id	sid	tid	token	lemma	pos
ejpam-2996	1	1	european	european	PROPN
ejpam-2996	1	2	journal	journal	PROPN
ejpam-2996	1	3	of	of	ADP
ejpam-2996	1	4	pure	pure	ADJ
ejpam-2996	1	5	and	and	CCONJ
ejpam-2996	1	6	applied	apply	VERB
ejpam-2996	1	7	mathematics	mathematic	NOUN
ejpam-2996	1	8	vol	vol	NOUN
ejpam-2996	1	9	.	.	PROPN
ejpam-2996	2	1	10	10	NUM
ejpam-2996	2	2	,	,	PUNCT
ejpam-2996	2	3	no	no	INTJ
ejpam-2996	2	4	.	.	NOUN
ejpam-2996	2	5	3	3	NUM
ejpam-2996	2	6	,	,	PUNCT
ejpam-2996	2	7	2017	2017	NUM
ejpam-2996	2	8	,	,	PUNCT
ejpam-2996	2	9	495	495	NUM
ejpam-2996	2	10	-	-	SYM
ejpam-2996	2	11	505	505	NUM
ejpam-2996	2	12	issn	issn	PROPN
ejpam-2996	2	13	1307	1307	NUM
ejpam-2996	2	14	-	-	SYM
ejpam-2996	2	15	5543	5543	NUM
ejpam-2996	2	16	–	–	PUNCT
ejpam-2996	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2996	2	18	published	publish	VERB
ejpam-2996	2	19	by	by	ADP
ejpam-2996	2	20	new	new	PROPN
ejpam-2996	2	21	york	york	PROPN
ejpam-2996	2	22	business	business	PROPN
ejpam-2996	2	23	global	global	ADJ
ejpam-2996	2	24	hermite	hermite	PROPN
ejpam-2996	2	25	-	-	PUNCT
ejpam-2996	2	26	hadamard	hadamard	ADJ
ejpam-2996	2	27	type	type	NOUN
ejpam-2996	2	28	fractional	fractional	ADJ
ejpam-2996	2	29	integral	integral	ADJ
ejpam-2996	2	30	inequalities	inequality	NOUN
ejpam-2996	2	31	for	for	ADP
ejpam-2996	2	32	generalized	generalized	ADJ
ejpam-2996	2	33	(	(	PUNCT
ejpam-2996	2	34	r	r	NOUN
ejpam-2996	2	35	;	;	PUNCT
ejpam-2996	2	36	s	s	X
ejpam-2996	2	37	,	,	PUNCT
ejpam-2996	2	38	m	m	PRON
ejpam-2996	2	39	,	,	PUNCT
ejpam-2996	2	40	ϕ)-preinvex	ϕ)-preinvex	NOUN
ejpam-2996	2	41	functions	function	NOUN
ejpam-2996	2	42	artion	artion	PROPN
ejpam-2996	2	43	kashuri1,∗	kashuri1,∗	NOUN
ejpam-2996	2	44	,	,	PUNCT
ejpam-2996	2	45	rozana	rozana	ADJ
ejpam-2996	2	46	liko1	liko1	PROPN
ejpam-2996	2	47	1	1	NUM
ejpam-2996	2	48	department	department	NOUN
ejpam-2996	2	49	of	of	ADP
ejpam-2996	2	50	mathematics	mathematic	NOUN
ejpam-2996	2	51	,	,	PUNCT
ejpam-2996	2	52	faculty	faculty	NOUN
ejpam-2996	2	53	of	of	ADP
ejpam-2996	2	54	technical	technical	ADJ
ejpam-2996	2	55	science	science	NOUN
ejpam-2996	2	56	,	,	PUNCT
ejpam-2996	2	57	university	university	NOUN
ejpam-2996	2	58	”	"	PUNCT
ejpam-2996	2	59	ismail	ismail	PROPN
ejpam-2996	2	60	qemali	qemali	PROPN
ejpam-2996	2	61	”	"	PUNCT
ejpam-2996	2	62	,	,	PUNCT
ejpam-2996	2	63	vlora	vlora	PROPN
ejpam-2996	2	64	,	,	PUNCT
ejpam-2996	2	65	albania	albania	PROPN
ejpam-2996	2	66	abstract	abstract	PROPN
ejpam-2996	2	67	.	.	PUNCT
ejpam-2996	3	1	in	in	ADP
ejpam-2996	3	2	the	the	DET
ejpam-2996	3	3	present	present	ADJ
ejpam-2996	3	4	paper	paper	NOUN
ejpam-2996	3	5	,	,	PUNCT
ejpam-2996	3	6	a	a	DET
ejpam-2996	3	7	new	new	ADJ
ejpam-2996	3	8	class	class	NOUN
ejpam-2996	3	9	of	of	ADP
ejpam-2996	3	10	generalized	generalized	ADJ
ejpam-2996	3	11	(	(	PUNCT
ejpam-2996	3	12	r	r	NOUN
ejpam-2996	3	13	;	;	PUNCT
ejpam-2996	3	14	s	s	X
ejpam-2996	3	15	,	,	PUNCT
ejpam-2996	3	16	m	m	PRON
ejpam-2996	3	17	,	,	PUNCT
ejpam-2996	3	18	ϕ)-preinvex	ϕ)-preinvex	NOUN
ejpam-2996	3	19	functions	function	NOUN
ejpam-2996	3	20	is	be	AUX
ejpam-2996	3	21	introduced	introduce	VERB
ejpam-2996	3	22	and	and	CCONJ
ejpam-2996	3	23	some	some	DET
ejpam-2996	3	24	new	new	ADJ
ejpam-2996	3	25	integral	integral	ADJ
ejpam-2996	3	26	inequalities	inequality	NOUN
ejpam-2996	3	27	for	for	ADP
ejpam-2996	3	28	the	the	DET
ejpam-2996	3	29	left	left	ADJ
ejpam-2996	3	30	hand	hand	NOUN
ejpam-2996	3	31	side	side	NOUN
ejpam-2996	3	32	of	of	ADP
ejpam-2996	3	33	gauss	gauss	ADJ
ejpam-2996	3	34	-	-	PUNCT
ejpam-2996	3	35	jacobi	jacobi	PROPN
ejpam-2996	3	36	type	type	NOUN
ejpam-2996	3	37	quadrature	quadrature	NOUN
ejpam-2996	3	38	formula	formula	NOUN
ejpam-2996	3	39	involving	involve	VERB
ejpam-2996	3	40	generalized	generalize	VERB
ejpam-2996	3	41	(	(	PUNCT
ejpam-2996	3	42	r	r	NOUN
ejpam-2996	3	43	;	;	PUNCT
ejpam-2996	3	44	s	s	X
ejpam-2996	3	45	,	,	PUNCT
ejpam-2996	3	46	m	m	PRON
ejpam-2996	3	47	,	,	PUNCT
ejpam-2996	3	48	ϕ)-preinvex	ϕ)-preinvex	NOUN
ejpam-2996	3	49	functions	function	NOUN
ejpam-2996	3	50	are	be	AUX
ejpam-2996	3	51	given	give	VERB
ejpam-2996	3	52	.	.	PUNCT
ejpam-2996	4	1	moreover	moreover	ADV
ejpam-2996	4	2	,	,	PUNCT
ejpam-2996	4	3	some	some	DET
ejpam-2996	4	4	generalizations	generalization	NOUN
ejpam-2996	4	5	of	of	ADP
ejpam-2996	4	6	hermite	hermite	ADJ
ejpam-2996	4	7	-	-	PUNCT
ejpam-2996	4	8	hadamard	hadamard	ADJ
ejpam-2996	4	9	type	type	NOUN
ejpam-2996	4	10	inequalities	inequality	NOUN
ejpam-2996	4	11	for	for	ADP
ejpam-2996	4	12	generalized	generalized	ADJ
ejpam-2996	4	13	(	(	PUNCT
ejpam-2996	4	14	r	r	NOUN
ejpam-2996	4	15	;	;	PUNCT
ejpam-2996	4	16	s	s	X
ejpam-2996	4	17	,	,	PUNCT
ejpam-2996	4	18	m	m	PRON
ejpam-2996	4	19	,	,	PUNCT
ejpam-2996	4	20	ϕ)-preinvex	ϕ)-preinvex	NOUN
ejpam-2996	4	21	functions	function	NOUN
ejpam-2996	4	22	via	via	ADP
ejpam-2996	4	23	riemann	riemann	PROPN
ejpam-2996	4	24	-	-	PUNCT
ejpam-2996	4	25	liouville	liouville	VERB
ejpam-2996	4	26	fractional	fractional	ADJ
ejpam-2996	4	27	integrals	integral	NOUN
ejpam-2996	4	28	are	be	AUX
ejpam-2996	4	29	established	establish	VERB
ejpam-2996	4	30	.	.	PUNCT
ejpam-2996	5	1	these	these	DET
ejpam-2996	5	2	results	result	VERB
ejpam-2996	5	3	not	not	PART
ejpam-2996	5	4	only	only	ADV
ejpam-2996	5	5	extend	extend	VERB
ejpam-2996	5	6	the	the	DET
ejpam-2996	5	7	results	result	NOUN
ejpam-2996	5	8	appeared	appear	VERB
ejpam-2996	5	9	in	in	ADP
ejpam-2996	5	10	the	the	DET
ejpam-2996	5	11	literature	literature	NOUN
ejpam-2996	5	12	(	(	PUNCT
ejpam-2996	5	13	see	see	VERB
ejpam-2996	5	14	[	[	X
ejpam-2996	5	15	1	1	NUM
ejpam-2996	5	16	]	]	PUNCT
ejpam-2996	5	17	,	,	PUNCT
ejpam-2996	5	18	[	[	X
ejpam-2996	5	19	2	2	NUM
ejpam-2996	5	20	]	]	NUM
ejpam-2996	5	21	)	)	PUNCT
ejpam-2996	5	22	,	,	PUNCT
ejpam-2996	5	23	but	but	CCONJ
ejpam-2996	5	24	also	also	ADV
ejpam-2996	5	25	provide	provide	VERB
ejpam-2996	5	26	new	new	ADJ
ejpam-2996	5	27	estimates	estimate	NOUN
ejpam-2996	5	28	on	on	ADP
ejpam-2996	5	29	these	these	DET
ejpam-2996	5	30	types	type	NOUN
ejpam-2996	5	31	.	.	PUNCT
ejpam-2996	6	1	2010	2010	NUM
ejpam-2996	6	2	mathematics	mathematic	NOUN
ejpam-2996	6	3	subject	subject	NOUN
ejpam-2996	6	4	classifications	classification	NOUN
ejpam-2996	6	5	:	:	PUNCT
ejpam-2996	6	6	primary	primary	ADJ
ejpam-2996	6	7	:	:	PUNCT
ejpam-2996	6	8	26a51	26a51	X
ejpam-2996	6	9	.	.	PUNCT
ejpam-2996	7	1	secondary	secondary	ADJ
ejpam-2996	7	2	:	:	PUNCT
ejpam-2996	7	3	26a33	26a33	NUM
ejpam-2996	7	4	,	,	PUNCT
ejpam-2996	7	5	26d07	26d07	NUM
ejpam-2996	7	6	,	,	PUNCT
ejpam-2996	7	7	26d10	26d10	NUM
ejpam-2996	7	8	,	,	PUNCT
ejpam-2996	7	9	26d15	26d15	NUM
ejpam-2996	7	10	.	.	PUNCT
ejpam-2996	8	1	key	key	ADJ
ejpam-2996	8	2	words	word	NOUN
ejpam-2996	8	3	and	and	CCONJ
ejpam-2996	8	4	phrases	phrase	NOUN
ejpam-2996	8	5	:	:	PUNCT
ejpam-2996	8	6	hermite	hermite	ADJ
ejpam-2996	8	7	-	-	PUNCT
ejpam-2996	8	8	hadamard	hadamard	ADJ
ejpam-2996	8	9	type	type	NOUN
ejpam-2996	8	10	inequality	inequality	NOUN
ejpam-2996	8	11	,	,	PUNCT
ejpam-2996	8	12	hölder	hölder	PROPN
ejpam-2996	8	13	’s	’s	PART
ejpam-2996	8	14	inequality	inequality	NOUN
ejpam-2996	8	15	,	,	PUNCT
ejpam-2996	8	16	minkowski	minkowski	PROPN
ejpam-2996	8	17	’s	’s	PART
ejpam-2996	8	18	inequality	inequality	NOUN
ejpam-2996	8	19	,	,	PUNCT
ejpam-2996	8	20	cauchy	cauchy	PROPN
ejpam-2996	8	21	’s	’s	PART
ejpam-2996	8	22	inequality	inequality	NOUN
ejpam-2996	8	23	,	,	PUNCT
ejpam-2996	8	24	power	power	NOUN
ejpam-2996	8	25	mean	mean	NOUN
ejpam-2996	8	26	inequality	inequality	NOUN
ejpam-2996	8	27	,	,	PUNCT
ejpam-2996	8	28	riemann	riemann	PROPN
ejpam-2996	8	29	-	-	PUNCT
ejpam-2996	8	30	liouville	liouville	VERB
ejpam-2996	8	31	fractional	fractional	ADJ
ejpam-2996	8	32	integral	integral	ADJ
ejpam-2996	8	33	,	,	PUNCT
ejpam-2996	8	34	sconvex	sconvex	ADJ
ejpam-2996	8	35	function	function	NOUN
ejpam-2996	8	36	in	in	ADP
ejpam-2996	8	37	the	the	DET
ejpam-2996	8	38	second	second	ADJ
ejpam-2996	8	39	sense	sense	NOUN
ejpam-2996	8	40	,	,	PUNCT
ejpam-2996	8	41	m	m	NOUN
ejpam-2996	8	42	-	-	PUNCT
ejpam-2996	8	43	invex	invex	ADJ
ejpam-2996	8	44	,	,	PUNCT
ejpam-2996	8	45	p	p	NOUN
ejpam-2996	8	46	-function	-function	NOUN
ejpam-2996	8	47	.	.	PUNCT
ejpam-2996	9	1	1	1	X
ejpam-2996	9	2	.	.	X
ejpam-2996	9	3	introduction	introduction	NOUN
ejpam-2996	9	4	and	and	CCONJ
ejpam-2996	9	5	preliminaries	preliminary	NOUN
ejpam-2996	9	6	the	the	DET
ejpam-2996	9	7	following	follow	VERB
ejpam-2996	9	8	notations	notation	NOUN
ejpam-2996	9	9	are	be	AUX
ejpam-2996	9	10	used	use	VERB
ejpam-2996	9	11	throughout	throughout	ADP
ejpam-2996	9	12	this	this	DET
ejpam-2996	9	13	paper	paper	NOUN
ejpam-2996	9	14	.	.	PUNCT
ejpam-2996	10	1	we	we	PRON
ejpam-2996	10	2	use	use	VERB
ejpam-2996	10	3	i	i	PRON
ejpam-2996	10	4	to	to	PART
ejpam-2996	10	5	denote	denote	VERB
ejpam-2996	10	6	an	an	DET
ejpam-2996	10	7	interval	interval	NOUN
ejpam-2996	10	8	on	on	ADP
ejpam-2996	10	9	the	the	DET
ejpam-2996	10	10	real	real	ADJ
ejpam-2996	10	11	line	line	NOUN
ejpam-2996	11	1	r	r	NOUN
ejpam-2996	11	2	=	=	PUNCT
ejpam-2996	11	3	(	(	PUNCT
ejpam-2996	11	4	−∞,+∞	−∞,+∞	ADV
ejpam-2996	11	5	)	)	PUNCT
ejpam-2996	11	6	and	and	CCONJ
ejpam-2996	11	7	i	i	PRON
ejpam-2996	11	8	◦	◦	VERB
ejpam-2996	11	9	to	to	PART
ejpam-2996	11	10	denote	denote	VERB
ejpam-2996	11	11	the	the	DET
ejpam-2996	11	12	interior	interior	NOUN
ejpam-2996	11	13	of	of	ADP
ejpam-2996	11	14	i.	i.	NOUN
ejpam-2996	11	15	for	for	ADP
ejpam-2996	11	16	any	any	DET
ejpam-2996	11	17	subset	subset	NOUN
ejpam-2996	11	18	k	k	PROPN
ejpam-2996	11	19	⊆	⊆	NUM
ejpam-2996	11	20	rn	rn	PROPN
ejpam-2996	11	21	,	,	PUNCT
ejpam-2996	11	22	k	k	NOUN
ejpam-2996	11	23	◦	◦	NOUN
ejpam-2996	11	24	is	be	AUX
ejpam-2996	11	25	used	use	VERB
ejpam-2996	11	26	to	to	PART
ejpam-2996	11	27	denote	denote	VERB
ejpam-2996	11	28	the	the	DET
ejpam-2996	11	29	interior	interior	NOUN
ejpam-2996	11	30	of	of	ADP
ejpam-2996	11	31	k.	k.	PROPN
ejpam-2996	11	32	rn	rn	PROPN
ejpam-2996	11	33	is	be	AUX
ejpam-2996	11	34	used	use	VERB
ejpam-2996	11	35	to	to	PART
ejpam-2996	11	36	denote	denote	VERB
ejpam-2996	11	37	a	a	DET
ejpam-2996	11	38	generic	generic	ADJ
ejpam-2996	11	39	n	n	CCONJ
ejpam-2996	11	40	-	-	PUNCT
ejpam-2996	11	41	dimensional	dimensional	ADJ
ejpam-2996	11	42	vector	vector	NOUN
ejpam-2996	11	43	space	space	NOUN
ejpam-2996	11	44	.	.	PUNCT
ejpam-2996	12	1	the	the	DET
ejpam-2996	12	2	nonnegative	nonnegative	ADJ
ejpam-2996	12	3	real	real	ADJ
ejpam-2996	12	4	numbers	number	NOUN
ejpam-2996	12	5	are	be	AUX
ejpam-2996	12	6	denoted	denote	VERB
ejpam-2996	12	7	by	by	ADP
ejpam-2996	12	8	r	r	NOUN
ejpam-2996	12	9	◦	◦	NOUN
ejpam-2996	12	10	=	=	SYM
ejpam-2996	13	1	[	[	X
ejpam-2996	13	2	0,+∞	0,+∞	NUM
ejpam-2996	13	3	)	)	PUNCT
ejpam-2996	13	4	.	.	PUNCT
ejpam-2996	14	1	the	the	DET
ejpam-2996	14	2	set	set	NOUN
ejpam-2996	14	3	of	of	ADP
ejpam-2996	14	4	integrable	integrable	ADJ
ejpam-2996	14	5	functions	function	NOUN
ejpam-2996	14	6	on	on	ADP
ejpam-2996	14	7	the	the	DET
ejpam-2996	14	8	interval	interval	NOUN
ejpam-2996	14	9	[	[	X
ejpam-2996	14	10	a	a	X
ejpam-2996	14	11	,	,	PUNCT
ejpam-2996	14	12	b	b	NOUN
ejpam-2996	14	13	]	]	PUNCT
ejpam-2996	14	14	is	be	AUX
ejpam-2996	14	15	denoted	denote	VERB
ejpam-2996	14	16	by	by	ADP
ejpam-2996	14	17	l1[a	l1[a	NOUN
ejpam-2996	14	18	,	,	PUNCT
ejpam-2996	14	19	b	b	NOUN
ejpam-2996	14	20	]	]	X
ejpam-2996	14	21	.	.	PUNCT
ejpam-2996	15	1	the	the	DET
ejpam-2996	15	2	following	follow	VERB
ejpam-2996	15	3	inequality	inequality	NOUN
ejpam-2996	15	4	,	,	PUNCT
ejpam-2996	15	5	named	name	VERB
ejpam-2996	15	6	hermite	hermite	ADJ
ejpam-2996	15	7	-	-	PUNCT
ejpam-2996	15	8	hadamard	hadamard	ADJ
ejpam-2996	15	9	inequality	inequality	NOUN
ejpam-2996	15	10	,	,	PUNCT
ejpam-2996	15	11	is	be	AUX
ejpam-2996	15	12	one	one	NUM
ejpam-2996	15	13	of	of	ADP
ejpam-2996	15	14	the	the	DET
ejpam-2996	15	15	most	most	ADV
ejpam-2996	15	16	famous	famous	ADJ
ejpam-2996	15	17	inequalities	inequality	NOUN
ejpam-2996	15	18	in	in	ADP
ejpam-2996	15	19	the	the	DET
ejpam-2996	15	20	literature	literature	NOUN
ejpam-2996	15	21	for	for	ADP
ejpam-2996	15	22	convex	convex	NOUN
ejpam-2996	15	23	functions	function	NOUN
ejpam-2996	15	24	.	.	PUNCT
ejpam-2996	16	1	theorem	theorem	NOUN
ejpam-2996	16	2	1	1	NUM
ejpam-2996	16	3	.	.	PUNCT
ejpam-2996	17	1	let	let	VERB
ejpam-2996	17	2	f	f	NOUN
ejpam-2996	17	3	:	:	PUNCT
ejpam-2996	17	4	i	i	PRON
ejpam-2996	18	1	⊆	⊆	NUM
ejpam-2996	18	2	r	r	NOUN
ejpam-2996	18	3	−→	−→	NOUN
ejpam-2996	18	4	r	r	NOUN
ejpam-2996	18	5	be	be	VERB
ejpam-2996	18	6	a	a	DET
ejpam-2996	18	7	convex	convex	ADJ
ejpam-2996	18	8	function	function	NOUN
ejpam-2996	18	9	on	on	ADP
ejpam-2996	18	10	an	an	DET
ejpam-2996	18	11	interval	interval	NOUN
ejpam-2996	18	12	i	i	PRON
ejpam-2996	18	13	of	of	ADP
ejpam-2996	18	14	real	real	ADJ
ejpam-2996	18	15	numbers	number	NOUN
ejpam-2996	18	16	and	and	CCONJ
ejpam-2996	18	17	a	a	DET
ejpam-2996	18	18	,	,	PUNCT
ejpam-2996	18	19	b	b	X
ejpam-2996	18	20	∈	∈	NOUN
ejpam-2996	18	21	i	i	PRON
ejpam-2996	18	22	with	with	ADP
ejpam-2996	18	23	a	a	DET
ejpam-2996	18	24	<	<	X
ejpam-2996	18	25	b.	b.	NOUN
ejpam-2996	18	26	then	then	ADV
ejpam-2996	18	27	the	the	DET
ejpam-2996	18	28	following	follow	VERB
ejpam-2996	18	29	inequality	inequality	NOUN
ejpam-2996	18	30	holds	hold	VERB
ejpam-2996	18	31	:	:	PUNCT
ejpam-2996	18	32	f	f	PROPN
ejpam-2996	18	33	(	(	PUNCT
ejpam-2996	18	34	a+	a+	PUNCT
ejpam-2996	18	35	b	b	PROPN
ejpam-2996	18	36	2	2	X
ejpam-2996	18	37	)	)	PUNCT
ejpam-2996	18	38	≤	≤	NOUN
ejpam-2996	18	39	1	1	NUM
ejpam-2996	18	40	b−	b−	PROPN
ejpam-2996	18	41	a	a	DET
ejpam-2996	18	42	∫	∫	PROPN
ejpam-2996	18	43	b	b	PROPN
ejpam-2996	18	44	a	a	DET
ejpam-2996	18	45	f(x)dx	f(x)dx	NUM
ejpam-2996	18	46	≤	≤	NUM
ejpam-2996	18	47	f(a	f(a	NOUN
ejpam-2996	18	48	)	)	PUNCT
ejpam-2996	19	1	+	+	CCONJ
ejpam-2996	19	2	f(b	f(b	X
ejpam-2996	19	3	)	)	PUNCT
ejpam-2996	19	4	2	2	NUM
ejpam-2996	19	5	.	.	PUNCT
ejpam-2996	20	1	(	(	PUNCT
ejpam-2996	20	2	1	1	X
ejpam-2996	20	3	)	)	PUNCT
ejpam-2996	20	4	∗corresponding	∗corresponde	VERB
ejpam-2996	20	5	author	author	NOUN
ejpam-2996	20	6	.	.	PUNCT
ejpam-2996	21	1	email	email	NOUN
ejpam-2996	21	2	addresses	address	NOUN
ejpam-2996	21	3	:	:	PUNCT
ejpam-2996	21	4	artionkashuri@gmail.com	artionkashuri@gmail.com	X
ejpam-2996	21	5	(	(	PUNCT
ejpam-2996	21	6	a.	a.	NOUN
ejpam-2996	21	7	kashuri	kashuri	PROPN
ejpam-2996	21	8	)	)	PUNCT
ejpam-2996	21	9	,	,	PUNCT
ejpam-2996	21	10	rozanaliko86@gmail.com	rozanaliko86@gmail.com	PROPN
ejpam-2996	21	11	(	(	PUNCT
ejpam-2996	21	12	r.	r.	PROPN
ejpam-2996	21	13	liko	liko	PROPN
ejpam-2996	21	14	)	)	PUNCT
ejpam-2996	21	15	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2996	22	1	495	495	NUM
ejpam-2996	23	1	c	c	NOUN
ejpam-2996	23	2	©	©	PROPN
ejpam-2996	23	3	2017	2017	NUM
ejpam-2996	23	4	ejpam	ejpam	NOUN
ejpam-2996	23	5	all	all	DET
ejpam-2996	23	6	rights	right	NOUN
ejpam-2996	23	7	reserved	reserve	VERB
ejpam-2996	23	8	.	.	PUNCT
ejpam-2996	24	1	a.	a.	PROPN
ejpam-2996	24	2	kashuri	kashuri	PROPN
ejpam-2996	24	3	,	,	PUNCT
ejpam-2996	24	4	r.	r.	PROPN
ejpam-2996	24	5	liko	liko	PROPN
ejpam-2996	24	6	/	/	SYM
ejpam-2996	24	7	eur	eur	PROPN
ejpam-2996	24	8	.	.	PUNCT
ejpam-2996	25	1	j.	j.	PROPN
ejpam-2996	25	2	pure	pure	PROPN
ejpam-2996	25	3	appl	appl	PROPN
ejpam-2996	25	4	.	.	PROPN
ejpam-2996	25	5	math	math	PROPN
ejpam-2996	25	6	,	,	PUNCT
ejpam-2996	25	7	10	10	NUM
ejpam-2996	25	8	(	(	PUNCT
ejpam-2996	25	9	3	3	NUM
ejpam-2996	25	10	)	)	PUNCT
ejpam-2996	25	11	(	(	PUNCT
ejpam-2996	25	12	2017	2017	NUM
ejpam-2996	25	13	)	)	PUNCT
ejpam-2996	25	14	,	,	PUNCT
ejpam-2996	25	15	495	495	NUM
ejpam-2996	25	16	-	-	SYM
ejpam-2996	25	17	505	505	NUM
ejpam-2996	25	18	496	496	NUM
ejpam-2996	25	19	fractional	fractional	ADJ
ejpam-2996	25	20	calculus	calculus	NOUN
ejpam-2996	25	21	(	(	PUNCT
ejpam-2996	25	22	see	see	VERB
ejpam-2996	25	23	[	[	X
ejpam-2996	25	24	14	14	NUM
ejpam-2996	25	25	]	]	PUNCT
ejpam-2996	25	26	)	)	PUNCT
ejpam-2996	25	27	and	and	CCONJ
ejpam-2996	25	28	the	the	DET
ejpam-2996	25	29	references	reference	NOUN
ejpam-2996	25	30	cited	cite	VERB
ejpam-2996	25	31	therein	therein	ADV
ejpam-2996	25	32	,	,	PUNCT
ejpam-2996	25	33	was	be	AUX
ejpam-2996	25	34	introduced	introduce	VERB
ejpam-2996	25	35	at	at	ADP
ejpam-2996	25	36	the	the	DET
ejpam-2996	25	37	end	end	NOUN
ejpam-2996	25	38	of	of	ADP
ejpam-2996	25	39	the	the	DET
ejpam-2996	25	40	nineteenth	nineteenth	ADJ
ejpam-2996	25	41	century	century	NOUN
ejpam-2996	25	42	by	by	ADP
ejpam-2996	25	43	liouville	liouville	NOUN
ejpam-2996	25	44	and	and	CCONJ
ejpam-2996	25	45	riemann	riemann	PROPN
ejpam-2996	25	46	,	,	PUNCT
ejpam-2996	25	47	the	the	DET
ejpam-2996	25	48	subject	subject	NOUN
ejpam-2996	25	49	of	of	ADP
ejpam-2996	25	50	which	which	PRON
ejpam-2996	25	51	has	have	AUX
ejpam-2996	25	52	become	become	VERB
ejpam-2996	25	53	a	a	DET
ejpam-2996	25	54	rapidly	rapidly	ADV
ejpam-2996	25	55	growing	grow	VERB
ejpam-2996	25	56	area	area	NOUN
ejpam-2996	25	57	and	and	CCONJ
ejpam-2996	25	58	has	have	AUX
ejpam-2996	25	59	found	find	VERB
ejpam-2996	25	60	applications	application	NOUN
ejpam-2996	25	61	in	in	ADP
ejpam-2996	25	62	diverse	diverse	ADJ
ejpam-2996	25	63	fields	field	NOUN
ejpam-2996	25	64	ranging	range	VERB
ejpam-2996	25	65	from	from	ADP
ejpam-2996	25	66	physical	physical	ADJ
ejpam-2996	25	67	sciences	science	NOUN
ejpam-2996	25	68	and	and	CCONJ
ejpam-2996	25	69	engineering	engineering	NOUN
ejpam-2996	25	70	to	to	ADP
ejpam-2996	25	71	biological	biological	ADJ
ejpam-2996	25	72	sciences	science	NOUN
ejpam-2996	25	73	and	and	CCONJ
ejpam-2996	25	74	economics	economic	NOUN
ejpam-2996	25	75	.	.	PUNCT
ejpam-2996	26	1	definition	definition	NOUN
ejpam-2996	26	2	1	1	NUM
ejpam-2996	26	3	.	.	PUNCT
ejpam-2996	27	1	let	let	VERB
ejpam-2996	27	2	f	f	PROPN
ejpam-2996	27	3	∈	∈	PROPN
ejpam-2996	27	4	l1[a	l1[a	NOUN
ejpam-2996	27	5	,	,	PUNCT
ejpam-2996	27	6	b	b	NOUN
ejpam-2996	27	7	]	]	X
ejpam-2996	27	8	.	.	PUNCT
ejpam-2996	28	1	the	the	DET
ejpam-2996	28	2	riemann	riemann	PROPN
ejpam-2996	28	3	-	-	PUNCT
ejpam-2996	28	4	liouville	liouville	NOUN
ejpam-2996	28	5	integrals	integral	NOUN
ejpam-2996	28	6	jαa+f	jαa+f	PROPN
ejpam-2996	28	7	and	and	CCONJ
ejpam-2996	28	8	jαb−f	jαb−f	NOUN
ejpam-2996	28	9	of	of	ADP
ejpam-2996	28	10	order	order	NOUN
ejpam-2996	28	11	α	α	X
ejpam-2996	28	12	>	>	X
ejpam-2996	28	13	0	0	PUNCT
ejpam-2996	28	14	with	with	ADP
ejpam-2996	28	15	a	a	DET
ejpam-2996	28	16	≥	≥	NOUN
ejpam-2996	28	17	0	0	NUM
ejpam-2996	28	18	are	be	AUX
ejpam-2996	28	19	defined	define	VERB
ejpam-2996	28	20	by	by	ADP
ejpam-2996	28	21	jαa+f(x	jαa+f(x	PROPN
ejpam-2996	28	22	)	)	PUNCT
ejpam-2996	28	23	=	=	SYM
ejpam-2996	28	24	1	1	NUM
ejpam-2996	28	25	γ(α	γ(α	NOUN
ejpam-2996	28	26	)	)	PUNCT
ejpam-2996	28	27	∫	∫	PROPN
ejpam-2996	29	1	x	x	X
ejpam-2996	29	2	a	a	DET
ejpam-2996	29	3	(	(	PUNCT
ejpam-2996	29	4	x−	x−	PROPN
ejpam-2996	29	5	t)α−1f(t)dt	t)α−1f(t)dt	PROPN
ejpam-2996	29	6	,	,	PUNCT
ejpam-2996	29	7	x	x	X
ejpam-2996	29	8	>	>	X
ejpam-2996	29	9	a	a	PRON
ejpam-2996	29	10	and	and	CCONJ
ejpam-2996	29	11	jαb−f(x	jαb−f(x	PROPN
ejpam-2996	29	12	)	)	PUNCT
ejpam-2996	29	13	=	=	SYM
ejpam-2996	29	14	1	1	NUM
ejpam-2996	29	15	γ(α	γ(α	NOUN
ejpam-2996	29	16	)	)	PUNCT
ejpam-2996	30	1	∫	∫	PROPN
ejpam-2996	31	1	b	b	PROPN
ejpam-2996	31	2	x	x	X
ejpam-2996	31	3	(	(	PUNCT
ejpam-2996	31	4	t−	t−	PROPN
ejpam-2996	31	5	x)α−1f(t)dt	x)α−1f(t)dt	PROPN
ejpam-2996	31	6	,	,	PUNCT
ejpam-2996	31	7	b	b	X
ejpam-2996	31	8	>	>	X
ejpam-2996	31	9	x	x	NOUN
ejpam-2996	31	10	,	,	PUNCT
ejpam-2996	31	11	where	where	SCONJ
ejpam-2996	31	12	γ(α	γ(α	NOUN
ejpam-2996	31	13	)	)	PUNCT
ejpam-2996	31	14	=	=	PUNCT
ejpam-2996	32	1	∫	∫	PROPN
ejpam-2996	33	1	+	+	NUM
ejpam-2996	33	2	∞	∞	NOUN
ejpam-2996	33	3	0	0	NUM
ejpam-2996	33	4	e−uuα−1du	e−uuα−1du	ADJ
ejpam-2996	33	5	.	.	PUNCT
ejpam-2996	34	1	here	here	ADV
ejpam-2996	34	2	j0	j0	PROPN
ejpam-2996	34	3	a+f(x	a+f(x	NOUN
ejpam-2996	34	4	)	)	PUNCT
ejpam-2996	34	5	=	=	PROPN
ejpam-2996	34	6	j0	j0	PROPN
ejpam-2996	34	7	b−f(x	b−f(x	PROPN
ejpam-2996	34	8	)	)	PUNCT
ejpam-2996	34	9	=	=	SYM
ejpam-2996	34	10	f(x	f(x	PROPN
ejpam-2996	34	11	)	)	PUNCT
ejpam-2996	34	12	.	.	PUNCT
ejpam-2996	35	1	in	in	ADP
ejpam-2996	35	2	the	the	DET
ejpam-2996	35	3	case	case	NOUN
ejpam-2996	35	4	of	of	ADP
ejpam-2996	35	5	α	α	NOUN
ejpam-2996	35	6	=	=	SYM
ejpam-2996	35	7	1	1	NUM
ejpam-2996	35	8	,	,	PUNCT
ejpam-2996	35	9	the	the	DET
ejpam-2996	35	10	fractional	fractional	ADJ
ejpam-2996	35	11	integral	integral	ADJ
ejpam-2996	35	12	reduces	reduce	NOUN
ejpam-2996	35	13	to	to	ADP
ejpam-2996	35	14	the	the	DET
ejpam-2996	35	15	classical	classical	ADJ
ejpam-2996	35	16	integral	integral	NOUN
ejpam-2996	35	17	.	.	PUNCT
ejpam-2996	36	1	due	due	ADP
ejpam-2996	36	2	to	to	ADP
ejpam-2996	36	3	the	the	DET
ejpam-2996	36	4	wide	wide	ADJ
ejpam-2996	36	5	application	application	NOUN
ejpam-2996	36	6	of	of	ADP
ejpam-2996	36	7	fractional	fractional	ADJ
ejpam-2996	36	8	integrals	integral	NOUN
ejpam-2996	36	9	,	,	PUNCT
ejpam-2996	36	10	some	some	DET
ejpam-2996	36	11	authors	author	NOUN
ejpam-2996	36	12	extended	extend	VERB
ejpam-2996	36	13	to	to	PART
ejpam-2996	36	14	study	study	VERB
ejpam-2996	36	15	fractional	fractional	ADJ
ejpam-2996	36	16	hermite	hermite	PROPN
