id	sid	tid	token	lemma	pos
iajs-399	1	1	fixed	fix	VERB
iajs-399	1	2	point	point	NOUN
iajs-399	1	3	for	for	ADP
iajs-399	1	4	asymptotically	asymptotically	ADV
iajs-399	1	5	non	non	ADJ
iajs-399	1	6	-	-	ADJ
iajs-399	1	7	expansive	expansive	ADJ
iajs-399	1	8	mappings	mapping	NOUN
iajs-399	1	9	in	in	ADP
iajs-399	1	10	2	2	NUM
iajs-399	1	11	-	-	PUNCT
iajs-399	1	12	banach	banach	NOUN
iajs-399	1	13	space	space	NOUN
iajs-399	1	14	salwa	salwa	PROPN
iajs-399	1	15	s.	s.	PROPN
iajs-399	1	16	abed	abed	PROPN
iajs-399	1	17	rafah	rafah	PROPN
iajs-399	1	18	s.	s.	PROPN
iajs-399	1	19	abed	abed	PROPN
iajs-399	1	20	ali	ali	PROPN
iajs-399	1	21	department	department	PROPN
iajs-399	1	22	of	of	ADP
iajs-399	1	23	mathematics	mathematics	PROPN
iajs-399	1	24	/	/	SYM
iajs-399	1	25	college	college	NOUN
iajs-399	1	26	of	of	ADP
iajs-399	1	27	education	education	NOUN
iajs-399	1	28	for	for	ADP
iajs-399	1	29	pure	pure	ADJ
iajs-399	1	30	science(ibn	science(ibn	NOUN
iajs-399	1	31	alhaitham	alhaitham	NOUN
iajs-399	1	32	)	)	PUNCT
iajs-399	1	33	/baghdad	/baghdad	PUNCT
iajs-399	2	1	university	university	NOUN
iajs-399	2	2	received	receive	VERB
iajs-399	2	3	in	in	ADP
iajs-399	2	4	:	:	PUNCT
iajs-399	2	5	23	23	NUM
iajs-399	2	6	june	june	PROPN
iajs-399	2	7	2013	2013	NUM
iajs-399	2	8	,	,	PUNCT
iajs-399	2	9	accepted	accept	VERB
iajs-399	2	10	in	in	ADP
iajs-399	2	11	:	:	PUNCT
iajs-399	2	12	4	4	NUM
iajs-399	2	13	december	december	PROPN
iajs-399	2	14	2013	2013	NUM
iajs-399	2	15	abstract	abstract	NOUN
iajs-399	2	16	in	in	ADP
iajs-399	2	17	this	this	DET
iajs-399	2	18	paper	paper	NOUN
iajs-399	2	19	,	,	PUNCT
iajs-399	2	20	we	we	PRON
iajs-399	2	21	introduced	introduce	VERB
iajs-399	2	22	some	some	DET
iajs-399	2	23	fact	fact	NOUN
iajs-399	2	24	in	in	ADP
iajs-399	2	25	2	2	NUM
iajs-399	2	26	-	-	PUNCT
iajs-399	2	27	banach	banach	NOUN
iajs-399	2	28	space	space	NOUN
iajs-399	2	29	.	.	PUNCT
iajs-399	3	1	also	also	ADV
iajs-399	3	2	,	,	PUNCT
iajs-399	3	3	we	we	PRON
iajs-399	3	4	define	define	VERB
iajs-399	3	5	asymptotically	asymptotically	ADV
iajs-399	3	6	non	non	ADJ
iajs-399	3	7	-	-	ADJ
iajs-399	3	8	expansive	expansive	ADJ
iajs-399	3	9	mappings	mapping	NOUN
iajs-399	3	10	in	in	ADP
iajs-399	3	11	the	the	DET
iajs-399	3	12	setting	setting	NOUN
iajs-399	3	13	of	of	ADP
iajs-399	3	14	2	2	NUM
iajs-399	3	15	-	-	PUNCT
iajs-399	3	16	normed	norme	VERB
iajs-399	3	17	spaces	space	NOUN
iajs-399	3	18	analogous	analogous	ADJ
iajs-399	3	19	to	to	ADP
iajs-399	3	20	asymptotically	asymptotically	ADV
iajs-399	3	21	non	non	ADJ
iajs-399	3	22	-	-	ADJ
iajs-399	3	23	expansive	expansive	ADJ
iajs-399	3	24	mappings	mapping	NOUN
iajs-399	3	25	in	in	ADP
iajs-399	3	26	usual	usual	ADJ
iajs-399	3	27	normed	norme	VERB
iajs-399	3	28	spaces	space	NOUN
iajs-399	3	29	.	.	PUNCT
iajs-399	4	1	and	and	CCONJ
iajs-399	4	2	then	then	ADV
iajs-399	4	3	prove	prove	VERB
iajs-399	4	4	the	the	DET
iajs-399	4	5	existence	existence	NOUN
iajs-399	4	6	of	of	ADP
iajs-399	4	7	fixed	fix	VERB
iajs-399	4	8	points	point	NOUN
iajs-399	4	9	for	for	ADP
iajs-399	4	10	this	this	DET
iajs-399	4	11	type	type	NOUN
iajs-399	4	12	of	of	ADP
iajs-399	4	13	mappings	mapping	NOUN
iajs-399	4	14	in	in	ADP
iajs-399	4	15	2	2	NUM
iajs-399	4	16	-	-	PUNCT
iajs-399	4	17	banach	banach	NOUN
iajs-399	4	18	spaces	space	NOUN
iajs-399	4	19	.	.	PUNCT
iajs-399	5	1	keywords	keyword	NOUN
iajs-399	5	2	:	:	PUNCT
iajs-399	5	3	2	2	NUM
iajs-399	5	4	-	-	PUNCT
iajs-399	5	5	banach	banach	NOUN
iajs-399	5	6	space	space	NOUN
iajs-399	5	7	,	,	PUNCT
iajs-399	5	8	non	non	ADJ
iajs-399	5	9	-	-	ADJ
iajs-399	5	10	expansive	expansive	ADJ
iajs-399	5	11	mapping	mapping	NOUN
iajs-399	5	12	,	,	PUNCT
