id	sid	tid	token	lemma	pos
easat-3054	1	1	edelweiss	edelweiss	PROPN
easat-3054	1	2	applied	apply	VERB
easat-3054	1	3	science	science	NOUN
easat-3054	1	4	and	and	CCONJ
easat-3054	1	5	technology	technology	NOUN
easat-3054	1	6	issn	issn	PROPN
easat-3054	1	7	:	:	PUNCT
easat-3054	1	8	2576	2576	NUM
easat-3054	1	9	-	-	SYM
easat-3054	1	10	8484	8484	NUM
easat-3054	1	11	vol	vol	NOUN
easat-3054	1	12	.	.	PROPN
easat-3054	1	13	8	8	NUM
easat-3054	1	14	,	,	PUNCT
easat-3054	1	15	no	no	INTJ
easat-3054	1	16	.	.	NOUN
easat-3054	1	17	6	6	NUM
easat-3054	1	18	,	,	PUNCT
easat-3054	1	19	4910	4910	NUM
easat-3054	1	20	-	-	SYM
easat-3054	1	21	4919	4919	NUM
easat-3054	1	22	2024	2024	NUM
easat-3054	1	23	publisher	publisher	NOUN
easat-3054	1	24	:	:	PUNCT
easat-3054	1	25	learning	learn	VERB
easat-3054	1	26	gate	gate	NOUN
easat-3054	1	27	doi	doi	PROPN
easat-3054	1	28	:	:	PUNCT
easat-3054	1	29	10.55214/25768484.v8i6.3054	10.55214/25768484.v8i6.3054	NUM
easat-3054	1	30	©	©	PROPN
easat-3054	1	31	2024	2024	NUM
easat-3054	1	32	by	by	ADP
easat-3054	1	33	the	the	DET
easat-3054	1	34	authors	author	NOUN
easat-3054	1	35	;	;	PUNCT
easat-3054	1	36	licensee	licensee	PROPN
easat-3054	1	37	learning	learning	NOUN
easat-3054	1	38	gate	gate	NOUN
easat-3054	1	39	©	©	PROPN
easat-3054	1	40	2024	2024	NUM
easat-3054	1	41	by	by	ADP
easat-3054	1	42	the	the	DET
easat-3054	1	43	authors	author	NOUN
easat-3054	1	44	;	;	PUNCT
easat-3054	1	45	licensee	licensee	PROPN
easat-3054	1	46	learning	learn	VERB
easat-3054	1	47	gate	gate	NOUN
easat-3054	1	48	*	*	PUNCT
easat-3054	1	49	correspondence	correspondence	NOUN
easat-3054	1	50	:	:	PUNCT
easat-3054	1	51	nadiah.a@uokerbala.edu.iq	nadiah.a@uokerbala.edu.iq	ADJ
easat-3054	1	52	fractional	fractional	ADJ
easat-3054	1	53	integral	integral	ADJ
easat-3054	1	54	ostrowski	ostrowski	ADJ
easat-3054	1	55	inequality	inequality	NOUN
easat-3054	1	56	on	on	ADP
easat-3054	1	57	l_p,0	l_p,0	PROPN
easat-3054	1	58	<	<	X
easat-3054	1	59	p<∞	p<∞	PROPN
easat-3054	1	60	spaces	space	VERB
easat-3054	1	61	nadia	nadia	PROPN
easat-3054	1	62	abed	abed	PROPN
easat-3054	1	63	habeeb1	habeeb1	PROPN
easat-3054	2	1	*	*	PUNCT
easat-3054	2	2	,	,	PUNCT
easat-3054	3	1	eman	eman	PROPN
easat-3054	3	2	samir	samir	PROPN
easat-3054	3	3	bhaya2	bhaya2	PROPN
easat-3054	3	4	1college	1college	PROPN
easat-3054	3	5	of	of	ADP
easat-3054	3	6	engineering	engineering	PROPN
easat-3054	3	7	,	,	PUNCT
easat-3054	3	8	kerbala	kerbala	PROPN
easat-3054	3	9	university	university	PROPN
easat-3054	3	10	,	,	PUNCT
easat-3054	3	11	iraq	iraq	PROPN
easat-3054	3	12	;	;	PUNCT
easat-3054	3	13	nadiah.a@uokerbala.edu.iq	nadiah.a@uokerbala.edu.iq	X
easat-3054	3	14	(	(	PUNCT
easat-3054	3	15	n.a.h	n.a.h	NOUN
easat-3054	3	16	.	.	PUNCT
easat-3054	3	17	)	)	PUNCT
easat-3054	3	18	.	.	PUNCT
easat-3054	4	1	2college	2college	NUM
easat-3054	4	2	of	of	ADP
easat-3054	4	3	education	education	NOUN
easat-3054	4	4	,	,	PUNCT
easat-3054	4	5	al	al	PROPN
easat-3054	4	6	-	-	PUNCT
easat-3054	4	7	zahraa	zahraa	PROPN
easat-3054	4	8	university	university	PROPN
easat-3054	4	9	for	for	ADP
easat-3054	4	10	women	woman	NOUN
easat-3054	4	11	,	,	PUNCT
easat-3054	4	12	iraq	iraq	PROPN
easat-3054	4	13	;	;	PUNCT
easat-3054	4	14	eman.bhaya@alzahraa.edu.iq	eman.bhaya@alzahraa.edu.iq	NOUN
easat-3054	4	15	(	(	PUNCT
easat-3054	4	16	e.s.b	e.s.b	NOUN
easat-3054	4	17	.	.	PUNCT
easat-3054	4	18	)	)	PUNCT
easat-3054	4	19	.	.	PUNCT
easat-3054	5	1	abstract	abstract	ADV
easat-3054	5	2	:	:	PUNCT
easat-3054	5	3	recently	recently	ADV
easat-3054	5	4	we	we	PRON
easat-3054	5	5	proved	prove	VERB
easat-3054	5	6	a	a	DET
easat-3054	5	7	type	type	NOUN
easat-3054	5	8	of	of	ADP
easat-3054	5	9	ostrowski	ostrowski	ADJ
easat-3054	5	10	inequality	inequality	NOUN
easat-3054	5	11	in	in	ADP
easat-3054	5	12	terms	term	NOUN
easat-3054	5	13	of	of	ADP
easat-3054	5	14	the	the	DET
easat-3054	5	15	quasi	quasi	ADJ
easat-3054	5	16	norm	norm	NOUN
easat-3054	5	17	of	of	ADP
easat-3054	5	18	the	the	DET
easat-3054	5	19	first	first	ADJ
easat-3054	5	20	derivative	derivative	NOUN
easat-3054	5	21	.	.	PUNCT
easat-3054	6	1	here	here	ADV
easat-3054	6	2	we	we	PRON
easat-3054	6	3	generalize	generalize	VERB
easat-3054	6	4	this	this	DET
easat-3054	6	5	inequality	inequality	NOUN
easat-3054	6	6	type	type	NOUN
easat-3054	6	7	for	for	ADP
easat-3054	6	8	fractional	fractional	ADJ
easat-3054	6	9	integral	integral	ADJ
easat-3054	6	10	.	.	PUNCT
easat-3054	7	1	keywords	keyword	NOUN
easat-3054	7	2	:	:	PUNCT
easat-3054	7	3	convex	convex	NOUN
easat-3054	7	4	function	function	NOUN
easat-3054	7	5	,	,	PUNCT
easat-3054	7	6	fractional	fractional	ADJ
easat-3054	7	7	integral	integral	ADJ
easat-3054	7	8	,	,	PUNCT
easat-3054	7	9	holder	holder	NOUN
easat-3054	7	10	inequality	inequality	NOUN
easat-3054	7	11	,	,	PUNCT
easat-3054	7	12	l_pspace	l_pspace	NOUN
easat-3054	7	13	.	.	PUNCT
easat-3054	8	1	classification	classification	NOUN
easat-3054	8	2	:	:	PUNCT
easat-3054	8	3	60e15	60e15	NUM
easat-3054	8	4	;	;	PUNCT
easat-3054	8	5	39b72	39b72	NUM
easat-3054	8	6	.	.	NOUN
easat-3054	9	1	1	1	X
easat-3054	9	2	.	.	X
easat-3054	9	3	introduction	introduction	NOUN
easat-3054	9	4	firstly	firstly	ADV
easat-3054	9	5	,	,	PUNCT
easat-3054	9	6	let	let	VERB
easat-3054	9	7	us	we	PRON
easat-3054	9	8	recall	recall	VERB
easat-3054	9	9	and	and	CCONJ
easat-3054	9	10	introduce	introduce	VERB
easat-3054	9	11	some	some	DET
easat-3054	9	12	definitions	definition	NOUN
easat-3054	9	13	notations	notation	NOUN
easat-3054	9	14	,	,	PUNCT
easat-3054	9	15	that	that	SCONJ
easat-3054	9	16	we	we	PRON
easat-3054	9	17	need	need	VERB
easat-3054	9	18	in	in	ADP
easat-3054	9	19	our	our	PRON
easat-3054	9	20	work	work	NOUN
easat-3054	9	21	.	.	PUNCT
easat-3054	10	1	the	the	DET
easat-3054	10	2	function	function	NOUN
easat-3054	10	3	𝑓	𝑓	X
easat-3054	10	4	:	:	PUNCT
easat-3054	10	5	[	[	X
easat-3054	10	6	𝑎	𝑎	X
easat-3054	10	7	,	,	PUNCT
easat-3054	10	8	𝑏	𝑏	NOUN
easat-3054	10	9	]	]	X
easat-3054	10	10	⊂	⊂	PROPN
easat-3054	10	11	𝑅	𝑅	PROPN
easat-3054	10	12	→	→	SYM
easat-3054	10	13	𝑅	𝑅	PROPN
easat-3054	10	14	is	be	AUX
easat-3054	10	15	said	say	VERB
easat-3054	10	16	to	to	PART
easat-3054	10	17	be	be	AUX
easat-3054	10	18	convex	convex	ADJ
easat-3054	10	19	if	if	SCONJ
easat-3054	10	20	the	the	DET
easat-3054	10	21	following	follow	VERB
easat-3054	10	22	inequality	inequality	NOUN
easat-3054	10	23	holds	hold	VERB
easat-3054	10	24	𝑓(𝑡𝑥	𝑓(𝑡𝑥	PROPN
easat-3054	10	25	+	+	CCONJ
easat-3054	10	26	(	(	PUNCT
easat-3054	10	27	1	1	NUM
easat-3054	10	28	−	−	NOUN
easat-3054	10	29	𝑡)𝑦	𝑡)𝑦	NOUN
easat-3054	10	30	)	)	PUNCT
easat-3054	10	31	≤	≤	NOUN
easat-3054	10	32	𝑡𝑓(𝑥	𝑡𝑓(𝑥	NOUN
easat-3054	10	33	)	)	PUNCT
easat-3054	11	1	+	+	CCONJ
easat-3054	11	2	(	(	PUNCT
easat-3054	11	3	1	1	NUM
easat-3054	11	4	−	−	NUM
easat-3054	11	5	𝑡)𝑓(𝑦	𝑡)𝑓(𝑦	PUNCT
easat-3054	12	1	[	[	X
easat-3054	12	2	4	4	X
easat-3054	12	3	]	]	PUNCT
easat-3054	12	4	for	for	ADP
easat-3054	12	5	all	all	DET
easat-3054	12	6	𝑥	𝑥	PROPN
easat-3054	12	7	,	,	PUNCT
easat-3054	12	8	𝑦	𝑦	PRON
easat-3054	12	9	∈	∈	NOUN
easat-3054	13	1	[	[	X
easat-3054	13	2	𝑎	𝑎	X
easat-3054	13	3	,	,	PUNCT
easat-3054	13	4	𝑏	𝑏	NOUN
easat-3054	13	5	]	]	PUNCT
easat-3054	13	6	and	and	CCONJ
easat-3054	13	7	𝑡	𝑡	PROPN
easat-3054	13	8	∈	∈	PROPN
easat-3054	13	9	[	[	X
easat-3054	13	10	0,1	0,1	NUM
easat-3054	13	11	]	]	PUNCT
easat-3054	13	12	,	,	PUNCT
easat-3054	13	13	we	we	PRON
easat-3054	13	14	say	say	VERB
easat-3054	13	15	that	that	SCONJ
easat-3054	13	16	f	f	PROPN
easat-3054	13	17	is	be	AUX
easat-3054	13	18	concave	concave	ADJ
easat-3054	13	19	if(−𝑓	if(−𝑓	NOUN
easat-3054	13	20	)	)	PUNCT
easat-3054	13	21	is	be	AUX
easat-3054	13	22	convex	convex	ADJ
easat-3054	13	23	.	.	PUNCT
easat-3054	14	1	𝑅∝is	𝑅∝is	ADP
easat-3054	14	2	the	the	DET
easat-3054	14	3	set	set	NOUN
easat-3054	14	4	of	of	ADP
easat-3054	14	5	real	real	ADJ
easat-3054	14	6	numbers	number	NOUN
easat-3054	14	7	,	,	PUNCT
easat-3054	14	8	𝑅∝	𝑅∝	NOUN
easat-3054	14	9	=	=	PUNCT
easat-3054	14	10	𝑄∝	𝑄∝	NOUN
easat-3054	14	11	∪	∪	PROPN
easat-3054	14	12	𝐽∝,where	𝐽∝,where	PROPN
easat-3054	14	13	𝑄∝	𝑄∝	PROPN
easat-3054	14	14	is	be	AUX
easat-3054	14	15	the	the	DET
easat-3054	14	16	𝛼	𝛼	PRON
easat-3054	14	17	−type	−type	NOUN
easat-3054	14	18	set	set	NOUN
easat-3054	14	19	of	of	ADP
easat-3054	14	20	the	the	DET
easat-3054	14	21	rational	rational	ADJ
easat-3054	14	22	numbers	number	NOUN
easat-3054	14	23	is	be	AUX
easat-3054	14	24	defined	define	VERB
easat-3054	14	25	as	as	ADP
easat-3054	14	26	the	the	DET
easat-3054	14	27	set	set	NOUN
easat-3054	14	28	{	{	PUNCT
easat-3054	14	29	𝑚∝	𝑚∝	X
easat-3054	14	30	=	=	SYM
easat-3054	14	31	(	(	PUNCT
easat-3054	14	32	𝑃	𝑃	PROPN
easat-3054	14	33	𝑞	𝑞	SYM
easat-3054	14	34	)	)	PUNCT
easat-3054	14	35	𝛼	𝛼	PROPN
easat-3054	14	36	,	,	PUNCT
easat-3054	14	37	𝑝	𝑝	NOUN
easat-3054	14	38	,	,	PUNCT
easat-3054	14	39	𝑞𝜖𝑍	𝑞𝜖𝑍	PROPN
easat-3054	14	40	,	,	PUNCT
easat-3054	14	41	𝑞	𝑞	NOUN
easat-3054	14	42	≠	≠	PROPN
easat-3054	14	43	0	0	NUM
easat-3054	14	44	}	}	PUNCT
easat-3054	14	45	,	,	PUNCT
easat-3054	14	46	also	also	ADV
easat-3054	14	47	𝐽∝	𝐽∝	PROPN
easat-3054	14	48	is	be	AUX
easat-3054	14	49	the	the	DET
easat-3054	14	50	𝛼	𝛼	PRON
easat-3054	14	51	−type	−type	NOUN
easat-3054	14	52	set	set	NOUN
easat-3054	14	53	of	of	ADP
easat-3054	14	54	the	the	DET
easat-3054	14	55	irrational	irrational	ADJ
easat-3054	14	56	numbers	number	NOUN
easat-3054	14	57	is	be	AUX
easat-3054	14	58	defined	define	VERB
easat-3054	14	59	as	as	ADP
easat-3054	14	60	the	the	DET
easat-3054	14	61	set	set	NOUN
easat-3054	14	62	{	{	PUNCT
easat-3054	14	63	𝑚∝	𝑚∝	PROPN
easat-3054	14	64	≠	≠	PROPN
easat-3054	14	65	(	(	PUNCT
easat-3054	14	66	𝑃	𝑃	PROPN
easat-3054	14	67	𝑞	𝑞	NOUN
easat-3054	14	68	)	)	PUNCT
easat-3054	14	69	𝛼	𝛼	PROPN
easat-3054	14	70	,	,	PUNCT
easat-3054	14	71	𝑝	𝑝	NOUN
easat-3054	14	72	,	,	PUNCT
easat-3054	14	73	𝑞𝜖𝑍	𝑞𝜖𝑍	PROPN
easat-3054	14	74	,	,	PUNCT
easat-3054	14	75	𝑞	𝑞	NOUN
easat-3054	14	76	≠	≠	PROPN
easat-3054	14	77	0	0	NUM
easat-3054	14	78	}	}	PUNCT
easat-3054	14	79	.	.	PUNCT
easat-3054	15	1	the	the	DET
easat-3054	15	2	local	local	ADJ
easat-3054	15	3	fractional	fractional	ADJ
easat-3054	15	4	derivative	derivative	NOUN
easat-3054	15	5	of	of	ADP
easat-3054	15	6	𝑓(𝑥	𝑓(𝑥	NOUN
easat-3054	15	7	)	)	PUNCT
easat-3054	15	8	of	of	ADP
easat-3054	15	9	order	order	NOUN
easat-3054	15	10	𝛼	𝛼	NOUN
easat-3054	15	11	at	at	ADP
easat-3054	15	12	𝑋	𝑋	PROPN
easat-3054	15	13	=	=	SYM
easat-3054	15	14	𝑋	𝑋	PROPN
easat-3054	15	15	°	°	PROPN
easat-3054	15	16	is	be	AUX
easat-3054	15	17	defined	define	VERB
easat-3054	15	18	as	as	ADP
easat-3054	15	19	:	:	PUNCT
easat-3054	15	20	𝑓𝛼(𝑋	𝑓𝛼(𝑋	NOUN
easat-3054	15	21	°	°	NUM
easat-3054	15	22	)	)	PUNCT
easat-3054	15	23	=	=	SYM
easat-3054	15	24	𝑑𝛼𝑓(𝑥	𝑑𝛼𝑓(𝑥	PROPN
easat-3054	15	25	)	)	PUNCT
easat-3054	15	26	𝑑𝑥𝛼	𝑑𝑥𝛼	NOUN
easat-3054	15	27	|	|	ADV
easat-3054	15	28	𝑋=𝑋	𝑋=𝑋	NOUN
easat-3054	15	29	°	°	PUNCT
easat-3054	16	1	=	=	SYM
easat-3054	16	2	lim	lim	PROPN
easat-3054	16	3	𝑋→𝑋	𝑋→𝑋	PROPN
easat-3054	16	4	°	°	NOUN
easat-3054	16	5	∆𝛼(𝑓(𝑋	∆𝛼(𝑓(𝑋	NUM
easat-3054	16	6	)	)	PUNCT
easat-3054	16	7	−	−	PROPN
easat-3054	16	8	𝑓(𝑋	𝑓(𝑋	PROPN
easat-3054	16	9	°	°	NUM
easat-3054	16	10	)	)	PUNCT
easat-3054	16	11	)	)	PUNCT
easat-3054	17	1	(	(	PUNCT
easat-3054	17	2	𝑋	𝑋	PROPN
easat-3054	17	3	−	−	PROPN
easat-3054	17	4	𝑋	𝑋	PROPN
easat-3054	17	5	°	°	PROPN
easat-3054	17	6	)	)	PUNCT
easat-3054	17	7	where	where	SCONJ
easat-3054	17	8	∆𝛼(𝑓(𝑋	∆𝛼(𝑓(𝑋	ADP
easat-3054	17	9	)	)	PUNCT
easat-3054	17	10	−	−	PROPN
easat-3054	17	11	𝑓(𝑋	𝑓(𝑋	PROPN
easat-3054	17	12	°	°	NUM
easat-3054	17	13	)	)	PUNCT
easat-3054	17	14	)	)	PUNCT
easat-3054	18	1	≅	≅	PROPN
easat-3054	18	2	γ(𝛼	γ(𝛼	PROPN
easat-3054	18	3	+	+	NUM
easat-3054	18	4	1)(𝑓(𝑋	1)(𝑓(𝑋	NUM
easat-3054	18	5	)	)	PUNCT
easat-3054	18	6	−	−	PROPN
easat-3054	18	7	𝑓(𝑋	𝑓(𝑋	PROPN
easat-3054	18	8	°	°	NUM
easat-3054	18	9	)	)	PUNCT
easat-3054	18	10	)	)	PUNCT
easat-3054	18	11	.	.	PUNCT
easat-3054	19	1	if	if	SCONJ
easat-3054	19	2	there	there	PRON
easat-3054	19	3	exists	exist	VERB
easat-3054	19	4	𝑓(𝑘+1)𝛼(𝑥	𝑓(𝑘+1)𝛼(𝑥	PROPN
easat-3054	19	5	)	)	PUNCT
easat-3054	19	6	=	=	SYM
easat-3054	20	1	𝐷𝑥	𝐷𝑥	PROPN
easat-3054	20	2	𝛼	𝛼	PROPN
easat-3054	20	3	…	…	PUNCT
easat-3054	20	4	𝐷𝑥	𝐷𝑥	PROPN
easat-3054	20	5	𝛼𝑓(𝑥	𝛼𝑓(𝑥	NOUN
easat-3054	20	6	)	)	PUNCT
easat-3054	20	7	mm	mm	PROPN
easat-3054	20	8	times	time	NOUN
easat-3054	20	9	for	for	ADP
easat-3054	20	10	any	any	DET
easat-3054	20	11	𝑋	𝑋	NOUN
easat-3054	20	12	∈	∈	NOUN
easat-3054	20	13	𝐼	𝐼	ADP
easat-3054	20	14	⊆	⊆	NUM
easat-3054	20	15	𝑅,then	𝑅,then	PUNCT
easat-3054	20	16	we	we	PRON
easat-3054	20	17	denoted	denote	VERB
easat-3054	20	18	𝑓	𝑓	DET
easat-3054	20	19	∈	∈	PROPN
easat-3054	20	20	𝐷(𝑘+1)𝛼(𝐼	𝐷(𝑘+1)𝛼(𝐼	PROPN
easat-3054	20	21	)	)	PUNCT
easat-3054	20	22	,	,	PUNCT
easat-3054	20	23	where	where	SCONJ
easat-3054	20	24	𝑘	𝑘	PRON
easat-3054	20	25	=	=	SYM
easat-3054	20	26	0,1	0,1	NUM
easat-3054	20	27	,	,	PUNCT
easat-3054	20	28	…	…	PUNCT
easat-3054	21	1	[	[	X
easat-3054	21	2	5	5	NUM
easat-3054	21	3	]	]	PUNCT
easat-3054	21	4	anon	anon	X
easat-3054	21	5	–	–	PUNCT
easat-3054	21	6	differentiable	differentiable	ADJ
easat-3054	21	7	function	function	NOUN
easat-3054	21	8	𝑓	𝑓	NOUN
easat-3054	21	9	:	:	PUNCT
easat-3054	21	10	𝑅	𝑅	PROPN
easat-3054	21	11	→	→	SYM
easat-3054	21	12	𝑅𝛼	𝑅𝛼	PROPN
easat-3054	21	13	,	,	PUNCT
easat-3054	21	14	𝑋	𝑋	NOUN
easat-3054	21	15	→	→	SYM
easat-3054	21	16	𝑓(𝑥	𝑓(𝑥	NOUN
easat-3054	21	17	)	)	PUNCT
easat-3054	21	18	is	be	AUX
easat-3054	21	19	called	call	VERB
easat-3054	21	20	to	to	PART
easat-3054	21	21	be	be	AUX
easat-3054	21	22	local	local	ADJ
easat-3054	21	23	fractional	fractional	ADJ
easat-3054	21	24	continuous	continuous	ADJ
easat-3054	21	25	at	at	ADP
easat-3054	21	26	𝑋	𝑋	PROPN
easat-3054	21	27	°	°	PROPN
easat-3054	21	28	.if	.if	PROPN
easat-3054	21	29	for	for	ADP
easat-3054	21	30	any	any	DET
easat-3054	21	31	∈	∈	PROPN
easat-3054	21	32	>	>	X
easat-3054	21	33	0	0	PROPN
easat-3054	21	34	,	,	PUNCT
easat-3054	21	35	there	there	PRON
easat-3054	21	36	exists	exist	VERB
easat-3054	21	37	𝛿	𝛿	PROPN
easat-3054	21	38	>	>	X
easat-3054	21	39	0	0	NUM
easat-3054	21	40	,	,	PUNCT
easat-3054	21	41	such	such	ADJ
easat-3054	21	42	that	that	SCONJ
easat-3054	21	43	|𝑓(𝑥	|𝑓(𝑥	NOUN
easat-3054	21	44	)	)	PUNCT
easat-3054	21	45	−	−	PROPN
easat-3054	21	46	𝑓(𝑋	𝑓(𝑋	PROPN
easat-3054	21	47	°	°	NOUN
easat-3054	21	48	)|	)|	NOUN
easat-3054	21	49	<	<	X
easat-3054	21	50	∈	∈	X
easat-3054	21	51	∝	∝	PROPN
easat-3054	21	52	holds	hold	VERB
easat-3054	21	53	for	for	ADP
easat-3054	21	54	|𝑋	|𝑋	PROPN
easat-3054	21	55	−	−	PROPN
easat-3054	21	56	𝑋	𝑋	PROPN
easat-3054	21	57	°	°	PROPN
easat-3054	21	58	|	|	NOUN
easat-3054	21	59	<	<	X
easat-3054	21	60	𝛿	𝛿	ADJ
easat-3054	21	61	,	,	PUNCT
easat-3054	21	62	where	where	SCONJ
easat-3054	21	63	∈	∈	PROPN
easat-3054	21	64	,	,	PUNCT
easat-3054	21	65	𝛿	𝛿	PRON
easat-3054	21	66	∈	∈	NOUN
easat-3054	21	67	𝑅.	𝑅.	NOUN
easat-3054	21	68	if	if	SCONJ
easat-3054	21	69	𝑓(𝑥	𝑓(𝑥	NOUN
easat-3054	21	70	)	)	PUNCT
easat-3054	21	71	is	be	AUX
easat-3054	21	72	local	local	ADJ
easat-3054	21	73	continuous	continuous	ADJ
easat-3054	21	74	on	on	ADP
easat-3054	21	75	the	the	DET
easat-3054	21	76	interval	interval	NOUN
easat-3054	21	77	(	(	PUNCT
easat-3054	21	78	𝑎	𝑎	X
easat-3054	21	79	,	,	PUNCT
easat-3054	21	80	𝑏).we	𝑏).we	NOUN
easat-3054	21	81	denote	denote	VERB
easat-3054	21	82	𝑓(𝑥	𝑓(𝑥	NOUN
easat-3054	21	83	)	)	PUNCT
easat-3054	21	84	∈	∈	NOUN
easat-3054	21	85	𝐶𝛼(𝑎	𝐶𝛼(𝑎	NOUN
easat-3054	21	86	,	,	PUNCT
easat-3054	21	87	𝑏	𝑏	NOUN
easat-3054	21	88	)	)	PUNCT
easat-3054	21	89	.	.	PUNCT
easat-3054	22	1	[	[	X
easat-3054	22	2	5	5	X
easat-3054	22	3	]	]	PUNCT
easat-3054	22	4	we	we	PRON
easat-3054	22	5	call	call	VERB
easat-3054	22	6	𝑓	𝑓	PRON
easat-3054	22	7	is	be	AUX
easat-3054	22	8	fractional	fractional	ADV
easat-3054	22	9	integrable	integrable	ADJ
easat-3054	22	10	if	if	SCONJ
easat-3054	22	11	1	1	NUM
easat-3054	22	12	γ(1	γ(1	NOUN
easat-3054	22	13	+	+	NUM
easat-3054	22	14	𝛼	𝛼	X
easat-3054	22	15	)	)	PUNCT
easat-3054	22	16	∫	∫	NOUN
easat-3054	22	17	𝑓(𝑥)(𝑑𝑡)𝛼	𝑓(𝑥)(𝑑𝑡)𝛼	NOUN
easat-3054	22	18	=	=	PUNCT
easat-3054	22	19	𝑏	𝑏	PROPN
easat-3054	22	20	𝑎	𝑎	SYM
easat-3054	22	21	1	1	NUM
easat-3054	22	22	γ(1	γ(1	PROPN
easat-3054	22	23	+	+	NUM
easat-3054	22	24	𝛼	𝛼	X
easat-3054	22	25	)	)	PUNCT
easat-3054	22	26	lim	lim	NOUN
easat-3054	22	27	∆𝑡→0	∆𝑡→0	VERB
easat-3054	22	28	∑𝑓(𝑡𝑗	∑𝑓(𝑡𝑗	X
easat-3054	22	29	)	)	PUNCT
easat-3054	22	30	𝑛−1	𝑛−1	PROPN
easat-3054	22	31	𝑗=0	𝑗=0	PROPN
easat-3054	22	32	(	(	PUNCT
easat-3054	22	33	∆𝑡𝑗	∆𝑡𝑗	NOUN
easat-3054	22	34	)	)	PUNCT
easat-3054	22	35	𝛼	𝛼	X
easat-3054	22	36	<	<	X
easat-3054	22	37	∞	∞	PROPN
easat-3054	22	38	(	(	PUNCT
easat-3054	22	39	1	1	NUM
easat-3054	22	40	)	)	PUNCT
easat-3054	22	41	and	and	CCONJ
easat-3054	22	42	the	the	DET
easat-3054	22	43	fractional	fractional	ADJ
easat-3054	22	44	integrable	integrable	ADJ
easat-3054	22	45	defined	define	VERB
easat-3054	22	46	by	by	ADP
easat-3054	22	47	:	:	PUNCT
easat-3054	22	48	𝑎𝐼𝑏	𝑎𝐼𝑏	NOUN
easat-3054	22	49	∝𝑓(𝑥	∝𝑓(𝑥	NOUN
easat-3054	22	50	)	)	PUNCT
easat-3054	22	51	=	=	SYM
easat-3054	22	52	1	1	NUM
easat-3054	22	53	γ(1	γ(1	NOUN
easat-3054	22	54	+	+	NUM
easat-3054	22	55	𝛼	𝛼	X
easat-3054	22	56	)	)	PUNCT
easat-3054	22	57	∫	∫	NOUN
easat-3054	22	58	𝑓(𝑥)(𝑑𝑡)𝛼	𝑓(𝑥)(𝑑𝑡)𝛼	NOUN
easat-3054	22	59	𝑏	𝑏	PROPN
easat-3054	22	60	𝑎	𝑎	NOUN
easat-3054	22	61	=	=	SYM
easat-3054	22	62	1	1	NUM
easat-3054	22	63	γ(1	γ(1	NOUN
easat-3054	22	64	+	+	NUM
easat-3054	22	65	𝛼	𝛼	X
easat-3054	22	66	)	)	PUNCT
easat-3054	22	67	lim	lim	NOUN
easat-3054	22	68	∆𝑡→0	∆𝑡→0	VERB
easat-3054	22	69	∑𝑓(𝑡𝑗	∑𝑓(𝑡𝑗	X
easat-3054	22	70	)	)	PUNCT
easat-3054	22	71	𝑛−1	𝑛−1	PROPN
easat-3054	22	72	𝑗=0	𝑗=0	PROPN
easat-3054	22	73	(	(	PUNCT
easat-3054	22	74	∆𝑡𝑗	∆𝑡𝑗	NOUN
easat-3054	22	75	)	)	PUNCT
easat-3054	22	76	𝛼	𝛼	NOUN
easat-3054	22	77	with	with	ADP
easat-3054	22	78	∆𝑡𝑗	∆𝑡𝑗	NOUN
easat-3054	22	79	=	=	SYM
easat-3054	22	80	𝑡𝑗+1	𝑡𝑗+1	PROPN
easat-3054	22	81	−	−	PROPN
easat-3054	22	82	𝑡,and	𝑡,and	NUM
easat-3054	22	83	∆𝑡	∆𝑡	PROPN
easat-3054	22	84	=	=	SYM
easat-3054	22	85	𝑚𝑎𝑥{∆𝑡1	𝑚𝑎𝑥{∆𝑡1	PROPN
easat-3054	22	86	,	,	PUNCT
easat-3054	22	87	∆𝑡2	∆𝑡2	PROPN
easat-3054	22	88	,	,	PUNCT
easat-3054	22	89	…	…	PUNCT
easat-3054	22	90	,	,	PUNCT
easat-3054	22	91	∆𝑡𝑛−1},where	∆𝑡𝑛−1},where	X
easat-3054	22	92	[	[	X
easat-3054	22	93	𝑡𝑗	𝑡𝑗	X
easat-3054	22	94	,	,	PUNCT
easat-3054	22	95	𝑡𝑗+1	𝑡𝑗+1	PROPN
easat-3054	22	96	]	]	PUNCT
easat-3054	22	97	,	,	PUNCT
easat-3054	22	98	4911	4911	NUM
easat-3054	22	99	edelweiss	edelweiss	PROPN
easat-3054	22	100	applied	apply	VERB
easat-3054	22	101	science	science	NOUN
easat-3054	22	102	and	and	CCONJ
easat-3054	22	103	technology	technology	NOUN
easat-3054	22	104	issn	issn	PROPN
easat-3054	22	105	:	:	PUNCT
easat-3054	22	106	2576	2576	NUM
easat-3054	22	107	-	-	SYM
easat-3054	22	108	8484	8484	NUM
easat-3054	22	109	vol	vol	NOUN
easat-3054	22	110	.	.	PROPN
easat-3054	23	1	8	8	NUM
