ejpam-4015	180	1	(	(	PUNCT
ejpam-4015	180	2	iv	iv	X
ejpam-4015	180	3	)	)	PUNCT
ejpam-4015	180	4	if	if	SCONJ
ejpam-4015	180	5	one	one	PRON
ejpam-4015	180	6	takes	take	VERB
ejpam-4015	180	7	p	p	NOUN
ejpam-4015	180	8	=	=	PUNCT
ejpam-4015	180	9	s	s	PART
ejpam-4015	180	10	=	=	SYM
ejpam-4015	180	11	1	1	NUM
ejpam-4015	180	12	,	,	PUNCT
ejpam-4015	180	13	then	then	ADV
ejpam-4015	180	14	one	one	PRON
ejpam-4015	180	15	has	have	VERB
ejpam-4015	180	16	the	the	DET
ejpam-4015	180	17	following	follow	VERB
ejpam-4015	180	18	hermite	hermite	ADJ
ejpam-4015	180	19	–	–	PUNCT
ejpam-4015	180	20	hadamard	hadamard	ADJ
ejpam-4015	180	21	type	type	NOUN
ejpam-4015	180	22	inequality	inequality	NOUN
ejpam-4015	180	23	for	for	ADP
ejpam-4015	180	24	s−convex	s−convex	X
ejpam-4015	180	25	functions	function	NOUN
ejpam-4015	180	26	in	in	ADP
ejpam-4015	180	27	1st	1st	ADJ
ejpam-4015	180	28	kind:∣∣∣∣∣∣	kind:∣∣∣∣∣∣	PROPN
ejpam-4015	180	29	b∫	b∫	PROPN
ejpam-4015	180	30	a	a	DET
ejpam-4015	180	31	f(x)dx−m1f	f(x)dx−m1f	NOUN
ejpam-4015	180	32	(	(	PUNCT
ejpam-4015	180	33	a+	a+	NOUN
ejpam-4015	180	34	b	b	NOUN
ejpam-4015	180	35	2	2	NUM
ejpam-4015	180	36	)	)	PUNCT
ejpam-4015	180	37	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4015	180	38	≤	≤	ADJ
ejpam-4015	180	39	m2	m2	PROPN
ejpam-4015	180	40	1	1	NUM
ejpam-4015	180	41	[	[	PUNCT
ejpam-4015	180	42	(	(	PUNCT
ejpam-4015	180	43	2s+1	2s+1	NOUN
ejpam-4015	180	44	−	−	NOUN
ejpam-4015	180	45	1	1	NUM
ejpam-4015	180	46	)	)	PUNCT
ejpam-4015	180	47	2s+1(s+	2s+1(s+	NUM
ejpam-4015	180	48	1)(s+	1)(s+	NUM
ejpam-4015	180	49	2	2	NUM
ejpam-4015	180	50	)	)	PUNCT
ejpam-4015	180	51	|f	|f	PROPN
ejpam-4015	181	1	′(a)|+	′(a)|+	PROPN
ejpam-4015	181	2	(	(	PUNCT
ejpam-4015	181	3	1	1	NUM
ejpam-4015	181	4	4	4	NUM
ejpam-4015	181	5	−	−	NOUN
ejpam-4015	181	6	(	(	PUNCT
ejpam-4015	181	7	2s+1	2s+1	NOUN
ejpam-4015	181	8	−	−	NOUN
ejpam-4015	181	9	1	1	NUM
ejpam-4015	181	10	)	)	PUNCT
ejpam-4015	181	11	2s+1(s+	2s+1(s+	NUM
ejpam-4015	181	12	1)(s+	1)(s+	NUM
ejpam-4015	181	13	2	2	NUM
ejpam-4015	181	14	)	)	PUNCT
ejpam-4015	181	15	)	)	PUNCT
ejpam-4015	182	1	|f	|f	PROPN
ejpam-4015	182	2	′(b)|	′(b)|	VERB
ejpam-4015	182	3	]	]	PUNCT
ejpam-4015	182	4	.	.	PUNCT
ejpam-4015	183	1	(	(	PUNCT
ejpam-4015	183	2	v	v	NOUN
ejpam-4015	183	3	)	)	PUNCT
ejpam-4015	183	4	if	if	SCONJ
ejpam-4015	183	5	one	one	PRON
ejpam-4015	183	6	takes	take	VERB
ejpam-4015	183	7	p	p	NOUN
ejpam-4015	183	8	=	=	PUNCT
ejpam-4015	183	9	r	r	NOUN
ejpam-4015	183	10	=	=	SYM
ejpam-4015	183	11	1	1	NUM
ejpam-4015	183	12	,	,	PUNCT
ejpam-4015	183	13	then	then	ADV
ejpam-4015	183	14	one	one	PRON
ejpam-4015	183	15	has	have	VERB
ejpam-4015	183	16	the	the	DET
ejpam-4015	183	17	following	follow	VERB
ejpam-4015	183	18	hermite	hermite	ADJ
ejpam-4015	183	19	–	–	PUNCT
ejpam-4015	183	20	hadamard	hadamard	ADJ
ejpam-4015	183	21	type	type	NOUN
ejpam-4015	183	22	inequality	inequality	NOUN
ejpam-4015	183	23	for	for	ADP
ejpam-4015	183	24	s−convex	s−convex	X
ejpam-4015	183	25	functions	function	NOUN
ejpam-4015	183	26	in	in	ADP
ejpam-4015	183	27	2nd	2nd	ADJ
ejpam-4015	183	28	kind:∣∣∣∣∣∣	kind:∣∣∣∣∣∣	NOUN
ejpam-4015	183	29	b∫	b∫	PROPN
ejpam-4015	183	30	a	a	DET
ejpam-4015	183	31	f(x)dx−m1f	f(x)dx−m1f	NOUN
ejpam-4015	183	32	(	(	PUNCT
ejpam-4015	183	33	a+	a+	NOUN
ejpam-4015	183	34	b	b	NOUN
ejpam-4015	183	35	2	2	NUM
ejpam-4015	183	36	)	)	PUNCT
ejpam-4015	183	37	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4015	183	38	≤	≤	ADJ
ejpam-4015	183	39	m2	m2	PROPN
ejpam-4015	183	40	1	1	NUM
ejpam-4015	183	41	(	(	PUNCT
ejpam-4015	183	42	2s+1	2s+1	NOUN
ejpam-4015	183	43	−	−	NOUN
ejpam-4015	183	44	1	1	NUM
ejpam-4015	183	45	)	)	PUNCT
ejpam-4015	183	46	2s+1(s+	2s+1(s+	NUM
ejpam-4015	183	47	1)(s+	1)(s+	NUM
ejpam-4015	183	48	2	2	NUM
ejpam-4015	183	49	)	)	PUNCT
ejpam-4015	183	50	(	(	PUNCT
ejpam-4015	183	51	|f	|f	PROPN
ejpam-4015	183	52	′(a)|+	′(a)|+	PROPN
ejpam-4015	183	53	|f	|f	PROPN
ejpam-4015	183	54	′(b)|	′(b)|	PROPN
ejpam-4015	183	55	)	)	PUNCT
ejpam-4015	183	56	.	.	PUNCT
ejpam-4015	184	1	theorem	theorem	NOUN
ejpam-4015	184	2	5	5	NUM
ejpam-4015	184	3	.	.	PUNCT
ejpam-4015	185	1	let	let	VERB
ejpam-4015	185	2	f	f	NOUN
ejpam-4015	185	3	:	:	PUNCT
ejpam-4015	186	1	i	i	PRON
ejpam-4015	186	2	⊂	⊂	PROPN
ejpam-4015	186	3	(	(	PUNCT
ejpam-4015	186	4	0,∞	0,∞	NUM
ejpam-4015	186	5	)	)	PUNCT
ejpam-4015	186	6	→	→	PUNCT
ejpam-4015	186	7	r	r	NOUN
ejpam-4015	186	8	be	be	AUX
ejpam-4015	186	9	a	a	DET
ejpam-4015	186	10	differentiable	differentiable	ADJ
ejpam-4015	186	11	mapping	mapping	NOUN
ejpam-4015	186	12	on	on	ADP
ejpam-4015	186	13	i	i	PRON
ejpam-4015	186	14	◦	◦	VERB
ejpam-4015	186	15	such	such	ADJ
ejpam-4015	186	16	that	that	SCONJ
ejpam-4015	186	17	f	f	PROPN
ejpam-4015	186	18	′	′	NUM
ejpam-4015	186	19	∈	∈	PROPN
ejpam-4015	186	20	l[a	l[a	NOUN
ejpam-4015	186	21	,	,	PUNCT
ejpam-4015	186	22	b	b	NOUN
ejpam-4015	186	23	]	]	X
ejpam-4015	186	24	,	,	PUNCT
ejpam-4015	186	25	where	where	SCONJ
ejpam-4015	186	26	a	a	X
ejpam-4015	186	27	,	,	PUNCT
ejpam-4015	186	28	b	b	X
ejpam-4015	186	29	∈	∈	PROPN
ejpam-4015	186	30	i	i	PRON
ejpam-4015	186	31	◦	◦	NOUN
ejpam-4015	186	32	and	and	CCONJ
ejpam-4015	186	33	a	a	DET
ejpam-4015	186	34	<	<	X
ejpam-4015	186	35	b.	b.	NOUN
ejpam-4015	187	1	if	if	SCONJ
ejpam-4015	187	2	|f	|f	PROPN
ejpam-4015	187	3	′|q	′|q	PROPN
ejpam-4015	187	4	,	,	PUNCT
ejpam-4015	187	5	q	q	X
ejpam-4015	187	6	≥	≥	NOUN
ejpam-4015	187	7	1	1	NUM
ejpam-4015	187	8	is	be	AUX
ejpam-4015	187	9	s−	s−	PROPN
ejpam-4015	187	10	p−convex	p−convex	NOUN
ejpam-4015	187	11	in	in	ADP
ejpam-4015	187	12	the	the	DET
ejpam-4015	187	13	mixed	mixed	ADJ
ejpam-4015	187	14	kind	kind	NOUN
ejpam-4015	187	15	on	on	ADP
ejpam-4015	187	16	i	i	PRON
ejpam-4015	187	17	for	for	ADP
ejpam-4015	187	18	some	some	DET
ejpam-4015	187	19	fixed	fix	VERB
ejpam-4015	187	20	r	r	NOUN
ejpam-4015	187	21	,	,	PUNCT
ejpam-4015	187	22	s	s	NOUN
ejpam-4015	187	23	∈	∈	PROPN
ejpam-4015	187	24	[	[	X
ejpam-4015	187	25	0	0	NUM
ejpam-4015	187	26	,	,	PUNCT
ejpam-4015	187	27	1	1	NUM
ejpam-4015	187	28	]	]	PUNCT
ejpam-4015	187	29	and	and	CCONJ
ejpam-4015	187	30	for	for	ADP
ejpam-4015	187	31	p	p	PROPN
ejpam-4015	187	32	∈	∈	PROPN
ejpam-4015	187	33	r	r	NOUN
ejpam-4015	187	34	\	\	PUNCT
ejpam-4015	187	35	{	{	PUNCT
ejpam-4015	187	36	0	0	NUM
ejpam-4015	187	37	}	}	PUNCT
ejpam-4015	187	38	,	,	PUNCT
ejpam-4015	187	39	then	then	ADV
ejpam-4015	187	40	following	follow	VERB
ejpam-4015	187	41	inequality	inequality	NOUN
ejpam-4015	187	42	holds:∣∣∣∣∣∣	holds:∣∣∣∣∣∣	PROPN
ejpam-4015	187	43	b∫	b∫	PROPN
ejpam-4015	187	44	a	a	DET
ejpam-4015	187	45	f(x	f(x	PROPN
ejpam-4015	187	46	)	)	PUNCT
ejpam-4015	187	47	x1−p	x1−p	PROPN
ejpam-4015	188	1	dx−mpf	dx−mpf	NOUN
ejpam-4015	188	2	(	(	PUNCT
ejpam-4015	188	3	[	[	PUNCT
ejpam-4015	188	4	ap	ap	PROPN
ejpam-4015	188	5	+	+	NUM
ejpam-4015	188	6	bp	bp	PROPN
ejpam-4015	188	7	2	2	NUM
ejpam-4015	188	8	]	]	PUNCT
ejpam-4015	188	9	1	1	NUM
ejpam-4015	188	10	p	p	NOUN
ejpam-4015	188	11	)	)	PUNCT
ejpam-4015	188	12	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4015	188	13	≤	≤	PROPN
ejpam-4015	188	14	m2	m2	PROPN
ejpam-4015	188	15	p	p	PROPN
ejpam-4015	188	16	{	{	PUNCT
ejpam-4015	188	17	(	(	PUNCT
ejpam-4015	188	18	z3(p	z3(p	NOUN
ejpam-4015	188	19	)	)	PUNCT
ejpam-4015	188	20	)	)	PUNCT
ejpam-4015	188	21	1−	1−	NUM
ejpam-4015	188	22	1	1	NUM
ejpam-4015	188	23	q	q	NOUN
ejpam-4015	188	24	[	[	PUNCT
ejpam-4015	188	25	(	(	PUNCT
ejpam-4015	188	26	z4(p))|f	z4(p))|f	NOUN
ejpam-4015	188	27	′(a)|q	′(a)|q	NOUN
ejpam-4015	188	28	+	+	NUM
ejpam-4015	188	29	z5(p)|f	z5(p)|f	NOUN
ejpam-4015	188	30	′(b)|q	′(b)|q	NOUN
ejpam-4015	188	31	]	]	PUNCT
ejpam-4015	189	1	1	1	NUM
ejpam-4015	189	2	q	q	X
ejpam-4015	189	3	+	+	ADJ
ejpam-4015	189	4	(	(	PUNCT
ejpam-4015	189	5	z6(p	z6(p	NUM
ejpam-4015	189	6	)	)	PUNCT
ejpam-4015	189	7	)	)	PUNCT
ejpam-4015	189	8	1−	1−	NUM
ejpam-4015	189	9	1	1	NUM
ejpam-4015	189	10	q	q	NOUN
ejpam-4015	189	11	[	[	PUNCT
ejpam-4015	189	12	(	(	PUNCT
ejpam-4015	189	13	z7(p))|f	z7(p))|f	NOUN
ejpam-4015	189	14	′(a)|q	′(a)|q	NOUN
ejpam-4015	189	15	+	+	CCONJ
ejpam-4015	189	16	z8(p)|f	z8(p)|f	NOUN
ejpam-4015	189	17	′(b)|q	′(b)|q	NOUN
ejpam-4015	189	18	]	]	PUNCT
ejpam-4015	189	19	1	1	NUM
ejpam-4015	189	20	q	q	NOUN
ejpam-4015	189	21	}	}	PUNCT
ejpam-4015	189	22	.	.	PUNCT
ejpam-4015	190	1	where	where	SCONJ
ejpam-4015	190	2	z3(p	z3(p	X
ejpam-4015	190	3	)	)	PUNCT
ejpam-4015	190	4	=	=	SYM
ejpam-4015	190	5	1/2∫	1/2∫	NOUN
ejpam-4015	190	6	0	0	NUM
ejpam-4015	190	7	t	t	NOUN
ejpam-4015	191	1	[	[	X
ejpam-4015	191	2	tap	tap	NOUN
ejpam-4015	191	3	+	+	CCONJ
ejpam-4015	191	4	(	(	PUNCT
ejpam-4015	191	5	1−	1−	NUM
ejpam-4015	191	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	191	7	1	1	NUM
ejpam-4015	191	8	p	p	NOUN
ejpam-4015	191	9	dt	dt	X
ejpam-4015	191	10	,	,	PUNCT
ejpam-4015	191	11	z4(p	z4(p	NUM
ejpam-4015	191	12	)	)	PUNCT
ejpam-4015	191	13	=	=	SYM
ejpam-4015	191	14	1/2∫	1/2∫	NUM
ejpam-4015	191	15	0	0	NUM
ejpam-4015	191	16	trs+1	trs+1	NOUN
ejpam-4015	191	17	[	[	X
ejpam-4015	191	18	tap	tap	NOUN
ejpam-4015	191	19	+	+	CCONJ
ejpam-4015	191	20	(	(	PUNCT
ejpam-4015	191	21	1−	1−	NUM
ejpam-4015	191	22	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	191	23	1	1	NUM
ejpam-4015	191	24	p	p	NOUN
ejpam-4015	191	25	dt	dt	X
ejpam-4015	191	26	z5(p	z5(p	NOUN
ejpam-4015	191	27	)	)	PUNCT
ejpam-4015	191	28	=	=	SYM
ejpam-4015	192	1	1/2∫	1/2∫	NOUN
ejpam-4015	192	2	0	0	NUM
ejpam-4015	193	1	t(1−	t(1−	PROPN
ejpam-4015	193	2	tr)s	tr)s	PROPN
ejpam-4015	193	3	[	[	X
ejpam-4015	193	4	tap	tap	NOUN
ejpam-4015	193	5	+	+	CCONJ
ejpam-4015	193	6	(	(	PUNCT
ejpam-4015	193	7	1−	1−	NUM
ejpam-4015	193	8	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	193	9	1	1	NUM
ejpam-4015	193	10	p	p	NOUN
ejpam-4015	193	11	dt	dt	X
ejpam-4015	193	12	,	,	PUNCT
ejpam-4015	193	13	z6(p	z6(p	NUM
ejpam-4015	193	14	)	)	PUNCT
ejpam-4015	193	15	=	=	PUNCT
ejpam-4015	194	1	1∫	1∫	NUM
ejpam-4015	194	2	1/2	1/2	NUM
ejpam-4015	194	3	(	(	PUNCT
ejpam-4015	194	4	1−	1−	NUM
ejpam-4015	194	5	t	t	NOUN
ejpam-4015	194	6	)	)	PUNCT
ejpam-4015	195	1	[	[	X
ejpam-4015	195	2	tap	tap	NOUN
ejpam-4015	195	3	+	+	CCONJ
ejpam-4015	195	4	(	(	PUNCT
ejpam-4015	195	5	1−	1−	NUM
ejpam-4015	195	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	195	7	1	1	NUM
ejpam-4015	195	8	p	p	NOUN
ejpam-4015	195	9	dt	dt	X
ejpam-4015	195	10	muhammad	muhammad	PROPN
ejpam-4015	195	11	bilal	bilal	PROPN
ejpam-4015	195	12	,	,	PUNCT
ejpam-4015	195	13	asif	asif	PROPN
ejpam-4015	195	14	r.	r.	PROPN
ejpam-4015	195	15	khan	khan	PROPN
ejpam-4015	195	16	/	/	SYM
ejpam-4015	195	17	eur	eur	PROPN
ejpam-4015	195	18	.	.	PUNCT
ejpam-4015	196	1	j.	j.	PROPN
ejpam-4015	196	2	pure	pure	PROPN
ejpam-4015	196	3	appl	appl	PROPN
ejpam-4015	196	4	.	.	PROPN
ejpam-4015	196	5	math	math	PROPN
ejpam-4015	196	6	,	,	PUNCT
ejpam-4015	196	7	14	14	NUM
ejpam-4015	196	8	(	(	PUNCT
ejpam-4015	196	9	3	3	NUM
ejpam-4015	196	10	)	)	PUNCT
ejpam-4015	196	11	(	(	PUNCT
ejpam-4015	196	12	2021	2021	NUM
ejpam-4015	196	13	)	)	PUNCT
ejpam-4015	196	14	,	,	PUNCT
ejpam-4015	196	15	863	863	NUM
ejpam-4015	196	16	-	-	SYM
ejpam-4015	196	17	880	880	NUM
ejpam-4015	196	18	871	871	NUM
ejpam-4015	196	19	z7(p	z7(p	NUM
ejpam-4015	196	20	)	)	PUNCT
ejpam-4015	196	21	=	=	PUNCT
ejpam-4015	197	1	1∫	1∫	NUM
ejpam-4015	197	2	1/2	1/2	NUM
ejpam-4015	197	3	trs(1−	trs(1−	NOUN
ejpam-4015	197	4	t	t	PROPN
ejpam-4015	197	5	)	)	PUNCT
ejpam-4015	198	1	[	[	X
ejpam-4015	198	2	tap	tap	NOUN
ejpam-4015	198	3	+	+	CCONJ
ejpam-4015	198	4	(	(	PUNCT
ejpam-4015	198	5	1−	1−	NUM
ejpam-4015	198	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	198	7	1	1	NUM
ejpam-4015	198	8	p	p	NOUN
ejpam-4015	198	9	dt	dt	X
ejpam-4015	198	10	,	,	PUNCT
ejpam-4015	198	11	z8(p	z8(p	NUM
ejpam-4015	198	12	)	)	PUNCT
ejpam-4015	198	13	=	=	PUNCT
ejpam-4015	199	1	1∫	1∫	NUM
ejpam-4015	199	2	1/2	1/2	NUM
ejpam-4015	199	3	(	(	PUNCT
ejpam-4015	199	4	1−	1−	NUM
ejpam-4015	199	5	t)(1−	t)(1−	NOUN
ejpam-4015	199	6	tr)s	tr)s	NUM
ejpam-4015	200	1	[	[	X
ejpam-4015	200	2	tap	tap	NOUN
ejpam-4015	200	3	+	+	CCONJ
ejpam-4015	200	4	(	(	PUNCT
ejpam-4015	200	5	1−	1−	NUM
ejpam-4015	200	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	200	7	1	1	NUM
ejpam-4015	200	8	p	p	NOUN
ejpam-4015	200	9	dt	dt	NOUN
ejpam-4015	200	10	proof	proof	NOUN
ejpam-4015	200	11	.	.	PUNCT
ejpam-4015	201	1	by	by	ADP
ejpam-4015	201	2	using	use	VERB
ejpam-4015	201	3	lemma	lemma	PROPN
ejpam-4015	201	4	1	1	NUM
ejpam-4015	201	5	,	,	PUNCT
ejpam-4015	201	6	power	power	NOUN
ejpam-4015	201	7	mean	mean	NOUN
ejpam-4015	201	8	inequality	inequality	NOUN
ejpam-4015	201	9	and	and	CCONJ
ejpam-4015	201	10	then	then	ADV
ejpam-4015	201	11	by	by	ADP
ejpam-4015	201	12	applying	apply	VERB
ejpam-4015	201	13	the	the	DET
ejpam-4015	201	14	definition	definition	NOUN
ejpam-4015	201	15	of	of	ADP
ejpam-4015	201	16	mixed	mixed	ADJ
ejpam-4015	201	17	kind	kind	NOUN
ejpam-4015	201	18	s−	s−	PROPN
ejpam-4015	201	19	p−convexity	p−convexity	PROPN
ejpam-4015	201	20	of	of	ADP
ejpam-4015	201	21	|f	|f	PROPN
ejpam-4015	201	22	|q	|q	NOUN
ejpam-4015	201	23	on	on	ADP
ejpam-4015	201	24	i	i	PRON
ejpam-4015	201	25	,	,	PUNCT
ejpam-4015	201	26	we	we	PRON
ejpam-4015	201	27	have,∣∣∣∣∣∣	have,∣∣∣∣∣∣	VERB
ejpam-4015	201	28	b∫	b∫	PROPN
ejpam-4015	201	29	a	a	DET
ejpam-4015	201	30	f(x	f(x	PROPN
ejpam-4015	201	31	)	)	PUNCT
ejpam-4015	202	1	x1−p	x1−p	PROPN
ejpam-4015	203	1	dx−mpf	dx−mpf	NOUN
ejpam-4015	203	2	(	(	PUNCT
ejpam-4015	203	3	[	[	PUNCT
ejpam-4015	203	4	ap	ap	PROPN
ejpam-4015	203	5	+	+	NUM
ejpam-4015	203	6	bp	bp	PROPN
ejpam-4015	203	7	2	2	NUM
ejpam-4015	203	8	]	]	PUNCT
ejpam-4015	203	9	1	1	NUM
ejpam-4015	203	10	p	p	NOUN
ejpam-4015	203	11	)	)	PUNCT
ejpam-4015	203	12	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4015	203	13	≤	≤	PROPN
ejpam-4015	203	14	m2	m2	PROPN
ejpam-4015	203	15	p	p	PROPN
ejpam-4015	203	16			NUM
ejpam-4015	203	17	1/2∫	1/2∫	NUM
ejpam-4015	203	18	0	0	NUM
ejpam-4015	203	19	t	t	NOUN
ejpam-4015	203	20	[	[	X
ejpam-4015	203	21	tap	tap	NOUN
ejpam-4015	203	22	+	+	CCONJ
ejpam-4015	203	23	(	(	PUNCT
ejpam-4015	203	24	1−	1−	NUM
ejpam-4015	203	25	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	203	26	1	1	NUM
ejpam-4015	203	27	p	p	NOUN
ejpam-4015	203	28	∣∣∣f	∣∣∣f	NOUN
ejpam-4015	204	1	′	′	NUM
ejpam-4015	204	2	(	(	PUNCT
ejpam-4015	204	3	[	[	X
ejpam-4015	204	4	tap	tap	NOUN
ejpam-4015	204	5	+	+	CCONJ
ejpam-4015	204	6	(	(	PUNCT
ejpam-4015	204	7	1−	1−	NUM
ejpam-4015	204	8	t)bp	t)bp	PROPN
ejpam-4015	204	9	]	]	X
ejpam-4015	204	10	1	1	NUM
ejpam-4015	204	11	p	p	NOUN
ejpam-4015	204	12	)	)	PUNCT
ejpam-4015	204	13	∣∣∣	∣∣∣	NOUN
ejpam-4015	204	14	dt	dt	ADP
ejpam-4015	205	1	+	+	CCONJ
ejpam-4015	205	2	1∫	1∫	NUM
ejpam-4015	205	3	1/2	1/2	NUM
ejpam-4015	205	4	1−	1−	NUM
ejpam-4015	205	5	t	t	NOUN
ejpam-4015	205	6	[	[	X
ejpam-4015	205	7	tap	tap	NOUN
ejpam-4015	205	8	+	+	CCONJ
ejpam-4015	205	9	(	(	PUNCT
ejpam-4015	205	10	1−	1−	NUM
ejpam-4015	205	11	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	205	12	1	1	NUM
ejpam-4015	205	13	p	p	NOUN