iajs-399	5	13	asymptotically	asymptotically	ADV
iajs-399	5	14	non	non	ADJ
iajs-399	5	15	-	-	ADJ
iajs-399	5	16	expansive	expansive	ADJ
iajs-399	5	17	mapping	mapping	NOUN
iajs-399	5	18	,	,	PUNCT
iajs-399	5	19	fixed	fix	VERB
iajs-399	5	20	point	point	NOUN
iajs-399	5	21	.	.	PUNCT
iajs-399	6	1	343	343	NUM
iajs-399	7	1	|	|	ADV
iajs-399	7	2	mathematics	mathematics	PROPN
iajs-399	7	3	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	NUM
iajs-399	7	4	�	�	NOUN
iajs-399	7	5	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	NUM
iajs-399	7	6	:	:	PUNCT
iajs-399	7	7	a@âig@ú‹	a@âig@ú‹	PROPN
iajs-399	8	1	©	©	PROPN
iajs-399	8	2	@ü‹127@@öü»€a@i1@‚b«@h2014	@ü‹127@@öü»€a@i1@‚b«@h2014	PROPN
iajs-399	8	3	ibn	ibn	PROPN
iajs-399	8	4	al	al	PROPN
iajs-399	8	5	-	-	PUNCT
iajs-399	8	6	haitham	haitham	PROPN
iajs-399	8	7	jour	jour	X
iajs-399	8	8	.	.	PROPN
iajs-399	8	9	for	for	ADP
iajs-399	8	10	pure	pure	ADJ
iajs-399	8	11	&	&	CCONJ
iajs-399	8	12	appl	appl	PROPN
iajs-399	8	13	.	.	PUNCT
iajs-399	9	1	sci	sci	PROPN
iajs-399	9	2	.	.	PUNCT
iajs-399	9	3	vol	vol	NOUN
iajs-399	9	4	.	.	PROPN
iajs-399	10	1	27	27	NUM
iajs-399	10	2	(	(	PUNCT
iajs-399	10	3	1	1	NUM
iajs-399	10	4	)	)	PUNCT
iajs-399	10	5	2014	2014	NUM
iajs-399	10	6	introduction	introduction	NOUN
iajs-399	10	7	and	and	CCONJ
iajs-399	10	8	preliminaries	preliminary	NOUN
iajs-399	10	9	the	the	DET
iajs-399	10	10	concept	concept	NOUN
iajs-399	10	11	of	of	ADP
iajs-399	10	12	linear	linear	ADJ
iajs-399	10	13	2	2	NUM
iajs-399	10	14	-	-	PUNCT
iajs-399	10	15	normed	norme	VERB
iajs-399	10	16	spaces	space	NOUN
iajs-399	10	17	(	(	PUNCT
iajs-399	10	18	breviary	breviary	ADJ
iajs-399	10	19	,	,	PUNCT
iajs-399	10	20	2	2	NUM
iajs-399	10	21	-	-	PUNCT
iajs-399	10	22	normed	norme	VERB
iajs-399	10	23	space	space	NOUN
iajs-399	10	24	)	)	PUNCT
iajs-399	10	25	was	be	AUX
iajs-399	10	26	initiated	initiate	VERB
iajs-399	10	27	by	by	ADP
iajs-399	10	28	sgahler	sgahler	NOUN
iajs-399	10	29	in	in	ADP
iajs-399	10	30	1965	1965	NUM
iajs-399	10	31	[	[	X
iajs-399	10	32	1	1	NUM
iajs-399	10	33	]	]	PUNCT
iajs-399	10	34	.	.	PUNCT
iajs-399	11	1	other	other	ADJ
iajs-399	11	2	papers	paper	NOUN
iajs-399	11	3	dealing	deal	VERB
iajs-399	11	4	with	with	ADP
iajs-399	11	5	2	2	NUM
iajs-399	11	6	-	-	PUNCT
iajs-399	11	7	normed	norme	VERB
iajs-399	11	8	spaces	space	NOUN
iajs-399	11	9	are	be	AUX
iajs-399	11	10	[	[	X
iajs-399	11	11	2	2	NUM
iajs-399	11	12	]	]	PUNCT
iajs-399	11	13	,	,	PUNCT
iajs-399	11	14	[	[	X
iajs-399	11	15	3	3	NUM
iajs-399	11	16	]	]	PUNCT
iajs-399	11	17	and	and	CCONJ
iajs-399	11	18	[	[	X
iajs-399	11	19	4	4	NUM
iajs-399	11	20	]	]	PUNCT
iajs-399	11	21	.	.	PUNCT
iajs-399	12	1	later	later	ADV
iajs-399	12	2	on	on	ADV
iajs-399	12	3	,	,	PUNCT
iajs-399	12	4	several	several	ADJ
iajs-399	12	5	researchers	researcher	NOUN
iajs-399	12	6	studied	study	VERB
iajs-399	12	7	2	2	NUM
iajs-399	12	8	-	-	PUNCT
iajs-399	12	9	normed	norme	VERB
iajs-399	12	10	spaces	space	NOUN
iajs-399	12	11	using	use	VERB
iajs-399	12	12	contractive	contractive	ADJ
iajs-399	12	13	map	map	NOUN
iajs-399	12	14	-	-	PUNCT
iajs-399	12	15	pings	ping	NOUN
iajs-399	12	16	(	(	PUNCT
iajs-399	12	17	see	see	VERB
iajs-399	12	18	[	[	X
iajs-399	12	19	5	5	NUM
iajs-399	12	20	]	]	PUNCT
iajs-399	12	21	and	and	CCONJ
iajs-399	12	22	[	[	X
iajs-399	12	23	6	6	NUM
iajs-399	12	24	]	]	PUNCT
iajs-399	12	25	)	)	PUNCT
iajs-399	12	26	.	.	PUNCT
iajs-399	13	1	also	also	ADV
iajs-399	13	2	,	,	PUNCT
iajs-399	13	3	mukti	mukti	PROPN
iajs-399	13	4	,	,	PUNCT
iajs-399	13	5	sahu	sahu	PROPN
iajs-399	13	6	and	and	CCONJ
iajs-399	13	7	baisnab	baisnab	VERB
iajs-399	14	1	[	[	X
iajs-399	14	2	7	7	X
iajs-399	14	3	]	]	PUNCT
iajs-399	14	4	proved	prove	VERB