easat-3054	23	2	,	,	PUNCT
easat-3054	23	3	no	no	INTJ
easat-3054	23	4	.	.	NOUN
easat-3054	24	1	6	6	NUM
easat-3054	24	2	:	:	SYM
easat-3054	24	3	4910	4910	NUM
easat-3054	24	4	-	-	SYM
easat-3054	24	5	4919	4919	NUM
easat-3054	24	6	,	,	PUNCT
easat-3054	24	7	2024	2024	NUM
easat-3054	24	8	doi	doi	NOUN
easat-3054	24	9	:	:	PUNCT
easat-3054	24	10	10.55214/25768484.v8i6.3054	10.55214/25768484.v8i6.3054	NUM
easat-3054	24	11	©	©	PROPN
easat-3054	24	12	2024	2024	NUM
easat-3054	24	13	by	by	ADP
easat-3054	24	14	the	the	DET
easat-3054	24	15	authors	author	NOUN
easat-3054	24	16	;	;	PUNCT
easat-3054	24	17	licensee	licensee	PROPN
easat-3054	24	18	learning	learning	NOUN
easat-3054	24	19	gate	gate	VERB
easat-3054	24	20	𝑗	𝑗	PROPN
easat-3054	24	21	=	=	SYM
easat-3054	24	22	0	0	NUM
easat-3054	24	23	,	,	PUNCT
easat-3054	24	24	…	…	PUNCT
easat-3054	24	25	,	,	PUNCT
easat-3054	24	26	𝑛	𝑛	PRON
easat-3054	24	27	−	−	PROPN
easat-3054	24	28	1	1	NUM
easat-3054	24	29	,	,	PUNCT
easat-3054	24	30	and	and	CCONJ
easat-3054	24	31	𝑎	𝑎	X
easat-3054	24	32	=	=	SYM
easat-3054	24	33	𝑡0	𝑡0	NOUN
easat-3054	24	34	<	<	X
easat-3054	24	35	𝑡1	𝑡1	X
easat-3054	24	36	<	<	X
easat-3054	24	37	⋯	⋯	X
easat-3054	24	38	<	<	X
easat-3054	24	39	𝑡𝑛−1	𝑡𝑛−1	NOUN
easat-3054	24	40	=	=	PUNCT
easat-3054	24	41	𝑏	𝑏	PROPN
easat-3054	24	42	is	be	AUX
easat-3054	24	43	a	a	DET
easat-3054	24	44	partition	partition	NOUN
easat-3054	24	45	of	of	ADP
easat-3054	24	46	interval	interval	NOUN
easat-3054	24	47	[	[	X
easat-3054	24	48	𝑎	𝑎	X
easat-3054	24	49	,	,	PUNCT
easat-3054	24	50	𝑏].here	𝑏].here	VERB
easat-3054	24	51	it	it	PRON
easat-3054	24	52	follows	follow	VERB
easat-3054	24	53	that	that	SCONJ
easat-3054	24	54	𝑎𝐼𝑏	𝑎𝐼𝑏	ADJ
easat-3054	24	55	∝𝑓(𝑥	∝𝑓(𝑥	NOUN
easat-3054	24	56	)	)	PUNCT
easat-3054	25	1	=	=	SYM
easat-3054	25	2	0	0	PUNCT
easat-3054	26	1	if	if	SCONJ
easat-3054	26	2	𝑎	𝑎	PRON
easat-3054	26	3	=	=	VERB
easat-3054	26	4	𝑏	𝑏	NOUN
easat-3054	26	5	and	and	CCONJ
easat-3054	26	6	𝑎𝐼𝑏	𝑎𝐼𝑏	PRON
easat-3054	26	7	∝𝑓(𝑥	∝𝑓(𝑥	NOUN
easat-3054	26	8	)	)	PUNCT
easat-3054	27	1	=	=	SYM
easat-3054	27	2	−𝑏	−𝑏	ADJ
easat-3054	27	3	𝑎𝐼𝑏	𝑎𝐼𝑏	ADJ
easat-3054	27	4	∝𝑓(𝑥	∝𝑓(𝑥	NOUN
easat-3054	27	5	)	)	PUNCT
easat-3054	27	6	if	if	SCONJ
easat-3054	27	7	𝑎	𝑎	PRON
easat-3054	27	8	<	<	X
easat-3054	27	9	𝑏.	𝑏.	NOUN
easat-3054	27	10	let	let	VERB
easat-3054	27	11	𝑓	𝑓	PRON
easat-3054	28	1	:	:	PUNCT
easat-3054	28	2	𝐼	𝐼	PROPN
easat-3054	28	3	⊂	⊂	PROPN
easat-3054	28	4	𝑅	𝑅	PROPN
easat-3054	28	5	→	→	SYM
easat-3054	28	6	𝑅𝛼	𝑅𝛼	PROPN
easat-3054	28	7	.for	.for	ADP
easat-3054	28	8	any	any	DET
easat-3054	28	9	𝑋1,𝑋2	𝑋1,𝑋2	NOUN
easat-3054	28	10	∈	∈	NOUN
easat-3054	28	11	𝐼and	𝐼and	PROPN
easat-3054	28	12	𝜆	𝜆	PROPN
easat-3054	28	13	∈	∈	PROPN
easat-3054	29	1	[	[	X
easat-3054	29	2	0,1	0,1	NUM
easat-3054	29	3	]	]	PUNCT
easat-3054	29	4	,	,	PUNCT
easat-3054	29	5	if	if	SCONJ
easat-3054	29	6	the	the	DET
easat-3054	29	7	following	follow	VERB
easat-3054	29	8	inequality	inequality	NOUN
easat-3054	29	9	𝑓(𝜆𝑋1	𝑓(𝜆𝑋1	NUM
easat-3054	29	10	)	)	PUNCT
easat-3054	29	11	+	+	CCONJ
easat-3054	29	12	(	(	PUNCT
easat-3054	29	13	1	1	NUM
easat-3054	29	14	−	−	NOUN
easat-3054	29	15	𝜆)𝑋2	𝜆)𝑋2	NOUN
easat-3054	29	16	≤	≤	NOUN
easat-3054	29	17	𝜆𝛼𝑓(𝑋1	𝜆𝛼𝑓(𝑋1	PUNCT
easat-3054	29	18	)	)	PUNCT
easat-3054	30	1	+	+	CCONJ
easat-3054	30	2	(	(	PUNCT
easat-3054	30	3	1	1	NUM
easat-3054	30	4	−	−	NOUN
easat-3054	30	5	𝜆	𝜆	NOUN
easat-3054	30	6	)	)	PUNCT
easat-3054	30	7	𝛼𝑓(𝑋2	𝛼𝑓(𝑋2	PROPN
easat-3054	30	8	)	)	PUNCT
easat-3054	30	9	holds	hold	VERB
easat-3054	30	10	,	,	PUNCT
easat-3054	30	11	then	then	ADV
easat-3054	30	12	f	f	PROPN
easat-3054	30	13	is	be	AUX
easat-3054	30	14	called	call	VERB
easat-3054	30	15	a	a	DET
easat-3054	30	16	generalized	generalize	VERB
easat-3054	30	17	convex	convex	NOUN
easat-3054	30	18	function	function	NOUN
easat-3054	30	19	on	on	ADP
easat-3054	30	20	i.	i.	PROPN
easat-3054	30	21	now	now	ADV
easat-3054	30	22	,	,	PUNCT
easat-3054	30	23	let	let	VERB
easat-3054	30	24	us	we	PRON
easat-3054	30	25	introduce	introduce	VERB
easat-3054	30	26	our	our	PRON
easat-3054	30	27	lp,∝	lp,∝	ADJ
easat-3054	30	28	space	space	NOUN
easat-3054	30	29	for	for	ADP
easat-3054	30	30	0	0	NUM
easat-3054	30	31	<	<	X
easat-3054	30	32	𝑃	𝑃	PROPN
easat-3054	30	33	<	<	X
easat-3054	30	34	∞.	∞.	PROPN
easat-3054	30	35	let	let	VERB
easat-3054	30	36	us	we	PRON
easat-3054	30	37	define	define	VERB
easat-3054	30	38	the	the	DET
easat-3054	30	39	fractional	fractional	ADJ
easat-3054	30	40	integrable	integrable	ADJ
easat-3054	30	41	quasi	quasi	NOUN
easat-3054	30	42	normed	normed	PROPN
easat-3054	30	43	space	space	NOUN
easat-3054	30	44	as	as	ADP
easat-3054	30	45	:	:	PUNCT
easat-3054	30	46	lp,∝[𝑎	lp,∝[𝑎	PROPN
easat-3054	30	47	,	,	PUNCT
easat-3054	30	48	𝑏	𝑏	NOUN
easat-3054	30	49	]	]	X
easat-3054	30	50	=	=	X
easat-3054	30	51	{	{	PUNCT
easat-3054	30	52	𝑓	𝑓	NOUN
easat-3054	30	53	:	:	PUNCT
easat-3054	30	54	[	[	X
easat-3054	30	55	𝑎	𝑎	X
easat-3054	30	56	,	,	PUNCT
easat-3054	30	57	𝑏	𝑏	NOUN
easat-3054	30	58	]	]	PUNCT
easat-3054	30	59	→	→	SYM
easat-3054	30	60	𝑅	𝑅	NOUN
easat-3054	30	61	:	:	PUNCT
easat-3054	30	62	‖𝑓‖𝑃,𝛼	‖𝑓‖𝑃,𝛼	PROPN
easat-3054	31	1	=	=	SYM
easat-3054	32	1	(	(	PUNCT
easat-3054	32	2	∫	∫	PROPN
easat-3054	32	3	|𝑓(𝑥)|𝑝	|𝑓(𝑥)|𝑝	PROPN
easat-3054	32	4	𝑏	𝑏	PROPN
easat-3054	32	5	𝑎	𝑎	PROPN
easat-3054	32	6	(	(	PUNCT
easat-3054	32	7	𝑑𝑥)𝛼	𝑑𝑥)𝛼	NOUN
easat-3054	32	8	)	)	PUNCT
easat-3054	32	9	1	1	NUM
easat-3054	32	10	𝑃	𝑃	NOUN
easat-3054	32	11	<	<	X
easat-3054	32	12	∞	∞	NOUN
easat-3054	32	13	}	}	PUNCT
easat-3054	32	14	and	and	CCONJ
easat-3054	32	15	‖.	‖.	PROPN
easat-3054	32	16	‖𝑃,𝛼	‖𝑃,𝛼	PROPN
easat-3054	32	17	is	be	AUX
easat-3054	32	18	a	a	DET
easat-3054	32	19	fractional	fractional	ADJ
easat-3054	32	20	lp	lp	ADJ
easat-3054	32	21	integrable	integrable	ADJ
easat-3054	32	22	norm	norm	NOUN
easat-3054	32	23	.	.	PUNCT
easat-3054	33	1	2	2	X
easat-3054	33	2	.	.	X
easat-3054	33	3	auxilary	auxilary	ADJ
easat-3054	33	4	results	result	NOUN
easat-3054	33	5	lemma	lemma	PROPN
easat-3054	33	6	2.1	2.1	NUM
easat-3054	33	7	[	[	X
easat-3054	33	8	6	6	NUM
easat-3054	33	9	]	]	SYM
easat-3054	33	10	:	:	PUNCT
easat-3054	33	11	dαf(x	dαf(x	PROPN
easat-3054	33	12	)	)	PUNCT
easat-3054	33	13	dxα	dxα	NOUN
easat-3054	34	1	=	=	SYM
easat-3054	34	2	γ(1	γ(1	PROPN
easat-3054	34	3	+	+	NUM
easat-3054	34	4	𝑘𝛼	𝑘𝛼	NOUN
easat-3054	34	5	)	)	PUNCT
easat-3054	35	1	γ(1	γ(1	PROPN
easat-3054	36	1	+	+	PUNCT
easat-3054	36	2	(	(	PUNCT
easat-3054	36	3	𝑘	𝑘	PRON
easat-3054	36	4	−	−	PROPN
easat-3054	36	5	1)𝛼	1)𝛼	NUM
easat-3054	36	6	)	)	PUNCT
easat-3054	36	7	𝑋(𝑘−1)𝛼	𝑋(𝑘−1)𝛼	NOUN
easat-3054	37	1	1	1	NUM
easat-3054	38	1	γ(1	γ(1	NOUN
easat-3054	38	2	+	+	NUM
easat-3054	38	3	𝛼	𝛼	X
easat-3054	38	4	)	)	PUNCT
easat-3054	38	5	∫𝑋𝑘𝛼(𝑑𝑥)𝛼	∫𝑋𝑘𝛼(𝑑𝑥)𝛼	NOUN
easat-3054	38	6	=	=	PUNCT
easat-3054	39	1	𝑏	𝑏	PROPN
easat-3054	39	2	𝑎	𝑎	X
easat-3054	39	3	γ(1	γ(1	PROPN
easat-3054	39	4	+	+	NUM
easat-3054	39	5	𝑘𝛼	𝑘𝛼	PROPN
easat-3054	39	6	)	)	PUNCT
easat-3054	40	1	γ(1	γ(1	PROPN
easat-3054	41	1	+	+	PUNCT
easat-3054	41	2	(	(	PUNCT
easat-3054	41	3	𝑘	𝑘	X
easat-3054	41	4	+	+	NOUN
easat-3054	41	5	1)𝛼	1)𝛼	NUM
easat-3054	41	6	)	)	PUNCT
easat-3054	41	7	(	(	PUNCT
easat-3054	41	8	𝑏(𝑘+1)𝛼	𝑏(𝑘+1)𝛼	PROPN
easat-3054	41	9	−	−	PROPN
easat-3054	41	10	𝑎(𝑘+1)𝛼	𝑎(𝑘+1)𝛼	PROPN
easat-3054	41	11	)	)	PUNCT
easat-3054	41	12	,	,	PUNCT
easat-3054	41	13	𝑘𝜖𝑅.	𝑘𝜖𝑅.	PRON
easat-3054	41	14	lemma	lemma	PROPN
easat-3054	41	15	2.2	2.2	NUM
easat-3054	42	1	[	[	X
easat-3054	42	2	1	1	NUM
easat-3054	42	3	]	]	NUM
easat-3054	42	4	:	:	PUNCT
easat-3054	42	5	generalized	generalized	ADJ
easat-3054	42	6	holder	holder	NOUN
easat-3054	42	7	,	,	PUNCT
easat-3054	42	8	s	s	PART
easat-3054	42	9	inequality	inequality	NOUN
easat-3054	42	10	let	let	VERB
easat-3054	42	11	𝑓	𝑓	PRON
easat-3054	42	12	,	,	PUNCT
easat-3054	42	13	𝑔	𝑔	PROPN
easat-3054	42	14	∈	∈	PROPN
easat-3054	42	15	𝐶𝛼[𝑎	𝐶𝛼[𝑎	NOUN
easat-3054	42	16	,	,	PUNCT
easat-3054	42	17	𝑏	𝑏	NOUN
easat-3054	42	18	]	]	X
easat-3054	42	19	,	,	PUNCT
easat-3054	42	20	𝑝	𝑝	NOUN
easat-3054	42	21	,	,	PUNCT
easat-3054	42	22	𝑞	𝑞	X
easat-3054	42	23	>	>	X
easat-3054	42	24	1	1	NUM
easat-3054	42	25	,	,	PUNCT
easat-3054	42	26	with	with	ADP
easat-3054	42	27	1	1	NUM
easat-3054	42	28	𝑝	𝑝	NOUN
easat-3054	43	1	+	+	NUM
easat-3054	43	2	1	1	NUM
easat-3054	43	3	𝑞	𝑞	NOUN
easat-3054	43	4	=	=	ADJ
easat-3054	43	5	1	1	NUM
easat-3054	43	6	,	,	PUNCT
easat-3054	43	7	then	then	ADV
easat-3054	43	8	1	1	X
easat-3054	44	1	γ(1	γ(1	NOUN
easat-3054	44	2	+	+	NUM
easat-3054	44	3	𝛼	𝛼	X
easat-3054	44	4	)	)	PUNCT
easat-3054	44	5	∫|𝑓(𝑥)𝑔(𝑥)|(𝑑𝑥)𝛼	∫|𝑓(𝑥)𝑔(𝑥)|(𝑑𝑥)𝛼	PROPN
easat-3054	44	6	≤	≤	NUM
easat-3054	44	7	(	(	PUNCT
easat-3054	44	8	1	1	NUM
easat-3054	44	9	γ(1	γ(1	NOUN
easat-3054	44	10	+	+	NUM
easat-3054	44	11	𝛼	𝛼	X
easat-3054	44	12	)	)	PUNCT
easat-3054	44	13	∫|𝑓(𝑥)|𝑝(𝑑𝑥)𝛼	∫|𝑓(𝑥)|𝑝(𝑑𝑥)𝛼	VERB
easat-3054	45	1	𝑏	𝑏	PRON
easat-3054	45	2	𝑎	𝑎	X
easat-3054	45	3	)	)	PUNCT
easat-3054	45	4	1	1	NUM
easat-3054	45	5	𝑝𝑏	𝑝𝑏	NOUN
easat-3054	45	6	𝑎	𝑎	NOUN
easat-3054	45	7	.	.	PUNCT
easat-3054	46	1	(	(	PUNCT
easat-3054	46	2	1	1	NUM
easat-3054	46	3	γ(1	γ(1	NOUN
easat-3054	46	4	+	+	NUM
easat-3054	46	5	𝛼	𝛼	X
easat-3054	46	6	)	)	PUNCT
easat-3054	46	7	∫|𝑔(𝑥)|𝑞(𝑑𝑥)𝛼	∫|𝑔(𝑥)|𝑞(𝑑𝑥)𝛼	NOUN
easat-3054	47	1	𝑏	𝑏	PRON
easat-3054	47	2	𝑎	𝑎	X
easat-3054	47	3	)	)	PUNCT
easat-3054	47	4	1	1	NUM
easat-3054	47	5	𝑞	𝑞	X
easat-3054	47	6	.	.	PUNCT
easat-3054	48	1	lemma	lemma	PROPN
easat-3054	48	2	2.3	2.3	NUM
easat-3054	49	1	[	[	X
easat-3054	49	2	1	1	NUM
easat-3054	49	3	]	]	X
easat-3054	49	4	:	:	PUNCT
easat-3054	49	5	in	in	ADP
easat-3054	49	6	𝐿𝑃-space	𝐿𝑃-space	PROPN
easat-3054	49	7	if	if	SCONJ
easat-3054	49	8	if	if	SCONJ
easat-3054	49	9	p	p	X
easat-3054	49	10	<	<	X
easat-3054	49	11	q	q	X
easat-3054	49	12	,	,	PUNCT
easat-3054	49	13	then	then	ADV
easat-3054	49	14	(	(	PUNCT
easat-3054	49	15	∑	∑	PUNCT
easat-3054	49	16	|𝑥𝑖|	|𝑥𝑖|	VERB
easat-3054	49	17	𝑞	𝑞	NOUN
easat-3054	49	18	∞	∞	PROPN
easat-3054	49	19	𝑖=1	𝑖=1	PROPN
easat-3054	49	20	)	)	PUNCT
easat-3054	49	21	1	1	NUM
easat-3054	49	22	𝑞	𝑞	SYM
easat-3054	49	23	≤	≤	X
easat-3054	49	24	(	(	PUNCT
easat-3054	49	25	∑	∑	ADP
easat-3054	49	26	|𝑥𝑖|	|𝑥𝑖|	NOUN
easat-3054	49	27	𝑝	𝑝	ADP
easat-3054	49	28	∞	∞	NUM
easat-3054	49	29	𝑖=1	𝑖=1	PROPN
easat-3054	49	30	)	)	PUNCT
easat-3054	49	31	1	1	NUM
easat-3054	49	32	𝑝	𝑝	NOUN
easat-3054	49	33	.	.	PUNCT
easat-3054	50	1	lemma	lemma	PROPN
easat-3054	50	2	2.4	2.4	NUM
easat-3054	50	3	[	[	SYM
easat-3054	50	4	2	2	NUM
easat-3054	50	5	]	]	NUM
easat-3054	50	6	:	:	PUNCT
easat-3054	50	7	generalized	generalize	VERB
easat-3054	50	8	montgomery	montgomery	PROPN
easat-3054	50	9	inequality	inequality	NOUN
easat-3054	50	10	let	let	VERB
easat-3054	50	11	𝐼	𝐼	PROPN
easat-3054	50	12	⊂	⊂	PROPN
easat-3054	50	13	𝑅	𝑅	PROPN
easat-3054	50	14	be	be	AUX
easat-3054	50	15	an	an	DET
easat-3054	50	16	interval,𝑓	interval,𝑓	NOUN
easat-3054	50	17	:	:	PUNCT
easat-3054	50	18	𝐼∘	𝐼∘	PROPN
easat-3054	50	19	⊂	⊂	PROPN
easat-3054	50	20	𝑅	𝑅	PROPN
easat-3054	50	21	→	→	SYM
easat-3054	50	22	𝑅𝛼	𝑅𝛼	PROPN
easat-3054	50	23	(	(	PUNCT
easat-3054	50	24	𝐼∘is	𝐼∘is	NOUN
easat-3054	50	25	the	the	DET
easat-3054	50	26	interior	interior	NOUN
easat-3054	50	27	of	of	ADP
easat-3054	50	28	i	i	PRON
easat-3054	50	29	)	)	PUNCT
easat-3054	50	30	such	such	ADJ
easat-3054	50	31	that	that	SCONJ
easat-3054	50	32	𝑓	𝑓	PROPN
easat-3054	50	33	is	be	AUX
easat-3054	50	34	∝	∝	PROPN
easat-3054	50	35	−integrable	−integrable	ADJ
easat-3054	50	36	for	for	ADP
easat-3054	50	37	𝑎	𝑎	PROPN
easat-3054	50	38	,	,	PUNCT
easat-3054	50	39	𝑏	𝑏	PROPN
easat-3054	50	40	∈	∈	PROPN
easat-3054	50	41	𝐼∘	𝐼∘	NOUN
easat-3054	50	42	with	with	ADP
easat-3054	50	43	𝑎	𝑎	ADJ
easat-3054	50	44	<	<	X
easat-3054	50	45	𝑏.then	𝑏.then	VERB
easat-3054	50	46	we	we	PRON
easat-3054	50	47	have	have	VERB
easat-3054	50	48	the	the	DET
easat-3054	50	49	identity	identity	NOUN
easat-3054	50	50	𝑓(𝑥	𝑓(𝑥	NOUN
easat-3054	50	51	)	)	PUNCT
easat-3054	50	52	−	−	PROPN
easat-3054	51	1	γ(1	γ(1	PROPN
easat-3054	51	2	+	+	NUM
easat-3054	51	3	𝛼	𝛼	X
easat-3054	51	4	)	)	PUNCT
easat-3054	51	5	(	(	PUNCT
easat-3054	51	6	𝑏	𝑏	PRON
easat-3054	51	7	−	−	PROPN
easat-3054	51	8	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	51	9	𝑎𝐼𝑏	𝑎𝐼𝑏	NOUN
easat-3054	51	10	∝𝑓(𝑥	∝𝑓(𝑥	NOUN
easat-3054	51	11	)	)	PUNCT
easat-3054	51	12	=	=	SYM
easat-3054	52	1	1	1	NUM
easat-3054	52	2	γ(1	γ(1	NOUN
easat-3054	52	3	+	+	NUM
easat-3054	52	4	𝛼	𝛼	X
easat-3054	52	5	)	)	PUNCT
easat-3054	52	6	∫	∫	PROPN
easat-3054	52	7	𝑝(𝑥	𝑝(𝑥	PROPN
easat-3054	52	8	,	,	PUNCT
easat-3054	52	9	𝑡)𝑓(𝑥)𝛼(𝑑𝑡)𝛼	𝑡)𝑓(𝑥)𝛼(𝑑𝑡)𝛼	PROPN
easat-3054	52	10	𝑏	𝑏	NOUN
easat-3054	52	11	𝑎	𝑎	NOUN
easat-3054	52	12	where	where	SCONJ
easat-3054	52	13	𝑝(𝑥	𝑝(𝑥	NOUN
easat-3054	52	14	,	,	PUNCT
easat-3054	52	15	𝑡	𝑡	X
easat-3054	52	16	)	)	PUNCT
easat-3054	52	17	=	=	SYM
easat-3054	52	18	{	{	PUNCT
easat-3054	52	19	(	(	PUNCT
easat-3054	52	20	𝑡	𝑡	X
easat-3054	52	21	−	−	NOUN
easat-3054	52	22	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	52	23	,	,	PUNCT
easat-3054	52	24	𝑡	𝑡	PROPN
easat-3054	52	25	∈	∈	PROPN
easat-3054	53	1	[	[	X
easat-3054	53	2	𝑎	𝑎	X
easat-3054	53	3	,	,	PUNCT
easat-3054	53	4	𝑥	𝑥	X
easat-3054	53	5	]	]	X
easat-3054	53	6	(	(	PUNCT
easat-3054	53	7	𝑡	𝑡	NOUN
easat-3054	53	8	−	−	NOUN
easat-3054	53	9	𝑏)𝛼	𝑏)𝛼	ADJ
easat-3054	53	10	,	,	PUNCT
easat-3054	53	11	𝑡	𝑡	PROPN
easat-3054	53	12	∈	∈	PROPN
easat-3054	53	13	[	[	X
easat-3054	53	14	𝑥	𝑥	X
easat-3054	53	15	,	,	PUNCT
easat-3054	53	16	𝑏	𝑏	NOUN
easat-3054	53	17	]	]	X
easat-3054	53	18	lemma	lemma	PROPN
easat-3054	53	19	2.5	2.5	NUM
easat-3054	53	20	[	[	X
easat-3054	53	21	6	6	NUM
easat-3054	53	22	]	]	PUNCT
easat-3054	53	23	:	:	PUNCT
easat-3054	53	24	a	a	DET
easat-3054	53	25	second	second	ADJ
easat-3054	53	26	type	type	NOUN
easat-3054	53	27	generalized	generalize	VERB
easat-3054	53	28	montgomery	montgomery	PROPN
easat-3054	53	29	inequality	inequality	NOUN
easat-3054	53	30	let	let	VERB
easat-3054	53	31	𝐼	𝐼	PROPN
easat-3054	53	32	⊂	⊂	PROPN
easat-3054	53	33	𝑅	𝑅	PROPN
easat-3054	53	34	be	be	AUX
easat-3054	53	35	an	an	DET
easat-3054	53	36	interval,𝑓	interval,𝑓	NOUN
easat-3054	53	37	:	:	PUNCT
easat-3054	53	38	𝐼∘	𝐼∘	PROPN
easat-3054	53	39	⊂	⊂	PROPN
easat-3054	53	40	𝑅	𝑅	PROPN
easat-3054	53	41	→	→	PROPN
easat-3054	53	42	𝑅𝛼(𝐼∘is	𝑅𝛼(𝐼∘is	ADP
easat-3054	53	43	the	the	DET
easat-3054	53	44	interior	interior	NOUN
easat-3054	53	45	of	of	ADP
easat-3054	53	46	i	i	PRON
easat-3054	53	47	)	)	PUNCT
easat-3054	53	48	such	such	ADJ
easat-3054	53	49	that	that	SCONJ
easat-3054	53	50	𝑓	𝑓	DET
easat-3054	53	51	∈	∈	PROPN
easat-3054	53	52	𝐷𝛼(𝐼	𝐷𝛼(𝐼	NOUN
easat-3054	53	53	∘	∘	X
easat-3054	53	54	)	)	PUNCT
easat-3054	53	55	and	and	CCONJ
easat-3054	53	56	𝑓	𝑓	PROPN
easat-3054	53	57	is	be	AUX
easat-3054	53	58	∝	∝	NOUN
easat-3054	53	59	−integrable	−integrable	ADJ
easat-3054	53	60	with	with	ADP
easat-3054	53	61	𝑎	𝑎	PROPN
easat-3054	53	62	<	<	X
easat-3054	53	63	𝑏	𝑏	NOUN
easat-3054	53	64	,	,	PUNCT
easat-3054	53	65	then	then	ADV
easat-3054	53	66	(	(	PUNCT
easat-3054	53	67	𝐼	𝐼	PROPN
easat-3054	53	68	−	−	PROPN
easat-3054	53	69	ℎ)𝛼𝑓(𝑥	ℎ)𝛼𝑓(𝑥	NOUN
easat-3054	53	70	)	)	PUNCT
easat-3054	54	1	+	+	CCONJ
easat-3054	54	2	ℎ𝛼	ℎ𝛼	DET
easat-3054	54	3	𝑓(𝑎	𝑓(𝑎	NUM
easat-3054	54	4	)	)	PUNCT
easat-3054	55	1	+	+	NUM
easat-3054	55	2	𝑓(𝑏	𝑓(𝑏	NOUN
easat-3054	55	3	)	)	PUNCT
easat-3054	55	4	2𝛼	2𝛼	PROPN
easat-3054	55	5	−	−	PROPN
easat-3054	56	1	γ(1	γ(1	NOUN
easat-3054	56	2	+	+	NUM
easat-3054	56	3	𝛼	𝛼	X
easat-3054	56	4	)	)	PUNCT
easat-3054	56	5	(	(	PUNCT
easat-3054	56	6	𝑏	𝑏	PRON
easat-3054	56	7	−	−	PROPN
easat-3054	56	8	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	56	9	𝑎𝐼𝑏	𝑎𝐼𝑏	NOUN
easat-3054	56	10	∝𝑓(𝑥	∝𝑓(𝑥	NOUN
easat-3054	56	11	)	)	PUNCT
easat-3054	57	1	=	=	SYM
easat-3054	57	2	1	1	NUM
easat-3054	58	1	γ(1	γ(1	NOUN
easat-3054	58	2	+	+	NUM
easat-3054	58	3	𝛼	𝛼	X
easat-3054	58	4	)	)	PUNCT
easat-3054	58	5	∫	∫	PROPN
easat-3054	58	6	𝑝(𝑥	𝑝(𝑥	PROPN
easat-3054	58	7	,	,	PUNCT
easat-3054	58	8	𝑡)𝑓(𝑥)𝛼(𝑑𝑡)𝛼	𝑡)𝑓(𝑥)𝛼(𝑑𝑡)𝛼	PROPN
easat-3054	58	9	𝑏	𝑏	PROPN
easat-3054	58	10	𝑎	𝑎	NOUN
easat-3054	58	11	.	.	PUNCT
easat-3054	59	1	where	where	SCONJ
easat-3054	59	2	4912	4912	NUM
easat-3054	59	3	edelweiss	edelweiss	PROPN
easat-3054	59	4	applied	apply	VERB
easat-3054	59	5	science	science	NOUN
easat-3054	59	6	and	and	CCONJ
easat-3054	59	7	technology	technology	NOUN
easat-3054	59	8	issn	issn	PROPN
easat-3054	59	9	:	:	PUNCT
easat-3054	59	10	2576	2576	NUM
easat-3054	59	11	-	-	SYM
easat-3054	59	12	8484	8484	NUM
easat-3054	59	13	vol	vol	NOUN
easat-3054	59	14	.	.	PROPN
easat-3054	59	15	8	8	NUM
easat-3054	59	16	,	,	PUNCT
easat-3054	59	17	no	no	INTJ
easat-3054	59	18	.	.	NOUN
easat-3054	60	1	6	6	NUM
easat-3054	60	2	:	:	SYM
easat-3054	60	3	4910	4910	NUM
easat-3054	60	4	-	-	SYM
easat-3054	60	5	4919	4919	NUM
easat-3054	60	6	,	,	PUNCT
easat-3054	60	7	2024	2024	NUM
easat-3054	60	8	doi	doi	NOUN
easat-3054	60	9	:	:	PUNCT
easat-3054	60	10	10.55214/25768484.v8i6.3054	10.55214/25768484.v8i6.3054	NUM
easat-3054	60	11	©	©	PROPN
easat-3054	60	12	2024	2024	NUM
easat-3054	60	13	by	by	ADP
easat-3054	60	14	the	the	DET
easat-3054	60	15	authors	author	NOUN
easat-3054	60	16	;	;	PUNCT
easat-3054	60	17	licensee	licensee	PROPN
easat-3054	60	18	learning	learn	VERB
easat-3054	60	19	gate	gate	PROPN
easat-3054	60	20	𝑝(𝑥	𝑝(𝑥	PROPN
easat-3054	60	21	,	,	PUNCT
easat-3054	60	22	𝑡	𝑡	X
easat-3054	60	23	)	)	PUNCT
easat-3054	60	24	=	=	PRON
easat-3054	60	25	{	{	PUNCT
easat-3054	60	26	𝑡	𝑡	X
easat-3054	60	27	−	−	PROPN
easat-3054	60	28	(	(	PUNCT
easat-3054	60	29	𝑎	𝑎	NOUN
easat-3054	60	30	+	+	X
easat-3054	60	31	ℎ	ℎ	X
easat-3054	60	32	(	(	PUNCT
easat-3054	60	33	𝑏	𝑏	PROPN
easat-3054	60	34	−	−	PROPN
easat-3054	60	35	𝑎	𝑎	PROPN
easat-3054	60	36	2	2	NUM
easat-3054	60	37	)	)	PUNCT
easat-3054	60	38	)	)	PUNCT
easat-3054	61	1	∝	∝	PROPN
easat-3054	61	2	,	,	PUNCT
easat-3054	61	3	𝑡	𝑡	PROPN
easat-3054	61	4	∈	∈	PROPN
easat-3054	61	5	[	[	X
easat-3054	61	6	𝑎	𝑎	X
easat-3054	61	7	,	,	PUNCT
easat-3054	61	8	𝑥	𝑥	X
easat-3054	61	9	]	]	X
easat-3054	61	10	𝑡	𝑡	X
easat-3054	61	11	−	−	PROPN
easat-3054	61	12	(	(	PUNCT
easat-3054	61	13	𝑏	𝑏	PROPN
easat-3054	61	14	−	−	PROPN
easat-3054	61	15	ℎ	ℎ	PROPN
easat-3054	61	16	(	(	PUNCT
easat-3054	61	17	𝑏	𝑏	PROPN
easat-3054	61	18	−	−	PROPN
easat-3054	61	19	𝑎	𝑎	PROPN
easat-3054	61	20	2	2	NUM
easat-3054	61	21	)	)	PUNCT
easat-3054	61	22	)	)	PUNCT
easat-3054	62	1	∝	∝	PROPN
easat-3054	62	2	,	,	PUNCT
easat-3054	62	3	𝑡	𝑡	PROPN
easat-3054	62	4	∈	∈	PROPN
easat-3054	63	1	[	[	X
easat-3054	63	2	𝑥	𝑥	X
easat-3054	63	3	,	,	PUNCT
easat-3054	63	4	𝑏	𝑏	NOUN
easat-3054	63	5	]	]	PUNCT
easat-3054	63	6	.	.	PUNCT
easat-3054	64	1	where	where	SCONJ
easat-3054	64	2	ℎ	ℎ	X
easat-3054	64	3	∈	∈	PROPN
easat-3054	64	4	[	[	X
easat-3054	64	5	0,1	0,1	NUM
easat-3054	64	6	]	]	PUNCT
easat-3054	64	7	and	and	CCONJ
easat-3054	64	8	𝑎	𝑎	X
easat-3054	64	9	+	+	NOUN
easat-3054	64	10	ℎ	ℎ	NOUN
easat-3054	64	11	(	(	PUNCT
easat-3054	64	12	𝑏−𝑎	𝑏−𝑎	ADP
easat-3054	64	13	2	2	X
easat-3054	64	14	)	)	PUNCT