ejpam-4015	205	14	∣∣∣f	∣∣∣f	NOUN
ejpam-4015	206	1	′	′	NUM
ejpam-4015	206	2	(	(	PUNCT
ejpam-4015	206	3	[	[	X
ejpam-4015	206	4	tap	tap	NOUN
ejpam-4015	206	5	+	+	CCONJ
ejpam-4015	206	6	(	(	PUNCT
ejpam-4015	206	7	1−	1−	NUM
ejpam-4015	206	8	t)bp	t)bp	PROPN
ejpam-4015	206	9	]	]	X
ejpam-4015	206	10	1	1	NUM
ejpam-4015	206	11	p	p	NOUN
ejpam-4015	206	12	)	)	PUNCT
ejpam-4015	206	13	∣∣∣	∣∣∣	ADJ
ejpam-4015	206	14	dt	dt	ADP
ejpam-4015	207	1			NUM
ejpam-4015	207	2	≤	≤	NOUN
ejpam-4015	207	3	m2	m2	PROPN
ejpam-4015	207	4	p	p	PROPN
ejpam-4015	207	5			NOUN
ejpam-4015	207	6			X
ejpam-4015	207	7	1/2∫	1/2∫	NUM
ejpam-4015	207	8	0	0	NUM
ejpam-4015	207	9	t	t	NOUN
ejpam-4015	208	1	[	[	X
ejpam-4015	208	2	tap	tap	NOUN
ejpam-4015	208	3	+	+	CCONJ
ejpam-4015	208	4	(	(	PUNCT
ejpam-4015	208	5	1−	1−	NUM
ejpam-4015	208	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	208	7	1	1	NUM
ejpam-4015	208	8	p	p	NOUN
ejpam-4015	208	9	dt	dt	NOUN
ejpam-4015	208	10			PROPN
ejpam-4015	208	11	1−	1−	NUM
ejpam-4015	208	12	1	1	NUM
ejpam-4015	208	13	q	q	NOUN
ejpam-4015	208	14			X
ejpam-4015	208	15	1/2∫	1/2∫	NUM
ejpam-4015	208	16	0	0	NUM
ejpam-4015	208	17	t	t	NOUN
ejpam-4015	209	1	[	[	X
ejpam-4015	209	2	tap	tap	NOUN
ejpam-4015	209	3	+	+	CCONJ
ejpam-4015	209	4	(	(	PUNCT
ejpam-4015	209	5	1−	1−	NUM
ejpam-4015	209	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	209	7	1	1	NUM
ejpam-4015	209	8	p	p	NOUN
ejpam-4015	209	9	∣∣∣f	∣∣∣f	NOUN
ejpam-4015	209	10	′	′	NUM
ejpam-4015	209	11	(	(	PUNCT
ejpam-4015	209	12	[	[	X
ejpam-4015	209	13	tap	tap	NOUN
ejpam-4015	209	14	+	+	CCONJ
ejpam-4015	209	15	(	(	PUNCT
ejpam-4015	209	16	1−	1−	NUM
ejpam-4015	209	17	t)bp	t)bp	PROPN
ejpam-4015	209	18	]	]	X
ejpam-4015	209	19	1	1	NUM
ejpam-4015	209	20	p	p	NOUN
ejpam-4015	209	21	)	)	PUNCT
ejpam-4015	209	22	∣∣∣q	∣∣∣q	NUM
ejpam-4015	209	23	dt	dt	NOUN
ejpam-4015	209	24			PROPN
ejpam-4015	209	25	1	1	NUM
ejpam-4015	209	26	q	q	NOUN
ejpam-4015	209	27	+	+	NUM
ejpam-4015	209	28			NUM
ejpam-4015	209	29	1∫	1∫	NUM
ejpam-4015	209	30	1/2	1/2	NUM
ejpam-4015	209	31	1−	1−	NUM
ejpam-4015	209	32	t	t	NOUN
ejpam-4015	210	1	[	[	X
ejpam-4015	210	2	tap	tap	NOUN
ejpam-4015	210	3	+	+	CCONJ
ejpam-4015	210	4	(	(	PUNCT
ejpam-4015	210	5	1−	1−	NUM
ejpam-4015	210	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	210	7	1	1	NUM
ejpam-4015	210	8	p	p	NOUN
ejpam-4015	210	9	dt	dt	NOUN
ejpam-4015	210	10			PROPN
ejpam-4015	210	11	1−	1−	NUM
ejpam-4015	210	12	1	1	NUM
ejpam-4015	210	13	q	q	NOUN
ejpam-4015	210	14			NUM
ejpam-4015	210	15	1∫	1∫	NUM
ejpam-4015	210	16	1/2	1/2	NUM
ejpam-4015	210	17	1−	1−	NUM
ejpam-4015	210	18	t	t	NOUN
ejpam-4015	211	1	[	[	X
ejpam-4015	211	2	tap	tap	NOUN
ejpam-4015	211	3	+	+	CCONJ
ejpam-4015	211	4	(	(	PUNCT
ejpam-4015	211	5	1−	1−	NUM
ejpam-4015	211	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	211	7	1	1	NUM
ejpam-4015	211	8	p	p	NOUN
ejpam-4015	211	9	∣∣∣f	∣∣∣f	NOUN
ejpam-4015	211	10	′	′	NUM
ejpam-4015	211	11	(	(	PUNCT
ejpam-4015	211	12	[	[	X
ejpam-4015	211	13	tap	tap	NOUN
ejpam-4015	211	14	+	+	CCONJ
ejpam-4015	211	15	(	(	PUNCT
ejpam-4015	211	16	1−	1−	NUM
ejpam-4015	211	17	t)bp	t)bp	PROPN
ejpam-4015	211	18	]	]	X
ejpam-4015	211	19	1	1	NUM
ejpam-4015	211	20	p	p	NOUN
ejpam-4015	211	21	)	)	PUNCT
ejpam-4015	211	22	∣∣∣q	∣∣∣q	NUM
ejpam-4015	211	23	dt	dt	NOUN
ejpam-4015	211	24			PROPN
ejpam-4015	211	25	1	1	NUM
ejpam-4015	211	26	q	q	NOUN
ejpam-4015	211	27			NOUN
ejpam-4015	211	28	≤	≤	NUM
ejpam-4015	211	29	m2	m2	PROPN
ejpam-4015	211	30	p	p	PROPN
ejpam-4015	211	31			NOUN
ejpam-4015	211	32			X
ejpam-4015	211	33	1/2∫	1/2∫	NUM
ejpam-4015	211	34	0	0	NUM
ejpam-4015	211	35	t	t	NOUN
ejpam-4015	212	1	[	[	X
ejpam-4015	212	2	tap	tap	NOUN
ejpam-4015	212	3	+	+	CCONJ
ejpam-4015	212	4	(	(	PUNCT
ejpam-4015	212	5	1−	1−	NUM
ejpam-4015	212	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	212	7	1	1	NUM
ejpam-4015	212	8	p	p	NOUN
ejpam-4015	212	9	dt	dt	NOUN
ejpam-4015	212	10			PROPN
ejpam-4015	212	11	1−	1−	NUM
ejpam-4015	212	12	1	1	NUM
ejpam-4015	212	13	q	q	NOUN
ejpam-4015	212	14			X
ejpam-4015	212	15	1/2∫	1/2∫	NUM
ejpam-4015	212	16	0	0	NUM
ejpam-4015	212	17	t	t	NOUN
ejpam-4015	213	1	[	[	X
ejpam-4015	213	2	tap	tap	NOUN
ejpam-4015	213	3	+	+	CCONJ
ejpam-4015	213	4	(	(	PUNCT
ejpam-4015	213	5	1−	1−	NUM
ejpam-4015	213	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	213	7	1	1	NUM
ejpam-4015	213	8	p	p	NOUN
ejpam-4015	213	9	{	{	PUNCT
ejpam-4015	213	10	trs|f	trs|f	PROPN
ejpam-4015	213	11	′(a)|q	′(a)|q	NOUN
ejpam-4015	213	12	+	+	CCONJ
ejpam-4015	213	13	(	(	PUNCT
ejpam-4015	213	14	1−	1−	NUM
ejpam-4015	213	15	tr)s|f	tr)s|f	PROPN
ejpam-4015	213	16	′(b)|q	′(b)|q	PROPN
ejpam-4015	213	17	}	}	PUNCT
ejpam-4015	213	18	dt	dt	PROPN
ejpam-4015	213	19			PROPN
ejpam-4015	213	20	1	1	NUM
ejpam-4015	213	21	q	q	PROPN
ejpam-4015	213	22	muhammad	muhammad	PROPN
ejpam-4015	213	23	bilal	bilal	PROPN
ejpam-4015	213	24	,	,	PUNCT
ejpam-4015	213	25	asif	asif	PROPN
ejpam-4015	213	26	r.	r.	PROPN
ejpam-4015	213	27	khan	khan	PROPN
ejpam-4015	213	28	/	/	SYM
ejpam-4015	213	29	eur	eur	PROPN
ejpam-4015	213	30	.	.	PUNCT
ejpam-4015	214	1	j.	j.	PROPN
ejpam-4015	214	2	pure	pure	PROPN
ejpam-4015	214	3	appl	appl	PROPN
ejpam-4015	214	4	.	.	PROPN
ejpam-4015	214	5	math	math	PROPN
ejpam-4015	214	6	,	,	PUNCT
ejpam-4015	214	7	14	14	NUM
ejpam-4015	214	8	(	(	PUNCT
ejpam-4015	214	9	3	3	NUM
ejpam-4015	214	10	)	)	PUNCT
ejpam-4015	214	11	(	(	PUNCT
ejpam-4015	214	12	2021	2021	NUM
ejpam-4015	214	13	)	)	PUNCT
ejpam-4015	214	14	,	,	PUNCT
ejpam-4015	214	15	863	863	NUM
ejpam-4015	214	16	-	-	SYM
ejpam-4015	214	17	880	880	NUM
ejpam-4015	214	18	872	872	NUM
ejpam-4015	214	19	+	+	CCONJ
ejpam-4015	214	20			NUM
ejpam-4015	214	21	1∫	1∫	NUM
ejpam-4015	214	22	1/2	1/2	NUM
ejpam-4015	214	23	1−	1−	NUM
ejpam-4015	214	24	t	t	NOUN
ejpam-4015	215	1	[	[	X
ejpam-4015	215	2	tap	tap	NOUN
ejpam-4015	215	3	+	+	CCONJ
ejpam-4015	215	4	(	(	PUNCT
ejpam-4015	215	5	1−	1−	NUM
ejpam-4015	215	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	215	7	1	1	NUM
ejpam-4015	215	8	p	p	NOUN
ejpam-4015	215	9	dt	dt	NOUN
ejpam-4015	215	10			PROPN
ejpam-4015	215	11	1−	1−	NUM
ejpam-4015	215	12	1	1	NUM
ejpam-4015	215	13	q	q	NOUN
ejpam-4015	215	14			NUM
ejpam-4015	215	15	1∫	1∫	NUM
ejpam-4015	215	16	1/2	1/2	NUM
ejpam-4015	215	17	1−	1−	NUM
ejpam-4015	215	18	t	t	NOUN
ejpam-4015	216	1	[	[	X
ejpam-4015	216	2	tap	tap	NOUN
ejpam-4015	216	3	+	+	CCONJ
ejpam-4015	216	4	(	(	PUNCT
ejpam-4015	216	5	1−	1−	NUM
ejpam-4015	216	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	216	7	1	1	NUM
ejpam-4015	216	8	p	p	NOUN
ejpam-4015	216	9	{	{	PUNCT
ejpam-4015	216	10	trs|f	trs|f	PROPN
ejpam-4015	216	11	′(a)|q	′(a)|q	NOUN
ejpam-4015	216	12	+	+	CCONJ
ejpam-4015	216	13	(	(	PUNCT
ejpam-4015	216	14	1−	1−	NUM
ejpam-4015	216	15	tr)s|f	tr)s|f	PROPN
ejpam-4015	216	16	′(b)|q	′(b)|q	PROPN
ejpam-4015	216	17	}	}	PUNCT
ejpam-4015	216	18	dt	dt	PROPN
ejpam-4015	216	19			PROPN
ejpam-4015	216	20	1	1	NUM
ejpam-4015	216	21	q	q	NOUN
ejpam-4015	216	22			NOUN
ejpam-4015	216	23	=	=	SYM
ejpam-4015	216	24	m2	m2	PROPN
ejpam-4015	216	25	p	p	PROPN
ejpam-4015	216	26			NOUN
ejpam-4015	216	27			X
ejpam-4015	216	28	1/2∫	1/2∫	NUM
ejpam-4015	216	29	0	0	NUM
ejpam-4015	216	30	t	t	NOUN
ejpam-4015	217	1	[	[	X
ejpam-4015	217	2	tap	tap	NOUN
ejpam-4015	217	3	+	+	CCONJ
ejpam-4015	217	4	(	(	PUNCT
ejpam-4015	217	5	1−	1−	NUM
ejpam-4015	217	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	217	7	1	1	NUM
ejpam-4015	217	8	p	p	NOUN
ejpam-4015	217	9	dt	dt	NOUN
ejpam-4015	217	10			PROPN
ejpam-4015	217	11	1−	1−	NUM
ejpam-4015	217	12	1	1	NUM
ejpam-4015	217	13	q	q	NOUN
ejpam-4015	217	14	|f	|f	PROPN
ejpam-4015	217	15	′(a)|q	′(a)|q	NOUN
ejpam-4015	217	16	1/2∫	1/2∫	NOUN
ejpam-4015	217	17	0	0	NUM
ejpam-4015	217	18	trs+1	trs+1	NOUN
ejpam-4015	218	1	[	[	X
ejpam-4015	218	2	tap	tap	NOUN
ejpam-4015	218	3	+	+	CCONJ
ejpam-4015	218	4	(	(	PUNCT
ejpam-4015	218	5	1−	1−	NUM
ejpam-4015	218	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	218	7	1	1	NUM
ejpam-4015	218	8	p	p	NOUN
ejpam-4015	218	9	dt+	dt+	NOUN
ejpam-4015	218	10	|f	|f	PROPN
ejpam-4015	218	11	′(b)|q	′(b)|q	PROPN
ejpam-4015	218	12	1/2∫	1/2∫	NOUN
ejpam-4015	218	13	0	0	NUM
ejpam-4015	219	1	t(1−	t(1−	PROPN
ejpam-4015	219	2	tr)s	tr)s	PROPN
ejpam-4015	219	3	[	[	X
ejpam-4015	219	4	tap	tap	NOUN
ejpam-4015	219	5	+	+	CCONJ
ejpam-4015	219	6	(	(	PUNCT
ejpam-4015	219	7	1−	1−	NUM
ejpam-4015	219	8	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	219	9	1	1	NUM
ejpam-4015	219	10	p	p	NOUN
ejpam-4015	219	11	dt	dt	NOUN
ejpam-4015	219	12			PROPN
ejpam-4015	219	13	1	1	NUM
ejpam-4015	219	14	q	q	NOUN
ejpam-4015	219	15	+	+	NUM
ejpam-4015	219	16			NUM
ejpam-4015	219	17	1∫	1∫	NUM
ejpam-4015	219	18	1/2	1/2	NUM
ejpam-4015	219	19	1−	1−	NUM
ejpam-4015	219	20	t	t	NOUN
ejpam-4015	220	1	[	[	X
ejpam-4015	220	2	tap	tap	NOUN
ejpam-4015	220	3	+	+	CCONJ
ejpam-4015	220	4	(	(	PUNCT
ejpam-4015	220	5	1−	1−	NUM
ejpam-4015	220	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	220	7	1	1	NUM
ejpam-4015	220	8	p	p	NOUN
ejpam-4015	220	9	dt	dt	NOUN
ejpam-4015	220	10			PROPN
ejpam-4015	220	11	1−	1−	NUM
ejpam-4015	220	12	1	1	NUM
ejpam-4015	220	13	q	q	NOUN
ejpam-4015	220	14	|f	|f	PROPN
ejpam-4015	220	15	′(a)|q	′(a)|q	NOUN
ejpam-4015	220	16	1∫	1∫	NUM
ejpam-4015	220	17	1/2	1/2	NUM
ejpam-4015	220	18	trs	trs	PROPN
ejpam-4015	220	19	−	−	PROPN
ejpam-4015	220	20	trs+1	trs+1	NOUN
ejpam-4015	220	21	[	[	X
ejpam-4015	220	22	tap	tap	NOUN
ejpam-4015	220	23	+	+	CCONJ
ejpam-4015	220	24	(	(	PUNCT
ejpam-4015	220	25	1−	1−	NUM
ejpam-4015	220	26	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	220	27	1	1	NUM
ejpam-4015	220	28	p	p	NOUN
ejpam-4015	220	29	dt+	dt+	NOUN
ejpam-4015	220	30	|f	|f	PROPN
ejpam-4015	220	31	′(b)|q	′(b)|q	PROPN
ejpam-4015	220	32	1∫	1∫	NUM
ejpam-4015	220	33	1/2	1/2	NUM
ejpam-4015	220	34	(	(	PUNCT
ejpam-4015	220	35	1−	1−	NUM
ejpam-4015	220	36	t)(1−	t)(1−	NOUN
ejpam-4015	220	37	tr)s	tr)s	NUM
ejpam-4015	221	1	[	[	X
ejpam-4015	221	2	tap	tap	NOUN
ejpam-4015	221	3	+	+	CCONJ
ejpam-4015	221	4	(	(	PUNCT
ejpam-4015	221	5	1−	1−	NUM
ejpam-4015	221	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	221	7	1	1	NUM
ejpam-4015	221	8	p	p	NOUN
ejpam-4015	221	9	dt	dt	X
ejpam-4015	221	10			PROPN
ejpam-4015	221	11	1	1	NUM
ejpam-4015	221	12	q	q	NOUN
ejpam-4015	221	13			NOUN
ejpam-4015	221	14	which	which	PRON
ejpam-4015	221	15	completes	complete	VERB
ejpam-4015	221	16	the	the	DET
ejpam-4015	221	17	proof	proof	NOUN
ejpam-4015	221	18	.	.	PUNCT
ejpam-4015	222	1	remark	remark	NOUN
ejpam-4015	222	2	9	9	NUM
ejpam-4015	222	3	.	.	PUNCT
ejpam-4015	223	1	in	in	ADP
ejpam-4015	223	2	theorem	theorem	NOUN
ejpam-4015	223	3	5	5	NUM
ejpam-4015	223	4	,	,	PUNCT
ejpam-4015	223	5	we	we	PRON
ejpam-4015	223	6	can	can	AUX
ejpam-4015	223	7	get	get	VERB
ejpam-4015	223	8	the	the	DET
ejpam-4015	223	9	following	follow	VERB
ejpam-4015	223	10	results	result	NOUN
ejpam-4015	223	11	:	:	PUNCT
ejpam-4015	223	12	(	(	PUNCT
ejpam-4015	223	13	i	i	NOUN
ejpam-4015	223	14	)	)	PUNCT
ejpam-4015	223	15	if	if	SCONJ
ejpam-4015	223	16	one	one	PRON
ejpam-4015	223	17	takes	take	VERB
ejpam-4015	223	18	p	p	NOUN
ejpam-4015	223	19	=	=	NOUN
ejpam-4015	223	20	r	r	NOUN
ejpam-4015	223	21	=	=	SYM
ejpam-4015	223	22	s	s	NOUN
ejpam-4015	223	23	=	=	SYM
ejpam-4015	223	24	1	1	NUM
ejpam-4015	223	25	,	,	PUNCT
ejpam-4015	223	26	then	then	ADV
ejpam-4015	223	27	one	one	PRON
ejpam-4015	223	28	has	have	VERB
ejpam-4015	223	29	first	first	ADJ
ejpam-4015	223	30	result	result	NOUN
ejpam-4015	223	31	of	of	ADP
ejpam-4015	223	32	corollary	corollary	ADJ
ejpam-4015	223	33	2	2	NUM
ejpam-4015	223	34	of	of	ADP
ejpam-4015	223	35	[	[	X
ejpam-4015	223	36	16	16	NUM
ejpam-4015	223	37	]	]	PUNCT
ejpam-4015	223	38	.	.	PUNCT
ejpam-4015	224	1	(	(	PUNCT
ejpam-4015	224	2	ii	ii	NOUN
ejpam-4015	224	3	)	)	PUNCT
ejpam-4015	224	4	if	if	SCONJ
ejpam-4015	224	5	one	one	PRON
ejpam-4015	224	6	takes	take	VERB
ejpam-4015	224	7	r	r	NOUN
ejpam-4015	224	8	=	=	SYM
ejpam-4015	224	9	s	s	NOUN
ejpam-4015	224	10	=	=	SYM
ejpam-4015	224	11	1	1	NUM
ejpam-4015	224	12	,	,	PUNCT
ejpam-4015	224	13	then	then	ADV
ejpam-4015	224	14	one	one	PRON
ejpam-4015	224	15	has	have	VERB
ejpam-4015	224	16	second	second	ADJ
ejpam-4015	224	17	result	result	NOUN
ejpam-4015	224	18	of	of	ADP
ejpam-4015	224	19	corollary	corollary	ADJ
ejpam-4015	224	20	2	2	NUM
ejpam-4015	224	21	of	of	ADP
ejpam-4015	224	22	[	[	X
ejpam-4015	224	23	16	16	NUM
ejpam-4015	224	24	]	]	PUNCT
ejpam-4015	224	25	.	.	PUNCT
ejpam-4015	225	1	(	(	PUNCT
ejpam-4015	225	2	iii	iii	X
ejpam-4015	225	3	)	)	PUNCT
ejpam-4015	225	4	if	if	SCONJ
ejpam-4015	225	5	one	one	PRON
ejpam-4015	225	6	takes	take	VERB
ejpam-4015	225	7	p	p	NOUN
ejpam-4015	225	8	=	=	PUNCT
ejpam-4015	225	9	−1	−1	NOUN
ejpam-4015	225	10	and	and	CCONJ
ejpam-4015	225	11	r	r	NOUN
ejpam-4015	225	12	=	=	SYM
ejpam-4015	225	13	s	s	NOUN
ejpam-4015	225	14	=	=	SYM
ejpam-4015	225	15	1	1	NUM
ejpam-4015	225	16	,	,	PUNCT
ejpam-4015	225	17	then	then	ADV
ejpam-4015	225	18	one	one	PRON
ejpam-4015	225	19	has	have	VERB
ejpam-4015	225	20	fifth	fifth	ADJ
ejpam-4015	225	21	result	result	NOUN
ejpam-4015	225	22	of	of	ADP
ejpam-4015	225	23	corollary	corollary	ADJ
ejpam-4015	225	24	2	2	NUM
ejpam-4015	225	25	of	of	ADP
ejpam-4015	225	26	[	[	X
ejpam-4015	225	27	16	16	NUM
ejpam-4015	225	28	]	]	PUNCT
ejpam-4015	225	29	.	.	PUNCT
ejpam-4015	226	1	corollary	corollary	ADJ
ejpam-4015	226	2	2	2	NUM
ejpam-4015	226	3	.	.	PUNCT
ejpam-4015	226	4	in	in	ADP
ejpam-4015	226	5	theorem	theorem	NOUN
ejpam-4015	226	6	5	5	NUM
ejpam-4015	226	7	,	,	PUNCT
ejpam-4015	226	8	one	one	PRON
ejpam-4015	226	9	can	can	AUX
ejpam-4015	226	10	see	see	VERB
ejpam-4015	226	11	the	the	DET
ejpam-4015	226	12	following	following	NOUN
ejpam-4015	226	13	:	:	PUNCT
ejpam-4015	226	14	(	(	PUNCT
ejpam-4015	226	15	i	i	NOUN
ejpam-4015	226	16	)	)	PUNCT
ejpam-4015	226	17	if	if	SCONJ
ejpam-4015	226	18	one	one	PRON
ejpam-4015	226	19	takes	take	VERB
ejpam-4015	226	20	s	s	NOUN
ejpam-4015	226	21	=	=	NOUN
ejpam-4015	226	22	1	1	NUM
ejpam-4015	226	23	then	then	ADV
ejpam-4015	226	24	one	one	NUM
ejpam-4015	226	25	has	have	VERB
ejpam-4015	226	26	the	the	DET
ejpam-4015	226	27	following	follow	VERB
ejpam-4015	226	28	hermite	hermite	ADJ
ejpam-4015	226	29	–	–	PUNCT
ejpam-4015	226	30	hadamard	hadamard	ADJ
ejpam-4015	226	31	type	type	NOUN
ejpam-4015	226	32	inequality	inequality	NOUN
ejpam-4015	226	33	for	for	ADP
ejpam-4015	226	34	s−	s−	PROPN
ejpam-4015	226	35	p−convex	p−convex	NOUN
ejpam-4015	226	36	functions	function	NOUN
ejpam-4015	226	37	in	in	ADP
ejpam-4015	226	38	1st	1st	ADJ
ejpam-4015	226	39	kind	kind	NOUN
ejpam-4015	226	40	:	:	PUNCT
ejpam-4015	226	41	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4015	226	42	b∫	b∫	PROPN
ejpam-4015	226	43	a	a	DET
ejpam-4015	226	44	f(x	f(x	PROPN
ejpam-4015	226	45	)	)	PUNCT
ejpam-4015	226	46	x1−p	x1−p	PROPN
ejpam-4015	226	47	dx−mpf	dx−mpf	NOUN
ejpam-4015	226	48	(	(	PUNCT
ejpam-4015	226	49	[	[	PUNCT
ejpam-4015	226	50	ap	ap	PROPN
ejpam-4015	226	51	+	+	NUM
ejpam-4015	226	52	bp	bp	PROPN
