id	sid	tid	token	lemma	pos
ejpam-5694	1	1	european	european	PROPN
ejpam-5694	1	2	journal	journal	PROPN
ejpam-5694	1	3	of	of	ADP
ejpam-5694	1	4	pure	pure	ADJ
ejpam-5694	1	5	and	and	CCONJ
ejpam-5694	1	6	applied	applied	ADJ
ejpam-5694	1	7	mathematics	mathematic	NOUN
ejpam-5694	1	8	2025	2025	NUM
ejpam-5694	1	9	,	,	PUNCT
ejpam-5694	1	10	vol	vol	NOUN
ejpam-5694	1	11	.	.	PROPN
ejpam-5694	1	12	18	18	NUM
ejpam-5694	1	13	,	,	PUNCT
ejpam-5694	1	14	issue	issue	NOUN
ejpam-5694	1	15	1	1	NUM
ejpam-5694	1	16	,	,	PUNCT
ejpam-5694	1	17	article	article	NOUN
ejpam-5694	1	18	number	number	NOUN
ejpam-5694	1	19	5694	5694	NUM
ejpam-5694	1	20	issn	issn	VERB
ejpam-5694	1	21	1307	1307	NUM
ejpam-5694	1	22	-	-	SYM
ejpam-5694	1	23	5543	5543	NUM
ejpam-5694	1	24	–	–	PUNCT
ejpam-5694	1	25	ejpam.com	ejpam.com	X
ejpam-5694	1	26	published	publish	VERB
ejpam-5694	1	27	by	by	ADP
ejpam-5694	1	28	new	new	PROPN
ejpam-5694	1	29	york	york	PROPN
ejpam-5694	1	30	business	business	PROPN
ejpam-5694	1	31	global	global	ADJ
ejpam-5694	1	32	analysis	analysis	NOUN
ejpam-5694	1	33	of	of	ADP
ejpam-5694	1	34	hardy	hardy	ADJ
ejpam-5694	1	35	-	-	PUNCT
ejpam-5694	1	36	type	type	NOUN
ejpam-5694	1	37	inequalities	inequality	NOUN
ejpam-5694	1	38	involving	involve	VERB
ejpam-5694	1	39	green	green	ADJ
ejpam-5694	1	40	functions	function	NOUN
ejpam-5694	1	41	and	and	CCONJ
ejpam-5694	1	42	taylor	taylor	PROPN
ejpam-5694	1	43	’s	’s	PART
ejpam-5694	1	44	polynomial	polynomial	PROPN
ejpam-5694	1	45	approximation	approximation	NOUN
ejpam-5694	1	46	anjum	anjum	PROPN
ejpam-5694	1	47	mustafa	mustafa	PROPN
ejpam-5694	1	48	khan	khan	PROPN
ejpam-5694	1	49	abbasi1,∗	abbasi1,∗	PROPN
ejpam-5694	1	50	,	,	PUNCT
ejpam-5694	1	51	matloob	matloob	ADJ
ejpam-5694	1	52	anwar1	anwar1	PROPN
ejpam-5694	1	53	1	1	NUM
ejpam-5694	1	54	department	department	NOUN
ejpam-5694	1	55	of	of	ADP
ejpam-5694	1	56	mathematics	mathematics	PROPN
ejpam-5694	1	57	school	school	NOUN
ejpam-5694	1	58	of	of	ADP
ejpam-5694	1	59	natural	natural	ADJ
ejpam-5694	1	60	sciences	science	NOUN
ejpam-5694	1	61	,	,	PUNCT
ejpam-5694	1	62	national	national	ADJ
ejpam-5694	1	63	university	university	PROPN
ejpam-5694	1	64	of	of	ADP
ejpam-5694	1	65	sciences	science	NOUN
ejpam-5694	1	66	and	and	CCONJ
ejpam-5694	1	67	technology	technology	NOUN
ejpam-5694	1	68	,	,	PUNCT
ejpam-5694	1	69	islamabad	islamabad	PROPN
ejpam-5694	1	70	,	,	PUNCT
ejpam-5694	1	71	pakistan	pakistan	PROPN
ejpam-5694	1	72	abstract	abstract	NOUN
ejpam-5694	1	73	.	.	PUNCT
ejpam-5694	2	1	herein	herein	NOUN
ejpam-5694	2	2	,	,	PUNCT
ejpam-5694	2	3	we	we	PRON
ejpam-5694	2	4	prove	prove	VERB
ejpam-5694	2	5	the	the	DET
ejpam-5694	2	6	hardy	hardy	ADJ
ejpam-5694	2	7	-	-	PUNCT
ejpam-5694	2	8	type	type	NOUN
ejpam-5694	2	9	inequalities	inequality	NOUN
ejpam-5694	2	10	using	use	VERB
ejpam-5694	2	11	the	the	DET
ejpam-5694	2	12	two	two	NUM
ejpam-5694	2	13	-	-	PUNCT
ejpam-5694	2	14	point	point	NOUN
ejpam-5694	2	15	right	right	ADJ
ejpam-5694	2	16	focal	focal	ADJ
ejpam-5694	2	17	problem	problem	NOUN
ejpam-5694	2	18	’s	’s	PART
ejpam-5694	2	19	green	green	ADJ
ejpam-5694	2	20	functions	function	NOUN
ejpam-5694	2	21	,	,	PUNCT
ejpam-5694	2	22	which	which	PRON
ejpam-5694	2	23	are	be	AUX
ejpam-5694	2	24	convex	convex	ADJ
ejpam-5694	2	25	and	and	CCONJ
ejpam-5694	2	26	continuous	continuous	ADJ
ejpam-5694	2	27	concerning	concern	VERB
ejpam-5694	2	28	both	both	DET
ejpam-5694	2	29	variables	variable	NOUN
ejpam-5694	2	30	.	.	PUNCT
ejpam-5694	3	1	along	along	ADP
ejpam-5694	3	2	with	with	ADP
ejpam-5694	3	3	the	the	DET
ejpam-5694	3	4	green	green	ADJ
ejpam-5694	3	5	functions	function	NOUN
ejpam-5694	3	6	,	,	PUNCT
ejpam-5694	3	7	taylor	taylor	PROPN
ejpam-5694	3	8	’s	’s	PART
ejpam-5694	3	9	polynomial	polynomial	ADJ
ejpam-5694	3	10	and	and	CCONJ
ejpam-5694	3	11	n−convex	n−convex	NOUN
ejpam-5694	3	12	functions	function	NOUN
ejpam-5694	3	13	are	be	AUX
ejpam-5694	3	14	also	also	ADV
ejpam-5694	3	15	considered	consider	VERB
ejpam-5694	3	16	.	.	PUNCT
ejpam-5694	4	1	in	in	ADP
ejpam-5694	4	2	addition	addition	NOUN
ejpam-5694	4	3	,	,	PUNCT
ejpam-5694	4	4	we	we	PRON
ejpam-5694	4	5	find	find	VERB
ejpam-5694	4	6	the	the	DET
ejpam-5694	4	7	bounds	bound	NOUN
ejpam-5694	4	8	on	on	ADP
ejpam-5694	4	9	the	the	DET
ejpam-5694	4	10	remainder	remainder	NOUN
ejpam-5694	4	11	using	use	VERB
ejpam-5694	4	12	čebyšev	čebyšev	PROPN
ejpam-5694	4	13	functional	functional	ADJ
ejpam-5694	4	14	in	in	ADP
ejpam-5694	4	15	the	the	DET
ejpam-5694	4	16	presence	presence	NOUN
ejpam-5694	4	17	of	of	ADP
ejpam-5694	4	18	obtained	obtain	VERB
ejpam-5694	4	19	results	result	NOUN
ejpam-5694	4	20	in	in	ADP
ejpam-5694	4	21	the	the	DET
ejpam-5694	4	22	form	form	NOUN
ejpam-5694	4	23	of	of	ADP
ejpam-5694	4	24	hardy	hardy	ADJ
ejpam-5694	4	25	-	-	PUNCT
ejpam-5694	4	26	type	type	NOUN
ejpam-5694	4	27	inequalities	inequality	NOUN
ejpam-5694	4	28	.	.	PUNCT
ejpam-5694	5	1	then	then	ADV
ejpam-5694	5	2	,	,	PUNCT
ejpam-5694	5	3	we	we	PRON
ejpam-5694	5	4	discuss	discuss	VERB
ejpam-5694	5	5	grüss	grüss	PROPN
ejpam-5694	5	6	-	-	PUNCT
ejpam-5694	5	7	type	type	NOUN
ejpam-5694	5	8	inequalities	inequality	NOUN
ejpam-5694	5	9	that	that	PRON
ejpam-5694	5	10	enable	enable	VERB
ejpam-5694	5	11	us	we	PRON
ejpam-5694	5	12	to	to	PART
ejpam-5694	5	13	find	find	VERB
ejpam-5694	5	14	the	the	DET
ejpam-5694	5	15	bounds	bound	NOUN
ejpam-5694	5	16	on	on	ADP
ejpam-5694	5	17	remainders	remainder	NOUN
ejpam-5694	5	18	and	and	CCONJ
ejpam-5694	5	19	then	then	ADV
ejpam-5694	5	20	ostrowski	ostrowski	ADJ
ejpam-5694	5	21	-	-	PUNCT
ejpam-5694	5	22	type	type	NOUN
ejpam-5694	5	23	inequalities	inequality	NOUN
ejpam-5694	5	24	are	be	AUX
ejpam-5694	5	25	discussed	discuss	VERB
ejpam-5694	5	26	.	.	PUNCT
ejpam-5694	6	1	in	in	ADP
ejpam-5694	6	2	the	the	DET
ejpam-5694	6	3	later	later	ADJ
ejpam-5694	6	4	part	part	NOUN
ejpam-5694	6	5	of	of	ADP
ejpam-5694	6	6	this	this	DET
ejpam-5694	6	7	study	study	NOUN
ejpam-5694	6	8	,	,	PUNCT
ejpam-5694	6	9	we	we	PRON
ejpam-5694	6	10	discuss	discuss	VERB
ejpam-5694	6	11	some	some	DET
ejpam-5694	6	12	results	result	NOUN
ejpam-5694	6	13	related	relate	VERB
ejpam-5694	6	14	to	to	ADP
ejpam-5694	6	15	the	the	DET
ejpam-5694	6	16	mean	mean	ADJ
ejpam-5694	6	17	value	value	NOUN
ejpam-5694	6	18	theorem	theorem	NOUN
ejpam-5694	6	19	and	and	CCONJ
ejpam-5694	6	20	n	n	CCONJ
ejpam-5694	6	21	-	-	PUNCT
ejpam-5694	6	22	exponential	exponential	ADJ
ejpam-5694	6	23	convexity	convexity	NOUN
ejpam-5694	6	24	.	.	PUNCT
ejpam-5694	7	1	2020	2020	NUM
ejpam-5694	7	2	mathematics	mathematic	NOUN
ejpam-5694	7	3	subject	subject	NOUN
ejpam-5694	7	4	classifications	classification	NOUN
ejpam-5694	7	5	:	:	PUNCT
ejpam-5694	7	6	26d10	26d10	NUM
ejpam-5694	7	7	,	,	PUNCT
ejpam-5694	7	8	26d15	26d15	NUM
ejpam-5694	7	9	,	,	PUNCT
ejpam-5694	7	10	26d25	26d25	NUM
ejpam-5694	7	11	,	,	PUNCT
ejpam-5694	7	12	26d30	26d30	ADV
ejpam-5694	7	13	key	key	ADJ
ejpam-5694	7	14	words	word	NOUN
ejpam-5694	7	15	and	and	CCONJ
ejpam-5694	7	16	phrases	phrase	NOUN
ejpam-5694	7	17	:	:	PUNCT
ejpam-5694	7	18	hardy	hardy	ADJ
ejpam-5694	7	19	-	-	PUNCT
ejpam-5694	7	20	type	type	NOUN
ejpam-5694	7	21	inequalities	inequality	NOUN
ejpam-5694	7	22	,	,	PUNCT
ejpam-5694	7	23	convex	convex	NOUN
ejpam-5694	7	24	functions	function	NOUN
ejpam-5694	7	25	,	,	PUNCT
ejpam-5694	7	26	n	n	CCONJ
ejpam-5694	7	27	-	-	PUNCT
ejpam-5694	7	28	exponential	exponential	ADJ
ejpam-5694	7	29	convex	convex	NOUN
ejpam-5694	7	30	functions	function	NOUN
ejpam-5694	7	31	,	,	PUNCT
ejpam-5694	7	32	green	green	ADJ
ejpam-5694	7	33	function	function	NOUN
ejpam-5694	7	34	,	,	PUNCT
ejpam-5694	7	35	taylor	taylor	PROPN
ejpam-5694	7	36	interpolating	interpolate	VERB
ejpam-5694	7	37	polynomial	polynomial	ADJ
ejpam-5694	7	38	,	,	PUNCT
ejpam-5694	7	39	čebyšev	čebyšev	PROPN
ejpam-5694	7	40	functional	functional	ADJ
ejpam-5694	7	41	,	,	PUNCT
ejpam-5694	7	42	grüss	grüss	NOUN
ejpam-5694	7	43	-	-	PUNCT
ejpam-5694	7	44	type	type	NOUN
ejpam-5694	7	45	inequalities	inequality	NOUN
ejpam-5694	7	46	,	,	PUNCT
ejpam-5694	7	47	ostrowski	ostrowski	ADJ
ejpam-5694	7	48	-	-	PUNCT
ejpam-5694	7	49	type	type	NOUN
ejpam-5694	7	50	inequalities	inequality	NOUN
ejpam-5694	7	51	,	,	PUNCT
ejpam-5694	7	52	bounds	bound	VERB
ejpam-5694	7	53	on	on	ADP
ejpam-5694	7	54	remainders	remainder	NOUN
ejpam-5694	7	55	1	1	NUM
ejpam-5694	7	56	.	.	PUNCT
ejpam-5694	8	1	introduction	introduction	NOUN
ejpam-5694	8	2	a	a	DET
ejpam-5694	8	3	remarkable	remarkable	ADJ
ejpam-5694	8	4	development	development	NOUN
ejpam-5694	8	5	in	in	ADP
ejpam-5694	8	6	the	the	DET
ejpam-5694	8	7	theory	theory	NOUN
ejpam-5694	8	8	of	of	ADP
ejpam-5694	8	9	green	green	ADJ
ejpam-5694	8	10	function	function	NOUN
ejpam-5694	8	11	was	be	AUX
ejpam-5694	8	12	introduced	introduce	VERB
ejpam-5694	8	13	by	by	ADP
ejpam-5694	8	14	green	green	ADJ
ejpam-5694	8	15	[	[	X
ejpam-5694	8	16	8	8	NUM
ejpam-5694	8	17	]	]	PUNCT
ejpam-5694	8	18	that	that	PRON
ejpam-5694	8	19	was	be	AUX
ejpam-5694	8	20	almost	almost	ADV
ejpam-5694	8	21	seminal	seminal	ADJ
ejpam-5694	8	22	and	and	CCONJ
ejpam-5694	8	23	later	later	ADV
ejpam-5694	8	24	on	on	ADP
ejpam-5694	8	25	theory	theory	NOUN
ejpam-5694	8	26	related	relate	VERB
ejpam-5694	8	27	to	to	ADP
ejpam-5694	8	28	green	green	ADJ
ejpam-5694	8	29	function	function	NOUN
ejpam-5694	8	30	plays	play	VERB
ejpam-5694	8	31	an	an	DET
ejpam-5694	8	32	important	important	ADJ
ejpam-5694	8	33	role	role	NOUN
ejpam-5694	8	34	in	in	ADP
ejpam-5694	8	35	dealing	deal	VERB
ejpam-5694	8	36	with	with	ADP
ejpam-5694	8	37	differential	differential	ADJ
ejpam-5694	8	38	equations	equation	NOUN
ejpam-5694	8	39	qualitatively	qualitatively	ADV
ejpam-5694	8	40	and	and	CCONJ
ejpam-5694	8	41	quantitatively	quantitatively	ADV
ejpam-5694	9	1	[	[	X
ejpam-5694	9	2	4],[13	4],[13	NOUN
ejpam-5694	9	3	]	]	PUNCT
ejpam-5694	9	4	.	.	PUNCT
ejpam-5694	10	1	mathematicians	mathematician	NOUN
ejpam-5694	10	2	used	use	VERB
ejpam-5694	10	3	green	green	ADJ
ejpam-5694	10	4	functions	function	NOUN
ejpam-5694	10	5	in	in	ADP
ejpam-5694	10	6	many	many	ADJ
ejpam-5694	10	7	other	other	ADJ
ejpam-5694	10	8	directions	direction	NOUN
ejpam-5694	10	9	of	of	ADP
ejpam-5694	10	10	mathematics	mathematic	NOUN
ejpam-5694	10	11	,	,	PUNCT
ejpam-5694	10	12	other	other	ADJ
ejpam-5694	10	13	than	than	ADP
ejpam-5694	10	14	differential	differential	ADJ
ejpam-5694	10	15	equations	equation	NOUN
ejpam-5694	10	16	.	.	PUNCT
ejpam-5694	11	1	in	in	ADP
ejpam-5694	11	2	resent	resent	NOUN
ejpam-5694	11	3	past	past	NOUN
ejpam-5694	11	4	,	,	PUNCT
ejpam-5694	11	5	it	it	PRON
ejpam-5694	11	6	has	have	AUX
ejpam-5694	11	7	been	be	AUX
ejpam-5694	11	8	used	use	VERB
ejpam-5694	11	9	diversely	diversely	ADV
ejpam-5694	11	10	in	in	ADP
ejpam-5694	11	11	the	the	DET
ejpam-5694	11	12	mathematical	mathematical	ADJ
ejpam-5694	11	13	inequalities	inequality	NOUN
ejpam-5694	11	14	along	along	ADP
ejpam-5694	11	15	with	with	ADP
ejpam-5694	11	16	the	the	DET
ejpam-5694	11	17	polynomial	polynomial	ADJ
ejpam-5694	11	18	interpolation	interpolation	NOUN
ejpam-5694	11	19	.	.	PUNCT
ejpam-5694	12	1	like	like	INTJ
ejpam-5694	12	2	in	in	ADP
ejpam-5694	12	3	[	[	X
ejpam-5694	12	4	2	2	NUM
ejpam-5694	12	5	]	]	X
ejpam-5694	12	6	different	different	ADJ
ejpam-5694	12	7	aspects	aspect	NOUN
ejpam-5694	12	8	have	have	AUX
ejpam-5694	12	9	been	be	AUX
ejpam-5694	12	10	extensively	extensively	ADV
ejpam-5694	12	11	discussed	discuss	VERB
ejpam-5694	12	12	.	.	PUNCT
ejpam-5694	13	1	then	then	ADV
ejpam-5694	13	2	further	further	ADJ
ejpam-5694	13	3	generalizations	generalization	NOUN
ejpam-5694	13	4	have	have	AUX
ejpam-5694	13	5	been	be	AUX
ejpam-5694	13	6	made	make	VERB
ejpam-5694	13	7	by	by	ADP
ejpam-5694	13	8	many	many	ADJ
ejpam-5694	13	9	researchers	researcher	NOUN
ejpam-5694	13	10	like	like	ADP
ejpam-5694	13	11	k.	k.	PROPN
ejpam-5694	13	12	k	k	PROPN
ejpam-5694	13	13	.himmelreich	.himmelreich	PRON
ejpam-5694	13	14	et	et	PROPN
ejpam-5694	13	15	al	al	PROPN
ejpam-5694	13	16	.	.	PUNCT
ejpam-5694	14	1	[	[	X
ejpam-5694	14	2	10	10	NUM
ejpam-5694	14	3	]	]	PUNCT
ejpam-5694	14	4	discuss	discuss	VERB
ejpam-5694	14	5	the	the	DET
ejpam-5694	14	6	hardy	hardy	ADJ
ejpam-5694	14	7	-	-	PUNCT
ejpam-5694	14	8	type	type	NOUN
ejpam-5694	14	9	inequalities	inequality	NOUN
ejpam-5694	14	10	by	by	ADP
ejpam-5694	14	11	tkaing	tkae	VERB
ejpam-5694	14	12	green	green	ADJ
ejpam-5694	14	13	function	function	NOUN
ejpam-5694	14	14	into	into	ADP
ejpam-5694	14	15	account	account	NOUN
ejpam-5694	14	16	along	along	ADP
ejpam-5694	14	17	with	with	ADP
ejpam-5694	14	18	montgomery	montgomery	PROPN
ejpam-5694	14	19	identity	identity	NOUN
ejpam-5694	14	20	.	.	PUNCT
ejpam-5694	15	1	d.	d.	PROPN
ejpam-5694	15	2	pokaz	pokaz	PROPN
ejpam-5694	16	1	[	[	X
ejpam-5694	16	2	20	20	NUM
ejpam-5694	16	3	]	]	PUNCT
ejpam-5694	16	4	studied	study	VERB
ejpam-5694	16	5	the	the	DET
ejpam-5694	16	6	hardytype	hardytype	NOUN
ejpam-5694	16	7	inequalities	inequality	NOUN
ejpam-5694	16	8	via	via	ADP
ejpam-5694	16	9	green	green	ADJ
ejpam-5694	16	10	functions	function	NOUN
ejpam-5694	16	11	,	,	PUNCT
ejpam-5694	16	12	n−convex	n−convex	NOUN
ejpam-5694	16	13	functions	function	NOUN
ejpam-5694	16	14	and	and	CCONJ
ejpam-5694	16	15	polynomial	polynomial	ADJ
ejpam-5694	16	16	interpolation	interpolation	NOUN
ejpam-5694	16	17	of	of	ADP
ejpam-5694	16	18	abel	abel	PROPN
ejpam-5694	16	19	gontschorf	gontschorf	PROPN
ejpam-5694	16	20	and	and	CCONJ
ejpam-5694	16	21	find	find	VERB
ejpam-5694	16	22	the	the	DET
ejpam-5694	16	23	bounds	bound	NOUN
ejpam-5694	16	24	on	on	ADP
ejpam-5694	16	25	the	the	DET
ejpam-5694	16	26	remainder	remainder	NOUN
ejpam-5694	16	27	obtained	obtain	VERB
ejpam-5694	16	28	from	from	ADP
ejpam-5694	16	29	the	the	DET
ejpam-5694	16	30	assumptions	assumption	NOUN
ejpam-5694	16	31	under	under	ADP
ejpam-5694	16	32	consideration	consideration	NOUN
ejpam-5694	16	33	.	.	PUNCT
ejpam-5694	17	1	a.	a.	NOUN
ejpam-5694	17	2	rasheed	rasheed	PROPN
ejpam-5694	17	3	et	et	PROPN
ejpam-5694	17	4	al	al	PROPN
ejpam-5694	17	5	.	.	PUNCT
ejpam-5694	18	1	[	[	X
ejpam-5694	18	2	22	22	NUM
ejpam-5694	18	3	]	]	PUNCT
ejpam-5694	18	4	investigate	investigate	VERB
ejpam-5694	18	5	the	the	DET
ejpam-5694	18	6	levinson	levinson	NOUN
ejpam-5694	18	7	-	-	PUNCT
ejpam-5694	18	8	type	type	NOUN
ejpam-5694	18	9	inequalities	inequality	NOUN
ejpam-5694	18	10	using	use	VERB
ejpam-5694	18	11	∗corresponding	∗corresponde	VERB
ejpam-5694	18	12	author	author	NOUN
ejpam-5694	18	13	.	.	PUNCT
ejpam-5694	19	1	doi	doi	NOUN
ejpam-5694	19	2	:	:	PUNCT
ejpam-5694	19	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5694	https://doi.org/10.29020/nybg.ejpam.v18i1.5694	DET
ejpam-5694	19	4	email	email	NOUN
ejpam-5694	19	5	addresses	address	VERB
ejpam-5694	19	6	:	:	PUNCT
ejpam-5694	19	7	aabbasi.phdmath19sns@student.nust.edu.pk	aabbasi.phdmath19sns@student.nust.edu.pk	PROPN
ejpam-5694	19	8	(	(	PUNCT
ejpam-5694	19	9	a.	a.	NOUN
ejpam-5694	19	10	m.	m.	PROPN
ejpam-5694	19	11	k.	k.	PROPN
ejpam-5694	19	12	abbasi	abbasi	PROPN
ejpam-5694	19	13	)	)	PUNCT
ejpam-5694	19	14	,	,	PUNCT
ejpam-5694	19	15	manwar@sns.nust.edu.pk	manwar@sns.nust.edu.pk	PROPN
ejpam-5694	19	16	(	(	PUNCT
ejpam-5694	19	17	m.	m.	NOUN
ejpam-5694	19	18	anwar	anwar	PROPN
ejpam-5694	19	19	)	)	PUNCT
ejpam-5694	19	20	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5694	20	1	1	1	NUM
ejpam-5694	20	2	copyright	copyright	NOUN
ejpam-5694	20	3	:	:	PUNCT
ejpam-5694	20	4	©	©	PROPN
ejpam-5694	20	5	2025	2025	NUM
ejpam-5694	20	6	the	the	DET
ejpam-5694	20	7	author(s	author(s	NOUN
ejpam-5694	20	8	)	)	PUNCT
ejpam-5694	20	9	.	.	PUNCT
ejpam-5694	21	1	(	(	PUNCT
ejpam-5694	21	2	cc	cc	NOUN
ejpam-5694	21	3	by	by	ADP
ejpam-5694	21	4	-	-	PUNCT
ejpam-5694	21	5	nc	nc	PROPN
ejpam-5694	21	6	4.0	4.0	NUM
ejpam-5694	21	7	)	)	PUNCT
ejpam-5694	21	8	a.	a.	NOUN
ejpam-5694	21	9	m.	m.	PROPN
ejpam-5694	21	10	k.	k.	PROPN
ejpam-5694	21	11	abbasi	abbasi	PROPN
ejpam-5694	21	12	,	,	PUNCT
ejpam-5694	21	13	m.	m.	PROPN
ejpam-5694	21	14	anwar	anwar	PROPN
ejpam-5694	21	15	/	/	PUNCT
ejpam-5694	21	16	eur	eur	PROPN
ejpam-5694	21	17	.	.	PUNCT
ejpam-5694	22	1	j.	j.	PROPN
ejpam-5694	22	2	pure	pure	PROPN
ejpam-5694	22	3	appl	appl	PROPN
ejpam-5694	22	4	.	.	PROPN
ejpam-5694	22	5	math	math	PROPN
ejpam-5694	22	6	,	,	PUNCT
ejpam-5694	22	7	18	18	NUM
ejpam-5694	22	8	(	(	PUNCT
ejpam-5694	22	9	1	1	NUM
ejpam-5694	22	10	)	)	PUNCT
ejpam-5694	22	11	(	(	PUNCT
ejpam-5694	22	12	2025	2025	NUM
ejpam-5694	22	13	)	)	PUNCT
ejpam-5694	22	14	,	,	PUNCT
ejpam-5694	22	15	5694	5694	NUM
ejpam-5694	22	16	2	2	NUM
ejpam-5694	22	17	of	of	ADP
ejpam-5694	22	18	18	18	NUM
ejpam-5694	22	19	green	green	ADJ
ejpam-5694	22	20	functions	function	NOUN
ejpam-5694	22	21	of	of	ADP
ejpam-5694	22	22	the	the	DET
ejpam-5694	22	23	two	two	NUM
ejpam-5694	22	24	-	-	PUNCT
ejpam-5694	22	25	point	point	NOUN
ejpam-5694	22	26	right	right	ADJ
ejpam-5694	22	27	focal	focal	ADJ
ejpam-5694	22	28	problems	problem	NOUN
ejpam-5694	22	29	.	.	PUNCT
ejpam-5694	23	1	muhammad	muhammad	PROPN
ejpam-5694	23	2	adeel	adeel	PROPN
ejpam-5694	23	3	et	et	PROPN
ejpam-5694	23	4	al	al	PROPN
ejpam-5694	23	5	.	.	PROPN
ejpam-5694	23	6	investigate	investigate	VERB
ejpam-5694	23	7	levisnson	levisnson	NOUN
ejpam-5694	23	8	type	type	NOUN
ejpam-5694	23	9	inequalities	inequality	NOUN
ejpam-5694	23	10	in	in	ADP
ejpam-5694	23	11	[	[	X
ejpam-5694	23	12	1	1	NUM
ejpam-5694	23	13	]	]	PUNCT
ejpam-5694	23	14	by	by	ADP
ejpam-5694	23	15	using	use	VERB
ejpam-5694	23	16	the	the	DET
ejpam-5694	23	17	green	green	ADJ
ejpam-5694	23	18	function	function	NOUN
ejpam-5694	23	19	and	and	CCONJ
ejpam-5694	23	20	lidstone	lidstone	NOUN
ejpam-5694	23	21	’s	’s	PART
ejpam-5694	23	22	polynomial	polynomial	ADJ
ejpam-5694	24	1	and	and	CCONJ
ejpam-5694	24	2	then	then	ADV
ejpam-5694	24	3	he	he	PRON
ejpam-5694	24	4	gave	give	VERB
ejpam-5694	24	5	the	the	DET
ejpam-5694	24	6	application	application	NOUN
ejpam-5694	24	7	of	of	ADP
ejpam-5694	24	8	these	these	DET
ejpam-5694	24	9	inequalities	inequality	NOUN
ejpam-5694	24	10	to	to	ADP
ejpam-5694	24	11	the	the	DET
ejpam-5694	24	12	estimate	estimate	NOUN
ejpam-5694	24	13	the	the	DET
ejpam-5694	24	14	f−divergence	f−divergence	NOUN
ejpam-5694	24	15	and	and	CCONJ
ejpam-5694	24	16	shannon	shannon	PROPN
ejpam-5694	24	17	entropy	entropy	PROPN
ejpam-5694	24	18	.	.	PUNCT
ejpam-5694	25	1	in	in	ADP
ejpam-5694	25	2	[	[	X
ejpam-5694	25	3	7	7	X
ejpam-5694	25	4	]	]	PUNCT
ejpam-5694	25	5	some	some	DET
ejpam-5694	25	6	real	real	ADJ
ejpam-5694	25	7	-	-	PUNCT
ejpam-5694	25	8	world	world	NOUN
ejpam-5694	25	9	problems	problem	NOUN
ejpam-5694	25	10	are	be	AUX
ejpam-5694	25	11	discussed	discuss	VERB
ejpam-5694	25	12	along	along	ADP
ejpam-5694	25	13	with	with	ADP
ejpam-5694	25	14	the	the	DET
ejpam-5694	25	15	hermitehadamard	hermitehadamard	NOUN
ejpam-5694	25	16	inequality	inequality	NOUN
ejpam-5694	25	17	and	and	CCONJ
ejpam-5694	25	18	green	green	ADJ
ejpam-5694	25	19	functions	function	NOUN
ejpam-5694	25	20	.	.	PUNCT
ejpam-5694	26	1	although	although	SCONJ
ejpam-5694	26	2	this	this	DET
ejpam-5694	26	3	inequality	inequality	NOUN
ejpam-5694	26	4	is	be	AUX
ejpam-5694	26	5	vastly	vastly	ADV
ejpam-5694	26	6	studied	study	VERB
ejpam-5694	26	7	in	in	ADP
ejpam-5694	26	8	many	many	ADJ
ejpam-5694	26	9	other	other	ADJ
ejpam-5694	26	10	ways	way	NOUN
ejpam-5694	26	11	like	like	SCONJ
ejpam-5694	26	12	it	it	PRON
ejpam-5694	26	13	’s	’	VERB
ejpam-5694	26	14	generalizations	generalization	NOUN
ejpam-5694	26	15	so	so	ADV
ejpam-5694	26	16	-	-	PUNCT
ejpam-5694	26	17	called	call	VERB
ejpam-5694	26	18	levinson	levinson	PROPN
ejpam-5694	26	19	’s	’s	PART
ejpam-5694	26	20	inequality	inequality	NOUN
ejpam-5694	26	21	or	or	CCONJ
ejpam-5694	26	22	involvement	involvement	NOUN
ejpam-5694	26	23	of	of	ADP
ejpam-5694	26	24	fractional	fractional	ADJ
ejpam-5694	26	25	calculus	calculus	NOUN
ejpam-5694	26	26	to	to	PART
ejpam-5694	26	27	study	study	VERB
ejpam-5694	26	28	this	this	DET
ejpam-5694	26	29	inequality	inequality	NOUN
ejpam-5694	26	30	but	but	CCONJ
ejpam-5694	26	31	we	we	PRON
ejpam-5694	26	32	analyze	analyze	VERB
ejpam-5694	26	33	the	the	DET
ejpam-5694	26	34	aforementioned	aforementioned	ADJ
ejpam-5694	26	35	inequality	inequality	NOUN
ejpam-5694	26	36	for	for	ADP
ejpam-5694	26	37	upcoming	upcoming	ADJ
ejpam-5694	26	38	green	green	ADJ
ejpam-5694	26	39	functions	function	NOUN
ejpam-5694	26	40	and	and	CCONJ
ejpam-5694	26	41	taylor	taylor	PROPN
ejpam-5694	26	42	’s	’s	PART
ejpam-5694	26	43	polynomial	polynomial	ADJ
ejpam-5694	26	44	.	.	PUNCT
ejpam-5694	27	1	due	due	ADP
ejpam-5694	27	2	to	to	ADP
ejpam-5694	27	3	the	the	DET
ejpam-5694	27	4	importance	importance	NOUN
ejpam-5694	27	5	of	of	ADP
ejpam-5694	27	6	the	the	DET
ejpam-5694	27	7	hardy	hardy	ADJ
ejpam-5694	27	8	-	-	PUNCT
ejpam-5694	27	9	type	type	NOUN
ejpam-5694	27	10	inequalities	inequality	NOUN
ejpam-5694	27	11	to	to	PART
ejpam-5694	27	12	find	find	VERB
ejpam-5694	27	13	the	the	DET
ejpam-5694	27	14	prior	prior	ADJ
ejpam-5694	27	15	estimation	estimation	NOUN
ejpam-5694	27	16	to	to	ADP
ejpam-5694	27	17	the	the	DET
ejpam-5694	27	18	solution	solution	NOUN
ejpam-5694	27	19	of	of	ADP
ejpam-5694	27	20	partial	partial	ADJ
ejpam-5694	27	21	differential	differential	NOUN
ejpam-5694	27	22	equations	equation	NOUN
ejpam-5694	27	23	,	,	PUNCT
ejpam-5694	27	24	approximation	approximation	NOUN
ejpam-5694	27	25	of	of	ADP
ejpam-5694	27	26	a	a	DET
ejpam-5694	27	27	function	function	NOUN
ejpam-5694	27	28	to	to	ADP
ejpam-5694	27	29	the	the	DET
ejpam-5694	27	30	basis	basis	NOUN
ejpam-5694	27	31	of	of	ADP
ejpam-5694	27	32	functions	function	NOUN
ejpam-5694	27	33	or	or	CCONJ
ejpam-5694	27	34	the	the	DET
ejpam-5694	27	35	polynomials	polynomial	NOUN
ejpam-5694	27	36	,	,	PUNCT
ejpam-5694	27	37	it	it	PRON
ejpam-5694	27	38	got	get	VERB
ejpam-5694	27	39	the	the	DET
ejpam-5694	27	40	attention	attention	NOUN
ejpam-5694	27	41	of	of	ADP
ejpam-5694	27	42	mathematicians	mathematician	NOUN
ejpam-5694	27	43	.	.	PUNCT
ejpam-5694	28	1	some	some	DET
ejpam-5694	28	2	nominal	nominal	ADJ
ejpam-5694	28	3	works	work	NOUN
ejpam-5694	28	4	and	and	CCONJ
ejpam-5694	28	5	discussion	discussion	NOUN
ejpam-5694	28	6	are	be	AUX
ejpam-5694	28	7	made	make	VERB
ejpam-5694	28	8	in	in	ADP
ejpam-5694	28	9	[	[	X
ejpam-5694	28	10	2	2	NUM
ejpam-5694	28	11	]	]	PUNCT
ejpam-5694	28	12	,	,	PUNCT
ejpam-5694	28	13	[	[	X
ejpam-5694	28	14	22	22	NUM
ejpam-5694	28	15	]	]	PUNCT
ejpam-5694	28	16	,	,	PUNCT
ejpam-5694	28	17	[	[	X
ejpam-5694	28	18	9	9	NUM
ejpam-5694	28	19	]	]	PUNCT
ejpam-5694	28	20	,	,	PUNCT
ejpam-5694	28	21	[	[	X
ejpam-5694	28	22	23	23	NUM
ejpam-5694	28	23	]	]	PUNCT
ejpam-5694	28	24	and	and	CCONJ
ejpam-5694	28	25	[	[	X
ejpam-5694	28	26	12	12	NUM
ejpam-5694	28	27	]	]	PUNCT
ejpam-5694	28	28	.	.	PUNCT
ejpam-5694	29	1	also	also	ADV
ejpam-5694	29	2	,	,	PUNCT
ejpam-5694	29	3	there	there	PRON
ejpam-5694	29	4	is	be	VERB
ejpam-5694	29	5	scope	scope	NOUN
ejpam-5694	29	6	to	to	PART
ejpam-5694	29	7	extend	extend	VERB
ejpam-5694	29	8	this	this	DET
ejpam-5694	29	9	work	work	NOUN
ejpam-5694	29	10	in	in	ADP
ejpam-5694	29	11	the	the	DET
ejpam-5694	29	12	fractional	fractional	ADJ
ejpam-5694	29	13	calculus	calculus	NOUN
ejpam-5694	29	14	side	side	NOUN
ejpam-5694	29	15	using	use	VERB
ejpam-5694	29	16	different	different	ADJ
ejpam-5694	29	17	operators	operator	NOUN
ejpam-5694	29	18	discussed	discuss	VERB
ejpam-5694	29	19	in	in	ADP
ejpam-5694	29	20	[	[	X
ejpam-5694	29	21	6	6	NUM
ejpam-5694	29	22	]	]	PUNCT
ejpam-5694	29	23	,	,	PUNCT
ejpam-5694	29	24	[	[	X
ejpam-5694	29	25	7	7	X
ejpam-5694	29	26	]	]	PUNCT
ejpam-5694	29	27	and	and	CCONJ
ejpam-5694	29	28	[	[	X
ejpam-5694	29	29	21	21	NUM
ejpam-5694	29	30	]	]	PUNCT
ejpam-5694	29	31	in	in	ADP
ejpam-5694	29	32	the	the	DET
ejpam-5694	29	33	presence	presence	NOUN
ejpam-5694	29	34	of	of	ADP
ejpam-5694	29	35	čebyšev	čebyšev	PROPN
ejpam-5694	29	36	functional	functional	ADJ
ejpam-5694	29	37	in	in	ADP
ejpam-5694	29	38	fractional	fractional	ADJ
ejpam-5694	29	39	sense	sense	NOUN
ejpam-5694	29	40	accordingly	accordingly	ADV
ejpam-5694	29	41	.	.	PUNCT
ejpam-5694	30	1	for	for	ADP
ejpam-5694	30	2	example	example	NOUN
ejpam-5694	30	3	,	,	PUNCT
ejpam-5694	30	4	while	while	SCONJ
ejpam-5694	30	5	discussing	discuss	VERB
ejpam-5694	30	6	the	the	DET
ejpam-5694	30	7	aforementioned	aforementioned	ADJ
ejpam-5694	30	8	inequality	inequality	NOUN
ejpam-5694	30	9	in	in	ADP
ejpam-5694	30	10	conformable	conformable	ADJ
ejpam-5694	30	11	fractional	fractional	ADJ
ejpam-5694	30	12	operator	operator	NOUN
ejpam-5694	30	13	we	we	PRON
ejpam-5694	30	14	use	use	VERB
ejpam-5694	30	15	čebyšev	čebyšev	PROPN
ejpam-5694	30	16	functional	functional	ADJ
ejpam-5694	30	17	given	give	VERB
ejpam-5694	30	18	in	in	ADP
ejpam-5694	30	19	[	[	X
ejpam-5694	30	20	24	24	NUM
ejpam-5694	30	21	]	]	PUNCT
ejpam-5694	30	22	,	,	PUNCT
ejpam-5694	30	23	but	but	CCONJ
ejpam-5694	30	24	in	in	ADP
ejpam-5694	30	25	the	the	DET
ejpam-5694	30	26	present	present	ADJ
ejpam-5694	30	27	study	study	NOUN
ejpam-5694	30	28	we	we	PRON
ejpam-5694	30	29	are	be	AUX
ejpam-5694	30	30	considering	consider	VERB
ejpam-5694	30	31	the	the	DET
ejpam-5694	30	32	ordinary	ordinary	ADJ
ejpam-5694	30	33	case	case	NOUN
ejpam-5694	30	34	.	.	PUNCT
ejpam-5694	31	1	for	for	ADP
ejpam-5694	31	2	further	further	ADJ
ejpam-5694	31	3	details	detail	NOUN
ejpam-5694	31	4	it	it	PRON
ejpam-5694	31	5	is	be	AUX
ejpam-5694	31	6	plausibe	plausibe	NOUN
ejpam-5694	31	7	to	to	PART
ejpam-5694	31	8	mention	mention	VERB
ejpam-5694	31	9	some	some	DET
ejpam-5694	31	10	important	important	ADJ
ejpam-5694	31	11	and	and	CCONJ
ejpam-5694	31	12	nominal	nominal	ADJ
ejpam-5694	31	13	work	work	NOUN
ejpam-5694	31	14	that	that	PRON
ejpam-5694	31	15	generalize	generalize	VERB
ejpam-5694	31	16	this	this	DET
ejpam-5694	31	17	inequaltiy	inequaltiy	PROPN
ejpam-5694	31	18	by	by	ADP
ejpam-5694	31	19	using	use	VERB
ejpam-5694	31	20	polynomial	polynomial	ADJ
ejpam-5694	31	21	interpolation	interpolation	NOUN
ejpam-5694	31	22	and	and	CCONJ
ejpam-5694	31	23	green	green	ADJ
ejpam-5694	31	24	function	function	NOUN
ejpam-5694	31	25	.	.	PUNCT
ejpam-5694	32	1	kristina	kristina	PROPN
ejpam-5694	32	2	krulić	krulić	PROPN
ejpam-5694	32	3	himmelreich	himmelreich	PROPN
ejpam-5694	33	1	[	[	X
ejpam-5694	33	2	15	15	NUM
ejpam-5694	33	3	]	]	PUNCT
ejpam-5694	33	4	discuss	discuss	VERB
ejpam-5694	33	5	hardy	hardy	ADJ
ejpam-5694	33	6	-	-	PUNCT
ejpam-5694	33	7	type	type	NOUN
ejpam-5694	33	8	inequalities	inequality	NOUN
ejpam-5694	33	9	via	via	ADP
ejpam-5694	33	10	taylor	taylor	PROPN
ejpam-5694	33	11	’s	’s	PART
ejpam-5694	33	12	polynomial	polynomial	ADJ
ejpam-5694	33	13	,	,	PUNCT
ejpam-5694	33	14	d	d	DET
ejpam-5694	33	15	pokaz	pokaz	NOUN
ejpam-5694	33	16	in	in	ADP
ejpam-5694	33	17	[	[	X
ejpam-5694	33	18	20	20	NUM
ejpam-5694	33	19	]	]	PUNCT
ejpam-5694	33	20	use	use	VERB
ejpam-5694	33	21	abel	abel	NOUN
ejpam-5694	33	22	-	-	PUNCT
ejpam-5694	33	23	gontscharoff	gontscharoff	NOUN
ejpam-5694	33	24	interpolation	interpolation	NOUN
ejpam-5694	33	25	and	and	CCONJ
ejpam-5694	33	26	the	the	DET
ejpam-5694	33	27	green	green	ADJ
ejpam-5694	33	28	functions	function	NOUN
ejpam-5694	33	29	as	as	ADV
ejpam-5694	33	30	well	well	ADV
ejpam-5694	33	31	to	to	PART
ejpam-5694	33	32	generalize	generalize	VERB
ejpam-5694	33	33	aforementioned	aforementioned	ADJ
ejpam-5694	33	34	inequality	inequality	NOUN
ejpam-5694	33	35	and	and	CCONJ
ejpam-5694	33	36	kristina	kristina	PROPN
ejpam-5694	33	37	krulić	krulić	PROPN
ejpam-5694	33	38	himmelreich	himmelreich	PROPN
ejpam-5694	33	39	et	et	PROPN
ejpam-5694	33	40	al	al	PROPN
ejpam-5694	33	41	.	.	PUNCT
ejpam-5694	34	1	[	[	X
ejpam-5694	34	2	14	14	NUM
ejpam-5694	34	3	]	]	PUNCT
ejpam-5694	34	4	generalize	generalize	VERB
ejpam-5694	34	5	hardytype	hardytype	NOUN
ejpam-5694	34	6	inequalities	inequality	NOUN
ejpam-5694	34	7	with	with	ADP
ejpam-5694	34	8	the	the	DET
ejpam-5694	34	9	hermite	hermite	ADJ
ejpam-5694	34	10	interpolating	interpolate	VERB
ejpam-5694	34	11	polynomials	polynomial	NOUN
ejpam-5694	34	12	.	.	PUNCT
ejpam-5694	35	1	we	we	PRON
ejpam-5694	35	2	observe	observe	VERB
ejpam-5694	35	3	that	that	SCONJ
ejpam-5694	35	4	the	the	DET
ejpam-5694	35	5	hardy	hardy	ADJ
ejpam-5694	35	6	-	-	PUNCT
ejpam-5694	35	7	type	type	NOUN
ejpam-5694	35	8	inequalities	inequality	NOUN
ejpam-5694	35	9	are	be	AUX
ejpam-5694	35	10	not	not	PART
ejpam-5694	35	11	yet	yet	ADV
ejpam-5694	35	12	studied	study	VERB
ejpam-5694	35	13	in	in	ADP
ejpam-5694	35	14	the	the	DET
ejpam-5694	35	15	presence	presence	NOUN
ejpam-5694	35	16	of	of	ADP
ejpam-5694	35	17	the	the	DET
ejpam-5694	35	18	green	green	ADJ
ejpam-5694	35	19	functions	function	NOUN
ejpam-5694	35	20	presented	present	VERB
ejpam-5694	35	21	in	in	ADP
ejpam-5694	35	22	lemma	lemma	PROPN
ejpam-5694	35	23	1	1	NUM
ejpam-5694	35	24	of	of	ADP
ejpam-5694	35	25	upcoming	upcoming	ADJ
ejpam-5694	35	26	section	section	NOUN
ejpam-5694	35	27	.	.	PUNCT
ejpam-5694	36	1	herein	herein	NOUN
ejpam-5694	36	2	,	,	PUNCT
ejpam-5694	36	3	we	we	PRON
ejpam-5694	36	4	are	be	AUX
ejpam-5694	36	5	interested	interested	ADJ
ejpam-5694	36	6	in	in	ADP
ejpam-5694	36	7	generalizing	generalize	VERB
ejpam-5694	36	8	hardy	hardy	ADJ
ejpam-5694	36	9	-	-	PUNCT
ejpam-5694	36	10	type	type	NOUN
ejpam-5694	36	11	inequalities	inequality	NOUN
ejpam-5694	36	12	via	via	ADP
ejpam-5694	36	13	taylor	taylor	PROPN
ejpam-5694	36	14	’s	’s	PART
ejpam-5694	36	15	polynomial	polynomial	ADJ
ejpam-5694	36	16	and	and	CCONJ
ejpam-5694	36	17	the	the	DET
ejpam-5694	36	18	two	two	NUM
ejpam-5694	36	19	-	-	PUNCT
ejpam-5694	36	20	point	point	NOUN
ejpam-5694	36	21	right	right	ADJ
ejpam-5694	36	22	focal	focal	ADJ
ejpam-5694	36	23	green	green	ADJ
ejpam-5694	36	24	function	function	NOUN
ejpam-5694	36	25	,	,	PUNCT
ejpam-5694	36	26	which	which	PRON
ejpam-5694	36	27	is	be	AUX
ejpam-5694	36	28	discussed	discuss	VERB
ejpam-5694	36	29	in	in	ADP
ejpam-5694	36	30	section	section	NOUN
ejpam-5694	36	31	3	3	NUM
ejpam-5694	36	32	.	.	PUNCT
ejpam-5694	37	1	after	after	ADP
ejpam-5694	37	2	that	that	PRON
ejpam-5694	37	3	,	,	PUNCT
ejpam-5694	37	4	we	we	PRON
ejpam-5694	37	5	find	find	VERB
ejpam-5694	37	6	the	the	DET
ejpam-5694	37	7	grüss	grüss	NOUN
ejpam-5694	37	8	-	-	PUNCT
ejpam-5694	37	9	type	type	NOUN
ejpam-5694	37	10	and	and	CCONJ
ejpam-5694	37	11	ostowski	ostowski	ADJ
ejpam-5694	37	12	-	-	PUNCT
ejpam-5694	37	13	type	type	NOUN
ejpam-5694	37	14	bounds	bound	NOUN
ejpam-5694	37	15	that	that	PRON
ejpam-5694	37	16	are	be	AUX
ejpam-5694	37	17	given	give	VERB
ejpam-5694	37	18	in	in	ADP
ejpam-5694	37	19	section	section	NOUN
ejpam-5694	37	20	4	4	NUM
ejpam-5694	37	21	.	.	PUNCT
ejpam-5694	38	1	the	the	DET
ejpam-5694	38	2	final	final	ADJ
ejpam-5694	38	3	section	section	NOUN
ejpam-5694	38	4	5	5	NUM
ejpam-5694	38	5	involves	involve	VERB
ejpam-5694	38	6	some	some	DET
ejpam-5694	38	7	results	result	NOUN
ejpam-5694	38	8	regarding	regard	VERB
ejpam-5694	38	9	the	the	DET
ejpam-5694	38	10	n	n	CCONJ
ejpam-5694	38	11	-	-	PUNCT
ejpam-5694	38	12	exponential	exponential	NOUN
ejpam-5694	38	13	convexity	convexity	NOUN
ejpam-5694	38	14	and	and	CCONJ
ejpam-5694	38	15	utility	utility	NOUN
ejpam-5694	38	16	of	of	ADP