easat-3054	64	15	≤	≤	NOUN
easat-3054	64	16	𝑥	𝑥	PRON
easat-3054	64	17	≤	≤	NUM
easat-3054	65	1	𝑏	𝑏	DET
easat-3054	65	2	−	−	NOUN
easat-3054	65	3	ℎ	ℎ	PROPN
easat-3054	65	4	(	(	PUNCT
easat-3054	65	5	𝑏−𝑎	𝑏−𝑎	ADP
easat-3054	65	6	2	2	NUM
easat-3054	65	7	)	)	PUNCT
easat-3054	65	8	.	.	PUNCT
easat-3054	66	1	3	3	X
easat-3054	66	2	.	.	X
easat-3054	66	3	main	main	ADJ
easat-3054	66	4	results	result	NOUN
easat-3054	66	5	let	let	VERB
easat-3054	66	6	us	we	PRON
easat-3054	66	7	now	now	ADV
easat-3054	66	8	introduce	introduce	VERB
easat-3054	66	9	our	our	PRON
easat-3054	66	10	main	main	ADJ
easat-3054	66	11	results	result	NOUN
easat-3054	66	12	.	.	PUNCT
easat-3054	67	1	we	we	PRON
easat-3054	67	2	use	use	VERB
easat-3054	67	3	two	two	NUM
easat-3054	67	4	kinds	kind	NOUN
easat-3054	67	5	of	of	ADP
easat-3054	67	6	generalized	generalize	VERB
easat-3054	67	7	montgomery	montgomery	PROPN
easat-3054	67	8	identity	identity	NOUN
easat-3054	67	9	to	to	PART
easat-3054	67	10	prove	prove	VERB
easat-3054	67	11	types	type	NOUN
easat-3054	67	12	generalized	generalize	VERB
easat-3054	67	13	ostrowski	ostrowski	ADJ
easat-3054	67	14	theorems	theorem	NOUN
easat-3054	67	15	.	.	PUNCT
easat-3054	67	16	theorem	theorem	VERB
easat-3054	67	17	3.1	3.1	NUM
easat-3054	67	18	:	:	PUNCT
easat-3054	67	19	if	if	SCONJ
easat-3054	67	20	𝑓	𝑓	PRON
easat-3054	67	21	⊂	⊂	PROPN
easat-3054	67	22	𝑅	𝑅	PROPN
easat-3054	67	23	,	,	PUNCT
easat-3054	67	24	𝑓	𝑓	PRON
easat-3054	67	25	:	:	PUNCT
easat-3054	67	26	𝐼∘	𝐼∘	PROPN
easat-3054	67	27	⊂	⊂	PROPN
easat-3054	67	28	𝑅	𝑅	PROPN
easat-3054	67	29	→	→	SYM
easat-3054	67	30	𝑅𝛼	𝑅𝛼	PROPN
easat-3054	67	31	be	be	AUX
easat-3054	67	32	a	a	DET
easat-3054	67	33	map	map	NOUN
easat-3054	68	1	[	[	X
easat-3054	68	2	𝑎	𝑎	X
easat-3054	68	3	,	,	PUNCT
easat-3054	68	4	𝑏	𝑏	NOUN
easat-3054	68	5	]	]	X
easat-3054	68	6	⊂	⊂	X
easat-3054	68	7	𝐼∘and	𝐼∘and	PUNCT
easat-3054	68	8	𝑓	𝑓	PRON
easat-3054	68	9	∈	∈	PROPN
easat-3054	68	10	𝐿𝑃,𝛼[𝑎	𝐿𝑃,𝛼[𝑎	NOUN
easat-3054	68	11	,	,	PUNCT
easat-3054	68	12	𝑏	𝑏	NOUN
easat-3054	68	13	]	]	PUNCT
easat-3054	68	14	.	.	PUNCT
easat-3054	69	1	then	then	ADV
easat-3054	69	2	(	(	PUNCT
easat-3054	69	3	1	1	X
easat-3054	69	4	)	)	PUNCT
easat-3054	69	5	|𝑓(𝑥	|𝑓(𝑥	NOUN
easat-3054	69	6	)	)	PUNCT
easat-3054	69	7	−	−	PROPN
easat-3054	70	1	γ(1	γ(1	PROPN
easat-3054	70	2	+	+	NUM
easat-3054	70	3	𝛼	𝛼	X
easat-3054	70	4	)	)	PUNCT
easat-3054	70	5	(	(	PUNCT
easat-3054	70	6	𝑏	𝑏	PROPN
easat-3054	70	7	−	−	PROPN
easat-3054	70	8	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	70	9	𝑎𝐼𝑏	𝑎𝐼𝑏	NOUN
easat-3054	70	10	∝𝑓(𝑥)|	∝𝑓(𝑥)|	PROPN
easat-3054	70	11	≤	≤	NOUN
easat-3054	70	12	(	(	PUNCT
easat-3054	70	13	γ(1	γ(1	PROPN
easat-3054	70	14	+	+	CCONJ
easat-3054	70	15	𝛼𝑞	𝛼𝑞	PROPN
easat-3054	70	16	)	)	PUNCT
easat-3054	70	17	)	)	PUNCT
easat-3054	70	18	1	1	NUM
easat-3054	71	1	𝑞(𝑏	𝑞(𝑏	NOUN
easat-3054	71	2	−	−	NUM
easat-3054	71	3	𝑎	𝑎	NOUN
easat-3054	71	4	)	)	PUNCT
easat-3054	71	5	∝	∝	PROPN
easat-3054	71	6	𝑞	𝑞	X
easat-3054	71	7	(	(	PUNCT
easat-3054	71	8	γ(1	γ(1	PROPN
easat-3054	71	9	+	+	CCONJ
easat-3054	71	10	(	(	PUNCT
easat-3054	71	11	𝑞	𝑞	X
easat-3054	71	12	+	+	X
easat-3054	71	13	1)𝛼	1)𝛼	NUM
easat-3054	71	14	)	)	PUNCT
easat-3054	71	15	)	)	PUNCT
easat-3054	72	1	1	1	NUM
easat-3054	72	2	𝑞(γ(1	𝑞(γ(1	NOUN
easat-3054	72	3	+	+	NUM
easat-3054	72	4	𝛼	𝛼	X
easat-3054	72	5	)	)	PUNCT
easat-3054	72	6	)	)	PUNCT
easat-3054	72	7	1	1	NUM
easat-3054	72	8	𝑝	𝑝	X
easat-3054	72	9	‖𝑓𝛼‖𝑝	‖𝑓𝛼‖𝑝	PROPN
easat-3054	72	10	,	,	PUNCT
easat-3054	72	11	1	1	NUM
easat-3054	72	12	≤	≤	NUM
easat-3054	72	13	𝑝	𝑝	PROPN
easat-3054	72	14	,	,	PUNCT
easat-3054	72	15	𝑞	𝑞	X
easat-3054	72	16	≤	≤	NOUN
easat-3054	72	17	∞	∞	PROPN
easat-3054	72	18	,	,	PUNCT
easat-3054	72	19	1	1	NUM
easat-3054	72	20	𝑝	𝑝	NOUN
easat-3054	72	21	+	+	NUM
easat-3054	72	22	1	1	NUM
easat-3054	72	23	𝑞	𝑞	NOUN
easat-3054	72	24	=	=	NOUN
easat-3054	72	25	1	1	X
easat-3054	72	26	.	.	PUNCT
easat-3054	72	27	(	(	PUNCT
easat-3054	72	28	2	2	X
easat-3054	72	29	)	)	PUNCT
easat-3054	72	30	|𝑓(𝑥	|𝑓(𝑥	NOUN
easat-3054	72	31	)	)	PUNCT
easat-3054	72	32	−	−	PROPN
easat-3054	73	1	γ(1	γ(1	PROPN
easat-3054	73	2	+	+	NUM
easat-3054	73	3	𝛼	𝛼	X
easat-3054	73	4	)	)	PUNCT
easat-3054	73	5	(	(	PUNCT
easat-3054	73	6	𝑏	𝑏	PROPN
easat-3054	73	7	−	−	PROPN
easat-3054	73	8	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	73	9	𝑎𝐼𝑏	𝑎𝐼𝑏	NOUN
easat-3054	73	10	∝𝑓(𝑥)|	∝𝑓(𝑥)|	SYM
easat-3054	73	11	≤	≤	NUM
easat-3054	73	12	𝐶(𝑝)(γ(1	𝐶(𝑝)(γ(1	NUM
easat-3054	73	13	+	+	CCONJ
easat-3054	73	14	𝛼𝑞	𝛼𝑞	X
easat-3054	73	15	)	)	PUNCT
easat-3054	73	16	)	)	PUNCT
easat-3054	73	17	1	1	NUM
easat-3054	73	18	𝑞(𝑏	𝑞(𝑏	NOUN
easat-3054	73	19	−	−	NUM
easat-3054	73	20	𝑎	𝑎	NOUN
easat-3054	73	21	)	)	PUNCT
easat-3054	73	22	∝	∝	PROPN
easat-3054	73	23	𝑞	𝑞	X
easat-3054	73	24	(	(	PUNCT
easat-3054	73	25	γ(1	γ(1	PROPN
easat-3054	73	26	+	+	CCONJ
easat-3054	73	27	(	(	PUNCT
easat-3054	73	28	𝑞	𝑞	X
easat-3054	73	29	+	+	X
easat-3054	73	30	1)𝛼	1)𝛼	NUM
easat-3054	73	31	)	)	PUNCT
easat-3054	73	32	)	)	PUNCT
easat-3054	74	1	1	1	NUM
easat-3054	74	2	𝑞(γ(1	𝑞(γ(1	NOUN
easat-3054	74	3	+	+	NUM
easat-3054	74	4	𝛼	𝛼	X
easat-3054	74	5	)	)	PUNCT
easat-3054	74	6	)	)	PUNCT
easat-3054	74	7	1	1	NUM
easat-3054	74	8	𝑝	𝑝	X
easat-3054	74	9	‖𝑓𝛼‖𝑝	‖𝑓𝛼‖𝑝	PROPN
easat-3054	74	10	,	,	PUNCT
easat-3054	74	11	0	0	NUM
easat-3054	74	12	<	<	X
easat-3054	74	13	𝑝	𝑝	X
easat-3054	74	14	<	<	X
easat-3054	74	15	1	1	NUM
easat-3054	74	16	.	.	PUNCT
easat-3054	74	17	where	where	SCONJ
easat-3054	74	18	,	,	PUNCT
easat-3054	74	19	𝐼∘	𝐼∘	PROPN
easat-3054	74	20	is	be	AUX
easat-3054	74	21	the	the	DET
easat-3054	74	22	interior	interior	NOUN
easat-3054	74	23	of	of	ADP
easat-3054	74	24	the	the	DET
easat-3054	74	25	interval	interval	NOUN
easat-3054	74	26	i.	i.	NOUN
easat-3054	74	27	proof	proof	PROPN
easat-3054	74	28	:	:	PUNCT
easat-3054	74	29	according	accord	VERB
easat-3054	74	30	to	to	ADP
easat-3054	74	31	p	p	PRON
easat-3054	74	32	,	,	PUNCT
easat-3054	74	33	let	let	VERB
easat-3054	74	34	us	we	PRON
easat-3054	74	35	divide	divide	VERB
easat-3054	74	36	our	our	PRON
easat-3054	74	37	proof	proof	NOUN
easat-3054	74	38	into	into	ADP
easat-3054	74	39	two	two	NUM
easat-3054	74	40	cases	case	NOUN
easat-3054	74	41	.	.	PUNCT
easat-3054	75	1	case1	case1	NOUN
easat-3054	75	2	:	:	PUNCT
easat-3054	75	3	1	1	NUM
easat-3054	75	4	≤	≤	NUM
easat-3054	75	5	𝑝	𝑝	NOUN
easat-3054	75	6	≤	≤	NOUN
easat-3054	75	7	∞	∞	NUM
easat-3054	75	8	by	by	ADP
easat-3054	75	9	using	use	VERB
easat-3054	75	10	the	the	DET
easat-3054	75	11	generalized	generalized	ADJ
easat-3054	75	12	holder	holder	NOUN
easat-3054	75	13	,	,	PUNCT
easat-3054	75	14	s	s	PART
easat-3054	75	15	inequality	inequality	NOUN
easat-3054	75	16	described	describe	VERB
easat-3054	75	17	in	in	ADP
easat-3054	75	18	lemma(2.2	lemma(2.2	NOUN
easat-3054	75	19	)	)	PUNCT
easat-3054	75	20	,	,	PUNCT
easat-3054	75	21	we	we	PRON
easat-3054	75	22	get	get	VERB
easat-3054	75	23	1	1	NUM
easat-3054	75	24	γ(1	γ(1	ADJ
easat-3054	75	25	+	+	CCONJ
easat-3054	75	26	𝛼)(𝑏	𝛼)(𝑏	NUM
easat-3054	75	27	−	−	PROPN
easat-3054	75	28	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	75	29	∫	∫	PROPN
easat-3054	75	30	|𝑝(𝑥	|𝑝(𝑥	PROPN
easat-3054	75	31	,	,	PUNCT
easat-3054	75	32	𝑡)||𝑓(𝑥)𝛼|	𝑡)||𝑓(𝑥)𝛼|	PROPN
easat-3054	75	33	(	(	PUNCT
easat-3054	75	34	𝑑𝑡)𝛼	𝑑𝑡)𝛼	NOUN
easat-3054	75	35	𝑏	𝑏	NOUN
easat-3054	75	36	𝑎	𝑎	PROPN
easat-3054	75	37	≤	≤	NUM
easat-3054	75	38	1	1	NUM
easat-3054	75	39	(	(	PUNCT
easat-3054	75	40	𝑏	𝑏	NOUN
easat-3054	75	41	−	−	PROPN
easat-3054	75	42	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	75	43	(	(	PUNCT
easat-3054	75	44	1	1	NUM
easat-3054	75	45	γ(1	γ(1	NOUN
easat-3054	75	46	+	+	NUM
easat-3054	75	47	𝛼	𝛼	X
easat-3054	75	48	)	)	PUNCT
easat-3054	75	49	∫|𝑝(𝑥	∫|𝑝(𝑥	ADJ
easat-3054	75	50	,	,	PUNCT
easat-3054	75	51	𝑡)|𝑞(𝑑𝑥)𝛼	𝑡)|𝑞(𝑑𝑥)𝛼	NOUN
easat-3054	75	52	𝑏	𝑏	PROPN
easat-3054	75	53	𝑎	𝑎	X
easat-3054	75	54	)	)	PUNCT
easat-3054	75	55	1	1	NUM
easat-3054	75	56	𝑞	𝑞	SYM
easat-3054	75	57	(	(	PUNCT
easat-3054	75	58	1	1	NUM
easat-3054	76	1	γ(1	γ(1	NOUN
easat-3054	76	2	+	+	NUM
easat-3054	76	3	𝛼	𝛼	X
easat-3054	76	4	)	)	PUNCT
easat-3054	76	5	∫|𝑓(𝑥)𝛼|𝑝(𝑑𝑥)𝛼	∫|𝑓(𝑥)𝛼|𝑝(𝑑𝑥)𝛼	PROPN
easat-3054	77	1	𝑏	𝑏	PROPN
easat-3054	77	2	𝑎	𝑎	X
easat-3054	77	3	)	)	PUNCT
easat-3054	77	4	1	1	NUM
easat-3054	77	5	𝑝	𝑝	PROPN
easat-3054	77	6	1	1	NUM
easat-3054	77	7	≤	≤	NUM
easat-3054	77	8	𝑝	𝑝	PROPN
easat-3054	77	9	,	,	PUNCT
easat-3054	77	10	𝑞	𝑞	X
easat-3054	77	11	≤	≤	NOUN
easat-3054	77	12	∞	∞	PROPN
easat-3054	77	13	,	,	PUNCT
easat-3054	77	14	1	1	NUM
easat-3054	77	15	𝑝	𝑝	NOUN
easat-3054	77	16	+	+	NUM
easat-3054	77	17	1	1	NUM
easat-3054	77	18	𝑞	𝑞	NOUN
easat-3054	77	19	=	=	SYM
easat-3054	77	20	1	1	NUM
easat-3054	77	21	(	(	PUNCT
easat-3054	77	22	2	2	NUM
easat-3054	77	23	)	)	PUNCT
easat-3054	77	24	let	let	VERB
easat-3054	77	25	us	we	PRON
easat-3054	77	26	calculate	calculate	VERB
easat-3054	77	27	(	(	PUNCT
easat-3054	77	28	1	1	NUM
easat-3054	77	29	γ(1+𝛼	γ(1+𝛼	ADJ
easat-3054	77	30	)	)	PUNCT
easat-3054	77	31	∫	∫	PROPN
easat-3054	78	1	|𝑝(𝑥	|𝑝(𝑥	PROPN
easat-3054	78	2	,	,	PUNCT
easat-3054	78	3	𝑡)|𝑞(𝑑𝑥)𝛼	𝑡)|𝑞(𝑑𝑥)𝛼	NOUN
easat-3054	78	4	𝑏	𝑏	PROPN
easat-3054	78	5	𝑎	𝑎	X
easat-3054	78	6	)	)	PUNCT
easat-3054	78	7	1	1	NUM
easat-3054	78	8	𝑞	𝑞	NOUN
easat-3054	78	9	,	,	PUNCT
easat-3054	78	10	we	we	PRON
easat-3054	78	11	have	have	VERB
easat-3054	78	12	(	(	PUNCT
easat-3054	78	13	1	1	NUM
easat-3054	78	14	γ(1	γ(1	NOUN
easat-3054	78	15	+	+	NUM
easat-3054	78	16	𝛼	𝛼	X
easat-3054	78	17	)	)	PUNCT
easat-3054	78	18	∫|(𝑡	∫|(𝑡	VERB
easat-3054	78	19	−	−	PROPN
easat-3054	78	20	𝑎)|𝑞(𝑑𝑡)𝛼	𝑎)|𝑞(𝑑𝑡)𝛼	NOUN
easat-3054	79	1	𝑥	𝑥	PRON
easat-3054	80	1	𝑎	𝑎	X
easat-3054	80	2	)	)	PUNCT
easat-3054	80	3	1	1	NUM
easat-3054	80	4	𝑞	𝑞	NOUN
easat-3054	80	5	+	+	X
easat-3054	80	6	(	(	PUNCT
easat-3054	80	7	1	1	NUM
easat-3054	80	8	γ(1	γ(1	NOUN
easat-3054	80	9	+	+	NUM
easat-3054	80	10	𝛼	𝛼	X
easat-3054	80	11	)	)	PUNCT
easat-3054	80	12	∫|(𝑡	∫|(𝑡	VERB
easat-3054	80	13	−	−	PROPN
easat-3054	80	14	𝑏)|𝑞(𝑑𝑡)𝛼	𝑏)|𝑞(𝑑𝑡)𝛼	NOUN
easat-3054	80	15	𝑏	𝑏	PROPN
easat-3054	80	16	𝑥	𝑥	PROPN
easat-3054	80	17	)	)	PUNCT
easat-3054	80	18	1	1	NUM
easat-3054	80	19	𝑞	𝑞	NOUN
easat-3054	80	20	=	=	PUNCT
easat-3054	80	21	(	(	PUNCT
easat-3054	80	22	𝐼1	𝐼1	NOUN
easat-3054	80	23	+	+	CCONJ
easat-3054	80	24	𝐼2	𝐼2	NOUN
easat-3054	80	25	)	)	PUNCT
easat-3054	80	26	1	1	NUM
easat-3054	80	27	𝑞	𝑞	PROPN
easat-3054	80	28	(	(	PUNCT
easat-3054	80	29	3	3	NUM
easat-3054	80	30	)	)	PUNCT
easat-3054	80	31	by	by	ADP
easat-3054	80	32	using	use	VERB
easat-3054	80	33	lemma	lemma	PROPN
easat-3054	80	34	2,1	2,1	NUM
easat-3054	80	35	,	,	PUNCT
easat-3054	80	36	𝐼1	𝐼1	NOUN
easat-3054	80	37	=	=	SYM
easat-3054	80	38	1	1	NUM
easat-3054	81	1	γ(1	γ(1	NOUN
easat-3054	81	2	+	+	NUM
easat-3054	81	3	𝛼	𝛼	X
easat-3054	81	4	)	)	PUNCT
easat-3054	81	5	∫|(𝑡	∫|(𝑡	VERB
easat-3054	81	6	−	−	PROPN
easat-3054	81	7	𝑎)|𝑞(𝑑𝑡)𝛼	𝑎)|𝑞(𝑑𝑡)𝛼	NOUN
easat-3054	82	1	𝑥	𝑥	PROPN
easat-3054	82	2	𝑎	𝑎	PROPN
easat-3054	82	3	4913	4913	NUM
easat-3054	82	4	edelweiss	edelweiss	PROPN
easat-3054	82	5	applied	apply	VERB
easat-3054	82	6	science	science	NOUN
easat-3054	82	7	and	and	CCONJ
easat-3054	82	8	technology	technology	NOUN
easat-3054	82	9	issn	issn	PROPN
easat-3054	82	10	:	:	PUNCT
easat-3054	82	11	2576	2576	NUM
easat-3054	82	12	-	-	SYM
easat-3054	82	13	8484	8484	NUM
easat-3054	82	14	vol	vol	NOUN
easat-3054	82	15	.	.	PROPN
easat-3054	82	16	8	8	NUM
easat-3054	82	17	,	,	PUNCT
easat-3054	82	18	no	no	INTJ
easat-3054	82	19	.	.	NOUN
easat-3054	83	1	6	6	NUM
easat-3054	83	2	:	:	SYM
easat-3054	83	3	4910	4910	NUM
easat-3054	83	4	-	-	SYM
easat-3054	83	5	4919	4919	NUM
easat-3054	83	6	,	,	PUNCT
easat-3054	83	7	2024	2024	NUM
easat-3054	83	8	doi	doi	NOUN
easat-3054	83	9	:	:	PUNCT
easat-3054	83	10	10.55214/25768484.v8i6.3054	10.55214/25768484.v8i6.3054	NUM
easat-3054	83	11	©	©	PROPN
easat-3054	83	12	2024	2024	NUM
easat-3054	83	13	by	by	ADP
easat-3054	83	14	the	the	DET
easat-3054	83	15	authors	author	NOUN
easat-3054	83	16	;	;	PUNCT
easat-3054	83	17	licensee	licensee	NOUN
easat-3054	83	18	learning	learning	NOUN
easat-3054	83	19	gate	gate	NOUN
easat-3054	83	20	=	=	PUNCT
easat-3054	84	1	γ(1	γ(1	PROPN
easat-3054	84	2	+	+	CCONJ
easat-3054	84	3	𝛼𝑞	𝛼𝑞	X
easat-3054	85	1	)	)	PUNCT
easat-3054	85	2	γ(1	γ(1	PROPN
easat-3054	86	1	+	+	CCONJ
easat-3054	86	2	(	(	PUNCT
easat-3054	86	3	𝑞	𝑞	X
easat-3054	86	4	+	+	NOUN
easat-3054	86	5	1)𝛼	1)𝛼	NUM
easat-3054	86	6	)	)	PUNCT
easat-3054	86	7	(	(	PUNCT
easat-3054	86	8	𝑥(𝑞+1)𝛼	𝑥(𝑞+1)𝛼	PROPN
easat-3054	86	9	−	−	PROPN
easat-3054	86	10	𝑎(𝑞+1)𝛼	𝑎(𝑞+1)𝛼	PROPN
easat-3054	86	11	)	)	PUNCT
easat-3054	86	12	(	(	PUNCT
easat-3054	86	13	4	4	X
easat-3054	86	14	)	)	PUNCT
easat-3054	86	15	𝐼2	𝐼2	NOUN
easat-3054	86	16	=	=	SYM
easat-3054	86	17	1	1	NUM
easat-3054	86	18	γ(1	γ(1	NOUN
easat-3054	86	19	+	+	NUM
easat-3054	86	20	𝛼	𝛼	X
easat-3054	86	21	)	)	PUNCT
easat-3054	86	22	∫|(𝑡	∫|(𝑡	VERB
easat-3054	86	23	−	−	PROPN
easat-3054	86	24	𝑏)|𝑞(𝑑𝑡)𝛼	𝑏)|𝑞(𝑑𝑡)𝛼	ADV
easat-3054	87	1	𝑏	𝑏	NOUN
easat-3054	88	1	𝑥	𝑥	NOUN
easat-3054	88	2	=	=	SYM
easat-3054	88	3	γ(1	γ(1	PROPN
easat-3054	88	4	+	+	CCONJ
easat-3054	88	5	𝛼𝑞	𝛼𝑞	X
easat-3054	89	1	)	)	PUNCT
easat-3054	89	2	γ(1	γ(1	PROPN
easat-3054	90	1	+	+	CCONJ
easat-3054	90	2	(	(	PUNCT
easat-3054	90	3	𝑞	𝑞	X
easat-3054	90	4	+	+	NOUN
easat-3054	90	5	1)𝛼	1)𝛼	NUM
easat-3054	90	6	)	)	PUNCT
easat-3054	90	7	(	(	PUNCT
easat-3054	90	8	𝑏(𝑞+1)𝛼	𝑏(𝑞+1)𝛼	PROPN
easat-3054	90	9	−	−	PROPN
easat-3054	90	10	𝑥(𝑞+1)𝛼	𝑥(𝑞+1)𝛼	PROPN
easat-3054	90	11	)	)	PUNCT
easat-3054	90	12	(	(	PUNCT
easat-3054	90	13	5	5	X
easat-3054	90	14	)	)	PUNCT
easat-3054	90	15	put	put	NOUN
easat-3054	90	16	(	(	PUNCT
easat-3054	90	17	4	4	NUM
easat-3054	90	18	)	)	PUNCT
easat-3054	90	19	and(5	and(5	ADV
easat-3054	90	20	)	)	PUNCT
easat-3054	91	1	in	in	ADP
easat-3054	91	2	(	(	PUNCT
easat-3054	91	3	3	3	NUM
easat-3054	91	4	)	)	PUNCT
easat-3054	91	5	,	,	PUNCT
easat-3054	91	6	we	we	PRON
easat-3054	91	7	get	get	VERB
easat-3054	91	8	(	(	PUNCT
easat-3054	91	9	1	1	NUM
easat-3054	91	10	γ(1	γ(1	NOUN
easat-3054	91	11	+	+	NUM
easat-3054	91	12	𝛼	𝛼	X
easat-3054	91	13	)	)	PUNCT
easat-3054	91	14	∫|𝑝(𝑥	∫|𝑝(𝑥	ADJ
easat-3054	91	15	,	,	PUNCT
easat-3054	91	16	𝑡)|𝑞(𝑑𝑥)𝛼	𝑡)|𝑞(𝑑𝑥)𝛼	NOUN
easat-3054	91	17	𝑏	𝑏	PROPN
easat-3054	91	18	𝑎	𝑎	X
easat-3054	91	19	)	)	PUNCT
easat-3054	91	20	1	1	NUM
easat-3054	91	21	𝑞	𝑞	NOUN
easat-3054	91	22	=	=	PUNCT
easat-3054	91	23	(	(	PUNCT
easat-3054	91	24	γ(1	γ(1	PROPN
easat-3054	91	25	+	+	CCONJ
easat-3054	91	26	𝛼𝑞	𝛼𝑞	X
easat-3054	92	1	)	)	PUNCT
easat-3054	92	2	γ(1	γ(1	PROPN
easat-3054	93	1	+	+	CCONJ
easat-3054	93	2	(	(	PUNCT
easat-3054	93	3	𝑞	𝑞	X
easat-3054	93	4	+	+	NOUN
easat-3054	93	5	1)𝛼	1)𝛼	NUM
easat-3054	93	6	)	)	PUNCT
easat-3054	93	7	(	(	PUNCT
easat-3054	93	8	𝑏(𝑞+1)𝛼	𝑏(𝑞+1)𝛼	PROPN
easat-3054	93	9	−	−	PROPN
easat-3054	93	10	𝑎(𝑞+1)𝛼	𝑎(𝑞+1)𝛼	PROPN
easat-3054	93	11	)	)	PUNCT
easat-3054	93	12	)	)	PUNCT
easat-3054	94	1	1	1	NUM
easat-3054	94	2	𝑞	𝑞	SYM
easat-3054	94	3	≤	≤	X
easat-3054	94	4	(	(	PUNCT
easat-3054	94	5	γ(1	γ(1	PROPN
easat-3054	94	6	+	+	CCONJ
easat-3054	94	7	𝛼𝑞	𝛼𝑞	X
easat-3054	94	8	)	)	PUNCT
easat-3054	94	9	γ(1	γ(1	PROPN
easat-3054	95	1	+	+	CCONJ
easat-3054	95	2	(	(	PUNCT
easat-3054	95	3	𝑞	𝑞	X
easat-3054	95	4	+	+	NOUN
easat-3054	95	5	1)𝛼	1)𝛼	NUM
easat-3054	95	6	)	)	PUNCT
easat-3054	95	7	)	)	PUNCT
easat-3054	96	1	1	1	NUM
easat-3054	96	2	𝑞	𝑞	SYM
easat-3054	96	3	(	(	PUNCT
easat-3054	96	4	𝑏	𝑏	PROPN
easat-3054	96	5	−	−	PROPN
easat-3054	96	6	𝑎	𝑎	NOUN
easat-3054	96	7	)	)	PUNCT
easat-3054	96	8	(	(	PUNCT
easat-3054	96	9	𝑞+1)𝛼	𝑞+1)𝛼	PROPN
easat-3054	96	10	𝑞	𝑞	X
easat-3054	96	11	(	(	PUNCT
easat-3054	96	12	6	6	NUM
easat-3054	96	13	)	)	PUNCT
easat-3054	96	14	since	since	SCONJ
easat-3054	96	15	(	(	PUNCT
easat-3054	96	16	1	1	NUM
easat-3054	96	17	γ(1+𝛼	γ(1+𝛼	ADJ
easat-3054	96	18	)	)	PUNCT
easat-3054	96	19	∫	∫	PROPN
easat-3054	96	20	|𝑓(𝑥)𝛼|𝑝(𝑑𝑥)𝛼	|𝑓(𝑥)𝛼|𝑝(𝑑𝑥)𝛼	PROPN
easat-3054	96	21	𝑏	𝑏	PROPN
easat-3054	96	22	𝑎	𝑎	X
easat-3054	96	23	)	)	PUNCT
easat-3054	96	24	1	1	NUM
easat-3054	96	25	𝑝	𝑝	NOUN
easat-3054	96	26	=	=	PUNCT
easat-3054	96	27	(	(	PUNCT
easat-3054	96	28	1	1	NUM
easat-3054	96	29	γ(1+𝛼	γ(1+𝛼	ADJ
easat-3054	96	30	)	)	PUNCT
easat-3054	96	31	)	)	PUNCT
easat-3054	96	32	1	1	NUM
easat-3054	96	33	𝑝	𝑝	X
easat-3054	96	34	‖𝑓𝛼‖𝑝	‖𝑓𝛼‖𝑝	PROPN
easat-3054	96	35	(	(	PUNCT
easat-3054	96	36	7	7	NUM
easat-3054	96	37	)	)	PUNCT
easat-3054	96	38	put	put	NOUN
easat-3054	96	39	(	(	PUNCT
easat-3054	96	40	6	6	NUM
easat-3054	96	41	)	)	PUNCT
easat-3054	96	42	and	and	CCONJ
easat-3054	96	43	(	(	PUNCT
easat-3054	96	44	7	7	X
easat-3054	96	45	)	)	PUNCT
easat-3054	96	46	in	in	ADP
easat-3054	96	47	(	(	PUNCT
easat-3054	96	48	2	2	NUM
easat-3054	96	49	)	)	PUNCT
easat-3054	96	50	,	,	PUNCT
easat-3054	96	51	we	we	PRON
easat-3054	96	52	get	get	VERB
easat-3054	96	53	1	1	NUM
easat-3054	96	54	γ(1	γ(1	ADJ
easat-3054	96	55	+	+	CCONJ
easat-3054	96	56	𝛼)(𝑏	𝛼)(𝑏	NUM
easat-3054	96	57	−	−	PROPN
easat-3054	96	58	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	96	59	∫	∫	PROPN
easat-3054	96	60	|𝑝(𝑥	|𝑝(𝑥	PROPN
easat-3054	96	61	,	,	PUNCT
easat-3054	96	62	𝑡)||𝑓(𝑥)𝛼|	𝑡)||𝑓(𝑥)𝛼|	PROPN
easat-3054	96	63	(	(	PUNCT
easat-3054	96	64	𝑑𝑡)𝛼	𝑑𝑡)𝛼	PROPN
easat-3054	96	65	≤	≤	NOUN
easat-3054	96	66	𝑏	𝑏	PRON
easat-3054	96	67	𝑎	𝑎	X
easat-3054	96	68	(	(	PUNCT
easat-3054	96	69	𝛤(1	𝛤(1	PUNCT
easat-3054	96	70	+	+	CCONJ
easat-3054	96	71	𝛼𝑞	𝛼𝑞	NOUN
easat-3054	96	72	)	)	PUNCT
easat-3054	96	73	)	)	PUNCT
easat-3054	96	74	1	1	NUM
easat-3054	96	75	𝑞(𝑏	𝑞(𝑏	NOUN
easat-3054	96	76	−	−	NUM
easat-3054	96	77	𝑎	𝑎	NOUN
easat-3054	96	78	)	)	PUNCT
easat-3054	96	79	(	(	PUNCT
easat-3054	96	80	𝑞+1)𝛼	𝑞+1)𝛼	PROPN
easat-3054	96	81	𝑞	𝑞	X
easat-3054	96	82	(	(	PUNCT
easat-3054	96	83	𝑏	𝑏	PROPN
easat-3054	96	84	−	−	PROPN
easat-3054	96	85	𝑎)𝛼(𝛤(1	𝑎)𝛼(𝛤(1	PROPN
easat-3054	97	1	+	+	CCONJ
easat-3054	97	2	(	(	PUNCT
easat-3054	97	3	𝑞	𝑞	X
easat-3054	97	4	+	+	X
easat-3054	97	5	1)𝛼	1)𝛼	NUM
easat-3054	97	6	)	)	PUNCT
easat-3054	97	7	)	)	PUNCT
easat-3054	97	8	1	1	NUM
easat-3054	98	1	𝑞(𝛤(1	𝑞(𝛤(1	NUM
easat-3054	98	2	+	+	NUM
easat-3054	98	3	𝛼	𝛼	X
easat-3054	98	4	)	)	PUNCT
easat-3054	98	5	)	)	PUNCT
easat-3054	98	6	1	1	NUM
easat-3054	98	7	𝑝	𝑝	X
easat-3054	98	8	‖𝑓𝛼‖𝑝	‖𝑓𝛼‖𝑝	PROPN
easat-3054	98	9	,	,	PUNCT
easat-3054	98	10	1	1	NUM
easat-3054	98	11	≤	≤	NUM
easat-3054	98	12	𝑝	𝑝	PROPN
easat-3054	98	13	,	,	PUNCT
easat-3054	98	14	𝑞	𝑞	X
easat-3054	98	15	≤	≤	NOUN
easat-3054	98	16	∞	∞	PROPN
easat-3054	98	17	,	,	PUNCT
easat-3054	98	18	1	1	NUM
easat-3054	98	19	𝑝	𝑝	NOUN
easat-3054	98	20	+	+	NUM
easat-3054	98	21	1	1	NUM
easat-3054	98	22	𝑞	𝑞	NOUN
easat-3054	98	23	=	=	NOUN
easat-3054	98	24	1	1	NUM
easat-3054	98	25	now	now	ADV
easat-3054	98	26	by	by	ADP
easat-3054	98	27	using	use	VERB
easat-3054	98	28	lemma	lemma	PROPN
easat-3054	98	29	2.4,we	2.4,we	PROPN
easat-3054	98	30	get	get	VERB
easat-3054	98	31	|𝑓(𝑥	|𝑓(𝑥	NOUN
easat-3054	98	32	)	)	PUNCT
easat-3054	98	33	−	−	PROPN
easat-3054	99	1	γ(1	γ(1	PROPN
easat-3054	99	2	+	+	NUM
easat-3054	99	3	𝛼	𝛼	X
easat-3054	99	4	)	)	PUNCT