ejpam-4015	226	53	2	2	NUM
ejpam-4015	226	54	]	]	PUNCT
ejpam-4015	226	55	1	1	NUM
ejpam-4015	226	56	p	p	NOUN
ejpam-4015	226	57	)	)	PUNCT
ejpam-4015	226	58	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4015	226	59	≤m2	≤m2	ADP
ejpam-4015	226	60	p	p	NOUN
ejpam-4015	226	61			NOUN
ejpam-4015	226	62			X
ejpam-4015	226	63	1/2∫	1/2∫	NUM
ejpam-4015	226	64	0	0	NUM
ejpam-4015	226	65	t	t	NOUN
ejpam-4015	226	66	[	[	X
ejpam-4015	226	67	tap	tap	NOUN
ejpam-4015	226	68	+	+	CCONJ
ejpam-4015	226	69	(	(	PUNCT
ejpam-4015	226	70	1−	1−	NUM
ejpam-4015	226	71	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	226	72	1	1	NUM
ejpam-4015	226	73	p	p	NOUN
ejpam-4015	226	74	dt	dt	NOUN
ejpam-4015	226	75			PROPN
ejpam-4015	226	76	1−	1−	NUM
ejpam-4015	226	77	1	1	NUM
ejpam-4015	226	78	q	q	PROPN
ejpam-4015	226	79	muhammad	muhammad	PROPN
ejpam-4015	226	80	bilal	bilal	PROPN
ejpam-4015	226	81	,	,	PUNCT
ejpam-4015	226	82	asif	asif	PROPN
ejpam-4015	226	83	r.	r.	PROPN
ejpam-4015	226	84	khan	khan	PROPN
ejpam-4015	226	85	/	/	SYM
ejpam-4015	226	86	eur	eur	PROPN
ejpam-4015	226	87	.	.	PUNCT
ejpam-4015	227	1	j.	j.	PROPN
ejpam-4015	227	2	pure	pure	PROPN
ejpam-4015	227	3	appl	appl	PROPN
ejpam-4015	227	4	.	.	PROPN
ejpam-4015	227	5	math	math	PROPN
ejpam-4015	227	6	,	,	PUNCT
ejpam-4015	227	7	14	14	NUM
ejpam-4015	227	8	(	(	PUNCT
ejpam-4015	227	9	3	3	NUM
ejpam-4015	227	10	)	)	PUNCT
ejpam-4015	227	11	(	(	PUNCT
ejpam-4015	227	12	2021	2021	NUM
ejpam-4015	227	13	)	)	PUNCT
ejpam-4015	227	14	,	,	PUNCT
ejpam-4015	227	15	863	863	NUM
ejpam-4015	227	16	-	-	SYM
ejpam-4015	227	17	880	880	NUM
ejpam-4015	227	18	873|f	873|f	NUM
ejpam-4015	227	19	′(a)|q	′(a)|q	NOUN
ejpam-4015	227	20	1/2∫	1/2∫	NUM
ejpam-4015	227	21	0	0	NUM
ejpam-4015	227	22	ts+1	ts+1	NOUN
ejpam-4015	228	1	[	[	X
ejpam-4015	228	2	tap	tap	NOUN
ejpam-4015	228	3	+	+	CCONJ
ejpam-4015	228	4	(	(	PUNCT
ejpam-4015	228	5	1−	1−	NUM
ejpam-4015	228	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	228	7	1	1	NUM
ejpam-4015	228	8	p	p	NOUN
ejpam-4015	228	9	dt+	dt+	NOUN
ejpam-4015	228	10	|f	|f	PROPN
ejpam-4015	228	11	′(b)|q	′(b)|q	PROPN
ejpam-4015	228	12	1/2∫	1/2∫	NOUN
ejpam-4015	228	13	0	0	NUM
ejpam-4015	229	1	t−	t−	PROPN
ejpam-4015	229	2	ts+1	ts+1	PROPN
ejpam-4015	230	1	[	[	X
ejpam-4015	230	2	tap	tap	NOUN
ejpam-4015	230	3	+	+	CCONJ
ejpam-4015	230	4	(	(	PUNCT
ejpam-4015	230	5	1−	1−	NUM
ejpam-4015	230	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	230	7	1	1	NUM
ejpam-4015	230	8	p	p	NOUN
ejpam-4015	230	9	dt	dt	NOUN
ejpam-4015	230	10			PROPN
ejpam-4015	230	11	1	1	NUM
ejpam-4015	230	12	q	q	NOUN
ejpam-4015	230	13	+	+	NUM
ejpam-4015	230	14			NUM
ejpam-4015	230	15	1∫	1∫	NUM
ejpam-4015	230	16	1/2	1/2	NUM
ejpam-4015	230	17	1−	1−	NUM
ejpam-4015	230	18	t	t	NOUN
ejpam-4015	231	1	[	[	X
ejpam-4015	231	2	tap	tap	NOUN
ejpam-4015	231	3	+	+	CCONJ
ejpam-4015	231	4	(	(	PUNCT
ejpam-4015	231	5	1−	1−	NUM
ejpam-4015	231	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	231	7	1	1	NUM
ejpam-4015	231	8	p	p	NOUN
ejpam-4015	231	9	dt	dt	NOUN
ejpam-4015	231	10			PROPN
ejpam-4015	231	11	1−	1−	NUM
ejpam-4015	231	12	1	1	NUM
ejpam-4015	231	13	q	q	NOUN
ejpam-4015	231	14	|f	|f	PROPN
ejpam-4015	231	15	′(a)|q	′(a)|q	NOUN
ejpam-4015	231	16	1∫	1∫	NUM
ejpam-4015	231	17	1/2	1/2	NUM
ejpam-4015	231	18	ts	ts	ADP
ejpam-4015	231	19	−	−	PROPN
ejpam-4015	231	20	ts+1	ts+1	PROPN
ejpam-4015	232	1	[	[	X
ejpam-4015	232	2	tap	tap	NOUN
ejpam-4015	232	3	+	+	CCONJ
ejpam-4015	232	4	(	(	PUNCT
ejpam-4015	232	5	1−	1−	NUM
ejpam-4015	232	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	232	7	1	1	NUM
ejpam-4015	232	8	p	p	NOUN
ejpam-4015	232	9	dt+	dt+	NOUN
ejpam-4015	232	10	|f	|f	PROPN
ejpam-4015	232	11	′(b)|q	′(b)|q	PROPN
ejpam-4015	232	12	1∫	1∫	NUM
ejpam-4015	232	13	1/2	1/2	NUM
ejpam-4015	232	14	1−	1−	NUM
ejpam-4015	233	1	t−	t−	PROPN
ejpam-4015	233	2	ts	ts	ADP
ejpam-4015	233	3	+	+	NUM
ejpam-4015	233	4	ts+1	ts+1	X
ejpam-4015	233	5	[	[	X
ejpam-4015	233	6	tap	tap	NOUN
ejpam-4015	233	7	+	+	CCONJ
ejpam-4015	233	8	(	(	PUNCT
ejpam-4015	233	9	1−	1−	NUM
ejpam-4015	233	10	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	233	11	1	1	NUM
ejpam-4015	233	12	p	p	NOUN
ejpam-4015	233	13	dt	dt	X
ejpam-4015	233	14			PROPN
ejpam-4015	233	15	1	1	NUM
ejpam-4015	233	16	q	q	NOUN
ejpam-4015	233	17			NOUN
ejpam-4015	233	18	.	.	PUNCT
ejpam-4015	234	1	(	(	PUNCT
ejpam-4015	234	2	ii	ii	NOUN
ejpam-4015	234	3	)	)	PUNCT
ejpam-4015	234	4	if	if	SCONJ
ejpam-4015	234	5	one	one	PRON
ejpam-4015	234	6	takes	take	VERB
ejpam-4015	234	7	r	r	NOUN
ejpam-4015	234	8	=	=	SYM
ejpam-4015	234	9	1	1	NUM
ejpam-4015	234	10	,	,	PUNCT
ejpam-4015	234	11	then	then	ADV
ejpam-4015	234	12	one	one	PRON
ejpam-4015	234	13	has	have	VERB
ejpam-4015	234	14	the	the	DET
ejpam-4015	234	15	following	follow	VERB
ejpam-4015	234	16	hermite	hermite	ADJ
ejpam-4015	234	17	–	–	PUNCT
ejpam-4015	234	18	hadamard	hadamard	ADJ
ejpam-4015	234	19	type	type	NOUN
ejpam-4015	234	20	inequality	inequality	NOUN
ejpam-4015	234	21	for	for	ADP
ejpam-4015	234	22	s−	s−	PROPN
ejpam-4015	234	23	p−convex	p−convex	NOUN
ejpam-4015	234	24	functions	function	NOUN
ejpam-4015	234	25	in	in	ADP
ejpam-4015	234	26	2nd	2nd	ADJ
ejpam-4015	234	27	kind:∣∣∣∣∣∣	kind:∣∣∣∣∣∣	PROPN
ejpam-4015	234	28	b∫	b∫	PROPN
ejpam-4015	234	29	a	a	DET
ejpam-4015	234	30	f(x	f(x	PROPN
ejpam-4015	234	31	)	)	PUNCT
ejpam-4015	235	1	x1−p	x1−p	PROPN
ejpam-4015	236	1	dx−mpf	dx−mpf	NOUN
ejpam-4015	236	2	(	(	PUNCT
ejpam-4015	236	3	[	[	PUNCT
ejpam-4015	236	4	ap	ap	PROPN
ejpam-4015	236	5	+	+	NUM
ejpam-4015	236	6	bp	bp	PROPN
ejpam-4015	236	7	2	2	NUM
ejpam-4015	236	8	]	]	PUNCT
ejpam-4015	236	9	1	1	NUM
ejpam-4015	236	10	p	p	NOUN
ejpam-4015	236	11	)	)	PUNCT
ejpam-4015	236	12	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4015	236	13	≤m2	≤m2	ADP
ejpam-4015	236	14	p	p	NOUN
ejpam-4015	236	15			NOUN
ejpam-4015	236	16			X
ejpam-4015	236	17	1/2∫	1/2∫	NUM
ejpam-4015	236	18	0	0	NUM
ejpam-4015	236	19	t	t	NOUN
ejpam-4015	237	1	[	[	X
ejpam-4015	237	2	tap	tap	NOUN
ejpam-4015	237	3	+	+	CCONJ
ejpam-4015	237	4	(	(	PUNCT
ejpam-4015	237	5	1−	1−	NUM
ejpam-4015	237	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	237	7	1	1	NUM
ejpam-4015	237	8	p	p	NOUN
ejpam-4015	237	9	dt	dt	NOUN
ejpam-4015	237	10			PROPN
ejpam-4015	237	11	1−	1−	NUM
ejpam-4015	237	12	1	1	NUM
ejpam-4015	237	13	q	q	NOUN
ejpam-4015	237	14	|f	|f	PROPN
ejpam-4015	237	15	′(a)|q	′(a)|q	NOUN
ejpam-4015	237	16	1/2∫	1/2∫	NOUN
ejpam-4015	237	17	0	0	NUM
ejpam-4015	237	18	ts+1	ts+1	NOUN
ejpam-4015	238	1	[	[	X
ejpam-4015	238	2	tap	tap	NOUN
ejpam-4015	238	3	+	+	CCONJ
ejpam-4015	238	4	(	(	PUNCT
ejpam-4015	238	5	1−	1−	NUM
ejpam-4015	238	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	238	7	1	1	NUM
ejpam-4015	238	8	p	p	NOUN
ejpam-4015	238	9	dt+	dt+	NOUN
ejpam-4015	238	10	|f	|f	PROPN
ejpam-4015	238	11	′(b)|q	′(b)|q	PROPN
ejpam-4015	238	12	1/2∫	1/2∫	NOUN
ejpam-4015	238	13	0	0	NUM
ejpam-4015	238	14	t(1−	t(1−	VERB
ejpam-4015	238	15	t)s	t)s	PROPN
ejpam-4015	239	1	[	[	X
ejpam-4015	239	2	tap	tap	NOUN
ejpam-4015	239	3	+	+	CCONJ
ejpam-4015	239	4	(	(	PUNCT
ejpam-4015	239	5	1−	1−	NUM
ejpam-4015	239	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	239	7	1	1	NUM
ejpam-4015	239	8	p	p	NOUN
ejpam-4015	239	9	dt	dt	NOUN
ejpam-4015	239	10			PROPN
ejpam-4015	239	11	1	1	NUM
ejpam-4015	239	12	q	q	NOUN
ejpam-4015	239	13	+	+	NUM
ejpam-4015	239	14			NUM
ejpam-4015	239	15	1∫	1∫	NUM
ejpam-4015	239	16	1/2	1/2	NUM
ejpam-4015	239	17	1−	1−	NUM
ejpam-4015	239	18	t	t	NOUN
ejpam-4015	240	1	[	[	X
ejpam-4015	240	2	tap	tap	NOUN
ejpam-4015	240	3	+	+	CCONJ
ejpam-4015	240	4	(	(	PUNCT
ejpam-4015	240	5	1−	1−	NUM
ejpam-4015	240	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	240	7	1	1	NUM
ejpam-4015	240	8	p	p	NOUN
ejpam-4015	240	9	dt	dt	NOUN
ejpam-4015	240	10			PROPN
ejpam-4015	240	11	1−	1−	NUM
ejpam-4015	240	12	1	1	NUM
ejpam-4015	240	13	q	q	NOUN
ejpam-4015	240	14	|f	|f	PROPN
ejpam-4015	240	15	′(a)|q	′(a)|q	NOUN
ejpam-4015	240	16	1∫	1∫	NUM
ejpam-4015	240	17	1/2	1/2	NUM
ejpam-4015	240	18	ts	ts	ADP
ejpam-4015	240	19	−	−	PROPN
ejpam-4015	240	20	ts+1	ts+1	PROPN
ejpam-4015	241	1	[	[	X
ejpam-4015	241	2	tap	tap	NOUN
ejpam-4015	241	3	+	+	CCONJ
ejpam-4015	241	4	(	(	PUNCT
ejpam-4015	241	5	1−	1−	NUM
ejpam-4015	241	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	241	7	1	1	NUM
ejpam-4015	241	8	p	p	NOUN
ejpam-4015	241	9	dt+	dt+	NOUN
ejpam-4015	241	10	|f	|f	PROPN
ejpam-4015	241	11	′(b)|q	′(b)|q	PROPN
ejpam-4015	241	12	1∫	1∫	NUM
ejpam-4015	241	13	1/2	1/2	NUM
ejpam-4015	241	14	(	(	PUNCT
ejpam-4015	241	15	1−	1−	NUM
ejpam-4015	241	16	t)s+1	t)s+1	NOUN
ejpam-4015	242	1	[	[	X
ejpam-4015	242	2	tap	tap	NOUN
ejpam-4015	242	3	+	+	CCONJ
ejpam-4015	242	4	(	(	PUNCT
ejpam-4015	242	5	1−	1−	NUM
ejpam-4015	242	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	242	7	1	1	NUM
ejpam-4015	242	8	p	p	NOUN
ejpam-4015	242	9	dt	dt	X
ejpam-4015	242	10			PROPN
ejpam-4015	242	11	1	1	NUM
ejpam-4015	242	12	q	q	NOUN
ejpam-4015	242	13			NOUN
ejpam-4015	242	14	.	.	PUNCT
ejpam-4015	243	1	(	(	PUNCT
ejpam-4015	243	2	iii	iii	X
ejpam-4015	243	3	)	)	PUNCT
ejpam-4015	243	4	if	if	SCONJ
ejpam-4015	243	5	one	one	PRON
ejpam-4015	243	6	takes	take	VERB
ejpam-4015	243	7	p	p	NOUN
ejpam-4015	243	8	=	=	NOUN
ejpam-4015	243	9	1	1	NUM
ejpam-4015	243	10	,	,	PUNCT
ejpam-4015	243	11	then	then	ADV
ejpam-4015	243	12	one	one	PRON
ejpam-4015	243	13	has	have	VERB
ejpam-4015	243	14	the	the	DET
ejpam-4015	243	15	following	follow	VERB
ejpam-4015	243	16	hermite	hermite	ADJ
ejpam-4015	243	17	–	–	PUNCT
ejpam-4015	243	18	hadamard	hadamard	ADJ
ejpam-4015	243	19	type	type	NOUN
ejpam-4015	243	20	inequality	inequality	NOUN
ejpam-4015	243	21	for	for	ADP
ejpam-4015	243	22	(	(	PUNCT
ejpam-4015	243	23	s	s	X
ejpam-4015	243	24	,	,	PUNCT
ejpam-4015	243	25	r)−convex	r)−convex	PROPN
ejpam-4015	243	26	functions	function	NOUN
ejpam-4015	243	27	in	in	ADP
ejpam-4015	243	28	mixed	mixed	ADJ
ejpam-4015	243	29	kind:∣∣∣∣∣∣	kind:∣∣∣∣∣∣	NOUN
ejpam-4015	243	30	b∫	b∫	PROPN
ejpam-4015	243	31	a	a	DET
ejpam-4015	243	32	f(x)dx−m1f	f(x)dx−m1f	NOUN
ejpam-4015	243	33	(	(	PUNCT
ejpam-4015	243	34	a+	a+	NOUN
ejpam-4015	243	35	b	b	NOUN
ejpam-4015	243	36	2	2	NUM
ejpam-4015	243	37	)	)	PUNCT
ejpam-4015	243	38	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4015	243	39	≤m2	≤m2	ADP
ejpam-4015	243	40	1	1	NUM
ejpam-4015	243	41	(	(	PUNCT
ejpam-4015	243	42	1	1	NUM
ejpam-4015	243	43	8	8	NUM
ejpam-4015	243	44	)	)	PUNCT
ejpam-4015	243	45	1−	1−	NUM
ejpam-4015	243	46	1	1	NUM
ejpam-4015	243	47	q	q	NOUN
ejpam-4015	243	48	[	[	X
ejpam-4015	243	49	{	{	PUNCT
ejpam-4015	243	50	|f	|f	PROPN
ejpam-4015	243	51	′(a)|q	′(a)|q	NOUN
ejpam-4015	243	52	2rs+2(rs+	2rs+2(rs+	NUM
ejpam-4015	243	53	2	2	NUM
ejpam-4015	243	54	)	)	PUNCT
ejpam-4015	243	55	+	+	NUM
ejpam-4015	243	56	|f	|f	PROPN
ejpam-4015	243	57	′(b)|q	′(b)|q	PROPN
ejpam-4015	243	58	r	r	VERB
ejpam-4015	243	59	β1/2r	β1/2r	NOUN
ejpam-4015	243	60	(	(	PUNCT
ejpam-4015	243	61	2	2	NUM
ejpam-4015	243	62	r	r	NOUN
ejpam-4015	243	63	,	,	PUNCT
ejpam-4015	243	64	s+	s+	X
ejpam-4015	243	65	1	1	NUM
ejpam-4015	243	66	)	)	PUNCT
ejpam-4015	243	67	}	}	PUNCT
ejpam-4015	243	68	1	1	NUM
ejpam-4015	243	69	q	q	NOUN
ejpam-4015	243	70	+	+	NUM
ejpam-4015	243	71	{	{	PUNCT
ejpam-4015	243	72	(	(	PUNCT
ejpam-4015	243	73	2rs+1	2rs+1	NUM
ejpam-4015	243	74	−	−	NUM
ejpam-4015	243	75	1)|f	1)|f	NUM
ejpam-4015	243	76	′(a)|q	′(a)|q	NOUN
ejpam-4015	243	77	2rs+1(rs+	2rs+1(rs+	VERB
ejpam-4015	243	78	1)(rs+	1)(rs+	NUM
ejpam-4015	243	79	2	2	NUM
ejpam-4015	243	80	)	)	PUNCT
ejpam-4015	243	81	+	+	NUM
ejpam-4015	243	82	|f	|f	PROPN
ejpam-4015	243	83	′(b)|q	′(b)|q	PROPN
ejpam-4015	243	84	r	r	NOUN
ejpam-4015	243	85	(	(	PUNCT
ejpam-4015	243	86	β1−1/2r	β1−1/2r	NOUN
ejpam-4015	243	87	(	(	PUNCT
ejpam-4015	243	88	s+	s+	NUM
ejpam-4015	243	89	1	1	NUM
ejpam-4015	243	90	,	,	PUNCT
ejpam-4015	243	91	1	1	NUM
ejpam-4015	243	92	r	r	NOUN
ejpam-4015	243	93	)	)	PUNCT
ejpam-4015	244	1	+	+	NUM
ejpam-4015	244	2	β1−1/2r	β1−1/2r	NOUN
ejpam-4015	244	3	(	(	PUNCT
ejpam-4015	244	4	s+	s+	NUM
ejpam-4015	244	5	1	1	NUM
ejpam-4015	244	6	,	,	PUNCT
ejpam-4015	244	7	2	2	NUM
ejpam-4015	244	8	r	r	NOUN
ejpam-4015	244	9	)	)	PUNCT
ejpam-4015	244	10	)	)	PUNCT
ejpam-4015	244	11	}	}	PUNCT
ejpam-4015	244	12	1	1	NUM
ejpam-4015	244	13	q	q	NOUN
ejpam-4015	244	14	]	]	PUNCT
ejpam-4015	244	15	.	.	PUNCT
ejpam-4015	245	1	muhammad	muhammad	PROPN
ejpam-4015	245	2	bilal	bilal	PROPN
ejpam-4015	245	3	,	,	PUNCT
ejpam-4015	245	4	asif	asif	PROPN
ejpam-4015	245	5	r.	r.	PROPN
ejpam-4015	245	6	khan	khan	PROPN
ejpam-4015	245	7	/	/	SYM
ejpam-4015	245	8	eur	eur	PROPN
ejpam-4015	245	9	.	.	PUNCT
ejpam-4015	246	1	j.	j.	PROPN
ejpam-4015	246	2	pure	pure	PROPN
ejpam-4015	246	3	appl	appl	PROPN
ejpam-4015	246	4	.	.	PROPN
ejpam-4015	246	5	math	math	PROPN
ejpam-4015	246	6	,	,	PUNCT
ejpam-4015	246	7	14	14	NUM
ejpam-4015	246	8	(	(	PUNCT
ejpam-4015	246	9	3	3	NUM
ejpam-4015	246	10	)	)	PUNCT
ejpam-4015	246	11	(	(	PUNCT
ejpam-4015	246	12	2021	2021	NUM
ejpam-4015	246	13	)	)	PUNCT
ejpam-4015	246	14	,	,	PUNCT
ejpam-4015	246	15	863	863	NUM
ejpam-4015	246	16	-	-	SYM
ejpam-4015	246	17	880	880	NUM
ejpam-4015	246	18	874	874	NUM
ejpam-4015	246	19	(	(	PUNCT
ejpam-4015	246	20	iv	iv	X
ejpam-4015	246	21	)	)	PUNCT
ejpam-4015	246	22	if	if	SCONJ
ejpam-4015	246	23	one	one	PRON
ejpam-4015	246	24	takes	take	VERB
ejpam-4015	246	25	p	p	NOUN
ejpam-4015	246	26	=	=	PUNCT
ejpam-4015	246	27	s	s	PART
ejpam-4015	246	28	=	=	SYM
ejpam-4015	246	29	1	1	NUM
ejpam-4015	246	30	,	,	PUNCT
ejpam-4015	246	31	then	then	ADV
ejpam-4015	246	32	one	one	PRON
ejpam-4015	246	33	has	have	AUX
ejpam-4015	246	34	the	the	DET
ejpam-4015	246	35	following	follow	VERB
ejpam-4015	246	36	hermite	hermite	ADJ
ejpam-4015	246	37	–	–	PUNCT
ejpam-4015	246	38	hadamard	hadamard	ADJ
ejpam-4015	246	39	type	type	NOUN
ejpam-4015	246	40	inequality	inequality	NOUN
ejpam-4015	246	41	for	for	ADP
ejpam-4015	246	42	s−convex	s−convex	X
ejpam-4015	246	43	functions	function	NOUN
ejpam-4015	246	44	in	in	ADP
ejpam-4015	246	45	1st	1st	ADJ
ejpam-4015	246	46	kind:∣∣∣∣∣∣	kind:∣∣∣∣∣∣	PROPN
ejpam-4015	247	1	b∫	b∫	PROPN
ejpam-4015	247	2	a	a	DET
ejpam-4015	247	3	f(x)dx−m1f	f(x)dx−m1f	NOUN
ejpam-4015	247	4	(	(	PUNCT
ejpam-4015	247	5	a+	a+	NOUN
ejpam-4015	247	6	b	b	NOUN
ejpam-4015	247	7	2	2	NUM
ejpam-4015	247	8	)	)	PUNCT
ejpam-4015	247	9	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4015	247	10	≤m2	≤m2	ADP
ejpam-4015	247	11	1	1	NUM
ejpam-4015	247	12	(	(	PUNCT
ejpam-4015	247	13	1	1	NUM
ejpam-4015	247	14	8	8	NUM
ejpam-4015	247	15	)	)	PUNCT
ejpam-4015	247	16	1−	1−	NUM
ejpam-4015	247	17	1	1	NUM
ejpam-4015	247	18	q	q	NOUN
ejpam-4015	248	1	[	[	X
ejpam-4015	248	2	{	{	PUNCT
ejpam-4015	248	3	|f	|f	PROPN
ejpam-4015	248	4	′(a)|q	′(a)|q	NOUN
ejpam-4015	248	5	2s+2(s+	2s+2(s+	NUM
ejpam-4015	248	6	2	2	NUM
ejpam-4015	248	7	)	)	PUNCT
ejpam-4015	248	8	+	+	CCONJ
ejpam-4015	248	9	(	(	PUNCT
ejpam-4015	248	10	1	1	NUM
ejpam-4015	248	11	8	8	NUM
ejpam-4015	248	12	−	−	NUM
ejpam-4015	248	13	1	1	NUM