ejpam-2996	36	17	-	-	PUNCT
ejpam-2996	36	18	hadamard	hadamard	ADJ
ejpam-2996	36	19	type	type	NOUN
ejpam-2996	36	20	inequalities	inequality	NOUN
ejpam-2996	36	21	for	for	ADP
ejpam-2996	36	22	functions	function	NOUN
ejpam-2996	36	23	of	of	ADP
ejpam-2996	36	24	different	different	ADJ
ejpam-2996	36	25	classes	class	NOUN
ejpam-2996	36	26	(	(	PUNCT
ejpam-2996	36	27	see	see	VERB
ejpam-2996	36	28	[	[	X
ejpam-2996	36	29	13	13	NUM
ejpam-2996	36	30	]	]	PUNCT
ejpam-2996	36	31	,	,	PUNCT
ejpam-2996	37	1	[	[	X
ejpam-2996	37	2	14	14	NUM
ejpam-2996	37	3	]	]	PUNCT
ejpam-2996	37	4	)	)	PUNCT
ejpam-2996	37	5	and	and	CCONJ
ejpam-2996	37	6	the	the	DET
ejpam-2996	37	7	references	reference	NOUN
ejpam-2996	37	8	cited	cite	VERB
ejpam-2996	37	9	therein	therein	ADV
ejpam-2996	37	10	.	.	PUNCT
ejpam-2996	38	1	now	now	ADV
ejpam-2996	38	2	,	,	PUNCT
ejpam-2996	38	3	let	let	VERB
ejpam-2996	38	4	us	we	PRON
ejpam-2996	38	5	recall	recall	VERB
ejpam-2996	38	6	some	some	DET
ejpam-2996	38	7	definitions	definition	NOUN
ejpam-2996	38	8	of	of	ADP
ejpam-2996	38	9	various	various	ADJ
ejpam-2996	38	10	convex	convex	NOUN
ejpam-2996	38	11	functions	function	NOUN
ejpam-2996	38	12	.	.	PUNCT
ejpam-2996	39	1	definition	definition	NOUN
ejpam-2996	39	2	2	2	NUM
ejpam-2996	39	3	.	.	PUNCT
ejpam-2996	40	1	(	(	PUNCT
ejpam-2996	40	2	see	see	VERB
ejpam-2996	40	3	[	[	X
ejpam-2996	40	4	4	4	NUM
ejpam-2996	40	5	]	]	PUNCT
ejpam-2996	40	6	)	)	PUNCT
ejpam-2996	40	7	a	a	DET
ejpam-2996	40	8	nonnegative	nonnegative	ADJ
ejpam-2996	40	9	function	function	NOUN
ejpam-2996	40	10	f	f	NOUN
ejpam-2996	40	11	:	:	PUNCT
ejpam-2996	40	12	i	i	PRON
ejpam-2996	40	13	⊆	⊆	NUM
ejpam-2996	40	14	r	r	NOUN
ejpam-2996	40	15	−→	−→	NOUN
ejpam-2996	40	16	r	r	NOUN
ejpam-2996	40	17	◦	◦	NOUN
ejpam-2996	40	18	is	be	AUX
ejpam-2996	40	19	said	say	VERB
ejpam-2996	40	20	to	to	PART
ejpam-2996	40	21	be	be	AUX
ejpam-2996	40	22	p	p	NOUN
ejpam-2996	40	23	-function	-function	NOUN
ejpam-2996	40	24	or	or	CCONJ
ejpam-2996	40	25	p	p	NOUN
ejpam-2996	40	26	-convex	-convex	NOUN
ejpam-2996	40	27	,	,	PUNCT
ejpam-2996	40	28	if	if	SCONJ
ejpam-2996	40	29	f(tx+	f(tx+	ADJ
ejpam-2996	40	30	(	(	PUNCT
ejpam-2996	40	31	1−	1−	NUM
ejpam-2996	40	32	t)y	t)y	ADJ
ejpam-2996	40	33	)	)	PUNCT
ejpam-2996	40	34	≤	≤	NUM
ejpam-2996	40	35	f(x	f(x	PROPN
ejpam-2996	40	36	)	)	PUNCT
ejpam-2996	41	1	+	+	SYM
ejpam-2996	41	2	f(y	f(y	NOUN
ejpam-2996	41	3	)	)	PUNCT
ejpam-2996	41	4	,	,	PUNCT
ejpam-2996	41	5	∀x	∀x	X
ejpam-2996	41	6	,	,	PUNCT
ejpam-2996	41	7	y	y	PROPN
ejpam-2996	41	8	∈	∈	PROPN
ejpam-2996	42	1	i	i	PROPN
ejpam-2996	42	2	,	,	PUNCT
ejpam-2996	42	3	t	t	PROPN
ejpam-2996	42	4	∈	∈	PROPN
ejpam-2996	43	1	[	[	X
ejpam-2996	43	2	0	0	NUM
ejpam-2996	43	3	,	,	PUNCT
ejpam-2996	43	4	1	1	NUM
ejpam-2996	43	5	]	]	PUNCT
ejpam-2996	43	6	.	.	PUNCT
ejpam-2996	44	1	definition	definition	NOUN
ejpam-2996	44	2	3	3	NUM
ejpam-2996	44	3	.	.	PUNCT
ejpam-2996	45	1	(	(	PUNCT
ejpam-2996	45	2	see	see	VERB
ejpam-2996	45	3	[	[	X
ejpam-2996	45	4	5	5	NUM
ejpam-2996	45	5	]	]	PUNCT
ejpam-2996	45	6	)	)	PUNCT
ejpam-2996	45	7	a	a	DET
ejpam-2996	45	8	function	function	NOUN
ejpam-2996	45	9	f	f	NOUN
ejpam-2996	45	10	:	:	PUNCT
ejpam-2996	45	11	r	r	AUX
ejpam-2996	45	12	◦	◦	NOUN
ejpam-2996	45	13	−→	−→	ADJ
ejpam-2996	45	14	r	r	NOUN
ejpam-2996	45	15	is	be	AUX
ejpam-2996	45	16	said	say	VERB
ejpam-2996	45	17	to	to	PART
ejpam-2996	45	18	be	be	AUX
ejpam-2996	45	19	s	s	NOUN
ejpam-2996	45	20	-	-	NOUN
ejpam-2996	45	21	convex	convex	ADJ
ejpam-2996	45	22	in	in	ADP
ejpam-2996	45	23	the	the	DET
ejpam-2996	45	24	second	second	ADJ
ejpam-2996	45	25	sense	sense	NOUN
ejpam-2996	45	26	,	,	PUNCT
ejpam-2996	46	1	if	if	SCONJ
ejpam-2996	46	2	f(λx+	f(λx+	PROPN
ejpam-2996	46	3	(	(	PUNCT
ejpam-2996	46	4	1−	1−	NUM
ejpam-2996	46	5	λ)y	λ)y	NOUN
ejpam-2996	46	6	)	)	PUNCT
ejpam-2996	46	7	≤	≤	NUM
ejpam-2996	46	8	λsf(x	λsf(x	PROPN
ejpam-2996	46	9	)	)	PUNCT
ejpam-2996	47	1	+	+	CCONJ
ejpam-2996	47	2	(	(	PUNCT
ejpam-2996	47	3	1−	1−	NUM
ejpam-2996	47	4	λ)sf(y	λ)sf(y	NUM
ejpam-2996	47	5	)	)	PUNCT
ejpam-2996	47	6	(	(	PUNCT
ejpam-2996	47	7	2	2	X
ejpam-2996	47	8	)	)	PUNCT
ejpam-2996	47	9	for	for	ADP
ejpam-2996	47	10	all	all	DET
ejpam-2996	47	11	x	x	NOUN
ejpam-2996	47	12	,	,	PUNCT
ejpam-2996	47	13	y	y	PROPN
ejpam-2996	47	14	∈	∈	PROPN
ejpam-2996	47	15	r	r	NOUN
ejpam-2996	47	16	◦	◦	NOUN
ejpam-2996	47	17	,	,	PUNCT
ejpam-2996	47	18	λ	λ	X
ejpam-2996	47	19	∈	∈	PROPN
ejpam-2996	48	1	[	[	X
ejpam-2996	48	2	0	0	NUM
ejpam-2996	48	3	,	,	PUNCT
ejpam-2996	48	4	1	1	NUM
ejpam-2996	48	5	]	]	PUNCT
ejpam-2996	48	6	and	and	CCONJ
ejpam-2996	48	7	s	s	PROPN
ejpam-2996	48	8	∈	∈	PROPN
ejpam-2996	48	9	(	(	PUNCT
ejpam-2996	48	10	0	0	NUM
ejpam-2996	48	11	,	,	PUNCT
ejpam-2996	48	12	1	1	NUM
ejpam-2996	48	13	]	]	PUNCT
ejpam-2996	48	14	.	.	PUNCT
ejpam-2996	49	1	it	it	PRON
ejpam-2996	49	2	is	be	AUX
ejpam-2996	49	3	clear	clear	ADJ
ejpam-2996	49	4	that	that	SCONJ
ejpam-2996	49	5	a	a	DET
ejpam-2996	49	6	1	1	NUM
ejpam-2996	49	7	-	-	PUNCT
ejpam-2996	49	8	convex	convex	NOUN
ejpam-2996	49	9	function	function	NOUN
ejpam-2996	49	10	must	must	AUX
ejpam-2996	49	11	be	be	AUX
ejpam-2996	49	12	convex	convex	ADJ
ejpam-2996	49	13	on	on	ADP
ejpam-2996	49	14	r	r	NOUN
ejpam-2996	49	15	◦	◦	NOUN
ejpam-2996	49	16	as	as	ADP
ejpam-2996	49	17	usual	usual	ADJ
ejpam-2996	49	18	.	.	PUNCT
ejpam-2996	50	1	the	the	DET
ejpam-2996	50	2	s	s	ADJ
ejpam-2996	50	3	-	-	PUNCT
ejpam-2996	50	4	convex	convex	ADJ
ejpam-2996	50	5	functions	function	NOUN
ejpam-2996	50	6	in	in	ADP
ejpam-2996	50	7	the	the	DET
ejpam-2996	50	8	second	second	ADJ
ejpam-2996	50	9	sense	sense	NOUN
ejpam-2996	50	10	have	have	AUX
ejpam-2996	50	11	been	be	AUX
ejpam-2996	50	12	investigated	investigate	VERB
ejpam-2996	50	13	in	in	ADP
ejpam-2996	50	14	(	(	PUNCT
ejpam-2996	50	15	see	see	VERB
ejpam-2996	50	16	[	[	X
ejpam-2996	50	17	5	5	NUM
ejpam-2996	50	18	]	]	NUM
ejpam-2996	50	19	)	)	PUNCT
ejpam-2996	50	20	.	.	PUNCT
ejpam-2996	51	1	definition	definition	NOUN
ejpam-2996	51	2	4	4	NUM
ejpam-2996	51	3	.	.	PUNCT
ejpam-2996	52	1	(	(	PUNCT
ejpam-2996	52	2	see	see	VERB
ejpam-2996	52	3	[	[	X
ejpam-2996	52	4	6	6	NUM
ejpam-2996	52	5	]	]	PUNCT
ejpam-2996	52	6	)	)	PUNCT
ejpam-2996	52	7	a	a	DET
ejpam-2996	52	8	set	set	NOUN
ejpam-2996	52	9	k	k	PROPN
ejpam-2996	52	10	⊆	⊆	NUM
ejpam-2996	52	11	rn	rn	PROPN
ejpam-2996	52	12	is	be	AUX
ejpam-2996	52	13	said	say	VERB
ejpam-2996	52	14	to	to	PART
ejpam-2996	52	15	be	be	AUX
ejpam-2996	52	16	invex	invex	NOUN
ejpam-2996	52	17	with	with	ADP
ejpam-2996	52	18	respect	respect	NOUN
ejpam-2996	52	19	to	to	ADP
ejpam-2996	52	20	the	the	DET
ejpam-2996	52	21	mapping	mapping	NOUN
ejpam-2996	52	22	η	η	NOUN
ejpam-2996	52	23	:	:	PUNCT
ejpam-2996	53	1	k	k	PROPN
ejpam-2996	53	2	×k	×k	PROPN
ejpam-2996	53	3	−→	−→	PROPN
ejpam-2996	53	4	rn	rn	PROPN
ejpam-2996	53	5	,	,	PUNCT
ejpam-2996	53	6	if	if	SCONJ
ejpam-2996	53	7	x+	x+	ADJ
ejpam-2996	53	8	tη(y	tη(y	NOUN
ejpam-2996	53	9	,	,	PUNCT
ejpam-2996	53	10	x	x	X
ejpam-2996	53	11	)	)	PUNCT
ejpam-2996	53	12	∈	∈	PROPN
ejpam-2996	53	13	k	k	PROPN
ejpam-2996	53	14	for	for	ADP
ejpam-2996	53	15	every	every	DET
ejpam-2996	53	16	x	x	NOUN
ejpam-2996	53	17	,	,	PUNCT
ejpam-2996	53	18	y	y	PROPN
ejpam-2996	53	19	∈	∈	PROPN
ejpam-2996	53	20	k	k	PROPN
ejpam-2996	53	21	and	and	CCONJ
ejpam-2996	53	22	t	t	PROPN
ejpam-2996	53	23	∈	∈	PROPN
ejpam-2996	54	1	[	[	X
ejpam-2996	54	2	0	0	NUM
ejpam-2996	54	3	,	,	PUNCT
ejpam-2996	54	4	1	1	NUM
ejpam-2996	54	5	]	]	PUNCT
ejpam-2996	54	6	.	.	PUNCT
ejpam-2996	55	1	notice	notice	VERB
ejpam-2996	55	2	that	that	SCONJ
ejpam-2996	55	3	every	every	DET
ejpam-2996	55	4	convex	convex	NOUN
ejpam-2996	55	5	set	set	VERB
ejpam-2996	55	6	is	be	AUX
ejpam-2996	55	7	invex	invex	NOUN
ejpam-2996	55	8	with	with	ADP
ejpam-2996	55	9	respect	respect	NOUN
ejpam-2996	55	10	to	to	ADP
ejpam-2996	55	11	the	the	DET
ejpam-2996	55	12	mapping	mapping	NOUN
ejpam-2996	55	13	η(y	η(y	NOUN
ejpam-2996	55	14	,	,	PUNCT
ejpam-2996	55	15	x	x	X
ejpam-2996	55	16	)	)	PUNCT
ejpam-2996	56	1	=	=	SYM
ejpam-2996	56	2	y	y	PROPN
ejpam-2996	56	3	−	−	NOUN
ejpam-2996	56	4	x	x	NOUN
ejpam-2996	56	5	,	,	PUNCT
ejpam-2996	56	6	but	but	CCONJ
ejpam-2996	56	7	the	the	DET
ejpam-2996	56	8	converse	converse	NOUN
ejpam-2996	56	9	is	be	AUX
ejpam-2996	56	10	not	not	PART
ejpam-2996	56	11	necessarily	necessarily	ADV
ejpam-2996	56	12	true	true	ADJ
ejpam-2996	56	13	.	.	PUNCT
ejpam-2996	57	1	for	for	SCONJ
ejpam-2996	57	2	more	more	ADJ
ejpam-2996	57	3	details	detail	NOUN
ejpam-2996	57	4	please	please	INTJ
ejpam-2996	57	5	see	see	VERB
ejpam-2996	57	6	(	(	PUNCT
ejpam-2996	57	7	see	see	VERB
ejpam-2996	57	8	[	[	X
ejpam-2996	57	9	6	6	NUM
ejpam-2996	57	10	]	]	PUNCT
ejpam-2996	57	11	,	,	PUNCT
ejpam-2996	57	12	[	[	X
ejpam-2996	57	13	7	7	NUM
ejpam-2996	57	14	]	]	PUNCT
ejpam-2996	57	15	)	)	PUNCT
ejpam-2996	57	16	and	and	CCONJ
ejpam-2996	57	17	the	the	DET
ejpam-2996	57	18	references	reference	NOUN
ejpam-2996	57	19	therein	therein	ADV
ejpam-2996	57	20	.	.	PUNCT
ejpam-2996	58	1	definition	definition	NOUN
ejpam-2996	58	2	5	5	NUM
ejpam-2996	58	3	.	.	PUNCT
ejpam-2996	59	1	(	(	PUNCT
ejpam-2996	59	2	see	see	VERB
ejpam-2996	59	3	[	[	X
ejpam-2996	59	4	8	8	NUM
ejpam-2996	59	5	]	]	PUNCT
ejpam-2996	59	6	)	)	PUNCT
ejpam-2996	59	7	the	the	DET
ejpam-2996	59	8	function	function	NOUN
ejpam-2996	59	9	f	f	PROPN
ejpam-2996	59	10	defined	define	VERB
ejpam-2996	59	11	on	on	ADP
ejpam-2996	59	12	the	the	DET
ejpam-2996	59	13	invex	invex	NOUN
ejpam-2996	59	14	set	set	VERB
ejpam-2996	59	15	k	k	PROPN
ejpam-2996	59	16	⊆	⊆	NUM
ejpam-2996	59	17	rn	rn	PROPN
ejpam-2996	59	18	is	be	AUX
ejpam-2996	59	19	said	say	VERB
ejpam-2996	59	20	to	to	PART
ejpam-2996	59	21	be	be	AUX
ejpam-2996	59	22	preinvex	preinvex	ADJ
ejpam-2996	59	23	with	with	ADP
ejpam-2996	59	24	respect	respect	NOUN
ejpam-2996	59	25	η	η	PROPN
ejpam-2996	59	26	,	,	PUNCT
ejpam-2996	59	27	if	if	SCONJ
ejpam-2996	59	28	for	for	ADP
ejpam-2996	59	29	every	every	DET
ejpam-2996	59	30	x	x	NOUN
ejpam-2996	59	31	,	,	PUNCT
ejpam-2996	59	32	y	y	PROPN
ejpam-2996	59	33	∈	∈	PROPN
ejpam-2996	59	34	k	k	PROPN
ejpam-2996	59	35	and	and	CCONJ
ejpam-2996	59	36	t	t	PROPN
ejpam-2996	59	37	∈	∈	PROPN
ejpam-2996	60	1	[	[	X
ejpam-2996	60	2	0	0	NUM
ejpam-2996	60	3	,	,	PUNCT
ejpam-2996	60	4	1	1	NUM
ejpam-2996	60	5	]	]	PUNCT
ejpam-2996	60	6	,	,	PUNCT
ejpam-2996	60	7	we	we	PRON
ejpam-2996	60	8	have	have	VERB
ejpam-2996	60	9	that	that	DET
ejpam-2996	60	10	f	f	PROPN
ejpam-2996	60	11	(	(	PUNCT
ejpam-2996	60	12	x+	x+	X
ejpam-2996	60	13	tη(y	tη(y	NOUN
ejpam-2996	60	14	,	,	PUNCT
ejpam-2996	60	15	x	x	NOUN
ejpam-2996	60	16	)	)	PUNCT
ejpam-2996	60	17	)	)	PUNCT
ejpam-2996	60	18	≤	≤	NOUN
ejpam-2996	60	19	(	(	PUNCT
ejpam-2996	60	20	1−	1−	NUM
ejpam-2996	60	21	t)f(x	t)f(x	NOUN
ejpam-2996	60	22	)	)	PUNCT
ejpam-2996	61	1	+	+	NUM
ejpam-2996	61	2	tf(y	tf(y	NUM
ejpam-2996	61	3	)	)	PUNCT
ejpam-2996	61	4	.	.	PUNCT
ejpam-2996	62	1	a.	a.	PROPN
ejpam-2996	62	2	kashuri	kashuri	PROPN
ejpam-2996	62	3	,	,	PUNCT
ejpam-2996	62	4	r.	r.	PROPN
ejpam-2996	62	5	liko	liko	PROPN
ejpam-2996	62	6	/	/	SYM
ejpam-2996	62	7	eur	eur	PROPN
ejpam-2996	62	8	.	.	PUNCT
ejpam-2996	63	1	j.	j.	PROPN
ejpam-2996	63	2	pure	pure	PROPN
ejpam-2996	63	3	appl	appl	PROPN
ejpam-2996	63	4	.	.	PROPN
ejpam-2996	63	5	math	math	PROPN
ejpam-2996	63	6	,	,	PUNCT
ejpam-2996	63	7	10	10	NUM
ejpam-2996	63	8	(	(	PUNCT
ejpam-2996	63	9	3	3	NUM
ejpam-2996	63	10	)	)	PUNCT
ejpam-2996	63	11	(	(	PUNCT
ejpam-2996	63	12	2017	2017	NUM
ejpam-2996	63	13	)	)	PUNCT
ejpam-2996	63	14	,	,	PUNCT
ejpam-2996	63	15	495	495	NUM
ejpam-2996	63	16	-	-	SYM
ejpam-2996	63	17	505	505	NUM
ejpam-2996	63	18	497	497	NUM
ejpam-2996	63	19	the	the	DET
ejpam-2996	63	20	concept	concept	NOUN
ejpam-2996	63	21	of	of	ADP
ejpam-2996	63	22	preinvexity	preinvexity	NOUN
ejpam-2996	63	23	is	be	AUX
ejpam-2996	63	24	more	more	ADV
ejpam-2996	63	25	general	general	ADJ
ejpam-2996	63	26	than	than	ADP
ejpam-2996	63	27	convexity	convexity	NOUN
ejpam-2996	63	28	since	since	SCONJ
ejpam-2996	63	29	every	every	DET
ejpam-2996	63	30	convex	convex	NOUN
ejpam-2996	63	31	function	function	NOUN
ejpam-2996	63	32	is	be	AUX
ejpam-2996	63	33	preinvex	preinvex	ADJ
ejpam-2996	63	34	with	with	ADP
ejpam-2996	63	35	respect	respect	NOUN
ejpam-2996	63	36	to	to	ADP
ejpam-2996	63	37	the	the	DET
ejpam-2996	63	38	mapping	mapping	NOUN
ejpam-2996	63	39	η(y	η(y	NOUN
ejpam-2996	63	40	,	,	PUNCT
ejpam-2996	63	41	x	x	X
ejpam-2996	63	42	)	)	PUNCT
ejpam-2996	63	43	=	=	SYM
ejpam-2996	64	1	y	y	PROPN
ejpam-2996	64	2	−	−	NOUN
ejpam-2996	64	3	x	x	NOUN
ejpam-2996	64	4	,	,	PUNCT
ejpam-2996	64	5	but	but	CCONJ
ejpam-2996	64	6	the	the	DET
ejpam-2996	64	7	converse	converse	NOUN
ejpam-2996	64	8	is	be	AUX
ejpam-2996	64	9	not	not	PART
ejpam-2996	64	10	true	true	ADJ
ejpam-2996	64	11	.	.	PUNCT
ejpam-2996	65	1	the	the	DET
ejpam-2996	65	2	gauss	gauss	PROPN
ejpam-2996	65	3	-	-	PUNCT
ejpam-2996	65	4	jacobi	jacobi	PROPN
ejpam-2996	65	5	type	type	NOUN
ejpam-2996	65	6	quadrature	quadrature	NOUN
ejpam-2996	65	7	formula	formula	NOUN
ejpam-2996	65	8	has	have	VERB
ejpam-2996	65	9	the	the	DET
ejpam-2996	65	10	following∫	following∫	PROPN
ejpam-2996	65	11	b	b	PROPN
ejpam-2996	65	12	a	a	PRON
ejpam-2996	65	13	(	(	PUNCT
ejpam-2996	65	14	x−	x−	PROPN
ejpam-2996	65	15	a)p(b−	a)p(b−	PROPN
ejpam-2996	65	16	x)qf(x)dx	x)qf(x)dx	X
ejpam-2996	66	1	=	=	PUNCT
ejpam-2996	67	1	+	+	ADJ
ejpam-2996	67	2	∞∑	∞∑	PRON
ejpam-2996	67	3	k=0	k=0	PROPN
ejpam-2996	67	4	bm	bm	PROPN
ejpam-2996	67	5	,	,	PUNCT
ejpam-2996	67	6	kf(γk	kf(γk	PROPN
ejpam-2996	67	7	)	)	PUNCT
ejpam-2996	68	1	+	+	NUM
ejpam-2996	68	2	r?m|f	r?m|f	PROPN
ejpam-2996	68	3	|	|	NOUN
ejpam-2996	68	4	,	,	PUNCT
ejpam-2996	68	5	(	(	PUNCT
ejpam-2996	68	6	3	3	X
ejpam-2996	68	7	)	)	PUNCT
ejpam-2996	68	8	for	for	ADP
ejpam-2996	68	9	certain	certain	ADJ
ejpam-2996	68	10	bm	bm	PROPN
ejpam-2996	68	11	,	,	PUNCT
ejpam-2996	68	12	k	k	PROPN
ejpam-2996	68	13	,	,	PUNCT
ejpam-2996	68	14	γk	γk	NOUN
ejpam-2996	68	15	and	and	CCONJ
ejpam-2996	68	16	rest	rest	VERB
ejpam-2996	68	17	r?m|f	r?m|f	PROPN
ejpam-2996	68	18	|	|	ADV
ejpam-2996	68	19	(	(	PUNCT
ejpam-2996	68	20	see	see	VERB
ejpam-2996	68	21	[	[	X
ejpam-2996	68	22	9	9	NUM
ejpam-2996	68	23	]	]	NUM
ejpam-2996	68	24	)	)	PUNCT
ejpam-2996	68	25	.	.	PUNCT
ejpam-2996	69	1	recently	recently	ADV
ejpam-2996	69	2	,	,	PUNCT
ejpam-2996	69	3	liu	liu	PROPN
ejpam-2996	69	4	(	(	PUNCT
ejpam-2996	69	5	see	see	VERB
ejpam-2996	69	6	[	[	X
ejpam-2996	69	7	10	10	NUM
ejpam-2996	69	8	]	]	PUNCT
ejpam-2996	69	9	)	)	PUNCT
ejpam-2996	69	10	obtained	obtain	VERB
ejpam-2996	69	11	several	several	ADJ
ejpam-2996	69	12	integral	integral	ADJ
ejpam-2996	69	13	inequalities	inequality	NOUN
ejpam-2996	69	14	for	for	ADP
ejpam-2996	69	15	the	the	DET
ejpam-2996	69	16	left	left	ADJ
ejpam-2996	69	17	hand	hand	NOUN
ejpam-2996	69	18	side	side	NOUN
ejpam-2996	69	19	of	of	ADP
ejpam-2996	69	20	(	(	PUNCT
ejpam-2996	69	21	3	3	NUM
ejpam-2996	69	22	)	)	PUNCT
ejpam-2996	69	23	under	under	ADP
ejpam-2996	69	24	the	the	DET
ejpam-2996	69	25	definition	definition	NOUN
ejpam-2996	69	26	2	2	NUM
ejpam-2996	69	27	of	of	ADP
ejpam-2996	69	28	p	p	NOUN
ejpam-2996	69	29	-function	-function	NOUN
ejpam-2996	69	30	.	.	PUNCT
ejpam-2996	70	1	also	also	ADV
ejpam-2996	70	2	in	in	AUX
ejpam-2996	70	3	(	(	PUNCT
ejpam-2996	70	4	see	see	VERB
ejpam-2996	70	5	[	[	X
ejpam-2996	70	6	11	11	NUM
ejpam-2996	70	7	]	]	NUM
ejpam-2996	70	8	)	)	PUNCT
ejpam-2996	70	9	,	,	PUNCT
ejpam-2996	70	10	özdemir	özdemir	PROPN
ejpam-2996	70	11	et	et	PROPN
ejpam-2996	70	12	al	al	PROPN
ejpam-2996	70	13	.	.	PROPN
ejpam-2996	70	14	established	establish	VERB
ejpam-2996	70	15	several	several	ADJ
ejpam-2996	70	16	integral	integral	ADJ
ejpam-2996	70	17	inequalities	inequality	NOUN
ejpam-2996	70	18	concerning	concern	VERB
ejpam-2996	70	19	the	the	DET
ejpam-2996	70	20	left	left	ADJ
ejpam-2996	70	21	-	-	PUNCT
ejpam-2996	70	22	hand	hand	NOUN
ejpam-2996	70	23	side	side	NOUN
ejpam-2996	70	24	of	of	ADP
ejpam-2996	70	25	(	(	PUNCT
ejpam-2996	70	26	3	3	NUM
ejpam-2996	70	27	)	)	PUNCT
ejpam-2996	70	28	via	via	ADP
ejpam-2996	70	29	some	some	DET
ejpam-2996	70	30	kinds	kind	NOUN
ejpam-2996	70	31	of	of	ADP
ejpam-2996	70	32	convexity	convexity	NOUN
ejpam-2996	70	33	.	.	PUNCT
ejpam-2996	71	1	motivated	motivate	VERB
ejpam-2996	71	2	by	by	ADP
ejpam-2996	71	3	these	these	DET
ejpam-2996	71	4	results	result	NOUN
ejpam-2996	71	5	,	,	PUNCT
ejpam-2996	71	6	in	in	ADP
ejpam-2996	71	7	section	section	NOUN
ejpam-2996	71	8	2	2	NUM
ejpam-2996	71	9	,	,	PUNCT
ejpam-2996	71	10	the	the	DET
ejpam-2996	71	11	notion	notion	NOUN
ejpam-2996	71	12	of	of	ADP
ejpam-2996	71	13	generalized	generalized	ADJ
ejpam-2996	71	14	(	(	PUNCT
ejpam-2996	71	15	r	r	NOUN
ejpam-2996	71	16	;	;	PUNCT
ejpam-2996	71	17	s	s	X
ejpam-2996	71	18	,	,	PUNCT
ejpam-2996	71	19	m	m	PRON
ejpam-2996	71	20	,	,	PUNCT
ejpam-2996	71	21	ϕ)-preinvex	ϕ)-preinvex	VERB
ejpam-2996	71	22	function	function	NOUN
ejpam-2996	71	23	is	be	AUX
ejpam-2996	71	24	introduced	introduce	VERB
ejpam-2996	71	25	and	and	CCONJ
ejpam-2996	71	26	some	some	DET
ejpam-2996	71	27	new	new	ADJ
ejpam-2996	71	28	integral	integral	ADJ
ejpam-2996	71	29	inequalities	inequality	NOUN
ejpam-2996	71	30	for	for	ADP
ejpam-2996	71	31	the	the	DET
ejpam-2996	71	32	left	left	ADJ
ejpam-2996	71	33	hand	hand	NOUN
ejpam-2996	71	34	side	side	NOUN
ejpam-2996	71	35	of	of	ADP
ejpam-2996	71	36	(	(	PUNCT
ejpam-2996	71	37	3	3	NUM
ejpam-2996	71	38	)	)	PUNCT
ejpam-2996	71	39	involving	involve	VERB
ejpam-2996	71	40	generalized	generalize	VERB
ejpam-2996	71	41	(	(	PUNCT
ejpam-2996	71	42	r	r	NOUN
ejpam-2996	71	43	;	;	PUNCT
ejpam-2996	71	44	s	s	X
ejpam-2996	71	45	,	,	PUNCT
ejpam-2996	71	46	m	m	PRON
ejpam-2996	71	47	,	,	PUNCT
ejpam-2996	71	48	ϕ)-preinvex	ϕ)-preinvex	NOUN
ejpam-2996	71	49	functions	function	NOUN
ejpam-2996	71	50	are	be	AUX
ejpam-2996	71	51	given	give	VERB
ejpam-2996	71	52	.	.	PUNCT
ejpam-2996	72	1	in	in	ADP
ejpam-2996	72	2	section	section	NOUN
ejpam-2996	72	3	3	3	NUM
ejpam-2996	72	4	,	,	PUNCT
ejpam-2996	72	5	some	some	DET
ejpam-2996	72	6	generalizations	generalization	NOUN
ejpam-2996	72	7	of	of	ADP
ejpam-2996	72	8	hermite	hermite	ADJ
ejpam-2996	72	9	-	-	PUNCT
ejpam-2996	72	10	hadamard	hadamard	ADJ
ejpam-2996	72	11	type	type	NOUN
ejpam-2996	72	12	inequalities	inequality	NOUN
ejpam-2996	72	13	for	for	ADP
ejpam-2996	72	14	generalized	generalized	ADJ
ejpam-2996	72	15	(	(	PUNCT
ejpam-2996	72	16	r	r	NOUN
ejpam-2996	72	17	;	;	PUNCT
ejpam-2996	72	18	s	s	X
ejpam-2996	72	19	,	,	PUNCT
ejpam-2996	72	20	m	m	PRON
ejpam-2996	72	21	,	,	PUNCT
ejpam-2996	72	22	ϕ)-preinvex	ϕ)-preinvex	NOUN
ejpam-2996	72	23	functions	function	NOUN
ejpam-2996	72	24	via	via	ADP
ejpam-2996	72	25	fractional	fractional	ADJ
ejpam-2996	72	26	integrals	integral	NOUN
ejpam-2996	72	27	are	be	AUX
ejpam-2996	72	28	given	give	VERB
ejpam-2996	72	29	.	.	PUNCT
ejpam-2996	73	1	these	these	DET
ejpam-2996	73	2	general	general	ADJ
ejpam-2996	73	3	inequalities	inequality	NOUN
ejpam-2996	73	4	give	give	VERB
ejpam-2996	73	5	us	we	PRON
ejpam-2996	73	6	some	some	DET
ejpam-2996	73	7	new	new	ADJ
ejpam-2996	73	8	estimates	estimate	NOUN
ejpam-2996	73	9	for	for	ADP
ejpam-2996	73	10	the	the	DET
ejpam-2996	73	11	left	left	ADJ
ejpam-2996	73	12	hand	hand	NOUN
ejpam-2996	73	13	side	side	NOUN
ejpam-2996	73	14	of	of	ADP
ejpam-2996	73	15	gauss	gauss	ADJ
ejpam-2996	73	16	-	-	PUNCT
ejpam-2996	73	17	jacobi	jacobi	PROPN
ejpam-2996	73	18	type	type	NOUN
ejpam-2996	73	19	quadrature	quadrature	NOUN
ejpam-2996	73	20	formula	formula	NOUN
ejpam-2996	73	21	and	and	CCONJ
ejpam-2996	73	22	hermite	hermite	ADJ
ejpam-2996	73	23	-	-	PUNCT
ejpam-2996	73	24	hadamard	hadamard	ADJ
ejpam-2996	73	25	type	type	NOUN
ejpam-2996	73	26	fractional	fractional	ADJ
ejpam-2996	73	27	integral	integral	ADJ
ejpam-2996	73	28	inequalities	inequality	NOUN
ejpam-2996	73	29	.	.	PUNCT
ejpam-2996	74	1	2	2	X
ejpam-2996	74	2	.	.	X
ejpam-2996	74	3	new	new	ADJ
ejpam-2996	74	4	integral	integral	ADJ
ejpam-2996	74	5	inequalities	inequality	NOUN
ejpam-2996	74	6	for	for	ADP
ejpam-2996	74	7	generalized	generalized	ADJ
ejpam-2996	74	8	(	(	PUNCT
ejpam-2996	74	9	r	r	NOUN
ejpam-2996	74	10	;	;	PUNCT
ejpam-2996	74	11	s	s	X
ejpam-2996	74	12	,	,	PUNCT
ejpam-2996	74	13	m	m	PRON
ejpam-2996	74	14	,	,	PUNCT
ejpam-2996	74	15	ϕ)-preinvex	ϕ)-preinvex	NOUN
ejpam-2996	74	16	functions	function	NOUN
ejpam-2996	74	17	definition	definition	NOUN
ejpam-2996	74	18	6	6	NUM
ejpam-2996	74	19	.	.	PUNCT
ejpam-2996	75	1	(	(	PUNCT
ejpam-2996	75	2	see	see	VERB
ejpam-2996	75	3	[	[	X
ejpam-2996	75	4	3	3	NUM
ejpam-2996	75	5	]	]	PUNCT
ejpam-2996	75	6	)	)	PUNCT
ejpam-2996	75	7	a	a	DET
ejpam-2996	75	8	set	set	NOUN
ejpam-2996	75	9	k	k	PROPN
ejpam-2996	75	10	⊆	⊆	NUM
ejpam-2996	75	11	rn	rn	PROPN
ejpam-2996	75	12	is	be	AUX
ejpam-2996	75	13	said	say	VERB
ejpam-2996	75	14	to	to	PART
ejpam-2996	75	15	be	be	AUX
ejpam-2996	75	16	m	m	NOUN
ejpam-2996	75	17	-	-	NOUN
ejpam-2996	75	18	invex	invex	ADJ
ejpam-2996	75	19	with	with	ADP
ejpam-2996	75	20	respect	respect	NOUN
ejpam-2996	75	21	to	to	ADP
ejpam-2996	75	22	the	the	DET
ejpam-2996	75	23	mapping	mapping	NOUN
ejpam-2996	75	24	η	η	NOUN
ejpam-2996	75	25	:	:	PUNCT
ejpam-2996	76	1	k	k	PROPN
ejpam-2996	76	2	×k	×k	PROPN
ejpam-2996	76	3	×	×	NOUN
ejpam-2996	76	4	(	(	PUNCT