easat-3054	99	5	(	(	PUNCT
easat-3054	99	6	𝑏	𝑏	PROPN
easat-3054	99	7	−	−	PROPN
easat-3054	99	8	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	99	9	𝑎𝐼𝑏	𝑎𝐼𝑏	NOUN
easat-3054	99	10	∝𝑓(𝑥)|	∝𝑓(𝑥)|	PROPN
easat-3054	99	11	≤	≤	NUM
easat-3054	99	12	(	(	PUNCT
easat-3054	99	13	𝛤(1	𝛤(1	X
easat-3054	99	14	+	+	CCONJ
easat-3054	99	15	𝛼𝑞	𝛼𝑞	NOUN
easat-3054	99	16	)	)	PUNCT
easat-3054	99	17	)	)	PUNCT
easat-3054	99	18	1	1	NUM
easat-3054	99	19	𝑞(𝑏	𝑞(𝑏	NOUN
easat-3054	99	20	−	−	NUM
easat-3054	99	21	𝑎	𝑎	NOUN
easat-3054	99	22	)	)	PUNCT
easat-3054	99	23	𝛼	𝛼	PROPN
easat-3054	99	24	𝑞	𝑞	X
easat-3054	99	25	(	(	PUNCT
easat-3054	99	26	𝛤(1	𝛤(1	PUNCT
easat-3054	99	27	+	+	CCONJ
easat-3054	99	28	(	(	PUNCT
easat-3054	99	29	𝑞	𝑞	X
easat-3054	99	30	+	+	X
easat-3054	99	31	1)𝛼	1)𝛼	NUM
easat-3054	99	32	)	)	PUNCT
easat-3054	99	33	)	)	PUNCT
easat-3054	100	1	1	1	NUM
easat-3054	100	2	𝑞(𝛤(1	𝑞(𝛤(1	NUM
easat-3054	100	3	+	+	NUM
easat-3054	100	4	𝛼	𝛼	X
easat-3054	100	5	)	)	PUNCT
easat-3054	100	6	)	)	PUNCT
easat-3054	100	7	1	1	NUM
easat-3054	100	8	𝑝	𝑝	PROPN
easat-3054	100	9	‖𝑓𝛼‖𝑝.	‖𝑓𝛼‖𝑝.	PUNCT
easat-3054	100	10	the	the	DET
easat-3054	100	11	first	first	ADJ
easat-3054	100	12	case	case	NOUN
easat-3054	100	13	is	be	AUX
easat-3054	100	14	proved	prove	VERB
easat-3054	100	15	.	.	PUNCT
easat-3054	101	1	case2	case2	PROPN
easat-3054	101	2	:	:	PUNCT
easat-3054	101	3	0	0	NUM
easat-3054	101	4	<	<	X
easat-3054	101	5	𝑃	𝑃	X
easat-3054	101	6	<	<	X
easat-3054	101	7	1	1	NUM
easat-3054	101	8	by	by	ADP
easat-3054	101	9	using	use	VERB
easat-3054	101	10	the	the	DET
easat-3054	101	11	generalized	generalized	ADJ
easat-3054	101	12	holder	holder	NOUN
easat-3054	101	13	,	,	PUNCT
easat-3054	101	14	s	s	PART
easat-3054	101	15	inequality	inequality	NOUN
easat-3054	101	16	described	describe	VERB
easat-3054	101	17	in	in	ADP
easat-3054	101	18	lemma2.2	lemma2.2	NOUN
easat-3054	101	19	,	,	PUNCT
easat-3054	101	20	we	we	PRON
easat-3054	101	21	obtain	obtain	VERB
easat-3054	101	22	.	.	PUNCT
easat-3054	102	1	1	1	NUM
easat-3054	102	2	𝛤(1	𝛤(1	NUM
easat-3054	102	3	+	+	CCONJ
easat-3054	102	4	𝛼)(𝑏	𝛼)(𝑏	NUM
easat-3054	102	5	−	−	PROPN
easat-3054	102	6	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	102	7	∫	∫	PROPN
easat-3054	102	8	|𝑝(𝑥	|𝑝(𝑥	PROPN
easat-3054	102	9	,	,	PUNCT
easat-3054	102	10	𝑡)||𝑓(𝑥)𝛼|	𝑡)||𝑓(𝑥)𝛼|	PROPN
easat-3054	102	11	(	(	PUNCT
easat-3054	102	12	𝑑𝑡)𝛼	𝑑𝑡)𝛼	NOUN
easat-3054	102	13	𝑏	𝑏	NOUN
easat-3054	102	14	𝑎	𝑎	PROPN
easat-3054	102	15	≤	≤	NUM
easat-3054	102	16	1	1	NUM
easat-3054	102	17	(	(	PUNCT
easat-3054	102	18	𝑏	𝑏	NOUN
easat-3054	102	19	−	−	PROPN
easat-3054	102	20	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	102	21	(	(	PUNCT
easat-3054	102	22	1	1	NUM
easat-3054	102	23	𝛤(1	𝛤(1	NUM
easat-3054	102	24	+	+	CCONJ
easat-3054	102	25	𝛼	𝛼	X
easat-3054	102	26	)	)	PUNCT
easat-3054	102	27	∫|𝑝(𝑥	∫|𝑝(𝑥	ADJ
easat-3054	102	28	,	,	PUNCT
easat-3054	102	29	𝑡)|𝑞(𝑑𝑥)𝛼	𝑡)|𝑞(𝑑𝑥)𝛼	NOUN
easat-3054	102	30	𝑏	𝑏	PROPN
easat-3054	102	31	𝑎	𝑎	X
easat-3054	102	32	)	)	PUNCT
easat-3054	102	33	1	1	NUM
easat-3054	102	34	𝑞	𝑞	PROPN
easat-3054	102	35	(	(	PUNCT
easat-3054	102	36	1	1	NUM
easat-3054	102	37	𝛤(1	𝛤(1	NUM
easat-3054	102	38	+	+	CCONJ
easat-3054	102	39	𝛼	𝛼	X
easat-3054	102	40	)	)	PUNCT
easat-3054	102	41	∫|𝑓(𝑥)𝛼|ℎ(𝑑𝑥)𝛼	∫|𝑓(𝑥)𝛼|ℎ(𝑑𝑥)𝛼	NUM
easat-3054	103	1	𝑏	𝑏	PRON
easat-3054	103	2	𝑎	𝑎	X
easat-3054	103	3	)	)	PUNCT
easat-3054	103	4	1	1	NUM
easat-3054	103	5	ℎ	ℎ	PART
easat-3054	103	6	1	1	NUM
easat-3054	103	7	≤	≤	NUM
easat-3054	103	8	𝑝	𝑝	PROPN
easat-3054	103	9	,	,	PUNCT
easat-3054	103	10	𝑞	𝑞	X
easat-3054	103	11	≤	≤	NOUN
easat-3054	103	12	∞	∞	PROPN
easat-3054	103	13	,	,	PUNCT
easat-3054	103	14	1	1	NUM
easat-3054	103	15	ℎ	ℎ	X
easat-3054	103	16	+	+	NOUN
easat-3054	103	17	1	1	NUM
easat-3054	103	18	𝑞	𝑞	NOUN
easat-3054	103	19	=	=	SYM
easat-3054	103	20	1	1	NUM
easat-3054	103	21	by	by	ADP
easat-3054	103	22	using	use	VERB
easat-3054	103	23	definition	definition	NOUN
easat-3054	103	24	of	of	ADP
easat-3054	103	25	the	the	DET
easat-3054	103	26	fractional	fractional	ADJ
easat-3054	103	27	integral	integral	ADJ
easat-3054	103	28	in(1	in(1	NOUN
easat-3054	103	29	)	)	PUNCT
easat-3054	103	30	and	and	CCONJ
easat-3054	103	31	(	(	PUNCT
easat-3054	103	32	6	6	NUM
easat-3054	103	33	)	)	SYM
easat-3054	103	34	1	1	NUM
easat-3054	103	35	𝛤(1	𝛤(1	NUM
easat-3054	103	36	+	+	CCONJ
easat-3054	104	1	𝛼)(𝑏	𝛼)(𝑏	NUM
easat-3054	104	2	−	−	PROPN
easat-3054	104	3	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	104	4	∫	∫	PROPN
easat-3054	104	5	|𝑝(𝑥	|𝑝(𝑥	PROPN
easat-3054	104	6	,	,	PUNCT
easat-3054	104	7	𝑡)||𝑓(𝑥)𝛼|	𝑡)||𝑓(𝑥)𝛼|	PROPN
easat-3054	104	8	(	(	PUNCT
easat-3054	104	9	𝑑𝑡)𝛼	𝑑𝑡)𝛼	NOUN
easat-3054	104	10	𝑏	𝑏	NOUN
easat-3054	104	11	𝑎	𝑎	PROPN
easat-3054	104	12	4914	4914	NUM
easat-3054	104	13	edelweiss	edelweiss	PROPN
easat-3054	104	14	applied	apply	VERB
easat-3054	104	15	science	science	NOUN
easat-3054	104	16	and	and	CCONJ
easat-3054	104	17	technology	technology	NOUN
easat-3054	104	18	issn	issn	PROPN
easat-3054	104	19	:	:	PUNCT
easat-3054	104	20	2576	2576	NUM
easat-3054	104	21	-	-	SYM
easat-3054	104	22	8484	8484	NUM
easat-3054	104	23	vol	vol	NOUN
easat-3054	104	24	.	.	PROPN
easat-3054	104	25	8	8	NUM
easat-3054	104	26	,	,	PUNCT
easat-3054	104	27	no	no	INTJ
easat-3054	104	28	.	.	NOUN
easat-3054	105	1	6	6	NUM
easat-3054	105	2	:	:	SYM
easat-3054	105	3	4910	4910	NUM
easat-3054	105	4	-	-	SYM
easat-3054	105	5	4919	4919	NUM
easat-3054	105	6	,	,	PUNCT
easat-3054	105	7	2024	2024	NUM
easat-3054	105	8	doi	doi	NOUN
easat-3054	105	9	:	:	PUNCT
easat-3054	105	10	10.55214/25768484.v8i6.3054	10.55214/25768484.v8i6.3054	NUM
easat-3054	105	11	©	©	PROPN
easat-3054	105	12	2024	2024	NUM
easat-3054	105	13	by	by	ADP
easat-3054	105	14	the	the	DET
easat-3054	105	15	authors	author	NOUN
easat-3054	105	16	;	;	PUNCT
easat-3054	105	17	licensee	licensee	PROPN
easat-3054	105	18	learning	learning	NOUN
easat-3054	105	19	gate	gate	VERB
easat-3054	105	20	≤	≤	NOUN
easat-3054	105	21	(	(	PUNCT
easat-3054	106	1	γ(1	γ(1	PROPN
easat-3054	106	2	+	+	CCONJ
easat-3054	106	3	𝛼𝑞	𝛼𝑞	X
easat-3054	107	1	)	)	PUNCT
easat-3054	107	2	γ(1	γ(1	PROPN
easat-3054	108	1	+	+	CCONJ
easat-3054	108	2	(	(	PUNCT
easat-3054	108	3	𝑞	𝑞	X
easat-3054	108	4	+	+	NOUN
easat-3054	108	5	1)𝛼	1)𝛼	NUM
easat-3054	108	6	)	)	PUNCT
easat-3054	108	7	)	)	PUNCT
easat-3054	109	1	1	1	NUM
easat-3054	109	2	𝑞	𝑞	SYM
easat-3054	109	3	(	(	PUNCT
easat-3054	109	4	𝑏	𝑏	PROPN
easat-3054	109	5	−	−	PROPN
easat-3054	109	6	𝑎	𝑎	NOUN
easat-3054	109	7	)	)	PUNCT
easat-3054	109	8	(	(	PUNCT
easat-3054	109	9	𝑞+1)𝛼	𝑞+1)𝛼	PROPN
easat-3054	109	10	𝑞	𝑞	PART
easat-3054	109	11	×	×	PROPN
easat-3054	109	12	(	(	PUNCT
easat-3054	109	13	1	1	NUM
easat-3054	109	14	𝛤(1	𝛤(1	NUM
easat-3054	109	15	+	+	CCONJ
easat-3054	109	16	𝛼	𝛼	X
easat-3054	109	17	)	)	PUNCT
easat-3054	109	18	∑|𝑓𝛼(𝑡𝑖)|	∑|𝑓𝛼(𝑡𝑖)|	NOUN
easat-3054	109	19	ℎ(∆𝑡𝑖	ℎ(∆𝑡𝑖	NOUN
easat-3054	109	20	)	)	PUNCT
easat-3054	109	21	𝛼	𝛼	PART
easat-3054	109	22	𝑛	𝑛	PROPN
easat-3054	109	23	𝑖=1	𝑖=1	PROPN
easat-3054	109	24	)	)	PUNCT
easat-3054	109	25	1	1	NUM
easat-3054	109	26	ℎ	ℎ	NOUN
easat-3054	109	27	where	where	SCONJ
easat-3054	109	28	0	0	NUM
easat-3054	109	29	<	<	X
easat-3054	109	30	𝑝	𝑝	X
easat-3054	109	31	<	<	X
easat-3054	109	32	1	1	NUM
easat-3054	109	33	and	and	CCONJ
easat-3054	109	34	by	by	ADP
easat-3054	109	35	using	use	VERB
easat-3054	109	36	(	(	PUNCT
easat-3054	109	37	1	1	NUM
easat-3054	109	38	)	)	PUNCT
easat-3054	109	39	,	,	PUNCT
easat-3054	109	40	we	we	PRON
easat-3054	109	41	get	get	VERB
easat-3054	109	42	1	1	NUM
easat-3054	109	43	γ(1	γ(1	ADJ
easat-3054	109	44	+	+	CCONJ
easat-3054	109	45	𝛼)(𝑏	𝛼)(𝑏	NUM
easat-3054	109	46	−	−	PROPN
easat-3054	109	47	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	109	48	∫	∫	PROPN
easat-3054	109	49	|𝑝(𝑥	|𝑝(𝑥	PROPN
easat-3054	109	50	,	,	PUNCT
easat-3054	109	51	𝑡)||𝑓(𝑥)𝛼|	𝑡)||𝑓(𝑥)𝛼|	PROPN
easat-3054	109	52	(	(	PUNCT
easat-3054	109	53	𝑑𝑡)𝛼	𝑑𝑡)𝛼	PROPN
easat-3054	109	54	≤	≤	PUNCT
easat-3054	109	55	𝑏	𝑏	NUM
easat-3054	109	56	𝑎	𝑎	NOUN
easat-3054	109	57	𝐶(𝑝)(𝛤(1	𝐶(𝑝)(𝛤(1	NOUN
easat-3054	109	58	+	+	CCONJ
easat-3054	109	59	𝛼𝑞	𝛼𝑞	PROPN
easat-3054	109	60	)	)	PUNCT
easat-3054	109	61	)	)	PUNCT
easat-3054	110	1	1	1	NUM
easat-3054	110	2	𝑞(𝑏	𝑞(𝑏	NOUN
easat-3054	110	3	−	−	NUM
easat-3054	110	4	𝑎	𝑎	NOUN
easat-3054	110	5	)	)	PUNCT
easat-3054	110	6	𝛼	𝛼	PROPN
easat-3054	110	7	𝑞	𝑞	X
easat-3054	110	8	(	(	PUNCT
easat-3054	110	9	𝛤(1	𝛤(1	PUNCT
easat-3054	110	10	+	+	CCONJ
easat-3054	110	11	(	(	PUNCT
easat-3054	110	12	𝑞	𝑞	X
easat-3054	110	13	+	+	X
easat-3054	110	14	1)𝛼	1)𝛼	NUM
easat-3054	110	15	)	)	PUNCT
easat-3054	110	16	)	)	PUNCT
easat-3054	111	1	1	1	NUM
easat-3054	111	2	𝑞(𝛤(1	𝑞(𝛤(1	NUM
easat-3054	111	3	+	+	NUM
easat-3054	111	4	𝛼	𝛼	X
easat-3054	111	5	)	)	PUNCT
easat-3054	111	6	)	)	PUNCT
easat-3054	111	7	1	1	NUM
easat-3054	111	8	𝑝	𝑝	X
easat-3054	111	9	‖𝑓𝛼‖𝑝	‖𝑓𝛼‖𝑝	PROPN
easat-3054	111	10	,	,	PUNCT
easat-3054	111	11	0	0	NUM
easat-3054	111	12	<	<	X
easat-3054	111	13	𝑝	𝑝	X
easat-3054	111	14	<	<	X
easat-3054	111	15	1	1	NUM
easat-3054	111	16	.	.	PUNCT
easat-3054	111	17	now	now	ADV
easat-3054	111	18	by	by	ADP
easat-3054	111	19	using	use	VERB
easat-3054	111	20	lemma	lemma	PROPN
easat-3054	111	21	2.4,we	2.4,we	PROPN
easat-3054	111	22	get	get	VERB
easat-3054	111	23	|𝑓(𝑥	|𝑓(𝑥	NOUN
easat-3054	111	24	)	)	PUNCT
easat-3054	111	25	−	−	PROPN
easat-3054	112	1	γ(1	γ(1	PROPN
easat-3054	112	2	+	+	NUM
easat-3054	112	3	𝛼	𝛼	X
easat-3054	112	4	)	)	PUNCT
easat-3054	112	5	(	(	PUNCT
easat-3054	112	6	𝑏	𝑏	PROPN
easat-3054	112	7	−	−	PROPN
easat-3054	112	8	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	112	9	𝑎𝐼𝑏	𝑎𝐼𝑏	NOUN
easat-3054	112	10	∝𝑓(𝑥)|	∝𝑓(𝑥)|	SYM
easat-3054	112	11	≤	≤	NUM
easat-3054	112	12	𝐶(𝑝)(𝛤(1	𝐶(𝑝)(𝛤(1	NOUN
easat-3054	112	13	+	+	CCONJ
easat-3054	112	14	𝛼𝑞	𝛼𝑞	PROPN
easat-3054	112	15	)	)	PUNCT
easat-3054	112	16	)	)	PUNCT
easat-3054	112	17	1	1	NUM
easat-3054	113	1	𝑞(𝑏	𝑞(𝑏	NOUN
easat-3054	113	2	−	−	NUM
easat-3054	113	3	𝑎	𝑎	NOUN
easat-3054	113	4	)	)	PUNCT
easat-3054	113	5	𝛼	𝛼	PROPN
easat-3054	113	6	𝑞	𝑞	X
easat-3054	113	7	(	(	PUNCT
easat-3054	113	8	𝛤(1	𝛤(1	PUNCT
easat-3054	113	9	+	+	CCONJ
easat-3054	113	10	(	(	PUNCT
easat-3054	113	11	𝑞	𝑞	X
easat-3054	113	12	+	+	X
easat-3054	113	13	1)𝛼	1)𝛼	NUM
easat-3054	113	14	)	)	PUNCT
easat-3054	113	15	)	)	PUNCT
easat-3054	114	1	1	1	NUM
easat-3054	114	2	𝑞(𝛤(1	𝑞(𝛤(1	NUM
easat-3054	114	3	+	+	NUM
easat-3054	114	4	𝛼	𝛼	X
easat-3054	114	5	)	)	PUNCT
easat-3054	114	6	)	)	PUNCT
easat-3054	114	7	1	1	NUM
easat-3054	114	8	𝑝	𝑝	X
easat-3054	114	9	‖𝑓𝛼‖𝑝	‖𝑓𝛼‖𝑝	PROPN
easat-3054	114	10	,	,	PUNCT
easat-3054	114	11	0	0	NUM
easat-3054	114	12	<	<	X
easat-3054	114	13	𝑝	𝑝	X
easat-3054	114	14	<	<	X
easat-3054	114	15	1	1	NUM
easat-3054	114	16	.	.	PUNCT
easat-3054	115	1	the	the	DET
easat-3054	115	2	second	second	ADJ
easat-3054	115	3	case	case	NOUN
easat-3054	115	4	is	be	AUX
easat-3054	115	5	proved	prove	VERB
easat-3054	115	6	.	.	PUNCT
easat-3054	116	1	theorem	theorem	ADJ
easat-3054	116	2	3.2	3.2	NUM
easat-3054	116	3	:	:	PUNCT
easat-3054	116	4	if	if	SCONJ
easat-3054	116	5	𝑓	𝑓	PRON
easat-3054	116	6	⊂	⊂	PROPN
easat-3054	116	7	𝑅	𝑅	PROPN
easat-3054	116	8	,	,	PUNCT
easat-3054	116	9	𝑓	𝑓	PRON
easat-3054	116	10	:	:	PUNCT
easat-3054	116	11	𝐼∘	𝐼∘	PROPN
easat-3054	116	12	⊂	⊂	PROPN
easat-3054	116	13	𝑅	𝑅	PROPN
easat-3054	116	14	→	→	SYM
easat-3054	116	15	𝑅𝛼	𝑅𝛼	PROPN
easat-3054	116	16	be	be	AUX
easat-3054	116	17	a	a	DET
easat-3054	116	18	map	map	NOUN
easat-3054	117	1	[	[	X
easat-3054	117	2	𝑎	𝑎	X
easat-3054	117	3	,	,	PUNCT
easat-3054	117	4	𝑏	𝑏	NOUN
easat-3054	117	5	]	]	X
easat-3054	117	6	⊂	⊂	PROPN
easat-3054	117	7	𝐼∘	𝐼∘	PROPN
easat-3054	117	8	,	,	PUNCT
easat-3054	117	9	𝑓	𝑓	DET
easat-3054	117	10	∈	∈	PROPN
easat-3054	117	11	𝐿𝑃,𝛼[𝑎	𝐿𝑃,𝛼[𝑎	NOUN
easat-3054	117	12	,	,	PUNCT
easat-3054	117	13	𝑏	𝑏	NOUN
easat-3054	117	14	]	]	PUNCT
easat-3054	117	15	.	.	PUNCT
easat-3054	118	1	then	then	ADV
easat-3054	118	2	(	(	PUNCT
easat-3054	118	3	1	1	X
easat-3054	118	4	)	)	PUNCT
easat-3054	118	5	|(𝐼	|(𝐼	NOUN
easat-3054	118	6	−	−	NOUN
easat-3054	118	7	ℎ)𝛼𝑓(𝑥	ℎ)𝛼𝑓(𝑥	NOUN
easat-3054	118	8	)	)	PUNCT
easat-3054	119	1	+	+	CCONJ
easat-3054	119	2	ℎ𝛼	ℎ𝛼	DET
easat-3054	119	3	𝑓(𝑎	𝑓(𝑎	NUM
easat-3054	119	4	)	)	PUNCT
easat-3054	120	1	+	+	NUM
easat-3054	120	2	𝑓(𝑏	𝑓(𝑏	NOUN
easat-3054	120	3	)	)	PUNCT
easat-3054	120	4	2𝛼	2𝛼	PROPN
easat-3054	120	5	−	−	PROPN
easat-3054	121	1	γ(1	γ(1	NOUN
easat-3054	121	2	+	+	NUM
easat-3054	121	3	𝛼	𝛼	X
easat-3054	121	4	)	)	PUNCT
easat-3054	121	5	(	(	PUNCT
easat-3054	121	6	𝑏	𝑏	PROPN
easat-3054	121	7	−	−	PROPN
easat-3054	121	8	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	121	9	𝑎𝐼𝑏	𝑎𝐼𝑏	NOUN
easat-3054	121	10	∝𝑓(𝑥)|	∝𝑓(𝑥)|	PROPN
easat-3054	121	11	≤	≤	NOUN
easat-3054	121	12	(	(	PUNCT
easat-3054	121	13	γ(1	γ(1	PROPN
easat-3054	121	14	+	+	CCONJ
easat-3054	121	15	𝛼𝑞	𝛼𝑞	PROPN
easat-3054	121	16	)	)	PUNCT
easat-3054	121	17	)	)	PUNCT
easat-3054	121	18	1	1	NUM
easat-3054	122	1	𝑞(𝑏	𝑞(𝑏	NOUN
easat-3054	122	2	−	−	NUM
easat-3054	122	3	𝑎	𝑎	NOUN
easat-3054	122	4	)	)	PUNCT
easat-3054	122	5	∝	∝	PROPN
easat-3054	122	6	𝑞	𝑞	X
easat-3054	122	7	(	(	PUNCT
easat-3054	122	8	γ(1	γ(1	PROPN
easat-3054	122	9	+	+	CCONJ
easat-3054	122	10	(	(	PUNCT
easat-3054	122	11	𝑞	𝑞	X
easat-3054	122	12	+	+	X
easat-3054	122	13	1)𝛼	1)𝛼	NUM
easat-3054	122	14	)	)	PUNCT
easat-3054	122	15	)	)	PUNCT
easat-3054	123	1	1	1	NUM
easat-3054	123	2	𝑞(γ(1	𝑞(γ(1	NOUN
easat-3054	123	3	+	+	NUM
easat-3054	123	4	𝛼	𝛼	X
easat-3054	123	5	)	)	PUNCT
easat-3054	123	6	)	)	PUNCT
easat-3054	123	7	1	1	NUM
easat-3054	123	8	𝑝	𝑝	X
easat-3054	123	9	‖𝑓𝛼‖𝑝	‖𝑓𝛼‖𝑝	PROPN
easat-3054	123	10	,	,	PUNCT
easat-3054	123	11	1	1	NUM
easat-3054	123	12	≤	≤	NUM
easat-3054	123	13	𝑝	𝑝	PROPN
easat-3054	123	14	,	,	PUNCT
easat-3054	123	15	𝑞	𝑞	X
easat-3054	123	16	≤	≤	NOUN
easat-3054	123	17	∞	∞	PROPN
easat-3054	123	18	,	,	PUNCT
easat-3054	123	19	1	1	NUM
easat-3054	123	20	𝑝	𝑝	NOUN
easat-3054	123	21	+	+	NUM
easat-3054	123	22	1	1	NUM
easat-3054	123	23	𝑞	𝑞	NOUN
easat-3054	123	24	=	=	NOUN
easat-3054	123	25	1	1	X
easat-3054	123	26	.	.	PUNCT
easat-3054	123	27	(	(	PUNCT
easat-3054	123	28	2	2	X
easat-3054	123	29	)	)	PUNCT
easat-3054	123	30	|(𝐼	|(𝐼	NOUN
easat-3054	123	31	−	−	NOUN
easat-3054	123	32	ℎ)𝛼𝑓(𝑥	ℎ)𝛼𝑓(𝑥	NOUN
easat-3054	123	33	)	)	PUNCT
easat-3054	123	34	+	+	CCONJ
easat-3054	123	35	ℎ𝛼	ℎ𝛼	DET
easat-3054	123	36	𝑓(𝑎	𝑓(𝑎	NUM
easat-3054	123	37	)	)	PUNCT
easat-3054	123	38	+	+	NUM
easat-3054	123	39	𝑓(𝑏	𝑓(𝑏	NOUN
easat-3054	123	40	)	)	PUNCT
easat-3054	123	41	2𝛼	2𝛼	PROPN
easat-3054	123	42	−	−	PROPN
easat-3054	124	1	γ(1	γ(1	NOUN
easat-3054	124	2	+	+	NUM
easat-3054	124	3	𝛼	𝛼	X
easat-3054	124	4	)	)	PUNCT
easat-3054	124	5	(	(	PUNCT
easat-3054	124	6	𝑏	𝑏	PROPN
easat-3054	124	7	−	−	PROPN
easat-3054	124	8	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	124	9	𝑎𝐼𝑏	𝑎𝐼𝑏	NOUN
easat-3054	124	10	∝𝑓(𝑥)|	∝𝑓(𝑥)|	SYM
easat-3054	124	11	≤	≤	NUM
easat-3054	124	12	𝐶(𝑝)(γ(1	𝐶(𝑝)(γ(1	NUM
easat-3054	124	13	+	+	CCONJ
easat-3054	124	14	𝛼𝑞	𝛼𝑞	X
easat-3054	124	15	)	)	PUNCT
easat-3054	124	16	)	)	PUNCT
easat-3054	124	17	1	1	NUM
easat-3054	124	18	𝑞(𝑏	𝑞(𝑏	NOUN
easat-3054	124	19	−	−	NUM
easat-3054	124	20	𝑎	𝑎	NOUN
easat-3054	124	21	)	)	PUNCT
easat-3054	124	22	∝	∝	PROPN
easat-3054	124	23	𝑞	𝑞	X
easat-3054	124	24	(	(	PUNCT
easat-3054	124	25	γ(1	γ(1	PROPN
easat-3054	124	26	+	+	CCONJ
easat-3054	124	27	(	(	PUNCT
easat-3054	124	28	𝑞	𝑞	X
easat-3054	124	29	+	+	X
easat-3054	124	30	1)𝛼	1)𝛼	NUM
easat-3054	124	31	)	)	PUNCT
easat-3054	124	32	)	)	PUNCT
easat-3054	124	33	1	1	NUM
easat-3054	125	1	𝑞(γ(1	𝑞(γ(1	NOUN
easat-3054	125	2	+	+	NUM
easat-3054	125	3	𝛼	𝛼	X
easat-3054	125	4	)	)	PUNCT
easat-3054	125	5	)	)	PUNCT
easat-3054	125	6	1	1	NUM
easat-3054	125	7	𝑝	𝑝	PROPN
easat-3054	125	8	‖𝑓𝛼‖𝑝	‖𝑓𝛼‖𝑝	PROPN
easat-3054	125	9	,	,	PUNCT
easat-3054	125	10	0	0	NUM
easat-3054	125	11	<	<	X
easat-3054	125	12	𝑝	𝑝	X
easat-3054	125	13	<	<	X
easat-3054	125	14	1	1	NUM
easat-3054	125	15	.	.	PUNCT
easat-3054	126	1	proof	proof	NOUN
easat-3054	126	2	:	:	PUNCT
easat-3054	126	3	we	we	PRON
easat-3054	126	4	take	take	VERB
easat-3054	126	5	two	two	NUM
easat-3054	126	6	cases	case	NOUN
easat-3054	126	7	to	to	PART
easat-3054	126	8	prove	prove	VERB
easat-3054	126	9	our	our	PRON
easat-3054	126	10	theorem	theorem	NOUN
easat-3054	126	11	.	.	PUNCT
easat-3054	127	1	case1	case1	PROPN
easat-3054	127	2	:	:	PUNCT
easat-3054	127	3	1	1	NUM
easat-3054	127	4	≤	≤	NUM
easat-3054	127	5	𝑝	𝑝	NOUN
easat-3054	127	6	≤	≤	NOUN
easat-3054	127	7	∞	∞	NUM
easat-3054	127	8	by	by	ADP
easat-3054	127	9	using	use	VERB
easat-3054	127	10	lemma	lemma	PROPN
easat-3054	127	11	2.5	2.5	NUM
easat-3054	127	12	,	,	PUNCT
easat-3054	127	13	we	we	PRON
easat-3054	127	14	obtain	obtain	VERB
easat-3054	127	15	.	.	PUNCT
easat-3054	128	1	|(𝐼	|(𝐼	NOUN
easat-3054	128	2	−	−	PROPN
easat-3054	128	3	ℎ)𝛼𝑓(𝑥	ℎ)𝛼𝑓(𝑥	NOUN
easat-3054	128	4	)	)	PUNCT
easat-3054	129	1	+	+	CCONJ
easat-3054	129	2	ℎ𝛼	ℎ𝛼	DET
easat-3054	129	3	𝑓(𝑎	𝑓(𝑎	NUM
easat-3054	129	4	)	)	PUNCT
easat-3054	130	1	+	+	NUM
easat-3054	130	2	𝑓(𝑏	𝑓(𝑏	NOUN
easat-3054	130	3	)	)	PUNCT
easat-3054	130	4	2𝛼	2𝛼	PROPN
easat-3054	130	5	−	−	PROPN
easat-3054	131	1	γ(1	γ(1	NOUN
easat-3054	131	2	+	+	NUM
easat-3054	131	3	𝛼	𝛼	X
easat-3054	131	4	)	)	PUNCT
easat-3054	131	5	(	(	PUNCT
easat-3054	131	6	𝑏	𝑏	PROPN
easat-3054	131	7	−	−	PROPN
easat-3054	131	8	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	131	9	𝑎𝐼𝑏	𝑎𝐼𝑏	NOUN
easat-3054	131	10	∝𝑓(𝑥)|	∝𝑓(𝑥)|	PROPN
easat-3054	131	11	=	=	SYM
easat-3054	131	12	1	1	NUM
easat-3054	131	13	𝛤(1	𝛤(1	NUM
easat-3054	131	14	+	+	CCONJ
easat-3054	131	15	𝛼)(𝑏	𝛼)(𝑏	NUM
easat-3054	131	16	−	−	PROPN
easat-3054	131	17	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	131	18	∫	∫	PROPN
easat-3054	131	19	|𝑝(𝑥	|𝑝(𝑥	PROPN
easat-3054	131	20	,	,	PUNCT
easat-3054	131	21	𝑡)||𝑓(𝑥)𝛼|	𝑡)||𝑓(𝑥)𝛼|	PROPN
easat-3054	131	22	(	(	PUNCT
easat-3054	131	23	𝑑𝑡)𝛼	𝑑𝑡)𝛼	NOUN
easat-3054	131	24	𝑏	𝑏	NOUN
easat-3054	131	25	𝑎	𝑎	NOUN
easat-3054	131	26	by	by	ADP
easat-3054	131	27	using	use	VERB
easat-3054	131	28	the	the	DET
easat-3054	131	29	generalized	generalized	ADJ
easat-3054	131	30	holder	holder	NOUN
easat-3054	131	31	,	,	PUNCT
easat-3054	131	32	s	s	PART
easat-3054	131	33	inequality	inequality	NOUN
easat-3054	131	34	described	describe	VERB
easat-3054	131	35	in	in	ADP
easat-3054	131	36	lemma2.1	lemma2.1	PROPN
easat-3054	131	37	,	,	PUNCT
easat-3054	131	38	we	we	PRON
easat-3054	131	39	obtain	obtain	VERB
easat-3054	131	40	.	.	PUNCT
easat-3054	132	1	4915	4915	NUM
easat-3054	132	2	edelweiss	edelweiss	PROPN
easat-3054	132	3	applied	apply	VERB
easat-3054	132	4	science	science	NOUN
easat-3054	132	5	and	and	CCONJ
easat-3054	132	6	technology	technology	NOUN
easat-3054	132	7	issn	issn	PROPN
easat-3054	132	8	:	:	PUNCT
easat-3054	132	9	2576	2576	NUM
easat-3054	132	10	-	-	SYM
easat-3054	132	11	8484	8484	NUM
easat-3054	132	12	vol	vol	NOUN
easat-3054	132	13	.	.	PROPN
easat-3054	132	14	8	8	NUM
easat-3054	132	15	,	,	PUNCT
easat-3054	132	16	no	no	INTJ