ejpam-4015	248	14	2s+2(s+	2s+2(s+	NUM
ejpam-4015	248	15	2	2	NUM
ejpam-4015	248	16	)	)	PUNCT
ejpam-4015	248	17	)	)	PUNCT
ejpam-4015	248	18	|f	|f	PROPN
ejpam-4015	249	1	′(b)|q	′(b)|q	PROPN
ejpam-4015	249	2	}	}	PUNCT
ejpam-4015	249	3	1	1	NUM
ejpam-4015	249	4	q	q	NOUN
ejpam-4015	249	5	+	+	NUM
ejpam-4015	249	6	{	{	PUNCT
ejpam-4015	249	7	(	(	PUNCT
ejpam-4015	249	8	2s+2	2s+2	PROPN
ejpam-4015	249	9	−	−	PROPN
ejpam-4015	249	10	(	(	PUNCT
ejpam-4015	249	11	s+	s+	NUM
ejpam-4015	249	12	3))|f	3))|f	NUM
ejpam-4015	249	13	′(a)|q	′(a)|q	NOUN
ejpam-4015	249	14	2s+2(s+	2s+2(s+	NUM
ejpam-4015	249	15	1)(s+	1)(s+	NUM
ejpam-4015	249	16	2	2	NUM
ejpam-4015	249	17	)	)	PUNCT
ejpam-4015	249	18	+	+	CCONJ
ejpam-4015	249	19	(	(	PUNCT
ejpam-4015	249	20	1	1	NUM
ejpam-4015	249	21	4	4	NUM
ejpam-4015	249	22	−	−	NOUN
ejpam-4015	249	23	(	(	PUNCT
ejpam-4015	249	24	2s+1	2s+1	NOUN
ejpam-4015	249	25	−	−	NOUN
ejpam-4015	249	26	1	1	NUM
ejpam-4015	249	27	)	)	PUNCT
ejpam-4015	249	28	2s+1(s+	2s+1(s+	NUM
ejpam-4015	249	29	1)(s+	1)(s+	NUM
ejpam-4015	249	30	2	2	NUM
ejpam-4015	249	31	)	)	PUNCT
ejpam-4015	249	32	)	)	PUNCT
ejpam-4015	249	33	|f	|f	PROPN
ejpam-4015	250	1	′(b)|q	′(b)|q	PROPN
ejpam-4015	250	2	}	}	PUNCT
ejpam-4015	250	3	1	1	NUM
ejpam-4015	250	4	q	q	NOUN
ejpam-4015	250	5	]	]	PUNCT
ejpam-4015	250	6	.	.	PUNCT
ejpam-4015	251	1	(	(	PUNCT
ejpam-4015	251	2	v	v	NOUN
ejpam-4015	251	3	)	)	PUNCT
ejpam-4015	251	4	if	if	SCONJ
ejpam-4015	251	5	one	one	PRON
ejpam-4015	251	6	takes	take	VERB
ejpam-4015	251	7	p	p	NOUN
ejpam-4015	251	8	=	=	PUNCT
ejpam-4015	251	9	r	r	NOUN
ejpam-4015	251	10	=	=	SYM
ejpam-4015	251	11	1	1	NUM
ejpam-4015	251	12	,	,	PUNCT
ejpam-4015	251	13	then	then	ADV
ejpam-4015	251	14	one	one	PRON
ejpam-4015	251	15	has	have	VERB
ejpam-4015	251	16	the	the	DET
ejpam-4015	251	17	following	follow	VERB
ejpam-4015	251	18	hermite	hermite	ADJ
ejpam-4015	251	19	–	–	PUNCT
ejpam-4015	251	20	hadamard	hadamard	ADJ
ejpam-4015	251	21	type	type	NOUN
ejpam-4015	251	22	inequality	inequality	NOUN
ejpam-4015	251	23	for	for	ADP
ejpam-4015	251	24	s−convex	s−convex	X
ejpam-4015	251	25	functions	function	NOUN
ejpam-4015	251	26	in	in	ADP
ejpam-4015	251	27	2nd	2nd	ADJ
ejpam-4015	251	28	kind:∣∣∣∣∣∣	kind:∣∣∣∣∣∣	NOUN
ejpam-4015	251	29	b∫	b∫	PROPN
ejpam-4015	251	30	a	a	DET
ejpam-4015	251	31	f(x)dx−m1f	f(x)dx−m1f	NOUN
ejpam-4015	251	32	(	(	PUNCT
ejpam-4015	251	33	a+	a+	NOUN
ejpam-4015	251	34	b	b	NOUN
ejpam-4015	251	35	2	2	NUM
ejpam-4015	251	36	)	)	PUNCT
ejpam-4015	251	37	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4015	251	38	≤m2	≤m2	ADP
ejpam-4015	251	39	1	1	NUM
ejpam-4015	251	40	(	(	PUNCT
ejpam-4015	251	41	1	1	NUM
ejpam-4015	251	42	8	8	NUM
ejpam-4015	251	43	)	)	PUNCT
ejpam-4015	251	44	1−	1−	NUM
ejpam-4015	251	45	1	1	NUM
ejpam-4015	251	46	q	q	NOUN
ejpam-4015	252	1	[	[	X
ejpam-4015	252	2	{	{	PUNCT
ejpam-4015	252	3	|f	|f	PROPN
ejpam-4015	252	4	′(a)|q	′(a)|q	NOUN
ejpam-4015	252	5	2s+2(s+	2s+2(s+	NUM
ejpam-4015	252	6	2	2	NUM
ejpam-4015	252	7	)	)	PUNCT
ejpam-4015	252	8	+	+	CCONJ
ejpam-4015	252	9	(	(	PUNCT
ejpam-4015	252	10	2s+2	2s+2	NUM
ejpam-4015	252	11	−	−	PROPN
ejpam-4015	252	12	(	(	PUNCT
ejpam-4015	252	13	s+	s+	NUM
ejpam-4015	252	14	3))|f	3))|f	NUM
ejpam-4015	252	15	′(b)|q	′(b)|q	PROPN
ejpam-4015	252	16	2s+2(s+	2s+2(s+	NUM
ejpam-4015	252	17	1)(s+	1)(s+	NUM
ejpam-4015	252	18	2	2	NUM
ejpam-4015	252	19	)	)	PUNCT
ejpam-4015	252	20	}	}	PUNCT
ejpam-4015	252	21	1	1	NUM
ejpam-4015	252	22	q	q	NOUN
ejpam-4015	252	23	+	+	NUM
ejpam-4015	252	24	{	{	PUNCT
ejpam-4015	252	25	(	(	PUNCT
ejpam-4015	252	26	2s+2	2s+2	PROPN
ejpam-4015	252	27	−	−	PROPN
ejpam-4015	252	28	(	(	PUNCT
ejpam-4015	252	29	s+	s+	NUM
ejpam-4015	252	30	3))|f	3))|f	NUM
ejpam-4015	252	31	′(a)|q	′(a)|q	NOUN
ejpam-4015	252	32	2s+2(s+	2s+2(s+	NUM
ejpam-4015	252	33	1)(s+	1)(s+	NUM
ejpam-4015	252	34	2	2	NUM
ejpam-4015	252	35	)	)	PUNCT
ejpam-4015	253	1	+	+	NUM
ejpam-4015	253	2	|f	|f	PROPN
ejpam-4015	253	3	′(b)|q	′(b)|q	PROPN
ejpam-4015	253	4	2s+2(s+	2s+2(s+	NUM
ejpam-4015	253	5	2	2	NUM
ejpam-4015	253	6	)	)	PUNCT
ejpam-4015	253	7	}	}	PUNCT
ejpam-4015	253	8	1	1	NUM
ejpam-4015	253	9	q	q	NOUN
ejpam-4015	253	10	]	]	PUNCT
ejpam-4015	253	11	.	.	PUNCT
ejpam-4015	254	1	theorem	theorem	ADJ
ejpam-4015	254	2	6	6	NUM
ejpam-4015	254	3	.	.	PUNCT
ejpam-4015	255	1	let	let	VERB
ejpam-4015	255	2	f	f	NOUN
ejpam-4015	255	3	:	:	PUNCT
ejpam-4015	256	1	i	i	PRON
ejpam-4015	256	2	⊂	⊂	PROPN
ejpam-4015	256	3	(	(	PUNCT
ejpam-4015	256	4	0,∞	0,∞	NUM
ejpam-4015	256	5	)	)	PUNCT
ejpam-4015	256	6	→	→	PUNCT
ejpam-4015	256	7	r	r	NOUN
ejpam-4015	256	8	be	be	AUX
ejpam-4015	256	9	a	a	DET
ejpam-4015	256	10	differentiable	differentiable	ADJ
ejpam-4015	256	11	mapping	mapping	NOUN
ejpam-4015	256	12	on	on	ADP
ejpam-4015	256	13	i	i	PRON
ejpam-4015	256	14	◦	◦	VERB
ejpam-4015	256	15	such	such	ADJ
ejpam-4015	256	16	that	that	SCONJ
ejpam-4015	256	17	f	f	PROPN
ejpam-4015	256	18	′	′	NUM
ejpam-4015	256	19	∈	∈	PROPN
ejpam-4015	256	20	l[a	l[a	NOUN
ejpam-4015	256	21	,	,	PUNCT
ejpam-4015	256	22	b	b	NOUN
ejpam-4015	256	23	]	]	X
ejpam-4015	256	24	,	,	PUNCT
ejpam-4015	256	25	where	where	SCONJ
ejpam-4015	256	26	a	a	X
ejpam-4015	256	27	,	,	PUNCT
ejpam-4015	256	28	b	b	X
ejpam-4015	256	29	∈	∈	PROPN
ejpam-4015	256	30	i	i	PRON
ejpam-4015	256	31	◦	◦	NOUN
ejpam-4015	256	32	and	and	CCONJ
ejpam-4015	256	33	a	a	DET
ejpam-4015	256	34	<	<	X
ejpam-4015	256	35	b.	b.	NOUN
ejpam-4015	256	36	if	if	SCONJ
ejpam-4015	256	37	|f	|f	PROPN
ejpam-4015	256	38	′|q2	′|q2	PROPN
ejpam-4015	256	39	,	,	PUNCT
ejpam-4015	256	40	q2	q2	NOUN
ejpam-4015	256	41	≥	≥	NUM
ejpam-4015	256	42	1	1	NUM
ejpam-4015	256	43	is	be	AUX
ejpam-4015	256	44	s−	s−	PROPN
ejpam-4015	256	45	p−convex	p−convex	NOUN
ejpam-4015	256	46	in	in	ADP
ejpam-4015	256	47	the	the	DET
ejpam-4015	256	48	mixed	mixed	ADJ
ejpam-4015	256	49	kind	kind	NOUN
ejpam-4015	256	50	on	on	ADP
ejpam-4015	256	51	i	i	PRON
ejpam-4015	256	52	for	for	ADP
ejpam-4015	256	53	some	some	DET
ejpam-4015	256	54	fixed	fix	VERB
ejpam-4015	256	55	r	r	NOUN
ejpam-4015	256	56	,	,	PUNCT
ejpam-4015	256	57	s	s	NOUN
ejpam-4015	256	58	∈	∈	PROPN
ejpam-4015	256	59	[	[	X
ejpam-4015	256	60	0	0	NUM
ejpam-4015	256	61	,	,	PUNCT
ejpam-4015	256	62	1	1	NUM
ejpam-4015	256	63	]	]	PUNCT
ejpam-4015	256	64	and	and	CCONJ
ejpam-4015	256	65	for	for	ADP
ejpam-4015	256	66	p	p	PROPN
ejpam-4015	256	67	∈	∈	PROPN
ejpam-4015	256	68	r	r	NOUN
ejpam-4015	256	69	\	\	PUNCT
ejpam-4015	256	70	{	{	PUNCT
ejpam-4015	256	71	0	0	NUM
ejpam-4015	256	72	}	}	PUNCT
ejpam-4015	256	73	,	,	PUNCT
ejpam-4015	256	74	then	then	ADV
ejpam-4015	256	75	following	follow	VERB
ejpam-4015	256	76	inequality	inequality	NOUN
ejpam-4015	256	77	holds:∣∣∣∣∣∣	holds:∣∣∣∣∣∣	PROPN
ejpam-4015	256	78	b∫	b∫	PROPN
ejpam-4015	256	79	a	a	DET
ejpam-4015	256	80	f(x	f(x	PROPN
ejpam-4015	256	81	)	)	PUNCT
ejpam-4015	256	82	x1−p	x1−p	PROPN
ejpam-4015	257	1	dx−mpf	dx−mpf	NOUN
ejpam-4015	257	2	(	(	PUNCT
ejpam-4015	257	3	[	[	PUNCT
ejpam-4015	257	4	ap	ap	PROPN
ejpam-4015	257	5	+	+	NUM
ejpam-4015	257	6	bp	bp	PROPN
ejpam-4015	257	7	2	2	NUM
ejpam-4015	257	8	]	]	PUNCT
ejpam-4015	257	9	1	1	NUM
ejpam-4015	257	10	p	p	NOUN
ejpam-4015	257	11	)	)	PUNCT
ejpam-4015	257	12	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4015	257	13	≤	≤	PROPN
ejpam-4015	257	14	m2	m2	PROPN
ejpam-4015	257	15	p	p	PROPN
ejpam-4015	257	16	z9(p	z9(p	NOUN
ejpam-4015	257	17	)	)	PUNCT
ejpam-4015	257	18	(	(	PUNCT
ejpam-4015	257	19	|f	|f	NOUN
ejpam-4015	257	20	′(a)|q2	′(a)|q2	VERB
ejpam-4015	257	21	2rs+1(rs+	2rs+1(rs+	NUM
ejpam-4015	257	22	1	1	NUM
ejpam-4015	257	23	)	)	PUNCT
ejpam-4015	257	24	+	+	CCONJ
ejpam-4015	258	1	β1/2r	β1/2r	ADJ
ejpam-4015	258	2	(	(	PUNCT
ejpam-4015	258	3	1	1	NUM
ejpam-4015	258	4	r	r	NOUN
ejpam-4015	258	5	,	,	PUNCT
ejpam-4015	258	6	s+	s+	X
ejpam-4015	258	7	1	1	X
ejpam-4015	258	8	)	)	PUNCT
ejpam-4015	258	9	|f	|f	PROPN
ejpam-4015	258	10	′(b)|q2	′(b)|q2	VERB
ejpam-4015	258	11	r	r	NOUN
ejpam-4015	258	12	)	)	PUNCT
ejpam-4015	258	13	1	1	NUM
ejpam-4015	258	14	q2	q2	NOUN
ejpam-4015	258	15	+	+	NOUN
ejpam-4015	258	16	z10(p	z10(p	NOUN
ejpam-4015	258	17	)	)	PUNCT
ejpam-4015	258	18	(	(	PUNCT
ejpam-4015	258	19	(	(	PUNCT
ejpam-4015	258	20	2rs+1	2rs+1	NUM
ejpam-4015	258	21	−	−	NUM
ejpam-4015	258	22	1)|f	1)|f	NUM
ejpam-4015	258	23	′(a)|q2	′(a)|q2	NOUN
ejpam-4015	258	24	2rs+1(rs+	2rs+1(rs+	NUM
ejpam-4015	258	25	1	1	NUM
ejpam-4015	258	26	)	)	PUNCT
ejpam-4015	258	27	+	+	NUM
ejpam-4015	258	28	β1−1/2r	β1−1/2r	NOUN
ejpam-4015	258	29	(	(	PUNCT
ejpam-4015	258	30	s+	s+	NUM
ejpam-4015	258	31	1	1	NUM
ejpam-4015	258	32	,	,	PUNCT
ejpam-4015	258	33	1r	1r	NUM
ejpam-4015	258	34	)	)	PUNCT
ejpam-4015	258	35	|f	|f	PROPN
ejpam-4015	258	36	′(b)|q2	′(b)|q2	VERB
ejpam-4015	258	37	r	r	NOUN
ejpam-4015	258	38	)	)	PUNCT
ejpam-4015	258	39	1	1	NUM
ejpam-4015	258	40	q2	q2	NOUN
ejpam-4015	258	41			NOUN
ejpam-4015	258	42	.	.	PUNCT
ejpam-4015	259	1	where	where	SCONJ
ejpam-4015	259	2	z9(p	z9(p	NUM
ejpam-4015	259	3	)	)	PUNCT
ejpam-4015	259	4	=	=	PRON
ejpam-4015	259	5			X
ejpam-4015	259	6	1/2∫	1/2∫	NUM
ejpam-4015	259	7	0	0	NUM
ejpam-4015	260	1	(	(	PUNCT
ejpam-4015	260	2	t	t	X
ejpam-4015	261	1	[	[	X
ejpam-4015	261	2	tap	tap	NOUN
ejpam-4015	261	3	+	+	CCONJ
ejpam-4015	261	4	(	(	PUNCT
ejpam-4015	261	5	1−	1−	NUM
ejpam-4015	261	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	261	7	1	1	NUM
ejpam-4015	261	8	p	p	NOUN
ejpam-4015	261	9	)	)	PUNCT
ejpam-4015	261	10	q1	q1	PROPN
ejpam-4015	261	11	dt	dt	NOUN
ejpam-4015	261	12			PROPN
ejpam-4015	261	13	1	1	NUM
ejpam-4015	261	14	q1	q1	PROPN
ejpam-4015	261	15	,	,	PUNCT
ejpam-4015	261	16	muhammad	muhammad	PROPN
ejpam-4015	261	17	bilal	bilal	PROPN
ejpam-4015	261	18	,	,	PUNCT
ejpam-4015	261	19	asif	asif	PROPN
ejpam-4015	261	20	r.	r.	PROPN
ejpam-4015	261	21	khan	khan	PROPN
ejpam-4015	261	22	/	/	SYM
ejpam-4015	261	23	eur	eur	PROPN
ejpam-4015	261	24	.	.	PUNCT
ejpam-4015	262	1	j.	j.	PROPN
ejpam-4015	262	2	pure	pure	PROPN
ejpam-4015	262	3	appl	appl	PROPN
ejpam-4015	262	4	.	.	PROPN
ejpam-4015	262	5	math	math	PROPN
ejpam-4015	262	6	,	,	PUNCT
ejpam-4015	262	7	14	14	NUM
ejpam-4015	262	8	(	(	PUNCT
ejpam-4015	262	9	3	3	NUM
ejpam-4015	262	10	)	)	PUNCT
ejpam-4015	262	11	(	(	PUNCT
ejpam-4015	262	12	2021	2021	NUM
ejpam-4015	262	13	)	)	PUNCT
ejpam-4015	262	14	,	,	PUNCT
ejpam-4015	262	15	863	863	NUM
ejpam-4015	262	16	-	-	SYM
ejpam-4015	262	17	880	880	NUM
ejpam-4015	262	18	875	875	NUM
ejpam-4015	262	19	z10(p	z10(p	NOUN
ejpam-4015	262	20	)	)	PUNCT
ejpam-4015	262	21	=	=	NOUN
ejpam-4015	262	22			NUM
ejpam-4015	262	23	1∫	1∫	NUM
ejpam-4015	262	24	1/2	1/2	NUM
ejpam-4015	262	25	(	(	PUNCT
ejpam-4015	262	26	1−	1−	NUM
ejpam-4015	262	27	t	t	NOUN
ejpam-4015	263	1	[	[	X
ejpam-4015	263	2	tap	tap	NOUN
ejpam-4015	263	3	+	+	CCONJ
ejpam-4015	263	4	(	(	PUNCT
ejpam-4015	263	5	1−	1−	NUM
ejpam-4015	263	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	263	7	1	1	NUM
ejpam-4015	263	8	p	p	NOUN
ejpam-4015	263	9	)	)	PUNCT
ejpam-4015	263	10	q1	q1	PROPN
ejpam-4015	263	11	dt	dt	NOUN
ejpam-4015	263	12			PROPN
ejpam-4015	263	13	1	1	NUM
ejpam-4015	263	14	q1	q1	NOUN
ejpam-4015	263	15	with	with	ADP
ejpam-4015	263	16	1	1	NUM
ejpam-4015	263	17	q1	q1	NOUN
ejpam-4015	263	18	+	+	CCONJ
ejpam-4015	263	19	1	1	NUM
ejpam-4015	263	20	q2	q2	NOUN
ejpam-4015	263	21	=	=	SYM
ejpam-4015	263	22	1	1	X
ejpam-4015	263	23	.	.	PUNCT
ejpam-4015	264	1	proof	proof	NOUN
ejpam-4015	264	2	.	.	PUNCT
ejpam-4015	265	1	by	by	ADP
ejpam-4015	265	2	using	use	VERB
ejpam-4015	265	3	lemma	lemma	PROPN
ejpam-4015	265	4	1	1	NUM
ejpam-4015	265	5	,	,	PUNCT
ejpam-4015	265	6	hölder	hölder	PROPN
ejpam-4015	265	7	’s	’s	PART
ejpam-4015	265	8	inequality	inequality	NOUN
ejpam-4015	265	9	and	and	CCONJ
ejpam-4015	265	10	then	then	ADV
ejpam-4015	265	11	by	by	ADP
ejpam-4015	265	12	applying	apply	VERB
ejpam-4015	265	13	the	the	DET
ejpam-4015	265	14	definition	definition	NOUN
ejpam-4015	265	15	of	of	ADP
ejpam-4015	265	16	mixed	mixed	ADJ
ejpam-4015	265	17	kind	kind	NOUN
ejpam-4015	265	18	s−	s−	PROPN
ejpam-4015	265	19	p−convexity	p−convexity	PROPN
ejpam-4015	265	20	of	of	ADP
ejpam-4015	265	21	|f	|f	PROPN
ejpam-4015	265	22	|q2	|q2	VERB
ejpam-4015	265	23	on	on	ADP
ejpam-4015	265	24	i	i	PRON
ejpam-4015	265	25	,	,	PUNCT
ejpam-4015	265	26	we	we	PRON
ejpam-4015	265	27	have,∣∣∣∣∣∣	have,∣∣∣∣∣∣	VERB
ejpam-4015	265	28	b∫	b∫	PROPN
ejpam-4015	265	29	a	a	DET
ejpam-4015	265	30	f(x	f(x	PROPN
ejpam-4015	265	31	)	)	PUNCT
ejpam-4015	266	1	x1−p	x1−p	PROPN
ejpam-4015	267	1	dx−mpf	dx−mpf	NOUN
ejpam-4015	267	2	(	(	PUNCT
ejpam-4015	267	3	[	[	PUNCT
ejpam-4015	267	4	ap	ap	PROPN
ejpam-4015	267	5	+	+	NUM
ejpam-4015	267	6	bp	bp	PROPN
ejpam-4015	267	7	2	2	NUM
ejpam-4015	267	8	]	]	PUNCT
ejpam-4015	267	9	1	1	NUM
ejpam-4015	267	10	p	p	NOUN
ejpam-4015	267	11	)	)	PUNCT
ejpam-4015	267	12	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4015	267	13	≤	≤	PROPN
ejpam-4015	267	14	m2	m2	PROPN
ejpam-4015	267	15	p	p	PROPN
ejpam-4015	267	16			NUM
ejpam-4015	267	17	1/2∫	1/2∫	NUM
ejpam-4015	267	18	0	0	NUM
ejpam-4015	267	19	t	t	NOUN
ejpam-4015	267	20	[	[	X
ejpam-4015	267	21	tap	tap	NOUN
ejpam-4015	267	22	+	+	CCONJ
ejpam-4015	267	23	(	(	PUNCT
ejpam-4015	267	24	1−	1−	NUM
ejpam-4015	267	25	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	267	26	1	1	NUM
ejpam-4015	267	27	p	p	NOUN
ejpam-4015	267	28	∣∣∣f	∣∣∣f	NOUN
ejpam-4015	268	1	′	′	NUM
ejpam-4015	268	2	(	(	PUNCT
ejpam-4015	268	3	[	[	X
ejpam-4015	268	4	tap	tap	NOUN
ejpam-4015	268	5	+	+	CCONJ
ejpam-4015	268	6	(	(	PUNCT
ejpam-4015	268	7	1−	1−	NUM
ejpam-4015	268	8	t)bp	t)bp	PROPN
ejpam-4015	268	9	]	]	X
ejpam-4015	268	10	1	1	NUM
ejpam-4015	268	11	p	p	NOUN
ejpam-4015	268	12	)	)	PUNCT
ejpam-4015	268	13	∣∣∣	∣∣∣	NOUN
ejpam-4015	268	14	dt	dt	ADP
ejpam-4015	269	1	+	+	CCONJ
ejpam-4015	269	2	1∫	1∫	NUM
ejpam-4015	269	3	1/2	1/2	NUM
ejpam-4015	269	4	1−	1−	NUM
ejpam-4015	269	5	t	t	NOUN
ejpam-4015	269	6	[	[	X
ejpam-4015	269	7	tap	tap	NOUN
ejpam-4015	269	8	+	+	CCONJ
ejpam-4015	269	9	(	(	PUNCT
ejpam-4015	269	10	1−	1−	NUM
ejpam-4015	269	11	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	269	12	1	1	NUM
ejpam-4015	269	13	p	p	NOUN
ejpam-4015	269	14	∣∣∣f	∣∣∣f	NOUN
ejpam-4015	270	1	′	′	NUM
ejpam-4015	270	2	(	(	PUNCT
ejpam-4015	270	3	[	[	X
ejpam-4015	270	4	tap	tap	NOUN
ejpam-4015	270	5	+	+	CCONJ
ejpam-4015	270	6	(	(	PUNCT
ejpam-4015	270	7	1−	1−	NUM
ejpam-4015	270	8	t)bp	t)bp	PROPN
ejpam-4015	270	9	]	]	X
ejpam-4015	270	10	1	1	NUM
ejpam-4015	270	11	p	p	NOUN
ejpam-4015	270	12	)	)	PUNCT
ejpam-4015	270	13	∣∣∣	∣∣∣	NOUN
ejpam-4015	270	14	dt	dt	NOUN
ejpam-4015	270	15			NUM
ejpam-4015	270	16	.	.	PUNCT
ejpam-4015	271	1	≤	≤	NUM
ejpam-4015	272	1	m2	m2	PROPN
ejpam-4015	272	2	p	p	PROPN
ejpam-4015	272	3			NOUN
ejpam-4015	272	4			X
ejpam-4015	272	5	1/2∫	1/2∫	NUM
ejpam-4015	272	6	0	0	NUM
ejpam-4015	272	7	(	(	PUNCT
ejpam-4015	272	8	t	t	X
ejpam-4015	272	9	[	[	X
ejpam-4015	272	10	tap	tap	NOUN
ejpam-4015	272	11	+	+	CCONJ
ejpam-4015	272	12	(	(	PUNCT
ejpam-4015	272	13	1−	1−	NUM
ejpam-4015	272	14	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	272	15	1	1	NUM
