id	sid	tid	token	lemma	pos
ejpam-440	1	1	2_440_gordji.dvi	2_440_gordji.dvi	NUM
ejpam-440	1	2	european	european	ADJ
ejpam-440	1	3	journal	journal	NOUN
ejpam-440	1	4	of	of	ADP
ejpam-440	1	5	pure	pure	ADJ
ejpam-440	1	6	and	and	CCONJ
ejpam-440	1	7	applied	apply	VERB
ejpam-440	1	8	mathematics	mathematic	NOUN
ejpam-440	1	9	vol	vol	NOUN
ejpam-440	1	10	.	.	PROPN
ejpam-440	2	1	2	2	NUM
ejpam-440	2	2	,	,	PUNCT
ejpam-440	2	3	no	no	INTJ
ejpam-440	2	4	.	.	NOUN
ejpam-440	2	5	4	4	NUM
ejpam-440	2	6	,	,	PUNCT
ejpam-440	2	7	2009	2009	NUM
ejpam-440	2	8	,	,	PUNCT
ejpam-440	2	9	(	(	PUNCT
ejpam-440	2	10	494	494	NUM
ejpam-440	2	11	-	-	SYM
ejpam-440	2	12	507	507	NUM
ejpam-440	2	13	)	)	PUNCT
ejpam-440	2	14	issn	issn	PROPN
ejpam-440	2	15	1307	1307	NUM
ejpam-440	2	16	-	-	SYM
ejpam-440	2	17	5543	5543	NUM
ejpam-440	2	18	–	–	PUNCT
ejpam-440	2	19	www.ejpam.com	www.ejpam.com	X
ejpam-440	2	20	approximation	approximation	NOUN
ejpam-440	2	21	of	of	ADP
ejpam-440	2	22	the	the	DET
ejpam-440	2	23	quadratic	quadratic	ADJ
ejpam-440	2	24	and	and	CCONJ
ejpam-440	2	25	cubic	cubic	ADJ
ejpam-440	2	26	functional	functional	ADJ
ejpam-440	2	27	equations	equation	NOUN
ejpam-440	2	28	in	in	ADP
ejpam-440	2	29	rn	rn	PROPN
ejpam-440	2	30	–	–	PUNCT
ejpam-440	2	31	spaces	space	NOUN
ejpam-440	2	32	m.	m.	PROPN
ejpam-440	2	33	eshaghi	eshaghi	PROPN
ejpam-440	2	34	gordji1∗	gordji1∗	PROPN
ejpam-440	2	35	,	,	PUNCT
ejpam-440	2	36	j.	j.	PROPN
ejpam-440	2	37	m.	m.	PROPN
ejpam-440	2	38	rassias2	rassias2	PROPN
ejpam-440	2	39	and	and	CCONJ
ejpam-440	2	40	m.	m.	NOUN
ejpam-440	2	41	bavand	bavand	PROPN
ejpam-440	3	1	savadkouhi1	savadkouhi1	PROPN
ejpam-440	3	2	1	1	NUM
ejpam-440	3	3	department	department	NOUN
ejpam-440	3	4	of	of	ADP
ejpam-440	3	5	mathematics	mathematic	NOUN
ejpam-440	3	6	,	,	PUNCT
ejpam-440	3	7	university	university	NOUN
ejpam-440	3	8	of	of	ADP
ejpam-440	3	9	semnan	semnan	PROPN
ejpam-440	3	10	,	,	PUNCT
ejpam-440	3	11	p.	p.	PROPN
ejpam-440	3	12	o.	o.	PROPN
ejpam-440	3	13	box	box	PROPN
ejpam-440	3	14	35195	35195	NUM
ejpam-440	3	15	-	-	SYM
ejpam-440	3	16	363	363	NUM
ejpam-440	3	17	,	,	PUNCT
ejpam-440	3	18	semnan	semnan	NOUN
ejpam-440	3	19	,	,	PUNCT
ejpam-440	3	20	iran	iran	PROPN
ejpam-440	3	21	2	2	NUM
ejpam-440	3	22	section	section	NOUN
ejpam-440	3	23	of	of	ADP
ejpam-440	3	24	mathematics	mathematic	NOUN
ejpam-440	3	25	and	and	CCONJ
ejpam-440	3	26	informatics	informatic	NOUN
ejpam-440	3	27	,	,	PUNCT
ejpam-440	3	28	pedagogical	pedagogical	ADJ
ejpam-440	3	29	department	department	PROPN
ejpam-440	3	30	national	national	ADJ
ejpam-440	3	31	and	and	CCONJ
ejpam-440	3	32	capodistrian	capodistrian	ADJ
ejpam-440	3	33	university	university	PROPN
ejpam-440	3	34	of	of	ADP
ejpam-440	3	35	athens	athens	PROPN
ejpam-440	3	36	,	,	PUNCT
ejpam-440	3	37	4	4	NUM
ejpam-440	3	38	,	,	PUNCT
ejpam-440	3	39	agamemnonos	agamemnonos	PROPN
ejpam-440	3	40	st	st	PROPN
ejpam-440	3	41	.	.	PROPN
ejpam-440	3	42	,	,	PUNCT
ejpam-440	3	43	aghia	aghia	VERB
ejpam-440	3	44	paraskevi	paraskevi	ADJ
ejpam-440	3	45	,	,	PUNCT
ejpam-440	3	46	athens	athens	PROPN
ejpam-440	3	47	15342	15342	NUM
ejpam-440	3	48	,	,	PUNCT
ejpam-440	3	49	greece	greece	PROPN
ejpam-440	3	50	abstract	abstract	PROPN
ejpam-440	3	51	.	.	PUNCT
ejpam-440	4	1	we	we	PRON
ejpam-440	4	2	prove	prove	VERB
ejpam-440	4	3	a	a	DET
ejpam-440	4	4	stability	stability	NOUN
ejpam-440	4	5	result	result	NOUN
ejpam-440	4	6	for	for	ADP
ejpam-440	4	7	the	the	DET
ejpam-440	4	8	quadratic	quadratic	ADJ
ejpam-440	4	9	and	and	CCONJ
ejpam-440	4	10	cubic	cubic	ADJ
ejpam-440	4	11	functional	functional	ADJ
ejpam-440	4	12	equations	equation	NOUN
ejpam-440	4	13	in	in	ADP
ejpam-440	4	14	random	random	ADJ
ejpam-440	4	15	normed	normed	PROPN
ejpam-440	4	16	(	(	PUNCT
ejpam-440	4	17	rn	rn	NOUN
ejpam-440	4	18	)	)	PUNCT
ejpam-440	4	19	spaces	space	NOUN
ejpam-440	4	20	(	(	PUNCT
ejpam-440	4	21	in	in	ADP
ejpam-440	4	22	the	the	DET
ejpam-440	4	23	sense	sense	NOUN
ejpam-440	4	24	of	of	ADP
ejpam-440	4	25	sherstnev	sherstnev	NOUN
ejpam-440	4	26	)	)	PUNCT
ejpam-440	4	27	under	under	ADP
ejpam-440	4	28	arbitrary	arbitrary	ADJ
ejpam-440	4	29	t	t	PROPN
ejpam-440	4	30	–	–	PUNCT
ejpam-440	4	31	norms	norm	NOUN
ejpam-440	4	32	.	.	PUNCT
ejpam-440	5	1	2000	2000	NUM
ejpam-440	5	2	mathematics	mathematic	NOUN
ejpam-440	5	3	subject	subject	NOUN
ejpam-440	5	4	classifications	classification	NOUN
ejpam-440	5	5	:	:	PUNCT
ejpam-440	5	6	primary	primary	ADJ
ejpam-440	5	7	54e40	54e40	ADV
ejpam-440	5	8	;	;	PUNCT
ejpam-440	5	9	secondary	secondary	ADJ
ejpam-440	5	10	39b82	39b82	NUM
ejpam-440	5	11	,	,	PUNCT
ejpam-440	5	12	46s50	46s50	NUM
ejpam-440	5	13	,	,	PUNCT
ejpam-440	5	14	46s40	46s40	NUM
ejpam-440	5	15	.	.	PUNCT
ejpam-440	6	1	key	key	ADJ
ejpam-440	6	2	words	word	NOUN
ejpam-440	6	3	and	and	CCONJ
ejpam-440	6	4	phrases	phrase	NOUN
ejpam-440	6	5	:	:	PUNCT
ejpam-440	6	6	stability	stability	NOUN
ejpam-440	6	7	;	;	PUNCT
ejpam-440	6	8	quadratic	quadratic	ADJ
ejpam-440	6	9	functional	functional	ADJ
ejpam-440	6	10	equation	equation	NOUN
ejpam-440	6	11	;	;	PUNCT
ejpam-440	6	12	cubic	cubic	ADJ
ejpam-440	6	13	functional	functional	ADJ
ejpam-440	6	14	equation	equation	NOUN
ejpam-440	6	15	;	;	PUNCT
ejpam-440	6	16	random	random	ADJ
ejpam-440	6	17	normed	normed	ADJ
ejpam-440	6	18	space	space	NOUN
ejpam-440	6	19	.	.	PUNCT
ejpam-440	7	1	1	1	X
ejpam-440	7	2	.	.	X
ejpam-440	7	3	introduction	introduction	NOUN
ejpam-440	7	4	the	the	DET
ejpam-440	7	5	study	study	NOUN
ejpam-440	7	6	of	of	ADP
ejpam-440	7	7	stability	stability	NOUN
ejpam-440	7	8	problems	problem	NOUN
ejpam-440	7	9	for	for	ADP
ejpam-440	7	10	functional	functional	ADJ
ejpam-440	7	11	equations	equation	NOUN
ejpam-440	7	12	is	be	AUX
ejpam-440	7	13	related	relate	VERB
ejpam-440	7	14	to	to	ADP
ejpam-440	7	15	a	a	DET
ejpam-440	7	16	question	question	NOUN
ejpam-440	7	17	of	of	ADP
ejpam-440	7	18	ulam	ulam	PROPN
ejpam-440	8	1	[	[	X
ejpam-440	8	2	37	37	NUM
ejpam-440	8	3	]	]	PUNCT
ejpam-440	8	4	,	,	PUNCT
ejpam-440	8	5	concerning	concern	VERB
ejpam-440	8	6	the	the	DET
ejpam-440	8	7	stability	stability	NOUN
ejpam-440	8	8	of	of	ADP
ejpam-440	8	9	group	group	NOUN
ejpam-440	8	10	homomorphisms	homomorphism	NOUN
ejpam-440	8	11	,	,	PUNCT
ejpam-440	8	12	affirmatively	affirmatively	ADV
ejpam-440	8	13	answered	answer	VERB
ejpam-440	8	14	∗corresponding	∗corresponde	VERB
ejpam-440	8	15	author	author	NOUN
ejpam-440	8	16	.	.	PUNCT
ejpam-440	9	1	email	email	NOUN
ejpam-440	9	2	addresses	address	NOUN
ejpam-440	9	3	:	:	PUNCT
ejpam-440	9	4	madjid.eshaghi	madjid.eshaghi	X
ejpam-440	9	5	�	�	NOUN
ejpam-440	9	6	gmail	gmail	NOUN
ejpam-440	9	7	.	.	PUNCT
ejpam-440	10	1	om	om	PROPN
ejpam-440	10	2	(	(	PUNCT
ejpam-440	10	3	m.	m.	NOUN
ejpam-440	10	4	gordji	gordji	PROPN
ejpam-440	10	5	)	)	PUNCT
ejpam-440	10	6	,	,	PUNCT
ejpam-440	11	1	jrassias�primedu.uoa.gr	jrassias�primedu.uoa.gr	PROPN
ejpam-440	11	2	(	(	PUNCT
ejpam-440	11	3	j.	j.	PROPN
ejpam-440	11	4	rassias	rassias	PROPN
ejpam-440	11	5	)	)	PUNCT
ejpam-440	11	6	,	,	PUNCT
ejpam-440	11	7	bavand.m	bavand.m	NOUN
ejpam-440	11	8	�	�	NOUN
ejpam-440	11	9	gmail	gmail	NOUN
ejpam-440	11	10	.	.	PUNCT
ejpam-440	12	1	om	om	PROPN
ejpam-440	12	2	(	(	PUNCT
ejpam-440	12	3	m.	m.	NOUN
ejpam-440	12	4	savadkouhi	savadkouhi	PROPN
ejpam-440	12	5	)	)	PUNCT
ejpam-440	12	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-440	13	1	494	494	NUM
ejpam-440	13	2	c	c	NOUN
ejpam-440	13	3	©	©	PROPN
ejpam-440	13	4	2009	2009	NUM
ejpam-440	13	5	ejpam	ejpam	NOUN
ejpam-440	13	6	all	all	DET
ejpam-440	13	7	rights	right	NOUN
ejpam-440	13	8	reserved	reserve	VERB
ejpam-440	13	9	.	.	PUNCT
ejpam-440	14	1	m.	m.	NOUN
ejpam-440	14	2	gordji	gordji	PROPN
ejpam-440	14	3	,	,	PUNCT
ejpam-440	14	4	j.	j.	PROPN
ejpam-440	14	5	rassias	rassias	PROPN
ejpam-440	14	6	,	,	PUNCT
ejpam-440	14	7	and	and	CCONJ
ejpam-440	14	8	m.	m.	NOUN
ejpam-440	14	9	savadkouhi	savadkouhi	PROPN
ejpam-440	14	10	/	/	SYM
ejpam-440	14	11	eur	eur	PROPN
ejpam-440	14	12	.	.	PUNCT
ejpam-440	15	1	j.	j.	PROPN
ejpam-440	15	2	pure	pure	PROPN
ejpam-440	15	3	appl	appl	PROPN
ejpam-440	15	4	.	.	PROPN
ejpam-440	15	5	math	math	PROPN
ejpam-440	15	6	,	,	PUNCT
ejpam-440	15	7	2	2	NUM
ejpam-440	15	8	(	(	PUNCT
ejpam-440	15	9	2009	2009	NUM
ejpam-440	15	10	)	)	PUNCT
ejpam-440	15	11	,	,	PUNCT
ejpam-440	15	12	(	(	PUNCT
ejpam-440	15	13	494	494	NUM
ejpam-440	15	14	-	-	SYM
ejpam-440	15	15	507	507	NUM
ejpam-440	15	16	)	)	PUNCT
ejpam-440	15	17	495	495	NUM
ejpam-440	15	18	for	for	ADP
ejpam-440	15	19	banach	banach	NOUN
ejpam-440	15	20	spaces	space	NOUN
ejpam-440	15	21	by	by	ADP
ejpam-440	15	22	hyers	hyer	NOUN
ejpam-440	15	23	[	[	X
ejpam-440	15	24	13	13	NUM
ejpam-440	15	25	]	]	PUNCT
ejpam-440	15	26	.	.	PUNCT
ejpam-440	16	1	subsequently	subsequently	ADV
ejpam-440	16	2	,	,	PUNCT
ejpam-440	16	3	the	the	DET
ejpam-440	16	4	result	result	NOUN
ejpam-440	16	5	of	of	ADP
ejpam-440	16	6	hyers	hyer	NOUN
ejpam-440	16	7	was	be	AUX
ejpam-440	16	8	generalized	generalize	VERB
ejpam-440	16	9	by	by	ADP
ejpam-440	16	10	aoki	aoki	PROPN
ejpam-440	17	1	[	[	X
ejpam-440	17	2	2	2	NUM
ejpam-440	17	3	]	]	PUNCT
ejpam-440	17	4	,	,	PUNCT
ejpam-440	17	5	bourgin	bourgin	NOUN
ejpam-440	17	6	[	[	X
ejpam-440	17	7	4	4	NUM
ejpam-440	17	8	]	]	PUNCT
ejpam-440	17	9	,	,	PUNCT
ejpam-440	17	10	gǎvruta	gǎvruta	NOUN
ejpam-440	17	11	[	[	X
ejpam-440	17	12	8	8	NUM
ejpam-440	17	13	]	]	PUNCT
ejpam-440	17	14	and	and	CCONJ
ejpam-440	17	15	rassias	rassia	VERB
ejpam-440	18	1	[	[	X
ejpam-440	18	2	24	24	NUM
ejpam-440	18	3	]	]	PUNCT
ejpam-440	18	4	(	(	PUNCT
ejpam-440	18	5	see	see	VERB
ejpam-440	18	6	also	also	ADV
ejpam-440	18	7	[	[	X
ejpam-440	18	8	9	9	NUM
ejpam-440	18	9	]	]	PUNCT
ejpam-440	18	10	and	and	CCONJ
ejpam-440	18	11	[	[	X
ejpam-440	18	12	31	31	NUM
ejpam-440	18	13	]	]	PUNCT
ejpam-440	18	14	)	)	PUNCT
ejpam-440	18	15	.	.	PUNCT
ejpam-440	19	1	the	the	DET
ejpam-440	19	2	functional	functional	ADJ
ejpam-440	19	3	equation	equation	NOUN
ejpam-440	19	4	f	f	X
ejpam-440	19	5	(	(	PUNCT
ejpam-440	19	6	x	x	PROPN
ejpam-440	19	7	+	+	NUM
ejpam-440	19	8	y	y	NOUN
ejpam-440	19	9	)	)	PUNCT
ejpam-440	20	1	+	+	NOUN
ejpam-440	20	2	f	f	X
ejpam-440	20	3	(	(	PUNCT
ejpam-440	20	4	x	x	INTJ
ejpam-440	20	5	−	−	PROPN
ejpam-440	20	6	y	y	PROPN
ejpam-440	20	7	)	)	PUNCT
ejpam-440	20	8	=	=	SYM
ejpam-440	20	9	2	2	NUM
ejpam-440	20	10	f	f	NOUN
ejpam-440	20	11	(	(	PUNCT
ejpam-440	20	12	x	x	X
ejpam-440	20	13	)	)	PUNCT
ejpam-440	20	14	+	+	CCONJ
ejpam-440	20	15	2	2	NUM
ejpam-440	20	16	f	f	NOUN
ejpam-440	20	17	(	(	PUNCT
ejpam-440	20	18	y	y	NOUN
ejpam-440	20	19	)	)	PUNCT
ejpam-440	20	20	(	(	PUNCT
ejpam-440	20	21	1	1	X
ejpam-440	20	22	)	)	PUNCT
ejpam-440	20	23	is	be	AUX
ejpam-440	20	24	related	relate	VERB
ejpam-440	20	25	to	to	ADP
ejpam-440	20	26	a	a	DET
ejpam-440	20	27	symmetric	symmetric	ADJ
ejpam-440	20	28	bi	bi	ADJ
ejpam-440	20	29	–	–	PUNCT
ejpam-440	20	30	additive	additive	ADJ
ejpam-440	20	31	function	function	NOUN
ejpam-440	20	32	.	.	PUNCT
ejpam-440	21	1	it	it	PRON
ejpam-440	21	2	is	be	AUX
ejpam-440	21	3	natural	natural	ADJ
ejpam-440	21	4	that	that	SCONJ
ejpam-440	21	5	this	this	DET
ejpam-440	21	6	equation	equation	NOUN
ejpam-440	21	7	is	be	AUX
ejpam-440	21	8	called	call	VERB
ejpam-440	21	9	a	a	DET
ejpam-440	21	10	quadratic	quadratic	ADJ
ejpam-440	21	11	functional	functional	ADJ
ejpam-440	21	12	equation	equation	NOUN
ejpam-440	21	13	.	.	PUNCT
ejpam-440	22	1	in	in	ADP
ejpam-440	22	2	particular	particular	ADJ
ejpam-440	22	3	,	,	PUNCT
ejpam-440	22	4	every	every	DET
ejpam-440	22	5	solution	solution	NOUN
ejpam-440	22	6	of	of	ADP
ejpam-440	22	7	the	the	DET
ejpam-440	22	8	quadratic	quadratic	ADJ
ejpam-440	22	9	equation	equation	NOUN
ejpam-440	22	10	(	(	PUNCT
ejpam-440	22	11	1	1	X
ejpam-440	22	12	)	)	PUNCT
ejpam-440	22	13	is	be	AUX
ejpam-440	22	14	said	say	VERB
ejpam-440	22	15	to	to	PART
ejpam-440	22	16	be	be	AUX
ejpam-440	22	17	a	a	DET
ejpam-440	22	18	quadratic	quadratic	ADJ
ejpam-440	22	19	function	function	NOUN
ejpam-440	22	20	.	.	PUNCT
ejpam-440	23	1	it	it	PRON
ejpam-440	23	2	is	be	AUX
ejpam-440	23	3	well	well	ADV
ejpam-440	23	4	known	know	VERB
ejpam-440	23	5	that	that	SCONJ
ejpam-440	23	6	a	a	DET
ejpam-440	23	7	function	function	NOUN
ejpam-440	23	8	f	f	NOUN
ejpam-440	23	9	between	between	ADP
ejpam-440	23	10	real	real	ADJ
ejpam-440	23	11	vector	vector	NOUN
ejpam-440	23	12	spaces	space	NOUN
ejpam-440	23	13	is	be	AUX
ejpam-440	23	14	quadratic	quadratic	ADJ
ejpam-440	23	15	if	if	SCONJ
ejpam-440	23	16	and	and	CCONJ
ejpam-440	23	17	only	only	ADV
ejpam-440	23	18	if	if	SCONJ
ejpam-440	23	19	there	there	PRON
ejpam-440	23	20	exists	exist	VERB
ejpam-440	23	21	a	a	DET
ejpam-440	23	22	unique	unique	ADJ
ejpam-440	23	23	symmetric	symmetric	ADJ
ejpam-440	23	24	bi	bi	ADJ
ejpam-440	23	25	–	–	PUNCT
ejpam-440	23	26	additive	additive	ADJ
ejpam-440	23	27	function	function	NOUN
ejpam-440	23	28	b	b	NOUN
ejpam-440	23	29	such	such	ADJ
ejpam-440	24	1	that	that	SCONJ
ejpam-440	24	2	f	f	PROPN
ejpam-440	24	3	(	(	PUNCT
ejpam-440	24	4	x	x	X
ejpam-440	24	5	)	)	PUNCT
ejpam-440	24	6	=	=	SYM
ejpam-440	24	7	b(x	b(x	NOUN
ejpam-440	24	8	,	,	PUNCT
ejpam-440	24	9	x	x	X
ejpam-440	24	10	)	)	PUNCT
ejpam-440	24	11	for	for	ADP
ejpam-440	24	12	all	all	PRON
ejpam-440	24	13	x	x	PUNCT
ejpam-440	24	14	(	(	PUNCT
ejpam-440	24	15	see	see	VERB
ejpam-440	24	16	[	[	X
ejpam-440	24	17	1	1	NUM
ejpam-440	24	18	,	,	PUNCT
ejpam-440	24	19	16	16	NUM
ejpam-440	24	20	]	]	PUNCT
ejpam-440	24	21	)	)	PUNCT
ejpam-440	24	22	.	.	PUNCT
ejpam-440	25	1	the	the	DET
ejpam-440	25	2	bi	bi	ADJ
ejpam-440	25	3	–	–	PUNCT
ejpam-440	25	4	additive	additive	ADJ
ejpam-440	25	5	function	function	NOUN
ejpam-440	25	6	b	b	PROPN
ejpam-440	25	7	is	be	AUX
ejpam-440	25	8	given	give	VERB
ejpam-440	25	9	by	by	ADP
ejpam-440	25	10	b(x	b(x	PROPN
ejpam-440	25	11	,	,	PUNCT
ejpam-440	25	12	y	y	PROPN
ejpam-440	25	13	)	)	PUNCT
ejpam-440	25	14	=	=	SYM
ejpam-440	25	15	1	1	NUM
ejpam-440	25	16	4	4	NUM
ejpam-440	25	17	[	[	PUNCT
ejpam-440	25	18	f	f	X
ejpam-440	25	19	(	(	PUNCT
ejpam-440	25	20	x	x	PROPN
ejpam-440	25	21	+	+	PUNCT
ejpam-440	25	22	y)−	y)−	PROPN
ejpam-440	25	23	f	f	NOUN
ejpam-440	25	24	(	(	PUNCT
ejpam-440	25	25	x	x	PROPN
ejpam-440	25	26	−	−	PROPN
ejpam-440	25	27	y	y	PROPN
ejpam-440	25	28	)	)	PUNCT
ejpam-440	25	29	]	]	PUNCT
ejpam-440	25	30	.	.	PUNCT
ejpam-440	26	1	(	(	PUNCT
ejpam-440	26	2	2	2	X
ejpam-440	26	3	)	)	PUNCT
ejpam-440	26	4	hyers	hyer	NOUN
ejpam-440	26	5	–	–	PUNCT
ejpam-440	26	6	ulam	ulam	X
ejpam-440	26	7	–	–	PUNCT
ejpam-440	26	8	rassias	rassias	PROPN
ejpam-440	26	9	stability	stability	NOUN
ejpam-440	26	10	problem	problem	NOUN
ejpam-440	26	11	for	for	ADP
ejpam-440	26	12	the	the	DET
ejpam-440	26	13	quadratic	quadratic	ADJ
ejpam-440	26	14	functional	functional	ADJ
ejpam-440	26	15	equation	equation	NOUN
ejpam-440	26	16	(	(	PUNCT
ejpam-440	26	17	1	1	X
ejpam-440	26	18	)	)	PUNCT
ejpam-440	26	19	was	be	AUX
ejpam-440	26	20	proved	prove	VERB
ejpam-440	26	21	by	by	ADP
ejpam-440	26	22	skof	skof	NOUN
ejpam-440	26	23	for	for	ADP
ejpam-440	26	24	functions	function	NOUN
ejpam-440	26	25	f	f	X
ejpam-440	26	26	:	:	PUNCT
ejpam-440	26	27	a→	a→	PROPN
ejpam-440	26	28	b	b	NOUN
ejpam-440	26	29	,	,	PUNCT
ejpam-440	26	30	where	where	SCONJ
ejpam-440	26	31	a	a	PRON
ejpam-440	26	32	is	be	AUX
ejpam-440	26	33	normed	normed	ADJ
ejpam-440	26	34	space	space	NOUN
ejpam-440	26	35	and	and	CCONJ
ejpam-440	26	36	b	b	NOUN
ejpam-440	26	37	is	be	AUX
ejpam-440	26	38	a	a	DET
ejpam-440	26	39	banach	banach	NOUN
ejpam-440	26	40	space	space	NOUN
ejpam-440	26	41	(	(	PUNCT
ejpam-440	26	42	see	see	VERB
ejpam-440	26	43	[	[	X
ejpam-440	26	44	36	36	NUM
ejpam-440	26	45	]	]	NUM
ejpam-440	26	46	)	)	PUNCT
ejpam-440	26	47	.	.	PUNCT
ejpam-440	27	1	cholewa	cholewa	PROPN
ejpam-440	28	1	[	[	X
ejpam-440	28	2	5	5	X
ejpam-440	28	3	]	]	PUNCT
ejpam-440	28	4	noticed	notice	VERB
ejpam-440	28	5	that	that	SCONJ
ejpam-440	28	6	the	the	DET
ejpam-440	28	7	theorem	theorem	NOUN
ejpam-440	28	8	of	of	ADP
ejpam-440	28	9	skof	skof	NOUN
ejpam-440	28	10	is	be	AUX
ejpam-440	28	11	still	still	ADV
ejpam-440	28	12	true	true	ADJ
ejpam-440	28	13	if	if	SCONJ
ejpam-440	28	14	relevant	relevant	ADJ
ejpam-440	28	15	domain	domain	NOUN
ejpam-440	28	16	a	a	PRON
ejpam-440	28	17	is	be	AUX
ejpam-440	28	18	replaced	replace	VERB
ejpam-440	28	19	by	by	ADP
ejpam-440	28	20	an	an	DET
ejpam-440	28	21	abelian	abelian	ADJ
ejpam-440	28	22	group	group	NOUN
ejpam-440	28	23	.	.	PUNCT
ejpam-440	29	1	in	in	ADP
ejpam-440	29	2	the	the	DET
ejpam-440	29	3	paper	paper	NOUN
ejpam-440	29	4	[	[	X
ejpam-440	29	5	7	7	NUM
ejpam-440	29	6	]	]	PUNCT
ejpam-440	29	7	,	,	PUNCT
ejpam-440	29	8	czerwik	czerwik	PROPN
ejpam-440	29	9	proved	prove	VERB
ejpam-440	29	10	the	the	DET
ejpam-440	29	11	hyers	hyer	NOUN
ejpam-440	29	12	–	–	PUNCT
ejpam-440	29	13	ulam	ulam	X
ejpam-440	29	14	–	–	PUNCT
ejpam-440	29	15	rassias	rassia	NOUN
ejpam-440	29	16	stability	stability	NOUN
ejpam-440	29	17	of	of	ADP
ejpam-440	29	18	the	the	DET
ejpam-440	29	19	functional	functional	ADJ
ejpam-440	29	20	equation	equation	NOUN
ejpam-440	29	21	(	(	PUNCT
ejpam-440	29	22	1	1	NUM
ejpam-440	29	23	)	)	PUNCT
ejpam-440	29	24	.	.	PUNCT
ejpam-440	30	1	grabiec	grabiec	PROPN
ejpam-440	31	1	[	[	X
ejpam-440	31	2	10	10	NUM
ejpam-440	31	3	]	]	PUNCT
ejpam-440	31	4	has	have	AUX
ejpam-440	31	5	generalized	generalize	VERB
ejpam-440	31	6	these	these	DET
ejpam-440	31	7	result	result	NOUN
ejpam-440	31	8	mentioned	mention	VERB
ejpam-440	31	9	above	above	ADV
ejpam-440	31	10	.	.	PUNCT
ejpam-440	32	1	we	we	PRON
ejpam-440	32	2	only	only	ADV
ejpam-440	32	3	mention	mention	VERB
ejpam-440	32	4	here	here	ADV
ejpam-440	32	5	the	the	DET
ejpam-440	32	6	papers	paper	NOUN
ejpam-440	32	7	[	[	X
ejpam-440	32	8	14	14	NUM
ejpam-440	32	9	]	]	PUNCT
ejpam-440	32	10	,	,	PUNCT
ejpam-440	32	11	[	[	X
ejpam-440	32	12	16	16	NUM
ejpam-440	32	13	]	]	PUNCT
ejpam-440	32	14	,	,	PUNCT
ejpam-440	32	15	[	[	X
ejpam-440	32	16	23	23	NUM
ejpam-440	32	17	]	]	PUNCT
ejpam-440	32	18	,	,	PUNCT
ejpam-440	32	19	[	[	X
ejpam-440	32	20	32	32	NUM
ejpam-440	32	21	]	]	PUNCT
ejpam-440	32	22	,	,	PUNCT
ejpam-440	32	23	[	[	X
ejpam-440	32	24	33	33	NUM
ejpam-440	32	25	]	]	X
ejpam-440	33	1	[	[	X
ejpam-440	33	2	27–30	27–30	NUM
ejpam-440	33	3	]	]	PUNCT
ejpam-440	33	4	concerning	concern	VERB
ejpam-440	33	5	the	the	DET
ejpam-440	33	6	stability	stability	NOUN
ejpam-440	33	7	of	of	ADP
ejpam-440	33	8	the	the	DET
ejpam-440	33	9	quadratic	quadratic	ADJ
ejpam-440	33	10	functional	functional	ADJ
ejpam-440	33	11	equations	equation	NOUN
ejpam-440	33	12	.	.	PUNCT
ejpam-440	34	1	the	the	DET
ejpam-440	34	2	following	follow	VERB
ejpam-440	34	3	cubic	cubic	ADJ
ejpam-440	34	4	functional	functional	ADJ
ejpam-440	34	5	equation	equation	NOUN
ejpam-440	34	6	,	,	PUNCT
ejpam-440	34	7	which	which	PRON
ejpam-440	34	8	is	be	AUX
ejpam-440	34	9	the	the	DET
ejpam-440	34	10	oldest	old	ADJ
ejpam-440	34	11	cubic	cubic	ADJ
ejpam-440	34	12	functional	functional	ADJ
ejpam-440	34	13	equation	equation	NOUN
ejpam-440	34	14	,	,	PUNCT
ejpam-440	34	15	and	and	CCONJ
ejpam-440	34	16	was	be	AUX
ejpam-440	34	17	introduced	introduce	VERB
ejpam-440	34	18	by	by	ADP
ejpam-440	34	19	j.	j.	PROPN
ejpam-440	34	20	m.	m.	PROPN
ejpam-440	34	21	rassias	rassia	VERB
ejpam-440	35	1	[	[	X
ejpam-440	35	2	25](in	25](in	NUM
ejpam-440	35	3	2001	2001	NUM
ejpam-440	35	4	):	):	PUNCT
ejpam-440	35	5	f	f	PROPN
ejpam-440	35	6	(	(	PUNCT
ejpam-440	35	7	x	x	X
ejpam-440	35	8	+	+	PUNCT
ejpam-440	35	9	2y	2y	NUM
ejpam-440	35	10	)	)	PUNCT
ejpam-440	35	11	+	+	CCONJ
ejpam-440	35	12	3	3	NUM
ejpam-440	35	13	f	f	NOUN
ejpam-440	35	14	(	(	PUNCT
ejpam-440	35	15	x	x	NOUN
ejpam-440	35	16	)	)	PUNCT
ejpam-440	35	17	=	=	SYM
ejpam-440	35	18	3	3	NUM
ejpam-440	35	19	f	f	X
ejpam-440	35	20	(	(	PUNCT
ejpam-440	35	21	x	x	PROPN
ejpam-440	35	22	+	+	NUM
ejpam-440	35	23	y	y	NOUN
ejpam-440	35	24	)	)	PUNCT
ejpam-440	36	1	+	+	NOUN
ejpam-440	36	2	f	f	X
ejpam-440	36	3	(	(	PUNCT
ejpam-440	36	4	x	x	INTJ
ejpam-440	36	5	−	−	PROPN
ejpam-440	36	6	y	y	PROPN
ejpam-440	36	7	)	)	PUNCT
ejpam-440	37	1	+	+	CCONJ
ejpam-440	37	2	6	6	NUM
ejpam-440	37	3	f	f	NOUN
ejpam-440	37	4	(	(	PUNCT
ejpam-440	37	5	y	y	PROPN
ejpam-440	37	6	)	)	PUNCT
ejpam-440	37	7	.	.	PUNCT
ejpam-440	38	1	jun	jun	PROPN
ejpam-440	38	2	and	and	CCONJ
ejpam-440	38	3	kim	kim	PROPN
ejpam-440	39	1	[	[	X
ejpam-440	39	2	15	15	NUM
ejpam-440	39	3	]	]	PUNCT
ejpam-440	39	4	introduced	introduce	VERB
ejpam-440	39	5	the	the	DET
ejpam-440	39	6	following	follow	VERB
ejpam-440	39	7	cubic	cubic	ADJ
ejpam-440	39	8	functional	functional	ADJ
ejpam-440	39	9	equation	equation	NOUN
ejpam-440	39	10	f	f	X
ejpam-440	39	11	(	(	PUNCT
ejpam-440	39	12	2x	2x	NUM
ejpam-440	39	13	+	+	CCONJ
ejpam-440	39	14	y	y	X
ejpam-440	39	15	)	)	PUNCT
ejpam-440	40	1	+	+	CCONJ
ejpam-440	40	2	f	f	X
ejpam-440	40	3	(	(	PUNCT
ejpam-440	40	4	2x	2x	NUM
ejpam-440	40	5	−	−	PROPN
ejpam-440	40	6	y	y	NOUN
ejpam-440	40	7	)	)	PUNCT
ejpam-440	40	8	=	=	SYM
ejpam-440	40	9	2	2	NUM
ejpam-440	40	10	f	f	X
ejpam-440	40	11	(	(	PUNCT
ejpam-440	40	12	x	x	PROPN
ejpam-440	40	13	+	+	NUM
ejpam-440	40	14	y	y	NOUN
ejpam-440	40	15	)	)	PUNCT
ejpam-440	41	1	+	+	CCONJ
ejpam-440	41	2	2	2	NUM
ejpam-440	41	3	f	f	X
ejpam-440	41	4	(	(	PUNCT
ejpam-440	41	5	x	x	PROPN
ejpam-440	41	6	−	−	PROPN
ejpam-440	41	7	y	y	PROPN
ejpam-440	41	8	)	)	PUNCT
ejpam-440	42	1	+	+	CCONJ
ejpam-440	42	2	12	12	NUM
ejpam-440	42	3	f	f	NOUN
ejpam-440	42	4	(	(	PUNCT
ejpam-440	42	5	x	x	X
ejpam-440	42	6	)	)	PUNCT
ejpam-440	42	7	(	(	PUNCT
ejpam-440	42	8	3	3	X
ejpam-440	42	9	)	)	PUNCT