ejpam-5694	38	17	our	our	PRON
ejpam-5694	38	18	previous	previous	ADJ
ejpam-5694	38	19	results	result	NOUN
ejpam-5694	38	20	,	,	PUNCT
ejpam-5694	38	21	especially	especially	ADV
ejpam-5694	38	22	the	the	DET
ejpam-5694	38	23	functional	functional	ADJ
ejpam-5694	38	24	obtained	obtain	VERB
ejpam-5694	38	25	from	from	ADP
ejpam-5694	38	26	theorem	theorem	ADJ
ejpam-5694	38	27	5	5	NUM
ejpam-5694	38	28	.	.	SYM
ejpam-5694	38	29	2	2	NUM
ejpam-5694	38	30	.	.	PUNCT
ejpam-5694	38	31	preliminaries	preliminary	NOUN
ejpam-5694	38	32	initiating	initiate	VERB
ejpam-5694	38	33	by	by	ADP
ejpam-5694	38	34	considering	consider	VERB
ejpam-5694	38	35	the	the	DET
ejpam-5694	38	36	following	follow	VERB
ejpam-5694	38	37	lemma	lemma	PROPN
ejpam-5694	38	38	involving	involve	VERB
ejpam-5694	38	39	the	the	DET
ejpam-5694	38	40	green	green	ADJ
ejpam-5694	38	41	functions	function	NOUN
ejpam-5694	38	42	that	that	PRON
ejpam-5694	38	43	are	be	AUX
ejpam-5694	38	44	3	3	NUM
ejpam-5694	38	45	-	-	NOUN
ejpam-5694	38	46	convex	convex	NOUN
ejpam-5694	38	47	.	.	PUNCT
ejpam-5694	39	1	also	also	ADV
ejpam-5694	39	2	,	,	PUNCT
ejpam-5694	39	3	these	these	DET
ejpam-5694	39	4	green	green	ADJ
ejpam-5694	39	5	functions	function	NOUN
ejpam-5694	39	6	are	be	AUX
ejpam-5694	39	7	continuous	continuous	ADJ
ejpam-5694	39	8	and	and	CCONJ
ejpam-5694	39	9	convex	convex	VERB
ejpam-5694	39	10	with	with	ADP
ejpam-5694	39	11	respect	respect	NOUN
ejpam-5694	39	12	to	to	ADP
ejpam-5694	39	13	the	the	DET
ejpam-5694	39	14	involved	involved	ADJ
ejpam-5694	39	15	variables	variable	NOUN
ejpam-5694	39	16	and	and	CCONJ
ejpam-5694	39	17	given	give	VERB
ejpam-5694	39	18	in	in	ADP
ejpam-5694	39	19	[	[	NOUN
ejpam-5694	39	20	22	22	NUM
ejpam-5694	39	21	]	]	PUNCT
ejpam-5694	39	22	as	as	ADP
ejpam-5694	39	23	;	;	PUNCT
ejpam-5694	39	24	lemma	lemma	PROPN
ejpam-5694	39	25	1	1	NUM
ejpam-5694	39	26	.	.	PUNCT
ejpam-5694	39	27	assuming	assume	VERB
ejpam-5694	39	28	the	the	DET
ejpam-5694	39	29	real	real	ADV
ejpam-5694	39	30	valued	value	VERB
ejpam-5694	39	31	function	function	NOUN
ejpam-5694	39	32	f	f	PROPN
ejpam-5694	39	33	defined	define	VERB
ejpam-5694	39	34	on	on	ADP
ejpam-5694	39	35	t	t	X
ejpam-5694	39	36	=	=	PUNCT
ejpam-5694	40	1	[	[	X
ejpam-5694	40	2	a1	a1	NOUN
ejpam-5694	40	3	,	,	PUNCT
ejpam-5694	40	4	a2	a2	PROPN
ejpam-5694	40	5	]	]	PUNCT
ejpam-5694	40	6	and	and	CCONJ
ejpam-5694	40	7	f	f	PROPN
ejpam-5694	40	8	is	be	AUX
ejpam-5694	40	9	thrice	thrice	NOUN
ejpam-5694	40	10	differentiable	differentiable	ADJ
ejpam-5694	40	11	therein	therein	ADV
ejpam-5694	40	12	.	.	PUNCT
ejpam-5694	41	1	let	let	VERB
ejpam-5694	41	2	gα(α	gα(α	VERB
ejpam-5694	41	3	=	=	SYM
ejpam-5694	41	4	{	{	PUNCT
ejpam-5694	41	5	1	1	NUM
ejpam-5694	41	6	,	,	PUNCT
ejpam-5694	41	7	2	2	NUM
ejpam-5694	41	8	,	,	PUNCT
ejpam-5694	41	9	3	3	NUM
ejpam-5694	41	10	,	,	PUNCT
ejpam-5694	41	11	4	4	NUM
ejpam-5694	41	12	}	}	PUNCT
ejpam-5694	41	13	)	)	PUNCT
ejpam-5694	41	14	be	be	AUX
ejpam-5694	41	15	the	the	DET
ejpam-5694	41	16	two	two	NUM
ejpam-5694	41	17	-	-	PUNCT
ejpam-5694	41	18	point	point	NOUN
ejpam-5694	41	19	right	right	ADJ
ejpam-5694	41	20	-	-	PUNCT
ejpam-5694	41	21	focal	focal	ADJ
ejpam-5694	41	22	problem	problem	NOUN
ejpam-5694	41	23	type	type	NOUN
ejpam-5694	41	24	green	green	ADJ
ejpam-5694	41	25	function	function	NOUN
ejpam-5694	41	26	.	.	PUNCT
ejpam-5694	42	1	then	then	ADV
ejpam-5694	42	2	f(ϖ	f(ϖ	NOUN
ejpam-5694	42	3	)	)	PUNCT
ejpam-5694	42	4	=	=	SYM
ejpam-5694	42	5	f(a1	f(a1	NOUN
ejpam-5694	42	6	)	)	PUNCT
ejpam-5694	42	7	+	+	CCONJ
ejpam-5694	42	8	(	(	PUNCT
ejpam-5694	42	9	ϖ	ϖ	X
ejpam-5694	42	10	−	−	PROPN
ejpam-5694	42	11	a1)f	a1)f	PROPN
ejpam-5694	42	12	′(a2	′(a2	NUM
ejpam-5694	42	13	)	)	PUNCT
ejpam-5694	43	1	+	+	CCONJ
ejpam-5694	43	2	(	(	PUNCT
ejpam-5694	43	3	ϖ	ϖ	X
ejpam-5694	43	4	−	−	PROPN
ejpam-5694	43	5	a1)(ϖ	a1)(ϖ	PROPN
ejpam-5694	43	6	−	−	PROPN
ejpam-5694	43	7	a2)f	a2)f	NOUN
ejpam-5694	43	8	′′(a1)−	′′(a1)−	PROPN
ejpam-5694	43	9	(	(	PUNCT
ejpam-5694	43	10	ϖ	ϖ	NOUN
ejpam-5694	43	11	−	−	PROPN
ejpam-5694	43	12	a1	a1	NOUN
ejpam-5694	43	13	)	)	PUNCT
ejpam-5694	43	14	2	2	NUM
ejpam-5694	43	15	2	2	NUM
ejpam-5694	43	16	f	f	NOUN
ejpam-5694	43	17	′′(a2	′′(a2	NOUN
ejpam-5694	43	18	)	)	PUNCT
ejpam-5694	43	19	a.	a.	NOUN
ejpam-5694	43	20	m.	m.	PROPN
ejpam-5694	43	21	k.	k.	PROPN
ejpam-5694	43	22	abbasi	abbasi	PROPN
ejpam-5694	43	23	,	,	PUNCT
ejpam-5694	43	24	m.	m.	PROPN
ejpam-5694	43	25	anwar	anwar	PROPN
ejpam-5694	43	26	/	/	PUNCT
ejpam-5694	43	27	eur	eur	PROPN
ejpam-5694	43	28	.	.	PUNCT
ejpam-5694	44	1	j.	j.	PROPN
ejpam-5694	44	2	pure	pure	PROPN
ejpam-5694	44	3	appl	appl	PROPN
ejpam-5694	44	4	.	.	PROPN
ejpam-5694	44	5	math	math	PROPN
ejpam-5694	44	6	,	,	PUNCT
ejpam-5694	44	7	18	18	NUM
ejpam-5694	44	8	(	(	PUNCT
ejpam-5694	44	9	1	1	NUM
ejpam-5694	44	10	)	)	PUNCT
ejpam-5694	44	11	(	(	PUNCT
ejpam-5694	44	12	2025	2025	NUM
ejpam-5694	44	13	)	)	PUNCT
ejpam-5694	44	14	,	,	PUNCT
ejpam-5694	44	15	5694	5694	NUM
ejpam-5694	44	16	3	3	NUM
ejpam-5694	44	17	of	of	ADP
ejpam-5694	44	18	18	18	NUM
ejpam-5694	44	19	+	+	NUM
ejpam-5694	44	20	∫	∫	PROPN
ejpam-5694	44	21	a2	a2	PROPN
ejpam-5694	44	22	a1	a1	NOUN
ejpam-5694	44	23	g1(ϖ	g1(ϖ	NOUN
ejpam-5694	44	24	,	,	PUNCT
ejpam-5694	44	25	τ)f	τ)f	PUNCT
ejpam-5694	44	26	′′′(τ)dτ	′′′(τ)dτ	PROPN
ejpam-5694	44	27	,	,	PUNCT
ejpam-5694	44	28	(	(	PUNCT
ejpam-5694	44	29	1	1	X
ejpam-5694	44	30	)	)	PUNCT
ejpam-5694	44	31	f(ϖ	f(ϖ	NOUN
ejpam-5694	44	32	)	)	PUNCT
ejpam-5694	44	33	=	=	SYM
ejpam-5694	44	34	f(a2	f(a2	NOUN
ejpam-5694	44	35	)	)	PUNCT
ejpam-5694	45	1	+	+	CCONJ
ejpam-5694	45	2	(	(	PUNCT
ejpam-5694	45	3	ϖ	ϖ	X
ejpam-5694	45	4	−	−	PROPN
ejpam-5694	45	5	a2)f	a2)f	PROPN
ejpam-5694	45	6	′(a1	′(a1	PROPN
ejpam-5694	45	7	)	)	PUNCT
ejpam-5694	46	1	+	+	CCONJ
ejpam-5694	46	2	(	(	PUNCT
ejpam-5694	46	3	ϖ	ϖ	X
ejpam-5694	46	4	−	−	PROPN
ejpam-5694	46	5	a1)(ϖ	a1)(ϖ	PROPN
ejpam-5694	46	6	−	−	PROPN
ejpam-5694	46	7	a2)f	a2)f	PROPN
ejpam-5694	46	8	′′(a2)−	′′(a2)−	NOUN
ejpam-5694	46	9	(	(	PUNCT
ejpam-5694	46	10	ϖ	ϖ	INTJ
ejpam-5694	46	11	−	−	PROPN
ejpam-5694	46	12	a2	a2	PROPN
ejpam-5694	46	13	)	)	PUNCT
ejpam-5694	46	14	2	2	NUM
ejpam-5694	46	15	2	2	NUM
ejpam-5694	46	16	f	f	NOUN
ejpam-5694	46	17	′′(a1	′′(a1	NOUN
ejpam-5694	46	18	)	)	PUNCT
ejpam-5694	46	19	−	−	PROPN
ejpam-5694	46	20	∫	∫	PROPN
ejpam-5694	46	21	a2	a2	PROPN
ejpam-5694	46	22	a1	a1	PROPN
ejpam-5694	46	23	g2(ϖ	g2(ϖ	PROPN
ejpam-5694	46	24	,	,	PUNCT
ejpam-5694	46	25	τ)f	τ)f	PUNCT
ejpam-5694	46	26	′′′(τ)dτ	′′′(τ)dτ	PROPN
ejpam-5694	46	27	,	,	PUNCT
ejpam-5694	46	28	(	(	PUNCT
ejpam-5694	46	29	2	2	X
ejpam-5694	46	30	)	)	PUNCT
ejpam-5694	46	31	f(ϖ	f(ϖ	NOUN
ejpam-5694	46	32	)	)	PUNCT
ejpam-5694	46	33	=	=	SYM
ejpam-5694	46	34	f(a2	f(a2	NOUN
ejpam-5694	46	35	)	)	PUNCT
ejpam-5694	47	1	+	+	CCONJ
ejpam-5694	47	2	(	(	PUNCT
ejpam-5694	47	3	ϖ	ϖ	X
ejpam-5694	47	4	−	−	PROPN
ejpam-5694	47	5	a1)f	a1)f	VERB
ejpam-5694	47	6	′(a1	′(a1	NUM
ejpam-5694	47	7	)	)	PUNCT
ejpam-5694	48	1	+	+	CCONJ
ejpam-5694	48	2	(	(	PUNCT
ejpam-5694	48	3	a2	a2	PROPN
ejpam-5694	48	4	−	−	PROPN
ejpam-5694	48	5	a1)f	a1)f	PROPN
ejpam-5694	48	6	′(a2)−	′(a2)−	PROPN
ejpam-5694	48	7	[	[	PUNCT
ejpam-5694	48	8	(	(	PUNCT
ejpam-5694	48	9	ϖ	ϖ	INTJ
ejpam-5694	48	10	−	−	PROPN
ejpam-5694	48	11	a1	a1	NOUN
ejpam-5694	48	12	)	)	PUNCT
ejpam-5694	48	13	2	2	NUM
ejpam-5694	48	14	2	2	NUM
ejpam-5694	48	15	+	+	CCONJ
ejpam-5694	48	16	(	(	PUNCT
ejpam-5694	48	17	ϖ	ϖ	INTJ
ejpam-5694	48	18	−	−	PROPN
ejpam-5694	48	19	a1)(a−	a1)(a−	PROPN
ejpam-5694	48	20	b	b	NOUN
ejpam-5694	48	21	)	)	PUNCT
ejpam-5694	48	22	]	]	PUNCT
ejpam-5694	49	1	f	f	PROPN
ejpam-5694	49	2	′′(a1	′′(a1	NOUN
ejpam-5694	49	3	)	)	PUNCT
ejpam-5694	49	4	+	+	CCONJ
ejpam-5694	49	5	[	[	PUNCT
ejpam-5694	49	6	(	(	PUNCT
ejpam-5694	49	7	a2	a2	PROPN
ejpam-5694	49	8	−	−	PROPN
ejpam-5694	49	9	a1	a1	NOUN
ejpam-5694	49	10	)	)	PUNCT
ejpam-5694	49	11	2	2	NUM
ejpam-5694	49	12	2	2	NUM
ejpam-5694	49	13	+	+	CCONJ
ejpam-5694	49	14	(	(	PUNCT
ejpam-5694	49	15	ϖ	ϖ	AUX
ejpam-5694	49	16	−	−	PROPN
ejpam-5694	49	17	a1)(ϖ	a1)(ϖ	PROPN
ejpam-5694	49	18	−	−	PROPN
ejpam-5694	49	19	a2	a2	PROPN
ejpam-5694	49	20	)	)	PUNCT
ejpam-5694	49	21	]	]	PUNCT
ejpam-5694	50	1	f	f	PROPN
ejpam-5694	50	2	′′(a2)−	′′(a2)−	PROPN
ejpam-5694	50	3	∫	∫	PROPN
ejpam-5694	50	4	a2	a2	PROPN
ejpam-5694	50	5	a1	a1	PROPN
ejpam-5694	50	6	g3(ϖ	g3(ϖ	PROPN
ejpam-5694	50	7	,	,	PUNCT
ejpam-5694	50	8	τ)f	τ)f	PUNCT
ejpam-5694	50	9	′′′(τ)dτ	′′′(τ)dτ	PROPN
ejpam-5694	50	10	(	(	PUNCT
ejpam-5694	50	11	3	3	NUM
ejpam-5694	50	12	)	)	PUNCT
ejpam-5694	50	13	and	and	CCONJ
ejpam-5694	50	14	f(ϖ	f(ϖ	NOUN
ejpam-5694	50	15	)	)	PUNCT
ejpam-5694	50	16	=	=	SYM
ejpam-5694	50	17	f(a2	f(a2	NOUN
ejpam-5694	50	18	)	)	PUNCT
ejpam-5694	51	1	+	+	CCONJ
ejpam-5694	51	2	(	(	PUNCT
ejpam-5694	51	3	a2	a2	PROPN
ejpam-5694	51	4	−	−	PROPN
ejpam-5694	51	5	a1)f	a1)f	PROPN
ejpam-5694	51	6	′(a1	′(a1	NUM
ejpam-5694	51	7	)	)	PUNCT
ejpam-5694	52	1	+	+	CCONJ
ejpam-5694	52	2	(	(	PUNCT
ejpam-5694	52	3	b−ϖ)f	b−ϖ)f	PROPN
ejpam-5694	52	4	′(a2	′(a2	PROPN
ejpam-5694	52	5	)	)	PUNCT
ejpam-5694	53	1	+	+	CCONJ
ejpam-5694	53	2	[	[	PUNCT
ejpam-5694	53	3	(	(	PUNCT
ejpam-5694	53	4	a2	a2	PROPN
ejpam-5694	53	5	−	−	PROPN
ejpam-5694	53	6	a1	a1	NOUN
ejpam-5694	53	7	)	)	PUNCT
ejpam-5694	53	8	2	2	NUM
ejpam-5694	53	9	2	2	NUM
ejpam-5694	53	10	+	+	CCONJ
ejpam-5694	53	11	(	(	PUNCT
ejpam-5694	53	12	ϖ	ϖ	X
ejpam-5694	53	13	−	−	PROPN
ejpam-5694	53	14	a2)(ϖ	a2)(ϖ	PROPN
ejpam-5694	53	15	−	−	PROPN
ejpam-5694	53	16	a1	a1	NOUN
ejpam-5694	53	17	)	)	PUNCT
ejpam-5694	53	18	]	]	PUNCT
ejpam-5694	54	1	f	f	PROPN
ejpam-5694	54	2	′′(a1	′′(a1	PROPN
ejpam-5694	54	3	)	)	PUNCT
ejpam-5694	54	4	−	−	PROPN
ejpam-5694	55	1	[	[	PUNCT
ejpam-5694	55	2	(	(	PUNCT
ejpam-5694	55	3	ϖ	ϖ	INTJ
ejpam-5694	55	4	−	−	PROPN
ejpam-5694	55	5	a2	a2	PROPN
ejpam-5694	55	6	)	)	PUNCT
ejpam-5694	55	7	2	2	NUM
ejpam-5694	55	8	2	2	NUM
ejpam-5694	55	9	+	+	CCONJ
ejpam-5694	55	10	(	(	PUNCT
ejpam-5694	55	11	ϖ	ϖ	NOUN
ejpam-5694	55	12	−	−	PROPN
ejpam-5694	55	13	a2)(a2	a2)(a2	NOUN
ejpam-5694	55	14	−	−	PROPN
ejpam-5694	55	15	a1	a1	NOUN
ejpam-5694	55	16	)	)	PUNCT
ejpam-5694	55	17	]	]	PUNCT
ejpam-5694	56	1	f	f	PROPN
ejpam-5694	56	2	′′(a2	′′(a2	NOUN
ejpam-5694	56	3	)	)	PUNCT
ejpam-5694	56	4	+	+	CCONJ
ejpam-5694	56	5	∫	∫	PROPN
ejpam-5694	56	6	a2	a2	PROPN
ejpam-5694	56	7	a1	a1	PROPN
ejpam-5694	56	8	g4(ϖ	g4(ϖ	PROPN
ejpam-5694	56	9	,	,	PUNCT
ejpam-5694	56	10	τ)f	τ)f	PUNCT
ejpam-5694	56	11	′′′(τ)dτ	′′′(τ)dτ	PROPN
ejpam-5694	56	12	.	.	PUNCT
ejpam-5694	56	13	(	(	PUNCT
ejpam-5694	56	14	4	4	NUM
ejpam-5694	56	15	)	)	PUNCT
ejpam-5694	56	16	where	where	SCONJ
ejpam-5694	56	17	the	the	DET
ejpam-5694	56	18	green	green	ADJ
ejpam-5694	56	19	functions	function	NOUN
ejpam-5694	56	20	are	be	AUX
ejpam-5694	56	21	given	give	VERB
ejpam-5694	56	22	as	as	ADP
ejpam-5694	56	23	g1(ϖ	g1(ϖ	PROPN
ejpam-5694	56	24	,	,	PUNCT
ejpam-5694	56	25	τ	τ	NOUN
ejpam-5694	56	26	)	)	PUNCT
ejpam-5694	56	27	=	=	PRON
ejpam-5694	56	28	{	{	PUNCT
ejpam-5694	56	29	(	(	PUNCT
ejpam-5694	56	30	τ−a1)2	τ−a1)2	NUM
ejpam-5694	56	31	2	2	NUM
ejpam-5694	57	1	+	+	CCONJ
ejpam-5694	57	2	(	(	PUNCT
ejpam-5694	57	3	ϖ	ϖ	X
ejpam-5694	57	4	−	−	PROPN
ejpam-5694	57	5	a1)(ϖ	a1)(ϖ	PROPN
ejpam-5694	57	6	−	−	PROPN
ejpam-5694	57	7	a2	a2	PROPN
ejpam-5694	57	8	)	)	PUNCT
ejpam-5694	57	9	a	a	DET
ejpam-5694	57	10	≤	≤	ADV
ejpam-5694	57	11	τ	τ	X
ejpam-5694	57	12	≤	≤	NUM
ejpam-5694	58	1	ϖ	ϖ	X
ejpam-5694	58	2	(	(	PUNCT
ejpam-5694	58	3	ϖ	ϖ	NOUN
ejpam-5694	58	4	−	−	PROPN
ejpam-5694	59	1	a1)(τ	a1)(τ	NUM
ejpam-5694	59	2	−	−	PROPN
ejpam-5694	59	3	a2	a2	PROPN
ejpam-5694	59	4	)	)	PUNCT
ejpam-5694	60	1	+	+	CCONJ
ejpam-5694	60	2	(	(	PUNCT
ejpam-5694	60	3	τ−a1)2	τ−a1)2	NUM
ejpam-5694	60	4	2	2	NUM
ejpam-5694	60	5	ϖ	ϖ	NOUN
ejpam-5694	60	6	≤	≤	NUM
ejpam-5694	60	7	τ	τ	PROPN
ejpam-5694	60	8	≤	≤	NUM
ejpam-5694	60	9	b	b	PROPN
ejpam-5694	60	10	,	,	PUNCT
ejpam-5694	60	11	(	(	PUNCT
ejpam-5694	60	12	5	5	X
ejpam-5694	60	13	)	)	PUNCT
ejpam-5694	60	14	g2(ϖ	g2(ϖ	PROPN
ejpam-5694	60	15	,	,	PUNCT
ejpam-5694	60	16	τ	τ	X
ejpam-5694	60	17	)	)	PUNCT
ejpam-5694	60	18	=	=	PRON
ejpam-5694	60	19	{	{	PUNCT
ejpam-5694	60	20	(	(	PUNCT
ejpam-5694	60	21	τ−a2)2	τ−a2)2	NOUN
ejpam-5694	60	22	2	2	NUM
ejpam-5694	60	23	+	+	CCONJ
ejpam-5694	60	24	(	(	PUNCT
ejpam-5694	60	25	τ	τ	PROPN
ejpam-5694	60	26	−	−	NOUN
ejpam-5694	60	27	a1)(ϖ	a1)(ϖ	PROPN
ejpam-5694	60	28	−	−	PROPN
ejpam-5694	60	29	a2	a2	PROPN
ejpam-5694	60	30	)	)	PUNCT
ejpam-5694	60	31	a	a	DET
ejpam-5694	60	32	≤	≤	ADV
ejpam-5694	60	33	τ	τ	X
ejpam-5694	60	34	≤	≤	NUM
ejpam-5694	61	1	ϖ	ϖ	X
ejpam-5694	61	2	(	(	PUNCT
ejpam-5694	61	3	ϖ	ϖ	NOUN
ejpam-5694	61	4	−	−	NOUN
ejpam-5694	61	5	a1)(ϖ	a1)(ϖ	PROPN
ejpam-5694	61	6	−	−	PROPN
ejpam-5694	61	7	a2	a2	PROPN
ejpam-5694	61	8	)	)	PUNCT
ejpam-5694	61	9	+	+	CCONJ
ejpam-5694	61	10	(	(	PUNCT
ejpam-5694	61	11	τ−a2)2	τ−a2)2	PROPN
ejpam-5694	61	12	2	2	NUM
ejpam-5694	61	13	ϖ	ϖ	SYM
ejpam-5694	61	14	≤	≤	NUM
ejpam-5694	61	15	τ	τ	PROPN
ejpam-5694	61	16	≤	≤	NUM
ejpam-5694	61	17	b	b	PROPN
ejpam-5694	61	18	,	,	PUNCT
ejpam-5694	61	19	(	(	PUNCT
ejpam-5694	61	20	6	6	NUM
ejpam-5694	61	21	)	)	PUNCT
ejpam-5694	61	22	g3(ϖ	g3(ϖ	PROPN
ejpam-5694	61	23	,	,	PUNCT
ejpam-5694	61	24	τ	τ	X
ejpam-5694	61	25	)	)	PUNCT
ejpam-5694	61	26	=	=	PRON
ejpam-5694	61	27	{	{	PUNCT
ejpam-5694	61	28	(	(	PUNCT
ejpam-5694	61	29	τ−a1)2	τ−a1)2	NUM
ejpam-5694	61	30	2	2	NUM
ejpam-5694	61	31	+	+	CCONJ
ejpam-5694	61	32	(	(	PUNCT
ejpam-5694	61	33	ϖ	ϖ	X
ejpam-5694	61	34	−	−	PROPN
ejpam-5694	62	1	a1)(τ	a1)(τ	NUM
ejpam-5694	62	2	−	−	PROPN
ejpam-5694	62	3	a2	a2	PROPN
ejpam-5694	62	4	)	)	PUNCT
ejpam-5694	62	5	a	a	DET
ejpam-5694	62	6	≤	≤	ADV
ejpam-5694	62	7	τ	τ	X
ejpam-5694	62	8	≤	≤	NUM
ejpam-5694	63	1	ϖ	ϖ	X
ejpam-5694	63	2	(	(	PUNCT
ejpam-5694	63	3	ϖ	ϖ	NOUN
ejpam-5694	63	4	−	−	NOUN
ejpam-5694	63	5	a1)(ϖ	a1)(ϖ	PROPN
ejpam-5694	63	6	−	−	PROPN
ejpam-5694	63	7	a2	a2	PROPN
ejpam-5694	63	8	)	)	PUNCT
ejpam-5694	63	9	+	+	CCONJ
ejpam-5694	63	10	(	(	PUNCT
ejpam-5694	63	11	τ−a1)2	τ−a1)2	NUM
ejpam-5694	63	12	2	2	NUM
ejpam-5694	63	13	ϖ	ϖ	NOUN
ejpam-5694	63	14	≤	≤	NUM
ejpam-5694	63	15	τ	τ	PROPN
ejpam-5694	63	16	≤	≤	NUM
ejpam-5694	63	17	b	b	PROPN
ejpam-5694	63	18	,	,	PUNCT
ejpam-5694	63	19	(	(	PUNCT
ejpam-5694	63	20	7	7	X
ejpam-5694	63	21	)	)	PUNCT
ejpam-5694	63	22	g4(ϖ	g4(ϖ	PROPN
ejpam-5694	63	23	,	,	PUNCT
ejpam-5694	63	24	τ	τ	X
ejpam-5694	63	25	)	)	PUNCT
ejpam-5694	63	26	=	=	PRON
ejpam-5694	63	27	{	{	PUNCT
ejpam-5694	63	28	(	(	PUNCT
ejpam-5694	63	29	τ−a2)2	τ−a2)2	NOUN
ejpam-5694	63	30	2	2	NUM
ejpam-5694	63	31	+	+	CCONJ
ejpam-5694	63	32	(	(	PUNCT
ejpam-5694	63	33	ϖ	ϖ	X
ejpam-5694	63	34	−	−	PROPN
ejpam-5694	63	35	a1)(ϖ	a1)(ϖ	PROPN
ejpam-5694	63	36	−	−	PROPN
ejpam-5694	63	37	a2	a2	PROPN
ejpam-5694	63	38	)	)	PUNCT
ejpam-5694	63	39	a	a	DET
ejpam-5694	63	40	≤	≤	ADV
ejpam-5694	63	41	τ	τ	X
ejpam-5694	63	42	≤	≤	NUM
ejpam-5694	64	1	ϖ	ϖ	X
ejpam-5694	64	2	(	(	PUNCT
ejpam-5694	64	3	ϖ	ϖ	NOUN
ejpam-5694	64	4	−	−	PROPN
ejpam-5694	64	5	a2)(τ	a2)(τ	PROPN
ejpam-5694	64	6	−	−	PROPN
ejpam-5694	64	7	a1	a1	NOUN
ejpam-5694	64	8	)	)	PUNCT
ejpam-5694	64	9	+	+	CCONJ
ejpam-5694	64	10	(	(	PUNCT
ejpam-5694	64	11	ϖ−a2)2	ϖ−a2)2	PROPN
ejpam-5694	64	12	2	2	NUM
ejpam-5694	64	13	ϖ	ϖ	NOUN
ejpam-5694	64	14	≤	≤	NUM
ejpam-5694	64	15	τ	τ	PROPN
ejpam-5694	64	16	≤	≤	PROPN
ejpam-5694	64	17	b.	b.	PROPN
ejpam-5694	64	18	(	(	PUNCT
ejpam-5694	64	19	8)	8)	NUM
ejpam-5694	64	20	the	the	DET
ejpam-5694	64	21	taylor	taylor	PROPN
ejpam-5694	64	22	’s	’s	PART
ejpam-5694	64	23	formula	formula	NOUN
ejpam-5694	64	24	for	for	ADP
ejpam-5694	64	25	the	the	DET
ejpam-5694	64	26	function	function	NOUN
ejpam-5694	64	27	f	f	NOUN
ejpam-5694	64	28	:	:	PUNCT
ejpam-5694	64	29	t	t	PROPN
ejpam-5694	64	30	=	=	PUNCT
ejpam-5694	65	1	[	[	X
ejpam-5694	65	2	a1	a1	NOUN
ejpam-5694	65	3	,	,	PUNCT
ejpam-5694	65	4	a2	a2	PROPN
ejpam-5694	65	5	]	]	PUNCT
ejpam-5694	65	6	→	→	SYM
ejpam-5694	65	7	r	r	NOUN
ejpam-5694	65	8	at	at	ADP
ejpam-5694	65	9	c	c	PROPN
ejpam-5694	65	10	∈	∈	PROPN
ejpam-5694	65	11	t	t	PROPN
ejpam-5694	65	12	and	and	CCONJ
ejpam-5694	65	13	f	f	PROPN
ejpam-5694	65	14	(	(	PUNCT
ejpam-5694	65	15	n−1	n−1	PROPN
ejpam-5694	65	16	)	)	PUNCT
ejpam-5694	65	17	have	have	VERB
ejpam-5694	65	18	the	the	DET
ejpam-5694	65	19	property	property	NOUN
ejpam-5694	65	20	of	of	ADP
ejpam-5694	65	21	absolutely	absolutely	ADV
ejpam-5694	65	22	continuity	continuity	NOUN
ejpam-5694	65	23	,	,	PUNCT
ejpam-5694	65	24	is	be	AUX
ejpam-5694	65	25	;	;	PUNCT
ejpam-5694	65	26	f(ϖ	f(ϖ	NOUN
ejpam-5694	65	27	)	)	PUNCT
ejpam-5694	65	28	=	=	SYM
ejpam-5694	66	1	n−1∑	n−1∑	PROPN
ejpam-5694	66	2	κ=0	κ=0	PROPN
ejpam-5694	66	3	f	f	X
ejpam-5694	66	4	(	(	PUNCT
ejpam-5694	66	5	κ)(ϖ	κ)(ϖ	PROPN
ejpam-5694	66	6	)	)	PUNCT
ejpam-5694	66	7	κ	κ	NOUN
ejpam-5694	66	8	!	!	PUNCT
ejpam-5694	67	1	(	(	PUNCT
ejpam-5694	67	2	ϖ	ϖ	NOUN
ejpam-5694	67	3	−	−	NOUN
ejpam-5694	67	4	c)κ	c)κ	NOUN
ejpam-5694	67	5	+	+	CCONJ
ejpam-5694	67	6	1	1	NUM
ejpam-5694	67	7	n−	n−	NOUN
ejpam-5694	67	8	1	1	NUM
ejpam-5694	67	9	∫	∫	NOUN
ejpam-5694	67	10	ϖ	ϖ	PROPN
ejpam-5694	67	11	c	c	PROPN
ejpam-5694	67	12	f	f	X
ejpam-5694	67	13	(	(	PUNCT
ejpam-5694	67	14	n)(τ)(ϖ	n)(τ)(ϖ	PROPN
ejpam-5694	67	15	−	−	PROPN
ejpam-5694	67	16	τ)m−1dτ	τ)m−1dτ	PROPN
ejpam-5694	67	17	.	.	PUNCT
ejpam-5694	68	1	(	(	PUNCT
ejpam-5694	68	2	9	9	X
ejpam-5694	68	3	)	)	PUNCT
ejpam-5694	68	4	a.	a.	NOUN
ejpam-5694	68	5	m.	m.	PROPN
ejpam-5694	68	6	k.	k.	PROPN
ejpam-5694	68	7	abbasi	abbasi	PROPN
ejpam-5694	68	8	,	,	PUNCT
ejpam-5694	68	9	m.	m.	PROPN
ejpam-5694	68	10	anwar	anwar	PROPN
ejpam-5694	68	11	/	/	PUNCT
ejpam-5694	68	12	eur	eur	PROPN
ejpam-5694	68	13	.	.	PUNCT
ejpam-5694	69	1	j.	j.	PROPN
ejpam-5694	69	2	pure	pure	PROPN
ejpam-5694	69	3	appl	appl	PROPN
ejpam-5694	69	4	.	.	PROPN
ejpam-5694	69	5	math	math	PROPN
ejpam-5694	69	6	,	,	PUNCT
ejpam-5694	69	7	18	18	NUM
ejpam-5694	69	8	(	(	PUNCT
ejpam-5694	69	9	1	1	NUM
ejpam-5694	69	10	)	)	PUNCT
ejpam-5694	69	11	(	(	PUNCT
ejpam-5694	69	12	2025	2025	NUM
ejpam-5694	69	13	)	)	PUNCT
ejpam-5694	69	14	,	,	PUNCT
ejpam-5694	69	15	5694	5694	NUM
ejpam-5694	69	16	4	4	NUM
ejpam-5694	69	17	of	of	ADP
ejpam-5694	69	18	18	18	NUM
ejpam-5694	69	19	lemma	lemma	PROPN
ejpam-5694	69	20	2	2	NUM
ejpam-5694	69	21	.	.	PUNCT
ejpam-5694	70	1	assuming	assume	VERB
ejpam-5694	70	2	that	that	SCONJ
ejpam-5694	70	3	f	f	PROPN
ejpam-5694	70	4	:	:	PUNCT
ejpam-5694	70	5	t	t	PROPN
ejpam-5694	71	1	=	=	PUNCT
ejpam-5694	72	1	[	[	X
ejpam-5694	72	2	a1	a1	NOUN
ejpam-5694	72	3	,	,	PUNCT
ejpam-5694	72	4	a2	a2	PROPN
ejpam-5694	72	5	]	]	PUNCT
ejpam-5694	72	6	→	→	SYM
ejpam-5694	72	7	r	r	NOUN
ejpam-5694	72	8	is	be	AUX
ejpam-5694	72	9	such	such	ADJ
ejpam-5694	72	10	that	that	SCONJ
ejpam-5694	72	11	f	f	PROPN
ejpam-5694	72	12	(	(	PUNCT
ejpam-5694	72	13	n−1	n−1	PROPN
ejpam-5694	72	14	)	)	PUNCT
ejpam-5694	72	15	is	be	AUX
ejpam-5694	72	16	absolute	absolute	ADJ
ejpam-5694	72	17	continuous	continuous	ADJ
ejpam-5694	72	18	and	and	CCONJ
ejpam-5694	72	19	ϖ	ϖ	NOUN
ejpam-5694	72	20	∈	∈	PROPN
ejpam-5694	72	21	t	t	NOUN
ejpam-5694	72	22	.	.	PUNCT
ejpam-5694	73	1	then	then	ADV
ejpam-5694	73	2	the	the	DET
ejpam-5694	73	3	taylor	taylor	PROPN
ejpam-5694	73	4	’s	’s	PART
ejpam-5694	73	5	formula	formula	NOUN
ejpam-5694	73	6	at	at	ADP
ejpam-5694	73	7	point	point	NOUN
ejpam-5694	73	8	a1	a1	NOUN
ejpam-5694	73	9	and	and	CCONJ
ejpam-5694	73	10	a2	a2	PROPN
ejpam-5694	73	11	is	be	AUX
ejpam-5694	73	12	given	give	VERB
ejpam-5694	73	13	in	in	ADP
ejpam-5694	73	14	[	[	X
ejpam-5694	73	15	2	2	NUM
ejpam-5694	73	16	]	]	PUNCT
ejpam-5694	73	17	as	as	ADP
ejpam-5694	73	18	;	;	PUNCT
ejpam-5694	73	19	f(ϖ	f(ϖ	NOUN
ejpam-5694	73	20	)	)	PUNCT
ejpam-5694	73	21	=	=	SYM
ejpam-5694	73	22	n−1∑	n−1∑	PROPN
ejpam-5694	73	23	κ=0	κ=0	PROPN
ejpam-5694	73	24	f	f	X
ejpam-5694	73	25	(	(	PUNCT
ejpam-5694	73	26	κ)(a1	κ)(a1	X
ejpam-5694	73	27	)	)	PUNCT
ejpam-5694	73	28	κ	κ	NOUN
ejpam-5694	73	29	!	!	PUNCT
ejpam-5694	73	30	(	(	PUNCT
ejpam-5694	73	31	ϖ	ϖ	X
ejpam-5694	73	32	−	−	PROPN
ejpam-5694	73	33	a1	a1	NOUN
ejpam-5694	73	34	)	)	PUNCT
ejpam-5694	73	35	κ	κ	NOUN
ejpam-5694	74	1	+	+	NOUN
ejpam-5694	74	2	1	1	NUM
ejpam-5694	74	3	(	(	PUNCT
ejpam-5694	74	4	n−	n−	NOUN
ejpam-5694	74	5	1	1	NUM
ejpam-5694	74	6	)	)	PUNCT
ejpam-5694	74	7	!	!	PUNCT
ejpam-5694	75	1	∫	∫	PROPN
ejpam-5694	75	2	a2	a2	PROPN
ejpam-5694	75	3	a1	a1	PROPN
ejpam-5694	75	4	f	f	PROPN
ejpam-5694	75	5	(	(	PUNCT
ejpam-5694	75	6	n)(τ)(ϖ	n)(τ)(ϖ	PROPN
ejpam-5694	75	7	−	−	PROPN
ejpam-5694	75	8	τ)n−1	τ)n−1	PROPN
ejpam-5694	75	9	+	+	CCONJ
ejpam-5694	75	10	dτ	dτ	PROPN
ejpam-5694	75	11	.	.	PROPN
ejpam-5694	75	12	(	(	PUNCT
ejpam-5694	75	13	10	10	NUM
ejpam-5694	75	14	)	)	PUNCT
ejpam-5694	76	1	where	where	SCONJ
ejpam-5694	76	2	∫	∫	PROPN
ejpam-5694	76	3	a2	a2	PROPN
ejpam-5694	76	4	a1	a1	PROPN
ejpam-5694	76	5	(	(	PUNCT
ejpam-5694	76	6	ϖ	ϖ	NOUN
ejpam-5694	76	7	−	−	PROPN
ejpam-5694	76	8	τ)n−1	τ)n−1	PROPN
ejpam-5694	76	9	+	+	CCONJ
ejpam-5694	76	10	dτ	dτ	NOUN
ejpam-5694	76	11	=	=	SYM
ejpam-5694	76	12	∫	∫	PROPN
ejpam-5694	76	13	ϖ	ϖ	X
ejpam-5694	76	14	a1	a1	NOUN
ejpam-5694	76	15	(	(	PUNCT
ejpam-5694	76	16	ϖ	ϖ	NOUN
ejpam-5694	76	17	−	−	ADP
ejpam-5694	76	18	τ)n−1dτ	τ)n−1dτ	VERB
ejpam-5694	76	19	+	+	NUM
ejpam-5694	76	20	∫	∫	PROPN
ejpam-5694	76	21	a2	a2	PROPN
ejpam-5694	76	22	ϖ	ϖ	PROPN
ejpam-5694	76	23	0dτ	0dτ	NOUN
ejpam-5694	76	24	,	,	PUNCT
ejpam-5694	76	25	and	and	CCONJ
ejpam-5694	76	26	f(ϖ	f(ϖ	NOUN
ejpam-5694	76	27	)	)	PUNCT
ejpam-5694	76	28	=	=	SYM
ejpam-5694	76	29	n−1∑	n−1∑	PROPN
ejpam-5694	76	30	κ=0	κ=0	PROPN
ejpam-5694	76	31	f	f	X
ejpam-5694	76	32	(	(	PUNCT
ejpam-5694	76	33	κ)(a2	κ)(a2	PROPN
ejpam-5694	76	34	)	)	PUNCT
ejpam-5694	76	35	κ	κ	NOUN
ejpam-5694	76	36	!	!	PUNCT
ejpam-5694	76	37	(	(	PUNCT
ejpam-5694	76	38	−1)κ(a2	−1)κ(a2	NOUN
ejpam-5694	76	39	−ϖ)κ	−ϖ)κ	NOUN
ejpam-5694	76	40	−	−	PROPN
ejpam-5694	76	41	(	(	PUNCT
ejpam-5694	76	42	−1)n−1	−1)n−1	PROPN
ejpam-5694	76	43	(	(	PUNCT
ejpam-5694	76	44	n−	n−	NOUN
ejpam-5694	76	45	1	1	NUM
ejpam-5694	76	46	)	)	PUNCT
ejpam-5694	76	47	!	!	PUNCT
ejpam-5694	76	48	∫	∫	PROPN
ejpam-5694	76	49	a2	a2	PROPN
ejpam-5694	76	50	a1	a1	PROPN
ejpam-5694	76	51	f	f	PROPN
ejpam-5694	76	52	(	(	PUNCT
ejpam-5694	76	53	n)(τ)(τ	n)(τ)(τ	PROPN
ejpam-5694	76	54	−ϖ)n−1	−ϖ)n−1	PROPN
ejpam-5694	76	55	+	+	CCONJ
ejpam-5694	76	56	dτ	dτ	PROPN
ejpam-5694	76	57	.	.	PROPN
ejpam-5694	76	58	(	(	PUNCT
ejpam-5694	76	59	11	11	NUM
ejpam-5694	76	60	)	)	PUNCT
ejpam-5694	77	1	where	where	SCONJ
ejpam-5694	77	2	∫	∫	PROPN
ejpam-5694	77	3	a2	a2	PROPN
ejpam-5694	77	4	a1	a1	PROPN
ejpam-5694	77	5	(	(	PUNCT
ejpam-5694	77	6	τ	τ	PROPN
ejpam-5694	77	7	−ϖ)n−1	−ϖ)n−1	PROPN
ejpam-5694	77	8	+	+	PROPN
ejpam-5694	77	9	dτ	dτ	NOUN
ejpam-5694	77	10	=	=	SYM
ejpam-5694	77	11	∫	∫	PROPN
ejpam-5694	77	12	ϖ	ϖ	INTJ
ejpam-5694	77	13	a1	a1	NOUN
ejpam-5694	77	14	0dτ	0dτ	NOUN
ejpam-5694	77	15	+	+	CCONJ
ejpam-5694	77	16	∫	∫	PROPN
ejpam-5694	77	17	a2	a2	PROPN
ejpam-5694	77	18	ϖ	ϖ	PROPN
ejpam-5694	77	19	(	(	PUNCT
ejpam-5694	77	20	τ	τ	PROPN
ejpam-5694	77	21	−ϖ)n−1dτ	−ϖ)n−1dτ	PROPN
ejpam-5694	77	22	,	,	PUNCT
ejpam-5694	77	23	(	(	PUNCT
ejpam-5694	77	24	τ	τ	PROPN
ejpam-5694	77	25	−ϖ)+	−ϖ)+	PROPN
ejpam-5694	77	26	=	=	PUNCT
ejpam-5694	77	27	{	{	PUNCT
ejpam-5694	77	28	τ	τ	X
ejpam-5694	77	29	−ϖ	−ϖ	NOUN
ejpam-5694	77	30	ϖ	ϖ	X
ejpam-5694	77	31	≤	≤	NUM
ejpam-5694	77	32	τ	τ	X
ejpam-5694	77	33	0	0	PUNCT
ejpam-5694	77	34	ϖ	ϖ	X
ejpam-5694	77	35	>	>	X
ejpam-5694	77	36	τ	τ	PROPN
ejpam-5694	77	37	.	.	PUNCT
ejpam-5694	77	38	(	(	PUNCT
ejpam-5694	77	39	12	12	NUM
ejpam-5694	77	40	)	)	PUNCT
ejpam-5694	77	41	definition	definition	NOUN
ejpam-5694	77	42	1	1	NUM
ejpam-5694	77	43	.	.	PUNCT
ejpam-5694	77	44	the	the	DET
ejpam-5694	77	45	n	n	ADV
ejpam-5694	77	46	-	-	PUNCT
ejpam-5694	77	47	th	th	VERB
ejpam-5694	77	48	order	order	NOUN
ejpam-5694	77	49	divided	divide	VERB
ejpam-5694	77	50	difference	difference	NOUN
ejpam-5694	77	51	of	of	ADP
ejpam-5694	77	52	a	a	DET
ejpam-5694	77	53	real	real	ADV
ejpam-5694	77	54	valued	value	VERB
ejpam-5694	77	55	function	function	NOUN
ejpam-5694	77	56	f	f	PROPN
ejpam-5694	77	57	defined	define	VERB
ejpam-5694	77	58	on	on	ADP
ejpam-5694	77	59	[	[	X
ejpam-5694	77	60	a1	a1	NOUN
ejpam-5694	77	61	,	,	PUNCT
ejpam-5694	77	62	a2	a2	PROPN
ejpam-5694	77	63	]	]	PUNCT
ejpam-5694	77	64	at	at	ADP
ejpam-5694	77	65	distinct	distinct	ADJ
ejpam-5694	77	66	points	point	NOUN
ejpam-5694	77	67	ϖ0	ϖ0	NOUN
ejpam-5694	77	68	,	,	PUNCT
ejpam-5694	77	69	...	...	PUNCT
ejpam-5694	77	70	,	,	PUNCT
ejpam-5694	77	71	ϖn	ϖn	ADP
ejpam-5694	77	72	∈	∈	PROPN
ejpam-5694	77	73	[	[	X
ejpam-5694	77	74	a1	a1	NOUN
ejpam-5694	77	75	,	,	PUNCT
ejpam-5694	77	76	a2	a2	PROPN
ejpam-5694	77	77	]	]	PUNCT
ejpam-5694	77	78	is	be	AUX
ejpam-5694	77	79	defined	define	VERB
ejpam-5694	77	80	for	for	ADP
ejpam-5694	77	81	(	(	PUNCT
ejpam-5694	77	82	i	i	NOUN
ejpam-5694	77	83	=	=	NOUN
ejpam-5694	77	84	0	0	NUM
ejpam-5694	77	85	,	,	PUNCT
ejpam-5694	77	86	1	1	NUM
ejpam-5694	77	87	,	,	PUNCT
ejpam-5694	77	88	...	...	PUNCT
ejpam-5694	77	89	,	,	PUNCT
ejpam-5694	77	90	n	n	CCONJ
ejpam-5694	77	91	)	)	PUNCT
ejpam-5694	77	92	as	as	ADP
ejpam-5694	77	93	f	f	PROPN
ejpam-5694	78	1	[	[	X
ejpam-5694	78	2	ϖi	ϖi	X
ejpam-5694	78	3	]	]	X
ejpam-5694	78	4	=	=	SYM
ejpam-5694	78	5	f(ϖi	f(ϖi	PROPN
ejpam-5694	78	6	)	)	PUNCT
ejpam-5694	78	7	,	,	PUNCT
ejpam-5694	78	8	f	f	PROPN
ejpam-5694	79	1	[	[	X
ejpam-5694	79	2	ϖ0	ϖ0	NOUN
ejpam-5694	79	3	,	,	PUNCT
ejpam-5694	79	4	...	...	PUNCT
ejpam-5694	79	5	,	,	PUNCT
ejpam-5694	79	6	ϖn	ϖn	ADP
ejpam-5694	79	7	]	]	PUNCT
ejpam-5694	79	8	=	=	SYM
ejpam-5694	79	9	f	f	X
ejpam-5694	80	1	[	[	X
ejpam-5694	80	2	ϖ1	ϖ1	X
ejpam-5694	80	3	,	,	PUNCT
ejpam-5694	80	4	...	...	PUNCT
ejpam-5694	80	5	,	,	PUNCT
ejpam-5694	80	6	ϖn]−	ϖn]−	INTJ
ejpam-5694	80	7	f	f	X
ejpam-5694	81	1	[	[	X
ejpam-5694	81	2	ϖ0	ϖ0	NOUN
ejpam-5694	81	3	,	,	PUNCT
ejpam-5694	81	4	...	...	PUNCT
ejpam-5694	81	5	,	,	PUNCT
ejpam-5694	81	6	ϖn−1	ϖn−1	PROPN
ejpam-5694	81	7	]	]	PUNCT
ejpam-5694	81	8	ϖn	ϖn	ADP
ejpam-5694	81	9	−ϖ0	−ϖ0	PROPN
ejpam-5694	81	10	.	.	PUNCT
ejpam-5694	82	1	here	here	ADV
ejpam-5694	82	2	the	the	DET
ejpam-5694	82	3	value	value	NOUN
ejpam-5694	82	4	obtained	obtain	VERB
ejpam-5694	82	5	from	from	ADP
ejpam-5694	82	6	f	f	PROPN
ejpam-5694	83	1	[	[	X
ejpam-5694	83	2	ϖ0	ϖ0	NOUN
ejpam-5694	83	3	,	,	PUNCT
ejpam-5694	83	4	...	...	PUNCT
ejpam-5694	83	5	,	,	PUNCT
ejpam-5694	83	6	ϖn	ϖn	NOUN
ejpam-5694	83	7	]	]	PUNCT
ejpam-5694	83	8	is	be	AUX
ejpam-5694	83	9	not	not	PART
ejpam-5694	83	10	depending	depend	VERB
ejpam-5694	83	11	on	on	ADP
ejpam-5694	83	12	the	the	DET
ejpam-5694	83	13	order	order	NOUN
ejpam-5694	83	14	of	of	ADP
ejpam-5694	83	15	points	point	NOUN
ejpam-5694	83	16	ϖ0	ϖ0	NOUN
ejpam-5694	83	17	,	,	PUNCT
ejpam-5694	83	18	...	...	PUNCT
ejpam-5694	83	19	,	,	PUNCT
ejpam-5694	83	20	ϖn	ϖn	NOUN
ejpam-5694	83	21	.	.	PUNCT
ejpam-5694	84	1	in	in	ADP
ejpam-5694	84	2	case	case	NOUN
ejpam-5694	84	3	when	when	SCONJ
ejpam-5694	84	4	all	all	DET
ejpam-5694	84	5	points	point	NOUN
ejpam-5694	84	6	coincides	coincide	VERB
ejpam-5694	84	7	then	then	ADV
ejpam-5694	84	8	this	this	DET
ejpam-5694	84	9	definition	definition	NOUN
ejpam-5694	84	10	will	will	AUX
ejpam-5694	84	11	be	be	AUX
ejpam-5694	84	12	extended	extend	VERB
ejpam-5694	84	13	to	to	ADP
ejpam-5694	84	14	the	the	DET
ejpam-5694	84	15	following	follow	VERB
ejpam-5694	84	16	form	form	NOUN
ejpam-5694	84	17	if	if	SCONJ
ejpam-5694	84	18	f	f	PROPN
ejpam-5694	84	19	(	(	PUNCT
ejpam-5694	84	20	j−1)(ϖ	j−1)(ϖ	PROPN
ejpam-5694	84	21	)	)	PUNCT
ejpam-5694	84	22	exists	exist	VERB
ejpam-5694	84	23	f	f	X
ejpam-5694	84	24	[	[	X
ejpam-5694	84	25	ϖ	ϖ	X
ejpam-5694	84	26	,	,	PUNCT
ejpam-5694	84	27	...	...	PUNCT
ejpam-5694	84	28	j−times	j−time	NOUN
ejpam-5694	84	29	,	,	PUNCT
ejpam-5694	84	30	ϖ	ϖ	X
ejpam-5694	84	31	]	]	X
ejpam-5694	84	32	=	=	SYM
ejpam-5694	84	33	f	f	X
ejpam-5694	84	34	(	(	PUNCT
ejpam-5694	84	35	j−1)(ϖ	j−1)(ϖ	PROPN
ejpam-5694	84	36	)	)	PUNCT
ejpam-5694	84	37	(	(	PUNCT
ejpam-5694	84	38	j	j	NOUN
ejpam-5694	84	39	−	−	PROPN
ejpam-5694	84	40	1	1	NUM
ejpam-5694	84	41	)	)	PUNCT
ejpam-5694	84	42	!	!	PUNCT
ejpam-5694	84	43	.	.	PUNCT
ejpam-5694	85	1	(	(	PUNCT
ejpam-5694	85	2	13	13	NUM
ejpam-5694	85	3	)	)	PUNCT
ejpam-5694	85	4	the	the	DET
ejpam-5694	85	5	british	british	ADJ
ejpam-5694	85	6	mathematician	mathematician	NOUN
ejpam-5694	85	7	g	g	PROPN
ejpam-5694	85	8	h	h	PROPN
ejpam-5694	85	9	hardy	hardy	ADJ
ejpam-5694	85	10	introduce	introduce	VERB
ejpam-5694	85	11	an	an	DET
ejpam-5694	85	12	inequality	inequality	NOUN
ejpam-5694	85	13	so	so	ADV
ejpam-5694	85	14	-	-	PUNCT
ejpam-5694	85	15	called	call	VERB
ejpam-5694	85	16	hardy	hardy	ADJ
ejpam-5694	85	17	inequality	inequality	NOUN
ejpam-5694	85	18	in	in	ADP
ejpam-5694	85	19	[	[	X
ejpam-5694	85	20	9	9	NUM
ejpam-5694	85	21	]	]	PUNCT
ejpam-5694	85	22	given	give	VERB
ejpam-5694	85	23	as;∫	as;∫	PROPN
ejpam-5694	85	24	∞	∞	PROPN
ejpam-5694	85	25	0	0	NUM
ejpam-5694	86	1	(	(	PUNCT
ejpam-5694	86	2	1	1	NUM
ejpam-5694	86	3	ϖ	ϖ	NUM
ejpam-5694	86	4	∫	∫	PROPN
ejpam-5694	86	5	ϖ	ϖ	NOUN
ejpam-5694	86	6	0	0	NUM
ejpam-5694	86	7	f(τ)dτ	f(τ)dτ	PROPN
ejpam-5694	86	8	)	)	PUNCT
ejpam-5694	86	9	γ	γ	X
ejpam-5694	86	10	dϖ	dϖ	ADP
ejpam-5694	86	11	≤	≤	PROPN
ejpam-5694	86	12	(	(	PUNCT
ejpam-5694	86	13	γ	γ	X
ejpam-5694	86	14	γ	γ	X
ejpam-5694	86	15	−	−	PROPN
ejpam-5694	86	16	1	1	NUM
ejpam-5694	86	17	)	)	PUNCT
ejpam-5694	86	18	γ	γ	X
ejpam-5694	86	19	∫	∫	PROPN
ejpam-5694	86	20	∞	∞	PROPN
ejpam-5694	86	21	0	0	NUM
ejpam-5694	87	1	fγ(ϖ)dϖ	fγ(ϖ)dϖ	ADJ
ejpam-5694	87	2	,	,	PUNCT
ejpam-5694	87	3	γ	γ	X
ejpam-5694	87	4	>	>	X
ejpam-5694	87	5	1	1	NUM
ejpam-5694	87	6	,	,	PUNCT
ejpam-5694	87	7	(	(	PUNCT
ejpam-5694	87	8	14	14	NUM
ejpam-5694	87	9	)	)	PUNCT
ejpam-5694	87	10	where	where	SCONJ
ejpam-5694	87	11	he	he	PRON
ejpam-5694	87	12	took	take	VERB
ejpam-5694	87	13	a	a	DET
ejpam-5694	87	14	non	non	ADJ
ejpam-5694	87	15	-	-	ADJ
ejpam-5694	87	16	negative	negative	ADJ
ejpam-5694	87	17	function	function	NOUN
ejpam-5694	87	18	f	f	PROPN
ejpam-5694	87	19	with	with	ADP
ejpam-5694	87	20	f	f	PROPN
ejpam-5694	87	21	∈	∈	PROPN
ejpam-5694	87	22	lγ(r+	lγ(r+	PROPN
ejpam-5694	87	23	)	)	PUNCT
ejpam-5694	87	24	and	and	CCONJ
ejpam-5694	87	25	r+	r+	NOUN
ejpam-5694	87	26	=	=	SYM
ejpam-5694	87	27	(	(	PUNCT
ejpam-5694	87	28	0,∞	0,∞	NOUN
ejpam-5694	87	29	)	)	PUNCT
ejpam-5694	87	30	along	along	ADP
ejpam-5694	87	31	with	with	ADP
ejpam-5694	87	32	sharp	sharp	ADJ
ejpam-5694	87	33	constant	constant	ADJ
ejpam-5694	87	34	(	(	PUNCT
ejpam-5694	87	35	γ	γ	X
ejpam-5694	87	36	γ−1	γ−1	ADJ
ejpam-5694	87	37	)	)	PUNCT
ejpam-5694	87	38	γ	γ	PROPN
ejpam-5694	87	39	.	.	PUNCT
ejpam-5694	88	1	with	with	ADP
ejpam-5694	88	2	the	the	DET
ejpam-5694	88	3	passage	passage	NOUN
ejpam-5694	88	4	of	of	ADP
ejpam-5694	88	5	time	time	NOUN
ejpam-5694	88	6	it	it	PRON
ejpam-5694	88	7	has	have	AUX
ejpam-5694	88	8	been	be	AUX
ejpam-5694	88	9	generalized	generalize	VERB
ejpam-5694	88	10	in	in	ADP
ejpam-5694	88	11	many	many	ADJ
ejpam-5694	88	12	ways	way	NOUN
ejpam-5694	88	13	.	.	PUNCT
ejpam-5694	89	1	a.	a.	PROPN
ejpam-5694	89	2	m.	m.	PROPN
ejpam-5694	89	3	k.	k.	PROPN
ejpam-5694	89	4	abbasi	abbasi	PROPN
ejpam-5694	89	5	,	,	PUNCT
ejpam-5694	89	6	m.	m.	PROPN
ejpam-5694	89	7	anwar	anwar	PROPN
ejpam-5694	89	8	/	/	PUNCT
ejpam-5694	89	9	eur	eur	PROPN
ejpam-5694	89	10	.	.	PUNCT