easat-3054	132	17	.	.	NOUN
easat-3054	133	1	6	6	NUM
easat-3054	133	2	:	:	SYM
easat-3054	133	3	4910	4910	NUM
easat-3054	133	4	-	-	SYM
easat-3054	133	5	4919	4919	NUM
easat-3054	133	6	,	,	PUNCT
easat-3054	133	7	2024	2024	NUM
easat-3054	133	8	doi	doi	NOUN
easat-3054	133	9	:	:	PUNCT
easat-3054	133	10	10.55214/25768484.v8i6.3054	10.55214/25768484.v8i6.3054	NUM
easat-3054	133	11	©	©	PROPN
easat-3054	133	12	2024	2024	NUM
easat-3054	133	13	by	by	ADP
easat-3054	133	14	the	the	DET
easat-3054	133	15	authors	author	NOUN
easat-3054	133	16	;	;	PUNCT
easat-3054	133	17	licensee	licensee	PROPN
easat-3054	133	18	learning	learning	NOUN
easat-3054	133	19	gate	gate	VERB
easat-3054	133	20	|(𝐼	|(𝐼	PROPN
easat-3054	133	21	−	−	PROPN
easat-3054	133	22	ℎ)𝛼𝑓(𝑥	ℎ)𝛼𝑓(𝑥	NOUN
easat-3054	133	23	)	)	PUNCT
easat-3054	134	1	+	+	CCONJ
easat-3054	134	2	ℎ𝛼	ℎ𝛼	DET
easat-3054	134	3	𝑓(𝑎	𝑓(𝑎	NUM
easat-3054	134	4	)	)	PUNCT
easat-3054	135	1	+	+	NUM
easat-3054	135	2	𝑓(𝑏	𝑓(𝑏	NOUN
easat-3054	135	3	)	)	PUNCT
easat-3054	135	4	2𝛼	2𝛼	PROPN
easat-3054	135	5	−	−	PROPN
easat-3054	136	1	γ(1	γ(1	NOUN
easat-3054	136	2	+	+	NUM
easat-3054	136	3	𝛼	𝛼	X
easat-3054	136	4	)	)	PUNCT
easat-3054	136	5	(	(	PUNCT
easat-3054	136	6	𝑏	𝑏	PROPN
easat-3054	136	7	−	−	PROPN
easat-3054	136	8	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	136	9	𝑎𝐼𝑏	𝑎𝐼𝑏	NOUN
easat-3054	136	10	∝𝑓(𝑥)|	∝𝑓(𝑥)|	PROPN
easat-3054	136	11	≤	≤	NUM
easat-3054	136	12	1	1	NUM
easat-3054	136	13	(	(	PUNCT
easat-3054	136	14	𝑏	𝑏	PROPN
easat-3054	136	15	−	−	PROPN
easat-3054	136	16	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	136	17	(	(	PUNCT
easat-3054	136	18	1	1	NUM
easat-3054	136	19	𝛤(1	𝛤(1	NUM
easat-3054	136	20	+	+	CCONJ
easat-3054	136	21	𝛼	𝛼	X
easat-3054	136	22	)	)	PUNCT
easat-3054	136	23	∫|𝑝(𝑥	∫|𝑝(𝑥	ADJ
easat-3054	136	24	,	,	PUNCT
easat-3054	136	25	𝑡)|𝑞(𝑑𝑥)𝛼	𝑡)|𝑞(𝑑𝑥)𝛼	NOUN
easat-3054	136	26	𝑏	𝑏	PROPN
easat-3054	136	27	𝑎	𝑎	X
easat-3054	136	28	)	)	PUNCT
easat-3054	136	29	1	1	NUM
easat-3054	136	30	𝑞	𝑞	PROPN
easat-3054	136	31	(	(	PUNCT
easat-3054	136	32	1	1	NUM
easat-3054	136	33	𝛤(1	𝛤(1	NUM
easat-3054	136	34	+	+	CCONJ
easat-3054	136	35	𝛼	𝛼	X
easat-3054	136	36	)	)	PUNCT
easat-3054	136	37	∫|𝑓(𝑥)𝛼|ℎ(𝑑𝑥)𝛼	∫|𝑓(𝑥)𝛼|ℎ(𝑑𝑥)𝛼	NUM
easat-3054	137	1	𝑏	𝑏	PRON
easat-3054	137	2	𝑎	𝑎	X
easat-3054	137	3	)	)	PUNCT
easat-3054	137	4	1	1	NUM
easat-3054	137	5	ℎ	ℎ	PART
easat-3054	137	6	1	1	NUM
easat-3054	137	7	≤	≤	NUM
easat-3054	137	8	𝑝	𝑝	PROPN
easat-3054	137	9	,	,	PUNCT
easat-3054	137	10	𝑞	𝑞	X
easat-3054	137	11	≤	≤	NOUN
easat-3054	137	12	∞	∞	PROPN
easat-3054	137	13	,	,	PUNCT
easat-3054	137	14	1	1	NUM
easat-3054	137	15	ℎ	ℎ	X
easat-3054	137	16	+	+	NOUN
easat-3054	137	17	1	1	NUM
easat-3054	137	18	𝑞	𝑞	NOUN
easat-3054	137	19	=	=	SYM
easat-3054	137	20	1	1	NUM
easat-3054	137	21	(	(	PUNCT
easat-3054	137	22	8)	8)	NUM
easat-3054	137	23	let	let	VERB
easat-3054	137	24	us	we	PRON
easat-3054	137	25	calculate	calculate	VERB
easat-3054	137	26	(	(	PUNCT
easat-3054	137	27	1	1	NUM
easat-3054	137	28	γ(1+𝛼	γ(1+𝛼	ADJ
easat-3054	137	29	)	)	PUNCT
easat-3054	137	30	∫	∫	PROPN
easat-3054	138	1	|𝑝(𝑥	|𝑝(𝑥	PROPN
easat-3054	138	2	,	,	PUNCT
easat-3054	138	3	𝑡)|𝑞(𝑑𝑥)𝛼	𝑡)|𝑞(𝑑𝑥)𝛼	NOUN
easat-3054	138	4	𝑏	𝑏	PROPN
easat-3054	138	5	𝑎	𝑎	X
easat-3054	138	6	)	)	PUNCT
easat-3054	138	7	1	1	NUM
easat-3054	138	8	𝑞	𝑞	NOUN
easat-3054	138	9	,	,	PUNCT
easat-3054	138	10	we	we	PRON
easat-3054	138	11	have	have	VERB
easat-3054	138	12	(	(	PUNCT
easat-3054	138	13	1	1	NUM
easat-3054	138	14	γ(1	γ(1	NOUN
easat-3054	138	15	+	+	NUM
easat-3054	138	16	𝛼	𝛼	X
easat-3054	138	17	)	)	PUNCT
easat-3054	138	18	∫	∫	PROPN
easat-3054	138	19	|𝑡	|𝑡	X
easat-3054	139	1	−	−	PROPN
easat-3054	139	2	(	(	PUNCT
easat-3054	139	3	𝑎	𝑎	X
easat-3054	139	4	+	+	X
easat-3054	139	5	ℎ	ℎ	X
easat-3054	139	6	(	(	PUNCT
easat-3054	139	7	𝑏	𝑏	PROPN
easat-3054	139	8	−	−	PROPN
easat-3054	139	9	𝑎	𝑎	PROPN
easat-3054	139	10	2	2	NUM
easat-3054	139	11	)	)	PUNCT
easat-3054	139	12	)	)	PUNCT
easat-3054	140	1	|	|	ADV
easat-3054	140	2	𝛼𝑞	𝛼𝑞	X
easat-3054	140	3	(	(	PUNCT
easat-3054	140	4	𝑑𝑡)𝛼	𝑑𝑡)𝛼	NOUN
easat-3054	140	5	𝑥	𝑥	NOUN
easat-3054	140	6	𝑎	𝑎	X
easat-3054	140	7	)	)	PUNCT
easat-3054	140	8	1	1	NUM
easat-3054	140	9	𝑞	𝑞	NOUN
easat-3054	140	10	+	+	ADJ
easat-3054	140	11	(	(	PUNCT
easat-3054	140	12	1	1	NUM
easat-3054	140	13	γ(1	γ(1	PROPN
easat-3054	140	14	+	+	NUM
easat-3054	140	15	𝛼	𝛼	X
easat-3054	140	16	)	)	PUNCT
easat-3054	140	17	∫	∫	PROPN
easat-3054	140	18	|𝑡	|𝑡	X
easat-3054	141	1	−	−	PROPN
easat-3054	141	2	(	(	PUNCT
easat-3054	141	3	𝑏	𝑏	PROPN
easat-3054	141	4	−	−	PROPN
easat-3054	141	5	ℎ	ℎ	PROPN
easat-3054	141	6	(	(	PUNCT
easat-3054	141	7	𝑏	𝑏	PROPN
easat-3054	141	8	−	−	PROPN
easat-3054	141	9	𝑎	𝑎	PROPN
easat-3054	141	10	2	2	NUM
easat-3054	141	11	)	)	PUNCT
easat-3054	141	12	)	)	PUNCT
easat-3054	142	1	|	|	ADV
easat-3054	142	2	𝛼𝑞	𝛼𝑞	X
easat-3054	142	3	(	(	PUNCT
easat-3054	142	4	𝑑𝑡)𝛼	𝑑𝑡)𝛼	PROPN
easat-3054	142	5	𝑏	𝑏	NOUN
easat-3054	142	6	𝑥	𝑥	PROPN
easat-3054	142	7	)	)	PUNCT
easat-3054	142	8	1	1	NUM
easat-3054	142	9	𝑞	𝑞	NOUN
easat-3054	142	10	=	=	PUNCT
easat-3054	142	11	(	(	PUNCT
easat-3054	142	12	𝑀1	𝑀1	PROPN
easat-3054	142	13	+	+	SYM
easat-3054	142	14	𝑀2	𝑀2	NOUN
easat-3054	142	15	)	)	PUNCT
easat-3054	142	16	1	1	NUM
easat-3054	142	17	𝑞	𝑞	SYM
easat-3054	142	18	(	(	PUNCT
easat-3054	142	19	9	9	NUM
easat-3054	142	20	)	)	PUNCT
easat-3054	142	21	𝑀1	𝑀1	NOUN
easat-3054	142	22	=	=	SYM
easat-3054	142	23	1	1	NUM
easat-3054	142	24	γ(1	γ(1	NOUN
easat-3054	142	25	+	+	NUM
easat-3054	142	26	𝛼	𝛼	X
easat-3054	142	27	)	)	PUNCT
easat-3054	142	28	∫	∫	PROPN
easat-3054	142	29	|𝑡	|𝑡	X
easat-3054	143	1	−	−	PROPN
easat-3054	143	2	(	(	PUNCT
easat-3054	143	3	𝑎	𝑎	X
easat-3054	143	4	+	+	X
easat-3054	143	5	ℎ	ℎ	X
easat-3054	143	6	(	(	PUNCT
easat-3054	143	7	𝑏	𝑏	PROPN
easat-3054	143	8	−	−	PROPN
easat-3054	143	9	𝑎	𝑎	PROPN
easat-3054	143	10	2	2	NUM
easat-3054	143	11	)	)	PUNCT
easat-3054	143	12	)	)	PUNCT
easat-3054	144	1	|	|	ADV
easat-3054	144	2	𝛼𝑞	𝛼𝑞	X
easat-3054	144	3	(	(	PUNCT
easat-3054	144	4	𝑑𝑡)𝛼	𝑑𝑡)𝛼	NOUN
easat-3054	144	5	𝑥	𝑥	NOUN
easat-3054	144	6	𝑎	𝑎	X
easat-3054	144	7	=	=	SYM
easat-3054	144	8	1	1	NUM
easat-3054	144	9	γ(1	γ(1	NOUN
easat-3054	144	10	+	+	NUM
easat-3054	144	11	𝛼	𝛼	X
easat-3054	144	12	)	)	PUNCT
easat-3054	144	13	∫	∫	PROPN
easat-3054	144	14	|𝑡	|𝑡	X
easat-3054	145	1	−	−	PROPN
easat-3054	145	2	(	(	PUNCT
easat-3054	145	3	𝑎	𝑎	X
easat-3054	145	4	+	+	X
easat-3054	145	5	ℎ	ℎ	X
easat-3054	145	6	(	(	PUNCT
easat-3054	145	7	𝑏	𝑏	PROPN
easat-3054	145	8	−	−	PROPN
easat-3054	145	9	𝑎	𝑎	PROPN
easat-3054	145	10	2	2	NUM
easat-3054	145	11	)	)	PUNCT
easat-3054	145	12	)	)	PUNCT
easat-3054	146	1	|	|	ADV
easat-3054	146	2	𝛼𝑞	𝛼𝑞	X
easat-3054	146	3	(	(	PUNCT
easat-3054	146	4	𝑑𝑡)𝛼	𝑑𝑡)𝛼	NOUN
easat-3054	146	5	+	+	NOUN
easat-3054	146	6	𝑎+ℎ	𝑎+ℎ	PROPN
easat-3054	146	7	(	(	PUNCT
easat-3054	146	8	𝑏−𝑎	𝑏−𝑎	ADP
easat-3054	146	9	2	2	X
easat-3054	146	10	)	)	PUNCT
easat-3054	146	11	𝑎	𝑎	PRON
easat-3054	146	12	1	1	NUM
easat-3054	146	13	γ(1	γ(1	PROPN
easat-3054	146	14	+	+	NUM
easat-3054	146	15	𝛼	𝛼	X
easat-3054	146	16	)	)	PUNCT
easat-3054	146	17	∫	∫	PROPN
easat-3054	146	18	|𝑡	|𝑡	X
easat-3054	147	1	−	−	PROPN
easat-3054	147	2	(	(	PUNCT
easat-3054	147	3	𝑎	𝑎	X
easat-3054	147	4	+	+	X
easat-3054	147	5	ℎ	ℎ	X
easat-3054	147	6	(	(	PUNCT
easat-3054	147	7	𝑏	𝑏	PROPN
easat-3054	147	8	−	−	PROPN
easat-3054	147	9	𝑎	𝑎	PROPN
easat-3054	147	10	2	2	NUM
easat-3054	147	11	)	)	PUNCT
easat-3054	147	12	)	)	PUNCT
easat-3054	148	1	|	|	ADV
easat-3054	148	2	𝛼𝑞	𝛼𝑞	X
easat-3054	148	3	(	(	PUNCT
easat-3054	148	4	𝑑𝑡)𝛼	𝑑𝑡)𝛼	PROPN
easat-3054	148	5	𝑥	𝑥	NOUN
easat-3054	148	6	𝑎+ℎ	𝑎+ℎ	PROPN
easat-3054	148	7	(	(	PUNCT
easat-3054	148	8	𝑏−𝑎	𝑏−𝑎	ADP
easat-3054	148	9	2	2	NUM
easat-3054	148	10	)	)	PUNCT
easat-3054	148	11	by	by	ADP
easat-3054	148	12	using	use	VERB
easat-3054	148	13	lemma	lemma	PROPN
easat-3054	148	14	2,1	2,1	NUM
easat-3054	148	15	𝑀1	𝑀1	NOUN
easat-3054	148	16	=	=	PUNCT
easat-3054	149	1	γ(1	γ(1	PROPN
easat-3054	149	2	+	+	CCONJ
easat-3054	149	3	𝛼𝑞	𝛼𝑞	X
easat-3054	150	1	)	)	PUNCT
easat-3054	150	2	γ(1	γ(1	PROPN
easat-3054	151	1	+	+	CCONJ
easat-3054	151	2	(	(	PUNCT
easat-3054	151	3	𝑞	𝑞	X
easat-3054	151	4	+	+	X
easat-3054	151	5	1)𝛼	1)𝛼	NUM
easat-3054	151	6	)	)	PUNCT
easat-3054	152	1	[	[	X
easat-3054	152	2	(	(	PUNCT
easat-3054	152	3	(	(	PUNCT
easat-3054	152	4	𝑎	𝑎	NOUN
easat-3054	152	5	+	+	NOUN
easat-3054	152	6	ℎ	ℎ	X
easat-3054	152	7	(	(	PUNCT
easat-3054	152	8	𝑏	𝑏	PROPN
easat-3054	152	9	−	−	PROPN
easat-3054	152	10	𝑎	𝑎	PROPN
easat-3054	152	11	2	2	NUM
easat-3054	152	12	)	)	PUNCT
easat-3054	152	13	)	)	PUNCT
easat-3054	153	1	(	(	PUNCT
easat-3054	153	2	𝑞+1)𝛼	𝑞+1)𝛼	PROPN
easat-3054	153	3	−	−	PROPN
easat-3054	153	4	𝑎(𝑞+1)𝛼	𝑎(𝑞+1)𝛼	PROPN
easat-3054	153	5	)	)	PUNCT
easat-3054	153	6	+	+	PROPN
easat-3054	153	7	(	(	PUNCT
easat-3054	153	8	𝑥(𝑞+1)𝛼	𝑥(𝑞+1)𝛼	NOUN
easat-3054	153	9	−	−	PROPN
easat-3054	153	10	(	(	PUNCT
easat-3054	153	11	𝑎	𝑎	NOUN
easat-3054	153	12	+	+	X
easat-3054	153	13	ℎ	ℎ	X
easat-3054	153	14	(	(	PUNCT
easat-3054	153	15	𝑏	𝑏	PROPN
easat-3054	153	16	−	−	PROPN
easat-3054	153	17	𝑎	𝑎	PROPN
easat-3054	153	18	2	2	NUM
easat-3054	153	19	)	)	PUNCT
easat-3054	153	20	)	)	PUNCT
easat-3054	153	21	(	(	PUNCT
easat-3054	153	22	𝑞+1)𝛼	𝑞+1)𝛼	PROPN
easat-3054	153	23	)	)	PUNCT
easat-3054	153	24	]	]	PUNCT
easat-3054	154	1	=	=	PUNCT
easat-3054	155	1	γ(1	γ(1	PROPN
easat-3054	155	2	+	+	CCONJ
easat-3054	155	3	𝛼𝑞	𝛼𝑞	X
easat-3054	156	1	)	)	PUNCT
easat-3054	156	2	γ(1	γ(1	PROPN
easat-3054	157	1	+	+	CCONJ
easat-3054	157	2	(	(	PUNCT
easat-3054	157	3	𝑞	𝑞	X
easat-3054	157	4	+	+	NOUN
easat-3054	157	5	1)𝛼	1)𝛼	NUM
easat-3054	157	6	)	)	PUNCT
easat-3054	157	7	(	(	PUNCT
easat-3054	157	8	𝑥(𝑞+1)𝛼	𝑥(𝑞+1)𝛼	PROPN
easat-3054	157	9	−	−	PROPN
easat-3054	157	10	𝑎(𝑞+1)𝛼	𝑎(𝑞+1)𝛼	PROPN
easat-3054	157	11	)	)	PUNCT
easat-3054	157	12	(	(	PUNCT
easat-3054	157	13	10	10	NUM
easat-3054	157	14	)	)	PUNCT
easat-3054	157	15	also	also	ADV
easat-3054	157	16	,	,	PUNCT
easat-3054	157	17	𝑀2	𝑀2	PROPN
easat-3054	157	18	=	=	SYM
easat-3054	157	19	1	1	NUM
easat-3054	157	20	γ(1	γ(1	PROPN
easat-3054	157	21	+	+	NUM
easat-3054	157	22	𝛼	𝛼	X
easat-3054	157	23	)	)	PUNCT
easat-3054	157	24	∫	∫	PROPN
easat-3054	157	25	|𝑡	|𝑡	X
easat-3054	158	1	−	−	PROPN
easat-3054	158	2	(	(	PUNCT
easat-3054	158	3	𝑏	𝑏	PROPN
easat-3054	158	4	−	−	PROPN
easat-3054	158	5	ℎ	ℎ	PROPN
easat-3054	158	6	(	(	PUNCT
easat-3054	158	7	𝑏	𝑏	PROPN
easat-3054	158	8	−	−	PROPN
easat-3054	158	9	𝑎	𝑎	PROPN
easat-3054	158	10	2	2	NUM
easat-3054	158	11	)	)	PUNCT
easat-3054	158	12	)	)	PUNCT
easat-3054	159	1	|	|	ADV
easat-3054	159	2	𝛼𝑞	𝛼𝑞	X
easat-3054	159	3	(	(	PUNCT
easat-3054	159	4	𝑑𝑡)𝛼	𝑑𝑡)𝛼	NOUN
easat-3054	159	5	𝑏	𝑏	NOUN
easat-3054	159	6	𝑥	𝑥	NOUN
easat-3054	159	7	=	=	SYM
easat-3054	159	8	1	1	NUM
easat-3054	159	9	γ(1	γ(1	NOUN
easat-3054	159	10	+	+	NUM
easat-3054	159	11	𝛼	𝛼	X
easat-3054	159	12	)	)	PUNCT
easat-3054	159	13	∫	∫	PROPN
easat-3054	159	14	|𝑡	|𝑡	X
easat-3054	160	1	−	−	PROPN
easat-3054	160	2	(	(	PUNCT
easat-3054	160	3	𝑏	𝑏	PROPN
easat-3054	160	4	−	−	PROPN
easat-3054	160	5	ℎ	ℎ	PROPN
easat-3054	160	6	(	(	PUNCT
easat-3054	160	7	𝑏	𝑏	PROPN
easat-3054	160	8	−	−	PROPN
easat-3054	160	9	𝑎	𝑎	PROPN
easat-3054	160	10	2	2	NUM
easat-3054	160	11	)	)	PUNCT
easat-3054	160	12	)	)	PUNCT
easat-3054	161	1	|	|	ADV
easat-3054	161	2	𝛼𝑞	𝛼𝑞	X
easat-3054	161	3	(	(	PUNCT
easat-3054	161	4	𝑑𝑡)𝛼	𝑑𝑡)𝛼	NOUN
easat-3054	161	5	+	+	CCONJ
easat-3054	161	6	𝑏−ℎ	𝑏−ℎ	PROPN
easat-3054	161	7	(	(	PUNCT
easat-3054	161	8	𝑏−𝑎	𝑏−𝑎	ADV
easat-3054	161	9	2	2	X
easat-3054	161	10	)	)	PUNCT
easat-3054	161	11	𝑎	𝑎	PRON
easat-3054	161	12	1	1	NUM
easat-3054	161	13	γ(1	γ(1	PROPN
easat-3054	161	14	+	+	NUM
easat-3054	161	15	𝛼	𝛼	X
easat-3054	161	16	)	)	PUNCT
easat-3054	161	17	∫	∫	PROPN
easat-3054	161	18	|𝑡	|𝑡	X
easat-3054	162	1	−	−	PROPN
easat-3054	162	2	(	(	PUNCT
easat-3054	162	3	𝑏	𝑏	PROPN
easat-3054	162	4	−	−	PROPN
easat-3054	162	5	ℎ	ℎ	PROPN
easat-3054	162	6	(	(	PUNCT
easat-3054	162	7	𝑏	𝑏	PROPN
easat-3054	162	8	−	−	PROPN
easat-3054	162	9	𝑎	𝑎	PROPN
easat-3054	162	10	2	2	NUM
easat-3054	162	11	)	)	PUNCT
easat-3054	162	12	)	)	PUNCT
easat-3054	163	1	|	|	ADV
easat-3054	163	2	𝛼𝑞	𝛼𝑞	X
easat-3054	163	3	(	(	PUNCT
easat-3054	163	4	𝑑𝑡)𝛼	𝑑𝑡)𝛼	PROPN
easat-3054	163	5	𝑥	𝑥	NOUN
easat-3054	163	6	𝑎+ℎ	𝑎+ℎ	PROPN
easat-3054	163	7	(	(	PUNCT
easat-3054	163	8	𝑏−𝑎	𝑏−𝑎	ADP
easat-3054	163	9	2	2	X
easat-3054	163	10	)	)	PUNCT
easat-3054	163	11	4916	4916	NUM
easat-3054	163	12	edelweiss	edelweiss	PROPN
easat-3054	163	13	applied	apply	VERB
easat-3054	163	14	science	science	NOUN
easat-3054	163	15	and	and	CCONJ
easat-3054	163	16	technology	technology	NOUN
easat-3054	163	17	issn	issn	PROPN
easat-3054	163	18	:	:	PUNCT
easat-3054	163	19	2576	2576	NUM
easat-3054	163	20	-	-	SYM
easat-3054	163	21	8484	8484	NUM
easat-3054	163	22	vol	vol	NOUN
easat-3054	163	23	.	.	PROPN
easat-3054	163	24	8	8	NUM
easat-3054	163	25	,	,	PUNCT
easat-3054	163	26	no	no	INTJ
easat-3054	163	27	.	.	NOUN
easat-3054	164	1	6	6	NUM
easat-3054	164	2	:	:	SYM
easat-3054	164	3	4910	4910	NUM
easat-3054	164	4	-	-	SYM
easat-3054	164	5	4919	4919	NUM
easat-3054	164	6	,	,	PUNCT
easat-3054	164	7	2024	2024	NUM
easat-3054	164	8	doi	doi	NOUN
easat-3054	164	9	:	:	PUNCT
easat-3054	164	10	10.55214/25768484.v8i6.3054	10.55214/25768484.v8i6.3054	NUM
easat-3054	164	11	©	©	PROPN
easat-3054	164	12	2024	2024	NUM
easat-3054	164	13	by	by	ADP
easat-3054	164	14	the	the	DET
easat-3054	164	15	authors	author	NOUN
easat-3054	164	16	;	;	PUNCT
easat-3054	164	17	licensee	licensee	PROPN
easat-3054	164	18	learning	learning	NOUN
easat-3054	164	19	gate	gate	PROPN
easat-3054	164	20	𝑀2	𝑀2	PROPN
easat-3054	165	1	=	=	PUNCT
easat-3054	165	2	γ(1	γ(1	PROPN
easat-3054	165	3	+	+	CCONJ
easat-3054	165	4	𝛼𝑞	𝛼𝑞	X
easat-3054	165	5	)	)	PUNCT
easat-3054	165	6	γ(1	γ(1	PROPN
easat-3054	165	7	+	+	CCONJ
easat-3054	165	8	(	(	PUNCT
easat-3054	165	9	𝑞	𝑞	X
easat-3054	165	10	+	+	X
easat-3054	165	11	1)𝛼	1)𝛼	NUM
easat-3054	165	12	)	)	PUNCT
easat-3054	166	1	[	[	X
easat-3054	166	2	(	(	PUNCT
easat-3054	166	3	(	(	PUNCT
easat-3054	166	4	𝑏	𝑏	NOUN
easat-3054	166	5	−	−	PROPN
easat-3054	166	6	ℎ	ℎ	PROPN
easat-3054	166	7	(	(	PUNCT
easat-3054	166	8	𝑏	𝑏	PROPN
easat-3054	166	9	−	−	PROPN
easat-3054	166	10	𝑎	𝑎	PROPN
easat-3054	166	11	2	2	NUM
easat-3054	166	12	)	)	PUNCT
easat-3054	166	13	)	)	PUNCT
easat-3054	167	1	(	(	PUNCT
easat-3054	167	2	𝑞+1)𝛼	𝑞+1)𝛼	PROPN
easat-3054	167	3	−	−	PROPN
easat-3054	167	4	𝑥(𝑞+1)𝛼	𝑥(𝑞+1)𝛼	PROPN
easat-3054	167	5	)	)	PUNCT
easat-3054	168	1	+	+	PROPN
easat-3054	168	2	(	(	PUNCT
easat-3054	168	3	𝑥(𝑞+1)𝛼	𝑥(𝑞+1)𝛼	NOUN
easat-3054	168	4	−	−	PROPN
easat-3054	168	5	(	(	PUNCT
easat-3054	168	6	𝑏	𝑏	PROPN
easat-3054	168	7	−	−	PROPN
easat-3054	168	8	ℎ	ℎ	PROPN
easat-3054	168	9	(	(	PUNCT
easat-3054	168	10	𝑏	𝑏	PROPN
easat-3054	168	11	−	−	PROPN
easat-3054	169	1	𝑎	𝑎	PROPN
easat-3054	169	2	2	2	NUM
easat-3054	169	3	)	)	PUNCT
easat-3054	169	4	)	)	PUNCT
easat-3054	170	1	(	(	PUNCT
easat-3054	170	2	𝑞+1)𝛼	𝑞+1)𝛼	PROPN
easat-3054	170	3	)	)	PUNCT
easat-3054	170	4	]	]	PUNCT
easat-3054	171	1	=	=	PUNCT
easat-3054	172	1	γ(1	γ(1	PROPN
easat-3054	172	2	+	+	CCONJ
easat-3054	172	3	𝛼𝑞	𝛼𝑞	X
easat-3054	173	1	)	)	PUNCT
easat-3054	173	2	γ(1	γ(1	PROPN
easat-3054	174	1	+	+	CCONJ
easat-3054	174	2	(	(	PUNCT
easat-3054	174	3	𝑞	𝑞	X
easat-3054	174	4	+	+	NOUN
easat-3054	174	5	1)𝛼	1)𝛼	NUM
easat-3054	174	6	)	)	PUNCT
easat-3054	174	7	(	(	PUNCT
easat-3054	174	8	𝑏(𝑞+1)𝛼	𝑏(𝑞+1)𝛼	PROPN
easat-3054	174	9	−	−	PROPN
easat-3054	174	10	𝑥(𝑞+1)𝛼	𝑥(𝑞+1)𝛼	PROPN
easat-3054	174	11	)	)	PUNCT
easat-3054	174	12	(	(	PUNCT
easat-3054	174	13	11	11	NUM
easat-3054	174	14	)	)	PUNCT
easat-3054	174	15	put	put	NOUN
easat-3054	174	16	(	(	PUNCT
easat-3054	174	17	10	10	NUM
easat-3054	174	18	)	)	PUNCT
easat-3054	174	19	and(11	and(11	PROPN
easat-3054	174	20	)	)	PUNCT
easat-3054	174	21	in	in	ADP
easat-3054	174	22	(	(	PUNCT
easat-3054	174	23	9	9	NUM
easat-3054	174	24	)	)	PUNCT
easat-3054	174	25	,	,	PUNCT
easat-3054	174	26	we	we	PRON
easat-3054	174	27	get	get	VERB
easat-3054	174	28	(	(	PUNCT
easat-3054	174	29	1	1	NUM
easat-3054	174	30	γ(1	γ(1	NOUN
easat-3054	174	31	+	+	NUM
easat-3054	174	32	𝛼	𝛼	X
easat-3054	174	33	)	)	PUNCT
easat-3054	174	34	∫|𝑝(𝑥	∫|𝑝(𝑥	ADJ
easat-3054	174	35	,	,	PUNCT
easat-3054	174	36	𝑡)|𝑞(𝑑𝑥)𝛼	𝑡)|𝑞(𝑑𝑥)𝛼	NOUN
easat-3054	174	37	𝑏	𝑏	PROPN
easat-3054	174	38	𝑎	𝑎	X
easat-3054	174	39	)	)	PUNCT
easat-3054	174	40	1	1	NUM
easat-3054	174	41	𝑞	𝑞	NOUN
easat-3054	174	42	=	=	X
easat-3054	174	43	[	[	PUNCT
easat-3054	174	44	γ(1	γ(1	PROPN
easat-3054	174	45	+	+	CCONJ
easat-3054	174	46	𝛼𝑞	𝛼𝑞	X
easat-3054	174	47	)	)	PUNCT
easat-3054	175	1	γ(1	γ(1	PROPN
easat-3054	176	1	+	+	CCONJ
easat-3054	176	2	(	(	PUNCT
easat-3054	176	3	𝑞	𝑞	X
easat-3054	176	4	+	+	NOUN
easat-3054	176	5	1)𝛼	1)𝛼	NUM
easat-3054	176	6	)	)	PUNCT
easat-3054	176	7	(	(	PUNCT
easat-3054	176	8	𝑥(𝑞+1)𝛼	𝑥(𝑞+1)𝛼	PROPN
easat-3054	176	9	−	−	PROPN
easat-3054	176	10	𝑎(𝑞+1)𝛼	𝑎(𝑞+1)𝛼	PROPN
easat-3054	176	11	)	)	PUNCT
easat-3054	176	12	+	+	CCONJ
easat-3054	176	13	(	(	PUNCT
easat-3054	176	14	𝑏(𝑞+1)𝛼	𝑏(𝑞+1)𝛼	PROPN
easat-3054	176	15	−	−	PROPN
easat-3054	176	16	𝑥(𝑞+1)𝛼	𝑥(𝑞+1)𝛼	PROPN
easat-3054	176	17	)	)	PUNCT
easat-3054	176	18	]	]	PUNCT
easat-3054	177	1	1	1	NUM
easat-3054	177	2	𝑞	𝑞	X
easat-3054	177	3	=	=	PUNCT
easat-3054	177	4	(	(	PUNCT
easat-3054	177	5	γ(1	γ(1	PROPN
easat-3054	177	6	+	+	CCONJ
easat-3054	177	7	𝛼𝑞	𝛼𝑞	X
easat-3054	177	8	)	)	PUNCT
easat-3054	177	9	γ(1	γ(1	PROPN
easat-3054	177	10	+	+	CCONJ
easat-3054	177	11	(	(	PUNCT
easat-3054	177	12	𝑞	𝑞	X
easat-3054	177	13	+	+	NOUN
easat-3054	177	14	1)𝛼	1)𝛼	NUM
easat-3054	177	15	)	)	PUNCT
easat-3054	177	16	(	(	PUNCT
easat-3054	177	17	𝑏(𝑞+1)𝛼	𝑏(𝑞+1)𝛼	PROPN
easat-3054	177	18	−	−	PROPN
easat-3054	177	19	𝑎(𝑞+1)𝛼	𝑎(𝑞+1)𝛼	PROPN
easat-3054	177	20	)	)	PUNCT
easat-3054	177	21	)	)	PUNCT
easat-3054	177	22	1	1	NUM
easat-3054	177	23	𝑞	𝑞	SYM
easat-3054	177	24	≤	≤	X
easat-3054	177	25	(	(	PUNCT
easat-3054	178	1	γ(1	γ(1	PROPN
easat-3054	178	2	+	+	CCONJ
easat-3054	178	3	𝛼𝑞	𝛼𝑞	X
easat-3054	179	1	)	)	PUNCT
easat-3054	179	2	γ(1	γ(1	PROPN
easat-3054	180	1	+	+	CCONJ
easat-3054	180	2	(	(	PUNCT
easat-3054	180	3	𝑞	𝑞	X
easat-3054	180	4	+	+	NOUN
easat-3054	180	5	1)𝛼	1)𝛼	NUM
easat-3054	180	6	)	)	PUNCT
easat-3054	180	7	)	)	PUNCT
easat-3054	181	1	1	1	NUM
easat-3054	181	2	𝑞	𝑞	SYM
easat-3054	181	3	(	(	PUNCT
easat-3054	181	4	𝑏	𝑏	PROPN
easat-3054	181	5	−	−	PROPN
easat-3054	181	6	𝑎	𝑎	NOUN
easat-3054	181	7	)	)	PUNCT
easat-3054	181	8	(	(	PUNCT
easat-3054	181	9	𝑞+1)𝛼	𝑞+1)𝛼	PROPN
easat-3054	181	10	𝑞	𝑞	X
easat-3054	181	11	(	(	PUNCT
easat-3054	181	12	12	12	NUM
easat-3054	181	13	)	)	PUNCT
easat-3054	181	14	put	put	NOUN
easat-3054	181	15	(	(	PUNCT
easat-3054	181	16	7	7	NUM
easat-3054	181	17	)	)	PUNCT
easat-3054	181	18	and	and	CCONJ
easat-3054	181	19	(	(	PUNCT
easat-3054	181	20	12	12	NUM
easat-3054	181	21	)	)	PUNCT
easat-3054	181	22	in	in	ADP
easat-3054	181	23	(	(	PUNCT
easat-3054	181	24	8)	8)	NUM
easat-3054	181	25	,	,	PUNCT
easat-3054	181	26	we	we	PRON