ejpam-440	42	10	m.	m.	NOUN
ejpam-440	42	11	gordji	gordji	PROPN
ejpam-440	42	12	,	,	PUNCT
ejpam-440	42	13	j.	j.	PROPN
ejpam-440	42	14	rassias	rassias	PROPN
ejpam-440	42	15	,	,	PUNCT
ejpam-440	42	16	and	and	CCONJ
ejpam-440	42	17	m.	m.	NOUN
ejpam-440	42	18	savadkouhi	savadkouhi	PROPN
ejpam-440	42	19	/	/	SYM
ejpam-440	42	20	eur	eur	PROPN
ejpam-440	42	21	.	.	PUNCT
ejpam-440	43	1	j.	j.	PROPN
ejpam-440	43	2	pure	pure	PROPN
ejpam-440	43	3	appl	appl	PROPN
ejpam-440	43	4	.	.	PROPN
ejpam-440	43	5	math	math	PROPN
ejpam-440	43	6	,	,	PUNCT
ejpam-440	43	7	2	2	NUM
ejpam-440	43	8	(	(	PUNCT
ejpam-440	43	9	2009	2009	NUM
ejpam-440	43	10	)	)	PUNCT
ejpam-440	43	11	,	,	PUNCT
ejpam-440	43	12	(	(	PUNCT
ejpam-440	43	13	494	494	NUM
ejpam-440	43	14	-	-	SYM
ejpam-440	43	15	507	507	NUM
ejpam-440	43	16	)	)	PUNCT
ejpam-440	43	17	496	496	NUM
ejpam-440	43	18	and	and	CCONJ
ejpam-440	43	19	they	they	PRON
ejpam-440	43	20	established	establish	VERB
ejpam-440	43	21	the	the	DET
ejpam-440	43	22	general	general	ADJ
ejpam-440	43	23	solution	solution	NOUN
ejpam-440	43	24	and	and	CCONJ
ejpam-440	43	25	the	the	DET
ejpam-440	43	26	generalized	generalized	ADJ
ejpam-440	43	27	hyers	hyer	NOUN
ejpam-440	43	28	–	–	PUNCT
ejpam-440	43	29	ulam	ulam	X
ejpam-440	43	30	–	–	PUNCT
ejpam-440	43	31	rassias	rassia	NOUN
ejpam-440	43	32	stability	stability	NOUN
ejpam-440	43	33	for	for	ADP
ejpam-440	43	34	the	the	DET
ejpam-440	43	35	functional	functional	ADJ
ejpam-440	43	36	equation	equation	NOUN
ejpam-440	43	37	(	(	PUNCT
ejpam-440	43	38	3	3	NUM
ejpam-440	43	39	)	)	PUNCT
ejpam-440	43	40	(	(	PUNCT
ejpam-440	43	41	in	in	ADP
ejpam-440	43	42	this	this	DET
ejpam-440	43	43	case	case	NOUN
ejpam-440	43	44	we	we	PRON
ejpam-440	43	45	have	have	VERB
ejpam-440	43	46	a	a	DET
ejpam-440	43	47	much	much	ADV
ejpam-440	43	48	better	well	ADJ
ejpam-440	43	49	possible	possible	ADJ
ejpam-440	43	50	upper	upper	ADJ
ejpam-440	43	51	bound	bind	VERB
ejpam-440	43	52	for	for	ADP
ejpam-440	43	53	(	(	PUNCT
ejpam-440	43	54	1.3	1.3	NUM
ejpam-440	43	55	)	)	PUNCT
ejpam-440	43	56	than	than	ADP
ejpam-440	43	57	the	the	DET
ejpam-440	43	58	hyers	hyer	NOUN
ejpam-440	43	59	–	–	PUNCT
ejpam-440	43	60	ulam	ulam	X
ejpam-440	43	61	–	–	PUNCT
ejpam-440	43	62	rassias	rassias	PROPN
ejpam-440	43	63	stability	stability	NOUN
ejpam-440	43	64	)	)	PUNCT
ejpam-440	43	65	.	.	PUNCT
ejpam-440	44	1	the	the	DET
ejpam-440	44	2	function	function	NOUN
ejpam-440	44	3	f	f	X
ejpam-440	44	4	(	(	PUNCT
ejpam-440	44	5	x	x	X
ejpam-440	44	6	)	)	PUNCT
ejpam-440	44	7	=	=	SYM
ejpam-440	44	8	x3	x3	ADJ
ejpam-440	44	9	satisfies	satisfy	VERB
ejpam-440	44	10	the	the	DET
ejpam-440	44	11	functional	functional	ADJ
ejpam-440	44	12	equation	equation	NOUN
ejpam-440	44	13	(	(	PUNCT
ejpam-440	44	14	3	3	NUM
ejpam-440	44	15	)	)	PUNCT
ejpam-440	44	16	,	,	PUNCT
ejpam-440	44	17	which	which	PRON
ejpam-440	44	18	is	be	AUX
ejpam-440	44	19	thus	thus	ADV
ejpam-440	44	20	called	call	VERB
ejpam-440	44	21	a	a	DET
ejpam-440	44	22	cubic	cubic	ADJ
ejpam-440	44	23	functional	functional	ADJ
ejpam-440	44	24	equation	equation	NOUN
ejpam-440	44	25	.	.	PUNCT
ejpam-440	45	1	every	every	DET
ejpam-440	45	2	solution	solution	NOUN
ejpam-440	45	3	of	of	ADP
ejpam-440	45	4	the	the	DET
ejpam-440	45	5	cubic	cubic	ADJ
ejpam-440	45	6	functional	functional	ADJ
ejpam-440	45	7	equation	equation	NOUN
ejpam-440	45	8	is	be	AUX
ejpam-440	45	9	said	say	VERB
ejpam-440	45	10	to	to	PART
ejpam-440	45	11	be	be	AUX
ejpam-440	45	12	a	a	DET
ejpam-440	45	13	cubic	cubic	ADJ
ejpam-440	45	14	function	function	NOUN
ejpam-440	45	15	.	.	PUNCT
ejpam-440	46	1	there	there	PRON
ejpam-440	46	2	are	be	VERB
ejpam-440	46	3	many	many	ADJ
ejpam-440	46	4	works	work	NOUN
ejpam-440	46	5	in	in	ADP
ejpam-440	46	6	the	the	DET
ejpam-440	46	7	very	very	ADV
ejpam-440	46	8	active	active	ADJ
ejpam-440	46	9	area	area	NOUN
ejpam-440	46	10	of	of	ADP
ejpam-440	46	11	the	the	DET
ejpam-440	46	12	stability	stability	NOUN
ejpam-440	46	13	of	of	ADP
ejpam-440	46	14	functional	functional	ADJ
ejpam-440	46	15	equations	equation	NOUN
ejpam-440	46	16	.	.	PUNCT
ejpam-440	47	1	we	we	PRON
ejpam-440	47	2	only	only	ADV
ejpam-440	47	3	mention	mention	VERB
ejpam-440	47	4	here	here	ADV
ejpam-440	47	5	the	the	DET
ejpam-440	47	6	papers	paper	NOUN
ejpam-440	47	7	[	[	X
ejpam-440	47	8	26	26	NUM
ejpam-440	47	9	]	]	PUNCT
ejpam-440	47	10	and	and	CCONJ
ejpam-440	47	11	[	[	X
ejpam-440	47	12	14	14	NUM
ejpam-440	47	13	]	]	PUNCT
ejpam-440	47	14	concerning	concern	VERB
ejpam-440	47	15	the	the	DET
ejpam-440	47	16	stability	stability	NOUN
ejpam-440	47	17	of	of	ADP
ejpam-440	47	18	the	the	DET
ejpam-440	47	19	cubic	cubic	ADJ
ejpam-440	47	20	functional	functional	ADJ
ejpam-440	47	21	equation	equation	NOUN
ejpam-440	47	22	.	.	PUNCT
ejpam-440	48	1	the	the	DET
ejpam-440	48	2	generalized	generalized	ADJ
ejpam-440	48	3	hyers	hyer	NOUN
ejpam-440	48	4	–	–	PUNCT
ejpam-440	48	5	ulam	ulam	X
ejpam-440	48	6	–	–	PUNCT
ejpam-440	48	7	rassias	rassia	NOUN
ejpam-440	48	8	stability	stability	NOUN
ejpam-440	48	9	of	of	ADP
ejpam-440	48	10	different	different	ADJ
ejpam-440	48	11	functional	functional	ADJ
ejpam-440	48	12	equations	equation	NOUN
ejpam-440	48	13	in	in	ADP
ejpam-440	48	14	random	random	ADJ
ejpam-440	48	15	normed	normed	ADJ
ejpam-440	48	16	and	and	CCONJ
ejpam-440	48	17	fuzzy	fuzzy	ADJ
ejpam-440	48	18	normed	normed	ADJ
ejpam-440	48	19	spaces	space	NOUN
ejpam-440	48	20	has	have	AUX
ejpam-440	48	21	been	be	AUX
ejpam-440	48	22	recently	recently	ADV
ejpam-440	48	23	studied	study	VERB
ejpam-440	48	24	in	in	ADP
ejpam-440	48	25	[	[	X
ejpam-440	48	26	17	17	NUM
ejpam-440	48	27	]	]	PUNCT
ejpam-440	48	28	–	–	PUNCT
ejpam-440	49	1	[	[	X
ejpam-440	49	2	22	22	NUM
ejpam-440	49	3	]	]	PUNCT
ejpam-440	49	4	.	.	PUNCT
ejpam-440	50	1	in	in	ADP
ejpam-440	50	2	the	the	DET
ejpam-440	50	3	sequel	sequel	NOUN
ejpam-440	50	4	we	we	PRON
ejpam-440	50	5	adopt	adopt	VERB
ejpam-440	50	6	the	the	DET
ejpam-440	50	7	usual	usual	ADJ
ejpam-440	50	8	terminology	terminology	NOUN
ejpam-440	50	9	,	,	PUNCT
ejpam-440	50	10	notations	notation	NOUN
ejpam-440	50	11	and	and	CCONJ
ejpam-440	50	12	conventions	convention	NOUN
ejpam-440	50	13	of	of	ADP
ejpam-440	50	14	the	the	DET
ejpam-440	50	15	theory	theory	NOUN
ejpam-440	50	16	of	of	ADP
ejpam-440	50	17	random	random	ADJ
ejpam-440	50	18	normed	normed	ADJ
ejpam-440	50	19	spaces	space	NOUN
ejpam-440	50	20	,	,	PUNCT
ejpam-440	50	21	as	as	ADP
ejpam-440	50	22	in	in	ADP
ejpam-440	50	23	[	[	X
ejpam-440	50	24	3	3	NUM
ejpam-440	50	25	,	,	PUNCT
ejpam-440	50	26	6	6	NUM
ejpam-440	50	27	,	,	PUNCT
ejpam-440	50	28	17	17	NUM
ejpam-440	50	29	,	,	PUNCT
ejpam-440	50	30	19	19	NUM
ejpam-440	50	31	,	,	PUNCT
ejpam-440	50	32	34	34	NUM
ejpam-440	50	33	,	,	PUNCT
ejpam-440	50	34	35	35	NUM
ejpam-440	50	35	]	]	PUNCT
ejpam-440	50	36	.	.	PUNCT
ejpam-440	51	1	throughout	throughout	ADP
ejpam-440	51	2	this	this	DET
ejpam-440	51	3	paper	paper	NOUN
ejpam-440	51	4	,	,	PUNCT
ejpam-440	51	5	∆+	∆+	NUM
ejpam-440	51	6	is	be	AUX
ejpam-440	51	7	the	the	DET
ejpam-440	51	8	space	space	NOUN
ejpam-440	51	9	of	of	ADP
ejpam-440	51	10	distribution	distribution	NOUN
ejpam-440	51	11	functions	function	NOUN
ejpam-440	51	12	,	,	PUNCT
ejpam-440	51	13	that	that	ADV
ejpam-440	51	14	is	is	ADV
ejpam-440	51	15	,	,	PUNCT
ejpam-440	51	16	the	the	DET
ejpam-440	51	17	space	space	NOUN
ejpam-440	51	18	of	of	ADP
ejpam-440	51	19	all	all	DET
ejpam-440	51	20	mappings	mapping	NOUN
ejpam-440	52	1	f	f	NOUN
ejpam-440	52	2	:	:	PUNCT
ejpam-440	52	3	r	r	NOUN
ejpam-440	52	4	∪	∪	NOUN
ejpam-440	52	5	{	{	PUNCT
ejpam-440	52	6	−∞,∞}→	−∞,∞}→	PROPN
ejpam-440	52	7	[	[	NOUN
ejpam-440	52	8	0	0	NUM
ejpam-440	52	9	,	,	PUNCT
ejpam-440	52	10	1	1	NUM
ejpam-440	52	11	]	]	PUNCT
ejpam-440	52	12	,	,	PUNCT
ejpam-440	52	13	such	such	ADJ
ejpam-440	52	14	that	that	SCONJ
ejpam-440	52	15	f	f	PROPN
ejpam-440	52	16	is	be	AUX
ejpam-440	52	17	left	leave	VERB
ejpam-440	52	18	-	-	PUNCT
ejpam-440	52	19	continuous	continuous	ADJ
ejpam-440	52	20	and	and	CCONJ
ejpam-440	52	21	non	non	ADJ
ejpam-440	52	22	-	-	ADJ
ejpam-440	52	23	decreasing	decrease	VERB
ejpam-440	52	24	on	on	ADP
ejpam-440	52	25	r	r	NOUN
ejpam-440	52	26	,	,	PUNCT
ejpam-440	52	27	f(0	f(0	NOUN
ejpam-440	52	28	)	)	PUNCT
ejpam-440	52	29	=	=	SYM
ejpam-440	52	30	0	0	NUM
ejpam-440	52	31	and	and	CCONJ
ejpam-440	52	32	f(+∞	f(+∞	NOUN
ejpam-440	52	33	)	)	PUNCT
ejpam-440	52	34	=	=	SYM
ejpam-440	52	35	1	1	X
ejpam-440	52	36	.	.	X
ejpam-440	52	37	d+	d+	NOUN
ejpam-440	52	38	is	be	AUX
ejpam-440	52	39	a	a	DET
ejpam-440	52	40	subset	subset	NOUN
ejpam-440	52	41	of	of	ADP
ejpam-440	52	42	∆+	∆+	PUNCT
ejpam-440	52	43	consisting	consist	VERB
ejpam-440	52	44	of	of	ADP
ejpam-440	52	45	all	all	DET
ejpam-440	52	46	functions	function	NOUN
ejpam-440	52	47	f	f	PROPN
ejpam-440	52	48	∈	∈	PROPN
ejpam-440	52	49	∆+	∆+	NUM
ejpam-440	52	50	for	for	ADP
ejpam-440	52	51	which	which	PRON
ejpam-440	52	52	l−f(+∞	l−f(+∞	ADP
ejpam-440	52	53	)	)	PUNCT
ejpam-440	52	54	=	=	SYM
ejpam-440	52	55	1	1	NUM
ejpam-440	52	56	,	,	PUNCT
ejpam-440	52	57	where	where	SCONJ
ejpam-440	52	58	l−	l−	PROPN
ejpam-440	52	59	f	f	X
ejpam-440	52	60	(	(	PUNCT
ejpam-440	52	61	x	x	X
ejpam-440	52	62	)	)	PUNCT
ejpam-440	52	63	denotes	denote	VERB
ejpam-440	52	64	the	the	DET
ejpam-440	52	65	left	left	ADJ
ejpam-440	52	66	limit	limit	NOUN
ejpam-440	52	67	of	of	ADP
ejpam-440	52	68	the	the	DET
ejpam-440	52	69	function	function	NOUN
ejpam-440	52	70	f	f	PROPN
ejpam-440	52	71	at	at	ADP
ejpam-440	52	72	the	the	DET
ejpam-440	52	73	point	point	NOUN
ejpam-440	52	74	x	x	X
ejpam-440	52	75	,	,	PUNCT
ejpam-440	52	76	that	that	ADV
ejpam-440	52	77	is	is	ADV
ejpam-440	52	78	,	,	PUNCT
ejpam-440	52	79	l−	l−	PROPN
ejpam-440	52	80	f	f	X
ejpam-440	52	81	(	(	PUNCT
ejpam-440	52	82	x	x	X
ejpam-440	52	83	)	)	PUNCT
ejpam-440	52	84	=	=	VERB
ejpam-440	52	85	limt→x−	limt→x−	ADP
ejpam-440	52	86	f	f	PROPN
ejpam-440	52	87	(	(	PUNCT
ejpam-440	52	88	t	t	PROPN
ejpam-440	52	89	)	)	PUNCT
ejpam-440	52	90	.	.	PUNCT
ejpam-440	53	1	the	the	DET
ejpam-440	53	2	space	space	NOUN
ejpam-440	53	3	∆+	∆+	NOUN
ejpam-440	53	4	is	be	AUX
ejpam-440	53	5	partially	partially	ADV
ejpam-440	53	6	ordered	order	VERB
ejpam-440	53	7	by	by	ADP
ejpam-440	53	8	the	the	DET
ejpam-440	53	9	usual	usual	ADJ
ejpam-440	53	10	point	point	NOUN
ejpam-440	53	11	–	–	PUNCT
ejpam-440	53	12	wise	wise	ADJ
ejpam-440	53	13	ordering	ordering	NOUN
ejpam-440	53	14	of	of	ADP
ejpam-440	53	15	functions	function	NOUN
ejpam-440	53	16	,	,	PUNCT
ejpam-440	53	17	i.e.	i.e.	X
ejpam-440	53	18	,	,	PUNCT
ejpam-440	53	19	f	f	PROPN
ejpam-440	53	20	≤	≤	X
ejpam-440	53	21	g	g	PROPN
ejpam-440	54	1	if	if	SCONJ
ejpam-440	54	2	and	and	CCONJ
ejpam-440	54	3	only	only	ADV
ejpam-440	54	4	if	if	SCONJ
ejpam-440	54	5	f(t	f(t	NOUN
ejpam-440	54	6	)	)	PUNCT
ejpam-440	54	7	≤	≤	NUM
ejpam-440	54	8	g(t	g(t	PROPN
ejpam-440	54	9	)	)	PUNCT
ejpam-440	54	10	for	for	ADP
ejpam-440	54	11	all	all	DET
ejpam-440	54	12	t	t	PROPN
ejpam-440	54	13	in	in	ADP
ejpam-440	54	14	r.	r.	PROPN
ejpam-440	54	15	the	the	DET
ejpam-440	54	16	maximal	maximal	ADJ
ejpam-440	54	17	element	element	NOUN
ejpam-440	54	18	for	for	ADP
ejpam-440	54	19	∆+	∆+	NUM
ejpam-440	54	20	in	in	ADP
ejpam-440	54	21	this	this	DET
ejpam-440	54	22	order	order	NOUN
ejpam-440	54	23	is	be	AUX
ejpam-440	54	24	the	the	DET
ejpam-440	54	25	distribution	distribution	NOUN
ejpam-440	54	26	function	function	NOUN
ejpam-440	54	27	ǫ0	ǫ0	NOUN
ejpam-440	54	28	given	give	VERB
ejpam-440	54	29	by	by	ADP
ejpam-440	54	30	ǫ0(t	ǫ0(t	NOUN
ejpam-440	54	31	)	)	PUNCT
ejpam-440	54	32	=	=	PUNCT
ejpam-440	54	33			PROPN
ejpam-440	54	34			PRON
ejpam-440	54	35			NOUN
ejpam-440	54	36	0	0	NUM
ejpam-440	54	37	,	,	PUNCT
ejpam-440	54	38	if	if	SCONJ
ejpam-440	54	39	t	t	PRON
ejpam-440	54	40	≤	≤	NUM
ejpam-440	54	41	0	0	NUM
ejpam-440	54	42	,	,	PUNCT
ejpam-440	54	43	1	1	NUM
ejpam-440	54	44	,	,	PUNCT
ejpam-440	54	45	if	if	SCONJ
ejpam-440	54	46	t	t	PROPN
ejpam-440	54	47	>	>	X
ejpam-440	54	48	0	0	X
ejpam-440	54	49	.	.	PUNCT
ejpam-440	55	1	definition	definition	NOUN
ejpam-440	55	2	1	1	NUM
ejpam-440	55	3	.	.	PUNCT
ejpam-440	56	1	(	(	PUNCT
ejpam-440	56	2	[	[	X
ejpam-440	56	3	34	34	NUM
ejpam-440	56	4	]	]	PUNCT
ejpam-440	56	5	)	)	PUNCT
ejpam-440	56	6	.	.	PUNCT
ejpam-440	57	1	a	a	DET
ejpam-440	57	2	mapping	mapping	NOUN
ejpam-440	57	3	t	t	NOUN
ejpam-440	57	4	:	:	PUNCT
ejpam-440	58	1	[	[	X
ejpam-440	58	2	0	0	NUM
ejpam-440	58	3	,	,	PUNCT
ejpam-440	58	4	1]×[0	1]×[0	NUM
ejpam-440	58	5	,	,	PUNCT
ejpam-440	58	6	1]→	1]→	NOUN
ejpam-440	59	1	[	[	X
ejpam-440	59	2	0	0	NUM
ejpam-440	59	3	,	,	PUNCT
ejpam-440	59	4	1	1	NUM
ejpam-440	59	5	]	]	PUNCT
ejpam-440	59	6	is	be	AUX
ejpam-440	59	7	a	a	DET
ejpam-440	59	8	continuous	continuous	ADJ
ejpam-440	59	9	triangular	triangular	NOUN
ejpam-440	59	10	norm	norm	NOUN
ejpam-440	59	11	(	(	PUNCT
ejpam-440	59	12	briefly	briefly	ADV
ejpam-440	59	13	,	,	PUNCT
ejpam-440	59	14	a	a	DET
ejpam-440	59	15	continuous	continuous	ADJ
ejpam-440	59	16	t	t	NOUN
ejpam-440	59	17	–	–	PUNCT
ejpam-440	59	18	norm	norm	NOUN
ejpam-440	59	19	)	)	PUNCT
ejpam-440	59	20	if	if	SCONJ
ejpam-440	59	21	t	t	PROPN
ejpam-440	59	22	satisfies	satisfy	VERB
ejpam-440	59	23	the	the	DET
ejpam-440	59	24	following	follow	VERB
ejpam-440	59	25	conditions	condition	NOUN
ejpam-440	59	26	:	:	PUNCT
ejpam-440	59	27	(	(	PUNCT
ejpam-440	59	28	a	a	X
ejpam-440	59	29	)	)	PUNCT
ejpam-440	59	30	t	t	PROPN
ejpam-440	59	31	is	be	AUX
ejpam-440	59	32	commutative	commutative	ADJ
ejpam-440	59	33	and	and	CCONJ
ejpam-440	59	34	associative	associative	ADJ
ejpam-440	59	35	;	;	PUNCT
ejpam-440	59	36	(	(	PUNCT
ejpam-440	59	37	b	b	X
ejpam-440	59	38	)	)	PUNCT
ejpam-440	59	39	t	t	PROPN
ejpam-440	59	40	is	be	AUX
ejpam-440	59	41	continuous	continuous	ADJ
ejpam-440	59	42	;	;	PUNCT
ejpam-440	59	43	(	(	PUNCT
ejpam-440	59	44	c	c	X
ejpam-440	59	45	)	)	PUNCT
ejpam-440	59	46	t	t	NOUN
ejpam-440	59	47	(	(	PUNCT
ejpam-440	59	48	a	a	DET
ejpam-440	59	49	,	,	PUNCT
ejpam-440	59	50	1	1	NUM
ejpam-440	59	51	)	)	PUNCT
ejpam-440	59	52	=	=	NOUN
ejpam-440	59	53	a	a	PRON
ejpam-440	59	54	for	for	ADP
ejpam-440	59	55	all	all	DET
ejpam-440	59	56	a	a	DET
ejpam-440	59	57	∈	∈	NOUN
ejpam-440	60	1	[	[	X
ejpam-440	60	2	0	0	NUM
ejpam-440	60	3	,	,	PUNCT
ejpam-440	60	4	1	1	NUM
ejpam-440	60	5	]	]	PUNCT
ejpam-440	60	6	;	;	PUNCT
ejpam-440	60	7	m.	m.	NOUN
ejpam-440	60	8	gordji	gordji	PROPN
ejpam-440	60	9	,	,	PUNCT
ejpam-440	60	10	j.	j.	PROPN
ejpam-440	60	11	rassias	rassias	PROPN
ejpam-440	60	12	,	,	PUNCT
ejpam-440	60	13	and	and	CCONJ
ejpam-440	60	14	m.	m.	NOUN
ejpam-440	60	15	savadkouhi	savadkouhi	PROPN
ejpam-440	60	16	/	/	SYM
ejpam-440	60	17	eur	eur	PROPN
ejpam-440	60	18	.	.	PUNCT
ejpam-440	61	1	j.	j.	PROPN
ejpam-440	61	2	pure	pure	PROPN
ejpam-440	61	3	appl	appl	PROPN
ejpam-440	61	4	.	.	PROPN
ejpam-440	61	5	math	math	PROPN
ejpam-440	61	6	,	,	PUNCT
ejpam-440	61	7	2	2	NUM
ejpam-440	61	8	(	(	PUNCT
ejpam-440	61	9	2009	2009	NUM
ejpam-440	61	10	)	)	PUNCT
ejpam-440	61	11	,	,	PUNCT
ejpam-440	61	12	(	(	PUNCT
ejpam-440	61	13	494	494	NUM
ejpam-440	61	14	-	-	SYM
ejpam-440	61	15	507	507	NUM
ejpam-440	61	16	)	)	PUNCT
ejpam-440	61	17	497	497	NUM
ejpam-440	61	18	(	(	PUNCT
ejpam-440	61	19	d	d	NOUN
ejpam-440	61	20	)	)	PUNCT
ejpam-440	61	21	t	t	PROPN
ejpam-440	61	22	(	(	PUNCT
ejpam-440	61	23	a	a	PRON
ejpam-440	61	24	,	,	PUNCT
ejpam-440	61	25	b	b	NOUN
ejpam-440	61	26	)	)	PUNCT
ejpam-440	61	27	≤	≤	NOUN
ejpam-440	61	28	t	t	NOUN
ejpam-440	61	29	(	(	PUNCT
ejpam-440	61	30	c	c	X
ejpam-440	61	31	,	,	PUNCT
ejpam-440	61	32	d	d	NOUN
ejpam-440	61	33	)	)	PUNCT
ejpam-440	62	1	whenever	whenever	SCONJ
ejpam-440	62	2	a	a	DET
ejpam-440	62	3	≤	≤	NUM
ejpam-440	62	4	c	c	NOUN
ejpam-440	62	5	and	and	CCONJ
ejpam-440	62	6	b	b	NOUN
ejpam-440	62	7	≤	≤	NUM
ejpam-440	62	8	d	d	NOUN
ejpam-440	62	9	for	for	ADP
ejpam-440	62	10	all	all	DET
ejpam-440	62	11	a	a	DET
ejpam-440	62	12	,	,	PUNCT
ejpam-440	62	13	b	b	NOUN
ejpam-440	62	14	,	,	PUNCT
ejpam-440	62	15	c	c	NOUN
ejpam-440	62	16	,	,	PUNCT
ejpam-440	62	17	d	d	PROPN
ejpam-440	62	18	∈	∈	PROPN
ejpam-440	63	1	[	[	X
ejpam-440	63	2	0	0	NUM
ejpam-440	63	3	,	,	PUNCT
ejpam-440	63	4	1	1	NUM
ejpam-440	63	5	]	]	PUNCT
ejpam-440	63	6	.	.	PUNCT
ejpam-440	64	1	typical	typical	ADJ
ejpam-440	64	2	examples	example	NOUN
ejpam-440	64	3	of	of	ADP
ejpam-440	64	4	continuous	continuous	ADJ
ejpam-440	64	5	t	t	PROPN
ejpam-440	64	6	–	–	PUNCT
ejpam-440	64	7	norms	norm	NOUN
ejpam-440	64	8	are	be	AUX
ejpam-440	64	9	tp(a	tp(a	PRON
ejpam-440	64	10	,	,	PUNCT
ejpam-440	64	11	b	b	NOUN
ejpam-440	64	12	)	)	PUNCT
ejpam-440	64	13	=	=	SYM
ejpam-440	64	14	ab	ab	PROPN
ejpam-440	64	15	,	,	PUNCT
ejpam-440	64	16	tm(a	tm(a	PROPN
ejpam-440	64	17	,	,	PUNCT
ejpam-440	64	18	b	b	NOUN
ejpam-440	64	19	)	)	PUNCT
ejpam-440	64	20	=	=	SYM
ejpam-440	64	21	min(a	min(a	PROPN
ejpam-440	64	22	,	,	PUNCT
ejpam-440	64	23	b	b	NOUN
ejpam-440	64	24	)	)	PUNCT
ejpam-440	64	25	and	and	CCONJ
ejpam-440	64	26	tl(a	tl(a	NUM
ejpam-440	64	27	,	,	PUNCT
ejpam-440	64	28	b	b	NOUN
ejpam-440	64	29	)	)	PUNCT
ejpam-440	64	30	=	=	SYM
ejpam-440	65	1	max(a	max(a	PROPN
ejpam-440	65	2	+	+	NUM
ejpam-440	65	3	b	b	X
ejpam-440	65	4	−	−	PROPN
ejpam-440	65	5	1	1	NUM
ejpam-440	65	6	,	,	PUNCT
ejpam-440	65	7	0	0	NUM
ejpam-440	65	8	)	)	PUNCT
ejpam-440	65	9	(	(	PUNCT
ejpam-440	65	10	the	the	DET
ejpam-440	65	11	lukasiewicz	lukasiewicz	ADJ
ejpam-440	65	12	t	t	NOUN
ejpam-440	65	13	-	-	PUNCT
ejpam-440	65	14	norm	norm	NOUN
ejpam-440	65	15	)	)	PUNCT
ejpam-440	65	16	.	.	PUNCT
ejpam-440	66	1	recall	recall	NOUN
ejpam-440	66	2	(	(	PUNCT
ejpam-440	66	3	see	see	VERB
ejpam-440	66	4	[	[	X
ejpam-440	66	5	11	11	NUM
ejpam-440	66	6	]	]	PUNCT
ejpam-440	66	7	,	,	PUNCT
ejpam-440	66	8	[	[	X
ejpam-440	66	9	12	12	NUM
ejpam-440	66	10	]	]	PUNCT
ejpam-440	66	11	)	)	PUNCT
ejpam-440	66	12	that	that	SCONJ
ejpam-440	66	13	if	if	SCONJ
ejpam-440	66	14	t	t	PROPN
ejpam-440	66	15	is	be	AUX
ejpam-440	66	16	a	a	DET
ejpam-440	66	17	t	t	NOUN
ejpam-440	66	18	-	-	PUNCT
ejpam-440	66	19	norm	norm	NOUN
ejpam-440	66	20	and	and	CCONJ
ejpam-440	66	21	{	{	PUNCT
ejpam-440	66	22	xn	xn	X
ejpam-440	66	23	}	}	PUNCT
ejpam-440	66	24	is	be	AUX
ejpam-440	66	25	a	a	DET
ejpam-440	66	26	given	give	VERB
ejpam-440	66	27	sequence	sequence	NOUN
ejpam-440	66	28	of	of	ADP
ejpam-440	66	29	numbers	number	NOUN
ejpam-440	66	30	in	in	ADP
ejpam-440	66	31	[	[	X
ejpam-440	66	32	0	0	NUM
ejpam-440	66	33	,	,	PUNCT
ejpam-440	66	34	1	1	NUM
ejpam-440	66	35	]	]	PUNCT
ejpam-440	66	36	,	,	PUNCT
ejpam-440	66	37	t	t	PROPN
ejpam-440	66	38	n	n	CCONJ
ejpam-440	66	39	i=1	i=1	PROPN
ejpam-440	66	40	x	x	VERB
ejpam-440	67	1	i	i	PRON
ejpam-440	67	2	is	be	AUX
ejpam-440	67	3	defined	define	VERB
ejpam-440	67	4	recurrently	recurrently	ADV
ejpam-440	67	5	by	by	ADP
ejpam-440	67	6	t	t	PROPN
ejpam-440	67	7	1	1	NUM
ejpam-440	67	8	i=1	i=1	PROPN
ejpam-440	67	9	x	x	PUNCT
ejpam-440	68	1	i	i	NOUN
ejpam-440	68	2	=	=	PUNCT
ejpam-440	68	3	x1	x1	PROPN
ejpam-440	68	4	and	and	CCONJ
ejpam-440	68	5	t	t	PROPN
ejpam-440	68	6	n	n	CCONJ
ejpam-440	68	7	i=1	i=1	PROPN
ejpam-440	68	8	x	x	PUNCT
ejpam-440	69	1	i	i	PROPN
ejpam-440	69	2	=	=	SYM
ejpam-440	69	3	t	t	PROPN
ejpam-440	69	4	(	(	PUNCT
ejpam-440	69	5	t	t	PROPN
ejpam-440	69	6	n−1	n−1	PROPN
ejpam-440	69	7	i=1	i=1	PROPN
ejpam-440	69	8	x	x	PROPN
ejpam-440	69	9	i	i	PROPN
ejpam-440	69	10	,	,	PUNCT
ejpam-440	69	11	xn	xn	PROPN
ejpam-440	69	12	)	)	PUNCT
ejpam-440	69	13	for	for	ADP
ejpam-440	69	14	n	n	X
ejpam-440	69	15	≥	≥	NUM
ejpam-440	69	16	2	2	NUM
ejpam-440	69	17	.	.	X
ejpam-440	69	18	t∞	t∞	NOUN
ejpam-440	70	1	i	i	PRON
ejpam-440	70	2	=	=	VERB
ejpam-440	70	3	n	n	NOUN
ejpam-440	70	4	x	x	VERB
ejpam-440	70	5	i	i	PRON
ejpam-440	70	6	is	be	AUX
ejpam-440	70	7	defined	define	VERB
ejpam-440	70	8	as	as	ADP
ejpam-440	70	9	t∞	t∞	NOUN
ejpam-440	70	10	i=1	i=1	PROPN
ejpam-440	70	11	xn+i	xn+i	PROPN
ejpam-440	70	12	.	.	PUNCT
ejpam-440	71	1	it	it	PRON
ejpam-440	71	2	is	be	AUX
ejpam-440	71	3	known	know	VERB
ejpam-440	71	4	(	(	PUNCT
ejpam-440	71	5	[	[	X
ejpam-440	71	6	12	12	NUM
ejpam-440	71	7	]	]	PUNCT
ejpam-440	71	8	)	)	PUNCT
ejpam-440	71	9	that	that	SCONJ
ejpam-440	71	10	for	for	ADP
ejpam-440	71	11	the	the	DET
ejpam-440	71	12	lukasiewicz	lukasiewicz	ADJ
ejpam-440	71	13	t	t	PROPN
ejpam-440	71	14	–	–	PUNCT
ejpam-440	71	15	norm	norm	NOUN
ejpam-440	71	16	the	the	DET
ejpam-440	71	17	following	follow	VERB
ejpam-440	71	18	implication	implication	NOUN
ejpam-440	71	19	holds	hold	VERB
ejpam-440	71	20	:	:	PUNCT
ejpam-440	71	21	lim	lim	PROPN
ejpam-440	71	22	n→∞	n→∞	X
ejpam-440	71	23	(	(	PUNCT
ejpam-440	71	24	tl	tl	PROPN
ejpam-440	71	25	)	)	PUNCT
ejpam-440	71	26	∞	∞	PROPN
ejpam-440	71	27	i=1	i=1	PROPN
ejpam-440	71	28	xn+i	xn+i	PROPN
ejpam-440	72	1	=	=	SYM
ejpam-440	72	2	1	1	NUM
ejpam-440	72	3	⇐	⇐	ADJ
ejpam-440	72	4	⇒	⇒	NOUN
ejpam-440	72	5	∞	∞	PROPN
ejpam-440	72	6	∑	∑	PROPN
ejpam-440	72	7	n=1	n=1	PROPN
ejpam-440	72	8	(	(	PUNCT
ejpam-440	72	9	1−	1−	NUM
ejpam-440	72	10	xn)<∞	xn)<∞	NOUN
ejpam-440	72	11	(	(	PUNCT
ejpam-440	72	12	4	4	NUM
ejpam-440	72	13	)	)	PUNCT
ejpam-440	72	14	for	for	ADP
ejpam-440	72	15	all	all	DET
ejpam-440	72	16	t	t	PROPN
ejpam-440	72	17	≥	≥	NOUN
ejpam-440	72	18	0	0	NUM
ejpam-440	72	19	.	.	PUNCT
ejpam-440	72	20	definition	definition	NOUN
ejpam-440	72	21	2	2	NUM
ejpam-440	72	22	.	.	PUNCT
ejpam-440	73	1	(	(	PUNCT
ejpam-440	73	2	[	[	X
ejpam-440	73	3	35	35	NUM
ejpam-440	73	4	]	]	NUM
ejpam-440	73	5	)	)	PUNCT
ejpam-440	73	6	.	.	PUNCT
ejpam-440	74	1	a	a	DET
ejpam-440	74	2	random	random	ADJ
ejpam-440	74	3	normed	normed	ADJ