ejpam-4015	272	16	p	p	NOUN
ejpam-4015	272	17	)	)	PUNCT
ejpam-4015	272	18	q1	q1	PROPN
ejpam-4015	272	19	dt	dt	NOUN
ejpam-4015	272	20			PROPN
ejpam-4015	272	21	1	1	NUM
ejpam-4015	272	22	q1	q1	PROPN
ejpam-4015	272	23			X
ejpam-4015	272	24	1/2∫	1/2∫	NUM
ejpam-4015	272	25	0	0	PUNCT
ejpam-4015	273	1	∣∣∣f	∣∣∣f	NOUN
ejpam-4015	273	2	′	′	NUM
ejpam-4015	273	3	(	(	PUNCT
ejpam-4015	273	4	[	[	X
ejpam-4015	273	5	tap	tap	NOUN
ejpam-4015	273	6	+	+	CCONJ
ejpam-4015	273	7	(	(	PUNCT
ejpam-4015	273	8	1−	1−	NUM
ejpam-4015	273	9	t)bp	t)bp	PROPN
ejpam-4015	273	10	]	]	X
ejpam-4015	273	11	1	1	NUM
ejpam-4015	273	12	p	p	NOUN
ejpam-4015	273	13	)	)	PUNCT
ejpam-4015	273	14	∣∣∣q2	∣∣∣q2	PROPN
ejpam-4015	273	15	dt	dt	NOUN
ejpam-4015	273	16			PROPN
ejpam-4015	273	17	1	1	NUM
ejpam-4015	273	18	q2	q2	NOUN
ejpam-4015	273	19	+	+	CCONJ
ejpam-4015	273	20			NUM
ejpam-4015	273	21	1∫	1∫	NUM
ejpam-4015	273	22	1/2	1/2	NUM
ejpam-4015	273	23	(	(	PUNCT
ejpam-4015	273	24	1−	1−	NUM
ejpam-4015	273	25	t	t	NOUN
ejpam-4015	274	1	[	[	X
ejpam-4015	274	2	tap	tap	NOUN
ejpam-4015	274	3	+	+	CCONJ
ejpam-4015	274	4	(	(	PUNCT
ejpam-4015	274	5	1−	1−	NUM
ejpam-4015	274	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	274	7	1	1	NUM
ejpam-4015	274	8	p	p	NOUN
ejpam-4015	274	9	)	)	PUNCT
ejpam-4015	274	10	q1	q1	PROPN
ejpam-4015	274	11	dt	dt	NOUN
ejpam-4015	274	12			PROPN
ejpam-4015	274	13	1	1	NUM
ejpam-4015	274	14	q1	q1	NOUN
ejpam-4015	274	15			NOUN
ejpam-4015	274	16	1∫	1∫	NUM
ejpam-4015	274	17	1/2	1/2	NUM
ejpam-4015	275	1	∣∣∣f	∣∣∣f	NOUN
ejpam-4015	275	2	′	′	NUM
ejpam-4015	276	1	(	(	PUNCT
ejpam-4015	276	2	[	[	X
ejpam-4015	276	3	tap	tap	NOUN
ejpam-4015	276	4	+	+	CCONJ
ejpam-4015	276	5	(	(	PUNCT
ejpam-4015	276	6	1−	1−	NUM
ejpam-4015	276	7	t)bp	t)bp	PROPN
ejpam-4015	276	8	]	]	X
ejpam-4015	276	9	1	1	NUM
ejpam-4015	276	10	p	p	NOUN
ejpam-4015	276	11	)	)	PUNCT
ejpam-4015	276	12	∣∣∣q2	∣∣∣q2	PROPN
ejpam-4015	276	13	dt	dt	NOUN
ejpam-4015	276	14			PROPN
ejpam-4015	276	15	1	1	NUM
ejpam-4015	276	16	q2	q2	NOUN
ejpam-4015	276	17			NOUN
ejpam-4015	276	18	≤	≤	PUNCT
ejpam-4015	276	19	m2	m2	PROPN
ejpam-4015	276	20	p	p	PROPN
ejpam-4015	276	21			NOUN
ejpam-4015	276	22			X
ejpam-4015	276	23	1/2∫	1/2∫	NUM
ejpam-4015	276	24	0	0	NUM
ejpam-4015	276	25	(	(	PUNCT
ejpam-4015	276	26	t	t	X
ejpam-4015	277	1	[	[	X
ejpam-4015	277	2	tap	tap	NOUN
ejpam-4015	277	3	+	+	CCONJ
ejpam-4015	277	4	(	(	PUNCT
ejpam-4015	277	5	1−	1−	NUM
ejpam-4015	277	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	277	7	1	1	NUM
ejpam-4015	277	8	p	p	NOUN
ejpam-4015	277	9	)	)	PUNCT
ejpam-4015	277	10	q1	q1	PROPN
ejpam-4015	277	11	dt	dt	NOUN
ejpam-4015	277	12			PROPN
ejpam-4015	277	13	1	1	NUM
ejpam-4015	277	14	q1	q1	PROPN
ejpam-4015	277	15			X
ejpam-4015	277	16	1/2∫	1/2∫	NUM
ejpam-4015	277	17	0	0	NUM
ejpam-4015	277	18	(	(	PUNCT
ejpam-4015	277	19	trs|f	trs|f	PROPN
ejpam-4015	277	20	′(a)|q2	′(a)|q2	VERB
ejpam-4015	277	21	+	+	CCONJ
ejpam-4015	277	22	(	(	PUNCT
ejpam-4015	277	23	1−	1−	NUM
ejpam-4015	277	24	tr)s|f	tr)s|f	NOUN
ejpam-4015	277	25	′(b)|q2	′(b)|q2	VERB
ejpam-4015	277	26	)	)	PUNCT
ejpam-4015	278	1	dt	dt	PROPN
ejpam-4015	278	2			PROPN
ejpam-4015	278	3	1	1	NUM
ejpam-4015	278	4	q2	q2	NOUN
ejpam-4015	278	5	+	+	CCONJ
ejpam-4015	278	6			NUM
ejpam-4015	279	1	1∫	1∫	NUM
ejpam-4015	279	2	1/2	1/2	NUM
ejpam-4015	279	3	(	(	PUNCT
ejpam-4015	279	4	1−	1−	NUM
ejpam-4015	279	5	t	t	NOUN
ejpam-4015	280	1	[	[	X
ejpam-4015	280	2	tap	tap	NOUN
ejpam-4015	280	3	+	+	CCONJ
ejpam-4015	280	4	(	(	PUNCT
ejpam-4015	280	5	1−	1−	NUM
ejpam-4015	280	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	280	7	1	1	NUM
ejpam-4015	280	8	p	p	NOUN
ejpam-4015	280	9	)	)	PUNCT
ejpam-4015	280	10	q1	q1	PROPN
ejpam-4015	280	11	dt	dt	NOUN
ejpam-4015	280	12			PROPN
ejpam-4015	280	13	1	1	NUM
ejpam-4015	280	14	q1	q1	PROPN
ejpam-4015	280	15	muhammad	muhammad	PROPN
ejpam-4015	280	16	bilal	bilal	PROPN
ejpam-4015	280	17	,	,	PUNCT
ejpam-4015	280	18	asif	asif	PROPN
ejpam-4015	280	19	r.	r.	PROPN
ejpam-4015	280	20	khan	khan	PROPN
ejpam-4015	280	21	/	/	SYM
ejpam-4015	280	22	eur	eur	PROPN
ejpam-4015	280	23	.	.	PUNCT
ejpam-4015	281	1	j.	j.	PROPN
ejpam-4015	281	2	pure	pure	PROPN
ejpam-4015	281	3	appl	appl	PROPN
ejpam-4015	281	4	.	.	PROPN
ejpam-4015	281	5	math	math	PROPN
ejpam-4015	281	6	,	,	PUNCT
ejpam-4015	281	7	14	14	NUM
ejpam-4015	281	8	(	(	PUNCT
ejpam-4015	281	9	3	3	NUM
ejpam-4015	281	10	)	)	PUNCT
ejpam-4015	281	11	(	(	PUNCT
ejpam-4015	281	12	2021	2021	NUM
ejpam-4015	281	13	)	)	PUNCT
ejpam-4015	281	14	,	,	PUNCT
ejpam-4015	281	15	863	863	NUM
ejpam-4015	281	16	-	-	SYM
ejpam-4015	281	17	880	880	NUM
ejpam-4015	281	18	876	876	NUM
ejpam-4015	281	19	1∫	1∫	NUM
ejpam-4015	281	20	1/2	1/2	NUM
ejpam-4015	281	21	(	(	PUNCT
ejpam-4015	281	22	trs|f	trs|f	VERB
ejpam-4015	281	23	′(a)|q2	′(a)|q2	VERB
ejpam-4015	281	24	+	+	CCONJ
ejpam-4015	281	25	(	(	PUNCT
ejpam-4015	281	26	1−	1−	NUM
ejpam-4015	281	27	tr)s|f	tr)s|f	NOUN
ejpam-4015	281	28	′(b)|q2	′(b)|q2	VERB
ejpam-4015	281	29	)	)	PUNCT
ejpam-4015	282	1	dt	dt	PROPN
ejpam-4015	282	2			PROPN
ejpam-4015	282	3	1	1	NUM
ejpam-4015	282	4	q2	q2	NOUN
ejpam-4015	282	5			NOUN
ejpam-4015	282	6	=	=	PUNCT
ejpam-4015	283	1	m2	m2	PROPN
ejpam-4015	283	2	p	p	PROPN
ejpam-4015	283	3			NOUN
ejpam-4015	283	4			X
ejpam-4015	283	5	1/2∫	1/2∫	NUM
ejpam-4015	283	6	0	0	NUM
ejpam-4015	283	7	(	(	PUNCT
ejpam-4015	283	8	t	t	X
ejpam-4015	284	1	[	[	X
ejpam-4015	284	2	tap	tap	NOUN
ejpam-4015	284	3	+	+	CCONJ
ejpam-4015	284	4	(	(	PUNCT
ejpam-4015	284	5	1−	1−	NUM
ejpam-4015	284	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	284	7	1	1	NUM
ejpam-4015	284	8	p	p	NOUN
ejpam-4015	284	9	)	)	PUNCT
ejpam-4015	284	10	q1	q1	PROPN
ejpam-4015	284	11	dt	dt	NOUN
ejpam-4015	284	12			PROPN
ejpam-4015	284	13	1	1	NUM
ejpam-4015	284	14	q1	q1	PROPN
ejpam-4015	284	15	(	(	PUNCT
ejpam-4015	284	16	|f	|f	NOUN
ejpam-4015	284	17	′(a)|q2	′(a)|q2	VERB
ejpam-4015	284	18	2rs+1(rs+	2rs+1(rs+	NUM
ejpam-4015	284	19	1	1	NUM
ejpam-4015	284	20	)	)	PUNCT
ejpam-4015	284	21	+	+	CCONJ
ejpam-4015	284	22	β1/2r	β1/2r	ADJ
ejpam-4015	284	23	(	(	PUNCT
ejpam-4015	284	24	1	1	NUM
ejpam-4015	284	25	r	r	NOUN
ejpam-4015	284	26	,	,	PUNCT
ejpam-4015	284	27	s+	s+	X
ejpam-4015	284	28	1	1	X
ejpam-4015	284	29	)	)	PUNCT
ejpam-4015	284	30	|f	|f	PROPN
ejpam-4015	284	31	′(b)|q2	′(b)|q2	VERB
ejpam-4015	284	32	r	r	NOUN
ejpam-4015	284	33	)	)	PUNCT
ejpam-4015	284	34	1	1	NUM
ejpam-4015	284	35	q2	q2	NOUN
ejpam-4015	284	36	+	+	CCONJ
ejpam-4015	284	37			NUM
ejpam-4015	284	38	1∫	1∫	NUM
ejpam-4015	284	39	1/2	1/2	NUM
ejpam-4015	284	40	(	(	PUNCT
ejpam-4015	284	41	1−	1−	NUM
ejpam-4015	284	42	t	t	NOUN
ejpam-4015	285	1	[	[	X
ejpam-4015	285	2	tap	tap	NOUN
ejpam-4015	285	3	+	+	CCONJ
ejpam-4015	285	4	(	(	PUNCT
ejpam-4015	285	5	1−	1−	NUM
ejpam-4015	285	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	285	7	1	1	NUM
ejpam-4015	285	8	p	p	NOUN
ejpam-4015	285	9	)	)	PUNCT
ejpam-4015	285	10	q1	q1	PROPN
ejpam-4015	285	11	dt	dt	NOUN
ejpam-4015	285	12			PROPN
ejpam-4015	285	13	1	1	NUM
ejpam-4015	285	14	q1	q1	NOUN
ejpam-4015	285	15	(	(	PUNCT
ejpam-4015	285	16	(	(	PUNCT
ejpam-4015	285	17	2rs+1	2rs+1	NUM
ejpam-4015	285	18	−	−	NUM
ejpam-4015	285	19	1)|f	1)|f	NUM
ejpam-4015	285	20	′(a)|q2	′(a)|q2	NOUN
ejpam-4015	285	21	2rs+1(rs+	2rs+1(rs+	NUM
ejpam-4015	285	22	1	1	NUM
ejpam-4015	285	23	)	)	PUNCT
ejpam-4015	285	24	+	+	NUM
ejpam-4015	285	25	β1−1/2r	β1−1/2r	NOUN
ejpam-4015	285	26	(	(	PUNCT
ejpam-4015	285	27	s+	s+	NUM
ejpam-4015	285	28	1	1	NUM
ejpam-4015	285	29	,	,	PUNCT
ejpam-4015	285	30	1r	1r	NUM
ejpam-4015	285	31	)	)	PUNCT
ejpam-4015	285	32	|f	|f	PROPN
ejpam-4015	285	33	′(b)|q2	′(b)|q2	VERB
ejpam-4015	285	34	r	r	NOUN
ejpam-4015	285	35	)	)	PUNCT
ejpam-4015	285	36	1	1	NUM
ejpam-4015	285	37	q2	q2	NOUN
ejpam-4015	285	38			NOUN
ejpam-4015	285	39	which	which	PRON
ejpam-4015	285	40	completes	complete	VERB
ejpam-4015	285	41	the	the	DET
ejpam-4015	285	42	proof	proof	NOUN
ejpam-4015	285	43	.	.	PUNCT
ejpam-4015	286	1	remark	remark	PROPN
ejpam-4015	286	2	10	10	NUM
ejpam-4015	286	3	.	.	PUNCT
ejpam-4015	287	1	in	in	ADP
ejpam-4015	287	2	theorem	theorem	NOUN
ejpam-4015	287	3	6	6	NUM
ejpam-4015	287	4	,	,	PUNCT
ejpam-4015	287	5	we	we	PRON
ejpam-4015	287	6	can	can	AUX
ejpam-4015	287	7	get	get	VERB
ejpam-4015	287	8	the	the	DET
ejpam-4015	287	9	following	follow	VERB
ejpam-4015	287	10	results	result	NOUN
ejpam-4015	287	11	:	:	PUNCT
ejpam-4015	287	12	(	(	PUNCT
ejpam-4015	287	13	i	i	NOUN
ejpam-4015	287	14	)	)	PUNCT
ejpam-4015	287	15	if	if	SCONJ
ejpam-4015	287	16	one	one	PRON
ejpam-4015	287	17	takes	take	VERB
ejpam-4015	287	18	p	p	NOUN
ejpam-4015	287	19	=	=	NOUN
ejpam-4015	287	20	r	r	NOUN
ejpam-4015	287	21	=	=	SYM
ejpam-4015	287	22	s	s	NOUN
ejpam-4015	287	23	=	=	SYM
ejpam-4015	287	24	1	1	NUM
ejpam-4015	287	25	,	,	PUNCT
ejpam-4015	287	26	then	then	ADV
ejpam-4015	287	27	one	one	PRON
ejpam-4015	287	28	has	have	AUX
ejpam-4015	287	29	theorem	theorem	VERB
ejpam-4015	287	30	2.3	2.3	NUM
ejpam-4015	287	31	of	of	ADP
ejpam-4015	287	32	[	[	X
ejpam-4015	287	33	15	15	NUM
ejpam-4015	287	34	]	]	PUNCT
ejpam-4015	287	35	.	.	PUNCT
ejpam-4015	288	1	(	(	PUNCT
ejpam-4015	288	2	ii	ii	NOUN
ejpam-4015	288	3	)	)	PUNCT
ejpam-4015	288	4	if	if	SCONJ
ejpam-4015	288	5	one	one	PRON
ejpam-4015	288	6	takes	take	VERB
ejpam-4015	288	7	r	r	NOUN
ejpam-4015	288	8	=	=	SYM
ejpam-4015	288	9	s	s	NOUN
ejpam-4015	288	10	=	=	SYM
ejpam-4015	288	11	1	1	NUM
ejpam-4015	288	12	,	,	PUNCT
ejpam-4015	288	13	then	then	ADV
ejpam-4015	288	14	one	one	PRON
ejpam-4015	288	15	has	have	VERB
ejpam-4015	288	16	first	first	ADJ
ejpam-4015	288	17	result	result	NOUN
ejpam-4015	288	18	of	of	ADP
ejpam-4015	288	19	corollary	corollary	ADJ
ejpam-4015	288	20	3	3	NUM
ejpam-4015	288	21	of	of	ADP
ejpam-4015	288	22	[	[	X
ejpam-4015	288	23	16	16	NUM
ejpam-4015	288	24	]	]	PUNCT
ejpam-4015	288	25	.	.	PUNCT
ejpam-4015	289	1	(	(	PUNCT
ejpam-4015	289	2	iii	iii	X
ejpam-4015	289	3	)	)	PUNCT
ejpam-4015	289	4	if	if	SCONJ
ejpam-4015	289	5	one	one	PRON
ejpam-4015	289	6	takes	take	VERB
ejpam-4015	289	7	p	p	NOUN
ejpam-4015	289	8	=	=	PUNCT
ejpam-4015	289	9	−1	−1	NOUN
ejpam-4015	289	10	and	and	CCONJ
ejpam-4015	289	11	r	r	NOUN
ejpam-4015	289	12	=	=	SYM
ejpam-4015	289	13	s	s	NOUN
ejpam-4015	289	14	=	=	SYM
ejpam-4015	289	15	1	1	NUM
ejpam-4015	289	16	,	,	PUNCT
ejpam-4015	289	17	then	then	ADV
ejpam-4015	289	18	one	one	PRON
ejpam-4015	289	19	has	have	VERB
ejpam-4015	289	20	fourth	fourth	ADJ
ejpam-4015	289	21	result	result	NOUN
ejpam-4015	289	22	of	of	ADP
ejpam-4015	289	23	corollary	corollary	ADJ
ejpam-4015	289	24	3	3	NUM
ejpam-4015	289	25	of	of	ADP
ejpam-4015	289	26	[	[	X
ejpam-4015	289	27	16	16	NUM
ejpam-4015	289	28	]	]	PUNCT
ejpam-4015	289	29	.	.	PUNCT
ejpam-4015	290	1	corollary	corollary	ADJ
ejpam-4015	290	2	3	3	X
ejpam-4015	290	3	.	.	PUNCT
ejpam-4015	291	1	in	in	ADP
ejpam-4015	291	2	theorem	theorem	NOUN
ejpam-4015	291	3	6	6	NUM
ejpam-4015	291	4	,	,	PUNCT
ejpam-4015	291	5	one	one	PRON
ejpam-4015	291	6	can	can	AUX
ejpam-4015	291	7	see	see	VERB
ejpam-4015	291	8	the	the	DET
ejpam-4015	291	9	following	following	NOUN
ejpam-4015	291	10	:	:	PUNCT
ejpam-4015	291	11	(	(	PUNCT
ejpam-4015	291	12	i	i	NOUN
ejpam-4015	291	13	)	)	PUNCT
ejpam-4015	291	14	if	if	SCONJ
ejpam-4015	291	15	one	one	PRON
ejpam-4015	291	16	takes	take	VERB
ejpam-4015	291	17	s	s	NOUN
ejpam-4015	291	18	=	=	NOUN
ejpam-4015	291	19	1	1	NUM
ejpam-4015	291	20	then	then	ADV
ejpam-4015	291	21	one	one	NUM
ejpam-4015	291	22	has	have	VERB
ejpam-4015	291	23	the	the	DET
ejpam-4015	291	24	following	follow	VERB
ejpam-4015	291	25	hermite	hermite	ADJ
ejpam-4015	291	26	–	–	PUNCT
ejpam-4015	291	27	hadamard	hadamard	ADJ
ejpam-4015	291	28	type	type	NOUN
ejpam-4015	291	29	inequality	inequality	NOUN
ejpam-4015	291	30	for	for	ADP
ejpam-4015	291	31	s−	s−	PROPN
ejpam-4015	291	32	p−convex	p−convex	NOUN
ejpam-4015	291	33	functions	function	NOUN
ejpam-4015	291	34	in	in	ADP
ejpam-4015	291	35	1st	1st	ADJ
ejpam-4015	291	36	kind:∣∣∣∣∣∣	kind:∣∣∣∣∣∣	PROPN
ejpam-4015	291	37	b∫	b∫	PROPN
ejpam-4015	291	38	a	a	DET
ejpam-4015	291	39	f(x	f(x	PROPN
ejpam-4015	291	40	)	)	PUNCT
ejpam-4015	292	1	x1−p	x1−p	PROPN
ejpam-4015	293	1	dx−mpf	dx−mpf	NOUN
ejpam-4015	293	2	(	(	PUNCT
ejpam-4015	293	3	[	[	PUNCT
ejpam-4015	293	4	ap	ap	PROPN
ejpam-4015	293	5	+	+	NUM
ejpam-4015	293	6	bp	bp	PROPN
ejpam-4015	293	7	2	2	NUM
ejpam-4015	293	8	]	]	PUNCT
ejpam-4015	293	9	1	1	NUM
ejpam-4015	293	10	p	p	NOUN
ejpam-4015	293	11	)	)	PUNCT
ejpam-4015	293	12	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4015	293	13	≤m2	≤m2	ADP
ejpam-4015	293	14	p	p	PROPN
ejpam-4015	293	15	×	×	NOUN
ejpam-4015	293	16			X
ejpam-4015	293	17	1/2∫	1/2∫	NUM
ejpam-4015	293	18	0	0	NUM
ejpam-4015	293	19	(	(	PUNCT
ejpam-4015	293	20	t	t	X
ejpam-4015	294	1	[	[	X
ejpam-4015	294	2	tap	tap	NOUN
ejpam-4015	294	3	+	+	CCONJ
ejpam-4015	294	4	(	(	PUNCT
ejpam-4015	294	5	1−	1−	NUM
ejpam-4015	294	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	294	7	1	1	NUM
ejpam-4015	294	8	p	p	NOUN
ejpam-4015	294	9	)	)	PUNCT
ejpam-4015	294	10	p	p	NOUN
ejpam-4015	294	11	dt	dt	X
ejpam-4015	294	12			PROPN
ejpam-4015	294	13	1	1	NUM
ejpam-4015	294	14	p	p	NOUN
ejpam-4015	294	15	(	(	PUNCT
ejpam-4015	294	16	|f	|f	PROPN
ejpam-4015	294	17	′(a)|q	′(a)|q	PROPN
ejpam-4015	294	18	+	+	CCONJ
ejpam-4015	294	19	(	(	PUNCT
ejpam-4015	294	20	2s	2s	NUM
ejpam-4015	294	21	−	−	PROPN
ejpam-4015	294	22	1	1	NUM
ejpam-4015	294	23	)	)	PUNCT
ejpam-4015	294	24	|f	|f	PROPN
ejpam-4015	295	1	′(b)|q	′(b)|q	PROPN
ejpam-4015	295	2	2s+1(s+	2s+1(s+	NUM
ejpam-4015	295	3	1	1	NUM
ejpam-4015	295	4	)	)	PUNCT
ejpam-4015	295	5	)	)	PUNCT
ejpam-4015	296	1	1	1	NUM
ejpam-4015	296	2	q	q	NOUN
ejpam-4015	296	3	+	+	NUM
ejpam-4015	296	4			X
ejpam-4015	296	5	1/2∫	1/2∫	NUM
ejpam-4015	296	6	0	0	NUM
ejpam-4015	297	1	(	(	PUNCT
ejpam-4015	297	2	1−	1−	NUM
ejpam-4015	297	3	t	t	NOUN
ejpam-4015	297	4	[	[	X
ejpam-4015	297	5	tap	tap	NOUN
ejpam-4015	297	6	+	+	CCONJ
ejpam-4015	297	7	(	(	PUNCT
ejpam-4015	297	8	1−	1−	NUM
ejpam-4015	297	9	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	297	10	1	1	NUM
ejpam-4015	297	11	p	p	NOUN
ejpam-4015	297	12	)	)	PUNCT
ejpam-4015	297	13	p	p	NOUN
ejpam-4015	297	14	dt	dt	X
ejpam-4015	297	15			PROPN
ejpam-4015	297	16	1	1	NUM
ejpam-4015	297	17	p	p	PROPN
ejpam-4015	297	18	muhammad	muhammad	PROPN
ejpam-4015	297	19	bilal	bilal	PROPN
ejpam-4015	297	20	,	,	PUNCT
ejpam-4015	297	21	asif	asif	PROPN
ejpam-4015	297	22	r.	r.	PROPN
ejpam-4015	297	23	khan	khan	PROPN
ejpam-4015	297	24	/	/	SYM
ejpam-4015	297	25	eur	eur	PROPN
ejpam-4015	297	26	.	.	PUNCT
ejpam-4015	298	1	j.	j.	PROPN
ejpam-4015	298	2	pure	pure	PROPN
ejpam-4015	298	3	appl	appl	PROPN
ejpam-4015	298	4	.	.	PROPN
ejpam-4015	298	5	math	math	PROPN
ejpam-4015	298	6	,	,	PUNCT
ejpam-4015	298	7	14	14	NUM
ejpam-4015	298	8	(	(	PUNCT
ejpam-4015	298	9	3	3	NUM
ejpam-4015	298	10	)	)	PUNCT
ejpam-4015	298	11	(	(	PUNCT
ejpam-4015	298	12	2021	2021	NUM
ejpam-4015	298	13	)	)	PUNCT
ejpam-4015	298	14	,	,	PUNCT