iajs-399	14	5	some	some	DET
iajs-399	14	6	fixed	fix	VERB
iajs-399	14	7	point	point	NOUN
iajs-399	14	8	theorems	theorem	NOUN
iajs-399	14	9	in	in	ADP
iajs-399	14	10	2	2	NUM
iajs-399	14	11	-	-	PUNCT
iajs-399	14	12	banach	banach	NOUN
iajs-399	14	13	spaces	space	NOUN
iajs-399	14	14	where	where	SCONJ
iajs-399	14	15	mappings	mapping	NOUN
iajs-399	14	16	involved	involve	VERB
iajs-399	14	17	are	be	AUX
iajs-399	14	18	of	of	ADP
iajs-399	14	19	caristis	caristis	NOUN
iajs-399	14	20	type	type	NOUN
iajs-399	14	21	.	.	PUNCT
iajs-399	15	1	the	the	DET
iajs-399	15	2	study	study	NOUN
iajs-399	15	3	of	of	ADP
iajs-399	15	4	2	2	NUM
iajs-399	15	5	-	-	PUNCT
iajs-399	15	6	normed	norme	VERB
iajs-399	15	7	spaces	space	NOUN
iajs-399	15	8	using	use	VERB
iajs-399	15	9	asymptotically	asymptotically	ADV
iajs-399	15	10	non	non	ADJ
iajs-399	15	11	-	-	ADJ
iajs-399	15	12	expansive	expansive	ADJ
iajs-399	15	13	mappings	mapping	NOUN
iajs-399	15	14	was	be	AUX
iajs-399	15	15	not	not	PART
iajs-399	15	16	initiated	initiate	VERB
iajs-399	15	17	by	by	ADP
iajs-399	15	18	researcher	researcher	NOUN
iajs-399	15	19	.	.	PUNCT
iajs-399	16	1	the	the	DET
iajs-399	16	2	purpose	purpose	NOUN
iajs-399	16	3	of	of	ADP
iajs-399	16	4	this	this	DET
iajs-399	16	5	paper	paper	NOUN
iajs-399	16	6	is	be	AUX
iajs-399	16	7	to	to	PART
iajs-399	16	8	continue	continue	VERB
iajs-399	16	9	studying	study	VERB
iajs-399	16	10	2	2	NUM
iajs-399	16	11	-	-	PUNCT
iajs-399	16	12	normed	norme	VERB
iajs-399	16	13	spaces	space	NOUN
iajs-399	16	14	using	use	VERB
iajs-399	16	15	asymptotically	asymptotically	ADV
iajs-399	16	16	non	non	ADJ
iajs-399	16	17	-	-	ADJ
iajs-399	16	18	expansive	expansive	ADJ
iajs-399	16	19	mappings	mapping	NOUN
iajs-399	16	20	.	.	PUNCT
iajs-399	17	1	now	now	ADV
iajs-399	17	2	,	,	PUNCT
iajs-399	17	3	we	we	PRON
iajs-399	17	4	recall	recall	VERB
iajs-399	17	5	the	the	DET
iajs-399	17	6	following	follow	VERB
iajs-399	17	7	definitions	definition	NOUN
iajs-399	17	8	:	:	PUNCT
iajs-399	17	9	definition	definition	NOUN
iajs-399	17	10	[	[	X
iajs-399	17	11	8	8	NUM
iajs-399	17	12	]	]	PUNCT
iajs-399	17	13	let	let	VERB
iajs-399	17	14	x	x	PRON
iajs-399	17	15	be	be	AUX
iajs-399	17	16	a	a	DET
iajs-399	17	17	real	real	ADJ
iajs-399	17	18	linear	linear	ADJ
iajs-399	17	19	space	space	NOUN
iajs-399	17	20	and	and	CCONJ
iajs-399	17	21	‖.	‖.	NOUN
iajs-399	17	22	,	,	PUNCT
iajs-399	17	23	.‖	.‖	PROPN
iajs-399	17	24	be	be	AUX
iajs-399	17	25	a	a	DET
iajs-399	17	26	nonnegative	nonnegative	ADJ
iajs-399	17	27	real	real	ADJ
iajs-399	17	28	valued	value	VERB
iajs-399	17	29	function	function	NOUN
iajs-399	17	30	defined	define	VERB
iajs-399	17	31	on	on	ADP
iajs-399	17	32	x	x	X
iajs-399	17	33	×	×	NOUN
iajs-399	17	34	x	x	PUNCT
iajs-399	17	35	satisfying	satisfy	VERB
iajs-399	17	36	the	the	DET
iajs-399	17	37	following	follow	VERB
iajs-399	17	38	conditions	condition	NOUN
iajs-399	17	39	:	:	PUNCT
iajs-399	17	40	‖𝑥,𝑦‖	‖𝑥,𝑦‖	NOUN
iajs-399	17	41	=	=	SYM
iajs-399	17	42	0	0	PUNCT
iajs-399	17	43	if	if	SCONJ
iajs-399	17	44	and	and	CCONJ
iajs-399	17	45	only	only	ADV
iajs-399	17	46	if	if	SCONJ
iajs-399	17	47	𝓍𝓍	𝓍𝓍	PRON
iajs-399	17	48	and	and	CCONJ
iajs-399	17	49	y	y	PROPN
iajs-399	17	50	are	be	AUX
iajs-399	17	51	linearly	linearly	ADV
iajs-399	17	52	dependent	dependent	ADJ
iajs-399	17	53	in	in	ADP
iajs-399	17	54	x.	x.	NOUN
iajs-399	17	55	1	1	NUM
iajs-399	17	56	)	)	PUNCT
iajs-399	18	1	‖𝑥,𝑦‖	‖𝑥,𝑦‖	NOUN
iajs-399	18	2	=	=	PUNCT
iajs-399	19	1	‖𝑦,𝑥‖	‖𝑦,𝑥‖	NOUN
iajs-399	19	2	,	,	PUNCT
iajs-399	19	3	for	for	ADP
iajs-399	19	4	all	all	DET
iajs-399	19	5	𝓍𝓍	𝓍𝓍	PROPN
iajs-399	19	6	,	,	PUNCT
iajs-399	19	7	y	y	PROPN
iajs-399	19	8	ϵx	ϵx	INTJ
iajs-399	19	9	.	.	PUNCT