ejpam-440	74	4	space	space	NOUN
ejpam-440	74	5	(	(	PUNCT
ejpam-440	74	6	briefly	briefly	ADV
ejpam-440	74	7	,	,	PUNCT
ejpam-440	74	8	rn	rn	PROPN
ejpam-440	74	9	–	–	NOUN
ejpam-440	74	10	space	space	NOUN
ejpam-440	74	11	)	)	PUNCT
ejpam-440	74	12	is	be	AUX
ejpam-440	74	13	a	a	DET
ejpam-440	74	14	triple	triple	ADJ
ejpam-440	74	15	(	(	PUNCT
ejpam-440	74	16	x	x	SYM
ejpam-440	74	17	,	,	PUNCT
ejpam-440	74	18	µ	µ	NOUN
ejpam-440	74	19	,	,	PUNCT
ejpam-440	74	20	t	t	PROPN
ejpam-440	74	21	)	)	PUNCT
ejpam-440	74	22	,	,	PUNCT
ejpam-440	74	23	where	where	SCONJ
ejpam-440	74	24	x	x	PRON
ejpam-440	74	25	is	be	AUX
ejpam-440	74	26	a	a	DET
ejpam-440	74	27	vector	vector	NOUN
ejpam-440	74	28	space	space	NOUN
ejpam-440	74	29	,	,	PUNCT
ejpam-440	74	30	t	t	PROPN
ejpam-440	74	31	is	be	AUX
ejpam-440	74	32	a	a	DET
ejpam-440	74	33	continuous	continuous	ADJ
ejpam-440	74	34	t	t	NOUN
ejpam-440	74	35	-	-	PUNCT
ejpam-440	74	36	norm	norm	NOUN
ejpam-440	74	37	,	,	PUNCT
ejpam-440	74	38	and	and	CCONJ
ejpam-440	74	39	µ	µ	NOUN
ejpam-440	74	40	is	be	AUX
ejpam-440	74	41	a	a	DET
ejpam-440	74	42	mapping	mapping	NOUN
ejpam-440	74	43	from	from	ADP
ejpam-440	74	44	x	x	PUNCT
ejpam-440	74	45	into	into	ADP
ejpam-440	74	46	d+	d+	NOUN
ejpam-440	74	47	such	such	ADJ
ejpam-440	74	48	that	that	SCONJ
ejpam-440	74	49	,	,	PUNCT
ejpam-440	74	50	the	the	DET
ejpam-440	74	51	following	follow	VERB
ejpam-440	74	52	conditions	condition	NOUN
ejpam-440	74	53	hold	hold	VERB
ejpam-440	74	54	:	:	PUNCT
ejpam-440	74	55	(	(	PUNCT
ejpam-440	74	56	rn1	rn1	NOUN
ejpam-440	74	57	)	)	PUNCT
ejpam-440	74	58	µx(t	µx(t	NUM
ejpam-440	74	59	)	)	PUNCT
ejpam-440	74	60	=	=	SYM
ejpam-440	75	1	ǫ0(t	ǫ0(t	X
ejpam-440	75	2	)	)	PUNCT
ejpam-440	75	3	for	for	ADP
ejpam-440	75	4	all	all	DET
ejpam-440	75	5	t	t	PROPN
ejpam-440	75	6	>	>	X
ejpam-440	75	7	0	0	PUNCT
ejpam-440	76	1	if	if	SCONJ
ejpam-440	76	2	and	and	CCONJ
ejpam-440	76	3	only	only	ADV
ejpam-440	76	4	if	if	SCONJ
ejpam-440	76	5	x	x	SYM
ejpam-440	76	6	=	=	SYM
ejpam-440	76	7	0	0	NUM
ejpam-440	76	8	;	;	PUNCT
ejpam-440	76	9	(	(	PUNCT
ejpam-440	76	10	rn2	rn2	NOUN
ejpam-440	76	11	)	)	PUNCT
ejpam-440	76	12	µαx(t	µαx(t	PROPN
ejpam-440	76	13	)	)	PUNCT
ejpam-440	76	14	=	=	PRON
ejpam-440	76	15	µx	µx	NOUN
ejpam-440	76	16	(	(	PUNCT
ejpam-440	76	17	t	t	PROPN
ejpam-440	76	18	|α|	|α|	PROPN
ejpam-440	76	19	)	)	PUNCT
ejpam-440	76	20	for	for	ADP
ejpam-440	76	21	all	all	DET
ejpam-440	76	22	x	x	SYM
ejpam-440	76	23	∈	∈	PROPN
ejpam-440	76	24	x	x	X
ejpam-440	76	25	,	,	PUNCT
ejpam-440	76	26	α	α	PROPN
ejpam-440	76	27	6=	6=	ADP
ejpam-440	76	28	0	0	NUM
ejpam-440	76	29	and	and	CCONJ
ejpam-440	76	30	all	all	DET
ejpam-440	76	31	t	t	PROPN
ejpam-440	76	32	≥	≥	NOUN
ejpam-440	76	33	0	0	NUM
ejpam-440	76	34	;	;	PUNCT
ejpam-440	76	35	(	(	PUNCT
ejpam-440	76	36	rn3	rn3	NOUN
ejpam-440	76	37	)	)	PUNCT
ejpam-440	77	1	µx+y(t	µx+y(t	PROPN
ejpam-440	77	2	+	+	CCONJ
ejpam-440	77	3	s	s	X
ejpam-440	77	4	)	)	PUNCT
ejpam-440	77	5	≥	≥	NOUN
ejpam-440	77	6	t	t	PROPN
ejpam-440	77	7	(	(	PUNCT
ejpam-440	77	8	µx(t),µy(s	µx(t),µy(s	PROPN
ejpam-440	77	9	)	)	PUNCT
ejpam-440	77	10	)	)	PUNCT
ejpam-440	77	11	for	for	ADP
ejpam-440	77	12	all	all	DET
ejpam-440	77	13	x	x	SYM
ejpam-440	77	14	,	,	PUNCT
ejpam-440	77	15	y	y	PROPN
ejpam-440	77	16	∈	∈	PROPN
ejpam-440	77	17	x	x	X
ejpam-440	77	18	and	and	CCONJ
ejpam-440	77	19	t	t	PROPN
ejpam-440	77	20	,	,	PUNCT
ejpam-440	77	21	s	s	VERB
ejpam-440	77	22	≥	≥	NOUN
ejpam-440	77	23	0	0	NUM
ejpam-440	77	24	.	.	PUNCT
ejpam-440	78	1	every	every	DET
ejpam-440	78	2	normed	normed	ADJ
ejpam-440	78	3	space	space	NOUN
ejpam-440	78	4	(	(	PUNCT
ejpam-440	78	5	x	x	NOUN
ejpam-440	78	6	,	,	PUNCT
ejpam-440	78	7	‖.‖	‖.‖	NOUN
ejpam-440	78	8	)	)	PUNCT
ejpam-440	78	9	defines	define	VERB
ejpam-440	78	10	a	a	DET
ejpam-440	78	11	random	random	ADJ
ejpam-440	78	12	normed	normed	ADJ
ejpam-440	78	13	space	space	NOUN
ejpam-440	78	14	(	(	PUNCT
ejpam-440	78	15	x	x	X
ejpam-440	78	16	,	,	PUNCT
ejpam-440	78	17	µ	µ	NOUN
ejpam-440	78	18	,	,	PUNCT
ejpam-440	78	19	tm	tm	NOUN
ejpam-440	78	20	)	)	PUNCT
ejpam-440	78	21	where	where	SCONJ
ejpam-440	78	22	µx(t	µx(t	PUNCT
ejpam-440	78	23	)	)	PUNCT
ejpam-440	78	24	=	=	SYM
ejpam-440	78	25	t	t	PROPN
ejpam-440	78	26	t	t	NOUN
ejpam-440	78	27	+	+	CCONJ
ejpam-440	78	28	‖x‖	‖x‖	PROPN
ejpam-440	78	29	,	,	PUNCT
ejpam-440	78	30	for	for	ADP
ejpam-440	78	31	all	all	DET
ejpam-440	78	32	t	t	PROPN
ejpam-440	78	33	>	>	X
ejpam-440	78	34	0	0	NUM
ejpam-440	78	35	,	,	PUNCT
ejpam-440	78	36	and	and	CCONJ
ejpam-440	78	37	tm	tm	NOUN
ejpam-440	78	38	is	be	AUX
ejpam-440	78	39	the	the	DET
ejpam-440	78	40	minimum	minimum	ADJ
ejpam-440	78	41	t	t	NOUN
ejpam-440	78	42	-	-	PUNCT
ejpam-440	78	43	norm	norm	NOUN
ejpam-440	78	44	.	.	PUNCT
ejpam-440	79	1	this	this	DET
ejpam-440	79	2	space	space	NOUN
ejpam-440	79	3	is	be	AUX
ejpam-440	79	4	called	call	VERB
ejpam-440	79	5	the	the	DET
ejpam-440	79	6	induced	induce	VERB
ejpam-440	79	7	random	random	ADJ
ejpam-440	79	8	normed	normed	ADJ
ejpam-440	79	9	space	space	NOUN
ejpam-440	79	10	.	.	PUNCT
ejpam-440	80	1	definition	definition	NOUN
ejpam-440	80	2	3	3	X
ejpam-440	80	3	.	.	PUNCT
ejpam-440	81	1	let	let	AUX
ejpam-440	81	2	(	(	PUNCT
ejpam-440	81	3	x	x	X
ejpam-440	81	4	,	,	PUNCT
ejpam-440	81	5	µ	µ	NOUN
ejpam-440	81	6	,	,	PUNCT
ejpam-440	81	7	t	t	PROPN
ejpam-440	81	8	)	)	PUNCT
ejpam-440	81	9	be	be	AUX
ejpam-440	81	10	an	an	DET
ejpam-440	81	11	rn	rn	ADJ
ejpam-440	81	12	–	–	PUNCT
ejpam-440	81	13	space	space	NOUN
ejpam-440	81	14	.	.	PUNCT
ejpam-440	82	1	(	(	PUNCT
ejpam-440	82	2	1	1	X
ejpam-440	82	3	)	)	PUNCT
ejpam-440	82	4	a	a	DET
ejpam-440	82	5	sequence	sequence	NOUN
ejpam-440	82	6	{	{	PUNCT
ejpam-440	82	7	xn	xn	NOUN
ejpam-440	82	8	}	}	PUNCT
ejpam-440	82	9	in	in	ADP
ejpam-440	82	10	x	x	VERB
ejpam-440	82	11	is	be	AUX
ejpam-440	82	12	said	say	VERB
ejpam-440	82	13	to	to	PART
ejpam-440	82	14	be	be	AUX
ejpam-440	82	15	convergent	convergent	ADJ
ejpam-440	82	16	to	to	ADP
ejpam-440	82	17	x	x	PUNCT
ejpam-440	82	18	in	in	ADP
ejpam-440	82	19	x	x	PUNCT
ejpam-440	82	20	if	if	SCONJ
ejpam-440	82	21	,	,	PUNCT
ejpam-440	82	22	for	for	ADP
ejpam-440	82	23	every	every	DET
ejpam-440	82	24	ε	ε	PROPN
ejpam-440	82	25	>	>	X
ejpam-440	82	26	0	0	PUNCT
ejpam-440	82	27	and	and	CCONJ
ejpam-440	82	28	λ	λ	X
ejpam-440	82	29	>	>	X
ejpam-440	82	30	0	0	NUM
ejpam-440	82	31	,	,	PUNCT
ejpam-440	82	32	there	there	PRON
ejpam-440	82	33	exists	exist	VERB
ejpam-440	82	34	positive	positive	ADJ
ejpam-440	82	35	integer	integer	NOUN
ejpam-440	82	36	n	n	CCONJ
ejpam-440	82	37	such	such	ADJ
ejpam-440	82	38	that	that	SCONJ
ejpam-440	82	39	µxn−x(ε	µxn−x(ε	PROPN
ejpam-440	82	40	)	)	PUNCT
ejpam-440	82	41	>	>	X
ejpam-440	83	1	1−λ	1−λ	NUM
ejpam-440	83	2	whenever	whenever	SCONJ
ejpam-440	83	3	n≥	n≥	X
ejpam-440	83	4	n.	n.	NOUN
ejpam-440	83	5	(	(	PUNCT
ejpam-440	83	6	2	2	NUM
ejpam-440	83	7	)	)	PUNCT
ejpam-440	83	8	a	a	DET
ejpam-440	83	9	sequence	sequence	NOUN
ejpam-440	83	10	{	{	PUNCT
ejpam-440	83	11	xn	xn	NOUN
ejpam-440	83	12	}	}	PUNCT
ejpam-440	83	13	in	in	ADP
ejpam-440	83	14	x	x	PROPN
ejpam-440	83	15	is	be	AUX
ejpam-440	83	16	called	call	VERB
ejpam-440	83	17	cauchy	cauchy	ADJ
ejpam-440	83	18	sequence	sequence	NOUN
ejpam-440	83	19	if	if	SCONJ
ejpam-440	83	20	,	,	PUNCT
ejpam-440	83	21	for	for	ADP
ejpam-440	83	22	every	every	DET
ejpam-440	83	23	ε	ε	PROPN
ejpam-440	83	24	>	>	X
ejpam-440	83	25	0	0	PUNCT
ejpam-440	83	26	and	and	CCONJ
ejpam-440	83	27	λ	λ	X
ejpam-440	83	28	>	>	X
ejpam-440	83	29	0	0	PROPN
ejpam-440	83	30	,	,	PUNCT
ejpam-440	83	31	there	there	PRON
ejpam-440	83	32	m.	m.	NOUN
ejpam-440	83	33	gordji	gordji	PROPN
ejpam-440	83	34	,	,	PUNCT
ejpam-440	83	35	j.	j.	PROPN
ejpam-440	83	36	rassias	rassias	PROPN
ejpam-440	83	37	,	,	PUNCT
ejpam-440	83	38	and	and	CCONJ
ejpam-440	83	39	m.	m.	NOUN
ejpam-440	83	40	savadkouhi	savadkouhi	PROPN
ejpam-440	83	41	/	/	SYM
ejpam-440	83	42	eur	eur	PROPN
ejpam-440	83	43	.	.	PUNCT
ejpam-440	84	1	j.	j.	PROPN
ejpam-440	84	2	pure	pure	PROPN
ejpam-440	84	3	appl	appl	PROPN
ejpam-440	84	4	.	.	PROPN
ejpam-440	84	5	math	math	PROPN
ejpam-440	84	6	,	,	PUNCT
ejpam-440	84	7	2	2	NUM
ejpam-440	84	8	(	(	PUNCT
ejpam-440	84	9	2009	2009	NUM
ejpam-440	84	10	)	)	PUNCT
ejpam-440	84	11	,	,	PUNCT
ejpam-440	84	12	(	(	PUNCT
ejpam-440	84	13	494	494	NUM
ejpam-440	84	14	-	-	SYM
ejpam-440	84	15	507	507	NUM
ejpam-440	84	16	)	)	PUNCT
ejpam-440	84	17	498	498	NUM
ejpam-440	84	18	exists	exist	VERB
ejpam-440	84	19	positive	positive	ADJ
ejpam-440	84	20	integer	integer	NOUN
ejpam-440	84	21	n	n	CCONJ
ejpam-440	84	22	such	such	ADJ
ejpam-440	84	23	that	that	DET
ejpam-440	84	24	µxn−xm	µxn−xm	ADJ
ejpam-440	84	25	(	(	PUNCT
ejpam-440	84	26	ε	ε	PROPN
ejpam-440	84	27	)	)	PUNCT
ejpam-440	84	28	>	>	X
ejpam-440	85	1	1−λ	1−λ	NUM
ejpam-440	86	1	whenever	whenever	SCONJ
ejpam-440	86	2	n	n	X
ejpam-440	86	3	≥	≥	NOUN
ejpam-440	86	4	m	m	PROPN
ejpam-440	86	5	≥	≥	PROPN
ejpam-440	86	6	n.	n.	NOUN
ejpam-440	86	7	(	(	PUNCT
ejpam-440	86	8	3	3	NUM
ejpam-440	86	9	)	)	PUNCT
ejpam-440	86	10	an	an	DET
ejpam-440	86	11	rn	rn	PROPN
ejpam-440	86	12	–	–	PUNCT
ejpam-440	86	13	space	space	NOUN
ejpam-440	86	14	(	(	PUNCT
ejpam-440	86	15	x	x	X
ejpam-440	86	16	,	,	PUNCT
ejpam-440	86	17	µ	µ	NOUN
ejpam-440	86	18	,	,	PUNCT
ejpam-440	86	19	t	t	PROPN
ejpam-440	86	20	)	)	PUNCT
ejpam-440	86	21	is	be	AUX
ejpam-440	86	22	said	say	VERB
ejpam-440	86	23	to	to	PART
ejpam-440	86	24	be	be	AUX
ejpam-440	86	25	complete	complete	ADJ
ejpam-440	86	26	if	if	SCONJ
ejpam-440	86	27	and	and	CCONJ
ejpam-440	86	28	only	only	ADV
ejpam-440	86	29	if	if	SCONJ
ejpam-440	86	30	every	every	DET
ejpam-440	86	31	cauchy	cauchy	ADJ
ejpam-440	86	32	sequence	sequence	NOUN
ejpam-440	86	33	in	in	ADP
ejpam-440	86	34	x	x	PROPN
ejpam-440	86	35	is	be	AUX
ejpam-440	86	36	convergent	convergent	ADJ
ejpam-440	86	37	to	to	ADP
ejpam-440	86	38	a	a	DET
ejpam-440	86	39	point	point	NOUN
ejpam-440	86	40	in	in	ADP
ejpam-440	86	41	x	x	X
ejpam-440	86	42	.	.	PUNCT
ejpam-440	87	1	theorem	theorem	NOUN
ejpam-440	87	2	1	1	NUM
ejpam-440	87	3	.	.	PUNCT
ejpam-440	88	1	(	(	PUNCT
ejpam-440	88	2	[	[	X
ejpam-440	88	3	34	34	NUM
ejpam-440	88	4	]	]	PUNCT
ejpam-440	88	5	)	)	PUNCT
ejpam-440	88	6	.	.	PUNCT
ejpam-440	89	1	if	if	SCONJ
ejpam-440	89	2	(	(	PUNCT
ejpam-440	89	3	x	x	X
ejpam-440	89	4	,	,	PUNCT
ejpam-440	89	5	µ	µ	NOUN
ejpam-440	89	6	,	,	PUNCT
ejpam-440	89	7	t	t	PROPN
ejpam-440	89	8	)	)	PUNCT
ejpam-440	89	9	is	be	AUX
ejpam-440	89	10	an	an	DET
ejpam-440	89	11	rn	rn	ADJ
ejpam-440	89	12	–	–	PUNCT
ejpam-440	89	13	space	space	NOUN
ejpam-440	89	14	and	and	CCONJ
ejpam-440	89	15	{	{	PUNCT
ejpam-440	89	16	xn	xn	X
ejpam-440	89	17	}	}	PUNCT
ejpam-440	89	18	is	be	AUX
ejpam-440	89	19	a	a	DET
ejpam-440	89	20	sequence	sequence	NOUN
ejpam-440	89	21	such	such	ADJ
ejpam-440	89	22	that	that	SCONJ
ejpam-440	89	23	xn→	xn→	PUNCT
ejpam-440	90	1	x	x	X
ejpam-440	90	2	,	,	PUNCT
ejpam-440	90	3	then	then	ADV
ejpam-440	90	4	limn→∞µxn	limn→∞µxn	VERB
ejpam-440	90	5	(	(	PUNCT
ejpam-440	90	6	t	t	NOUN
ejpam-440	90	7	)	)	PUNCT
ejpam-440	90	8	=	=	PUNCT
ejpam-440	90	9	µx(t	µx(t	NOUN
ejpam-440	90	10	)	)	PUNCT
ejpam-440	90	11	almost	almost	ADV
ejpam-440	90	12	everywhere	everywhere	ADV
ejpam-440	90	13	.	.	PUNCT
ejpam-440	91	1	the	the	DET
ejpam-440	91	2	aim	aim	NOUN
ejpam-440	91	3	of	of	ADP
ejpam-440	91	4	this	this	DET
ejpam-440	91	5	paper	paper	NOUN
ejpam-440	91	6	is	be	AUX
ejpam-440	91	7	to	to	PART
ejpam-440	91	8	investigate	investigate	VERB
ejpam-440	91	9	the	the	DET
ejpam-440	91	10	stability	stability	NOUN
ejpam-440	91	11	of	of	ADP
ejpam-440	91	12	the	the	DET
ejpam-440	91	13	quadratic	quadratic	ADJ
ejpam-440	91	14	and	and	CCONJ
ejpam-440	91	15	cubic	cubic	ADJ
ejpam-440	91	16	functional	functional	ADJ
ejpam-440	91	17	equations	equation	NOUN
ejpam-440	91	18	in	in	ADP
ejpam-440	91	19	random	random	ADJ
ejpam-440	91	20	normed	normed	ADJ
ejpam-440	91	21	spaces	space	NOUN
ejpam-440	91	22	(	(	PUNCT
ejpam-440	91	23	in	in	ADP
ejpam-440	91	24	the	the	DET
ejpam-440	91	25	sense	sense	NOUN
ejpam-440	91	26	of	of	ADP
ejpam-440	91	27	sherstnev	sherstnev	NOUN
ejpam-440	91	28	)	)	PUNCT
ejpam-440	91	29	,	,	PUNCT
ejpam-440	91	30	under	under	ADP
ejpam-440	91	31	arbitrary	arbitrary	ADJ
ejpam-440	91	32	continuous	continuous	ADJ
ejpam-440	91	33	t	t	PROPN
ejpam-440	91	34	–	–	PUNCT
ejpam-440	91	35	norms	norm	NOUN
ejpam-440	91	36	.	.	PUNCT
ejpam-440	92	1	2	2	X
ejpam-440	92	2	.	.	X
ejpam-440	92	3	main	main	ADJ
ejpam-440	92	4	results	result	NOUN
ejpam-440	92	5	in	in	ADP
ejpam-440	92	6	this	this	DET
ejpam-440	92	7	section	section	NOUN
ejpam-440	92	8	we	we	PRON
ejpam-440	92	9	establish	establish	VERB
ejpam-440	92	10	the	the	DET
ejpam-440	92	11	stability	stability	NOUN
ejpam-440	92	12	of	of	ADP
ejpam-440	92	13	the	the	DET
ejpam-440	92	14	quadratic	quadratic	ADJ
ejpam-440	92	15	and	and	CCONJ
ejpam-440	92	16	cubic	cubic	ADJ
ejpam-440	92	17	functional	functional	ADJ
ejpam-440	92	18	equation	equation	NOUN
ejpam-440	92	19	f	f	X
ejpam-440	92	20	(	(	PUNCT
ejpam-440	92	21	2x	2x	NUM
ejpam-440	92	22	+	+	CCONJ
ejpam-440	92	23	y	y	X
ejpam-440	92	24	)	)	PUNCT
ejpam-440	93	1	+	+	CCONJ
ejpam-440	93	2	f	f	X
ejpam-440	93	3	(	(	PUNCT
ejpam-440	93	4	2x	2x	NUM
ejpam-440	93	5	−	−	PROPN
ejpam-440	94	1	y)−	y)−	PROPN
ejpam-440	94	2	2	2	NUM
ejpam-440	94	3	f	f	NOUN
ejpam-440	94	4	(	(	PUNCT
ejpam-440	94	5	x	x	PROPN
ejpam-440	94	6	+	+	PUNCT
ejpam-440	94	7	y)−	y)−	PROPN
ejpam-440	94	8	2	2	NUM
ejpam-440	94	9	f	f	NOUN
ejpam-440	94	10	(	(	PUNCT
ejpam-440	94	11	x	x	X
ejpam-440	94	12	−	−	PUNCT
ejpam-440	94	13	y)−	y)−	PROPN
ejpam-440	94	14	12	12	NUM
ejpam-440	94	15	f	f	NOUN
ejpam-440	94	16	(	(	PUNCT
ejpam-440	94	17	x	x	NOUN
ejpam-440	94	18	)	)	PUNCT
ejpam-440	94	19	=	=	SYM
ejpam-440	94	20	0	0	PUNCT
ejpam-440	94	21	(	(	PUNCT
ejpam-440	94	22	5	5	NUM
ejpam-440	94	23	)	)	PUNCT
ejpam-440	94	24	in	in	ADP
ejpam-440	94	25	the	the	DET
ejpam-440	94	26	setting	setting	NOUN
ejpam-440	94	27	of	of	ADP
ejpam-440	94	28	random	random	ADJ
ejpam-440	94	29	normed	normed	ADJ
ejpam-440	94	30	spaces	space	NOUN
ejpam-440	94	31	.	.	PUNCT
ejpam-440	95	1	theorem	theorem	NOUN
ejpam-440	95	2	2	2	NUM
ejpam-440	95	3	.	.	PUNCT
ejpam-440	96	1	let	let	VERB
ejpam-440	96	2	x	x	PRON
ejpam-440	96	3	be	be	AUX
ejpam-440	96	4	a	a	DET
ejpam-440	96	5	real	real	ADJ
ejpam-440	96	6	linear	linear	ADJ
ejpam-440	96	7	space	space	NOUN
ejpam-440	96	8	,	,	PUNCT
ejpam-440	96	9	(	(	PUNCT
ejpam-440	96	10	y,µ	y,µ	PROPN
ejpam-440	96	11	,	,	PUNCT
ejpam-440	96	12	t	t	PROPN
ejpam-440	96	13	)	)	PUNCT
ejpam-440	96	14	be	be	AUX
ejpam-440	96	15	a	a	DET
ejpam-440	96	16	complete	complete	ADJ
ejpam-440	96	17	rn	rn	NOUN
ejpam-440	96	18	-	-	NOUN
ejpam-440	96	19	space	space	NOUN
ejpam-440	96	20	and	and	CCONJ
ejpam-440	96	21	f	f	NOUN
ejpam-440	96	22	:	:	PUNCT
ejpam-440	96	23	x	x	X
ejpam-440	96	24	→	→	SYM
ejpam-440	96	25	y	y	X
ejpam-440	96	26	be	be	AUX
ejpam-440	96	27	a	a	DET
ejpam-440	96	28	mapping	mapping	NOUN
ejpam-440	96	29	with	with	ADP
ejpam-440	96	30	f	f	PROPN
ejpam-440	96	31	(	(	PUNCT
ejpam-440	96	32	0	0	NUM
ejpam-440	96	33	)	)	PUNCT
ejpam-440	96	34	=	=	SYM
ejpam-440	96	35	0	0	NUM
ejpam-440	96	36	for	for	ADP
ejpam-440	96	37	which	which	PRON
ejpam-440	96	38	there	there	PRON
ejpam-440	96	39	is	be	VERB
ejpam-440	96	40	ρ	ρ	NOUN
ejpam-440	96	41	:	:	PUNCT
ejpam-440	96	42	x	x	SYM
ejpam-440	96	43	×	×	NOUN
ejpam-440	96	44	x	x	SYM
ejpam-440	96	45	→	→	SYM
ejpam-440	96	46	d+	d+	PRON
ejpam-440	96	47	(	(	PUNCT
ejpam-440	96	48	ρ(x	ρ(x	NOUN
ejpam-440	96	49	,	,	PUNCT
ejpam-440	96	50	y	y	PROPN
ejpam-440	96	51	)	)	PUNCT
ejpam-440	96	52	is	be	AUX
ejpam-440	96	53	denoted	denote	VERB
ejpam-440	96	54	by	by	ADP
ejpam-440	96	55	ρx	ρx	PRON
ejpam-440	96	56	,	,	PUNCT
ejpam-440	96	57	y	y	PROPN
ejpam-440	96	58	)	)	PUNCT
ejpam-440	96	59	with	with	ADP
ejpam-440	96	60	the	the	DET
ejpam-440	96	61	property	property	NOUN
ejpam-440	96	62	:	:	PUNCT
ejpam-440	96	63	µ	µ	PROPN
ejpam-440	96	64	f	f	X
ejpam-440	96	65	(	(	PUNCT
ejpam-440	96	66	x+y)+	x+y)+	PROPN
ejpam-440	96	67	f	f	PROPN
ejpam-440	96	68	(	(	PUNCT
ejpam-440	96	69	x−y)−2	x−y)−2	PROPN
ejpam-440	96	70	f	f	PROPN
ejpam-440	96	71	(	(	PUNCT
ejpam-440	96	72	x)−2	x)−2	NOUN
ejpam-440	96	73	f	f	X
ejpam-440	96	74	(	(	PUNCT
ejpam-440	96	75	y)(t)≥	y)(t)≥	PRON
ejpam-440	96	76	ρx	ρx	VERB
ejpam-440	96	77	,	,	PUNCT
ejpam-440	96	78	y(t	y(t	PROPN
ejpam-440	96	79	)	)	PUNCT
ejpam-440	96	80	(	(	PUNCT
ejpam-440	96	81	6	6	NUM
ejpam-440	96	82	)	)	PUNCT
ejpam-440	96	83	for	for	ADP
ejpam-440	96	84	all	all	PRON
ejpam-440	96	85	x	x	SYM
ejpam-440	96	86	,	,	PUNCT
ejpam-440	96	87	y	y	PROPN
ejpam-440	96	88	∈	∈	PROPN
ejpam-440	96	89	x	x	X
ejpam-440	96	90	and	and	CCONJ
ejpam-440	96	91	all	all	DET
ejpam-440	96	92	t	t	NOUN
ejpam-440	96	93	>	>	X
ejpam-440	96	94	0	0	X
ejpam-440	96	95	.	.	PUNCT
ejpam-440	97	1	if	if	SCONJ
ejpam-440	97	2	lim	lim	PROPN
ejpam-440	97	3	n→∞	n→∞	X
ejpam-440	97	4	t∞	t∞	X
ejpam-440	97	5	i=1	i=1	PROPN
ejpam-440	97	6	(	(	PUNCT
ejpam-440	97	7	ρ2n+i−1	ρ2n+i−1	PROPN
ejpam-440	97	8	x	x	SYM
ejpam-440	97	9	,	,	PUNCT
ejpam-440	97	10	2n+i−1	2n+i−1	PROPN
ejpam-440	97	11	x(2	x(2	PROPN
ejpam-440	97	12	2n+2i	2n+2i	NUM
ejpam-440	97	13	t	t	NOUN
ejpam-440	97	14	)	)	PUNCT
ejpam-440	97	15	)	)	PUNCT
ejpam-440	98	1	=	=	SYM
ejpam-440	98	2	1	1	NUM
ejpam-440	98	3	(	(	PUNCT
ejpam-440	98	4	7	7	NUM
ejpam-440	98	5	)	)	PUNCT
ejpam-440	98	6	and	and	CCONJ
ejpam-440	98	7	lim	lim	PROPN
ejpam-440	98	8	n→∞	n→∞	PROPN
ejpam-440	98	9	ρ2n	ρ2n	PROPN
ejpam-440	99	1	x	x	SYM
ejpam-440	99	2	,	,	PUNCT
ejpam-440	99	3	2n	2n	NUM
ejpam-440	99	4	y(2	y(2	PROPN
ejpam-440	99	5	2n	2n	NUM
ejpam-440	99	6	t	t	PROPN
ejpam-440	99	7	)	)	PUNCT
ejpam-440	99	8	=	=	SYM
ejpam-440	99	9	1	1	NUM
ejpam-440	99	10	(	(	PUNCT
ejpam-440	99	11	8)	8)	NUM
ejpam-440	99	12	m.	m.	NOUN
ejpam-440	99	13	gordji	gordji	PROPN
ejpam-440	99	14	,	,	PUNCT
ejpam-440	99	15	j.	j.	PROPN
ejpam-440	99	16	rassias	rassias	PROPN
ejpam-440	99	17	,	,	PUNCT
ejpam-440	99	18	and	and	CCONJ
ejpam-440	99	19	m.	m.	NOUN
ejpam-440	99	20	savadkouhi	savadkouhi	PROPN
ejpam-440	99	21	/	/	SYM
ejpam-440	99	22	eur	eur	PROPN
ejpam-440	99	23	.	.	PUNCT
ejpam-440	100	1	j.	j.	PROPN
ejpam-440	100	2	pure	pure	PROPN
ejpam-440	100	3	appl	appl	PROPN
ejpam-440	100	4	.	.	PROPN
ejpam-440	100	5	math	math	PROPN
ejpam-440	100	6	,	,	PUNCT
ejpam-440	100	7	2	2	NUM
ejpam-440	100	8	(	(	PUNCT
ejpam-440	100	9	2009	2009	NUM
ejpam-440	100	10	)	)	PUNCT
ejpam-440	100	11	,	,	PUNCT
ejpam-440	100	12	(	(	PUNCT
ejpam-440	100	13	494	494	NUM
ejpam-440	100	14	-	-	SYM
ejpam-440	100	15	507	507	NUM
ejpam-440	100	16	)	)	PUNCT
ejpam-440	100	17	499	499	NUM
ejpam-440	100	18	for	for	ADP
ejpam-440	100	19	all	all	PRON
ejpam-440	100	20	x	x	SYM
ejpam-440	100	21	,	,	PUNCT
ejpam-440	100	22	y	y	PROPN
ejpam-440	100	23	∈	∈	PROPN
ejpam-440	100	24	x	x	X
ejpam-440	100	25	and	and	CCONJ
ejpam-440	100	26	all	all	DET
ejpam-440	100	27	t	t	PROPN
ejpam-440	100	28	>	>	X
ejpam-440	100	29	0	0	PROPN
ejpam-440	100	30	,	,	PUNCT
ejpam-440	100	31	then	then	ADV
ejpam-440	100	32	there	there	PRON
ejpam-440	100	33	exists	exist	VERB
ejpam-440	100	34	a	a	DET
ejpam-440	100	35	unique	unique	ADJ
ejpam-440	100	36	quadratic	quadratic	ADJ
ejpam-440	100	37	mapping	mapping	NOUN
ejpam-440	100	38	q	q	NOUN
ejpam-440	100	39	:	:	PUNCT
ejpam-440	100	40	x	x	X
ejpam-440	100	41	→	→	SYM
ejpam-440	100	42	y	y	NUM
ejpam-440	100	43	such	such	ADJ
ejpam-440	100	44	that	that	SCONJ
ejpam-440	100	45	µq(x)−	µq(x)−	PROPN
ejpam-440	100	46	f	f	X
ejpam-440	100	47	(	(	PUNCT
ejpam-440	100	48	x)(t)≥	x)(t)≥	PROPN
ejpam-440	100	49	t∞	t∞	NUM
ejpam-440	100	50	i=1	i=1	PROPN
ejpam-440	101	1	(	(	PUNCT
ejpam-440	101	2	ρ2i−1	ρ2i−1	PROPN
ejpam-440	101	3	x	x	PROPN
ejpam-440	101	4	,	,	PUNCT
ejpam-440	101	5	2i−1	2i−1	PROPN
ejpam-440	101	6	x(2	x(2	PROPN
ejpam-440	101	7	2i	2i	PROPN
ejpam-440	101	8	t	t	PROPN
ejpam-440	101	9	)	)	PUNCT
ejpam-440	101	10	)	)	PUNCT
ejpam-440	101	11	.	.	PUNCT
ejpam-440	102	1	(	(	PUNCT
ejpam-440	102	2	9	9	X
ejpam-440	102	3	)	)	PUNCT
ejpam-440	102	4	for	for	ADP
ejpam-440	102	5	all	all	DET
ejpam-440	102	6	x	x	SYM
ejpam-440	102	7	∈	∈	ADJ
ejpam-440	102	8	x	x	X
ejpam-440	102	9	and	and	CCONJ
ejpam-440	102	10	all	all	DET
ejpam-440	102	11	t	t	NOUN
ejpam-440	102	12	>	>	X
ejpam-440	102	13	0	0	X
ejpam-440	102	14	.	.	PUNCT
ejpam-440	102	15	proof	proof	NOUN
ejpam-440	102	16	.	.	PUNCT
ejpam-440	103	1	putting	put	VERB
ejpam-440	103	2	y	y	NOUN
ejpam-440	103	3	=	=	PUNCT
ejpam-440	103	4	x	x	PROPN
ejpam-440	103	5	in	in	ADP
ejpam-440	103	6	(	(	PUNCT
ejpam-440	103	7	6	6	NUM
ejpam-440	103	8	)	)	PUNCT
ejpam-440	103	9	,	,	PUNCT
ejpam-440	103	10	we	we	PRON
ejpam-440	103	11	get	get	VERB
ejpam-440	103	12	µ	µ	PRON
ejpam-440	103	13	f	f	X
ejpam-440	103	14	(	(	PUNCT
ejpam-440	103	15	2x	2x	NUM
ejpam-440	103	16	)	)	PUNCT
ejpam-440	103	17	22	22	NUM
ejpam-440	103	18	−	−	PROPN
ejpam-440	103	19	f	f	PROPN
ejpam-440	103	20	(	(	PUNCT
ejpam-440	103	21	x	x	X
ejpam-440	103	22	)	)	PUNCT
ejpam-440	103	23	(	(	PUNCT
ejpam-440	103	24	t)≥	t)≥	PROPN
ejpam-440	103	25	ρx	ρx	VERB
ejpam-440	103	26	,	,	PUNCT
ejpam-440	103	27	x(2	x(2	PROPN
ejpam-440	103	28	2	2	NUM
ejpam-440	103	29	t	t	PROPN
ejpam-440	103	30	)	)	PUNCT
ejpam-440	103	31	.	.	PUNCT
ejpam-440	104	1	(	(	PUNCT
ejpam-440	104	2	10	10	NUM
ejpam-440	104	3	)	)	PUNCT
ejpam-440	104	4	therefore	therefore	ADV
ejpam-440	104	5	,	,	PUNCT
ejpam-440	104	6	µ	µ	PROPN
ejpam-440	104	7	f	f	X
ejpam-440	104	8	(	(	PUNCT
ejpam-440	104	9	2k+1	2k+1	PROPN
ejpam-440	104	10	x	x	SYM
ejpam-440	104	11	)	)	PUNCT
ejpam-440	104	12	22(k+1	22(k+1	NUM