ejpam-4015	298	15	863	863	NUM
ejpam-4015	298	16	-	-	SYM
ejpam-4015	298	17	880	880	NUM
ejpam-4015	298	18	877	877	NUM
ejpam-4015	298	19	(	(	PUNCT
ejpam-4015	298	20	(	(	PUNCT
ejpam-4015	298	21	2s	2s	NUM
ejpam-4015	298	22	−	−	NOUN
ejpam-4015	298	23	1	1	NUM
ejpam-4015	298	24	)	)	PUNCT
ejpam-4015	298	25	|f	|f	PROPN
ejpam-4015	298	26	′(a)|q	′(a)|q	PROPN
ejpam-4015	298	27	+	+	CCONJ
ejpam-4015	298	28	(	(	PUNCT
ejpam-4015	298	29	2s	2s	NUM
ejpam-4015	298	30	−	−	PROPN
ejpam-4015	298	31	2s+1	2s+1	PROPN
ejpam-4015	298	32	+	+	CCONJ
ejpam-4015	298	33	1	1	NUM
ejpam-4015	298	34	)	)	PUNCT
ejpam-4015	298	35	|f	|f	PROPN
ejpam-4015	299	1	′(b)|q	′(b)|q	PROPN
ejpam-4015	299	2	2s+1(s+	2s+1(s+	NUM
ejpam-4015	299	3	1	1	NUM
ejpam-4015	299	4	)	)	PUNCT
ejpam-4015	299	5	)	)	PUNCT
ejpam-4015	299	6	1	1	NUM
ejpam-4015	299	7	q	q	NOUN
ejpam-4015	299	8			NOUN
ejpam-4015	299	9	.	.	PUNCT
ejpam-4015	300	1	(	(	PUNCT
ejpam-4015	300	2	ii	ii	NOUN
ejpam-4015	300	3	)	)	PUNCT
ejpam-4015	300	4	if	if	SCONJ
ejpam-4015	300	5	one	one	PRON
ejpam-4015	300	6	takes	take	VERB
ejpam-4015	300	7	r	r	NOUN
ejpam-4015	300	8	=	=	SYM
ejpam-4015	300	9	1	1	NUM
ejpam-4015	300	10	,	,	PUNCT
ejpam-4015	300	11	then	then	ADV
ejpam-4015	300	12	one	one	PRON
ejpam-4015	300	13	has	have	VERB
ejpam-4015	300	14	the	the	DET
ejpam-4015	300	15	following	follow	VERB
ejpam-4015	300	16	hermite	hermite	ADJ
ejpam-4015	300	17	–	–	PUNCT
ejpam-4015	300	18	hadamard	hadamard	ADJ
ejpam-4015	300	19	type	type	NOUN
ejpam-4015	300	20	inequality	inequality	NOUN
ejpam-4015	300	21	for	for	ADP
ejpam-4015	300	22	s−	s−	PROPN
ejpam-4015	300	23	p−convex	p−convex	NOUN
ejpam-4015	300	24	functions	function	NOUN
ejpam-4015	300	25	in	in	ADP
ejpam-4015	300	26	2nd	2nd	ADJ
ejpam-4015	300	27	kind:∣∣∣∣∣∣	kind:∣∣∣∣∣∣	PROPN
ejpam-4015	300	28	b∫	b∫	PROPN
ejpam-4015	300	29	a	a	DET
ejpam-4015	300	30	f(x	f(x	PROPN
ejpam-4015	300	31	)	)	PUNCT
ejpam-4015	301	1	x1−p	x1−p	PROPN
ejpam-4015	302	1	dx−mpf	dx−mpf	NOUN
ejpam-4015	302	2	(	(	PUNCT
ejpam-4015	302	3	[	[	PUNCT
ejpam-4015	302	4	ap	ap	PROPN
ejpam-4015	302	5	+	+	NUM
ejpam-4015	302	6	bp	bp	PROPN
ejpam-4015	302	7	2	2	NUM
ejpam-4015	302	8	]	]	PUNCT
ejpam-4015	302	9	1	1	NUM
ejpam-4015	302	10	p	p	NOUN
ejpam-4015	302	11	)	)	PUNCT
ejpam-4015	302	12	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4015	302	13	≤m2	≤m2	ADP
ejpam-4015	302	14	p	p	PROPN
ejpam-4015	302	15	×	×	NOUN
ejpam-4015	302	16			X
ejpam-4015	302	17	1/2∫	1/2∫	NUM
ejpam-4015	302	18	0	0	NUM
ejpam-4015	302	19	(	(	PUNCT
ejpam-4015	302	20	t	t	X
ejpam-4015	303	1	[	[	X
ejpam-4015	303	2	tap	tap	NOUN
ejpam-4015	303	3	+	+	CCONJ
ejpam-4015	303	4	(	(	PUNCT
ejpam-4015	303	5	1−	1−	NUM
ejpam-4015	303	6	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	303	7	1	1	NUM
ejpam-4015	303	8	p	p	NOUN
ejpam-4015	303	9	)	)	PUNCT
ejpam-4015	303	10	p	p	NOUN
ejpam-4015	303	11	dt	dt	X
ejpam-4015	303	12			PROPN
ejpam-4015	303	13	1	1	NUM
ejpam-4015	303	14	p	p	NOUN
ejpam-4015	303	15	(	(	PUNCT
ejpam-4015	303	16	|f	|f	PROPN
ejpam-4015	303	17	′(a)|q	′(a)|q	PROPN
ejpam-4015	303	18	+	+	CCONJ
ejpam-4015	303	19	(	(	PUNCT
ejpam-4015	303	20	2s+1	2s+1	PROPN
ejpam-4015	303	21	−	−	PROPN
ejpam-4015	303	22	1	1	NUM
ejpam-4015	303	23	)	)	PUNCT
ejpam-4015	303	24	|f	|f	PROPN
ejpam-4015	304	1	′(b)|q	′(b)|q	PROPN
ejpam-4015	304	2	2s+1(s+	2s+1(s+	NUM
ejpam-4015	304	3	1	1	NUM
ejpam-4015	304	4	)	)	PUNCT
ejpam-4015	304	5	)	)	PUNCT
ejpam-4015	305	1	1	1	NUM
ejpam-4015	305	2	q	q	NOUN
ejpam-4015	305	3	+	+	NUM
ejpam-4015	305	4			X
ejpam-4015	305	5	1/2∫	1/2∫	NUM
ejpam-4015	305	6	0	0	NUM
ejpam-4015	306	1	(	(	PUNCT
ejpam-4015	306	2	1−	1−	NUM
ejpam-4015	306	3	t	t	NOUN
ejpam-4015	306	4	[	[	X
ejpam-4015	306	5	tap	tap	NOUN
ejpam-4015	306	6	+	+	CCONJ
ejpam-4015	306	7	(	(	PUNCT
ejpam-4015	306	8	1−	1−	NUM
ejpam-4015	306	9	t)bp]1−	t)bp]1−	NOUN
ejpam-4015	306	10	1	1	NUM
ejpam-4015	306	11	p	p	NOUN
ejpam-4015	306	12	)	)	PUNCT
ejpam-4015	306	13	p	p	NOUN
ejpam-4015	306	14	dt	dt	X
ejpam-4015	306	15			PROPN
ejpam-4015	306	16	1	1	NUM
ejpam-4015	306	17	p	p	NOUN
ejpam-4015	306	18	(	(	PUNCT
ejpam-4015	306	19	(	(	PUNCT
ejpam-4015	306	20	2s+1	2s+1	PROPN
ejpam-4015	306	21	−	−	PROPN
ejpam-4015	306	22	1	1	NUM
ejpam-4015	306	23	)	)	PUNCT
ejpam-4015	306	24	|f	|f	PROPN
ejpam-4015	306	25	′(a)|q	′(a)|q	PROPN
ejpam-4015	306	26	+	+	CCONJ
ejpam-4015	306	27	|f	|f	PROPN
ejpam-4015	306	28	′(b)|q	′(b)|q	PROPN
ejpam-4015	306	29	2s+1(s+	2s+1(s+	NUM
ejpam-4015	306	30	1	1	NUM
ejpam-4015	306	31	)	)	PUNCT
ejpam-4015	306	32	)	)	PUNCT
ejpam-4015	306	33	1	1	NUM
ejpam-4015	306	34	q	q	NOUN
ejpam-4015	306	35			NOUN
ejpam-4015	306	36	.	.	PUNCT
ejpam-4015	307	1	(	(	PUNCT
ejpam-4015	307	2	iii	iii	X
ejpam-4015	307	3	)	)	PUNCT
ejpam-4015	307	4	if	if	SCONJ
ejpam-4015	307	5	one	one	PRON
ejpam-4015	307	6	takes	take	VERB
ejpam-4015	307	7	p	p	NOUN
ejpam-4015	307	8	=	=	NOUN
ejpam-4015	307	9	1	1	NUM
ejpam-4015	307	10	,	,	PUNCT
ejpam-4015	307	11	then	then	ADV
ejpam-4015	307	12	one	one	PRON
ejpam-4015	307	13	has	have	VERB
ejpam-4015	307	14	the	the	DET
ejpam-4015	307	15	following	follow	VERB
ejpam-4015	307	16	hermite	hermite	ADJ
ejpam-4015	307	17	–	–	PUNCT
ejpam-4015	307	18	hadamard	hadamard	ADJ
ejpam-4015	307	19	type	type	NOUN
ejpam-4015	307	20	inequality	inequality	NOUN
ejpam-4015	307	21	for	for	ADP
ejpam-4015	307	22	(	(	PUNCT
ejpam-4015	307	23	s	s	X
ejpam-4015	307	24	,	,	PUNCT
ejpam-4015	307	25	r)−convex	r)−convex	PROPN
ejpam-4015	307	26	functions	function	NOUN
ejpam-4015	307	27	in	in	ADP
ejpam-4015	307	28	mixed	mixed	ADJ
ejpam-4015	307	29	kind:∣∣∣∣∣∣	kind:∣∣∣∣∣∣	NOUN
ejpam-4015	307	30	b∫	b∫	PROPN
ejpam-4015	307	31	a	a	DET
ejpam-4015	307	32	f(x)dx−m1f	f(x)dx−m1f	NOUN
ejpam-4015	307	33	(	(	PUNCT
ejpam-4015	307	34	a+	a+	NOUN
ejpam-4015	307	35	b	b	NOUN
ejpam-4015	307	36	2	2	NUM
ejpam-4015	307	37	)	)	PUNCT
ejpam-4015	307	38	∣∣∣∣∣∣	∣∣∣∣∣∣	NOUN
ejpam-4015	307	39	≤m2	≤m2	ADP
ejpam-4015	307	40	1	1	NUM
ejpam-4015	307	41	×	×	NOUN
ejpam-4015	307	42	(	(	PUNCT
ejpam-4015	307	43	1	1	NUM
ejpam-4015	307	44	2p+1(p+	2p+1(p+	NUM
ejpam-4015	307	45	1	1	NUM
ejpam-4015	307	46	)	)	PUNCT
ejpam-4015	307	47	)	)	PUNCT
ejpam-4015	307	48	1	1	NUM
ejpam-4015	307	49	p	p	PRON
ejpam-4015	307	50			PROPN
ejpam-4015	307	51	(	(	PUNCT
ejpam-4015	307	52	|f	|f	PROPN
ejpam-4015	307	53	′(a)|q	′(a)|q	NOUN
ejpam-4015	307	54	2rs+1(rs+	2rs+1(rs+	NUM
ejpam-4015	307	55	1	1	NUM
ejpam-4015	307	56	)	)	PUNCT
ejpam-4015	307	57	+	+	CCONJ
ejpam-4015	308	1	β1/2r	β1/2r	ADJ
ejpam-4015	308	2	(	(	PUNCT
ejpam-4015	308	3	1	1	NUM
ejpam-4015	308	4	r	r	NOUN
ejpam-4015	308	5	,	,	PUNCT
ejpam-4015	308	6	s+	s+	X
ejpam-4015	308	7	1	1	X
ejpam-4015	308	8	)	)	PUNCT
ejpam-4015	308	9	|f	|f	PROPN
ejpam-4015	308	10	′(b)|q	′(b)|q	PROPN
ejpam-4015	308	11	r	r	NOUN
ejpam-4015	308	12	)	)	PUNCT
ejpam-4015	308	13	1	1	NUM
ejpam-4015	308	14	q	q	NOUN
ejpam-4015	308	15	+	+	NUM
ejpam-4015	308	16	(	(	PUNCT
ejpam-4015	308	17	(	(	PUNCT
ejpam-4015	308	18	2rs+1	2rs+1	NUM
ejpam-4015	308	19	−	−	NUM
ejpam-4015	308	20	1)|f	1)|f	NUM
ejpam-4015	308	21	′(a)|q	′(a)|q	NOUN
ejpam-4015	308	22	2rs+1(rs+	2rs+1(rs+	NUM
ejpam-4015	308	23	1	1	NUM
ejpam-4015	308	24	)	)	PUNCT
ejpam-4015	308	25	+	+	NUM
ejpam-4015	308	26	β1−1/2r	β1−1/2r	NOUN
ejpam-4015	308	27	(	(	PUNCT
ejpam-4015	308	28	s+	s+	NUM
ejpam-4015	308	29	1	1	NUM
ejpam-4015	308	30	,	,	PUNCT
ejpam-4015	308	31	1r	1r	NUM
ejpam-4015	308	32	)	)	PUNCT
ejpam-4015	308	33	|f	|f	PROPN
ejpam-4015	309	1	′(b)|q	′(b)|q	PROPN
ejpam-4015	309	2	r	r	NOUN
ejpam-4015	309	3	)	)	PUNCT
ejpam-4015	309	4	1	1	NUM
ejpam-4015	309	5	q	q	NOUN
ejpam-4015	309	6			NOUN
ejpam-4015	309	7	.	.	PUNCT
ejpam-4015	310	1	(	(	PUNCT
ejpam-4015	310	2	iv	iv	X
ejpam-4015	310	3	)	)	PUNCT
ejpam-4015	310	4	if	if	SCONJ
ejpam-4015	310	5	one	one	PRON
ejpam-4015	310	6	takes	take	VERB
ejpam-4015	310	7	p	p	NOUN
ejpam-4015	310	8	=	=	PUNCT
ejpam-4015	310	9	s	s	PART
ejpam-4015	310	10	=	=	SYM
ejpam-4015	310	11	1	1	NUM
ejpam-4015	310	12	,	,	PUNCT
ejpam-4015	310	13	then	then	ADV
ejpam-4015	310	14	one	one	PRON
ejpam-4015	310	15	has	have	VERB
ejpam-4015	310	16	the	the	DET
ejpam-4015	310	17	following	follow	VERB
ejpam-4015	310	18	hermite	hermite	ADJ
ejpam-4015	310	19	–	–	PUNCT
ejpam-4015	310	20	hadamard	hadamard	ADJ
ejpam-4015	310	21	type	type	NOUN
ejpam-4015	310	22	inequality	inequality	NOUN
ejpam-4015	310	23	for	for	ADP
ejpam-4015	310	24	s−convex	s−convex	X
ejpam-4015	310	25	functions	function	NOUN
ejpam-4015	310	26	in	in	ADP
ejpam-4015	310	27	1st	1st	ADJ
ejpam-4015	310	28	kind:∣∣∣∣∣∣	kind:∣∣∣∣∣∣	PROPN
ejpam-4015	310	29	b∫	b∫	PROPN
ejpam-4015	310	30	a	a	DET
ejpam-4015	310	31	f(x)dx−m1f	f(x)dx−m1f	NOUN
ejpam-4015	310	32	(	(	PUNCT
ejpam-4015	310	33	a+	a+	NOUN
ejpam-4015	310	34	b	b	NOUN
ejpam-4015	310	35	2	2	NUM
ejpam-4015	310	36	)	)	PUNCT
ejpam-4015	310	37	∣∣∣∣∣∣	∣∣∣∣∣∣	NOUN
ejpam-4015	310	38	≤m2	≤m2	ADP
ejpam-4015	310	39	1	1	NUM
ejpam-4015	310	40	×	×	NOUN
ejpam-4015	310	41	(	(	PUNCT
ejpam-4015	310	42	1	1	NUM
ejpam-4015	310	43	2p+1(p+	2p+1(p+	NUM
ejpam-4015	310	44	1	1	NUM
ejpam-4015	310	45	)	)	PUNCT
ejpam-4015	310	46	)	)	PUNCT
ejpam-4015	311	1	1	1	NUM
ejpam-4015	311	2	p	p	NOUN
ejpam-4015	311	3	[	[	X
ejpam-4015	311	4	(	(	PUNCT
ejpam-4015	311	5	|f	|f	PROPN
ejpam-4015	311	6	′(a)|q	′(a)|q	NOUN
ejpam-4015	311	7	+	+	CCONJ
ejpam-4015	311	8	(	(	PUNCT
ejpam-4015	311	9	2s	2s	NUM
ejpam-4015	311	10	−	−	PROPN
ejpam-4015	311	11	1	1	NUM
ejpam-4015	311	12	)	)	PUNCT
ejpam-4015	311	13	|f	|f	PROPN
ejpam-4015	312	1	′(b)|q	′(b)|q	PROPN
ejpam-4015	312	2	2s+1(s+	2s+1(s+	NUM
ejpam-4015	312	3	1	1	NUM
ejpam-4015	312	4	)	)	PUNCT
ejpam-4015	312	5	)	)	PUNCT
ejpam-4015	313	1	1	1	NUM
ejpam-4015	313	2	q	q	NOUN
ejpam-4015	313	3	+	+	CCONJ
ejpam-4015	313	4	(	(	PUNCT
ejpam-4015	313	5	(	(	PUNCT
ejpam-4015	313	6	2s	2s	NUM
ejpam-4015	313	7	−	−	NOUN
ejpam-4015	313	8	1	1	NUM
ejpam-4015	313	9	)	)	PUNCT
ejpam-4015	313	10	|f	|f	PROPN
ejpam-4015	313	11	′(a)|q	′(a)|q	PROPN
ejpam-4015	313	12	+	+	CCONJ
ejpam-4015	313	13	(	(	PUNCT
ejpam-4015	313	14	2s	2s	NUM
ejpam-4015	313	15	−	−	PROPN
ejpam-4015	313	16	2s+1	2s+1	PROPN
ejpam-4015	313	17	+	+	CCONJ
ejpam-4015	313	18	1	1	NUM
ejpam-4015	313	19	)	)	PUNCT
ejpam-4015	313	20	|f	|f	PROPN
ejpam-4015	314	1	′(b)|q	′(b)|q	PROPN
ejpam-4015	314	2	2s+1(s+	2s+1(s+	NUM
ejpam-4015	314	3	1	1	NUM
ejpam-4015	314	4	)	)	PUNCT
ejpam-4015	314	5	)	)	PUNCT
ejpam-4015	314	6	1	1	NUM
ejpam-4015	314	7	q	q	NOUN
ejpam-4015	314	8			NOUN
ejpam-4015	314	9	.	.	PUNCT
ejpam-4015	315	1	muhammad	muhammad	PROPN
ejpam-4015	315	2	bilal	bilal	PROPN
ejpam-4015	315	3	,	,	PUNCT
ejpam-4015	315	4	asif	asif	PROPN
ejpam-4015	315	5	r.	r.	PROPN
ejpam-4015	315	6	khan	khan	PROPN
ejpam-4015	315	7	/	/	SYM
ejpam-4015	315	8	eur	eur	PROPN
ejpam-4015	315	9	.	.	PUNCT
ejpam-4015	316	1	j.	j.	PROPN
ejpam-4015	316	2	pure	pure	PROPN
ejpam-4015	316	3	appl	appl	PROPN
ejpam-4015	316	4	.	.	PROPN
ejpam-4015	316	5	math	math	PROPN
ejpam-4015	316	6	,	,	PUNCT
ejpam-4015	316	7	14	14	NUM
ejpam-4015	316	8	(	(	PUNCT
ejpam-4015	316	9	3	3	NUM
ejpam-4015	316	10	)	)	PUNCT
ejpam-4015	316	11	(	(	PUNCT
ejpam-4015	316	12	2021	2021	NUM
ejpam-4015	316	13	)	)	PUNCT
ejpam-4015	316	14	,	,	PUNCT
ejpam-4015	316	15	863	863	NUM
ejpam-4015	316	16	-	-	SYM
ejpam-4015	316	17	880	880	NUM
ejpam-4015	316	18	878	878	NUM
ejpam-4015	316	19	(	(	PUNCT
ejpam-4015	316	20	v	v	NOUN
ejpam-4015	316	21	)	)	PUNCT
ejpam-4015	316	22	if	if	SCONJ
ejpam-4015	316	23	one	one	PRON
ejpam-4015	316	24	takes	take	VERB
ejpam-4015	316	25	p	p	NOUN
ejpam-4015	316	26	=	=	PUNCT
ejpam-4015	316	27	r	r	NOUN
ejpam-4015	316	28	=	=	SYM
ejpam-4015	316	29	1	1	NUM
ejpam-4015	316	30	,	,	PUNCT
ejpam-4015	316	31	then	then	ADV
ejpam-4015	316	32	one	one	PRON
ejpam-4015	316	33	has	have	VERB
ejpam-4015	316	34	the	the	DET
ejpam-4015	316	35	following	follow	VERB
ejpam-4015	316	36	hermite	hermite	ADJ
ejpam-4015	316	37	–	–	PUNCT
ejpam-4015	316	38	hadamard	hadamard	ADJ
ejpam-4015	316	39	type	type	NOUN
ejpam-4015	316	40	inequality	inequality	NOUN
ejpam-4015	316	41	for	for	ADP
ejpam-4015	316	42	s−convex	s−convex	X
ejpam-4015	316	43	functions	function	NOUN
ejpam-4015	316	44	in	in	ADP
ejpam-4015	316	45	2nd	2nd	ADJ
ejpam-4015	316	46	kind:∣∣∣∣∣∣	kind:∣∣∣∣∣∣	NOUN
ejpam-4015	316	47	b∫	b∫	PROPN
ejpam-4015	316	48	a	a	DET
ejpam-4015	316	49	f(x)dx−m1f	f(x)dx−m1f	NOUN
ejpam-4015	316	50	(	(	PUNCT
ejpam-4015	316	51	a+	a+	NOUN
ejpam-4015	316	52	b	b	NOUN
ejpam-4015	316	53	2	2	NUM
ejpam-4015	316	54	)	)	PUNCT
ejpam-4015	316	55	∣∣∣∣∣∣	∣∣∣∣∣∣	NOUN
ejpam-4015	316	56	≤m2	≤m2	ADP
ejpam-4015	316	57	1	1	NUM
ejpam-4015	316	58	×	×	NOUN
ejpam-4015	316	59	(	(	PUNCT
ejpam-4015	316	60	1	1	NUM
ejpam-4015	316	61	2p+1(p+	2p+1(p+	NUM
ejpam-4015	316	62	1	1	NUM
ejpam-4015	316	63	)	)	PUNCT
ejpam-4015	316	64	)	)	PUNCT
ejpam-4015	316	65	1	1	NUM
ejpam-4015	316	66	p	p	PRON
ejpam-4015	316	67			PROPN
ejpam-4015	316	68	(	(	PUNCT
ejpam-4015	316	69	|f	|f	PROPN
ejpam-4015	316	70	′(a)|q	′(a)|q	PROPN
ejpam-4015	316	71	+	+	CCONJ
ejpam-4015	316	72	(	(	PUNCT
ejpam-4015	316	73	2s+1	2s+1	PROPN
ejpam-4015	316	74	−	−	PROPN
ejpam-4015	316	75	1	1	NUM
ejpam-4015	316	76	)	)	PUNCT
ejpam-4015	316	77	|f	|f	PROPN
ejpam-4015	317	1	′(b)|q	′(b)|q	PROPN
ejpam-4015	317	2	2s+1(s+	2s+1(s+	NUM
ejpam-4015	317	3	1	1	NUM
ejpam-4015	317	4	)	)	PUNCT
ejpam-4015	317	5	)	)	PUNCT
ejpam-4015	318	1	1	1	NUM
ejpam-4015	318	2	q	q	NOUN
ejpam-4015	318	3	+	+	NUM
ejpam-4015	318	4	(	(	PUNCT
ejpam-4015	318	5	(	(	PUNCT
ejpam-4015	318	6	2s+1	2s+1	NOUN
ejpam-4015	318	7	−	−	NOUN
ejpam-4015	318	8	1	1	NUM
ejpam-4015	318	9	)	)	PUNCT
ejpam-4015	318	10	|f	|f	PROPN
ejpam-4015	318	11	′(a)|q	′(a)|q	PROPN
ejpam-4015	318	12	+	+	CCONJ
ejpam-4015	318	13	|f	|f	PROPN
ejpam-4015	318	14	′(b)|q	′(b)|q	PROPN
ejpam-4015	318	15	2s+1(s+	2s+1(s+	NUM
ejpam-4015	318	16	1	1	NUM
ejpam-4015	318	17	)	)	PUNCT
ejpam-4015	318	18	)	)	PUNCT
ejpam-4015	318	19	1	1	NUM
ejpam-4015	318	20	q	q	NOUN
ejpam-4015	318	21			NOUN
ejpam-4015	318	22	.	.	PUNCT
ejpam-4015	319	1	3	3	X
ejpam-4015	319	2	.	.	X
ejpam-4015	319	3	conclusion	conclusion	NOUN
ejpam-4015	319	4	and	and	CCONJ
ejpam-4015	319	5	remarks	remark	NOUN
ejpam-4015	319	6	3.1	3.1	NUM
ejpam-4015	319	7	.	.	PUNCT
ejpam-4015	320	1	conclusion	conclusion	NOUN
ejpam-4015	320	2	hermite−hadamard	hermite−hadamard	PART
ejpam-4015	320	3	dual	dual	ADJ
ejpam-4015	320	4	inequality	inequality	NOUN
ejpam-4015	320	5	is	be	AUX
ejpam-4015	320	6	one	one	NUM
ejpam-4015	320	7	of	of	ADP
ejpam-4015	320	8	the	the	DET
ejpam-4015	320	9	most	most	ADV
ejpam-4015	320	10	celebrated	celebrated	ADJ
ejpam-4015	320	11	inequalities	inequality	NOUN
ejpam-4015	320	12	.	.	PUNCT
ejpam-4015	321	1	we	we	PRON
ejpam-4015	321	2	can	can	AUX
ejpam-4015	321	3	find	find	VERB
ejpam-4015	321	4	its	its	PRON
ejpam-4015	321	5	various	various	ADJ
ejpam-4015	321	6	generalizations	generalization	NOUN
ejpam-4015	321	7	and	and	CCONJ
ejpam-4015	321	8	variants	variant	NOUN
ejpam-4015	321	9	in	in	ADP
ejpam-4015	321	10	literature	literature	NOUN
ejpam-4015	321	11	.	.	PUNCT
ejpam-4015	322	1	we	we	PRON
ejpam-4015	322	2	have	have	AUX