ejpam-5694	90	1	j.	j.	PROPN
ejpam-5694	90	2	pure	pure	PROPN
ejpam-5694	90	3	appl	appl	PROPN
ejpam-5694	90	4	.	.	PROPN
ejpam-5694	90	5	math	math	PROPN
ejpam-5694	90	6	,	,	PUNCT
ejpam-5694	90	7	18	18	NUM
ejpam-5694	90	8	(	(	PUNCT
ejpam-5694	90	9	1	1	NUM
ejpam-5694	90	10	)	)	PUNCT
ejpam-5694	90	11	(	(	PUNCT
ejpam-5694	90	12	2025	2025	NUM
ejpam-5694	90	13	)	)	PUNCT
ejpam-5694	90	14	,	,	PUNCT
ejpam-5694	90	15	5694	5694	NUM
ejpam-5694	90	16	5	5	NUM
ejpam-5694	90	17	of	of	ADP
ejpam-5694	90	18	18	18	NUM
ejpam-5694	90	19	like	like	ADP
ejpam-5694	90	20	in	in	ADP
ejpam-5694	90	21	1964	1964	NUM
ejpam-5694	90	22	n	n	CCONJ
ejpam-5694	90	23	levinson	levinson	PROPN
ejpam-5694	90	24	generalized	generalize	VERB
ejpam-5694	90	25	hardy	hardy	ADJ
ejpam-5694	90	26	inequality	inequality	NOUN
ejpam-5694	90	27	given	give	VERB
ejpam-5694	90	28	[	[	PROPN
ejpam-5694	90	29	19	19	NUM
ejpam-5694	90	30	]	]	PUNCT
ejpam-5694	90	31	,	,	PUNCT
ejpam-5694	90	32	[	[	X
ejpam-5694	90	33	18	18	NUM
ejpam-5694	90	34	]	]	PUNCT
ejpam-5694	90	35	.	.	PUNCT
ejpam-5694	91	1	but	but	CCONJ
ejpam-5694	91	2	[	[	X
ejpam-5694	91	3	18	18	NUM
ejpam-5694	91	4	]	]	PUNCT
ejpam-5694	91	5	,	,	PUNCT
ejpam-5694	91	6	[	[	X
ejpam-5694	91	7	16	16	NUM
ejpam-5694	91	8	]	]	PUNCT
ejpam-5694	91	9	and	and	CCONJ
ejpam-5694	92	1	[	[	X
ejpam-5694	92	2	17	17	NUM
ejpam-5694	92	3	]	]	PUNCT
ejpam-5694	92	4	generalized	generalize	VERB
ejpam-5694	92	5	the	the	DET
ejpam-5694	92	6	hardy	hardy	ADJ
ejpam-5694	92	7	-	-	PUNCT
ejpam-5694	92	8	type	type	NOUN
ejpam-5694	92	9	inequalities	inequality	NOUN
ejpam-5694	92	10	and	and	CCONJ
ejpam-5694	92	11	operator	operator	NOUN
ejpam-5694	92	12	.	.	PUNCT
ejpam-5694	93	1	after	after	ADP
ejpam-5694	93	2	some	some	DET
ejpam-5694	93	3	generalizations	generalization	NOUN
ejpam-5694	93	4	s.	s.	PROPN
ejpam-5694	93	5	kaisjer	kaisjer	PROPN
ejpam-5694	93	6	et	et	PROPN
ejpam-5694	93	7	al	al	PROPN
ejpam-5694	93	8	.	.	PUNCT
ejpam-5694	94	1	[	[	X
ejpam-5694	94	2	12	12	NUM
ejpam-5694	94	3	]	]	PUNCT
ejpam-5694	94	4	gave	give	VERB
ejpam-5694	94	5	some	some	DET
ejpam-5694	94	6	nominal	nominal	ADJ
ejpam-5694	94	7	concept	concept	NOUN
ejpam-5694	94	8	of	of	ADP
ejpam-5694	94	9	hardy	hardy	ADJ
ejpam-5694	94	10	-	-	PUNCT
ejpam-5694	94	11	type	type	NOUN
ejpam-5694	94	12	inequalities	inequality	NOUN
ejpam-5694	94	13	via	via	ADP
ejpam-5694	94	14	convexity	convexity	NOUN
ejpam-5694	94	15	.	.	PUNCT
ejpam-5694	95	1	here	here	ADV
ejpam-5694	95	2	we	we	PRON
ejpam-5694	95	3	throw	throw	VERB
ejpam-5694	95	4	a	a	DET
ejpam-5694	95	5	glance	glance	NOUN
ejpam-5694	95	6	on	on	ADP
ejpam-5694	95	7	some	some	PRON
ejpam-5694	95	8	of	of	ADP
ejpam-5694	95	9	their	their	PRON
ejpam-5694	95	10	important	important	ADJ
ejpam-5694	95	11	results	result	NOUN
ejpam-5694	95	12	.	.	PUNCT
ejpam-5694	96	1	for	for	ADP
ejpam-5694	96	2	positive	positive	ADJ
ejpam-5694	96	3	σ−finite	σ−finite	PROPN
ejpam-5694	96	4	measures	measure	NOUN
ejpam-5694	96	5	,	,	PUNCT
ejpam-5694	96	6	the	the	DET
ejpam-5694	96	7	two	two	NUM
ejpam-5694	96	8	measure	measure	NOUN
ejpam-5694	96	9	spaces	space	NOUN
ejpam-5694	96	10	(	(	PUNCT
ejpam-5694	96	11	∑	∑	PROPN
ejpam-5694	96	12	1,ω1	1,ω1	NUM
ejpam-5694	96	13	,	,	PUNCT
ejpam-5694	96	14	σ1	σ1	PROPN
ejpam-5694	96	15	)	)	PUNCT
ejpam-5694	96	16	and	and	CCONJ
ejpam-5694	96	17	(	(	PUNCT
ejpam-5694	96	18	∑	∑	PROPN
ejpam-5694	96	19	2,ω2	2,ω2	NUM
ejpam-5694	96	20	,	,	PUNCT
ejpam-5694	96	21	σ2	σ2	NOUN
ejpam-5694	96	22	)	)	PUNCT
ejpam-5694	96	23	,	,	PUNCT
ejpam-5694	96	24	we	we	PRON
ejpam-5694	96	25	have	have	VERB
ejpam-5694	96	26	ak	ak	PROPN
ejpam-5694	96	27	the	the	DET
ejpam-5694	96	28	operator	operator	NOUN
ejpam-5694	96	29	given	give	VERB
ejpam-5694	96	30	in	in	ADP
ejpam-5694	96	31	[	[	X
ejpam-5694	96	32	12	12	NUM
ejpam-5694	96	33	]	]	PUNCT
ejpam-5694	96	34	as	as	ADP
ejpam-5694	96	35	akf(ϖ	akf(ϖ	NOUN
ejpam-5694	96	36	)	)	PUNCT
ejpam-5694	96	37	=	=	SYM
ejpam-5694	96	38	1	1	NUM
ejpam-5694	96	39	k(ϖ	k(ϖ	X
ejpam-5694	96	40	)	)	PUNCT
ejpam-5694	96	41	∫	∫	PROPN
ejpam-5694	97	1	ω2	ω2	PROPN
ejpam-5694	97	2	g(ϖ	g(ϖ	PROPN
ejpam-5694	97	3	,	,	PUNCT
ejpam-5694	97	4	τ)f(τ)dµ2(τ	τ)f(τ)dµ2(τ	PROPN
ejpam-5694	97	5	)	)	PUNCT
ejpam-5694	97	6	,	,	PUNCT
ejpam-5694	97	7	(	(	PUNCT
ejpam-5694	97	8	15	15	NUM
ejpam-5694	97	9	)	)	PUNCT
ejpam-5694	97	10	where	where	SCONJ
ejpam-5694	97	11	f	f	PROPN
ejpam-5694	97	12	is	be	AUX
ejpam-5694	97	13	the	the	DET
ejpam-5694	97	14	measurable	measurable	ADJ
ejpam-5694	97	15	function	function	NOUN
ejpam-5694	97	16	and	and	CCONJ
ejpam-5694	97	17	g	g	NOUN
ejpam-5694	97	18	:	:	PUNCT
ejpam-5694	97	19	ω1×ω2	ω1×ω2	NOUN
ejpam-5694	97	20	→	→	PUNCT
ejpam-5694	97	21	r	r	NOUN
ejpam-5694	97	22	is	be	AUX
ejpam-5694	97	23	nonnegative	nonnegative	ADJ
ejpam-5694	97	24	measurable	measurable	ADJ
ejpam-5694	97	25	kernel	kernel	NOUN
ejpam-5694	97	26	and	and	CCONJ
ejpam-5694	97	27	obeys	obey	VERB
ejpam-5694	97	28	the	the	DET
ejpam-5694	97	29	following	follow	VERB
ejpam-5694	97	30	inequality	inequality	NOUN
ejpam-5694	97	31	0	0	NUM
ejpam-5694	97	32	<	<	X
ejpam-5694	97	33	k(ϖ	k(ϖ	X
ejpam-5694	97	34	)	)	PUNCT
ejpam-5694	97	35	=	=	SYM
ejpam-5694	98	1	∫	∫	PROPN
ejpam-5694	98	2	ω2	ω2	PROPN
ejpam-5694	98	3	g(ϖ	g(ϖ	PROPN
ejpam-5694	98	4	,	,	PUNCT
ejpam-5694	98	5	τ)dµ2(τ	τ)dµ2(τ	PROPN
ejpam-5694	98	6	)	)	PUNCT
ejpam-5694	98	7	,	,	PUNCT
ejpam-5694	98	8	ϖ	ϖ	PROPN
ejpam-5694	98	9	∈	∈	PROPN
ejpam-5694	98	10	ω1	ω1	PROPN
ejpam-5694	98	11	.	.	PUNCT
ejpam-5694	99	1	(	(	PUNCT
ejpam-5694	99	2	16	16	NUM
ejpam-5694	99	3	)	)	PUNCT
ejpam-5694	99	4	furthermore	furthermore	ADV
ejpam-5694	99	5	s.	s.	PROPN
ejpam-5694	99	6	kaisjer	kaisjer	PROPN
ejpam-5694	99	7	et	et	PROPN
ejpam-5694	99	8	al	al	PROPN
ejpam-5694	99	9	.	.	PROPN
ejpam-5694	99	10	gave	give	VERB
ejpam-5694	99	11	another	another	DET
ejpam-5694	99	12	useful	useful	ADJ
ejpam-5694	99	13	result	result	NOUN
ejpam-5694	99	14	in	in	ADP
ejpam-5694	99	15	[	[	X
ejpam-5694	99	16	12	12	NUM
ejpam-5694	99	17	]	]	PUNCT
ejpam-5694	99	18	in	in	ADP
ejpam-5694	99	19	the	the	DET
ejpam-5694	99	20	form	form	NOUN
ejpam-5694	99	21	of	of	ADP
ejpam-5694	99	22	following	follow	VERB
ejpam-5694	99	23	theorem	theorem	VERB
ejpam-5694	99	24	.	.	PUNCT
ejpam-5694	99	25	theorem	theorem	NOUN
ejpam-5694	99	26	1	1	NUM
ejpam-5694	99	27	.	.	PUNCT
ejpam-5694	99	28	assuming	assume	VERB
ejpam-5694	99	29	that	that	SCONJ
ejpam-5694	99	30	g(ϖ,s	g(ϖ,s	NOUN
ejpam-5694	99	31	)	)	PUNCT
ejpam-5694	99	32	k(ϖ	k(ϖ	PROPN
ejpam-5694	99	33	)	)	PUNCT
ejpam-5694	99	34	u(ϖ	u(ϖ	NUM
ejpam-5694	99	35	)	)	PUNCT
ejpam-5694	99	36	is	be	AUX
ejpam-5694	99	37	integrable	integrable	ADJ
ejpam-5694	99	38	locally	locally	ADV
ejpam-5694	99	39	on	on	ADP
ejpam-5694	99	40	ω1	ω1	PROPN
ejpam-5694	99	41	for	for	ADP
ejpam-5694	99	42	each	each	DET
ejpam-5694	99	43	fixed	fix	VERB
ejpam-5694	99	44	s	s	PROPN
ejpam-5694	99	45	∈	∈	PROPN
ejpam-5694	99	46	ω2	ω2	NUM
ejpam-5694	99	47	,	,	PUNCT
ejpam-5694	99	48	where	where	SCONJ
ejpam-5694	99	49	u	u	PRON
ejpam-5694	99	50	be	be	VERB
ejpam-5694	99	51	the	the	DET
ejpam-5694	99	52	weight	weight	NOUN
ejpam-5694	99	53	function	function	NOUN
ejpam-5694	99	54	,	,	PUNCT
ejpam-5694	99	55	g(ϖ	g(ϖ	PROPN
ejpam-5694	99	56	,	,	PUNCT
ejpam-5694	99	57	s	s	PART
ejpam-5694	99	58	)	)	PUNCT
ejpam-5694	99	59	≥	≥	NOUN
ejpam-5694	99	60	0	0	NUM
ejpam-5694	99	61	.	.	PUNCT
ejpam-5694	100	1	define	define	VERB
ejpam-5694	100	2	v	v	NOUN
ejpam-5694	100	3	as	as	ADP
ejpam-5694	100	4	ν(s	ν(s	NOUN
ejpam-5694	100	5	)	)	PUNCT
ejpam-5694	101	1	=	=	SYM
ejpam-5694	101	2	∫	∫	PROPN
ejpam-5694	101	3	ω1	ω1	PROPN
ejpam-5694	101	4	g(ϖ	g(ϖ	PROPN
ejpam-5694	101	5	,	,	PUNCT
ejpam-5694	101	6	s	s	NOUN
ejpam-5694	101	7	)	)	PUNCT
ejpam-5694	101	8	k(ϖ	k(ϖ	PROPN
ejpam-5694	101	9	)	)	PUNCT
ejpam-5694	101	10	u(ϖ)dµ1(ϖ	u(ϖ)dµ1(ϖ	PUNCT
ejpam-5694	101	11	)	)	PUNCT
ejpam-5694	102	1	<	<	X
ejpam-5694	102	2	∞.	∞.	PROPN
ejpam-5694	102	3	(	(	PUNCT
ejpam-5694	102	4	17	17	NUM
ejpam-5694	102	5	)	)	PUNCT
ejpam-5694	102	6	if	if	SCONJ
ejpam-5694	102	7	f	f	PROPN
ejpam-5694	102	8	is	be	AUX
ejpam-5694	102	9	supposed	suppose	VERB
ejpam-5694	102	10	to	to	PART
ejpam-5694	102	11	be	be	AUX
ejpam-5694	102	12	the	the	DET
ejpam-5694	102	13	convex	convex	ADJ
ejpam-5694	102	14	function	function	NOUN
ejpam-5694	102	15	on	on	ADP
ejpam-5694	102	16	i	i	PRON
ejpam-5694	102	17	⊂	⊂	PROPN
ejpam-5694	102	18	r	r	NOUN
ejpam-5694	102	19	which	which	PRON
ejpam-5694	102	20	is	be	AUX
ejpam-5694	102	21	open	open	ADJ
ejpam-5694	102	22	,	,	PUNCT
ejpam-5694	102	23	then	then	ADV
ejpam-5694	102	24	following	follow	VERB
ejpam-5694	102	25	relation	relation	NOUN
ejpam-5694	102	26	holds	hold	VERB
ejpam-5694	102	27	∫	∫	PROPN
ejpam-5694	102	28	ω1	ω1	PROPN
ejpam-5694	102	29	f(akf(ϖ))u(ϖ)dµ1(ϖ	f(akf(ϖ))u(ϖ)dµ1(ϖ	NUM
ejpam-5694	102	30	)	)	PUNCT
ejpam-5694	102	31	≤	≤	NUM
ejpam-5694	102	32	∫	∫	PROPN
ejpam-5694	102	33	ω2	ω2	PROPN
ejpam-5694	102	34	f(f(s))ν(s)dµ2(s	f(f(s))ν(s)dµ2(s	NUM
ejpam-5694	102	35	)	)	PUNCT
ejpam-5694	102	36	.	.	PUNCT
ejpam-5694	103	1	(	(	PUNCT
ejpam-5694	103	2	18	18	NUM
ejpam-5694	103	3	)	)	PUNCT
ejpam-5694	103	4	for	for	ADP
ejpam-5694	103	5	measurable	measurable	ADJ
ejpam-5694	103	6	function	function	NOUN
ejpam-5694	103	7	f	f	PROPN
ejpam-5694	103	8	:	:	PUNCT
ejpam-5694	103	9	ω1	ω1	PROPN
ejpam-5694	103	10	→	→	SYM
ejpam-5694	103	11	r	r	PROPN
ejpam-5694	103	12	,	,	PUNCT
ejpam-5694	103	13	with	with	SCONJ
ejpam-5694	103	14	image	image	NOUN
ejpam-5694	103	15	of	of	ADP
ejpam-5694	103	16	f	f	PROPN
ejpam-5694	103	17	is	be	AUX
ejpam-5694	103	18	subset	subset	VERB
ejpam-5694	103	19	of	of	ADP
ejpam-5694	103	20	i	i	PRON
ejpam-5694	103	21	,	,	PUNCT
ejpam-5694	103	22	and	and	CCONJ
ejpam-5694	103	23	ak	ak	PROPN
ejpam-5694	103	24	is	be	AUX
ejpam-5694	103	25	given	give	VERB
ejpam-5694	103	26	in	in	ADP
ejpam-5694	103	27	(	(	PUNCT
ejpam-5694	103	28	15	15	NUM
ejpam-5694	103	29	)	)	PUNCT
ejpam-5694	103	30	.	.	PUNCT
ejpam-5694	104	1	now	now	ADV
ejpam-5694	104	2	we	we	PRON
ejpam-5694	104	3	are	be	AUX
ejpam-5694	104	4	discussing	discuss	VERB
ejpam-5694	104	5	some	some	PRON
ejpam-5694	104	6	of	of	ADP
ejpam-5694	104	7	the	the	DET
ejpam-5694	104	8	existing	exist	VERB
ejpam-5694	104	9	results	result	NOUN
ejpam-5694	104	10	from	from	ADP
ejpam-5694	104	11	literature	literature	NOUN
ejpam-5694	104	12	which	which	PRON
ejpam-5694	104	13	help	help	VERB
ejpam-5694	104	14	us	we	PRON
ejpam-5694	104	15	to	to	PART
ejpam-5694	104	16	find	find	VERB
ejpam-5694	104	17	some	some	DET
ejpam-5694	104	18	important	important	ADJ
ejpam-5694	104	19	bounds	bound	NOUN
ejpam-5694	104	20	using	use	VERB
ejpam-5694	104	21	ostrowski	ostrowski	PROPN
ejpam-5694	104	22	and	and	CCONJ
ejpam-5694	104	23	grüss	grüss	PROPN
ejpam-5694	104	24	-	-	PUNCT
ejpam-5694	104	25	type	type	NOUN
ejpam-5694	104	26	inequalities	inequality	NOUN
ejpam-5694	104	27	presented	present	VERB
ejpam-5694	104	28	in	in	ADP
ejpam-5694	104	29	section	section	NOUN
ejpam-5694	104	30	4	4	NUM
ejpam-5694	104	31	.	.	PUNCT
ejpam-5694	104	32	considering	consider	VERB
ejpam-5694	104	33	the	the	DET
ejpam-5694	104	34	following	follow	VERB
ejpam-5694	104	35	functional	functional	NOUN
ejpam-5694	104	36	for	for	ADP
ejpam-5694	104	37	two	two	NUM
ejpam-5694	104	38	real	real	ADV
ejpam-5694	104	39	valued	value	VERB
ejpam-5694	104	40	lebesgue	lebesgue	NOUN
ejpam-5694	104	41	integrable	integrable	ADJ
ejpam-5694	104	42	functions	function	NOUN
ejpam-5694	104	43	f	f	X
ejpam-5694	104	44	,	,	PUNCT
ejpam-5694	104	45	g	g	PROPN
ejpam-5694	104	46	over	over	ADP
ejpam-5694	104	47	an	an	DET
ejpam-5694	104	48	interval	interval	NOUN
ejpam-5694	104	49	t	t	NOUN
ejpam-5694	104	50	so	so	ADV
ejpam-5694	104	51	-	-	PUNCT
ejpam-5694	104	52	called	call	VERB
ejpam-5694	104	53	čebyšev	čebyšev	PROPN
ejpam-5694	104	54	functional	functional	NOUN
ejpam-5694	104	55	given	give	VERB
ejpam-5694	104	56	by	by	ADP
ejpam-5694	104	57	p.	p.	PROPN
ejpam-5694	104	58	cerone	cerone	NOUN
ejpam-5694	104	59	et	et	PROPN
ejpam-5694	104	60	al	al	PROPN
ejpam-5694	104	61	.	.	PUNCT
ejpam-5694	105	1	in	in	ADP
ejpam-5694	105	2	[	[	X
ejpam-5694	105	3	5	5	NUM
ejpam-5694	105	4	]	]	PUNCT
ejpam-5694	105	5	as	as	ADP
ejpam-5694	105	6	f(f	f(f	PROPN
ejpam-5694	105	7	,	,	PUNCT
ejpam-5694	105	8	g	g	NOUN
ejpam-5694	105	9	)	)	PUNCT
ejpam-5694	105	10	=	=	SYM
ejpam-5694	105	11	1	1	NUM
ejpam-5694	105	12	a2	a2	PROPN
ejpam-5694	105	13	−	−	PROPN
ejpam-5694	105	14	a1	a1	PROPN
ejpam-5694	105	15	∫	∫	PROPN
ejpam-5694	105	16	a2	a2	PROPN
ejpam-5694	105	17	a1	a1	NOUN
ejpam-5694	105	18	f(η)g(η)dη	f(η)g(η)dη	NOUN
ejpam-5694	105	19	−	−	PROPN
ejpam-5694	105	20	1	1	NUM
ejpam-5694	105	21	a2	a2	PROPN
ejpam-5694	105	22	−	−	PROPN
ejpam-5694	105	23	a1	a1	PROPN
ejpam-5694	105	24	∫	∫	PROPN
ejpam-5694	105	25	a2	a2	PROPN
ejpam-5694	105	26	a1	a1	PROPN
ejpam-5694	105	27	f(η)dη	f(η)dη	PROPN
ejpam-5694	105	28	.	.	PROPN
ejpam-5694	105	29	1	1	NUM
ejpam-5694	105	30	a2	a2	PROPN
ejpam-5694	105	31	−	−	PROPN
ejpam-5694	105	32	a1	a1	PROPN
ejpam-5694	105	33	∫	∫	PROPN
ejpam-5694	105	34	a2	a2	PROPN
ejpam-5694	105	35	a1	a1	PROPN
ejpam-5694	105	36	g(η)dη	g(η)dη	PROPN
ejpam-5694	105	37	.	.	PUNCT
ejpam-5694	106	1	(	(	PUNCT
ejpam-5694	106	2	19	19	NUM
ejpam-5694	106	3	)	)	PUNCT
ejpam-5694	106	4	next	next	ADJ
ejpam-5694	106	5	result	result	NOUN
ejpam-5694	106	6	is	be	AUX
ejpam-5694	106	7	given	give	VERB
ejpam-5694	106	8	in	in	ADP
ejpam-5694	106	9	the	the	DET
ejpam-5694	106	10	same	same	ADJ
ejpam-5694	106	11	article	article	NOUN
ejpam-5694	106	12	[	[	X
ejpam-5694	106	13	5	5	X
ejpam-5694	106	14	]	]	PUNCT
ejpam-5694	106	15	which	which	PRON
ejpam-5694	106	16	is	be	AUX
ejpam-5694	106	17	used	use	VERB
ejpam-5694	106	18	to	to	PART
ejpam-5694	106	19	find	find	VERB
ejpam-5694	106	20	the	the	DET
ejpam-5694	106	21	bounds	bound	NOUN
ejpam-5694	106	22	of	of	ADP
ejpam-5694	106	23	the	the	DET
ejpam-5694	106	24	remainder	remainder	NOUN
ejpam-5694	106	25	of	of	ADP
ejpam-5694	106	26	hardy	hardy	ADJ
ejpam-5694	106	27	-	-	PUNCT
ejpam-5694	106	28	type	type	NOUN
ejpam-5694	106	29	inequalities	inequality	NOUN
ejpam-5694	106	30	using	use	VERB
ejpam-5694	106	31	taylor	taylor	PROPN
ejpam-5694	106	32	’s	’s	PART
ejpam-5694	106	33	polynimial	polynimial	ADJ
ejpam-5694	106	34	and	and	CCONJ
ejpam-5694	106	35	green	green	ADJ
ejpam-5694	106	36	function	function	NOUN
ejpam-5694	106	37	.	.	PUNCT
ejpam-5694	107	1	a.	a.	PROPN
ejpam-5694	107	2	m.	m.	PROPN
ejpam-5694	107	3	k.	k.	PROPN
ejpam-5694	107	4	abbasi	abbasi	PROPN
ejpam-5694	107	5	,	,	PUNCT
ejpam-5694	107	6	m.	m.	PROPN
ejpam-5694	107	7	anwar	anwar	PROPN
ejpam-5694	107	8	/	/	PUNCT
ejpam-5694	107	9	eur	eur	PROPN
ejpam-5694	107	10	.	.	PUNCT
ejpam-5694	108	1	j.	j.	PROPN
ejpam-5694	108	2	pure	pure	PROPN
ejpam-5694	108	3	appl	appl	PROPN
ejpam-5694	108	4	.	.	PROPN
ejpam-5694	108	5	math	math	PROPN
ejpam-5694	108	6	,	,	PUNCT
ejpam-5694	108	7	18	18	NUM
ejpam-5694	108	8	(	(	PUNCT
ejpam-5694	108	9	1	1	NUM
ejpam-5694	108	10	)	)	PUNCT
ejpam-5694	108	11	(	(	PUNCT
ejpam-5694	108	12	2025	2025	NUM
ejpam-5694	108	13	)	)	PUNCT
ejpam-5694	108	14	,	,	PUNCT
ejpam-5694	108	15	5694	5694	NUM
ejpam-5694	108	16	6	6	NUM
ejpam-5694	108	17	of	of	ADP
ejpam-5694	108	18	18	18	NUM
ejpam-5694	108	19	theorem	theorem	NOUN
ejpam-5694	108	20	2	2	NUM
ejpam-5694	108	21	.	.	PUNCT
ejpam-5694	109	1	let	let	VERB
ejpam-5694	109	2	the	the	DET
ejpam-5694	109	3	functions	function	NOUN
ejpam-5694	109	4	f	f	X
ejpam-5694	109	5	,	,	PUNCT
ejpam-5694	109	6	g	g	PROPN
ejpam-5694	109	7	are	be	AUX
ejpam-5694	109	8	as	as	ADV
ejpam-5694	109	9	taken	take	VERB
ejpam-5694	109	10	in	in	ADP
ejpam-5694	109	11	(	(	PUNCT
ejpam-5694	109	12	19	19	NUM
ejpam-5694	109	13	)	)	PUNCT
ejpam-5694	109	14	and	and	CCONJ
ejpam-5694	109	15	uniformly	uniformly	ADV
ejpam-5694	109	16	continuous	continuous	ADJ
ejpam-5694	109	17	on	on	ADP
ejpam-5694	109	18	[	[	X
ejpam-5694	109	19	a1	a1	NOUN
ejpam-5694	109	20	,	,	PUNCT
ejpam-5694	109	21	a2	a2	PROPN
ejpam-5694	109	22	]	]	PUNCT
ejpam-5694	109	23	as	as	ADV
ejpam-5694	109	24	well	well	ADV
ejpam-5694	109	25	.	.	PUNCT
ejpam-5694	110	1	additionally	additionally	ADV
ejpam-5694	110	2	assuming	assume	VERB
ejpam-5694	110	3	(	(	PUNCT
ejpam-5694	110	4	.	.	PUNCT
ejpam-5694	111	1	−	−	PROPN
ejpam-5694	111	2	a	a	X
ejpam-5694	111	3	)	)	PUNCT
ejpam-5694	111	4	,	,	PUNCT
ejpam-5694	111	5	(	(	PUNCT
ejpam-5694	111	6	b	b	X
ejpam-5694	111	7	−	−	PROPN
ejpam-5694	111	8	.)(g′)2	.)(g′)2	SYM
ejpam-5694	111	9	∈	∈	PROPN
ejpam-5694	111	10	l[a1	l[a1	NOUN
ejpam-5694	111	11	,	,	PUNCT
ejpam-5694	111	12	a2	a2	PROPN
ejpam-5694	111	13	]	]	PUNCT
ejpam-5694	111	14	,	,	PUNCT
ejpam-5694	111	15	then	then	ADV
ejpam-5694	111	16	following	follow	VERB
ejpam-5694	111	17	inequality	inequality	NOUN
ejpam-5694	111	18	holds	hold	VERB
ejpam-5694	111	19	∣∣∣f(f	∣∣∣f(f	NOUN
ejpam-5694	111	20	,	,	PUNCT
ejpam-5694	111	21	g)∣∣∣	g)∣∣∣	PROPN
ejpam-5694	111	22	≤	≤	PROPN
ejpam-5694	111	23	1√	1√	PROPN
ejpam-5694	111	24	2	2	NUM
ejpam-5694	111	25	(	(	PUNCT
ejpam-5694	111	26	f(f	f(f	PROPN
ejpam-5694	111	27	,	,	PUNCT
ejpam-5694	111	28	f	f	PROPN
ejpam-5694	111	29	)	)	PUNCT
ejpam-5694	111	30	)	)	PUNCT
ejpam-5694	111	31	1	1	NUM
ejpam-5694	111	32	2	2	NUM
ejpam-5694	111	33	1√	1√	PROPN
ejpam-5694	111	34	a2	a2	PROPN
ejpam-5694	111	35	−	−	PROPN
ejpam-5694	112	1	a1	a1	NOUN
ejpam-5694	112	2	(	(	PUNCT
ejpam-5694	112	3	∫	∫	PROPN
ejpam-5694	112	4	a2	a2	PROPN
ejpam-5694	112	5	a1	a1	PROPN
ejpam-5694	112	6	(	(	PUNCT
ejpam-5694	112	7	η	η	PROPN
ejpam-5694	112	8	−	−	PROPN
ejpam-5694	112	9	a1)(a2	a1)(a2	PROPN
ejpam-5694	112	10	−	−	PROPN
ejpam-5694	112	11	η)(g′(η))2dη	η)(g′(η))2dη	PROPN
ejpam-5694	112	12	)	)	PUNCT
ejpam-5694	112	13	2	2	NUM
ejpam-5694	112	14	,	,	PUNCT
ejpam-5694	112	15	(	(	PUNCT
ejpam-5694	112	16	20	20	NUM
ejpam-5694	112	17	)	)	PUNCT
ejpam-5694	112	18	where	where	SCONJ
ejpam-5694	112	19	1√	1√	PROPN
ejpam-5694	112	20	2	2	NUM
ejpam-5694	112	21	is	be	AUX
ejpam-5694	112	22	the	the	DET
ejpam-5694	112	23	best	good	ADJ
ejpam-5694	112	24	possible	possible	ADJ
ejpam-5694	112	25	approximation	approximation	NOUN
ejpam-5694	112	26	.	.	PUNCT
ejpam-5694	113	1	also	also	ADV
ejpam-5694	113	2	,	,	PUNCT
ejpam-5694	113	3	the	the	DET
ejpam-5694	113	4	grüss	grüss	NOUN
ejpam-5694	113	5	-	-	PUNCT
ejpam-5694	113	6	type	type	NOUN
ejpam-5694	113	7	inequality	inequality	NOUN
ejpam-5694	113	8	was	be	AUX
ejpam-5694	113	9	given	give	VERB
ejpam-5694	113	10	in	in	ADP
ejpam-5694	113	11	[	[	X
ejpam-5694	113	12	5	5	NUM
ejpam-5694	113	13	]	]	PUNCT
ejpam-5694	113	14	,	,	PUNCT
ejpam-5694	113	15	which	which	PRON
ejpam-5694	113	16	is	be	AUX
ejpam-5694	113	17	given	give	VERB
ejpam-5694	113	18	as	as	SCONJ
ejpam-5694	113	19	follows	follow	VERB
ejpam-5694	113	20	;	;	PUNCT
ejpam-5694	113	21	theorem	theorem	VERB
ejpam-5694	113	22	3	3	X
ejpam-5694	113	23	.	.	PUNCT
ejpam-5694	114	1	let	let	VERB
ejpam-5694	114	2	f	f	PROPN
ejpam-5694	114	3	is	be	AUX
ejpam-5694	114	4	absolutely	absolutely	ADV
ejpam-5694	114	5	continuous	continuous	ADJ
ejpam-5694	114	6	on	on	ADP
ejpam-5694	114	7	[	[	X
ejpam-5694	114	8	a1	a1	NOUN
ejpam-5694	114	9	,	,	PUNCT
ejpam-5694	114	10	a2	a2	PROPN
ejpam-5694	114	11	]	]	PUNCT
ejpam-5694	114	12	and	and	CCONJ
ejpam-5694	114	13	f	f	PROPN
ejpam-5694	114	14	′	′	NOUN
ejpam-5694	114	15	∈	∈	PROPN
ejpam-5694	114	16	l∞[a1	l∞[a1	NOUN
ejpam-5694	114	17	,	,	PUNCT
ejpam-5694	114	18	a2	a2	PROPN
ejpam-5694	114	19	]	]	PUNCT
ejpam-5694	114	20	and	and	CCONJ
ejpam-5694	114	21	g	g	NOUN
ejpam-5694	114	22	:	:	PUNCT
ejpam-5694	115	1	[	[	X
ejpam-5694	115	2	a1	a1	NOUN
ejpam-5694	115	3	,	,	PUNCT
ejpam-5694	115	4	a2	a2	PROPN
ejpam-5694	115	5	]	]	PUNCT
ejpam-5694	115	6	→	→	SYM
ejpam-5694	115	7	r	r	NOUN
ejpam-5694	115	8	is	be	AUX
ejpam-5694	115	9	monotonic	monotonic	ADJ
ejpam-5694	115	10	nondecreasing	nondecrease	VERB
ejpam-5694	115	11	then	then	ADV
ejpam-5694	115	12	following	follow	VERB
ejpam-5694	115	13	result	result	VERB
ejpam-5694	115	14	holds∣∣∣f(f	holds∣∣∣f(f	NOUN
ejpam-5694	115	15	,	,	PUNCT
ejpam-5694	115	16	g)∣∣∣	g)∣∣∣	PROPN
ejpam-5694	115	17	≤	≤	NUM
ejpam-5694	116	1	1	1	NUM
ejpam-5694	116	2	2(a2	2(a2	NUM
ejpam-5694	116	3	−	−	NOUN
ejpam-5694	116	4	a1	a1	NOUN
ejpam-5694	116	5	)	)	PUNCT
ejpam-5694	116	6	||f	||f	PROPN
ejpam-5694	116	7	′||∞	′||∞	NOUN
ejpam-5694	116	8	∫	∫	PROPN
ejpam-5694	116	9	a2	a2	PROPN
ejpam-5694	116	10	a1	a1	PROPN
ejpam-5694	116	11	(	(	PUNCT
ejpam-5694	116	12	η	η	PROPN
ejpam-5694	116	13	−	−	PROPN
ejpam-5694	116	14	a1)(a2	a1)(a2	PROPN
ejpam-5694	116	15	−	−	PROPN
ejpam-5694	116	16	η)(g′(η))2dg(η	η)(g′(η))2dg(η	PROPN
ejpam-5694	116	17	)	)	PUNCT
ejpam-5694	116	18	,	,	PUNCT
ejpam-5694	116	19	(	(	PUNCT
ejpam-5694	116	20	21	21	NUM
ejpam-5694	116	21	)	)	PUNCT
ejpam-5694	116	22	where	where	SCONJ
ejpam-5694	116	23	1	1	NUM
ejpam-5694	116	24	2	2	NUM
ejpam-5694	116	25	is	be	AUX
ejpam-5694	116	26	the	the	DET
ejpam-5694	116	27	best	good	ADJ
ejpam-5694	116	28	possible	possible	ADJ
ejpam-5694	116	29	approximation	approximation	NOUN
ejpam-5694	116	30	.	.	PUNCT
ejpam-5694	117	1	the	the	DET
ejpam-5694	117	2	following	follow	VERB
ejpam-5694	117	3	definitions	definition	NOUN
ejpam-5694	117	4	of	of	ADP
ejpam-5694	117	5	n	n	CCONJ
ejpam-5694	117	6	-	-	PUNCT
ejpam-5694	117	7	exponential	exponential	NOUN
ejpam-5694	117	8	convexity	convexity	NOUN
ejpam-5694	117	9	from	from	ADP
ejpam-5694	117	10	[	[	X
ejpam-5694	117	11	11	11	NUM
ejpam-5694	117	12	]	]	PUNCT
ejpam-5694	117	13	is	be	AUX
ejpam-5694	117	14	used	use	VERB
ejpam-5694	117	15	in	in	ADP
ejpam-5694	117	16	section	section	NOUN
ejpam-5694	117	17	5	5	NUM
ejpam-5694	117	18	and	and	CCONJ
ejpam-5694	117	19	related	related	ADJ
ejpam-5694	117	20	results	result	NOUN
ejpam-5694	117	21	of	of	ADP
ejpam-5694	117	22	exponential	exponential	ADJ
ejpam-5694	117	23	convexity	convexity	NOUN
ejpam-5694	117	24	are	be	AUX
ejpam-5694	117	25	under	under	ADP
ejpam-5694	117	26	consideration	consideration	NOUN
ejpam-5694	117	27	there	there	ADV
ejpam-5694	117	28	.	.	PUNCT
ejpam-5694	118	1	definition	definition	NOUN
ejpam-5694	118	2	2	2	NUM
ejpam-5694	118	3	.	.	PUNCT
ejpam-5694	119	1	a	a	DET
ejpam-5694	119	2	function	function	NOUN
ejpam-5694	119	3	f	f	NOUN
ejpam-5694	119	4	:	:	PUNCT
ejpam-5694	119	5	t	t	PROPN
ejpam-5694	119	6	→	→	SYM
ejpam-5694	119	7	r	r	NOUN
ejpam-5694	119	8	is	be	AUX
ejpam-5694	119	9	n	n	ADV
ejpam-5694	119	10	-	-	PUNCT
ejpam-5694	119	11	exponentially	exponentially	ADV
ejpam-5694	119	12	convex	convex	NOUN
ejpam-5694	119	13	in	in	ADP
ejpam-5694	119	14	jensen	jensen	PROPN
ejpam-5694	119	15	sense	sense	NOUN
ejpam-5694	119	16	on	on	ADP
ejpam-5694	119	17	t	t	PROPN
ejpam-5694	119	18	if	if	SCONJ
ejpam-5694	119	19	n∑	n∑	PROPN
ejpam-5694	119	20	i	i	PROPN
ejpam-5694	119	21	,	,	PUNCT
ejpam-5694	119	22	j	j	PROPN
ejpam-5694	119	23	cicjf	cicjf	NOUN
ejpam-5694	119	24	(	(	PUNCT
ejpam-5694	119	25	ζi	ζi	PROPN
ejpam-5694	119	26	+	+	X
ejpam-5694	119	27	ζj	ζj	ADP
ejpam-5694	119	28	2	2	NUM
ejpam-5694	119	29	)	)	PUNCT
ejpam-5694	119	30	≥	≥	NOUN
ejpam-5694	119	31	0	0	NUM
ejpam-5694	119	32	,	,	PUNCT
ejpam-5694	119	33	(	(	PUNCT
ejpam-5694	119	34	22	22	NUM
ejpam-5694	119	35	)	)	PUNCT
ejpam-5694	119	36	holds	hold	VERB
ejpam-5694	119	37	for	for	ADP
ejpam-5694	119	38	all	all	DET
ejpam-5694	119	39	c1	c1	NOUN
ejpam-5694	119	40	,	,	PUNCT
ejpam-5694	119	41	c2	c2	PROPN
ejpam-5694	119	42	,	,	PUNCT
ejpam-5694	119	43	...	...	PUNCT
ejpam-5694	119	44	,	,	PUNCT
ejpam-5694	119	45	cn	cn	PROPN
ejpam-5694	119	46	∈	∈	PROPN
ejpam-5694	119	47	r	r	NOUN
ejpam-5694	119	48	and	and	CCONJ
ejpam-5694	119	49	all	all	DET
ejpam-5694	119	50	choices	choice	NOUN
ejpam-5694	119	51	of	of	ADP
ejpam-5694	119	52	ζ1	ζ1	NOUN
ejpam-5694	119	53	,	,	PUNCT
ejpam-5694	119	54	...	...	PUNCT
ejpam-5694	119	55	,	,	PUNCT
ejpam-5694	119	56	ζn	ζn	DET
ejpam-5694	119	57	∈	∈	PROPN
ejpam-5694	119	58	t	t	NOUN
ejpam-5694	119	59	.	.	PUNCT
ejpam-5694	120	1	a	a	DET
ejpam-5694	120	2	function	function	NOUN
ejpam-5694	120	3	f	f	NOUN
ejpam-5694	120	4	:	:	PUNCT
ejpam-5694	120	5	t	t	PROPN
ejpam-5694	120	6	→	→	SYM
ejpam-5694	120	7	r	r	NOUN
ejpam-5694	120	8	will	will	AUX
ejpam-5694	120	9	be	be	AUX
ejpam-5694	120	10	n	n	ADV
ejpam-5694	120	11	-	-	PUNCT
ejpam-5694	120	12	exponentially	exponentially	ADV
ejpam-5694	120	13	convex	convex	NOUN
ejpam-5694	120	14	if	if	SCONJ
ejpam-5694	120	15	it	it	PRON
ejpam-5694	120	16	meets	meet	VERB
ejpam-5694	120	17	the	the	DET
ejpam-5694	120	18	criteria	criterion	NOUN
ejpam-5694	120	19	for	for	ADP
ejpam-5694	120	20	n	n	CCONJ
ejpam-5694	120	21	-	-	PUNCT
ejpam-5694	120	22	exponential	exponential	ADJ
ejpam-5694	120	23	convexity	convexity	NOUN
ejpam-5694	120	24	in	in	ADP
ejpam-5694	120	25	jensen	jensen	PROPN
ejpam-5694	120	26	sense	sense	NOUN
ejpam-5694	120	27	and	and	CCONJ
ejpam-5694	120	28	continuous	continuous	ADJ
ejpam-5694	120	29	on	on	ADP
ejpam-5694	120	30	t	t	PROPN
ejpam-5694	120	31	.	.	PUNCT
ejpam-5694	121	1	remark	remark	PROPN
ejpam-5694	121	2	1	1	NUM
ejpam-5694	121	3	.	.	PUNCT
ejpam-5694	122	1	the	the	DET
ejpam-5694	122	2	aforementioned	aforementioned	ADJ
ejpam-5694	122	3	definition	definition	NOUN
ejpam-5694	122	4	ensures	ensure	VERB
ejpam-5694	122	5	that	that	SCONJ
ejpam-5694	122	6	the	the	DET
ejpam-5694	122	7	function	function	NOUN
ejpam-5694	122	8	which	which	PRON
ejpam-5694	122	9	is	be	AUX
ejpam-5694	122	10	1	1	NUM
ejpam-5694	122	11	-	-	PUNCT
ejpam-5694	122	12	exponentially	exponentially	ADV
ejpam-5694	122	13	convex	convex	NOUN
ejpam-5694	122	14	in	in	ADP
ejpam-5694	122	15	jensen	jensen	PROPN
ejpam-5694	122	16	sense	sense	NOUN
ejpam-5694	122	17	is	be	AUX
ejpam-5694	122	18	indeed	indeed	ADV
ejpam-5694	122	19	non	non	ADJ
ejpam-5694	122	20	-	-	ADJ
ejpam-5694	122	21	negative	negative	ADJ
ejpam-5694	122	22	.	.	PUNCT
ejpam-5694	123	1	furthermore	furthermore	ADV
ejpam-5694	123	2	,	,	PUNCT
ejpam-5694	123	3	an	an	DET
ejpam-5694	123	4	n	n	ADV
ejpam-5694	123	5	-	-	PUNCT
ejpam-5694	123	6	exponentially	exponentially	ADV
ejpam-5694	123	7	convex	convex	ADJ
ejpam-5694	123	8	function	function	NOUN
ejpam-5694	123	9	in	in	ADP
ejpam-5694	123	10	jensen	jensen	PROPN
ejpam-5694	123	11	sense	sense	NOUN
ejpam-5694	123	12	is	be	AUX
ejpam-5694	123	13	also	also	ADV
ejpam-5694	123	14	l	l	NOUN
ejpam-5694	123	15	-	-	ADJ
ejpam-5694	123	16	exponentially	exponentially	ADV
ejpam-5694	123	17	convex	convex	NOUN
ejpam-5694	123	18	in	in	ADP
ejpam-5694	123	19	jensen	jensen	PROPN
ejpam-5694	123	20	sense	sense	NOUN
ejpam-5694	123	21	for	for	ADP
ejpam-5694	123	22	each	each	DET
ejpam-5694	123	23	l	l	NOUN
ejpam-5694	123	24	∈	∈	PROPN
ejpam-5694	123	25	n	n	CCONJ
ejpam-5694	123	26	,	,	PUNCT
ejpam-5694	123	27	where	where	SCONJ
ejpam-5694	123	28	l	l	NOUN
ejpam-5694	123	29	≤	≤	ADJ
ejpam-5694	123	30	n.	n.	NOUN
ejpam-5694	123	31	employing	employ	VERB
ejpam-5694	123	32	the	the	DET
ejpam-5694	123	33	definition	definition	NOUN
ejpam-5694	123	34	of	of	ADP
ejpam-5694	123	35	semi	semi	ADJ
ejpam-5694	123	36	-	-	ADJ
ejpam-5694	123	37	definite	definite	ADJ
ejpam-5694	123	38	matrices	matrix	NOUN
ejpam-5694	123	39	and	and	CCONJ
ejpam-5694	123	40	some	some	DET
ejpam-5694	123	41	fundamental	fundamental	ADJ
ejpam-5694	123	42	results	result	NOUN
ejpam-5694	123	43	from	from	ADP
ejpam-5694	123	44	linear	linear	PROPN
ejpam-5694	123	45	algebra	algebra	PROPN
ejpam-5694	123	46	,	,	PUNCT
ejpam-5694	123	47	j.pečarić	j.pečarić	VERB
ejpam-5694	123	48	[	[	X
ejpam-5694	123	49	11	11	NUM
ejpam-5694	123	50	]	]	PUNCT
ejpam-5694	123	51	propose	propose	VERB
ejpam-5694	123	52	the	the	DET
ejpam-5694	123	53	following	following	ADJ
ejpam-5694	123	54	result	result	NOUN
ejpam-5694	123	55	:	:	PUNCT
ejpam-5694	123	56	proposition	proposition	NOUN
ejpam-5694	123	57	1	1	NUM
ejpam-5694	123	58	.	.	PUNCT
ejpam-5694	124	1	if	if	SCONJ
ejpam-5694	124	2	f	f	PROPN
ejpam-5694	124	3	is	be	AUX
ejpam-5694	124	4	n	n	ADV
ejpam-5694	124	5	-	-	PUNCT
ejpam-5694	124	6	exponentially	exponentially	ADV
ejpam-5694	124	7	convex	convex	NOUN
ejpam-5694	124	8	in	in	ADP
ejpam-5694	124	9	jensen	jensen	PROPN
ejpam-5694	124	10	sense	sense	NOUN
ejpam-5694	124	11	,	,	PUNCT
ejpam-5694	124	12	then	then	ADV
ejpam-5694	124	13	the	the	DET
ejpam-5694	124	14	matrix	matrix	NOUN
ejpam-5694	124	15	[	[	PUNCT
ejpam-5694	124	16	f	f	X
ejpam-5694	124	17	(	(	PUNCT
ejpam-5694	124	18	ζi	ζi	PROPN
ejpam-5694	124	19	+	+	X
ejpam-5694	124	20	ζj	ζj	ADP
ejpam-5694	124	21	2	2	NUM
ejpam-5694	124	22	)	)	PUNCT
ejpam-5694	124	23	]	]	PUNCT
ejpam-5694	124	24	l	l	X
ejpam-5694	125	1	i	i	PRON
ejpam-5694	125	2	,	,	PUNCT
ejpam-5694	125	3	j=1	j=1	NOUN
ejpam-5694	125	4	,	,	PUNCT
ejpam-5694	125	5	∀	∀	PUNCT
ejpam-5694	125	6	l	l	NOUN
ejpam-5694	125	7	∈	∈	PROPN
ejpam-5694	125	8	n	n	CCONJ
ejpam-5694	125	9	,	,	PUNCT
ejpam-5694	125	10	l	l	PROPN
ejpam-5694	125	11	≤	≤	NOUN
ejpam-5694	125	12	n	n	CCONJ
ejpam-5694	125	13	,	,	PUNCT
ejpam-5694	125	14	is	be	AUX
ejpam-5694	125	15	positive	positive	ADJ
ejpam-5694	125	16	semi	semi	ADJ
ejpam-5694	125	17	definite	definite	ADJ
ejpam-5694	125	18	.	.	PUNCT
ejpam-5694	126	1	in	in	ADP
ejpam-5694	126	2	particular	particular	ADJ
ejpam-5694	126	3	following	follow	VERB
ejpam-5694	126	4	result	result	NOUN
ejpam-5694	126	5	holds	hold	VERB
ejpam-5694	126	6	for	for	ADP
ejpam-5694	126	7	all	all	DET
ejpam-5694	126	8	such	such	ADJ
ejpam-5694	126	9	l	l	NOUN
ejpam-5694	126	10	det	det	X
ejpam-5694	126	11	[	[	PUNCT
ejpam-5694	126	12	f	f	X
ejpam-5694	126	13	(	(	PUNCT
ejpam-5694	126	14	ζi	ζi	PROPN
ejpam-5694	126	15	+	+	X
ejpam-5694	126	16	ζj	ζj	ADP
ejpam-5694	126	17	2	2	NUM
ejpam-5694	126	18	)	)	PUNCT
ejpam-5694	126	19	]	]	PUNCT
ejpam-5694	127	1	l	l	X
ejpam-5694	128	1	i	i	PRON
ejpam-5694	128	2	,	,	PUNCT
ejpam-5694	128	3	j=1	j=1	PROPN
ejpam-5694	128	4	≥	≥	NUM
ejpam-5694	128	5	0	0	NUM
ejpam-5694	128	6	.	.	PUNCT
ejpam-5694	128	7	a.	a.	PROPN
ejpam-5694	128	8	m.	m.	PROPN
ejpam-5694	128	9	k.	k.	PROPN
ejpam-5694	128	10	abbasi	abbasi	PROPN
ejpam-5694	128	11	,	,	PUNCT
ejpam-5694	128	12	m.	m.	PROPN
ejpam-5694	128	13	anwar	anwar	PROPN
ejpam-5694	128	14	/	/	PUNCT
ejpam-5694	128	15	eur	eur	PROPN
ejpam-5694	128	16	.	.	PUNCT
ejpam-5694	129	1	j.	j.	PROPN
ejpam-5694	129	2	pure	pure	PROPN
ejpam-5694	129	3	appl	appl	PROPN
ejpam-5694	129	4	.	.	PROPN
ejpam-5694	129	5	math	math	PROPN
ejpam-5694	129	6	,	,	PUNCT
ejpam-5694	129	7	18	18	NUM
ejpam-5694	129	8	(	(	PUNCT
ejpam-5694	129	9	1	1	NUM
ejpam-5694	129	10	)	)	PUNCT
ejpam-5694	129	11	(	(	PUNCT
ejpam-5694	129	12	2025	2025	NUM
ejpam-5694	129	13	)	)	PUNCT
ejpam-5694	129	14	,	,	PUNCT
ejpam-5694	129	15	5694	5694	NUM
ejpam-5694	129	16	7	7	NUM
ejpam-5694	129	17	of	of	ADP
ejpam-5694	129	18	18	18	NUM
ejpam-5694	129	19	definition	definition	NOUN
ejpam-5694	129	20	3	3	NUM
ejpam-5694	129	21	.	.	PUNCT
ejpam-5694	130	1	if	if	SCONJ
ejpam-5694	130	2	a	a	DET
ejpam-5694	130	3	function	function	NOUN
ejpam-5694	130	4	f	f	X
ejpam-5694	130	5	:	:	PUNCT
ejpam-5694	130	6	t	t	PROPN
ejpam-5694	130	7	→	→	SYM
ejpam-5694	130	8	r	r	NOUN
ejpam-5694	130	9	is	be	AUX
ejpam-5694	130	10	n	n	ADV
ejpam-5694	130	11	-	-	PUNCT
ejpam-5694	130	12	exponentially	exponentially	ADV
ejpam-5694	130	13	convex	convex	NOUN
ejpam-5694	130	14	in	in	ADP
ejpam-5694	130	15	jensen	jensen	PROPN
ejpam-5694	130	16	sense	sense	NOUN
ejpam-5694	130	17	for	for	ADP
ejpam-5694	130	18	all	all	DET
ejpam-5694	130	19	n	n	PRON