ejpam-440	104	13	)	)	PUNCT
ejpam-440	104	14	−	−	PROPN
ejpam-440	104	15	f	f	PROPN
ejpam-440	104	16	(	(	PUNCT
ejpam-440	104	17	2k	2k	NUM
ejpam-440	104	18	x	x	SYM
ejpam-440	104	19	)	)	PUNCT
ejpam-440	104	20	22k	22k	NOUN
ejpam-440	104	21	(	(	PUNCT
ejpam-440	104	22	t)≥	t)≥	PROPN
ejpam-440	104	23	ρ2k	ρ2k	VERB
ejpam-440	104	24	x	x	X
ejpam-440	104	25	,	,	PUNCT
ejpam-440	104	26	2k	2k	NUM
ejpam-440	104	27	x(2	x(2	PROPN
ejpam-440	104	28	2(k+1	2(k+1	NUM
ejpam-440	104	29	)	)	PUNCT
ejpam-440	104	30	t	t	PROPN
ejpam-440	104	31	)	)	PUNCT
ejpam-440	104	32	,	,	PUNCT
ejpam-440	104	33	(	(	PUNCT
ejpam-440	104	34	11	11	NUM
ejpam-440	104	35	)	)	PUNCT
ejpam-440	104	36	for	for	ADP
ejpam-440	104	37	all	all	DET
ejpam-440	104	38	k	k	PROPN
ejpam-440	104	39	∈	∈	PROPN
ejpam-440	104	40	n	n	ADV
ejpam-440	104	41	and	and	CCONJ
ejpam-440	104	42	all	all	PRON
ejpam-440	104	43	t	t	NOUN
ejpam-440	104	44	>	>	X
ejpam-440	104	45	0	0	X
ejpam-440	104	46	.	.	PUNCT
ejpam-440	105	1	by	by	ADP
ejpam-440	105	2	the	the	DET
ejpam-440	105	3	triangle	triangle	NOUN
ejpam-440	105	4	inequality	inequality	NOUN
ejpam-440	105	5	it	it	PRON
ejpam-440	105	6	follows	follow	VERB
ejpam-440	105	7	that	that	SCONJ
ejpam-440	105	8	µ	µ	ADJ
ejpam-440	105	9	f	f	X
ejpam-440	105	10	(	(	PUNCT
ejpam-440	105	11	2n	2n	NUM
ejpam-440	105	12	x	x	NOUN
ejpam-440	105	13	)	)	PUNCT
ejpam-440	105	14	22n	22n	NOUN
ejpam-440	105	15	−	−	PROPN
ejpam-440	105	16	f	f	X
ejpam-440	105	17	(	(	PUNCT
ejpam-440	105	18	x	x	X
ejpam-440	105	19	)	)	PUNCT
ejpam-440	105	20	(	(	PUNCT
ejpam-440	105	21	t)≥	t)≥	PROPN
ejpam-440	105	22	t	t	PROPN
ejpam-440	105	23	n−1	n−1	PROPN
ejpam-440	105	24	k=0	k=0	PROPN
ejpam-440	105	25	(	(	PUNCT
ejpam-440	105	26	µ	µ	X
ejpam-440	105	27	f	f	X
ejpam-440	105	28	(	(	PUNCT
ejpam-440	105	29	2k+1	2k+1	PROPN
ejpam-440	105	30	x	x	SYM
ejpam-440	105	31	)	)	PUNCT
ejpam-440	105	32	22(k+1	22(k+1	NUM
ejpam-440	105	33	)	)	PUNCT
ejpam-440	105	34	−	−	PROPN
ejpam-440	105	35	f	f	PROPN
ejpam-440	105	36	(	(	PUNCT
ejpam-440	105	37	2k	2k	NUM
ejpam-440	105	38	x	x	SYM
ejpam-440	105	39	)	)	PUNCT
ejpam-440	105	40	22k	22k	NOUN
ejpam-440	105	41	(	(	PUNCT
ejpam-440	105	42	t))≥	t))≥	NOUN
ejpam-440	105	43	t	t	PROPN
ejpam-440	105	44	n−1	n−1	PROPN
ejpam-440	105	45	k=0	k=0	PROPN
ejpam-440	105	46	(	(	PUNCT
ejpam-440	105	47	ρ2k	ρ2k	PROPN
ejpam-440	105	48	x	x	X
ejpam-440	105	49	,	,	PUNCT
ejpam-440	105	50	2k	2k	NUM
ejpam-440	105	51	x(2	x(2	PROPN
ejpam-440	105	52	2(k+1	2(k+1	NUM
ejpam-440	105	53	)	)	PUNCT
ejpam-440	105	54	t	t	PROPN
ejpam-440	105	55	)	)	PUNCT
ejpam-440	105	56	)	)	PUNCT
ejpam-440	106	1	=	=	SYM
ejpam-440	106	2	t	t	PROPN
ejpam-440	106	3	n	n	PROPN
ejpam-440	106	4	i=1	i=1	PROPN
ejpam-440	107	1	(	(	PUNCT
ejpam-440	107	2	ρ2i−1	ρ2i−1	PROPN
ejpam-440	107	3	x	x	PROPN
ejpam-440	107	4	,	,	PUNCT
ejpam-440	107	5	2i−1	2i−1	PROPN
ejpam-440	107	6	x(2	x(2	PROPN
ejpam-440	107	7	2i	2i	PROPN
ejpam-440	107	8	t	t	PROPN
ejpam-440	107	9	)	)	PUNCT
ejpam-440	107	10	)	)	PUNCT
ejpam-440	107	11	(	(	PUNCT
ejpam-440	107	12	12	12	NUM
ejpam-440	107	13	)	)	PUNCT
ejpam-440	107	14	for	for	ADP
ejpam-440	107	15	all	all	DET
ejpam-440	107	16	x	x	SYM
ejpam-440	107	17	∈	∈	ADJ
ejpam-440	107	18	x	x	X
ejpam-440	107	19	and	and	CCONJ
ejpam-440	107	20	all	all	DET
ejpam-440	107	21	t	t	PROPN
ejpam-440	107	22	>	>	X
ejpam-440	107	23	0	0	X
ejpam-440	107	24	.	.	PUNCT
ejpam-440	108	1	in	in	ADP
ejpam-440	108	2	order	order	NOUN
ejpam-440	108	3	to	to	PART
ejpam-440	108	4	prove	prove	VERB
ejpam-440	108	5	the	the	DET
ejpam-440	108	6	convergence	convergence	NOUN
ejpam-440	108	7	of	of	ADP
ejpam-440	108	8	the	the	DET
ejpam-440	108	9	sequence	sequence	NOUN
ejpam-440	108	10	{	{	PUNCT
ejpam-440	108	11	f	f	PROPN
ejpam-440	108	12	(	(	PUNCT
ejpam-440	108	13	2n	2n	NUM
ejpam-440	108	14	x	x	NOUN
ejpam-440	108	15	)	)	PUNCT
ejpam-440	108	16	22n	22n	NOUN
ejpam-440	108	17	}	}	PUNCT
ejpam-440	108	18	,	,	PUNCT
ejpam-440	108	19	we	we	PRON
ejpam-440	108	20	replace	replace	VERB
ejpam-440	108	21	x	x	PUNCT
ejpam-440	108	22	with	with	ADP
ejpam-440	108	23	2mx	2mx	PROPN
ejpam-440	108	24	in	in	ADP
ejpam-440	108	25	(	(	PUNCT
ejpam-440	108	26	12	12	NUM
ejpam-440	108	27	)	)	PUNCT
ejpam-440	108	28	to	to	PART
ejpam-440	108	29	find	find	VERB
ejpam-440	108	30	that	that	SCONJ
ejpam-440	108	31	µ	µ	ADJ
ejpam-440	108	32	f	f	X
ejpam-440	108	33	(	(	PUNCT
ejpam-440	108	34	2n+m	2n+m	NUM
ejpam-440	108	35	x	x	SYM
ejpam-440	108	36	)	)	PUNCT
ejpam-440	108	37	22(n+m	22(n+m	NUM
ejpam-440	108	38	)	)	PUNCT
ejpam-440	108	39	−	−	PROPN
ejpam-440	108	40	f	f	PROPN
ejpam-440	108	41	(	(	PUNCT
ejpam-440	108	42	2	2	NUM
ejpam-440	108	43	m	m	NOUN
ejpam-440	108	44	x	x	NOUN
ejpam-440	108	45	)	)	PUNCT
ejpam-440	108	46	22	22	NUM
ejpam-440	108	47	m	m	PROPN
ejpam-440	108	48	(	(	PUNCT
ejpam-440	108	49	t	t	PROPN
ejpam-440	108	50	)	)	PUNCT
ejpam-440	108	51	=	=	PUNCT
ejpam-440	108	52	µ	µ	X
ejpam-440	108	53	f	f	X
ejpam-440	108	54	(	(	PUNCT
ejpam-440	108	55	2n+m	2n+m	NUM
ejpam-440	108	56	x	x	NOUN
ejpam-440	108	57	)	)	PUNCT
ejpam-440	108	58	22n	22n	NOUN
ejpam-440	108	59	−	−	PROPN
ejpam-440	108	60	f	f	NOUN
ejpam-440	108	61	(	(	PUNCT
ejpam-440	108	62	2	2	NUM
ejpam-440	108	63	m	m	NOUN
ejpam-440	108	64	x	x	NOUN
ejpam-440	108	65	)	)	PUNCT
ejpam-440	108	66	(	(	PUNCT
ejpam-440	108	67	22	22	NUM
ejpam-440	108	68	m	m	NOUN
ejpam-440	108	69	t	t	PROPN
ejpam-440	108	70	)	)	PUNCT
ejpam-440	108	71	≥	≥	PROPN
ejpam-440	108	72	t	t	PROPN
ejpam-440	108	73	n	n	PRON
ejpam-440	108	74	i=1	i=1	PROPN
ejpam-440	108	75	(	(	PUNCT
ejpam-440	108	76	ρ2i+m−1	ρ2i+m−1	NOUN
ejpam-440	108	77	x	x	X
ejpam-440	108	78	,	,	PUNCT
ejpam-440	108	79	2i+m−1	2i+m−1	NUM
ejpam-440	108	80	x(2	x(2	PROPN
ejpam-440	108	81	2i+2	2i+2	PROPN
ejpam-440	108	82	m	m	PROPN
ejpam-440	108	83	t	t	PROPN
ejpam-440	108	84	)	)	PUNCT
ejpam-440	108	85	)	)	PUNCT
ejpam-440	108	86	.	.	PUNCT
ejpam-440	109	1	(	(	PUNCT
ejpam-440	109	2	13	13	NUM
ejpam-440	109	3	)	)	PUNCT
ejpam-440	109	4	since	since	SCONJ
ejpam-440	109	5	the	the	DET
ejpam-440	109	6	right	right	ADJ
ejpam-440	109	7	hand	hand	NOUN
ejpam-440	109	8	side	side	NOUN
ejpam-440	109	9	of	of	ADP
ejpam-440	109	10	the	the	DET
ejpam-440	109	11	inequality	inequality	NOUN
ejpam-440	109	12	tends	tend	VERB
ejpam-440	109	13	to	to	ADP
ejpam-440	109	14	1	1	NUM
ejpam-440	109	15	as	as	ADP
ejpam-440	109	16	m	m	PROPN
ejpam-440	109	17	and	and	CCONJ
ejpam-440	109	18	n	n	ADV
ejpam-440	109	19	tend	tend	VERB
ejpam-440	109	20	to	to	PART
ejpam-440	109	21	infinity	infinity	VERB
ejpam-440	109	22	,	,	PUNCT
ejpam-440	109	23	the	the	DET
ejpam-440	109	24	sequence	sequence	NOUN
ejpam-440	109	25	{	{	PUNCT
ejpam-440	109	26	f	f	PROPN
ejpam-440	109	27	(	(	PUNCT
ejpam-440	109	28	2n	2n	NUM
ejpam-440	109	29	x	x	NOUN
ejpam-440	109	30	)	)	PUNCT
ejpam-440	109	31	22n	22n	NOUN
ejpam-440	109	32	}	}	PUNCT
ejpam-440	109	33	is	be	AUX
ejpam-440	109	34	a	a	DET
ejpam-440	109	35	cauchy	cauchy	ADJ
ejpam-440	109	36	sequence	sequence	NOUN
ejpam-440	109	37	.	.	PUNCT
ejpam-440	110	1	therefore	therefore	ADV
ejpam-440	110	2	,	,	PUNCT
ejpam-440	110	3	we	we	PRON
ejpam-440	110	4	may	may	AUX
ejpam-440	110	5	define	define	VERB
ejpam-440	110	6	q(x	q(x	NOUN
ejpam-440	110	7	)	)	PUNCT
ejpam-440	110	8	=	=	PUNCT
ejpam-440	111	1	limn→∞	limn→∞	X
ejpam-440	111	2	f	f	X
ejpam-440	111	3	(	(	PUNCT
ejpam-440	111	4	2n	2n	NUM
ejpam-440	111	5	x	x	NOUN
ejpam-440	111	6	)	)	PUNCT
ejpam-440	111	7	22n	22n	X
ejpam-440	111	8	for	for	ADP
ejpam-440	111	9	all	all	DET
ejpam-440	111	10	x	x	SYM
ejpam-440	111	11	∈	∈	PROPN
ejpam-440	111	12	x	x	X
ejpam-440	111	13	.	.	PUNCT
ejpam-440	112	1	now	now	ADV
ejpam-440	112	2	,	,	PUNCT
ejpam-440	112	3	we	we	PRON
ejpam-440	112	4	show	show	VERB
ejpam-440	112	5	that	that	SCONJ
ejpam-440	112	6	q	q	NOUN
ejpam-440	112	7	is	be	AUX
ejpam-440	112	8	a	a	DET
ejpam-440	112	9	quadratic	quadratic	ADJ
ejpam-440	112	10	function	function	NOUN
ejpam-440	112	11	.	.	PUNCT
ejpam-440	113	1	replacing	replace	VERB
ejpam-440	113	2	x	x	SYM
ejpam-440	113	3	,	,	PUNCT
ejpam-440	113	4	y	y	PROPN
ejpam-440	113	5	with	with	ADP
ejpam-440	113	6	2n	2n	NUM
ejpam-440	113	7	x	x	SYM
ejpam-440	113	8	and	and	CCONJ
ejpam-440	113	9	2n	2n	NUM
ejpam-440	113	10	y	y	PROPN
ejpam-440	113	11	,	,	PUNCT
ejpam-440	113	12	respectively	respectively	ADV
ejpam-440	113	13	,	,	PUNCT
ejpam-440	113	14	in	in	ADP
ejpam-440	113	15	(	(	PUNCT
ejpam-440	113	16	6	6	NUM
ejpam-440	113	17	)	)	PUNCT
ejpam-440	113	18	,	,	PUNCT
ejpam-440	113	19	it	it	PRON
ejpam-440	113	20	follows	follow	VERB
ejpam-440	113	21	that	that	SCONJ
ejpam-440	113	22	µ	µ	ADJ
ejpam-440	113	23	f	f	X
ejpam-440	113	24	(	(	PUNCT
ejpam-440	113	25	2n	2n	NUM
ejpam-440	113	26	x+2n	x+2n	PROPN
ejpam-440	113	27	y	y	PROPN
ejpam-440	113	28	)	)	PUNCT
ejpam-440	113	29	22n	22n	NOUN
ejpam-440	113	30	+	+	CCONJ
ejpam-440	113	31	f	f	X
ejpam-440	113	32	(	(	PUNCT
ejpam-440	113	33	2n	2n	NUM
ejpam-440	113	34	x−2n	x−2n	SYM
ejpam-440	113	35	y	y	PROPN
ejpam-440	113	36	)	)	PUNCT
ejpam-440	113	37	22n	22n	NUM
ejpam-440	113	38	−2	−2	PROPN
ejpam-440	113	39	f	f	PROPN
ejpam-440	113	40	(	(	PUNCT
ejpam-440	113	41	2n	2n	NUM
ejpam-440	113	42	x	x	NOUN
ejpam-440	113	43	)	)	PUNCT
ejpam-440	113	44	22n	22n	NUM
ejpam-440	113	45	−2	−2	PROPN
ejpam-440	113	46	f	f	PROPN
ejpam-440	113	47	(	(	PUNCT
ejpam-440	113	48	2n	2n	NUM
ejpam-440	113	49	y	y	NOUN
ejpam-440	113	50	)	)	PUNCT
ejpam-440	113	51	22n	22n	NOUN
ejpam-440	113	52	(	(	PUNCT
ejpam-440	113	53	t)≥	t)≥	PROPN
ejpam-440	113	54	ρ2n	ρ2n	PUNCT
ejpam-440	113	55	x	x	SYM
ejpam-440	113	56	,	,	PUNCT
ejpam-440	113	57	2n	2n	NUM
ejpam-440	113	58	y(2	y(2	PROPN
ejpam-440	113	59	2n	2n	NUM
ejpam-440	113	60	t	t	PROPN
ejpam-440	113	61	)	)	PUNCT
ejpam-440	113	62	.	.	PUNCT
ejpam-440	114	1	(	(	PUNCT
ejpam-440	114	2	14	14	X
ejpam-440	114	3	)	)	PUNCT
ejpam-440	114	4	taking	take	VERB
ejpam-440	114	5	the	the	DET
ejpam-440	114	6	limit	limit	NOUN
ejpam-440	114	7	as	as	ADP
ejpam-440	114	8	n→∞	n→∞	NUM
ejpam-440	114	9	,	,	PUNCT
ejpam-440	114	10	we	we	PRON
ejpam-440	114	11	find	find	VERB
ejpam-440	114	12	that	that	SCONJ
ejpam-440	114	13	q	q	NOUN
ejpam-440	114	14	satisfies	satisfie	NOUN
ejpam-440	114	15	(	(	PUNCT
ejpam-440	114	16	5	5	NUM
ejpam-440	114	17	)	)	PUNCT
ejpam-440	114	18	for	for	ADP
ejpam-440	114	19	all	all	PRON
ejpam-440	114	20	x	x	SYM
ejpam-440	114	21	,	,	PUNCT
ejpam-440	114	22	y	y	PROPN
ejpam-440	114	23	∈	∈	PROPN
ejpam-440	114	24	x	x	X
ejpam-440	114	25	.	.	PUNCT
ejpam-440	115	1	to	to	PART
ejpam-440	115	2	prove	prove	VERB
ejpam-440	115	3	(	(	PUNCT
ejpam-440	115	4	9	9	NUM
ejpam-440	115	5	)	)	PUNCT
ejpam-440	115	6	,	,	PUNCT
ejpam-440	115	7	take	take	VERB
ejpam-440	115	8	the	the	DET
ejpam-440	115	9	limit	limit	NOUN
ejpam-440	115	10	as	as	ADP
ejpam-440	115	11	n	n	PROPN
ejpam-440	115	12	→	→	SYM
ejpam-440	115	13	∞	∞	NUM
ejpam-440	115	14	in	in	ADP
ejpam-440	115	15	(	(	PUNCT
ejpam-440	115	16	12	12	NUM
ejpam-440	115	17	)	)	PUNCT
ejpam-440	115	18	.	.	PUNCT
ejpam-440	116	1	finally	finally	ADV
ejpam-440	116	2	,	,	PUNCT
ejpam-440	116	3	to	to	PART
ejpam-440	116	4	prove	prove	VERB
ejpam-440	116	5	the	the	DET
ejpam-440	116	6	uniqueness	uniqueness	NOUN
ejpam-440	116	7	of	of	ADP
ejpam-440	116	8	m.	m.	NOUN
ejpam-440	116	9	gordji	gordji	PROPN
ejpam-440	116	10	,	,	PUNCT
ejpam-440	116	11	j.	j.	PROPN
ejpam-440	116	12	rassias	rassias	PROPN
ejpam-440	116	13	,	,	PUNCT
ejpam-440	116	14	and	and	CCONJ
ejpam-440	116	15	m.	m.	NOUN
ejpam-440	116	16	savadkouhi	savadkouhi	PROPN
ejpam-440	116	17	/	/	SYM
ejpam-440	116	18	eur	eur	PROPN
ejpam-440	116	19	.	.	PUNCT
ejpam-440	117	1	j.	j.	PROPN
ejpam-440	117	2	pure	pure	PROPN
ejpam-440	117	3	appl	appl	PROPN
ejpam-440	117	4	.	.	PROPN
ejpam-440	117	5	math	math	PROPN
ejpam-440	117	6	,	,	PUNCT
ejpam-440	117	7	2	2	NUM
ejpam-440	117	8	(	(	PUNCT
ejpam-440	117	9	2009	2009	NUM
ejpam-440	117	10	)	)	PUNCT
ejpam-440	117	11	,	,	PUNCT
ejpam-440	117	12	(	(	PUNCT
ejpam-440	117	13	494	494	NUM
ejpam-440	117	14	-	-	SYM
ejpam-440	117	15	507	507	NUM
ejpam-440	117	16	)	)	PUNCT
ejpam-440	117	17	500	500	NUM
ejpam-440	117	18	the	the	DET
ejpam-440	117	19	quadratic	quadratic	ADJ
ejpam-440	117	20	function	function	NOUN
ejpam-440	117	21	q	q	PROPN
ejpam-440	117	22	subject	subject	NOUN
ejpam-440	117	23	to	to	ADP
ejpam-440	117	24	(	(	PUNCT
ejpam-440	117	25	9	9	NUM
ejpam-440	117	26	)	)	PUNCT
ejpam-440	117	27	,	,	PUNCT
ejpam-440	117	28	let	let	VERB
ejpam-440	117	29	us	we	PRON
ejpam-440	117	30	assume	assume	VERB
ejpam-440	117	31	that	that	SCONJ
ejpam-440	117	32	there	there	PRON
ejpam-440	117	33	exists	exist	VERB
ejpam-440	117	34	a	a	DET
ejpam-440	117	35	quadratic	quadratic	ADJ
ejpam-440	117	36	function	function	NOUN
ejpam-440	117	37	q′	q′	NOUN
ejpam-440	117	38	which	which	PRON
ejpam-440	117	39	satisfies	satisfy	VERB
ejpam-440	117	40	(	(	PUNCT
ejpam-440	117	41	9	9	NUM
ejpam-440	117	42	)	)	PUNCT
ejpam-440	117	43	since	since	SCONJ
ejpam-440	117	44	q(2nx	q(2nx	NOUN
ejpam-440	117	45	)	)	PUNCT
ejpam-440	118	1	=	=	SYM
ejpam-440	118	2	22nq(x	22nq(x	PROPN
ejpam-440	118	3	)	)	PUNCT
ejpam-440	118	4	and	and	CCONJ
ejpam-440	118	5	q′(2nx	q′(2nx	X
ejpam-440	118	6	)	)	PUNCT
ejpam-440	118	7	=	=	SYM
ejpam-440	118	8	22nq′(x	22nq′(x	NUM
ejpam-440	118	9	)	)	PUNCT
ejpam-440	118	10	for	for	ADP
ejpam-440	118	11	all	all	PRON
ejpam-440	118	12	x	x	SYM
ejpam-440	118	13	∈	∈	ADJ
ejpam-440	118	14	x	x	X
ejpam-440	118	15	and	and	CCONJ
ejpam-440	118	16	all	all	DET
ejpam-440	118	17	n	n	PRON
ejpam-440	118	18	∈	∈	PROPN
ejpam-440	118	19	n	n	CCONJ
ejpam-440	118	20	,	,	PUNCT
ejpam-440	118	21	from	from	ADP
ejpam-440	118	22	(	(	PUNCT
ejpam-440	118	23	9	9	X
ejpam-440	118	24	)	)	PUNCT
ejpam-440	118	25	it	it	PRON
ejpam-440	118	26	follows	follow	VERB
ejpam-440	118	27	that	that	SCONJ
ejpam-440	118	28	µq(x)−q′(x)(2	µq(x)−q′(x)(2	PROPN
ejpam-440	118	29	t	t	NOUN
ejpam-440	118	30	)	)	PUNCT
ejpam-440	118	31	=	=	PUNCT
ejpam-440	118	32	µq(2n	µq(2n	ADJ
ejpam-440	118	33	x)−q′(2n	x)−q′(2n	PROPN
ejpam-440	118	34	x)(2	x)(2	NUM
ejpam-440	119	1	2n+1	2n+1	PROPN
ejpam-440	119	2	t	t	PROPN
ejpam-440	119	3	)	)	PUNCT
ejpam-440	119	4	≥	≥	PROPN
ejpam-440	119	5	t	t	PROPN
ejpam-440	119	6	(	(	PUNCT
ejpam-440	119	7	µq(2n	µq(2n	ADJ
ejpam-440	119	8	x)−	x)−	PROPN
ejpam-440	119	9	f	f	PROPN
ejpam-440	119	10	(	(	PUNCT
ejpam-440	119	11	2n	2n	NUM
ejpam-440	119	12	x)(2	x)(2	X
ejpam-440	119	13	2n	2n	NUM
ejpam-440	119	14	t),µ	t),µ	PROPN
ejpam-440	119	15	f	f	PROPN
ejpam-440	119	16	(	(	PUNCT
ejpam-440	119	17	2n	2n	NUM
ejpam-440	119	18	x)−q′(2n	x)−q′(2n	PROPN
ejpam-440	119	19	x)(2	x)(2	NUM
ejpam-440	119	20	2n	2n	NUM
ejpam-440	119	21	t	t	PROPN
ejpam-440	119	22	)	)	PUNCT
ejpam-440	119	23	)	)	PUNCT
ejpam-440	119	24	≥	≥	PROPN
ejpam-440	120	1	t	t	NOUN
ejpam-440	120	2	(	(	PUNCT
ejpam-440	120	3	t∞	t∞	PROPN
ejpam-440	120	4	i=1	i=1	PROPN
ejpam-440	120	5	(	(	PUNCT
ejpam-440	120	6	ρ2n+i−1	ρ2n+i−1	PROPN
ejpam-440	120	7	x	x	SYM
ejpam-440	120	8	,	,	PUNCT
ejpam-440	120	9	2n+i−1	2n+i−1	PROPN
ejpam-440	120	10	x(2	x(2	PROPN
ejpam-440	120	11	2n+2i	2n+2i	NUM
ejpam-440	120	12	t	t	PROPN
ejpam-440	120	13	)	)	PUNCT
ejpam-440	120	14	)	)	PUNCT
ejpam-440	120	15	,	,	PUNCT
ejpam-440	120	16	t∞	t∞	X
ejpam-440	120	17	i=1	i=1	PROPN
ejpam-440	120	18	(	(	PUNCT
ejpam-440	120	19	ρ2n+i−1	ρ2n+i−1	PROPN
ejpam-440	120	20	x	x	SYM
ejpam-440	120	21	,	,	PUNCT
ejpam-440	120	22	2n+i−1(22n+2i	2n+i−1(22n+2i	PROPN
ejpam-440	120	23	t	t	PROPN
ejpam-440	120	24	)	)	PUNCT
ejpam-440	120	25	)	)	PUNCT
ejpam-440	120	26	)	)	PUNCT
ejpam-440	120	27	(	(	PUNCT
ejpam-440	120	28	15	15	NUM
ejpam-440	120	29	)	)	PUNCT
ejpam-440	120	30	for	for	ADP
ejpam-440	120	31	all	all	DET
ejpam-440	120	32	x	x	SYM
ejpam-440	120	33	∈	∈	ADJ
ejpam-440	120	34	x	x	X
ejpam-440	120	35	and	and	CCONJ
ejpam-440	120	36	all	all	DET
ejpam-440	120	37	t	t	PROPN
ejpam-440	120	38	>	>	X
ejpam-440	120	39	0	0	X
ejpam-440	120	40	.	.	PUNCT
ejpam-440	120	41	by	by	ADP
ejpam-440	120	42	letting	let	VERB
ejpam-440	120	43	n→∞	n→∞	PRON
ejpam-440	120	44	in	in	ADP
ejpam-440	120	45	(	(	PUNCT
ejpam-440	120	46	15	15	NUM
ejpam-440	120	47	)	)	PUNCT
ejpam-440	120	48	,	,	PUNCT
ejpam-440	120	49	we	we	PRON
ejpam-440	120	50	find	find	VERB
ejpam-440	120	51	that	that	SCONJ
ejpam-440	120	52	q	q	NOUN
ejpam-440	120	53	=	=	ADJ
ejpam-440	120	54	q′.	q′.	ADV
ejpam-440	120	55	theorem	theorem	VERB
ejpam-440	120	56	3	3	X
ejpam-440	120	57	.	.	PUNCT
ejpam-440	121	1	let	let	VERB
ejpam-440	121	2	x	x	PRON
ejpam-440	121	3	be	be	AUX
ejpam-440	121	4	a	a	DET
ejpam-440	121	5	real	real	ADJ
ejpam-440	121	6	linear	linear	ADJ
ejpam-440	121	7	space	space	NOUN
ejpam-440	121	8	,	,	PUNCT
ejpam-440	121	9	(	(	PUNCT
ejpam-440	121	10	y,µ	y,µ	PROPN
ejpam-440	121	11	,	,	PUNCT
ejpam-440	121	12	t	t	PROPN
ejpam-440	121	13	)	)	PUNCT
ejpam-440	121	14	be	be	AUX
ejpam-440	121	15	a	a	DET
ejpam-440	121	16	complete	complete	ADJ
ejpam-440	121	17	rn	rn	NOUN
ejpam-440	121	18	-	-	NOUN
ejpam-440	121	19	space	space	NOUN
ejpam-440	121	20	and	and	CCONJ
ejpam-440	121	21	f	f	NOUN
ejpam-440	121	22	:	:	PUNCT
ejpam-440	121	23	x	x	X
ejpam-440	121	24	→	→	SYM
ejpam-440	121	25	y	y	X
ejpam-440	121	26	be	be	AUX
ejpam-440	121	27	a	a	DET
ejpam-440	121	28	mapping	mapping	NOUN
ejpam-440	121	29	which	which	PRON
ejpam-440	121	30	there	there	PRON
ejpam-440	121	31	is	be	VERB
ejpam-440	121	32	τ	τ	PROPN
ejpam-440	121	33	:	:	PUNCT
ejpam-440	121	34	x	x	SYM
ejpam-440	121	35	×	×	NOUN
ejpam-440	121	36	x	x	INTJ
ejpam-440	121	37	→	→	SYM
ejpam-440	121	38	d+	d+	PRON
ejpam-440	121	39	(	(	PUNCT
ejpam-440	121	40	τ(x	τ(x	PROPN
ejpam-440	121	41	,	,	PUNCT
ejpam-440	121	42	y	y	PROPN
ejpam-440	121	43	)	)	PUNCT
ejpam-440	121	44	is	be	AUX
ejpam-440	121	45	denoted	denote	VERB
ejpam-440	121	46	by	by	ADP
ejpam-440	121	47	τx	τx	PROPN
ejpam-440	121	48	,	,	PUNCT
ejpam-440	121	49	y	y	PROPN
ejpam-440	121	50	)	)	PUNCT
ejpam-440	121	51	with	with	ADP
ejpam-440	121	52	the	the	DET
ejpam-440	121	53	property	property	NOUN
ejpam-440	121	54	:	:	PUNCT
ejpam-440	121	55	µ	µ	PROPN
ejpam-440	121	56	f	f	X
ejpam-440	121	57	(	(	PUNCT
ejpam-440	121	58	2x+y)+	2x+y)+	NUM
ejpam-440	121	59	f	f	NOUN
ejpam-440	121	60	(	(	PUNCT
ejpam-440	121	61	2x−y)−2	2x−y)−2	NUM
ejpam-440	121	62	f	f	X
ejpam-440	121	63	(	(	PUNCT
ejpam-440	121	64	x+y)−2	x+y)−2	PROPN
ejpam-440	121	65	f	f	PROPN
ejpam-440	121	66	(	(	PUNCT
ejpam-440	121	67	x−y)−12	x−y)−12	PROPN
ejpam-440	121	68	f	f	PROPN
ejpam-440	122	1	(	(	PUNCT
ejpam-440	122	2	x)(t)≥	x)(t)≥	PRON
ejpam-440	122	3	τx	τx	PROPN
ejpam-440	122	4	,	,	PUNCT
ejpam-440	122	5	y(t	y(t	PROPN
ejpam-440	122	6	)	)	PUNCT
ejpam-440	122	7	(	(	PUNCT
ejpam-440	122	8	16	16	NUM
ejpam-440	122	9	)	)	PUNCT
ejpam-440	122	10	for	for	ADP
ejpam-440	122	11	all	all	PRON
ejpam-440	122	12	x	x	SYM
ejpam-440	122	13	,	,	PUNCT
ejpam-440	122	14	y	y	PROPN
ejpam-440	122	15	∈	∈	PROPN
ejpam-440	122	16	x	x	X
ejpam-440	122	17	and	and	CCONJ
ejpam-440	122	18	all	all	DET
ejpam-440	122	19	t	t	NOUN
ejpam-440	122	20	>	>	X
ejpam-440	122	21	0	0	X
ejpam-440	122	22	.	.	PUNCT
ejpam-440	123	1	if	if	SCONJ
ejpam-440	123	2	lim	lim	PROPN
ejpam-440	123	3	n→∞	n→∞	X
ejpam-440	123	4	t∞	t∞	X
ejpam-440	123	5	i=1	i=1	PROPN
ejpam-440	123	6	(	(	PUNCT
ejpam-440	123	7	τ2n+i−1	τ2n+i−1	NOUN
ejpam-440	123	8	x	x	SYM
ejpam-440	123	9	,	,	PUNCT
ejpam-440	123	10	0(2	0(2	NUM
ejpam-440	123	11	3n+2i	3n+2i	NUM
ejpam-440	123	12	t	t	NOUN
ejpam-440	123	13	)	)	PUNCT
ejpam-440	123	14	)	)	PUNCT
ejpam-440	124	1	=	=	SYM
ejpam-440	124	2	1	1	NUM
ejpam-440	124	3	(	(	PUNCT
ejpam-440	124	4	17	17	NUM
ejpam-440	124	5	)	)	PUNCT
ejpam-440	124	6	and	and	CCONJ
ejpam-440	124	7	lim	lim	PROPN
ejpam-440	124	8	n→∞	n→∞	X
ejpam-440	124	9	τ2n	τ2n	PROPN
ejpam-440	124	10	x	x	SYM
ejpam-440	124	11	,	,	PUNCT
ejpam-440	124	12	2n	2n	NUM
ejpam-440	124	13	y(2	y(2	NOUN
ejpam-440	124	14	3n	3n	NUM
ejpam-440	124	15	t	t	PROPN
ejpam-440	124	16	)	)	PUNCT
ejpam-440	124	17	=	=	SYM
ejpam-440	124	18	1	1	NUM
ejpam-440	124	19	(	(	PUNCT
ejpam-440	124	20	18	18	NUM
ejpam-440	124	21	)	)	PUNCT
ejpam-440	124	22	for	for	ADP
ejpam-440	124	23	all	all	PRON
ejpam-440	124	24	x	x	SYM
ejpam-440	124	25	,	,	PUNCT
ejpam-440	124	26	y	y	PROPN
ejpam-440	124	27	∈	∈	PROPN
ejpam-440	124	28	x	x	X
ejpam-440	124	29	and	and	CCONJ
ejpam-440	124	30	all	all	DET
ejpam-440	124	31	t	t	PROPN
ejpam-440	124	32	>	>	X
ejpam-440	124	33	0	0	PROPN
ejpam-440	124	34	,	,	PUNCT
ejpam-440	124	35	then	then	ADV
ejpam-440	124	36	there	there	PRON
ejpam-440	124	37	exists	exist	VERB
ejpam-440	124	38	a	a	DET
ejpam-440	124	39	unique	unique	ADJ
ejpam-440	124	40	cubic	cubic	ADJ
ejpam-440	124	41	mapping	mapping	NOUN
ejpam-440	124	42	c	c	NOUN
ejpam-440	124	43	:	:	PUNCT
ejpam-440	124	44	x	x	X
ejpam-440	124	45	→	→	PUNCT
ejpam-440	124	46	y	y	PROPN
ejpam-440	124	47	such	such	ADJ
ejpam-440	124	48	that	that	SCONJ
ejpam-440	124	49	µc(x)−	µc(x)−	PROPN
ejpam-440	124	50	f	f	PROPN
ejpam-440	124	51	(	(	PUNCT
ejpam-440	124	52	x)(t)≥	x)(t)≥	PROPN
ejpam-440	124	53	t∞	t∞	PROPN
ejpam-440	124	54	i=1	i=1	PROPN
ejpam-440	124	55	(	(	PUNCT
ejpam-440	124	56	τ2i−1	τ2i−1	PROPN
ejpam-440	124	57	x	x	SYM
ejpam-440	124	58	,	,	PUNCT
ejpam-440	124	59	0(2	0(2	NUM
ejpam-440	124	60	2i	2i	PROPN
ejpam-440	124	61	t	t	PROPN
ejpam-440	124	62	)	)	PUNCT
ejpam-440	124	63	)	)	PUNCT
ejpam-440	124	64	.	.	PUNCT
ejpam-440	125	1	(	(	PUNCT
ejpam-440	125	2	19	19	NUM
ejpam-440	125	3	)	)	PUNCT
ejpam-440	125	4	for	for	ADP
ejpam-440	125	5	all	all	PRON
ejpam-440	125	6	x	x	SYM
ejpam-440	125	7	∈	∈	ADJ
ejpam-440	125	8	x	x	X
ejpam-440	125	9	and	and	CCONJ
ejpam-440	125	10	all	all	DET
ejpam-440	125	11	t	t	NOUN
ejpam-440	125	12	>	>	X
ejpam-440	125	13	0	0	X
ejpam-440	125	14	.	.	PUNCT