iajs-399	20	1	2	2	NUM
iajs-399	20	2	)	)	PUNCT
iajs-399	20	3	3	3	NUM
iajs-399	20	4	)	)	PUNCT
iajs-399	20	5	‖𝑥,𝛼𝑦‖	‖𝑥,𝛼𝑦‖	NOUN
iajs-399	20	6	=	=	SYM
iajs-399	20	7	|𝛼|‖𝑥	|𝛼|‖𝑥	NOUN
iajs-399	20	8	,	,	PUNCT
iajs-399	20	9	𝑦‖	𝑦‖	PROPN
iajs-399	20	10	,	,	PUNCT
iajs-399	20	11	α	α	NOUN
iajs-399	20	12	ϵ	ϵ	X
iajs-399	20	13	r	r	NOUN
iajs-399	20	14	,	,	PUNCT
iajs-399	20	15	𝓍𝓍	𝓍𝓍	PROPN
iajs-399	20	16	,	,	PUNCT
iajs-399	20	17	y	y	PROPN
iajs-399	20	18	ϵ	ϵ	X
iajs-399	20	19	x.	x.	NOUN
iajs-399	20	20	4	4	X
iajs-399	20	21	)	)	PUNCT
iajs-399	20	22	‖𝑥,𝑦	‖𝑥,𝑦	NOUN
iajs-399	20	23	+	+	CCONJ
iajs-399	20	24	𝑧‖	𝑧‖	PROPN
iajs-399	20	25	≤	≤	NUM
iajs-399	20	26	‖𝑥	‖𝑥	NOUN
iajs-399	20	27	,	,	PUNCT
iajs-399	20	28	𝑦‖	𝑦‖	PROPN
iajs-399	20	29	+	+	CCONJ
iajs-399	20	30	‖𝑥	‖𝑥	NOUN
iajs-399	20	31	,	,	PUNCT
iajs-399	20	32	𝑧‖	𝑧‖	PROPN
iajs-399	20	33	,	,	PUNCT
iajs-399	20	34	for	for	ADP
iajs-399	20	35	all	all	DET
iajs-399	20	36	𝓍𝓍	𝓍𝓍	PROPN
iajs-399	20	37	,	,	PUNCT
iajs-399	20	38	𝑦	𝑦	PRON
iajs-399	20	39	,	,	PUNCT
iajs-399	20	40	𝑧	𝑧	PROPN
iajs-399	20	41	ϵ	ϵ	NOUN
iajs-399	20	42	x.	x.	NOUN
iajs-399	20	43	then	then	ADV
iajs-399	20	44	(	(	PUNCT
iajs-399	20	45	x	x	X
iajs-399	20	46	,	,	PUNCT
iajs-399	20	47	‖.	‖.	INTJ
iajs-399	20	48	,	,	PUNCT
iajs-399	20	49	.‖	.‖	PROPN
iajs-399	20	50	)	)	PUNCT
iajs-399	20	51	is	be	AUX
iajs-399	20	52	called	call	VERB
iajs-399	20	53	a	a	DET
iajs-399	20	54	2	2	NUM
iajs-399	20	55	-	-	PUNCT
iajs-399	20	56	normed	norme	VERB
iajs-399	20	57	space	space	NOUN
iajs-399	20	58	.	.	PUNCT
iajs-399	21	1	note	note	VERB
iajs-399	21	2	that	that	SCONJ
iajs-399	21	3	the	the	DET
iajs-399	21	4	2	2	NUM
iajs-399	21	5	-	-	PUNCT
iajs-399	21	6	normed	norme	VERB
iajs-399	21	7	space	space	NOUN
iajs-399	21	8	is	be	AUX
iajs-399	21	9	hausdorff	hausdorff	NOUN
iajs-399	21	10	space	space	NOUN
iajs-399	21	11	and	and	CCONJ
iajs-399	21	12	‖.	‖.	INTJ
iajs-399	21	13	,	,	PUNCT
iajs-399	21	14	.‖	.‖	PROPN
iajs-399	21	15	is	be	AUX
iajs-399	21	16	continuous	continuous	ADJ
iajs-399	21	17	function	function	NOUN
iajs-399	21	18	,	,	PUNCT
iajs-399	21	19	for	for	ADP
iajs-399	21	20	examples	example	NOUN
iajs-399	21	21	of	of	ADP
iajs-399	21	22	2	2	NUM
iajs-399	21	23	-	-	PUNCT
iajs-399	21	24	normed	norme	VERB
iajs-399	21	25	spaces	space	NOUN
iajs-399	21	26	see	see	VERB
iajs-399	21	27	[	[	X
iajs-399	21	28	1	1	X
iajs-399	21	29	]	]	PUNCT
iajs-399	21	30	.	.	PUNCT
iajs-399	22	1	the	the	DET
iajs-399	22	2	ball	ball	NOUN
iajs-399	22	3	in	in	ADP
iajs-399	22	4	2	2	NUM
iajs-399	22	5	-	-	PUNCT
iajs-399	22	6	normed	norme	VERB
iajs-399	22	7	space	space	NOUN
iajs-399	22	8	x	x	PUNCT
iajs-399	22	9	with	with	ADP
iajs-399	22	10	center	center	NOUN
iajs-399	22	11	x	x	NOUN
iajs-399	22	12	,	,	PUNCT
iajs-399	22	13	radius	radius	NOUN
iajs-399	22	14	r	r	NOUN
iajs-399	22	15	>	>	X
iajs-399	22	16	0	0	PUNCT
iajs-399	22	17	and	and	CCONJ
iajs-399	22	18	is	be	AUX
iajs-399	22	19	defined	define	VERB
iajs-399	22	20	by	by	ADP
iajs-399	22	21	br(x	br(x	X
iajs-399	22	22	)	)	PUNCT
iajs-399	23	1	=	=	PRON
iajs-399	23	2	{	{	PUNCT
iajs-399	23	3	y	y	PROPN
iajs-399	23	4	,	,	PUNCT
iajs-399	23	5	u	u	NOUN
iajs-399	23	6	ϵ	ϵ	X
iajs-399	23	7	x	x	PROPN
iajs-399	23	8	,	,	PUNCT
iajs-399	23	9	||	||	NOUN
iajs-399	23	10	x	x	X
iajs-399	23	11	–	–	PUNCT
iajs-399	23	12	y	y	NOUN
iajs-399	23	13	,	,	PUNCT
iajs-399	23	14	u	u	NOUN
iajs-399	23	15	||	||	NOUN
iajs-399	24	1	˂	˂	NOUN
iajs-399	24	2	r	r	NOUN
iajs-399	24	3	}	}	PUNCT
iajs-399	24	4	,	,	PUNCT
iajs-399	24	5	and	and	CCONJ
iajs-399	24	6	the	the	DET
iajs-399	24	7	open	open	ADJ
iajs-399	24	8	subset	subset	NOUN
iajs-399	24	9	m	m	NOUN
iajs-399	24	10	of	of	ADP
iajs-399	24	11	x	x	PUNCT
iajs-399	24	12	is	be	AUX