ejpam-5694	130	20	∈	∈	NOUN
ejpam-5694	131	1	n	n	CCONJ
ejpam-5694	131	2	then	then	ADV
ejpam-5694	131	3	f	f	PROPN
ejpam-5694	131	4	is	be	AUX
ejpam-5694	131	5	eponentially	eponentially	ADV
ejpam-5694	131	6	convex	convex	ADJ
ejpam-5694	131	7	in	in	ADP
ejpam-5694	131	8	jensen	jensen	PROPN
ejpam-5694	131	9	sense	sense	NOUN
ejpam-5694	131	10	.	.	PUNCT
ejpam-5694	132	1	a	a	DET
ejpam-5694	132	2	continuous	continuous	ADJ
ejpam-5694	132	3	function	function	NOUN
ejpam-5694	132	4	f	f	NOUN
ejpam-5694	132	5	:	:	PUNCT
ejpam-5694	132	6	t	t	PROPN
ejpam-5694	132	7	→	→	PUNCT
ejpam-5694	132	8	r	r	NOUN
ejpam-5694	132	9	that	that	PRON
ejpam-5694	132	10	is	be	AUX
ejpam-5694	132	11	eponentially	eponentially	ADV
ejpam-5694	132	12	convex	convex	ADJ
ejpam-5694	132	13	in	in	ADP
ejpam-5694	132	14	jensen	jensen	PROPN
ejpam-5694	132	15	sense	sense	NOUN
ejpam-5694	132	16	is	be	AUX
ejpam-5694	132	17	exponentially	exponentially	ADV
ejpam-5694	132	18	convex	convex	ADJ
ejpam-5694	132	19	.	.	PUNCT
ejpam-5694	133	1	remark	remark	PROPN
ejpam-5694	133	2	2	2	NUM
ejpam-5694	133	3	.	.	PUNCT
ejpam-5694	134	1	it	it	PRON
ejpam-5694	134	2	is	be	AUX
ejpam-5694	134	3	easy	easy	ADJ
ejpam-5694	134	4	to	to	PART
ejpam-5694	134	5	show	show	VERB
ejpam-5694	134	6	that	that	SCONJ
ejpam-5694	134	7	f	f	NOUN
ejpam-5694	134	8	:	:	PUNCT
ejpam-5694	134	9	t	t	PROPN
ejpam-5694	134	10	→	→	SYM
ejpam-5694	134	11	r	r	NOUN
ejpam-5694	134	12	is	be	AUX
ejpam-5694	134	13	a	a	DET
ejpam-5694	134	14	log	log	NOUN
ejpam-5694	134	15	-	-	PUNCT
ejpam-5694	134	16	convex	convex	NOUN
ejpam-5694	134	17	in	in	ADP
ejpam-5694	134	18	the	the	DET
ejpam-5694	134	19	jensen	jensen	PROPN
ejpam-5694	134	20	sense	sense	NOUN
ejpam-5694	134	21	if	if	SCONJ
ejpam-5694	134	22	and	and	CCONJ
ejpam-5694	134	23	only	only	ADV
ejpam-5694	134	24	if	if	SCONJ
ejpam-5694	134	25	a21f(ζ1	a21f(ζ1	PROPN
ejpam-5694	134	26	)	)	PUNCT
ejpam-5694	135	1	+	+	CCONJ
ejpam-5694	135	2	2a1a2f	2a1a2f	NUM
ejpam-5694	135	3	(	(	PUNCT
ejpam-5694	135	4	ζ1	ζ1	NOUN
ejpam-5694	135	5	+	+	CCONJ
ejpam-5694	135	6	ζ2	ζ2	NOUN
ejpam-5694	135	7	2	2	NUM
ejpam-5694	135	8	)	)	PUNCT
ejpam-5694	136	1	+	+	CCONJ
ejpam-5694	136	2	a22f(ζ2	a22f(ζ2	ADJ
ejpam-5694	136	3	)	)	PUNCT
ejpam-5694	136	4	≥	≥	NOUN
ejpam-5694	136	5	0	0	NUM
ejpam-5694	136	6	,	,	PUNCT
ejpam-5694	136	7	(	(	PUNCT
ejpam-5694	136	8	23	23	NUM
ejpam-5694	136	9	)	)	PUNCT
ejpam-5694	136	10	holds	hold	VERB
ejpam-5694	136	11	for	for	ADP
ejpam-5694	136	12	all	all	DET
ejpam-5694	136	13	a1	a1	NOUN
ejpam-5694	136	14	,	,	PUNCT
ejpam-5694	136	15	a2	a2	PROPN
ejpam-5694	136	16	∈	∈	PROPN
ejpam-5694	136	17	r	r	NOUN
ejpam-5694	136	18	and	and	CCONJ
ejpam-5694	136	19	ζ1	ζ1	NOUN
ejpam-5694	136	20	,	,	PUNCT
ejpam-5694	136	21	ζ2	ζ2	NOUN
ejpam-5694	136	22	∈	∈	PROPN
ejpam-5694	136	23	t	t	NOUN
ejpam-5694	136	24	.	.	PUNCT
ejpam-5694	137	1	consequently	consequently	ADV
ejpam-5694	137	2	,	,	PUNCT
ejpam-5694	137	3	the	the	DET
ejpam-5694	137	4	function	function	NOUN
ejpam-5694	137	5	is	be	AUX
ejpam-5694	137	6	2	2	NUM
ejpam-5694	137	7	-	-	PUNCT
ejpam-5694	137	8	exponentially	exponentially	ADV
ejpam-5694	137	9	convex	convex	NOUN
ejpam-5694	137	10	in	in	ADP
ejpam-5694	137	11	the	the	DET
ejpam-5694	137	12	jensen	jensen	PROPN
ejpam-5694	137	13	sense	sense	NOUN
ejpam-5694	137	14	if	if	SCONJ
ejpam-5694	138	1	and	and	CCONJ
ejpam-5694	138	2	only	only	ADV
ejpam-5694	138	3	if	if	SCONJ
ejpam-5694	138	4	it	it	PRON
ejpam-5694	138	5	is	be	AUX
ejpam-5694	138	6	log	log	NOUN
ejpam-5694	138	7	-	-	PUNCT
ejpam-5694	138	8	convex	convex	NOUN
ejpam-5694	138	9	in	in	ADP
ejpam-5694	138	10	the	the	DET
ejpam-5694	138	11	jensen	jensen	PROPN
ejpam-5694	138	12	sense	sense	NOUN
ejpam-5694	138	13	.	.	PUNCT
ejpam-5694	139	1	a	a	DET
ejpam-5694	139	2	positive	positive	ADJ
ejpam-5694	139	3	function	function	NOUN
ejpam-5694	139	4	is	be	AUX
ejpam-5694	139	5	log	log	NOUN
ejpam-5694	139	6	-	-	PUNCT
ejpam-5694	139	7	convex	convex	NOUN
ejpam-5694	139	8	if	if	SCONJ
ejpam-5694	139	9	and	and	CCONJ
ejpam-5694	139	10	only	only	ADV
ejpam-5694	139	11	if	if	SCONJ
ejpam-5694	139	12	it	it	PRON
ejpam-5694	139	13	is	be	AUX
ejpam-5694	139	14	2	2	NUM
ejpam-5694	139	15	-	-	PUNCT
ejpam-5694	139	16	exponentially	exponentially	ADV
ejpam-5694	139	17	convex	convex	NOUN
ejpam-5694	139	18	.	.	PUNCT
ejpam-5694	140	1	3	3	X
ejpam-5694	140	2	.	.	X
ejpam-5694	140	3	main	main	ADJ
ejpam-5694	140	4	results	result	NOUN
ejpam-5694	140	5	in	in	ADP
ejpam-5694	140	6	this	this	DET
ejpam-5694	140	7	section	section	NOUN
ejpam-5694	140	8	,	,	PUNCT
ejpam-5694	140	9	we	we	PRON
ejpam-5694	140	10	present	present	VERB
ejpam-5694	140	11	hardy	hardy	ADJ
ejpam-5694	140	12	-	-	PUNCT
ejpam-5694	140	13	type	type	NOUN
ejpam-5694	140	14	inequalities	inequality	NOUN
ejpam-5694	140	15	as	as	ADP
ejpam-5694	140	16	a	a	DET
ejpam-5694	140	17	fundamental	fundamental	ADJ
ejpam-5694	140	18	result	result	NOUN
ejpam-5694	140	19	,	,	PUNCT
ejpam-5694	140	20	employing	employ	VERB
ejpam-5694	140	21	green	green	ADJ
ejpam-5694	140	22	functions	function	NOUN
ejpam-5694	140	23	obtained	obtain	VERB
ejpam-5694	140	24	from	from	ADP
ejpam-5694	140	25	the	the	DET
ejpam-5694	140	26	two	two	NUM
ejpam-5694	140	27	-	-	PUNCT
ejpam-5694	140	28	point	point	NOUN
ejpam-5694	140	29	right	right	ADJ
ejpam-5694	140	30	focal	focal	ADJ
ejpam-5694	140	31	problem	problem	NOUN
ejpam-5694	140	32	in	in	ADP
ejpam-5694	140	33	addition	addition	NOUN
ejpam-5694	140	34	to	to	ADP
ejpam-5694	140	35	this	this	PRON
ejpam-5694	140	36	,	,	PUNCT
ejpam-5694	140	37	taylor	taylor	PROPN
ejpam-5694	140	38	’s	’s	PART
ejpam-5694	140	39	polynomial	polynomial	NOUN
ejpam-5694	140	40	is	be	AUX
ejpam-5694	140	41	also	also	ADV
ejpam-5694	140	42	taken	take	VERB
ejpam-5694	140	43	into	into	ADP
ejpam-5694	140	44	account	account	NOUN
ejpam-5694	140	45	,	,	PUNCT
ejpam-5694	140	46	after	after	ADP
ejpam-5694	140	47	that	that	PRON
ejpam-5694	140	48	,	,	PUNCT
ejpam-5694	140	49	using	use	VERB
ejpam-5694	140	50	these	these	DET
ejpam-5694	140	51	fundamental	fundamental	ADJ
ejpam-5694	140	52	inequalities	inequality	NOUN
ejpam-5694	140	53	we	we	PRON
ejpam-5694	140	54	analyze	analyze	VERB
ejpam-5694	140	55	the	the	DET
ejpam-5694	140	56	grüss	grüss	NOUN
ejpam-5694	140	57	-	-	PUNCT
ejpam-5694	140	58	type	type	NOUN
ejpam-5694	140	59	and	and	CCONJ
ejpam-5694	140	60	ostrowski	ostrowski	ADJ
ejpam-5694	140	61	-	-	PUNCT
ejpam-5694	140	62	type	type	NOUN
ejpam-5694	140	63	bounds	bound	NOUN
ejpam-5694	140	64	.	.	PUNCT
ejpam-5694	141	1	starting	start	VERB
ejpam-5694	141	2	with	with	ADP
ejpam-5694	141	3	our	our	PRON
ejpam-5694	141	4	first	first	ADJ
ejpam-5694	141	5	result	result	NOUN
ejpam-5694	141	6	which	which	PRON
ejpam-5694	141	7	is	be	AUX
ejpam-5694	141	8	given	give	VERB
ejpam-5694	141	9	as	as	ADP
ejpam-5694	141	10	;	;	PUNCT
ejpam-5694	141	11	theorem	theorem	NOUN
ejpam-5694	141	12	4	4	NUM
ejpam-5694	141	13	.	.	PUNCT
ejpam-5694	142	1	let	let	VERB
ejpam-5694	142	2	f	f	PRON
ejpam-5694	142	3	be	be	AUX
ejpam-5694	142	4	defined	define	VERB
ejpam-5694	142	5	on	on	ADP
ejpam-5694	142	6	t	t	NOUN
ejpam-5694	142	7	such	such	ADJ
ejpam-5694	142	8	that	that	SCONJ
ejpam-5694	142	9	f	f	PROPN
ejpam-5694	142	10	′′′	′′′	PROPN
ejpam-5694	142	11	exists	exist	VERB
ejpam-5694	142	12	and	and	CCONJ
ejpam-5694	142	13	f	f	PROPN
ejpam-5694	142	14	(	(	PUNCT
ejpam-5694	142	15	n−1	n−1	PROPN
ejpam-5694	142	16	)	)	PUNCT
ejpam-5694	142	17	is	be	AUX
ejpam-5694	142	18	absolutely	absolutely	ADV
ejpam-5694	142	19	continuous	continuous	ADJ
ejpam-5694	142	20	therein	therein	ADV
ejpam-5694	142	21	,	,	PUNCT
ejpam-5694	142	22	for	for	ADP
ejpam-5694	142	23	n	n	DET
ejpam-5694	142	24	∈	∈	PROPN
ejpam-5694	142	25	n.	n.	NOUN
ejpam-5694	142	26	considering	consider	VERB
ejpam-5694	142	27	two	two	NUM
ejpam-5694	142	28	measure	measure	NOUN
ejpam-5694	142	29	spaces	space	NOUN
ejpam-5694	142	30	(	(	PUNCT
ejpam-5694	142	31	∑	∑	PROPN
ejpam-5694	142	32	1,ω1	1,ω1	NUM
ejpam-5694	142	33	,	,	PUNCT
ejpam-5694	142	34	σ1	σ1	PROPN
ejpam-5694	142	35	)	)	PUNCT
ejpam-5694	142	36	and	and	CCONJ
ejpam-5694	142	37	(	(	PUNCT
ejpam-5694	142	38	∑	∑	PROPN
ejpam-5694	142	39	2,ω2	2,ω2	NUM
ejpam-5694	142	40	,	,	PUNCT
ejpam-5694	142	41	σ2	σ2	NOUN
ejpam-5694	142	42	)	)	PUNCT
ejpam-5694	142	43	with	with	ADP
ejpam-5694	142	44	positive	positive	ADJ
ejpam-5694	142	45	σ−finite	σ−finite	PROPN
ejpam-5694	142	46	measures	measure	NOUN
ejpam-5694	142	47	and	and	CCONJ
ejpam-5694	142	48	ak	ak	PROPN
ejpam-5694	142	49	and	and	CCONJ
ejpam-5694	142	50	k	k	PROPN
ejpam-5694	142	51	are	be	AUX
ejpam-5694	142	52	mentioned	mention	VERB
ejpam-5694	142	53	in	in	ADP
ejpam-5694	142	54	(	(	PUNCT
ejpam-5694	142	55	15	15	NUM
ejpam-5694	142	56	)	)	PUNCT
ejpam-5694	142	57	and	and	CCONJ
ejpam-5694	142	58	(	(	PUNCT
ejpam-5694	142	59	16	16	NUM
ejpam-5694	142	60	)	)	PUNCT
ejpam-5694	142	61	respectively	respectively	ADV
ejpam-5694	142	62	.	.	PUNCT
ejpam-5694	143	1	let	let	VERB
ejpam-5694	143	2	gα	gα	VERB
ejpam-5694	143	3	,	,	PUNCT
ejpam-5694	143	4	{	{	PUNCT
ejpam-5694	143	5	α	α	NOUN
ejpam-5694	143	6	=	=	SYM
ejpam-5694	143	7	1	1	NUM
ejpam-5694	143	8	,	,	PUNCT
ejpam-5694	143	9	2	2	NUM
ejpam-5694	143	10	,	,	PUNCT
ejpam-5694	143	11	3	3	NUM
ejpam-5694	143	12	,	,	PUNCT
ejpam-5694	143	13	4	4	NUM
ejpam-5694	143	14	}	}	PUNCT
ejpam-5694	143	15	be	be	AUX
ejpam-5694	143	16	defined	define	VERB
ejpam-5694	143	17	in	in	ADP
ejpam-5694	143	18	(	(	PUNCT
ejpam-5694	143	19	5	5	NUM
ejpam-5694	143	20	)	)	PUNCT
ejpam-5694	143	21	,	,	PUNCT
ejpam-5694	143	22	(	(	PUNCT
ejpam-5694	143	23	6	6	NUM
ejpam-5694	143	24	)	)	PUNCT
ejpam-5694	143	25	,	,	PUNCT
ejpam-5694	143	26	(	(	PUNCT
ejpam-5694	143	27	7	7	X
ejpam-5694	143	28	)	)	PUNCT
ejpam-5694	143	29	and	and	CCONJ
ejpam-5694	143	30	(	(	PUNCT
ejpam-5694	143	31	8)	8)	NUM
ejpam-5694	143	32	respectively	respectively	ADV
ejpam-5694	143	33	and	and	CCONJ
ejpam-5694	143	34	u	u	NOUN
ejpam-5694	143	35	:	:	PUNCT
ejpam-5694	143	36	ω1	ω1	PROPN
ejpam-5694	143	37	→	→	SYM
ejpam-5694	143	38	r	r	NOUN
ejpam-5694	143	39	be	be	VERB
ejpam-5694	143	40	the	the	DET
ejpam-5694	143	41	weight	weight	NOUN
ejpam-5694	143	42	function	function	NOUN
ejpam-5694	143	43	and	and	CCONJ
ejpam-5694	143	44	v	v	NOUN
ejpam-5694	143	45	is	be	AUX
ejpam-5694	143	46	given	give	VERB
ejpam-5694	143	47	in	in	ADP
ejpam-5694	143	48	(	(	PUNCT
ejpam-5694	143	49	17	17	NUM
ejpam-5694	143	50	)	)	PUNCT
ejpam-5694	143	51	,	,	PUNCT
ejpam-5694	143	52	then	then	ADV
ejpam-5694	143	53	:	:	PUNCT
ejpam-5694	144	1	•	•	NUM
ejpam-5694	144	2	∫	∫	PROPN
ejpam-5694	145	1	ω2	ω2	PROPN
ejpam-5694	145	2	f(f(s))ν(s)dµ2(s)−	f(f(s))ν(s)dµ2(s)−	PROPN
ejpam-5694	145	3	∫	∫	PROPN
ejpam-5694	145	4	ω1	ω1	PROPN
ejpam-5694	145	5	f(akf(ϖ))u(ϖ)dµ1(ϖ	f(akf(ϖ))u(ϖ)dµ1(ϖ	PROPN
ejpam-5694	145	6	)	)	PUNCT
ejpam-5694	145	7	=	=	SYM
ejpam-5694	145	8	∫	∫	PROPN
ejpam-5694	145	9	a2	a2	PROPN
ejpam-5694	145	10	a1	a1	PROPN
ejpam-5694	145	11	jgα(f	jgα(f	PROPN
ejpam-5694	145	12	,	,	PUNCT
ejpam-5694	145	13	τ	τ	X
ejpam-5694	145	14	)	)	PUNCT
ejpam-5694	146	1	[	[	X
ejpam-5694	146	2	∑	∑	X
ejpam-5694	146	3	κ	κ	PROPN
ejpam-5694	146	4	f	f	PROPN
ejpam-5694	146	5	(	(	PUNCT
ejpam-5694	146	6	κ)(a1	κ)(a1	X
ejpam-5694	146	7	)	)	PUNCT
ejpam-5694	146	8	κ	κ	NOUN
ejpam-5694	146	9	!	!	PUNCT
ejpam-5694	146	10	(	(	PUNCT
ejpam-5694	146	11	τ	τ	PROPN
ejpam-5694	146	12	−	−	PROPN
ejpam-5694	146	13	a1	a1	PROPN
ejpam-5694	146	14	)	)	PUNCT
ejpam-5694	146	15	κ	κ	NOUN
ejpam-5694	147	1	+	+	NOUN
ejpam-5694	147	2	1	1	NUM
ejpam-5694	147	3	(	(	PUNCT
ejpam-5694	147	4	n−	n−	NOUN
ejpam-5694	147	5	4	4	NUM
ejpam-5694	147	6	)	)	PUNCT
ejpam-5694	147	7	!	!	PUNCT
ejpam-5694	148	1	∫	∫	PROPN
ejpam-5694	148	2	a2	a2	PROPN
ejpam-5694	148	3	a1	a1	PROPN
ejpam-5694	148	4	f	f	PROPN
ejpam-5694	148	5	(	(	PUNCT
ejpam-5694	148	6	n)(η)(τ	n)(η)(τ	PROPN
ejpam-5694	148	7	−	−	PROPN
ejpam-5694	148	8	η)n−4	η)n−4	NOUN
ejpam-5694	148	9	+	+	CCONJ
ejpam-5694	148	10	dη	dη	X
ejpam-5694	148	11	]	]	X
ejpam-5694	148	12	dτ	dτ	NOUN
ejpam-5694	148	13	,	,	PUNCT
ejpam-5694	148	14	(	(	PUNCT
ejpam-5694	148	15	24	24	NUM
ejpam-5694	148	16	)	)	PUNCT
ejpam-5694	148	17	•	•	NUM
ejpam-5694	148	18	∫	∫	PROPN
ejpam-5694	149	1	ω2	ω2	PROPN
ejpam-5694	149	2	f(f(s))ν(s)dµ2(s)−	f(f(s))ν(s)dµ2(s)−	PROPN
ejpam-5694	149	3	∫	∫	PROPN
ejpam-5694	149	4	ω1	ω1	PROPN
ejpam-5694	149	5	f(akf(ϖ))u(ϖ)dµ1(ϖ	f(akf(ϖ))u(ϖ)dµ1(ϖ	PROPN
ejpam-5694	149	6	)	)	PUNCT
ejpam-5694	149	7	=	=	SYM
ejpam-5694	149	8	∫	∫	PROPN
ejpam-5694	149	9	a2	a2	PROPN
ejpam-5694	149	10	a1	a1	PROPN
ejpam-5694	149	11	jgα(f	jgα(f	PROPN
ejpam-5694	149	12	,	,	PUNCT
ejpam-5694	149	13	τ	τ	X
ejpam-5694	149	14	)	)	PUNCT
ejpam-5694	150	1	[	[	X
ejpam-5694	150	2	∑	∑	X
ejpam-5694	150	3	κ	κ	X
ejpam-5694	150	4	(	(	PUNCT
ejpam-5694	150	5	−1)κf	−1)κf	PROPN
ejpam-5694	150	6	(	(	PUNCT
ejpam-5694	150	7	κ)(a2	κ)(a2	NOUN
ejpam-5694	150	8	)	)	PUNCT
ejpam-5694	150	9	κ	κ	NOUN
ejpam-5694	150	10	!	!	PUNCT
ejpam-5694	150	11	(	(	PUNCT
ejpam-5694	150	12	a2	a2	PROPN
ejpam-5694	150	13	−	−	PROPN
ejpam-5694	150	14	τ)κ	τ)κ	PROPN
ejpam-5694	150	15	−(−1)n−4	−(−1)n−4	X
ejpam-5694	150	16	(	(	PUNCT
ejpam-5694	150	17	n−	n−	NOUN
ejpam-5694	150	18	4	4	NUM
ejpam-5694	150	19	)	)	PUNCT
ejpam-5694	150	20	!	!	PUNCT
ejpam-5694	151	1	∫	∫	PROPN
ejpam-5694	151	2	a2	a2	PROPN
ejpam-5694	151	3	a1	a1	PROPN
ejpam-5694	151	4	f	f	PROPN
ejpam-5694	151	5	(	(	PUNCT
ejpam-5694	151	6	n)(η)(τ	n)(η)(τ	PROPN
ejpam-5694	151	7	−	−	PROPN
ejpam-5694	151	8	η)n−4	η)n−4	NOUN
ejpam-5694	151	9	+	+	CCONJ
ejpam-5694	151	10	dη	dη	X
ejpam-5694	151	11	]	]	X
ejpam-5694	151	12	dτ	dτ	PROPN
ejpam-5694	151	13	,	,	PUNCT
ejpam-5694	151	14	(	(	PUNCT
ejpam-5694	151	15	25	25	NUM
ejpam-5694	151	16	)	)	PUNCT
ejpam-5694	151	17	a.	a.	NOUN
ejpam-5694	151	18	m.	m.	PROPN
ejpam-5694	151	19	k.	k.	PROPN
ejpam-5694	151	20	abbasi	abbasi	PROPN
ejpam-5694	151	21	,	,	PUNCT
ejpam-5694	151	22	m.	m.	PROPN
ejpam-5694	151	23	anwar	anwar	PROPN
ejpam-5694	151	24	/	/	PUNCT
ejpam-5694	151	25	eur	eur	PROPN
ejpam-5694	151	26	.	.	PUNCT
ejpam-5694	152	1	j.	j.	PROPN
ejpam-5694	152	2	pure	pure	PROPN
ejpam-5694	152	3	appl	appl	PROPN
ejpam-5694	152	4	.	.	PROPN
ejpam-5694	152	5	math	math	PROPN
ejpam-5694	152	6	,	,	PUNCT
ejpam-5694	152	7	18	18	NUM
ejpam-5694	152	8	(	(	PUNCT
ejpam-5694	152	9	1	1	NUM
ejpam-5694	152	10	)	)	PUNCT
ejpam-5694	152	11	(	(	PUNCT
ejpam-5694	152	12	2025	2025	NUM
ejpam-5694	152	13	)	)	PUNCT
ejpam-5694	152	14	,	,	PUNCT
ejpam-5694	152	15	5694	5694	NUM
ejpam-5694	152	16	8	8	NUM
ejpam-5694	152	17	of	of	ADP
ejpam-5694	152	18	18	18	NUM
ejpam-5694	152	19	where	where	SCONJ
ejpam-5694	152	20	jgα(f	jgα(f	PROPN
ejpam-5694	152	21	,	,	PUNCT
ejpam-5694	152	22	τ	τ	X
ejpam-5694	152	23	)	)	PUNCT
ejpam-5694	152	24	=	=	SYM
ejpam-5694	153	1	∫	∫	PROPN
ejpam-5694	153	2	ω2	ω2	NUM
ejpam-5694	153	3	gα(f(s	gα(f(	NOUN
ejpam-5694	153	4	)	)	PUNCT
ejpam-5694	153	5	,	,	PUNCT
ejpam-5694	153	6	τ)ν(s)dµ2(s)−	τ)ν(s)dµ2(s)−	X
ejpam-5694	153	7	∫	∫	PROPN
ejpam-5694	153	8	ω1	ω1	PROPN
ejpam-5694	153	9	gα(akf(ϖ	gα(akf(ϖ	PROPN
ejpam-5694	153	10	)	)	PUNCT
ejpam-5694	153	11	,	,	PUNCT
ejpam-5694	153	12	τ)u(ϖ)dµ1(ϖ	τ)u(ϖ)dµ1(ϖ	PROPN
ejpam-5694	153	13	)	)	PUNCT
ejpam-5694	153	14	(	(	PUNCT
ejpam-5694	153	15	26	26	NUM
ejpam-5694	153	16	)	)	PUNCT
ejpam-5694	153	17	and	and	CCONJ
ejpam-5694	153	18	notation	notation	NOUN
ejpam-5694	153	19	∑	∑	PROPN
ejpam-5694	153	20	κ	κ	PROPN
ejpam-5694	153	21	is	be	AUX
ejpam-5694	153	22	used	use	VERB
ejpam-5694	153	23	for	for	ADP
ejpam-5694	153	24	∑n−1	∑n−1	PRON
ejpam-5694	153	25	κ=3	κ=3	PUNCT
ejpam-5694	153	26	throughout	throughout	ADP
ejpam-5694	153	27	this	this	DET
ejpam-5694	153	28	paper	paper	NOUN
ejpam-5694	153	29	.	.	PUNCT
ejpam-5694	154	1	proof	proof	NOUN
ejpam-5694	154	2	.	.	PUNCT
ejpam-5694	155	1	•	•	NUM
ejpam-5694	155	2	first	first	ADV
ejpam-5694	155	3	we	we	PRON
ejpam-5694	155	4	consider	consider	VERB
ejpam-5694	155	5	α	α	NOUN
ejpam-5694	155	6	=	=	SYM
ejpam-5694	155	7	1	1	NUM
ejpam-5694	155	8	and	and	CCONJ
ejpam-5694	155	9	from	from	ADP
ejpam-5694	155	10	(	(	PUNCT
ejpam-5694	155	11	1	1	NUM
ejpam-5694	155	12	)	)	PUNCT
ejpam-5694	155	13	and	and	CCONJ
ejpam-5694	155	14	we	we	PRON
ejpam-5694	155	15	can	can	AUX
ejpam-5694	155	16	write∫	write∫	VERB
ejpam-5694	155	17	ω2	ω2	ADJ
ejpam-5694	155	18	f(f(s))ν(s)dµ2(s	f(f(s))ν(s)dµ2(s	NUM
ejpam-5694	155	19	)	)	PUNCT
ejpam-5694	155	20	=	=	SYM
ejpam-5694	156	1	∫	∫	PROPN
ejpam-5694	156	2	ω2	ω2	ADJ
ejpam-5694	156	3	[	[	PUNCT
ejpam-5694	156	4	f(a1	f(a1	NOUN
ejpam-5694	156	5	)	)	PUNCT
ejpam-5694	156	6	+	+	CCONJ
ejpam-5694	156	7	(	(	PUNCT
ejpam-5694	156	8	f(s)−	f(s)−	PROPN
ejpam-5694	156	9	a)f	a)f	ADJ
ejpam-5694	156	10	′(a2	′(a2	PROPN
ejpam-5694	156	11	)	)	PUNCT
ejpam-5694	157	1	+	+	CCONJ
ejpam-5694	157	2	(	(	PUNCT
ejpam-5694	157	3	f(s)−	f(s)−	X
ejpam-5694	157	4	a)(f(s)−	a)(f(s)−	ADV
ejpam-5694	157	5	b)f	b)f	NOUN
ejpam-5694	157	6	′′(a1	′′(a1	NOUN
ejpam-5694	157	7	)	)	PUNCT
ejpam-5694	157	8	−(f(s)−	−(f(s)−	ADP
ejpam-5694	157	9	a)2	a)2	PROPN
ejpam-5694	157	10	2	2	NUM
ejpam-5694	157	11	f	f	NOUN
ejpam-5694	157	12	′′(a2	′′(a2	NOUN
ejpam-5694	157	13	)	)	PUNCT
ejpam-5694	158	1	+	+	CCONJ
ejpam-5694	158	2	∫	∫	PROPN
ejpam-5694	158	3	a2	a2	PROPN
ejpam-5694	158	4	a1	a1	PROPN
ejpam-5694	158	5	g1(f(s	g1(f(s	X
ejpam-5694	158	6	)	)	PUNCT
ejpam-5694	158	7	,	,	PUNCT
ejpam-5694	158	8	τ)f	τ)f	PUNCT
ejpam-5694	158	9	′′′(τ)dτ	′′′(τ)dτ	PROPN
ejpam-5694	158	10	]	]	PUNCT
ejpam-5694	158	11	ν(s)dµ2(s	ν(s)dµ2(s	NOUN
ejpam-5694	158	12	)	)	PUNCT
ejpam-5694	158	13	.	.	PUNCT
ejpam-5694	159	1	(	(	PUNCT
ejpam-5694	159	2	27	27	NUM
ejpam-5694	159	3	)	)	PUNCT
ejpam-5694	159	4	similarly	similarly	ADV
ejpam-5694	159	5	,	,	PUNCT
ejpam-5694	159	6	we	we	PRON
ejpam-5694	159	7	can	can	AUX
ejpam-5694	159	8	write	write	VERB
ejpam-5694	159	9	∫	∫	PROPN
ejpam-5694	159	10	ω1	ω1	PROPN
ejpam-5694	159	11	f(akf(ϖ))u(ϖ)dµ1(ϖ	f(akf(ϖ))u(ϖ)dµ1(ϖ	PROPN
ejpam-5694	159	12	)	)	PUNCT
ejpam-5694	160	1	=	=	SYM
ejpam-5694	160	2	∫	∫	PROPN
ejpam-5694	160	3	ω2	ω2	ADJ
ejpam-5694	160	4	[	[	PUNCT
ejpam-5694	160	5	f(a1	f(a1	NOUN
ejpam-5694	160	6	)	)	PUNCT
ejpam-5694	160	7	+	+	CCONJ
ejpam-5694	160	8	(	(	PUNCT
ejpam-5694	160	9	akf(ϖ)−	akf(ϖ)−	ADV
ejpam-5694	160	10	a)f	a)f	ADJ
ejpam-5694	160	11	′(a2	′(a2	NOUN
ejpam-5694	160	12	)	)	PUNCT
ejpam-5694	161	1	+	+	CCONJ
ejpam-5694	161	2	(	(	PUNCT
ejpam-5694	161	3	akf(ϖ)−	akf(ϖ)−	PROPN
ejpam-5694	161	4	a)(akf(ϖ)−	a)(akf(ϖ)−	PROPN
ejpam-5694	161	5	b)f	b)f	NOUN
ejpam-5694	161	6	′′(a1	′′(a1	NOUN
ejpam-5694	161	7	)	)	PUNCT
ejpam-5694	161	8	−(akf(ϖ)−	−(akf(ϖ)−	NUM
ejpam-5694	161	9	a)2	a)2	NOUN
ejpam-5694	161	10	2	2	NUM
ejpam-5694	161	11	f	f	NOUN
ejpam-5694	161	12	′′(a2	′′(a2	NOUN
ejpam-5694	161	13	)	)	PUNCT
ejpam-5694	162	1	+	+	CCONJ
ejpam-5694	162	2	∫	∫	PROPN
ejpam-5694	162	3	a2	a2	PROPN
ejpam-5694	162	4	a1	a1	PROPN
ejpam-5694	162	5	g1(akf(ϖ	g1(akf(ϖ	PROPN
ejpam-5694	162	6	)	)	PUNCT
ejpam-5694	162	7	,	,	PUNCT
ejpam-5694	162	8	τ)f	τ)f	PUNCT
ejpam-5694	162	9	′′′(τ)dτ	′′′(τ)dτ	PROPN
ejpam-5694	162	10	]	]	PUNCT
ejpam-5694	162	11	u(ϖ)dµ1(ϖ	u(ϖ)dµ1(ϖ	NUM
ejpam-5694	162	12	)	)	PUNCT
ejpam-5694	162	13	.	.	PUNCT
ejpam-5694	163	1	(	(	PUNCT
ejpam-5694	163	2	28	28	NUM
ejpam-5694	163	3	)	)	PUNCT
ejpam-5694	163	4	now	now	ADV
ejpam-5694	163	5	subtracting	subtract	VERB
ejpam-5694	163	6	(	(	PUNCT
ejpam-5694	163	7	28	28	NUM
ejpam-5694	163	8	)	)	PUNCT
ejpam-5694	163	9	from	from	ADP
ejpam-5694	163	10	(	(	PUNCT
ejpam-5694	163	11	27	27	NUM
ejpam-5694	163	12	)	)	PUNCT
ejpam-5694	163	13	we	we	PRON
ejpam-5694	163	14	obtain	obtain	VERB
ejpam-5694	163	15	∫	∫	PROPN
ejpam-5694	163	16	ω2	ω2	PROPN
ejpam-5694	163	17	f(f(s))ν(s)dµ2(s)−	f(f(s))ν(s)dµ2(s)−	PROPN
ejpam-5694	163	18	∫	∫	PROPN
ejpam-5694	163	19	ω1	ω1	PROPN
ejpam-5694	163	20	f(akf(ϖ))u(ϖ)dµ1(ϖ	f(akf(ϖ))u(ϖ)dµ1(ϖ	PROPN
ejpam-5694	163	21	)	)	PUNCT
ejpam-5694	163	22	=	=	SYM
ejpam-5694	164	1	∫	∫	PROPN
ejpam-5694	164	2	ω2	ω2	PROPN
ejpam-5694	164	3	[	[	PUNCT
ejpam-5694	164	4	∫	∫	PROPN
ejpam-5694	164	5	a2	a2	PROPN
ejpam-5694	164	6	a1	a1	PROPN
ejpam-5694	164	7	g1(f(s	g1(f(s	X
ejpam-5694	164	8	)	)	PUNCT
ejpam-5694	164	9	,	,	PUNCT
ejpam-5694	164	10	τ)f	τ)f	PUNCT
ejpam-5694	164	11	′′′(τ)dτ	′′′(τ)dτ	PROPN
ejpam-5694	164	12	]	]	PUNCT
ejpam-5694	164	13	ν(s)dµ2(s	ν(s)dµ2(s	NOUN
ejpam-5694	164	14	)	)	PUNCT
ejpam-5694	164	15	−	−	NUM
ejpam-5694	165	1	∫	∫	PROPN
ejpam-5694	165	2	ω1	ω1	PROPN
ejpam-5694	165	3	[	[	PUNCT
ejpam-5694	165	4	∫	∫	PROPN
ejpam-5694	165	5	a2	a2	PROPN
ejpam-5694	165	6	a1	a1	PROPN
ejpam-5694	165	7	g1(akf(ϖ	g1(akf(ϖ	PROPN
ejpam-5694	165	8	)	)	PUNCT
ejpam-5694	165	9	,	,	PUNCT
ejpam-5694	165	10	τ)f	τ)f	PUNCT
ejpam-5694	165	11	′′′(τ)dτ	′′′(τ)dτ	PROPN
ejpam-5694	165	12	]	]	PUNCT
ejpam-5694	165	13	u(ϖ)dµ1(ϖ	u(ϖ)dµ1(ϖ	NUM
ejpam-5694	165	14	)	)	PUNCT
ejpam-5694	165	15	.	.	PUNCT
ejpam-5694	166	1	(	(	PUNCT
ejpam-5694	166	2	29	29	NUM
ejpam-5694	166	3	)	)	PUNCT
ejpam-5694	166	4	the	the	DET
ejpam-5694	166	5	fact	fact	NOUN
ejpam-5694	166	6	used	use	VERB
ejpam-5694	166	7	in	in	ADP
ejpam-5694	166	8	obtaining	obtain	VERB
ejpam-5694	166	9	the	the	DET
ejpam-5694	166	10	equation	equation	NOUN
ejpam-5694	166	11	(	(	PUNCT
ejpam-5694	166	12	29	29	NUM
ejpam-5694	166	13	)	)	PUNCT
ejpam-5694	166	14	is	be	AUX
ejpam-5694	166	15	as	as	ADP
ejpam-5694	166	16	follows;∫	follows;∫	PROPN
ejpam-5694	166	17	ω2	ω2	PROPN
ejpam-5694	166	18	ν(s)dµ2(s	ν(s)dµ2(s	PROPN
ejpam-5694	166	19	)	)	PUNCT
ejpam-5694	167	1	=	=	SYM
ejpam-5694	168	1	∫	∫	PROPN
ejpam-5694	169	1	ω2	ω2	NUM
ejpam-5694	169	2	∫	∫	PROPN
ejpam-5694	169	3	ω1	ω1	PROPN
ejpam-5694	169	4	k(ϖ	k(ϖ	PROPN
ejpam-5694	169	5	,	,	PUNCT
ejpam-5694	169	6	s	s	NOUN
ejpam-5694	169	7	)	)	PUNCT
ejpam-5694	169	8	k(ϖ	k(ϖ	NOUN
ejpam-5694	169	9	)	)	PUNCT
ejpam-5694	169	10	u(ϖ)dµ1(ϖ)dµ2(s	u(ϖ)dµ1(ϖ)dµ2(s	NOUN
ejpam-5694	169	11	)	)	PUNCT
ejpam-5694	170	1	=	=	SYM
ejpam-5694	170	2	∫	∫	PROPN
ejpam-5694	170	3	ω1	ω1	PROPN
ejpam-5694	170	4	u(ϖ	u(ϖ	PROPN
ejpam-5694	170	5	)	)	PUNCT
ejpam-5694	170	6	k(ϖ	k(ϖ	PROPN
ejpam-5694	170	7	)	)	PUNCT
ejpam-5694	170	8	∫	∫	PROPN
ejpam-5694	171	1	ω2	ω2	PROPN
ejpam-5694	171	2	g(ϖ	g(ϖ	PROPN
ejpam-5694	171	3	,	,	PUNCT
ejpam-5694	171	4	s)dµ2(s)dµ1(ϖ	s)dµ2(s)dµ1(ϖ	NOUN
ejpam-5694	171	5	)	)	PUNCT
ejpam-5694	171	6	=	=	SYM
ejpam-5694	172	1	∫	∫	PROPN
ejpam-5694	172	2	ω1	ω1	PROPN
ejpam-5694	172	3	u(ϖ	u(ϖ	PROPN
ejpam-5694	172	4	)	)	PUNCT
ejpam-5694	172	5	k(ϖ	k(ϖ	PROPN
ejpam-5694	172	6	)	)	PUNCT
ejpam-5694	172	7	k(ϖ)dµ1(ϖ	k(ϖ)dµ1(ϖ	PROPN
ejpam-5694	172	8	)	)	PUNCT
ejpam-5694	173	1	=	=	SYM
ejpam-5694	173	2	∫	∫	PROPN
ejpam-5694	173	3	ω1	ω1	PROPN
ejpam-5694	173	4	u(ϖ)dµ1(ϖ	u(ϖ)dµ1(ϖ	PUNCT
ejpam-5694	173	5	)	)	PUNCT
ejpam-5694	173	6	a.	a.	NOUN
ejpam-5694	173	7	m.	m.	PROPN
ejpam-5694	173	8	k.	k.	PROPN
ejpam-5694	173	9	abbasi	abbasi	PROPN
ejpam-5694	173	10	,	,	PUNCT
ejpam-5694	173	11	m.	m.	PROPN
ejpam-5694	173	12	anwar	anwar	PROPN
ejpam-5694	173	13	/	/	PUNCT
ejpam-5694	173	14	eur	eur	PROPN
ejpam-5694	173	15	.	.	PUNCT
ejpam-5694	174	1	j.	j.	PROPN
ejpam-5694	174	2	pure	pure	PROPN
ejpam-5694	174	3	appl	appl	PROPN
ejpam-5694	174	4	.	.	PROPN
ejpam-5694	174	5	math	math	PROPN
ejpam-5694	174	6	,	,	PUNCT
ejpam-5694	174	7	18	18	NUM
ejpam-5694	174	8	(	(	PUNCT
ejpam-5694	174	9	1	1	NUM
ejpam-5694	174	10	)	)	PUNCT
ejpam-5694	174	11	(	(	PUNCT
ejpam-5694	174	12	2025	2025	NUM
ejpam-5694	174	13	)	)	PUNCT
ejpam-5694	174	14	,	,	PUNCT
ejpam-5694	174	15	5694	5694	NUM
ejpam-5694	174	16	9	9	NUM
ejpam-5694	174	17	of	of	ADP
ejpam-5694	174	18	18	18	NUM
ejpam-5694	174	19	and	and	CCONJ
ejpam-5694	174	20	∫	∫	PROPN
ejpam-5694	174	21	ω2	ω2	PROPN
ejpam-5694	174	22	akf(ϖ)u(ϖ)dµ1(ϖ	akf(ϖ)u(ϖ)dµ1(ϖ	PROPN
ejpam-5694	174	23	)	)	PUNCT
ejpam-5694	174	24	=	=	SYM
ejpam-5694	174	25	∫	∫	PROPN
ejpam-5694	174	26	ω1	ω1	PROPN
ejpam-5694	174	27	[	[	PUNCT
ejpam-5694	174	28	1	1	NUM
ejpam-5694	174	29	k(ϖ	k(ϖ	X
ejpam-5694	174	30	)	)	PUNCT
ejpam-5694	174	31	∫	∫	PROPN
ejpam-5694	174	32	ω2	ω2	PROPN
ejpam-5694	174	33	g(ϖ	g(ϖ	PROPN
ejpam-5694	174	34	,	,	PUNCT
ejpam-5694	174	35	s)f(s)dµ2(s	s)f(s)dµ2(s	NOUN
ejpam-5694	174	36	)	)	PUNCT
ejpam-5694	174	37	]	]	PUNCT
ejpam-5694	174	38	u(ϖ)dµ1(ϖ	u(ϖ)dµ1(ϖ	X
ejpam-5694	174	39	)	)	PUNCT
ejpam-5694	174	40	=	=	SYM
ejpam-5694	175	1	∫	∫	PROPN
ejpam-5694	175	2	ω2	ω2	NUM
ejpam-5694	175	3	f(s	f(s	PROPN
ejpam-5694	175	4	)	)	PUNCT
ejpam-5694	175	5	∫	∫	PROPN
ejpam-5694	175	6	ω1	ω1	PROPN
ejpam-5694	175	7	g(ϖ	g(ϖ	PROPN
ejpam-5694	175	8	,	,	PUNCT
ejpam-5694	175	9	s	s	NOUN
ejpam-5694	175	10	)	)	PUNCT
ejpam-5694	175	11	k(ϖ	k(ϖ	NOUN
ejpam-5694	175	12	)	)	PUNCT
ejpam-5694	175	13	u(ϖ)dµ1(ϖ)dµ2(s	u(ϖ)dµ1(ϖ)dµ2(s	NOUN
ejpam-5694	175	14	)	)	PUNCT
ejpam-5694	175	15	=	=	SYM
ejpam-5694	176	1	∫	∫	PROPN
ejpam-5694	176	2	ω2	ω2	NUM
ejpam-5694	176	3	f(s)ν(s)dµ2(s	f(s)ν(s)dµ2(s	PROPN
ejpam-5694	176	4	)	)	PUNCT
ejpam-5694	176	5	.	.	PUNCT
ejpam-5694	177	1	now	now	ADV
ejpam-5694	177	2	applying	apply	VERB
ejpam-5694	177	3	(	(	PUNCT
ejpam-5694	177	4	10	10	NUM
ejpam-5694	177	5	)	)	PUNCT
ejpam-5694	177	6	in	in	ADP
ejpam-5694	177	7	f	f	PROPN
ejpam-5694	177	8	′′′	′′′	PROPN
ejpam-5694	177	9	at	at	ADP
ejpam-5694	177	10	point	point	NOUN
ejpam-5694	177	11	a	a	PRON
ejpam-5694	177	12	we	we	PRON
ejpam-5694	177	13	obtain	obtain	VERB
ejpam-5694	177	14	f	f	PROPN
ejpam-5694	177	15	′′′(τ	′′′(τ	PROPN
ejpam-5694	177	16	)	)	PUNCT
ejpam-5694	177	17	=	=	PUNCT
ejpam-5694	178	1	∑	∑	PUNCT
ejpam-5694	178	2	κ	κ	PROPN
ejpam-5694	178	3	f	f	PROPN
ejpam-5694	178	4	(	(	PUNCT
ejpam-5694	178	5	κ)(a1	κ)(a1	X
ejpam-5694	178	6	)	)	PUNCT
ejpam-5694	178	7	κ	κ	NOUN
ejpam-5694	178	8	!	!	PUNCT
ejpam-5694	179	1	(	(	PUNCT
ejpam-5694	179	2	τ	τ	PROPN
ejpam-5694	179	3	−	−	PROPN
ejpam-5694	179	4	a1	a1	PROPN
ejpam-5694	179	5	)	)	PUNCT
ejpam-5694	180	1	j−3	j−3	NOUN
ejpam-5694	180	2	+	+	CCONJ
ejpam-5694	180	3	1	1	NUM
ejpam-5694	180	4	(	(	PUNCT
ejpam-5694	180	5	n−	n−	NOUN
ejpam-5694	180	6	4	4	NUM
ejpam-5694	180	7	)	)	PUNCT
ejpam-5694	180	8	!	!	PUNCT
ejpam-5694	181	1	∫	∫	PROPN
ejpam-5694	181	2	a2	a2	PROPN
ejpam-5694	181	3	a1	a1	PROPN
ejpam-5694	181	4	f	f	PROPN
ejpam-5694	181	5	(	(	PUNCT
ejpam-5694	181	6	n)(η)(τ	n)(η)(τ	PROPN
ejpam-5694	181	7	−	−	PROPN
ejpam-5694	181	8	η)n−4	η)n−4	NOUN
ejpam-5694	181	9	+	+	CCONJ
ejpam-5694	181	10	dη	dη	NOUN
ejpam-5694	181	11	.	.	PUNCT
ejpam-5694	182	1	(	(	PUNCT
ejpam-5694	182	2	30	30	NUM
ejpam-5694	182	3	)	)	PUNCT
ejpam-5694	182	4	using	use	VERB
ejpam-5694	182	5	(	(	PUNCT
ejpam-5694	182	6	30	30	NUM
ejpam-5694	182	7	)	)	PUNCT
ejpam-5694	182	8	in	in	ADP
ejpam-5694	182	9	(	(	PUNCT
ejpam-5694	182	10	29	29	NUM
ejpam-5694	182	11	)	)	PUNCT
ejpam-5694	182	12	we	we	PRON
ejpam-5694	182	13	obtain	obtain	VERB
ejpam-5694	182	14	for	for	ADP
ejpam-5694	182	15	α	α	NOUN
ejpam-5694	182	16	=	=	SYM
ejpam-5694	182	17	1	1	NUM
ejpam-5694	182	18	as	as	ADP
ejpam-5694	182	19	∫	∫	PROPN
ejpam-5694	182	20	ω2	ω2	PROPN
ejpam-5694	182	21	f(f(s))ν(s)dµ2(s)−	f(f(s))ν(s)dµ2(s)−	PROPN
ejpam-5694	182	22	∫	∫	PROPN
ejpam-5694	182	23	ω1	ω1	PROPN
ejpam-5694	182	24	f(akf(ϖ))u(ϖ)dµ1(ϖ	f(akf(ϖ))u(ϖ)dµ1(ϖ	PROPN
ejpam-5694	182	25	)	)	PUNCT
ejpam-5694	182	26	=	=	SYM
ejpam-5694	182	27	∫	∫	PROPN
ejpam-5694	182	28	a2	a2	PROPN
ejpam-5694	182	29	a1	a1	PROPN
ejpam-5694	183	1	[	[	X
ejpam-5694	183	2	∫	∫	X
ejpam-5694	183	3	ω2	ω2	ADJ
ejpam-5694	183	4	gα(f(s	gα(f(	NOUN
ejpam-5694	183	5	)	)	PUNCT
ejpam-5694	183	6	,	,	PUNCT
ejpam-5694	183	7	τ)ν(s)dµ2(s)−	τ)ν(s)dµ2(s)−	X
ejpam-5694	183	8	∫	∫	PROPN
ejpam-5694	183	9	ω1	ω1	PROPN
ejpam-5694	183	10	gα(akf(ϖ	gα(akf(ϖ	PROPN
ejpam-5694	183	11	)	)	PUNCT
ejpam-5694	183	12	,	,	PUNCT
ejpam-5694	183	13	τ)u(ϖ)dµ1(ϖ	τ)u(ϖ)dµ1(ϖ	NOUN
ejpam-5694	183	14	)	)	PUNCT
ejpam-5694	183	15	]	]	PUNCT
ejpam-5694	184	1	×	×	INTJ
ejpam-5694	184	2	∑	∑	PUNCT
ejpam-5694	184	3	κ	κ	PROPN
ejpam-5694	184	4	f	f	PROPN
ejpam-5694	184	5	(	(	PUNCT
ejpam-5694	184	6	κ)(a1	κ)(a1	X
ejpam-5694	184	7	)	)	PUNCT
ejpam-5694	184	8	κ	κ	NOUN
ejpam-5694	184	9	!	!	PUNCT
ejpam-5694	185	1	(	(	PUNCT
ejpam-5694	185	2	τ	τ	PROPN
ejpam-5694	185	3	−	−	PROPN
ejpam-5694	185	4	a1	a1	PROPN
ejpam-5694	185	5	)	)	PUNCT
ejpam-5694	185	6	κ−3dτ	κ−3dτ	NOUN
ejpam-5694	185	7	+	+	CCONJ
ejpam-5694	185	8	∫	∫	PROPN
ejpam-5694	185	9	a2	a2	PROPN
ejpam-5694	185	10	a1	a1	NOUN
ejpam-5694	185	11	(	(	PUNCT
ejpam-5694	185	12	[	[	X
ejpam-5694	185	13	∫	∫	X
ejpam-5694	185	14	ω2	ω2	ADJ
ejpam-5694	185	15	gα(f(s	gα(f(	NOUN
ejpam-5694	185	16	)	)	PUNCT
ejpam-5694	185	17	,	,	PUNCT
ejpam-5694	185	18	τ)ν(s)dµ2(s)−	τ)ν(s)dµ2(s)−	X
ejpam-5694	185	19	∫	∫	PROPN
ejpam-5694	185	20	ω1	ω1	PROPN
ejpam-5694	185	21	gα(akf(ϖ	gα(akf(ϖ	PROPN
ejpam-5694	185	22	)	)	PUNCT
ejpam-5694	185	23	,	,	PUNCT
ejpam-5694	185	24	τ)u(ϖ)dµ1(ϖ	τ)u(ϖ)dµ1(ϖ	PROPN
ejpam-5694	185	25	)	)	PUNCT
ejpam-5694	185	26	]	]	PUNCT
ejpam-5694	185	27	×	×	NOUN
ejpam-5694	185	28	1	1	NUM
ejpam-5694	185	29	(	(	PUNCT
ejpam-5694	185	30	n−	n−	NOUN
ejpam-5694	185	31	4	4	NUM
ejpam-5694	185	32	)	)	PUNCT
ejpam-5694	185	33	!	!	PUNCT
ejpam-5694	186	1	∫	∫	PROPN
ejpam-5694	186	2	a2	a2	PROPN
ejpam-5694	186	3	a1	a1	PROPN
ejpam-5694	186	4	f	f	PROPN
ejpam-5694	186	5	(	(	PUNCT
ejpam-5694	186	6	n)(η)(τ	n)(η)(τ	PROPN
ejpam-5694	186	7	−	−	PROPN
ejpam-5694	186	8	η)n−4	η)n−4	NOUN
ejpam-5694	186	9	+	+	CCONJ
ejpam-5694	186	10	dη	dη	NOUN
ejpam-5694	186	11	)	)	PUNCT
ejpam-5694	186	12	dτ	dτ	NOUN
ejpam-5694	186	13	.	.	PUNCT
ejpam-5694	186	14	after	after	ADP
ejpam-5694	186	15	giving	give	VERB
ejpam-5694	186	16	the	the	DET
ejpam-5694	186	17	notation	notation	NOUN
ejpam-5694	186	18	mentioned	mention	VERB
ejpam-5694	186	19	in	in	ADP
ejpam-5694	186	20	(	(	PUNCT
ejpam-5694	186	21	26	26	NUM
ejpam-5694	186	22	)	)	PUNCT
ejpam-5694	186	23	we	we	PRON
ejpam-5694	186	24	arrived	arrive	VERB
ejpam-5694	186	25	at	at	ADP
ejpam-5694	186	26	the	the	DET
ejpam-5694	186	27	required	require	VERB
ejpam-5694	186	28	result	result	NOUN
ejpam-5694	186	29	.	.	PUNCT
ejpam-5694	187	1	for	for	ADP
ejpam-5694	187	2	α	α	NOUN
ejpam-5694	187	3	=	=	SYM
ejpam-5694	187	4	2	2	NUM
ejpam-5694	187	5	,	,	PUNCT
ejpam-5694	187	6	3	3	NUM
ejpam-5694	187	7	,	,	PUNCT
ejpam-5694	187	8	4	4	NUM
ejpam-5694	187	9	consider	consider	VERB
ejpam-5694	187	10	the	the	DET
ejpam-5694	187	11	left	left	ADJ
ejpam-5694	187	12	hand	hand	NOUN
ejpam-5694	187	13	sides	side	NOUN
ejpam-5694	187	14	of	of	ADP
ejpam-5694	187	15	(	(	PUNCT
ejpam-5694	187	16	27	27	NUM
ejpam-5694	187	17	)	)	PUNCT
ejpam-5694	187	18	and	and	CCONJ
ejpam-5694	187	19	(	(	PUNCT
ejpam-5694	187	20	28	28	NUM
ejpam-5694	187	21	)	)	PUNCT
ejpam-5694	187	22	,	,	PUNCT
ejpam-5694	187	23	then	then	ADV
ejpam-5694	187	24	make	make	VERB
ejpam-5694	187	25	use	use	NOUN
ejpam-5694	187	26	of	of	ADP
ejpam-5694	187	27	(	(	PUNCT
ejpam-5694	187	28	2	2	NUM
ejpam-5694	187	29	)	)	PUNCT
ejpam-5694	187	30	,	,	PUNCT
ejpam-5694	187	31	(	(	PUNCT
ejpam-5694	187	32	3	3	X
ejpam-5694	187	33	)	)	PUNCT
ejpam-5694	187	34	and	and	CCONJ
ejpam-5694	187	35	(	(	PUNCT
ejpam-5694	187	36	4	4	NUM
ejpam-5694	187	37	)	)	PUNCT
ejpam-5694	187	38	,	,	PUNCT
ejpam-5694	187	39	after	after	ADP
ejpam-5694	187	40	that	that	PRON
ejpam-5694	187	41	subtracting	subtract	VERB
ejpam-5694	187	42	the	the	DET
ejpam-5694	187	43	obtained	obtain	VERB
ejpam-5694	187	44	results	result	NOUN
ejpam-5694	187	45	to	to	PART
ejpam-5694	187	46	get	get	VERB
ejpam-5694	187	47	(	(	PUNCT
ejpam-5694	187	48	29	29	NUM
ejpam-5694	187	49	)	)	PUNCT
ejpam-5694	187	50	then	then	ADV
ejpam-5694	187	51	follow	follow	VERB