ejpam-440	126	1	proof	proof	NOUN
ejpam-440	126	2	.	.	PUNCT
ejpam-440	127	1	putting	put	VERB
ejpam-440	127	2	y	y	NOUN
ejpam-440	127	3	=	=	PUNCT
ejpam-440	127	4	0	0	NUM
ejpam-440	127	5	in	in	ADP
ejpam-440	127	6	(	(	PUNCT
ejpam-440	127	7	16	16	NUM
ejpam-440	127	8	)	)	PUNCT
ejpam-440	127	9	,	,	PUNCT
ejpam-440	127	10	we	we	PRON
ejpam-440	127	11	get	get	VERB
ejpam-440	127	12	µ	µ	PRON
ejpam-440	127	13	f	f	X
ejpam-440	127	14	(	(	PUNCT
ejpam-440	127	15	2x	2x	NUM
ejpam-440	127	16	)	)	PUNCT
ejpam-440	127	17	23	23	NUM
ejpam-440	127	18	−	−	PROPN
ejpam-440	127	19	f	f	X
ejpam-440	127	20	(	(	PUNCT
ejpam-440	127	21	x	x	X
ejpam-440	127	22	)	)	PUNCT
ejpam-440	127	23	(	(	PUNCT
ejpam-440	127	24	t)≥	t)≥	PROPN
ejpam-440	127	25	τx	τx	VERB
ejpam-440	127	26	,	,	PUNCT
ejpam-440	127	27	0(2	0(2	NUM
ejpam-440	127	28	4	4	NUM
ejpam-440	127	29	t)≥	t)≥	NOUN
ejpam-440	127	30	τx	τx	X
ejpam-440	127	31	,	,	PUNCT
ejpam-440	127	32	0(2	0(2	NUM
ejpam-440	127	33	3	3	NUM
ejpam-440	127	34	t	t	NOUN
ejpam-440	127	35	)	)	PUNCT
ejpam-440	127	36	.	.	PUNCT
ejpam-440	128	1	(	(	PUNCT
ejpam-440	128	2	20	20	NUM
ejpam-440	128	3	)	)	PUNCT
ejpam-440	128	4	therefore	therefore	ADV
ejpam-440	128	5	,	,	PUNCT
ejpam-440	128	6	µ	µ	PROPN
ejpam-440	128	7	f	f	X
ejpam-440	128	8	(	(	PUNCT
ejpam-440	128	9	2k+1	2k+1	PROPN
ejpam-440	128	10	x	x	SYM
ejpam-440	128	11	)	)	PUNCT
ejpam-440	128	12	23(k+1	23(k+1	NUM
ejpam-440	128	13	)	)	PUNCT
ejpam-440	128	14	−	−	PROPN
ejpam-440	128	15	f	f	PROPN
ejpam-440	128	16	(	(	PUNCT
ejpam-440	128	17	2k	2k	NUM
ejpam-440	128	18	x	x	SYM
ejpam-440	128	19	)	)	PUNCT
ejpam-440	128	20	23k	23k	NOUN
ejpam-440	128	21	(	(	PUNCT
ejpam-440	128	22	t)≥	t)≥	PROPN
ejpam-440	128	23	τ2k	τ2k	PUNCT
ejpam-440	128	24	x	x	SYM
ejpam-440	128	25	,	,	PUNCT
ejpam-440	128	26	0(2	0(2	NUM
ejpam-440	128	27	3(k+1	3(k+1	NUM
ejpam-440	128	28	)	)	PUNCT
ejpam-440	128	29	t	t	PROPN
ejpam-440	128	30	)	)	PUNCT
ejpam-440	128	31	,	,	PUNCT
ejpam-440	128	32	(	(	PUNCT
ejpam-440	128	33	21	21	NUM
ejpam-440	128	34	)	)	PUNCT
ejpam-440	128	35	m.	m.	NOUN
ejpam-440	128	36	gordji	gordji	PROPN
ejpam-440	128	37	,	,	PUNCT
ejpam-440	128	38	j.	j.	PROPN
ejpam-440	128	39	rassias	rassias	PROPN
ejpam-440	128	40	,	,	PUNCT
ejpam-440	128	41	and	and	CCONJ
ejpam-440	128	42	m.	m.	NOUN
ejpam-440	128	43	savadkouhi	savadkouhi	PROPN
ejpam-440	128	44	/	/	SYM
ejpam-440	128	45	eur	eur	PROPN
ejpam-440	128	46	.	.	PUNCT
ejpam-440	129	1	j.	j.	PROPN
ejpam-440	129	2	pure	pure	PROPN
ejpam-440	129	3	appl	appl	PROPN
ejpam-440	129	4	.	.	PROPN
ejpam-440	129	5	math	math	PROPN
ejpam-440	129	6	,	,	PUNCT
ejpam-440	129	7	2	2	NUM
ejpam-440	129	8	(	(	PUNCT
ejpam-440	129	9	2009	2009	NUM
ejpam-440	129	10	)	)	PUNCT
ejpam-440	129	11	,	,	PUNCT
ejpam-440	129	12	(	(	PUNCT
ejpam-440	129	13	494	494	NUM
ejpam-440	129	14	-	-	SYM
ejpam-440	129	15	507	507	NUM
ejpam-440	129	16	)	)	PUNCT
ejpam-440	129	17	501	501	NUM
ejpam-440	129	18	for	for	ADP
ejpam-440	129	19	every	every	DET
ejpam-440	129	20	k	k	PROPN
ejpam-440	129	21	∈	∈	PROPN
ejpam-440	129	22	n	n	PROPN
ejpam-440	129	23	and	and	CCONJ
ejpam-440	129	24	t	t	PROPN
ejpam-440	129	25	>	>	X
ejpam-440	129	26	0	0	X
ejpam-440	129	27	.	.	PUNCT
ejpam-440	130	1	thus	thus	ADV
ejpam-440	130	2	we	we	PRON
ejpam-440	130	3	have	have	VERB
ejpam-440	130	4	µ	µ	PRON
ejpam-440	130	5	f	f	X
ejpam-440	130	6	(	(	PUNCT
ejpam-440	130	7	2k+1	2k+1	PROPN
ejpam-440	130	8	x	x	SYM
ejpam-440	130	9	)	)	PUNCT
ejpam-440	130	10	23(k+1	23(k+1	NUM
ejpam-440	130	11	)	)	PUNCT
ejpam-440	130	12	−	−	PROPN
ejpam-440	130	13	f	f	PROPN
ejpam-440	130	14	(	(	PUNCT
ejpam-440	130	15	2k	2k	NUM
ejpam-440	130	16	x	x	SYM
ejpam-440	130	17	)	)	PUNCT
ejpam-440	130	18	23k	23k	NOUN
ejpam-440	130	19	(	(	PUNCT
ejpam-440	130	20	t	t	PROPN
ejpam-440	130	21	2k+1	2k+1	PROPN
ejpam-440	130	22	)	)	PUNCT
ejpam-440	130	23	≥	≥	NOUN
ejpam-440	130	24	τ2k	τ2k	PUNCT
ejpam-440	130	25	x	x	X
ejpam-440	130	26	,	,	PUNCT
ejpam-440	130	27	0(2	0(2	X
ejpam-440	130	28	2(k+1	2(k+1	NOUN
ejpam-440	130	29	)	)	PUNCT
ejpam-440	130	30	t	t	PROPN
ejpam-440	130	31	)	)	PUNCT
ejpam-440	130	32	,	,	PUNCT
ejpam-440	130	33	(	(	PUNCT
ejpam-440	130	34	22	22	NUM
ejpam-440	130	35	)	)	PUNCT
ejpam-440	130	36	for	for	ADP
ejpam-440	130	37	every	every	DET
ejpam-440	130	38	k	k	PROPN
ejpam-440	130	39	∈	∈	PROPN
ejpam-440	130	40	n	n	PROPN
ejpam-440	130	41	and	and	CCONJ
ejpam-440	130	42	t	t	PROPN
ejpam-440	130	43	>	>	X
ejpam-440	130	44	0	0	X
ejpam-440	130	45	.	.	PUNCT
ejpam-440	131	1	as	as	ADP
ejpam-440	131	2	1	1	NUM
ejpam-440	131	3	>	>	SYM
ejpam-440	131	4	1	1	NUM
ejpam-440	131	5	2	2	NUM
ejpam-440	131	6	+	+	CCONJ
ejpam-440	131	7	1	1	NUM
ejpam-440	131	8	22	22	NUM
ejpam-440	131	9	+	+	CCONJ
ejpam-440	131	10	...	...	PUNCT
ejpam-440	131	11	+	+	CCONJ
ejpam-440	131	12	1	1	NUM
ejpam-440	131	13	2n	2n	NUM
ejpam-440	131	14	,	,	PUNCT
ejpam-440	131	15	by	by	ADP
ejpam-440	131	16	the	the	DET
ejpam-440	131	17	triangle	triangle	NOUN
ejpam-440	131	18	inequality	inequality	NOUN
ejpam-440	131	19	it	it	PRON
ejpam-440	131	20	follows	follow	VERB
ejpam-440	131	21	µ	µ	PROPN
ejpam-440	131	22	f	f	X
ejpam-440	131	23	(	(	PUNCT
ejpam-440	131	24	2n	2n	NUM
ejpam-440	131	25	x	x	NOUN
ejpam-440	131	26	)	)	PUNCT
ejpam-440	131	27	23n	23n	NOUN
ejpam-440	131	28	−	−	PROPN
ejpam-440	131	29	f	f	PROPN
ejpam-440	131	30	(	(	PUNCT
ejpam-440	131	31	x	x	X
ejpam-440	131	32	)	)	PUNCT
ejpam-440	131	33	(	(	PUNCT
ejpam-440	131	34	t)≥	t)≥	PROPN
ejpam-440	131	35	t	t	PROPN
ejpam-440	131	36	n−1	n−1	PROPN
ejpam-440	131	37	k=0	k=0	PROPN
ejpam-440	131	38	(	(	PUNCT
ejpam-440	131	39	µ	µ	X
ejpam-440	131	40	f	f	X
ejpam-440	131	41	(	(	PUNCT
ejpam-440	131	42	2k+1	2k+1	PROPN
ejpam-440	131	43	x	x	SYM
ejpam-440	131	44	)	)	PUNCT
ejpam-440	131	45	23(k+1	23(k+1	NUM
ejpam-440	131	46	)	)	PUNCT
ejpam-440	131	47	−	−	PROPN
ejpam-440	131	48	f	f	PROPN
ejpam-440	131	49	(	(	PUNCT
ejpam-440	131	50	2k	2k	NUM
ejpam-440	131	51	x	x	SYM
ejpam-440	131	52	)	)	PUNCT
ejpam-440	131	53	23k	23k	NOUN
ejpam-440	131	54	(	(	PUNCT
ejpam-440	131	55	t	t	PROPN
ejpam-440	131	56	2k+1	2k+1	PROPN
ejpam-440	131	57	)	)	PUNCT
ejpam-440	131	58	)	)	PUNCT
ejpam-440	131	59	≥	≥	PROPN
ejpam-440	131	60	t	t	PROPN
ejpam-440	131	61	n−1	n−1	PROPN
ejpam-440	131	62	k=0	k=0	PROPN
ejpam-440	131	63	(	(	PUNCT
ejpam-440	131	64	τ2k	τ2k	PUNCT
ejpam-440	131	65	x	x	SYM
ejpam-440	131	66	,	,	PUNCT
ejpam-440	131	67	0(2	0(2	X
ejpam-440	131	68	2(k+1	2(k+1	NOUN
ejpam-440	131	69	)	)	PUNCT
ejpam-440	131	70	t	t	PROPN
ejpam-440	131	71	)	)	PUNCT
ejpam-440	131	72	)	)	PUNCT
ejpam-440	132	1	=	=	SYM
ejpam-440	132	2	t	t	PROPN
ejpam-440	132	3	n	n	X
ejpam-440	132	4	i=1	i=1	PROPN
ejpam-440	132	5	(	(	PUNCT
ejpam-440	132	6	τ2i−1	τ2i−1	PROPN
ejpam-440	132	7	x	x	SYM
ejpam-440	132	8	,	,	PUNCT
ejpam-440	132	9	0(2	0(2	NUM
ejpam-440	132	10	2i	2i	PROPN
ejpam-440	132	11	t	t	PROPN
ejpam-440	132	12	)	)	PUNCT
ejpam-440	132	13	)	)	PUNCT
ejpam-440	133	1	(	(	PUNCT
ejpam-440	133	2	23	23	NUM
ejpam-440	133	3	)	)	PUNCT
ejpam-440	133	4	for	for	ADP
ejpam-440	133	5	all	all	PRON
ejpam-440	133	6	x	x	SYM
ejpam-440	133	7	∈	∈	ADJ
ejpam-440	133	8	x	x	X
ejpam-440	133	9	and	and	CCONJ
ejpam-440	133	10	all	all	DET
ejpam-440	133	11	t	t	PROPN
ejpam-440	133	12	>	>	X
ejpam-440	133	13	0	0	X
ejpam-440	133	14	.	.	PUNCT
ejpam-440	134	1	in	in	ADP
ejpam-440	134	2	order	order	NOUN
ejpam-440	134	3	to	to	PART
ejpam-440	134	4	prove	prove	VERB
ejpam-440	134	5	the	the	DET
ejpam-440	134	6	convergence	convergence	NOUN
ejpam-440	134	7	of	of	ADP
ejpam-440	134	8	the	the	DET
ejpam-440	134	9	sequence	sequence	NOUN
ejpam-440	134	10	{	{	PUNCT
ejpam-440	134	11	f	f	PROPN
ejpam-440	134	12	(	(	PUNCT
ejpam-440	134	13	2n	2n	NUM
ejpam-440	134	14	x	x	NOUN
ejpam-440	134	15	)	)	PUNCT
ejpam-440	134	16	23n	23n	NOUN
ejpam-440	134	17	}	}	PUNCT
ejpam-440	134	18	,	,	PUNCT
ejpam-440	134	19	we	we	PRON
ejpam-440	134	20	replace	replace	VERB
ejpam-440	134	21	x	x	PUNCT
ejpam-440	134	22	with	with	ADP
ejpam-440	134	23	2mx	2mx	PROPN
ejpam-440	134	24	in	in	ADP
ejpam-440	134	25	(	(	PUNCT
ejpam-440	134	26	23	23	NUM
ejpam-440	134	27	)	)	PUNCT
ejpam-440	134	28	to	to	PART
ejpam-440	134	29	find	find	VERB
ejpam-440	134	30	that	that	SCONJ
ejpam-440	134	31	µ	µ	ADJ
ejpam-440	134	32	f	f	X
ejpam-440	134	33	(	(	PUNCT
ejpam-440	134	34	2n+m	2n+m	NUM
ejpam-440	134	35	x	x	X
ejpam-440	134	36	)	)	PUNCT
ejpam-440	134	37	23(n+m	23(n+m	NUM
ejpam-440	134	38	)	)	PUNCT
ejpam-440	134	39	−	−	PROPN
ejpam-440	134	40	f	f	PROPN
ejpam-440	134	41	(	(	PUNCT
ejpam-440	134	42	2	2	NUM
ejpam-440	134	43	m	m	NOUN
ejpam-440	134	44	x	x	NOUN
ejpam-440	134	45	)	)	PUNCT
ejpam-440	134	46	23	23	NUM
ejpam-440	134	47	m	m	PROPN
ejpam-440	134	48	(	(	PUNCT
ejpam-440	134	49	t	t	PROPN
ejpam-440	134	50	)	)	PUNCT
ejpam-440	134	51	=	=	PUNCT
ejpam-440	134	52	µ	µ	X
ejpam-440	134	53	f	f	X
ejpam-440	134	54	(	(	PUNCT
ejpam-440	134	55	2n+m	2n+m	NUM
ejpam-440	134	56	x	x	NOUN
ejpam-440	134	57	)	)	PUNCT
ejpam-440	134	58	23n	23n	NOUN
ejpam-440	134	59	−	−	PROPN
ejpam-440	134	60	f	f	NOUN
ejpam-440	134	61	(	(	PUNCT
ejpam-440	134	62	2	2	NUM
ejpam-440	134	63	m	m	NOUN
ejpam-440	134	64	x	x	NOUN
ejpam-440	134	65	)	)	PUNCT
ejpam-440	134	66	(	(	PUNCT
ejpam-440	134	67	23	23	NUM
ejpam-440	134	68	m	m	NOUN
ejpam-440	134	69	t	t	PROPN
ejpam-440	134	70	)	)	PUNCT
ejpam-440	134	71	≥	≥	PROPN
ejpam-440	134	72	t	t	PROPN
ejpam-440	134	73	n	n	X
ejpam-440	134	74	i=1	i=1	PROPN
ejpam-440	134	75	(	(	PUNCT
ejpam-440	134	76	τ2i+m−1	τ2i+m−1	NOUN
ejpam-440	134	77	x	x	SYM
ejpam-440	134	78	,	,	PUNCT
ejpam-440	134	79	0(2	0(2	NUM
ejpam-440	134	80	2i+3	2i+3	PROPN
ejpam-440	134	81	m	m	NOUN
ejpam-440	134	82	t	t	PROPN
ejpam-440	134	83	)	)	PUNCT
ejpam-440	134	84	)	)	PUNCT
ejpam-440	134	85	.	.	PUNCT
ejpam-440	135	1	(	(	PUNCT
ejpam-440	135	2	24	24	NUM
ejpam-440	135	3	)	)	PUNCT
ejpam-440	135	4	since	since	SCONJ
ejpam-440	135	5	the	the	DET
ejpam-440	135	6	right	right	ADJ
ejpam-440	135	7	hand	hand	NOUN
ejpam-440	135	8	side	side	NOUN
ejpam-440	135	9	of	of	ADP
ejpam-440	135	10	the	the	DET
ejpam-440	135	11	inequality	inequality	NOUN
ejpam-440	135	12	tends	tend	VERB
ejpam-440	135	13	to	to	ADP
ejpam-440	135	14	1	1	NUM
ejpam-440	135	15	as	as	ADP
ejpam-440	135	16	m	m	PROPN
ejpam-440	135	17	and	and	CCONJ
ejpam-440	135	18	n	n	ADV
ejpam-440	135	19	tend	tend	VERB
ejpam-440	135	20	to	to	PART
ejpam-440	135	21	infinity	infinity	VERB
ejpam-440	135	22	,	,	PUNCT
ejpam-440	135	23	the	the	DET
ejpam-440	135	24	sequence	sequence	NOUN
ejpam-440	135	25	{	{	PUNCT
ejpam-440	135	26	f	f	PROPN
ejpam-440	135	27	(	(	PUNCT
ejpam-440	135	28	2n	2n	NUM
ejpam-440	135	29	x	x	NOUN
ejpam-440	135	30	)	)	PUNCT
ejpam-440	135	31	23n	23n	NOUN
ejpam-440	135	32	}	}	PUNCT
ejpam-440	135	33	is	be	AUX
ejpam-440	135	34	a	a	DET
ejpam-440	135	35	cauchy	cauchy	ADJ
ejpam-440	135	36	sequence	sequence	NOUN
ejpam-440	135	37	.	.	PUNCT
ejpam-440	136	1	therefore	therefore	ADV
ejpam-440	136	2	,	,	PUNCT
ejpam-440	136	3	we	we	PRON
ejpam-440	136	4	may	may	AUX
ejpam-440	136	5	define	define	VERB
ejpam-440	136	6	c(x	c(x	NOUN
ejpam-440	136	7	)	)	PUNCT
ejpam-440	136	8	=	=	SYM
ejpam-440	137	1	limn→∞	limn→∞	X
ejpam-440	137	2	f	f	X
ejpam-440	137	3	(	(	PUNCT
ejpam-440	137	4	2n	2n	NUM
ejpam-440	137	5	x	x	NOUN
ejpam-440	137	6	)	)	PUNCT
ejpam-440	137	7	23n	23n	NOUN
ejpam-440	137	8	for	for	ADP
ejpam-440	137	9	all	all	DET
ejpam-440	137	10	x	x	SYM
ejpam-440	137	11	∈	∈	PROPN
ejpam-440	137	12	x	x	X
ejpam-440	137	13	.	.	PUNCT
ejpam-440	138	1	now	now	ADV
ejpam-440	138	2	,	,	PUNCT
ejpam-440	138	3	we	we	PRON
ejpam-440	138	4	show	show	VERB
ejpam-440	138	5	that	that	SCONJ
ejpam-440	138	6	c	c	PROPN
ejpam-440	138	7	is	be	AUX
ejpam-440	138	8	a	a	DET
ejpam-440	138	9	cubic	cubic	ADJ
ejpam-440	138	10	function	function	NOUN
ejpam-440	138	11	.	.	PUNCT
ejpam-440	139	1	replacing	replace	VERB
ejpam-440	139	2	x	x	SYM
ejpam-440	139	3	,	,	PUNCT
ejpam-440	139	4	y	y	PROPN
ejpam-440	139	5	with	with	ADP
ejpam-440	139	6	2n	2n	NUM
ejpam-440	139	7	x	x	SYM
ejpam-440	139	8	and	and	CCONJ
ejpam-440	139	9	2n	2n	NUM
ejpam-440	139	10	y	y	PROPN
ejpam-440	139	11	respectively	respectively	ADV
ejpam-440	139	12	in	in	ADP
ejpam-440	139	13	(	(	PUNCT
ejpam-440	139	14	16	16	NUM
ejpam-440	139	15	)	)	PUNCT
ejpam-440	139	16	,	,	PUNCT
ejpam-440	139	17	it	it	PRON
ejpam-440	139	18	follows	follow	VERB
ejpam-440	139	19	that	that	SCONJ
ejpam-440	139	20	µ	µ	ADJ
ejpam-440	139	21	f	f	X
ejpam-440	139	22	(	(	PUNCT
ejpam-440	139	23	2n+1	2n+1	PROPN
ejpam-440	139	24	x+2n	x+2n	PROPN
ejpam-440	139	25	y	y	NOUN
ejpam-440	139	26	)	)	PUNCT
ejpam-440	139	27	23n	23n	NOUN
ejpam-440	139	28	+	+	CCONJ
ejpam-440	139	29	f	f	X
ejpam-440	139	30	(	(	PUNCT
ejpam-440	139	31	2n+1x−2n	2n+1x−2n	NUM
ejpam-440	139	32	y	y	NOUN
ejpam-440	139	33	)	)	PUNCT
ejpam-440	139	34	23n	23n	PROPN
ejpam-440	139	35	−2	−2	PROPN
ejpam-440	139	36	f	f	PROPN
ejpam-440	139	37	(	(	PUNCT
ejpam-440	139	38	2n	2n	NUM
ejpam-440	139	39	x+2n	x+2n	PROPN
ejpam-440	139	40	y	y	NOUN
ejpam-440	139	41	)	)	PUNCT
ejpam-440	139	42	23n	23n	PROPN
ejpam-440	139	43	−2	−2	PROPN
ejpam-440	139	44	f	f	PROPN
ejpam-440	139	45	(	(	PUNCT
ejpam-440	139	46	2n	2n	NUM
ejpam-440	139	47	x−2n	x−2n	SYM
ejpam-440	139	48	y	y	PROPN
ejpam-440	139	49	)	)	PUNCT
ejpam-440	139	50	23n	23n	PROPN
ejpam-440	139	51	−12	−12	NUM
ejpam-440	139	52	f	f	X
ejpam-440	139	53	(	(	PUNCT
ejpam-440	139	54	2n	2n	NUM
ejpam-440	139	55	x	x	NOUN
ejpam-440	139	56	)	)	PUNCT
ejpam-440	139	57	23n	23n	NOUN
ejpam-440	139	58	(	(	PUNCT
ejpam-440	139	59	t)≥	t)≥	PROPN
ejpam-440	139	60	τ2n	τ2n	PROPN
ejpam-440	139	61	x	x	SYM
ejpam-440	139	62	,	,	PUNCT
ejpam-440	139	63	2n	2n	NUM
ejpam-440	139	64	y(2	y(2	NOUN
ejpam-440	139	65	3n	3n	NUM
ejpam-440	139	66	t	t	PROPN
ejpam-440	139	67	)	)	PUNCT
ejpam-440	139	68	.	.	PUNCT
ejpam-440	140	1	(	(	PUNCT
ejpam-440	140	2	25	25	NUM
ejpam-440	140	3	)	)	PUNCT
ejpam-440	140	4	taking	take	VERB
ejpam-440	140	5	the	the	DET
ejpam-440	140	6	limit	limit	NOUN
ejpam-440	140	7	as	as	ADP
ejpam-440	140	8	n→∞	n→∞	NUM
ejpam-440	140	9	,	,	PUNCT
ejpam-440	140	10	we	we	PRON
ejpam-440	140	11	find	find	VERB
ejpam-440	140	12	that	that	SCONJ
ejpam-440	140	13	c	c	NOUN
ejpam-440	140	14	satisfies	satisfie	NOUN
ejpam-440	140	15	(	(	PUNCT
ejpam-440	140	16	25	25	NUM
ejpam-440	140	17	)	)	PUNCT
ejpam-440	140	18	for	for	ADP
ejpam-440	140	19	all	all	PRON
ejpam-440	140	20	x	x	SYM
ejpam-440	140	21	,	,	PUNCT
ejpam-440	140	22	y	y	PROPN
ejpam-440	140	23	∈	∈	PROPN
ejpam-440	140	24	x	x	X
ejpam-440	140	25	.	.	PUNCT
ejpam-440	141	1	to	to	PART
ejpam-440	141	2	prove	prove	VERB
ejpam-440	141	3	(	(	PUNCT
ejpam-440	141	4	19	19	NUM
ejpam-440	141	5	)	)	PUNCT
ejpam-440	141	6	,	,	PUNCT
ejpam-440	141	7	take	take	VERB
ejpam-440	141	8	the	the	DET
ejpam-440	141	9	limit	limit	NOUN
ejpam-440	141	10	as	as	ADP
ejpam-440	141	11	n→∞	n→∞	NUM
ejpam-440	141	12	in	in	ADP
ejpam-440	141	13	(	(	PUNCT
ejpam-440	141	14	23	23	NUM
ejpam-440	141	15	)	)	PUNCT
ejpam-440	141	16	.	.	PUNCT
ejpam-440	142	1	finally	finally	ADV
ejpam-440	142	2	,	,	PUNCT
ejpam-440	142	3	to	to	PART
ejpam-440	142	4	prove	prove	VERB
ejpam-440	142	5	the	the	DET
ejpam-440	142	6	uniqueness	uniqueness	NOUN
ejpam-440	142	7	of	of	ADP
ejpam-440	142	8	the	the	DET
ejpam-440	142	9	cubic	cubic	ADJ
ejpam-440	142	10	function	function	NOUN
ejpam-440	142	11	c	c	PROPN
ejpam-440	142	12	subject	subject	NOUN
ejpam-440	142	13	to	to	ADP
ejpam-440	142	14	(	(	PUNCT
ejpam-440	142	15	19	19	NUM
ejpam-440	142	16	)	)	PUNCT
ejpam-440	142	17	,	,	PUNCT
ejpam-440	142	18	let	let	VERB
ejpam-440	142	19	us	we	PRON
ejpam-440	142	20	assume	assume	VERB
ejpam-440	142	21	that	that	SCONJ
ejpam-440	142	22	there	there	PRON
ejpam-440	142	23	exists	exist	VERB
ejpam-440	142	24	a	a	DET
ejpam-440	142	25	cubic	cubic	ADJ
ejpam-440	142	26	function	function	NOUN
ejpam-440	142	27	c	c	NOUN
ejpam-440	142	28	′	′	NUM
ejpam-440	142	29	which	which	PRON
ejpam-440	142	30	satisfies	satisfy	VERB
ejpam-440	142	31	(	(	PUNCT
ejpam-440	142	32	19	19	NUM
ejpam-440	142	33	)	)	PUNCT
ejpam-440	142	34	.	.	PUNCT
ejpam-440	143	1	since	since	SCONJ
ejpam-440	143	2	c(2n	c(2n	NOUN
ejpam-440	143	3	x	x	SYM
ejpam-440	143	4	)	)	PUNCT
ejpam-440	143	5	=	=	SYM
ejpam-440	143	6	23nc(x	23nc(x	NOUN
ejpam-440	143	7	)	)	PUNCT
ejpam-440	143	8	and	and	CCONJ
ejpam-440	143	9	c	c	PROPN
ejpam-440	143	10	′(2n	′(2n	NOUN
ejpam-440	143	11	x	x	SYM
ejpam-440	143	12	)	)	PUNCT
ejpam-440	143	13	=	=	SYM
ejpam-440	143	14	23nc	23nc	ADJ
ejpam-440	143	15	′(x	′(x	NOUN
ejpam-440	143	16	)	)	PUNCT
ejpam-440	143	17	for	for	ADP
ejpam-440	143	18	all	all	DET
ejpam-440	143	19	x	x	SYM
ejpam-440	143	20	∈	∈	PROPN
ejpam-440	143	21	x	x	X
ejpam-440	143	22	and	and	CCONJ
ejpam-440	143	23	n	n	CCONJ
ejpam-440	143	24	∈	∈	PROPN
ejpam-440	143	25	n	n	CCONJ
ejpam-440	143	26	,	,	PUNCT
ejpam-440	143	27	from	from	ADP
ejpam-440	143	28	(	(	PUNCT
ejpam-440	143	29	19	19	NUM
ejpam-440	143	30	)	)	PUNCT
ejpam-440	143	31	it	it	PRON
ejpam-440	143	32	follows	follow	VERB
ejpam-440	143	33	that	that	SCONJ
ejpam-440	143	34	µc(x)−c	µc(x)−c	PROPN
ejpam-440	143	35	′(x)(2	′(x)(2	PROPN
ejpam-440	143	36	t	t	PROPN
ejpam-440	143	37	)	)	PUNCT
ejpam-440	143	38	=	=	PUNCT
ejpam-440	144	1	µc(2n	µc(2n	ADJ
ejpam-440	144	2	x)−c	x)−c	PROPN
ejpam-440	144	3	′(2n	′(2n	NOUN
ejpam-440	144	4	x)(2	x)(2	X
ejpam-440	145	1	3n+1	3n+1	PROPN
ejpam-440	145	2	t	t	PROPN
ejpam-440	145	3	)	)	PUNCT
ejpam-440	145	4	≥	≥	PROPN
ejpam-440	145	5	t	t	PROPN
ejpam-440	145	6	(	(	PUNCT
ejpam-440	145	7	µc(2n	µc(2n	X
ejpam-440	145	8	x)−	x)−	PROPN
ejpam-440	145	9	f	f	PROPN
ejpam-440	145	10	(	(	PUNCT
ejpam-440	145	11	2n	2n	NUM
ejpam-440	145	12	x)(2	x)(2	X
ejpam-440	145	13	3n	3n	NUM
ejpam-440	145	14	t),µ	t),µ	PROPN
ejpam-440	145	15	f	f	PROPN
ejpam-440	145	16	(	(	PUNCT
ejpam-440	145	17	2n	2n	NUM
ejpam-440	145	18	x)−c	x)−c	PROPN
ejpam-440	145	19	′(2n	′(2n	NOUN
ejpam-440	145	20	x)(2	x)(2	ADP
ejpam-440	145	21	3n	3n	NUM
ejpam-440	145	22	t	t	PROPN
ejpam-440	145	23	)	)	PUNCT
ejpam-440	145	24	)	)	PUNCT
ejpam-440	145	25	≥	≥	PROPN
ejpam-440	145	26	t	t	NOUN
ejpam-440	145	27	(	(	PUNCT
ejpam-440	145	28	t∞	t∞	NOUN
ejpam-440	145	29	i=1	i=1	PROPN
ejpam-440	145	30	(	(	PUNCT
ejpam-440	145	31	τ2n+i−1	τ2n+i−1	NOUN
ejpam-440	145	32	x	x	SYM
ejpam-440	145	33	,	,	PUNCT
ejpam-440	145	34	0(2	0(2	NUM
ejpam-440	145	35	3n+2i	3n+2i	NUM
ejpam-440	145	36	t	t	NOUN
ejpam-440	145	37	)	)	PUNCT
ejpam-440	145	38	)	)	PUNCT
ejpam-440	145	39	,	,	PUNCT
ejpam-440	145	40	t∞	t∞	X
ejpam-440	145	41	i=1	i=1	X
ejpam-440	145	42	(	(	PUNCT
ejpam-440	145	43	τ2n+i−1	τ2n+i−1	NOUN
ejpam-440	145	44	x	x	SYM
ejpam-440	145	45	,	,	PUNCT
ejpam-440	145	46	0(2	0(2	NUM
ejpam-440	145	47	3n+2i	3n+2i	NUM
ejpam-440	145	48	t	t	NOUN
ejpam-440	145	49	)	)	PUNCT
ejpam-440	145	50	)	)	PUNCT
ejpam-440	145	51	)	)	PUNCT
ejpam-440	145	52	,	,	PUNCT
ejpam-440	145	53	(	(	PUNCT
ejpam-440	145	54	26	26	NUM
ejpam-440	145	55	)	)	PUNCT
ejpam-440	145	56	for	for	ADP
ejpam-440	145	57	all	all	PRON
ejpam-440	145	58	x	x	SYM
ejpam-440	145	59	∈	∈	ADJ
ejpam-440	145	60	x	x	X
ejpam-440	145	61	and	and	CCONJ
ejpam-440	145	62	all	all	DET
ejpam-440	145	63	t	t	PROPN
ejpam-440	145	64	>	>	X
ejpam-440	145	65	0	0	X
ejpam-440	145	66	.	.	PUNCT
ejpam-440	145	67	by	by	ADP
ejpam-440	145	68	letting	let	VERB
ejpam-440	145	69	n→∞	n→∞	PRON
ejpam-440	145	70	in	in	ADP
ejpam-440	145	71	(	(	PUNCT
ejpam-440	145	72	26	26	NUM
ejpam-440	145	73	)	)	PUNCT
ejpam-440	145	74	,	,	PUNCT
ejpam-440	145	75	we	we	PRON
ejpam-440	145	76	find	find	VERB
ejpam-440	145	77	that	that	SCONJ
ejpam-440	145	78	c	c	NOUN
ejpam-440	145	79	=	=	SYM
ejpam-440	145	80	c	c	PROPN
ejpam-440	145	81	′.	′.	PROPN
ejpam-440	145	82	m.	m.	PROPN
ejpam-440	145	83	gordji	gordji	PROPN
ejpam-440	145	84	,	,	PUNCT
ejpam-440	145	85	j.	j.	PROPN
ejpam-440	145	86	rassias	rassias	PROPN
ejpam-440	145	87	,	,	PUNCT
ejpam-440	145	88	and	and	CCONJ
ejpam-440	145	89	m.	m.	NOUN
ejpam-440	145	90	savadkouhi	savadkouhi	PROPN
ejpam-440	145	91	/	/	SYM
ejpam-440	145	92	eur	eur	PROPN
ejpam-440	145	93	.	.	PUNCT
ejpam-440	146	1	j.	j.	PROPN
ejpam-440	146	2	pure	pure	PROPN
ejpam-440	146	3	appl	appl	PROPN
ejpam-440	146	4	.	.	PROPN
ejpam-440	146	5	math	math	PROPN
ejpam-440	146	6	,	,	PUNCT
ejpam-440	146	7	2	2	NUM
ejpam-440	146	8	(	(	PUNCT
ejpam-440	146	9	2009	2009	NUM
ejpam-440	146	10	)	)	PUNCT
ejpam-440	146	11	,	,	PUNCT
ejpam-440	146	12	(	(	PUNCT
ejpam-440	146	13	494	494	NUM
ejpam-440	146	14	-	-	SYM
ejpam-440	146	15	507	507	NUM
ejpam-440	146	16	)	)	PUNCT
ejpam-440	146	17	502	502	NUM
ejpam-440	146	18	example	example	NOUN
ejpam-440	146	19	1	1	X
ejpam-440	146	20	.	.	X
ejpam-440	147	1	let	let	AUX
ejpam-440	147	2	(	(	PUNCT
ejpam-440	147	3	a,‖.‖	a,‖.‖	PROPN
ejpam-440	147	4	)	)	PUNCT
ejpam-440	147	5	be	be	AUX
ejpam-440	147	6	a	a	DET
ejpam-440	147	7	banach	banach	NOUN
ejpam-440	147	8	algebra	algebra	NOUN
ejpam-440	147	9	and	and	CCONJ
ejpam-440	147	10	µx(t	µx(t	NOUN
ejpam-440	147	11	)	)	PUNCT
ejpam-440	147	12	=	=	PUNCT
ejpam-440	148	1			PROPN
ejpam-440	148	2			PRON
ejpam-440	148	3			NOUN
ejpam-440	148	4	max{1−	max{1−	PROPN
ejpam-440	148	5	‖x‖	‖x‖	PROPN
ejpam-440	148	6	t	t	PROPN
ejpam-440	148	7	,	,	PUNCT
ejpam-440	148	8	0	0	NUM
ejpam-440	148	9	}	}	PUNCT
ejpam-440	148	10	,	,	PUNCT
ejpam-440	148	11	if	if	SCONJ
ejpam-440	148	12	t	t	PROPN
ejpam-440	148	13	>	>	X
ejpam-440	148	14	0	0	NUM
ejpam-440	148	15	,	,	PUNCT
ejpam-440	148	16	0	0	NUM
ejpam-440	148	17	,	,	PUNCT
ejpam-440	148	18	if	if	SCONJ
ejpam-440	148	19	t	t	PRON
ejpam-440	148	20	≤	≤	NUM
ejpam-440	148	21	0	0	NUM
ejpam-440	148	22	,	,	PUNCT
ejpam-440	148	23	for	for	ADP
ejpam-440	148	24	every	every	PRON
ejpam-440	148	25	x	x	X
ejpam-440	148	26	,	,	PUNCT