iajs-399	24	13	defined	define	VERB
iajs-399	24	14	as	as	SCONJ
iajs-399	24	15	follows	follow	VERB
iajs-399	24	16	:	:	PUNCT
iajs-399	24	17	for	for	ADP
iajs-399	24	18	any	any	DET
iajs-399	24	19	x	x	SYM
iajs-399	24	20	ϵ	ϵ	NOUN
iajs-399	24	21	m	m	ADV
iajs-399	24	22	there	there	PRON
iajs-399	24	23	is	be	VERB
iajs-399	24	24	r	r	NOUN
iajs-399	24	25	>	>	X
iajs-399	24	26	0	0	NUM
iajs-399	24	27	such	such	ADJ
iajs-399	24	28	that	that	DET
iajs-399	24	29	br(x	br(x	NUM
iajs-399	24	30	)	)	PUNCT
iajs-399	25	1	⊂	⊂	PROPN
iajs-399	25	2	m.	m.	NOUN
iajs-399	25	3	therefore	therefore	ADV
iajs-399	25	4	m	m	PROPN
iajs-399	25	5	is	be	AUX
iajs-399	25	6	called	call	VERB
iajs-399	25	7	closed	closed	ADJ
iajs-399	25	8	subset	subset	NOUN
iajs-399	25	9	of	of	ADP
iajs-399	25	10	x	x	PRON
iajs-399	25	11	if	if	SCONJ
iajs-399	25	12	its	its	PRON
iajs-399	25	13	complement	complement	NOUN
iajs-399	25	14	is	be	AUX
iajs-399	25	15	open	open	ADJ
iajs-399	25	16	.	.	PUNCT
iajs-399	26	1	definition	definition	NOUN
iajs-399	27	1	[	[	X
iajs-399	27	2	9	9	NUM
iajs-399	27	3	]	]	PUNCT
iajs-399	27	4	a	a	DET
iajs-399	27	5	sequence	sequence	NOUN
iajs-399	27	6	(	(	PUNCT
iajs-399	27	7	xn	xn	PROPN
iajs-399	27	8	)	)	PUNCT
iajs-399	27	9	in	in	ADP
iajs-399	27	10	a	a	DET
iajs-399	27	11	2	2	NUM
iajs-399	27	12	-	-	PUNCT
iajs-399	27	13	normed	norme	VERB
iajs-399	27	14	space	space	NOUN
iajs-399	27	15	(	(	PUNCT
iajs-399	27	16	x,||.,.||	x,||.,.||	PROPN
iajs-399	27	17	)	)	PUNCT
iajs-399	27	18	is	be	AUX
iajs-399	27	19	called	call	VERB
iajs-399	27	20	a	a	DET
iajs-399	27	21	convergent	convergent	NOUN
iajs-399	27	22	sequence	sequence	NOUN
iajs-399	27	23	if	if	SCONJ
iajs-399	27	24	there	there	PRON
iajs-399	27	25	is	be	VERB
iajs-399	27	26	,	,	PUNCT
iajs-399	27	27	x	x	PROPN
iajs-399	27	28	ϵ	ϵ	X
iajs-399	27	29	x	x	NOUN
iajs-399	27	30	,	,	PUNCT
iajs-399	27	31	such	such	ADJ
iajs-399	27	32	that	that	PRON
iajs-399	27	33	lim𝑛→∞‖𝑥𝑛	lim𝑛→∞‖𝑥𝑛	PROPN
iajs-399	27	34	−	−	PROPN
iajs-399	28	1	𝑥	𝑥	NOUN
iajs-399	28	2	,	,	PUNCT
iajs-399	28	3	𝑢‖=	𝑢‖=	NOUN
iajs-399	28	4	0	0	NUM
iajs-399	28	5	,	,	PUNCT
iajs-399	28	6	for	for	ADP
iajs-399	28	7	all	all	DET
iajs-399	28	8	u	u	NOUN
iajs-399	28	9	ϵ	ϵ	NOUN
iajs-399	28	10	x.	x.	NOUN
iajs-399	28	11	definition	definition	NOUN
iajs-399	29	1	[	[	X
iajs-399	29	2	9	9	NUM
iajs-399	29	3	]	]	PUNCT
iajs-399	29	4	a	a	DET
iajs-399	29	5	sequence	sequence	NOUN
iajs-399	29	6	(	(	PUNCT
iajs-399	29	7	xn	xn	PROPN
iajs-399	29	8	)	)	PUNCT
iajs-399	29	9	in	in	ADP
iajs-399	29	10	a	a	DET
iajs-399	29	11	2	2	NUM
iajs-399	29	12	-	-	PUNCT
iajs-399	29	13	normed	norme	VERB
iajs-399	29	14	space	space	NOUN
iajs-399	29	15	(	(	PUNCT
iajs-399	29	16	x,||.,.||	x,||.,.||	PROPN
iajs-399	29	17	)	)	PUNCT
iajs-399	29	18	is	be	AUX
iajs-399	29	19	called	call	VERB
iajs-399	29	20	a	a	DET
iajs-399	29	21	cauchy	cauchy	ADJ
iajs-399	29	22	sequence	sequence	NOUN
iajs-399	29	23	if	if	SCONJ
iajs-399	29	24	lim𝑚,𝑛→∞‖𝑥𝑚	lim𝑚,𝑛→∞‖𝑥𝑚	VERB
iajs-399	29	25	−	−	PROPN
iajs-399	29	26	𝑥𝑛	𝑥𝑛	PROPN
iajs-399	29	27	,	,	PUNCT
iajs-399	29	28	𝑦‖	𝑦‖	PROPN
iajs-399	29	29	=	=	SYM
iajs-399	29	30	0	0	NUM
iajs-399	29	31	,	,	PUNCT
iajs-399	29	32	for	for	ADP
iajs-399	29	33	all	all	DET
iajs-399	29	34	𝑦	𝑦	NOUN
iajs-399	29	35	∈	∈	NOUN
iajs-399	29	36	x.	x.	NOUN
iajs-399	29	37	definition	definition	NOUN
iajs-399	30	1	[	[	X
iajs-399	30	2	9	9	NUM
iajs-399	30	3	]	]	X
iajs-399	30	4	a	a	DET
iajs-399	30	5	linear	linear	ADJ
iajs-399	30	6	2	2	NUM
iajs-399	30	7	-	-	PUNCT
iajs-399	30	8	normed	norme	VERB
iajs-399	30	9	space	space	NOUN
iajs-399	30	10	x	x	PUNCT
iajs-399	30	11	is	be	AUX
iajs-399	30	12	said	say	VERB
iajs-399	30	13	to	to	PART
iajs-399	30	14	be	be	AUX
iajs-399	30	15	complete	complete	ADJ