ejpam-4015	322	3	given	give	VERB
ejpam-4015	322	4	its	its	PRON
ejpam-4015	322	5	generalization	generalization	NOUN
ejpam-4015	322	6	by	by	ADP
ejpam-4015	322	7	introducing	introduce	VERB
ejpam-4015	322	8	new	new	ADJ
ejpam-4015	322	9	generalized	generalized	ADJ
ejpam-4015	322	10	notion	notion	NOUN
ejpam-4015	322	11	of	of	ADP
ejpam-4015	322	12	(	(	PUNCT
ejpam-4015	322	13	s	s	X
ejpam-4015	322	14	,	,	PUNCT
ejpam-4015	322	15	r)−convex	r)−convex	PROPN
ejpam-4015	322	16	functions	function	NOUN
ejpam-4015	322	17	in	in	ADP
ejpam-4015	322	18	the	the	DET
ejpam-4015	322	19	mixed	mixed	ADJ
ejpam-4015	322	20	kind	kind	NOUN
ejpam-4015	322	21	.	.	PUNCT
ejpam-4015	323	1	this	this	DET
ejpam-4015	323	2	new	new	ADJ
ejpam-4015	323	3	class	class	NOUN
ejpam-4015	323	4	of	of	ADP
ejpam-4015	323	5	functions	function	NOUN
ejpam-4015	323	6	contains	contain	VERB
ejpam-4015	323	7	many	many	ADJ
ejpam-4015	323	8	important	important	ADJ
ejpam-4015	323	9	classes	class	NOUN
ejpam-4015	323	10	including	include	VERB
ejpam-4015	323	11	class	class	NOUN
ejpam-4015	323	12	of	of	ADP
ejpam-4015	323	13	s−convex	s−convex	X
ejpam-4015	323	14	in	in	ADP
ejpam-4015	323	15	the	the	DET
ejpam-4015	323	16	first	first	ADJ
ejpam-4015	323	17	and	and	CCONJ
ejpam-4015	323	18	in	in	ADP
ejpam-4015	323	19	the	the	DET
ejpam-4015	323	20	second	second	ADJ
ejpam-4015	323	21	kind	kind	NOUN
ejpam-4015	323	22	(	(	PUNCT
ejpam-4015	323	23	and	and	CCONJ
ejpam-4015	323	24	hence	hence	ADV
ejpam-4015	323	25	contains	contain	VERB
ejpam-4015	323	26	class	class	NOUN
ejpam-4015	323	27	of	of	ADP
ejpam-4015	323	28	convex	convex	NOUN
ejpam-4015	323	29	functions	function	NOUN
ejpam-4015	323	30	)	)	PUNCT
ejpam-4015	323	31	.	.	PUNCT
ejpam-4015	324	1	it	it	PRON
ejpam-4015	324	2	also	also	ADV
ejpam-4015	324	3	contains	contain	VERB
ejpam-4015	324	4	class	class	NOUN
ejpam-4015	324	5	of	of	ADP
ejpam-4015	324	6	p−convex	p−convex	NOUN
ejpam-4015	324	7	functions	function	NOUN
ejpam-4015	324	8	and	and	CCONJ
ejpam-4015	324	9	class	class	NOUN
ejpam-4015	324	10	of	of	ADP
ejpam-4015	324	11	quasi−convex	quasi−convex	NUM
ejpam-4015	324	12	functions	function	NOUN
ejpam-4015	324	13	.	.	PUNCT
ejpam-4015	325	1	in	in	ADP
ejpam-4015	325	2	section	section	NOUN
ejpam-4015	325	3	2	2	NUM
ejpam-4015	325	4	,	,	PUNCT
ejpam-4015	325	5	we	we	PRON
ejpam-4015	325	6	have	have	AUX
ejpam-4015	325	7	stated	state	VERB
ejpam-4015	325	8	three	three	NUM
ejpam-4015	325	9	different	different	ADJ
ejpam-4015	325	10	results	result	NOUN
ejpam-4015	325	11	related	relate	VERB
ejpam-4015	325	12	to	to	ADP
ejpam-4015	325	13	estimation	estimation	NOUN
ejpam-4015	325	14	of	of	ADP
ejpam-4015	325	15	bound	bind	VERB
ejpam-4015	325	16	of	of	ADP
ejpam-4015	325	17	difference	difference	NOUN
ejpam-4015	325	18	of	of	ADP
ejpam-4015	325	19	left	left	ADJ
ejpam-4015	325	20	and	and	CCONJ
ejpam-4015	325	21	middle	middle	ADJ
ejpam-4015	325	22	term	term	NOUN
ejpam-4015	325	23	of	of	ADP
ejpam-4015	325	24	hermite−hadamard	hermite−hadamard	ADJ
ejpam-4015	325	25	dual	dual	ADJ
ejpam-4015	325	26	inequality	inequality	NOUN
ejpam-4015	325	27	in	in	ADP
ejpam-4015	325	28	absolute	absolute	ADJ
ejpam-4015	325	29	sense	sense	NOUN
ejpam-4015	325	30	.	.	PUNCT
ejpam-4015	326	1	here	here	ADV
ejpam-4015	326	2	we	we	PRON
ejpam-4015	326	3	used	use	VERB
ejpam-4015	326	4	different	different	ADJ
ejpam-4015	326	5	techniques	technique	NOUN
ejpam-4015	326	6	including	include	VERB
ejpam-4015	326	7	power	power	NOUN
ejpam-4015	326	8	mean	mean	NOUN
ejpam-4015	326	9	inequality	inequality	NOUN
ejpam-4015	326	10	and	and	CCONJ
ejpam-4015	326	11	hölder	hölder	NOUN
ejpam-4015	326	12	’s	’s	PART
ejpam-4015	326	13	inequality	inequality	NOUN
ejpam-4015	326	14	.	.	PUNCT
ejpam-4015	327	1	these	these	DET
ejpam-4015	327	2	results	result	NOUN
ejpam-4015	327	3	capture	capture	VERB
ejpam-4015	327	4	various	various	ADJ
ejpam-4015	327	5	results	result	NOUN
ejpam-4015	327	6	stated	state	VERB
ejpam-4015	327	7	in	in	ADP
ejpam-4015	327	8	articles	article	NOUN
ejpam-4015	327	9	[	[	X
ejpam-4015	327	10	15	15	NUM
ejpam-4015	327	11	]	]	PUNCT
ejpam-4015	327	12	,	,	PUNCT
ejpam-4015	327	13	[	[	X
ejpam-4015	327	14	16	16	NUM
ejpam-4015	327	15	]	]	PUNCT
ejpam-4015	327	16	and	and	CCONJ
ejpam-4015	327	17	[	[	X
ejpam-4015	327	18	20	20	NUM
ejpam-4015	327	19	]	]	PUNCT
ejpam-4015	327	20	.	.	PUNCT
ejpam-4015	328	1	now	now	ADV
ejpam-4015	328	2	we	we	PRON
ejpam-4015	328	3	are	be	AUX
ejpam-4015	328	4	going	go	VERB
ejpam-4015	328	5	to	to	PART
ejpam-4015	328	6	give	give	VERB
ejpam-4015	328	7	some	some	DET
ejpam-4015	328	8	remarks	remark	NOUN
ejpam-4015	328	9	and	and	CCONJ
ejpam-4015	328	10	future	future	ADJ
ejpam-4015	328	11	ideas	idea	NOUN
ejpam-4015	328	12	for	for	ADP
ejpam-4015	328	13	readers	reader	NOUN
ejpam-4015	328	14	.	.	PUNCT
ejpam-4015	329	1	3.2	3.2	NUM
ejpam-4015	329	2	.	.	PUNCT
ejpam-4015	329	3	remarks	remark	NOUN
ejpam-4015	329	4	and	and	CCONJ
ejpam-4015	329	5	future	future	ADJ
ejpam-4015	329	6	ideas	idea	NOUN
ejpam-4015	329	7	(	(	PUNCT
ejpam-4015	329	8	i	i	NOUN
ejpam-4015	329	9	)	)	PUNCT
ejpam-4015	329	10	we	we	PRON
ejpam-4015	329	11	can	can	AUX
ejpam-4015	329	12	also	also	ADV
ejpam-4015	329	13	state	state	VERB
ejpam-4015	329	14	all	all	DET
ejpam-4015	329	15	the	the	DET
ejpam-4015	329	16	inequalities	inequality	NOUN
ejpam-4015	329	17	given	give	VERB
ejpam-4015	329	18	in	in	ADP
ejpam-4015	329	19	this	this	DET
ejpam-4015	329	20	article	article	NOUN
ejpam-4015	329	21	in	in	ADP
ejpam-4015	329	22	reverse	reverse	ADJ
ejpam-4015	329	23	direction	direction	NOUN
ejpam-4015	329	24	for	for	ADP
ejpam-4015	329	25	concave	concave	ADJ
ejpam-4015	329	26	function	function	NOUN
ejpam-4015	329	27	by	by	ADP
ejpam-4015	329	28	using	use	VERB
ejpam-4015	329	29	simple	simple	ADJ
ejpam-4015	329	30	relation	relation	NOUN
ejpam-4015	329	31	f	f	PROPN
ejpam-4015	329	32	is	be	AUX
ejpam-4015	329	33	concave	concave	VERB
ejpam-4015	329	34	iff	iff	PROPN
ejpam-4015	329	35	−f	−f	PROPN
ejpam-4015	329	36	is	be	AUX
ejpam-4015	329	37	convex	convex	NOUN
ejpam-4015	329	38	.	.	PUNCT
ejpam-4015	330	1	(	(	PUNCT
ejpam-4015	330	2	ii	ii	NOUN
ejpam-4015	330	3	)	)	PUNCT
ejpam-4015	330	4	one	one	NOUN
ejpam-4015	330	5	may	may	AUX
ejpam-4015	330	6	also	also	ADV
ejpam-4015	330	7	work	work	VERB
ejpam-4015	330	8	on	on	ADP
ejpam-4015	330	9	fejer	fejer	ADJ
ejpam-4015	330	10	inequality	inequality	NOUN
ejpam-4015	330	11	by	by	ADP
ejpam-4015	330	12	introducing	introduce	VERB
ejpam-4015	330	13	weights	weight	NOUN
ejpam-4015	330	14	in	in	ADP
ejpam-4015	330	15	hermite−hadamard	hermite−hadamard	ADJ
ejpam-4015	330	16	dual	dual	ADJ
ejpam-4015	330	17	inequality	inequality	NOUN
ejpam-4015	330	18	.	.	PUNCT
ejpam-4015	331	1	(	(	PUNCT
ejpam-4015	331	2	iii	iii	X
ejpam-4015	331	3	)	)	PUNCT
ejpam-4015	331	4	one	one	NOUN
ejpam-4015	331	5	may	may	AUX
ejpam-4015	331	6	do	do	VERB
ejpam-4015	331	7	similar	similar	ADJ
ejpam-4015	331	8	work	work	NOUN
ejpam-4015	331	9	by	by	ADP
ejpam-4015	331	10	using	use	VERB
ejpam-4015	331	11	various	various	ADJ
ejpam-4015	331	12	different	different	ADJ
ejpam-4015	331	13	classes	class	NOUN
ejpam-4015	331	14	of	of	ADP
ejpam-4015	331	15	functions	function	NOUN
ejpam-4015	331	16	.	.	PUNCT
ejpam-4015	332	1	(	(	PUNCT
ejpam-4015	332	2	iv	iv	X
ejpam-4015	332	3	)	)	PUNCT
ejpam-4015	332	4	one	one	NOUN
ejpam-4015	332	5	may	may	AUX
ejpam-4015	332	6	try	try	VERB
ejpam-4015	332	7	to	to	PART
ejpam-4015	332	8	state	state	VERB
ejpam-4015	332	9	all	all	DET
ejpam-4015	332	10	results	result	NOUN
ejpam-4015	332	11	stated	state	VERB
ejpam-4015	332	12	in	in	ADP
ejpam-4015	332	13	this	this	DET
ejpam-4015	332	14	article	article	NOUN
ejpam-4015	332	15	in	in	ADP
ejpam-4015	332	16	discrete	discrete	ADJ
ejpam-4015	332	17	case	case	NOUN
ejpam-4015	332	18	.	.	PUNCT
ejpam-4015	333	1	(	(	PUNCT
ejpam-4015	333	2	v	v	NOUN
ejpam-4015	333	3	)	)	PUNCT
ejpam-4015	333	4	one	one	NOUN
ejpam-4015	333	5	may	may	AUX
ejpam-4015	333	6	also	also	ADV
ejpam-4015	333	7	state	state	VERB
ejpam-4015	333	8	all	all	DET
ejpam-4015	333	9	results	result	NOUN
ejpam-4015	333	10	stated	state	VERB
ejpam-4015	333	11	in	in	ADP
ejpam-4015	333	12	this	this	DET
ejpam-4015	333	13	article	article	NOUN
ejpam-4015	333	14	in	in	ADP
ejpam-4015	333	15	higher	high	ADJ
ejpam-4015	333	16	dimensions	dimension	NOUN
ejpam-4015	333	17	.	.	PUNCT
ejpam-4015	334	1	references	reference	NOUN
ejpam-4015	334	2	879	879	NUM
ejpam-4015	334	3	references	reference	NOUN
ejpam-4015	334	4	[	[	X
ejpam-4015	334	5	1	1	NUM
ejpam-4015	334	6	]	]	PUNCT
ejpam-4015	334	7	a.	a.	NOUN
ejpam-4015	334	8	arshad	arshad	PROPN
ejpam-4015	334	9	and	and	CCONJ
ejpam-4015	334	10	a.	a.	PROPN
ejpam-4015	334	11	r.	r.	PROPN
ejpam-4015	334	12	khan	khan	PROPN
ejpam-4015	334	13	.	.	PUNCT
ejpam-4015	335	1	hermite	hermite	ADJ
ejpam-4015	335	2	–	–	PUNCT
ejpam-4015	335	3	hadamard	hadamard	ADJ
ejpam-4015	335	4	–	–	PUNCT
ejpam-4015	335	5	fejer	fejer	ADJ
ejpam-4015	335	6	type	type	NOUN
ejpam-4015	335	7	inequalities	inequality	NOUN
ejpam-4015	335	8	for	for	ADP
ejpam-4015	335	9	s	s	NOUN
ejpam-4015	335	10	–	–	PUNCT
ejpam-4015	335	11	p	p	NOUN
ejpam-4015	335	12	–	–	PUNCT
ejpam-4015	335	13	convex	convex	NOUN
ejpam-4015	335	14	functions	function	NOUN
ejpam-4015	335	15	of	of	ADP
ejpam-4015	335	16	several	several	ADJ
ejpam-4015	335	17	senses	sense	NOUN
ejpam-4015	335	18	.	.	PUNCT
ejpam-4015	336	1	tjmm	tjmm	NOUN
ejpam-4015	336	2	.	.	PUNCT
ejpam-4015	336	3	,	,	PUNCT
ejpam-4015	336	4	11:25–40	11:25–40	NUM
ejpam-4015	336	5	,	,	PUNCT
ejpam-4015	336	6	2019	2019	NUM
ejpam-4015	336	7	.	.	PUNCT
ejpam-4015	337	1	[	[	X
ejpam-4015	337	2	2	2	NUM
ejpam-4015	337	3	]	]	PUNCT
ejpam-4015	337	4	m.	m.	NOUN
ejpam-4015	337	5	k.	k.	PROPN
ejpam-4015	337	6	bakula	bakula	PROPN
ejpam-4015	337	7	,	,	PUNCT
ejpam-4015	337	8	u.	u.	PROPN
ejpam-4015	337	9	s.	s.	PROPN
ejpam-4015	337	10	kiramaci	kiramaci	PROPN
ejpam-4015	337	11	,	,	PUNCT
ejpam-4015	337	12	m.	m.	PROPN
ejpam-4015	337	13	e.	e.	PROPN
ejpam-4015	337	14	ozdemir	ozdemir	PROPN
ejpam-4015	337	15	,	,	PUNCT
ejpam-4015	337	16	and	and	CCONJ
ejpam-4015	337	17	j.	j.	PROPN
ejpam-4015	337	18	e.	e.	PROPN
ejpam-4015	337	19	pečarić.	pečarić.	PROPN
ejpam-4015	337	20	hadamard	hadamard	PROPN
ejpam-4015	337	21	–	–	PUNCT
ejpam-4015	337	22	type	type	NOUN
ejpam-4015	337	23	inequalities	inequality	NOUN
ejpam-4015	337	24	for	for	ADP
ejpam-4015	337	25	s−convex	s−convex	NOUN
ejpam-4015	337	26	functions	function	NOUN
ejpam-4015	337	27	.	.	PUNCT
ejpam-4015	338	1	appl	appl	PROPN
ejpam-4015	338	2	.	.	PROPN
ejpam-4015	338	3	math	math	PROPN
ejpam-4015	338	4	.	.	PUNCT
ejpam-4015	339	1	comput	comput	NOUN
ejpam-4015	339	2	.	.	PUNCT
ejpam-4015	339	3	,	,	PUNCT
ejpam-4015	339	4	193:26–35	193:26–35	NUM
ejpam-4015	339	5	,	,	PUNCT
ejpam-4015	339	6	2007	2007	NUM
ejpam-4015	339	7	.	.	PUNCT
ejpam-4015	340	1	[	[	X
ejpam-4015	340	2	3	3	X
ejpam-4015	340	3	]	]	PUNCT
ejpam-4015	340	4	m.	m.	NOUN
ejpam-4015	340	5	k.	k.	PROPN
ejpam-4015	340	6	bakula	bakula	PROPN
ejpam-4015	340	7	and	and	CCONJ
ejpam-4015	340	8	j.	j.	PROPN
ejpam-4015	340	9	e.	e.	PROPN
ejpam-4015	340	10	pečarić.	pečarić.	PROPN
ejpam-4015	340	11	note	note	NOUN
ejpam-4015	340	12	on	on	ADP
ejpam-4015	340	13	some	some	DET
ejpam-4015	340	14	hadamard	hadamard	ADJ
ejpam-4015	340	15	–	–	PUNCT
ejpam-4015	340	16	type	type	NOUN
ejpam-4015	340	17	inequalities	inequality	NOUN
ejpam-4015	340	18	.	.	PUNCT
ejpam-4015	341	1	j.	j.	PROPN
ejpam-4015	341	2	ineq	ineq	PROPN
ejpam-4015	341	3	.	.	PUNCT
ejpam-4015	342	1	pure	pure	ADJ
ejpam-4015	342	2	&	&	CCONJ
ejpam-4015	342	3	appl	appl	PROPN
ejpam-4015	342	4	.	.	PROPN
ejpam-4015	342	5	math	math	PROPN
ejpam-4015	342	6	.	.	PUNCT
ejpam-4015	342	7	,	,	PUNCT
ejpam-4015	342	8	5(74	5(74	NUM
ejpam-4015	342	9	)	)	PUNCT
ejpam-4015	342	10	,	,	PUNCT
ejpam-4015	342	11	2004	2004	NUM
ejpam-4015	342	12	.	.	PUNCT
ejpam-4015	343	1	[	[	X
ejpam-4015	343	2	4	4	X
ejpam-4015	343	3	]	]	PUNCT
ejpam-4015	343	4	e.	e.	PROPN
ejpam-4015	343	5	f.	f.	PROPN
ejpam-4015	343	6	beckenbach	beckenbach	PROPN
ejpam-4015	343	7	.	.	PUNCT
ejpam-4015	344	1	convex	convex	NOUN
ejpam-4015	344	2	functions	function	NOUN
ejpam-4015	344	3	.	.	PUNCT
ejpam-4015	345	1	bull	bull	NOUN
ejpam-4015	345	2	.	.	PUNCT
ejpam-4015	346	1	amer	amer	PROPN
ejpam-4015	346	2	.	.	PUNCT
ejpam-4015	346	3	math	math	PROPN
ejpam-4015	346	4	.	.	PUNCT
ejpam-4015	347	1	soc	soc	PROPN
ejpam-4015	347	2	.	.	PUNCT
ejpam-4015	347	3	,	,	PUNCT
ejpam-4015	347	4	54:439–460	54:439–460	NUM
ejpam-4015	347	5	,	,	PUNCT
ejpam-4015	347	6	1948	1948	NUM
ejpam-4015	347	7	.	.	PUNCT
ejpam-4015	348	1	[	[	X
ejpam-4015	348	2	5	5	NUM
ejpam-4015	348	3	]	]	PUNCT
ejpam-4015	348	4	m.	m.	NOUN
ejpam-4015	348	5	bilal	bilal	PROPN
ejpam-4015	348	6	,	,	PUNCT
ejpam-4015	348	7	m.	m.	PROPN
ejpam-4015	348	8	imtiaz	imtiaz	PROPN
ejpam-4015	348	9	,	,	PUNCT
ejpam-4015	348	10	a.	a.	PROPN
ejpam-4015	348	11	r.	r.	PROPN
ejpam-4015	348	12	khan	khan	PROPN
ejpam-4015	348	13	,	,	PUNCT
ejpam-4015	348	14	i.	i.	PROPN
ejpam-4015	348	15	u.	u.	PROPN
ejpam-4015	348	16	khan	khan	PROPN
ejpam-4015	348	17	,	,	PUNCT
ejpam-4015	348	18	and	and	CCONJ
ejpam-4015	348	19	m.	m.	NOUN
ejpam-4015	348	20	zafran	zafran	PROPN
ejpam-4015	348	21	.	.	PUNCT
ejpam-4015	349	1	generalized	generalize	VERB
ejpam-4015	349	2	hermite	hermite	ADJ
ejpam-4015	349	3	–	–	PUNCT
ejpam-4015	349	4	hadamard	hadamard	ADJ
ejpam-4015	349	5	inequalities	inequality	NOUN
ejpam-4015	349	6	for	for	ADP
ejpam-4015	349	7	s	s	NOUN
ejpam-4015	349	8	–	–	PUNCT
ejpam-4015	349	9	convex	convex	NOUN
ejpam-4015	349	10	functions	function	NOUN
ejpam-4015	349	11	in	in	ADP
ejpam-4015	349	12	the	the	DET
ejpam-4015	349	13	mixed	mixed	ADJ
ejpam-4015	349	14	kind	kind	NOUN
ejpam-4015	349	15	.	.	PUNCT
ejpam-4015	350	1	2021(submitted	2021(submitted	NUM
ejpam-4015	350	2	)	)	PUNCT
ejpam-4015	350	3	.	.	PUNCT
ejpam-4015	351	1	[	[	X
ejpam-4015	351	2	6	6	NUM
ejpam-4015	351	3	]	]	PUNCT
ejpam-4015	351	4	m.	m.	NOUN
ejpam-4015	351	5	bilal	bilal	PROPN
ejpam-4015	351	6	,	,	PUNCT
ejpam-4015	351	7	n.	n.	PROPN
ejpam-4015	351	8	irshad	irshad	PROPN
ejpam-4015	351	9	,	,	PUNCT
ejpam-4015	351	10	and	and	CCONJ
ejpam-4015	351	11	a.	a.	PROPN
ejpam-4015	351	12	r.	r.	PROPN
ejpam-4015	351	13	khan	khan	PROPN
ejpam-4015	351	14	.	.	PUNCT
ejpam-4015	352	1	new	new	ADJ
ejpam-4015	352	2	version	version	NOUN
ejpam-4015	352	3	of	of	ADP
ejpam-4015	352	4	generalized	generalized	ADJ
ejpam-4015	352	5	ostrowski	ostrowski	NOUN
ejpam-4015	352	6	–	–	PUNCT
ejpam-4015	352	7	grüss	grüss	PROPN
ejpam-4015	352	8	type	type	NOUN
ejpam-4015	352	9	inequality	inequality	NOUN
ejpam-4015	352	10	.	.	PUNCT
ejpam-4015	353	1	stud	stud	PROPN
ejpam-4015	353	2	.	.	PUNCT
ejpam-4015	354	1	univ	univ	PROPN
ejpam-4015	354	2	.	.	PUNCT
ejpam-4015	355	1	babeş-bolyai	babeş-bolyai	PROPN
ejpam-4015	355	2	math	math	NOUN
ejpam-4015	355	3	.	.	PUNCT
ejpam-4015	355	4	,	,	PUNCT
ejpam-4015	355	5	2019(accepted	2019(accepted	NUM
ejpam-4015	355	6	)	)	PUNCT
ejpam-4015	355	7	.	.	PUNCT
ejpam-4015	356	1	[	[	X
ejpam-4015	356	2	7	7	X