ejpam-440	148	27	y	y	PROPN
ejpam-440	148	28	∈	∈	PROPN
ejpam-440	148	29	a.	a.	NOUN
ejpam-440	148	30	let	let	VERB
ejpam-440	148	31	ρx	ρx	VERB
ejpam-440	148	32	,	,	PUNCT
ejpam-440	148	33	y(t	y(t	PROPN
ejpam-440	148	34	)	)	PUNCT
ejpam-440	149	1	=	=	NOUN
ejpam-440	149	2	max{1−	max{1−	PROPN
ejpam-440	149	3	32‖x‖+	32‖x‖+	NUM
ejpam-440	150	1	32‖y‖	32‖y‖	PROPN
ejpam-440	150	2	t	t	NOUN
ejpam-440	150	3	,	,	PUNCT
ejpam-440	150	4	0	0	NUM
ejpam-440	150	5	}	}	PUNCT
ejpam-440	150	6	(	(	PUNCT
ejpam-440	150	7	t	t	X
ejpam-440	150	8	>	>	X
ejpam-440	150	9	0	0	NUM
ejpam-440	150	10	)	)	PUNCT
ejpam-440	150	11	and	and	CCONJ
ejpam-440	150	12	ρx	ρx	VERB
ejpam-440	150	13	,	,	PUNCT
ejpam-440	150	14	y(t	y(t	PROPN
ejpam-440	150	15	)	)	PUNCT
ejpam-440	151	1	=	=	SYM
ejpam-440	151	2	0	0	PUNCT
ejpam-440	152	1	if	if	SCONJ
ejpam-440	152	2	t	t	PRON
ejpam-440	152	3	≤	≤	NOUN
ejpam-440	152	4	0	0	NUM
ejpam-440	152	5	.	.	PUNCT
ejpam-440	153	1	we	we	PRON
ejpam-440	153	2	note	note	VERB
ejpam-440	153	3	that	that	SCONJ
ejpam-440	153	4	ρx	ρx	VERB
ejpam-440	153	5	,	,	PUNCT
ejpam-440	153	6	y	y	PROPN
ejpam-440	153	7	is	be	AUX
ejpam-440	153	8	a	a	DET
ejpam-440	153	9	distribution	distribution	NOUN
ejpam-440	153	10	function	function	NOUN
ejpam-440	153	11	and	and	CCONJ
ejpam-440	153	12	lim	lim	PROPN
ejpam-440	153	13	n→∞	n→∞	PROPN
ejpam-440	153	14	ρ2n	ρ2n	PROPN
ejpam-440	154	1	x	x	SYM
ejpam-440	154	2	,	,	PUNCT
ejpam-440	154	3	2n	2n	NUM
ejpam-440	154	4	y(2	y(2	PROPN
ejpam-440	154	5	2n	2n	NUM
ejpam-440	154	6	t	t	PROPN
ejpam-440	154	7	)	)	PUNCT
ejpam-440	154	8	=	=	SYM
ejpam-440	154	9	1	1	NUM
ejpam-440	154	10	for	for	ADP
ejpam-440	154	11	all	all	DET
ejpam-440	154	12	x	x	SYM
ejpam-440	154	13	,	,	PUNCT
ejpam-440	154	14	y	y	PROPN
ejpam-440	154	15	∈	∈	PROPN
ejpam-440	154	16	a	a	PRON
ejpam-440	154	17	and	and	CCONJ
ejpam-440	154	18	all	all	PRON
ejpam-440	154	19	t	t	NOUN
ejpam-440	154	20	>	>	X
ejpam-440	154	21	0	0	X
ejpam-440	154	22	.	.	PUNCT
ejpam-440	155	1	it	it	PRON
ejpam-440	155	2	is	be	AUX
ejpam-440	155	3	straightforward	straightforward	ADJ
ejpam-440	155	4	to	to	PART
ejpam-440	155	5	show	show	VERB
ejpam-440	155	6	that	that	SCONJ
ejpam-440	155	7	(	(	PUNCT
ejpam-440	155	8	a,µ	a,µ	PROPN
ejpam-440	155	9	,	,	PUNCT
ejpam-440	155	10	tl	tl	PROPN
ejpam-440	155	11	)	)	PUNCT
ejpam-440	155	12	is	be	AUX
ejpam-440	155	13	an	an	DET
ejpam-440	155	14	rn	rn	NOUN
ejpam-440	155	15	-	-	NOUN
ejpam-440	155	16	space	space	NOUN
ejpam-440	155	17	.	.	PUNCT
ejpam-440	156	1	indeed	indeed	ADV
ejpam-440	156	2	,	,	PUNCT
ejpam-440	156	3	(	(	PUNCT
ejpam-440	156	4	∀t	∀t	PROPN
ejpam-440	156	5	>	>	X
ejpam-440	156	6	0	0	NUM
ejpam-440	156	7	;	;	PUNCT
ejpam-440	156	8	µx(t	µx(t	NUM
ejpam-440	156	9	)	)	PUNCT
ejpam-440	156	10	=	=	SYM
ejpam-440	156	11	1	1	X
ejpam-440	156	12	)	)	PUNCT
ejpam-440	156	13	=	=	NOUN
ejpam-440	156	14	⇒	⇒	NOUN
ejpam-440	156	15	(	(	PUNCT
ejpam-440	156	16	∀t	∀t	PROPN
ejpam-440	156	17	>	>	X
ejpam-440	156	18	0	0	NUM
ejpam-440	156	19	;	;	PUNCT
ejpam-440	156	20	‖x‖	‖x‖	PROPN
ejpam-440	156	21	t	t	NOUN
ejpam-440	156	22	=	=	SYM
ejpam-440	156	23	0	0	X
ejpam-440	156	24	)	)	PUNCT
ejpam-440	157	1	=	=	NOUN
ejpam-440	157	2	⇒	⇒	NOUN
ejpam-440	157	3	x	x	PUNCT
ejpam-440	157	4	=	=	SYM
ejpam-440	157	5	0	0	NUM
ejpam-440	157	6	and	and	CCONJ
ejpam-440	157	7	µλx(t	µλx(t	PROPN
ejpam-440	157	8	)	)	PUNCT
ejpam-440	157	9	=	=	SYM
ejpam-440	157	10	1−	1−	NUM
ejpam-440	157	11	‖λx‖	‖λx‖	PROPN
ejpam-440	157	12	t	t	NOUN
ejpam-440	157	13	=	=	SYM
ejpam-440	157	14	1−	1−	NUM
ejpam-440	157	15	|λ|‖x‖	|λ|‖x‖	NOUN
ejpam-440	157	16	t	t	NOUN
ejpam-440	157	17	=	=	SYM
ejpam-440	157	18	1−	1−	NUM
ejpam-440	157	19	‖x‖	‖x‖	PROPN
ejpam-440	157	20	t	t	PROPN
ejpam-440	157	21	λ	λ	X
ejpam-440	157	22	=	=	PRON
ejpam-440	157	23	µx	µx	PROPN
ejpam-440	157	24	(	(	PUNCT
ejpam-440	157	25	t	t	PROPN
ejpam-440	157	26	λ	λ	PROPN
ejpam-440	157	27	)	)	PUNCT
ejpam-440	157	28	(	(	PUNCT
ejpam-440	157	29	27	27	NUM
ejpam-440	157	30	)	)	PUNCT
ejpam-440	157	31	for	for	ADP
ejpam-440	157	32	all	all	DET
ejpam-440	157	33	x	x	SYM
ejpam-440	157	34	∈	∈	PROPN
ejpam-440	157	35	a	a	PRON
ejpam-440	158	1	and	and	CCONJ
ejpam-440	158	2	all	all	PRON
ejpam-440	158	3	t	t	NOUN
ejpam-440	158	4	>	>	X
ejpam-440	158	5	0	0	X
ejpam-440	158	6	.	.	PUNCT
ejpam-440	159	1	also	also	ADV
ejpam-440	159	2	,	,	PUNCT
ejpam-440	159	3	for	for	ADP
ejpam-440	159	4	every	every	DET
ejpam-440	159	5	x	x	X
ejpam-440	159	6	,	,	PUNCT
ejpam-440	159	7	y	y	PROPN
ejpam-440	159	8	∈	∈	PROPN
ejpam-440	159	9	a	a	PRON
ejpam-440	159	10	and	and	CCONJ
ejpam-440	159	11	t	t	PROPN
ejpam-440	159	12	,	,	PUNCT
ejpam-440	159	13	s	s	VERB
ejpam-440	159	14	>	>	X
ejpam-440	159	15	0	0	NUM
ejpam-440	160	1	we	we	PRON
ejpam-440	160	2	have	have	AUX
ejpam-440	160	3	µx+y(t	µx+y(t	X
ejpam-440	160	4	+	+	CCONJ
ejpam-440	160	5	s	s	X
ejpam-440	160	6	)	)	PUNCT
ejpam-440	161	1	=	=	NOUN
ejpam-440	161	2	max{1−	max{1−	NOUN
ejpam-440	161	3	‖x	‖x	NOUN
ejpam-440	162	1	+	+	CCONJ
ejpam-440	162	2	y‖	y‖	PROPN
ejpam-440	162	3	t	t	PROPN
ejpam-440	162	4	+	+	CCONJ
ejpam-440	162	5	s	s	X
ejpam-440	162	6	,	,	PUNCT
ejpam-440	162	7	0}=max{1−‖	0}=max{1−‖	NOUN
ejpam-440	162	8	x	x	PUNCT
ejpam-440	163	1	+	+	CCONJ
ejpam-440	163	2	y	y	PROPN
ejpam-440	163	3	t	t	PROPN
ejpam-440	163	4	+	+	CCONJ
ejpam-440	163	5	s	s	PROPN
ejpam-440	163	6	‖	‖	ADJ
ejpam-440	163	7	,	,	PUNCT
ejpam-440	163	8	0	0	NUM
ejpam-440	163	9	}	}	PUNCT
ejpam-440	163	10	=	=	NOUN
ejpam-440	163	11	max{1−‖	max{1−‖	NOUN
ejpam-440	163	12	x	x	X
ejpam-440	163	13	t	t	PROPN
ejpam-440	164	1	+	+	SYM
ejpam-440	164	2	s	s	PART
ejpam-440	164	3	+	+	CCONJ
ejpam-440	164	4	y	y	PROPN
ejpam-440	164	5	t	t	PROPN
ejpam-440	164	6	+	+	CCONJ
ejpam-440	164	7	s	s	PROPN
ejpam-440	165	1	‖	‖	ADJ
ejpam-440	165	2	,	,	PUNCT
ejpam-440	165	3	0	0	NUM
ejpam-440	165	4	}	}	PUNCT
ejpam-440	165	5	≥max{1−‖	≥max{1−‖	NOUN
ejpam-440	165	6	x	x	PROPN
ejpam-440	165	7	t	t	PROPN
ejpam-440	165	8	+	+	CCONJ
ejpam-440	165	9	y	y	PROPN
ejpam-440	165	10	s	s	PROPN
ejpam-440	165	11	‖	‖	PROPN
ejpam-440	165	12	,	,	PUNCT
ejpam-440	165	13	0	0	NUM
ejpam-440	165	14	}	}	PUNCT
ejpam-440	165	15	≥max{1−‖	≥max{1−‖	NOUN
ejpam-440	165	16	x	x	PROPN
ejpam-440	165	17	t	t	PROPN
ejpam-440	165	18	‖−	‖−	PROPN
ejpam-440	165	19	‖	‖	PROPN
ejpam-440	165	20	y	y	PROPN
ejpam-440	165	21	s	s	PROPN
ejpam-440	165	22	‖	‖	PROPN
ejpam-440	165	23	,	,	PUNCT
ejpam-440	165	24	0	0	NUM
ejpam-440	165	25	}	}	PUNCT
ejpam-440	165	26	=	=	SYM
ejpam-440	165	27	tl(µx(t),µy(s	tl(µx(t),µy(s	PROPN
ejpam-440	165	28	)	)	PUNCT
ejpam-440	165	29	)	)	PUNCT
ejpam-440	165	30	.	.	PUNCT
ejpam-440	166	1	it	it	PRON
ejpam-440	166	2	is	be	AUX
ejpam-440	166	3	also	also	ADV
ejpam-440	166	4	easy	easy	ADJ
ejpam-440	166	5	to	to	PART
ejpam-440	166	6	see	see	VERB
ejpam-440	166	7	that	that	PRON
ejpam-440	166	8	(	(	PUNCT
ejpam-440	166	9	a,µ	a,µ	PROPN
ejpam-440	166	10	,	,	PUNCT
ejpam-440	166	11	tl	tl	PROPN
ejpam-440	166	12	)	)	PUNCT
ejpam-440	166	13	is	be	AUX
ejpam-440	166	14	complete	complete	ADJ
ejpam-440	166	15	,	,	PUNCT
ejpam-440	166	16	for	for	ADP
ejpam-440	166	17	µx−y(t)≥	µx−y(t)≥	PRON
ejpam-440	166	18	1−	1−	NUM
ejpam-440	166	19	‖x	‖x	NUM
ejpam-440	167	1	−	−	PROPN
ejpam-440	167	2	y‖	y‖	PROPN
ejpam-440	167	3	t	t	PROPN
ejpam-440	167	4	;	;	PUNCT
ejpam-440	167	5	(	(	PUNCT
ejpam-440	167	6	x	x	X
ejpam-440	167	7	,	,	PUNCT
ejpam-440	167	8	y	y	PROPN
ejpam-440	167	9	∈	∈	PROPN
ejpam-440	167	10	a	a	PRON
ejpam-440	167	11	,	,	PUNCT
ejpam-440	167	12	t	t	X
ejpam-440	167	13	>	>	X
ejpam-440	167	14	0	0	NUM
ejpam-440	167	15	)	)	PUNCT
ejpam-440	167	16	(	(	PUNCT
ejpam-440	167	17	28	28	NUM
ejpam-440	167	18	)	)	PUNCT
ejpam-440	167	19	m.	m.	NOUN
ejpam-440	167	20	gordji	gordji	PROPN
ejpam-440	167	21	,	,	PUNCT
ejpam-440	167	22	j.	j.	PROPN
ejpam-440	167	23	rassias	rassias	PROPN
ejpam-440	167	24	,	,	PUNCT
ejpam-440	167	25	and	and	CCONJ
ejpam-440	167	26	m.	m.	NOUN
ejpam-440	167	27	savadkouhi	savadkouhi	PROPN
ejpam-440	167	28	/	/	SYM
ejpam-440	167	29	eur	eur	PROPN
ejpam-440	167	30	.	.	PUNCT
ejpam-440	168	1	j.	j.	PROPN
ejpam-440	168	2	pure	pure	PROPN
ejpam-440	168	3	appl	appl	PROPN
ejpam-440	168	4	.	.	PROPN
ejpam-440	168	5	math	math	PROPN
ejpam-440	168	6	,	,	PUNCT
ejpam-440	168	7	2	2	NUM
ejpam-440	168	8	(	(	PUNCT
ejpam-440	168	9	2009	2009	NUM
ejpam-440	168	10	)	)	PUNCT
ejpam-440	168	11	,	,	PUNCT
ejpam-440	168	12	(	(	PUNCT
ejpam-440	168	13	494	494	NUM
ejpam-440	168	14	-	-	SYM
ejpam-440	168	15	507	507	NUM
ejpam-440	168	16	)	)	PUNCT
ejpam-440	168	17	503	503	NUM
ejpam-440	168	18	and	and	CCONJ
ejpam-440	168	19	(	(	PUNCT
ejpam-440	168	20	a,‖.‖	a,‖.‖	PROPN
ejpam-440	168	21	)	)	PUNCT
ejpam-440	168	22	is	be	AUX
ejpam-440	168	23	complete	complete	ADJ
ejpam-440	168	24	.	.	PUNCT
ejpam-440	169	1	define	define	VERB
ejpam-440	169	2	f	f	PROPN
ejpam-440	169	3	:	:	PUNCT
ejpam-440	169	4	a→	a→	PUNCT
ejpam-440	169	5	a	a	X
ejpam-440	169	6	,	,	PUNCT
ejpam-440	169	7	f	f	PROPN
ejpam-440	169	8	(	(	PUNCT
ejpam-440	169	9	x	x	X
ejpam-440	169	10	)	)	PUNCT
ejpam-440	169	11	=	=	SYM
ejpam-440	169	12	‖x‖x0	‖x‖x0	NUM
ejpam-440	169	13	,	,	PUNCT
ejpam-440	169	14	where	where	SCONJ
ejpam-440	169	15	x0	x0	PROPN
ejpam-440	169	16	is	be	AUX
ejpam-440	169	17	a	a	DET
ejpam-440	169	18	unit	unit	NOUN
ejpam-440	169	19	vector	vector	NOUN
ejpam-440	169	20	in	in	ADP
ejpam-440	169	21	a.	a.	NOUN
ejpam-440	169	22	a	a	DET
ejpam-440	169	23	simple	simple	ADJ
ejpam-440	169	24	computation	computation	NOUN
ejpam-440	169	25	shows	show	VERB
ejpam-440	169	26	that	that	SCONJ
ejpam-440	169	27	‖	‖	PROPN
ejpam-440	169	28	f	f	X
ejpam-440	169	29	(	(	PUNCT
ejpam-440	169	30	x	x	PROPN
ejpam-440	169	31	+	+	NUM
ejpam-440	169	32	y	y	NOUN
ejpam-440	169	33	)	)	PUNCT
ejpam-440	170	1	+	+	NOUN
ejpam-440	170	2	f	f	X
ejpam-440	170	3	(	(	PUNCT
ejpam-440	170	4	x	x	X
ejpam-440	170	5	−	−	PUNCT
ejpam-440	170	6	y)−	y)−	PROPN
ejpam-440	170	7	2	2	NUM
ejpam-440	170	8	f	f	NOUN
ejpam-440	170	9	(	(	PUNCT
ejpam-440	170	10	x)−	x)−	PROPN
ejpam-440	170	11	2	2	NUM
ejpam-440	170	12	f	f	NOUN
ejpam-440	170	13	(	(	PUNCT
ejpam-440	170	14	y)‖	y)‖	NOUN
ejpam-440	170	15	=	=	PUNCT
ejpam-440	170	16	‖x	‖x	NOUN
ejpam-440	171	1	+	+	PUNCT
ejpam-440	172	1	y‖+	y‖+	ADJ
ejpam-440	172	2	‖x	‖x	PUNCT
ejpam-440	172	3	−	−	PROPN
ejpam-440	172	4	y‖	y‖	PROPN
ejpam-440	172	5	−	−	PROPN
ejpam-440	173	1	2‖x‖−	2‖x‖−	NUM
ejpam-440	173	2	2‖y‖	2‖y‖	NUM
ejpam-440	173	3	≤	≤	NOUN
ejpam-440	173	4	32‖x‖+	32‖x‖+	NUM
ejpam-440	173	5	32‖y‖	32‖y‖	NUM
ejpam-440	173	6	for	for	ADP
ejpam-440	173	7	all	all	DET
ejpam-440	173	8	x	x	SYM
ejpam-440	173	9	,	,	PUNCT
ejpam-440	173	10	y	y	PROPN
ejpam-440	173	11	∈	∈	PROPN
ejpam-440	173	12	a	a	PRON
ejpam-440	173	13	,	,	PUNCT
ejpam-440	173	14	hence	hence	ADV
ejpam-440	173	15	µ	µ	X
ejpam-440	173	16	f	f	X
ejpam-440	173	17	(	(	PUNCT
ejpam-440	173	18	x+y)+	x+y)+	PROPN
ejpam-440	173	19	f	f	PROPN
ejpam-440	173	20	(	(	PUNCT
ejpam-440	173	21	x−y)−2	x−y)−2	PROPN
ejpam-440	173	22	f	f	PROPN
ejpam-440	174	1	(	(	PUNCT
ejpam-440	174	2	x)−2	x)−2	NOUN
ejpam-440	174	3	f	f	X
ejpam-440	174	4	(	(	PUNCT
ejpam-440	174	5	y)(t)≥	y)(t)≥	PRON
ejpam-440	174	6	ρx	ρx	VERB
ejpam-440	174	7	,	,	PUNCT
ejpam-440	174	8	y(t	y(t	PROPN
ejpam-440	174	9	)	)	PUNCT
ejpam-440	174	10	,	,	PUNCT
ejpam-440	174	11	(	(	PUNCT
ejpam-440	174	12	29	29	NUM
ejpam-440	174	13	)	)	PUNCT
ejpam-440	174	14	for	for	ADP
ejpam-440	174	15	all	all	DET
ejpam-440	174	16	x	x	SYM
ejpam-440	174	17	,	,	PUNCT
ejpam-440	174	18	y	y	PROPN
ejpam-440	174	19	∈	∈	PROPN
ejpam-440	174	20	a	a	PRON
ejpam-440	175	1	and	and	CCONJ
ejpam-440	176	1	all	all	DET
ejpam-440	176	2	t	t	NOUN
ejpam-440	176	3	>	>	X
ejpam-440	176	4	0	0	X
ejpam-440	176	5	.	.	PUNCT
ejpam-440	177	1	fix	fix	VERB
ejpam-440	177	2	x	x	X
ejpam-440	177	3	∈	∈	PROPN
ejpam-440	177	4	a	a	NOUN
ejpam-440	177	5	and	and	CCONJ
ejpam-440	177	6	t	t	PROPN
ejpam-440	177	7	>	>	X
ejpam-440	177	8	0	0	PROPN
ejpam-440	177	9	,	,	PUNCT
ejpam-440	177	10	then	then	ADV
ejpam-440	177	11	(	(	PUNCT
ejpam-440	177	12	tl	tl	PROPN
ejpam-440	177	13	)	)	PUNCT
ejpam-440	178	1	∞	∞	PROPN
ejpam-440	178	2	i=1	i=1	PROPN
ejpam-440	178	3	(	(	PUNCT
ejpam-440	178	4	ρ2n+i−1	ρ2n+i−1	PROPN
ejpam-440	178	5	x	x	SYM
ejpam-440	178	6	,	,	PUNCT
ejpam-440	178	7	2n+i−1	2n+i−1	PROPN
ejpam-440	178	8	x(2	x(2	PROPN
ejpam-440	178	9	2n+2i	2n+2i	NUM
ejpam-440	178	10	t	t	NOUN
ejpam-440	178	11	)	)	PUNCT
ejpam-440	178	12	)	)	PUNCT
ejpam-440	179	1	=	=	X
ejpam-440	179	2	max	max	X
ejpam-440	179	3	{	{	PUNCT
ejpam-440	179	4	∞	∞	PROPN
ejpam-440	179	5	∑	∑	PROPN
ejpam-440	179	6	i=1	i=1	PROPN
ejpam-440	179	7	(	(	PUNCT
ejpam-440	179	8	ρ2n+i−1	ρ2n+i−1	PROPN
ejpam-440	179	9	x	x	SYM
ejpam-440	179	10	,	,	PUNCT
ejpam-440	179	11	2n+i−1	2n+i−1	PROPN
ejpam-440	179	12	x(2	x(2	PROPN
ejpam-440	179	13	2n+2i	2n+2i	NUM
ejpam-440	179	14	t)−	t)−	PROPN
ejpam-440	179	15	1	1	NUM
ejpam-440	179	16	)	)	PUNCT
ejpam-440	179	17	+	+	CCONJ
ejpam-440	179	18	1	1	NUM
ejpam-440	179	19	,	,	PUNCT
ejpam-440	179	20	0	0	NUM
ejpam-440	179	21	}	}	PUNCT
ejpam-440	179	22	=	=	NOUN
ejpam-440	179	23	max{1−	max{1−	NOUN
ejpam-440	179	24	32‖x‖	32‖x‖	NUM
ejpam-440	179	25	2nt	2nt	NOUN
ejpam-440	179	26	,	,	PUNCT
ejpam-440	179	27	0	0	NUM
ejpam-440	179	28	}	}	PUNCT
ejpam-440	179	29	,	,	PUNCT
ejpam-440	179	30	hence	hence	ADV
ejpam-440	179	31	limn→∞(tl	limn→∞(tl	NUM
ejpam-440	179	32	)	)	PUNCT
ejpam-440	180	1	∞	∞	NUM
ejpam-440	180	2	i=1	i=1	PROPN
ejpam-440	180	3	(	(	PUNCT
ejpam-440	180	4	ρ2n+i−1	ρ2n+i−1	PROPN
ejpam-440	180	5	x	x	SYM
ejpam-440	180	6	,	,	PUNCT
ejpam-440	180	7	2n+i−1	2n+i−1	PROPN
ejpam-440	180	8	x(2	x(2	PROPN
ejpam-440	180	9	2n+2i	2n+2i	NUM
ejpam-440	180	10	t	t	NOUN
ejpam-440	180	11	)	)	PUNCT
ejpam-440	180	12	)	)	PUNCT
ejpam-440	181	1	=	=	PUNCT
ejpam-440	181	2	1	1	X
ejpam-440	181	3	.	.	PUNCT
ejpam-440	182	1	hence	hence	ADV
ejpam-440	182	2	,	,	PUNCT
ejpam-440	182	3	all	all	DET
ejpam-440	182	4	the	the	DET
ejpam-440	182	5	conditions	condition	NOUN
ejpam-440	182	6	of	of	ADP
ejpam-440	182	7	theorem	theorem	ADJ
ejpam-440	182	8	3	3	NUM
ejpam-440	182	9	hold	hold	NOUN
ejpam-440	182	10	.	.	PUNCT
ejpam-440	183	1	since	since	SCONJ
ejpam-440	183	2	(	(	PUNCT
ejpam-440	183	3	tl	tl	PROPN
ejpam-440	183	4	)	)	PUNCT
ejpam-440	183	5	∞	∞	PROPN
ejpam-440	183	6	i=1	i=1	PROPN
ejpam-440	184	1	(	(	PUNCT
ejpam-440	184	2	ρ2i−1	ρ2i−1	PROPN
ejpam-440	184	3	x	x	PROPN
ejpam-440	184	4	,	,	PUNCT
ejpam-440	184	5	2i−1	2i−1	PROPN
ejpam-440	184	6	x(2	x(2	PROPN
ejpam-440	184	7	2i	2i	PROPN
ejpam-440	184	8	t	t	PROPN
ejpam-440	184	9	)	)	PUNCT
ejpam-440	184	10	)	)	PUNCT
ejpam-440	185	1	=	=	X
ejpam-440	185	2	max	max	X
ejpam-440	185	3	{	{	PUNCT
ejpam-440	185	4	∞	∞	PROPN
ejpam-440	185	5	∑	∑	PROPN
ejpam-440	185	6	i=1	i=1	PROPN
ejpam-440	185	7	(	(	PUNCT
ejpam-440	185	8	ρ2i−1	ρ2i−1	PROPN
ejpam-440	185	9	x	x	PROPN
ejpam-440	185	10	,	,	PUNCT
ejpam-440	185	11	2i−1	2i−1	PROPN
ejpam-440	185	12	x(2	x(2	PROPN
ejpam-440	185	13	2i	2i	NOUN
ejpam-440	185	14	t)−	t)−	PROPN
ejpam-440	185	15	1	1	NUM
ejpam-440	185	16	)	)	PUNCT
ejpam-440	185	17	+	+	CCONJ
ejpam-440	185	18	1	1	NUM
ejpam-440	185	19	,	,	PUNCT
ejpam-440	185	20	0	0	NUM
ejpam-440	185	21	}	}	PUNCT
ejpam-440	185	22	=	=	NOUN
ejpam-440	185	23	max{1−	max{1−	NOUN
ejpam-440	185	24	32‖x‖	32‖x‖	NUM
ejpam-440	185	25	t	t	NOUN
ejpam-440	185	26	,	,	PUNCT
ejpam-440	185	27	0	0	NUM
ejpam-440	185	28	}	}	PUNCT
ejpam-440	185	29	,	,	PUNCT
ejpam-440	185	30	we	we	PRON
ejpam-440	185	31	obtain	obtain	VERB
ejpam-440	185	32	that	that	SCONJ
ejpam-440	185	33	there	there	PRON
ejpam-440	185	34	exists	exist	VERB
ejpam-440	185	35	a	a	DET
ejpam-440	185	36	unique	unique	ADJ
ejpam-440	185	37	quadratic	quadratic	ADJ
ejpam-440	185	38	mapping	mapping	NOUN
ejpam-440	185	39	q	q	NOUN
ejpam-440	185	40	:	:	PUNCT
ejpam-440	185	41	a−→	a−→	NOUN
ejpam-440	185	42	a	a	DET
ejpam-440	185	43	such	such	ADJ
ejpam-440	185	44	that	that	SCONJ
ejpam-440	185	45	µq(x)−	µq(x)−	PROPN
ejpam-440	185	46	f	f	X
ejpam-440	185	47	(	(	PUNCT
ejpam-440	185	48	x)(t)≥max{1−	x)(t)≥max{1−	PROPN
ejpam-440	185	49	32‖x‖	32‖x‖	NUM
ejpam-440	185	50	t	t	NOUN
ejpam-440	185	51	,	,	PUNCT
ejpam-440	185	52	0	0	NUM
ejpam-440	185	53	}	}	PUNCT
ejpam-440	185	54	(	(	PUNCT
ejpam-440	185	55	30	30	NUM
ejpam-440	185	56	)	)	PUNCT
ejpam-440	185	57	for	for	ADP
ejpam-440	185	58	all	all	DET
ejpam-440	185	59	x	x	SYM
ejpam-440	185	60	∈	∈	PROPN
ejpam-440	185	61	a	a	PRON
ejpam-440	186	1	and	and	CCONJ
ejpam-440	186	2	all	all	PRON
ejpam-440	186	3	t	t	NOUN
ejpam-440	186	4	>	>	X
ejpam-440	186	5	0	0	X
ejpam-440	186	6	.	.	PUNCT
ejpam-440	187	1	let	let	VERB
ejpam-440	187	2	τx	τx	INTJ
ejpam-440	187	3	,	,	PUNCT
ejpam-440	187	4	y(t	y(t	PROPN
ejpam-440	187	5	)	)	PUNCT
ejpam-440	188	1	=	=	NOUN
ejpam-440	188	2	max{1−	max{1−	ADJ
ejpam-440	188	3	64‖x‖+	64‖x‖+	NUM
ejpam-440	188	4	64‖y‖	64‖y‖	NUM
ejpam-440	188	5	t	t	NOUN
ejpam-440	188	6	,	,	PUNCT
ejpam-440	188	7	0	0	NUM
ejpam-440	188	8	}	}	PUNCT
ejpam-440	188	9	(	(	PUNCT
ejpam-440	188	10	t	t	X
ejpam-440	188	11	>	>	X
ejpam-440	188	12	0	0	NUM
ejpam-440	188	13	)	)	PUNCT
ejpam-440	188	14	(	(	PUNCT
ejpam-440	188	15	31	31	NUM
ejpam-440	188	16	)	)	PUNCT
ejpam-440	188	17	and	and	CCONJ
ejpam-440	188	18	τx	τx	INTJ
ejpam-440	188	19	,	,	PUNCT
ejpam-440	188	20	y(t	y(t	PROPN
ejpam-440	188	21	)	)	PUNCT
ejpam-440	189	1	=	=	SYM
ejpam-440	189	2	0	0	PUNCT
ejpam-440	190	1	if	if	SCONJ
ejpam-440	190	2	t	t	PRON
ejpam-440	190	3	≤	≤	NOUN
ejpam-440	190	4	0	0	NUM
ejpam-440	190	5	.	.	PUNCT
ejpam-440	191	1	we	we	PRON
ejpam-440	191	2	note	note	VERB
ejpam-440	191	3	that	that	SCONJ
ejpam-440	191	4	τx	τx	INTJ
ejpam-440	191	5	,	,	PUNCT
ejpam-440	191	6	y	y	PROPN
ejpam-440	191	7	is	be	AUX
ejpam-440	191	8	a	a	DET
ejpam-440	191	9	distribution	distribution	NOUN
ejpam-440	191	10	function	function	NOUN
ejpam-440	191	11	and	and	CCONJ
ejpam-440	191	12	lim	lim	PROPN
ejpam-440	191	13	n→∞	n→∞	X
ejpam-440	191	14	τ2n	τ2n	PROPN
ejpam-440	191	15	x	x	SYM
ejpam-440	191	16	,	,	PUNCT
ejpam-440	191	17	2n	2n	NUM
ejpam-440	191	18	y(2	y(2	NOUN
ejpam-440	191	19	3n	3n	NUM
ejpam-440	191	20	t	t	PROPN
ejpam-440	191	21	)	)	PUNCT
ejpam-440	191	22	=	=	SYM
ejpam-440	191	23	1	1	NUM
ejpam-440	191	24	(	(	PUNCT
ejpam-440	191	25	32	32	NUM
ejpam-440	191	26	)	)	PUNCT
ejpam-440	191	27	m.	m.	NOUN
ejpam-440	191	28	gordji	gordji	PROPN
ejpam-440	191	29	,	,	PUNCT
ejpam-440	191	30	j.	j.	PROPN
ejpam-440	191	31	rassias	rassias	PROPN
ejpam-440	191	32	,	,	PUNCT
ejpam-440	191	33	and	and	CCONJ
ejpam-440	191	34	m.	m.	NOUN
ejpam-440	191	35	savadkouhi	savadkouhi	PROPN
ejpam-440	191	36	/	/	SYM
ejpam-440	191	37	eur	eur	PROPN
ejpam-440	191	38	.	.	PUNCT
ejpam-440	192	1	j.	j.	PROPN
ejpam-440	192	2	pure	pure	PROPN
ejpam-440	192	3	appl	appl	PROPN
ejpam-440	192	4	.	.	PROPN
ejpam-440	192	5	math	math	PROPN
ejpam-440	192	6	,	,	PUNCT
ejpam-440	192	7	2	2	NUM
ejpam-440	192	8	(	(	PUNCT
ejpam-440	192	9	2009	2009	NUM
ejpam-440	192	10	)	)	PUNCT
ejpam-440	192	11	,	,	PUNCT
ejpam-440	192	12	(	(	PUNCT
ejpam-440	192	13	494	494	NUM
ejpam-440	192	14	-	-	SYM
ejpam-440	192	15	507	507	NUM
ejpam-440	192	16	)	)	PUNCT
ejpam-440	192	17	504	504	NUM
ejpam-440	192	18	for	for	ADP
ejpam-440	192	19	all	all	DET
ejpam-440	192	20	x	x	SYM
ejpam-440	192	21	,	,	PUNCT
ejpam-440	192	22	y	y	PROPN
ejpam-440	192	23	∈	∈	PROPN
ejpam-440	192	24	a	a	PRON
ejpam-440	193	1	and	and	CCONJ
ejpam-440	193	2	all	all	PRON
ejpam-440	193	3	t	t	NOUN
ejpam-440	193	4	>	>	X
ejpam-440	193	5	0	0	X
ejpam-440	193	6	.	.	PUNCT
ejpam-440	194	1	it	it	PRON
ejpam-440	194	2	is	be	AUX
ejpam-440	194	3	obviously	obviously	ADV
ejpam-440	194	4	that	that	PRON
ejpam-440	194	5	(	(	PUNCT
ejpam-440	194	6	a,µ	a,µ	PROPN
ejpam-440	194	7	,	,	PUNCT
ejpam-440	194	8	tl	tl	PROPN
ejpam-440	194	9	)	)	PUNCT
ejpam-440	194	10	is	be	AUX
ejpam-440	194	11	an	an	DET
ejpam-440	194	12	rn	rn	ADJ
ejpam-440	194	13	–	–	PUNCT
ejpam-440	194	14	space	space	NOUN
ejpam-440	194	15	.	.	PUNCT
ejpam-440	195	1	it	it	PRON
ejpam-440	195	2	is	be	AUX
ejpam-440	195	3	also	also	ADV
ejpam-440	195	4	easy	easy	ADJ
ejpam-440	195	5	to	to	PART
ejpam-440	195	6	see	see	VERB
ejpam-440	195	7	that	that	PRON
ejpam-440	195	8	(	(	PUNCT
ejpam-440	195	9	a,µ	a,µ	PROPN
ejpam-440	195	10	,	,	PUNCT
ejpam-440	195	11	tl	tl	PROPN
ejpam-440	195	12	)	)	PUNCT
ejpam-440	195	13	is	be	AUX
ejpam-440	195	14	complete	complete	ADJ
ejpam-440	195	15	,	,	PUNCT
ejpam-440	195	16	for	for	ADP
ejpam-440	195	17	µx−y(t)≥	µx−y(t)≥	PRON
ejpam-440	195	18	1−	1−	NUM
ejpam-440	195	19	‖x	‖x	NUM
ejpam-440	196	1	−	−	PROPN
ejpam-440	196	2	y‖	y‖	PROPN
ejpam-440	196	3	t	t	PROPN
ejpam-440	196	4	(	(	PUNCT
ejpam-440	196	5	x	x	X
ejpam-440	196	6	,	,	PUNCT
ejpam-440	196	7	y	y	PROPN
ejpam-440	196	8	∈	∈	PROPN
ejpam-440	196	9	a	a	PRON
ejpam-440	196	10	,	,	PUNCT
ejpam-440	196	11	t	t	X
ejpam-440	196	12	>	>	X
ejpam-440	196	13	0	0	NUM
ejpam-440	196	14	)	)	PUNCT
ejpam-440	196	15	(	(	PUNCT
ejpam-440	196	16	33	33	NUM
ejpam-440	196	17	)	)	PUNCT
ejpam-440	196	18	and	and	CCONJ
ejpam-440	196	19	(	(	PUNCT
ejpam-440	196	20	a,‖.‖	a,‖.‖	PROPN
ejpam-440	196	21	)	)	PUNCT
ejpam-440	196	22	is	be	AUX
ejpam-440	196	23	complete	complete	ADJ
ejpam-440	196	24	.	.	PUNCT
ejpam-440	197	1	define	define	VERB
ejpam-440	197	2	g	g	NOUN
ejpam-440	197	3	:	:	PUNCT
ejpam-440	197	4	a→	a→	PROPN
ejpam-440	197	5	a	a	DET
ejpam-440	197	6	,	,	PUNCT
ejpam-440	197	7	g(x	g(x	NOUN
ejpam-440	197	8	)	)	PUNCT
ejpam-440	197	9	=	=	SYM
ejpam-440	198	1	x3	x3	PROPN
ejpam-440	198	2	+	+	CCONJ
ejpam-440	198	3	‖x‖x0	‖x‖x0	NUM
ejpam-440	198	4	,	,	PUNCT
ejpam-440	198	5	where	where	SCONJ
ejpam-440	198	6	x0	x0	PROPN
ejpam-440	198	7	is	be	AUX
ejpam-440	198	8	a	a	DET
ejpam-440	198	9	unit	unit	NOUN