iajs-399	30	16	if	if	SCONJ
iajs-399	30	17	every	every	DET
iajs-399	30	18	cauchy	cauchy	ADJ
iajs-399	30	19	sequence	sequence	NOUN
iajs-399	30	20	is	be	AUX
iajs-399	30	21	convergent	convergent	ADJ
iajs-399	30	22	to	to	ADP
iajs-399	30	23	an	an	DET
iajs-399	30	24	element	element	NOUN
iajs-399	30	25	of	of	ADP
iajs-399	30	26	x.	x.	NOUN
iajs-399	30	27	then	then	ADV
iajs-399	30	28	x	x	VERB
iajs-399	30	29	is	be	AUX
iajs-399	30	30	called	call	VERB
iajs-399	30	31	a	a	DET
iajs-399	30	32	2	2	NUM
iajs-399	30	33	-	-	PUNCT
iajs-399	30	34	banach	banach	NOUN
iajs-399	30	35	space	space	NOUN
iajs-399	30	36	.	.	PUNCT
iajs-399	31	1	definition	definition	NOUN
iajs-399	31	2	[	[	X
iajs-399	31	3	9	9	X
iajs-399	31	4	]	]	PUNCT
iajs-399	31	5	let	let	VERB
iajs-399	31	6	x	x	PRON
iajs-399	31	7	be	be	AUX
iajs-399	31	8	a	a	DET
iajs-399	31	9	2	2	NUM
iajs-399	31	10	-	-	PUNCT
iajs-399	31	11	banach	banach	NOUN
iajs-399	31	12	space	space	NOUN
iajs-399	31	13	and	and	CCONJ
iajs-399	31	14	t	t	PROPN
iajs-399	31	15	:	:	PUNCT
iajs-399	31	16	x→x	x→x	NUM
iajs-399	31	17	be	be	AUX
iajs-399	31	18	a	a	DET
iajs-399	31	19	mapping	mapping	NOUN
iajs-399	31	20	t	t	NOUN
iajs-399	31	21	is	be	AUX
iajs-399	31	22	said	say	VERB
iajs-399	31	23	to	to	PART
iajs-399	31	24	be	be	AUX
iajs-399	31	25	continuous	continuous	ADJ
iajs-399	31	26	at	at	ADP
iajs-399	31	27	x	x	PUNCT
iajs-399	31	28	if	if	SCONJ
iajs-399	31	29	for	for	ADP
iajs-399	31	30	every	every	DET
iajs-399	31	31	sequence	sequence	NOUN
iajs-399	31	32	(	(	PUNCT
iajs-399	31	33	𝓍𝓍n	𝓍𝓍n	NOUN
iajs-399	31	34	)	)	PUNCT
iajs-399	31	35	in	in	ADP
iajs-399	31	36	x	x	PRON
iajs-399	31	37	,	,	PUNCT
iajs-399	31	38	(	(	PUNCT
iajs-399	31	39	𝓍𝓍n	𝓍𝓍n	NOUN
iajs-399	31	40	)	)	PUNCT
iajs-399	31	41	→𝓍𝓍	→𝓍𝓍	NOUN
iajs-399	31	42	as	as	SCONJ
iajs-399	31	43	n→∞	n→∞	PRON
iajs-399	31	44	implies	imply	VERB
iajs-399	31	45	that	that	SCONJ
iajs-399	31	46	{	{	PUNCT
iajs-399	31	47	t(𝓍𝓍n	t(𝓍𝓍n	NOUN
iajs-399	31	48	)	)	PUNCT
iajs-399	31	49	}	}	PUNCT
iajs-399	31	50	→t(𝓍𝓍	→t(𝓍𝓍	PROPN
iajs-399	31	51	)	)	PUNCT
iajs-399	31	52	as	as	ADP
iajs-399	31	53	n→∞.	n→∞.	NUM
iajs-399	31	54	we	we	PRON
iajs-399	31	55	need	need	VERB
iajs-399	31	56	to	to	PART
iajs-399	31	57	give	give	VERB
iajs-399	31	58	some	some	DET
iajs-399	31	59	concepts	concept	NOUN
iajs-399	31	60	in	in	ADP
iajs-399	31	61	the	the	DET
iajs-399	31	62	setting	setting	NOUN
iajs-399	31	63	of	of	ADP
iajs-399	31	64	2	2	NUM
iajs-399	31	65	-	-	PUNCT
iajs-399	31	66	normed	norme	VERB
iajs-399	31	67	space	space	NOUN
iajs-399	31	68	x	x	PUNCT
iajs-399	31	69	as	as	SCONJ
iajs-399	31	70	the	the	DET
iajs-399	31	71	first	first	ADJ
iajs-399	31	72	dual	dual	ADJ
iajs-399	31	73	and	and	CCONJ
iajs-399	31	74	the	the	DET
iajs-399	31	75	second	second	ADJ
iajs-399	31	76	dual	dual	ADJ
iajs-399	31	77	of	of	ADP
iajs-399	31	78	x	x	SYM
iajs-399	31	79	are	be	AUX
iajs-399	31	80	defined	define	VERB
iajs-399	31	81	by	by	ADP
iajs-399	31	82	x*=	x*=	PROPN
iajs-399	31	83	{	{	PUNCT
iajs-399	31	84	f	f	PROPN
iajs-399	31	85	l	l	NOUN
iajs-399	31	86	f	f	PROPN
iajs-399	31	87	:x	:x	PROPN
iajs-399	31	88	→ℝ	→ℝ	PROPN
iajs-399	31	89	,	,	PUNCT
iajs-399	31	90	bounded	bound	VERB
iajs-399	31	91	linear	linear	PROPN
iajs-399	31	92	function	function	PROPN
iajs-399	31	93	}	}	PUNCT
iajs-399	31	94	,	,	PUNCT
iajs-399	31	95	x**=	x**=	PROPN
iajs-399	31	96	{	{	PUNCT
iajs-399	31	97	g	g	NOUN
iajs-399	31	98	l	l	NOUN
iajs-399	31	99	g	g	PROPN
iajs-399	31	100	:	:	PUNCT
iajs-399	32	1	x*→	x*→	PROPN
iajs-399	32	2	ℝ	ℝ	PROPN
iajs-399	32	3	,	,	PUNCT
iajs-399	32	4	bounded	bound	VERB
iajs-399	32	5	linear	linear	PROPN
iajs-399	32	6	function	function	PROPN
iajs-399	32	7	}	}	PUNCT
iajs-399	32	8	.	.	PUNCT