easat-3054	181	27	get	get	VERB
easat-3054	181	28	|(𝐼	|(𝐼	PROPN
easat-3054	181	29	−	−	PROPN
easat-3054	181	30	ℎ)𝛼𝑓(𝑥	ℎ)𝛼𝑓(𝑥	NOUN
easat-3054	181	31	)	)	PUNCT
easat-3054	182	1	+	+	CCONJ
easat-3054	182	2	ℎ𝛼	ℎ𝛼	DET
easat-3054	182	3	𝑓(𝑎	𝑓(𝑎	NUM
easat-3054	182	4	)	)	PUNCT
easat-3054	183	1	+	+	NUM
easat-3054	183	2	𝑓(𝑏	𝑓(𝑏	NOUN
easat-3054	183	3	)	)	PUNCT
easat-3054	183	4	2𝛼	2𝛼	PROPN
easat-3054	183	5	−	−	PROPN
easat-3054	184	1	γ(1	γ(1	NOUN
easat-3054	184	2	+	+	NUM
easat-3054	184	3	𝛼	𝛼	X
easat-3054	184	4	)	)	PUNCT
easat-3054	184	5	(	(	PUNCT
easat-3054	184	6	𝑏	𝑏	PROPN
easat-3054	184	7	−	−	PROPN
easat-3054	184	8	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	184	9	𝑎𝐼𝑏	𝑎𝐼𝑏	NOUN
easat-3054	184	10	∝𝑓(𝑥)|	∝𝑓(𝑥)|	PROPN
easat-3054	184	11	≤	≤	NUM
easat-3054	184	12	1	1	NUM
easat-3054	184	13	(	(	PUNCT
easat-3054	184	14	𝑏	𝑏	PROPN
easat-3054	184	15	−	−	PROPN
easat-3054	184	16	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	184	17	(	(	PUNCT
easat-3054	184	18	(	(	PUNCT
easat-3054	184	19	𝛤(1	𝛤(1	X
easat-3054	184	20	+	+	CCONJ
easat-3054	184	21	𝛼𝑞	𝛼𝑞	NOUN
easat-3054	184	22	)	)	PUNCT
easat-3054	184	23	)	)	PUNCT
easat-3054	184	24	𝛤(1	𝛤(1	PUNCT
easat-3054	185	1	+	+	CCONJ
easat-3054	185	2	(	(	PUNCT
easat-3054	185	3	𝑞	𝑞	X
easat-3054	185	4	+	+	NOUN
easat-3054	185	5	1)𝛼	1)𝛼	NUM
easat-3054	185	6	)	)	PUNCT
easat-3054	185	7	(	(	PUNCT
easat-3054	185	8	𝑏(𝑞+1)𝛼	𝑏(𝑞+1)𝛼	PROPN
easat-3054	185	9	−	−	PROPN
easat-3054	185	10	𝑎(𝑞+1)𝛼	𝑎(𝑞+1)𝛼	PROPN
easat-3054	185	11	)	)	PUNCT
easat-3054	185	12	)	)	PUNCT
easat-3054	185	13	1	1	NUM
easat-3054	185	14	𝑞	𝑞	SYM
easat-3054	185	15	×	×	NOUN
easat-3054	185	16	(	(	PUNCT
easat-3054	185	17	1	1	NUM
easat-3054	185	18	𝛤(1	𝛤(1	NUM
easat-3054	185	19	+	+	CCONJ
easat-3054	185	20	𝛼	𝛼	X
easat-3054	185	21	)	)	PUNCT
easat-3054	185	22	)	)	PUNCT
easat-3054	185	23	1	1	NUM
easat-3054	185	24	𝑝	𝑝	PROPN
easat-3054	185	25	‖𝑓𝛼‖𝑝	‖𝑓𝛼‖𝑝	PROPN
easat-3054	185	26	.	.	PUNCT
easat-3054	186	1	this	this	PRON
easat-3054	186	2	implies	imply	VERB
easat-3054	186	3	,	,	PUNCT
easat-3054	186	4	|(𝐼	|(𝐼	PROPN
easat-3054	186	5	−	−	NOUN
easat-3054	186	6	ℎ)𝛼𝑓(𝑥	ℎ)𝛼𝑓(𝑥	VERB
easat-3054	186	7	)	)	PUNCT
easat-3054	187	1	+	+	CCONJ
easat-3054	187	2	ℎ𝛼	ℎ𝛼	DET
easat-3054	187	3	𝑓(𝑎	𝑓(𝑎	NUM
easat-3054	187	4	)	)	PUNCT
easat-3054	188	1	+	+	NUM
easat-3054	188	2	𝑓(𝑏	𝑓(𝑏	NOUN
easat-3054	188	3	)	)	PUNCT
easat-3054	188	4	2𝛼	2𝛼	PROPN
easat-3054	188	5	−	−	PROPN
easat-3054	189	1	γ(1	γ(1	NOUN
easat-3054	189	2	+	+	NUM
easat-3054	189	3	𝛼	𝛼	X
easat-3054	189	4	)	)	PUNCT
easat-3054	189	5	(	(	PUNCT
easat-3054	189	6	𝑏	𝑏	PROPN
easat-3054	189	7	−	−	PROPN
easat-3054	189	8	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	189	9	𝑎𝐼𝑏	𝑎𝐼𝑏	NOUN
easat-3054	189	10	∝𝑓(𝑥)|	∝𝑓(𝑥)|	PROPN
easat-3054	189	11	≤	≤	NUM
easat-3054	189	12	(	(	PUNCT
easat-3054	189	13	𝛤(1	𝛤(1	X
easat-3054	189	14	+	+	CCONJ
easat-3054	189	15	𝛼𝑞	𝛼𝑞	NOUN
easat-3054	189	16	)	)	PUNCT
easat-3054	189	17	)	)	PUNCT
easat-3054	189	18	1	1	NUM
easat-3054	189	19	𝑞(𝑏	𝑞(𝑏	NOUN
easat-3054	189	20	−	−	NUM
easat-3054	189	21	𝑎	𝑎	NOUN
easat-3054	189	22	)	)	PUNCT
easat-3054	189	23	𝛼	𝛼	PROPN
easat-3054	189	24	𝑞	𝑞	X
easat-3054	189	25	(	(	PUNCT
easat-3054	189	26	𝛤(1	𝛤(1	PUNCT
easat-3054	189	27	+	+	CCONJ
easat-3054	189	28	(	(	PUNCT
easat-3054	189	29	𝑞	𝑞	X
easat-3054	189	30	+	+	X
easat-3054	189	31	1)𝛼	1)𝛼	NUM
easat-3054	189	32	)	)	PUNCT
easat-3054	189	33	)	)	PUNCT
easat-3054	190	1	1	1	NUM
easat-3054	190	2	𝑞(𝛤(1	𝑞(𝛤(1	NUM
easat-3054	190	3	+	+	NUM
easat-3054	190	4	𝛼	𝛼	X
easat-3054	190	5	)	)	PUNCT
easat-3054	190	6	)	)	PUNCT
easat-3054	190	7	1	1	NUM
easat-3054	190	8	𝑝	𝑝	X
easat-3054	190	9	‖𝑓𝛼‖𝑝	‖𝑓𝛼‖𝑝	PROPN
easat-3054	190	10	,	,	PUNCT
easat-3054	190	11	1	1	NUM
easat-3054	190	12	≤	≤	NUM
easat-3054	190	13	𝑝	𝑝	PROPN
easat-3054	190	14	,	,	PUNCT
easat-3054	190	15	𝑞	𝑞	X
easat-3054	190	16	≤	≤	NOUN
easat-3054	190	17	∞	∞	PROPN
easat-3054	190	18	,	,	PUNCT
easat-3054	190	19	1	1	NUM
easat-3054	190	20	𝑝	𝑝	NOUN
easat-3054	190	21	+	+	NUM
easat-3054	190	22	1	1	NUM
easat-3054	190	23	𝑞	𝑞	NOUN
easat-3054	190	24	=	=	PROPN
easat-3054	190	25	1	1	NUM
easat-3054	190	26	the	the	DET
easat-3054	190	27	first	first	ADJ
easat-3054	190	28	case	case	NOUN
easat-3054	190	29	is	be	AUX
easat-3054	190	30	proved	prove	VERB
easat-3054	190	31	.	.	PUNCT
easat-3054	191	1	case2	case2	PROPN
easat-3054	191	2	:	:	PUNCT
easat-3054	191	3	0	0	NUM
easat-3054	191	4	<	<	X
easat-3054	191	5	𝑃	𝑃	X
easat-3054	191	6	<	<	X
easat-3054	191	7	1	1	NUM
easat-3054	191	8	by	by	ADP
easat-3054	191	9	using	use	VERB
easat-3054	191	10	the	the	DET
easat-3054	191	11	generalized	generalized	ADJ
easat-3054	191	12	holder	holder	NOUN
easat-3054	191	13	,	,	PUNCT
easat-3054	191	14	s	s	PART
easat-3054	191	15	inequality	inequality	NOUN
easat-3054	191	16	described	describe	VERB
easat-3054	191	17	in	in	ADP
easat-3054	191	18	lemma2.2	lemma2.2	NOUN
easat-3054	191	19	,	,	PUNCT
easat-3054	191	20	we	we	PRON
easat-3054	191	21	obtain	obtain	VERB
easat-3054	191	22	.	.	PUNCT
easat-3054	192	1	1	1	NUM
easat-3054	192	2	𝛤(1	𝛤(1	NUM
easat-3054	192	3	+	+	CCONJ
easat-3054	192	4	𝛼)(𝑏	𝛼)(𝑏	NUM
easat-3054	192	5	−	−	PROPN
easat-3054	192	6	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	192	7	∫	∫	PROPN
easat-3054	192	8	|𝑝(𝑥	|𝑝(𝑥	PROPN
easat-3054	192	9	,	,	PUNCT
easat-3054	192	10	𝑡)||𝑓(𝑥)𝛼|	𝑡)||𝑓(𝑥)𝛼|	PROPN
easat-3054	192	11	(	(	PUNCT
easat-3054	192	12	𝑑𝑡)𝛼	𝑑𝑡)𝛼	NOUN
easat-3054	192	13	𝑏	𝑏	NOUN
easat-3054	192	14	𝑎	𝑎	PROPN
easat-3054	192	15	≤	≤	NUM
easat-3054	192	16	1	1	NUM
easat-3054	192	17	(	(	PUNCT
easat-3054	192	18	𝑏	𝑏	NOUN
easat-3054	192	19	−	−	PROPN
easat-3054	192	20	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	192	21	(	(	PUNCT
easat-3054	192	22	1	1	NUM
easat-3054	192	23	𝛤(1	𝛤(1	NUM
easat-3054	192	24	+	+	CCONJ
easat-3054	192	25	𝛼	𝛼	X
easat-3054	192	26	)	)	PUNCT
easat-3054	192	27	∫|𝑝(𝑥	∫|𝑝(𝑥	ADJ
easat-3054	192	28	,	,	PUNCT
easat-3054	192	29	𝑡)|𝑞(𝑑𝑥)𝛼	𝑡)|𝑞(𝑑𝑥)𝛼	NOUN
easat-3054	192	30	𝑏	𝑏	PROPN
easat-3054	192	31	𝑎	𝑎	X
easat-3054	192	32	)	)	PUNCT
easat-3054	192	33	1	1	NUM
easat-3054	192	34	𝑞	𝑞	PROPN
easat-3054	192	35	(	(	PUNCT
easat-3054	192	36	1	1	NUM
easat-3054	192	37	𝛤(1	𝛤(1	NUM
easat-3054	192	38	+	+	CCONJ
easat-3054	192	39	𝛼	𝛼	X
easat-3054	192	40	)	)	PUNCT
easat-3054	192	41	∫|𝑓(𝑥)𝛼|𝐿(𝑑𝑥)𝛼	∫|𝑓(𝑥)𝛼|𝐿(𝑑𝑥)𝛼	NOUN
easat-3054	193	1	𝑏	𝑏	PROPN
easat-3054	193	2	𝑎	𝑎	X
easat-3054	193	3	)	)	PUNCT
easat-3054	193	4	1	1	NUM
easat-3054	193	5	𝐿	𝐿	PROPN
easat-3054	193	6	4917	4917	NUM
easat-3054	193	7	edelweiss	edelweiss	PROPN
easat-3054	193	8	applied	apply	VERB
easat-3054	193	9	science	science	NOUN
easat-3054	193	10	and	and	CCONJ
easat-3054	193	11	technology	technology	NOUN
easat-3054	193	12	issn	issn	PROPN
easat-3054	193	13	:	:	PUNCT
easat-3054	193	14	2576	2576	NUM
easat-3054	193	15	-	-	SYM
easat-3054	193	16	8484	8484	NUM
easat-3054	193	17	vol	vol	NOUN
easat-3054	193	18	.	.	PROPN
easat-3054	193	19	8	8	NUM
easat-3054	193	20	,	,	PUNCT
easat-3054	193	21	no	no	INTJ
easat-3054	193	22	.	.	NOUN
easat-3054	194	1	6	6	NUM
easat-3054	194	2	:	:	SYM
easat-3054	194	3	4910	4910	NUM
easat-3054	194	4	-	-	SYM
easat-3054	194	5	4919	4919	NUM
easat-3054	194	6	,	,	PUNCT
easat-3054	194	7	2024	2024	NUM
easat-3054	194	8	doi	doi	NOUN
easat-3054	194	9	:	:	PUNCT
easat-3054	194	10	10.55214/25768484.v8i6.3054	10.55214/25768484.v8i6.3054	NUM
easat-3054	194	11	©	©	PROPN
easat-3054	194	12	2024	2024	NUM
easat-3054	194	13	by	by	ADP
easat-3054	194	14	the	the	DET
easat-3054	194	15	authors	author	NOUN
easat-3054	194	16	;	;	PUNCT
easat-3054	194	17	licensee	licensee	PROPN
easat-3054	194	18	learning	learning	NOUN
easat-3054	194	19	gate	gate	NOUN
easat-3054	194	20	1	1	NUM
easat-3054	194	21	≤	≤	PROPN
easat-3054	194	22	𝑝	𝑝	PROPN
easat-3054	194	23	,	,	PUNCT
easat-3054	194	24	𝑞	𝑞	X
easat-3054	194	25	≤	≤	NOUN
easat-3054	194	26	∞	∞	PROPN
easat-3054	194	27	,	,	PUNCT
easat-3054	194	28	1	1	NUM
easat-3054	194	29	𝐿	𝐿	NOUN
easat-3054	194	30	+	+	NOUN
easat-3054	194	31	1	1	NUM
easat-3054	194	32	𝑞	𝑞	NOUN
easat-3054	194	33	=	=	SYM
easat-3054	194	34	1	1	NUM
easat-3054	194	35	by	by	ADP
easat-3054	194	36	using	use	VERB
easat-3054	194	37	(	(	PUNCT
easat-3054	194	38	1	1	NUM
easat-3054	194	39	)	)	PUNCT
easat-3054	194	40	and	and	CCONJ
easat-3054	194	41	using(12	using(12	ADJ
easat-3054	194	42	)	)	PUNCT
easat-3054	194	43	implies	imply	VERB
easat-3054	194	44	1	1	NUM
easat-3054	194	45	𝛤(1	𝛤(1	NUM
easat-3054	194	46	+	+	CCONJ
easat-3054	194	47	𝛼)(𝑏	𝛼)(𝑏	NUM
easat-3054	194	48	−	−	PROPN
easat-3054	194	49	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	194	50	∫	∫	PROPN
easat-3054	194	51	|𝑝(𝑥	|𝑝(𝑥	PROPN
easat-3054	194	52	,	,	PUNCT
easat-3054	194	53	𝑡)||𝑓(𝑥)𝛼|	𝑡)||𝑓(𝑥)𝛼|	PROPN
easat-3054	194	54	(	(	PUNCT
easat-3054	194	55	𝑑𝑡)𝛼	𝑑𝑡)𝛼	NOUN
easat-3054	194	56	𝑏	𝑏	NOUN
easat-3054	194	57	𝑎	𝑎	NOUN
easat-3054	194	58	≤	≤	NOUN
easat-3054	194	59	(	(	PUNCT
easat-3054	194	60	γ(1	γ(1	PROPN
easat-3054	194	61	+	+	CCONJ
easat-3054	194	62	𝛼𝑞	𝛼𝑞	X
easat-3054	194	63	)	)	PUNCT
easat-3054	194	64	γ(1	γ(1	PROPN
easat-3054	195	1	+	+	CCONJ
easat-3054	195	2	(	(	PUNCT
easat-3054	195	3	𝑞	𝑞	X
easat-3054	195	4	+	+	NOUN
easat-3054	195	5	1)𝛼	1)𝛼	NUM
easat-3054	195	6	)	)	PUNCT
easat-3054	195	7	)	)	PUNCT
easat-3054	196	1	1	1	NUM
easat-3054	196	2	𝑞	𝑞	SYM
easat-3054	196	3	(	(	PUNCT
easat-3054	196	4	𝑏	𝑏	PROPN
easat-3054	196	5	−	−	PROPN
easat-3054	196	6	𝑎	𝑎	NOUN
easat-3054	196	7	)	)	PUNCT
easat-3054	196	8	(	(	PUNCT
easat-3054	196	9	𝑞+1)𝛼	𝑞+1)𝛼	PROPN
easat-3054	196	10	𝑞	𝑞	PART
easat-3054	196	11	×	×	PROPN
easat-3054	196	12	(	(	PUNCT
easat-3054	196	13	1	1	NUM
easat-3054	196	14	𝛤(1	𝛤(1	NUM
easat-3054	196	15	+	+	CCONJ
easat-3054	196	16	𝛼	𝛼	X
easat-3054	196	17	)	)	PUNCT
easat-3054	196	18	∑|𝑓𝛼(𝑡𝑖)|	∑|𝑓𝛼(𝑡𝑖)|	NOUN
easat-3054	196	19	𝐿(∆𝑡𝑖	𝐿(∆𝑡𝑖	NOUN
easat-3054	196	20	)	)	PUNCT
easat-3054	196	21	𝛼	𝛼	PROPN
easat-3054	196	22	𝑛	𝑛	PROPN
easat-3054	196	23	𝑖=1	𝑖=1	PROPN
easat-3054	196	24	)	)	PUNCT
easat-3054	196	25	1	1	NUM
easat-3054	196	26	𝐿	𝐿	PROPN
easat-3054	196	27	where	where	SCONJ
easat-3054	196	28	0	0	NUM
easat-3054	196	29	<	<	X
easat-3054	196	30	𝑝	𝑝	X
easat-3054	196	31	<	<	X
easat-3054	196	32	1	1	NUM
easat-3054	196	33	,	,	PUNCT
easat-3054	196	34	by	by	ADP
easat-3054	196	35	using	use	VERB
easat-3054	196	36	lemma	lemma	PROPN
easat-3054	196	37	2.3,we	2.3,we	PROPN
easat-3054	196	38	get	get	VERB
easat-3054	196	39	1	1	NUM
easat-3054	196	40	𝛤(1	𝛤(1	NUM
easat-3054	196	41	+	+	CCONJ
easat-3054	196	42	𝛼)(𝑏	𝛼)(𝑏	NUM
easat-3054	196	43	−	−	PROPN
easat-3054	196	44	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	196	45	∫	∫	PROPN
easat-3054	196	46	|𝑝(𝑥	|𝑝(𝑥	PROPN
easat-3054	196	47	,	,	PUNCT
easat-3054	196	48	𝑡)||𝑓(𝑥)𝛼|	𝑡)||𝑓(𝑥)𝛼|	PROPN
easat-3054	196	49	(	(	PUNCT
easat-3054	196	50	𝑑𝑡)𝛼	𝑑𝑡)𝛼	NOUN
easat-3054	196	51	𝑏	𝑏	NOUN
easat-3054	196	52	𝑎	𝑎	NOUN
easat-3054	196	53	≤	≤	NOUN
easat-3054	196	54	(	(	PUNCT
easat-3054	197	1	γ(1	γ(1	PROPN
easat-3054	197	2	+	+	CCONJ
easat-3054	197	3	𝛼𝑞	𝛼𝑞	X
easat-3054	198	1	)	)	PUNCT
easat-3054	198	2	γ(1	γ(1	PROPN
easat-3054	199	1	+	+	CCONJ
easat-3054	199	2	(	(	PUNCT
easat-3054	199	3	𝑞	𝑞	X
easat-3054	199	4	+	+	NOUN
easat-3054	199	5	1)𝛼	1)𝛼	NUM
easat-3054	199	6	)	)	PUNCT
easat-3054	199	7	)	)	PUNCT
easat-3054	200	1	1	1	NUM
easat-3054	200	2	𝑞	𝑞	SYM
easat-3054	200	3	(	(	PUNCT
easat-3054	200	4	𝑏	𝑏	PROPN
easat-3054	200	5	−	−	PROPN
easat-3054	200	6	𝑎	𝑎	NOUN
easat-3054	200	7	)	)	PUNCT
easat-3054	200	8	(	(	PUNCT
easat-3054	200	9	𝑞+1)𝛼	𝑞+1)𝛼	PROPN
easat-3054	200	10	𝑞	𝑞	PART
easat-3054	200	11	×	×	PROPN
easat-3054	200	12	(	(	PUNCT
easat-3054	200	13	1	1	NUM
easat-3054	200	14	𝛤(1	𝛤(1	NUM
easat-3054	200	15	+	+	CCONJ
easat-3054	200	16	𝛼	𝛼	X
easat-3054	200	17	)	)	PUNCT
easat-3054	200	18	∑|𝑓𝛼(𝑡𝑖)|	∑|𝑓𝛼(𝑡𝑖)|	X
easat-3054	200	19	𝑃(∆𝑡𝑖	𝑃(∆𝑡𝑖	NOUN
easat-3054	200	20	)	)	PUNCT
easat-3054	200	21	𝛼	𝛼	PART
easat-3054	200	22	𝑛	𝑛	PROPN
easat-3054	200	23	𝑖=1	𝑖=1	PROPN
easat-3054	200	24	)	)	PUNCT
easat-3054	200	25	1	1	NUM
easat-3054	200	26	𝑃	𝑃	NOUN
easat-3054	200	27	by	by	ADP
easat-3054	200	28	using	use	VERB
easat-3054	200	29	(	(	PUNCT
easat-3054	200	30	1	1	NUM
easat-3054	200	31	)	)	PUNCT
easat-3054	200	32	,	,	PUNCT
easat-3054	200	33	we	we	PRON
easat-3054	200	34	get	get	VERB
easat-3054	200	35	1	1	NUM
easat-3054	200	36	𝛤(1	𝛤(1	NUM
easat-3054	200	37	+	+	CCONJ
easat-3054	200	38	𝛼)(𝑏	𝛼)(𝑏	NUM
easat-3054	200	39	−	−	PROPN
easat-3054	200	40	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	200	41	∫	∫	PROPN
easat-3054	200	42	|𝑝(𝑥	|𝑝(𝑥	PROPN
easat-3054	200	43	,	,	PUNCT
easat-3054	200	44	𝑡)||𝑓(𝑥)𝛼|	𝑡)||𝑓(𝑥)𝛼|	PROPN
easat-3054	200	45	(	(	PUNCT
easat-3054	200	46	𝑑𝑡)𝛼	𝑑𝑡)𝛼	NOUN
easat-3054	200	47	𝑏	𝑏	NOUN
easat-3054	200	48	𝑎	𝑎	PROPN
easat-3054	200	49	≤	≤	NUM
easat-3054	200	50	𝐶(𝑝)(𝛤(1	𝐶(𝑝)(𝛤(1	NOUN
easat-3054	200	51	+	+	CCONJ
easat-3054	200	52	𝛼𝑞	𝛼𝑞	PROPN
easat-3054	200	53	)	)	PUNCT
easat-3054	200	54	)	)	PUNCT
easat-3054	201	1	1	1	NUM
easat-3054	201	2	𝑞(𝑏	𝑞(𝑏	NOUN
easat-3054	201	3	−	−	NUM
easat-3054	201	4	𝑎	𝑎	NOUN
easat-3054	201	5	)	)	PUNCT
easat-3054	201	6	𝛼	𝛼	PROPN
easat-3054	201	7	𝑞	𝑞	X
easat-3054	201	8	(	(	PUNCT
easat-3054	201	9	𝛤(1	𝛤(1	PUNCT
easat-3054	201	10	+	+	CCONJ
easat-3054	201	11	(	(	PUNCT
easat-3054	201	12	𝑞	𝑞	X
easat-3054	201	13	+	+	X
easat-3054	201	14	1)𝛼	1)𝛼	NUM
easat-3054	201	15	)	)	PUNCT
easat-3054	201	16	)	)	PUNCT
easat-3054	202	1	1	1	NUM
easat-3054	202	2	𝑞(𝛤(1	𝑞(𝛤(1	NUM
easat-3054	202	3	+	+	NUM
easat-3054	202	4	𝛼	𝛼	X
easat-3054	202	5	)	)	PUNCT
easat-3054	202	6	)	)	PUNCT
easat-3054	202	7	1	1	NUM
easat-3054	202	8	𝑝	𝑝	X
easat-3054	202	9	‖𝑓𝛼‖𝑝	‖𝑓𝛼‖𝑝	PROPN
easat-3054	202	10	,	,	PUNCT
easat-3054	202	11	0	0	NUM
easat-3054	202	12	<	<	X
easat-3054	202	13	𝑝	𝑝	X
easat-3054	202	14	<	<	X
easat-3054	202	15	1	1	NUM
easat-3054	202	16	.	.	PUNCT
easat-3054	202	17	now	now	ADV
easat-3054	202	18	by	by	ADP
easat-3054	202	19	using	use	VERB
easat-3054	202	20	lemma	lemma	PROPN
easat-3054	202	21	2.5	2.5	NUM
easat-3054	202	22	,	,	PUNCT
easat-3054	202	23	we	we	PRON
easat-3054	202	24	get	get	VERB
easat-3054	202	25	|(𝐼	|(𝐼	PROPN
easat-3054	202	26	−	−	PROPN
easat-3054	202	27	ℎ)𝛼𝑓(𝑥	ℎ)𝛼𝑓(𝑥	NOUN
easat-3054	202	28	)	)	PUNCT
easat-3054	203	1	+	+	CCONJ
easat-3054	203	2	ℎ𝛼	ℎ𝛼	DET
easat-3054	203	3	𝑓(𝑎	𝑓(𝑎	NUM
easat-3054	203	4	)	)	PUNCT
easat-3054	204	1	+	+	NUM
easat-3054	204	2	𝑓(𝑏	𝑓(𝑏	NOUN
easat-3054	204	3	)	)	PUNCT
easat-3054	204	4	2𝛼	2𝛼	PROPN
easat-3054	204	5	−	−	PROPN
easat-3054	205	1	γ(1	γ(1	NOUN
easat-3054	205	2	+	+	NUM
easat-3054	205	3	𝛼	𝛼	X
easat-3054	205	4	)	)	PUNCT
easat-3054	205	5	(	(	PUNCT
easat-3054	205	6	𝑏	𝑏	PROPN
easat-3054	205	7	−	−	PROPN
easat-3054	205	8	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	205	9	𝑎𝐼𝑏	𝑎𝐼𝑏	NOUN
easat-3054	205	10	∝𝑓(𝑥)|	∝𝑓(𝑥)|	SYM
easat-3054	205	11	≤	≤	NUM
easat-3054	205	12	𝐶(𝑝)(γ(1	𝐶(𝑝)(γ(1	NUM
easat-3054	205	13	+	+	CCONJ
easat-3054	205	14	𝛼𝑞	𝛼𝑞	X
easat-3054	205	15	)	)	PUNCT
easat-3054	205	16	)	)	PUNCT
easat-3054	205	17	1	1	NUM
easat-3054	205	18	𝑞(𝑏	𝑞(𝑏	NOUN
easat-3054	205	19	−	−	NUM
easat-3054	205	20	𝑎	𝑎	NOUN
easat-3054	205	21	)	)	PUNCT
easat-3054	205	22	∝	∝	PROPN
easat-3054	205	23	𝑞	𝑞	X
easat-3054	205	24	(	(	PUNCT
easat-3054	205	25	γ(1	γ(1	PROPN
easat-3054	205	26	+	+	CCONJ
easat-3054	205	27	(	(	PUNCT
easat-3054	205	28	𝑞	𝑞	X
easat-3054	205	29	+	+	X
easat-3054	205	30	1)𝛼	1)𝛼	NUM
easat-3054	205	31	)	)	PUNCT
easat-3054	205	32	)	)	PUNCT
easat-3054	205	33	1	1	NUM
easat-3054	206	1	𝑞(γ(1	𝑞(γ(1	NOUN
easat-3054	206	2	+	+	NUM
easat-3054	206	3	𝛼	𝛼	X
easat-3054	206	4	)	)	PUNCT
easat-3054	206	5	)	)	PUNCT
easat-3054	206	6	1	1	NUM
easat-3054	206	7	𝑝	𝑝	X
easat-3054	206	8	‖𝑓𝛼‖𝑝	‖𝑓𝛼‖𝑝	PROPN
easat-3054	206	9	,	,	PUNCT
easat-3054	206	10	0	0	NUM
easat-3054	206	11	<	<	X
easat-3054	206	12	𝑝	𝑝	X
easat-3054	206	13	<	<	X
easat-3054	206	14	1	1	NUM
easat-3054	206	15	.	.	PUNCT
easat-3054	207	1	the	the	DET
easat-3054	207	2	second	second	ADJ
easat-3054	207	3	case	case	NOUN
easat-3054	207	4	is	be	AUX
easat-3054	207	5	proved	prove	VERB
easat-3054	207	6	.	.	PUNCT
easat-3054	208	1	corollary3.3	corollary3.3	NOUN
easat-3054	208	2	:	:	PUNCT
easat-3054	208	3	if	if	SCONJ
easat-3054	208	4	𝑓	𝑓	PRON
easat-3054	208	5	⊂	⊂	PROPN
easat-3054	208	6	𝑅	𝑅	PROPN
easat-3054	208	7	,	,	PUNCT
easat-3054	208	8	𝑓	𝑓	PRON
easat-3054	208	9	:	:	PUNCT
easat-3054	208	10	𝐼∘	𝐼∘	PROPN
easat-3054	208	11	⊂	⊂	PROPN
easat-3054	208	12	𝑅	𝑅	PROPN
easat-3054	208	13	→	→	SYM
easat-3054	208	14	𝑅𝛼	𝑅𝛼	PROPN
easat-3054	208	15	be	be	AUX
easat-3054	208	16	a	a	DET
easat-3054	208	17	map	map	NOUN
easat-3054	209	1	[	[	X
easat-3054	209	2	𝑎	𝑎	X
easat-3054	209	3	,	,	PUNCT
easat-3054	209	4	𝑏	𝑏	NOUN
easat-3054	209	5	]	]	X
easat-3054	209	6	⊂	⊂	X
easat-3054	209	7	𝐼∘and	𝐼∘and	PUNCT
easat-3054	209	8	𝑓	𝑓	PRON
easat-3054	209	9	∈	∈	PROPN
easat-3054	209	10	𝐿𝑃,𝛼[𝑎	𝐿𝑃,𝛼[𝑎	NOUN
easat-3054	209	11	,	,	PUNCT
easat-3054	209	12	𝑏	𝑏	NOUN
easat-3054	209	13	]	]	PUNCT
easat-3054	209	14	.	.	PUNCT
easat-3054	210	1	then	then	ADV
easat-3054	210	2	(	(	PUNCT
easat-3054	210	3	1	1	X
easat-3054	210	4	)	)	PUNCT
easat-3054	210	5	|𝑓(𝑥	|𝑓(𝑥	NOUN
easat-3054	210	6	)	)	PUNCT
easat-3054	210	7	−	−	PROPN
easat-3054	211	1	γ(1	γ(1	PROPN
easat-3054	211	2	+	+	NUM
easat-3054	211	3	𝛼	𝛼	X
easat-3054	211	4	)	)	PUNCT
easat-3054	211	5	(	(	PUNCT
easat-3054	211	6	𝑏	𝑏	PROPN
easat-3054	211	7	−	−	PROPN
easat-3054	211	8	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	211	9	𝑎𝐼𝑏	𝑎𝐼𝑏	NOUN
easat-3054	211	10	∝𝑓(𝑥)|	∝𝑓(𝑥)|	PROPN
easat-3054	211	11	≤	≤	NOUN
easat-3054	211	12	(	(	PUNCT
easat-3054	211	13	γ(1	γ(1	PROPN
easat-3054	211	14	+	+	CCONJ
easat-3054	211	15	𝛼𝑞	𝛼𝑞	PROPN
easat-3054	211	16	)	)	PUNCT
easat-3054	211	17	)	)	PUNCT
easat-3054	211	18	1	1	NUM
easat-3054	212	1	𝑞(𝑏	𝑞(𝑏	NOUN
easat-3054	212	2	−	−	NUM
easat-3054	212	3	𝑎	𝑎	NOUN
easat-3054	212	4	)	)	PUNCT
easat-3054	212	5	∝	∝	PROPN
easat-3054	212	6	𝑞	𝑞	X
easat-3054	212	7	(	(	PUNCT
easat-3054	212	8	γ(1	γ(1	PROPN
easat-3054	212	9	+	+	CCONJ
easat-3054	212	10	(	(	PUNCT
easat-3054	212	11	𝑞	𝑞	X
easat-3054	212	12	+	+	X
easat-3054	212	13	1)𝛼	1)𝛼	NUM
easat-3054	212	14	)	)	PUNCT
easat-3054	212	15	)	)	PUNCT
easat-3054	213	1	1	1	NUM
easat-3054	213	2	𝑞(γ(1	𝑞(γ(1	NOUN
easat-3054	213	3	+	+	NUM
easat-3054	213	4	𝛼	𝛼	X
easat-3054	213	5	)	)	PUNCT
easat-3054	213	6	)	)	PUNCT
easat-3054	213	7	1	1	NUM
easat-3054	213	8	𝑝	𝑝	X
easat-3054	213	9	‖𝑓𝛼‖𝑝	‖𝑓𝛼‖𝑝	PROPN
easat-3054	213	10	,	,	PUNCT
easat-3054	213	11	1	1	NUM
easat-3054	213	12	≤	≤	NUM
easat-3054	213	13	𝑝	𝑝	PROPN
easat-3054	213	14	,	,	PUNCT
easat-3054	213	15	𝑞	𝑞	X
easat-3054	213	16	≤	≤	NOUN
easat-3054	213	17	∞	∞	PROPN
easat-3054	213	18	,	,	PUNCT
easat-3054	213	19	1	1	NUM
easat-3054	213	20	𝑝	𝑝	NOUN
easat-3054	213	21	+	+	NUM
easat-3054	213	22	1	1	NUM
easat-3054	213	23	𝑞	𝑞	NOUN
easat-3054	213	24	=	=	NOUN
easat-3054	213	25	1	1	X
easat-3054	213	26	.	.	PUNCT
easat-3054	213	27	(	(	PUNCT
easat-3054	213	28	2	2	X
easat-3054	213	29	)	)	PUNCT
easat-3054	213	30	|𝑓(𝑥	|𝑓(𝑥	NOUN
easat-3054	213	31	)	)	PUNCT
easat-3054	213	32	−	−	PROPN
easat-3054	214	1	γ(1	γ(1	PROPN
easat-3054	214	2	+	+	NUM
easat-3054	214	3	𝛼	𝛼	X
easat-3054	214	4	)	)	PUNCT