ejpam-440	198	10	vector	vector	NOUN
ejpam-440	198	11	in	in	ADP
ejpam-440	198	12	a.	a.	NOUN
ejpam-440	198	13	a	a	DET
ejpam-440	198	14	simple	simple	ADJ
ejpam-440	198	15	computation	computation	NOUN
ejpam-440	198	16	shows	show	VERB
ejpam-440	198	17	that	that	SCONJ
ejpam-440	198	18	‖g(2x	‖g(2x	PROPN
ejpam-440	198	19	+	+	NUM
ejpam-440	198	20	y	y	NOUN
ejpam-440	198	21	)	)	PUNCT
ejpam-440	199	1	+	+	CCONJ
ejpam-440	199	2	g(2x	g(2x	VERB
ejpam-440	199	3	−	−	PROPN
ejpam-440	199	4	y)−	y)−	PROPN
ejpam-440	199	5	2g(x	2g(x	NUM
ejpam-440	200	1	+	+	CCONJ
ejpam-440	200	2	y)−	y)−	PROPN
ejpam-440	200	3	2g(x	2g(x	NUM
ejpam-440	200	4	−	−	NOUN
ejpam-440	201	1	y)−	y)−	PROPN
ejpam-440	201	2	12g(x)‖	12g(x)‖	NUM
ejpam-440	201	3	≤	≤	NUM
ejpam-440	201	4	64‖x‖+	64‖x‖+	NUM
ejpam-440	201	5	64‖y‖	64‖y‖	NUM
ejpam-440	201	6	for	for	ADP
ejpam-440	201	7	all	all	DET
ejpam-440	201	8	x	x	SYM
ejpam-440	201	9	,	,	PUNCT
ejpam-440	201	10	y	y	PROPN
ejpam-440	201	11	∈	∈	PROPN
ejpam-440	201	12	a	a	PRON
ejpam-440	201	13	,	,	PUNCT
ejpam-440	201	14	hence	hence	ADV
ejpam-440	201	15	µg(2x+y)+g(2x−y)−2g(x−y)−2g(x−y)−12g(x)(t)≥	µg(2x+y)+g(2x−y)−2g(x−y)−2g(x−y)−12g(x)(t)≥	VERB
ejpam-440	201	16	τx	τx	INTJ
ejpam-440	201	17	,	,	PUNCT
ejpam-440	201	18	y(t	y(t	PROPN
ejpam-440	201	19	)	)	PUNCT
ejpam-440	201	20	,	,	PUNCT
ejpam-440	201	21	for	for	ADP
ejpam-440	201	22	all	all	DET
ejpam-440	201	23	x	x	SYM
ejpam-440	201	24	,	,	PUNCT
ejpam-440	201	25	y	y	PROPN
ejpam-440	201	26	∈	∈	PROPN
ejpam-440	201	27	a	a	PRON
ejpam-440	201	28	and	and	CCONJ
ejpam-440	201	29	all	all	PRON
ejpam-440	201	30	t	t	NOUN
ejpam-440	201	31	>	>	X
ejpam-440	201	32	0	0	X
ejpam-440	201	33	.	.	PUNCT
ejpam-440	202	1	fix	fix	VERB
ejpam-440	202	2	x	x	X
ejpam-440	202	3	∈	∈	PROPN
ejpam-440	202	4	a	a	NOUN
ejpam-440	202	5	and	and	CCONJ
ejpam-440	202	6	t	t	PROPN
ejpam-440	202	7	>	>	X
ejpam-440	202	8	0	0	PROPN
ejpam-440	202	9	,	,	PUNCT
ejpam-440	202	10	then	then	ADV
ejpam-440	202	11	(	(	PUNCT
ejpam-440	202	12	tl	tl	PROPN
ejpam-440	202	13	)	)	PUNCT
ejpam-440	203	1	∞	∞	PROPN
ejpam-440	203	2	i=1	i=1	PROPN
ejpam-440	203	3	(	(	PUNCT
ejpam-440	203	4	τ2n+i−1	τ2n+i−1	NOUN
ejpam-440	203	5	x	x	SYM
ejpam-440	203	6	,	,	PUNCT
ejpam-440	203	7	0(2	0(2	NUM
ejpam-440	203	8	3n+2i	3n+2i	NUM
ejpam-440	203	9	t	t	NOUN
ejpam-440	203	10	)	)	PUNCT
ejpam-440	203	11	)	)	PUNCT
ejpam-440	204	1	=	=	X
ejpam-440	204	2	max	max	X
ejpam-440	204	3	{	{	PUNCT
ejpam-440	204	4	∞	∞	PROPN
ejpam-440	204	5	∑	∑	PROPN
ejpam-440	204	6	i=1	i=1	PROPN
ejpam-440	204	7	(	(	PUNCT
ejpam-440	204	8	τ2n+i−1	τ2n+i−1	NOUN
ejpam-440	204	9	x	x	SYM
ejpam-440	204	10	,	,	PUNCT
ejpam-440	204	11	0(2	0(2	NUM
ejpam-440	204	12	3n+2i	3n+2i	NUM
ejpam-440	204	13	t)−	t)−	PROPN
ejpam-440	204	14	1	1	NUM
ejpam-440	204	15	)	)	PUNCT
ejpam-440	204	16	+	+	CCONJ
ejpam-440	204	17	1	1	NUM
ejpam-440	204	18	,	,	PUNCT
ejpam-440	204	19	0	0	NUM
ejpam-440	204	20	}	}	PUNCT
ejpam-440	204	21	=	=	NOUN
ejpam-440	204	22	max{1−	max{1−	PROPN
ejpam-440	204	23	32‖x‖	32‖x‖	NUM
ejpam-440	204	24	22n	22n	NOUN
ejpam-440	204	25	t	t	NOUN
ejpam-440	204	26	,	,	PUNCT
ejpam-440	204	27	0	0	NUM
ejpam-440	204	28	}	}	PUNCT
ejpam-440	204	29	,	,	PUNCT
ejpam-440	204	30	hence	hence	ADV
ejpam-440	204	31	limn→∞(tl	limn→∞(tl	NUM
ejpam-440	204	32	)	)	PUNCT
ejpam-440	205	1	∞	∞	NUM
ejpam-440	205	2	i=1	i=1	PROPN
ejpam-440	205	3	(	(	PUNCT
ejpam-440	205	4	τ2n+i−1	τ2n+i−1	NOUN
ejpam-440	205	5	x	x	SYM
ejpam-440	205	6	,	,	PUNCT
ejpam-440	205	7	0(2	0(2	NUM
ejpam-440	205	8	3n+2i	3n+2i	NUM
ejpam-440	205	9	t	t	NOUN
ejpam-440	205	10	)	)	PUNCT
ejpam-440	205	11	)	)	PUNCT
ejpam-440	206	1	=	=	PUNCT
ejpam-440	206	2	1	1	X
ejpam-440	206	3	.	.	PUNCT
ejpam-440	206	4	thus	thus	ADV
ejpam-440	206	5	,	,	PUNCT
ejpam-440	206	6	all	all	DET
ejpam-440	206	7	the	the	DET
ejpam-440	206	8	conditions	condition	NOUN
ejpam-440	206	9	of	of	ADP
ejpam-440	206	10	theorem	theorem	ADJ
ejpam-440	206	11	3	3	NUM
ejpam-440	206	12	hold	hold	NOUN
ejpam-440	206	13	.	.	PUNCT
ejpam-440	207	1	since	since	SCONJ
ejpam-440	207	2	(	(	PUNCT
ejpam-440	207	3	tl	tl	PROPN
ejpam-440	207	4	)	)	PUNCT
ejpam-440	207	5	∞	∞	PROPN
ejpam-440	207	6	i=1	i=1	PROPN
ejpam-440	207	7	(	(	PUNCT
ejpam-440	207	8	τ2i−1	τ2i−1	PROPN
ejpam-440	207	9	x	x	SYM
ejpam-440	207	10	,	,	PUNCT
ejpam-440	207	11	0(2	0(2	NUM
ejpam-440	207	12	2i	2i	PROPN
ejpam-440	207	13	t	t	PROPN
ejpam-440	207	14	)	)	PUNCT
ejpam-440	207	15	)	)	PUNCT
ejpam-440	208	1	=	=	X
ejpam-440	208	2	max	max	X
ejpam-440	208	3	{	{	PUNCT
ejpam-440	208	4	∞	∞	PROPN
ejpam-440	208	5	∑	∑	PROPN
ejpam-440	208	6	i=1	i=1	PROPN
ejpam-440	208	7	(	(	PUNCT
ejpam-440	208	8	τ2i−1	τ2i−1	PROPN
ejpam-440	208	9	x	x	SYM
ejpam-440	208	10	,	,	PUNCT
ejpam-440	208	11	0(2	0(2	NUM
ejpam-440	208	12	2i	2i	NOUN
ejpam-440	208	13	t)−	t)−	PROPN
ejpam-440	208	14	1	1	NUM
ejpam-440	208	15	)	)	PUNCT
ejpam-440	208	16	+	+	CCONJ
ejpam-440	208	17	1	1	NUM
ejpam-440	208	18	,	,	PUNCT
ejpam-440	208	19	0	0	NUM
ejpam-440	208	20	}	}	PUNCT
ejpam-440	208	21	=	=	NOUN
ejpam-440	208	22	max{1−	max{1−	NOUN
ejpam-440	208	23	32‖x‖	32‖x‖	NUM
ejpam-440	208	24	t	t	NOUN
ejpam-440	208	25	,	,	PUNCT
ejpam-440	208	26	0	0	NUM
ejpam-440	208	27	}	}	PUNCT
ejpam-440	208	28	,	,	PUNCT
ejpam-440	208	29	we	we	PRON
ejpam-440	208	30	obtain	obtain	VERB
ejpam-440	208	31	that	that	SCONJ
ejpam-440	208	32	there	there	PRON
ejpam-440	208	33	exists	exist	VERB
ejpam-440	208	34	a	a	DET
ejpam-440	208	35	unique	unique	ADJ
ejpam-440	208	36	cubic	cubic	ADJ
ejpam-440	208	37	mapping	mapping	NOUN
ejpam-440	208	38	c	c	NOUN
ejpam-440	208	39	:	:	PUNCT
ejpam-440	208	40	a−→	a−→	NOUN
ejpam-440	208	41	a	a	DET
ejpam-440	208	42	such	such	ADJ
ejpam-440	208	43	that	that	SCONJ
ejpam-440	208	44	µc(x)−g(x)(t)≥max{1−	µc(x)−g(x)(t)≥max{1−	VERB
ejpam-440	208	45	32‖x‖	32‖x‖	NUM
ejpam-440	208	46	t	t	NOUN
ejpam-440	208	47	,	,	PUNCT
ejpam-440	208	48	0	0	NUM
ejpam-440	208	49	}	}	PUNCT
ejpam-440	208	50	(	(	PUNCT
ejpam-440	208	51	34	34	NUM
ejpam-440	208	52	)	)	PUNCT
ejpam-440	208	53	for	for	ADP
ejpam-440	208	54	all	all	DET
ejpam-440	208	55	x	x	SYM
ejpam-440	208	56	∈	∈	PROPN
ejpam-440	208	57	a	a	PRON
ejpam-440	209	1	and	and	CCONJ
ejpam-440	209	2	all	all	PRON
ejpam-440	209	3	t	t	NOUN
ejpam-440	209	4	>	>	X
ejpam-440	209	5	0	0	X
ejpam-440	209	6	.	.	PUNCT
ejpam-440	210	1	references	reference	NOUN
ejpam-440	210	2	505	505	NUM
ejpam-440	210	3	references	reference	NOUN
ejpam-440	210	4	[	[	X
ejpam-440	210	5	1	1	NUM
ejpam-440	210	6	]	]	PUNCT
ejpam-440	210	7	j.	j.	PROPN
ejpam-440	210	8	aczel	aczel	PROPN
ejpam-440	210	9	and	and	CCONJ
ejpam-440	210	10	j.	j.	PROPN
ejpam-440	210	11	dhombres	dhombres	PROPN
ejpam-440	210	12	,	,	PUNCT
ejpam-440	210	13	functional	functional	ADJ
ejpam-440	210	14	equations	equation	NOUN
ejpam-440	210	15	in	in	ADP
ejpam-440	210	16	several	several	ADJ
ejpam-440	210	17	variables	variable	NOUN
ejpam-440	210	18	,	,	PUNCT
ejpam-440	210	19	cambridge	cambridge	PROPN
ejpam-440	210	20	univ	univ	PROPN
ejpam-440	210	21	.	.	PUNCT
ejpam-440	211	1	press	press	PROPN
ejpam-440	211	2	,	,	PUNCT
ejpam-440	211	3	1989	1989	NUM
ejpam-440	211	4	.	.	PUNCT
ejpam-440	212	1	[	[	X
ejpam-440	212	2	2	2	X
ejpam-440	212	3	]	]	PUNCT
ejpam-440	212	4	t.	t.	PROPN
ejpam-440	212	5	aoki	aoki	PROPN
ejpam-440	212	6	,	,	PUNCT
ejpam-440	212	7	on	on	ADP
ejpam-440	212	8	the	the	DET
ejpam-440	212	9	stability	stability	NOUN
ejpam-440	212	10	of	of	ADP
ejpam-440	212	11	the	the	DET
ejpam-440	212	12	linear	linear	ADJ
ejpam-440	212	13	transformation	transformation	NOUN
ejpam-440	212	14	in	in	ADP
ejpam-440	212	15	banach	banach	NOUN
ejpam-440	212	16	spaces	space	NOUN
ejpam-440	212	17	,	,	PUNCT
ejpam-440	212	18	j.	j.	PROPN
ejpam-440	212	19	math	math	PROPN
ejpam-440	212	20	.	.	PUNCT
ejpam-440	212	21	soc	soc	PROPN
ejpam-440	212	22	.	.	PUNCT
ejpam-440	213	1	japan	japan	PROPN
ejpam-440	213	2	.	.	PROPN
ejpam-440	214	1	2	2	NUM
ejpam-440	214	2	(	(	PUNCT
ejpam-440	214	3	1950	1950	NUM
ejpam-440	214	4	)	)	PUNCT
ejpam-440	214	5	,	,	PUNCT
ejpam-440	214	6	64–66	64–66	NUM
ejpam-440	214	7	.	.	PUNCT
ejpam-440	215	1	[	[	X
ejpam-440	215	2	3	3	X
ejpam-440	215	3	]	]	X
ejpam-440	215	4	e.	e.	PROPN
ejpam-440	215	5	baktash	baktash	PROPN
ejpam-440	215	6	,	,	PUNCT
ejpam-440	215	7	y.j	y.j	PROPN
ejpam-440	215	8	.	.	PUNCT
ejpam-440	215	9	cho	cho	PROPN
ejpam-440	215	10	,	,	PUNCT
ejpam-440	215	11	m.	m.	NOUN
ejpam-440	215	12	jalili	jalili	PROPN
ejpam-440	215	13	,	,	PUNCT
ejpam-440	215	14	r.	r.	PROPN
ejpam-440	215	15	saadati	saadati	PROPN
ejpam-440	215	16	and	and	CCONJ
ejpam-440	215	17	s.	s.	PROPN
ejpam-440	215	18	m.	m.	PROPN
ejpam-440	215	19	vaezpour	vaezpour	NOUN
ejpam-440	215	20	,	,	PUNCT
ejpam-440	215	21	on	on	ADP
ejpam-440	215	22	the	the	DET
ejpam-440	215	23	stability	stability	NOUN
ejpam-440	215	24	of	of	ADP
ejpam-440	215	25	cubic	cubic	ADJ
ejpam-440	215	26	mappings	mapping	NOUN
ejpam-440	215	27	and	and	CCONJ
ejpam-440	215	28	quadratic	quadratic	ADJ
ejpam-440	215	29	mappings	mapping	NOUN
ejpam-440	215	30	in	in	ADP
ejpam-440	215	31	random	random	ADJ
ejpam-440	215	32	normed	normed	ADJ
ejpam-440	215	33	spaces	space	NOUN
ejpam-440	215	34	,	,	PUNCT
ejpam-440	215	35	to	to	PART
ejpam-440	215	36	appear	appear	VERB
ejpam-440	215	37	in	in	ADP
ejpam-440	215	38	jia	jia	PROPN
ejpam-440	215	39	.	.	PUNCT
ejpam-440	216	1	[	[	X
ejpam-440	216	2	4	4	X
ejpam-440	216	3	]	]	X
ejpam-440	216	4	d.	d.	PROPN
ejpam-440	216	5	g.	g.	PROPN
ejpam-440	216	6	bourgin	bourgin	PROPN
ejpam-440	216	7	,	,	PUNCT
ejpam-440	216	8	classes	class	NOUN
ejpam-440	216	9	of	of	ADP
ejpam-440	216	10	transformations	transformation	NOUN
ejpam-440	216	11	and	and	CCONJ
ejpam-440	216	12	bordering	border	VERB
ejpam-440	216	13	transformations	transformation	NOUN
ejpam-440	216	14	,	,	PUNCT
ejpam-440	216	15	bull	bull	NOUN
ejpam-440	216	16	.	.	PUNCT
ejpam-440	217	1	amer	amer	PROPN
ejpam-440	217	2	.	.	PUNCT
ejpam-440	217	3	math	math	PROPN
ejpam-440	217	4	.	.	PUNCT
ejpam-440	218	1	soc	soc	PROPN
ejpam-440	218	2	.	.	PUNCT
ejpam-440	219	1	57	57	NUM
ejpam-440	219	2	(	(	PUNCT
ejpam-440	219	3	1951	1951	NUM
ejpam-440	219	4	)	)	PUNCT
ejpam-440	219	5	223	223	NUM
ejpam-440	219	6	-	-	SYM
ejpam-440	219	7	ű237	ű237	PRON
ejpam-440	219	8	.	.	PUNCT
ejpam-440	220	1	[	[	X
ejpam-440	220	2	5	5	X
ejpam-440	220	3	]	]	PUNCT
ejpam-440	220	4	p.	p.	PROPN
ejpam-440	220	5	w.	w.	PROPN
ejpam-440	220	6	cholewa	cholewa	PROPN
ejpam-440	220	7	,	,	PUNCT
ejpam-440	220	8	remarks	remark	VERB
ejpam-440	220	9	on	on	ADP
ejpam-440	220	10	the	the	DET
ejpam-440	220	11	stability	stability	NOUN
ejpam-440	220	12	of	of	ADP
ejpam-440	220	13	functional	functional	ADJ
ejpam-440	220	14	equations	equation	NOUN
ejpam-440	220	15	,	,	PUNCT
ejpam-440	220	16	aequationes	aequatione	VERB
ejpam-440	220	17	math	math	NOUN
ejpam-440	220	18	.	.	PUNCT
ejpam-440	221	1	27	27	NUM
ejpam-440	221	2	(	(	PUNCT
ejpam-440	221	3	1984	1984	NUM
ejpam-440	221	4	)	)	PUNCT
ejpam-440	221	5	76	76	NUM
ejpam-440	221	6	-	-	PUNCT
ejpam-440	221	7	ű86	ű86	NOUN
ejpam-440	221	8	.	.	PUNCT
ejpam-440	222	1	[	[	X
ejpam-440	222	2	6	6	NUM
ejpam-440	222	3	]	]	PUNCT
ejpam-440	222	4	s.	s.	PROPN
ejpam-440	222	5	s.	s.	PROPN
ejpam-440	222	6	chang	chang	PROPN
ejpam-440	222	7	,	,	PUNCT
ejpam-440	222	8	y.	y.	PROPN
ejpam-440	222	9	j.	j.	PROPN
ejpam-440	222	10	cho	cho	PROPN
ejpam-440	222	11	and	and	CCONJ
ejpam-440	222	12	s.	s.	PROPN
ejpam-440	222	13	m.	m.	PROPN
ejpam-440	222	14	kang	kang	PROPN
ejpam-440	222	15	,	,	PUNCT
ejpam-440	222	16	nonlinear	nonlinear	ADJ
ejpam-440	222	17	operator	operator	NOUN
ejpam-440	222	18	theory	theory	NOUN
ejpam-440	222	19	in	in	ADP
ejpam-440	222	20	probabilistic	probabilistic	ADJ
ejpam-440	222	21	metric	metric	ADJ
ejpam-440	222	22	spaces	space	NOUN
ejpam-440	222	23	,	,	PUNCT
ejpam-440	222	24	nova	nova	PROPN
ejpam-440	222	25	science	science	NOUN
ejpam-440	222	26	publishers	publisher	NOUN
ejpam-440	222	27	,	,	PUNCT
ejpam-440	222	28	inc	inc	PROPN
ejpam-440	222	29	.	.	PROPN
ejpam-440	222	30	new	new	PROPN
ejpam-440	222	31	york	york	PROPN
ejpam-440	222	32	,	,	PUNCT
ejpam-440	222	33	2001	2001	NUM
ejpam-440	222	34	.	.	PUNCT
ejpam-440	223	1	[	[	X
ejpam-440	223	2	7	7	X
ejpam-440	223	3	]	]	X
ejpam-440	223	4	s.	s.	PROPN
ejpam-440	223	5	czerwik	czerwik	PROPN
ejpam-440	223	6	,	,	PUNCT
ejpam-440	223	7	on	on	ADP
ejpam-440	223	8	the	the	DET
ejpam-440	223	9	stability	stability	NOUN
ejpam-440	223	10	of	of	ADP
ejpam-440	223	11	the	the	DET
ejpam-440	223	12	quadratic	quadratic	ADJ
ejpam-440	223	13	mapping	mapping	NOUN
ejpam-440	223	14	in	in	ADP
ejpam-440	223	15	normed	normed	ADJ
ejpam-440	223	16	spaces	space	NOUN
ejpam-440	223	17	,	,	PUNCT
ejpam-440	223	18	abh	abh	PROPN
ejpam-440	223	19	.	.	PUNCT
ejpam-440	223	20	math	math	PROPN
ejpam-440	223	21	.	.	PUNCT
ejpam-440	224	1	sem	sem	PROPN
ejpam-440	224	2	.	.	PUNCT
ejpam-440	224	3	univ	univ	PROPN
ejpam-440	224	4	.	.	PUNCT
ejpam-440	225	1	hamburg	hamburg	PROPN
ejpam-440	225	2	.	.	PUNCT
ejpam-440	226	1	62	62	NUM
ejpam-440	226	2	(	(	PUNCT
ejpam-440	226	3	1992	1992	NUM
ejpam-440	226	4	)	)	PUNCT
ejpam-440	226	5	,	,	PUNCT
ejpam-440	226	6	59–64	59–64	NUM
ejpam-440	226	7	.	.	PUNCT
ejpam-440	227	1	[	[	X
ejpam-440	227	2	8	8	NUM
ejpam-440	227	3	]	]	PUNCT
ejpam-440	227	4	p.	p.	NOUN
ejpam-440	227	5	gǎvruta	gǎvruta	PROPN
ejpam-440	227	6	,	,	PUNCT
ejpam-440	227	7	a	a	DET
ejpam-440	227	8	generalization	generalization	NOUN
ejpam-440	227	9	of	of	ADP
ejpam-440	227	10	the	the	DET
ejpam-440	227	11	hyers	hyers	PROPN
ejpam-440	227	12	-	-	PUNCT
ejpam-440	227	13	ulam	ulam	ADJ
ejpam-440	227	14	-	-	PUNCT
ejpam-440	227	15	rassias	rassias	PROPN
ejpam-440	227	16	stability	stability	NOUN
ejpam-440	227	17	of	of	ADP
ejpam-440	227	18	approximately	approximately	ADV
ejpam-440	227	19	additive	additive	ADJ
ejpam-440	227	20	mappings	mapping	NOUN
ejpam-440	227	21	,	,	PUNCT
ejpam-440	227	22	j.	j.	PROPN
ejpam-440	227	23	math	math	PROPN
ejpam-440	227	24	.	.	PUNCT
ejpam-440	228	1	anal	anal	PROPN
ejpam-440	228	2	.	.	PUNCT
ejpam-440	228	3	appl	appl	PROPN
ejpam-440	228	4	.	.	PUNCT
ejpam-440	229	1	184	184	NUM
ejpam-440	229	2	(	(	PUNCT
ejpam-440	229	3	1994	1994	NUM
ejpam-440	229	4	)	)	PUNCT
ejpam-440	229	5	,	,	PUNCT
ejpam-440	229	6	431–436	431–436	NUM
ejpam-440	229	7	.	.	PUNCT
ejpam-440	230	1	[	[	X
ejpam-440	230	2	9	9	NUM
ejpam-440	230	3	]	]	PUNCT
ejpam-440	230	4	z.	z.	PROPN
ejpam-440	230	5	gajda	gajda	PROPN
ejpam-440	230	6	,	,	PUNCT
ejpam-440	230	7	on	on	ADP
ejpam-440	230	8	stability	stability	NOUN
ejpam-440	230	9	of	of	ADP
ejpam-440	230	10	additive	additive	ADJ
ejpam-440	230	11	mappings	mapping	NOUN
ejpam-440	230	12	,	,	PUNCT
ejpam-440	230	13	internat	internat	NOUN
ejpam-440	230	14	.	.	PUNCT
ejpam-440	231	1	j.	j.	PROPN
ejpam-440	231	2	math	math	PROPN
ejpam-440	231	3	.	.	PUNCT
ejpam-440	232	1	math	math	NOUN
ejpam-440	232	2	.	.	PUNCT
ejpam-440	233	1	sci	sci	PROPN
ejpam-440	233	2	.	.	PROPN
ejpam-440	233	3	14	14	NUM
ejpam-440	233	4	(	(	PUNCT
ejpam-440	233	5	1991	1991	NUM
ejpam-440	233	6	)	)	PUNCT
ejpam-440	233	7	,	,	PUNCT
ejpam-440	233	8	431–434	431–434	NUM
ejpam-440	233	9	.	.	PUNCT
ejpam-440	234	1	[	[	X
ejpam-440	234	2	10	10	NUM
ejpam-440	234	3	]	]	PUNCT
ejpam-440	234	4	a.	a.	NOUN
ejpam-440	234	5	grabiec	grabiec	PROPN
ejpam-440	234	6	,	,	PUNCT
ejpam-440	234	7	the	the	DET
ejpam-440	234	8	generalized	generalize	VERB
ejpam-440	234	9	hyersűulam	hyersűulam	PROPN
ejpam-440	234	10	stability	stability	NOUN
ejpam-440	234	11	of	of	ADP
ejpam-440	234	12	a	a	DET
ejpam-440	234	13	class	class	NOUN
ejpam-440	234	14	of	of	ADP
ejpam-440	234	15	functional	functional	ADJ
ejpam-440	234	16	equations	equation	NOUN
ejpam-440	234	17	,	,	PUNCT
ejpam-440	234	18	publ	publ	NOUN
ejpam-440	234	19	.	.	PUNCT
ejpam-440	235	1	math	math	NOUN
ejpam-440	235	2	.	.	PUNCT
ejpam-440	236	1	debrecen	debrecen	PROPN
ejpam-440	236	2	48	48	NUM
ejpam-440	236	3	(	(	PUNCT
ejpam-440	236	4	1996	1996	NUM
ejpam-440	236	5	)	)	PUNCT
ejpam-440	237	1	217ű-235	217ű-235	X
ejpam-440	237	2	.	.	PUNCT
ejpam-440	238	1	[	[	X
ejpam-440	238	2	11	11	NUM
ejpam-440	238	3	]	]	X
ejpam-440	238	4	o.	o.	PROPN
ejpam-440	238	5	hadžić	hadžić	PROPN
ejpam-440	238	6	and	and	CCONJ
ejpam-440	238	7	e.	e.	PROPN
ejpam-440	238	8	pap	pap	PROPN
ejpam-440	238	9	,	,	PUNCT
ejpam-440	238	10	fixed	fix	VERB
ejpam-440	238	11	point	point	NOUN
ejpam-440	238	12	theory	theory	NOUN
ejpam-440	238	13	in	in	ADP
ejpam-440	238	14	pm	pm	NOUN
ejpam-440	238	15	spaces	space	NOUN
ejpam-440	238	16	,	,	PUNCT
ejpam-440	238	17	kluwer	kluwer	NOUN
ejpam-440	238	18	academic	academic	ADJ
ejpam-440	238	19	publishers	publisher	NOUN
ejpam-440	238	20	,	,	PUNCT
ejpam-440	238	21	dordrecht	dordrecht	PROPN
ejpam-440	238	22	,	,	PUNCT
ejpam-440	238	23	2001	2001	NUM
ejpam-440	238	24	.	.	PUNCT
ejpam-440	239	1	[	[	X
ejpam-440	239	2	12	12	NUM
ejpam-440	239	3	]	]	X
ejpam-440	239	4	o.	o.	PROPN
ejpam-440	239	5	hadžić	hadžić	PROPN
ejpam-440	239	6	,	,	PUNCT
ejpam-440	239	7	e.	e.	PROPN
ejpam-440	239	8	pap	pap	PROPN
ejpam-440	239	9	and	and	CCONJ
ejpam-440	239	10	m.	m.	NOUN
ejpam-440	239	11	budincević	budincević	PROPN
ejpam-440	239	12	,	,	PUNCT
ejpam-440	239	13	countable	countable	ADJ
ejpam-440	239	14	extension	extension	NOUN
ejpam-440	239	15	of	of	ADP
ejpam-440	239	16	triangular	triangular	NOUN
ejpam-440	239	17	norms	norm	NOUN
ejpam-440	239	18	and	and	CCONJ
ejpam-440	239	19	their	their	PRON
ejpam-440	239	20	applications	application	NOUN
ejpam-440	239	21	to	to	ADP
ejpam-440	239	22	the	the	DET
ejpam-440	239	23	fixed	fix	VERB
ejpam-440	239	24	point	point	NOUN
ejpam-440	239	25	theory	theory	NOUN
ejpam-440	239	26	in	in	ADP
ejpam-440	239	27	probabilistic	probabilistic	ADJ
ejpam-440	239	28	metric	metric	ADJ
ejpam-440	239	29	spaces	space	NOUN
ejpam-440	239	30	,	,	PUNCT
ejpam-440	239	31	kybernetica	kybernetica	PROPN
ejpam-440	239	32	,	,	PUNCT
ejpam-440	239	33	38	38	NUM
ejpam-440	239	34	(	(	PUNCT
ejpam-440	239	35	3	3	NUM
ejpam-440	239	36	)	)	PUNCT
ejpam-440	239	37	(	(	PUNCT
ejpam-440	239	38	2002	2002	NUM
ejpam-440	239	39	)	)	PUNCT
ejpam-440	239	40	,	,	PUNCT
ejpam-440	239	41	363–381	363–381	NUM
ejpam-440	239	42	.	.	PUNCT
ejpam-440	240	1	[	[	X
ejpam-440	240	2	13	13	NUM
ejpam-440	240	3	]	]	X
ejpam-440	240	4	d.	d.	PROPN
ejpam-440	240	5	h.	h.	PROPN
ejpam-440	240	6	hyers	hyers	PROPN
ejpam-440	240	7	,	,	PUNCT
ejpam-440	240	8	on	on	ADP
ejpam-440	240	9	the	the	DET
ejpam-440	240	10	stability	stability	NOUN
ejpam-440	240	11	of	of	ADP
ejpam-440	240	12	the	the	DET
ejpam-440	240	13	linear	linear	ADJ
ejpam-440	240	14	functional	functional	ADJ
ejpam-440	240	15	equation	equation	NOUN
ejpam-440	240	16	,	,	PUNCT
ejpam-440	240	17	proc	proc	NOUN
ejpam-440	240	18	.	.	PUNCT
ejpam-440	241	1	nat	nat	PROPN
ejpam-440	241	2	.	.	PUNCT
ejpam-440	242	1	acad	acad	PROPN
ejpam-440	242	2	.	.	PUNCT
ejpam-440	243	1	sci	sci	PROPN
ejpam-440	243	2	.	.	PROPN
ejpam-440	243	3	usa	usa	PROPN
ejpam-440	243	4	27	27	NUM
ejpam-440	243	5	(	(	PUNCT
ejpam-440	243	6	1941	1941	NUM
ejpam-440	243	7	)	)	PUNCT
ejpam-440	243	8	,	,	PUNCT
ejpam-440	243	9	222ű-224	222ű-224	NUM
ejpam-440	243	10	.	.	PUNCT
ejpam-440	244	1	references	reference	NOUN
ejpam-440	244	2	506	506	NUM
ejpam-440	244	3	[	[	X
ejpam-440	244	4	14	14	NUM
ejpam-440	244	5	]	]	PUNCT
ejpam-440	244	6	k.	k.	PROPN
ejpam-440	244	7	jun	jun	PROPN
ejpam-440	244	8	and	and	CCONJ
ejpam-440	244	9	y.	y.	PROPN
ejpam-440	244	10	lee	lee	PROPN
ejpam-440	244	11	,	,	PUNCT
ejpam-440	244	12	on	on	ADP
ejpam-440	244	13	the	the	DET
ejpam-440	244	14	hyers	hyers	PROPN
ejpam-440	244	15	-	-	PUNCT
ejpam-440	244	16	ulam	ulam	ADJ
ejpam-440	244	17	-	-	PUNCT
ejpam-440	244	18	rassias	rassias	PROPN
ejpam-440	244	19	stability	stability	NOUN
ejpam-440	244	20	of	of	ADP
ejpam-440	244	21	a	a	DET
ejpam-440	244	22	pexiderized	pexiderize	VERB
ejpam-440	244	23	quadratic	quadratic	ADJ
ejpam-440	244	24	inequality	inequality	NOUN
ejpam-440	244	25	,	,	PUNCT
ejpam-440	244	26	math	math	NOUN
ejpam-440	244	27	.	.	PUNCT
ejpam-440	245	1	inequal	inequal	PROPN
ejpam-440	245	2	.	.	PUNCT
ejpam-440	246	1	appl	appl	PROPN
ejpam-440	246	2	.	.	PROPN
ejpam-440	247	1	4	4	NUM
ejpam-440	247	2	(	(	PUNCT
ejpam-440	247	3	2001	2001	NUM
ejpam-440	247	4	)	)	PUNCT
ejpam-440	247	5	,	,	PUNCT
ejpam-440	247	6	no	no	INTJ
ejpam-440	247	7	.	.	NOUN
ejpam-440	247	8	1	1	NUM
ejpam-440	247	9	,	,	PUNCT
ejpam-440	247	10	93–118	93–118	NUM
ejpam-440	247	11	.	.	PUNCT
ejpam-440	248	1	[	[	X
ejpam-440	248	2	15	15	NUM
ejpam-440	248	3	]	]	PUNCT
ejpam-440	248	4	k.	k.	PROPN
ejpam-440	248	5	w.	w.	PROPN
ejpam-440	248	6	jung	jung	PROPN
ejpam-440	248	7	and	and	CCONJ
ejpam-440	248	8	h.	h.	PROPN
ejpam-440	248	9	m.	m.	PROPN
ejpam-440	248	10	kim	kim	PROPN
ejpam-440	248	11	,	,	PUNCT
ejpam-440	248	12	the	the	DET
ejpam-440	248	13	generalized	generalize	VERB
ejpam-440	248	14	hyers	hyer	NOUN
ejpam-440	248	15	-	-	PUNCT
ejpam-440	248	16	ulam	ulam	ADJ
ejpam-440	248	17	-	-	PUNCT
ejpam-440	248	18	russias	russia	NOUN
ejpam-440	248	19	stability	stability	NOUN
ejpam-440	248	20	of	of	ADP
ejpam-440	248	21	a	a	DET
ejpam-440	248	22	cubic	cubic	ADJ
ejpam-440	248	23	functional	functional	ADJ
ejpam-440	248	24	equation	equation	NOUN
ejpam-440	248	25	,	,	PUNCT
ejpam-440	248	26	j.	j.	PROPN
ejpam-440	248	27	math	math	PROPN
ejpam-440	248	28	.	.	PUNCT
ejpam-440	249	1	anal	anal	PROPN
ejpam-440	249	2	.	.	PUNCT
ejpam-440	250	1	appl	appl	PROPN
ejpam-440	250	2	.	.	PROPN
ejpam-440	251	1	274	274	NUM
ejpam-440	251	2	(	(	PUNCT
ejpam-440	251	3	2002	2002	NUM
ejpam-440	251	4	)	)	PUNCT
ejpam-440	251	5	,	,	PUNCT
ejpam-440	251	6	no	no	INTJ
ejpam-440	251	7	.	.	NOUN
ejpam-440	251	8	2	2	NUM
ejpam-440	251	9	,	,	PUNCT