ejpam-2996	76	5	0	0	NUM
ejpam-2996	76	6	,	,	PUNCT
ejpam-2996	76	7	1	1	NUM
ejpam-2996	76	8	]	]	X
ejpam-2996	76	9	−→	−→	PROPN
ejpam-2996	76	10	rn	rn	NOUN
ejpam-2996	76	11	for	for	ADP
ejpam-2996	76	12	some	some	DET
ejpam-2996	76	13	fixed	fix	VERB
ejpam-2996	76	14	m	m	VERB
ejpam-2996	76	15	∈	∈	NOUN
ejpam-2996	76	16	(	(	PUNCT
ejpam-2996	76	17	0	0	NUM
ejpam-2996	76	18	,	,	PUNCT
ejpam-2996	76	19	1	1	NUM
ejpam-2996	76	20	]	]	PUNCT
ejpam-2996	76	21	,	,	PUNCT
ejpam-2996	76	22	if	if	SCONJ
ejpam-2996	76	23	mx+	mx+	NOUN
ejpam-2996	76	24	tη(y	tη(y	NOUN
ejpam-2996	76	25	,	,	PUNCT
ejpam-2996	76	26	x	x	X
ejpam-2996	76	27	,	,	PUNCT
ejpam-2996	76	28	m	m	NOUN
ejpam-2996	76	29	)	)	PUNCT
ejpam-2996	76	30	∈	∈	PROPN
ejpam-2996	76	31	k	k	PROPN
ejpam-2996	76	32	holds	hold	VERB
ejpam-2996	76	33	for	for	ADP
ejpam-2996	76	34	each	each	DET
ejpam-2996	76	35	x	x	NOUN
ejpam-2996	76	36	,	,	PUNCT
ejpam-2996	76	37	y	y	PROPN
ejpam-2996	76	38	∈	∈	PROPN
ejpam-2996	76	39	k	k	PROPN
ejpam-2996	76	40	and	and	CCONJ
ejpam-2996	76	41	any	any	DET
ejpam-2996	76	42	t	t	NOUN
ejpam-2996	76	43	∈	∈	PROPN
ejpam-2996	77	1	[	[	X
ejpam-2996	77	2	0	0	NUM
ejpam-2996	77	3	,	,	PUNCT
ejpam-2996	77	4	1	1	NUM
ejpam-2996	77	5	]	]	PUNCT
ejpam-2996	77	6	.	.	PUNCT
ejpam-2996	78	1	remark	remark	PROPN
ejpam-2996	78	2	1	1	NUM
ejpam-2996	78	3	.	.	PUNCT
ejpam-2996	79	1	in	in	ADP
ejpam-2996	79	2	definition	definition	NOUN
ejpam-2996	79	3	6	6	NUM
ejpam-2996	79	4	,	,	PUNCT
ejpam-2996	79	5	under	under	ADP
ejpam-2996	79	6	certain	certain	ADJ
ejpam-2996	79	7	conditions	condition	NOUN
ejpam-2996	79	8	,	,	PUNCT
ejpam-2996	79	9	the	the	DET
ejpam-2996	79	10	mapping	mapping	NOUN
ejpam-2996	79	11	η(y	η(y	NOUN
ejpam-2996	79	12	,	,	PUNCT
ejpam-2996	79	13	x	x	X
ejpam-2996	79	14	,	,	PUNCT
ejpam-2996	79	15	m	m	VERB
ejpam-2996	79	16	)	)	PUNCT
ejpam-2996	79	17	could	could	AUX
ejpam-2996	79	18	reduce	reduce	VERB
ejpam-2996	79	19	to	to	ADP
ejpam-2996	79	20	η(y	η(y	NOUN
ejpam-2996	79	21	,	,	PUNCT
ejpam-2996	79	22	x	x	NOUN
ejpam-2996	79	23	)	)	PUNCT
ejpam-2996	79	24	.	.	PUNCT
ejpam-2996	80	1	for	for	ADP
ejpam-2996	80	2	example	example	NOUN
ejpam-2996	80	3	when	when	SCONJ
ejpam-2996	80	4	m	m	VERB
ejpam-2996	80	5	=	=	SYM
ejpam-2996	80	6	1	1	NUM
ejpam-2996	80	7	,	,	PUNCT
ejpam-2996	80	8	then	then	ADV
ejpam-2996	80	9	the	the	DET
ejpam-2996	80	10	m	m	NOUN
ejpam-2996	80	11	-	-	PUNCT
ejpam-2996	80	12	invex	invex	NOUN
ejpam-2996	80	13	set	set	VERB
ejpam-2996	80	14	degenerates	degenerate	NOUN
ejpam-2996	80	15	an	an	DET
ejpam-2996	80	16	invex	invex	NOUN
ejpam-2996	80	17	set	set	VERB
ejpam-2996	80	18	on	on	ADP
ejpam-2996	80	19	k.	k.	PROPN
ejpam-2996	80	20	definition	definition	PROPN
ejpam-2996	80	21	7	7	NUM
ejpam-2996	80	22	.	.	PUNCT
ejpam-2996	81	1	(	(	PUNCT
ejpam-2996	81	2	see	see	VERB
ejpam-2996	81	3	[	[	X
ejpam-2996	81	4	12	12	NUM
ejpam-2996	81	5	]	]	PUNCT
ejpam-2996	81	6	)	)	PUNCT
ejpam-2996	81	7	a	a	DET
ejpam-2996	81	8	positive	positive	ADJ
ejpam-2996	81	9	function	function	NOUN
ejpam-2996	81	10	f	f	PROPN
ejpam-2996	81	11	on	on	ADP
ejpam-2996	81	12	the	the	DET
ejpam-2996	81	13	invex	invex	NOUN
ejpam-2996	81	14	set	set	NOUN
ejpam-2996	81	15	k	k	PROPN
ejpam-2996	81	16	is	be	AUX
ejpam-2996	81	17	said	say	VERB
ejpam-2996	81	18	to	to	PART
ejpam-2996	81	19	be	be	AUX
ejpam-2996	81	20	logarithmically	logarithmically	ADV
ejpam-2996	81	21	preinvex	preinvex	ADJ
ejpam-2996	81	22	,	,	PUNCT
ejpam-2996	81	23	if	if	SCONJ
ejpam-2996	81	24	f(u+	f(u+	NOUN
ejpam-2996	81	25	tη(v	tη(v	NOUN
ejpam-2996	81	26	,	,	PUNCT
ejpam-2996	81	27	u	u	NOUN
ejpam-2996	81	28	)	)	PUNCT
ejpam-2996	81	29	)	)	PUNCT
ejpam-2996	81	30	≤	≤	NUM
ejpam-2996	81	31	f1−t(u)f	f1−t(u)f	ADP
ejpam-2996	81	32	t(v	t(v	NOUN
ejpam-2996	81	33	)	)	PUNCT
ejpam-2996	81	34	for	for	ADP
ejpam-2996	81	35	all	all	DET
ejpam-2996	81	36	u	u	NOUN
ejpam-2996	81	37	,	,	PUNCT
ejpam-2996	81	38	v	v	ADP
ejpam-2996	81	39	∈	∈	PROPN
ejpam-2996	81	40	k	k	NOUN
ejpam-2996	81	41	and	and	CCONJ
ejpam-2996	81	42	t	t	PROPN
ejpam-2996	81	43	∈	∈	PROPN
ejpam-2996	82	1	[	[	X
ejpam-2996	82	2	0	0	NUM
ejpam-2996	82	3	,	,	PUNCT
ejpam-2996	82	4	1	1	NUM
ejpam-2996	82	5	]	]	PUNCT
ejpam-2996	82	6	.	.	PUNCT
ejpam-2996	83	1	definition	definition	NOUN
ejpam-2996	83	2	8	8	NUM
ejpam-2996	83	3	.	.	PUNCT
ejpam-2996	84	1	(	(	PUNCT
ejpam-2996	84	2	see	see	VERB
ejpam-2996	84	3	[	[	X
ejpam-2996	84	4	12	12	NUM
ejpam-2996	84	5	]	]	PUNCT
ejpam-2996	84	6	)	)	PUNCT
ejpam-2996	84	7	the	the	DET
ejpam-2996	84	8	function	function	NOUN
ejpam-2996	84	9	f	f	PROPN
ejpam-2996	84	10	on	on	ADP
ejpam-2996	84	11	the	the	DET
ejpam-2996	84	12	invex	invex	NOUN
ejpam-2996	84	13	set	set	NOUN
ejpam-2996	84	14	k	k	PROPN
ejpam-2996	84	15	is	be	AUX
ejpam-2996	84	16	said	say	VERB
ejpam-2996	84	17	to	to	PART
ejpam-2996	84	18	be	be	AUX
ejpam-2996	84	19	r	r	NOUN
ejpam-2996	84	20	-	-	PUNCT
ejpam-2996	84	21	preinvex	preinvex	NOUN
ejpam-2996	84	22	with	with	ADP
ejpam-2996	84	23	respect	respect	NOUN
ejpam-2996	84	24	to	to	ADP
ejpam-2996	84	25	η	η	NOUN
ejpam-2996	84	26	,	,	PUNCT
ejpam-2996	84	27	if	if	SCONJ
ejpam-2996	84	28	f(u+	f(u+	NOUN
ejpam-2996	84	29	tη(v	tη(v	NOUN
ejpam-2996	84	30	,	,	PUNCT
ejpam-2996	84	31	u	u	NOUN
ejpam-2996	84	32	)	)	PUNCT
ejpam-2996	84	33	)	)	PUNCT
ejpam-2996	84	34	≤mr(f(u	≤mr(f(u	PROPN
ejpam-2996	84	35	)	)	PUNCT
ejpam-2996	84	36	,	,	PUNCT
ejpam-2996	84	37	f(v	f(v	PROPN
ejpam-2996	84	38	)	)	PUNCT
ejpam-2996	84	39	;	;	PUNCT
ejpam-2996	84	40	t	t	X
ejpam-2996	84	41	)	)	PUNCT
ejpam-2996	84	42	holds	hold	VERB
ejpam-2996	84	43	for	for	ADP
ejpam-2996	84	44	all	all	DET
ejpam-2996	84	45	u	u	NOUN
ejpam-2996	84	46	,	,	PUNCT
ejpam-2996	84	47	v	v	ADP
ejpam-2996	84	48	∈	∈	PROPN
ejpam-2996	84	49	k	k	NOUN
ejpam-2996	84	50	and	and	CCONJ
ejpam-2996	84	51	t	t	PROPN
ejpam-2996	84	52	∈	∈	PROPN
ejpam-2996	85	1	[	[	X
ejpam-2996	85	2	0	0	NUM
ejpam-2996	85	3	,	,	PUNCT
ejpam-2996	85	4	1	1	NUM
ejpam-2996	85	5	]	]	PUNCT
ejpam-2996	85	6	,	,	PUNCT
ejpam-2996	85	7	where	where	SCONJ
ejpam-2996	85	8	mr(x	mr(x	PROPN
ejpam-2996	85	9	,	,	PUNCT
ejpam-2996	85	10	y	y	PROPN
ejpam-2996	85	11	;	;	PUNCT
ejpam-2996	85	12	t	t	PROPN
ejpam-2996	85	13	)	)	PUNCT
ejpam-2996	85	14	=	=	PRON
ejpam-2996	85	15	{	{	PUNCT
ejpam-2996	85	16	[	[	PUNCT
ejpam-2996	85	17	(	(	PUNCT
ejpam-2996	85	18	1−	1−	NUM
ejpam-2996	85	19	t)xr	t)xr	NOUN
ejpam-2996	85	20	+	+	NUM
ejpam-2996	85	21	tyr	tyr	NOUN
ejpam-2996	85	22	]	]	PUNCT
ejpam-2996	85	23	1	1	NUM
ejpam-2996	85	24	r	r	NOUN
ejpam-2996	85	25	,	,	PUNCT
ejpam-2996	85	26	if	if	SCONJ
ejpam-2996	85	27	r	r	NOUN
ejpam-2996	85	28	6=	6=	ADP
ejpam-2996	85	29	0	0	NUM
ejpam-2996	85	30	;	;	PUNCT
ejpam-2996	85	31	x1−tyt	x1−tyt	X
ejpam-2996	85	32	,	,	PUNCT
ejpam-2996	85	33	if	if	SCONJ
ejpam-2996	85	34	r	r	NOUN
ejpam-2996	85	35	=	=	SYM
ejpam-2996	85	36	0	0	NUM
ejpam-2996	85	37	,	,	PUNCT
ejpam-2996	85	38	is	be	AUX
ejpam-2996	85	39	the	the	DET
ejpam-2996	85	40	weighted	weight	VERB
ejpam-2996	85	41	power	power	NOUN
ejpam-2996	85	42	mean	mean	NOUN
ejpam-2996	85	43	of	of	ADP
ejpam-2996	85	44	order	order	NOUN
ejpam-2996	85	45	r	r	NOUN
ejpam-2996	85	46	for	for	ADP
ejpam-2996	85	47	positive	positive	ADJ
ejpam-2996	85	48	numbers	number	NOUN
ejpam-2996	85	49	x	x	PUNCT
ejpam-2996	85	50	and	and	CCONJ
ejpam-2996	85	51	y.	y.	PROPN
ejpam-2996	85	52	a.	a.	PROPN
ejpam-2996	85	53	kashuri	kashuri	PROPN
ejpam-2996	85	54	,	,	PUNCT
ejpam-2996	85	55	r.	r.	PROPN
ejpam-2996	85	56	liko	liko	PROPN
ejpam-2996	85	57	/	/	SYM
ejpam-2996	85	58	eur	eur	PROPN
ejpam-2996	85	59	.	.	PUNCT
ejpam-2996	86	1	j.	j.	PROPN
ejpam-2996	86	2	pure	pure	PROPN
ejpam-2996	86	3	appl	appl	PROPN
ejpam-2996	86	4	.	.	PROPN
ejpam-2996	86	5	math	math	PROPN
ejpam-2996	86	6	,	,	PUNCT
ejpam-2996	86	7	10	10	NUM
ejpam-2996	86	8	(	(	PUNCT
ejpam-2996	86	9	3	3	NUM
ejpam-2996	86	10	)	)	PUNCT
ejpam-2996	86	11	(	(	PUNCT
ejpam-2996	86	12	2017	2017	NUM
ejpam-2996	86	13	)	)	PUNCT
ejpam-2996	86	14	,	,	PUNCT
ejpam-2996	86	15	495	495	NUM
ejpam-2996	86	16	-	-	SYM
ejpam-2996	86	17	505	505	NUM
ejpam-2996	86	18	498	498	NUM
ejpam-2996	86	19	we	we	PRON
ejpam-2996	86	20	next	next	ADV
ejpam-2996	86	21	give	give	VERB
ejpam-2996	86	22	new	new	ADJ
ejpam-2996	86	23	definition	definition	NOUN
ejpam-2996	86	24	,	,	PUNCT
ejpam-2996	86	25	to	to	PART
ejpam-2996	86	26	be	be	AUX
ejpam-2996	86	27	referred	refer	VERB
ejpam-2996	86	28	as	as	ADP
ejpam-2996	86	29	generalized	generalize	VERB
ejpam-2996	86	30	(	(	PUNCT
ejpam-2996	86	31	r	r	NOUN
ejpam-2996	86	32	;	;	PUNCT
ejpam-2996	86	33	s	s	X
ejpam-2996	86	34	,	,	PUNCT
ejpam-2996	86	35	m	m	PRON
ejpam-2996	86	36	,	,	PUNCT
ejpam-2996	86	37	ϕ)-preinvex	ϕ)-preinvex	NOUN
ejpam-2996	86	38	function	function	NOUN
ejpam-2996	86	39	.	.	PUNCT
ejpam-2996	87	1	definition	definition	NOUN
ejpam-2996	87	2	9	9	NUM
ejpam-2996	87	3	.	.	PUNCT
ejpam-2996	88	1	let	let	VERB
ejpam-2996	88	2	k	k	PROPN
ejpam-2996	88	3	⊆	⊆	NUM
ejpam-2996	88	4	rn	rn	AUX
ejpam-2996	88	5	be	be	AUX
ejpam-2996	88	6	an	an	DET
ejpam-2996	88	7	open	open	ADJ
ejpam-2996	88	8	m	m	NOUN
ejpam-2996	88	9	-	-	PUNCT
ejpam-2996	88	10	invex	invex	NOUN
ejpam-2996	88	11	set	set	VERB
ejpam-2996	88	12	with	with	ADP
ejpam-2996	88	13	respect	respect	NOUN
ejpam-2996	88	14	to	to	ADP
ejpam-2996	88	15	η	η	PROPN
ejpam-2996	88	16	:	:	PUNCT
ejpam-2996	88	17	k×k×(0	k×k×(0	PROPN
ejpam-2996	88	18	,	,	PUNCT
ejpam-2996	88	19	1	1	NUM
ejpam-2996	88	20	]	]	X
ejpam-2996	88	21	−→	−→	PROPN
ejpam-2996	88	22	rn	rn	PROPN
ejpam-2996	88	23	,	,	PUNCT
ejpam-2996	88	24	and	and	CCONJ
ejpam-2996	88	25	ϕ	ϕ	X
ejpam-2996	88	26	:	:	PUNCT
ejpam-2996	88	27	i	i	PRON
ejpam-2996	88	28	−→	−→	VERB
ejpam-2996	88	29	k	k	PROPN
ejpam-2996	88	30	is	be	AUX
ejpam-2996	88	31	a	a	DET
ejpam-2996	88	32	continuous	continuous	ADJ
ejpam-2996	88	33	increasing	increase	VERB
ejpam-2996	88	34	function	function	NOUN
ejpam-2996	88	35	.	.	PUNCT
ejpam-2996	89	1	the	the	DET
ejpam-2996	89	2	function	function	NOUN
ejpam-2996	89	3	f	f	NOUN
ejpam-2996	89	4	:	:	PUNCT
ejpam-2996	89	5	k	k	X
ejpam-2996	89	6	−→	−→	NOUN
ejpam-2996	89	7	(	(	PUNCT
ejpam-2996	89	8	0,∞	0,∞	NUM
ejpam-2996	89	9	)	)	PUNCT
ejpam-2996	89	10	is	be	AUX
ejpam-2996	89	11	said	say	VERB
ejpam-2996	89	12	to	to	PART
ejpam-2996	89	13	be	be	AUX
ejpam-2996	89	14	generalized	generalize	VERB
ejpam-2996	89	15	(	(	PUNCT
ejpam-2996	89	16	r	r	NOUN
ejpam-2996	89	17	;	;	PUNCT
ejpam-2996	89	18	s	s	X
ejpam-2996	89	19	,	,	PUNCT
ejpam-2996	89	20	m	m	PRON
ejpam-2996	89	21	,	,	PUNCT
ejpam-2996	89	22	ϕ)-preinvex	ϕ)-preinvex	VERB
ejpam-2996	89	23	with	with	ADP
ejpam-2996	89	24	respect	respect	NOUN
ejpam-2996	89	25	to	to	ADP
ejpam-2996	89	26	η	η	PROPN
ejpam-2996	89	27	,	,	PUNCT
ejpam-2996	89	28	if	if	SCONJ
ejpam-2996	89	29	f	f	PROPN
ejpam-2996	89	30	(	(	PUNCT
ejpam-2996	89	31	mϕ(x	mϕ(x	NOUN
ejpam-2996	89	32	)	)	PUNCT
ejpam-2996	89	33	+	+	CCONJ
ejpam-2996	89	34	tη(ϕ(y	tη(ϕ(y	X
ejpam-2996	89	35	)	)	PUNCT
ejpam-2996	89	36	,	,	PUNCT
ejpam-2996	89	37	ϕ(x),m	ϕ(x),m	ADJ
ejpam-2996	89	38	)	)	PUNCT
ejpam-2996	89	39	)	)	PUNCT
ejpam-2996	90	1	≤mr(f(ϕ(x	≤mr(f(ϕ(x	PROPN
ejpam-2996	90	2	)	)	PUNCT
ejpam-2996	90	3	)	)	PUNCT
ejpam-2996	91	1	,	,	PUNCT
ejpam-2996	91	2	f(ϕ(y)),m	f(ϕ(y)),m	NOUN
ejpam-2996	91	3	,	,	PUNCT
ejpam-2996	91	4	s	s	PROPN
ejpam-2996	91	5	;	;	PUNCT
ejpam-2996	91	6	t	t	PROPN
ejpam-2996	91	7	)	)	PUNCT
ejpam-2996	91	8	(	(	PUNCT
ejpam-2996	91	9	4	4	X
ejpam-2996	91	10	)	)	PUNCT
ejpam-2996	91	11	holds	hold	VERB
ejpam-2996	91	12	for	for	ADP
ejpam-2996	91	13	any	any	DET
ejpam-2996	91	14	fixed	fix	VERB
ejpam-2996	91	15	s	s	NOUN
ejpam-2996	91	16	,	,	PUNCT
ejpam-2996	91	17	m	m	VERB
ejpam-2996	91	18	∈	∈	ADJ
ejpam-2996	91	19	(	(	PUNCT
ejpam-2996	91	20	0	0	NUM
ejpam-2996	91	21	,	,	PUNCT
ejpam-2996	91	22	1	1	NUM
ejpam-2996	91	23	]	]	PUNCT
ejpam-2996	91	24	and	and	CCONJ
ejpam-2996	91	25	for	for	ADP
ejpam-2996	91	26	all	all	DET
ejpam-2996	91	27	x	x	NOUN
ejpam-2996	91	28	,	,	PUNCT
ejpam-2996	91	29	y	y	PROPN
ejpam-2996	91	30	∈	∈	PROPN
ejpam-2996	91	31	i	i	PRON
ejpam-2996	91	32	,	,	PUNCT
ejpam-2996	91	33	t	t	PROPN
ejpam-2996	91	34	∈	∈	PROPN
ejpam-2996	92	1	[	[	X
ejpam-2996	92	2	0	0	NUM
ejpam-2996	92	3	,	,	PUNCT
ejpam-2996	92	4	1	1	NUM
ejpam-2996	92	5	]	]	PUNCT
ejpam-2996	92	6	,	,	PUNCT
ejpam-2996	92	7	where	where	SCONJ
ejpam-2996	92	8	mr(f(ϕ(x	mr(f(ϕ(x	NOUN
ejpam-2996	92	9	)	)	PUNCT
ejpam-2996	92	10	)	)	PUNCT
ejpam-2996	92	11	,	,	PUNCT
ejpam-2996	92	12	f(ϕ(y)),m	f(ϕ(y)),m	NOUN
ejpam-2996	92	13	,	,	PUNCT
ejpam-2996	92	14	s	s	PROPN
ejpam-2996	92	15	;	;	PUNCT
ejpam-2996	92	16	t	t	PROPN
ejpam-2996	92	17	)	)	PUNCT
ejpam-2996	92	18	=	=	PUNCT
ejpam-2996	92	19			PUNCT
ejpam-2996	92	20	[	[	PUNCT
ejpam-2996	92	21	m(1−	m(1−	PROPN
ejpam-2996	92	22	t)sf	t)sf	PROPN
ejpam-2996	92	23	r(ϕ(x	r(ϕ(x	PROPN
ejpam-2996	92	24	)	)	PUNCT
ejpam-2996	92	25	)	)	PUNCT
ejpam-2996	93	1	+	+	CCONJ
ejpam-2996	93	2	tsf	tsf	PROPN
ejpam-2996	93	3	r(ϕ(y	r(ϕ(y	PROPN
ejpam-2996	93	4	)	)	PUNCT
ejpam-2996	93	5	)	)	PUNCT
ejpam-2996	93	6	]	]	PUNCT
ejpam-2996	94	1	1	1	NUM
ejpam-2996	94	2	r	r	NOUN
ejpam-2996	94	3	,	,	PUNCT
ejpam-2996	94	4	if	if	SCONJ
ejpam-2996	94	5	r	r	NOUN
ejpam-2996	94	6	6=	6=	ADP
ejpam-2996	94	7	0	0	NUM
ejpam-2996	94	8	;	;	PUNCT
ejpam-2996	94	9	f(ϕ(x))m(1−t)sf(ϕ(y))t	f(ϕ(x))m(1−t)sf(ϕ(y))t	PRON
ejpam-2996	94	10	s	s	X
ejpam-2996	94	11	,	,	PUNCT
ejpam-2996	94	12	if	if	SCONJ
ejpam-2996	94	13	r	r	NOUN
ejpam-2996	94	14	=	=	SYM
ejpam-2996	94	15	0	0	NUM
ejpam-2996	94	16	,	,	PUNCT
ejpam-2996	94	17	is	be	AUX
ejpam-2996	94	18	the	the	DET
ejpam-2996	94	19	weighted	weight	VERB
ejpam-2996	94	20	power	power	NOUN
ejpam-2996	94	21	mean	mean	NOUN
ejpam-2996	94	22	of	of	ADP
ejpam-2996	94	23	order	order	NOUN
ejpam-2996	94	24	r	r	NOUN
ejpam-2996	94	25	for	for	ADP
ejpam-2996	94	26	positive	positive	ADJ
ejpam-2996	94	27	numbers	number	NOUN
ejpam-2996	94	28	f(ϕ(x	f(ϕ(x	PROPN
ejpam-2996	94	29	)	)	PUNCT
ejpam-2996	94	30	)	)	PUNCT
ejpam-2996	94	31	and	and	CCONJ
ejpam-2996	94	32	f(ϕ(y	f(ϕ(y	PROPN
ejpam-2996	94	33	)	)	PUNCT
ejpam-2996	94	34	)	)	PUNCT
ejpam-2996	94	35	.	.	PUNCT
ejpam-2996	95	1	remark	remark	NOUN
ejpam-2996	95	2	2	2	NUM
ejpam-2996	95	3	.	.	PUNCT
ejpam-2996	96	1	in	in	ADP
ejpam-2996	96	2	definition	definition	NOUN
ejpam-2996	96	3	9	9	NUM
ejpam-2996	96	4	,	,	PUNCT
ejpam-2996	96	5	it	it	PRON
ejpam-2996	96	6	is	be	AUX
ejpam-2996	96	7	worthwhile	worthwhile	ADJ
ejpam-2996	96	8	to	to	PART
ejpam-2996	96	9	note	note	VERB
ejpam-2996	96	10	that	that	SCONJ
ejpam-2996	96	11	the	the	DET
ejpam-2996	96	12	class	class	NOUN
ejpam-2996	96	13	of	of	ADP
ejpam-2996	96	14	generalized	generalized	ADJ
ejpam-2996	96	15	(	(	PUNCT
ejpam-2996	96	16	r	r	NOUN
ejpam-2996	96	17	;	;	PUNCT
ejpam-2996	96	18	s	s	X
ejpam-2996	96	19	,	,	PUNCT
ejpam-2996	96	20	m	m	PROPN
ejpam-2996	96	21	,	,	PUNCT
ejpam-2996	96	22	ϕ)preinvex	ϕ)preinvex	PROPN
ejpam-2996	96	23	function	function	PROPN
ejpam-2996	96	24	is	be	AUX
ejpam-2996	96	25	a	a	DET
ejpam-2996	96	26	generalization	generalization	NOUN
ejpam-2996	96	27	of	of	ADP
ejpam-2996	96	28	the	the	DET
ejpam-2996	96	29	class	class	NOUN
ejpam-2996	96	30	of	of	ADP
ejpam-2996	96	31	s	s	NOUN
ejpam-2996	96	32	-	-	NOUN
ejpam-2996	96	33	convex	convex	NOUN
ejpam-2996	96	34	in	in	ADP
ejpam-2996	96	35	the	the	DET
ejpam-2996	96	36	second	second	ADJ
ejpam-2996	96	37	sense	sense	NOUN
ejpam-2996	96	38	function	function	NOUN
ejpam-2996	96	39	given	give	VERB
ejpam-2996	96	40	in	in	ADP
ejpam-2996	96	41	definition	definition	NOUN
ejpam-2996	96	42	3	3	NUM
ejpam-2996	96	43	.	.	PUNCT
ejpam-2996	97	1	also	also	ADV
ejpam-2996	97	2	,	,	PUNCT
ejpam-2996	97	3	for	for	ADP
ejpam-2996	97	4	r	r	NOUN
ejpam-2996	97	5	=	=	SYM
ejpam-2996	97	6	1	1	NUM
ejpam-2996	97	7	and	and	CCONJ
ejpam-2996	97	8	ϕ(x	ϕ(x	NOUN
ejpam-2996	97	9	)	)	PUNCT
ejpam-2996	97	10	=	=	SYM
ejpam-2996	98	1	x	x	NOUN
ejpam-2996	98	2	,	,	PUNCT
ejpam-2996	98	3	∀x	∀x	X
ejpam-2996	98	4	∈	∈	PROPN
ejpam-2996	99	1	i	i	PRON
ejpam-2996	99	2	,	,	PUNCT
ejpam-2996	99	3	we	we	PRON
ejpam-2996	99	4	get	get	VERB
ejpam-2996	99	5	the	the	DET
ejpam-2996	99	6	notion	notion	NOUN
ejpam-2996	99	7	of	of	ADP
ejpam-2996	99	8	generalized	generalized	ADJ
ejpam-2996	99	9	(	(	PUNCT
ejpam-2996	99	10	s	s	X
ejpam-2996	99	11	,	,	PUNCT
ejpam-2996	99	12	m)-preinvex	m)-preinvex	X
ejpam-2996	99	13	function	function	VERB
ejpam-2996	99	14	(	(	PUNCT
ejpam-2996	99	15	see	see	VERB
ejpam-2996	99	16	[	[	X
ejpam-2996	99	17	3	3	NUM
ejpam-2996	99	18	]	]	NUM
ejpam-2996	99	19	)	)	PUNCT
ejpam-2996	99	20	.	.	PUNCT
ejpam-2996	100	1	example	example	NOUN
ejpam-2996	101	1	1	1	NUM
ejpam-2996	101	2	.	.	PUNCT
ejpam-2996	101	3	let	let	VERB
ejpam-2996	101	4	f(x	f(x	PROPN
ejpam-2996	101	5	)	)	PUNCT
ejpam-2996	102	1	=	=	SYM
ejpam-2996	102	2	|x|	|x|	PROPN
ejpam-2996	102	3	,	,	PUNCT
ejpam-2996	102	4	ϕ(x	ϕ(x	X
ejpam-2996	102	5	)	)	PUNCT
ejpam-2996	102	6	=	=	SYM
ejpam-2996	103	1	x	x	X
ejpam-2996	103	2	,	,	PUNCT
ejpam-2996	103	3	r	r	NOUN
ejpam-2996	103	4	=	=	SYM
ejpam-2996	103	5	s	s	NOUN
ejpam-2996	103	6	=	=	SYM
ejpam-2996	103	7	1	1	NUM
ejpam-2996	103	8	and	and	CCONJ
ejpam-2996	103	9	η(y	η(y	NOUN
ejpam-2996	103	10	,	,	PUNCT
ejpam-2996	103	11	x	x	X
ejpam-2996	103	12	,	,	PUNCT
ejpam-2996	103	13	m	m	NOUN
ejpam-2996	103	14	)	)	PUNCT
ejpam-2996	103	15	=	=	SYM
ejpam-2996	103	16			PUNCT
ejpam-2996	103	17	y	y	PROPN
ejpam-2996	103	18	−mx	−mx	PROPN
ejpam-2996	103	19	,	,	PUNCT
ejpam-2996	103	20	if	if	SCONJ
ejpam-2996	103	21	x	x	PRON
ejpam-2996	103	22	≥	≥	NOUN
ejpam-2996	103	23	0	0	NUM
ejpam-2996	103	24	,	,	PUNCT
ejpam-2996	103	25	y	y	PROPN
ejpam-2996	103	26	≥	≥	NUM
ejpam-2996	103	27	0	0	NUM
ejpam-2996	103	28	;	;	PUNCT
ejpam-2996	103	29	y	y	PROPN
ejpam-2996	103	30	−mx	−mx	NOUN
ejpam-2996	103	31	,	,	PUNCT
ejpam-2996	103	32	if	if	SCONJ
ejpam-2996	103	33	x	x	ADP
ejpam-2996	103	34	≤	≤	NUM
ejpam-2996	103	35	0	0	NUM
ejpam-2996	103	36	,	,	PUNCT
ejpam-2996	103	37	y	y	PROPN
ejpam-2996	103	38	≤	≤	PROPN
ejpam-2996	103	39	0	0	NUM
ejpam-2996	103	40	;	;	PUNCT
ejpam-2996	103	41	mx−	mx−	PROPN
ejpam-2996	103	42	y	y	PROPN
ejpam-2996	103	43	,	,	PUNCT
ejpam-2996	103	44	if	if	SCONJ
ejpam-2996	103	45	x	x	PRON
ejpam-2996	103	46	≥	≥	NOUN
ejpam-2996	103	47	0	0	NUM
ejpam-2996	103	48	,	,	PUNCT
ejpam-2996	103	49	y	y	PROPN
ejpam-2996	103	50	≤	≤	PROPN
ejpam-2996	103	51	0	0	NUM
ejpam-2996	103	52	;	;	PUNCT
ejpam-2996	103	53	mx−	mx−	PROPN
ejpam-2996	103	54	y	y	PROPN
ejpam-2996	103	55	,	,	PUNCT
ejpam-2996	103	56	if	if	SCONJ
ejpam-2996	103	57	x	x	ADP
ejpam-2996	103	58	≤	≤	NUM
ejpam-2996	103	59	0	0	NUM
ejpam-2996	103	60	,	,	PUNCT
ejpam-2996	103	61	y	y	PROPN
ejpam-2996	103	62	≥	≥	NUM
ejpam-2996	103	63	0	0	NUM
ejpam-2996	103	64	.	.	PUNCT
ejpam-2996	104	1	then	then	ADV
ejpam-2996	104	2	f(x	f(x	PROPN
ejpam-2996	104	3	)	)	PUNCT
ejpam-2996	104	4	is	be	AUX
ejpam-2996	104	5	a	a	DET
ejpam-2996	104	6	generalized	generalized	ADJ
ejpam-2996	104	7	(	(	PUNCT
ejpam-2996	104	8	1	1	NUM
ejpam-2996	104	9	;	;	PUNCT
ejpam-2996	104	10	1,m	1,m	NUM
ejpam-2996	104	11	,	,	PUNCT
ejpam-2996	104	12	x)-preinvex	x)-preinvex	PUNCT
ejpam-2996	104	13	function	function	NOUN
ejpam-2996	104	14	of	of	ADP
ejpam-2996	104	15	with	with	ADP
ejpam-2996	104	16	respect	respect	NOUN
ejpam-2996	104	17	to	to	ADP
ejpam-2996	104	18	η	η	PROPN
ejpam-2996	104	19	:	:	PUNCT
ejpam-2996	104	20	r	r	NOUN
ejpam-2996	104	21	×	×	NOUN
ejpam-2996	104	22	r	r	NOUN
ejpam-2996	104	23	×	×	NOUN
ejpam-2996	104	24	(	(	PUNCT
ejpam-2996	104	25	0	0	NUM
ejpam-2996	104	26	,	,	PUNCT
ejpam-2996	104	27	1	1	NUM
ejpam-2996	104	28	]	]	X
ejpam-2996	104	29	−→	−→	ADJ
ejpam-2996	104	30	r	r	NOUN
ejpam-2996	104	31	and	and	CCONJ
ejpam-2996	104	32	any	any	DET
ejpam-2996	104	33	fixed	fix	VERB
ejpam-2996	104	34	m	m	NOUN
ejpam-2996	104	35	∈	∈	NOUN
ejpam-2996	104	36	(	(	PUNCT
ejpam-2996	104	37	0	0	NUM
ejpam-2996	104	38	,	,	PUNCT
ejpam-2996	104	39	1	1	NUM
ejpam-2996	104	40	]	]	PUNCT
ejpam-2996	104	41	.	.	PUNCT
ejpam-2996	105	1	however	however	ADV
ejpam-2996	105	2	,	,	PUNCT
ejpam-2996	105	3	it	it	PRON
ejpam-2996	105	4	is	be	AUX
ejpam-2996	105	5	obvious	obvious	ADJ
ejpam-2996	105	6	that	that	SCONJ
ejpam-2996	105	7	f(x	f(x	NOUN
ejpam-2996	105	8	)	)	PUNCT
ejpam-2996	106	1	=	=	PUNCT
ejpam-2996	106	2	|x|	|x|	PROPN
ejpam-2996	106	3	is	be	AUX
ejpam-2996	106	4	not	not	PART
ejpam-2996	106	5	a	a	DET
ejpam-2996	106	6	convex	convex	NOUN
ejpam-2996	106	7	function	function	NOUN
ejpam-2996	106	8	on	on	ADP
ejpam-2996	106	9	r.	r.	PROPN
ejpam-2996	106	10	in	in	ADP
ejpam-2996	106	11	this	this	DET
ejpam-2996	106	12	section	section	NOUN
ejpam-2996	106	13	,	,	PUNCT
ejpam-2996	106	14	in	in	ADP
ejpam-2996	106	15	order	order	NOUN
ejpam-2996	106	16	to	to	PART
ejpam-2996	106	17	prove	prove	VERB
ejpam-2996	106	18	our	our	PRON
ejpam-2996	106	19	main	main	ADJ
ejpam-2996	106	20	results	result	NOUN
ejpam-2996	106	21	regarding	regard	VERB
ejpam-2996	106	22	some	some	DET
ejpam-2996	106	23	new	new	ADJ
ejpam-2996	106	24	integral	integral	ADJ
ejpam-2996	106	25	inequalities	inequality	NOUN
ejpam-2996	106	26	involving	involve	VERB
ejpam-2996	106	27	generalized	generalize	VERB
ejpam-2996	106	28	(	(	PUNCT
ejpam-2996	106	29	r	r	NOUN
ejpam-2996	106	30	;	;	PUNCT
ejpam-2996	106	31	s	s	X
ejpam-2996	106	32	,	,	PUNCT
ejpam-2996	106	33	m	m	PRON
ejpam-2996	106	34	,	,	PUNCT
ejpam-2996	106	35	ϕ)-preinvex	ϕ)-preinvex	NOUN
ejpam-2996	106	36	functions	function	NOUN
ejpam-2996	106	37	,	,	PUNCT