ejpam-4015	356	3	]	]	X
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ejpam-4015	356	5	w.	w.	PROPN
ejpam-4015	356	6	breckner	breckner	PROPN
ejpam-4015	356	7	.	.	PUNCT
ejpam-4015	357	1	stetigkeitsaussagen	stetigkeitsaussagen	PROPN
ejpam-4015	357	2	fur	fur	PROPN
ejpam-4015	357	3	eine	eine	PROPN
ejpam-4015	357	4	klasse	klasse	PROPN
ejpam-4015	357	5	verallgemeinerter	verallgemeinerter	PROPN
ejpam-4015	357	6	konvexer	konvexer	PROPN
ejpam-4015	357	7	funktionen	funktionen	PROPN
ejpam-4015	357	8	in	in	ADP
ejpam-4015	357	9	topologischen	topologischen	PROPN
ejpam-4015	357	10	linearen	linearen	PROPN
ejpam-4015	357	11	raumen	raumen	PROPN
ejpam-4015	357	12	(	(	PUNCT
ejpam-4015	357	13	german	german	ADJ
ejpam-4015	357	14	)	)	PUNCT
ejpam-4015	357	15	.	.	PUNCT
ejpam-4015	358	1	publ	publ	PROPN
ejpam-4015	358	2	.	.	PUNCT
ejpam-4015	359	1	inst	inst	PROPN
ejpam-4015	359	2	.	.	PUNCT
ejpam-4015	359	3	math	math	NOUN
ejpam-4015	359	4	.	.	PUNCT
ejpam-4015	359	5	,	,	PUNCT
ejpam-4015	359	6	23(37):13–20	23(37):13–20	NUM
ejpam-4015	359	7	,	,	PUNCT
ejpam-4015	359	8	1978	1978	NUM
ejpam-4015	359	9	.	.	PUNCT
ejpam-4015	360	1	[	[	X
ejpam-4015	360	2	8	8	NUM
ejpam-4015	360	3	]	]	PUNCT
ejpam-4015	360	4	s.	s.	PROPN
ejpam-4015	360	5	s.	s.	PROPN
ejpam-4015	360	6	dragomir	dragomir	PROPN
ejpam-4015	360	7	,	,	PUNCT
ejpam-4015	360	8	j.	j.	PROPN
ejpam-4015	360	9	pečarić	pečarić	PROPN
ejpam-4015	360	10	,	,	PUNCT
ejpam-4015	360	11	and	and	CCONJ
ejpam-4015	360	12	l.	l.	PROPN
ejpam-4015	360	13	persson	persson	PROPN
ejpam-4015	360	14	.	.	PUNCT
ejpam-4015	361	1	some	some	DET
ejpam-4015	361	2	inequalities	inequality	NOUN
ejpam-4015	361	3	of	of	ADP
ejpam-4015	361	4	hadamard	hadamard	ADJ
ejpam-4015	361	5	type	type	NOUN
ejpam-4015	361	6	.	.	PUNCT
ejpam-4015	362	1	soochow	soochow	PROPN
ejpam-4015	362	2	j.	j.	PROPN
ejpam-4015	362	3	math	math	PROPN
ejpam-4015	362	4	.	.	PROPN
ejpam-4015	362	5	,	,	PUNCT
ejpam-4015	362	6	21(3):335–341	21(3):335–341	NUM
ejpam-4015	362	7	,	,	PUNCT
ejpam-4015	362	8	1995	1995	NUM
ejpam-4015	362	9	.	.	PUNCT
ejpam-4015	363	1	[	[	X
ejpam-4015	363	2	9	9	NUM
ejpam-4015	363	3	]	]	PUNCT
ejpam-4015	363	4	m.	m.	NOUN
ejpam-4015	363	5	feckan	feckan	PROPN
ejpam-4015	363	6	,	,	PUNCT
ejpam-4015	363	7	x.	x.	PROPN
ejpam-4015	363	8	li	li	PROPN
ejpam-4015	363	9	,	,	PUNCT
ejpam-4015	363	10	j.	j.	PROPN
ejpam-4015	363	11	wang	wang	PROPN
ejpam-4015	363	12	,	,	PUNCT
ejpam-4015	363	13	and	and	CCONJ
ejpam-4015	363	14	y.	y.	PROPN
ejpam-4015	363	15	zhou	zhou	PROPN
ejpam-4015	363	16	.	.	PUNCT
ejpam-4015	364	1	hermite	hermite	ADJ
ejpam-4015	364	2	–	–	PUNCT
ejpam-4015	364	3	hadamard	hadamard	ADJ
ejpam-4015	364	4	–	–	PUNCT
ejpam-4015	364	5	type	type	NOUN
ejpam-4015	364	6	inequalities	inequality	NOUN
ejpam-4015	364	7	for	for	ADP
ejpam-4015	364	8	riemann	riemann	PROPN
ejpam-4015	364	9	–	–	PUNCT
ejpam-4015	364	10	liouville	liouville	VERB
ejpam-4015	364	11	fractional	fractional	ADJ
ejpam-4015	364	12	integrals	integral	NOUN
ejpam-4015	364	13	via	via	ADP
ejpam-4015	364	14	two	two	NUM
ejpam-4015	364	15	senses	sense	NOUN
ejpam-4015	364	16	of	of	ADP
ejpam-4015	364	17	convexity	convexity	NOUN
ejpam-4015	364	18	.	.	PUNCT
ejpam-4015	365	1	applicable	applicable	ADJ
ejpam-4015	365	2	analysis	analysis	NOUN
ejpam-4015	365	3	,	,	PUNCT
ejpam-4015	365	4	92:2241–2253	92:2241–2253	NUM
ejpam-4015	365	5	,	,	PUNCT
ejpam-4015	365	6	2013	2013	NUM
ejpam-4015	365	7	.	.	PUNCT
ejpam-4015	366	1	[	[	X
ejpam-4015	366	2	10	10	NUM
ejpam-4015	366	3	]	]	X
ejpam-4015	366	4	ch	ch	NOUN
ejpam-4015	366	5	.	.	PUNCT
ejpam-4015	366	6	hermite	hermite	PROPN
ejpam-4015	366	7	.	.	PUNCT
ejpam-4015	367	1	sur	sur	PROPN
ejpam-4015	367	2	deux	deux	PROPN
ejpam-4015	367	3	limites	limites	PROPN
ejpam-4015	367	4	d’une	d’une	PROPN
ejpam-4015	367	5	int’egrale	int’egrale	PROPN
ejpam-4015	367	6	d’efinie	d’efinie	PROPN
ejpam-4015	367	7	.	.	PUNCT
ejpam-4015	368	1	mathesis	mathesis	PROPN
ejpam-4015	368	2	3	3	NUM
ejpam-4015	368	3	,	,	PUNCT
ejpam-4015	368	4	1883	1883	NUM
ejpam-4015	368	5	.	.	PUNCT
ejpam-4015	369	1	[	[	X
ejpam-4015	369	2	11	11	NUM
ejpam-4015	369	3	]	]	PUNCT
ejpam-4015	369	4	i̇.	i̇.	PROPN
ejpam-4015	369	5	işcan	işcan	PROPN
ejpam-4015	369	6	.	.	PUNCT
ejpam-4015	369	7	hermite−hadamard	hermite−hadamard	PROPN
ejpam-4015	369	8	and	and	CCONJ
ejpam-4015	369	9	simpson	simpson	PROPN
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ejpam-4015	369	11	inequalities	inequality	NOUN
ejpam-4015	369	12	for	for	ADP
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ejpam-4015	369	14	harmonically	harmonically	ADV
ejpam-4015	369	15	convex	convex	NOUN
ejpam-4015	369	16	functions	function	NOUN
ejpam-4015	369	17	.	.	PUNCT
ejpam-4015	370	1	j.	j.	PROPN
ejpam-4015	370	2	math	math	PROPN
ejpam-4015	370	3	.	.	PROPN
ejpam-4015	370	4	,	,	PUNCT
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ejpam-4015	370	6	,	,	PUNCT
ejpam-4015	370	7	2014	2014	NUM
ejpam-4015	370	8	.	.	PUNCT
ejpam-4015	371	1	[	[	X
ejpam-4015	371	2	12	12	NUM
ejpam-4015	371	3	]	]	PUNCT
ejpam-4015	371	4	i̇.	i̇.	PROPN
ejpam-4015	371	5	işcan	işcan	PROPN
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ejpam-4015	371	7	hermite−hadamard	hermite−hadamard	PART
ejpam-4015	371	8	type	type	NOUN
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ejpam-4015	371	10	for	for	ADP
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ejpam-4015	371	12	functions	function	NOUN
ejpam-4015	371	13	.	.	PUNCT
ejpam-4015	372	1	in	in	ADP
ejpam-4015	372	2	.	.	PUNCT
ejpam-4015	373	1	j.	j.	PROPN
ejpam-4015	373	2	anal	anal	PROPN
ejpam-4015	373	3	.	.	PUNCT
ejpam-4015	374	1	appl	appl	PROPN
ejpam-4015	374	2	.	.	PROPN
ejpam-4015	374	3	,	,	PUNCT
ejpam-4015	374	4	11(2):137–145	11(2):137–145	NUM
ejpam-4015	374	5	,	,	PUNCT
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ejpam-4015	374	7	.	.	PUNCT
ejpam-4015	375	1	[	[	X
ejpam-4015	375	2	13	13	NUM
ejpam-4015	375	3	]	]	PUNCT
ejpam-4015	375	4	i̇.	i̇.	PROPN
ejpam-4015	375	5	işcan	işcan	PROPN
ejpam-4015	375	6	.	.	PUNCT
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ejpam-4015	375	8	type	type	NOUN
ejpam-4015	375	9	inequalities	inequality	NOUN
ejpam-4015	375	10	for	for	ADP
ejpam-4015	375	11	p	p	NOUN
ejpam-4015	375	12	-	-	PUNCT
ejpam-4015	375	13	convex	convex	NOUN
ejpam-4015	375	14	functions	function	NOUN
ejpam-4015	375	15	.	.	PUNCT
ejpam-4015	376	1	new	new	ADJ
ejpam-4015	376	2	trends	trend	NOUN
ejpam-4015	376	3	math	math	NOUN
ejpam-4015	376	4	.	.	PUNCT
ejpam-4015	377	1	sci	sci	PROPN
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ejpam-4015	377	5	,	,	PUNCT
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ejpam-4015	377	7	.	.	PUNCT
ejpam-4015	378	1	[	[	X
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ejpam-4015	378	3	]	]	PUNCT
ejpam-4015	378	4	a.	a.	PROPN
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ejpam-4015	378	8	i.	i.	PROPN
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ejpam-4015	378	15	.	.	PUNCT
ejpam-4015	378	16	hermite	hermite	PROPN
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ejpam-4015	378	24	-	-	PUNCT
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ejpam-4015	378	28	mixed	mixed	ADJ
ejpam-4015	378	29	kind	kind	NOUN
ejpam-4015	378	30	.	.	PUNCT
ejpam-4015	379	1	tmcs	tmcs	NOUN
ejpam-4015	379	2	.	.	PUNCT
ejpam-4015	379	3	,	,	PUNCT
ejpam-4015	379	4	1:25–37	1:25–37	NUM
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ejpam-4015	379	7	.	.	PUNCT
ejpam-4015	380	1	[	[	X
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ejpam-4015	380	7	.	.	PUNCT
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ejpam-4015	381	13	and	and	CCONJ
ejpam-4015	381	14	to	to	PART
ejpam-4015	381	15	midpoint	midpoint	VERB
ejpam-4015	381	16	formula	formula	NOUN
ejpam-4015	381	17	.	.	PUNCT
ejpam-4015	382	1	appl	appl	PROPN
ejpam-4015	382	2	.	.	PROPN
ejpam-4015	382	3	math	math	PROPN
ejpam-4015	382	4	.	.	PUNCT
ejpam-4015	383	1	comput	comput	NOUN
ejpam-4015	383	2	.	.	PUNCT
ejpam-4015	383	3	,	,	PUNCT
ejpam-4015	383	4	147:137–146	147:137–146	NUM
ejpam-4015	383	5	,	,	PUNCT
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ejpam-4015	383	7	.	.	PUNCT
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ejpam-4015	384	2	880	880	NUM
ejpam-4015	384	3	[	[	SYM
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ejpam-4015	384	5	]	]	PUNCT
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ejpam-4015	384	9	i̇.	i̇.	PROPN
ejpam-4015	384	10	işcan	işcan	PROPN
ejpam-4015	384	11	.	.	PUNCT
ejpam-4015	385	1	hermite−hadamard	hermite−hadamard	ADV
ejpam-4015	385	2	–	–	PUNCT
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ejpam-4015	385	4	type	type	NOUN
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ejpam-4015	385	6	for	for	ADP
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ejpam-4015	385	9	.	.	PUNCT
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ejpam-4015	387	1	j.	j.	PROPN
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ejpam-4015	387	4	,	,	PUNCT
ejpam-4015	387	5	23(1):215–230	23(1):215–230	PROPN
ejpam-4015	387	6	,	,	PUNCT
ejpam-4015	387	7	2017	2017	NUM
ejpam-4015	387	8	.	.	PUNCT
ejpam-4015	388	1	[	[	X
ejpam-4015	388	2	17	17	NUM
ejpam-4015	388	3	]	]	X
ejpam-4015	388	4	f.	f.	PROPN
ejpam-4015	388	5	mehmood	mehmood	PROPN
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ejpam-4015	388	8	r.	r.	PROPN
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ejpam-4015	388	17	shaikh	shaikh	PROPN
ejpam-4015	388	18	.	.	PUNCT
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ejpam-4015	389	9	.	.	PUNCT
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ejpam-4015	390	6	and	and	CCONJ
ejpam-4015	390	7	mathematical	mathematical	ADJ
ejpam-4015	390	8	sciences	science	NOUN
ejpam-4015	390	9	,	,	PUNCT
ejpam-4015	390	10	15(4):13–20	15(4):13–20	NUM
ejpam-4015	390	11	,	,	PUNCT
ejpam-4015	390	12	2020	2020	NUM
ejpam-4015	390	13	.	.	PUNCT
ejpam-4015	391	1	[	[	X
ejpam-4015	391	2	18	18	NUM
ejpam-4015	391	3	]	]	X
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ejpam-4015	391	5	s.	s.	PROPN
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ejpam-4015	391	8	j.	j.	PROPN
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ejpam-4015	391	11	,	,	PUNCT
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ejpam-4015	391	14	m.	m.	NOUN
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ejpam-4015	391	16	.	.	PUNCT
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ejpam-4015	392	7	.	.	PUNCT
ejpam-4015	393	1	kluwer	kluwer	NOUN
ejpam-4015	393	2	academic	academic	ADJ
ejpam-4015	393	3	publishers	publisher	NOUN
ejpam-4015	393	4	,	,	PUNCT
ejpam-4015	393	5	dordrecht	dordrecht	PROPN
ejpam-4015	393	6	,	,	PUNCT
ejpam-4015	393	7	1993	1993	NUM
ejpam-4015	393	8	.	.	PUNCT
ejpam-4015	394	1	[	[	X
ejpam-4015	394	2	19	19	NUM
ejpam-4015	394	3	]	]	PUNCT
ejpam-4015	394	4	m.	m.	NOUN
ejpam-4015	394	5	a.	a.	PROPN
ejpam-4015	394	6	noor	noor	PROPN
ejpam-4015	394	7	and	and	CCONJ
ejpam-4015	394	8	m.	m.	PROPN
ejpam-4015	394	9	u.	u.	PROPN
ejpam-4015	394	10	awan	awan	PROPN
ejpam-4015	394	11	.	.	PUNCT
ejpam-4015	395	1	some	some	DET
ejpam-4015	395	2	integral	integral	ADJ
ejpam-4015	395	3	inequalities	inequality	NOUN
ejpam-4015	395	4	for	for	ADP
ejpam-4015	395	5	two	two	NUM
ejpam-4015	395	6	kinds	kind	NOUN
ejpam-4015	395	7	of	of	ADP
ejpam-4015	395	8	convexities	convexity	NOUN
ejpam-4015	395	9	via	via	ADP
ejpam-4015	395	10	fractional	fractional	ADJ
ejpam-4015	395	11	integrals	integral	NOUN
ejpam-4015	395	12	.	.	PUNCT
ejpam-4015	396	1	tjmm	tjmm	NOUN
ejpam-4015	396	2	.	.	PUNCT
ejpam-4015	396	3	,	,	PUNCT
ejpam-4015	396	4	5:129–136	5:129–136	PROPN
ejpam-4015	396	5	,	,	PUNCT
ejpam-4015	396	6	2013	2013	NUM
ejpam-4015	396	7	.	.	PUNCT
ejpam-4015	397	1	[	[	X
ejpam-4015	397	2	20	20	NUM
ejpam-4015	397	3	]	]	PUNCT
ejpam-4015	397	4	m.	m.	NOUN
ejpam-4015	397	5	a.	a.	PROPN
ejpam-4015	397	6	noor	noor	PROPN
ejpam-4015	397	7	,	,	PUNCT
ejpam-4015	397	8	k.	k.	PROPN
ejpam-4015	397	9	i.	i.	PROPN
ejpam-4015	397	10	noor	noor	PROPN
ejpam-4015	397	11	,	,	PUNCT
ejpam-4015	397	12	m.	m.	NOUN
ejpam-4015	397	13	v.	v.	PROPN
ejpam-4015	397	14	mihai	mihai	PROPN
ejpam-4015	397	15	,	,	PUNCT
ejpam-4015	397	16	and	and	CCONJ
ejpam-4015	397	17	m.	m.	NOUN
ejpam-4015	397	18	u.	u.	PROPN
ejpam-4015	397	19	awan	awan	PROPN
ejpam-4015	397	20	.	.	PUNCT
ejpam-4015	398	1	hermite−hadamard	hermite−hadamard	PART
ejpam-4015	398	2	inequalities	inequality	NOUN
ejpam-4015	398	3	for	for	ADP
ejpam-4015	398	4	differentiable	differentiable	ADJ
ejpam-4015	398	5	p−convex	p−convex	NOUN
ejpam-4015	398	6	functions	function	NOUN
ejpam-4015	398	7	using	use	VERB
ejpam-4015	398	8	hypergeometric	hypergeometric	ADJ
ejpam-4015	398	9	functions	function	NOUN
ejpam-4015	398	10	.	.	PUNCT
ejpam-4015	399	1	publications	publication	NOUN
ejpam-4015	399	2	de	de	X
ejpam-4015	399	3	l’institut	l’institut	X
ejpam-4015	399	4	mathématique	mathématique	NOUN
ejpam-4015	399	5	,	,	PUNCT
ejpam-4015	399	6	100(114):251–257	100(114):251–257	NOUN
ejpam-4015	399	7	,	,	PUNCT
ejpam-4015	399	8	2015	2015	NUM
ejpam-4015	399	9	.	.	PUNCT
ejpam-4015	400	1	[	[	X
ejpam-4015	400	2	21	21	NUM
ejpam-4015	400	3	]	]	X
ejpam-4015	400	4	s.	s.	PROPN
ejpam-4015	400	5	özcan	özcan	PROPN
ejpam-4015	400	6	and	and	CCONJ
ejpam-4015	400	7	i.	i.	PROPN
ejpam-4015	400	8	işcan	işcan	PROPN
ejpam-4015	400	9	.	.	PUNCT
ejpam-4015	401	1	some	some	DET
ejpam-4015	401	2	new	new	ADJ
ejpam-4015	401	3	hermite	hermite	ADJ
ejpam-4015	401	4	–	–	PUNCT
ejpam-4015	401	5	hadamard	hadamard	ADJ
ejpam-4015	401	6	type	type	NOUN
ejpam-4015	401	7	inequalities	inequality	NOUN
ejpam-4015	401	8	for	for	ADP
ejpam-4015	401	9	s−convex	s−convex	NOUN
ejpam-4015	401	10	functions	function	NOUN
ejpam-4015	401	11	and	and	CCONJ
ejpam-4015	401	12	their	their	PRON
ejpam-4015	401	13	applications	application	NOUN
ejpam-4015	401	14	.	.	PUNCT
ejpam-4015	402	1	j.	j.	PROPN
ejpam-4015	402	2	ineq	ineq	PROPN
ejpam-4015	402	3	.	.	PUNCT
ejpam-4015	403	1	app	app	PROPN
ejpam-4015	403	2	.	.	PROPN
ejpam-4015	403	3	,	,	PUNCT
ejpam-4015	403	4	2019(201	2019(201	NUM
ejpam-4015	403	5	)	)	PUNCT
ejpam-4015	403	6	,	,	PUNCT
ejpam-4015	403	7	2019	2019	NUM
ejpam-4015	403	8	.	.	PUNCT
ejpam-4015	404	1	[	[	X
ejpam-4015	404	2	22	22	NUM
ejpam-4015	404	3	]	]	X
ejpam-4015	404	4	s.	s.	PROPN
ejpam-4015	404	5	simić	simić	PROPN
ejpam-4015	404	6	and	and	CCONJ
ejpam-4015	404	7	s.	s.	PROPN
ejpam-4015	405	1	radenović.	radenović.	PROPN
ejpam-4015	405	2	a	a	DET
ejpam-4015	405	3	functional	functional	ADJ
ejpam-4015	405	4	inequality	inequality	NOUN
ejpam-4015	405	5	.	.	PUNCT
ejpam-4015	406	1	journal	journal	PROPN
ejpam-4015	406	2	of	of	ADP
ejpam-4015	406	3	mathematical	mathematical	ADJ
ejpam-4015	406	4	analysis	analysis	NOUN
ejpam-4015	406	5	and	and	CCONJ
ejpam-4015	406	6	applications	application	NOUN
ejpam-4015	406	7	,	,	PUNCT
ejpam-4015	406	8	197:489–494	197:489–494	NUM
ejpam-4015	406	9	,	,	PUNCT
ejpam-4015	406	10	1996	1996	NUM
ejpam-4015	406	11	.	.	PUNCT