ejpam-440	251	10	267–278	267–278	NUM
ejpam-440	251	11	.	.	PUNCT
ejpam-440	252	1	[	[	X
ejpam-440	252	2	16	16	NUM
ejpam-440	252	3	]	]	X
ejpam-440	252	4	pl	pl	PROPN
ejpam-440	252	5	.	.	PROPN
ejpam-440	252	6	kannappan	kannappan	PROPN
ejpam-440	252	7	,	,	PUNCT
ejpam-440	252	8	quadratic	quadratic	ADJ
ejpam-440	252	9	functional	functional	ADJ
ejpam-440	252	10	equation	equation	NOUN
ejpam-440	252	11	and	and	CCONJ
ejpam-440	252	12	inner	inner	ADJ
ejpam-440	252	13	product	product	NOUN
ejpam-440	252	14	spaces	space	NOUN
ejpam-440	252	15	,	,	PUNCT
ejpam-440	252	16	results	result	VERB
ejpam-440	252	17	math	math	NOUN
ejpam-440	252	18	.	.	PUNCT
ejpam-440	253	1	27	27	NUM
ejpam-440	253	2	(	(	PUNCT
ejpam-440	253	3	1995	1995	NUM
ejpam-440	253	4	)	)	PUNCT
ejpam-440	253	5	,	,	PUNCT
ejpam-440	253	6	no	no	INTJ
ejpam-440	253	7	.	.	NOUN
ejpam-440	253	8	3	3	NUM
ejpam-440	253	9	-	-	SYM
ejpam-440	253	10	4	4	NUM
ejpam-440	253	11	,	,	PUNCT
ejpam-440	253	12	368–372	368–372	NUM
ejpam-440	253	13	.	.	PUNCT
ejpam-440	254	1	[	[	X
ejpam-440	254	2	17	17	NUM
ejpam-440	254	3	]	]	X
ejpam-440	254	4	d.	d.	PROPN
ejpam-440	254	5	mihȩt	mihȩt	ADV
ejpam-440	254	6	and	and	CCONJ
ejpam-440	254	7	v.	v.	ADP
ejpam-440	254	8	radu	radu	PROPN
ejpam-440	254	9	,	,	PUNCT
ejpam-440	254	10	on	on	ADP
ejpam-440	254	11	the	the	DET
ejpam-440	254	12	stability	stability	NOUN
ejpam-440	254	13	of	of	ADP
ejpam-440	254	14	the	the	DET
ejpam-440	254	15	additive	additive	ADJ
ejpam-440	254	16	cauchy	cauchy	ADJ
ejpam-440	254	17	functional	functional	ADJ
ejpam-440	254	18	equation	equation	NOUN
ejpam-440	254	19	in	in	ADP
ejpam-440	254	20	random	random	ADJ
ejpam-440	254	21	normed	normed	ADJ
ejpam-440	254	22	spaces	space	NOUN
ejpam-440	254	23	,	,	PUNCT
ejpam-440	254	24	j.	j.	PROPN
ejpam-440	254	25	math	math	PROPN
ejpam-440	254	26	.	.	PUNCT
ejpam-440	255	1	anal	anal	PROPN
ejpam-440	255	2	.	.	PUNCT
ejpam-440	255	3	appl	appl	PROPN
ejpam-440	255	4	.	.	PUNCT
ejpam-440	256	1	343	343	NUM
ejpam-440	256	2	(	(	PUNCT
ejpam-440	256	3	2008	2008	NUM
ejpam-440	256	4	)	)	PUNCT
ejpam-440	256	5	,	,	PUNCT
ejpam-440	256	6	567ű-572	567ű-572	NOUN
ejpam-440	256	7	.	.	PUNCT
ejpam-440	257	1	[	[	X
ejpam-440	257	2	18	18	NUM
ejpam-440	257	3	]	]	X
ejpam-440	257	4	d.	d.	PROPN
ejpam-440	257	5	mihȩt	mihȩt	PROPN
ejpam-440	257	6	,	,	PUNCT
ejpam-440	257	7	the	the	DET
ejpam-440	257	8	probabilistic	probabilistic	ADJ
ejpam-440	257	9	stability	stability	NOUN
ejpam-440	257	10	for	for	ADP
ejpam-440	257	11	a	a	DET
ejpam-440	257	12	functional	functional	ADJ
ejpam-440	257	13	equation	equation	NOUN
ejpam-440	257	14	in	in	ADP
ejpam-440	257	15	a	a	DET
ejpam-440	257	16	single	single	ADJ
ejpam-440	257	17	variable	variable	NOUN
ejpam-440	257	18	,	,	PUNCT
ejpam-440	257	19	acta	acta	PROPN
ejpam-440	257	20	math	math	PROPN
ejpam-440	257	21	.	.	PUNCT
ejpam-440	258	1	hungar	hungar	NOUN
ejpam-440	258	2	.	.	PUNCT
ejpam-440	259	1	2008	2008	NUM
ejpam-440	259	2	doi	doi	NOUN
ejpam-440	259	3	:	:	PUNCT
ejpam-440	259	4	10.1007	10.1007	NUM
ejpam-440	259	5	/	/	SYM
ejpam-440	259	6	s10474	s10474	NOUN
ejpam-440	259	7	-	-	PUNCT
ejpam-440	259	8	008	008	NUM
ejpam-440	259	9	-	-	PUNCT
ejpam-440	259	10	8101	8101	NUM
ejpam-440	259	11	-	-	PUNCT
ejpam-440	259	12	y.	y.	PROPN
ejpam-440	260	1	[	[	X
ejpam-440	260	2	19	19	NUM
ejpam-440	260	3	]	]	X
ejpam-440	260	4	d.	d.	PROPN
ejpam-440	260	5	mihȩt	mihȩt	PROPN
ejpam-440	260	6	,	,	PUNCT
ejpam-440	260	7	the	the	DET
ejpam-440	260	8	fixed	fix	VERB
ejpam-440	260	9	point	point	NOUN
ejpam-440	260	10	method	method	NOUN
ejpam-440	260	11	for	for	ADP
ejpam-440	260	12	fuzzy	fuzzy	ADJ
ejpam-440	260	13	stability	stability	NOUN
ejpam-440	260	14	of	of	ADP
ejpam-440	260	15	the	the	DET
ejpam-440	260	16	jensen	jensen	PROPN
ejpam-440	260	17	functional	functional	ADJ
ejpam-440	260	18	equation	equation	NOUN
ejpam-440	260	19	,	,	PUNCT
ejpam-440	260	20	fuzzy	fuzzy	ADJ
ejpam-440	260	21	sets	set	NOUN
ejpam-440	260	22	and	and	CCONJ
ejpam-440	260	23	systems	system	NOUN
ejpam-440	260	24	,	,	PUNCT
ejpam-440	260	25	doi:10.1016	doi:10.1016	PROPN
ejpam-440	260	26	/	/	SYM
ejpam-440	260	27	j.fss.2008.06.014	j.fss.2008.06.014	PROPN
ejpam-440	260	28	.	.	PUNCT
ejpam-440	261	1	[	[	X
ejpam-440	261	2	20	20	NUM
ejpam-440	261	3	]	]	PUNCT
ejpam-440	261	4	m.	m.	NOUN
ejpam-440	261	5	mirmostafaee	mirmostafaee	PROPN
ejpam-440	261	6	,	,	PUNCT
ejpam-440	261	7	m.	m.	NOUN
ejpam-440	261	8	mirzavaziri	mirzavaziri	PROPN
ejpam-440	261	9	and	and	CCONJ
ejpam-440	261	10	m.	m.	PROPN
ejpam-440	261	11	s.	s.	PROPN
ejpam-440	261	12	moslehian	moslehian	PROPN
ejpam-440	261	13	,	,	PUNCT
ejpam-440	261	14	fuzzy	fuzzy	ADJ
ejpam-440	261	15	stability	stability	NOUN
ejpam-440	261	16	of	of	ADP
ejpam-440	261	17	the	the	DET
ejpam-440	261	18	jensen	jensen	PROPN
ejpam-440	261	19	functional	functional	ADJ
ejpam-440	261	20	equation	equation	NOUN
ejpam-440	261	21	,	,	PUNCT
ejpam-440	261	22	fuzzy	fuzzy	ADJ
ejpam-440	261	23	sets	set	NOUN
ejpam-440	261	24	and	and	CCONJ
ejpam-440	261	25	systems	system	NOUN
ejpam-440	261	26	,	,	PUNCT
ejpam-440	261	27	159	159	NUM
ejpam-440	261	28	(	(	PUNCT
ejpam-440	261	29	2008	2008	NUM
ejpam-440	261	30	)	)	PUNCT
ejpam-440	261	31	,	,	PUNCT
ejpam-440	261	32	730–738	730–738	NUM
ejpam-440	261	33	.	.	PUNCT
ejpam-440	262	1	[	[	X
ejpam-440	262	2	21	21	NUM
ejpam-440	262	3	]	]	PUNCT
ejpam-440	262	4	a.	a.	PROPN
ejpam-440	262	5	k.	k.	PROPN
ejpam-440	262	6	mirmostafee	mirmostafee	PROPN
ejpam-440	262	7	and	and	CCONJ
ejpam-440	262	8	m.	m.	PROPN
ejpam-440	262	9	s.	s.	PROPN
ejpam-440	262	10	moslehian	moslehian	PROPN
ejpam-440	262	11	,	,	PUNCT
ejpam-440	262	12	fuzzy	fuzzy	ADJ
ejpam-440	262	13	versions	version	NOUN
ejpam-440	262	14	of	of	ADP
ejpam-440	262	15	hyers	hyer	NOUN
ejpam-440	262	16	-	-	PUNCT
ejpam-440	262	17	ulam	ulam	NOUN
ejpam-440	262	18	-	-	PUNCT
ejpam-440	262	19	rassias	rassias	NOUN
ejpam-440	262	20	theorem	theorem	VERB
ejpam-440	262	21	,	,	PUNCT
ejpam-440	262	22	fuzzy	fuzzy	ADJ
ejpam-440	262	23	sets	set	NOUN
ejpam-440	262	24	and	and	CCONJ
ejpam-440	262	25	systems	system	NOUN
ejpam-440	262	26	,	,	PUNCT
ejpam-440	262	27	159	159	NUM
ejpam-440	262	28	(	(	PUNCT
ejpam-440	262	29	2008	2008	NUM
ejpam-440	262	30	)	)	PUNCT
ejpam-440	262	31	,	,	PUNCT
ejpam-440	262	32	720–729	720–729	NUM
ejpam-440	262	33	.	.	PUNCT
ejpam-440	263	1	[	[	X
ejpam-440	263	2	22	22	NUM
ejpam-440	263	3	]	]	PUNCT
ejpam-440	263	4	a.	a.	PROPN
ejpam-440	263	5	k.	k.	PROPN
ejpam-440	263	6	mirmostafaee	mirmostafaee	PROPN
ejpam-440	263	7	and	and	CCONJ
ejpam-440	263	8	m.	m.	PROPN
ejpam-440	263	9	s.	s.	PROPN
ejpam-440	263	10	moslehian	moslehian	PROPN
ejpam-440	263	11	,	,	PUNCT
ejpam-440	263	12	fuzzy	fuzzy	ADJ
ejpam-440	263	13	approximately	approximately	ADV
ejpam-440	263	14	cubic	cubic	ADJ
ejpam-440	263	15	mappings	mapping	NOUN
ejpam-440	263	16	,	,	PUNCT
ejpam-440	263	17	inform	inform	NOUN
ejpam-440	263	18	.	.	PUNCT
ejpam-440	264	1	sci	sci	PROPN
ejpam-440	264	2	.	.	PROPN
ejpam-440	264	3	178	178	NUM
ejpam-440	264	4	(	(	PUNCT
ejpam-440	264	5	2008	2008	NUM
ejpam-440	264	6	)	)	PUNCT
ejpam-440	264	7	,	,	PUNCT
ejpam-440	264	8	3791–3798	3791–3798	NUM
ejpam-440	264	9	.	.	PUNCT
ejpam-440	265	1	[	[	X
ejpam-440	265	2	23	23	NUM
ejpam-440	265	3	]	]	X
ejpam-440	265	4	c.	c.	PROPN
ejpam-440	265	5	park	park	PROPN
ejpam-440	265	6	,	,	PUNCT
ejpam-440	265	7	generalized	generalize	VERB
ejpam-440	265	8	quadratic	quadratic	ADJ
ejpam-440	265	9	mappings	mapping	NOUN
ejpam-440	265	10	in	in	ADP
ejpam-440	265	11	several	several	ADJ
ejpam-440	265	12	variables	variable	NOUN
ejpam-440	265	13	,	,	PUNCT
ejpam-440	265	14	nonlinear	nonlinear	ADJ
ejpam-440	265	15	anal	anal	NOUN
ejpam-440	265	16	.	.	PUNCT
ejpam-440	266	1	tma	tma	PROPN
ejpam-440	266	2	57	57	NUM
ejpam-440	266	3	(	(	PUNCT
ejpam-440	266	4	2004	2004	NUM
ejpam-440	266	5	)	)	PUNCT
ejpam-440	266	6	,	,	PUNCT
ejpam-440	266	7	713–722	713–722	NUM
ejpam-440	266	8	.	.	PUNCT
ejpam-440	267	1	[	[	X
ejpam-440	267	2	24	24	NUM
ejpam-440	267	3	]	]	X
ejpam-440	267	4	j.	j.	PROPN
ejpam-440	267	5	m.	m.	PROPN
ejpam-440	267	6	rassias	rassias	PROPN
ejpam-440	267	7	,	,	PUNCT
ejpam-440	267	8	solution	solution	NOUN
ejpam-440	267	9	of	of	ADP
ejpam-440	267	10	a	a	DET
ejpam-440	267	11	stability	stability	NOUN
ejpam-440	267	12	problem	problem	NOUN
ejpam-440	267	13	of	of	ADP
ejpam-440	267	14	ulam	ulam	PROPN
ejpam-440	267	15	,	,	PUNCT
ejpam-440	267	16	discuss	discuss	PROPN
ejpam-440	267	17	.	.	PUNCT
ejpam-440	268	1	math	math	NOUN
ejpam-440	268	2	.	.	PUNCT
ejpam-440	269	1	12	12	NUM
ejpam-440	269	2	(	(	PUNCT
ejpam-440	269	3	1992	1992	NUM
ejpam-440	269	4	)	)	PUNCT
ejpam-440	269	5	,	,	PUNCT
ejpam-440	269	6	95ű103	95ű103	NUM
ejpam-440	269	7	.	.	PUNCT
ejpam-440	270	1	[	[	X
ejpam-440	270	2	25	25	NUM
ejpam-440	270	3	]	]	PUNCT
ejpam-440	270	4	j.	j.	PROPN
ejpam-440	270	5	m.	m.	PROPN
ejpam-440	270	6	rassias	rassias	PROPN
ejpam-440	270	7	,	,	PUNCT
ejpam-440	270	8	solution	solution	NOUN
ejpam-440	270	9	of	of	ADP
ejpam-440	270	10	the	the	DET
ejpam-440	270	11	ulam	ulam	PROPN
ejpam-440	270	12	stability	stability	PROPN
ejpam-440	270	13	problem	problem	NOUN
ejpam-440	270	14	for	for	ADP
ejpam-440	270	15	cubic	cubic	ADJ
ejpam-440	270	16	mappings	mapping	NOUN
ejpam-440	270	17	,	,	PUNCT
ejpam-440	270	18	glas	glas	PROPN
ejpam-440	270	19	.	.	PUNCT
ejpam-440	270	20	mat	mat	PROPN
ejpam-440	270	21	.	.	PUNCT
ejpam-440	270	22	ser	ser	PROPN
ejpam-440	270	23	.	.	PUNCT
ejpam-440	270	24	iii	iii	NUM
ejpam-440	270	25	36	36	NUM
ejpam-440	270	26	(	(	PUNCT
ejpam-440	270	27	56	56	NUM
ejpam-440	270	28	)	)	PUNCT
ejpam-440	270	29	(	(	PUNCT
ejpam-440	270	30	2001	2001	NUM
ejpam-440	270	31	)	)	PUNCT
ejpam-440	270	32	,	,	PUNCT
ejpam-440	270	33	no	no	INTJ
ejpam-440	270	34	.	.	NOUN
ejpam-440	270	35	1	1	NUM
ejpam-440	270	36	,	,	PUNCT
ejpam-440	270	37	63	63	NUM
ejpam-440	270	38	-	-	NUM
ejpam-440	270	39	ű72	ű72	NOUN
ejpam-440	270	40	.	.	PUNCT
ejpam-440	271	1	[	[	X
ejpam-440	271	2	26	26	NUM
ejpam-440	271	3	]	]	X
ejpam-440	271	4	j.	j.	PROPN
ejpam-440	271	5	m.	m.	PROPN
ejpam-440	271	6	rassias	rassias	PROPN
ejpam-440	271	7	,	,	PUNCT
ejpam-440	271	8	solution	solution	NOUN
ejpam-440	271	9	of	of	ADP
ejpam-440	271	10	the	the	DET
ejpam-440	271	11	ulam	ulam	PROPN
ejpam-440	271	12	stability	stability	PROPN
ejpam-440	271	13	problem	problem	NOUN
ejpam-440	271	14	for	for	ADP
ejpam-440	271	15	cubic	cubic	ADJ
ejpam-440	271	16	mappings	mapping	NOUN
ejpam-440	271	17	,	,	PUNCT
ejpam-440	271	18	an	an	PRON
ejpam-440	271	19	.	.	PUNCT
ejpam-440	271	20	univ	univ	PROPN
ejpam-440	271	21	.	.	PUNCT
ejpam-440	272	1	timi	timi	PROPN
ejpam-440	272	2	c	c	PROPN
ejpam-440	272	3	soara	soara	PROPN
ejpam-440	272	4	ser	ser	PROPN
ejpam-440	272	5	.	.	PUNCT
ejpam-440	273	1	mat.-inform	mat.-inform	PROPN
ejpam-440	273	2	.	.	PUNCT
ejpam-440	274	1	38	38	NUM
ejpam-440	274	2	(	(	PUNCT
ejpam-440	274	3	2000	2000	NUM
ejpam-440	274	4	)	)	PUNCT
ejpam-440	274	5	,	,	PUNCT
ejpam-440	274	6	no	no	INTJ
ejpam-440	274	7	.	.	NOUN
ejpam-440	274	8	1	1	NUM
ejpam-440	274	9	,	,	PUNCT
ejpam-440	274	10	121	121	NUM
ejpam-440	274	11	-	-	PUNCT
ejpam-440	274	12	ű132	ű132	NOUN
ejpam-440	274	13	.	.	PUNCT
ejpam-440	275	1	[	[	X
ejpam-440	275	2	27	27	NUM
ejpam-440	275	3	]	]	X
ejpam-440	275	4	j.	j.	PROPN
ejpam-440	275	5	m.	m.	PROPN
ejpam-440	275	6	rassias	rassias	PROPN
ejpam-440	275	7	,	,	PUNCT
ejpam-440	275	8	on	on	ADP
ejpam-440	275	9	approximation	approximation	NOUN
ejpam-440	275	10	of	of	ADP
ejpam-440	275	11	approximately	approximately	ADV
ejpam-440	275	12	linear	linear	ADJ
ejpam-440	275	13	mappings	mapping	NOUN
ejpam-440	275	14	by	by	ADP
ejpam-440	275	15	linear	linear	ADJ
ejpam-440	275	16	mappings	mapping	NOUN
ejpam-440	275	17	.	.	PUNCT
ejpam-440	276	1	j.funct	j.funct	ADJ
ejpam-440	276	2	.	.	PUNCT
ejpam-440	277	1	anal	anal	ADJ
ejpam-440	277	2	.	.	PUNCT
ejpam-440	278	1	46	46	NUM
ejpam-440	278	2	(	(	PUNCT
ejpam-440	278	3	1982	1982	NUM
ejpam-440	278	4	)	)	PUNCT
ejpam-440	278	5	,	,	PUNCT
ejpam-440	278	6	no	no	INTJ
ejpam-440	278	7	.	.	NOUN
ejpam-440	278	8	1	1	NUM
ejpam-440	278	9	,	,	PUNCT
ejpam-440	278	10	126–130	126–130	NUM
ejpam-440	278	11	.	.	PUNCT
ejpam-440	279	1	[	[	X
ejpam-440	279	2	28	28	NUM
ejpam-440	279	3	]	]	X
ejpam-440	279	4	j.	j.	PROPN
ejpam-440	279	5	m.	m.	PROPN
ejpam-440	279	6	rassias	rassias	PROPN
ejpam-440	279	7	,	,	PUNCT
ejpam-440	279	8	solution	solution	NOUN
ejpam-440	279	9	of	of	ADP
ejpam-440	279	10	a	a	DET
ejpam-440	279	11	problem	problem	NOUN
ejpam-440	279	12	of	of	ADP
ejpam-440	279	13	ulam	ulam	PROPN
ejpam-440	279	14	.	.	PUNCT
ejpam-440	280	1	j.	j.	PROPN
ejpam-440	280	2	approx	approx	PROPN
ejpam-440	280	3	.	.	PUNCT
ejpam-440	281	1	theory	theory	NOUN
ejpam-440	281	2	57	57	NUM
ejpam-440	281	3	(	(	PUNCT
ejpam-440	281	4	1989	1989	NUM
ejpam-440	281	5	)	)	PUNCT
ejpam-440	281	6	,	,	PUNCT
ejpam-440	281	7	no	no	INTJ
ejpam-440	281	8	.	.	NOUN
ejpam-440	281	9	3	3	NUM
ejpam-440	281	10	,	,	PUNCT
ejpam-440	281	11	268	268	NUM
ejpam-440	281	12	–	–	PUNCT
ejpam-440	281	13	references	reference	NOUN
ejpam-440	281	14	507	507	NUM
ejpam-440	281	15	273	273	NUM
ejpam-440	281	16	.	.	PUNCT
ejpam-440	282	1	[	[	X
ejpam-440	282	2	29	29	NUM
ejpam-440	282	3	]	]	X
ejpam-440	282	4	j.	j.	PROPN
ejpam-440	282	5	m.	m.	PROPN
ejpam-440	282	6	rassias	rassias	PROPN
ejpam-440	282	7	,	,	PUNCT
ejpam-440	282	8	on	on	ADP
ejpam-440	282	9	a	a	DET
ejpam-440	282	10	new	new	ADJ
ejpam-440	282	11	approximation	approximation	NOUN
ejpam-440	282	12	of	of	ADP
ejpam-440	282	13	approximately	approximately	ADV
ejpam-440	282	14	linear	linear	ADJ
ejpam-440	282	15	mappings	mapping	NOUN
ejpam-440	282	16	by	by	ADP
ejpam-440	282	17	linear	linear	ADJ
ejpam-440	282	18	mappings	mapping	NOUN
ejpam-440	282	19	,	,	PUNCT
ejpam-440	282	20	discuss	discuss	NOUN
ejpam-440	282	21	.	.	PUNCT
ejpam-440	283	1	math.7	math.7	NOUN
ejpam-440	283	2	(	(	PUNCT
ejpam-440	283	3	1985	1985	NUM
ejpam-440	283	4	)	)	PUNCT
ejpam-440	283	5	,	,	PUNCT
ejpam-440	283	6	193	193	NUM
ejpam-440	283	7	-	-	SYM
ejpam-440	283	8	196	196	NUM
ejpam-440	283	9	.	.	PUNCT
ejpam-440	284	1	[	[	X
ejpam-440	284	2	30	30	NUM
ejpam-440	284	3	]	]	X
ejpam-440	284	4	j.	j.	PROPN
ejpam-440	284	5	m.	m.	PROPN
ejpam-440	284	6	rassias	rassias	PROPN
ejpam-440	284	7	,	,	PUNCT
ejpam-440	284	8	on	on	ADP
ejpam-440	284	9	approximation	approximation	NOUN
ejpam-440	284	10	of	of	ADP
ejpam-440	284	11	approximately	approximately	ADV
ejpam-440	284	12	linear	linear	ADJ
ejpam-440	284	13	mappings	mapping	NOUN
ejpam-440	284	14	by	by	ADP
ejpam-440	284	15	linear	linear	ADJ
ejpam-440	284	16	mappings	mapping	NOUN
ejpam-440	284	17	,	,	PUNCT
ejpam-440	284	18	bull	bull	NOUN
ejpam-440	284	19	.	.	PUNCT
ejpam-440	285	1	sci	sci	PROPN
ejpam-440	285	2	.	.	PROPN
ejpam-440	285	3	math	math	PROPN
ejpam-440	285	4	.	.	PUNCT
ejpam-440	286	1	(	(	PUNCT
ejpam-440	286	2	2	2	NUM
ejpam-440	286	3	)	)	PUNCT
ejpam-440	286	4	108	108	NUM
ejpam-440	286	5	(	(	PUNCT
ejpam-440	286	6	1984	1984	NUM
ejpam-440	286	7	)	)	PUNCT
ejpam-440	286	8	,	,	PUNCT
ejpam-440	286	9	no.4	no.4	PROPN
ejpam-440	286	10	,	,	PUNCT
ejpam-440	286	11	445	445	NUM
ejpam-440	286	12	-	-	SYM
ejpam-440	286	13	446	446	NUM
ejpam-440	286	14	.	.	PUNCT
ejpam-440	287	1	[	[	X
ejpam-440	287	2	31	31	NUM
ejpam-440	287	3	]	]	SYM
ejpam-440	287	4	th	th	X
ejpam-440	287	5	.	.	PUNCT
ejpam-440	287	6	m.	m.	NOUN
ejpam-440	287	7	rassias	rassias	PROPN
ejpam-440	287	8	,	,	PUNCT
ejpam-440	287	9	on	on	ADP
ejpam-440	287	10	the	the	DET
ejpam-440	287	11	stability	stability	NOUN
ejpam-440	287	12	of	of	ADP
ejpam-440	287	13	the	the	DET
ejpam-440	287	14	linear	linear	ADJ
ejpam-440	287	15	mapping	mapping	NOUN
ejpam-440	287	16	in	in	ADP
ejpam-440	287	17	banach	banach	NOUN
ejpam-440	287	18	spaces	space	NOUN
ejpam-440	287	19	,	,	PUNCT
ejpam-440	287	20	proc	proc	NOUN
ejpam-440	287	21	.	.	PUNCT
ejpam-440	288	1	amer	amer	PROPN
ejpam-440	288	2	.	.	PUNCT
ejpam-440	288	3	math	math	PROPN
ejpam-440	288	4	.	.	PUNCT
ejpam-440	289	1	soc	soc	PROPN
ejpam-440	289	2	.	.	PUNCT
ejpam-440	290	1	72	72	NUM
ejpam-440	290	2	(	(	PUNCT
ejpam-440	290	3	1978	1978	NUM
ejpam-440	290	4	)	)	PUNCT
ejpam-440	290	5	,	,	PUNCT
ejpam-440	290	6	297–300	297–300	NUM
ejpam-440	290	7	.	.	PUNCT
ejpam-440	291	1	[	[	X
ejpam-440	291	2	32	32	NUM
ejpam-440	291	3	]	]	SYM
ejpam-440	291	4	th	th	X
ejpam-440	291	5	.	.	PUNCT
ejpam-440	291	6	m.	m.	NOUN
ejpam-440	291	7	rassias	rassias	PROPN
ejpam-440	291	8	,	,	PUNCT
ejpam-440	291	9	on	on	ADP
ejpam-440	291	10	the	the	DET
ejpam-440	291	11	stability	stability	NOUN
ejpam-440	291	12	of	of	ADP
ejpam-440	291	13	the	the	DET
ejpam-440	291	14	quadratic	quadratic	ADJ
ejpam-440	291	15	functional	functional	ADJ
ejpam-440	291	16	equation	equation	NOUN
ejpam-440	291	17	and	and	CCONJ
ejpam-440	291	18	its	its	PRON
ejpam-440	291	19	applications	application	NOUN
ejpam-440	291	20	,	,	PUNCT
ejpam-440	291	21	studia	studia	PROPN
ejpam-440	291	22	univ	univ	PROPN
ejpam-440	291	23	.	.	PUNCT
ejpam-440	292	1	babes	babe	NOUN
ejpam-440	292	2	-	-	PUNCT
ejpam-440	292	3	bolyai	bolyai	NOUN
ejpam-440	292	4	(	(	PUNCT
ejpam-440	292	5	1998	1998	NUM
ejpam-440	292	6	)	)	PUNCT
ejpam-440	292	7	,	,	PUNCT
ejpam-440	292	8	89–124	89–124	NUM
ejpam-440	292	9	.	.	PUNCT
ejpam-440	293	1	[	[	X
ejpam-440	293	2	33	33	NUM
ejpam-440	293	3	]	]	SYM
ejpam-440	293	4	th	th	X
ejpam-440	293	5	.	.	PUNCT
ejpam-440	293	6	m.	m.	NOUN
ejpam-440	293	7	rassias	rassias	PROPN
ejpam-440	293	8	and	and	CCONJ
ejpam-440	293	9	k.	k.	PROPN
ejpam-440	293	10	shibata	shibata	PROPN
ejpam-440	293	11	,	,	PUNCT
ejpam-440	293	12	variational	variational	ADJ
ejpam-440	293	13	problem	problem	NOUN
ejpam-440	293	14	of	of	ADP
ejpam-440	293	15	some	some	DET
ejpam-440	293	16	quadratic	quadratic	ADJ
ejpam-440	293	17	functionals	functional	NOUN
ejpam-440	293	18	in	in	ADP
ejpam-440	293	19	complex	complex	ADJ
ejpam-440	293	20	analysis	analysis	NOUN
ejpam-440	293	21	,	,	PUNCT
ejpam-440	293	22	j.	j.	PROPN
ejpam-440	293	23	math	math	PROPN
ejpam-440	293	24	.	.	PUNCT
ejpam-440	294	1	anal	anal	PROPN
ejpam-440	294	2	.	.	PUNCT
ejpam-440	294	3	appl	appl	PROPN
ejpam-440	294	4	.	.	PUNCT
ejpam-440	295	1	228	228	NUM
ejpam-440	295	2	(	(	PUNCT
ejpam-440	295	3	1998	1998	NUM
ejpam-440	295	4	)	)	PUNCT
ejpam-440	295	5	,	,	PUNCT
ejpam-440	295	6	234–253	234–253	NUM
ejpam-440	295	7	.	.	PUNCT
ejpam-440	296	1	[	[	X
ejpam-440	296	2	34	34	NUM
ejpam-440	296	3	]	]	X
ejpam-440	296	4	b.	b.	PROPN
ejpam-440	296	5	schweizer	schweizer	PROPN
ejpam-440	296	6	and	and	CCONJ
ejpam-440	296	7	a.	a.	NOUN
ejpam-440	296	8	sklar	sklar	PROPN
ejpam-440	296	9	,	,	PUNCT
ejpam-440	296	10	probabilistic	probabilistic	ADJ
ejpam-440	296	11	metric	metric	ADJ
ejpam-440	296	12	spaces	space	NOUN
ejpam-440	296	13	,	,	PUNCT
ejpam-440	296	14	elsevier	elsevier	NOUN
ejpam-440	296	15	,	,	PUNCT
ejpam-440	296	16	north	north	NOUN
ejpam-440	296	17	holand	holand	PROPN
ejpam-440	296	18	,	,	PUNCT
ejpam-440	296	19	new	new	PROPN
ejpam-440	296	20	york	york	PROPN
ejpam-440	296	21	,	,	PUNCT
ejpam-440	296	22	1983	1983	NUM
ejpam-440	296	23	.	.	PUNCT
ejpam-440	297	1	[	[	X
ejpam-440	297	2	35	35	NUM
ejpam-440	297	3	]	]	PUNCT
ejpam-440	297	4	a.	a.	NOUN
ejpam-440	297	5	n.	n.	PROPN
ejpam-440	297	6	sherstnev	sherstnev	PROPN
ejpam-440	297	7	,	,	PUNCT
ejpam-440	297	8	on	on	ADP
ejpam-440	297	9	the	the	DET
ejpam-440	297	10	notion	notion	NOUN
ejpam-440	297	11	of	of	ADP
ejpam-440	297	12	a	a	DET
ejpam-440	297	13	random	random	ADJ
ejpam-440	297	14	normed	normed	ADJ
ejpam-440	297	15	space	space	NOUN
ejpam-440	297	16	,	,	PUNCT
ejpam-440	297	17	dokl	dokl	NOUN
ejpam-440	297	18	.	.	PUNCT
ejpam-440	297	19	akad	akad	PROPN
ejpam-440	297	20	.	.	PUNCT
ejpam-440	298	1	nauk	nauk	PROPN
ejpam-440	298	2	sssr	sssr	NOUN
ejpam-440	298	3	149	149	NUM
ejpam-440	298	4	(	(	PUNCT
ejpam-440	298	5	1963	1963	NUM
ejpam-440	298	6	)	)	PUNCT
ejpam-440	298	7	,	,	PUNCT
ejpam-440	298	8	280ű-283	280ű-283	NUM
ejpam-440	298	9	(	(	PUNCT
ejpam-440	298	10	in	in	ADP
ejpam-440	298	11	russian	russian	NOUN
ejpam-440	298	12	)	)	PUNCT
ejpam-440	298	13	.	.	PUNCT
ejpam-440	299	1	[	[	X
ejpam-440	299	2	36	36	NUM
ejpam-440	299	3	]	]	X
ejpam-440	299	4	f.	f.	PROPN
ejpam-440	299	5	skof	skof	PROPN
ejpam-440	299	6	,	,	PUNCT
ejpam-440	299	7	propriet	propriet	PROPN
ejpam-440	299	8	locali	locali	PROPN
ejpam-440	299	9	e	e	PROPN
ejpam-440	299	10	approssimazione	approssimazione	PROPN
ejpam-440	299	11	di	di	PROPN
ejpam-440	299	12	operatori	operatori	PROPN
ejpam-440	299	13	,	,	PUNCT
ejpam-440	299	14	rend	rend	VERB
ejpam-440	299	15	.	.	PUNCT
ejpam-440	299	16	sem	sem	PROPN
ejpam-440	299	17	.	.	PUNCT
ejpam-440	299	18	mat	mat	PROPN
ejpam-440	299	19	.	.	PROPN
ejpam-440	299	20	fis	fis	PROPN
ejpam-440	299	21	.	.	PUNCT
ejpam-440	300	1	milano	milano	PROPN
ejpam-440	300	2	,	,	PUNCT
ejpam-440	300	3	53	53	NUM
ejpam-440	300	4	(	(	PUNCT
ejpam-440	300	5	1983	1983	NUM
ejpam-440	300	6	)	)	PUNCT
ejpam-440	300	7	,	,	PUNCT
ejpam-440	300	8	113–129	113–129	NUM
ejpam-440	300	9	.	.	PUNCT
ejpam-440	301	1	[	[	X
ejpam-440	301	2	37	37	NUM
ejpam-440	301	3	]	]	PUNCT
ejpam-440	301	4	s.	s.	PROPN
ejpam-440	301	5	m.	m.	PROPN
ejpam-440	301	6	ulam	ulam	PROPN
ejpam-440	301	7	,	,	PUNCT
ejpam-440	301	8	problems	problem	NOUN
ejpam-440	301	9	in	in	ADP
ejpam-440	301	10	modern	modern	ADJ
ejpam-440	301	11	mathematics	mathematic	NOUN
ejpam-440	301	12	,	,	PUNCT
ejpam-440	301	13	wiley	wiley	NOUN
ejpam-440	301	14	,	,	PUNCT
ejpam-440	301	15	new	new	PROPN
ejpam-440	301	16	york	york	PROPN
ejpam-440	301	17	,	,	PUNCT
ejpam-440	301	18	1964	1964	NUM
ejpam-440	301	19	.	.	PUNCT