ejpam-2996	106	38	we	we	PRON
ejpam-2996	106	39	need	need	VERB
ejpam-2996	106	40	the	the	DET
ejpam-2996	106	41	following	follow	VERB
ejpam-2996	106	42	new	new	ADJ
ejpam-2996	106	43	lemma	lemma	PROPN
ejpam-2996	106	44	:	:	PUNCT
ejpam-2996	106	45	lemma	lemma	PROPN
ejpam-2996	106	46	1	1	X
ejpam-2996	106	47	.	.	PUNCT
ejpam-2996	107	1	let	let	VERB
ejpam-2996	107	2	ϕ	ϕ	NOUN
ejpam-2996	107	3	:	:	PUNCT
ejpam-2996	108	1	i	i	PRON
ejpam-2996	108	2	−→	−→	VERB
ejpam-2996	108	3	k	k	X
ejpam-2996	108	4	be	be	AUX
ejpam-2996	108	5	a	a	DET
ejpam-2996	108	6	continuous	continuous	ADJ
ejpam-2996	108	7	increasing	increase	VERB
ejpam-2996	108	8	function	function	NOUN
ejpam-2996	108	9	.	.	PUNCT
ejpam-2996	109	1	assume	assume	VERB
ejpam-2996	109	2	that	that	SCONJ
ejpam-2996	109	3	f	f	X
ejpam-2996	109	4	:	:	PUNCT
ejpam-2996	110	1	k	k	X
ejpam-2996	110	2	=	=	PUNCT
ejpam-2996	111	1	[	[	X
ejpam-2996	111	2	mϕ(a),mϕ(a	mϕ(a),mϕ(a	NOUN
ejpam-2996	111	3	)	)	PUNCT
ejpam-2996	111	4	+	+	NUM
ejpam-2996	111	5	η(ϕ(b	η(ϕ(b	PROPN
ejpam-2996	111	6	)	)	PUNCT
ejpam-2996	111	7	,	,	PUNCT
ejpam-2996	111	8	ϕ(a),m	ϕ(a),m	ADJ
ejpam-2996	111	9	)	)	PUNCT
ejpam-2996	111	10	]	]	PUNCT
ejpam-2996	112	1	−→	−→	NOUN
ejpam-2996	112	2	r	r	NOUN
ejpam-2996	112	3	is	be	AUX
ejpam-2996	112	4	a	a	DET
ejpam-2996	112	5	continuous	continuous	ADJ
ejpam-2996	112	6	function	function	NOUN
ejpam-2996	112	7	on	on	ADP
ejpam-2996	112	8	the	the	DET
ejpam-2996	112	9	interval	interval	NOUN
ejpam-2996	112	10	of	of	ADP
ejpam-2996	112	11	real	real	ADJ
ejpam-2996	112	12	numbers	number	NOUN
ejpam-2996	112	13	k	k	X
ejpam-2996	112	14	◦	◦	NOUN
ejpam-2996	112	15	with	with	ADP
ejpam-2996	112	16	respect	respect	NOUN
ejpam-2996	112	17	to	to	ADP
ejpam-2996	112	18	η	η	PROPN
ejpam-2996	112	19	:	:	PUNCT
ejpam-2996	112	20	k×k×(0	k×k×(0	PROPN
ejpam-2996	112	21	,	,	PUNCT
ejpam-2996	112	22	1	1	NUM
ejpam-2996	112	23	]	]	X
ejpam-2996	112	24	−→	−→	ADJ
ejpam-2996	112	25	r	r	NOUN
ejpam-2996	112	26	,	,	PUNCT
ejpam-2996	112	27	for	for	ADP
ejpam-2996	112	28	mϕ(a	mϕ(a	NOUN
ejpam-2996	112	29	)	)	PUNCT
ejpam-2996	112	30	<	<	X
ejpam-2996	112	31	mϕ(a)+η(ϕ(b	mϕ(a)+η(ϕ(b	PROPN
ejpam-2996	112	32	)	)	PUNCT
ejpam-2996	112	33	,	,	PUNCT
ejpam-2996	112	34	ϕ(a),m	ϕ(a),m	ADJ
ejpam-2996	112	35	)	)	PUNCT
ejpam-2996	112	36	.	.	PUNCT
ejpam-2996	113	1	then	then	ADV
ejpam-2996	113	2	for	for	ADP
ejpam-2996	113	3	any	any	DET
ejpam-2996	113	4	fixed	fix	VERB
ejpam-2996	113	5	m	m	NOUN
ejpam-2996	113	6	∈	∈	NOUN
ejpam-2996	113	7	(	(	PUNCT
ejpam-2996	113	8	0	0	NUM
ejpam-2996	113	9	,	,	PUNCT
ejpam-2996	113	10	1	1	NUM
ejpam-2996	113	11	]	]	PUNCT
ejpam-2996	113	12	and	and	CCONJ
ejpam-2996	113	13	p	p	X
ejpam-2996	113	14	,	,	PUNCT
ejpam-2996	113	15	q	q	ADJ
ejpam-2996	113	16	>	>	X
ejpam-2996	113	17	0	0	NUM
ejpam-2996	113	18	,	,	PUNCT
ejpam-2996	113	19	we	we	PRON
ejpam-2996	113	20	have∫	have∫	VERB
ejpam-2996	113	21	mϕ(a)+η(ϕ(b),ϕ(a),m	mϕ(a)+η(ϕ(b),ϕ(a),m	SYM
ejpam-2996	113	22	)	)	PUNCT
ejpam-2996	113	23	mϕ(a	mϕ(a	NOUN
ejpam-2996	113	24	)	)	PUNCT
ejpam-2996	113	25	(	(	PUNCT
ejpam-2996	113	26	x−mϕ(a))p(mϕ(a	x−mϕ(a))p(mϕ(a	PROPN
ejpam-2996	113	27	)	)	PUNCT
ejpam-2996	114	1	+	+	CCONJ
ejpam-2996	114	2	η(ϕ(b	η(ϕ(b	PROPN
ejpam-2996	114	3	)	)	PUNCT
ejpam-2996	114	4	,	,	PUNCT
ejpam-2996	114	5	ϕ(a),m)−	ϕ(a),m)−	VERB
ejpam-2996	114	6	x)qf(x)dx	x)qf(x)dx	PRON
ejpam-2996	115	1	=	=	PUNCT
ejpam-2996	115	2	η(ϕ(b	η(ϕ(b	PROPN
ejpam-2996	115	3	)	)	PUNCT
ejpam-2996	115	4	,	,	PUNCT
ejpam-2996	115	5	ϕ(a),m)p+q+1	ϕ(a),m)p+q+1	PROPN
ejpam-2996	115	6	∫	∫	PROPN
ejpam-2996	116	1	1	1	NUM
ejpam-2996	116	2	0	0	NUM
ejpam-2996	116	3	tp(1−	tp(1−	PROPN
ejpam-2996	116	4	t)qf(mϕ(a	t)qf(mϕ(a	NOUN
ejpam-2996	116	5	)	)	PUNCT
ejpam-2996	117	1	+	+	CCONJ
ejpam-2996	117	2	tη(ϕ(b	tη(ϕ(b	NUM
ejpam-2996	117	3	)	)	PUNCT
ejpam-2996	117	4	,	,	PUNCT
ejpam-2996	117	5	ϕ(a),m))dt	ϕ(a),m))dt	PROPN
ejpam-2996	117	6	.	.	PUNCT
ejpam-2996	118	1	a.	a.	PROPN
ejpam-2996	118	2	kashuri	kashuri	PROPN
ejpam-2996	118	3	,	,	PUNCT
ejpam-2996	118	4	r.	r.	PROPN
ejpam-2996	118	5	liko	liko	PROPN
ejpam-2996	118	6	/	/	SYM
ejpam-2996	118	7	eur	eur	PROPN
ejpam-2996	118	8	.	.	PUNCT
ejpam-2996	119	1	j.	j.	PROPN
ejpam-2996	119	2	pure	pure	PROPN
ejpam-2996	119	3	appl	appl	PROPN
ejpam-2996	119	4	.	.	PROPN
ejpam-2996	119	5	math	math	PROPN
ejpam-2996	119	6	,	,	PUNCT
ejpam-2996	119	7	10	10	NUM
ejpam-2996	119	8	(	(	PUNCT
ejpam-2996	119	9	3	3	NUM
ejpam-2996	119	10	)	)	PUNCT
ejpam-2996	119	11	(	(	PUNCT
ejpam-2996	119	12	2017	2017	NUM
ejpam-2996	119	13	)	)	PUNCT
ejpam-2996	119	14	,	,	PUNCT
ejpam-2996	119	15	495	495	NUM
ejpam-2996	119	16	-	-	SYM
ejpam-2996	119	17	505	505	NUM
ejpam-2996	119	18	499	499	NUM
ejpam-2996	119	19	proof	proof	NOUN
ejpam-2996	119	20	.	.	PUNCT
ejpam-2996	120	1	it	it	PRON
ejpam-2996	120	2	is	be	AUX
ejpam-2996	120	3	easy	easy	ADJ
ejpam-2996	120	4	to	to	PART
ejpam-2996	120	5	observe	observe	VERB
ejpam-2996	120	6	that∫	that∫	PROPN
ejpam-2996	120	7	mϕ(a)+η(ϕ(b),ϕ(a),m	mϕ(a)+η(ϕ(b),ϕ(a),m	PROPN
ejpam-2996	120	8	)	)	PUNCT
ejpam-2996	120	9	mϕ(a	mϕ(a	NOUN
ejpam-2996	120	10	)	)	PUNCT
ejpam-2996	120	11	(	(	PUNCT
ejpam-2996	120	12	x−mϕ(a))p(mϕ(a	x−mϕ(a))p(mϕ(a	PROPN
ejpam-2996	120	13	)	)	PUNCT
ejpam-2996	121	1	+	+	CCONJ
ejpam-2996	121	2	η(ϕ(b	η(ϕ(b	PROPN
ejpam-2996	121	3	)	)	PUNCT
ejpam-2996	121	4	,	,	PUNCT
ejpam-2996	121	5	ϕ(a),m)−	ϕ(a),m)−	VERB
ejpam-2996	121	6	x)qf(x)dx	x)qf(x)dx	PRON
ejpam-2996	122	1	=	=	PUNCT
ejpam-2996	122	2	η(ϕ(b	η(ϕ(b	PROPN
ejpam-2996	122	3	)	)	PUNCT
ejpam-2996	122	4	,	,	PUNCT
ejpam-2996	122	5	ϕ(a),m	ϕ(a),m	PROPN
ejpam-2996	122	6	)	)	PUNCT
ejpam-2996	122	7	∫	∫	PROPN
ejpam-2996	123	1	1	1	NUM
ejpam-2996	123	2	0	0	NUM
ejpam-2996	123	3	(	(	PUNCT
ejpam-2996	123	4	mϕ(a	mϕ(a	NOUN
ejpam-2996	123	5	)	)	PUNCT
ejpam-2996	123	6	+	+	CCONJ
ejpam-2996	123	7	tη(ϕ(b	tη(ϕ(b	NUM
ejpam-2996	123	8	)	)	PUNCT
ejpam-2996	123	9	,	,	PUNCT
ejpam-2996	123	10	ϕ(a),m)−mϕ(a))p	ϕ(a),m)−mϕ(a))p	PROPN
ejpam-2996	123	11	×(mϕ(a	×(mϕ(a	PROPN
ejpam-2996	123	12	)	)	PUNCT
ejpam-2996	124	1	+	+	CCONJ
ejpam-2996	124	2	η(ϕ(b	η(ϕ(b	PROPN
ejpam-2996	124	3	)	)	PUNCT
ejpam-2996	124	4	,	,	PUNCT
ejpam-2996	124	5	ϕ(a),m)−mϕ(a)−	ϕ(a),m)−mϕ(a)−	NOUN
ejpam-2996	124	6	tη(ϕ(b	tη(ϕ(b	ADJ
ejpam-2996	124	7	)	)	PUNCT
ejpam-2996	124	8	,	,	PUNCT
ejpam-2996	124	9	ϕ(a),m))q	ϕ(a),m))q	PROPN
ejpam-2996	124	10	×f(mϕ(a	×f(mϕ(a	NOUN
ejpam-2996	124	11	)	)	PUNCT
ejpam-2996	124	12	+	+	CCONJ
ejpam-2996	124	13	tη(ϕ(b	tη(ϕ(b	NUM
ejpam-2996	124	14	)	)	PUNCT
ejpam-2996	124	15	,	,	PUNCT
ejpam-2996	124	16	ϕ(a),m))dt	ϕ(a),m))dt	PROPN
ejpam-2996	124	17	=	=	SYM
ejpam-2996	124	18	η(ϕ(b	η(ϕ(b	PROPN
ejpam-2996	124	19	)	)	PUNCT
ejpam-2996	124	20	,	,	PUNCT
ejpam-2996	124	21	ϕ(a),m)p+q+1	ϕ(a),m)p+q+1	PROPN
ejpam-2996	124	22	∫	∫	PROPN
ejpam-2996	124	23	1	1	NUM
ejpam-2996	124	24	0	0	NUM
ejpam-2996	124	25	tp(1−	tp(1−	PROPN
ejpam-2996	124	26	t)qf(mϕ(a	t)qf(mϕ(a	NOUN
ejpam-2996	124	27	)	)	PUNCT
ejpam-2996	124	28	+	+	CCONJ
ejpam-2996	124	29	tη(ϕ(b	tη(ϕ(b	NUM
ejpam-2996	124	30	)	)	PUNCT
ejpam-2996	124	31	,	,	PUNCT
ejpam-2996	124	32	ϕ(a),m))dt	ϕ(a),m))dt	PROPN
ejpam-2996	124	33	.	.	PUNCT
ejpam-2996	125	1	the	the	DET
ejpam-2996	125	2	following	follow	VERB
ejpam-2996	125	3	definition	definition	NOUN
ejpam-2996	125	4	will	will	AUX
ejpam-2996	125	5	be	be	AUX
ejpam-2996	125	6	used	use	VERB
ejpam-2996	125	7	in	in	ADP
ejpam-2996	125	8	the	the	DET
ejpam-2996	125	9	sequel	sequel	NOUN
ejpam-2996	125	10	.	.	PUNCT
ejpam-2996	126	1	definition	definition	NOUN
ejpam-2996	126	2	10	10	NUM
ejpam-2996	126	3	.	.	PUNCT
ejpam-2996	127	1	the	the	DET
ejpam-2996	127	2	euler	euler	NOUN
ejpam-2996	127	3	beta	beta	NOUN
ejpam-2996	127	4	function	function	NOUN
ejpam-2996	127	5	is	be	AUX
ejpam-2996	127	6	defined	define	VERB
ejpam-2996	127	7	for	for	ADP
ejpam-2996	127	8	x	x	X
ejpam-2996	127	9	,	,	PUNCT
ejpam-2996	127	10	y	y	PROPN
ejpam-2996	127	11	>	>	X
ejpam-2996	127	12	0	0	PUNCT
ejpam-2996	128	1	as	as	ADP
ejpam-2996	128	2	β(x	β(x	NOUN
ejpam-2996	128	3	,	,	PUNCT
ejpam-2996	128	4	y	y	NOUN
ejpam-2996	128	5	)	)	PUNCT
ejpam-2996	128	6	=	=	SYM
ejpam-2996	128	7	∫	∫	PROPN
ejpam-2996	128	8	1	1	NUM
ejpam-2996	128	9	0	0	NUM
ejpam-2996	128	10	tx−1(1−	tx−1(1−	NOUN
ejpam-2996	128	11	t)y−1dt	t)y−1dt	NOUN
ejpam-2996	128	12	=	=	SYM
ejpam-2996	128	13	γ(x)γ(y	γ(x)γ(y	NOUN
ejpam-2996	128	14	)	)	PUNCT
ejpam-2996	128	15	γ(x+	γ(x+	NOUN
ejpam-2996	128	16	y	y	X
ejpam-2996	128	17	)	)	PUNCT
ejpam-2996	128	18	.	.	PUNCT
ejpam-2996	129	1	theorem	theorem	NOUN
ejpam-2996	129	2	2	2	NUM
ejpam-2996	129	3	.	.	PUNCT
ejpam-2996	130	1	let	let	VERB
ejpam-2996	130	2	ϕ	ϕ	NOUN
ejpam-2996	130	3	:	:	PUNCT
ejpam-2996	131	1	i	i	PRON
ejpam-2996	131	2	−→	−→	VERB
ejpam-2996	131	3	k	k	X
ejpam-2996	131	4	be	be	AUX
ejpam-2996	131	5	a	a	DET
ejpam-2996	131	6	continuous	continuous	ADJ
ejpam-2996	131	7	increasing	increase	VERB
ejpam-2996	131	8	function	function	NOUN
ejpam-2996	131	9	.	.	PUNCT
ejpam-2996	132	1	assume	assume	VERB
ejpam-2996	132	2	that	that	SCONJ
ejpam-2996	132	3	f	f	X
ejpam-2996	132	4	:	:	PUNCT
ejpam-2996	133	1	k	k	X
ejpam-2996	133	2	=	=	PUNCT
ejpam-2996	134	1	[	[	X
ejpam-2996	134	2	mϕ(a),mϕ(a	mϕ(a),mϕ(a	NOUN
ejpam-2996	134	3	)	)	PUNCT
ejpam-2996	134	4	+	+	NUM
ejpam-2996	134	5	η(ϕ(b	η(ϕ(b	PROPN
ejpam-2996	134	6	)	)	PUNCT
ejpam-2996	134	7	,	,	PUNCT
ejpam-2996	134	8	ϕ(a),m	ϕ(a),m	ADJ
ejpam-2996	134	9	)	)	PUNCT
ejpam-2996	134	10	]	]	PUNCT
ejpam-2996	135	1	−→	−→	NOUN
ejpam-2996	135	2	(	(	PUNCT
ejpam-2996	135	3	0,∞	0,∞	NOUN
ejpam-2996	135	4	)	)	PUNCT
ejpam-2996	135	5	is	be	AUX
ejpam-2996	135	6	a	a	DET
ejpam-2996	135	7	continuous	continuous	ADJ
ejpam-2996	135	8	function	function	NOUN
ejpam-2996	135	9	on	on	ADP
ejpam-2996	135	10	the	the	DET
ejpam-2996	135	11	interval	interval	NOUN
ejpam-2996	135	12	of	of	ADP
ejpam-2996	135	13	real	real	ADJ
ejpam-2996	135	14	numbers	number	NOUN
ejpam-2996	135	15	k	k	X
ejpam-2996	135	16	◦	◦	NOUN
ejpam-2996	135	17	with	with	ADP
ejpam-2996	135	18	mϕ(a	mϕ(a	NOUN
ejpam-2996	135	19	)	)	PUNCT
ejpam-2996	135	20	<	<	X
ejpam-2996	135	21	mϕ(a	mϕ(a	NOUN
ejpam-2996	135	22	)	)	PUNCT
ejpam-2996	136	1	+	+	CCONJ
ejpam-2996	136	2	η(ϕ(b	η(ϕ(b	PROPN
ejpam-2996	136	3	)	)	PUNCT
ejpam-2996	136	4	,	,	PUNCT
ejpam-2996	136	5	ϕ(a),m	ϕ(a),m	ADJ
ejpam-2996	136	6	)	)	PUNCT
ejpam-2996	136	7	.	.	PUNCT
ejpam-2996	137	1	let	let	VERB
ejpam-2996	137	2	k	k	PRON
ejpam-2996	137	3	>	>	X
ejpam-2996	137	4	1	1	NUM
ejpam-2996	137	5	and	and	CCONJ
ejpam-2996	137	6	0	0	NUM
ejpam-2996	138	1	<	<	X
ejpam-2996	138	2	r	r	NOUN
ejpam-2996	138	3	≤	≤	NUM
ejpam-2996	138	4	1	1	NUM
ejpam-2996	138	5	.	.	PUNCT
ejpam-2996	139	1	if	if	SCONJ
ejpam-2996	139	2	f	f	PROPN
ejpam-2996	139	3	k	k	PROPN
ejpam-2996	139	4	k−1	k−1	PROPN
ejpam-2996	139	5	is	be	AUX
ejpam-2996	139	6	a	a	DET
ejpam-2996	139	7	generalized	generalized	ADJ
ejpam-2996	139	8	(	(	PUNCT
ejpam-2996	139	9	r	r	NOUN
ejpam-2996	139	10	;	;	PUNCT
ejpam-2996	139	11	s	s	X
ejpam-2996	139	12	,	,	PUNCT
ejpam-2996	139	13	m	m	PRON
ejpam-2996	139	14	,	,	PUNCT
ejpam-2996	139	15	ϕ)-preinvex	ϕ)-preinvex	AUX
ejpam-2996	139	16	function	function	VERB
ejpam-2996	139	17	on	on	ADP
ejpam-2996	139	18	an	an	DET
ejpam-2996	139	19	open	open	ADJ
ejpam-2996	139	20	m	m	NOUN
ejpam-2996	139	21	-	-	PUNCT
ejpam-2996	139	22	invex	invex	NOUN
ejpam-2996	139	23	set	set	VERB
ejpam-2996	139	24	k	k	PROPN
ejpam-2996	139	25	with	with	ADP
ejpam-2996	139	26	respect	respect	NOUN
ejpam-2996	139	27	to	to	ADP
ejpam-2996	139	28	η	η	PROPN
ejpam-2996	139	29	:	:	PUNCT
ejpam-2996	139	30	k	k	PROPN
ejpam-2996	139	31	×k	×k	PROPN
ejpam-2996	139	32	×	×	NOUN
ejpam-2996	139	33	(	(	PUNCT
ejpam-2996	139	34	0	0	NUM
ejpam-2996	139	35	,	,	PUNCT
ejpam-2996	139	36	1	1	NUM
ejpam-2996	139	37	]	]	X
ejpam-2996	139	38	−→	−→	ADJ
ejpam-2996	139	39	r	r	NOUN
ejpam-2996	139	40	for	for	ADP
ejpam-2996	139	41	any	any	DET
ejpam-2996	139	42	fixed	fix	VERB
ejpam-2996	139	43	s	s	NOUN
ejpam-2996	139	44	,	,	PUNCT
ejpam-2996	139	45	m	m	VERB
ejpam-2996	139	46	∈	∈	ADJ
ejpam-2996	139	47	(	(	PUNCT
ejpam-2996	139	48	0	0	NUM
ejpam-2996	139	49	,	,	PUNCT
ejpam-2996	139	50	1	1	NUM
ejpam-2996	139	51	]	]	PUNCT
ejpam-2996	139	52	,	,	PUNCT
ejpam-2996	139	53	then	then	ADV
ejpam-2996	139	54	for	for	ADP
ejpam-2996	139	55	any	any	DET
ejpam-2996	139	56	fixed	fix	VERB
ejpam-2996	139	57	p	p	NOUN
ejpam-2996	139	58	,	,	PUNCT
ejpam-2996	139	59	q	q	X
ejpam-2996	139	60	>	>	X
ejpam-2996	139	61	0,∫	0,∫	PROPN
ejpam-2996	139	62	mϕ(a)+η(ϕ(b),ϕ(a),m	mϕ(a)+η(ϕ(b),ϕ(a),m	PROPN
ejpam-2996	139	63	)	)	PUNCT
ejpam-2996	139	64	mϕ(a	mϕ(a	NOUN
ejpam-2996	139	65	)	)	PUNCT
ejpam-2996	139	66	(	(	PUNCT
ejpam-2996	139	67	x−mϕ(a))p(mϕ(a	x−mϕ(a))p(mϕ(a	PROPN
ejpam-2996	139	68	)	)	PUNCT
ejpam-2996	140	1	+	+	CCONJ
ejpam-2996	140	2	η(ϕ(b	η(ϕ(b	PROPN
ejpam-2996	140	3	)	)	PUNCT
ejpam-2996	140	4	,	,	PUNCT
ejpam-2996	140	5	ϕ(a),m)−	ϕ(a),m)−	VERB
ejpam-2996	140	6	x)qf(x)dx	x)qf(x)dx	DET
ejpam-2996	140	7	≤	≤	NUM
ejpam-2996	140	8	|η(ϕ(b	|η(ϕ(b	PROPN
ejpam-2996	140	9	)	)	PUNCT
ejpam-2996	140	10	,	,	PUNCT
ejpam-2996	140	11	ϕ(a),m)|p+q+1	ϕ(a),m)|p+q+1	X
ejpam-2996	141	1	(	(	PUNCT
ejpam-2996	141	2	r	r	NOUN
ejpam-2996	141	3	s+	s+	NOUN
ejpam-2996	141	4	r	r	NOUN
ejpam-2996	141	5	)	)	PUNCT
ejpam-2996	142	1	k−1	k−1	PROPN
ejpam-2996	142	2	k	k	NOUN
ejpam-2996	142	3	β	β	PROPN
ejpam-2996	142	4	1	1	NUM
ejpam-2996	142	5	k	k	X
ejpam-2996	142	6	(	(	PUNCT
ejpam-2996	142	7	kp+	kp+	PROPN
ejpam-2996	142	8	1	1	NUM
ejpam-2996	142	9	,	,	PUNCT
ejpam-2996	142	10	kq	kq	PROPN
ejpam-2996	142	11	+	+	CCONJ
ejpam-2996	142	12	1	1	X
ejpam-2996	142	13	)	)	PUNCT
ejpam-2996	142	14	×	×	NOUN
ejpam-2996	142	15	[	[	PUNCT
ejpam-2996	142	16	mf	mf	X
ejpam-2996	142	17	rk	rk	NOUN
ejpam-2996	142	18	k−1	k−1	PROPN
ejpam-2996	142	19	(	(	PUNCT
ejpam-2996	142	20	ϕ(a	ϕ(a	NOUN
ejpam-2996	142	21	)	)	PUNCT
ejpam-2996	142	22	)	)	PUNCT
ejpam-2996	143	1	+	+	CCONJ
ejpam-2996	143	2	f	f	X
ejpam-2996	143	3	rk	rk	NOUN
ejpam-2996	143	4	k−1	k−1	PROPN
ejpam-2996	143	5	(	(	PUNCT
ejpam-2996	143	6	ϕ(b	ϕ(b	PROPN
ejpam-2996	143	7	)	)	PUNCT
ejpam-2996	143	8	)	)	PUNCT
ejpam-2996	143	9	]	]	PUNCT
ejpam-2996	144	1	k−1	k−1	PROPN
ejpam-2996	144	2	rk	rk	INTJ
ejpam-2996	144	3	.	.	PUNCT
ejpam-2996	145	1	(	(	PUNCT
ejpam-2996	145	2	5	5	X
ejpam-2996	145	3	)	)	PUNCT
ejpam-2996	145	4	proof	proof	NOUN
ejpam-2996	145	5	.	.	PUNCT
ejpam-2996	146	1	let	let	VERB
ejpam-2996	146	2	k	k	PRON
ejpam-2996	146	3	>	>	X
ejpam-2996	146	4	1	1	NUM
ejpam-2996	146	5	and	and	CCONJ
ejpam-2996	146	6	0	0	NUM
ejpam-2996	147	1	<	<	X
ejpam-2996	147	2	r	r	NOUN
ejpam-2996	147	3	≤	≤	NUM
ejpam-2996	147	4	1	1	NUM
ejpam-2996	147	5	.	.	PUNCT
ejpam-2996	148	1	since	since	SCONJ
ejpam-2996	148	2	f	f	PROPN
ejpam-2996	148	3	k	k	PROPN
ejpam-2996	148	4	k−1	k−1	PROPN
ejpam-2996	148	5	is	be	AUX
ejpam-2996	148	6	a	a	DET
ejpam-2996	148	7	generalized	generalized	ADJ
ejpam-2996	148	8	(	(	PUNCT
ejpam-2996	148	9	r	r	NOUN
ejpam-2996	148	10	;	;	PUNCT
ejpam-2996	148	11	s	s	X
ejpam-2996	148	12	,	,	PUNCT
ejpam-2996	148	13	m	m	PRON
ejpam-2996	148	14	,	,	PUNCT
ejpam-2996	148	15	ϕ)-preinvex	ϕ)-preinvex	AUX
ejpam-2996	148	16	function	function	NOUN
ejpam-2996	148	17	on	on	ADP
ejpam-2996	148	18	k	k	PROPN
ejpam-2996	148	19	,	,	PUNCT
ejpam-2996	148	20	combining	combine	VERB
ejpam-2996	148	21	with	with	ADP
ejpam-2996	148	22	lemma	lemma	PROPN
ejpam-2996	148	23	1	1	NUM
ejpam-2996	148	24	,	,	PUNCT
ejpam-2996	148	25	hölder	hölder	NOUN
ejpam-2996	148	26	inequality	inequality	NOUN
ejpam-2996	148	27	and	and	CCONJ
ejpam-2996	148	28	minkowski	minkowski	ADJ
ejpam-2996	148	29	inequality	inequality	NOUN
ejpam-2996	148	30	for	for	ADP
ejpam-2996	148	31	all	all	DET
ejpam-2996	148	32	t	t	NOUN
ejpam-2996	148	33	∈	∈	PROPN
ejpam-2996	149	1	[	[	X
ejpam-2996	149	2	0	0	NUM
ejpam-2996	149	3	,	,	PUNCT
ejpam-2996	149	4	1	1	NUM
ejpam-2996	149	5	]	]	PUNCT
ejpam-2996	149	6	and	and	CCONJ
ejpam-2996	149	7	for	for	ADP
ejpam-2996	149	8	any	any	DET
ejpam-2996	149	9	fixed	fix	VERB
ejpam-2996	149	10	s	s	NOUN
ejpam-2996	149	11	,	,	PUNCT
ejpam-2996	149	12	m	m	VERB
ejpam-2996	149	13	∈	∈	ADJ
ejpam-2996	149	14	(	(	PUNCT
ejpam-2996	149	15	0	0	NUM
ejpam-2996	149	16	,	,	PUNCT
ejpam-2996	149	17	1	1	NUM
ejpam-2996	149	18	]	]	PUNCT
ejpam-2996	149	19	,	,	PUNCT
ejpam-2996	149	20	we	we	PRON
ejpam-2996	149	21	get∫	get∫	PROPN
ejpam-2996	149	22	mϕ(a)+η(ϕ(b),ϕ(a),m	mϕ(a)+η(ϕ(b),ϕ(a),m	PROPN
ejpam-2996	149	23	)	)	PUNCT
ejpam-2996	149	24	mϕ(a	mϕ(a	NOUN
ejpam-2996	149	25	)	)	PUNCT
ejpam-2996	149	26	(	(	PUNCT
ejpam-2996	149	27	x−mϕ(a))p(mϕ(a	x−mϕ(a))p(mϕ(a	PROPN
ejpam-2996	149	28	)	)	PUNCT
ejpam-2996	149	29	+	+	CCONJ
ejpam-2996	149	30	η(ϕ(b	η(ϕ(b	PROPN
ejpam-2996	149	31	)	)	PUNCT
ejpam-2996	149	32	,	,	PUNCT
ejpam-2996	149	33	ϕ(a),m)−	ϕ(a),m)−	VERB
ejpam-2996	149	34	x)qf(x)dx	x)qf(x)dx	DET
ejpam-2996	149	35	≤	≤	NUM
ejpam-2996	149	36	|η(ϕ(b	|η(ϕ(b	PROPN
ejpam-2996	149	37	)	)	PUNCT
ejpam-2996	149	38	,	,	PUNCT
ejpam-2996	149	39	ϕ(a),m)|p+q+1	ϕ(a),m)|p+q+1	X
ejpam-2996	150	1	[	[	X
ejpam-2996	150	2	∫	∫	X
ejpam-2996	150	3	1	1	NUM
ejpam-2996	150	4	0	0	NUM
ejpam-2996	150	5	tkp(1−	tkp(1−	PROPN
ejpam-2996	150	6	t)kqdt	t)kqdt	NOUN
ejpam-2996	150	7	]	]	PUNCT
ejpam-2996	150	8	1	1	NUM
ejpam-2996	150	9	k	k	PROPN
ejpam-2996	150	10	a.	a.	NOUN
ejpam-2996	150	11	kashuri	kashuri	PROPN
ejpam-2996	150	12	,	,	PUNCT
ejpam-2996	150	13	r.	r.	PROPN
ejpam-2996	150	14	liko	liko	PROPN
ejpam-2996	150	15	/	/	SYM
ejpam-2996	150	16	eur	eur	PROPN
ejpam-2996	150	17	.	.	PUNCT
ejpam-2996	151	1	j.	j.	PROPN
ejpam-2996	151	2	pure	pure	PROPN
ejpam-2996	151	3	appl	appl	PROPN
ejpam-2996	151	4	.	.	PROPN
ejpam-2996	151	5	math	math	PROPN
ejpam-2996	151	6	,	,	PUNCT
ejpam-2996	151	7	10	10	NUM
ejpam-2996	151	8	(	(	PUNCT
ejpam-2996	151	9	3	3	NUM
ejpam-2996	151	10	)	)	PUNCT
ejpam-2996	151	11	(	(	PUNCT
ejpam-2996	151	12	2017	2017	NUM
ejpam-2996	151	13	)	)	PUNCT
ejpam-2996	151	14	,	,	PUNCT
ejpam-2996	151	15	495	495	NUM
ejpam-2996	151	16	-	-	SYM
ejpam-2996	151	17	505	505	NUM
ejpam-2996	151	18	500	500	NUM
ejpam-2996	151	19	×	×	NOUN
ejpam-2996	152	1	[	[	X
ejpam-2996	152	2	∫	∫	PROPN
ejpam-2996	152	3	1	1	NUM
ejpam-2996	152	4	0	0	NUM
ejpam-2996	152	5	f	f	PROPN
ejpam-2996	152	6	k	k	PROPN
ejpam-2996	152	7	k−1	k−1	PROPN
ejpam-2996	152	8	(	(	PUNCT
ejpam-2996	152	9	mϕ(a	mϕ(a	NOUN
ejpam-2996	152	10	)	)	PUNCT
ejpam-2996	152	11	+	+	CCONJ
ejpam-2996	152	12	tη(ϕ(b	tη(ϕ(b	NUM
ejpam-2996	152	13	)	)	PUNCT
ejpam-2996	152	14	,	,	PUNCT
ejpam-2996	152	15	ϕ(a),m))dt	ϕ(a),m))dt	PROPN
ejpam-2996	152	16	]	]	PUNCT
ejpam-2996	153	1	k−1	k−1	PROPN
ejpam-2996	153	2	k	k	PROPN
ejpam-2996	153	3	≤	≤	PROPN
ejpam-2996	153	4	|η(ϕ(b	|η(ϕ(b	PROPN
ejpam-2996	153	5	)	)	PUNCT
ejpam-2996	153	6	,	,	PUNCT
ejpam-2996	154	1	ϕ(a),m)|p+q+1β	ϕ(a),m)|p+q+1β	PROPN
ejpam-2996	154	2	1	1	NUM
ejpam-2996	155	1	k	k	X
ejpam-2996	155	2	(	(	PUNCT
ejpam-2996	155	3	kp+	kp+	PROPN
ejpam-2996	155	4	1	1	NUM
ejpam-2996	155	5	,	,	PUNCT
ejpam-2996	155	6	kq	kq	PROPN
ejpam-2996	155	7	+	+	CCONJ
ejpam-2996	155	8	1	1	X
ejpam-2996	155	9	)	)	PUNCT
ejpam-2996	155	10	×	×	NOUN
ejpam-2996	156	1	[	[	X
ejpam-2996	156	2	∫	∫	PROPN
ejpam-2996	156	3	1	1	NUM
ejpam-2996	156	4	0	0	NUM
ejpam-2996	156	5	(	(	PUNCT
ejpam-2996	156	6	m(1−	m(1−	PROPN
ejpam-2996	156	7	t)sf	t)sf	PROPN
ejpam-2996	156	8	r(ϕ(a	r(ϕ(a	NOUN
ejpam-2996	156	9	)	)	PUNCT
ejpam-2996	156	10	)	)	PUNCT
ejpam-2996	157	1	k	k	PROPN
ejpam-2996	157	2	k−1	k−1	PROPN
ejpam-2996	157	3	+	+	CCONJ
ejpam-2996	157	4	tsf	tsf	PROPN
ejpam-2996	157	5	r(ϕ(b	r(ϕ(b	PROPN
ejpam-2996	157	6	)	)	PUNCT
ejpam-2996	157	7	)	)	PUNCT
ejpam-2996	158	1	k	k	PROPN
ejpam-2996	158	2	k−1	k−1	PROPN
ejpam-2996	158	3	)	)	PUNCT
ejpam-2996	158	4	1	1	NUM
ejpam-2996	158	5	r	r	NOUN
ejpam-2996	158	6	dt	dt	NOUN
ejpam-2996	158	7	]	]	X
ejpam-2996	158	8	k−1	k−1	PROPN
ejpam-2996	158	9	k	k	PROPN
ejpam-2996	158	10	≤	≤	PROPN
ejpam-2996	158	11	|η(ϕ(b	|η(ϕ(b	PROPN
ejpam-2996	158	12	)	)	PUNCT
ejpam-2996	158	13	,	,	PUNCT
ejpam-2996	159	1	ϕ(a),m)|p+q+1β	ϕ(a),m)|p+q+1β	PROPN
ejpam-2996	159	2	1	1	NUM
ejpam-2996	159	3	k	k	X
ejpam-2996	159	4	(	(	PUNCT
ejpam-2996	159	5	kp+	kp+	PROPN
ejpam-2996	159	6	1	1	NUM
ejpam-2996	159	7	,	,	PUNCT
ejpam-2996	159	8	kq	kq	PROPN
ejpam-2996	159	9	+	+	CCONJ
ejpam-2996	159	10	1	1	X
ejpam-2996	159	11	)	)	PUNCT
ejpam-2996	159	12	×	×	NOUN
ejpam-2996	160	1	[	[	X
ejpam-2996	160	2	(	(	PUNCT
ejpam-2996	160	3	∫	∫	PROPN
ejpam-2996	160	4	1	1	NUM
ejpam-2996	160	5	0	0	NUM
ejpam-2996	160	6	m	m	VERB
ejpam-2996	160	7	1	1	NUM
ejpam-2996	160	8	r	r	NOUN
ejpam-2996	160	9	(	(	PUNCT
ejpam-2996	160	10	1−	1−	NUM
ejpam-2996	160	11	t	t	PROPN
ejpam-2996	160	12	)	)	PUNCT
ejpam-2996	160	13	s	s	PART
ejpam-2996	160	14	r	r	NOUN
ejpam-2996	160	15	f	f	PROPN
ejpam-2996	160	16	k	k	PROPN
ejpam-2996	160	17	k−1	k−1	PROPN
ejpam-2996	160	18	(	(	PUNCT
ejpam-2996	160	19	ϕ(a))dt	ϕ(a))dt	PROPN
ejpam-2996	160	20	)	)	PUNCT
ejpam-2996	160	21	r	r	NOUN
ejpam-2996	160	22	+	+	CCONJ
ejpam-2996	160	23	(	(	PUNCT
ejpam-2996	160	24	∫	∫	PROPN
ejpam-2996	160	25	1	1	NUM
ejpam-2996	160	26	0	0	NUM
ejpam-2996	160	27	t	t	NOUN
ejpam-2996	160	28	s	s	NOUN
ejpam-2996	160	29	r	r	NOUN
ejpam-2996	160	30	f	f	PROPN
ejpam-2996	160	31	k	k	PROPN
ejpam-2996	160	32	k−1	k−1	PROPN
ejpam-2996	160	33	(	(	PUNCT
ejpam-2996	160	34	ϕ(b))dt	ϕ(b))dt	NOUN
ejpam-2996	160	35	)	)	PUNCT
ejpam-2996	161	1	r	r	NOUN
ejpam-2996	161	2	]	]	PUNCT
ejpam-2996	161	3	k−1	k−1	PROPN
ejpam-2996	161	4	rk	rk	PROPN