ejpam-5694	187	52	the	the	DET
ejpam-5694	187	53	same	same	ADJ
ejpam-5694	187	54	steps	step	NOUN
ejpam-5694	187	55	as	as	ADP
ejpam-5694	187	56	for	for	ADP
ejpam-5694	187	57	α	α	NOUN
ejpam-5694	187	58	=	=	SYM
ejpam-5694	187	59	1	1	NUM
ejpam-5694	187	60	to	to	PART
ejpam-5694	187	61	obtain	obtain	VERB
ejpam-5694	187	62	the	the	DET
ejpam-5694	187	63	required	require	VERB
ejpam-5694	187	64	result	result	NOUN
ejpam-5694	187	65	.	.	PUNCT
ejpam-5694	188	1	•	•	ADJ
ejpam-5694	188	2	proof	proof	NOUN
ejpam-5694	188	3	is	be	AUX
ejpam-5694	188	4	analogous	analogous	ADJ
ejpam-5694	188	5	to	to	ADP
ejpam-5694	188	6	the	the	DET
ejpam-5694	188	7	first	first	ADJ
ejpam-5694	188	8	part	part	NOUN
ejpam-5694	188	9	,	,	PUNCT
ejpam-5694	188	10	use	use	VERB
ejpam-5694	188	11	the	the	DET
ejpam-5694	188	12	taylor	taylor	PROPN
ejpam-5694	188	13	polynomial	polynomial	NOUN
ejpam-5694	188	14	(	(	PUNCT
ejpam-5694	188	15	11	11	NUM
ejpam-5694	188	16	)	)	PUNCT
ejpam-5694	188	17	and	and	CCONJ
ejpam-5694	188	18	simplify	simplify	NOUN
ejpam-5694	188	19	we	we	PRON
ejpam-5694	188	20	get	get	AUX
ejpam-5694	188	21	required	require	VERB
ejpam-5694	188	22	.	.	PUNCT
ejpam-5694	189	1	remark	remark	NOUN
ejpam-5694	189	2	3	3	NUM
ejpam-5694	189	3	.	.	PUNCT
ejpam-5694	190	1	as	as	SCONJ
ejpam-5694	190	2	gα	gα	ADV
ejpam-5694	190	3	are	be	VERB
ejpam-5694	190	4	convex	convex	ADJ
ejpam-5694	190	5	with	with	ADP
ejpam-5694	190	6	respect	respect	NOUN
ejpam-5694	190	7	to	to	ADP
ejpam-5694	190	8	both	both	DET
ejpam-5694	190	9	variables	variable	NOUN
ejpam-5694	190	10	,	,	PUNCT
ejpam-5694	190	11	replacing	replace	VERB
ejpam-5694	190	12	the	the	DET
ejpam-5694	190	13	convex	convex	NOUN
ejpam-5694	190	14	function	function	NOUN
ejpam-5694	190	15	f	f	X
ejpam-5694	190	16	(	(	PUNCT
ejpam-5694	190	17	.	.	PUNCT
ejpam-5694	190	18	)	)	PUNCT
ejpam-5694	190	19	by	by	ADP
ejpam-5694	190	20	gα	gα	PROPN
ejpam-5694	190	21	(	(	PUNCT
ejpam-5694	190	22	.	.	NUM
ejpam-5694	190	23	,	,	PUNCT
ejpam-5694	190	24	τ	τ	PROPN
ejpam-5694	190	25	)	)	PUNCT
ejpam-5694	190	26	ensures	ensure	VERB
ejpam-5694	190	27	that	that	SCONJ
ejpam-5694	190	28	relation	relation	NOUN
ejpam-5694	190	29	in	in	ADP
ejpam-5694	190	30	(	(	PUNCT
ejpam-5694	190	31	18	18	NUM
ejpam-5694	190	32	)	)	PUNCT
ejpam-5694	190	33	remains	remain	VERB
ejpam-5694	190	34	valid	valid	ADJ
ejpam-5694	190	35	,	,	PUNCT
ejpam-5694	191	1	that	that	SCONJ
ejpam-5694	191	2	is;∫	is;∫	PRON
ejpam-5694	191	3	ω1	ω1	PROPN
ejpam-5694	191	4	gα(akf(ϖ	gα(akf(ϖ	PROPN
ejpam-5694	191	5	)	)	PUNCT
ejpam-5694	191	6	,	,	PUNCT
ejpam-5694	191	7	τ)u(ϖ)dµ1(ϖ	τ)u(ϖ)dµ1(ϖ	NOUN
ejpam-5694	191	8	)	)	PUNCT
ejpam-5694	191	9	≤	≤	NUM
ejpam-5694	191	10	∫	∫	PROPN
ejpam-5694	191	11	ω2	ω2	NOUN
ejpam-5694	191	12	gα(f(s	gα(f(	NOUN
ejpam-5694	191	13	)	)	PUNCT
ejpam-5694	191	14	,	,	PUNCT
ejpam-5694	191	15	τ)ν(s)dµ2(s	τ)ν(s)dµ2(s	NOUN
ejpam-5694	191	16	)	)	PUNCT
ejpam-5694	191	17	.	.	PUNCT
ejpam-5694	192	1	(	(	PUNCT
ejpam-5694	192	2	31	31	NUM
ejpam-5694	192	3	)	)	PUNCT
ejpam-5694	192	4	a.	a.	NOUN
ejpam-5694	192	5	m.	m.	PROPN
ejpam-5694	192	6	k.	k.	PROPN
ejpam-5694	192	7	abbasi	abbasi	PROPN
ejpam-5694	192	8	,	,	PUNCT
ejpam-5694	192	9	m.	m.	PROPN
ejpam-5694	192	10	anwar	anwar	PROPN
ejpam-5694	192	11	/	/	PUNCT
ejpam-5694	192	12	eur	eur	PROPN
ejpam-5694	192	13	.	.	PUNCT
ejpam-5694	193	1	j.	j.	PROPN
ejpam-5694	193	2	pure	pure	PROPN
ejpam-5694	193	3	appl	appl	PROPN
ejpam-5694	193	4	.	.	PROPN
ejpam-5694	193	5	math	math	PROPN
ejpam-5694	193	6	,	,	PUNCT
ejpam-5694	193	7	18	18	NUM
ejpam-5694	193	8	(	(	PUNCT
ejpam-5694	193	9	1	1	NUM
ejpam-5694	193	10	)	)	PUNCT
ejpam-5694	193	11	(	(	PUNCT
ejpam-5694	193	12	2025	2025	NUM
ejpam-5694	193	13	)	)	PUNCT
ejpam-5694	193	14	,	,	PUNCT
ejpam-5694	193	15	5694	5694	NUM
ejpam-5694	193	16	10	10	NUM
ejpam-5694	193	17	of	of	ADP
ejpam-5694	193	18	18	18	NUM
ejpam-5694	193	19	theorem	theorem	NOUN
ejpam-5694	193	20	5	5	NUM
ejpam-5694	193	21	.	.	PUNCT
ejpam-5694	194	1	let	let	VERB
ejpam-5694	194	2	all	all	DET
ejpam-5694	194	3	conditions	condition	NOUN
ejpam-5694	194	4	of	of	ADP
ejpam-5694	194	5	theorem	theorem	ADJ
ejpam-5694	194	6	4	4	NUM
ejpam-5694	194	7	holds	hold	VERB
ejpam-5694	194	8	and	and	CCONJ
ejpam-5694	194	9	if	if	SCONJ
ejpam-5694	194	10	f	f	PROPN
ejpam-5694	194	11	is	be	AUX
ejpam-5694	194	12	n−	n−	PROPN
ejpam-5694	194	13	convex	convex	VERB
ejpam-5694	194	14	on	on	ADP
ejpam-5694	194	15	t	t	PROPN
ejpam-5694	194	16	,	,	PUNCT
ejpam-5694	194	17	then	then	ADV
ejpam-5694	194	18	;	;	PUNCT
ejpam-5694	194	19	•	•	X
ejpam-5694	194	20	(	(	PUNCT
ejpam-5694	194	21	i	i	NOUN
ejpam-5694	194	22	)	)	PUNCT
ejpam-5694	194	23	∫	∫	PROPN
ejpam-5694	195	1	ω2	ω2	PROPN
ejpam-5694	196	1	f(f(s))ν(s)dµ2(s)−	f(f(s))ν(s)dµ2(s)−	PROPN
ejpam-5694	196	2	∫	∫	PROPN
ejpam-5694	196	3	ω1	ω1	PROPN
ejpam-5694	196	4	f(akf(ϖ))u(ϖ)dµ1(ϖ	f(akf(ϖ))u(ϖ)dµ1(ϖ	PROPN
ejpam-5694	196	5	)	)	PUNCT
ejpam-5694	196	6	≥	≥	PROPN
ejpam-5694	196	7	∫	∫	PROPN
ejpam-5694	196	8	a2	a2	PROPN
ejpam-5694	196	9	a1	a1	PROPN
ejpam-5694	196	10	jgα(f	jgα(f	PROPN
ejpam-5694	196	11	,	,	PUNCT
ejpam-5694	196	12	τ)×	τ)×	X
ejpam-5694	196	13	∑	∑	PROPN
ejpam-5694	196	14	κ	κ	PROPN
ejpam-5694	196	15	f	f	PROPN
ejpam-5694	196	16	(	(	PUNCT
ejpam-5694	196	17	κ)(a1	κ)(a1	X
ejpam-5694	196	18	)	)	PUNCT
ejpam-5694	196	19	κ	κ	NOUN
ejpam-5694	196	20	!	!	PUNCT
ejpam-5694	197	1	(	(	PUNCT
ejpam-5694	197	2	τ	τ	PROPN
ejpam-5694	197	3	−	−	PROPN
ejpam-5694	197	4	a1	a1	PROPN
ejpam-5694	197	5	)	)	PUNCT
ejpam-5694	197	6	κdτ	κdτ	NOUN
ejpam-5694	197	7	.	.	PUNCT
ejpam-5694	198	1	(	(	PUNCT
ejpam-5694	198	2	32	32	NUM
ejpam-5694	198	3	)	)	PUNCT
ejpam-5694	198	4	•	•	NUM
ejpam-5694	198	5	(	(	PUNCT
ejpam-5694	198	6	ii	ii	NOUN
ejpam-5694	198	7	)	)	PUNCT
ejpam-5694	198	8	for	for	ADP
ejpam-5694	198	9	any	any	DET
ejpam-5694	198	10	odd	odd	ADJ
ejpam-5694	198	11	n	n	NOUN
ejpam-5694	198	12	>	>	SYM
ejpam-5694	198	13	4;∫	4;∫	NUM
ejpam-5694	199	1	ω2	ω2	ADV
ejpam-5694	200	1	f(f(s))ν(s)dµ2(s)−	f(f(s))ν(s)dµ2(s)−	PROPN
ejpam-5694	200	2	∫	∫	PROPN
ejpam-5694	200	3	ω1	ω1	PROPN
ejpam-5694	200	4	f(akf(ϖ))u(ϖ)dµ1(ϖ	f(akf(ϖ))u(ϖ)dµ1(ϖ	PROPN
ejpam-5694	200	5	)	)	PUNCT
ejpam-5694	200	6	≥	≥	PROPN
ejpam-5694	200	7	∫	∫	PROPN
ejpam-5694	200	8	a2	a2	PROPN
ejpam-5694	200	9	a1	a1	PROPN
ejpam-5694	200	10	jgα(f	jgα(f	PROPN
ejpam-5694	200	11	,	,	PUNCT
ejpam-5694	200	12	τ)×	τ)×	X
ejpam-5694	200	13	∑	∑	PROPN
ejpam-5694	200	14	κ	κ	X
ejpam-5694	200	15	(	(	PUNCT
ejpam-5694	200	16	−1)κ	−1)κ	X
ejpam-5694	200	17	f	f	X
ejpam-5694	200	18	(	(	PUNCT
ejpam-5694	200	19	κ)(a2	κ)(a2	PROPN
ejpam-5694	200	20	)	)	PUNCT
ejpam-5694	200	21	κ	κ	NOUN
ejpam-5694	200	22	!	!	PUNCT
ejpam-5694	201	1	(	(	PUNCT
ejpam-5694	201	2	a2	a2	PROPN
ejpam-5694	201	3	−	−	PROPN
ejpam-5694	201	4	τ)κdτ	τ)κdτ	PROPN
ejpam-5694	201	5	.	.	PUNCT
ejpam-5694	202	1	(	(	PUNCT
ejpam-5694	202	2	33	33	NUM
ejpam-5694	202	3	)	)	PUNCT
ejpam-5694	202	4	proof	proof	NOUN
ejpam-5694	202	5	.	.	PUNCT
ejpam-5694	203	1	•	•	INTJ
ejpam-5694	203	2	as	as	SCONJ
ejpam-5694	203	3	f	f	PROPN
ejpam-5694	203	4	is	be	AUX
ejpam-5694	203	5	n−convex	n−convex	NOUN
ejpam-5694	203	6	for	for	ADP
ejpam-5694	203	7	all	all	DET
ejpam-5694	203	8	n	n	PRON
ejpam-5694	203	9	∈	∈	NOUN
ejpam-5694	203	10	n	n	NOUN
ejpam-5694	203	11	implies	imply	VERB
ejpam-5694	203	12	f	f	PROPN
ejpam-5694	203	13	(	(	PUNCT
ejpam-5694	203	14	n	n	CCONJ
ejpam-5694	203	15	)	)	PUNCT
ejpam-5694	203	16	≥	≥	X
ejpam-5694	203	17	0	0	NUM
ejpam-5694	203	18	for	for	ADP
ejpam-5694	203	19	τ	τ	PROPN
ejpam-5694	203	20	∈	∈	PROPN
ejpam-5694	203	21	t	t	PROPN
ejpam-5694	203	22	.	.	PUNCT
ejpam-5694	204	1	also	also	ADV
ejpam-5694	204	2	,	,	PUNCT
ejpam-5694	204	3	(	(	PUNCT
ejpam-5694	204	4	τ	τ	X
ejpam-5694	204	5	−	−	PROPN
ejpam-5694	204	6	η)n−4	η)n−4	NOUN
ejpam-5694	204	7	+	+	PUNCT
ejpam-5694	204	8	is	be	AUX
ejpam-5694	204	9	non	non	ADJ
ejpam-5694	204	10	-	-	ADJ
ejpam-5694	204	11	negative	negative	ADJ
ejpam-5694	204	12	for	for	ADP
ejpam-5694	204	13	all	all	DET
ejpam-5694	204	14	n	n	PRON
ejpam-5694	204	15	∈	∈	NOUN
ejpam-5694	204	16	n	n	NOUN
ejpam-5694	204	17	because	because	SCONJ
ejpam-5694	204	18	τ	τ	PROPN
ejpam-5694	204	19	≥	≥	PROPN
ejpam-5694	204	20	η	η	PROPN
ejpam-5694	204	21	.	.	PROPN
ejpam-5694	204	22	by	by	ADP
ejpam-5694	204	23	using	use	VERB
ejpam-5694	204	24	aforementioned	aforementioned	ADJ
ejpam-5694	204	25	reasons	reason	NOUN
ejpam-5694	204	26	in	in	ADP
ejpam-5694	204	27	equation	equation	NOUN
ejpam-5694	204	28	(	(	PUNCT
ejpam-5694	204	29	24	24	NUM
ejpam-5694	204	30	)	)	PUNCT
ejpam-5694	204	31	we	we	PRON
ejpam-5694	204	32	obtain	obtain	VERB
ejpam-5694	204	33	the	the	DET
ejpam-5694	204	34	required	require	VERB
ejpam-5694	204	35	result	result	NOUN
ejpam-5694	204	36	.	.	PUNCT
ejpam-5694	205	1	•	•	INTJ
ejpam-5694	205	2	as	as	SCONJ
ejpam-5694	205	3	f	f	PROPN
ejpam-5694	205	4	is	be	AUX
ejpam-5694	205	5	n−convex	n−convex	NOUN
ejpam-5694	205	6	this	this	PRON
ejpam-5694	205	7	implies	imply	VERB
ejpam-5694	205	8	f	f	PROPN
ejpam-5694	205	9	(	(	PUNCT
ejpam-5694	205	10	n	n	CCONJ
ejpam-5694	205	11	)	)	PUNCT
ejpam-5694	205	12	≥	≥	NOUN
ejpam-5694	205	13	0	0	NUM
ejpam-5694	205	14	on	on	ADP
ejpam-5694	205	15	t	t	PROPN
ejpam-5694	205	16	.	.	PUNCT
ejpam-5694	206	1	also	also	ADV
ejpam-5694	206	2	,	,	PUNCT
ejpam-5694	206	3	(	(	PUNCT
ejpam-5694	206	4	−1)n−4(τ	−1)n−4(τ	NOUN
ejpam-5694	206	5	−	−	PROPN
ejpam-5694	206	6	η)n−4	η)n−4	NOUN
ejpam-5694	206	7	+	+	NOUN
ejpam-5694	206	8	=	=	X
ejpam-5694	206	9	{	{	PUNCT
ejpam-5694	206	10	0	0	NUM
ejpam-5694	206	11	τ	τ	PROPN
ejpam-5694	206	12	≤	≤	PROPN
ejpam-5694	206	13	η	η	PROPN
ejpam-5694	206	14	(	(	PUNCT
ejpam-5694	206	15	η	η	PROPN
ejpam-5694	206	16	−	−	PROPN
ejpam-5694	206	17	τ)n−4	τ)n−4	PROPN
ejpam-5694	206	18	τ	τ	PROPN
ejpam-5694	206	19	≥	≥	PROPN
ejpam-5694	206	20	η	η	PROPN
ejpam-5694	206	21	,	,	PUNCT
ejpam-5694	206	22	(	(	PUNCT
ejpam-5694	206	23	34	34	NUM
ejpam-5694	206	24	)	)	PUNCT
ejpam-5694	206	25	since	since	SCONJ
ejpam-5694	206	26	for	for	ADP
ejpam-5694	206	27	τ	τ	PROPN
ejpam-5694	206	28	≥	≥	PROPN
ejpam-5694	206	29	η	η	PROPN
ejpam-5694	206	30	,	,	PUNCT
ejpam-5694	206	31	so	so	SCONJ
ejpam-5694	206	32	for	for	ADP
ejpam-5694	206	33	any	any	DET
ejpam-5694	206	34	odd	odd	ADJ
ejpam-5694	206	35	n	n	PRON
ejpam-5694	206	36	≥	≥	NOUN
ejpam-5694	206	37	4	4	NUM
ejpam-5694	206	38	,	,	PUNCT
ejpam-5694	206	39	(	(	PUNCT
ejpam-5694	206	40	η	η	PROPN
ejpam-5694	206	41	−	−	PROPN
ejpam-5694	206	42	τ)n−4	τ)n−4	NOUN
ejpam-5694	206	43	is	be	AUX
ejpam-5694	206	44	negative	negative	ADJ
ejpam-5694	206	45	and	and	CCONJ
ejpam-5694	206	46	−(η	−(η	PROPN
ejpam-5694	206	47	−	−	PROPN
ejpam-5694	206	48	τ)n−4	τ)n−4	NOUN
ejpam-5694	206	49	will	will	AUX
ejpam-5694	206	50	be	be	AUX
ejpam-5694	206	51	nonnegative	nonnegative	ADJ
ejpam-5694	206	52	.	.	PUNCT
ejpam-5694	207	1	thus	thus	ADV
ejpam-5694	207	2	last	last	ADJ
ejpam-5694	207	3	term	term	NOUN
ejpam-5694	207	4	in	in	ADP
ejpam-5694	207	5	(	(	PUNCT
ejpam-5694	207	6	25	25	NUM
ejpam-5694	207	7	)	)	PUNCT
ejpam-5694	207	8	is	be	AUX
ejpam-5694	207	9	nonnegative	nonnegative	ADJ
ejpam-5694	207	10	.	.	PUNCT
ejpam-5694	208	1	hence	hence	ADV
ejpam-5694	208	2	we	we	PRON
ejpam-5694	208	3	can	can	AUX
ejpam-5694	208	4	write	write	VERB
ejpam-5694	208	5	(	(	PUNCT
ejpam-5694	208	6	33	33	NUM
ejpam-5694	208	7	)	)	PUNCT
ejpam-5694	208	8	.	.	PUNCT
ejpam-5694	209	1	theorem	theorem	VERB
ejpam-5694	209	2	6	6	NUM
ejpam-5694	209	3	.	.	PUNCT
ejpam-5694	210	1	let	let	VERB
ejpam-5694	210	2	the	the	DET
ejpam-5694	210	3	conditions	condition	NOUN
ejpam-5694	210	4	of	of	ADP
ejpam-5694	210	5	theorem	theorem	ADJ
ejpam-5694	210	6	4	4	NUM
ejpam-5694	210	7	hold	hold	VERB
ejpam-5694	210	8	entirely	entirely	ADV
ejpam-5694	210	9	.	.	PUNCT
ejpam-5694	211	1	additionally	additionally	ADV
ejpam-5694	211	2	,	,	PUNCT
ejpam-5694	211	3	if	if	SCONJ
ejpam-5694	211	4	f	f	PROPN
ejpam-5694	211	5	is	be	AUX
ejpam-5694	211	6	n−convex	n−convex	PRON
ejpam-5694	211	7	and	and	CCONJ
ejpam-5694	211	8	the	the	DET
ejpam-5694	211	9	function	function	NOUN
ejpam-5694	211	10	;	;	PUNCT
ejpam-5694	211	11	(	(	PUNCT
ejpam-5694	211	12	i	i	NOUN
ejpam-5694	211	13	)	)	PUNCT
ejpam-5694	211	14	l1	l1	PROPN
ejpam-5694	211	15	(	(	PUNCT
ejpam-5694	211	16	.	.	PUNCT
ejpam-5694	211	17	)	)	PUNCT
ejpam-5694	212	1	=	=	PUNCT
ejpam-5694	213	1	∑	∑	PUNCT
ejpam-5694	213	2	κ	κ	PROPN
ejpam-5694	213	3	f	f	PROPN
ejpam-5694	213	4	(	(	PUNCT
ejpam-5694	213	5	κ)(a1	κ)(a1	X
ejpam-5694	213	6	)	)	PUNCT
ejpam-5694	213	7	κ	κ	NOUN
ejpam-5694	213	8	!	!	PUNCT
ejpam-5694	213	9	∫	∫	PROPN
ejpam-5694	213	10	a2	a2	PROPN
ejpam-5694	213	11	a1	a1	PROPN
ejpam-5694	213	12	gα	gα	PROPN
ejpam-5694	213	13	(	(	PUNCT
ejpam-5694	213	14	.	.	PUNCT
ejpam-5694	213	15	,	,	PUNCT
ejpam-5694	213	16	τ)(τ	τ)(τ	PROPN
ejpam-5694	213	17	−	−	PROPN
ejpam-5694	213	18	a1	a1	PROPN
ejpam-5694	213	19	)	)	PUNCT
ejpam-5694	213	20	κdτ	κdτ	NOUN
ejpam-5694	213	21	,	,	PUNCT
ejpam-5694	213	22	(	(	PUNCT
ejpam-5694	213	23	35	35	NUM
ejpam-5694	213	24	)	)	PUNCT
ejpam-5694	213	25	is	be	AUX
ejpam-5694	213	26	convex	convex	ADJ
ejpam-5694	213	27	on	on	ADP
ejpam-5694	213	28	[	[	X
ejpam-5694	213	29	a1	a1	NOUN
ejpam-5694	213	30	,	,	PUNCT
ejpam-5694	213	31	a2	a2	PROPN
ejpam-5694	213	32	]	]	PUNCT
ejpam-5694	213	33	,	,	PUNCT
ejpam-5694	213	34	then	then	ADV
ejpam-5694	213	35	∫	∫	PROPN
ejpam-5694	213	36	ω1	ω1	PROPN
ejpam-5694	213	37	f(akf(ϖ))u(ϖ)dµ1(ϖ	f(akf(ϖ))u(ϖ)dµ1(ϖ	PROPN
ejpam-5694	213	38	)	)	PUNCT
ejpam-5694	213	39	≤	≤	NUM
ejpam-5694	213	40	∫	∫	PROPN
ejpam-5694	213	41	ω2	ω2	PROPN
ejpam-5694	213	42	f(f(s))ν(s)dµ2(s	f(f(s))ν(s)dµ2(s	NUM
ejpam-5694	213	43	)	)	PUNCT
ejpam-5694	213	44	.	.	PUNCT
ejpam-5694	214	1	(	(	PUNCT
ejpam-5694	214	2	36	36	NUM
ejpam-5694	214	3	)	)	PUNCT
ejpam-5694	214	4	a.	a.	NOUN
ejpam-5694	214	5	m.	m.	PROPN
ejpam-5694	214	6	k.	k.	PROPN
ejpam-5694	214	7	abbasi	abbasi	PROPN
ejpam-5694	214	8	,	,	PUNCT
ejpam-5694	214	9	m.	m.	PROPN
ejpam-5694	214	10	anwar	anwar	PROPN
ejpam-5694	214	11	/	/	PUNCT
ejpam-5694	214	12	eur	eur	PROPN
ejpam-5694	214	13	.	.	PUNCT
ejpam-5694	215	1	j.	j.	PROPN
ejpam-5694	215	2	pure	pure	PROPN
ejpam-5694	215	3	appl	appl	PROPN
ejpam-5694	215	4	.	.	PROPN
ejpam-5694	215	5	math	math	PROPN
ejpam-5694	215	6	,	,	PUNCT
ejpam-5694	215	7	18	18	NUM
ejpam-5694	215	8	(	(	PUNCT
ejpam-5694	215	9	1	1	NUM
ejpam-5694	215	10	)	)	PUNCT
ejpam-5694	215	11	(	(	PUNCT
ejpam-5694	215	12	2025	2025	NUM
ejpam-5694	215	13	)	)	PUNCT
ejpam-5694	215	14	,	,	PUNCT
ejpam-5694	215	15	5694	5694	NUM
ejpam-5694	215	16	11	11	NUM
ejpam-5694	215	17	of	of	ADP
ejpam-5694	215	18	18	18	NUM
ejpam-5694	215	19	(	(	PUNCT
ejpam-5694	215	20	ii	ii	NOUN
ejpam-5694	215	21	)	)	PUNCT
ejpam-5694	215	22	l2	l2	NOUN
ejpam-5694	215	23	(	(	PUNCT
ejpam-5694	215	24	.	.	PUNCT
ejpam-5694	215	25	)	)	PUNCT
ejpam-5694	216	1	=	=	PUNCT
ejpam-5694	216	2	∑	∑	PUNCT
ejpam-5694	216	3	κ	κ	X
ejpam-5694	216	4	(	(	PUNCT
ejpam-5694	216	5	−1)κf	−1)κf	PROPN
ejpam-5694	216	6	(	(	PUNCT
ejpam-5694	216	7	κ)(a1	κ)(a1	X
ejpam-5694	216	8	)	)	PUNCT
ejpam-5694	216	9	κ	κ	NOUN
ejpam-5694	216	10	!	!	PUNCT
ejpam-5694	216	11	∫	∫	PROPN
ejpam-5694	216	12	a2	a2	PROPN
ejpam-5694	216	13	a1	a1	PROPN
ejpam-5694	216	14	gα	gα	PROPN
ejpam-5694	216	15	(	(	PUNCT
ejpam-5694	216	16	.	.	PUNCT
ejpam-5694	216	17	,	,	PUNCT
ejpam-5694	216	18	τ)(τ	τ)(τ	PROPN
ejpam-5694	216	19	−	−	PROPN
ejpam-5694	216	20	a1	a1	PROPN
ejpam-5694	216	21	)	)	PUNCT
ejpam-5694	216	22	κdτ	κdτ	NOUN
ejpam-5694	216	23	,	,	PUNCT
ejpam-5694	216	24	(	(	PUNCT
ejpam-5694	216	25	37	37	NUM
ejpam-5694	216	26	)	)	PUNCT
ejpam-5694	216	27	is	be	AUX
ejpam-5694	216	28	convex	convex	ADJ
ejpam-5694	216	29	on	on	ADP
ejpam-5694	216	30	[	[	X
ejpam-5694	216	31	a1	a1	NOUN
ejpam-5694	216	32	,	,	PUNCT
ejpam-5694	216	33	a2	a2	PROPN
ejpam-5694	216	34	]	]	PUNCT
ejpam-5694	216	35	,	,	PUNCT
ejpam-5694	216	36	then∫	then∫	NOUN
ejpam-5694	216	37	ω1	ω1	PROPN
ejpam-5694	216	38	f(akf(ϖ))u(ϖ)dµ1(ϖ	f(akf(ϖ))u(ϖ)dµ1(ϖ	NUM
ejpam-5694	216	39	)	)	PUNCT
ejpam-5694	216	40	≤	≤	NUM
ejpam-5694	216	41	∫	∫	PROPN
ejpam-5694	216	42	ω2	ω2	PROPN
ejpam-5694	216	43	f(f(s))ν(s)dµ2(s	f(f(s))ν(s)dµ2(s	NUM
ejpam-5694	216	44	)	)	PUNCT
ejpam-5694	216	45	.	.	PUNCT
ejpam-5694	217	1	proof	proof	NOUN
ejpam-5694	217	2	.	.	PUNCT
ejpam-5694	218	1	•	•	NUM
ejpam-5694	218	2	from	from	ADP
ejpam-5694	218	3	right	right	ADJ
ejpam-5694	218	4	hand	hand	NOUN
ejpam-5694	218	5	side	side	NOUN
ejpam-5694	218	6	of	of	ADP
ejpam-5694	218	7	(	(	PUNCT
ejpam-5694	218	8	32	32	NUM
ejpam-5694	218	9	)	)	PUNCT
ejpam-5694	218	10	we	we	PRON
ejpam-5694	218	11	can	can	AUX
ejpam-5694	218	12	write∫	write∫	VERB
ejpam-5694	218	13	ω2	ω2	PROPN
ejpam-5694	218	14	l1(f(s))ν(s)dµ2(s)−	l1(f(s))ν(s)dµ2(s)−	PROPN
ejpam-5694	218	15	∫	∫	PROPN
ejpam-5694	218	16	ω1	ω1	PROPN
ejpam-5694	218	17	l1(akf(ϖ))u(ϖ)dµ1(ϖ	l1(akf(ϖ))u(ϖ)dµ1(ϖ	PROPN
ejpam-5694	218	18	)	)	PUNCT
ejpam-5694	218	19	.	.	PUNCT
ejpam-5694	219	1	since	since	SCONJ
ejpam-5694	219	2	l1	l1	PROPN
ejpam-5694	219	3	is	be	AUX
ejpam-5694	219	4	convex	convex	PROPN
ejpam-5694	219	5	,	,	PUNCT
ejpam-5694	219	6	using	use	VERB
ejpam-5694	219	7	theorem	theorem	NOUN
ejpam-5694	219	8	1	1	NUM
ejpam-5694	219	9	we	we	PRON
ejpam-5694	219	10	find	find	VERB
ejpam-5694	219	11	that	that	SCONJ
ejpam-5694	219	12	the	the	DET
ejpam-5694	219	13	last	last	ADJ
ejpam-5694	219	14	relation	relation	NOUN
ejpam-5694	219	15	is	be	AUX
ejpam-5694	219	16	nonnegative	nonnegative	ADJ
ejpam-5694	219	17	.	.	PUNCT
ejpam-5694	220	1	consequently	consequently	ADV
ejpam-5694	220	2	,	,	PUNCT
ejpam-5694	220	3	our	our	PRON
ejpam-5694	220	4	stated	state	VERB
ejpam-5694	220	5	inequality	inequality	NOUN
ejpam-5694	220	6	results	result	VERB
ejpam-5694	220	7	from	from	ADP
ejpam-5694	220	8	(	(	PUNCT
ejpam-5694	220	9	32	32	NUM
ejpam-5694	220	10	)	)	PUNCT
ejpam-5694	220	11	.	.	PUNCT
ejpam-5694	221	1	•	•	NOUN
ejpam-5694	221	2	analogously	analogously	ADV
ejpam-5694	221	3	,	,	PUNCT
ejpam-5694	221	4	the	the	DET
ejpam-5694	221	5	assertion	assertion	NOUN
ejpam-5694	221	6	for	for	ADP
ejpam-5694	221	7	the	the	DET
ejpam-5694	221	8	functional	functional	ADJ
ejpam-5694	221	9	l2	l2	NOUN
ejpam-5694	221	10	can	can	AUX
ejpam-5694	221	11	be	be	AUX
ejpam-5694	221	12	derived	derive	VERB
ejpam-5694	221	13	from	from	ADP
ejpam-5694	221	14	(	(	PUNCT
ejpam-5694	221	15	33	33	NUM
ejpam-5694	221	16	)	)	PUNCT
ejpam-5694	221	17	.	.	PUNCT
ejpam-5694	222	1	4	4	X
ejpam-5694	222	2	.	.	NUM
ejpam-5694	222	3	bounds	bound	NOUN
ejpam-5694	222	4	on	on	ADP
ejpam-5694	222	5	remainders	remainder	NOUN
ejpam-5694	222	6	in	in	ADP
ejpam-5694	222	7	this	this	DET
ejpam-5694	222	8	section	section	NOUN
ejpam-5694	222	9	,	,	PUNCT
ejpam-5694	222	10	we	we	PRON
ejpam-5694	222	11	make	make	VERB
ejpam-5694	222	12	use	use	NOUN
ejpam-5694	222	13	of	of	ADP
ejpam-5694	222	14	the	the	DET
ejpam-5694	222	15	theorems	theorem	NOUN
ejpam-5694	222	16	2	2	NUM
ejpam-5694	222	17	and	and	CCONJ
ejpam-5694	222	18	3	3	NUM
ejpam-5694	222	19	to	to	PART
ejpam-5694	222	20	discuss	discuss	VERB
ejpam-5694	222	21	the	the	DET
ejpam-5694	222	22	grüss	grüss	PROPN
ejpam-5694	222	23	and	and	CCONJ
ejpam-5694	222	24	ostrowski	ostrowski	ADJ
ejpam-5694	222	25	-	-	PUNCT
ejpam-5694	222	26	type	type	NOUN
ejpam-5694	222	27	inequalities	inequality	NOUN
ejpam-5694	222	28	and	and	CCONJ
ejpam-5694	222	29	bounds	bound	NOUN
ejpam-5694	222	30	on	on	ADP
ejpam-5694	222	31	the	the	DET
ejpam-5694	222	32	remainders	remainder	NOUN
ejpam-5694	222	33	.	.	PUNCT
ejpam-5694	223	1	consider	consider	VERB
ejpam-5694	223	2	the	the	DET
ejpam-5694	223	3	following	follow	VERB
ejpam-5694	223	4	notations	notation	NOUN
ejpam-5694	223	5	for	for	ADP
ejpam-5694	223	6	the	the	DET
ejpam-5694	223	7	sake	sake	NOUN
ejpam-5694	223	8	of	of	ADP
ejpam-5694	223	9	brevity	brevity	NOUN
ejpam-5694	223	10	.	.	PUNCT
ejpam-5694	224	1	b1(τ	b1(τ	NOUN
ejpam-5694	224	2	)	)	PUNCT
ejpam-5694	224	3	=	=	SYM
ejpam-5694	224	4	∫	∫	PROPN
ejpam-5694	224	5	a2	a2	PROPN
ejpam-5694	224	6	a1	a1	PROPN
ejpam-5694	224	7	jgα(f	jgα(f	PROPN
ejpam-5694	224	8	,	,	PUNCT
ejpam-5694	224	9	τ)×	τ)×	X
ejpam-5694	224	10	(	(	PUNCT
ejpam-5694	224	11	τ	τ	X
ejpam-5694	224	12	−	−	PROPN
ejpam-5694	224	13	η)n−4	η)n−4	NOUN
ejpam-5694	224	14	+	+	X
ejpam-5694	224	15	dτ	dτ	PROPN
ejpam-5694	224	16	(	(	PUNCT
ejpam-5694	224	17	38	38	NUM
ejpam-5694	224	18	)	)	PUNCT
ejpam-5694	224	19	and	and	CCONJ
ejpam-5694	224	20	b2(τ	b2(τ	NUM
ejpam-5694	224	21	)	)	PUNCT
ejpam-5694	224	22	=	=	SYM
ejpam-5694	224	23	(	(	PUNCT
ejpam-5694	224	24	−1)n−4	−1)n−4	NOUN
ejpam-5694	224	25	∫	∫	PROPN
ejpam-5694	224	26	a2	a2	PROPN
ejpam-5694	224	27	a1	a1	PROPN
ejpam-5694	224	28	jgα(f	jgα(f	PROPN
ejpam-5694	224	29	,	,	PUNCT
ejpam-5694	224	30	τ)×	τ)×	X
ejpam-5694	224	31	(	(	PUNCT
ejpam-5694	224	32	τ	τ	X
ejpam-5694	224	33	−	−	PROPN
ejpam-5694	224	34	η)n−4	η)n−4	NOUN
ejpam-5694	224	35	+	+	CCONJ
ejpam-5694	224	36	dτ	dτ	PROPN
ejpam-5694	224	37	.	.	PROPN
ejpam-5694	224	38	(	(	PUNCT
ejpam-5694	224	39	39	39	NUM
ejpam-5694	224	40	)	)	PUNCT
ejpam-5694	224	41	theorem	theorem	VERB
ejpam-5694	224	42	7	7	NUM
ejpam-5694	224	43	.	.	PUNCT
ejpam-5694	225	1	let	let	VERB
ejpam-5694	225	2	f	f	PRON
ejpam-5694	225	3	be	be	AUX
ejpam-5694	225	4	defined	define	VERB
ejpam-5694	225	5	on	on	ADP
ejpam-5694	225	6	t	t	PROPN
ejpam-5694	225	7	,	,	PUNCT
ejpam-5694	225	8	for	for	ADP
ejpam-5694	225	9	n	n	PRON
ejpam-5694	225	10	∈	∈	PROPN
ejpam-5694	225	11	n	n	CCONJ
ejpam-5694	225	12	,	,	PUNCT
ejpam-5694	225	13	f	f	PROPN
ejpam-5694	225	14	(	(	PUNCT
ejpam-5694	225	15	n−1	n−1	PROPN
ejpam-5694	225	16	)	)	PUNCT
ejpam-5694	225	17	has	have	VERB
ejpam-5694	225	18	the	the	DET
ejpam-5694	225	19	property	property	NOUN
ejpam-5694	225	20	that	that	PRON
ejpam-5694	225	21	it	it	PRON
ejpam-5694	225	22	is	be	AUX
ejpam-5694	225	23	absolutely	absolutely	ADV
ejpam-5694	225	24	continuous	continuous	ADJ
ejpam-5694	225	25	therein	therein	ADV
ejpam-5694	225	26	and	and	CCONJ
ejpam-5694	225	27	(	(	PUNCT
ejpam-5694	225	28	τ	τ	PROPN
ejpam-5694	225	29	−	−	PROPN
ejpam-5694	225	30	a1)(a2	a1)(a2	PROPN
ejpam-5694	225	31	−	−	PROPN
ejpam-5694	225	32	τ)[f	τ)[f	NOUN
ejpam-5694	225	33	(	(	PUNCT
ejpam-5694	225	34	n+1)]2	n+1)]2	PROPN
ejpam-5694	225	35	∈	∈	PROPN
ejpam-5694	225	36	l1([a1	l1([a1	NOUN
ejpam-5694	225	37	,	,	PUNCT
ejpam-5694	225	38	a2	a2	PROPN
ejpam-5694	225	39	]	]	PUNCT
ejpam-5694	225	40	)	)	PUNCT
ejpam-5694	225	41	.	.	PUNCT
ejpam-5694	226	1	let	let	VERB
ejpam-5694	226	2	(	(	PUNCT
ejpam-5694	226	3	∑	∑	ADV
ejpam-5694	226	4	1,ω1	1,ω1	NUM
ejpam-5694	226	5	,	,	PUNCT
ejpam-5694	226	6	σ1	σ1	PROPN
ejpam-5694	226	7	)	)	PUNCT
ejpam-5694	226	8	and	and	CCONJ
ejpam-5694	226	9	(	(	PUNCT
ejpam-5694	226	10	∑	∑	PROPN
ejpam-5694	226	11	2,ω2	2,ω2	NUM
ejpam-5694	226	12	,	,	PUNCT
ejpam-5694	226	13	σ2	σ2	NOUN
ejpam-5694	226	14	)	)	PUNCT
ejpam-5694	226	15	with	with	ADP
ejpam-5694	226	16	positive	positive	ADJ
ejpam-5694	226	17	σ−finite	σ−finite	PROPN
ejpam-5694	226	18	measures	measure	NOUN
ejpam-5694	226	19	,	,	PUNCT
ejpam-5694	226	20	ak	ak	PROPN
ejpam-5694	226	21	and	and	CCONJ
ejpam-5694	226	22	k	k	PROPN
ejpam-5694	226	23	are	be	AUX
ejpam-5694	226	24	given	give	VERB
ejpam-5694	226	25	in	in	ADP
ejpam-5694	226	26	(	(	PUNCT
ejpam-5694	226	27	15	15	NUM
ejpam-5694	226	28	)	)	PUNCT
ejpam-5694	226	29	and	and	CCONJ
ejpam-5694	226	30	(	(	PUNCT
ejpam-5694	226	31	16	16	NUM
ejpam-5694	226	32	)	)	PUNCT
ejpam-5694	226	33	respectively	respectively	ADV
ejpam-5694	226	34	.	.	PUNCT
ejpam-5694	227	1	let	let	VERB
ejpam-5694	227	2	gα	gα	VERB
ejpam-5694	227	3	,	,	PUNCT
ejpam-5694	227	4	{	{	PUNCT
ejpam-5694	227	5	α	α	NOUN
ejpam-5694	227	6	=	=	SYM
ejpam-5694	227	7	1	1	NUM
ejpam-5694	227	8	,	,	PUNCT
ejpam-5694	227	9	2	2	NUM
ejpam-5694	227	10	,	,	PUNCT
ejpam-5694	227	11	3	3	NUM
ejpam-5694	227	12	,	,	PUNCT
ejpam-5694	227	13	4	4	NUM
ejpam-5694	227	14	}	}	PUNCT
ejpam-5694	227	15	be	be	AUX
ejpam-5694	227	16	defined	define	VERB
ejpam-5694	227	17	in	in	ADP
ejpam-5694	227	18	(	(	PUNCT
ejpam-5694	227	19	5	5	NUM
ejpam-5694	227	20	)	)	PUNCT
ejpam-5694	227	21	,	,	PUNCT
ejpam-5694	227	22	(	(	PUNCT
ejpam-5694	227	23	6	6	NUM
ejpam-5694	227	24	)	)	PUNCT
ejpam-5694	227	25	,	,	PUNCT
ejpam-5694	227	26	(	(	PUNCT
ejpam-5694	227	27	7	7	X
ejpam-5694	227	28	)	)	PUNCT
ejpam-5694	227	29	and	and	CCONJ
ejpam-5694	227	30	(	(	PUNCT
ejpam-5694	227	31	8)	8)	NUM
ejpam-5694	227	32	respectively	respectively	ADV
ejpam-5694	227	33	,	,	PUNCT
ejpam-5694	227	34	jgα	jgα	PROPN
ejpam-5694	227	35	is	be	AUX
ejpam-5694	227	36	defined	define	VERB
ejpam-5694	227	37	in	in	ADP
ejpam-5694	227	38	(	(	PUNCT
ejpam-5694	227	39	26	26	NUM
ejpam-5694	227	40	)	)	PUNCT
ejpam-5694	227	41	u	u	NOUN
ejpam-5694	227	42	:	:	PUNCT
ejpam-5694	227	43	ω1	ω1	PROPN
ejpam-5694	227	44	→	→	SYM
ejpam-5694	227	45	r	r	NOUN
ejpam-5694	227	46	be	be	VERB
ejpam-5694	227	47	the	the	DET
ejpam-5694	227	48	weight	weight	NOUN
ejpam-5694	227	49	function	function	NOUN
ejpam-5694	227	50	and	and	CCONJ
ejpam-5694	227	51	v	v	NOUN
ejpam-5694	227	52	is	be	AUX
ejpam-5694	227	53	given	give	VERB
ejpam-5694	227	54	in	in	ADP
ejpam-5694	227	55	(	(	PUNCT
ejpam-5694	227	56	17	17	NUM
ejpam-5694	227	57	)	)	PUNCT
ejpam-5694	227	58	and	and	CCONJ
ejpam-5694	227	59	b1,b2	b1,b2	PROPN
ejpam-5694	227	60	are	be	AUX
ejpam-5694	227	61	given	give	VERB
ejpam-5694	227	62	in	in	ADP
ejpam-5694	227	63	(	(	PUNCT
ejpam-5694	227	64	38	38	NUM
ejpam-5694	227	65	)	)	PUNCT
ejpam-5694	227	66	and	and	CCONJ
ejpam-5694	227	67	(	(	PUNCT
ejpam-5694	227	68	39	39	NUM
ejpam-5694	227	69	)	)	PUNCT
ejpam-5694	227	70	respectively	respectively	ADV
ejpam-5694	227	71	and	and	CCONJ
ejpam-5694	227	72	f	f	PROPN
ejpam-5694	227	73	is	be	AUX
ejpam-5694	227	74	measurable	measurable	ADJ
ejpam-5694	227	75	,	,	PUNCT
ejpam-5694	227	76	then	then	ADV
ejpam-5694	227	77	;	;	PUNCT
ejpam-5694	227	78	(	(	PUNCT
ejpam-5694	227	79	i	i	NOUN
ejpam-5694	227	80	)	)	PUNCT
ejpam-5694	227	81	the	the	DET
ejpam-5694	227	82	remainder	remainder	NOUN
ejpam-5694	227	83	r1	r1	NOUN
ejpam-5694	227	84	is	be	AUX
ejpam-5694	227	85	r1(f	r1(f	PROPN
ejpam-5694	227	86	;	;	PUNCT
ejpam-5694	227	87	a1	a1	PROPN
ejpam-5694	227	88	,	,	PUNCT
ejpam-5694	227	89	a2	a2	PROPN
ejpam-5694	227	90	)	)	PUNCT
ejpam-5694	227	91	a.	a.	NOUN
ejpam-5694	227	92	m.	m.	PROPN
ejpam-5694	227	93	k.	k.	PROPN
ejpam-5694	227	94	abbasi	abbasi	PROPN
ejpam-5694	227	95	,	,	PUNCT
ejpam-5694	227	96	m.	m.	PROPN
ejpam-5694	227	97	anwar	anwar	PROPN
ejpam-5694	227	98	/	/	PUNCT
ejpam-5694	227	99	eur	eur	PROPN
ejpam-5694	227	100	.	.	PUNCT
ejpam-5694	228	1	j.	j.	PROPN
ejpam-5694	228	2	pure	pure	PROPN
ejpam-5694	228	3	appl	appl	PROPN
ejpam-5694	228	4	.	.	PROPN
ejpam-5694	228	5	math	math	PROPN
ejpam-5694	228	6	,	,	PUNCT
ejpam-5694	228	7	18	18	NUM
ejpam-5694	228	8	(	(	PUNCT
ejpam-5694	228	9	1	1	NUM
ejpam-5694	228	10	)	)	PUNCT
ejpam-5694	228	11	(	(	PUNCT
ejpam-5694	228	12	2025	2025	NUM
ejpam-5694	228	13	)	)	PUNCT
ejpam-5694	228	14	,	,	PUNCT
ejpam-5694	228	15	5694	5694	NUM
ejpam-5694	228	16	12	12	NUM
ejpam-5694	228	17	of	of	ADP
ejpam-5694	228	18	18	18	NUM
ejpam-5694	228	19	=	=	SYM
ejpam-5694	228	20	∫	∫	PROPN
ejpam-5694	229	1	ω2	ω2	PROPN
ejpam-5694	229	2	f(f(s))ν(s)dµ2(s)−	f(f(s))ν(s)dµ2(s)−	PROPN
ejpam-5694	229	3	∫	∫	PROPN
ejpam-5694	229	4	ω1	ω1	PROPN
ejpam-5694	229	5	f(akf(ϖ))u(ϖ)dµ1(ϖ	f(akf(ϖ))u(ϖ)dµ1(ϖ	PROPN
ejpam-5694	229	6	)	)	PUNCT
ejpam-5694	229	7	−	−	PROPN
ejpam-5694	230	1	∑	∑	PUNCT
ejpam-5694	230	2	κ	κ	PROPN
ejpam-5694	230	3	f	f	PROPN
ejpam-5694	230	4	(	(	PUNCT
ejpam-5694	230	5	κ)(a1	κ)(a1	X
ejpam-5694	230	6	)	)	PUNCT
ejpam-5694	230	7	κ	κ	NOUN
ejpam-5694	230	8	!	!	PUNCT
ejpam-5694	230	9	∫	∫	PROPN
ejpam-5694	230	10	a2	a2	PROPN
ejpam-5694	230	11	a1	a1	PROPN
ejpam-5694	230	12	jgα(f	jgα(f	PROPN
ejpam-5694	230	13	,	,	PUNCT
ejpam-5694	230	14	τ)(τ	τ)(τ	PROPN
ejpam-5694	230	15	−	−	PROPN
ejpam-5694	230	16	a1	a1	NOUN
ejpam-5694	230	17	)	)	PUNCT
ejpam-5694	230	18	κdτ	κdτ	NOUN
ejpam-5694	230	19	−f	−f	NOUN
ejpam-5694	230	20	(	(	PUNCT
ejpam-5694	230	21	n−1)(a2)−f	n−1)(a2)−f	X
ejpam-5694	230	22	(	(	PUNCT
ejpam-5694	230	23	n−1)(a1	n−1)(a1	NOUN
ejpam-5694	230	24	)	)	PUNCT
ejpam-5694	230	25	(	(	PUNCT
ejpam-5694	230	26	a2	a2	PROPN
ejpam-5694	230	27	−	−	PROPN
ejpam-5694	230	28	a1)(n−	a1)(n−	NUM
ejpam-5694	230	29	4	4	NUM
ejpam-5694	230	30	)	)	PUNCT
ejpam-5694	230	31	!	!	PUNCT
ejpam-5694	231	1	∫	∫	PROPN
ejpam-5694	231	2	a2	a2	PROPN
ejpam-5694	231	3	a1	a1	PROPN
ejpam-5694	231	4	b1(τ)dτ	b1(τ)dτ	NOUN
ejpam-5694	231	5	,	,	PUNCT
ejpam-5694	231	6	(	(	PUNCT
ejpam-5694	231	7	40	40	NUM
ejpam-5694	231	8	)	)	PUNCT
ejpam-5694	231	9	bounded	bound	VERB
ejpam-5694	231	10	by	by	ADP
ejpam-5694	231	11	|r1(f	|r1(f	PROPN
ejpam-5694	231	12	;	;	PUNCT
ejpam-5694	231	13	a1	a1	PROPN
ejpam-5694	231	14	,	,	PUNCT
ejpam-5694	231	15	a2)|	a2)|	PROPN
ejpam-5694	231	16	≤	≤	PROPN
ejpam-5694	231	17	√	√	NUM
ejpam-5694	231	18	a2	a2	PROPN
ejpam-5694	231	19	−	−	PROPN
ejpam-5694	232	1	a1√	a1√	NOUN
ejpam-5694	232	2	2(n−	2(n−	NUM
ejpam-5694	232	3	4	4	NUM
ejpam-5694	232	4	)	)	PUNCT
ejpam-5694	232	5	!	!	PUNCT
ejpam-5694	233	1	(	(	PUNCT
ejpam-5694	233	2	f(b1,b1	f(b1,b1	NOUN
ejpam-5694	233	3	)	)	PUNCT
ejpam-5694	233	4	)	)	PUNCT
ejpam-5694	233	5	1	1	NUM
ejpam-5694	233	6	2	2	NUM
ejpam-5694	233	7	(	(	PUNCT
ejpam-5694	233	8	∫	∫	PROPN
ejpam-5694	233	9	a2	a2	PROPN
ejpam-5694	233	10	a1	a1	PROPN
ejpam-5694	233	11	(	(	PUNCT
ejpam-5694	233	12	τ	τ	PROPN
ejpam-5694	233	13	−	−	PROPN
ejpam-5694	233	14	a1)(a2	a1)(a2	PROPN
ejpam-5694	234	1	−	−	PROPN
ejpam-5694	234	2	τ)[f	τ)[f	PROPN
ejpam-5694	234	3	(	(	PUNCT
ejpam-5694	234	4	n+1)]2dτ	n+1)]2dτ	PROPN
ejpam-5694	234	5	)	)	PUNCT
ejpam-5694	234	6	1	1	NUM
ejpam-5694	234	7	2	2	NUM
ejpam-5694	234	8	.(41	.(41	NUM
ejpam-5694	234	9	)	)	PUNCT
ejpam-5694	234	10	(	(	PUNCT
ejpam-5694	234	11	ii	ii	NOUN
ejpam-5694	234	12	)	)	PUNCT
ejpam-5694	234	13	and	and	CCONJ
ejpam-5694	234	14	the	the	DET
ejpam-5694	234	15	remainder	remainder	NOUN
ejpam-5694	234	16	r2	r2	NOUN
ejpam-5694	234	17	is	be	AUX
ejpam-5694	234	18	r2(f	r2(f	X
ejpam-5694	234	19	;	;	PUNCT
ejpam-5694	234	20	a1	a1	NOUN
ejpam-5694	234	21	,	,	PUNCT
ejpam-5694	234	22	a2	a2	PROPN
ejpam-5694	234	23	)	)	PUNCT
ejpam-5694	234	24	=	=	SYM
ejpam-5694	235	1	∫	∫	PROPN
ejpam-5694	236	1	ω2	ω2	PROPN
ejpam-5694	236	2	f(f(s))ν(s)dµ2(s)−	f(f(s))ν(s)dµ2(s)−	PROPN
ejpam-5694	237	1	∫	∫	PROPN
ejpam-5694	238	1	ω1	ω1	PROPN
ejpam-5694	238	2	f(akf(ϖ))u(ϖ)dµ1(ϖ	f(akf(ϖ))u(ϖ)dµ1(ϖ	PROPN
ejpam-5694	238	3	)	)	PUNCT
ejpam-5694	239	1	−	−	PROPN
ejpam-5694	239	2	∑	∑	PUNCT
ejpam-5694	239	3	κ	κ	PROPN
ejpam-5694	239	4	(	(	PUNCT
ejpam-5694	239	5	−1)κf	−1)κf	PROPN
ejpam-5694	239	6	(	(	PUNCT
ejpam-5694	239	7	κ)(a2	κ)(a2	NOUN
ejpam-5694	239	8	)	)	PUNCT
ejpam-5694	239	9	κ	κ	NOUN
ejpam-5694	239	10	!	!	PUNCT
ejpam-5694	239	11	∫	∫	PROPN
ejpam-5694	239	12	a2	a2	PROPN
ejpam-5694	239	13	a1	a1	PROPN
ejpam-5694	239	14	jgα(f	jgα(f	PROPN
ejpam-5694	239	15	,	,	PUNCT
ejpam-5694	239	16	τ)(a2	τ)(a2	PROPN
ejpam-5694	239	17	−	−	ADP
ejpam-5694	239	18	τ)κdτ	τ)κdτ	PROPN
ejpam-5694	239	19	−f	−f	NOUN
ejpam-5694	239	20	(	(	PUNCT
ejpam-5694	239	21	n−1)(a2)−f	n−1)(a2)−f	X
ejpam-5694	239	22	(	(	PUNCT
ejpam-5694	239	23	n−1)(a1	n−1)(a1	NOUN
ejpam-5694	239	24	)	)	PUNCT
ejpam-5694	239	25	(	(	PUNCT
ejpam-5694	239	26	a2	a2	PROPN
ejpam-5694	239	27	−	−	PROPN
ejpam-5694	239	28	a1)(n−	a1)(n−	NUM
ejpam-5694	239	29	4	4	NUM