iajs-399	33	1	respectively	respectively	ADV
iajs-399	33	2	,	,	PUNCT
iajs-399	33	3	then	then	ADV
iajs-399	33	4	the	the	DET
iajs-399	33	5	mapping	mapping	NOUN
iajs-399	33	6	j	j	PROPN
iajs-399	33	7	:	:	PUNCT
iajs-399	33	8	x→	x→	PUNCT
iajs-399	34	1	x	x	X
iajs-399	34	2	*	*	PUNCT
iajs-399	34	3	,	,	PUNCT
iajs-399	34	4	where	where	SCONJ
iajs-399	34	5	j(x	j(x	NOUN
iajs-399	34	6	)	)	PUNCT
iajs-399	34	7	=	=	SYM
iajs-399	34	8	fx(f	fx(f	X
iajs-399	34	9	)	)	PUNCT
iajs-399	34	10	=	=	SYM
iajs-399	34	11	f(x	f(x	PROPN
iajs-399	34	12	)	)	PUNCT
iajs-399	34	13	,	,	PUNCT
iajs-399	35	1	f	f	PROPN
iajs-399	36	1	ϵ	ϵ	X
iajs-399	36	2	x	x	X
iajs-399	36	3	*	*	VERB
iajs-399	36	4	is	be	AUX
iajs-399	36	5	called	call	VERB
iajs-399	36	6	a	a	DET
iajs-399	36	7	natural	natural	ADJ
iajs-399	36	8	embedding	embedding	NOUN
iajs-399	36	9	,	,	PUNCT
iajs-399	36	10	so	so	SCONJ
iajs-399	36	11	we	we	PRON
iajs-399	36	12	say	say	VERB
iajs-399	36	13	that	that	SCONJ
iajs-399	36	14	x	x	PRON
iajs-399	36	15	is	be	AUX
iajs-399	36	16	reflexive	reflexive	ADJ
iajs-399	36	17	if	if	SCONJ
iajs-399	36	18	the	the	DET
iajs-399	36	19	natural	natural	ADJ
iajs-399	36	20	embedding	embedding	NOUN
iajs-399	36	21	is	be	AUX
iajs-399	36	22	an	an	PRON
iajs-399	36	23	onto	onto	ADP
iajs-399	36	24	mapping	mapping	NOUN
iajs-399	36	25	.	.	PUNCT
iajs-399	37	1	344	344	NUM
iajs-399	38	1	|	|	ADV
iajs-399	38	2	mathematics	mathematics	PROPN
iajs-399	38	3	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	NUM
iajs-399	38	4	�	�	NOUN
iajs-399	38	5	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	NUM
iajs-399	38	6	:	:	PUNCT
iajs-399	38	7	a@âig@ú‹	a@âig@ú‹	PROPN
iajs-399	39	1	©	©	PROPN
iajs-399	39	2	@ü‹127@@öü»€a@i1@‚b«@h2014	@ü‹127@@öü»€a@i1@‚b«@h2014	PROPN
iajs-399	39	3	ibn	ibn	PROPN
iajs-399	39	4	al	al	PROPN
iajs-399	39	5	-	-	PUNCT
iajs-399	39	6	haitham	haitham	PROPN
iajs-399	39	7	jour	jour	X
iajs-399	39	8	.	.	PROPN
iajs-399	39	9	for	for	ADP
iajs-399	39	10	pure	pure	ADJ
iajs-399	39	11	&	&	CCONJ
iajs-399	39	12	appl	appl	PROPN
iajs-399	39	13	.	.	PUNCT
iajs-399	40	1	sci	sci	PROPN
iajs-399	40	2	.	.	PUNCT
iajs-399	40	3	vol	vol	NOUN
iajs-399	40	4	.	.	PROPN
iajs-399	41	1	27	27	NUM
iajs-399	41	2	(	(	PUNCT
iajs-399	41	3	1	1	NUM
iajs-399	41	4	)	)	PUNCT
iajs-399	41	5	2014	2014	NUM
iajs-399	41	6	definition	definition	NOUN
iajs-399	41	7	[	[	X
iajs-399	41	8	10	10	NUM
iajs-399	41	9	]	]	PUNCT
iajs-399	41	10	let	let	VERB
iajs-399	41	11	x	x	PRON
iajs-399	41	12	be	be	AUX
iajs-399	41	13	a	a	DET
iajs-399	41	14	2	2	NUM
iajs-399	41	15	-	-	PUNCT
iajs-399	41	16	normed	normed	ADJ
iajs-399	41	17	space	space	NOUN
iajs-399	41	18	,	,	PUNCT
iajs-399	41	19	(	(	PUNCT
iajs-399	41	20	𝓍𝓍n	𝓍𝓍n	NOUN
iajs-399	41	21	)	)	PUNCT
iajs-399	41	22	be	be	AUX
iajs-399	41	23	a	a	DET
iajs-399	41	24	sequence	sequence	NOUN
iajs-399	41	25	in	in	ADP
iajs-399	41	26	x	x	SYM
iajs-399	41	27	,	,	PUNCT
iajs-399	41	28	then	then	ADV
iajs-399	41	29	(	(	PUNCT
iajs-399	41	30	𝓍𝓍n	𝓍𝓍n	NOUN
iajs-399	41	31	)	)	PUNCT
iajs-399	41	32	is	be	AUX
iajs-399	41	33	said	say	VERB
iajs-399	41	34	to	to	PART
iajs-399	41	35	be	be	AUX
iajs-399	41	36	converges	converge	NOUN
iajs-399	41	37	weakly	weakly	ADJ
iajs-399	41	38	to	to	ADP
iajs-399	41	39	𝓍𝓍	𝓍𝓍	PRON
iajs-399	41	40	denoted	denote	VERB
iajs-399	41	41	by	by	ADP
iajs-399	41	42	𝓍𝓍n	𝓍𝓍n	NOUN
iajs-399	41	43	→𝓍𝓍	→𝓍𝓍	PROPN
iajs-399	41	44	as	as	ADP
iajs-399	41	45	n	n	PROPN
iajs-399	41	46	→	→	SYM
iajs-399	41	47	∞	∞	PROPN
iajs-399	41	48	,	,	PUNCT
iajs-399	41	49	if	if	SCONJ
iajs-399	41	50	f(𝓍𝓍n	f(𝓍𝓍n	ADJ
iajs-399	41	51	)	)	PUNCT
iajs-399	41	52	→	→	SYM
iajs-399	41	53	f(𝓍𝓍	f(𝓍𝓍	NUM
iajs-399	41	54	)	)	PUNCT
iajs-399	41	55	as	as	ADP
iajs-399	41	56	n	n	PROPN