ejpam-2996	161	5	=	=	SYM
ejpam-2996	161	6	|η(ϕ(b	|η(ϕ(b	PROPN
ejpam-2996	161	7	)	)	PUNCT
ejpam-2996	161	8	,	,	PUNCT
ejpam-2996	161	9	ϕ(a),m)|p+q+1	ϕ(a),m)|p+q+1	X
ejpam-2996	162	1	(	(	PUNCT
ejpam-2996	162	2	r	r	NOUN
ejpam-2996	162	3	s+	s+	NOUN
ejpam-2996	162	4	r	r	NOUN
ejpam-2996	162	5	)	)	PUNCT
ejpam-2996	163	1	k−1	k−1	PROPN
ejpam-2996	163	2	k	k	NOUN
ejpam-2996	163	3	β	β	PROPN
ejpam-2996	163	4	1	1	NUM
ejpam-2996	163	5	k	k	X
ejpam-2996	163	6	(	(	PUNCT
ejpam-2996	163	7	kp+	kp+	PROPN
ejpam-2996	163	8	1	1	NUM
ejpam-2996	163	9	,	,	PUNCT
ejpam-2996	163	10	kq	kq	PROPN
ejpam-2996	163	11	+	+	CCONJ
ejpam-2996	163	12	1	1	X
ejpam-2996	163	13	)	)	PUNCT
ejpam-2996	163	14	×	×	NOUN
ejpam-2996	163	15	[	[	PUNCT
ejpam-2996	163	16	mf	mf	X
ejpam-2996	163	17	rk	rk	NOUN
ejpam-2996	163	18	k−1	k−1	PROPN
ejpam-2996	163	19	(	(	PUNCT
ejpam-2996	163	20	ϕ(a	ϕ(a	NOUN
ejpam-2996	163	21	)	)	PUNCT
ejpam-2996	163	22	)	)	PUNCT
ejpam-2996	164	1	+	+	CCONJ
ejpam-2996	165	1	f	f	X
ejpam-2996	165	2	rk	rk	NOUN
ejpam-2996	165	3	k−1	k−1	PROPN
ejpam-2996	165	4	(	(	PUNCT
ejpam-2996	165	5	ϕ(b	ϕ(b	PROPN
ejpam-2996	165	6	)	)	PUNCT
ejpam-2996	165	7	)	)	PUNCT
ejpam-2996	165	8	]	]	PUNCT
ejpam-2996	166	1	k−1	k−1	PROPN
ejpam-2996	166	2	rk	rk	INTJ
ejpam-2996	166	3	.	.	PUNCT
ejpam-2996	167	1	corollary	corollary	ADJ
ejpam-2996	167	2	1	1	NUM
ejpam-2996	167	3	.	.	PUNCT
ejpam-2996	168	1	under	under	ADP
ejpam-2996	168	2	the	the	DET
ejpam-2996	168	3	same	same	ADJ
ejpam-2996	168	4	conditions	condition	NOUN
ejpam-2996	168	5	as	as	ADP
ejpam-2996	168	6	in	in	ADP
ejpam-2996	168	7	theorem	theorem	NOUN
ejpam-2996	168	8	2	2	NUM
ejpam-2996	168	9	for	for	ADP
ejpam-2996	168	10	r	r	NOUN
ejpam-2996	168	11	=	=	SYM
ejpam-2996	168	12	1	1	NUM
ejpam-2996	168	13	,	,	PUNCT
ejpam-2996	168	14	we	we	PRON
ejpam-2996	168	15	get	get	AUX
ejpam-2996	168	16	(	(	PUNCT
ejpam-2996	168	17	see	see	VERB
ejpam-2996	168	18	[	[	X
ejpam-2996	168	19	1	1	NUM
ejpam-2996	168	20	]	]	PUNCT
ejpam-2996	168	21	,	,	PUNCT
ejpam-2996	168	22	theorem	theorem	VERB
ejpam-2996	168	23	2.2	2.2	NUM
ejpam-2996	168	24	)	)	PUNCT
ejpam-2996	168	25	.	.	PUNCT
ejpam-2996	169	1	theorem	theorem	NOUN
ejpam-2996	169	2	3	3	X
ejpam-2996	169	3	.	.	PUNCT
ejpam-2996	170	1	let	let	VERB
ejpam-2996	170	2	ϕ	ϕ	NOUN
ejpam-2996	170	3	:	:	PUNCT
ejpam-2996	171	1	i	i	PRON
ejpam-2996	171	2	−→	−→	VERB
ejpam-2996	171	3	k	k	X
ejpam-2996	171	4	be	be	AUX
ejpam-2996	171	5	a	a	DET
ejpam-2996	171	6	continuous	continuous	ADJ
ejpam-2996	171	7	increasing	increase	VERB
ejpam-2996	171	8	function	function	NOUN
ejpam-2996	171	9	.	.	PUNCT
ejpam-2996	172	1	assume	assume	VERB
ejpam-2996	172	2	that	that	SCONJ
ejpam-2996	172	3	f	f	X
ejpam-2996	172	4	:	:	PUNCT
ejpam-2996	173	1	k	k	X
ejpam-2996	173	2	=	=	PUNCT
ejpam-2996	174	1	[	[	X
ejpam-2996	174	2	mϕ(a),mϕ(a	mϕ(a),mϕ(a	NOUN
ejpam-2996	174	3	)	)	PUNCT
ejpam-2996	174	4	+	+	NUM
ejpam-2996	174	5	η(ϕ(b	η(ϕ(b	PROPN
ejpam-2996	174	6	)	)	PUNCT
ejpam-2996	174	7	,	,	PUNCT
ejpam-2996	174	8	ϕ(a),m	ϕ(a),m	ADJ
ejpam-2996	174	9	)	)	PUNCT
ejpam-2996	174	10	]	]	PUNCT
ejpam-2996	175	1	−→	−→	NOUN
ejpam-2996	175	2	(	(	PUNCT
ejpam-2996	175	3	0,∞	0,∞	NOUN
ejpam-2996	175	4	)	)	PUNCT
ejpam-2996	175	5	is	be	AUX
ejpam-2996	175	6	a	a	DET
ejpam-2996	175	7	continuous	continuous	ADJ
ejpam-2996	175	8	function	function	NOUN
ejpam-2996	175	9	on	on	ADP
ejpam-2996	175	10	the	the	DET
ejpam-2996	175	11	interval	interval	NOUN
ejpam-2996	175	12	of	of	ADP
ejpam-2996	175	13	real	real	ADJ
ejpam-2996	175	14	numbers	number	NOUN
ejpam-2996	175	15	k	k	X
ejpam-2996	175	16	◦	◦	NOUN
ejpam-2996	175	17	with	with	ADP
ejpam-2996	175	18	mϕ(a	mϕ(a	NOUN
ejpam-2996	175	19	)	)	PUNCT
ejpam-2996	175	20	<	<	X
ejpam-2996	175	21	mϕ(a	mϕ(a	NOUN
ejpam-2996	175	22	)	)	PUNCT
ejpam-2996	176	1	+	+	CCONJ
ejpam-2996	176	2	η(ϕ(b	η(ϕ(b	PROPN
ejpam-2996	176	3	)	)	PUNCT
ejpam-2996	176	4	,	,	PUNCT
ejpam-2996	176	5	ϕ(a),m	ϕ(a),m	ADJ
ejpam-2996	176	6	)	)	PUNCT
ejpam-2996	176	7	.	.	PUNCT
ejpam-2996	177	1	let	let	VERB
ejpam-2996	177	2	l	l	NOUN
ejpam-2996	177	3	≥	≥	NUM
ejpam-2996	177	4	1	1	NUM
ejpam-2996	177	5	and	and	CCONJ
ejpam-2996	177	6	0	0	NUM
ejpam-2996	177	7	<	<	X
ejpam-2996	177	8	r	r	NOUN
ejpam-2996	177	9	≤	≤	NUM
ejpam-2996	177	10	1	1	NUM
ejpam-2996	177	11	.	.	PUNCT
ejpam-2996	178	1	if	if	SCONJ
ejpam-2996	178	2	f	f	PROPN
ejpam-2996	178	3	l	l	NOUN
ejpam-2996	178	4	is	be	AUX
ejpam-2996	178	5	a	a	DET
ejpam-2996	178	6	generalized	generalized	ADJ
ejpam-2996	178	7	(	(	PUNCT
ejpam-2996	178	8	r	r	NOUN
ejpam-2996	178	9	;	;	PUNCT
ejpam-2996	178	10	s	s	X
ejpam-2996	178	11	,	,	PUNCT
ejpam-2996	178	12	m	m	PRON
ejpam-2996	178	13	,	,	PUNCT
ejpam-2996	178	14	ϕ)-preinvex	ϕ)-preinvex	AUX
ejpam-2996	178	15	function	function	VERB
ejpam-2996	178	16	on	on	ADP
ejpam-2996	178	17	an	an	DET
ejpam-2996	178	18	open	open	ADJ
ejpam-2996	178	19	m	m	NOUN
ejpam-2996	178	20	-	-	PUNCT
ejpam-2996	178	21	invex	invex	NOUN
ejpam-2996	178	22	set	set	VERB
ejpam-2996	178	23	k	k	PROPN
ejpam-2996	178	24	with	with	ADP
ejpam-2996	178	25	respect	respect	NOUN
ejpam-2996	178	26	to	to	ADP
ejpam-2996	178	27	η	η	PROPN
ejpam-2996	178	28	:	:	PUNCT
ejpam-2996	178	29	k	k	PROPN
ejpam-2996	178	30	×k	×k	PROPN
ejpam-2996	178	31	×	×	NOUN
ejpam-2996	178	32	(	(	PUNCT
ejpam-2996	178	33	0	0	NUM
ejpam-2996	178	34	,	,	PUNCT
ejpam-2996	178	35	1	1	NUM
ejpam-2996	178	36	]	]	X
ejpam-2996	178	37	−→	−→	ADJ
ejpam-2996	178	38	r	r	NOUN
ejpam-2996	178	39	for	for	ADP
ejpam-2996	178	40	any	any	DET
ejpam-2996	178	41	fixed	fix	VERB
ejpam-2996	178	42	s	s	NOUN
ejpam-2996	178	43	,	,	PUNCT
ejpam-2996	178	44	m	m	VERB
ejpam-2996	178	45	∈	∈	ADJ
ejpam-2996	178	46	(	(	PUNCT
ejpam-2996	178	47	0	0	NUM
ejpam-2996	178	48	,	,	PUNCT
ejpam-2996	178	49	1	1	NUM
ejpam-2996	178	50	]	]	PUNCT
ejpam-2996	178	51	,	,	PUNCT
ejpam-2996	178	52	then	then	ADV
ejpam-2996	178	53	for	for	ADP
ejpam-2996	178	54	any	any	DET
ejpam-2996	178	55	fixed	fix	VERB
ejpam-2996	178	56	p	p	NOUN
ejpam-2996	178	57	,	,	PUNCT
ejpam-2996	178	58	q	q	X
ejpam-2996	178	59	>	>	X
ejpam-2996	178	60	0,∫	0,∫	PROPN
ejpam-2996	178	61	mϕ(a)+η(ϕ(b),ϕ(a),m	mϕ(a)+η(ϕ(b),ϕ(a),m	PROPN
ejpam-2996	178	62	)	)	PUNCT
ejpam-2996	178	63	mϕ(a	mϕ(a	NOUN
ejpam-2996	178	64	)	)	PUNCT
ejpam-2996	178	65	(	(	PUNCT
ejpam-2996	178	66	x−mϕ(a))p(mϕ(a	x−mϕ(a))p(mϕ(a	PROPN
ejpam-2996	178	67	)	)	PUNCT
ejpam-2996	179	1	+	+	CCONJ
ejpam-2996	179	2	η(ϕ(b	η(ϕ(b	PROPN
ejpam-2996	179	3	)	)	PUNCT
ejpam-2996	179	4	,	,	PUNCT
ejpam-2996	179	5	ϕ(a),m)−	ϕ(a),m)−	VERB
ejpam-2996	179	6	x)qf(x)dx	x)qf(x)dx	DET
ejpam-2996	179	7	≤	≤	NUM
ejpam-2996	179	8	|η(ϕ(b	|η(ϕ(b	PROPN
ejpam-2996	179	9	)	)	PUNCT
ejpam-2996	179	10	,	,	PUNCT
ejpam-2996	179	11	ϕ(a),m)|p+q+1β	ϕ(a),m)|p+q+1β	PROPN
ejpam-2996	179	12	l−1	l−1	PROPN
ejpam-2996	179	13	l	l	NOUN
ejpam-2996	179	14	(	(	PUNCT
ejpam-2996	179	15	p+	p+	NOUN
ejpam-2996	179	16	1	1	NUM
ejpam-2996	179	17	,	,	PUNCT
ejpam-2996	179	18	q	q	X
ejpam-2996	180	1	+	+	NUM
ejpam-2996	180	2	1	1	X
ejpam-2996	180	3	)	)	PUNCT
ejpam-2996	180	4	×	×	NOUN
ejpam-2996	180	5	[	[	PUNCT
ejpam-2996	180	6	mf	mf	X
ejpam-2996	180	7	rl(ϕ(a))βr	rl(ϕ(a))βr	NOUN
ejpam-2996	180	8	(	(	PUNCT
ejpam-2996	180	9	p+	p+	NOUN
ejpam-2996	180	10	1	1	NUM
ejpam-2996	180	11	,	,	PUNCT
ejpam-2996	180	12	q	q	X
ejpam-2996	181	1	+	+	NUM
ejpam-2996	181	2	s	s	NOUN
ejpam-2996	181	3	r	r	NOUN
ejpam-2996	181	4	+	+	NOUN
ejpam-2996	181	5	1	1	NUM
ejpam-2996	181	6	)	)	PUNCT
ejpam-2996	182	1	+	+	CCONJ
ejpam-2996	182	2	f	f	X
ejpam-2996	182	3	rl(ϕ(b))βr	rl(ϕ(b))βr	NOUN
ejpam-2996	182	4	(	(	PUNCT
ejpam-2996	182	5	p+	p+	NOUN
ejpam-2996	182	6	s	s	NOUN
ejpam-2996	182	7	r	r	NOUN
ejpam-2996	182	8	+	+	NUM
ejpam-2996	182	9	1	1	NUM
ejpam-2996	182	10	,	,	PUNCT
ejpam-2996	182	11	q	q	X
ejpam-2996	182	12	+	+	NOUN
ejpam-2996	182	13	1	1	NUM
ejpam-2996	182	14	)	)	PUNCT
ejpam-2996	182	15	]	]	PUNCT
ejpam-2996	182	16	1	1	NUM
ejpam-2996	182	17	rl	rl	X
ejpam-2996	182	18	.	.	PUNCT
ejpam-2996	183	1	(	(	PUNCT
ejpam-2996	183	2	6	6	X
ejpam-2996	183	3	)	)	PUNCT
ejpam-2996	183	4	proof	proof	NOUN
ejpam-2996	183	5	.	.	PUNCT
ejpam-2996	184	1	let	let	VERB
ejpam-2996	184	2	l	l	NOUN
ejpam-2996	184	3	≥	≥	NUM
ejpam-2996	184	4	1	1	NUM
ejpam-2996	184	5	and	and	CCONJ
ejpam-2996	184	6	0	0	NUM
ejpam-2996	184	7	<	<	X
ejpam-2996	184	8	r	r	NOUN
ejpam-2996	184	9	≤	≤	NUM
ejpam-2996	184	10	1	1	NUM
ejpam-2996	184	11	.	.	PUNCT
ejpam-2996	185	1	since	since	SCONJ
ejpam-2996	185	2	f	f	PROPN
ejpam-2996	185	3	l	l	PROPN
ejpam-2996	185	4	is	be	AUX
ejpam-2996	185	5	a	a	DET
ejpam-2996	185	6	generalized	generalized	ADJ
ejpam-2996	185	7	(	(	PUNCT
ejpam-2996	185	8	r	r	NOUN
ejpam-2996	185	9	;	;	PUNCT
ejpam-2996	185	10	s	s	X
ejpam-2996	185	11	,	,	PUNCT
ejpam-2996	185	12	m	m	PRON
ejpam-2996	185	13	,	,	PUNCT
ejpam-2996	185	14	ϕ)-preinvex	ϕ)-preinvex	AUX
ejpam-2996	185	15	function	function	NOUN
ejpam-2996	185	16	on	on	ADP
ejpam-2996	185	17	k	k	PROPN
ejpam-2996	185	18	,	,	PUNCT
ejpam-2996	185	19	combining	combine	VERB
ejpam-2996	185	20	with	with	ADP
ejpam-2996	185	21	lemma	lemma	PROPN
ejpam-2996	185	22	1	1	NUM
ejpam-2996	185	23	,	,	PUNCT
ejpam-2996	185	24	the	the	DET
ejpam-2996	185	25	well	well	ADV
ejpam-2996	185	26	-	-	PUNCT
ejpam-2996	185	27	known	know	VERB
ejpam-2996	185	28	power	power	NOUN
ejpam-2996	185	29	mean	mean	VERB
ejpam-2996	185	30	inequality	inequality	NOUN
ejpam-2996	185	31	and	and	CCONJ
ejpam-2996	185	32	minkowski	minkowski	ADJ
ejpam-2996	185	33	inequality	inequality	NOUN
ejpam-2996	185	34	for	for	ADP
ejpam-2996	185	35	all	all	DET
ejpam-2996	185	36	t	t	NOUN
ejpam-2996	185	37	∈	∈	PROPN
ejpam-2996	186	1	[	[	X
ejpam-2996	186	2	0	0	NUM
ejpam-2996	186	3	,	,	PUNCT
ejpam-2996	186	4	1	1	NUM
ejpam-2996	186	5	]	]	PUNCT
ejpam-2996	186	6	and	and	CCONJ
ejpam-2996	186	7	for	for	ADP
ejpam-2996	186	8	any	any	DET
ejpam-2996	186	9	fixed	fix	VERB
ejpam-2996	186	10	s	s	NOUN
ejpam-2996	186	11	,	,	PUNCT
ejpam-2996	186	12	m	m	VERB
ejpam-2996	186	13	∈	∈	ADJ
ejpam-2996	186	14	(	(	PUNCT
ejpam-2996	186	15	0	0	NUM
ejpam-2996	186	16	,	,	PUNCT
ejpam-2996	186	17	1	1	NUM
ejpam-2996	186	18	]	]	PUNCT
ejpam-2996	186	19	,	,	PUNCT
ejpam-2996	186	20	we	we	PRON
ejpam-2996	186	21	get∫	get∫	PROPN
ejpam-2996	186	22	mϕ(a)+η(ϕ(b),ϕ(a),m	mϕ(a)+η(ϕ(b),ϕ(a),m	PROPN
ejpam-2996	186	23	)	)	PUNCT
ejpam-2996	186	24	mϕ(a	mϕ(a	NOUN
ejpam-2996	186	25	)	)	PUNCT
ejpam-2996	186	26	(	(	PUNCT
ejpam-2996	186	27	x−mϕ(a))p(mϕ(a	x−mϕ(a))p(mϕ(a	PROPN
ejpam-2996	186	28	)	)	PUNCT
ejpam-2996	186	29	+	+	CCONJ
ejpam-2996	186	30	η(ϕ(b	η(ϕ(b	PROPN
ejpam-2996	186	31	)	)	PUNCT
ejpam-2996	186	32	,	,	PUNCT
ejpam-2996	186	33	ϕ(a),m)−	ϕ(a),m)−	VERB
ejpam-2996	187	1	x)qf(x)dx	x)qf(x)dx	PRON
ejpam-2996	187	2	=	=	PUNCT
ejpam-2996	187	3	η(ϕ(b	η(ϕ(b	PROPN
ejpam-2996	187	4	)	)	PUNCT
ejpam-2996	187	5	,	,	PUNCT
ejpam-2996	187	6	ϕ(a),m)p+q+1	ϕ(a),m)p+q+1	PROPN
ejpam-2996	187	7	a.	a.	NOUN
ejpam-2996	187	8	kashuri	kashuri	PROPN
ejpam-2996	187	9	,	,	PUNCT
ejpam-2996	187	10	r.	r.	PROPN
ejpam-2996	187	11	liko	liko	PROPN
ejpam-2996	187	12	/	/	SYM
ejpam-2996	187	13	eur	eur	PROPN
ejpam-2996	187	14	.	.	PUNCT
ejpam-2996	188	1	j.	j.	PROPN
ejpam-2996	188	2	pure	pure	PROPN
ejpam-2996	188	3	appl	appl	PROPN
ejpam-2996	188	4	.	.	PROPN
ejpam-2996	188	5	math	math	PROPN
ejpam-2996	188	6	,	,	PUNCT
ejpam-2996	188	7	10	10	NUM
ejpam-2996	188	8	(	(	PUNCT
ejpam-2996	188	9	3	3	NUM
ejpam-2996	188	10	)	)	PUNCT
ejpam-2996	188	11	(	(	PUNCT
ejpam-2996	188	12	2017	2017	NUM
ejpam-2996	188	13	)	)	PUNCT
ejpam-2996	188	14	,	,	PUNCT
ejpam-2996	188	15	495	495	NUM
ejpam-2996	188	16	-	-	SYM
ejpam-2996	188	17	505	505	NUM
ejpam-2996	188	18	501	501	NUM
ejpam-2996	188	19	×	×	NOUN
ejpam-2996	188	20	∫	∫	NOUN
ejpam-2996	188	21	1	1	NUM
ejpam-2996	188	22	0	0	NUM
ejpam-2996	188	23	[	[	PUNCT
ejpam-2996	188	24	tp(1−	tp(1−	PROPN
ejpam-2996	188	25	t)q	t)q	PUNCT
ejpam-2996	188	26	]	]	PUNCT
ejpam-2996	189	1	l−1	l−1	NOUN
ejpam-2996	189	2	l	l	NOUN
ejpam-2996	189	3	[	[	PUNCT
ejpam-2996	189	4	tp(1−	tp(1−	PROPN
ejpam-2996	189	5	t)q	t)q	PUNCT
ejpam-2996	189	6	]	]	PUNCT
ejpam-2996	189	7	1	1	NUM
ejpam-2996	189	8	l	l	NOUN
ejpam-2996	189	9	f(mϕ(a	f(mϕ(a	PROPN
ejpam-2996	189	10	)	)	PUNCT
ejpam-2996	189	11	+	+	CCONJ
ejpam-2996	189	12	tη(ϕ(b	tη(ϕ(b	NUM
ejpam-2996	189	13	)	)	PUNCT
ejpam-2996	189	14	,	,	PUNCT
ejpam-2996	189	15	ϕ(a),m))dt	ϕ(a),m))dt	PROPN
ejpam-2996	189	16	≤	≤	NUM
ejpam-2996	189	17	|η(ϕ(b	|η(ϕ(b	PROPN
ejpam-2996	189	18	)	)	PUNCT
ejpam-2996	189	19	,	,	PUNCT
ejpam-2996	189	20	ϕ(a),m)|p+q+1	ϕ(a),m)|p+q+1	X
ejpam-2996	190	1	[	[	X
ejpam-2996	190	2	∫	∫	X
ejpam-2996	190	3	1	1	NUM
ejpam-2996	190	4	0	0	NUM
ejpam-2996	190	5	tp(1−	tp(1−	PROPN
ejpam-2996	190	6	t)qdt	t)qdt	NOUN
ejpam-2996	190	7	]	]	PUNCT
ejpam-2996	190	8	l−1	l−1	NOUN
ejpam-2996	190	9	l	l	NOUN
ejpam-2996	190	10	×	×	NOUN
ejpam-2996	191	1	[	[	X
ejpam-2996	191	2	∫	∫	PROPN
ejpam-2996	191	3	1	1	NUM
ejpam-2996	191	4	0	0	NUM
ejpam-2996	191	5	tp(1−	tp(1−	PROPN
ejpam-2996	192	1	t)qf	t)qf	PROPN
ejpam-2996	192	2	l(mϕ(a	l(mϕ(a	PROPN
ejpam-2996	192	3	)	)	PUNCT
ejpam-2996	193	1	+	+	CCONJ
ejpam-2996	193	2	tη(ϕ(b	tη(ϕ(b	NUM
ejpam-2996	193	3	)	)	PUNCT
ejpam-2996	193	4	,	,	PUNCT
ejpam-2996	193	5	ϕ(a),m))dt	ϕ(a),m))dt	NOUN
ejpam-2996	193	6	]	]	PUNCT
ejpam-2996	193	7	1	1	NUM
ejpam-2996	193	8	l	l	NOUN
ejpam-2996	193	9	≤	≤	NUM
ejpam-2996	193	10	|η(ϕ(b	|η(ϕ(b	NOUN
ejpam-2996	193	11	)	)	PUNCT
ejpam-2996	193	12	,	,	PUNCT
ejpam-2996	194	1	ϕ(a),m)|p+q+1β	ϕ(a),m)|p+q+1β	PROPN
ejpam-2996	194	2	l−1	l−1	PROPN
ejpam-2996	194	3	l	l	NOUN
ejpam-2996	194	4	(	(	PUNCT
ejpam-2996	194	5	p+	p+	NOUN
ejpam-2996	194	6	1	1	NUM
ejpam-2996	194	7	,	,	PUNCT
ejpam-2996	194	8	q	q	X
ejpam-2996	195	1	+	+	NUM
ejpam-2996	195	2	1	1	X
ejpam-2996	195	3	)	)	PUNCT
ejpam-2996	195	4	×	×	NOUN
ejpam-2996	196	1	[	[	X
ejpam-2996	196	2	∫	∫	PROPN
ejpam-2996	196	3	1	1	NUM
ejpam-2996	196	4	0	0	NUM
ejpam-2996	196	5	tp(1−	tp(1−	NOUN
ejpam-2996	196	6	t)q	t)q	PUNCT
ejpam-2996	196	7	(	(	PUNCT
ejpam-2996	196	8	m(1−	m(1−	PROPN
ejpam-2996	196	9	t)sf	t)sf	PROPN
ejpam-2996	196	10	r(ϕ(a))l	r(ϕ(a))l	NOUN
ejpam-2996	196	11	+	+	CCONJ
ejpam-2996	196	12	tsf	tsf	NOUN
ejpam-2996	196	13	r(ϕ(b))l	r(ϕ(b))l	NOUN
ejpam-2996	196	14	)	)	PUNCT
ejpam-2996	196	15	1	1	NUM
ejpam-2996	196	16	r	r	NOUN
ejpam-2996	196	17	dt	dt	NOUN
ejpam-2996	196	18	]	]	PUNCT
ejpam-2996	196	19	1	1	NUM
ejpam-2996	196	20	l	l	NOUN
ejpam-2996	196	21	≤	≤	NUM
ejpam-2996	196	22	|η(ϕ(b	|η(ϕ(b	NOUN
ejpam-2996	196	23	)	)	PUNCT
ejpam-2996	196	24	,	,	PUNCT
ejpam-2996	196	25	ϕ(a),m)|p+q+1β	ϕ(a),m)|p+q+1β	PROPN
ejpam-2996	196	26	l−1	l−1	PROPN
ejpam-2996	196	27	l	l	NOUN
ejpam-2996	196	28	(	(	PUNCT
ejpam-2996	196	29	p+	p+	NOUN
ejpam-2996	196	30	1	1	NUM
ejpam-2996	196	31	,	,	PUNCT
ejpam-2996	196	32	q	q	X
ejpam-2996	197	1	+	+	NUM
ejpam-2996	197	2	1	1	X
ejpam-2996	197	3	)	)	PUNCT
ejpam-2996	197	4	×	×	NOUN
ejpam-2996	198	1	[	[	X
ejpam-2996	198	2	(	(	PUNCT
ejpam-2996	198	3	∫	∫	PROPN
ejpam-2996	198	4	1	1	NUM
ejpam-2996	198	5	0	0	NUM
ejpam-2996	198	6	m	m	VERB
ejpam-2996	198	7	1	1	NUM
ejpam-2996	198	8	r	r	NOUN
ejpam-2996	198	9	tp(1−	tp(1−	NOUN
ejpam-2996	198	10	t)q+	t)q+	NOUN
ejpam-2996	198	11	s	s	NOUN
ejpam-2996	198	12	r	r	NOUN
ejpam-2996	198	13	f	f	NOUN
ejpam-2996	198	14	l(ϕ(a))dt	l(ϕ(a))dt	NOUN
ejpam-2996	198	15	)	)	PUNCT
ejpam-2996	199	1	r	r	NOUN
ejpam-2996	199	2	+	+	CCONJ
ejpam-2996	199	3	(	(	PUNCT
ejpam-2996	199	4	∫	∫	PROPN
ejpam-2996	199	5	1	1	NUM
ejpam-2996	199	6	0	0	NUM
ejpam-2996	199	7	tp+	tp+	NOUN
ejpam-2996	199	8	s	s	PART
ejpam-2996	199	9	r	r	NOUN
ejpam-2996	199	10	(	(	PUNCT
ejpam-2996	199	11	1−	1−	NUM
ejpam-2996	199	12	t)qf	t)qf	PROPN
ejpam-2996	199	13	l(ϕ(b))dt	l(ϕ(b))dt	NOUN
ejpam-2996	199	14	)	)	PUNCT
ejpam-2996	200	1	r	r	NOUN
ejpam-2996	200	2	]	]	PUNCT
ejpam-2996	200	3	1	1	NUM
ejpam-2996	200	4	rl	rl	PROPN
ejpam-2996	200	5	=	=	SYM
ejpam-2996	200	6	|η(ϕ(b	|η(ϕ(b	PROPN
ejpam-2996	200	7	)	)	PUNCT
ejpam-2996	200	8	,	,	PUNCT
ejpam-2996	200	9	ϕ(a),m)|p+q+1β	ϕ(a),m)|p+q+1β	PROPN
ejpam-2996	200	10	l−1	l−1	PROPN
ejpam-2996	200	11	l	l	NOUN
ejpam-2996	200	12	(	(	PUNCT
ejpam-2996	200	13	p+	p+	NOUN
ejpam-2996	200	14	1	1	NUM
ejpam-2996	200	15	,	,	PUNCT
ejpam-2996	200	16	q	q	X
ejpam-2996	201	1	+	+	NUM
ejpam-2996	201	2	1	1	X
ejpam-2996	201	3	)	)	PUNCT
ejpam-2996	201	4	×	×	NOUN
ejpam-2996	201	5	[	[	PUNCT
ejpam-2996	201	6	mf	mf	X
ejpam-2996	201	7	rl(ϕ(a))βr	rl(ϕ(a))βr	NOUN
ejpam-2996	201	8	(	(	PUNCT
ejpam-2996	201	9	p+	p+	NOUN
ejpam-2996	201	10	1	1	NUM
ejpam-2996	201	11	,	,	PUNCT
ejpam-2996	201	12	q	q	X
ejpam-2996	202	1	+	+	NUM
ejpam-2996	202	2	s	s	NOUN
ejpam-2996	202	3	r	r	NOUN
ejpam-2996	202	4	+	+	NOUN
ejpam-2996	202	5	1	1	NUM
ejpam-2996	202	6	)	)	PUNCT
ejpam-2996	203	1	+	+	CCONJ
ejpam-2996	203	2	f	f	X
ejpam-2996	203	3	rl(ϕ(b))βr	rl(ϕ(b))βr	NOUN
ejpam-2996	203	4	(	(	PUNCT
ejpam-2996	203	5	p+	p+	NOUN
ejpam-2996	203	6	s	s	NOUN
ejpam-2996	203	7	r	r	NOUN
ejpam-2996	203	8	+	+	NUM
ejpam-2996	203	9	1	1	NUM
ejpam-2996	203	10	,	,	PUNCT
ejpam-2996	203	11	q	q	X
ejpam-2996	203	12	+	+	NOUN
ejpam-2996	203	13	1	1	NUM
ejpam-2996	203	14	)	)	PUNCT
ejpam-2996	203	15	]	]	PUNCT
ejpam-2996	203	16	1	1	NUM
ejpam-2996	203	17	rl	rl	X
ejpam-2996	203	18	.	.	PUNCT
ejpam-2996	203	19	corollary	corollary	ADJ
ejpam-2996	203	20	2	2	NUM
ejpam-2996	203	21	.	.	PUNCT
ejpam-2996	204	1	under	under	ADP
ejpam-2996	204	2	the	the	DET
ejpam-2996	204	3	same	same	ADJ
ejpam-2996	204	4	conditions	condition	NOUN
ejpam-2996	204	5	as	as	ADP
ejpam-2996	204	6	in	in	ADP
ejpam-2996	204	7	theorem	theorem	NOUN
ejpam-2996	204	8	3	3	NUM
ejpam-2996	204	9	for	for	ADP
ejpam-2996	204	10	r	r	NOUN
ejpam-2996	204	11	=	=	SYM
ejpam-2996	204	12	1	1	NUM
ejpam-2996	204	13	,	,	PUNCT
ejpam-2996	204	14	we	we	PRON
ejpam-2996	204	15	get	get	AUX
ejpam-2996	204	16	(	(	PUNCT
ejpam-2996	204	17	see	see	VERB
ejpam-2996	204	18	[	[	X
ejpam-2996	204	19	1	1	NUM
ejpam-2996	204	20	]	]	PUNCT
ejpam-2996	204	21	,	,	PUNCT
ejpam-2996	204	22	theorem	theorem	VERB
ejpam-2996	204	23	2.3	2.3	NUM
ejpam-2996	204	24	)	)	PUNCT
ejpam-2996	204	25	.	.	PUNCT
ejpam-2996	205	1	3	3	X
ejpam-2996	205	2	.	.	X
ejpam-2996	205	3	hermite	hermite	PROPN
ejpam-2996	205	4	-	-	PUNCT
ejpam-2996	205	5	hadamard	hadamard	ADJ
ejpam-2996	205	6	type	type	NOUN
ejpam-2996	205	7	fractional	fractional	ADJ
ejpam-2996	205	8	integral	integral	ADJ
ejpam-2996	205	9	inequalities	inequality	NOUN
ejpam-2996	205	10	for	for	ADP
ejpam-2996	205	11	generalized	generalized	ADJ
ejpam-2996	205	12	(	(	PUNCT
ejpam-2996	205	13	r	r	NOUN
ejpam-2996	205	14	;	;	PUNCT
ejpam-2996	205	15	s	s	X
ejpam-2996	205	16	,	,	PUNCT
ejpam-2996	205	17	m	m	PRON
ejpam-2996	205	18	,	,	PUNCT
ejpam-2996	205	19	ϕ)-preinvex	ϕ)-preinvex	NOUN
ejpam-2996	205	20	functions	function	NOUN
ejpam-2996	205	21	in	in	ADP
ejpam-2996	205	22	this	this	DET
ejpam-2996	205	23	section	section	NOUN
ejpam-2996	205	24	,	,	PUNCT
ejpam-2996	205	25	we	we	PRON
ejpam-2996	205	26	prove	prove	VERB
ejpam-2996	205	27	our	our	PRON
ejpam-2996	205	28	main	main	ADJ
ejpam-2996	205	29	results	result	NOUN
ejpam-2996	205	30	regarding	regard	VERB
ejpam-2996	205	31	some	some	DET
ejpam-2996	205	32	generalizations	generalization	NOUN
ejpam-2996	205	33	of	of	ADP
ejpam-2996	205	34	hermitehadamard	hermitehadamard	NOUN
ejpam-2996	205	35	type	type	NOUN
ejpam-2996	205	36	inequalities	inequality	NOUN
ejpam-2996	205	37	for	for	ADP
ejpam-2996	205	38	generalized	generalized	ADJ
ejpam-2996	205	39	(	(	PUNCT
ejpam-2996	205	40	r	r	NOUN
ejpam-2996	205	41	;	;	PUNCT
ejpam-2996	205	42	s	s	X
ejpam-2996	205	43	,	,	PUNCT
ejpam-2996	205	44	m	m	PRON
ejpam-2996	205	45	,	,	PUNCT
ejpam-2996	205	46	ϕ)-preinvex	ϕ)-preinvex	NOUN
ejpam-2996	205	47	functions	function	NOUN
ejpam-2996	205	48	via	via	ADP
ejpam-2996	205	49	fractional	fractional	ADJ
ejpam-2996	205	50	integrals	integral	NOUN
ejpam-2996	205	51	.	.	PUNCT
ejpam-2996	206	1	theorem	theorem	NOUN
ejpam-2996	206	2	4	4	NUM
ejpam-2996	206	3	.	.	PUNCT
ejpam-2996	207	1	let	let	VERB
ejpam-2996	207	2	ϕ	ϕ	NOUN
ejpam-2996	207	3	:	:	PUNCT
ejpam-2996	208	1	i	i	PRON
ejpam-2996	208	2	−→	−→	VERB
ejpam-2996	208	3	k	k	X
ejpam-2996	208	4	be	be	AUX
ejpam-2996	208	5	a	a	DET
ejpam-2996	208	6	continuous	continuous	ADJ
ejpam-2996	208	7	increasing	increase	VERB
ejpam-2996	208	8	function	function	NOUN
ejpam-2996	208	9	.	.	PUNCT
ejpam-2996	209	1	suppose	suppose	VERB
ejpam-2996	209	2	k	k	PROPN
ejpam-2996	209	3	⊆	⊆	NUM
ejpam-2996	209	4	r	r	NOUN
ejpam-2996	209	5	be	be	VERB
ejpam-2996	209	6	an	an	DET
ejpam-2996	209	7	open	open	ADJ
ejpam-2996	209	8	m	m	NOUN
ejpam-2996	209	9	-	-	PUNCT
ejpam-2996	209	10	invex	invex	NOUN
ejpam-2996	209	11	subset	subset	VERB
ejpam-2996	209	12	with	with	ADP
ejpam-2996	209	13	respect	respect	NOUN
ejpam-2996	209	14	to	to	ADP
ejpam-2996	209	15	η	η	PROPN
ejpam-2996	209	16	:	:	PUNCT
ejpam-2996	210	1	k	k	PROPN
ejpam-2996	210	2	×	×	PROPN
ejpam-2996	210	3	k	k	PROPN
ejpam-2996	210	4	×	×	PROPN
ejpam-2996	210	5	(	(	PUNCT
ejpam-2996	210	6	0	0	NUM
ejpam-2996	210	7	,	,	PUNCT
ejpam-2996	210	8	1	1	NUM
ejpam-2996	210	9	]	]	X
ejpam-2996	210	10	−→	−→	ADJ
ejpam-2996	210	11	r	r	NOUN
ejpam-2996	210	12	for	for	ADP
ejpam-2996	210	13	any	any	DET
ejpam-2996	210	14	fixed	fix	VERB
ejpam-2996	210	15	s	s	NOUN
ejpam-2996	210	16	,	,	PUNCT
ejpam-2996	210	17	m	m	VERB
ejpam-2996	210	18	∈	∈	ADJ
ejpam-2996	210	19	(	(	PUNCT
ejpam-2996	210	20	0	0	NUM
ejpam-2996	210	21	,	,	PUNCT
ejpam-2996	210	22	1	1	NUM
ejpam-2996	210	23	]	]	PUNCT