ejpam-5694	239	30	)	)	PUNCT
ejpam-5694	239	31	!	!	PUNCT
ejpam-5694	240	1	∫	∫	PROPN
ejpam-5694	240	2	a2	a2	PROPN
ejpam-5694	240	3	a1	a1	PROPN
ejpam-5694	240	4	b2(τ)dτ	b2(τ)dτ	ADV
ejpam-5694	240	5	,	,	PUNCT
ejpam-5694	240	6	(	(	PUNCT
ejpam-5694	240	7	42	42	NUM
ejpam-5694	240	8	)	)	PUNCT
ejpam-5694	240	9	bounded	bound	VERB
ejpam-5694	240	10	by	by	ADP
ejpam-5694	240	11	|r2(f	|r2(f	NOUN
ejpam-5694	240	12	;	;	PUNCT
ejpam-5694	240	13	a1	a1	PROPN
ejpam-5694	240	14	,	,	PUNCT
ejpam-5694	240	15	a2)|	a2)|	PROPN
ejpam-5694	240	16	≤	≤	PROPN
ejpam-5694	240	17	√	√	NUM
ejpam-5694	240	18	a2	a2	PROPN
ejpam-5694	240	19	−	−	PROPN
ejpam-5694	241	1	a1√	a1√	NOUN
ejpam-5694	242	1	2(n−	2(n−	NUM
ejpam-5694	242	2	4	4	NUM
ejpam-5694	242	3	)	)	PUNCT
ejpam-5694	242	4	!	!	PUNCT
ejpam-5694	243	1	(	(	PUNCT
ejpam-5694	243	2	f(b2,b2	f(b2,b2	NOUN
ejpam-5694	243	3	)	)	PUNCT
ejpam-5694	243	4	)	)	PUNCT
ejpam-5694	244	1	1	1	NUM
ejpam-5694	244	2	2	2	NUM
ejpam-5694	244	3	(	(	PUNCT
ejpam-5694	244	4	∫	∫	PROPN
ejpam-5694	244	5	a2	a2	PROPN
ejpam-5694	244	6	a1	a1	PROPN
ejpam-5694	244	7	(	(	PUNCT
ejpam-5694	244	8	τ	τ	PROPN
ejpam-5694	244	9	−	−	PROPN
ejpam-5694	244	10	a1)(a2	a1)(a2	PROPN
ejpam-5694	244	11	−	−	PROPN
ejpam-5694	244	12	τ)[f	τ)[f	PROPN
ejpam-5694	244	13	(	(	PUNCT
ejpam-5694	244	14	n+1)]2dτ	n+1)]2dτ	PROPN
ejpam-5694	244	15	)	)	PUNCT
ejpam-5694	244	16	1	1	NUM
ejpam-5694	244	17	2	2	NUM
ejpam-5694	244	18	.(43	.(43	NUM
ejpam-5694	244	19	)	)	PUNCT
ejpam-5694	244	20	proof	proof	NOUN
ejpam-5694	244	21	.	.	PUNCT
ejpam-5694	245	1	•	•	NUM
ejpam-5694	245	2	from	from	ADP
ejpam-5694	245	3	(	(	PUNCT
ejpam-5694	245	4	24	24	NUM
ejpam-5694	245	5	)	)	PUNCT
ejpam-5694	245	6	and	and	CCONJ
ejpam-5694	245	7	(	(	PUNCT
ejpam-5694	245	8	40	40	NUM
ejpam-5694	245	9	)	)	PUNCT
ejpam-5694	245	10	we	we	PRON
ejpam-5694	245	11	have	have	VERB
ejpam-5694	245	12	r1(f	r1(f	NUM
ejpam-5694	245	13	;	;	PUNCT
ejpam-5694	245	14	a1	a1	PROPN
ejpam-5694	245	15	,	,	PUNCT
ejpam-5694	245	16	a2	a2	PROPN
ejpam-5694	245	17	)	)	PUNCT
ejpam-5694	245	18	=	=	SYM
ejpam-5694	246	1	1	1	NUM
ejpam-5694	246	2	(	(	PUNCT
ejpam-5694	246	3	n−	n−	NOUN
ejpam-5694	246	4	4	4	NUM
ejpam-5694	246	5	)	)	PUNCT
ejpam-5694	246	6	!	!	PUNCT
ejpam-5694	247	1	(	(	PUNCT
ejpam-5694	247	2	∫	∫	PROPN
ejpam-5694	247	3	a2	a2	PROPN
ejpam-5694	247	4	a1	a1	PROPN
ejpam-5694	247	5	b1(τ)f	b1(τ)f	NOUN
ejpam-5694	247	6	(	(	PUNCT
ejpam-5694	247	7	n)(τ)dτ	n)(τ)dτ	NOUN
ejpam-5694	247	8	−	−	PROPN
ejpam-5694	247	9	f	f	PROPN
ejpam-5694	247	10	(	(	PUNCT
ejpam-5694	247	11	n−1)(a2)−f	n−1)(a2)−f	X
ejpam-5694	247	12	(	(	PUNCT
ejpam-5694	247	13	n−1)(a1	n−1)(a1	NOUN
ejpam-5694	247	14	)	)	PUNCT
ejpam-5694	247	15	(	(	PUNCT
ejpam-5694	247	16	a2	a2	PROPN
ejpam-5694	247	17	−	−	PROPN
ejpam-5694	247	18	a1	a1	PROPN
ejpam-5694	247	19	)	)	PUNCT
ejpam-5694	247	20	∫	∫	PROPN
ejpam-5694	247	21	a2	a2	PROPN
ejpam-5694	247	22	a1	a1	PROPN
ejpam-5694	247	23	b1(τ)dτ	b1(τ)dτ	NOUN
ejpam-5694	247	24	)	)	PUNCT
ejpam-5694	247	25	.(44	.(44	PUNCT
ejpam-5694	247	26	)	)	PUNCT
ejpam-5694	248	1	taking	take	VERB
ejpam-5694	248	2	f	f	NOUN
ejpam-5694	248	3	=	=	PUNCT
ejpam-5694	248	4	b1	b1	PROPN
ejpam-5694	248	5	and	and	CCONJ
ejpam-5694	248	6	g	g	NOUN
ejpam-5694	248	7	=	=	SYM
ejpam-5694	248	8	f	f	PROPN
ejpam-5694	248	9	(	(	PUNCT
ejpam-5694	248	10	n	n	CCONJ
ejpam-5694	248	11	)	)	PUNCT
ejpam-5694	248	12	along	along	ADP
ejpam-5694	248	13	with	with	ADP
ejpam-5694	248	14	(	(	PUNCT
ejpam-5694	248	15	44	44	NUM
ejpam-5694	248	16	)	)	PUNCT
ejpam-5694	248	17	,	,	PUNCT
ejpam-5694	248	18	then	then	ADV
ejpam-5694	248	19	using	use	VERB
ejpam-5694	248	20	theorem	theorem	NOUN
ejpam-5694	248	21	2	2	NUM
ejpam-5694	248	22	we	we	PRON
ejpam-5694	248	23	obtain	obtain	VERB
ejpam-5694	248	24	1	1	NUM
ejpam-5694	248	25	a2	a2	NOUN
ejpam-5694	248	26	−	−	PROPN
ejpam-5694	248	27	a1	a1	PROPN
ejpam-5694	248	28	∣∣∣r1(f	∣∣∣r1(f	PROPN
ejpam-5694	248	29	;	;	PUNCT
ejpam-5694	248	30	a1	a1	PROPN
ejpam-5694	248	31	,	,	PUNCT
ejpam-5694	248	32	a2	a2	NOUN
ejpam-5694	248	33	)	)	PUNCT
ejpam-5694	248	34	∣∣∣	∣∣∣	NOUN
ejpam-5694	249	1	=	=	SYM
ejpam-5694	249	2	1	1	X
ejpam-5694	249	3	(	(	PUNCT
ejpam-5694	249	4	n−	n−	NOUN
ejpam-5694	249	5	4	4	NUM
ejpam-5694	249	6	)	)	PUNCT
ejpam-5694	249	7	!	!	PUNCT
ejpam-5694	250	1	∣∣∣∣∣	∣∣∣∣∣	ADJ
ejpam-5694	250	2	1	1	NUM
ejpam-5694	250	3	a2	a2	PROPN
ejpam-5694	250	4	−	−	PROPN
ejpam-5694	250	5	a1	a1	PROPN
ejpam-5694	250	6	∫	∫	PROPN
ejpam-5694	250	7	a2	a2	PROPN
ejpam-5694	250	8	a1	a1	PROPN
ejpam-5694	250	9	b1(τ)f	b1(τ)f	NOUN
ejpam-5694	250	10	(	(	PUNCT
ejpam-5694	250	11	n)(τ)dτ	n)(τ)dτ	NOUN
ejpam-5694	250	12	−	−	PROPN
ejpam-5694	250	13	1	1	NUM
ejpam-5694	250	14	(	(	PUNCT
ejpam-5694	250	15	a2	a2	PROPN
ejpam-5694	250	16	−	−	PROPN
ejpam-5694	250	17	a1	a1	PROPN
ejpam-5694	250	18	)	)	PUNCT
ejpam-5694	250	19	∫	∫	PROPN
ejpam-5694	250	20	a2	a2	PROPN
ejpam-5694	250	21	a1	a1	PROPN
ejpam-5694	250	22	b1(τ)dτ	b1(τ)dτ	NOUN
ejpam-5694	250	23	1	1	NUM
ejpam-5694	250	24	(	(	PUNCT
ejpam-5694	250	25	a2	a2	PROPN
ejpam-5694	250	26	−	−	PROPN
ejpam-5694	250	27	a1	a1	PROPN
ejpam-5694	250	28	)	)	PUNCT
ejpam-5694	250	29	∫	∫	PROPN
ejpam-5694	250	30	a2	a2	PROPN
ejpam-5694	250	31	a1	a1	PROPN
ejpam-5694	250	32	f	f	PROPN
ejpam-5694	250	33	(	(	PUNCT
ejpam-5694	250	34	n)(τ)dτ	n)(τ)dτ	PROPN
ejpam-5694	250	35	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5694	250	36	≤	≤	PROPN
ejpam-5694	250	37	1√	1√	PROPN
ejpam-5694	250	38	2(n−	2(n−	NUM
ejpam-5694	250	39	4	4	NUM
ejpam-5694	250	40	)	)	PUNCT
ejpam-5694	250	41	!	!	PUNCT
ejpam-5694	251	1	1√	1√	PROPN
ejpam-5694	251	2	a2	a2	PROPN
ejpam-5694	251	3	−	−	PROPN
ejpam-5694	251	4	a1	a1	NOUN
ejpam-5694	251	5	(	(	PUNCT
ejpam-5694	251	6	f(b1,b1	f(b1,b1	NOUN
ejpam-5694	251	7	)	)	PUNCT
ejpam-5694	251	8	)	)	PUNCT
ejpam-5694	251	9	1	1	NUM
ejpam-5694	251	10	2	2	NUM
ejpam-5694	251	11	(	(	PUNCT
ejpam-5694	251	12	∫	∫	PROPN
ejpam-5694	251	13	a2	a2	PROPN
ejpam-5694	251	14	a1	a1	PROPN
ejpam-5694	251	15	(	(	PUNCT
ejpam-5694	251	16	τ	τ	PROPN
ejpam-5694	251	17	−	−	PROPN
ejpam-5694	251	18	a1)(a2	a1)(a2	PROPN
ejpam-5694	251	19	−	−	PROPN
ejpam-5694	251	20	τ)[f	τ)[f	PROPN
ejpam-5694	251	21	(	(	PUNCT
ejpam-5694	251	22	n+1)]2dτ	n+1)]2dτ	PROPN
ejpam-5694	251	23	)	)	PUNCT
ejpam-5694	251	24	1	1	NUM
ejpam-5694	251	25	2	2	NUM
ejpam-5694	251	26	.	.	PUNCT
ejpam-5694	252	1	(	(	PUNCT
ejpam-5694	252	2	45	45	NUM
ejpam-5694	252	3	)	)	PUNCT
ejpam-5694	252	4	after	after	ADP
ejpam-5694	252	5	simplification	simplification	NOUN
ejpam-5694	252	6	of	of	ADP
ejpam-5694	252	7	involved	involved	ADJ
ejpam-5694	252	8	integral	integral	ADJ
ejpam-5694	252	9	we	we	PRON
ejpam-5694	252	10	get	get	VERB
ejpam-5694	252	11	the	the	DET
ejpam-5694	252	12	required	require	VERB
ejpam-5694	252	13	result	result	NOUN
ejpam-5694	252	14	.	.	PUNCT
ejpam-5694	253	1	a.	a.	PROPN
ejpam-5694	253	2	m.	m.	PROPN
ejpam-5694	253	3	k.	k.	PROPN
ejpam-5694	253	4	abbasi	abbasi	PROPN
ejpam-5694	253	5	,	,	PUNCT
ejpam-5694	253	6	m.	m.	PROPN
ejpam-5694	253	7	anwar	anwar	PROPN
ejpam-5694	253	8	/	/	PUNCT
ejpam-5694	253	9	eur	eur	PROPN
ejpam-5694	253	10	.	.	PUNCT
ejpam-5694	254	1	j.	j.	PROPN
ejpam-5694	254	2	pure	pure	PROPN
ejpam-5694	254	3	appl	appl	PROPN
ejpam-5694	254	4	.	.	PROPN
ejpam-5694	254	5	math	math	PROPN
ejpam-5694	254	6	,	,	PUNCT
ejpam-5694	254	7	18	18	NUM
ejpam-5694	254	8	(	(	PUNCT
ejpam-5694	254	9	1	1	NUM
ejpam-5694	254	10	)	)	PUNCT
ejpam-5694	254	11	(	(	PUNCT
ejpam-5694	254	12	2025	2025	NUM
ejpam-5694	254	13	)	)	PUNCT
ejpam-5694	254	14	,	,	PUNCT
ejpam-5694	254	15	5694	5694	NUM
ejpam-5694	254	16	13	13	NUM
ejpam-5694	254	17	of	of	ADP
ejpam-5694	254	18	18	18	NUM
ejpam-5694	254	19	•	•	NOUN
ejpam-5694	254	20	following	follow	VERB
ejpam-5694	254	21	similar	similar	ADJ
ejpam-5694	254	22	steps	step	NOUN
ejpam-5694	254	23	of	of	ADP
ejpam-5694	254	24	first	first	ADJ
ejpam-5694	254	25	part	part	NOUN
ejpam-5694	254	26	we	we	PRON
ejpam-5694	254	27	obtain	obtain	VERB
ejpam-5694	254	28	the	the	DET
ejpam-5694	254	29	required	require	VERB
ejpam-5694	254	30	result	result	NOUN
ejpam-5694	254	31	.	.	PUNCT
ejpam-5694	255	1	now	now	ADV
ejpam-5694	255	2	we	we	PRON
ejpam-5694	255	3	use	use	VERB
ejpam-5694	255	4	theorem	theorem	NOUN
ejpam-5694	255	5	3	3	NUM
ejpam-5694	255	6	to	to	PART
ejpam-5694	255	7	discuss	discuss	VERB
ejpam-5694	255	8	the	the	DET
ejpam-5694	255	9	grüss	grüss	NOUN
ejpam-5694	255	10	-	-	PUNCT
ejpam-5694	255	11	type	type	NOUN
ejpam-5694	255	12	inequalities	inequality	NOUN
ejpam-5694	255	13	that	that	PRON
ejpam-5694	255	14	enable	enable	VERB
ejpam-5694	255	15	us	we	PRON
ejpam-5694	255	16	to	to	PART
ejpam-5694	255	17	find	find	VERB
ejpam-5694	255	18	the	the	DET
ejpam-5694	255	19	bounds	bound	NOUN
ejpam-5694	255	20	of	of	ADP
ejpam-5694	255	21	remainder	remainder	NOUN
ejpam-5694	255	22	.	.	PUNCT
ejpam-5694	256	1	theorem	theorem	ADJ
ejpam-5694	256	2	8	8	NUM
ejpam-5694	256	3	.	.	PUNCT
ejpam-5694	257	1	let	let	VERB
ejpam-5694	257	2	(	(	PUNCT
ejpam-5694	257	3	∑	∑	ADV
ejpam-5694	257	4	1,ω1	1,ω1	NUM
ejpam-5694	257	5	,	,	PUNCT
ejpam-5694	257	6	σ1	σ1	PROPN
ejpam-5694	257	7	)	)	PUNCT
ejpam-5694	257	8	and	and	CCONJ
ejpam-5694	257	9	(	(	PUNCT
ejpam-5694	257	10	∑	∑	PROPN
ejpam-5694	257	11	2,ω2	2,ω2	NUM
ejpam-5694	257	12	,	,	PUNCT
ejpam-5694	257	13	σ2	σ2	NOUN
ejpam-5694	257	14	)	)	PUNCT
ejpam-5694	257	15	with	with	ADP
ejpam-5694	257	16	positive	positive	ADJ
ejpam-5694	257	17	σ−finite	σ−finite	PROPN
ejpam-5694	257	18	measures	measure	NOUN
ejpam-5694	257	19	and	and	CCONJ
ejpam-5694	257	20	ak	ak	PROPN
ejpam-5694	257	21	and	and	CCONJ
ejpam-5694	257	22	k	k	PROPN
ejpam-5694	257	23	be	be	AUX
ejpam-5694	257	24	given	give	VERB
ejpam-5694	257	25	in	in	ADP
ejpam-5694	257	26	(	(	PUNCT
ejpam-5694	257	27	15	15	NUM
ejpam-5694	257	28	)	)	PUNCT
ejpam-5694	257	29	and	and	CCONJ
ejpam-5694	257	30	(	(	PUNCT
ejpam-5694	257	31	16	16	NUM
ejpam-5694	257	32	)	)	PUNCT
ejpam-5694	257	33	respectively	respectively	ADV
ejpam-5694	257	34	.	.	PUNCT
ejpam-5694	258	1	let	let	VERB
ejpam-5694	258	2	f	f	PRON
ejpam-5694	258	3	be	be	AUX
ejpam-5694	258	4	defined	define	VERB
ejpam-5694	258	5	on	on	ADP
ejpam-5694	258	6	t	t	NOUN
ejpam-5694	258	7	such	such	ADJ
ejpam-5694	258	8	that	that	PRON
ejpam-5694	258	9	for	for	ADP
ejpam-5694	258	10	n	n	PRON
ejpam-5694	258	11	∈	∈	PROPN
ejpam-5694	258	12	n	n	CCONJ
ejpam-5694	258	13	,	,	PUNCT
ejpam-5694	258	14	f	f	PROPN
ejpam-5694	258	15	(	(	PUNCT
ejpam-5694	258	16	n	n	CCONJ
ejpam-5694	258	17	)	)	PUNCT
ejpam-5694	258	18	is	be	AUX
ejpam-5694	258	19	absolutely	absolutely	ADV
ejpam-5694	258	20	continuous	continuous	ADJ
ejpam-5694	258	21	and	and	CCONJ
ejpam-5694	258	22	f	f	X
ejpam-5694	258	23	(	(	PUNCT
ejpam-5694	258	24	n+1	n+1	PROPN
ejpam-5694	258	25	)	)	PUNCT
ejpam-5694	258	26	≥	≥	NOUN
ejpam-5694	258	27	0	0	NUM
ejpam-5694	259	1	therein	therein	ADV
ejpam-5694	259	2	.	.	PUNCT
ejpam-5694	260	1	let	let	VERB
ejpam-5694	260	2	gα	gα	VERB
ejpam-5694	260	3	,	,	PUNCT
ejpam-5694	260	4	{	{	PUNCT
ejpam-5694	260	5	α	α	NOUN
ejpam-5694	260	6	=	=	SYM
ejpam-5694	260	7	1	1	NUM
ejpam-5694	260	8	,	,	PUNCT
ejpam-5694	260	9	2	2	NUM
ejpam-5694	260	10	,	,	PUNCT
ejpam-5694	260	11	3	3	NUM
ejpam-5694	260	12	,	,	PUNCT
ejpam-5694	260	13	4	4	NUM
ejpam-5694	260	14	}	}	PUNCT
ejpam-5694	260	15	be	be	AUX
ejpam-5694	260	16	defined	define	VERB
ejpam-5694	260	17	in	in	ADP
ejpam-5694	260	18	(	(	PUNCT
ejpam-5694	260	19	5	5	NUM
ejpam-5694	260	20	)	)	PUNCT
ejpam-5694	260	21	,	,	PUNCT
ejpam-5694	260	22	(	(	PUNCT
ejpam-5694	260	23	6	6	NUM
ejpam-5694	260	24	)	)	PUNCT
ejpam-5694	260	25	,	,	PUNCT
ejpam-5694	260	26	(	(	PUNCT
ejpam-5694	260	27	7	7	X
ejpam-5694	260	28	)	)	PUNCT
ejpam-5694	260	29	and	and	CCONJ
ejpam-5694	260	30	(	(	PUNCT
ejpam-5694	260	31	8)	8)	NUM
ejpam-5694	260	32	respectively	respectively	ADV
ejpam-5694	260	33	and	and	CCONJ
ejpam-5694	260	34	u	u	NOUN
ejpam-5694	260	35	:	:	PUNCT
ejpam-5694	260	36	ω1	ω1	PROPN
ejpam-5694	260	37	→	→	SYM
ejpam-5694	260	38	r	r	NOUN
ejpam-5694	260	39	be	be	VERB
ejpam-5694	260	40	the	the	DET
ejpam-5694	260	41	weight	weight	NOUN
ejpam-5694	260	42	function	function	NOUN
ejpam-5694	260	43	and	and	CCONJ
ejpam-5694	260	44	v	v	NOUN
ejpam-5694	260	45	is	be	AUX
ejpam-5694	260	46	given	give	VERB
ejpam-5694	260	47	in	in	ADP
ejpam-5694	260	48	(	(	PUNCT
ejpam-5694	260	49	17	17	NUM
ejpam-5694	260	50	)	)	PUNCT
ejpam-5694	260	51	,	,	PUNCT
ejpam-5694	260	52	b1,b2	b1,b2	PROPN
ejpam-5694	260	53	are	be	AUX
ejpam-5694	260	54	given	give	VERB
ejpam-5694	260	55	in	in	ADP
ejpam-5694	260	56	(	(	PUNCT
ejpam-5694	260	57	38	38	NUM
ejpam-5694	260	58	)	)	PUNCT
ejpam-5694	260	59	and	and	CCONJ
ejpam-5694	260	60	(	(	PUNCT
ejpam-5694	260	61	39	39	NUM
ejpam-5694	260	62	)	)	PUNCT
ejpam-5694	260	63	respectively	respectively	ADV
ejpam-5694	260	64	such	such	ADJ
ejpam-5694	260	65	that	that	SCONJ
ejpam-5694	260	66	b′	b′	NUM
ejpam-5694	260	67	1	1	NUM
ejpam-5694	260	68	and	and	CCONJ
ejpam-5694	260	69	b′	b′	NUM
ejpam-5694	260	70	2	2	NUM
ejpam-5694	260	71	∈	∈	NOUN
ejpam-5694	260	72	l∞([a1	l∞([a1	ADJ
ejpam-5694	260	73	,	,	PUNCT
ejpam-5694	260	74	a2	a2	PROPN
ejpam-5694	260	75	]	]	PUNCT
ejpam-5694	260	76	)	)	PUNCT
ejpam-5694	260	77	,	,	PUNCT
ejpam-5694	260	78	then	then	ADV
ejpam-5694	260	79	;	;	PUNCT
ejpam-5694	260	80	|r1(f	|r1(f	X
ejpam-5694	260	81	;	;	PUNCT
ejpam-5694	260	82	a1	a1	PROPN
ejpam-5694	260	83	,	,	PUNCT
ejpam-5694	260	84	a2)|	a2)|	PROPN
ejpam-5694	260	85	≤	≤	NOUN
ejpam-5694	260	86	(	(	PUNCT
ejpam-5694	260	87	a2	a2	PROPN
ejpam-5694	260	88	−	−	PROPN
ejpam-5694	260	89	a1)||b	a1)||b	ADJ
ejpam-5694	260	90	′	′	NOUN
ejpam-5694	260	91	1||∞	1||∞	NUM
ejpam-5694	260	92	(	(	PUNCT
ejpam-5694	260	93	n−	n−	NOUN
ejpam-5694	260	94	4	4	NUM
ejpam-5694	260	95	)	)	PUNCT
ejpam-5694	260	96	!	!	PUNCT
ejpam-5694	261	1	[	[	PUNCT
ejpam-5694	261	2	f	f	X
ejpam-5694	261	3	(	(	PUNCT
ejpam-5694	261	4	n−1)(a2	n−1)(a2	PROPN
ejpam-5694	261	5	)	)	PUNCT
ejpam-5694	262	1	+	+	NUM
ejpam-5694	262	2	f	f	X
ejpam-5694	262	3	(	(	PUNCT
ejpam-5694	262	4	n−1)(a1	n−1)(a1	NOUN
ejpam-5694	262	5	)	)	PUNCT
ejpam-5694	262	6	2	2	NUM
ejpam-5694	262	7	−	−	PROPN
ejpam-5694	262	8	f	f	NOUN
ejpam-5694	262	9	(	(	PUNCT
ejpam-5694	262	10	n−2)(a2)−f	n−2)(a2)−f	PROPN
ejpam-5694	262	11	(	(	PUNCT
ejpam-5694	262	12	n−2)(a1	n−2)(a1	NOUN
ejpam-5694	262	13	)	)	PUNCT
ejpam-5694	262	14	a2	a2	PROPN
ejpam-5694	262	15	−	−	PROPN
ejpam-5694	263	1	a1	a1	NOUN
ejpam-5694	263	2	]	]	PUNCT
ejpam-5694	263	3	,	,	PUNCT
ejpam-5694	263	4	(	(	PUNCT
ejpam-5694	263	5	46	46	NUM
ejpam-5694	263	6	)	)	PUNCT
ejpam-5694	263	7	|r2(f	|r2(f	PROPN
ejpam-5694	263	8	;	;	PUNCT
ejpam-5694	263	9	a1	a1	PROPN
ejpam-5694	263	10	,	,	PUNCT
ejpam-5694	263	11	a2)|	a2)|	PROPN
ejpam-5694	263	12	≤	≤	NOUN
ejpam-5694	263	13	(	(	PUNCT
ejpam-5694	263	14	a2	a2	PROPN
ejpam-5694	263	15	−	−	PROPN
ejpam-5694	263	16	a1)||b	a1)||b	PROPN
ejpam-5694	263	17	′	′	NOUN
ejpam-5694	263	18	2||∞	2||∞	NUM
ejpam-5694	263	19	(	(	PUNCT
ejpam-5694	263	20	n−	n−	NOUN
ejpam-5694	263	21	4	4	NUM
ejpam-5694	263	22	)	)	PUNCT
ejpam-5694	263	23	!	!	PUNCT
ejpam-5694	264	1	[	[	PUNCT
ejpam-5694	264	2	f	f	X
ejpam-5694	264	3	(	(	PUNCT
ejpam-5694	264	4	n−1)(a2	n−1)(a2	PROPN
ejpam-5694	264	5	)	)	PUNCT
ejpam-5694	265	1	+	+	NUM
ejpam-5694	265	2	f	f	X
ejpam-5694	265	3	(	(	PUNCT
ejpam-5694	265	4	n−1)(a1	n−1)(a1	NOUN
ejpam-5694	265	5	)	)	PUNCT
ejpam-5694	265	6	2	2	NUM
ejpam-5694	265	7	−	−	PROPN
ejpam-5694	265	8	f	f	NOUN
ejpam-5694	265	9	(	(	PUNCT
ejpam-5694	265	10	n−2)(a2)−f	n−2)(a2)−f	PROPN
ejpam-5694	265	11	(	(	PUNCT
ejpam-5694	265	12	n−2)(a1	n−2)(a1	NOUN
ejpam-5694	265	13	)	)	PUNCT
ejpam-5694	265	14	a2	a2	PROPN
ejpam-5694	265	15	−	−	PROPN
ejpam-5694	266	1	a1	a1	PROPN
ejpam-5694	266	2	]	]	PUNCT
ejpam-5694	266	3	.(47	.(47	PROPN
ejpam-5694	266	4	)	)	PUNCT
ejpam-5694	266	5	where	where	SCONJ
ejpam-5694	266	6	r1(f	r1(f	X
ejpam-5694	266	7	;	;	PUNCT
ejpam-5694	266	8	a1	a1	PROPN
ejpam-5694	266	9	,	,	PUNCT
ejpam-5694	266	10	a2	a2	PROPN
ejpam-5694	266	11	)	)	PUNCT
ejpam-5694	266	12	and	and	CCONJ
ejpam-5694	266	13	r2(f	r2(f	X
ejpam-5694	266	14	;	;	PUNCT
ejpam-5694	266	15	a1	a1	PROPN
ejpam-5694	266	16	,	,	PUNCT
ejpam-5694	266	17	a2	a2	PROPN
ejpam-5694	266	18	)	)	PUNCT
ejpam-5694	266	19	are	be	AUX
ejpam-5694	266	20	given	give	VERB
ejpam-5694	266	21	in	in	ADP
ejpam-5694	266	22	(	(	PUNCT
ejpam-5694	266	23	40	40	NUM
ejpam-5694	266	24	)	)	PUNCT
ejpam-5694	266	25	and	and	CCONJ
ejpam-5694	266	26	(	(	PUNCT
ejpam-5694	266	27	42	42	NUM
ejpam-5694	266	28	)	)	PUNCT
ejpam-5694	266	29	respectively	respectively	ADV
ejpam-5694	266	30	.	.	PUNCT
ejpam-5694	267	1	proof	proof	NOUN
ejpam-5694	267	2	.	.	PUNCT
ejpam-5694	268	1	•	•	INTJ
ejpam-5694	268	2	as	as	ADV
ejpam-5694	268	3	all	all	DET
ejpam-5694	268	4	the	the	DET
ejpam-5694	268	5	conditions	condition	NOUN
ejpam-5694	268	6	stated	state	VERB
ejpam-5694	268	7	in	in	ADP
ejpam-5694	268	8	theorem	theorem	ADJ
ejpam-5694	268	9	3	3	NUM
ejpam-5694	268	10	are	be	AUX
ejpam-5694	268	11	obayed	obaye	VERB
ejpam-5694	268	12	if	if	SCONJ
ejpam-5694	268	13	we	we	PRON
ejpam-5694	268	14	take	take	VERB
ejpam-5694	268	15	f	f	NOUN
ejpam-5694	268	16	=	=	PUNCT
ejpam-5694	268	17	b1	b1	PROPN
ejpam-5694	268	18	and	and	CCONJ
ejpam-5694	268	19	g	g	NOUN
ejpam-5694	268	20	=	=	SYM
ejpam-5694	268	21	f	f	PROPN
ejpam-5694	268	22	(	(	PUNCT
ejpam-5694	268	23	n	n	CCONJ
ejpam-5694	268	24	)	)	PUNCT
ejpam-5694	268	25	.	.	PUNCT
ejpam-5694	269	1	so	so	ADV
ejpam-5694	269	2	considering	consider	VERB
ejpam-5694	269	3	(	(	PUNCT
ejpam-5694	269	4	44	44	NUM
ejpam-5694	269	5	)	)	PUNCT
ejpam-5694	269	6	we	we	PRON
ejpam-5694	269	7	can	can	AUX
ejpam-5694	269	8	have	have	VERB
ejpam-5694	269	9	1	1	NUM
ejpam-5694	269	10	a2	a2	PROPN
ejpam-5694	269	11	−	−	PROPN
ejpam-5694	269	12	a1	a1	PROPN
ejpam-5694	269	13	∣∣∣r1(f	∣∣∣r1(f	PROPN
ejpam-5694	269	14	;	;	PUNCT
ejpam-5694	269	15	a1	a1	PROPN
ejpam-5694	269	16	,	,	PUNCT
ejpam-5694	269	17	a2	a2	NOUN
ejpam-5694	269	18	)	)	PUNCT
ejpam-5694	269	19	∣∣∣	∣∣∣	NOUN
ejpam-5694	269	20	=	=	SYM
ejpam-5694	269	21	1	1	X
ejpam-5694	269	22	(	(	PUNCT
ejpam-5694	269	23	n−	n−	NOUN
ejpam-5694	269	24	4	4	NUM
ejpam-5694	269	25	)	)	PUNCT
ejpam-5694	269	26	!	!	PUNCT
ejpam-5694	270	1	∣∣∣∣∣	∣∣∣∣∣	ADJ
ejpam-5694	270	2	1	1	NUM
ejpam-5694	270	3	a2	a2	PROPN
ejpam-5694	270	4	−	−	PROPN
ejpam-5694	270	5	a1	a1	PROPN
ejpam-5694	270	6	∫	∫	PROPN
ejpam-5694	270	7	a2	a2	PROPN
ejpam-5694	270	8	a1	a1	PROPN
ejpam-5694	270	9	b1(τ)f	b1(τ)f	NOUN
ejpam-5694	270	10	(	(	PUNCT
ejpam-5694	270	11	n)(τ)dτ	n)(τ)dτ	NOUN
ejpam-5694	270	12	−	−	PROPN
ejpam-5694	270	13	1	1	NUM
ejpam-5694	270	14	(	(	PUNCT
ejpam-5694	270	15	a2	a2	PROPN
ejpam-5694	270	16	−	−	PROPN
ejpam-5694	270	17	a1	a1	PROPN
ejpam-5694	270	18	)	)	PUNCT
ejpam-5694	270	19	∫	∫	PROPN
ejpam-5694	270	20	a2	a2	PROPN
ejpam-5694	270	21	a1	a1	PROPN
ejpam-5694	270	22	b1(τ)dτ	b1(τ)dτ	NOUN
ejpam-5694	270	23	1	1	NUM
ejpam-5694	270	24	(	(	PUNCT
ejpam-5694	270	25	a2	a2	PROPN
ejpam-5694	270	26	−	−	PROPN
ejpam-5694	270	27	a1	a1	PROPN
ejpam-5694	270	28	)	)	PUNCT
ejpam-5694	270	29	∫	∫	PROPN
ejpam-5694	270	30	a2	a2	PROPN
ejpam-5694	270	31	a1	a1	PROPN
ejpam-5694	270	32	f	f	PROPN
ejpam-5694	270	33	(	(	PUNCT
ejpam-5694	270	34	n)(τ)dτ	n)(τ)dτ	PROPN
ejpam-5694	270	35	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5694	270	36	≤	≤	ADV
ejpam-5694	270	37	1	1	NUM
ejpam-5694	270	38	2(n−	2(n−	NUM
ejpam-5694	270	39	4	4	NUM
ejpam-5694	270	40	)	)	PUNCT
ejpam-5694	270	41	!	!	PUNCT
ejpam-5694	271	1	||b′	||b′	NOUN
ejpam-5694	271	2	1||∞	1||∞	NUM
ejpam-5694	271	3	a2	a2	PROPN
ejpam-5694	271	4	−	−	NOUN
ejpam-5694	271	5	a1	a1	NOUN
ejpam-5694	271	6	(	(	PUNCT
ejpam-5694	271	7	∫	∫	PROPN
ejpam-5694	271	8	a2	a2	PROPN
ejpam-5694	271	9	a1	a1	PROPN
ejpam-5694	271	10	(	(	PUNCT
ejpam-5694	271	11	τ	τ	PROPN
ejpam-5694	271	12	−	−	PROPN
ejpam-5694	271	13	a1)(a2	a1)(a2	PROPN
ejpam-5694	271	14	−	−	NOUN
ejpam-5694	271	15	τ)f	τ)f	PUNCT
ejpam-5694	271	16	(	(	PUNCT
ejpam-5694	271	17	n+1)(τ)dτ	n+1)(τ)dτ	PROPN
ejpam-5694	271	18	)	)	PUNCT
ejpam-5694	271	19	.	.	PUNCT
ejpam-5694	272	1	(	(	PUNCT
ejpam-5694	272	2	48	48	NUM
ejpam-5694	272	3	)	)	PUNCT
ejpam-5694	272	4	after	after	ADP
ejpam-5694	272	5	simplifying	simplify	VERB
ejpam-5694	272	6	integral	integral	ADJ
ejpam-5694	272	7	in	in	ADP
ejpam-5694	272	8	last	last	ADJ
ejpam-5694	272	9	step	step	NOUN
ejpam-5694	272	10	and	and	CCONJ
ejpam-5694	272	11	taking	take	VERB
ejpam-5694	272	12	(	(	PUNCT
ejpam-5694	272	13	44	44	NUM
ejpam-5694	272	14	)	)	PUNCT
ejpam-5694	272	15	into	into	ADP
ejpam-5694	272	16	account	account	NOUN
ejpam-5694	272	17	we	we	PRON
ejpam-5694	272	18	get	get	VERB
ejpam-5694	272	19	the	the	DET
ejpam-5694	272	20	required	require	VERB
ejpam-5694	272	21	result	result	NOUN
ejpam-5694	272	22	.	.	PUNCT
ejpam-5694	273	1	•	•	NUM
ejpam-5694	273	2	following	follow	VERB
ejpam-5694	273	3	smiliar	smiliar	NOUN
ejpam-5694	273	4	steps	step	NOUN
ejpam-5694	273	5	of	of	ADP
ejpam-5694	273	6	first	first	ADJ
ejpam-5694	273	7	part	part	NOUN
ejpam-5694	273	8	we	we	PRON
ejpam-5694	273	9	obtain	obtain	VERB
ejpam-5694	273	10	the	the	DET
ejpam-5694	273	11	required	require	VERB
ejpam-5694	273	12	result	result	NOUN
ejpam-5694	273	13	.	.	PUNCT
ejpam-5694	274	1	now	now	ADV
ejpam-5694	274	2	moving	move	VERB
ejpam-5694	274	3	forward	forward	ADV
ejpam-5694	274	4	for	for	ADP
ejpam-5694	274	5	the	the	DET
ejpam-5694	274	6	analysis	analysis	NOUN
ejpam-5694	274	7	of	of	ADP
ejpam-5694	274	8	ostrowski	ostrowski	ADJ
ejpam-5694	274	9	-	-	PUNCT
ejpam-5694	274	10	type	type	NOUN
ejpam-5694	274	11	inequalities	inequality	NOUN
ejpam-5694	274	12	related	relate	VERB
ejpam-5694	274	13	to	to	ADP
ejpam-5694	274	14	the	the	DET
ejpam-5694	274	15	case	case	NOUN
ejpam-5694	274	16	under	under	ADP
ejpam-5694	274	17	consideration	consideration	NOUN
ejpam-5694	274	18	i.e	i.e	PRON
ejpam-5694	274	19	generalized	generalize	VERB
ejpam-5694	274	20	hardy	hardy	ADJ
ejpam-5694	274	21	-	-	PUNCT
ejpam-5694	274	22	type	type	NOUN
ejpam-5694	274	23	inequalities	inequality	NOUN
ejpam-5694	274	24	of	of	ADP
ejpam-5694	274	25	convex	convex	NOUN
ejpam-5694	274	26	functions	function	NOUN
ejpam-5694	274	27	via	via	ADP
ejpam-5694	274	28	taylor	taylor	PROPN
ejpam-5694	274	29	polynomial	polynomial	PROPN
ejpam-5694	274	30	and	and	CCONJ
ejpam-5694	274	31	green	green	ADJ
ejpam-5694	274	32	function	function	NOUN
ejpam-5694	274	33	a.	a.	NOUN
ejpam-5694	274	34	m.	m.	PROPN
ejpam-5694	274	35	k.	k.	PROPN
ejpam-5694	274	36	abbasi	abbasi	PROPN
ejpam-5694	274	37	,	,	PUNCT
ejpam-5694	274	38	m.	m.	PROPN
ejpam-5694	274	39	anwar	anwar	PROPN
ejpam-5694	274	40	/	/	PUNCT
ejpam-5694	274	41	eur	eur	PROPN
ejpam-5694	274	42	.	.	PUNCT
ejpam-5694	275	1	j.	j.	PROPN
ejpam-5694	275	2	pure	pure	PROPN
ejpam-5694	275	3	appl	appl	PROPN
ejpam-5694	275	4	.	.	PROPN
ejpam-5694	275	5	math	math	PROPN
ejpam-5694	275	6	,	,	PUNCT
ejpam-5694	275	7	18	18	NUM
ejpam-5694	275	8	(	(	PUNCT
ejpam-5694	275	9	1	1	NUM
ejpam-5694	275	10	)	)	PUNCT
ejpam-5694	275	11	(	(	PUNCT
ejpam-5694	275	12	2025	2025	NUM
ejpam-5694	275	13	)	)	PUNCT
ejpam-5694	275	14	,	,	PUNCT
ejpam-5694	275	15	5694	5694	NUM
ejpam-5694	275	16	14	14	NUM
ejpam-5694	275	17	of	of	ADP
ejpam-5694	275	18	18	18	NUM
ejpam-5694	275	19	theorem	theorem	NOUN
ejpam-5694	275	20	9	9	NUM
ejpam-5694	275	21	.	.	PUNCT
ejpam-5694	276	1	let	let	VERB
ejpam-5694	276	2	all	all	DET
ejpam-5694	276	3	the	the	DET
ejpam-5694	276	4	conditions	condition	NOUN
ejpam-5694	276	5	of	of	ADP
ejpam-5694	276	6	theorem	theorem	ADJ
ejpam-5694	276	7	4	4	NUM
ejpam-5694	276	8	holds	hold	VERB
ejpam-5694	276	9	with	with	ADP
ejpam-5694	276	10	n	n	PRON
ejpam-5694	276	11	∈	∈	PROPN
ejpam-5694	276	12	n	n	NOUN
ejpam-5694	276	13	and	and	CCONJ
ejpam-5694	276	14	n	n	PRON
ejpam-5694	276	15	≥	≥	NOUN
ejpam-5694	276	16	4	4	NUM
ejpam-5694	276	17	.	.	PUNCT
ejpam-5694	277	1	let	let	VERB
ejpam-5694	277	2	jgα	jgα	NOUN
ejpam-5694	277	3	,	,	PUNCT
ejpam-5694	277	4	b1	b1	NOUN
ejpam-5694	277	5	and	and	CCONJ
ejpam-5694	277	6	b2	b2	NOUN
ejpam-5694	277	7	be	be	AUX
ejpam-5694	277	8	given	give	VERB
ejpam-5694	277	9	in	in	ADP
ejpam-5694	277	10	(	(	PUNCT
ejpam-5694	277	11	26	26	NUM
ejpam-5694	277	12	)	)	PUNCT
ejpam-5694	277	13	,	,	PUNCT
ejpam-5694	277	14	(	(	PUNCT
ejpam-5694	277	15	38	38	NUM
ejpam-5694	277	16	)	)	PUNCT
ejpam-5694	277	17	and	and	CCONJ
ejpam-5694	277	18	(	(	PUNCT
ejpam-5694	277	19	39	39	NUM
ejpam-5694	277	20	)	)	PUNCT
ejpam-5694	277	21	respectively	respectively	ADV
ejpam-5694	277	22	.	.	PUNCT
ejpam-5694	278	1	assuming	assume	VERB
ejpam-5694	278	2	that	that	SCONJ
ejpam-5694	278	3	p	p	X
ejpam-5694	278	4	,	,	PUNCT
ejpam-5694	278	5	q	q	ADJ
ejpam-5694	278	6	be	be	AUX
ejpam-5694	278	7	the	the	DET
ejpam-5694	278	8	conjugate	conjugate	ADJ
ejpam-5694	278	9	exponents	exponent	NOUN
ejpam-5694	278	10	with	with	ADP
ejpam-5694	278	11	1	1	NUM
ejpam-5694	278	12	≤	≤	NOUN
ejpam-5694	278	13	p	p	NOUN
ejpam-5694	278	14	,	,	PUNCT
ejpam-5694	278	15	q	q	PROPN
ejpam-5694	278	16	≤	≤	NUM
ejpam-5694	278	17	∞	∞	NUM
ejpam-5694	278	18	such	such	ADJ
ejpam-5694	278	19	that	that	SCONJ
ejpam-5694	278	20	1	1	NUM
ejpam-5694	278	21	q	q	NOUN
ejpam-5694	278	22	+	+	NUM
ejpam-5694	278	23	1	1	NUM
ejpam-5694	278	24	p	p	NOUN
ejpam-5694	278	25	=	=	NOUN
ejpam-5694	278	26	1	1	NUM
ejpam-5694	278	27	and	and	CCONJ
ejpam-5694	278	28	f	f	PROPN
ejpam-5694	278	29	:	:	PUNCT
ejpam-5694	278	30	t	t	PROPN
ejpam-5694	278	31	→	→	SYM
ejpam-5694	278	32	r	r	NOUN
ejpam-5694	278	33	be	be	AUX
ejpam-5694	278	34	such	such	ADJ
ejpam-5694	278	35	that	that	DET
ejpam-5694	278	36	||f	||f	NOUN
ejpam-5694	278	37	(	(	PUNCT
ejpam-5694	278	38	n)||p	n)||p	X
ejpam-5694	278	39	<	<	X
ejpam-5694	278	40	∞.	∞.	PROPN
ejpam-5694	278	41	then	then	ADV
ejpam-5694	278	42	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5694	278	43	∫	∫	PROPN
ejpam-5694	279	1	ω2	ω2	PROPN
ejpam-5694	280	1	f(f(s))ν(s)dµ2(s)−	f(f(s))ν(s)dµ2(s)−	PROPN
ejpam-5694	280	2	∫	∫	PROPN
ejpam-5694	280	3	ω1	ω1	PROPN
ejpam-5694	280	4	f(akf(ϖ))u(ϖ)dµ1(ϖ	f(akf(ϖ))u(ϖ)dµ1(ϖ	PROPN
ejpam-5694	280	5	)	)	PUNCT
ejpam-5694	280	6	−	−	PROPN
ejpam-5694	281	1	∑	∑	PUNCT
ejpam-5694	281	2	κ	κ	PROPN
ejpam-5694	281	3	f	f	PROPN
ejpam-5694	281	4	(	(	PUNCT
ejpam-5694	281	5	κ)(a1	κ)(a1	X
ejpam-5694	281	6	)	)	PUNCT
ejpam-5694	281	7	κ	κ	NOUN
ejpam-5694	281	8	!	!	PUNCT
ejpam-5694	281	9	∫	∫	PROPN
ejpam-5694	281	10	a2	a2	PROPN
ejpam-5694	281	11	a1	a1	PROPN
ejpam-5694	281	12	jgα(f	jgα(f	PROPN
ejpam-5694	281	13	,	,	PUNCT
ejpam-5694	281	14	τ)ν(s)dµ2(s)(τ	τ)ν(s)dµ2(s)(τ	ADJ
ejpam-5694	281	15	−	−	PROPN
ejpam-5694	281	16	a1	a1	NOUN
ejpam-5694	281	17	)	)	PUNCT
ejpam-5694	281	18	κ	κ	NOUN
ejpam-5694	281	19	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5694	281	20	≤	≤	NOUN
ejpam-5694	281	21	1	1	NUM
ejpam-5694	281	22	(	(	PUNCT
ejpam-5694	281	23	n−	n−	NOUN
ejpam-5694	281	24	4	4	NUM
ejpam-5694	281	25	)	)	PUNCT
ejpam-5694	281	26	!	!	PUNCT
ejpam-5694	282	1	||f	||f	NOUN
ejpam-5694	282	2	(	(	PUNCT
ejpam-5694	282	3	n)||p||b1||q	n)||p||b1||q	PROPN
ejpam-5694	282	4	(	(	PUNCT
ejpam-5694	282	5	49	49	NUM
ejpam-5694	282	6	)	)	PUNCT
ejpam-5694	282	7	and	and	CCONJ
ejpam-5694	283	1	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5694	283	2	∫	∫	PROPN
ejpam-5694	284	1	ω2	ω2	PROPN
ejpam-5694	285	1	f(f(s))ν(s)dµ2(s)−	f(f(s))ν(s)dµ2(s)−	PROPN
ejpam-5694	285	2	∫	∫	PROPN
ejpam-5694	285	3	ω1	ω1	PROPN
ejpam-5694	285	4	f(akf(ϖ))u(ϖ)dµ1(ϖ	f(akf(ϖ))u(ϖ)dµ1(ϖ	PROPN
ejpam-5694	285	5	)	)	PUNCT
ejpam-5694	285	6	−	−	PROPN
ejpam-5694	286	1	∑	∑	PUNCT
ejpam-5694	286	2	κ	κ	PROPN
ejpam-5694	286	3	f	f	PROPN
ejpam-5694	286	4	(	(	PUNCT
ejpam-5694	286	5	κ)(a2	κ)(a2	PROPN
ejpam-5694	286	6	)	)	PUNCT
ejpam-5694	286	7	κ	κ	NOUN
ejpam-5694	286	8	!	!	PUNCT
ejpam-5694	286	9	∫	∫	PROPN
ejpam-5694	286	10	a2	a2	PROPN
ejpam-5694	286	11	a1	a1	PROPN
ejpam-5694	286	12	jgα(f	jgα(f	PROPN
ejpam-5694	286	13	,	,	PUNCT
ejpam-5694	286	14	τ)(τ	τ)(τ	PROPN
ejpam-5694	286	15	−	−	PROPN
ejpam-5694	286	16	a2	a2	PROPN
ejpam-5694	286	17	)	)	PUNCT
ejpam-5694	286	18	κdτ	κdτ	NOUN
ejpam-5694	286	19	∣∣∣∣∣	∣∣∣∣∣	SYM
ejpam-5694	286	20	≤	≤	NOUN
ejpam-5694	286	21	1	1	NUM
ejpam-5694	286	22	(	(	PUNCT
ejpam-5694	286	23	n−	n−	NOUN
ejpam-5694	286	24	4	4	NUM
ejpam-5694	286	25	)	)	PUNCT
ejpam-5694	286	26	!	!	PUNCT
ejpam-5694	287	1	||f	||f	NOUN
ejpam-5694	287	2	(	(	PUNCT
ejpam-5694	287	3	n)||p||b1||q	n)||p||b1||q	PROPN
ejpam-5694	287	4	.	.	PUNCT
ejpam-5694	288	1	(	(	PUNCT
ejpam-5694	288	2	50	50	NUM
ejpam-5694	288	3	)	)	PUNCT
ejpam-5694	288	4	proof	proof	NOUN
ejpam-5694	288	5	.	.	PUNCT
ejpam-5694	289	1	•	•	NOUN
ejpam-5694	289	2	using	use	VERB
ejpam-5694	289	3	hölder	hölder	NOUN
ejpam-5694	289	4	inequality	inequality	NOUN
ejpam-5694	289	5	in	in	ADP
ejpam-5694	289	6	(	(	PUNCT
ejpam-5694	289	7	24	24	NUM
ejpam-5694	289	8	)	)	PUNCT
ejpam-5694	289	9	we	we	PRON
ejpam-5694	289	10	arrive	arrive	VERB
ejpam-5694	289	11	at∣∣∣∣∣	at∣∣∣∣∣	PROPN
ejpam-5694	289	12	∫	∫	PROPN
ejpam-5694	290	1	ω2	ω2	PROPN
ejpam-5694	290	2	f(f(s))ν(s)dµ2(s)−	f(f(s))ν(s)dµ2(s)−	PROPN
ejpam-5694	290	3	∫	∫	PROPN
ejpam-5694	290	4	ω1	ω1	PROPN
ejpam-5694	290	5	f(akf(ϖ))u(ϖ)dµ1(ϖ	f(akf(ϖ))u(ϖ)dµ1(ϖ	PROPN
ejpam-5694	290	6	)	)	PUNCT
ejpam-5694	290	7	−	−	PROPN
ejpam-5694	291	1	∑	∑	PUNCT
ejpam-5694	291	2	κ	κ	PROPN
ejpam-5694	291	3	f	f	PROPN
ejpam-5694	291	4	(	(	PUNCT
ejpam-5694	291	5	κ)(a1	κ)(a1	X
ejpam-5694	291	6	)	)	PUNCT
ejpam-5694	291	7	κ	κ	NOUN
ejpam-5694	291	8	!	!	PUNCT
ejpam-5694	291	9	∫	∫	PROPN
ejpam-5694	291	10	a2	a2	PROPN
ejpam-5694	291	11	a1	a1	PROPN
ejpam-5694	291	12	jgα(f	jgα(f	PROPN
ejpam-5694	291	13	,	,	PUNCT
ejpam-5694	291	14	τ)(τ	τ)(τ	PROPN
ejpam-5694	291	15	−	−	PROPN
ejpam-5694	291	16	a1	a1	PROPN
ejpam-5694	291	17	)	)	PUNCT
ejpam-5694	291	18	κdτ	κdτ	NOUN
ejpam-5694	291	19	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5694	292	1	=	=	SYM
ejpam-5694	292	2	1	1	NUM
ejpam-5694	292	3	(	(	PUNCT
ejpam-5694	292	4	n−	n−	NOUN
ejpam-5694	292	5	4	4	NUM
ejpam-5694	292	6	)	)	PUNCT
ejpam-5694	292	7	!	!	PUNCT
ejpam-5694	293	1	∣∣∣	∣∣∣	PROPN
ejpam-5694	293	2	∫	∫	PROPN
ejpam-5694	293	3	a2	a2	PROPN
ejpam-5694	293	4	a1	a1	PROPN
ejpam-5694	293	5	b1(τ)f	b1(τ)f	NOUN
ejpam-5694	293	6	(	(	PUNCT
ejpam-5694	293	7	n)(τ)dτ	n)(τ)dτ	NOUN
ejpam-5694	293	8	∣∣∣	∣∣∣	NOUN
ejpam-5694	293	9	≤	≤	ADV
ejpam-5694	293	10	1	1	NUM
ejpam-5694	293	11	(	(	PUNCT
ejpam-5694	293	12	n−	n−	NOUN
ejpam-5694	293	13	4	4	NUM
ejpam-5694	293	14	)	)	PUNCT
ejpam-5694	293	15	!	!	PUNCT
ejpam-5694	294	1	||f	||f	NOUN
ejpam-5694	294	2	(	(	PUNCT
ejpam-5694	294	3	n)||p	n)||p	X
ejpam-5694	294	4	(	(	PUNCT
ejpam-5694	294	5	∫	∫	PROPN
ejpam-5694	294	6	a2	a2	PROPN
ejpam-5694	294	7	a1	a1	PROPN
ejpam-5694	294	8	|b1(τ)|qdτ	|b1(τ)|qdτ	PROPN
ejpam-5694	294	9	)	)	PUNCT
ejpam-5694	294	10	1	1	NUM
ejpam-5694	294	11	q	q	NOUN
ejpam-5694	294	12	.	.	PUNCT
ejpam-5694	295	1	from	from	ADP
ejpam-5694	295	2	this	this	PRON
ejpam-5694	295	3	we	we	PRON
ejpam-5694	295	4	can	can	AUX
ejpam-5694	295	5	write	write	VERB
ejpam-5694	295	6	(	(	PUNCT
ejpam-5694	295	7	49	49	NUM
ejpam-5694	295	8	)	)	PUNCT
ejpam-5694	295	9	.	.	PUNCT
ejpam-5694	296	1	•	•	NUM
ejpam-5694	296	2	following	follow	VERB
ejpam-5694	296	3	similar	similar	ADJ
ejpam-5694	296	4	steps	step	NOUN
ejpam-5694	296	5	of	of	ADP
ejpam-5694	296	6	part	part	NOUN
ejpam-5694	296	7	one	one	NUM
ejpam-5694	296	8	after	after	ADP
ejpam-5694	296	9	using	use	VERB