easat-3054	214	5	(	(	PUNCT
easat-3054	214	6	𝑏	𝑏	PROPN
easat-3054	214	7	−	−	PROPN
easat-3054	214	8	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	214	9	𝑎𝐼𝑏	𝑎𝐼𝑏	NOUN
easat-3054	214	10	∝𝑓(𝑥)|	∝𝑓(𝑥)|	SYM
easat-3054	214	11	≤	≤	NUM
easat-3054	214	12	𝐶(𝑝)(γ(1	𝐶(𝑝)(γ(1	NUM
easat-3054	214	13	+	+	CCONJ
easat-3054	214	14	𝛼𝑞	𝛼𝑞	X
easat-3054	214	15	)	)	PUNCT
easat-3054	214	16	)	)	PUNCT
easat-3054	214	17	1	1	NUM
easat-3054	214	18	𝑞(𝑏	𝑞(𝑏	NOUN
easat-3054	214	19	−	−	NUM
easat-3054	214	20	𝑎	𝑎	NOUN
easat-3054	214	21	)	)	PUNCT
easat-3054	214	22	∝	∝	PROPN
easat-3054	214	23	𝑞	𝑞	X
easat-3054	214	24	(	(	PUNCT
easat-3054	214	25	γ(1	γ(1	PROPN
easat-3054	214	26	+	+	CCONJ
easat-3054	214	27	(	(	PUNCT
easat-3054	214	28	𝑞	𝑞	X
easat-3054	214	29	+	+	X
easat-3054	214	30	1)𝛼	1)𝛼	NUM
easat-3054	214	31	)	)	PUNCT
easat-3054	214	32	)	)	PUNCT
easat-3054	215	1	1	1	NUM
easat-3054	215	2	𝑞(γ(1	𝑞(γ(1	NOUN
easat-3054	215	3	+	+	NUM
easat-3054	215	4	𝛼	𝛼	X
easat-3054	215	5	)	)	PUNCT
easat-3054	215	6	)	)	PUNCT
easat-3054	215	7	1	1	NUM
easat-3054	215	8	𝑝	𝑝	PROPN
easat-3054	215	9	‖𝑓𝛼‖𝑝	‖𝑓𝛼‖𝑝	PROPN
easat-3054	215	10	,	,	PUNCT
easat-3054	215	11	0	0	NUM
easat-3054	215	12	<	<	X
easat-3054	215	13	𝑝	𝑝	X
easat-3054	215	14	<	<	X
easat-3054	215	15	1	1	NUM
easat-3054	215	16	.	.	PUNCT
easat-3054	216	1	proof	proof	NOUN
easat-3054	216	2	:	:	PUNCT
easat-3054	216	3	by	by	ADP
easat-3054	216	4	usingtheorem	usingtheorem	ADJ
easat-3054	216	5	3.2	3.2	NUM
easat-3054	216	6	,	,	PUNCT
easat-3054	216	7	we	we	PRON
easat-3054	216	8	get	get	VERB
easat-3054	216	9	case	case	NOUN
easat-3054	216	10	1	1	NUM
easat-3054	216	11	:	:	SYM
easat-3054	216	12	4918	4918	NUM
easat-3054	216	13	edelweiss	edelweiss	PROPN
easat-3054	216	14	applied	apply	VERB
easat-3054	216	15	science	science	NOUN
easat-3054	216	16	and	and	CCONJ
easat-3054	216	17	technology	technology	NOUN
easat-3054	216	18	issn	issn	PROPN
easat-3054	216	19	:	:	PUNCT
easat-3054	216	20	2576	2576	NUM
easat-3054	216	21	-	-	SYM
easat-3054	216	22	8484	8484	NUM
easat-3054	216	23	vol	vol	NOUN
easat-3054	216	24	.	.	PROPN
easat-3054	216	25	8	8	NUM
easat-3054	216	26	,	,	PUNCT
easat-3054	216	27	no	no	INTJ
easat-3054	216	28	.	.	NOUN
easat-3054	217	1	6	6	NUM
easat-3054	217	2	:	:	SYM
easat-3054	217	3	4910	4910	NUM
easat-3054	217	4	-	-	SYM
easat-3054	217	5	4919	4919	NUM
easat-3054	217	6	,	,	PUNCT
easat-3054	217	7	2024	2024	NUM
easat-3054	217	8	doi	doi	NOUN
easat-3054	217	9	:	:	PUNCT
easat-3054	217	10	10.55214/25768484.v8i6.3054	10.55214/25768484.v8i6.3054	NUM
easat-3054	217	11	©	©	PROPN
easat-3054	217	12	2024	2024	NUM
easat-3054	217	13	by	by	ADP
easat-3054	217	14	the	the	DET
easat-3054	217	15	authors	author	NOUN
easat-3054	217	16	;	;	PUNCT
easat-3054	217	17	licensee	licensee	PROPN
easat-3054	217	18	learning	learning	NOUN
easat-3054	217	19	gate	gate	VERB
easat-3054	217	20	|(𝐼	|(𝐼	PROPN
easat-3054	217	21	−	−	PROPN
easat-3054	217	22	ℎ)𝛼𝑓(𝑥	ℎ)𝛼𝑓(𝑥	NOUN
easat-3054	217	23	)	)	PUNCT
easat-3054	218	1	+	+	CCONJ
easat-3054	218	2	ℎ𝛼	ℎ𝛼	DET
easat-3054	218	3	𝑓(𝑎	𝑓(𝑎	NUM
easat-3054	218	4	)	)	PUNCT
easat-3054	219	1	+	+	NUM
easat-3054	219	2	𝑓(𝑏	𝑓(𝑏	NOUN
easat-3054	219	3	)	)	PUNCT
easat-3054	219	4	2𝛼	2𝛼	PROPN
easat-3054	219	5	−	−	PROPN
easat-3054	220	1	γ(1	γ(1	NOUN
easat-3054	220	2	+	+	NUM
easat-3054	220	3	𝛼	𝛼	X
easat-3054	220	4	)	)	PUNCT
easat-3054	220	5	(	(	PUNCT
easat-3054	220	6	𝑏	𝑏	PROPN
easat-3054	220	7	−	−	PROPN
easat-3054	220	8	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	220	9	𝑎𝐼𝑏	𝑎𝐼𝑏	NOUN
easat-3054	220	10	∝𝑓(𝑥)|	∝𝑓(𝑥)|	PROPN
easat-3054	220	11	≤	≤	NOUN
easat-3054	220	12	(	(	PUNCT
easat-3054	220	13	γ(1	γ(1	PROPN
easat-3054	220	14	+	+	CCONJ
easat-3054	220	15	𝛼𝑞	𝛼𝑞	PROPN
easat-3054	220	16	)	)	PUNCT
easat-3054	220	17	)	)	PUNCT
easat-3054	220	18	1	1	NUM
easat-3054	221	1	𝑞(𝑏	𝑞(𝑏	NOUN
easat-3054	221	2	−	−	NUM
easat-3054	221	3	𝑎	𝑎	NOUN
easat-3054	221	4	)	)	PUNCT
easat-3054	221	5	∝	∝	PROPN
easat-3054	221	6	𝑞	𝑞	X
easat-3054	221	7	(	(	PUNCT
easat-3054	221	8	γ(1	γ(1	PROPN
easat-3054	221	9	+	+	CCONJ
easat-3054	221	10	(	(	PUNCT
easat-3054	221	11	𝑞	𝑞	X
easat-3054	221	12	+	+	X
easat-3054	221	13	1)𝛼	1)𝛼	NUM
easat-3054	221	14	)	)	PUNCT
easat-3054	221	15	)	)	PUNCT
easat-3054	222	1	1	1	NUM
easat-3054	222	2	𝑞(γ(1	𝑞(γ(1	NOUN
easat-3054	222	3	+	+	NUM
easat-3054	222	4	𝛼	𝛼	X
easat-3054	222	5	)	)	PUNCT
easat-3054	222	6	)	)	PUNCT
easat-3054	222	7	1	1	NUM
easat-3054	222	8	𝑝	𝑝	X
easat-3054	222	9	‖𝑓𝛼‖𝑝	‖𝑓𝛼‖𝑝	NOUN
easat-3054	222	10	,	,	PUNCT
easat-3054	222	11	if	if	SCONJ
easat-3054	222	12	ℎ	ℎ	PROPN
easat-3054	222	13	=	=	SYM
easat-3054	222	14	0	0	NUM
easat-3054	222	15	,	,	PUNCT
easat-3054	222	16	we	we	PRON
easat-3054	222	17	get	get	VERB
easat-3054	222	18	|𝑓(𝑥	|𝑓(𝑥	NOUN
easat-3054	222	19	)	)	PUNCT
easat-3054	222	20	−	−	PROPN
easat-3054	223	1	γ(1	γ(1	PROPN
easat-3054	223	2	+	+	NUM
easat-3054	223	3	𝛼	𝛼	X
easat-3054	223	4	)	)	PUNCT
easat-3054	223	5	(	(	PUNCT
easat-3054	223	6	𝑏	𝑏	PROPN
easat-3054	223	7	−	−	PROPN
easat-3054	223	8	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	223	9	𝑎𝐼𝑏	𝑎𝐼𝑏	NOUN
easat-3054	223	10	∝𝑓(𝑥)|	∝𝑓(𝑥)|	PROPN
easat-3054	223	11	≤	≤	NOUN
easat-3054	223	12	(	(	PUNCT
easat-3054	223	13	γ(1	γ(1	PROPN
easat-3054	223	14	+	+	CCONJ
easat-3054	223	15	𝛼𝑞	𝛼𝑞	PROPN
easat-3054	223	16	)	)	PUNCT
easat-3054	223	17	)	)	PUNCT
easat-3054	223	18	1	1	NUM
easat-3054	224	1	𝑞(𝑏	𝑞(𝑏	NOUN
easat-3054	224	2	−	−	NUM
easat-3054	224	3	𝑎	𝑎	NOUN
easat-3054	224	4	)	)	PUNCT
easat-3054	224	5	∝	∝	PROPN
easat-3054	224	6	𝑞	𝑞	X
easat-3054	224	7	(	(	PUNCT
easat-3054	224	8	γ(1	γ(1	PROPN
easat-3054	224	9	+	+	CCONJ
easat-3054	224	10	(	(	PUNCT
easat-3054	224	11	𝑞	𝑞	X
easat-3054	224	12	+	+	X
easat-3054	224	13	1)𝛼	1)𝛼	NUM
easat-3054	224	14	)	)	PUNCT
easat-3054	224	15	)	)	PUNCT
easat-3054	225	1	1	1	NUM
easat-3054	225	2	𝑞(γ(1	𝑞(γ(1	NOUN
easat-3054	225	3	+	+	NUM
easat-3054	225	4	𝛼	𝛼	X
easat-3054	225	5	)	)	PUNCT
easat-3054	225	6	)	)	PUNCT
easat-3054	225	7	1	1	NUM
easat-3054	225	8	𝑝	𝑝	X
easat-3054	225	9	‖𝑓𝛼‖𝑝	‖𝑓𝛼‖𝑝	PROPN
easat-3054	225	10	,	,	PUNCT
easat-3054	225	11	1	1	NUM
easat-3054	225	12	≤	≤	NUM
easat-3054	225	13	𝑝	𝑝	PROPN
easat-3054	225	14	,	,	PUNCT
easat-3054	225	15	𝑞	𝑞	X
easat-3054	225	16	≤	≤	NOUN
easat-3054	225	17	∞	∞	PROPN
easat-3054	225	18	,	,	PUNCT
easat-3054	225	19	1	1	NUM
easat-3054	225	20	𝑝	𝑝	NOUN
easat-3054	225	21	+	+	NUM
easat-3054	225	22	1	1	NUM
easat-3054	225	23	𝑞	𝑞	NOUN
easat-3054	225	24	=	=	NOUN
easat-3054	225	25	1	1	X
easat-3054	225	26	.	.	PUNCT
easat-3054	225	27	case	case	NOUN
easat-3054	225	28	2	2	NUM
easat-3054	225	29	:	:	PUNCT
easat-3054	225	30	|(𝐼	|(𝐼	PROPN
easat-3054	225	31	−	−	PROPN
easat-3054	225	32	ℎ)𝛼𝑓(𝑥	ℎ)𝛼𝑓(𝑥	VERB
easat-3054	225	33	)	)	PUNCT
easat-3054	225	34	+	+	CCONJ
easat-3054	225	35	ℎ𝛼	ℎ𝛼	DET
easat-3054	225	36	𝑓(𝑎	𝑓(𝑎	NUM
easat-3054	225	37	)	)	PUNCT
easat-3054	225	38	+	+	NUM
easat-3054	225	39	𝑓(𝑏	𝑓(𝑏	NOUN
easat-3054	225	40	)	)	PUNCT
easat-3054	225	41	2𝛼	2𝛼	PROPN
easat-3054	225	42	−	−	PROPN
easat-3054	226	1	γ(1	γ(1	NOUN
easat-3054	226	2	+	+	NUM
easat-3054	226	3	𝛼	𝛼	X
easat-3054	226	4	)	)	PUNCT
easat-3054	226	5	(	(	PUNCT
easat-3054	226	6	𝑏	𝑏	PROPN
easat-3054	226	7	−	−	PROPN
easat-3054	226	8	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	226	9	𝑎𝐼𝑏	𝑎𝐼𝑏	NOUN
easat-3054	226	10	∝𝑓(𝑥)|	∝𝑓(𝑥)|	PROPN
easat-3054	226	11	≤	≤	NUM
easat-3054	226	12	𝐶(𝑃)(γ(1	𝐶(𝑃)(γ(1	NOUN
easat-3054	226	13	+	+	CCONJ
easat-3054	226	14	𝛼𝑞	𝛼𝑞	PROPN
easat-3054	226	15	)	)	PUNCT
easat-3054	226	16	)	)	PUNCT
easat-3054	227	1	1	1	NUM
easat-3054	227	2	𝑞(𝑏	𝑞(𝑏	NOUN
easat-3054	227	3	−	−	NUM
easat-3054	227	4	𝑎	𝑎	NOUN
easat-3054	227	5	)	)	PUNCT
easat-3054	227	6	∝	∝	PROPN
easat-3054	227	7	𝑞	𝑞	X
easat-3054	227	8	(	(	PUNCT
easat-3054	227	9	γ(1	γ(1	PROPN
easat-3054	227	10	+	+	CCONJ
easat-3054	227	11	(	(	PUNCT
easat-3054	227	12	𝑞	𝑞	X
easat-3054	227	13	+	+	X
easat-3054	227	14	1)𝛼	1)𝛼	NUM
easat-3054	227	15	)	)	PUNCT
easat-3054	227	16	)	)	PUNCT
easat-3054	227	17	1	1	NUM
easat-3054	228	1	𝑞(γ(1	𝑞(γ(1	NOUN
easat-3054	228	2	+	+	NUM
easat-3054	228	3	𝛼	𝛼	X
easat-3054	228	4	)	)	PUNCT
easat-3054	228	5	)	)	PUNCT
easat-3054	228	6	1	1	NUM
easat-3054	228	7	𝑝	𝑝	X
easat-3054	228	8	‖𝑓𝛼‖𝑝	‖𝑓𝛼‖𝑝	NOUN
easat-3054	228	9	,	,	PUNCT
easat-3054	228	10	if	if	SCONJ
easat-3054	228	11	ℎ	ℎ	PROPN
easat-3054	228	12	=	=	SYM
easat-3054	228	13	0	0	NUM
easat-3054	228	14	,	,	PUNCT
easat-3054	228	15	we	we	PRON
easat-3054	228	16	get	get	VERB
easat-3054	228	17	|𝑓(𝑥	|𝑓(𝑥	NOUN
easat-3054	228	18	)	)	PUNCT
easat-3054	228	19	−	−	PROPN
easat-3054	229	1	γ(1	γ(1	PROPN
easat-3054	229	2	+	+	NUM
easat-3054	229	3	𝛼	𝛼	X
easat-3054	229	4	)	)	PUNCT
easat-3054	229	5	(	(	PUNCT
easat-3054	229	6	𝑏	𝑏	PROPN
easat-3054	229	7	−	−	PROPN
easat-3054	229	8	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	229	9	𝑎𝐼𝑏	𝑎𝐼𝑏	NOUN
easat-3054	229	10	∝𝑓(𝑥)|	∝𝑓(𝑥)|	PROPN
easat-3054	229	11	≤	≤	NUM
easat-3054	229	12	𝐶(𝑃)(γ(1	𝐶(𝑃)(γ(1	NOUN
easat-3054	229	13	+	+	CCONJ
easat-3054	229	14	𝛼𝑞	𝛼𝑞	PROPN
easat-3054	229	15	)	)	PUNCT
easat-3054	229	16	)	)	PUNCT
easat-3054	230	1	1	1	NUM
easat-3054	230	2	𝑞(𝑏	𝑞(𝑏	NOUN
easat-3054	230	3	−	−	NUM
easat-3054	230	4	𝑎	𝑎	NOUN
easat-3054	230	5	)	)	PUNCT
easat-3054	230	6	∝	∝	PROPN
easat-3054	230	7	𝑞	𝑞	X
easat-3054	230	8	(	(	PUNCT
easat-3054	230	9	γ(1	γ(1	PROPN
easat-3054	230	10	+	+	CCONJ
easat-3054	230	11	(	(	PUNCT
easat-3054	230	12	𝑞	𝑞	X
easat-3054	230	13	+	+	X
easat-3054	230	14	1)𝛼	1)𝛼	NUM
easat-3054	230	15	)	)	PUNCT
easat-3054	230	16	)	)	PUNCT
easat-3054	230	17	1	1	NUM
easat-3054	231	1	𝑞(γ(1	𝑞(γ(1	NOUN
easat-3054	231	2	+	+	NUM
easat-3054	231	3	𝛼	𝛼	X
easat-3054	231	4	)	)	PUNCT
easat-3054	231	5	)	)	PUNCT
easat-3054	231	6	1	1	NUM
easat-3054	231	7	𝑝	𝑝	X
easat-3054	231	8	‖𝑓𝛼‖𝑝	‖𝑓𝛼‖𝑝	PROPN
easat-3054	231	9	,	,	PUNCT
easat-3054	231	10	0	0	NUM
easat-3054	231	11	<	<	X
easat-3054	231	12	𝑃	𝑃	X
easat-3054	231	13	<	<	X
easat-3054	231	14	1	1	NUM
easat-3054	231	15	.	.	PUNCT
easat-3054	231	16	corollary	corollary	ADJ
easat-3054	231	17	3.4	3.4	NUM
easat-3054	231	18	:	:	PUNCT
easat-3054	231	19	if	if	SCONJ
easat-3054	231	20	𝑓	𝑓	PRON
easat-3054	231	21	⊂	⊂	PROPN
easat-3054	231	22	𝑅	𝑅	PROPN
easat-3054	231	23	,	,	PUNCT
easat-3054	231	24	𝑓	𝑓	PRON
easat-3054	231	25	:	:	PUNCT
easat-3054	231	26	𝐼∘	𝐼∘	PROPN
easat-3054	231	27	⊂	⊂	PROPN
easat-3054	231	28	𝑅	𝑅	PROPN
easat-3054	231	29	→	→	SYM
easat-3054	231	30	𝑅𝛼	𝑅𝛼	PROPN
easat-3054	231	31	be	be	AUX
easat-3054	231	32	a	a	DET
easat-3054	231	33	map	map	NOUN
easat-3054	232	1	[	[	X
easat-3054	232	2	𝑎	𝑎	X
easat-3054	232	3	,	,	PUNCT
easat-3054	232	4	𝑏	𝑏	NOUN
easat-3054	232	5	]	]	X
easat-3054	232	6	⊂	⊂	X
easat-3054	232	7	𝐼∘and	𝐼∘and	PUNCT
easat-3054	232	8	𝑓	𝑓	PRON
easat-3054	232	9	∈	∈	PROPN
easat-3054	232	10	𝐿𝑃,𝛼[𝑎	𝐿𝑃,𝛼[𝑎	NOUN
easat-3054	232	11	,	,	PUNCT
easat-3054	232	12	𝑏	𝑏	NOUN
easat-3054	232	13	]	]	PUNCT
easat-3054	232	14	.	.	PUNCT
easat-3054	233	1	then	then	ADV
easat-3054	233	2	(	(	PUNCT
easat-3054	233	3	1	1	X
easat-3054	233	4	)	)	PUNCT
easat-3054	233	5	|𝑓(𝑥	|𝑓(𝑥	NOUN
easat-3054	233	6	)	)	PUNCT
easat-3054	233	7	+	+	NOUN
easat-3054	233	8	𝑓(𝑎	𝑓(𝑎	X
easat-3054	233	9	)	)	PUNCT
easat-3054	233	10	+	+	NUM
easat-3054	233	11	𝑓(𝑏	𝑓(𝑏	NOUN
easat-3054	233	12	)	)	PUNCT
easat-3054	233	13	2𝛼	2𝛼	PROPN
easat-3054	234	1	−	−	PROPN
easat-3054	235	1	γ(1	γ(1	NOUN
easat-3054	235	2	+	+	NUM
easat-3054	235	3	𝛼	𝛼	X
easat-3054	235	4	)	)	PUNCT
easat-3054	235	5	(	(	PUNCT
easat-3054	235	6	𝑏	𝑏	PROPN
easat-3054	235	7	−	−	PROPN
easat-3054	235	8	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	235	9	𝑎𝐼𝑏	𝑎𝐼𝑏	NOUN
easat-3054	235	10	∝𝑓(𝑥)|	∝𝑓(𝑥)|	PROPN
easat-3054	235	11	≤	≤	NOUN
easat-3054	235	12	(	(	PUNCT
easat-3054	235	13	γ(1	γ(1	PROPN
easat-3054	235	14	+	+	CCONJ
easat-3054	235	15	𝛼𝑞	𝛼𝑞	PROPN
easat-3054	235	16	)	)	PUNCT
easat-3054	235	17	)	)	PUNCT
easat-3054	235	18	1	1	NUM
easat-3054	236	1	𝑞(𝑏	𝑞(𝑏	NOUN
easat-3054	236	2	−	−	NUM
easat-3054	236	3	𝑎	𝑎	NOUN
easat-3054	236	4	)	)	PUNCT
easat-3054	236	5	∝	∝	PROPN
easat-3054	236	6	𝑞	𝑞	X
easat-3054	236	7	(	(	PUNCT
easat-3054	236	8	γ(1	γ(1	PROPN
easat-3054	236	9	+	+	CCONJ
easat-3054	236	10	(	(	PUNCT
easat-3054	236	11	𝑞	𝑞	X
easat-3054	236	12	+	+	X
easat-3054	236	13	1)𝛼	1)𝛼	NUM
easat-3054	236	14	)	)	PUNCT
easat-3054	236	15	)	)	PUNCT
easat-3054	237	1	1	1	NUM
easat-3054	237	2	𝑞(γ(1	𝑞(γ(1	NOUN
easat-3054	237	3	+	+	NUM
easat-3054	237	4	𝛼	𝛼	X
easat-3054	237	5	)	)	PUNCT
easat-3054	237	6	)	)	PUNCT
easat-3054	237	7	1	1	NUM
easat-3054	237	8	𝑝	𝑝	PROPN
easat-3054	237	9	‖𝑓𝛼‖𝑝	‖𝑓𝛼‖𝑝	PROPN
easat-3054	237	10	,	,	PUNCT
easat-3054	237	11	1	1	NUM
easat-3054	237	12	≤	≤	NUM
easat-3054	237	13	𝑝	𝑝	PROPN
easat-3054	237	14	,	,	PUNCT
easat-3054	237	15	𝑞	𝑞	X
easat-3054	237	16	≤	≤	NOUN
easat-3054	237	17	∞	∞	PROPN
easat-3054	237	18	,	,	PUNCT
easat-3054	237	19	1	1	NUM
easat-3054	237	20	𝑝	𝑝	NOUN
easat-3054	237	21	+	+	NUM
easat-3054	237	22	1	1	NUM
easat-3054	237	23	𝑞	𝑞	NOUN
easat-3054	237	24	=	=	NOUN
easat-3054	237	25	1	1	X
easat-3054	237	26	.	.	PUNCT
easat-3054	237	27	(	(	PUNCT
easat-3054	237	28	2	2	X
easat-3054	237	29	)	)	PUNCT
easat-3054	237	30	|𝑓(𝑥	|𝑓(𝑥	NOUN
easat-3054	237	31	)	)	PUNCT
easat-3054	237	32	+	+	NOUN
easat-3054	237	33	𝑓(𝑎	𝑓(𝑎	X
easat-3054	237	34	)	)	PUNCT
easat-3054	237	35	+	+	NUM
easat-3054	237	36	𝑓(𝑏	𝑓(𝑏	NOUN
easat-3054	237	37	)	)	PUNCT
easat-3054	237	38	2𝛼	2𝛼	PROPN
easat-3054	237	39	−	−	PROPN
easat-3054	238	1	γ(1	γ(1	NOUN
easat-3054	238	2	+	+	NUM
easat-3054	238	3	𝛼	𝛼	X
easat-3054	238	4	)	)	PUNCT
easat-3054	238	5	(	(	PUNCT
easat-3054	238	6	𝑏	𝑏	PROPN
easat-3054	238	7	−	−	PROPN
easat-3054	238	8	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	238	9	𝑎𝐼𝑏	𝑎𝐼𝑏	NOUN
easat-3054	238	10	∝𝑓(𝑥)|	∝𝑓(𝑥)|	SYM
easat-3054	238	11	≤	≤	NUM
easat-3054	238	12	𝐶(𝑝)(γ(1	𝐶(𝑝)(γ(1	NUM
easat-3054	238	13	+	+	CCONJ
easat-3054	238	14	𝛼𝑞	𝛼𝑞	X
easat-3054	238	15	)	)	PUNCT
easat-3054	238	16	)	)	PUNCT
easat-3054	238	17	1	1	NUM
easat-3054	238	18	𝑞(𝑏	𝑞(𝑏	NOUN
easat-3054	238	19	−	−	NUM
easat-3054	238	20	𝑎	𝑎	NOUN
easat-3054	238	21	)	)	PUNCT
easat-3054	238	22	∝	∝	PROPN
easat-3054	238	23	𝑞	𝑞	X
easat-3054	238	24	(	(	PUNCT
easat-3054	238	25	γ(1	γ(1	PROPN
easat-3054	238	26	+	+	CCONJ
easat-3054	238	27	(	(	PUNCT
easat-3054	238	28	𝑞	𝑞	X
easat-3054	238	29	+	+	X
easat-3054	238	30	1)𝛼	1)𝛼	NUM
easat-3054	238	31	)	)	PUNCT
easat-3054	238	32	)	)	PUNCT
easat-3054	238	33	1	1	NUM
easat-3054	239	1	𝑞(γ(1	𝑞(γ(1	NOUN
easat-3054	239	2	+	+	NUM
easat-3054	239	3	𝛼	𝛼	X
easat-3054	239	4	)	)	PUNCT
easat-3054	239	5	)	)	PUNCT
easat-3054	239	6	1	1	NUM
easat-3054	239	7	𝑝	𝑝	PROPN
easat-3054	239	8	‖𝑓𝛼‖𝑝	‖𝑓𝛼‖𝑝	PROPN
easat-3054	239	9	,	,	PUNCT
easat-3054	239	10	0	0	NUM
easat-3054	239	11	<	<	X
easat-3054	239	12	𝑝	𝑝	X
easat-3054	239	13	<	<	X
easat-3054	239	14	1	1	NUM
easat-3054	239	15	.	.	PUNCT
easat-3054	240	1	proof	proof	NOUN
easat-3054	240	2	:	:	PUNCT
easat-3054	240	3	by	by	ADP
easat-3054	240	4	using	use	VERB
easat-3054	240	5	theorem	theorem	NOUN
easat-3054	240	6	3.2	3.2	NUM
easat-3054	240	7	,	,	PUNCT
easat-3054	240	8	we	we	PRON
easat-3054	240	9	get	get	VERB
easat-3054	240	10	case	case	NOUN
easat-3054	240	11	1	1	NUM
easat-3054	240	12	:	:	PUNCT
easat-3054	240	13	|(𝐼	|(𝐼	PROPN
easat-3054	240	14	−	−	PROPN
easat-3054	240	15	ℎ)𝛼𝑓(𝑥	ℎ)𝛼𝑓(𝑥	VERB
easat-3054	240	16	)	)	PUNCT
easat-3054	241	1	+	+	CCONJ
easat-3054	241	2	ℎ𝛼	ℎ𝛼	DET
easat-3054	241	3	𝑓(𝑎	𝑓(𝑎	NUM
easat-3054	241	4	)	)	PUNCT
easat-3054	242	1	+	+	NUM
easat-3054	242	2	𝑓(𝑏	𝑓(𝑏	NOUN
easat-3054	242	3	)	)	PUNCT
easat-3054	242	4	2𝛼	2𝛼	PROPN
easat-3054	242	5	−	−	PROPN
easat-3054	243	1	γ(1	γ(1	NOUN
easat-3054	243	2	+	+	NUM
easat-3054	243	3	𝛼	𝛼	X
easat-3054	243	4	)	)	PUNCT
easat-3054	243	5	(	(	PUNCT
easat-3054	243	6	𝑏	𝑏	PROPN
easat-3054	243	7	−	−	PROPN
easat-3054	243	8	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	243	9	𝑎𝐼𝑏	𝑎𝐼𝑏	NOUN
easat-3054	243	10	∝𝑓(𝑥)|	∝𝑓(𝑥)|	PROPN
easat-3054	243	11	≤	≤	NOUN
easat-3054	243	12	(	(	PUNCT
easat-3054	243	13	γ(1	γ(1	PROPN
easat-3054	243	14	+	+	CCONJ
easat-3054	243	15	𝛼𝑞	𝛼𝑞	PROPN
easat-3054	243	16	)	)	PUNCT
easat-3054	243	17	)	)	PUNCT
easat-3054	243	18	1	1	NUM
easat-3054	244	1	𝑞(𝑏	𝑞(𝑏	NOUN
easat-3054	244	2	−	−	NUM
easat-3054	244	3	𝑎	𝑎	NOUN
easat-3054	244	4	)	)	PUNCT
easat-3054	244	5	∝	∝	PROPN
easat-3054	244	6	𝑞	𝑞	X
easat-3054	244	7	(	(	PUNCT
easat-3054	244	8	γ(1	γ(1	PROPN
easat-3054	244	9	+	+	CCONJ
easat-3054	244	10	(	(	PUNCT
easat-3054	244	11	𝑞	𝑞	X
easat-3054	244	12	+	+	X
easat-3054	244	13	1)𝛼	1)𝛼	NUM
easat-3054	244	14	)	)	PUNCT
easat-3054	244	15	)	)	PUNCT
easat-3054	245	1	1	1	NUM
easat-3054	245	2	𝑞(γ(1	𝑞(γ(1	NOUN
easat-3054	245	3	+	+	NUM
easat-3054	245	4	𝛼	𝛼	X
easat-3054	245	5	)	)	PUNCT
easat-3054	245	6	)	)	PUNCT
easat-3054	245	7	1	1	NUM
easat-3054	245	8	𝑝	𝑝	X
easat-3054	245	9	‖𝑓𝛼‖𝑝	‖𝑓𝛼‖𝑝	NOUN
easat-3054	245	10	,	,	PUNCT
easat-3054	245	11	if	if	SCONJ
easat-3054	245	12	ℎ	ℎ	PROPN
easat-3054	245	13	=	=	SYM
easat-3054	245	14	1	1	NUM
easat-3054	245	15	,	,	PUNCT
easat-3054	245	16	we	we	PRON
easat-3054	245	17	get	get	VERB
easat-3054	245	18	|𝑓(𝑥	|𝑓(𝑥	NOUN
easat-3054	245	19	)	)	PUNCT
easat-3054	245	20	+	+	CCONJ
easat-3054	245	21	𝑓(𝑎	𝑓(𝑎	X
easat-3054	245	22	)	)	PUNCT
easat-3054	246	1	+	+	NUM
easat-3054	246	2	𝑓(𝑏	𝑓(𝑏	NOUN
easat-3054	246	3	)	)	PUNCT
easat-3054	246	4	2𝛼	2𝛼	PROPN
easat-3054	246	5	−	−	PROPN
easat-3054	247	1	γ(1	γ(1	NOUN
easat-3054	247	2	+	+	NUM
easat-3054	247	3	𝛼	𝛼	X
easat-3054	247	4	)	)	PUNCT
easat-3054	247	5	(	(	PUNCT
easat-3054	247	6	𝑏	𝑏	PROPN
easat-3054	247	7	−	−	PROPN
easat-3054	247	8	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	247	9	𝑎𝐼𝑏	𝑎𝐼𝑏	NOUN
easat-3054	247	10	∝𝑓(𝑥)|	∝𝑓(𝑥)|	PROPN
easat-3054	247	11	≤	≤	NOUN
easat-3054	247	12	(	(	PUNCT
easat-3054	247	13	γ(1	γ(1	PROPN
easat-3054	247	14	+	+	CCONJ
easat-3054	247	15	𝛼𝑞	𝛼𝑞	PROPN
easat-3054	247	16	)	)	PUNCT
easat-3054	247	17	)	)	PUNCT
easat-3054	247	18	1	1	NUM
easat-3054	248	1	𝑞(𝑏	𝑞(𝑏	NOUN
easat-3054	248	2	−	−	NUM
easat-3054	248	3	𝑎	𝑎	NOUN
easat-3054	248	4	)	)	PUNCT
easat-3054	248	5	∝	∝	PROPN
easat-3054	248	6	𝑞	𝑞	X
easat-3054	248	7	(	(	PUNCT
easat-3054	248	8	γ(1	γ(1	PROPN
easat-3054	248	9	+	+	CCONJ
easat-3054	248	10	(	(	PUNCT
easat-3054	248	11	𝑞	𝑞	X
easat-3054	248	12	+	+	X
easat-3054	248	13	1)𝛼	1)𝛼	NUM
easat-3054	248	14	)	)	PUNCT
easat-3054	248	15	)	)	PUNCT
easat-3054	249	1	1	1	NUM
easat-3054	249	2	𝑞(γ(1	𝑞(γ(1	NOUN
easat-3054	249	3	+	+	NUM
easat-3054	249	4	𝛼	𝛼	X
easat-3054	249	5	)	)	PUNCT
easat-3054	249	6	)	)	PUNCT
easat-3054	249	7	1	1	NUM
easat-3054	249	8	𝑝	𝑝	X
easat-3054	249	9	‖𝑓𝛼‖𝑝	‖𝑓𝛼‖𝑝	PROPN
easat-3054	249	10	,	,	PUNCT
easat-3054	249	11	1	1	NUM
easat-3054	249	12	≤	≤	NUM
easat-3054	249	13	𝑝	𝑝	PROPN
easat-3054	249	14	,	,	PUNCT
easat-3054	249	15	𝑞	𝑞	X
easat-3054	249	16	≤	≤	NOUN
easat-3054	249	17	∞	∞	PROPN
easat-3054	249	18	,	,	PUNCT
easat-3054	249	19	1	1	NUM
easat-3054	249	20	𝑝	𝑝	NOUN
easat-3054	249	21	+	+	NUM
easat-3054	249	22	1	1	NUM
easat-3054	249	23	𝑞	𝑞	NOUN
easat-3054	249	24	=	=	NOUN
easat-3054	249	25	1	1	X
easat-3054	249	26	.	.	PUNCT
easat-3054	249	27	case	case	NOUN
easat-3054	249	28	2	2	NUM
easat-3054	249	29	:	:	SYM
easat-3054	249	30	4919	4919	NUM