ejpam-2996	210	24	with	with	ADP
ejpam-2996	210	25	mϕ(a	mϕ(a	NOUN
ejpam-2996	210	26	)	)	PUNCT
ejpam-2996	210	27	<	<	X
ejpam-2996	210	28	mϕ(a	mϕ(a	NOUN
ejpam-2996	210	29	)	)	PUNCT
ejpam-2996	210	30	+	+	CCONJ
ejpam-2996	210	31	η(ϕ(b	η(ϕ(b	PROPN
ejpam-2996	210	32	)	)	PUNCT
ejpam-2996	210	33	,	,	PUNCT
ejpam-2996	210	34	ϕ(a),m	ϕ(a),m	ADJ
ejpam-2996	210	35	)	)	PUNCT
ejpam-2996	210	36	.	.	PUNCT
ejpam-2996	211	1	assume	assume	VERB
ejpam-2996	211	2	that	that	SCONJ
ejpam-2996	211	3	f	f	X
ejpam-2996	211	4	:	:	PUNCT
ejpam-2996	212	1	k	k	X
ejpam-2996	212	2	=	=	PUNCT
ejpam-2996	213	1	[	[	X
ejpam-2996	213	2	mϕ(a),mϕ(a	mϕ(a),mϕ(a	NOUN
ejpam-2996	213	3	)	)	PUNCT
ejpam-2996	213	4	+	+	NUM
ejpam-2996	213	5	η(ϕ(b	η(ϕ(b	PROPN
ejpam-2996	213	6	)	)	PUNCT
ejpam-2996	213	7	,	,	PUNCT
ejpam-2996	213	8	ϕ(a),m	ϕ(a),m	ADJ
ejpam-2996	213	9	)	)	PUNCT
ejpam-2996	213	10	]	]	PUNCT
ejpam-2996	214	1	−→	−→	NOUN
ejpam-2996	214	2	(	(	PUNCT
ejpam-2996	214	3	0,∞	0,∞	NOUN
ejpam-2996	214	4	)	)	PUNCT
ejpam-2996	214	5	be	be	AUX
ejpam-2996	214	6	a	a	DET
ejpam-2996	214	7	generalized	generalized	ADJ
ejpam-2996	214	8	(	(	PUNCT
ejpam-2996	214	9	r	r	NOUN
ejpam-2996	214	10	;	;	PUNCT
ejpam-2996	214	11	s	s	X
ejpam-2996	214	12	,	,	PUNCT
ejpam-2996	214	13	m	m	PRON
ejpam-2996	214	14	,	,	PUNCT
ejpam-2996	214	15	ϕ)-preinvex	ϕ)-preinvex	AUX
ejpam-2996	214	16	function	function	VERB
ejpam-2996	214	17	on	on	ADP
ejpam-2996	214	18	an	an	DET
ejpam-2996	214	19	open	open	ADJ
ejpam-2996	214	20	minvex	minvex	NOUN
ejpam-2996	214	21	set	set	VERB
ejpam-2996	214	22	k	k	NOUN
ejpam-2996	214	23	◦	◦	NOUN
ejpam-2996	214	24	.	.	PUNCT
ejpam-2996	215	1	then	then	ADV
ejpam-2996	215	2	for	for	ADP
ejpam-2996	215	3	α	α	PROPN
ejpam-2996	215	4	>	>	X
ejpam-2996	215	5	0	0	PUNCT
ejpam-2996	215	6	and	and	CCONJ
ejpam-2996	215	7	0	0	NUM
ejpam-2996	215	8	<	<	X
ejpam-2996	215	9	r	r	NOUN
ejpam-2996	215	10	≤	≤	NUM
ejpam-2996	215	11	1	1	NUM
ejpam-2996	215	12	,	,	PUNCT
ejpam-2996	215	13	we	we	PRON
ejpam-2996	215	14	have	have	VERB
ejpam-2996	215	15	γ(α	γ(α	NOUN
ejpam-2996	215	16	)	)	PUNCT
ejpam-2996	215	17	ηα(ϕ(b	ηα(ϕ(b	PROPN
ejpam-2996	215	18	)	)	PUNCT
ejpam-2996	215	19	,	,	PUNCT
ejpam-2996	215	20	ϕ(a),m	ϕ(a),m	ADJ
ejpam-2996	215	21	)	)	PUNCT
ejpam-2996	215	22	jα(mϕ(a)+η(ϕ(b),ϕ(a),m))−f(mϕ(a	jα(mϕ(a)+η(ϕ(b),ϕ(a),m))−f(mϕ(a	NOUN
ejpam-2996	215	23	)	)	PUNCT
ejpam-2996	215	24	)	)	PUNCT
ejpam-2996	215	25	≤	≤	NOUN
ejpam-2996	215	26	[	[	PUNCT
ejpam-2996	215	27	mf	mf	X
ejpam-2996	215	28	r(ϕ(a))βr	r(ϕ(a))βr	NOUN
ejpam-2996	215	29	(	(	PUNCT
ejpam-2996	215	30	α	α	NOUN
ejpam-2996	215	31	,	,	PUNCT
ejpam-2996	215	32	s	s	NOUN
ejpam-2996	215	33	r	r	NOUN
ejpam-2996	215	34	+	+	NOUN
ejpam-2996	215	35	1	1	NUM
ejpam-2996	215	36	)	)	PUNCT
ejpam-2996	216	1	+	+	CCONJ
ejpam-2996	216	2	f	f	PROPN
ejpam-2996	216	3	r(ϕ(b	r(ϕ(b	PROPN
ejpam-2996	216	4	)	)	PUNCT
ejpam-2996	216	5	)	)	PUNCT
ejpam-2996	217	1	(	(	PUNCT
ejpam-2996	217	2	r	r	NOUN
ejpam-2996	217	3	αr	αr	NUM
ejpam-2996	217	4	+	+	SYM
ejpam-2996	217	5	s	s	PART
ejpam-2996	217	6	)	)	PUNCT
ejpam-2996	217	7	r	r	NOUN
ejpam-2996	217	8	]	]	PUNCT
ejpam-2996	217	9	1	1	NUM
ejpam-2996	217	10	r	r	NOUN
ejpam-2996	217	11	.	.	PUNCT
ejpam-2996	218	1	(	(	PUNCT
ejpam-2996	218	2	7	7	X
ejpam-2996	218	3	)	)	PUNCT
ejpam-2996	218	4	a.	a.	NOUN
ejpam-2996	218	5	kashuri	kashuri	PROPN
ejpam-2996	218	6	,	,	PUNCT
ejpam-2996	218	7	r.	r.	PROPN
ejpam-2996	218	8	liko	liko	PROPN
ejpam-2996	218	9	/	/	SYM
ejpam-2996	218	10	eur	eur	PROPN
ejpam-2996	218	11	.	.	PUNCT
ejpam-2996	219	1	j.	j.	PROPN
ejpam-2996	219	2	pure	pure	PROPN
ejpam-2996	219	3	appl	appl	PROPN
ejpam-2996	219	4	.	.	PROPN
ejpam-2996	219	5	math	math	PROPN
ejpam-2996	219	6	,	,	PUNCT
ejpam-2996	219	7	10	10	NUM
ejpam-2996	219	8	(	(	PUNCT
ejpam-2996	219	9	3	3	NUM
ejpam-2996	219	10	)	)	PUNCT
ejpam-2996	219	11	(	(	PUNCT
ejpam-2996	219	12	2017	2017	NUM
ejpam-2996	219	13	)	)	PUNCT
ejpam-2996	219	14	,	,	PUNCT
ejpam-2996	219	15	495	495	NUM
ejpam-2996	219	16	-	-	SYM
ejpam-2996	219	17	505	505	NUM
ejpam-2996	219	18	502	502	NUM
ejpam-2996	219	19	proof	proof	NOUN
ejpam-2996	219	20	.	.	PUNCT
ejpam-2996	220	1	let	let	VERB
ejpam-2996	220	2	0	0	NUM
ejpam-2996	220	3	<	<	X
ejpam-2996	220	4	r	r	NOUN
ejpam-2996	220	5	≤	≤	NUM
ejpam-2996	220	6	1	1	NUM
ejpam-2996	220	7	.	.	PUNCT
ejpam-2996	221	1	since	since	SCONJ
ejpam-2996	221	2	f	f	PROPN
ejpam-2996	221	3	is	be	AUX
ejpam-2996	221	4	a	a	DET
ejpam-2996	221	5	generalized	generalized	ADJ
ejpam-2996	221	6	(	(	PUNCT
ejpam-2996	221	7	r	r	NOUN
ejpam-2996	221	8	;	;	PUNCT
ejpam-2996	221	9	s	s	X
ejpam-2996	221	10	,	,	PUNCT
ejpam-2996	221	11	m	m	PRON
ejpam-2996	221	12	,	,	PUNCT
ejpam-2996	221	13	ϕ)-preinvex	ϕ)-preinvex	AUX
ejpam-2996	221	14	function	function	VERB
ejpam-2996	221	15	on	on	ADP
ejpam-2996	221	16	an	an	DET
ejpam-2996	221	17	open	open	ADJ
ejpam-2996	221	18	m	m	NOUN
ejpam-2996	221	19	-	-	PUNCT
ejpam-2996	221	20	invex	invex	NOUN
ejpam-2996	221	21	set	set	VERB
ejpam-2996	221	22	k	k	PROPN
ejpam-2996	221	23	◦	◦	NOUN
ejpam-2996	221	24	,	,	PUNCT
ejpam-2996	221	25	combining	combine	VERB
ejpam-2996	221	26	with	with	ADP
ejpam-2996	221	27	minkowski	minkowski	ADJ
ejpam-2996	221	28	inequality	inequality	NOUN
ejpam-2996	221	29	for	for	ADP
ejpam-2996	221	30	all	all	DET
ejpam-2996	221	31	t	t	NOUN
ejpam-2996	221	32	∈	∈	PROPN
ejpam-2996	222	1	[	[	X
ejpam-2996	222	2	0	0	NUM
ejpam-2996	222	3	,	,	PUNCT
ejpam-2996	222	4	1	1	NUM
ejpam-2996	222	5	]	]	PUNCT
ejpam-2996	222	6	and	and	CCONJ
ejpam-2996	222	7	for	for	ADP
ejpam-2996	222	8	any	any	DET
ejpam-2996	222	9	fixed	fix	VERB
ejpam-2996	222	10	s	s	NOUN
ejpam-2996	222	11	,	,	PUNCT
ejpam-2996	222	12	m	m	VERB
ejpam-2996	222	13	∈	∈	ADJ
ejpam-2996	222	14	(	(	PUNCT
ejpam-2996	222	15	0	0	NUM
ejpam-2996	222	16	,	,	PUNCT
ejpam-2996	222	17	1	1	NUM
ejpam-2996	222	18	]	]	PUNCT
ejpam-2996	222	19	,	,	PUNCT
ejpam-2996	222	20	we	we	PRON
ejpam-2996	222	21	get	get	VERB
ejpam-2996	222	22	γ(α	γ(α	NOUN
ejpam-2996	222	23	)	)	PUNCT
ejpam-2996	222	24	ηα(ϕ(b	ηα(ϕ(b	NOUN
ejpam-2996	222	25	)	)	PUNCT
ejpam-2996	222	26	,	,	PUNCT
ejpam-2996	222	27	ϕ(a),m	ϕ(a),m	ADJ
ejpam-2996	222	28	)	)	PUNCT
ejpam-2996	222	29	jα(mϕ(a)+η(ϕ(b),ϕ(a),m))−f(mϕ(a	jα(mϕ(a)+η(ϕ(b),ϕ(a),m))−f(mϕ(a	NOUN
ejpam-2996	222	30	)	)	PUNCT
ejpam-2996	222	31	)	)	PUNCT
ejpam-2996	223	1	=	=	PUNCT
ejpam-2996	223	2	∫	∫	PROPN
ejpam-2996	223	3	1	1	NUM
ejpam-2996	223	4	0	0	NUM
ejpam-2996	223	5	tα−1f(mϕ(a	tα−1f(mϕ(a	NOUN
ejpam-2996	223	6	)	)	PUNCT
ejpam-2996	223	7	+	+	CCONJ
ejpam-2996	223	8	tη(ϕ(b	tη(ϕ(b	NUM
ejpam-2996	223	9	)	)	PUNCT
ejpam-2996	223	10	,	,	PUNCT
ejpam-2996	223	11	ϕ(a),m))dt	ϕ(a),m))dt	PROPN
ejpam-2996	223	12	≤	≤	NUM
ejpam-2996	223	13	∫	∫	PROPN
ejpam-2996	223	14	1	1	NUM
ejpam-2996	223	15	0	0	NUM
ejpam-2996	223	16	tα−1	tα−1	NOUN
ejpam-2996	223	17	[	[	PUNCT
ejpam-2996	223	18	m(1−	m(1−	PROPN
ejpam-2996	223	19	t)sf	t)sf	PROPN
ejpam-2996	223	20	r(ϕ(a	r(ϕ(a	NOUN
ejpam-2996	223	21	)	)	PUNCT
ejpam-2996	223	22	)	)	PUNCT
ejpam-2996	224	1	+	+	CCONJ
ejpam-2996	224	2	tsf	tsf	NOUN
ejpam-2996	224	3	r(ϕ(b	r(ϕ(b	PROPN
ejpam-2996	224	4	)	)	PUNCT
ejpam-2996	224	5	)	)	PUNCT
ejpam-2996	224	6	]	]	PUNCT
ejpam-2996	225	1	1	1	NUM
ejpam-2996	225	2	r	r	NOUN
ejpam-2996	225	3	dt	dt	NOUN
ejpam-2996	225	4	≤	≤	NOUN
ejpam-2996	225	5	{	{	PUNCT
ejpam-2996	226	1	[	[	X
ejpam-2996	226	2	∫	∫	X
ejpam-2996	226	3	1	1	NUM
ejpam-2996	226	4	0	0	NUM
ejpam-2996	227	1	tα−1	tα−1	NOUN
ejpam-2996	227	2	+	+	NOUN
ejpam-2996	227	3	s	s	NOUN
ejpam-2996	227	4	r	r	NOUN
ejpam-2996	227	5	f(ϕ(b))dt	f(ϕ(b))dt	NOUN
ejpam-2996	227	6	]	]	X
ejpam-2996	227	7	r	r	NOUN
ejpam-2996	228	1	+	+	SYM
ejpam-2996	228	2	[	[	X
ejpam-2996	228	3	∫	∫	X
ejpam-2996	228	4	1	1	NUM
ejpam-2996	228	5	0	0	NUM
ejpam-2996	228	6	m	m	VERB
ejpam-2996	228	7	1	1	NUM
ejpam-2996	228	8	r	r	NOUN
ejpam-2996	228	9	tα−1(1−	tα−1(1−	PROPN
ejpam-2996	228	10	t	t	PROPN
ejpam-2996	228	11	)	)	PUNCT
ejpam-2996	228	12	s	s	PART
ejpam-2996	228	13	r	r	NOUN
ejpam-2996	228	14	f(ϕ(a))dt	f(ϕ(a))dt	NOUN
ejpam-2996	228	15	]	]	X
ejpam-2996	228	16	r	r	NOUN
ejpam-2996	228	17	}	}	SYM
ejpam-2996	228	18	1	1	NUM
ejpam-2996	228	19	r	r	NOUN
ejpam-2996	228	20	=	=	SYM
ejpam-2996	228	21	[	[	PUNCT
ejpam-2996	228	22	mf	mf	X
ejpam-2996	228	23	r(ϕ(a))βr	r(ϕ(a))βr	NOUN
ejpam-2996	228	24	(	(	PUNCT
ejpam-2996	228	25	α	α	NOUN
ejpam-2996	228	26	,	,	PUNCT
ejpam-2996	228	27	s	s	NOUN
ejpam-2996	228	28	r	r	NOUN
ejpam-2996	228	29	+	+	NOUN
ejpam-2996	228	30	1	1	NUM
ejpam-2996	228	31	)	)	PUNCT
ejpam-2996	229	1	+	+	CCONJ
ejpam-2996	229	2	f	f	PROPN
ejpam-2996	229	3	r(ϕ(b	r(ϕ(b	PROPN
ejpam-2996	229	4	)	)	PUNCT
ejpam-2996	229	5	)	)	PUNCT
ejpam-2996	230	1	(	(	PUNCT
ejpam-2996	230	2	r	r	NOUN
ejpam-2996	230	3	αr	αr	NUM
ejpam-2996	230	4	+	+	SYM
ejpam-2996	230	5	s	s	PART
ejpam-2996	230	6	)	)	PUNCT
ejpam-2996	230	7	r	r	NOUN
ejpam-2996	230	8	]	]	PUNCT
ejpam-2996	230	9	1	1	NUM
ejpam-2996	230	10	r	r	NOUN
ejpam-2996	230	11	.	.	PUNCT
ejpam-2996	231	1	corollary	corollary	ADJ
ejpam-2996	231	2	3	3	NUM
ejpam-2996	231	3	.	.	PUNCT
ejpam-2996	232	1	under	under	ADP
ejpam-2996	232	2	the	the	DET
ejpam-2996	232	3	same	same	ADJ
ejpam-2996	232	4	conditions	condition	NOUN
ejpam-2996	232	5	as	as	ADP
ejpam-2996	232	6	in	in	ADP
ejpam-2996	232	7	theorem	theorem	NOUN
ejpam-2996	232	8	4	4	NUM
ejpam-2996	232	9	for	for	ADP
ejpam-2996	232	10	m	m	NOUN
ejpam-2996	232	11	=	=	SYM
ejpam-2996	232	12	s	s	PART
ejpam-2996	232	13	=	=	SYM
ejpam-2996	232	14	1	1	NUM
ejpam-2996	232	15	,	,	PUNCT
ejpam-2996	232	16	ϕ(x	ϕ(x	X
ejpam-2996	232	17	)	)	PUNCT
ejpam-2996	232	18	=	=	SYM
ejpam-2996	232	19	x	x	PUNCT
ejpam-2996	232	20	and	and	CCONJ
ejpam-2996	232	21	η(ϕ(b	η(ϕ(b	PROPN
ejpam-2996	232	22	)	)	PUNCT
ejpam-2996	232	23	,	,	PUNCT
ejpam-2996	232	24	ϕ(a),m	ϕ(a),m	ADJ
ejpam-2996	232	25	)	)	PUNCT
ejpam-2996	232	26	=	=	PUNCT
ejpam-2996	232	27	η(b	η(b	PROPN
ejpam-2996	232	28	,	,	PUNCT
ejpam-2996	232	29	a	a	PRON
ejpam-2996	232	30	)	)	PUNCT
ejpam-2996	232	31	,	,	PUNCT
ejpam-2996	232	32	we	we	PRON
ejpam-2996	232	33	get	get	AUX
ejpam-2996	232	34	(	(	PUNCT
ejpam-2996	232	35	see	see	VERB
ejpam-2996	232	36	[	[	X
ejpam-2996	232	37	2	2	NUM
ejpam-2996	232	38	]	]	PUNCT
ejpam-2996	232	39	,	,	PUNCT
ejpam-2996	232	40	theorem	theorem	VERB
ejpam-2996	232	41	3.1	3.1	NUM
ejpam-2996	232	42	)	)	PUNCT
ejpam-2996	232	43	.	.	PUNCT
ejpam-2996	233	1	theorem	theorem	NOUN
ejpam-2996	233	2	5	5	NUM
ejpam-2996	233	3	.	.	PUNCT
ejpam-2996	234	1	let	let	VERB
ejpam-2996	234	2	ϕ	ϕ	NOUN
ejpam-2996	234	3	:	:	PUNCT
ejpam-2996	235	1	i	i	PRON
ejpam-2996	235	2	−→	−→	VERB
ejpam-2996	235	3	k	k	X
ejpam-2996	235	4	be	be	AUX
ejpam-2996	235	5	a	a	DET
ejpam-2996	235	6	continuous	continuous	ADJ
ejpam-2996	235	7	increasing	increase	VERB
ejpam-2996	235	8	function	function	NOUN
ejpam-2996	235	9	.	.	PUNCT
ejpam-2996	236	1	suppose	suppose	VERB
ejpam-2996	236	2	k	k	PROPN
ejpam-2996	236	3	⊆	⊆	NUM
ejpam-2996	236	4	r	r	NOUN
ejpam-2996	236	5	be	be	VERB
ejpam-2996	236	6	an	an	DET
ejpam-2996	236	7	open	open	ADJ
ejpam-2996	236	8	m	m	NOUN
ejpam-2996	236	9	-	-	PUNCT
ejpam-2996	236	10	invex	invex	NOUN
ejpam-2996	236	11	subset	subset	VERB
ejpam-2996	236	12	with	with	ADP
ejpam-2996	236	13	respect	respect	NOUN
ejpam-2996	236	14	to	to	ADP
ejpam-2996	236	15	η	η	PROPN
ejpam-2996	236	16	:	:	PUNCT
ejpam-2996	237	1	k	k	PROPN
ejpam-2996	237	2	×	×	PROPN
ejpam-2996	237	3	k	k	PROPN
ejpam-2996	237	4	×	×	PROPN
ejpam-2996	237	5	(	(	PUNCT
ejpam-2996	237	6	0	0	NUM
ejpam-2996	237	7	,	,	PUNCT
ejpam-2996	237	8	1	1	NUM
ejpam-2996	237	9	]	]	X
ejpam-2996	237	10	−→	−→	ADJ
ejpam-2996	237	11	r	r	NOUN
ejpam-2996	237	12	for	for	ADP
ejpam-2996	237	13	any	any	DET
ejpam-2996	237	14	fixed	fix	VERB
ejpam-2996	237	15	s	s	NOUN
ejpam-2996	237	16	,	,	PUNCT
ejpam-2996	237	17	m	m	VERB
ejpam-2996	237	18	∈	∈	ADJ
ejpam-2996	237	19	(	(	PUNCT
ejpam-2996	237	20	0	0	NUM
ejpam-2996	237	21	,	,	PUNCT
ejpam-2996	237	22	1	1	NUM
ejpam-2996	237	23	]	]	PUNCT
ejpam-2996	237	24	with	with	ADP
ejpam-2996	237	25	mϕ(a	mϕ(a	NOUN
ejpam-2996	237	26	)	)	PUNCT
ejpam-2996	237	27	<	<	X
ejpam-2996	237	28	mϕ(a	mϕ(a	NOUN
ejpam-2996	237	29	)	)	PUNCT
ejpam-2996	237	30	+	+	CCONJ
ejpam-2996	237	31	η(ϕ(b	η(ϕ(b	PROPN
ejpam-2996	237	32	)	)	PUNCT
ejpam-2996	237	33	,	,	PUNCT
ejpam-2996	237	34	ϕ(a),m	ϕ(a),m	ADJ
ejpam-2996	237	35	)	)	PUNCT
ejpam-2996	237	36	.	.	PUNCT
ejpam-2996	238	1	assume	assume	VERB
ejpam-2996	238	2	that	that	SCONJ
ejpam-2996	238	3	f	f	X
ejpam-2996	238	4	,	,	PUNCT
ejpam-2996	238	5	h	h	NOUN
ejpam-2996	238	6	:	:	PUNCT
ejpam-2996	239	1	k	k	X
ejpam-2996	239	2	=	=	PUNCT
ejpam-2996	240	1	[	[	X
ejpam-2996	240	2	mϕ(a),mϕ(a	mϕ(a),mϕ(a	NOUN
ejpam-2996	240	3	)	)	PUNCT
ejpam-2996	240	4	+	+	NUM
ejpam-2996	240	5	η(ϕ(b	η(ϕ(b	PROPN
ejpam-2996	240	6	)	)	PUNCT
ejpam-2996	240	7	,	,	PUNCT
ejpam-2996	240	8	ϕ(a),m	ϕ(a),m	ADJ
ejpam-2996	240	9	)	)	PUNCT
ejpam-2996	240	10	]	]	PUNCT
ejpam-2996	241	1	−→	−→	NOUN
ejpam-2996	241	2	(	(	PUNCT
ejpam-2996	241	3	0,∞	0,∞	NOUN
ejpam-2996	241	4	)	)	PUNCT
ejpam-2996	241	5	are	be	AUX
ejpam-2996	241	6	respectively	respectively	ADV
ejpam-2996	241	7	generalized	generalize	VERB
ejpam-2996	241	8	(	(	PUNCT
ejpam-2996	241	9	r	r	NOUN
ejpam-2996	241	10	;	;	PUNCT
ejpam-2996	241	11	s	s	X
ejpam-2996	241	12	,	,	PUNCT
ejpam-2996	241	13	m	m	PRON
ejpam-2996	241	14	,	,	PUNCT
ejpam-2996	241	15	ϕ)-preinvex	ϕ)-preinvex	NOUN
ejpam-2996	241	16	function	function	NOUN
ejpam-2996	241	17	and	and	CCONJ
ejpam-2996	241	18	generalized	generalize	VERB
ejpam-2996	241	19	(	(	PUNCT
ejpam-2996	241	20	l	l	NOUN
ejpam-2996	241	21	;	;	PUNCT
ejpam-2996	241	22	s	s	X
ejpam-2996	241	23	,	,	PUNCT
ejpam-2996	241	24	m	m	PRON
ejpam-2996	241	25	,	,	PUNCT
ejpam-2996	241	26	ϕ)-preinvex	ϕ)-preinvex	AUX
ejpam-2996	241	27	function	function	VERB
ejpam-2996	241	28	on	on	ADP
ejpam-2996	241	29	an	an	DET
ejpam-2996	241	30	open	open	ADJ
ejpam-2996	241	31	m	m	NOUN
ejpam-2996	241	32	-	-	PUNCT
ejpam-2996	241	33	invex	invex	NOUN
ejpam-2996	241	34	set	set	VERB
ejpam-2996	241	35	k	k	PROPN
ejpam-2996	241	36	◦	◦	NOUN
ejpam-2996	241	37	.	.	PUNCT
ejpam-2996	242	1	then	then	ADV
ejpam-2996	242	2	for	for	ADP
ejpam-2996	242	3	α	α	PROPN
ejpam-2996	242	4	>	>	X
ejpam-2996	242	5	0	0	NUM
ejpam-2996	242	6	,	,	PUNCT
ejpam-2996	242	7	r	r	NOUN
ejpam-2996	242	8	>	>	X
ejpam-2996	242	9	1	1	NUM
ejpam-2996	242	10	and	and	CCONJ
ejpam-2996	242	11	r−1	r−1	PROPN
ejpam-2996	242	12	+	+	CCONJ
ejpam-2996	242	13	l−1	l−1	PROPN
ejpam-2996	242	14	=	=	SYM
ejpam-2996	242	15	1	1	NUM
ejpam-2996	242	16	,	,	PUNCT
ejpam-2996	242	17	we	we	PRON
ejpam-2996	242	18	have	have	VERB
ejpam-2996	242	19	γ(α	γ(α	NOUN
ejpam-2996	242	20	)	)	PUNCT
ejpam-2996	242	21	ηα(ϕ(b	ηα(ϕ(b	PROPN
ejpam-2996	242	22	)	)	PUNCT
ejpam-2996	242	23	,	,	PUNCT
ejpam-2996	242	24	ϕ(a),m	ϕ(a),m	ADJ
ejpam-2996	242	25	)	)	PUNCT
ejpam-2996	242	26	jα(mϕ(a)+η(ϕ(b),ϕ(a),m))−f(mϕ(a))h(mϕ(a	jα(mϕ(a)+η(ϕ(b),ϕ(a),m))−f(mϕ(a))h(mϕ(a	PROPN
ejpam-2996	242	27	)	)	PUNCT
ejpam-2996	242	28	)	)	PUNCT
ejpam-2996	242	29	≤	≤	NUM
ejpam-2996	242	30	1	1	NUM
ejpam-2996	242	31	2	2	NUM
ejpam-2996	242	32	{	{	PUNCT
ejpam-2996	242	33	[	[	PUNCT
ejpam-2996	242	34	mf	mf	X
ejpam-2996	242	35	r(ϕ(a))β	r(ϕ(a))β	NUM
ejpam-2996	242	36	r	r	NOUN
ejpam-2996	242	37	2	2	NUM
ejpam-2996	242	38	(	(	PUNCT
ejpam-2996	242	39	2(α−	2(α−	NUM
ejpam-2996	242	40	1	1	NUM
ejpam-2996	242	41	)	)	PUNCT
ejpam-2996	242	42	r	r	NOUN
ejpam-2996	242	43	+	+	NUM
ejpam-2996	242	44	1	1	NUM
ejpam-2996	242	45	,	,	PUNCT
ejpam-2996	242	46	2s	2s	NUM
ejpam-2996	242	47	r	r	NOUN
ejpam-2996	242	48	+	+	NOUN
ejpam-2996	242	49	1	1	NUM
ejpam-2996	242	50	)	)	PUNCT
ejpam-2996	243	1	+	+	CCONJ
ejpam-2996	243	2	f	f	PROPN
ejpam-2996	243	3	r(ϕ(b	r(ϕ(b	PROPN
ejpam-2996	243	4	)	)	PUNCT
ejpam-2996	243	5	)	)	PUNCT
ejpam-2996	244	1	(	(	PUNCT
ejpam-2996	244	2	r	r	NOUN
ejpam-2996	244	3	2(α−	2(α−	NUM
ejpam-2996	244	4	1	1	NUM
ejpam-2996	244	5	+	+	NUM
ejpam-2996	244	6	s	s	X
ejpam-2996	244	7	)	)	PUNCT
ejpam-2996	245	1	+	+	NUM
ejpam-2996	245	2	r	r	NOUN
ejpam-2996	245	3	)	)	PUNCT
ejpam-2996	245	4	r	r	NOUN
ejpam-2996	245	5	2	2	NUM
ejpam-2996	245	6	]	]	SYM
ejpam-2996	245	7	2	2	NUM
ejpam-2996	245	8	r	r	NOUN
ejpam-2996	245	9	(	(	PUNCT
ejpam-2996	245	10	8)	8)	NUM
ejpam-2996	245	11	+	+	CCONJ
ejpam-2996	245	12	[	[	PUNCT
ejpam-2996	245	13	mhl(ϕ(a))β	mhl(ϕ(a))β	ADJ
ejpam-2996	245	14	l	l	NOUN
ejpam-2996	245	15	2	2	NUM
ejpam-2996	245	16	(	(	PUNCT
ejpam-2996	245	17	2(α−	2(α−	NUM
ejpam-2996	245	18	1	1	NUM
ejpam-2996	245	19	)	)	PUNCT
ejpam-2996	245	20	l	l	NOUN
ejpam-2996	246	1	+	+	NUM
ejpam-2996	246	2	1	1	NUM
ejpam-2996	246	3	,	,	PUNCT
ejpam-2996	246	4	2s	2	VERB
ejpam-2996	246	5	l	l	NOUN
ejpam-2996	247	1	+	+	NOUN
ejpam-2996	247	2	1	1	NUM
ejpam-2996	247	3	)	)	PUNCT
ejpam-2996	247	4	+	+	CCONJ
ejpam-2996	247	5	hl(ϕ(b	hl(ϕ(b	NOUN
ejpam-2996	247	6	)	)	PUNCT
ejpam-2996	247	7	)	)	PUNCT
ejpam-2996	248	1	(	(	PUNCT
ejpam-2996	248	2	l	l	NOUN
ejpam-2996	248	3	2(α−	2(α−	NUM
ejpam-2996	248	4	1	1	NUM
ejpam-2996	248	5	+	+	NUM
ejpam-2996	248	6	s	s	X
ejpam-2996	248	7	)	)	PUNCT
ejpam-2996	248	8	+	+	NUM
ejpam-2996	248	9	l	l	NOUN
ejpam-2996	248	10	)	)	PUNCT
ejpam-2996	248	11	l	l	NOUN
ejpam-2996	248	12	2	2	X
ejpam-2996	248	13	]	]	SYM
ejpam-2996	248	14	2	2	NUM
ejpam-2996	248	15	l	l	NOUN
ejpam-2996	248	16	}	}	PUNCT
ejpam-2996	248	17	.	.	PUNCT
ejpam-2996	249	1	proof	proof	NOUN
ejpam-2996	249	2	.	.	PUNCT
ejpam-2996	250	1	let	let	VERB
ejpam-2996	251	1	r	r	PRON
ejpam-2996	251	2	>	>	X
ejpam-2996	251	3	1	1	NUM
ejpam-2996	251	4	and	and	CCONJ
ejpam-2996	251	5	r−1	r−1	PROPN
ejpam-2996	252	1	+	+	CCONJ
ejpam-2996	252	2	l−1	l−1	PROPN
ejpam-2996	252	3	=	=	SYM
ejpam-2996	252	4	1	1	X
ejpam-2996	252	5	.	.	PUNCT
ejpam-2996	253	1	since	since	SCONJ
ejpam-2996	253	2	f	f	PROPN
ejpam-2996	253	3	and	and	CCONJ
ejpam-2996	253	4	h	h	PROPN
ejpam-2996	253	5	are	be	AUX
ejpam-2996	253	6	respectively	respectively	ADV
ejpam-2996	253	7	generalized	generalize	VERB
ejpam-2996	253	8	(	(	PUNCT
ejpam-2996	253	9	r	r	NOUN
ejpam-2996	253	10	;	;	PUNCT
ejpam-2996	253	11	s	s	X
ejpam-2996	253	12	,	,	PUNCT
ejpam-2996	253	13	m	m	PRON
ejpam-2996	253	14	,	,	PUNCT
ejpam-2996	253	15	ϕ)-preinvex	ϕ)-preinvex	NOUN
ejpam-2996	253	16	function	function	NOUN
ejpam-2996	253	17	and	and	CCONJ
ejpam-2996	253	18	generalized	generalize	VERB
ejpam-2996	253	19	(	(	PUNCT
ejpam-2996	253	20	l	l	NOUN
ejpam-2996	253	21	;	;	PUNCT
ejpam-2996	253	22	s	s	X
ejpam-2996	253	23	,	,	PUNCT
ejpam-2996	253	24	m	m	PRON
ejpam-2996	253	25	,	,	PUNCT
ejpam-2996	253	26	ϕ)-preinvex	ϕ)-preinvex	AUX
ejpam-2996	253	27	function	function	VERB
ejpam-2996	253	28	on	on	ADP
ejpam-2996	253	29	an	an	DET
ejpam-2996	253	30	open	open	ADJ
ejpam-2996	253	31	minvex	minvex	NOUN
ejpam-2996	253	32	set	set	VERB
ejpam-2996	253	33	k	k	NOUN
ejpam-2996	253	34	◦	◦	NOUN
ejpam-2996	253	35	,	,	PUNCT
ejpam-2996	253	36	combining	combine	VERB
ejpam-2996	253	37	with	with	ADP
ejpam-2996	253	38	cauchy	cauchy	ADJ
ejpam-2996	253	39	and	and	CCONJ
ejpam-2996	253	40	minkowski	minkowski	ADJ
ejpam-2996	253	41	inequalities	inequality	NOUN
ejpam-2996	253	42	for	for	ADP
ejpam-2996	253	43	all	all	DET
ejpam-2996	253	44	t	t	NOUN
ejpam-2996	253	45	∈	∈	PROPN
ejpam-2996	254	1	[	[	X
ejpam-2996	254	2	0	0	NUM
ejpam-2996	254	3	,	,	PUNCT
ejpam-2996	254	4	1	1	NUM
ejpam-2996	254	5	]	]	PUNCT
ejpam-2996	254	6	and	and	CCONJ
ejpam-2996	254	7	for	for	ADP
ejpam-2996	254	8	any	any	DET
ejpam-2996	254	9	fixed	fix	VERB
ejpam-2996	254	10	s	s	NOUN
ejpam-2996	254	11	,	,	PUNCT
ejpam-2996	254	12	m	m	VERB
ejpam-2996	254	13	∈	∈	ADJ
ejpam-2996	254	14	(	(	PUNCT
ejpam-2996	254	15	0	0	NUM
ejpam-2996	254	16	,	,	PUNCT
ejpam-2996	254	17	1	1	NUM
ejpam-2996	254	18	]	]	PUNCT
ejpam-2996	254	19	,	,	PUNCT
ejpam-2996	254	20	we	we	PRON
ejpam-2996	254	21	get	get	VERB
ejpam-2996	254	22	γ(α	γ(α	NOUN
ejpam-2996	254	23	)	)	PUNCT
ejpam-2996	254	24	ηα(ϕ(b	ηα(ϕ(b	NOUN
ejpam-2996	254	25	)	)	PUNCT
ejpam-2996	254	26	,	,	PUNCT
ejpam-2996	254	27	ϕ(a),m	ϕ(a),m	ADJ
ejpam-2996	254	28	)	)	PUNCT
ejpam-2996	254	29	jα(mϕ(a)+η(ϕ(b),ϕ(a),m))−f(mϕ(a))h(mϕ(a	jα(mϕ(a)+η(ϕ(b),ϕ(a),m))−f(mϕ(a))h(mϕ(a	PROPN
ejpam-2996	254	30	)	)	PUNCT
ejpam-2996	254	31	)	)	PUNCT
ejpam-2996	254	32	a.	a.	NOUN
ejpam-2996	254	33	kashuri	kashuri	PROPN
ejpam-2996	254	34	,	,	PUNCT
ejpam-2996	254	35	r.	r.	PROPN
ejpam-2996	254	36	liko	liko	PROPN
ejpam-2996	254	37	/	/	SYM
ejpam-2996	254	38	eur	eur	PROPN
ejpam-2996	254	39	.	.	PUNCT
ejpam-2996	255	1	j.	j.	PROPN
ejpam-2996	255	2	pure	pure	PROPN
ejpam-2996	255	3	appl	appl	PROPN
ejpam-2996	255	4	.	.	PROPN
ejpam-2996	255	5	math	math	PROPN
ejpam-2996	255	6	,	,	PUNCT
ejpam-2996	255	7	10	10	NUM
ejpam-2996	255	8	(	(	PUNCT
ejpam-2996	255	9	3	3	NUM
ejpam-2996	255	10	)	)	PUNCT
ejpam-2996	255	11	(	(	PUNCT
ejpam-2996	255	12	2017	2017	NUM
ejpam-2996	255	13	)	)	PUNCT
ejpam-2996	255	14	,	,	PUNCT
ejpam-2996	255	15	495	495	NUM
ejpam-2996	255	16	-	-	SYM
ejpam-2996	255	17	505	505	NUM
ejpam-2996	255	18	503	503	NUM
ejpam-2996	255	19	=	=	SYM
ejpam-2996	255	20	∫	∫	PROPN
ejpam-2996	255	21	1	1	NUM
ejpam-2996	255	22	0	0	NUM
ejpam-2996	255	23	t(α−1	t(α−1	NOUN
ejpam-2996	255	24	)	)	PUNCT
ejpam-2996	255	25	(	(	PUNCT
ejpam-2996	255	26	1	1	NUM
ejpam-2996	255	27	r	r	NOUN
ejpam-2996	255	28	+	+	NOUN
ejpam-2996	255	29	1	1	NUM
ejpam-2996	255	30	l	l	NOUN
ejpam-2996	255	31	)	)	PUNCT
ejpam-2996	255	32	f(mϕ(a	f(mϕ(a	NOUN
ejpam-2996	255	33	)	)	PUNCT
ejpam-2996	255	34	+	+	CCONJ