ejpam-5694	296	10	hölder	hölder	NOUN
ejpam-5694	296	11	inequality	inequality	NOUN
ejpam-5694	296	12	in	in	ADP
ejpam-5694	296	13	(	(	PUNCT
ejpam-5694	296	14	25	25	NUM
ejpam-5694	296	15	)	)	PUNCT
ejpam-5694	296	16	we	we	PRON
ejpam-5694	296	17	get	get	VERB
ejpam-5694	296	18	the	the	DET
ejpam-5694	296	19	required	require	VERB
ejpam-5694	296	20	result	result	NOUN
ejpam-5694	296	21	.	.	PUNCT
ejpam-5694	297	1	5	5	X
ejpam-5694	297	2	.	.	X
ejpam-5694	297	3	mean	mean	ADJ
ejpam-5694	297	4	value	value	NOUN
ejpam-5694	297	5	theorem	theorem	NOUN
ejpam-5694	297	6	(	(	PUNCT
ejpam-5694	297	7	mvt	mvt	PROPN
ejpam-5694	297	8	)	)	PUNCT
ejpam-5694	297	9	and	and	CCONJ
ejpam-5694	297	10	n	n	CCONJ
ejpam-5694	297	11	-	-	PUNCT
ejpam-5694	297	12	exponential	exponential	NOUN
ejpam-5694	297	13	convexity	convexity	NOUN
ejpam-5694	297	14	it	it	PRON
ejpam-5694	297	15	is	be	AUX
ejpam-5694	297	16	clear	clear	ADJ
ejpam-5694	297	17	that	that	SCONJ
ejpam-5694	297	18	inequalities	inequality	NOUN
ejpam-5694	297	19	(	(	PUNCT
ejpam-5694	297	20	32	32	NUM
ejpam-5694	297	21	)	)	PUNCT
ejpam-5694	297	22	and	and	CCONJ
ejpam-5694	297	23	(	(	PUNCT
ejpam-5694	297	24	33	33	NUM
ejpam-5694	297	25	)	)	PUNCT
ejpam-5694	297	26	are	be	AUX
ejpam-5694	297	27	linear	linear	ADJ
ejpam-5694	297	28	in	in	ADP
ejpam-5694	297	29	f	f	PROPN
ejpam-5694	297	30	.	.	PUNCT
ejpam-5694	298	1	keeping	keep	VERB
ejpam-5694	298	2	in	in	ADP
ejpam-5694	298	3	mind	mind	NOUN
ejpam-5694	298	4	all	all	DET
ejpam-5694	298	5	the	the	DET
ejpam-5694	298	6	assumptions	assumption	NOUN
ejpam-5694	298	7	stated	state	VERB
ejpam-5694	298	8	in	in	ADP
ejpam-5694	298	9	theorem	theorem	NOUN
ejpam-5694	298	10	5	5	NUM
ejpam-5694	298	11	,	,	PUNCT
ejpam-5694	298	12	two	two	NUM
ejpam-5694	298	13	linear	linear	ADJ
ejpam-5694	298	14	functionals	functional	NOUN
ejpam-5694	298	15	can	can	AUX
ejpam-5694	298	16	be	be	AUX
ejpam-5694	298	17	defined	define	VERB
ejpam-5694	298	18	as	as	ADP
ejpam-5694	298	19	following	follow	VERB
ejpam-5694	298	20	;	;	PUNCT
ejpam-5694	298	21	h1	h1	PROPN
ejpam-5694	298	22	=	=	SYM
ejpam-5694	298	23	∫	∫	PROPN
ejpam-5694	299	1	ω2	ω2	PROPN
ejpam-5694	299	2	f(f(s))ν(s)dµ2(s)−	f(f(s))ν(s)dµ2(s)−	PROPN
ejpam-5694	299	3	∫	∫	PROPN
ejpam-5694	299	4	ω1	ω1	PROPN
ejpam-5694	299	5	f(akf(ϖ))u(ϖ)dµ1(ϖ	f(akf(ϖ))u(ϖ)dµ1(ϖ	PROPN
ejpam-5694	299	6	)	)	PUNCT
ejpam-5694	299	7	a.	a.	NOUN
ejpam-5694	299	8	m.	m.	PROPN
ejpam-5694	299	9	k.	k.	PROPN
ejpam-5694	299	10	abbasi	abbasi	PROPN
ejpam-5694	299	11	,	,	PUNCT
ejpam-5694	299	12	m.	m.	PROPN
ejpam-5694	299	13	anwar	anwar	PROPN
ejpam-5694	299	14	/	/	PUNCT
ejpam-5694	299	15	eur	eur	PROPN
ejpam-5694	299	16	.	.	PUNCT
ejpam-5694	300	1	j.	j.	PROPN
ejpam-5694	300	2	pure	pure	PROPN
ejpam-5694	300	3	appl	appl	PROPN
ejpam-5694	300	4	.	.	PROPN
ejpam-5694	300	5	math	math	PROPN
ejpam-5694	300	6	,	,	PUNCT
ejpam-5694	300	7	18	18	NUM
ejpam-5694	300	8	(	(	PUNCT
ejpam-5694	300	9	1	1	NUM
ejpam-5694	300	10	)	)	PUNCT
ejpam-5694	300	11	(	(	PUNCT
ejpam-5694	300	12	2025	2025	NUM
ejpam-5694	300	13	)	)	PUNCT
ejpam-5694	300	14	,	,	PUNCT
ejpam-5694	300	15	5694	5694	NUM
ejpam-5694	300	16	15	15	NUM
ejpam-5694	300	17	of	of	ADP
ejpam-5694	300	18	18	18	NUM
ejpam-5694	300	19	−	−	PROPN
ejpam-5694	300	20	∫	∫	PROPN
ejpam-5694	300	21	a2	a2	PROPN
ejpam-5694	300	22	a1	a1	PROPN
ejpam-5694	300	23	jgα(f	jgα(f	PROPN
ejpam-5694	300	24	,	,	PUNCT
ejpam-5694	300	25	τ)×	τ)×	X
ejpam-5694	300	26	∑	∑	PROPN
ejpam-5694	300	27	κ	κ	PROPN
ejpam-5694	300	28	f	f	PROPN
ejpam-5694	300	29	(	(	PUNCT
ejpam-5694	300	30	κ)(a1	κ)(a1	X
ejpam-5694	300	31	)	)	PUNCT
ejpam-5694	300	32	κ	κ	NOUN
ejpam-5694	300	33	!	!	PUNCT
ejpam-5694	301	1	(	(	PUNCT
ejpam-5694	301	2	τ	τ	PROPN
ejpam-5694	301	3	−	−	PROPN
ejpam-5694	301	4	a1	a1	PROPN
ejpam-5694	301	5	)	)	PUNCT
ejpam-5694	301	6	κdτ	κdτ	NOUN
ejpam-5694	301	7	(	(	PUNCT
ejpam-5694	301	8	51	51	NUM
ejpam-5694	301	9	)	)	PUNCT
ejpam-5694	301	10	and	and	CCONJ
ejpam-5694	301	11	h2	h2	PROPN
ejpam-5694	301	12	=	=	SYM
ejpam-5694	302	1	∫	∫	PROPN
ejpam-5694	303	1	ω2	ω2	PROPN
ejpam-5694	304	1	f(f(s))ν(s)dµ2(s)−	f(f(s))ν(s)dµ2(s)−	PROPN
ejpam-5694	304	2	∫	∫	PROPN
ejpam-5694	304	3	ω1	ω1	PROPN
ejpam-5694	304	4	f(akf(ϖ))u(ϖ)dµ1(ϖ	f(akf(ϖ))u(ϖ)dµ1(ϖ	PROPN
ejpam-5694	304	5	)	)	PUNCT
ejpam-5694	305	1	−	−	PROPN
ejpam-5694	305	2	∫	∫	PROPN
ejpam-5694	305	3	a2	a2	PROPN
ejpam-5694	305	4	a1	a1	PROPN
ejpam-5694	305	5	jgα(f	jgα(f	PROPN
ejpam-5694	305	6	,	,	PUNCT
ejpam-5694	305	7	τ)×	τ)×	X
ejpam-5694	305	8	∑	∑	PROPN
ejpam-5694	305	9	κ	κ	X
ejpam-5694	305	10	(	(	PUNCT
ejpam-5694	305	11	−1)κ	−1)κ	X
ejpam-5694	305	12	f	f	X
ejpam-5694	305	13	(	(	PUNCT
ejpam-5694	305	14	κ)(a2	κ)(a2	PROPN
ejpam-5694	305	15	)	)	PUNCT
ejpam-5694	305	16	κ	κ	NOUN
ejpam-5694	305	17	!	!	PUNCT
ejpam-5694	305	18	(	(	PUNCT
ejpam-5694	305	19	a2	a2	PROPN
ejpam-5694	305	20	−	−	PROPN
ejpam-5694	305	21	τ)κdτ	τ)κdτ	PROPN
ejpam-5694	305	22	.	.	PUNCT
ejpam-5694	306	1	(	(	PUNCT
ejpam-5694	306	2	52	52	NUM
ejpam-5694	306	3	)	)	PUNCT
ejpam-5694	306	4	for	for	ADP
ejpam-5694	306	5	any	any	DET
ejpam-5694	306	6	n	n	PRON
ejpam-5694	306	7	-	-	PUNCT
ejpam-5694	306	8	convex	convex	NOUN
ejpam-5694	306	9	function	function	NOUN
ejpam-5694	306	10	f	f	PROPN
ejpam-5694	306	11	∈	∈	PROPN
ejpam-5694	306	12	cn([a1	cn([a1	PROPN
ejpam-5694	306	13	,	,	PUNCT
ejpam-5694	306	14	a2	a2	PROPN
ejpam-5694	306	15	]	]	PUNCT
ejpam-5694	306	16	)	)	PUNCT
ejpam-5694	306	17	,	,	PUNCT
ejpam-5694	306	18	we	we	PRON
ejpam-5694	306	19	have	have	VERB
ejpam-5694	306	20	hγ(f	hγ(f	PROPN
ejpam-5694	306	21	)	)	PUNCT
ejpam-5694	306	22	≥	≥	NOUN
ejpam-5694	306	23	0	0	NUM
ejpam-5694	306	24	,	,	PUNCT
ejpam-5694	306	25	for	for	ADP
ejpam-5694	306	26	γ	γ	X
ejpam-5694	306	27	=	=	SYM
ejpam-5694	306	28	1	1	NUM
ejpam-5694	306	29	,	,	PUNCT
ejpam-5694	306	30	2	2	NUM
ejpam-5694	306	31	.	.	X
ejpam-5694	306	32	employing	employ	VERB
ejpam-5694	306	33	the	the	DET
ejpam-5694	306	34	linearity	linearity	NOUN
ejpam-5694	306	35	and	and	CCONJ
ejpam-5694	306	36	non	non	ADJ
ejpam-5694	306	37	-	-	NOUN
ejpam-5694	306	38	negativity	negativity	NOUN
ejpam-5694	306	39	of	of	ADP
ejpam-5694	306	40	the	the	DET
ejpam-5694	306	41	functionals	functional	NOUN
ejpam-5694	306	42	given	give	VERB
ejpam-5694	306	43	above	above	ADV
ejpam-5694	306	44	,	,	PUNCT
ejpam-5694	306	45	we	we	PRON
ejpam-5694	306	46	can	can	AUX
ejpam-5694	306	47	obtain	obtain	VERB
ejpam-5694	306	48	the	the	DET
ejpam-5694	306	49	corresponding	corresponding	ADJ
ejpam-5694	306	50	mvt	mvt	PROPN
ejpam-5694	306	51	.	.	PUNCT
ejpam-5694	307	1	theorem	theorem	NOUN
ejpam-5694	307	2	10	10	NUM
ejpam-5694	307	3	.	.	PUNCT
ejpam-5694	308	1	consider	consider	VERB
ejpam-5694	308	2	the	the	DET
ejpam-5694	308	3	aforementioned	aforementioned	ADJ
ejpam-5694	308	4	functionals	functional	NOUN
ejpam-5694	308	5	hγ	hγ	PRON
ejpam-5694	308	6	,	,	PUNCT
ejpam-5694	308	7	γ	γ	NOUN
ejpam-5694	308	8	=	=	SYM
ejpam-5694	308	9	1	1	NUM
ejpam-5694	308	10	,	,	PUNCT
ejpam-5694	308	11	2	2	NUM
ejpam-5694	308	12	defined	define	VERB
ejpam-5694	308	13	in	in	ADP
ejpam-5694	308	14	(	(	PUNCT
ejpam-5694	308	15	51)and	51)and	NUM
ejpam-5694	308	16	(	(	PUNCT
ejpam-5694	308	17	52	52	NUM
ejpam-5694	308	18	)	)	PUNCT
ejpam-5694	308	19	and	and	CCONJ
ejpam-5694	308	20	f	f	PROPN
ejpam-5694	308	21	∈	∈	PROPN
ejpam-5694	308	22	cn([a1	cn([a1	PROPN
ejpam-5694	308	23	,	,	PUNCT
ejpam-5694	308	24	a2	a2	PROPN
ejpam-5694	308	25	]	]	PUNCT
ejpam-5694	308	26	)	)	PUNCT
ejpam-5694	308	27	.	.	PUNCT
ejpam-5694	309	1	then	then	ADV
ejpam-5694	309	2	there	there	PRON
ejpam-5694	309	3	exist	exist	VERB
ejpam-5694	309	4	a1	a1	NOUN
ejpam-5694	309	5	≤	≤	NUM
ejpam-5694	309	6	cγ	cγ	NOUN
ejpam-5694	309	7	≤	≤	NOUN
ejpam-5694	309	8	a2	a2	NOUN
ejpam-5694	309	9	such	such	ADJ
ejpam-5694	309	10	that	that	DET
ejpam-5694	309	11	hγ(f	hγ(f	PROPN
ejpam-5694	309	12	)	)	PUNCT
ejpam-5694	310	1	=	=	SYM
ejpam-5694	310	2	f	f	PROPN
ejpam-5694	310	3	(	(	PUNCT
ejpam-5694	310	4	n)(cγ)hγ(f0	n)(cγ)hγ(f0	NOUN
ejpam-5694	310	5	)	)	PUNCT
ejpam-5694	310	6	γ	γ	NOUN
ejpam-5694	310	7	=	=	SYM
ejpam-5694	310	8	1	1	NUM
ejpam-5694	310	9	,	,	PUNCT
ejpam-5694	310	10	2	2	NUM
ejpam-5694	310	11	,	,	PUNCT
ejpam-5694	310	12	(	(	PUNCT
ejpam-5694	310	13	53	53	NUM
ejpam-5694	310	14	)	)	PUNCT
ejpam-5694	310	15	where	where	SCONJ
ejpam-5694	310	16	f0(x	f0(x	NOUN
ejpam-5694	310	17	)	)	PUNCT
ejpam-5694	310	18	=	=	SYM
ejpam-5694	310	19	xn	xn	PROPN
ejpam-5694	310	20	n	n	CCONJ
ejpam-5694	310	21	!	!	PUNCT
ejpam-5694	310	22	proof	proof	NOUN
ejpam-5694	310	23	.	.	PUNCT
ejpam-5694	311	1	denote	denote	VERB
ejpam-5694	311	2	m	m	NOUN
ejpam-5694	311	3	=	=	ADJ
ejpam-5694	311	4	minf	minf	ADJ
ejpam-5694	311	5	(	(	PUNCT
ejpam-5694	311	6	n	n	CCONJ
ejpam-5694	311	7	)	)	PUNCT
ejpam-5694	311	8	and	and	CCONJ
ejpam-5694	311	9	m	m	VERB
ejpam-5694	311	10	=	=	VERB
ejpam-5694	311	11	maxf	maxf	ADJ
ejpam-5694	311	12	(	(	PUNCT
ejpam-5694	311	13	n	n	CCONJ
ejpam-5694	311	14	)	)	PUNCT
ejpam-5694	311	15	.	.	PUNCT
ejpam-5694	312	1	firstly	firstly	ADV
ejpam-5694	312	2	,	,	PUNCT
ejpam-5694	312	3	we	we	PRON
ejpam-5694	312	4	consider	consider	VERB
ejpam-5694	312	5	h(ϖ	h(ϖ	NOUN
ejpam-5694	312	6	)	)	PUNCT
ejpam-5694	312	7	=	=	SYM
ejpam-5694	312	8	mϖn	mϖn	NOUN
ejpam-5694	312	9	n	n	CCONJ
ejpam-5694	312	10	!	!	PUNCT
ejpam-5694	313	1	−	−	PROPN
ejpam-5694	313	2	f(ϖ	f(ϖ	PROPN
ejpam-5694	313	3	)	)	PUNCT
ejpam-5694	313	4	.	.	PUNCT
ejpam-5694	314	1	then	then	ADV
ejpam-5694	314	2	h(n	h(n	PROPN
ejpam-5694	314	3	)	)	PUNCT
ejpam-5694	314	4	1	1	NUM
ejpam-5694	314	5	(	(	PUNCT
ejpam-5694	314	6	ϖ	ϖ	NOUN
ejpam-5694	314	7	)	)	PUNCT
ejpam-5694	314	8	=	=	NOUN
ejpam-5694	314	9	m	m	VERB
ejpam-5694	314	10	−	−	NOUN
ejpam-5694	314	11	fn	fn	NOUN
ejpam-5694	314	12	≥	≥	NOUN
ejpam-5694	314	13	0	0	NUM
ejpam-5694	314	14	,	,	PUNCT
ejpam-5694	314	15	ϖ	ϖ	PROPN
ejpam-5694	314	16	∈	∈	PROPN
ejpam-5694	314	17	t	t	NOUN
ejpam-5694	314	18	.	.	PUNCT
ejpam-5694	315	1	so	so	ADV
ejpam-5694	315	2	we	we	PRON
ejpam-5694	315	3	can	can	AUX
ejpam-5694	315	4	say	say	VERB
ejpam-5694	315	5	h1	h1	PROPN
ejpam-5694	315	6	is	be	AUX
ejpam-5694	315	7	n	n	PRON
ejpam-5694	315	8	-	-	PUNCT
ejpam-5694	315	9	convex	convex	NOUN
ejpam-5694	315	10	function	function	NOUN
ejpam-5694	315	11	.	.	PUNCT
ejpam-5694	316	1	similarly	similarly	ADV
ejpam-5694	316	2	,	,	PUNCT
ejpam-5694	316	3	h2(ϖ	h2(ϖ	NUM
ejpam-5694	316	4	)	)	PUNCT
ejpam-5694	316	5	=	=	SYM
ejpam-5694	316	6	f(ϖ	f(ϖ	PROPN
ejpam-5694	316	7	)	)	PUNCT
ejpam-5694	316	8	−	−	NOUN
ejpam-5694	316	9	mϖn	mϖn	NOUN
ejpam-5694	316	10	n	n	CCONJ
ejpam-5694	316	11	!	!	PROPN
ejpam-5694	316	12	is	be	AUX
ejpam-5694	316	13	n	n	PRON
ejpam-5694	316	14	-	-	PUNCT
ejpam-5694	316	15	convex	convex	NOUN
ejpam-5694	316	16	.	.	PUNCT
ejpam-5694	317	1	following	follow	VERB
ejpam-5694	317	2	similar	similar	ADJ
ejpam-5694	317	3	steps	step	NOUN
ejpam-5694	317	4	of	of	ADP
ejpam-5694	317	5	[	[	X
ejpam-5694	317	6	3	3	NUM
ejpam-5694	317	7	,	,	PUNCT
ejpam-5694	317	8	theorem	theorem	VERB
ejpam-5694	317	9	7	7	NUM
ejpam-5694	317	10	]	]	PUNCT
ejpam-5694	317	11	for	for	ADP
ejpam-5694	317	12	convex	convex	NOUN
ejpam-5694	317	13	functions	function	NOUN
ejpam-5694	317	14	h1	h1	VERB
ejpam-5694	317	15	and	and	CCONJ
ejpam-5694	317	16	h2	h2	NOUN
ejpam-5694	317	17	we	we	PRON
ejpam-5694	317	18	have	have	VERB
ejpam-5694	317	19	that	that	SCONJ
ejpam-5694	317	20	there	there	PRON
ejpam-5694	317	21	exist	exist	VERB
ejpam-5694	317	22	cγ	cγ	NOUN
ejpam-5694	317	23	for	for	ADP
ejpam-5694	317	24	which	which	PRON
ejpam-5694	317	25	(	(	PUNCT
ejpam-5694	317	26	53	53	NUM
ejpam-5694	317	27	)	)	PUNCT
ejpam-5694	317	28	holds	hold	VERB
ejpam-5694	317	29	.	.	PUNCT
ejpam-5694	318	1	theorem	theorem	NOUN
ejpam-5694	318	2	11	11	NUM
ejpam-5694	318	3	.	.	PUNCT
ejpam-5694	319	1	let	let	VERB
ejpam-5694	319	2	f1,f2	f1,f2	PROPN
ejpam-5694	319	3	∈	∈	PROPN
ejpam-5694	319	4	cn([a1	cn([a1	PROPN
ejpam-5694	319	5	,	,	PUNCT
ejpam-5694	319	6	a2	a2	PROPN
ejpam-5694	319	7	]	]	PUNCT
ejpam-5694	319	8	)	)	PUNCT
ejpam-5694	319	9	and	and	CCONJ
ejpam-5694	319	10	hγ	hγ	ADV
ejpam-5694	319	11	,	,	PUNCT
ejpam-5694	319	12	γ	γ	NOUN
ejpam-5694	319	13	=	=	SYM
ejpam-5694	319	14	1	1	NUM
ejpam-5694	319	15	,	,	PUNCT
ejpam-5694	319	16	2	2	NUM
ejpam-5694	319	17	be	be	AUX
ejpam-5694	319	18	defined	define	VERB
ejpam-5694	319	19	in	in	ADP
ejpam-5694	319	20	(	(	PUNCT
ejpam-5694	319	21	51	51	NUM
ejpam-5694	319	22	)	)	PUNCT
ejpam-5694	319	23	and	and	CCONJ
ejpam-5694	319	24	(	(	PUNCT
ejpam-5694	319	25	52	52	NUM
ejpam-5694	319	26	)	)	PUNCT
ejpam-5694	319	27	.	.	PUNCT
ejpam-5694	320	1	then	then	ADV
ejpam-5694	320	2	there	there	PRON
ejpam-5694	320	3	exist	exist	VERB
ejpam-5694	320	4	cγ	cγ	NOUN
ejpam-5694	320	5	,	,	PUNCT
ejpam-5694	320	6	γ	γ	X
ejpam-5694	320	7	=	=	SYM
ejpam-5694	320	8	1	1	NUM
ejpam-5694	320	9	,	,	PUNCT
ejpam-5694	320	10	2	2	NUM
ejpam-5694	320	11	such	such	ADJ
ejpam-5694	320	12	that	that	SCONJ
ejpam-5694	320	13	f	f	PROPN
ejpam-5694	320	14	(	(	PUNCT
ejpam-5694	320	15	n	n	CCONJ
ejpam-5694	320	16	)	)	PUNCT
ejpam-5694	320	17	1	1	NUM
ejpam-5694	320	18	(	(	PUNCT
ejpam-5694	320	19	cγ	cγ	NOUN
ejpam-5694	320	20	)	)	PUNCT
ejpam-5694	320	21	f	f	PROPN
ejpam-5694	320	22	(	(	PUNCT
ejpam-5694	320	23	n	n	CCONJ
ejpam-5694	320	24	)	)	PUNCT
ejpam-5694	320	25	2	2	NUM
ejpam-5694	320	26	(	(	PUNCT
ejpam-5694	320	27	cγ	cγ	NOUN
ejpam-5694	320	28	)	)	PUNCT
ejpam-5694	320	29	=	=	SYM
ejpam-5694	320	30	hγ(f1	hγ(f1	X
ejpam-5694	320	31	)	)	PUNCT
ejpam-5694	320	32	hγ(f2	hγ(f2	NOUN
ejpam-5694	320	33	)	)	PUNCT
ejpam-5694	320	34	,	,	PUNCT
ejpam-5694	320	35	γ	γ	X
ejpam-5694	320	36	=	=	SYM
ejpam-5694	320	37	1	1	NUM
ejpam-5694	320	38	,	,	PUNCT
ejpam-5694	320	39	2	2	NUM
ejpam-5694	320	40	,	,	PUNCT
ejpam-5694	320	41	(	(	PUNCT
ejpam-5694	320	42	54	54	NUM
ejpam-5694	320	43	)	)	PUNCT
ejpam-5694	320	44	for	for	ADP
ejpam-5694	320	45	denominators	denominator	NOUN
ejpam-5694	320	46	that	that	PRON
ejpam-5694	320	47	are	be	AUX
ejpam-5694	320	48	not	not	PART
ejpam-5694	320	49	equal	equal	ADJ
ejpam-5694	320	50	to	to	ADP
ejpam-5694	320	51	zero	zero	NUM
ejpam-5694	320	52	.	.	PUNCT
ejpam-5694	321	1	proof	proof	NOUN
ejpam-5694	321	2	.	.	PUNCT
ejpam-5694	322	1	the	the	DET
ejpam-5694	322	2	proof	proof	NOUN
ejpam-5694	322	3	follows	follow	VERB
ejpam-5694	322	4	from	from	ADP
ejpam-5694	322	5	[	[	X
ejpam-5694	322	6	3	3	NUM
ejpam-5694	322	7	,	,	PUNCT
ejpam-5694	322	8	corollary	corollary	NOUN
ejpam-5694	322	9	12	12	NUM
ejpam-5694	322	10	]	]	PUNCT
ejpam-5694	322	11	the	the	DET
ejpam-5694	322	12	seminal	seminal	ADJ
ejpam-5694	322	13	concept	concept	NOUN
ejpam-5694	322	14	of	of	ADP
ejpam-5694	322	15	obtaining	obtain	VERB
ejpam-5694	322	16	n	n	CCONJ
ejpam-5694	322	17	-	-	PUNCT
ejpam-5694	322	18	exponentially	exponentially	ADV
ejpam-5694	322	19	convex	convex	NOUN
ejpam-5694	322	20	and	and	CCONJ
ejpam-5694	322	21	exponentially	exponentially	ADV
ejpam-5694	322	22	convex	convex	NOUN
ejpam-5694	322	23	functions	function	NOUN
ejpam-5694	322	24	was	be	AUX
ejpam-5694	322	25	given	give	VERB
ejpam-5694	322	26	in	in	ADP
ejpam-5694	322	27	[	[	X
ejpam-5694	322	28	11	11	NUM
ejpam-5694	322	29	]	]	PUNCT
ejpam-5694	322	30	.	.	PUNCT
ejpam-5694	323	1	we	we	PRON
ejpam-5694	323	2	apply	apply	VERB
ejpam-5694	323	3	aforementioned	aforementioned	ADJ
ejpam-5694	323	4	functionals	functional	NOUN
ejpam-5694	323	5	on	on	ADP
ejpam-5694	323	6	specific	specific	ADJ
ejpam-5694	323	7	family	family	NOUN
ejpam-5694	323	8	given	give	VERB
ejpam-5694	323	9	in	in	ADP
ejpam-5694	323	10	the	the	DET
ejpam-5694	323	11	upcoming	upcoming	ADJ
ejpam-5694	323	12	theorem	theorem	NOUN
ejpam-5694	323	13	which	which	PRON
ejpam-5694	323	14	is	be	AUX
ejpam-5694	323	15	enough	enough	ADJ
ejpam-5694	323	16	to	to	PART
ejpam-5694	323	17	get	get	VERB
ejpam-5694	323	18	criteria	criterion	NOUN
ejpam-5694	323	19	for	for	ADP
ejpam-5694	323	20	the	the	DET
ejpam-5694	323	21	exponential	exponential	ADJ
ejpam-5694	323	22	convexity	convexity	NOUN
ejpam-5694	323	23	of	of	ADP
ejpam-5694	323	24	the	the	DET
ejpam-5694	323	25	family	family	NOUN
ejpam-5694	323	26	of	of	ADP
ejpam-5694	323	27	functions	function	NOUN
ejpam-5694	323	28	on	on	ADP
ejpam-5694	323	29	selection	selection	NOUN
ejpam-5694	323	30	of	of	ADP
ejpam-5694	323	31	any	any	DET
ejpam-5694	323	32	distinct	distinct	ADJ
ejpam-5694	323	33	points	point	NOUN
ejpam-5694	323	34	.	.	PUNCT
ejpam-5694	324	1	theorem	theorem	NOUN
ejpam-5694	324	2	12	12	NUM
ejpam-5694	324	3	.	.	PUNCT
ejpam-5694	325	1	consider	consider	VERB
ejpam-5694	325	2	hγ	hγ	PRON
ejpam-5694	325	3	,	,	PUNCT
ejpam-5694	325	4	γ	γ	X
ejpam-5694	325	5	=	=	SYM
ejpam-5694	325	6	1	1	NUM
ejpam-5694	325	7	,	,	PUNCT
ejpam-5694	325	8	2	2	NUM
ejpam-5694	325	9	be	be	AUX
ejpam-5694	325	10	the	the	DET
ejpam-5694	325	11	functionals	functional	NOUN
ejpam-5694	325	12	defined	define	VERB
ejpam-5694	325	13	in	in	ADP
ejpam-5694	325	14	(	(	PUNCT
ejpam-5694	325	15	51	51	NUM
ejpam-5694	325	16	)	)	PUNCT
ejpam-5694	325	17	and	and	CCONJ
ejpam-5694	325	18	(	(	PUNCT
ejpam-5694	325	19	52	52	NUM
ejpam-5694	325	20	)	)	PUNCT
ejpam-5694	325	21	.	.	PUNCT
ejpam-5694	326	1	let	let	VERB
ejpam-5694	326	2	s	s	PRON
ejpam-5694	326	3	=	=	NOUN
ejpam-5694	326	4	{	{	PUNCT
ejpam-5694	326	5	fµ	fµ	X
ejpam-5694	326	6	:	:	PUNCT
ejpam-5694	326	7	[	[	X
ejpam-5694	326	8	a1	a1	NOUN
ejpam-5694	326	9	,	,	PUNCT
ejpam-5694	326	10	a2	a2	PROPN
ejpam-5694	326	11	]	]	PUNCT
ejpam-5694	326	12	→	→	SYM
ejpam-5694	326	13	r	r	NOUN
ejpam-5694	326	14	}	}	PUNCT
ejpam-5694	326	15	represents	represent	VERB
ejpam-5694	326	16	the	the	DET
ejpam-5694	326	17	class	class	NOUN
ejpam-5694	326	18	of	of	ADP
ejpam-5694	326	19	functions	function	NOUN
ejpam-5694	326	20	having	have	VERB
ejpam-5694	326	21	property	property	NOUN
ejpam-5694	326	22	that	that	PRON
ejpam-5694	326	23	on	on	ADP
ejpam-5694	326	24	choosing	choose	VERB
ejpam-5694	326	25	any	any	PRON
ejpam-5694	326	26	of	of	ADP
ejpam-5694	326	27	r	r	NOUN
ejpam-5694	326	28	+	+	CCONJ
ejpam-5694	326	29	1	1	NUM
ejpam-5694	326	30	distinct	distinct	ADJ
ejpam-5694	326	31	points	point	NOUN
ejpam-5694	326	32	s0	s0	PROPN
ejpam-5694	326	33	,	,	PUNCT
ejpam-5694	326	34	...	...	PUNCT
ejpam-5694	326	35	,	,	PUNCT
ejpam-5694	326	36	sr	sr	PROPN
ejpam-5694	326	37	∈	∈	PROPN
ejpam-5694	326	38	[	[	X
ejpam-5694	326	39	a1	a1	NOUN
ejpam-5694	326	40	,	,	PUNCT
ejpam-5694	326	41	a2	a2	PROPN
ejpam-5694	326	42	]	]	PUNCT
ejpam-5694	326	43	,	,	PUNCT
ejpam-5694	326	44	the	the	DET
ejpam-5694	326	45	mapping	mapping	NOUN
ejpam-5694	326	46	µ	µ	X
ejpam-5694	326	47	→	→	SYM
ejpam-5694	327	1	[	[	X
ejpam-5694	327	2	s0	s0	NOUN
ejpam-5694	327	3	,	,	PUNCT
ejpam-5694	327	4	...	...	PUNCT
ejpam-5694	327	5	,	,	PUNCT
ejpam-5694	327	6	sr	sr	PROPN
ejpam-5694	327	7	;	;	PUNCT
ejpam-5694	327	8	fµ	fµ	PROPN
ejpam-5694	327	9	]	]	X
ejpam-5694	327	10	is	be	AUX
ejpam-5694	327	11	n	n	ADV
ejpam-5694	327	12	-	-	PUNCT
ejpam-5694	327	13	exponentially	exponentially	ADV
ejpam-5694	327	14	convex	convex	NOUN
ejpam-5694	327	15	in	in	ADP
ejpam-5694	327	16	jensen	jensen	PROPN
ejpam-5694	327	17	sense	sense	NOUN
ejpam-5694	327	18	on	on	ADP
ejpam-5694	327	19	t	t	PROPN
ejpam-5694	327	20	so	so	ADV
ejpam-5694	327	21	does	do	VERB
ejpam-5694	327	22	the	the	DET
ejpam-5694	327	23	function	function	NOUN
ejpam-5694	327	24	µ	µ	PROPN
ejpam-5694	327	25	→	→	SYM
ejpam-5694	327	26	hγ(fµ	hγ(fµ	PROPN
ejpam-5694	327	27	)	)	PUNCT
ejpam-5694	327	28	on	on	ADP
ejpam-5694	327	29	t	t	PROPN
ejpam-5694	327	30	.	.	PUNCT
ejpam-5694	328	1	furthermore	furthermore	ADV
ejpam-5694	328	2	,	,	PUNCT
ejpam-5694	328	3	if	if	SCONJ
ejpam-5694	328	4	µ	µ	X
ejpam-5694	328	5	→	→	SYM
ejpam-5694	328	6	hγ(fµ	hγ(fµ	PROPN
ejpam-5694	328	7	)	)	PUNCT
ejpam-5694	328	8	is	be	AUX
ejpam-5694	328	9	continuous	continuous	ADJ
ejpam-5694	328	10	t	t	NOUN
ejpam-5694	328	11	,	,	PUNCT
ejpam-5694	328	12	then	then	ADV
ejpam-5694	328	13	it	it	PRON
ejpam-5694	328	14	is	be	AUX
ejpam-5694	328	15	n	n	ADV
ejpam-5694	328	16	-	-	PUNCT
ejpam-5694	328	17	exponentially	exponentially	ADV
ejpam-5694	328	18	convex	convex	NOUN
ejpam-5694	328	19	on	on	ADP
ejpam-5694	328	20	t	t	PROPN
ejpam-5694	328	21	.	.	PUNCT
ejpam-5694	329	1	a.	a.	PROPN
ejpam-5694	329	2	m.	m.	PROPN
ejpam-5694	329	3	k.	k.	PROPN
ejpam-5694	329	4	abbasi	abbasi	PROPN
ejpam-5694	329	5	,	,	PUNCT
ejpam-5694	329	6	m.	m.	PROPN
ejpam-5694	329	7	anwar	anwar	PROPN
ejpam-5694	329	8	/	/	PUNCT
ejpam-5694	329	9	eur	eur	PROPN
ejpam-5694	329	10	.	.	PUNCT
ejpam-5694	330	1	j.	j.	PROPN
ejpam-5694	330	2	pure	pure	PROPN
ejpam-5694	330	3	appl	appl	PROPN
ejpam-5694	330	4	.	.	PROPN
ejpam-5694	330	5	math	math	PROPN
ejpam-5694	330	6	,	,	PUNCT
ejpam-5694	330	7	18	18	NUM
ejpam-5694	330	8	(	(	PUNCT
ejpam-5694	330	9	1	1	NUM
ejpam-5694	330	10	)	)	PUNCT
ejpam-5694	330	11	(	(	PUNCT
ejpam-5694	330	12	2025	2025	NUM
ejpam-5694	330	13	)	)	PUNCT
ejpam-5694	330	14	,	,	PUNCT
ejpam-5694	330	15	5694	5694	NUM
ejpam-5694	330	16	16	16	NUM
ejpam-5694	330	17	of	of	ADP
ejpam-5694	330	18	18	18	NUM
ejpam-5694	330	19	proof	proof	NOUN
ejpam-5694	330	20	.	.	PUNCT
ejpam-5694	331	1	define	define	VERB
ejpam-5694	331	2	a	a	DET
ejpam-5694	331	3	function	function	NOUN
ejpam-5694	331	4	for	for	ADP
ejpam-5694	331	5	cj	cj	NOUN
ejpam-5694	331	6	∈	∈	PROPN
ejpam-5694	331	7	r	r	NOUN
ejpam-5694	331	8	and	and	CCONJ
ejpam-5694	331	9	µj	µj	PROPN
ejpam-5694	331	10	∈	∈	PROPN
ejpam-5694	331	11	t	t	PROPN
ejpam-5694	331	12	,	,	PUNCT
ejpam-5694	331	13	j	j	PROPN
ejpam-5694	331	14	=	=	SYM
ejpam-5694	331	15	1	1	NUM
ejpam-5694	331	16	,	,	PUNCT
ejpam-5694	331	17	...	...	PUNCT
ejpam-5694	331	18	,	,	PUNCT
ejpam-5694	331	19	n	n	PROPN
ejpam-5694	331	20	and	and	CCONJ
ejpam-5694	331	21	µk	µk	DET
ejpam-5694	331	22	j	j	PROPN
ejpam-5694	332	1	=	=	PUNCT
ejpam-5694	332	2	µi+µj	µi+µj	X
ejpam-5694	332	3	2	2	NUM
ejpam-5694	332	4	,	,	PUNCT
ejpam-5694	332	5	1	1	NUM
ejpam-5694	332	6	≤	≤	PROPN
ejpam-5694	332	7	j	j	PROPN
ejpam-5694	332	8	,	,	PUNCT
ejpam-5694	332	9	k	k	PROPN
ejpam-5694	332	10	≤	≤	PROPN
ejpam-5694	332	11	n	n	CCONJ
ejpam-5694	332	12	as	as	ADP
ejpam-5694	332	13	;	;	PUNCT
ejpam-5694	332	14	ξ(x	ξ(x	NOUN
ejpam-5694	332	15	)	)	PUNCT
ejpam-5694	332	16	=	=	SYM
ejpam-5694	333	1	n∑	n∑	PROPN
ejpam-5694	333	2	j	j	PROPN
ejpam-5694	333	3	,	,	PUNCT
ejpam-5694	333	4	k=1	k=1	PROPN
ejpam-5694	333	5	cjckfµk	cjckfµk	ADV
ejpam-5694	333	6	j	j	PROPN
ejpam-5694	333	7	(	(	PUNCT
ejpam-5694	333	8	x	x	NOUN
ejpam-5694	333	9	)	)	PUNCT
ejpam-5694	333	10	,	,	PUNCT
ejpam-5694	333	11	(	(	PUNCT
ejpam-5694	333	12	55	55	NUM
ejpam-5694	333	13	)	)	PUNCT
ejpam-5694	333	14	where	where	SCONJ
ejpam-5694	333	15	fµk	fµk	PROPN
ejpam-5694	333	16	j	j	X
ejpam-5694	333	17	(	(	PUNCT
ejpam-5694	333	18	x	x	X
ejpam-5694	333	19	)	)	PUNCT
ejpam-5694	333	20	∈	∈	PROPN
ejpam-5694	333	21	s.	s.	PROPN
ejpam-5694	333	22	imploying	imploye	VERB
ejpam-5694	333	23	the	the	DET
ejpam-5694	333	24	assumption	assumption	NOUN
ejpam-5694	333	25	that	that	SCONJ
ejpam-5694	333	26	µ	µ	X
ejpam-5694	333	27	→	→	SYM
ejpam-5694	333	28	[	[	X
ejpam-5694	333	29	s0	s0	NOUN
ejpam-5694	333	30	,	,	PUNCT
ejpam-5694	333	31	...	...	PUNCT
ejpam-5694	333	32	,	,	PUNCT
ejpam-5694	333	33	sn	sn	INTJ
ejpam-5694	333	34	;	;	PUNCT
ejpam-5694	333	35	fµ	fµ	NOUN
ejpam-5694	333	36	]	]	X
ejpam-5694	333	37	is	be	AUX
ejpam-5694	333	38	n	n	ADV
ejpam-5694	333	39	-	-	PUNCT
ejpam-5694	333	40	exponentially	exponentially	ADV
ejpam-5694	333	41	convex	convex	NOUN
ejpam-5694	333	42	in	in	ADP
ejpam-5694	333	43	jensen	jensen	PROPN
ejpam-5694	333	44	sense	sense	NOUN
ejpam-5694	333	45	,	,	PUNCT
ejpam-5694	333	46	we	we	PRON
ejpam-5694	333	47	have	have	AUX
ejpam-5694	333	48	[	[	X
ejpam-5694	333	49	s0	s0	NOUN
ejpam-5694	333	50	,	,	PUNCT
ejpam-5694	333	51	...	...	PUNCT
ejpam-5694	333	52	,	,	PUNCT
ejpam-5694	333	53	sn	sn	PROPN
ejpam-5694	333	54	;	;	PUNCT
ejpam-5694	333	55	ξ	ξ	X
ejpam-5694	333	56	]	]	PUNCT
ejpam-5694	333	57	=	=	SYM
ejpam-5694	333	58	n∑	n∑	PROPN
ejpam-5694	333	59	j	j	PROPN
ejpam-5694	333	60	,	,	PUNCT
ejpam-5694	333	61	k=1	k=1	PROPN
ejpam-5694	334	1	cjck[s0	cjck[s0	PROPN
ejpam-5694	334	2	,	,	PUNCT
ejpam-5694	334	3	...	...	PUNCT
ejpam-5694	334	4	,	,	PUNCT
ejpam-5694	334	5	sn	sn	INTJ
ejpam-5694	334	6	;	;	PUNCT
ejpam-5694	334	7	fµk	fµk	PROPN
ejpam-5694	334	8	j	j	X
ejpam-5694	334	9	]	]	PUNCT
ejpam-5694	334	10	≥	≥	PROPN
ejpam-5694	334	11	0	0	NUM
ejpam-5694	334	12	.	.	PUNCT
ejpam-5694	335	1	(	(	PUNCT
ejpam-5694	335	2	56	56	NUM
ejpam-5694	335	3	)	)	PUNCT
ejpam-5694	335	4	consequently	consequently	ADV
ejpam-5694	335	5	,	,	PUNCT
ejpam-5694	335	6	we	we	PRON
ejpam-5694	335	7	have	have	VERB
ejpam-5694	335	8	hγ(ξ	hγ(ξ	NOUN
ejpam-5694	335	9	)	)	PUNCT
ejpam-5694	336	1	=	=	SYM
ejpam-5694	336	2	n∑	n∑	PROPN
ejpam-5694	336	3	j	j	PROPN
ejpam-5694	336	4	,	,	PUNCT
ejpam-5694	336	5	k=1	k=1	PROPN
ejpam-5694	336	6	cjckhγ(fµk	cjckhγ(fµk	PROPN
ejpam-5694	336	7	j	j	PROPN
ejpam-5694	336	8	)	)	PUNCT
ejpam-5694	336	9	≥	≥	PROPN
ejpam-5694	336	10	0	0	NUM
ejpam-5694	336	11	,	,	PUNCT
ejpam-5694	336	12	(	(	PUNCT
ejpam-5694	336	13	57	57	NUM
ejpam-5694	336	14	)	)	PUNCT
ejpam-5694	336	15	for	for	ADP
ejpam-5694	336	16	each	each	DET
ejpam-5694	336	17	γ	γ	X
ejpam-5694	336	18	=	=	SYM
ejpam-5694	336	19	1	1	NUM
ejpam-5694	336	20	,	,	PUNCT
ejpam-5694	336	21	2	2	NUM
ejpam-5694	336	22	.	.	X
ejpam-5694	336	23	from	from	ADP
ejpam-5694	336	24	this	this	DET
ejpam-5694	336	25	relation	relation	NOUN
ejpam-5694	336	26	,	,	PUNCT
ejpam-5694	336	27	it	it	PRON
ejpam-5694	336	28	is	be	AUX
ejpam-5694	336	29	evident	evident	ADJ
ejpam-5694	336	30	that	that	SCONJ
ejpam-5694	336	31	hγ(fµ	hγ(fµ	PROPN
ejpam-5694	336	32	)	)	PUNCT
ejpam-5694	336	33	is	be	AUX
ejpam-5694	336	34	n	n	ADV
ejpam-5694	336	35	-	-	PUNCT
ejpam-5694	336	36	exponentially	exponentially	ADV
ejpam-5694	336	37	convex	convex	NOUN
ejpam-5694	336	38	in	in	ADP
ejpam-5694	336	39	jensen	jensen	PROPN
ejpam-5694	336	40	sense	sense	NOUN
ejpam-5694	336	41	on	on	ADP
ejpam-5694	336	42	t	t	PROPN
ejpam-5694	336	43	.	.	PUNCT
ejpam-5694	337	1	also	also	ADV
ejpam-5694	337	2	if	if	SCONJ
ejpam-5694	337	3	we	we	PRON
ejpam-5694	337	4	take	take	VERB
ejpam-5694	337	5	continuity	continuity	NOUN
ejpam-5694	337	6	of	of	ADP
ejpam-5694	337	7	µ	µ	X
ejpam-5694	337	8	→	→	SYM
ejpam-5694	337	9	hγ(fµ	hγ(fµ	PROPN
ejpam-5694	337	10	)	)	PUNCT
ejpam-5694	337	11	under	under	ADP
ejpam-5694	337	12	consideration	consideration	NOUN
ejpam-5694	337	13	then	then	ADV
ejpam-5694	337	14	it	it	PRON
ejpam-5694	337	15	is	be	AUX
ejpam-5694	337	16	n	n	ADV
ejpam-5694	337	17	-	-	PUNCT
ejpam-5694	337	18	exponentially	exponentially	ADV
ejpam-5694	337	19	convex	convex	NOUN
ejpam-5694	337	20	on	on	ADP
ejpam-5694	337	21	t	t	PROPN
ejpam-5694	337	22	.	.	PUNCT
ejpam-5694	338	1	some	some	PRON
ejpam-5694	338	2	of	of	ADP
ejpam-5694	338	3	the	the	DET
ejpam-5694	338	4	consequences	consequence	NOUN
ejpam-5694	338	5	of	of	ADP
ejpam-5694	338	6	theorem	theorem	NOUN
ejpam-5694	338	7	12	12	NUM
ejpam-5694	338	8	can	can	AUX
ejpam-5694	338	9	be	be	AUX
ejpam-5694	338	10	obtained	obtain	VERB
ejpam-5694	338	11	in	in	ADP
ejpam-5694	338	12	the	the	DET
ejpam-5694	338	13	form	form	NOUN
ejpam-5694	338	14	of	of	ADP
ejpam-5694	338	15	results	result	NOUN
ejpam-5694	338	16	given	give	VERB
ejpam-5694	338	17	in	in	ADP
ejpam-5694	338	18	corollary	corollary	ADJ
ejpam-5694	338	19	4.4.1	4.4.1	NUM
ejpam-5694	338	20	and	and	CCONJ
ejpam-5694	338	21	4.4.2	4.4.2	NUM
ejpam-5694	338	22	in	in	ADP
ejpam-5694	338	23	[	[	X
ejpam-5694	338	24	15	15	NUM
ejpam-5694	338	25	]	]	SYM
ejpam-5694	338	26	6	6	NUM
ejpam-5694	338	27	.	.	X
ejpam-5694	338	28	conclusion	conclusion	VERB
ejpam-5694	338	29	the	the	DET
ejpam-5694	338	30	study	study	NOUN
ejpam-5694	338	31	under	under	ADP
ejpam-5694	338	32	consideration	consideration	NOUN
ejpam-5694	338	33	is	be	AUX
ejpam-5694	338	34	the	the	DET
ejpam-5694	338	35	advancement	advancement	NOUN
ejpam-5694	338	36	and	and	CCONJ
ejpam-5694	338	37	analysis	analysis	NOUN
ejpam-5694	338	38	of	of	ADP
ejpam-5694	338	39	hardy	hardy	ADJ
ejpam-5694	338	40	-	-	PUNCT
ejpam-5694	338	41	type	type	NOUN
ejpam-5694	338	42	inequalities	inequality	NOUN
ejpam-5694	338	43	using	use	VERB
ejpam-5694	338	44	the	the	DET
ejpam-5694	338	45	two	two	NUM
ejpam-5694	338	46	-	-	PUNCT
ejpam-5694	338	47	point	point	NOUN
ejpam-5694	338	48	right	right	ADJ
ejpam-5694	338	49	focal	focal	ADJ
ejpam-5694	338	50	problem	problem	NOUN
ejpam-5694	338	51	-	-	PUNCT
ejpam-5694	338	52	type	type	NOUN
ejpam-5694	338	53	green	green	ADJ
ejpam-5694	338	54	functions	function	NOUN
ejpam-5694	338	55	and	and	CCONJ
ejpam-5694	338	56	taylor	taylor	PROPN
ejpam-5694	338	57	’s	’s	PART
ejpam-5694	338	58	polynomial	polynomial	NOUN
ejpam-5694	338	59	that	that	PRON
ejpam-5694	338	60	can	can	AUX
ejpam-5694	338	61	be	be	AUX
ejpam-5694	338	62	seen	see	VERB
ejpam-5694	338	63	in	in	ADP
ejpam-5694	338	64	theorem	theorem	ADJ
ejpam-5694	338	65	4	4	NUM
ejpam-5694	338	66	,	,	PUNCT
ejpam-5694	338	67	theorem	theorem	VERB
ejpam-5694	338	68	5	5	NUM
ejpam-5694	338	69	and	and	CCONJ
ejpam-5694	338	70	theorem	theorem	VERB
ejpam-5694	338	71	6	6	NUM
ejpam-5694	338	72	.	.	PUNCT
ejpam-5694	338	73	also	also	ADV
ejpam-5694	338	74	,	,	PUNCT
ejpam-5694	338	75	bounds	bound	VERB
ejpam-5694	338	76	on	on	ADP
ejpam-5694	338	77	the	the	DET
ejpam-5694	338	78	remainders	remainder	NOUN
ejpam-5694	338	79	are	be	AUX
ejpam-5694	338	80	found	find	VERB
ejpam-5694	338	81	in	in	ADP
ejpam-5694	338	82	theorem	theorem	NOUN
ejpam-5694	338	83	7	7	NUM
ejpam-5694	338	84	by	by	ADP
ejpam-5694	338	85	using	use	VERB
ejpam-5694	338	86	čebyšev	čebyšev	PROPN
ejpam-5694	338	87	functional	functional	ADJ
ejpam-5694	338	88	.	.	PUNCT
ejpam-5694	339	1	in	in	ADP
ejpam-5694	339	2	the	the	DET
ejpam-5694	339	3	same	same	ADJ
ejpam-5694	339	4	section	section	NOUN
ejpam-5694	339	5	4	4	NUM
ejpam-5694	339	6	we	we	PRON
ejpam-5694	339	7	discussed	discuss	VERB
ejpam-5694	339	8	the	the	DET
ejpam-5694	339	9	grüss	grüss	NOUN
ejpam-5694	339	10	-	-	PUNCT
ejpam-5694	339	11	type	type	NOUN
ejpam-5694	339	12	inequalities	inequality	NOUN
ejpam-5694	339	13	in	in	ADP
ejpam-5694	339	14	theorem	theorem	NOUN
ejpam-5694	339	15	8	8	NUM
ejpam-5694	339	16	to	to	PART
ejpam-5694	339	17	find	find	VERB
ejpam-5694	339	18	the	the	DET
ejpam-5694	339	19	bound	bind	VERB
ejpam-5694	339	20	and	and	CCONJ
ejpam-5694	339	21	ostrowski	ostrowski	ADJ
ejpam-5694	339	22	-	-	PUNCT
ejpam-5694	339	23	type	type	NOUN
ejpam-5694	339	24	inequalities	inequality	NOUN
ejpam-5694	339	25	in	in	ADP
ejpam-5694	339	26	theorem	theorem	NOUN
ejpam-5694	339	27	9	9	NUM
ejpam-5694	339	28	related	relate	VERB
ejpam-5694	339	29	to	to	ADP
ejpam-5694	339	30	the	the	DET
ejpam-5694	339	31	hardy	hardy	ADJ
ejpam-5694	339	32	-	-	PUNCT
ejpam-5694	339	33	type	type	NOUN
ejpam-5694	339	34	inequalities	inequality	NOUN
ejpam-5694	339	35	via	via	ADP
ejpam-5694	339	36	taylor	taylor	PROPN
ejpam-5694	339	37	’s	’s	PART
ejpam-5694	339	38	polynomial	polynomial	ADJ
ejpam-5694	339	39	and	and	CCONJ
ejpam-5694	339	40	green	green	ADJ
ejpam-5694	339	41	function	function	NOUN
ejpam-5694	339	42	.	.	PUNCT
ejpam-5694	340	1	next	next	ADV
ejpam-5694	340	2	,	,	PUNCT
ejpam-5694	340	3	we	we	PRON
ejpam-5694	340	4	discuss	discuss	VERB
ejpam-5694	340	5	the	the	DET
ejpam-5694	340	6	mean	mean	ADJ
ejpam-5694	340	7	value	value	NOUN
ejpam-5694	340	8	theorem	theorem	NOUN