easat-3054	249	31	edelweiss	edelweiss	PROPN
easat-3054	249	32	applied	apply	VERB
easat-3054	249	33	science	science	NOUN
easat-3054	249	34	and	and	CCONJ
easat-3054	249	35	technology	technology	NOUN
easat-3054	249	36	issn	issn	PROPN
easat-3054	249	37	:	:	PUNCT
easat-3054	249	38	2576	2576	NUM
easat-3054	249	39	-	-	SYM
easat-3054	249	40	8484	8484	NUM
easat-3054	249	41	vol	vol	NOUN
easat-3054	249	42	.	.	PROPN
easat-3054	250	1	8	8	NUM
easat-3054	250	2	,	,	PUNCT
easat-3054	250	3	no	no	INTJ
easat-3054	250	4	.	.	NOUN
easat-3054	251	1	6	6	NUM
easat-3054	251	2	:	:	SYM
easat-3054	251	3	4910	4910	NUM
easat-3054	251	4	-	-	SYM
easat-3054	251	5	4919	4919	NUM
easat-3054	251	6	,	,	PUNCT
easat-3054	251	7	2024	2024	NUM
easat-3054	251	8	doi	doi	NOUN
easat-3054	251	9	:	:	PUNCT
easat-3054	251	10	10.55214/25768484.v8i6.3054	10.55214/25768484.v8i6.3054	NUM
easat-3054	251	11	©	©	PROPN
easat-3054	251	12	2024	2024	NUM
easat-3054	251	13	by	by	ADP
easat-3054	251	14	the	the	DET
easat-3054	251	15	authors	author	NOUN
easat-3054	251	16	;	;	PUNCT
easat-3054	251	17	licensee	licensee	PROPN
easat-3054	251	18	learning	learning	NOUN
easat-3054	251	19	gate	gate	VERB
easat-3054	251	20	|(𝐼	|(𝐼	PROPN
easat-3054	251	21	−	−	PROPN
easat-3054	251	22	ℎ)𝛼𝑓(𝑥	ℎ)𝛼𝑓(𝑥	NOUN
easat-3054	251	23	)	)	PUNCT
easat-3054	252	1	+	+	CCONJ
easat-3054	252	2	ℎ𝛼	ℎ𝛼	DET
easat-3054	252	3	𝑓(𝑎	𝑓(𝑎	NUM
easat-3054	252	4	)	)	PUNCT
easat-3054	253	1	+	+	NUM
easat-3054	253	2	𝑓(𝑏	𝑓(𝑏	NOUN
easat-3054	253	3	)	)	PUNCT
easat-3054	253	4	2𝛼	2𝛼	PROPN
easat-3054	253	5	−	−	PROPN
easat-3054	254	1	γ(1	γ(1	NOUN
easat-3054	254	2	+	+	NUM
easat-3054	254	3	𝛼	𝛼	X
easat-3054	254	4	)	)	PUNCT
easat-3054	254	5	(	(	PUNCT
easat-3054	254	6	𝑏	𝑏	PROPN
easat-3054	254	7	−	−	PROPN
easat-3054	254	8	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	254	9	𝑎𝐼𝑏	𝑎𝐼𝑏	NOUN
easat-3054	254	10	∝𝑓(𝑥)|	∝𝑓(𝑥)|	PROPN
easat-3054	254	11	≤	≤	NUM
easat-3054	254	12	𝐶(𝑃)(γ(1	𝐶(𝑃)(γ(1	NOUN
easat-3054	254	13	+	+	CCONJ
easat-3054	254	14	𝛼𝑞	𝛼𝑞	PROPN
easat-3054	254	15	)	)	PUNCT
easat-3054	254	16	)	)	PUNCT
easat-3054	255	1	1	1	NUM
easat-3054	255	2	𝑞(𝑏	𝑞(𝑏	NOUN
easat-3054	255	3	−	−	NUM
easat-3054	255	4	𝑎	𝑎	NOUN
easat-3054	255	5	)	)	PUNCT
easat-3054	255	6	∝	∝	PROPN
easat-3054	255	7	𝑞	𝑞	X
easat-3054	255	8	(	(	PUNCT
easat-3054	255	9	γ(1	γ(1	PROPN
easat-3054	255	10	+	+	CCONJ
easat-3054	255	11	(	(	PUNCT
easat-3054	255	12	𝑞	𝑞	X
easat-3054	255	13	+	+	X
easat-3054	255	14	1)𝛼	1)𝛼	NUM
easat-3054	255	15	)	)	PUNCT
easat-3054	255	16	)	)	PUNCT
easat-3054	255	17	1	1	NUM
easat-3054	256	1	𝑞(γ(1	𝑞(γ(1	NOUN
easat-3054	256	2	+	+	NUM
easat-3054	256	3	𝛼	𝛼	X
easat-3054	256	4	)	)	PUNCT
easat-3054	256	5	)	)	PUNCT
easat-3054	256	6	1	1	NUM
easat-3054	256	7	𝑝	𝑝	X
easat-3054	256	8	‖𝑓𝛼‖𝑝	‖𝑓𝛼‖𝑝	NOUN
easat-3054	256	9	,	,	PUNCT
easat-3054	256	10	if	if	SCONJ
easat-3054	256	11	ℎ	ℎ	PROPN
easat-3054	256	12	=	=	SYM
easat-3054	256	13	1	1	NUM
easat-3054	256	14	,	,	PUNCT
easat-3054	256	15	we	we	PRON
easat-3054	256	16	get	get	VERB
easat-3054	256	17	|𝑓(𝑥	|𝑓(𝑥	NOUN
easat-3054	256	18	)	)	PUNCT
easat-3054	256	19	+	+	CCONJ
easat-3054	256	20	𝑓(𝑎	𝑓(𝑎	X
easat-3054	256	21	)	)	PUNCT
easat-3054	257	1	+	+	NUM
easat-3054	257	2	𝑓(𝑏	𝑓(𝑏	NOUN
easat-3054	257	3	)	)	PUNCT
easat-3054	257	4	2𝛼	2𝛼	PROPN
easat-3054	257	5	−	−	PROPN
easat-3054	258	1	γ(1	γ(1	NOUN
easat-3054	258	2	+	+	NUM
easat-3054	258	3	𝛼	𝛼	X
easat-3054	258	4	)	)	PUNCT
easat-3054	258	5	(	(	PUNCT
easat-3054	258	6	𝑏	𝑏	PROPN
easat-3054	258	7	−	−	PROPN
easat-3054	258	8	𝑎)𝛼	𝑎)𝛼	ADJ
easat-3054	258	9	𝑎𝐼𝑏	𝑎𝐼𝑏	NOUN
easat-3054	258	10	∝𝑓(𝑥)|	∝𝑓(𝑥)|	PROPN
easat-3054	258	11	≤	≤	NUM
easat-3054	258	12	𝐶(𝑃)(γ(1	𝐶(𝑃)(γ(1	NOUN
easat-3054	258	13	+	+	CCONJ
easat-3054	258	14	𝛼𝑞	𝛼𝑞	PROPN
easat-3054	258	15	)	)	PUNCT
easat-3054	258	16	)	)	PUNCT
easat-3054	259	1	1	1	NUM
easat-3054	259	2	𝑞(𝑏	𝑞(𝑏	NOUN
easat-3054	259	3	−	−	NUM
easat-3054	259	4	𝑎	𝑎	NOUN
easat-3054	259	5	)	)	PUNCT
easat-3054	259	6	∝	∝	PROPN
easat-3054	259	7	𝑞	𝑞	X
easat-3054	259	8	(	(	PUNCT
easat-3054	259	9	γ(1	γ(1	PROPN
easat-3054	259	10	+	+	CCONJ
easat-3054	259	11	(	(	PUNCT
easat-3054	259	12	𝑞	𝑞	X
easat-3054	259	13	+	+	X
easat-3054	259	14	1)𝛼	1)𝛼	NUM
easat-3054	259	15	)	)	PUNCT
easat-3054	259	16	)	)	PUNCT
easat-3054	259	17	1	1	NUM
easat-3054	260	1	𝑞(γ(1	𝑞(γ(1	NOUN
easat-3054	260	2	+	+	NUM
easat-3054	260	3	𝛼	𝛼	X
easat-3054	260	4	)	)	PUNCT
easat-3054	260	5	)	)	PUNCT
easat-3054	260	6	1	1	NUM
easat-3054	260	7	𝑝	𝑝	X
easat-3054	260	8	‖𝑓𝛼‖𝑝	‖𝑓𝛼‖𝑝	NOUN
easat-3054	260	9	0	0	PUNCT
easat-3054	260	10	<	<	X
easat-3054	260	11	𝑃	𝑃	X
easat-3054	260	12	<	<	X
easat-3054	260	13	1	1	NUM
easat-3054	260	14	.	.	PUNCT
easat-3054	261	1	copyright	copyright	NOUN
easat-3054	261	2	:	:	PUNCT
easat-3054	261	3	©	©	PROPN
easat-3054	261	4	2024	2024	NUM
easat-3054	261	5	by	by	ADP
easat-3054	261	6	the	the	DET
easat-3054	261	7	authors	author	NOUN
easat-3054	261	8	.	.	PUNCT
easat-3054	262	1	this	this	DET
easat-3054	262	2	article	article	NOUN
easat-3054	262	3	is	be	AUX
easat-3054	262	4	an	an	DET
easat-3054	262	5	open	open	ADJ
easat-3054	262	6	access	access	NOUN
easat-3054	262	7	article	article	NOUN
easat-3054	262	8	distributed	distribute	VERB
easat-3054	262	9	under	under	ADP
easat-3054	262	10	the	the	DET
easat-3054	262	11	terms	term	NOUN
easat-3054	262	12	and	and	CCONJ
easat-3054	262	13	conditions	condition	NOUN
easat-3054	262	14	of	of	ADP
easat-3054	262	15	the	the	DET
easat-3054	262	16	creative	creative	ADJ
easat-3054	262	17	commons	common	NOUN
easat-3054	262	18	attribution	attribution	NOUN
easat-3054	262	19	(	(	PUNCT
easat-3054	262	20	cc	cc	NOUN
easat-3054	262	21	by	by	ADP
easat-3054	262	22	)	)	PUNCT
easat-3054	262	23	license	license	NOUN
easat-3054	262	24	(	(	PUNCT
easat-3054	262	25	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
easat-3054	262	26	)	)	PUNCT
easat-3054	262	27	.	.	PUNCT
easat-3054	263	1	references	reference	NOUN
easat-3054	263	2	[	[	X
easat-3054	263	3	1	1	NUM
easat-3054	263	4	]	]	PUNCT
easat-3054	263	5	b.	b.	PROPN
easat-3054	263	6	meftah	meftah	PROPN
easat-3054	263	7	&	&	CCONJ
easat-3054	263	8	boukerrioua	boukerrioua	PROPN
easat-3054	263	9	khaled	khaled	PROPN
easat-3054	263	10	(	(	PUNCT
easat-3054	263	11	2017	2017	NUM
easat-3054	263	12	)	)	PUNCT
easat-3054	263	13	some	some	DET
easat-3054	263	14	new	new	ADJ
easat-3054	263	15	ostrowski	ostrowski	ADJ
easat-3054	263	16	type	type	NOUN
easat-3054	263	17	inequalities	inequality	NOUN
easat-3054	263	18	on	on	ADP
easat-3054	263	19	time	time	NOUN
easat-3054	263	20	scales	scale	NOUN
easat-3054	263	21	for	for	ADP
easat-3054	263	22	functions	function	NOUN
easat-3054	263	23	of	of	ADP
easat-3054	263	24	two	two	NUM
easat-3054	263	25	independent	independent	ADJ
easat-3054	263	26	variables	variable	NOUN
easat-3054	263	27	,	,	PUNCT
easat-3054	263	28	journal	journal	NOUN
easat-3054	263	29	of	of	ADP
easat-3054	263	30	interdisciplinary	interdisciplinary	ADJ
easat-3054	263	31	mathematics	mathematic	NOUN
easat-3054	263	32	,	,	PUNCT
easat-3054	263	33	20:2	20:2	NUM
easat-3054	263	34	,	,	PUNCT
easat-3054	263	35	397	397	NUM
easat-3054	263	36	-	-	SYM
easat-3054	263	37	415	415	NUM
easat-3054	263	38	,	,	PUNCT
easat-3054	263	39	doi	doi	NOUN
easat-3054	263	40	:	:	PUNCT
easat-3054	263	41	10.1080/09720502.2015.1026463	10.1080/09720502.2015.1026463	NUM
easat-3054	263	42	.	.	PUNCT
easat-3054	264	1	[	[	X
easat-3054	264	2	2	2	NUM
easat-3054	264	3	]	]	X
easat-3054	264	4	b.	b.	PROPN
easat-3054	264	5	meftah	meftah	PROPN
easat-3054	264	6	,	,	PUNCT
easat-3054	264	7	m.	m.	NOUN
easat-3054	264	8	merad	merad	PROPN
easat-3054	264	9	&	&	CCONJ
easat-3054	264	10	a.	a.	PROPN
easat-3054	264	11	souahi	souahi	PROPN
easat-3054	264	12	(	(	PUNCT
easat-3054	264	13	2019	2019	NUM
easat-3054	264	14	)	)	PUNCT
easat-3054	264	15	fractional	fractional	ADJ
easat-3054	264	16	ostrowski	ostrowski	ADJ
easat-3054	264	17	type	type	NOUN
easat-3054	264	18	inequalities	inequality	NOUN
easat-3054	264	19	for	for	ADP
easat-3054	264	20	functions	function	NOUN
easat-3054	264	21	whose	whose	DET
easat-3054	264	22	mixed	mixed	ADJ
easat-3054	264	23	derivatives	derivative	NOUN
easat-3054	264	24	are	be	AUX
easat-3054	264	25	prequasiinvex	prequasiinvex	NOUN
easat-3054	264	26	functions	function	NOUN
easat-3054	264	27	,	,	PUNCT
easat-3054	264	28	journal	journal	NOUN
easat-3054	264	29	of	of	ADP
easat-3054	264	30	interdisciplinary	interdisciplinary	ADJ
easat-3054	264	31	mathematics	mathematic	NOUN
easat-3054	264	32	,	,	PUNCT
easat-3054	264	33	22:6	22:6	NUM
easat-3054	264	34	,	,	PUNCT
easat-3054	264	35	951	951	NUM
easat-3054	264	36	-	-	SYM
easat-3054	264	37	967	967	NUM
easat-3054	264	38	,	,	PUNCT
easat-3054	264	39	doi	doi	NOUN
easat-3054	264	40	:	:	PUNCT
easat-3054	264	41	10.1080/09720502.2019.1696562	10.1080/09720502.2019.1696562	NUM
easat-3054	264	42	.	.	PUNCT
easat-3054	265	1	[	[	X
easat-3054	265	2	3	3	X
easat-3054	265	3	]	]	X
easat-3054	265	4	eman	eman	PROPN
easat-3054	265	5	samir	samir	PROPN
easat-3054	265	6	bhayah	bhayah	PROPN
easat-3054	265	7	,	,	PUNCT
easat-3054	265	8	"	"	PUNCT
easat-3054	265	9	a	a	DET
easat-3054	265	10	study	study	NOUN
easat-3054	265	11	on	on	ADP
easat-3054	265	12	approximations	approximation	NOUN
easat-3054	265	13	of	of	ADP
easat-3054	265	14	bounded	bounded	ADJ
easat-3054	265	15	measurable	measurable	ADJ
easat-3054	265	16	functions	function	NOUN
easat-3054	265	17	with	with	ADP
easat-3054	265	18	sone	sone	NOUN
easat-3054	265	19	discrete	discrete	ADJ
easat-3054	265	20	series	series	NOUN
easat-3054	265	21	in	in	ADP
easat-3054	265	22	lp	lp	PROPN
easat-3054	265	23	spaces	space	NOUN
easat-3054	265	24	(	(	PUNCT
easat-3054	265	25	0	0	NUM
easat-3054	265	26	<	<	X
easat-3054	265	27	p	p	X
easat-3054	265	28	thesis	thesis	NOUN
easat-3054	265	29	,	,	PUNCT
easat-3054	265	30	baghdad	baghdad	PROPN
easat-3054	265	31	,	,	PUNCT
easat-3054	265	32	1999	1999	NUM
easat-3054	265	33	.	.	PUNCT
easat-3054	266	1	[	[	X
easat-3054	266	2	4	4	NUM
easat-3054	266	3	]	]	X
easat-3054	266	4	g	g	PROPN
easat-3054	266	5	-	-	PUNCT
easat-3054	266	6	s.	s.	PROPN
easat-3054	266	7	chen	chen	PROPN
easat-3054	266	8	,	,	PUNCT
easat-3054	266	9	generalizations	generalization	NOUN
easat-3054	266	10	of	of	ADP
easat-3054	266	11	hölder	hölder	PROPN
easat-3054	266	12	’s	’s	PART
easat-3054	266	13	and	and	CCONJ
easat-3054	266	14	some	some	DET
easat-3054	266	15	related	relate	VERB
easat-3054	266	16	integral	integral	ADJ
easat-3054	266	17	inequalities	inequality	NOUN
easat-3054	266	18	on	on	ADP
easat-3054	266	19	fractal	fractal	ADJ
easat-3054	266	20	space	space	NOUN
easat-3054	266	21	,	,	PUNCT
easat-3054	266	22	journal	journal	NOUN
easat-3054	266	23	of	of	ADP
easat-3054	266	24	function	function	NOUN
easat-3054	266	25	spaces	space	NOUN
easat-3054	266	26	and	and	CCONJ
easat-3054	266	27	applications	application	NOUN
easat-3054	266	28	volume	volume	NOUN
easat-3054	266	29	2013	2013	NUM
easat-3054	266	30	,	,	PUNCT
easat-3054	266	31	article	article	NOUN
easat-3054	266	32	i	i	PROPN
easat-3054	266	33	d	d	PROPN
easat-3054	266	34	198405	198405	NUM
easat-3054	266	35	,	,	PUNCT
easat-3054	266	36	9	9	NUM
easat-3054	266	37	pages	page	NOUN
easat-3054	266	38	.	.	PUNCT
easat-3054	267	1	[	[	X
easat-3054	267	2	5	5	NUM
easat-3054	267	3	]	]	X
easat-3054	267	4	m.w.alomari	m.w.alomari	NOUN
easat-3054	267	5	and	and	CCONJ
easat-3054	267	6	m.darus	m.darus	VERB
easat-3054	267	7	some	some	DET
easat-3054	267	8	ostromski	ostromski	NOUN
easat-3054	267	9	’s	’s	PART
easat-3054	267	10	type	type	NOUN
easat-3054	267	11	inequalities	inequality	NOUN
easat-3054	267	12	for	for	ADP
easat-3054	267	13	convex	convex	NOUN
easat-3054	267	14	functions	function	NOUN
easat-3054	267	15	mith	mith	ADP
easat-3054	267	16	application	application	NOUN
easat-3054	267	17	,	,	PUNCT
easat-3054	267	18	rgmia	rgmia	NOUN
easat-3054	267	19	res	re	NOUN
easat-3054	267	20	.	.	PUNCT
easat-3054	267	21	rep	rep	PROPN
easat-3054	267	22	.	.	PROPN
easat-3054	267	23	coll	coll	PROPN
easat-3054	267	24	.	.	PUNCT
easat-3054	268	1	13(1	13(1	NUM
easat-3054	268	2	)	)	PUNCT
easat-3054	268	3	2010	2010	NUM
easat-3054	268	4	,	,	PUNCT
easat-3054	268	5	art	art	NOUN
easat-3054	268	6	.	.	PUNCT
easat-3054	269	1	[	[	X
easat-3054	269	2	6	6	NUM
easat-3054	269	3	]	]	SYM
easat-3054	269	4	n.s.barnett	n.s.barnett	NOUN
easat-3054	269	5	and	and	CCONJ
easat-3054	269	6	s.s.dragomir	s.s.dragomir	NOUN
easat-3054	269	7	,	,	PUNCT
easat-3054	269	8	an	an	DET
easat-3054	269	9	ostromski	ostromski	ADJ
easat-3054	269	10	type	type	NOUN
easat-3054	269	11	inequality	inequality	NOUN
easat-3054	269	12	for	for	ADP
easat-3054	269	13	double	double	ADJ
easat-3054	269	14	integrals	integral	NOUN
easat-3054	269	15	and	and	CCONJ
easat-3054	269	16	applications	application	NOUN
easat-3054	269	17	for	for	ADP
easat-3054	269	18	cubature	cubature	ADJ
easat-3054	269	19	formulae	formulae	NOUN
easat-3054	269	20	,	,	PUNCT
easat-3054	269	21	soochow	soochow	PROPN
easat-3054	269	22	j.	j.	PROPN
easat-3054	269	23	math	math	PROPN
easat-3054	269	24	.	.	PUNCT
easat-3054	269	25	,	,	PUNCT
easat-3054	269	26	27(1	27(1	NUM
easat-3054	269	27	)	)	PUNCT
easat-3054	269	28	,	,	PUNCT
easat-3054	269	29	(	(	PUNCT
easat-3054	269	30	2001	2001	NUM
easat-3054	269	31	)	)	PUNCT
easat-3054	269	32	,	,	PUNCT
easat-3054	269	33	109	109	NUM
easat-3054	269	34	-	-	SYM
easat-3054	269	35	114	114	NUM
easat-3054	269	36	.	.	PUNCT
easat-3054	270	1	[	[	X
easat-3054	270	2	7	7	X
easat-3054	270	3	]	]	PUNCT
easat-3054	270	4	nadiha	nadiha	NOUN
easat-3054	270	5	abed	abe	VERB
easat-3054	270	6	habeeb	habeeb	PROPN
easat-3054	270	7	and	and	CCONJ
easat-3054	270	8	eman	eman	PROPN
easat-3054	270	9	samir	samir	PROPN
easat-3054	270	10	bhaya	bhaya	PROPN
easat-3054	270	11	,	,	PUNCT
easat-3054	270	12	a	a	DET
easat-3054	270	13	modified	modified	ADJ
easat-3054	270	14	ostrowski	ostrowski	ADJ
easat-3054	270	15	inequality	inequality	NOUN
easat-3054	270	16	with	with	ADP
easat-3054	270	17	random	random	ADJ
easat-3054	270	18	variable	variable	ADJ
easat-3054	270	19	application	application	NOUN
easat-3054	270	20	on	on	ADP
easat-3054	270	21	lp[a	lp[a	PROPN
easat-3054	270	22	,	,	PUNCT
easat-3054	270	23	b],0	b],0	X
easat-3054	270	24	<	<	X
easat-3054	270	25	p<1,spaces	p<1,space	NOUN
easat-3054	270	26	,	,	PUNCT
easat-3054	270	27	international	international	ADJ
easat-3054	270	28	journal	journal	NOUN
easat-3054	270	29	of	of	ADP
easat-3054	270	30	mechanical	mechanical	ADJ
easat-3054	270	31	engineering	engineering	NOUN
easat-3054	270	32	,	,	PUNCT
easat-3054	270	33	vol	vol	NOUN
easat-3054	270	34	.	.	PROPN
easat-3054	270	35	7	7	NUM
easat-3054	271	1	no	no	NOUN
easat-3054	271	2	.	.	NOUN
easat-3054	271	3	3	3	NUM
easat-3054	271	4	march	march	NOUN
easat-3054	271	5	,	,	PUNCT
easat-3054	271	6	2022	2022	NUM
easat-3054	272	1	[	[	X
easat-3054	272	2	8	8	X
easat-3054	272	3	]	]	PUNCT
easat-3054	272	4	nadiha	nadiha	NOUN
easat-3054	272	5	abed	abe	VERB
easat-3054	272	6	habeeb	habeeb	PROPN
easat-3054	272	7	and	and	CCONJ
easat-3054	272	8	eman	eman	PROPN
easat-3054	272	9	samir	samir	PROPN
easat-3054	272	10	bhaya	bhaya	PROPN
easat-3054	272	11	,	,	PUNCT
easat-3054	272	12	approximation	approximation	NOUN
easat-3054	272	13	of	of	ADP
easat-3054	272	14	expectation	expectation	NOUN
easat-3054	272	15	and	and	CCONJ
easat-3054	272	16	variance	variance	NOUN
easat-3054	272	17	on	on	ADP
easat-3054	272	18	[	[	X
easat-3054	272	19	𝑎,𝑏	𝑎,𝑏	NOUN
easat-3054	272	20	]	]	X
easat-3054	272	21	interval	interval	NOUN
easat-3054	272	22	,	,	PUNCT
easat-3054	272	23	with	with	ADP
easat-3054	272	24	probability	probability	NOUN
easat-3054	272	25	density	density	NOUN
easat-3054	272	26	function	function	NOUN
easat-3054	272	27	in	in	ADP
easat-3054	272	28	𝐿𝑝[𝑎,𝑏],0<𝑝<1	𝐿𝑝[𝑎,𝑏],0<𝑝<1	PROPN
easat-3054	272	29	,	,	PUNCT
easat-3054	272	30	international	international	ADJ
easat-3054	272	31	journal	journal	NOUN
easat-3054	272	32	of	of	ADP
easat-3054	272	33	mechanical	mechanical	ADJ
easat-3054	272	34	engineering	engineering	NOUN
easat-3054	272	35	,	,	PUNCT
easat-3054	272	36	vol	vol	NOUN
easat-3054	272	37	.	.	PROPN
easat-3054	272	38	7	7	NUM
easat-3054	273	1	no	no	NOUN
easat-3054	273	2	.	.	NOUN
easat-3054	273	3	3	3	NUM
easat-3054	273	4	march	march	NOUN
easat-3054	273	5	,	,	PUNCT
easat-3054	273	6	2022	2022	NUM
easat-3054	273	7	[	[	X
easat-3054	273	8	9	9	NUM
easat-3054	273	9	]	]	PUNCT
easat-3054	273	10	p.	p.	NOUN
easat-3054	273	11	cerone	cerone	NOUN
easat-3054	273	12	and	and	CCONJ
easat-3054	273	13	s.s	s.s	PROPN
easat-3054	273	14	.	.	PROPN
easat-3054	273	15	dragomir	dragomir	PROPN
easat-3054	273	16	,	,	PUNCT
easat-3054	273	17	ostromski	ostromski	ADP
easat-3054	273	18	type	type	NOUN
easat-3054	273	19	inequalities	inequality	NOUN
easat-3054	273	20	for	for	ADP
easat-3054	273	21	functions	function	NOUN
easat-3054	273	22	mhose	mhose	NOUN
easat-3054	273	23	derivatives	derivative	NOUN
easat-3054	273	24	satisfy	satisfy	VERB
easat-3054	273	25	certain	certain	ADJ
easat-3054	273	26	convexity	convexity	NOUN
easat-3054	273	27	assumptions	assumption	NOUN
easat-3054	273	28	,	,	PUNCT
easat-3054	273	29	demonstratio	demonstratio	PROPN
easat-3054	273	30	math	math	PROPN
easat-3054	273	31	.	.	PUNCT
easat-3054	274	1	,	,	PUNCT
easat-3054	274	2	37	37	NUM
easat-3054	274	3	(	(	PUNCT
easat-3054	274	4	2004	2004	NUM
easat-3054	274	5	)	)	PUNCT
easat-3054	274	6	,	,	PUNCT
easat-3054	274	7	no.2,299–308	no.2,299–308	PROPN
easat-3054	274	8	.	.	PUNCT
easat-3054	275	1	[	[	X
easat-3054	275	2	10	10	NUM
easat-3054	275	3	]	]	X
easat-3054	275	4	s.s.dragomir	s.s.dragomir	NOUN
easat-3054	275	5	and	and	CCONJ
easat-3054	275	6	r.	r.	PROPN
easat-3054	275	7	p.	p.	PROPN
easat-3054	275	8	agarwal	agarwal	PROPN
easat-3054	275	9	,	,	PUNCT
easat-3054	275	10	two	two	NUM
easat-3054	275	11	inequalities	inequality	NOUN
easat-3054	275	12	for	for	ADP
easat-3054	275	13	differentiable	differentiable	ADJ
easat-3054	275	14	mappings	mapping	NOUN
easat-3054	275	15	and	and	CCONJ
easat-3054	275	16	applications	application	NOUN
easat-3054	275	17	to	to	ADP
easat-3054	275	18	special	special	ADJ
easat-3054	275	19	means	mean	NOUN
easat-3054	275	20	of	of	ADP
easat-3054	275	21	real	real	ADJ
easat-3054	275	22	numbers	number	NOUN
easat-3054	275	23	and	and	CCONJ
easat-3054	275	24	to	to	ADP
easat-3054	275	25	trapezoidal	trapezoidal	ADJ
easat-3054	275	26	formula	formula	NOUN
easat-3054	275	27	,	,	PUNCT
easat-3054	275	28	appl	appl	PROPN
easat-3054	275	29	.	.	PROPN
easat-3054	275	30	math	math	PROPN
easat-3054	275	31	.	.	PUNCT
easat-3054	276	1	lett.vol	lett.vol	X
easat-3054	276	2	.	.	PROPN
easat-3054	276	3	11	11	NUM
easat-3054	276	4	,	,	PUNCT
easat-3054	276	5	no.5	no.5	PROPN
easat-3054	276	6	,	,	PUNCT
easat-3054	276	7	pp.91	pp.91	PROPN
easat-3054	276	8	-	-	PROPN
easat-3054	276	9	95	95	NUM
easat-3054	276	10	,	,	PUNCT
easat-3054	276	11	1998	1998	NUM
easat-3054	276	12	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	NOUN