ejpam-2996	255	35	tη(ϕ(b	tη(ϕ(b	NUM
ejpam-2996	255	36	)	)	PUNCT
ejpam-2996	255	37	,	,	PUNCT
ejpam-2996	255	38	ϕ(a),m	ϕ(a),m	ADJ
ejpam-2996	255	39	)	)	PUNCT
ejpam-2996	255	40	)	)	PUNCT
ejpam-2996	256	1	×h(mϕ(a	×h(mϕ(a	NOUN
ejpam-2996	256	2	)	)	PUNCT
ejpam-2996	256	3	+	+	CCONJ
ejpam-2996	256	4	tη(ϕ(b	tη(ϕ(b	NUM
ejpam-2996	256	5	)	)	PUNCT
ejpam-2996	256	6	,	,	PUNCT
ejpam-2996	256	7	ϕ(a),m))dt	ϕ(a),m))dt	PROPN
ejpam-2996	256	8	≤	≤	NUM
ejpam-2996	256	9	∫	∫	PROPN
ejpam-2996	256	10	1	1	NUM
ejpam-2996	256	11	0	0	NUM
ejpam-2996	256	12	t(α−1	t(α−1	NOUN
ejpam-2996	256	13	)	)	PUNCT
ejpam-2996	256	14	(	(	PUNCT
ejpam-2996	256	15	1	1	NUM
ejpam-2996	256	16	r	r	NOUN
ejpam-2996	256	17	+	+	NOUN
ejpam-2996	256	18	1	1	NUM
ejpam-2996	256	19	l	l	NOUN
ejpam-2996	256	20	)	)	PUNCT
ejpam-2996	257	1	[	[	PUNCT
ejpam-2996	257	2	m(1−	m(1−	PROPN
ejpam-2996	257	3	t)sf	t)sf	PROPN
ejpam-2996	257	4	r(ϕ(a	r(ϕ(a	NOUN
ejpam-2996	257	5	)	)	PUNCT
ejpam-2996	257	6	)	)	PUNCT
ejpam-2996	258	1	+	+	CCONJ
ejpam-2996	258	2	tsf	tsf	NOUN
ejpam-2996	258	3	r(ϕ(b	r(ϕ(b	PROPN
ejpam-2996	258	4	)	)	PUNCT
ejpam-2996	258	5	)	)	PUNCT
ejpam-2996	258	6	]	]	PUNCT
ejpam-2996	259	1	1	1	NUM
ejpam-2996	259	2	r	r	NOUN
ejpam-2996	259	3	×	×	NOUN
ejpam-2996	259	4	[	[	PUNCT
ejpam-2996	259	5	m(1−	m(1−	PROPN
ejpam-2996	259	6	t)shl(ϕ(a	t)shl(ϕ(a	PROPN
ejpam-2996	259	7	)	)	PUNCT
ejpam-2996	259	8	)	)	PUNCT
ejpam-2996	260	1	+	+	CCONJ
ejpam-2996	260	2	tshl(ϕ(b	tshl(ϕ(b	NOUN
ejpam-2996	260	3	)	)	PUNCT
ejpam-2996	260	4	)	)	PUNCT
ejpam-2996	260	5	]	]	PUNCT
ejpam-2996	260	6	1	1	NUM
ejpam-2996	260	7	l	l	NOUN
ejpam-2996	260	8	dt	dt	NOUN
ejpam-2996	260	9	≤	≤	NUM
ejpam-2996	260	10	1	1	NUM
ejpam-2996	260	11	2	2	NUM
ejpam-2996	260	12	{	{	PUNCT
ejpam-2996	260	13	∫	∫	PROPN
ejpam-2996	260	14	1	1	NUM
ejpam-2996	260	15	0	0	NUM
ejpam-2996	260	16	[	[	PUNCT
ejpam-2996	260	17	tα−1+sf	tα−1+sf	NOUN
ejpam-2996	260	18	r(ϕ(b	r(ϕ(b	NOUN
ejpam-2996	260	19	)	)	PUNCT
ejpam-2996	260	20	)	)	PUNCT
ejpam-2996	261	1	+	+	ADP
ejpam-2996	261	2	mtα−1(1−	mtα−1(1−	NOUN
ejpam-2996	261	3	t)sf	t)sf	PROPN
ejpam-2996	261	4	r(ϕ(a	r(ϕ(a	NOUN
ejpam-2996	261	5	)	)	PUNCT
ejpam-2996	261	6	)	)	PUNCT
ejpam-2996	261	7	]	]	PUNCT
ejpam-2996	261	8	2	2	NUM
ejpam-2996	261	9	r	r	NOUN
ejpam-2996	261	10	dt	dt	NOUN
ejpam-2996	261	11	+	+	CCONJ
ejpam-2996	261	12	∫	∫	PROPN
ejpam-2996	261	13	1	1	NUM
ejpam-2996	261	14	0	0	NUM
ejpam-2996	261	15	[	[	PUNCT
ejpam-2996	261	16	tα−1+shl(ϕ(b	tα−1+shl(ϕ(b	NOUN
ejpam-2996	261	17	)	)	PUNCT
ejpam-2996	261	18	)	)	PUNCT
ejpam-2996	262	1	+	+	PROPN
ejpam-2996	262	2	mtα−1(1−	mtα−1(1−	PROPN
ejpam-2996	262	3	t)shl(ϕ(a	t)shl(ϕ(a	PROPN
ejpam-2996	262	4	)	)	PUNCT
ejpam-2996	262	5	)	)	PUNCT
ejpam-2996	262	6	]	]	PUNCT
ejpam-2996	262	7	2	2	NUM
ejpam-2996	262	8	l	l	NOUN
ejpam-2996	262	9	dt	dt	NOUN
ejpam-2996	262	10	}	}	PUNCT
ejpam-2996	262	11	≤	≤	NUM
ejpam-2996	262	12	1	1	NUM
ejpam-2996	262	13	2	2	NUM
ejpam-2996	262	14	[	[	X
ejpam-2996	262	15	{	{	PUNCT
ejpam-2996	262	16	(	(	PUNCT
ejpam-2996	262	17	∫	∫	PROPN
ejpam-2996	262	18	1	1	NUM
ejpam-2996	262	19	0	0	NUM
ejpam-2996	262	20	t	t	NOUN
ejpam-2996	262	21	2(α−1+s	2(α−1+s	NUM
ejpam-2996	262	22	)	)	PUNCT
ejpam-2996	262	23	r	r	NOUN
ejpam-2996	262	24	f2(ϕ(b))dt	f2(ϕ(b))dt	NOUN
ejpam-2996	262	25	)	)	PUNCT
ejpam-2996	262	26	r	r	NOUN
ejpam-2996	262	27	2	2	NUM
ejpam-2996	262	28	+	+	CCONJ
ejpam-2996	262	29	(	(	PUNCT
ejpam-2996	262	30	∫	∫	PROPN
ejpam-2996	262	31	1	1	NUM
ejpam-2996	262	32	0	0	NUM
ejpam-2996	262	33	m	m	VERB
ejpam-2996	262	34	2	2	NUM
ejpam-2996	262	35	r	r	NOUN
ejpam-2996	262	36	t	t	NOUN
ejpam-2996	262	37	2(α−1	2(α−1	NOUN
ejpam-2996	262	38	)	)	PUNCT
ejpam-2996	262	39	r	r	NOUN
ejpam-2996	262	40	(	(	PUNCT
ejpam-2996	262	41	1−	1−	NUM
ejpam-2996	262	42	t	t	NOUN
ejpam-2996	262	43	)	)	PUNCT
ejpam-2996	262	44	2s	2s	NOUN
ejpam-2996	262	45	r	r	NOUN
ejpam-2996	262	46	f2(ϕ(a))dt	f2(ϕ(a))dt	NOUN
ejpam-2996	262	47	)	)	PUNCT
ejpam-2996	262	48	r	r	NOUN
ejpam-2996	262	49	2	2	NUM
ejpam-2996	262	50	}	}	SYM
ejpam-2996	262	51	2	2	NUM
ejpam-2996	262	52	r	r	NOUN
ejpam-2996	262	53	+	+	NUM
ejpam-2996	262	54	{	{	PUNCT
ejpam-2996	262	55	(	(	PUNCT
ejpam-2996	262	56	∫	∫	PROPN
ejpam-2996	262	57	1	1	NUM
ejpam-2996	262	58	0	0	NUM
ejpam-2996	262	59	t	t	NOUN
ejpam-2996	262	60	2(α−1+s	2(α−1+s	NUM
ejpam-2996	262	61	)	)	PUNCT
ejpam-2996	262	62	l	l	NOUN
ejpam-2996	262	63	h2(ϕ(b))dt	h2(ϕ(b))dt	NOUN
ejpam-2996	262	64	)	)	PUNCT
ejpam-2996	262	65	l	l	NOUN
ejpam-2996	262	66	2	2	NUM
ejpam-2996	262	67	+	+	CCONJ
ejpam-2996	262	68	(	(	PUNCT
ejpam-2996	262	69	∫	∫	PROPN
ejpam-2996	262	70	1	1	NUM
ejpam-2996	262	71	0	0	NUM
ejpam-2996	262	72	m	m	VERB
ejpam-2996	262	73	2	2	NUM
ejpam-2996	262	74	l	l	NOUN
ejpam-2996	262	75	t	t	NOUN
ejpam-2996	262	76	2(α−1	2(α−1	NOUN
ejpam-2996	262	77	)	)	PUNCT
ejpam-2996	262	78	l	l	NOUN
ejpam-2996	262	79	(	(	PUNCT
ejpam-2996	262	80	1−	1−	NUM
ejpam-2996	262	81	t	t	NOUN
ejpam-2996	262	82	)	)	PUNCT
ejpam-2996	262	83	2s	2s	NUM
ejpam-2996	262	84	l	l	NOUN
ejpam-2996	262	85	h2(ϕ(a))dt	h2(ϕ(a))dt	X
ejpam-2996	262	86	)	)	PUNCT
ejpam-2996	262	87	l	l	NOUN
ejpam-2996	262	88	2	2	X
ejpam-2996	262	89	}	}	SYM
ejpam-2996	262	90	2	2	NUM
ejpam-2996	262	91	l	l	NOUN
ejpam-2996	262	92	]	]	PUNCT
ejpam-2996	262	93	=	=	SYM
ejpam-2996	262	94	1	1	NUM
ejpam-2996	262	95	2	2	NUM
ejpam-2996	262	96	{	{	PUNCT
ejpam-2996	262	97	[	[	PUNCT
ejpam-2996	262	98	mf	mf	X
ejpam-2996	262	99	r(ϕ(a))β	r(ϕ(a))β	NUM
ejpam-2996	262	100	r	r	NOUN
ejpam-2996	262	101	2	2	NUM
ejpam-2996	262	102	(	(	PUNCT
ejpam-2996	262	103	2(α−	2(α−	NUM
ejpam-2996	262	104	1	1	NUM
ejpam-2996	262	105	)	)	PUNCT
ejpam-2996	262	106	r	r	NOUN
ejpam-2996	262	107	+	+	NUM
ejpam-2996	262	108	1	1	NUM
ejpam-2996	262	109	,	,	PUNCT
ejpam-2996	262	110	2s	2s	NUM
ejpam-2996	262	111	r	r	NOUN
ejpam-2996	262	112	+	+	NOUN
ejpam-2996	262	113	1	1	NUM
ejpam-2996	262	114	)	)	PUNCT
ejpam-2996	262	115	+	+	CCONJ
ejpam-2996	262	116	f	f	PROPN
ejpam-2996	262	117	r(ϕ(b	r(ϕ(b	PROPN
ejpam-2996	262	118	)	)	PUNCT
ejpam-2996	262	119	)	)	PUNCT
ejpam-2996	263	1	(	(	PUNCT
ejpam-2996	263	2	r	r	NOUN
ejpam-2996	263	3	2(α−	2(α−	NUM
ejpam-2996	263	4	1	1	NUM
ejpam-2996	263	5	+	+	NUM
ejpam-2996	263	6	s	s	X
ejpam-2996	263	7	)	)	PUNCT
ejpam-2996	264	1	+	+	NUM
ejpam-2996	264	2	r	r	NOUN
ejpam-2996	264	3	)	)	PUNCT
ejpam-2996	264	4	r	r	NOUN
ejpam-2996	264	5	2	2	NUM
ejpam-2996	264	6	]	]	SYM
ejpam-2996	264	7	2	2	NUM
ejpam-2996	264	8	r	r	NOUN
ejpam-2996	264	9	+	+	CCONJ
ejpam-2996	264	10	[	[	PUNCT
ejpam-2996	264	11	mhl(ϕ(a))β	mhl(ϕ(a))β	ADJ
ejpam-2996	264	12	l	l	NOUN
ejpam-2996	264	13	2	2	NUM
ejpam-2996	264	14	(	(	PUNCT
ejpam-2996	264	15	2(α−	2(α−	NUM
ejpam-2996	264	16	1	1	NUM
ejpam-2996	264	17	)	)	PUNCT
ejpam-2996	264	18	l	l	NOUN
ejpam-2996	265	1	+	+	NUM
ejpam-2996	265	2	1	1	NUM
ejpam-2996	265	3	,	,	PUNCT
ejpam-2996	265	4	2s	2	VERB
ejpam-2996	265	5	l	l	NOUN
ejpam-2996	266	1	+	+	NOUN
ejpam-2996	266	2	1	1	NUM
ejpam-2996	266	3	)	)	PUNCT
ejpam-2996	266	4	+	+	CCONJ
ejpam-2996	266	5	hl(ϕ(b	hl(ϕ(b	NOUN
ejpam-2996	266	6	)	)	PUNCT
ejpam-2996	266	7	)	)	PUNCT
ejpam-2996	267	1	(	(	PUNCT
ejpam-2996	267	2	l	l	NOUN
ejpam-2996	267	3	2(α−	2(α−	NUM
ejpam-2996	267	4	1	1	NUM
ejpam-2996	267	5	+	+	NUM
ejpam-2996	267	6	s	s	X
ejpam-2996	267	7	)	)	PUNCT
ejpam-2996	267	8	+	+	NUM
ejpam-2996	267	9	l	l	NOUN
ejpam-2996	267	10	)	)	PUNCT
ejpam-2996	267	11	l	l	NOUN
ejpam-2996	267	12	2	2	X
ejpam-2996	267	13	]	]	SYM
ejpam-2996	267	14	2	2	NUM
ejpam-2996	267	15	l	l	NOUN
ejpam-2996	267	16	}	}	PUNCT
ejpam-2996	267	17	.	.	PUNCT
ejpam-2996	268	1	corollary	corollary	ADJ
ejpam-2996	268	2	4	4	NUM
ejpam-2996	268	3	.	.	PUNCT
ejpam-2996	269	1	under	under	ADP
ejpam-2996	269	2	the	the	DET
ejpam-2996	269	3	same	same	ADJ
ejpam-2996	269	4	conditions	condition	NOUN
ejpam-2996	269	5	as	as	ADP
ejpam-2996	269	6	in	in	ADP
ejpam-2996	269	7	theorem	theorem	NOUN
ejpam-2996	269	8	5	5	NUM
ejpam-2996	269	9	for	for	ADP
ejpam-2996	269	10	m	m	PROPN
ejpam-2996	269	11	=	=	SYM
ejpam-2996	269	12	s	s	PART
ejpam-2996	269	13	=	=	SYM
ejpam-2996	269	14	1	1	NUM
ejpam-2996	269	15	,	,	PUNCT
ejpam-2996	269	16	ϕ(x	ϕ(x	X
ejpam-2996	269	17	)	)	PUNCT
ejpam-2996	269	18	=	=	SYM
ejpam-2996	269	19	x	x	PUNCT
ejpam-2996	269	20	and	and	CCONJ
ejpam-2996	269	21	η(ϕ(b	η(ϕ(b	PROPN
ejpam-2996	269	22	)	)	PUNCT
ejpam-2996	269	23	,	,	PUNCT
ejpam-2996	269	24	ϕ(a),m	ϕ(a),m	ADJ
ejpam-2996	269	25	)	)	PUNCT
ejpam-2996	270	1	=	=	PUNCT
ejpam-2996	270	2	η(b	η(b	PROPN
ejpam-2996	270	3	,	,	PUNCT
ejpam-2996	270	4	a	a	PRON
ejpam-2996	270	5	)	)	PUNCT
ejpam-2996	270	6	,	,	PUNCT
ejpam-2996	270	7	we	we	PRON
ejpam-2996	270	8	get	get	AUX
ejpam-2996	270	9	(	(	PUNCT
ejpam-2996	270	10	see	see	VERB
ejpam-2996	270	11	[	[	X
ejpam-2996	270	12	2	2	NUM
ejpam-2996	270	13	]	]	PUNCT
ejpam-2996	270	14	,	,	PUNCT
ejpam-2996	270	15	theorem	theorem	VERB
ejpam-2996	270	16	3.3	3.3	NUM
ejpam-2996	270	17	)	)	PUNCT
ejpam-2996	270	18	.	.	PUNCT
ejpam-2996	271	1	theorem	theorem	VERB
ejpam-2996	271	2	6	6	NUM
ejpam-2996	271	3	.	.	PUNCT
ejpam-2996	272	1	let	let	VERB
ejpam-2996	272	2	ϕ	ϕ	NOUN
ejpam-2996	272	3	:	:	PUNCT
ejpam-2996	273	1	i	i	PRON
ejpam-2996	273	2	−→	−→	VERB
ejpam-2996	273	3	k	k	X
ejpam-2996	273	4	be	be	AUX
ejpam-2996	273	5	a	a	DET
ejpam-2996	273	6	continuous	continuous	ADJ
ejpam-2996	273	7	increasing	increase	VERB
ejpam-2996	273	8	function	function	NOUN
ejpam-2996	273	9	.	.	PUNCT
ejpam-2996	274	1	suppose	suppose	VERB
ejpam-2996	274	2	k	k	PROPN
ejpam-2996	274	3	⊆	⊆	NUM
ejpam-2996	274	4	r	r	NOUN
ejpam-2996	274	5	be	be	VERB
ejpam-2996	274	6	an	an	DET
ejpam-2996	274	7	open	open	ADJ
ejpam-2996	274	8	m	m	NOUN
ejpam-2996	274	9	-	-	PUNCT
ejpam-2996	274	10	invex	invex	NOUN
ejpam-2996	274	11	subset	subset	VERB
ejpam-2996	274	12	with	with	ADP
ejpam-2996	274	13	respect	respect	NOUN
ejpam-2996	274	14	to	to	ADP
ejpam-2996	274	15	η	η	PROPN
ejpam-2996	274	16	:	:	PUNCT
ejpam-2996	275	1	k	k	PROPN
ejpam-2996	275	2	×	×	PROPN
ejpam-2996	275	3	k	k	PROPN
ejpam-2996	275	4	×	×	PROPN
ejpam-2996	275	5	(	(	PUNCT
ejpam-2996	275	6	0	0	NUM
ejpam-2996	275	7	,	,	PUNCT
ejpam-2996	275	8	1	1	NUM
ejpam-2996	275	9	]	]	X
ejpam-2996	275	10	−→	−→	ADJ
ejpam-2996	275	11	r	r	NOUN
ejpam-2996	275	12	for	for	ADP
ejpam-2996	275	13	any	any	DET
ejpam-2996	275	14	fixed	fix	VERB
ejpam-2996	275	15	s	s	NOUN
ejpam-2996	275	16	,	,	PUNCT
ejpam-2996	275	17	m	m	VERB
ejpam-2996	275	18	∈	∈	ADJ
ejpam-2996	275	19	(	(	PUNCT
ejpam-2996	275	20	0	0	NUM
ejpam-2996	275	21	,	,	PUNCT
ejpam-2996	275	22	1	1	NUM
ejpam-2996	275	23	]	]	PUNCT
ejpam-2996	275	24	with	with	ADP
ejpam-2996	275	25	mϕ(a	mϕ(a	NOUN
ejpam-2996	275	26	)	)	PUNCT
ejpam-2996	275	27	<	<	X
ejpam-2996	275	28	mϕ(a	mϕ(a	NOUN
ejpam-2996	275	29	)	)	PUNCT
ejpam-2996	275	30	+	+	CCONJ
ejpam-2996	275	31	η(ϕ(b	η(ϕ(b	PROPN
ejpam-2996	275	32	)	)	PUNCT
ejpam-2996	275	33	,	,	PUNCT
ejpam-2996	275	34	ϕ(a),m	ϕ(a),m	ADJ
ejpam-2996	275	35	)	)	PUNCT
ejpam-2996	275	36	.	.	PUNCT
ejpam-2996	276	1	assume	assume	VERB
ejpam-2996	276	2	that	that	SCONJ
ejpam-2996	276	3	f	f	X
ejpam-2996	276	4	,	,	PUNCT
ejpam-2996	276	5	h	h	NOUN
ejpam-2996	276	6	:	:	PUNCT
ejpam-2996	277	1	k	k	X
ejpam-2996	277	2	=	=	PUNCT
ejpam-2996	278	1	[	[	X
ejpam-2996	278	2	mϕ(a),mϕ(a	mϕ(a),mϕ(a	NOUN
ejpam-2996	278	3	)	)	PUNCT
ejpam-2996	278	4	+	+	NUM
ejpam-2996	278	5	η(ϕ(b	η(ϕ(b	PROPN
ejpam-2996	278	6	)	)	PUNCT
ejpam-2996	278	7	,	,	PUNCT
ejpam-2996	278	8	ϕ(a),m	ϕ(a),m	ADJ
ejpam-2996	278	9	)	)	PUNCT
ejpam-2996	278	10	]	]	PUNCT
ejpam-2996	279	1	−→	−→	NOUN
ejpam-2996	279	2	(	(	PUNCT
ejpam-2996	279	3	0,∞	0,∞	NOUN
ejpam-2996	279	4	)	)	PUNCT
ejpam-2996	279	5	are	be	AUX
ejpam-2996	279	6	respectively	respectively	ADV
ejpam-2996	279	7	generalized	generalize	VERB
ejpam-2996	279	8	(	(	PUNCT
ejpam-2996	279	9	r	r	NOUN
ejpam-2996	279	10	;	;	PUNCT
ejpam-2996	279	11	s	s	X
ejpam-2996	279	12	,	,	PUNCT
ejpam-2996	279	13	m	m	PRON
ejpam-2996	279	14	,	,	PUNCT
ejpam-2996	279	15	ϕ)-preinvex	ϕ)-preinvex	NOUN
ejpam-2996	279	16	function	function	NOUN
ejpam-2996	279	17	and	and	CCONJ
ejpam-2996	279	18	generalized	generalize	VERB
ejpam-2996	279	19	(	(	PUNCT
ejpam-2996	279	20	l	l	NOUN
ejpam-2996	279	21	;	;	PUNCT
ejpam-2996	279	22	s	s	X
ejpam-2996	279	23	,	,	PUNCT
ejpam-2996	279	24	m	m	PRON
ejpam-2996	279	25	,	,	PUNCT
ejpam-2996	279	26	ϕ)-preinvex	ϕ)-preinvex	AUX
ejpam-2996	279	27	function	function	VERB
ejpam-2996	279	28	on	on	ADP
ejpam-2996	279	29	an	an	DET
ejpam-2996	279	30	open	open	ADJ
ejpam-2996	279	31	m	m	NOUN
ejpam-2996	279	32	-	-	PUNCT
ejpam-2996	279	33	invex	invex	NOUN
ejpam-2996	279	34	set	set	VERB
ejpam-2996	279	35	k	k	PROPN
ejpam-2996	279	36	◦	◦	NOUN
ejpam-2996	279	37	.	.	PUNCT
ejpam-2996	280	1	then	then	ADV
ejpam-2996	280	2	for	for	ADP
ejpam-2996	280	3	α	α	PROPN
ejpam-2996	280	4	>	>	X
ejpam-2996	280	5	0	0	NUM
ejpam-2996	280	6	,	,	PUNCT
ejpam-2996	280	7	r	r	NOUN
ejpam-2996	280	8	>	>	X
ejpam-2996	280	9	1	1	NUM
ejpam-2996	280	10	and	and	CCONJ
ejpam-2996	280	11	r−1	r−1	PROPN
ejpam-2996	280	12	+	+	CCONJ
ejpam-2996	280	13	l−1	l−1	PROPN
ejpam-2996	280	14	=	=	SYM
ejpam-2996	280	15	1	1	NUM
ejpam-2996	280	16	,	,	PUNCT
ejpam-2996	280	17	we	we	PRON
ejpam-2996	280	18	have	have	VERB
ejpam-2996	280	19	γ(α	γ(α	NOUN
ejpam-2996	280	20	)	)	PUNCT
ejpam-2996	280	21	ηα(ϕ(b	ηα(ϕ(b	PROPN
ejpam-2996	280	22	)	)	PUNCT
ejpam-2996	280	23	,	,	PUNCT
ejpam-2996	280	24	ϕ(a),m	ϕ(a),m	ADJ
ejpam-2996	280	25	)	)	PUNCT
ejpam-2996	280	26	jα(mϕ(a)+η(ϕ(b),ϕ(a),m))−f(mϕ(a))h(mϕ(a	jα(mϕ(a)+η(ϕ(b),ϕ(a),m))−f(mϕ(a))h(mϕ(a	PROPN
ejpam-2996	280	27	)	)	PUNCT
ejpam-2996	280	28	)	)	PUNCT
ejpam-2996	281	1	≤	≤	NOUN
ejpam-2996	281	2	{	{	PUNCT
ejpam-2996	281	3	f	f	PROPN
ejpam-2996	281	4	r(ϕ(b	r(ϕ(b	PROPN
ejpam-2996	281	5	)	)	PUNCT
ejpam-2996	281	6	)	)	PUNCT
ejpam-2996	282	1	s+	s+	PUNCT
ejpam-2996	282	2	α	α	PROPN
ejpam-2996	283	1	+	+	PROPN
ejpam-2996	283	2	mf	mf	X
ejpam-2996	283	3	r(ϕ(a))β(α	r(ϕ(a))β(α	NOUN
ejpam-2996	283	4	,	,	PUNCT
ejpam-2996	283	5	s+	s+	PUNCT
ejpam-2996	283	6	1	1	NUM
ejpam-2996	283	7	)	)	PUNCT
ejpam-2996	283	8	}	}	PUNCT
ejpam-2996	283	9	1	1	NUM
ejpam-2996	283	10	r	r	NOUN
ejpam-2996	283	11	+	+	CCONJ
ejpam-2996	283	12	{	{	PUNCT
ejpam-2996	283	13	hl(ϕ(b	hl(ϕ(b	NOUN
ejpam-2996	283	14	)	)	PUNCT
ejpam-2996	283	15	)	)	PUNCT
ejpam-2996	284	1	s+	s+	PUNCT
ejpam-2996	284	2	α	α	PROPN
ejpam-2996	284	3	+	+	PROPN
ejpam-2996	284	4	mhl(ϕ(a))β(α	mhl(ϕ(a))β(α	NOUN
ejpam-2996	284	5	,	,	PUNCT
ejpam-2996	284	6	s+	s+	X
ejpam-2996	284	7	1	1	NUM
ejpam-2996	284	8	)	)	PUNCT
ejpam-2996	284	9	}	}	PUNCT
ejpam-2996	284	10	1	1	NUM
ejpam-2996	284	11	l	l	NOUN
ejpam-2996	284	12	.	.	PUNCT
ejpam-2996	285	1	(	(	PUNCT
ejpam-2996	285	2	9	9	X
ejpam-2996	285	3	)	)	PUNCT
ejpam-2996	285	4	references	reference	NOUN
ejpam-2996	285	5	504	504	NUM
ejpam-2996	285	6	proof	proof	NOUN
ejpam-2996	285	7	.	.	PUNCT
ejpam-2996	286	1	let	let	VERB
ejpam-2996	287	1	r	r	PRON
ejpam-2996	287	2	>	>	X
ejpam-2996	287	3	1	1	NUM
ejpam-2996	287	4	and	and	CCONJ
ejpam-2996	287	5	r−1	r−1	PROPN
ejpam-2996	288	1	+	+	CCONJ
ejpam-2996	288	2	l−1	l−1	PROPN
ejpam-2996	288	3	=	=	SYM
ejpam-2996	288	4	1	1	X
ejpam-2996	288	5	.	.	PUNCT
ejpam-2996	289	1	since	since	SCONJ
ejpam-2996	289	2	f	f	PROPN
ejpam-2996	289	3	and	and	CCONJ
ejpam-2996	289	4	h	h	PROPN
ejpam-2996	289	5	are	be	AUX
ejpam-2996	289	6	respectively	respectively	ADV
ejpam-2996	289	7	generalized	generalize	VERB
ejpam-2996	289	8	(	(	PUNCT
ejpam-2996	289	9	r	r	NOUN
ejpam-2996	289	10	;	;	PUNCT
ejpam-2996	289	11	s	s	X
ejpam-2996	289	12	,	,	PUNCT
ejpam-2996	289	13	m	m	PRON
ejpam-2996	289	14	,	,	PUNCT
ejpam-2996	289	15	ϕ)-preinvex	ϕ)-preinvex	NOUN
ejpam-2996	289	16	function	function	NOUN
ejpam-2996	289	17	and	and	CCONJ
ejpam-2996	289	18	generalized	generalize	VERB
ejpam-2996	289	19	(	(	PUNCT
ejpam-2996	289	20	l	l	NOUN
ejpam-2996	289	21	;	;	PUNCT
ejpam-2996	289	22	s	s	X
ejpam-2996	289	23	,	,	PUNCT
ejpam-2996	289	24	m	m	PRON
ejpam-2996	289	25	,	,	PUNCT
ejpam-2996	289	26	ϕ)-preinvex	ϕ)-preinvex	AUX
ejpam-2996	289	27	function	function	VERB
ejpam-2996	289	28	on	on	ADP
ejpam-2996	289	29	an	an	DET
ejpam-2996	289	30	open	open	ADJ
ejpam-2996	289	31	minvex	minvex	NOUN
ejpam-2996	289	32	set	set	VERB
ejpam-2996	289	33	k	k	NOUN
ejpam-2996	289	34	◦	◦	NOUN
ejpam-2996	289	35	,	,	PUNCT
ejpam-2996	289	36	combining	combine	VERB
ejpam-2996	289	37	with	with	ADP
ejpam-2996	289	38	hölder	hölder	NOUN
ejpam-2996	289	39	inequality	inequality	NOUN
ejpam-2996	289	40	for	for	ADP
ejpam-2996	289	41	all	all	DET
ejpam-2996	289	42	t	t	NOUN
ejpam-2996	289	43	∈	∈	PROPN
ejpam-2996	290	1	[	[	X
ejpam-2996	290	2	0	0	NUM
ejpam-2996	290	3	,	,	PUNCT
ejpam-2996	290	4	1	1	NUM
ejpam-2996	290	5	]	]	PUNCT
ejpam-2996	290	6	and	and	CCONJ
ejpam-2996	290	7	for	for	ADP
ejpam-2996	290	8	any	any	DET
ejpam-2996	290	9	fixed	fix	VERB
ejpam-2996	290	10	s	s	NOUN
ejpam-2996	290	11	,	,	PUNCT
ejpam-2996	290	12	m	m	VERB
ejpam-2996	290	13	∈	∈	ADJ
ejpam-2996	290	14	(	(	PUNCT
ejpam-2996	290	15	0	0	NUM
ejpam-2996	290	16	,	,	PUNCT
ejpam-2996	290	17	1	1	NUM
ejpam-2996	290	18	]	]	PUNCT
ejpam-2996	290	19	,	,	PUNCT
ejpam-2996	290	20	we	we	PRON
ejpam-2996	290	21	get	get	VERB
ejpam-2996	290	22	γ(α	γ(α	NOUN
ejpam-2996	290	23	)	)	PUNCT
ejpam-2996	290	24	ηα(ϕ(b	ηα(ϕ(b	NOUN
ejpam-2996	290	25	)	)	PUNCT
ejpam-2996	290	26	,	,	PUNCT
ejpam-2996	290	27	ϕ(a),m	ϕ(a),m	ADJ
ejpam-2996	290	28	)	)	PUNCT
ejpam-2996	290	29	jα(mϕ(a)+η(ϕ(b),ϕ(a),m))−f(mϕ(a))h(mϕ(a	jα(mϕ(a)+η(ϕ(b),ϕ(a),m))−f(mϕ(a))h(mϕ(a	PROPN
ejpam-2996	290	30	)	)	PUNCT
ejpam-2996	290	31	)	)	PUNCT
ejpam-2996	291	1	=	=	PUNCT
ejpam-2996	291	2	∫	∫	PROPN
ejpam-2996	291	3	1	1	NUM
ejpam-2996	291	4	0	0	NUM
ejpam-2996	291	5	t(α−1	t(α−1	NOUN
ejpam-2996	291	6	)	)	PUNCT
ejpam-2996	291	7	(	(	PUNCT
ejpam-2996	291	8	1	1	NUM
ejpam-2996	291	9	r	r	NOUN
ejpam-2996	291	10	+	+	NOUN
ejpam-2996	291	11	1	1	NUM
ejpam-2996	291	12	l	l	NOUN
ejpam-2996	291	13	)	)	PUNCT
ejpam-2996	291	14	f(mϕ(a	f(mϕ(a	NOUN
ejpam-2996	291	15	)	)	PUNCT
ejpam-2996	291	16	+	+	CCONJ
ejpam-2996	291	17	tη(ϕ(b	tη(ϕ(b	NUM
ejpam-2996	291	18	)	)	PUNCT
ejpam-2996	291	19	,	,	PUNCT
ejpam-2996	291	20	ϕ(a),m	ϕ(a),m	ADJ
ejpam-2996	291	21	)	)	PUNCT
ejpam-2996	291	22	)	)	PUNCT
ejpam-2996	292	1	×h(mϕ(a	×h(mϕ(a	NOUN
ejpam-2996	292	2	)	)	PUNCT
ejpam-2996	292	3	+	+	CCONJ
ejpam-2996	292	4	tη(ϕ(b	tη(ϕ(b	NUM
ejpam-2996	292	5	)	)	PUNCT
ejpam-2996	292	6	,	,	PUNCT
ejpam-2996	292	7	ϕ(a),m))dt	ϕ(a),m))dt	PROPN
ejpam-2996	292	8	≤	≤	PROPN
ejpam-2996	292	9	{	{	PUNCT
ejpam-2996	292	10	∫	∫	PROPN
ejpam-2996	292	11	1	1	NUM
ejpam-2996	292	12	0	0	NUM
ejpam-2996	293	1	[	[	PUNCT
ejpam-2996	293	2	tα−1+sf	tα−1+sf	NOUN
ejpam-2996	293	3	r(ϕ(b	r(ϕ(b	NOUN
ejpam-2996	293	4	)	)	PUNCT
ejpam-2996	293	5	)	)	PUNCT
ejpam-2996	294	1	+	+	ADP
ejpam-2996	294	2	mtα−1(1−	mtα−1(1−	NOUN
ejpam-2996	294	3	t)sf	t)sf	PROPN
ejpam-2996	294	4	r(ϕ(a	r(ϕ(a	NOUN
ejpam-2996	294	5	)	)	PUNCT
ejpam-2996	294	6	)	)	PUNCT
ejpam-2996	294	7	]	]	PUNCT
ejpam-2996	294	8	1	1	NUM
ejpam-2996	294	9	r	r	NOUN
ejpam-2996	294	10	×	×	NOUN
ejpam-2996	294	11	[	[	PUNCT
ejpam-2996	294	12	tα−1+shl(ϕ(b	tα−1+shl(ϕ(b	NOUN
ejpam-2996	294	13	)	)	PUNCT
ejpam-2996	294	14	)	)	PUNCT
ejpam-2996	295	1	+	+	PROPN
ejpam-2996	295	2	mtα−1(1−	mtα−1(1−	PROPN
ejpam-2996	295	3	t)shl(ϕ(a	t)shl(ϕ(a	PROPN
ejpam-2996	295	4	)	)	PUNCT
ejpam-2996	295	5	)	)	PUNCT
ejpam-2996	295	6	]	]	PUNCT
ejpam-2996	295	7	1	1	NUM
ejpam-2996	295	8	l	l	NOUN
ejpam-2996	295	9	dt	dt	X
ejpam-2996	295	10	}	}	PUNCT
ejpam-2996	295	11	≤	≤	NUM
ejpam-2996	295	12	{	{	PUNCT
ejpam-2996	295	13	∫	∫	PROPN
ejpam-2996	295	14	1	1	NUM
ejpam-2996	295	15	0	0	NUM
ejpam-2996	296	1	[	[	PUNCT
ejpam-2996	296	2	tα−1+sf	tα−1+sf	NOUN
ejpam-2996	296	3	r(ϕ(b	r(ϕ(b	NOUN
ejpam-2996	296	4	)	)	PUNCT
ejpam-2996	296	5	)	)	PUNCT
ejpam-2996	297	1	+	+	ADP
ejpam-2996	297	2	mtα−1(1−	mtα−1(1−	NOUN
ejpam-2996	297	3	t)sf	t)sf	PROPN
ejpam-2996	297	4	r(ϕ(a	r(ϕ(a	NOUN
ejpam-2996	297	5	)	)	PUNCT
ejpam-2996	297	6	)	)	PUNCT
ejpam-2996	297	7	]	]	PUNCT
ejpam-2996	297	8	dt	dt	X
ejpam-2996	297	9	}	}	PUNCT
ejpam-2996	297	10	1	1	NUM
ejpam-2996	297	11	r	r	NOUN
ejpam-2996	297	12	+	+	CCONJ
ejpam-2996	297	13	{	{	PUNCT
ejpam-2996	297	14	∫	∫	PROPN
ejpam-2996	297	15	1	1	NUM
ejpam-2996	297	16	0	0	NUM
ejpam-2996	297	17	[	[	PUNCT
ejpam-2996	297	18	tα−1+shl(ϕ(b	tα−1+shl(ϕ(b	NOUN
ejpam-2996	297	19	)	)	PUNCT
ejpam-2996	297	20	)	)	PUNCT
ejpam-2996	298	1	+	+	PROPN
ejpam-2996	298	2	mtα−1(1−	mtα−1(1−	PROPN
ejpam-2996	298	3	t)shl(ϕ(a	t)shl(ϕ(a	PROPN
ejpam-2996	298	4	)	)	PUNCT
ejpam-2996	298	5	)	)	PUNCT
ejpam-2996	298	6	]	]	PUNCT
ejpam-2996	299	1	dt	dt	X
ejpam-2996	300	1	}	}	PUNCT
ejpam-2996	300	2	1	1	NUM
ejpam-2996	300	3	l	l	NOUN
ejpam-2996	300	4	=	=	PUNCT
ejpam-2996	300	5	{	{	PUNCT
ejpam-2996	300	6	f	f	PROPN
ejpam-2996	300	7	r(ϕ(b	r(ϕ(b	PROPN
ejpam-2996	300	8	)	)	PUNCT
ejpam-2996	300	9	)	)	PUNCT
ejpam-2996	301	1	s+	s+	PUNCT
ejpam-2996	301	2	α	α	PROPN
ejpam-2996	302	1	+	+	PROPN
ejpam-2996	302	2	mf	mf	X
ejpam-2996	302	3	r(ϕ(a))β(α	r(ϕ(a))β(α	NOUN
ejpam-2996	302	4	,	,	PUNCT
ejpam-2996	302	5	s+	s+	PUNCT
ejpam-2996	302	6	1	1	NUM
ejpam-2996	302	7	)	)	PUNCT
ejpam-2996	302	8	}	}	PUNCT
ejpam-2996	302	9	1	1	NUM
ejpam-2996	302	10	r	r	NOUN
ejpam-2996	302	11	+	+	CCONJ
ejpam-2996	302	12	{	{	PUNCT
ejpam-2996	302	13	hl(ϕ(b	hl(ϕ(b	NOUN
ejpam-2996	302	14	)	)	PUNCT
ejpam-2996	302	15	)	)	PUNCT
ejpam-2996	303	1	s+	s+	PUNCT
ejpam-2996	303	2	α	α	PROPN
ejpam-2996	303	3	+	+	PROPN