ejpam-5694	340	9	for	for	ADP
ejpam-5694	340	10	the	the	DET
ejpam-5694	340	11	functionals	functional	NOUN
ejpam-5694	340	12	(	(	PUNCT
ejpam-5694	340	13	51	51	NUM
ejpam-5694	340	14	)	)	PUNCT
ejpam-5694	340	15	and	and	CCONJ
ejpam-5694	340	16	(	(	PUNCT
ejpam-5694	340	17	52	52	NUM
ejpam-5694	340	18	)	)	PUNCT
ejpam-5694	340	19	obtained	obtain	VERB
ejpam-5694	340	20	from	from	ADP
ejpam-5694	340	21	our	our	PRON
ejpam-5694	340	22	main	main	ADJ
ejpam-5694	340	23	results	result	NOUN
ejpam-5694	340	24	and	and	CCONJ
ejpam-5694	340	25	then	then	ADV
ejpam-5694	340	26	make	make	VERB
ejpam-5694	340	27	use	use	NOUN
ejpam-5694	340	28	of	of	ADP
ejpam-5694	340	29	them	they	PRON
ejpam-5694	340	30	to	to	PART
ejpam-5694	340	31	get	get	VERB
ejpam-5694	340	32	results	result	NOUN
ejpam-5694	340	33	in	in	ADP
ejpam-5694	340	34	the	the	DET
ejpam-5694	340	35	form	form	NOUN
ejpam-5694	340	36	of	of	ADP
ejpam-5694	340	37	mvt	mvt	NOUN
ejpam-5694	340	38	given	give	VERB
ejpam-5694	340	39	in	in	ADP
ejpam-5694	340	40	theorem	theorem	ADJ
ejpam-5694	340	41	10	10	NUM
ejpam-5694	340	42	and	and	CCONJ
ejpam-5694	340	43	theorem	theorem	VERB
ejpam-5694	340	44	11	11	NUM
ejpam-5694	340	45	.	.	PUNCT
ejpam-5694	341	1	finally	finally	ADV
ejpam-5694	341	2	,	,	PUNCT
ejpam-5694	341	3	using	use	VERB
ejpam-5694	341	4	obtained	obtain	VERB
ejpam-5694	341	5	functionals	functional	NOUN
ejpam-5694	341	6	(	(	PUNCT
ejpam-5694	341	7	51	51	NUM
ejpam-5694	341	8	)	)	PUNCT
ejpam-5694	341	9	and	and	CCONJ
ejpam-5694	341	10	(	(	PUNCT
ejpam-5694	341	11	52	52	NUM
ejpam-5694	341	12	)	)	PUNCT
ejpam-5694	341	13	the	the	DET
ejpam-5694	341	14	n	n	CCONJ
ejpam-5694	341	15	-	-	PUNCT
ejpam-5694	341	16	exponential	exponential	ADJ
ejpam-5694	341	17	convexity	convexity	NOUN
ejpam-5694	341	18	is	be	AUX
ejpam-5694	341	19	discussed	discuss	VERB
ejpam-5694	341	20	as	as	ADP
ejpam-5694	341	21	in	in	ADP
ejpam-5694	341	22	theorem	theorem	NOUN
ejpam-5694	341	23	12	12	NUM
ejpam-5694	341	24	.	.	PUNCT
ejpam-5694	342	1	acknowledgements	acknowledgement	NOUN
ejpam-5694	342	2	the	the	DET
ejpam-5694	342	3	authors	author	NOUN
ejpam-5694	342	4	appreciate	appreciate	VERB
ejpam-5694	342	5	indebtedly	indebtedly	ADV
ejpam-5694	342	6	,	,	PUNCT
ejpam-5694	342	7	the	the	DET
ejpam-5694	342	8	anonymous	anonymous	ADJ
ejpam-5694	342	9	referees	referee	NOUN
ejpam-5694	342	10	for	for	ADP
ejpam-5694	342	11	their	their	PRON
ejpam-5694	342	12	meticulous	meticulous	ADJ
ejpam-5694	342	13	reading	reading	NOUN
ejpam-5694	342	14	of	of	ADP
ejpam-5694	342	15	the	the	DET
ejpam-5694	342	16	manuscript	manuscript	NOUN
ejpam-5694	342	17	and	and	CCONJ
ejpam-5694	342	18	for	for	ADP
ejpam-5694	342	19	fruitful	fruitful	ADJ
ejpam-5694	342	20	comments	comment	NOUN
ejpam-5694	342	21	and	and	CCONJ
ejpam-5694	342	22	suggestions	suggestion	NOUN
ejpam-5694	342	23	.	.	PUNCT
ejpam-5694	343	1	a.	a.	PROPN
ejpam-5694	343	2	m.	m.	PROPN
ejpam-5694	343	3	k.	k.	PROPN
ejpam-5694	343	4	abbasi	abbasi	PROPN
ejpam-5694	343	5	,	,	PUNCT
ejpam-5694	343	6	m.	m.	PROPN
ejpam-5694	343	7	anwar	anwar	PROPN
ejpam-5694	343	8	/	/	PUNCT
ejpam-5694	343	9	eur	eur	PROPN
ejpam-5694	343	10	.	.	PUNCT
ejpam-5694	344	1	j.	j.	PROPN
ejpam-5694	344	2	pure	pure	PROPN
ejpam-5694	344	3	appl	appl	PROPN
ejpam-5694	344	4	.	.	PROPN
ejpam-5694	344	5	math	math	PROPN
ejpam-5694	344	6	,	,	PUNCT
ejpam-5694	344	7	18	18	NUM
ejpam-5694	344	8	(	(	PUNCT
ejpam-5694	344	9	1	1	NUM
ejpam-5694	344	10	)	)	PUNCT
ejpam-5694	344	11	(	(	PUNCT
ejpam-5694	344	12	2025	2025	NUM
ejpam-5694	344	13	)	)	PUNCT
ejpam-5694	344	14	,	,	PUNCT
ejpam-5694	344	15	5694	5694	NUM
ejpam-5694	344	16	17	17	NUM
ejpam-5694	344	17	of	of	ADP
ejpam-5694	344	18	18	18	NUM
ejpam-5694	344	19	references	reference	NOUN
ejpam-5694	344	20	[	[	X
ejpam-5694	344	21	1	1	X
ejpam-5694	344	22	]	]	PUNCT
ejpam-5694	344	23	muhammad	muhammad	PROPN
ejpam-5694	344	24	adeel	adeel	PROPN
ejpam-5694	344	25	,	,	PUNCT
ejpam-5694	344	26	khuram	khuram	PROPN
ejpam-5694	344	27	ali	ali	PROPN
ejpam-5694	344	28	khan	khan	PROPN
ejpam-5694	344	29	,	,	PUNCT
ejpam-5694	344	30	dilda	dilda	NOUN
ejpam-5694	344	31	pečarić	pečarić	PROPN
ejpam-5694	344	32	,	,	PUNCT
ejpam-5694	344	33	and	and	CCONJ
ejpam-5694	344	34	josip	josip	PROPN
ejpam-5694	344	35	pečarić.	pečarić.	PROPN
ejpam-5694	344	36	estimation	estimation	NOUN
ejpam-5694	344	37	of	of	ADP
ejpam-5694	344	38	f	f	NOUN
ejpam-5694	344	39	-	-	PUNCT
ejpam-5694	344	40	divergence	divergence	NOUN
ejpam-5694	344	41	and	and	CCONJ
ejpam-5694	344	42	shannon	shannon	PROPN
ejpam-5694	344	43	entropy	entropy	PROPN
ejpam-5694	344	44	by	by	ADP
ejpam-5694	344	45	levinson	levinson	PROPN
ejpam-5694	344	46	type	type	PROPN
ejpam-5694	344	47	inequalities	inequality	NOUN
ejpam-5694	344	48	via	via	ADP
ejpam-5694	344	49	new	new	ADJ
ejpam-5694	344	50	green	green	PROPN
ejpam-5694	344	51	’s	’s	PART
ejpam-5694	344	52	functions	function	NOUN
ejpam-5694	344	53	and	and	CCONJ
ejpam-5694	344	54	lidstone	lidstone	VERB
ejpam-5694	344	55	polynomial	polynomial	ADJ
ejpam-5694	344	56	.	.	PUNCT
ejpam-5694	345	1	advances	advance	NOUN
ejpam-5694	345	2	in	in	ADP
ejpam-5694	345	3	difference	difference	NOUN
ejpam-5694	345	4	equations	equation	NOUN
ejpam-5694	345	5	,	,	PUNCT
ejpam-5694	345	6	2020(1):27	2020(1):27	NUM
ejpam-5694	345	7	,	,	PUNCT
ejpam-5694	345	8	2020	2020	NUM
ejpam-5694	345	9	.	.	PUNCT
ejpam-5694	346	1	[	[	X
ejpam-5694	346	2	2	2	NUM
ejpam-5694	346	3	]	]	PUNCT
ejpam-5694	346	4	ravi	ravi	NOUN
ejpam-5694	346	5	p	p	PROPN
ejpam-5694	346	6	agarwal	agarwal	PROPN
ejpam-5694	346	7	and	and	CCONJ
ejpam-5694	346	8	patricia	patricia	PROPN
ejpam-5694	346	9	jy	jy	PROPN
ejpam-5694	346	10	wong	wong	PROPN
ejpam-5694	346	11	.	.	PUNCT
ejpam-5694	347	1	error	error	NOUN
ejpam-5694	347	2	inequalities	inequality	NOUN
ejpam-5694	347	3	in	in	ADP
ejpam-5694	347	4	polynomial	polynomial	ADJ
ejpam-5694	347	5	interpolation	interpolation	NOUN
ejpam-5694	347	6	and	and	CCONJ
ejpam-5694	347	7	their	their	PRON
ejpam-5694	347	8	applications	application	NOUN
ejpam-5694	347	9	,	,	PUNCT
ejpam-5694	347	10	volume	volume	NOUN
ejpam-5694	347	11	262	262	NUM
ejpam-5694	347	12	.	.	PUNCT
ejpam-5694	348	1	springer	springer	PROPN
ejpam-5694	348	2	science	science	PROPN
ejpam-5694	348	3	&	&	CCONJ
ejpam-5694	348	4	business	business	NOUN
ejpam-5694	348	5	media	medium	NOUN
ejpam-5694	348	6	,	,	PUNCT
ejpam-5694	348	7	2012	2012	NUM
ejpam-5694	348	8	.	.	PUNCT
ejpam-5694	349	1	[	[	X
ejpam-5694	349	2	3	3	X
ejpam-5694	349	3	]	]	X
ejpam-5694	349	4	gorana	gorana	PROPN
ejpam-5694	349	5	aras	aras	PROPN
ejpam-5694	349	6	-	-	PUNCT
ejpam-5694	349	7	gazić	gazić	ADJ
ejpam-5694	349	8	,	,	PUNCT
ejpam-5694	349	9	vera	vera	NOUN
ejpam-5694	349	10	čuljak	čuljak	X
ejpam-5694	349	11	,	,	PUNCT
ejpam-5694	349	12	josip	josip	PROPN
ejpam-5694	349	13	pečarić	pečarić	PROPN
ejpam-5694	349	14	,	,	PUNCT
ejpam-5694	349	15	and	and	CCONJ
ejpam-5694	349	16	ana	ana	PROPN
ejpam-5694	349	17	vukelić.	vukelić.	PROPN
ejpam-5694	349	18	generalization	generalization	NOUN
ejpam-5694	349	19	of	of	ADP
ejpam-5694	349	20	jensen	jensen	PROPN
ejpam-5694	349	21	’s	’s	PART
ejpam-5694	349	22	inequality	inequality	NOUN
ejpam-5694	349	23	by	by	ADP
ejpam-5694	349	24	lidstone	lidstone	PROPN
ejpam-5694	349	25	’s	’s	PART
ejpam-5694	349	26	polynomial	polynomial	ADJ
ejpam-5694	349	27	and	and	CCONJ
ejpam-5694	349	28	related	related	ADJ
ejpam-5694	349	29	results	result	NOUN
ejpam-5694	349	30	.	.	PUNCT
ejpam-5694	350	1	mathematical	mathematical	ADJ
ejpam-5694	350	2	inequalities	inequality	NOUN
ejpam-5694	350	3	&	&	CCONJ
ejpam-5694	350	4	applications	application	NOUN
ejpam-5694	350	5	,	,	PUNCT
ejpam-5694	350	6	16(4):1243–1267	16(4):1243–1267	NUM
ejpam-5694	350	7	,	,	PUNCT
ejpam-5694	350	8	2013	2013	NUM
ejpam-5694	350	9	.	.	PUNCT
ejpam-5694	351	1	[	[	X
ejpam-5694	351	2	4	4	NUM
ejpam-5694	351	3	]	]	X
ejpam-5694	351	4	alberto	alberto	PROPN
ejpam-5694	351	5	cabada	cabada	PROPN
ejpam-5694	351	6	and	and	CCONJ
ejpam-5694	351	7	alberto	alberto	PROPN
ejpam-5694	351	8	cabada	cabada	PROPN
ejpam-5694	351	9	.	.	PUNCT
ejpam-5694	352	1	green	green	PROPN
ejpam-5694	352	2	’s	’s	PART
ejpam-5694	352	3	functions	function	NOUN
ejpam-5694	352	4	in	in	ADP
ejpam-5694	352	5	the	the	DET
ejpam-5694	352	6	theory	theory	NOUN
ejpam-5694	352	7	of	of	ADP
ejpam-5694	352	8	ordinary	ordinary	ADJ
ejpam-5694	352	9	differential	differential	ADJ
ejpam-5694	352	10	equations	equation	NOUN
ejpam-5694	352	11	.	.	PUNCT
ejpam-5694	353	1	springer	springer	NOUN
ejpam-5694	353	2	,	,	PUNCT
ejpam-5694	353	3	2014	2014	NUM
ejpam-5694	353	4	.	.	PUNCT
ejpam-5694	354	1	[	[	X
ejpam-5694	354	2	5	5	X
ejpam-5694	354	3	]	]	X
ejpam-5694	354	4	p	p	X
ejpam-5694	354	5	cerone	cerone	NOUN
ejpam-5694	354	6	and	and	CCONJ
ejpam-5694	354	7	ss	ss	NOUN
ejpam-5694	354	8	dragomir	dragomir	NOUN
ejpam-5694	354	9	.	.	PUNCT
ejpam-5694	355	1	some	some	DET
ejpam-5694	355	2	new	new	ADJ
ejpam-5694	355	3	ostrowski	ostrowski	ADJ
ejpam-5694	355	4	-	-	PUNCT
ejpam-5694	355	5	type	type	NOUN
ejpam-5694	355	6	bounds	bound	NOUN
ejpam-5694	355	7	for	for	ADP
ejpam-5694	355	8	the	the	DET
ejpam-5694	355	9	cebyšev	cebyšev	PROPN
ejpam-5694	355	10	functional	functional	ADJ
ejpam-5694	355	11	and	and	CCONJ
ejpam-5694	355	12	applications	application	NOUN
ejpam-5694	355	13	.	.	PUNCT
ejpam-5694	356	1	j.	j.	PROPN
ejpam-5694	356	2	math	math	PROPN
ejpam-5694	356	3	.	.	PUNCT
ejpam-5694	357	1	inequal	inequal	ADJ
ejpam-5694	357	2	,	,	PUNCT
ejpam-5694	357	3	8(1):159–170	8(1):159–170	NUM
ejpam-5694	357	4	,	,	PUNCT
ejpam-5694	357	5	2014	2014	NUM
ejpam-5694	357	6	.	.	PUNCT
ejpam-5694	358	1	[	[	X
ejpam-5694	358	2	6	6	NUM
ejpam-5694	358	3	]	]	X
ejpam-5694	358	4	smina	smina	ADJ
ejpam-5694	358	5	djennadi	djennadi	NOUN
ejpam-5694	358	6	,	,	PUNCT
ejpam-5694	358	7	nabil	nabil	NOUN
ejpam-5694	358	8	shawagfeh	shawagfeh	NOUN
ejpam-5694	358	9	,	,	PUNCT
ejpam-5694	358	10	and	and	CCONJ
ejpam-5694	358	11	omar	omar	PROPN
ejpam-5694	358	12	abu	abu	PROPN
ejpam-5694	358	13	arqub	arqub	PROPN
ejpam-5694	358	14	.	.	PUNCT
ejpam-5694	359	1	a	a	DET
ejpam-5694	359	2	fractional	fractional	ADJ
ejpam-5694	359	3	tikhonov	tikhonov	NOUN
ejpam-5694	359	4	regularization	regularization	NOUN
ejpam-5694	359	5	method	method	NOUN
ejpam-5694	359	6	for	for	ADP
ejpam-5694	359	7	an	an	DET
ejpam-5694	359	8	inverse	inverse	NOUN
ejpam-5694	359	9	backward	backward	NOUN
ejpam-5694	359	10	and	and	CCONJ
ejpam-5694	359	11	source	source	NOUN
ejpam-5694	359	12	problems	problem	NOUN
ejpam-5694	359	13	in	in	ADP
ejpam-5694	359	14	the	the	DET
ejpam-5694	359	15	time	time	NOUN
ejpam-5694	359	16	-	-	PUNCT
ejpam-5694	359	17	space	space	NOUN
ejpam-5694	359	18	fractional	fractional	ADJ
ejpam-5694	359	19	diffusion	diffusion	NOUN
ejpam-5694	359	20	equations	equation	NOUN
ejpam-5694	359	21	.	.	PUNCT
ejpam-5694	360	1	chaos	chaos	NOUN
ejpam-5694	360	2	,	,	PUNCT
ejpam-5694	360	3	solitons	soliton	NOUN
ejpam-5694	360	4	&	&	CCONJ
ejpam-5694	360	5	fractals	fractal	NOUN
ejpam-5694	360	6	,	,	PUNCT
ejpam-5694	360	7	150:111127	150:111127	NUM
ejpam-5694	360	8	,	,	PUNCT
ejpam-5694	360	9	2021	2021	NUM
ejpam-5694	360	10	.	.	PUNCT
ejpam-5694	361	1	[	[	X
ejpam-5694	361	2	7	7	NUM
ejpam-5694	361	3	]	]	X
ejpam-5694	361	4	smina	smina	ADJ
ejpam-5694	361	5	djennadi	djennadi	NOUN
ejpam-5694	361	6	,	,	PUNCT
ejpam-5694	361	7	nabil	nabil	NOUN
ejpam-5694	361	8	shawagfeh	shawagfeh	NOUN
ejpam-5694	361	9	,	,	PUNCT
ejpam-5694	361	10	ms	ms	PROPN
ejpam-5694	361	11	osman	osman	PROPN
ejpam-5694	361	12	,	,	PUNCT
ejpam-5694	361	13	jf	jf	PROPN
ejpam-5694	361	14	gómez	gómez	NOUN
ejpam-5694	361	15	-	-	PUNCT
ejpam-5694	361	16	aguilar	aguilar	ADJ
ejpam-5694	361	17	,	,	PUNCT
ejpam-5694	361	18	omar	omar	PROPN
ejpam-5694	361	19	abu	abu	PROPN
ejpam-5694	361	20	arqub	arqub	PROPN
ejpam-5694	361	21	,	,	PUNCT
ejpam-5694	361	22	et	et	PROPN
ejpam-5694	361	23	al	al	PROPN
ejpam-5694	361	24	.	.	PUNCT
ejpam-5694	362	1	the	the	DET
ejpam-5694	362	2	tikhonov	tikhonov	NOUN
ejpam-5694	362	3	regularization	regularization	NOUN
ejpam-5694	362	4	method	method	NOUN
ejpam-5694	362	5	for	for	ADP
ejpam-5694	362	6	the	the	DET
ejpam-5694	362	7	inverse	inverse	NOUN
ejpam-5694	362	8	source	source	NOUN
ejpam-5694	362	9	problem	problem	NOUN
ejpam-5694	362	10	of	of	ADP
ejpam-5694	362	11	time	time	NOUN
ejpam-5694	362	12	fractional	fractional	ADJ
ejpam-5694	362	13	heat	heat	NOUN
ejpam-5694	362	14	equation	equation	NOUN
ejpam-5694	362	15	in	in	ADP
ejpam-5694	362	16	the	the	DET
ejpam-5694	362	17	view	view	NOUN
ejpam-5694	362	18	of	of	ADP
ejpam-5694	362	19	abc	abc	PROPN
ejpam-5694	362	20	-	-	PUNCT
ejpam-5694	362	21	fractional	fractional	ADJ
ejpam-5694	362	22	technique	technique	NOUN
ejpam-5694	362	23	.	.	PUNCT
ejpam-5694	363	1	physica	physica	PROPN
ejpam-5694	363	2	scripta	scripta	PROPN
ejpam-5694	363	3	,	,	PUNCT
ejpam-5694	363	4	96(9):094006	96(9):094006	NUM
ejpam-5694	363	5	,	,	PUNCT
ejpam-5694	363	6	2021	2021	NUM
ejpam-5694	363	7	.	.	PUNCT
ejpam-5694	364	1	[	[	X
ejpam-5694	364	2	8	8	NUM
ejpam-5694	364	3	]	]	X
ejpam-5694	364	4	george	george	PROPN
ejpam-5694	364	5	green	green	PROPN
ejpam-5694	364	6	.	.	PUNCT
ejpam-5694	365	1	an	an	DET
ejpam-5694	365	2	essay	essay	NOUN
ejpam-5694	365	3	on	on	ADP
ejpam-5694	365	4	the	the	DET
ejpam-5694	365	5	application	application	NOUN
ejpam-5694	365	6	of	of	ADP
ejpam-5694	365	7	mathematical	mathematical	ADJ
ejpam-5694	365	8	analysis	analysis	NOUN
ejpam-5694	365	9	to	to	ADP
ejpam-5694	365	10	the	the	DET
ejpam-5694	365	11	theories	theory	NOUN
ejpam-5694	365	12	of	of	ADP
ejpam-5694	365	13	electricity	electricity	NOUN
ejpam-5694	365	14	and	and	CCONJ
ejpam-5694	365	15	magnetism	magnetism	NOUN
ejpam-5694	365	16	.	.	PUNCT
ejpam-5694	366	1	1852	1852	NUM
ejpam-5694	366	2	.	.	PUNCT
ejpam-5694	367	1	[	[	X
ejpam-5694	367	2	9	9	NUM
ejpam-5694	367	3	]	]	X
ejpam-5694	367	4	gh	gh	PROPN
ejpam-5694	367	5	hardy	hardy	PROPN
ejpam-5694	367	6	.	.	PUNCT
ejpam-5694	368	1	notes	note	NOUN
ejpam-5694	368	2	on	on	ADP
ejpam-5694	368	3	some	some	DET
ejpam-5694	368	4	points	point	NOUN
ejpam-5694	368	5	in	in	ADP
ejpam-5694	368	6	the	the	DET
ejpam-5694	368	7	integral	integral	ADJ
ejpam-5694	368	8	calculus	calculus	NOUN
ejpam-5694	368	9	(	(	PUNCT
ejpam-5694	368	10	lx	lx	NOUN
ejpam-5694	368	11	)	)	PUNCT
ejpam-5694	368	12	.	.	PUNCT
ejpam-5694	369	1	messenger	messenger	NOUN
ejpam-5694	369	2	of	of	ADP
ejpam-5694	369	3	math	math	NOUN
ejpam-5694	369	4	,	,	PUNCT
ejpam-5694	369	5	54:150–156	54:150–156	PROPN
ejpam-5694	369	6	,	,	PUNCT
ejpam-5694	369	7	1925	1925	NUM
ejpam-5694	369	8	.	.	PUNCT
ejpam-5694	370	1	[	[	X
ejpam-5694	370	2	10	10	NUM
ejpam-5694	370	3	]	]	X
ejpam-5694	370	4	kristina	kristina	PROPN
ejpam-5694	370	5	krulić	krulić	PROPN
ejpam-5694	370	6	himmelreich	himmelreich	PROPN
ejpam-5694	370	7	,	,	PUNCT
ejpam-5694	370	8	josip	josip	PROPN
ejpam-5694	370	9	pečarić	pečarić	PROPN
ejpam-5694	370	10	,	,	PUNCT
ejpam-5694	370	11	dora	dora	PROPN
ejpam-5694	370	12	pokaz	pokaz	PROPN
ejpam-5694	370	13	,	,	PUNCT
ejpam-5694	370	14	and	and	CCONJ
ejpam-5694	370	15	marjan	marjan	PROPN
ejpam-5694	370	16	praljak	praljak	PROPN
ejpam-5694	370	17	.	.	PUNCT
ejpam-5694	371	1	generalizations	generalization	NOUN
ejpam-5694	371	2	of	of	ADP
ejpam-5694	371	3	hardy	hardy	ADJ
ejpam-5694	371	4	-	-	PUNCT
ejpam-5694	371	5	type	type	NOUN
ejpam-5694	371	6	inequalities	inequality	NOUN
ejpam-5694	371	7	by	by	ADP
ejpam-5694	371	8	montgomery	montgomery	PROPN
ejpam-5694	371	9	identity	identity	NOUN
ejpam-5694	371	10	and	and	CCONJ
ejpam-5694	371	11	new	new	ADJ
ejpam-5694	371	12	green	green	ADJ
ejpam-5694	371	13	functions	function	NOUN
ejpam-5694	371	14	.	.	PUNCT
ejpam-5694	372	1	axioms	axiom	NOUN
ejpam-5694	372	2	,	,	PUNCT
ejpam-5694	372	3	12(5):434	12(5):434	NUM
ejpam-5694	372	4	,	,	PUNCT
ejpam-5694	372	5	2023	2023	NUM
ejpam-5694	372	6	.	.	PUNCT
ejpam-5694	373	1	[	[	X
ejpam-5694	373	2	11	11	NUM
ejpam-5694	373	3	]	]	SYM
ejpam-5694	373	4	julije	julije	PROPN
ejpam-5694	373	5	jakšetić	jakšetić	PROPN
ejpam-5694	373	6	and	and	CCONJ
ejpam-5694	373	7	josip	josip	PROPN
ejpam-5694	373	8	pečarić.	pečarić.	PROPN
ejpam-5694	373	9	exponential	exponential	NOUN
ejpam-5694	373	10	convexity	convexity	NOUN
ejpam-5694	373	11	method	method	NOUN
ejpam-5694	373	12	.	.	PUNCT
ejpam-5694	374	1	journal	journal	NOUN
ejpam-5694	374	2	of	of	ADP
ejpam-5694	374	3	convex	convex	PROPN
ejpam-5694	374	4	analysis	analysis	NOUN
ejpam-5694	374	5	,	,	PUNCT
ejpam-5694	374	6	20(1):181–197	20(1):181–197	PROPN
ejpam-5694	374	7	,	,	PUNCT
ejpam-5694	374	8	2013	2013	NUM
ejpam-5694	374	9	.	.	PUNCT
ejpam-5694	375	1	[	[	X
ejpam-5694	375	2	12	12	NUM
ejpam-5694	375	3	]	]	PUNCT
ejpam-5694	375	4	sten	sten	NOUN
ejpam-5694	375	5	kaijser	kaijser	PROPN
ejpam-5694	375	6	,	,	PUNCT
ejpam-5694	375	7	ludmila	ludmila	PROPN
ejpam-5694	375	8	nikolova	nikolova	PROPN
ejpam-5694	375	9	,	,	PUNCT
ejpam-5694	375	10	lars	lars	PROPN
ejpam-5694	375	11	-	-	PUNCT
ejpam-5694	375	12	erik	erik	PROPN
ejpam-5694	375	13	persson	persson	PROPN
ejpam-5694	375	14	,	,	PUNCT
ejpam-5694	375	15	and	and	CCONJ
ejpam-5694	375	16	anna	anna	PROPN
ejpam-5694	375	17	wedestig	wedestig	PROPN
ejpam-5694	375	18	.	.	PUNCT
ejpam-5694	376	1	hardy	hardy	ADJ
ejpam-5694	376	2	-	-	PUNCT
ejpam-5694	376	3	type	type	NOUN
ejpam-5694	376	4	inequalities	inequality	NOUN
ejpam-5694	376	5	via	via	ADP
ejpam-5694	376	6	convexity	convexity	NOUN
ejpam-5694	376	7	.	.	PUNCT
ejpam-5694	377	1	mathematical	mathematical	ADJ
ejpam-5694	377	2	inequalities	inequality	NOUN
ejpam-5694	377	3	&	&	CCONJ
ejpam-5694	377	4	applications	application	NOUN
ejpam-5694	377	5	,	,	PUNCT
ejpam-5694	377	6	8(3):403–417	8(3):403–417	NUM
ejpam-5694	377	7	,	,	PUNCT
ejpam-5694	377	8	2005	2005	NUM
ejpam-5694	377	9	.	.	PUNCT
ejpam-5694	378	1	[	[	X
ejpam-5694	378	2	13	13	NUM
ejpam-5694	378	3	]	]	X
ejpam-5694	378	4	w.g	w.g	PROPN
ejpam-5694	378	5	.	.	PROPN
ejpam-5694	378	6	kelley	kelley	PROPN
ejpam-5694	378	7	and	and	CCONJ
ejpam-5694	378	8	a.c	a.c	PROPN
ejpam-5694	378	9	.	.	PROPN
ejpam-5694	378	10	peterson	peterson	PROPN
ejpam-5694	378	11	.	.	PUNCT
ejpam-5694	379	1	the	the	DET
ejpam-5694	379	2	theory	theory	NOUN
ejpam-5694	379	3	of	of	ADP
ejpam-5694	379	4	differential	differential	ADJ
ejpam-5694	379	5	equations	equation	NOUN
ejpam-5694	379	6	:	:	PUNCT
ejpam-5694	379	7	classical	classical	ADJ
ejpam-5694	379	8	and	and	CCONJ
ejpam-5694	379	9	qualitative	qualitative	NOUN
ejpam-5694	379	10	.	.	PUNCT
ejpam-5694	380	1	universitext	universitext	PROPN
ejpam-5694	380	2	.	.	PUNCT
ejpam-5694	381	1	springer	springer	PROPN
ejpam-5694	381	2	new	new	PROPN
ejpam-5694	381	3	york	york	PROPN
ejpam-5694	381	4	,	,	PUNCT
ejpam-5694	381	5	2010	2010	NUM
ejpam-5694	381	6	.	.	PUNCT
ejpam-5694	382	1	[	[	X
ejpam-5694	382	2	14	14	NUM
ejpam-5694	382	3	]	]	X
ejpam-5694	382	4	kristina	kristina	PROPN
ejpam-5694	382	5	kruli	kruli	PROPN
ejpam-5694	382	6	,	,	PUNCT
ejpam-5694	382	7	josip	josip	PROPN
ejpam-5694	382	8	pe	pe	PROPN
ejpam-5694	382	9	himmelreich	himmelreich	PROPN
ejpam-5694	382	10	,	,	PUNCT
ejpam-5694	382	11	dora	dora	PROPN
ejpam-5694	382	12	pokaz	pokaz	PROPN
ejpam-5694	382	13	,	,	PUNCT
ejpam-5694	382	14	and	and	CCONJ
ejpam-5694	382	15	marjan	marjan	PROPN
ejpam-5694	382	16	praljak	praljak	PROPN
ejpam-5694	382	17	.	.	PUNCT
ejpam-5694	383	1	generalization	generalization	NOUN
ejpam-5694	383	2	of	of	ADP
ejpam-5694	383	3	hardy	hardy	ADJ
ejpam-5694	383	4	–	–	PUNCT
ejpam-5694	383	5	type	type	NOUN
ejpam-5694	383	6	inequalities	inequality	NOUN
ejpam-5694	383	7	by	by	ADP
ejpam-5694	383	8	the	the	DET
ejpam-5694	383	9	hermite	hermite	PROPN
ejpam-5694	383	10	interpolating	interpolate	VERB
ejpam-5694	383	11	polynomial	polynomial	ADJ
ejpam-5694	383	12	.	.	PUNCT
ejpam-5694	384	1	[	[	X
ejpam-5694	384	2	15	15	NUM
ejpam-5694	384	3	]	]	X
ejpam-5694	384	4	kristina	kristina	PROPN
ejpam-5694	384	5	krulić	krulić	PROPN
ejpam-5694	384	6	himmelreich	himmelreich	PROPN
ejpam-5694	384	7	.	.	PUNCT
ejpam-5694	385	1	generalizations	generalization	NOUN
ejpam-5694	385	2	of	of	ADP
ejpam-5694	385	3	hardy	hardy	ADJ
ejpam-5694	385	4	type	type	NOUN
ejpam-5694	385	5	inequalities	inequality	NOUN
ejpam-5694	385	6	by	by	ADP
ejpam-5694	385	7	taylor	taylor	PROPN
ejpam-5694	385	8	’s	’s	PART
ejpam-5694	385	9	formula	formula	NOUN
ejpam-5694	385	10	.	.	PUNCT
ejpam-5694	386	1	mathematica	mathematica	PROPN
ejpam-5694	386	2	slovaca	slovaca	PROPN
ejpam-5694	386	3	,	,	PUNCT
ejpam-5694	386	4	72(1):67–84	72(1):67–84	NOUN
ejpam-5694	386	5	,	,	PUNCT
ejpam-5694	386	6	2022	2022	NUM
ejpam-5694	386	7	.	.	PUNCT
ejpam-5694	387	1	[	[	X
ejpam-5694	387	2	16	16	NUM
ejpam-5694	387	3	]	]	X
ejpam-5694	387	4	marek	marek	PROPN
ejpam-5694	387	5	kuczma	kuczma	PROPN
ejpam-5694	387	6	.	.	PUNCT
ejpam-5694	388	1	an	an	DET
ejpam-5694	388	2	introduction	introduction	NOUN
ejpam-5694	388	3	to	to	ADP
ejpam-5694	388	4	the	the	DET
ejpam-5694	388	5	theory	theory	NOUN
ejpam-5694	388	6	of	of	ADP
ejpam-5694	388	7	functional	functional	ADJ
ejpam-5694	388	8	equations	equation	NOUN
ejpam-5694	388	9	and	and	CCONJ
ejpam-5694	388	10	inequalities	inequality	NOUN
ejpam-5694	388	11	.	.	PUNCT
ejpam-5694	389	1	(	(	PUNCT
ejpam-5694	389	2	no	no	DET
ejpam-5694	389	3	title	title	NOUN
ejpam-5694	389	4	)	)	PUNCT
ejpam-5694	389	5	,	,	PUNCT
ejpam-5694	389	6	2009	2009	NUM
ejpam-5694	389	7	.	.	PUNCT
ejpam-5694	390	1	[	[	X
ejpam-5694	390	2	17	17	NUM
ejpam-5694	390	3	]	]	X
ejpam-5694	390	4	alois	alois	PROPN
ejpam-5694	390	5	kufner	kufner	PROPN
ejpam-5694	390	6	,	,	PUNCT
ejpam-5694	390	7	lech	lech	PROPN
ejpam-5694	390	8	maligranda	maligranda	PROPN
ejpam-5694	390	9	,	,	PUNCT
ejpam-5694	390	10	and	and	CCONJ
ejpam-5694	390	11	lars	lars	PROPN
ejpam-5694	390	12	-	-	PUNCT
ejpam-5694	390	13	erik	erik	PROPN
ejpam-5694	390	14	persson	persson	PROPN
ejpam-5694	390	15	.	.	PUNCT
ejpam-5694	391	1	the	the	DET
ejpam-5694	391	2	prehistory	prehistory	NOUN
ejpam-5694	391	3	of	of	ADP
ejpam-5694	391	4	the	the	DET
ejpam-5694	391	5	hardy	hardy	ADJ
ejpam-5694	391	6	inequality	inequality	NOUN
ejpam-5694	391	7	.	.	PUNCT
ejpam-5694	392	1	the	the	DET
ejpam-5694	392	2	american	american	PROPN
ejpam-5694	392	3	mathematical	mathematical	PROPN
ejpam-5694	392	4	monthly	monthly	ADV
ejpam-5694	392	5	,	,	PUNCT
ejpam-5694	392	6	113(8):715–732	113(8):715–732	NUM
ejpam-5694	392	7	,	,	PUNCT
ejpam-5694	392	8	2006	2006	NUM
ejpam-5694	392	9	.	.	PUNCT
ejpam-5694	393	1	a.	a.	PROPN
ejpam-5694	393	2	m.	m.	PROPN
ejpam-5694	393	3	k.	k.	PROPN
ejpam-5694	393	4	abbasi	abbasi	PROPN
ejpam-5694	393	5	,	,	PUNCT
ejpam-5694	393	6	m.	m.	PROPN
ejpam-5694	393	7	anwar	anwar	PROPN
ejpam-5694	393	8	/	/	PUNCT
ejpam-5694	393	9	eur	eur	PROPN
ejpam-5694	393	10	.	.	PUNCT
ejpam-5694	394	1	j.	j.	PROPN
ejpam-5694	394	2	pure	pure	PROPN
ejpam-5694	394	3	appl	appl	PROPN
ejpam-5694	394	4	.	.	PROPN
ejpam-5694	394	5	math	math	PROPN
ejpam-5694	394	6	,	,	PUNCT
ejpam-5694	394	7	18	18	NUM
ejpam-5694	394	8	(	(	PUNCT
ejpam-5694	394	9	1	1	NUM
ejpam-5694	394	10	)	)	PUNCT
ejpam-5694	394	11	(	(	PUNCT
ejpam-5694	394	12	2025	2025	NUM
ejpam-5694	394	13	)	)	PUNCT
ejpam-5694	394	14	,	,	PUNCT
ejpam-5694	394	15	5694	5694	NUM
ejpam-5694	394	16	18	18	NUM
ejpam-5694	394	17	of	of	ADP
ejpam-5694	394	18	18	18	NUM
ejpam-5694	394	19	[	[	SYM
ejpam-5694	394	20	18	18	NUM
ejpam-5694	394	21	]	]	X
ejpam-5694	394	22	alois	alois	PROPN
ejpam-5694	394	23	kufner	kufner	PROPN
ejpam-5694	394	24	,	,	PUNCT
ejpam-5694	394	25	lech	lech	PROPN
ejpam-5694	394	26	maligranda	maligranda	PROPN
ejpam-5694	394	27	,	,	PUNCT
ejpam-5694	394	28	and	and	CCONJ
ejpam-5694	394	29	lars	lars	PROPN
ejpam-5694	394	30	-	-	PUNCT
ejpam-5694	394	31	erik	erik	PROPN
ejpam-5694	394	32	persson	persson	PROPN
ejpam-5694	394	33	.	.	PUNCT
ejpam-5694	395	1	the	the	DET
ejpam-5694	395	2	hardy	hardy	ADJ
ejpam-5694	395	3	inequality	inequality	NOUN
ejpam-5694	395	4	:	:	PUNCT
ejpam-5694	395	5	about	about	ADP
ejpam-5694	395	6	its	its	PRON
ejpam-5694	395	7	history	history	NOUN
ejpam-5694	395	8	and	and	CCONJ
ejpam-5694	395	9	some	some	DET
ejpam-5694	395	10	related	related	ADJ
ejpam-5694	395	11	results	result	NOUN
ejpam-5694	395	12	.	.	PUNCT
ejpam-5694	396	1	vydavatelskỳ	vydavatelskỳ	NOUN
ejpam-5694	396	2	servis	servis	PROPN
ejpam-5694	396	3	,	,	PUNCT
ejpam-5694	396	4	2007	2007	NUM
ejpam-5694	396	5	.	.	PUNCT
ejpam-5694	397	1	[	[	X
ejpam-5694	397	2	19	19	NUM
ejpam-5694	397	3	]	]	PUNCT
ejpam-5694	397	4	n	n	PRON
ejpam-5694	397	5	levinson	levinson	PROPN
ejpam-5694	397	6	.	.	PUNCT
ejpam-5694	398	1	generalizations	generalization	NOUN
ejpam-5694	398	2	of	of	ADP
ejpam-5694	398	3	an	an	DET
ejpam-5694	398	4	inequality	inequality	NOUN
ejpam-5694	398	5	of	of	ADP
ejpam-5694	398	6	hardy	hardy	NOUN
ejpam-5694	398	7	.	.	PUNCT
ejpam-5694	398	8	1964	1964	NUM
ejpam-5694	398	9	.	.	PUNCT
ejpam-5694	399	1	[	[	X
ejpam-5694	399	2	20	20	NUM
ejpam-5694	399	3	]	]	X
ejpam-5694	399	4	dora	dora	PROPN
ejpam-5694	399	5	pokaz	pokaz	PROPN
ejpam-5694	399	6	.	.	PUNCT
ejpam-5694	400	1	inequality	inequality	NOUN
ejpam-5694	400	2	of	of	ADP
ejpam-5694	400	3	hardy	hardy	ADJ
ejpam-5694	400	4	–	–	PUNCT
ejpam-5694	400	5	type	type	NOUN
ejpam-5694	400	6	for	for	ADP
ejpam-5694	400	7	n	n	CCONJ
ejpam-5694	400	8	–	–	PUNCT
ejpam-5694	400	9	convex	convex	NOUN
ejpam-5694	400	10	function	function	NOUN
ejpam-5694	400	11	via	via	ADP
ejpam-5694	400	12	interpolation	interpolation	NOUN
ejpam-5694	400	13	polynomial	polynomial	ADJ
ejpam-5694	400	14	and	and	CCONJ
ejpam-5694	400	15	green	green	ADJ
ejpam-5694	400	16	functions	function	NOUN
ejpam-5694	400	17	.	.	PUNCT
ejpam-5694	401	1	mathematical	mathematical	ADJ
ejpam-5694	401	2	inequalities	inequality	NOUN
ejpam-5694	401	3	&	&	CCONJ
ejpam-5694	401	4	applications	application	NOUN
ejpam-5694	401	5	,	,	PUNCT
ejpam-5694	401	6	2023	2023	NUM
ejpam-5694	401	7	.	.	PUNCT
ejpam-5694	402	1	[	[	X
ejpam-5694	402	2	21	21	NUM
ejpam-5694	402	3	]	]	X
ejpam-5694	402	4	gauhar	gauhar	PROPN
ejpam-5694	402	5	rahman	rahman	PROPN
ejpam-5694	402	6	,	,	PUNCT
ejpam-5694	402	7	kottakkaran	kottakkaran	VERB
ejpam-5694	402	8	sooppy	sooppy	ADJ
ejpam-5694	402	9	nisar	nisar	PROPN
ejpam-5694	402	10	,	,	PUNCT
ejpam-5694	402	11	thabet	thabet	ADJ
ejpam-5694	402	12	abdeljawad	abdeljawad	NOUN
ejpam-5694	402	13	,	,	PUNCT
ejpam-5694	402	14	and	and	CCONJ
ejpam-5694	402	15	samee	samee	PROPN
ejpam-5694	402	16	ullah	ullah	PROPN
ejpam-5694	402	17	.	.	PUNCT
ejpam-5694	403	1	certain	certain	ADJ
ejpam-5694	403	2	fractional	fractional	ADJ
ejpam-5694	403	3	proportional	proportional	ADJ
ejpam-5694	403	4	integral	integral	ADJ
ejpam-5694	403	5	inequalities	inequality	NOUN
ejpam-5694	403	6	via	via	ADP
ejpam-5694	403	7	convex	convex	NOUN
ejpam-5694	403	8	functions	function	NOUN
ejpam-5694	403	9	.	.	PUNCT
ejpam-5694	404	1	mathematics	mathematic	NOUN
ejpam-5694	404	2	,	,	PUNCT
ejpam-5694	404	3	8(2):222	8(2):222	NUM
ejpam-5694	404	4	,	,	PUNCT
ejpam-5694	404	5	2020	2020	NUM
ejpam-5694	404	6	.	.	PUNCT
ejpam-5694	405	1	[	[	X
ejpam-5694	405	2	22	22	NUM
ejpam-5694	405	3	]	]	PUNCT
ejpam-5694	405	4	awais	awais	PROPN
ejpam-5694	405	5	rasheed	rasheed	PROPN
ejpam-5694	405	6	,	,	PUNCT
ejpam-5694	405	7	khuram	khuram	PROPN
ejpam-5694	405	8	ali	ali	PROPN
ejpam-5694	405	9	khan	khan	PROPN
ejpam-5694	405	10	,	,	PUNCT
ejpam-5694	405	11	josip	josip	PROPN
ejpam-5694	405	12	pečarić	pečarić	PROPN
ejpam-5694	405	13	,	,	PUNCT
ejpam-5694	405	14	and	and	CCONJ
ejpam-5694	405	15	ilda	ilda	VERB
ejpam-5694	405	16	pečarić.	pečarić.	ADJ
ejpam-5694	405	17	generalizations	generalization	NOUN
ejpam-5694	405	18	of	of	ADP
ejpam-5694	405	19	levinson	levinson	PROPN
ejpam-5694	405	20	type	type	NOUN
ejpam-5694	405	21	inequalities	inequality	NOUN
ejpam-5694	405	22	via	via	ADP
ejpam-5694	405	23	new	new	ADJ
ejpam-5694	405	24	green	green	ADJ
ejpam-5694	405	25	functions	function	NOUN
ejpam-5694	405	26	with	with	ADP
ejpam-5694	405	27	applications	application	NOUN
ejpam-5694	405	28	to	to	ADP
ejpam-5694	405	29	information	information	NOUN
ejpam-5694	405	30	theory	theory	NOUN
ejpam-5694	405	31	.	.	PUNCT
ejpam-5694	406	1	journal	journal	PROPN
ejpam-5694	406	2	of	of	ADP
ejpam-5694	406	3	inequalities	inequality	NOUN
ejpam-5694	406	4	and	and	CCONJ
ejpam-5694	406	5	applications	application	NOUN
ejpam-5694	406	6	,	,	PUNCT
ejpam-5694	406	7	2023(1):124	2023(1):124	NUM
ejpam-5694	406	8	,	,	PUNCT
ejpam-5694	406	9	2023	2023	NUM
ejpam-5694	406	10	.	.	PUNCT
ejpam-5694	407	1	[	[	X
ejpam-5694	407	2	23	23	NUM
ejpam-5694	407	3	]	]	X
ejpam-5694	407	4	muhammad	muhammad	PROPN
ejpam-5694	407	5	samraiz	samraiz	PROPN
ejpam-5694	407	6	,	,	PUNCT
ejpam-5694	407	7	saima	saima	PROPN
ejpam-5694	407	8	naheed	naheed	PROPN
ejpam-5694	407	9	,	,	PUNCT
ejpam-5694	407	10	ayesha	ayesha	PROPN
ejpam-5694	407	11	gul	gul	PROPN
ejpam-5694	407	12	,	,	PUNCT
ejpam-5694	407	13	gauhar	gauhar	PROPN
ejpam-5694	407	14	rahman	rahman	PROPN
ejpam-5694	407	15	,	,	PUNCT
ejpam-5694	407	16	and	and	CCONJ
ejpam-5694	407	17	miguel	miguel	PROPN
ejpam-5694	407	18	vivas	vivas	PROPN
ejpam-5694	407	19	-	-	PROPN
ejpam-5694	407	20	cortez	cortez	PROPN
ejpam-5694	407	21	.	.	PUNCT
ejpam-5694	408	1	innovative	innovative	ADJ
ejpam-5694	408	2	interpolating	interpolate	VERB
ejpam-5694	408	3	polynomial	polynomial	ADJ
ejpam-5694	408	4	approach	approach	NOUN
ejpam-5694	408	5	to	to	ADP
ejpam-5694	408	6	fractional	fractional	ADJ
ejpam-5694	408	7	integral	integral	ADJ
ejpam-5694	408	8	inequalities	inequality	NOUN
ejpam-5694	408	9	and	and	CCONJ
ejpam-5694	408	10	real	real	ADJ
ejpam-5694	408	11	-	-	PUNCT
ejpam-5694	408	12	world	world	NOUN
ejpam-5694	408	13	implementations	implementation	NOUN
ejpam-5694	408	14	.	.	PUNCT
ejpam-5694	409	1	axioms	axiom	NOUN
ejpam-5694	409	2	,	,	PUNCT
ejpam-5694	409	3	12(10):914	12(10):914	NUM
ejpam-5694	409	4	,	,	PUNCT
ejpam-5694	409	5	2023	2023	NUM
ejpam-5694	409	6	.	.	PUNCT
ejpam-5694	410	1	[	[	X
ejpam-5694	410	2	24	24	NUM
ejpam-5694	410	3	]	]	PUNCT
ejpam-5694	410	4	asifa	asifa	PROPN
ejpam-5694	410	5	tassaddiq	tassaddiq	NOUN
ejpam-5694	410	6	,	,	PUNCT
ejpam-5694	410	7	gauhar	gauhar	PROPN
ejpam-5694	410	8	rahman	rahman	PROPN
ejpam-5694	410	9	,	,	PUNCT
ejpam-5694	410	10	kottakkaran	kottakkaran	VERB
ejpam-5694	410	11	sooppy	sooppy	ADJ
ejpam-5694	410	12	nisar	nisar	PROPN
ejpam-5694	410	13	,	,	PUNCT
ejpam-5694	410	14	and	and	CCONJ
ejpam-5694	410	15	muhammad	muhammad	PROPN
ejpam-5694	410	16	samraiz	samraiz	PROPN
ejpam-5694	410	17	.	.	PUNCT
ejpam-5694	411	1	certain	certain	ADJ
ejpam-5694	411	2	fractional	fractional	ADJ
ejpam-5694	411	3	conformable	conformable	ADJ
ejpam-5694	411	4	inequalities	inequality	NOUN
ejpam-5694	411	5	for	for	ADP
ejpam-5694	411	6	the	the	DET
ejpam-5694	411	7	weighted	weighted	NOUN
ejpam-5694	411	8	and	and	CCONJ
ejpam-5694	411	9	the	the	DET
ejpam-5694	411	10	extended	extended	ADJ
ejpam-5694	411	11	chebyshev	chebyshev	NOUN
ejpam-5694	411	12	functionals	functional	NOUN
ejpam-5694	411	13	.	.	PUNCT
ejpam-5694	412	1	advances	advance	NOUN
ejpam-5694	412	2	in	in	ADP
ejpam-5694	412	3	difference	difference	NOUN
ejpam-5694	412	4	equations	equation	NOUN
ejpam-5694	412	5	,	,	PUNCT
ejpam-5694	412	6	2020:1–9	2020:1–9	NUM
ejpam-5694	412	7	,	,	PUNCT
ejpam-5694	412	8	2020	2020	NUM
ejpam-5694	412	9	.	.	PUNCT