ejpam-2996	303	4	mhl(ϕ(a))β(α	mhl(ϕ(a))β(α	NOUN
ejpam-2996	303	5	,	,	PUNCT
ejpam-2996	303	6	s+	s+	X
ejpam-2996	303	7	1	1	NUM
ejpam-2996	303	8	)	)	PUNCT
ejpam-2996	303	9	}	}	PUNCT
ejpam-2996	303	10	1	1	NUM
ejpam-2996	303	11	l	l	NOUN
ejpam-2996	303	12	.	.	PUNCT
ejpam-2996	304	1	corollary	corollary	ADJ
ejpam-2996	304	2	5	5	NUM
ejpam-2996	304	3	.	.	PUNCT
ejpam-2996	305	1	under	under	ADP
ejpam-2996	305	2	the	the	DET
ejpam-2996	305	3	same	same	ADJ
ejpam-2996	305	4	conditions	condition	NOUN
ejpam-2996	305	5	as	as	ADP
ejpam-2996	305	6	in	in	ADP
ejpam-2996	305	7	theorem	theorem	NOUN
ejpam-2996	305	8	6	6	NUM
ejpam-2996	305	9	for	for	ADP
ejpam-2996	305	10	m	m	NOUN
ejpam-2996	305	11	=	=	SYM
ejpam-2996	305	12	s	s	PART
ejpam-2996	305	13	=	=	SYM
ejpam-2996	305	14	1	1	NUM
ejpam-2996	305	15	,	,	PUNCT
ejpam-2996	305	16	ϕ(x	ϕ(x	X
ejpam-2996	305	17	)	)	PUNCT
ejpam-2996	305	18	=	=	SYM
ejpam-2996	305	19	x	x	PUNCT
ejpam-2996	305	20	and	and	CCONJ
ejpam-2996	305	21	η(ϕ(b	η(ϕ(b	PROPN
ejpam-2996	305	22	)	)	PUNCT
ejpam-2996	305	23	,	,	PUNCT
ejpam-2996	305	24	ϕ(a),m	ϕ(a),m	ADJ
ejpam-2996	305	25	)	)	PUNCT
ejpam-2996	306	1	=	=	PUNCT
ejpam-2996	306	2	η(b	η(b	PROPN
ejpam-2996	306	3	,	,	PUNCT
ejpam-2996	306	4	a	a	PRON
ejpam-2996	306	5	)	)	PUNCT
ejpam-2996	306	6	,	,	PUNCT
ejpam-2996	306	7	we	we	PRON
ejpam-2996	306	8	get	get	AUX
ejpam-2996	306	9	(	(	PUNCT
ejpam-2996	306	10	see	see	VERB
ejpam-2996	306	11	[	[	X
ejpam-2996	306	12	2	2	NUM
ejpam-2996	306	13	]	]	PUNCT
ejpam-2996	306	14	,	,	PUNCT
ejpam-2996	306	15	theorem	theorem	VERB
ejpam-2996	306	16	3.9	3.9	NUM
ejpam-2996	306	17	)	)	PUNCT
ejpam-2996	306	18	.	.	PUNCT
ejpam-2996	307	1	remark	remark	PROPN
ejpam-2996	307	2	3	3	NUM
ejpam-2996	307	3	.	.	PUNCT
ejpam-2996	308	1	for	for	ADP
ejpam-2996	308	2	different	different	ADJ
ejpam-2996	308	3	choices	choice	NOUN
ejpam-2996	308	4	of	of	ADP
ejpam-2996	308	5	positive	positive	ADJ
ejpam-2996	308	6	values	value	NOUN
ejpam-2996	308	7	r	r	NOUN
ejpam-2996	308	8	,	,	PUNCT
ejpam-2996	308	9	l	l	NOUN
ejpam-2996	308	10	=	=	SYM
ejpam-2996	308	11	1	1	NUM
ejpam-2996	308	12	2	2	NUM
ejpam-2996	308	13	,	,	PUNCT
ejpam-2996	308	14	1	1	NUM
ejpam-2996	308	15	3	3	NUM
ejpam-2996	308	16	,	,	PUNCT
ejpam-2996	308	17	2	2	NUM
ejpam-2996	308	18	,	,	PUNCT
ejpam-2996	308	19	etc	etc	X
ejpam-2996	308	20	.	.	X
ejpam-2996	308	21	,	,	PUNCT
ejpam-2996	308	22	for	for	ADP
ejpam-2996	308	23	any	any	DET
ejpam-2996	308	24	fixed	fix	VERB
ejpam-2996	308	25	s	s	NOUN
ejpam-2996	308	26	,	,	PUNCT
ejpam-2996	308	27	m	m	VERB
ejpam-2996	308	28	∈	∈	ADJ
ejpam-2996	308	29	(	(	PUNCT
ejpam-2996	308	30	0	0	NUM
ejpam-2996	308	31	,	,	PUNCT
ejpam-2996	308	32	1	1	NUM
ejpam-2996	308	33	]	]	PUNCT
ejpam-2996	308	34	and	and	CCONJ
ejpam-2996	308	35	a	a	DET
ejpam-2996	308	36	particular	particular	ADJ
ejpam-2996	308	37	choices	choice	NOUN
ejpam-2996	308	38	of	of	ADP
ejpam-2996	308	39	a	a	DET
ejpam-2996	308	40	continuous	continuous	ADJ
ejpam-2996	308	41	increasing	increase	VERB
ejpam-2996	308	42	function	function	NOUN
ejpam-2996	308	43	ϕ(x	ϕ(x	X
ejpam-2996	308	44	)	)	PUNCT
ejpam-2996	308	45	=	=	SYM
ejpam-2996	309	1	ex	ex	X
ejpam-2996	309	2	for	for	ADP
ejpam-2996	309	3	all	all	DET
ejpam-2996	309	4	x	x	SYM
ejpam-2996	309	5	∈	∈	PROPN
ejpam-2996	309	6	r	r	NOUN
ejpam-2996	309	7	,	,	PUNCT
ejpam-2996	309	8	xn	xn	PROPN
ejpam-2996	309	9	for	for	ADP
ejpam-2996	309	10	all	all	DET
ejpam-2996	309	11	x	x	SYM
ejpam-2996	309	12	>	>	PUNCT
ejpam-2996	309	13	0	0	PUNCT
ejpam-2996	309	14	and	and	CCONJ
ejpam-2996	309	15	for	for	ADP
ejpam-2996	309	16	all	all	PRON
ejpam-2996	309	17	n	n	PRON
ejpam-2996	309	18	∈	∈	PROPN
ejpam-2996	309	19	n	n	CCONJ
ejpam-2996	309	20	,	,	PUNCT
ejpam-2996	309	21	etc	etc	X
ejpam-2996	309	22	.	.	X
ejpam-2996	309	23	,	,	PUNCT
ejpam-2996	309	24	by	by	ADP
ejpam-2996	309	25	theorem	theorem	NOUN
ejpam-2996	309	26	4	4	NUM
ejpam-2996	309	27	,	,	PUNCT
ejpam-2996	309	28	theorem	theorem	VERB
ejpam-2996	309	29	5	5	NUM
ejpam-2996	309	30	and	and	CCONJ
ejpam-2996	309	31	theorem	theorem	VERB
ejpam-2996	309	32	6	6	NUM
ejpam-2996	309	33	we	we	PRON
ejpam-2996	309	34	can	can	AUX
ejpam-2996	309	35	get	get	VERB
ejpam-2996	309	36	some	some	DET
ejpam-2996	309	37	special	special	ADJ
ejpam-2996	309	38	kinds	kind	NOUN
ejpam-2996	309	39	of	of	ADP
ejpam-2996	309	40	hermite	hermite	ADJ
ejpam-2996	309	41	-	-	PUNCT
ejpam-2996	309	42	hadamard	hadamard	ADJ
ejpam-2996	309	43	type	type	NOUN
ejpam-2996	309	44	fractional	fractional	ADJ
ejpam-2996	309	45	integral	integral	ADJ
ejpam-2996	309	46	inequalities	inequality	NOUN
ejpam-2996	309	47	.	.	PUNCT
ejpam-2996	310	1	references	reference	NOUN
ejpam-2996	310	2	[	[	X
ejpam-2996	310	3	1	1	NUM
ejpam-2996	310	4	]	]	PUNCT
ejpam-2996	310	5	a.	a.	NOUN
ejpam-2996	310	6	kashuri	kashuri	PROPN
ejpam-2996	310	7	,	,	PUNCT
ejpam-2996	310	8	r.	r.	PROPN
ejpam-2996	310	9	liko	liko	PROPN
ejpam-2996	310	10	,	,	PUNCT
ejpam-2996	310	11	ostrowski	ostrowski	ADJ
ejpam-2996	310	12	type	type	NOUN
ejpam-2996	310	13	fractional	fractional	ADJ
ejpam-2996	310	14	integral	integral	ADJ
ejpam-2996	310	15	inequalities	inequality	NOUN
ejpam-2996	310	16	for	for	ADP
ejpam-2996	310	17	generalized	generalized	ADJ
ejpam-2996	310	18	(	(	PUNCT
ejpam-2996	310	19	s	s	PROPN
ejpam-2996	310	20	,	,	PUNCT
ejpam-2996	310	21	m	m	PRON
ejpam-2996	310	22	,	,	PUNCT
ejpam-2996	310	23	ϕ)-preinvex	ϕ)-preinvex	NOUN
ejpam-2996	310	24	functions	function	NOUN
ejpam-2996	310	25	,	,	PUNCT
ejpam-2996	310	26	aust	aust	PROPN
ejpam-2996	310	27	.	.	PUNCT
ejpam-2996	311	1	j.	j.	PROPN
ejpam-2996	311	2	math	math	PROPN
ejpam-2996	311	3	.	.	PUNCT
ejpam-2996	312	1	anal	anal	PROPN
ejpam-2996	312	2	.	.	PUNCT
ejpam-2996	313	1	appl	appl	PROPN
ejpam-2996	313	2	.	.	PROPN
ejpam-2996	313	3	,	,	PUNCT
ejpam-2996	313	4	13	13	NUM
ejpam-2996	313	5	,	,	PUNCT
ejpam-2996	313	6	1	1	NUM
ejpam-2996	313	7	(	(	PUNCT
ejpam-2996	313	8	2016	2016	NUM
ejpam-2996	313	9	)	)	PUNCT
ejpam-2996	313	10	,	,	PUNCT
ejpam-2996	313	11	article	article	NOUN
ejpam-2996	313	12	16	16	NUM
ejpam-2996	313	13	,	,	PUNCT
ejpam-2996	313	14	1	1	NUM
ejpam-2996	313	15	-	-	SYM
ejpam-2996	313	16	11	11	NUM
ejpam-2996	313	17	.	.	PUNCT
ejpam-2996	314	1	[	[	X
ejpam-2996	314	2	2	2	NUM
ejpam-2996	314	3	]	]	PUNCT
ejpam-2996	314	4	a.	a.	NOUN
ejpam-2996	314	5	akkurt	akkurt	PROPN
ejpam-2996	314	6	,	,	PUNCT
ejpam-2996	314	7	h.	h.	PROPN
ejpam-2996	314	8	yildirim	yildirim	PROPN
ejpam-2996	314	9	,	,	PUNCT
ejpam-2996	314	10	on	on	ADP
ejpam-2996	314	11	some	some	DET
ejpam-2996	314	12	fractional	fractional	ADJ
ejpam-2996	314	13	integral	integral	ADJ
ejpam-2996	314	14	inequalities	inequality	NOUN
ejpam-2996	314	15	of	of	ADP
ejpam-2996	314	16	hermite	hermite	ADJ
ejpam-2996	314	17	-	-	PUNCT
ejpam-2996	314	18	hadamard	hadamard	ADJ
ejpam-2996	314	19	type	type	NOUN
ejpam-2996	314	20	for	for	ADP
ejpam-2996	314	21	r	r	NOUN
ejpam-2996	314	22	-	-	PUNCT
ejpam-2996	314	23	preinvex	preinvex	NOUN
ejpam-2996	314	24	functions	function	NOUN
ejpam-2996	314	25	,	,	PUNCT
ejpam-2996	314	26	khayyam	khayyam	PROPN
ejpam-2996	314	27	j.	j.	PROPN
ejpam-2996	314	28	math	math	PROPN
ejpam-2996	314	29	.	.	PUNCT
ejpam-2996	314	30	,	,	PUNCT
ejpam-2996	314	31	2	2	NUM
ejpam-2996	314	32	,	,	PUNCT
ejpam-2996	314	33	2	2	NUM
ejpam-2996	314	34	(	(	PUNCT
ejpam-2996	314	35	2016	2016	NUM
ejpam-2996	314	36	)	)	PUNCT
ejpam-2996	314	37	,	,	PUNCT
ejpam-2996	314	38	119	119	NUM
ejpam-2996	314	39	-	-	SYM
ejpam-2996	314	40	126	126	NUM
ejpam-2996	314	41	.	.	PUNCT
ejpam-2996	315	1	references	reference	NOUN
ejpam-2996	315	2	505	505	NUM
ejpam-2996	316	1	[	[	X
ejpam-2996	316	2	3	3	X
ejpam-2996	316	3	]	]	PUNCT
ejpam-2996	316	4	t.	t.	PROPN
ejpam-2996	316	5	s.	s.	PROPN
ejpam-2996	316	6	du	du	PROPN
ejpam-2996	316	7	,	,	PUNCT
ejpam-2996	316	8	j.	j.	PROPN
ejpam-2996	316	9	g.	g.	PROPN
ejpam-2996	316	10	liao	liao	PROPN
ejpam-2996	316	11	,	,	PUNCT
ejpam-2996	316	12	y.	y.	PROPN
ejpam-2996	316	13	j.	j.	PROPN
ejpam-2996	316	14	li	li	PROPN
ejpam-2996	316	15	,	,	PUNCT
ejpam-2996	316	16	properties	property	NOUN
ejpam-2996	316	17	and	and	CCONJ
ejpam-2996	316	18	integral	integral	ADJ
ejpam-2996	316	19	inequalities	inequality	NOUN
ejpam-2996	316	20	of	of	ADP
ejpam-2996	316	21	hadamardsimpson	hadamardsimpson	PROPN
ejpam-2996	316	22	type	type	NOUN
ejpam-2996	316	23	for	for	ADP
ejpam-2996	316	24	the	the	DET
ejpam-2996	316	25	generalized	generalized	ADJ
ejpam-2996	316	26	(	(	PUNCT
ejpam-2996	316	27	s	s	X
ejpam-2996	316	28	,	,	PUNCT
ejpam-2996	316	29	m)-preinvex	m)-preinvex	NOUN
ejpam-2996	316	30	functions	function	NOUN
ejpam-2996	316	31	,	,	PUNCT
ejpam-2996	316	32	j.	j.	PROPN
ejpam-2996	316	33	nonlinear	nonlinear	PROPN
ejpam-2996	316	34	sci	sci	PROPN
ejpam-2996	316	35	.	.	PUNCT
ejpam-2996	316	36	appl	appl	PROPN
ejpam-2996	316	37	.	.	PROPN
ejpam-2996	316	38	,	,	PUNCT
ejpam-2996	316	39	9	9	NUM
ejpam-2996	316	40	,	,	PUNCT
ejpam-2996	316	41	(	(	PUNCT
ejpam-2996	316	42	2016	2016	NUM
ejpam-2996	316	43	)	)	PUNCT
ejpam-2996	316	44	,	,	PUNCT
ejpam-2996	316	45	3112	3112	NUM
ejpam-2996	316	46	-	-	SYM
ejpam-2996	316	47	3126	3126	NUM
ejpam-2996	316	48	.	.	PUNCT
ejpam-2996	317	1	[	[	X
ejpam-2996	317	2	4	4	X
ejpam-2996	317	3	]	]	PUNCT
ejpam-2996	317	4	s.	s.	PROPN
ejpam-2996	317	5	s.	s.	PROPN
ejpam-2996	317	6	dragomir	dragomir	PROPN
ejpam-2996	317	7	,	,	PUNCT
ejpam-2996	317	8	j.	j.	PROPN
ejpam-2996	317	9	pečarić	pečarić	PROPN
ejpam-2996	317	10	,	,	PUNCT
ejpam-2996	317	11	l.	l.	PROPN
ejpam-2996	317	12	e.	e.	PROPN
ejpam-2996	317	13	persson	persson	PROPN
ejpam-2996	317	14	,	,	PUNCT
ejpam-2996	317	15	some	some	DET
ejpam-2996	317	16	inequalities	inequality	NOUN
ejpam-2996	317	17	of	of	ADP
ejpam-2996	317	18	hadamard	hadamard	ADJ
ejpam-2996	317	19	type	type	NOUN
ejpam-2996	317	20	,	,	PUNCT
ejpam-2996	317	21	soochow	soochow	PROPN
ejpam-2996	317	22	j.	j.	PROPN
ejpam-2996	317	23	math	math	PROPN
ejpam-2996	317	24	.	.	PROPN
ejpam-2996	317	25	,	,	PUNCT
ejpam-2996	317	26	21	21	NUM
ejpam-2996	317	27	,	,	PUNCT
ejpam-2996	317	28	(	(	PUNCT
ejpam-2996	317	29	1995	1995	NUM
ejpam-2996	317	30	)	)	PUNCT
ejpam-2996	317	31	,	,	PUNCT
ejpam-2996	317	32	335	335	NUM
ejpam-2996	317	33	-	-	SYM
ejpam-2996	317	34	341	341	NUM
ejpam-2996	317	35	.	.	PUNCT
ejpam-2996	318	1	[	[	X
ejpam-2996	318	2	5	5	X
ejpam-2996	318	3	]	]	PUNCT
ejpam-2996	318	4	h.	h.	PROPN
ejpam-2996	318	5	hudzik	hudzik	PROPN
ejpam-2996	318	6	,	,	PUNCT
ejpam-2996	318	7	l.	l.	PROPN
ejpam-2996	318	8	maligranda	maligranda	PROPN
ejpam-2996	318	9	,	,	PUNCT
ejpam-2996	318	10	some	some	DET
ejpam-2996	318	11	remarks	remark	NOUN
ejpam-2996	318	12	on	on	ADP
ejpam-2996	318	13	s	s	ADJ
ejpam-2996	318	14	-	-	PUNCT
ejpam-2996	318	15	convex	convex	ADJ
ejpam-2996	318	16	functions	function	NOUN
ejpam-2996	318	17	,	,	PUNCT
ejpam-2996	318	18	aequationes	aequatione	VERB
ejpam-2996	318	19	math	math	PROPN
ejpam-2996	318	20	.	.	PUNCT
ejpam-2996	318	21	,	,	PUNCT
ejpam-2996	318	22	48	48	NUM
ejpam-2996	318	23	,	,	PUNCT
ejpam-2996	318	24	(	(	PUNCT
ejpam-2996	318	25	1994	1994	NUM
ejpam-2996	318	26	)	)	PUNCT
ejpam-2996	318	27	,	,	PUNCT
ejpam-2996	318	28	100	100	NUM
ejpam-2996	318	29	-	-	SYM
ejpam-2996	318	30	111	111	NUM
ejpam-2996	318	31	.	.	PUNCT
ejpam-2996	319	1	[	[	X
ejpam-2996	319	2	6	6	NUM
ejpam-2996	319	3	]	]	PUNCT
ejpam-2996	319	4	t.	t.	PROPN
ejpam-2996	319	5	antczak	antczak	PROPN
ejpam-2996	319	6	,	,	PUNCT
ejpam-2996	319	7	mean	mean	ADJ
ejpam-2996	319	8	value	value	NOUN
ejpam-2996	319	9	in	in	ADP
ejpam-2996	319	10	invexity	invexity	NOUN
ejpam-2996	319	11	analysis	analysis	NOUN
ejpam-2996	319	12	,	,	PUNCT
ejpam-2996	319	13	nonlinear	nonlinear	ADJ
ejpam-2996	319	14	anal	anal	NOUN
ejpam-2996	319	15	.	.	PUNCT
ejpam-2996	319	16	,	,	PUNCT
ejpam-2996	319	17	60	60	NUM
ejpam-2996	319	18	,	,	PUNCT
ejpam-2996	319	19	(	(	PUNCT
ejpam-2996	319	20	2005	2005	NUM
ejpam-2996	319	21	)	)	PUNCT
ejpam-2996	319	22	,	,	PUNCT
ejpam-2996	319	23	1473	1473	NUM
ejpam-2996	319	24	-	-	SYM
ejpam-2996	319	25	1484	1484	NUM
ejpam-2996	319	26	.	.	PUNCT
ejpam-2996	320	1	[	[	X
ejpam-2996	320	2	7	7	X
ejpam-2996	320	3	]	]	PUNCT
ejpam-2996	320	4	x.	x.	NOUN
ejpam-2996	320	5	m.	m.	PROPN
ejpam-2996	320	6	yang	yang	PROPN
ejpam-2996	320	7	,	,	PUNCT
ejpam-2996	320	8	x.	x.	PROPN
ejpam-2996	320	9	q.	q.	PROPN
ejpam-2996	320	10	yang	yang	PROPN
ejpam-2996	320	11	,	,	PUNCT
ejpam-2996	320	12	k.	k.	PROPN
ejpam-2996	320	13	l.	l.	PROPN
ejpam-2996	320	14	teo	teo	PROPN
ejpam-2996	320	15	,	,	PUNCT
ejpam-2996	320	16	generalized	generalized	ADJ
ejpam-2996	320	17	invexity	invexity	NOUN
ejpam-2996	320	18	and	and	CCONJ
ejpam-2996	320	19	generalized	generalize	VERB
ejpam-2996	320	20	invariant	invariant	ADJ
ejpam-2996	320	21	monotonicity	monotonicity	NOUN
ejpam-2996	320	22	,	,	PUNCT
ejpam-2996	320	23	j.	j.	PROPN
ejpam-2996	320	24	optim	optim	PROPN
ejpam-2996	320	25	.	.	PUNCT
ejpam-2996	321	1	theory	theory	NOUN
ejpam-2996	321	2	appl	appl	PROPN
ejpam-2996	321	3	.	.	PROPN
ejpam-2996	321	4	,	,	PUNCT
ejpam-2996	321	5	117	117	NUM
ejpam-2996	321	6	,	,	PUNCT
ejpam-2996	321	7	(	(	PUNCT
ejpam-2996	321	8	2003	2003	NUM
ejpam-2996	321	9	)	)	PUNCT
ejpam-2996	321	10	,	,	PUNCT
ejpam-2996	321	11	607	607	NUM
ejpam-2996	321	12	-	-	SYM
ejpam-2996	321	13	625	625	NUM
ejpam-2996	321	14	.	.	PUNCT
ejpam-2996	322	1	[	[	X
ejpam-2996	322	2	8	8	NUM
ejpam-2996	322	3	]	]	X
ejpam-2996	322	4	r.	r.	PROPN
ejpam-2996	322	5	pini	pini	PROPN
ejpam-2996	322	6	,	,	PUNCT
ejpam-2996	322	7	invexity	invexity	NOUN
ejpam-2996	322	8	and	and	CCONJ
ejpam-2996	322	9	generalized	generalized	ADJ
ejpam-2996	322	10	convexity	convexity	NOUN
ejpam-2996	322	11	,	,	PUNCT
ejpam-2996	322	12	optimization	optimization	NOUN
ejpam-2996	322	13	.	.	PUNCT
ejpam-2996	322	14	,	,	PUNCT
ejpam-2996	322	15	22	22	NUM
ejpam-2996	322	16	,	,	PUNCT
ejpam-2996	322	17	(	(	PUNCT
ejpam-2996	322	18	1991	1991	NUM
ejpam-2996	322	19	)	)	PUNCT
ejpam-2996	322	20	,	,	PUNCT
ejpam-2996	322	21	513	513	NUM
ejpam-2996	322	22	-	-	SYM
ejpam-2996	322	23	525	525	NUM
ejpam-2996	322	24	.	.	PUNCT
ejpam-2996	323	1	[	[	X
ejpam-2996	323	2	9	9	NUM
ejpam-2996	323	3	]	]	X
ejpam-2996	323	4	d.	d.	PROPN
ejpam-2996	323	5	d.	d.	PROPN
ejpam-2996	323	6	stancu	stancu	PROPN
ejpam-2996	323	7	,	,	PUNCT
ejpam-2996	323	8	g.	g.	PROPN
ejpam-2996	323	9	coman	coman	PROPN
ejpam-2996	323	10	,	,	PUNCT
ejpam-2996	323	11	p.	p.	PROPN
ejpam-2996	323	12	blaga	blaga	PROPN
ejpam-2996	323	13	,	,	PUNCT
ejpam-2996	323	14	analiză	analiză	VERB
ejpam-2996	323	15	numerică	numerică	NOUN
ejpam-2996	323	16	şi	şi	PROPN
ejpam-2996	323	17	teoria	teoria	NOUN
ejpam-2996	323	18	aproximării	aproximării	PROPN
ejpam-2996	323	19	,	,	PUNCT
ejpam-2996	323	20	clujnapoca	clujnapoca	NOUN
ejpam-2996	323	21	:	:	PUNCT
ejpam-2996	323	22	presa	presa	PROPN
ejpam-2996	323	23	universitară	universitară	PROPN
ejpam-2996	323	24	clujeană.	clujeană.	PROPN
ejpam-2996	323	25	,	,	PUNCT
ejpam-2996	323	26	2	2	NUM
ejpam-2996	323	27	,	,	PUNCT
ejpam-2996	323	28	(	(	PUNCT
ejpam-2996	323	29	2002	2002	NUM
ejpam-2996	323	30	)	)	PUNCT
ejpam-2996	323	31	.	.	PUNCT
ejpam-2996	324	1	[	[	X
ejpam-2996	324	2	10	10	NUM
ejpam-2996	324	3	]	]	X
ejpam-2996	324	4	w.	w.	PROPN
ejpam-2996	324	5	liu	liu	PROPN
ejpam-2996	324	6	,	,	PUNCT
ejpam-2996	324	7	new	new	ADJ
ejpam-2996	324	8	integral	integral	ADJ
ejpam-2996	324	9	inequalities	inequality	NOUN
ejpam-2996	324	10	involving	involve	VERB
ejpam-2996	324	11	beta	beta	ADJ
ejpam-2996	324	12	function	function	NOUN
ejpam-2996	324	13	via	via	ADP
ejpam-2996	324	14	p	p	NOUN
ejpam-2996	324	15	-convexity	-convexity	NOUN
ejpam-2996	324	16	,	,	PUNCT
ejpam-2996	324	17	miskolc	miskolc	ADJ
ejpam-2996	324	18	math	math	NOUN
ejpam-2996	324	19	notes	note	NOUN
ejpam-2996	324	20	.	.	PUNCT
ejpam-2996	324	21	,	,	PUNCT
ejpam-2996	324	22	15	15	NUM
ejpam-2996	324	23	,	,	PUNCT
ejpam-2996	324	24	2	2	NUM
ejpam-2996	324	25	(	(	PUNCT
ejpam-2996	324	26	2014	2014	NUM
ejpam-2996	324	27	)	)	PUNCT
ejpam-2996	324	28	,	,	PUNCT
ejpam-2996	324	29	585	585	NUM
ejpam-2996	324	30	-	-	SYM
ejpam-2996	324	31	591	591	NUM
ejpam-2996	324	32	.	.	PUNCT
ejpam-2996	325	1	[	[	X
ejpam-2996	325	2	11	11	NUM
ejpam-2996	325	3	]	]	PUNCT
ejpam-2996	325	4	m.	m.	NOUN
ejpam-2996	325	5	e.	e.	PROPN
ejpam-2996	325	6	özdemir	özdemir	PROPN
ejpam-2996	325	7	,	,	PUNCT
ejpam-2996	325	8	e.	e.	PROPN
ejpam-2996	325	9	set	set	PROPN
ejpam-2996	325	10	,	,	PUNCT
ejpam-2996	325	11	m.	m.	NOUN
ejpam-2996	325	12	alomari	alomari	PROPN
ejpam-2996	325	13	,	,	PUNCT
ejpam-2996	325	14	integral	integral	ADJ
ejpam-2996	325	15	inequalities	inequality	NOUN
ejpam-2996	325	16	via	via	ADP
ejpam-2996	325	17	several	several	ADJ
ejpam-2996	325	18	kinds	kind	NOUN
ejpam-2996	325	19	of	of	ADP
ejpam-2996	325	20	convexity	convexity	NOUN
ejpam-2996	325	21	,	,	PUNCT
ejpam-2996	325	22	creat	creat	PROPN
ejpam-2996	325	23	.	.	PUNCT
ejpam-2996	325	24	math	math	PROPN
ejpam-2996	325	25	.	.	PUNCT
ejpam-2996	326	1	inform	inform	NOUN
ejpam-2996	326	2	.	.	PUNCT
ejpam-2996	326	3	,	,	PUNCT
ejpam-2996	326	4	20	20	NUM
ejpam-2996	326	5	,	,	PUNCT
ejpam-2996	326	6	1	1	NUM
ejpam-2996	326	7	(	(	PUNCT
ejpam-2996	326	8	2011	2011	NUM
ejpam-2996	326	9	)	)	PUNCT
ejpam-2996	326	10	,	,	PUNCT
ejpam-2996	326	11	62	62	NUM
ejpam-2996	326	12	-	-	SYM
ejpam-2996	326	13	73	73	NUM
ejpam-2996	326	14	.	.	PUNCT
ejpam-2996	327	1	[	[	X
ejpam-2996	327	2	12	12	NUM
ejpam-2996	327	3	]	]	PUNCT
ejpam-2996	327	4	w.	w.	PROPN
ejpam-2996	327	5	dong	dong	PROPN
ejpam-2996	327	6	jiang	jiang	PROPN
ejpam-2996	327	7	,	,	PUNCT
ejpam-2996	327	8	d.	d.	PROPN
ejpam-2996	327	9	wei	wei	PROPN
ejpam-2996	327	10	niu	niu	PROPN
ejpam-2996	327	11	,	,	PUNCT
ejpam-2996	327	12	f.	f.	PROPN
ejpam-2996	327	13	qi	qi	PROPN
ejpam-2996	327	14	,	,	PUNCT
ejpam-2996	327	15	some	some	DET
ejpam-2996	327	16	fractional	fractional	ADJ
ejpam-2996	327	17	inequalties	inequaltie	NOUN
ejpam-2996	327	18	of	of	ADP
ejpam-2996	327	19	hermite	hermite	ADJ
ejpam-2996	327	20	-	-	PUNCT
ejpam-2996	327	21	hadamard	hadamard	ADJ
ejpam-2996	327	22	type	type	NOUN
ejpam-2996	327	23	for	for	ADP
ejpam-2996	327	24	r-ϕ-preinvex	r-ϕ-preinvex	NOUN
ejpam-2996	327	25	functions	function	NOUN
ejpam-2996	327	26	,	,	PUNCT
ejpam-2996	327	27	tamkang	tamkang	PROPN
ejpam-2996	327	28	j.	j.	PROPN
ejpam-2996	327	29	math	math	PROPN
ejpam-2996	327	30	.	.	PROPN
ejpam-2996	327	31	,	,	PUNCT
ejpam-2996	327	32	45	45	NUM
ejpam-2996	327	33	,	,	PUNCT
ejpam-2996	327	34	1	1	NUM
ejpam-2996	327	35	(	(	PUNCT
ejpam-2996	327	36	2014	2014	NUM
ejpam-2996	327	37	)	)	PUNCT
ejpam-2996	327	38	,	,	PUNCT
ejpam-2996	327	39	31	31	NUM
ejpam-2996	327	40	-	-	SYM
ejpam-2996	327	41	38	38	NUM
ejpam-2996	327	42	.	.	PUNCT
ejpam-2996	328	1	[	[	X
ejpam-2996	328	2	13	13	NUM
ejpam-2996	328	3	]	]	X
ejpam-2996	328	4	f.	f.	PROPN
ejpam-2996	328	5	qi	qi	PROPN
ejpam-2996	328	6	,	,	PUNCT
ejpam-2996	328	7	b.	b.	PROPN
ejpam-2996	329	1	y.	y.	PROPN
ejpam-2996	329	2	xi	xi	PROPN
ejpam-2996	329	3	,	,	PUNCT
ejpam-2996	329	4	some	some	DET
ejpam-2996	329	5	integral	integral	ADJ
ejpam-2996	329	6	inequalities	inequality	NOUN
ejpam-2996	329	7	of	of	ADP
ejpam-2996	329	8	simpson	simpson	PROPN
ejpam-2996	329	9	type	type	PROPN
ejpam-2996	329	10	for	for	ADP
ejpam-2996	329	11	ga	ga	PROPN
ejpam-2996	329	12	−	−	PROPN
ejpam-2996	329	13	ε	ε	PROPN
ejpam-2996	329	14	-	-	PUNCT
ejpam-2996	329	15	convex	convex	NOUN
ejpam-2996	329	16	functions	function	NOUN
ejpam-2996	329	17	,	,	PUNCT
ejpam-2996	329	18	georgian	georgian	PROPN
ejpam-2996	329	19	math	math	NOUN
ejpam-2996	329	20	.	.	PUNCT
ejpam-2996	330	1	j.	j.	PROPN
ejpam-2996	330	2	,	,	PUNCT
ejpam-2996	330	3	20	20	NUM
ejpam-2996	330	4	,	,	PUNCT
ejpam-2996	330	5	5	5	NUM
ejpam-2996	330	6	(	(	PUNCT
ejpam-2996	330	7	2013	2013	NUM
ejpam-2996	330	8	)	)	PUNCT
ejpam-2996	330	9	,	,	PUNCT
ejpam-2996	330	10	775	775	NUM
ejpam-2996	330	11	-	-	SYM
ejpam-2996	330	12	788	788	NUM
ejpam-2996	330	13	.	.	PUNCT
ejpam-2996	331	1	[	[	X
ejpam-2996	331	2	14	14	NUM
ejpam-2996	331	3	]	]	X
ejpam-2996	331	4	w.	w.	PROPN
ejpam-2996	331	5	liu	liu	PROPN
ejpam-2996	331	6	,	,	PUNCT
ejpam-2996	331	7	w.	w.	PROPN
ejpam-2996	331	8	wen	wen	PROPN
ejpam-2996	331	9	,	,	PUNCT
ejpam-2996	331	10	j.	j.	PROPN
ejpam-2996	331	11	park	park	PROPN
ejpam-2996	331	12	,	,	PUNCT
ejpam-2996	331	13	hermite	hermite	PROPN
ejpam-2996	331	14	-	-	PUNCT
ejpam-2996	331	15	hadamard	hadamard	ADJ
ejpam-2996	331	16	type	type	NOUN
ejpam-2996	331	17	inequalities	inequality	NOUN
ejpam-2996	331	18	for	for	ADP
ejpam-2996	331	19	mt	mt	NOUN
ejpam-2996	331	20	-	-	PUNCT
ejpam-2996	331	21	convex	convex	NOUN
ejpam-2996	331	22	functions	function	NOUN
ejpam-2996	331	23	via	via	ADP
ejpam-2996	331	24	classical	classical	ADJ
ejpam-2996	331	25	integrals	integral	NOUN
ejpam-2996	331	26	and	and	CCONJ
ejpam-2996	331	27	fractional	fractional	ADJ
ejpam-2996	331	28	integrals	integral	NOUN
ejpam-2996	331	29	,	,	PUNCT
ejpam-2996	331	30	j.	j.	PROPN
ejpam-2996	331	31	nonlinear	nonlinear	PROPN
ejpam-2996	331	32	sci	sci	PROPN
ejpam-2996	331	33	.	.	PUNCT
ejpam-2996	331	34	appl	appl	PROPN
ejpam-2996	331	35	.	.	PROPN
ejpam-2996	331	36	,	,	PUNCT
ejpam-2996	331	37	9	9	NUM
ejpam-2996	331	38	,	,	PUNCT
ejpam-2996	331	39	(	(	PUNCT
ejpam-2996	331	40	2016	2016	NUM
ejpam-2996	331	41	)	)	PUNCT
ejpam-2996	331	42	,	,	PUNCT
ejpam-2996	331	43	766	766	NUM
ejpam-2996	331	44	-	-	SYM
ejpam-2996	331	45	777	777	NUM
ejpam-2996	331	46	.	.	PUNCT