iajs-399	41	57	→	→	SYM
iajs-399	41	58	∞.	∞.	PROPN
iajs-399	41	59	definition	definition	NOUN
iajs-399	41	60	[	[	X
iajs-399	41	61	11	11	NUM
iajs-399	41	62	]	]	X
iajs-399	41	63	a	a	DET
iajs-399	41	64	2	2	NUM
iajs-399	41	65	-	-	PUNCT
iajs-399	41	66	normed	norme	VERB
iajs-399	41	67	space	space	NOUN
iajs-399	41	68	(	(	PUNCT
iajs-399	41	69	x,||.,.||	x,||.,.||	PROPN
iajs-399	41	70	)	)	PUNCT
iajs-399	41	71	is	be	AUX
iajs-399	41	72	said	say	VERB
iajs-399	41	73	to	to	PART
iajs-399	41	74	be	be	AUX
iajs-399	41	75	uniformly	uniformly	ADV
iajs-399	41	76	convex	convex	ADJ
iajs-399	41	77	if	if	SCONJ
iajs-399	41	78	for	for	ADP
iajs-399	41	79	every	every	DET
iajs-399	41	80	ε	ε	PROPN
iajs-399	41	81	ϵ	ϵ	X
iajs-399	41	82	(	(	PUNCT
iajs-399	41	83	0,2	0,2	NUM
iajs-399	41	84	]	]	PUNCT
iajs-399	41	85	and	and	CCONJ
iajs-399	41	86	u	u	NOUN
iajs-399	41	87	≠	≠	PROPN
iajs-399	41	88	0	0	NUM
iajs-399	41	89	in	in	ADP
iajs-399	41	90	x	x	SYM
iajs-399	41	91	,	,	PUNCT
iajs-399	41	92	there	there	PRON
iajs-399	41	93	exists	exist	VERB
iajs-399	41	94	α	α	PROPN
iajs-399	41	95	>	>	X
iajs-399	41	96	0	0	NUM
iajs-399	42	1	such	such	ADJ
iajs-399	42	2	that	that	PRON
iajs-399	42	3	||	||	NOUN
iajs-399	43	1	𝓍𝓍	𝓍𝓍	INTJ
iajs-399	43	2	,	,	PUNCT
iajs-399	43	3	u	u	NOUN
iajs-399	43	4	||	||	NOUN
iajs-399	43	5	≤	≤	NUM
iajs-399	43	6	1	1	NUM
iajs-399	43	7	;	;	PUNCT
iajs-399	43	8	||	||	X
iajs-399	44	1	y	y	PROPN
iajs-399	44	2	,	,	PUNCT
iajs-399	44	3	u	u	NOUN
iajs-399	44	4	||	||	NOUN
iajs-399	44	5	≤	≤	NUM
iajs-399	44	6	1	1	NUM
iajs-399	44	7	and	and	CCONJ
iajs-399	44	8	||	||	NUM
iajs-399	44	9	𝓍𝓍	𝓍𝓍	PROPN
iajs-399	44	10	–	–	PUNCT
iajs-399	44	11	y	y	PROPN
iajs-399	44	12	,	,	PUNCT
iajs-399	44	13	u	u	PROPN
iajs-399	44	14	||	||	NOUN
iajs-399	44	15	≥	≥	NUM
iajs-399	44	16	ε	ε	PROPN
iajs-399	44	17	implies	imply	VERB
iajs-399	44	18	that	that	SCONJ
iajs-399	44	19	||	||	NOUN
iajs-399	44	20	12	12	NUM
iajs-399	44	21	(	(	PUNCT
iajs-399	44	22	𝓍𝓍	𝓍𝓍	PROPN
iajs-399	44	23	+	+	NUM
iajs-399	44	24	y	y	PROPN
iajs-399	44	25	)	)	PUNCT
iajs-399	44	26	,	,	PUNCT
iajs-399	45	1	u	u	NOUN
iajs-399	45	2	||	||	NOUN
iajs-399	45	3	≤	≤	NUM
iajs-399	45	4	1	1	NUM
iajs-399	45	5	α	α	NOUN
iajs-399	45	6	.	.	PUNCT
iajs-399	46	1	definition	definition	NOUN
iajs-399	46	2	let	let	VERB
iajs-399	46	3	x	x	PRON
iajs-399	46	4	be	be	AUX
iajs-399	46	5	a	a	DET
iajs-399	46	6	2	2	NUM
iajs-399	46	7	-	-	PUNCT
iajs-399	46	8	normed	normed	ADJ
iajs-399	46	9	space	space	NOUN
iajs-399	46	10	,	,	PUNCT
iajs-399	46	11	then	then	ADV
iajs-399	46	12	we	we	PRON
iajs-399	46	13	say	say	VERB
iajs-399	46	14	that	that	SCONJ
iajs-399	46	15	x	x	PRON
iajs-399	46	16	satisfies	satisfy	VERB
iajs-399	46	17	opial	opial	ADJ
iajs-399	46	18	condition	condition	NOUN
iajs-399	46	19	if	if	SCONJ
iajs-399	46	20	for	for	ADP
iajs-399	46	21	every	every	DET
iajs-399	46	22	bounded	bounded	ADJ
iajs-399	46	23	sequence	sequence	NOUN
iajs-399	46	24	(	(	PUNCT
iajs-399	46	25	𝓍𝓍n	𝓍𝓍n	NOUN
iajs-399	46	26	)	)	PUNCT
iajs-399	46	27	ϵ	ϵ	NOUN
iajs-399	46	28	x	x	PUNCT
iajs-399	46	29	converges	converge	VERB
iajs-399	46	30	weakly	weakly	ADJ
iajs-399	46	31	to	to	ADP
iajs-399	46	32	𝓍𝓍	𝓍𝓍	PRON
iajs-399	46	33	ϵ	ϵ	ADP
iajs-399	46	34	x	x	NOUN
iajs-399	46	35	,	,	PUNCT
iajs-399	46	36	then	then	ADV
iajs-399	46	37	lim𝑛→∞	lim𝑛→∞	PROPN
iajs-399	46	38	inf	inf	PROPN
iajs-399	46	39	�	�	PROPN
iajs-399	46	40	|xn	|xn	NOUN
iajs-399	46	41	−	−	PROPN
iajs-399	46	42	x	x	SYM
iajs-399	46	43	,	,	PUNCT
iajs-399	46	44	u|	u|	PROPN
iajs-399	46	45	�	�	PROPN
iajs-399	46	46	˂	˂	PROPN
iajs-399	46	47	limn→∞	limn→∞	PROPN
iajs-399	46	48	𝑖𝑛𝑓	𝑖𝑛𝑓	SYM
iajs-399	46	49	�	�	PROPN
iajs-399	46	50	|xn	|xn	NOUN
iajs-399	46	51	−	−	PROPN
iajs-399	46	52	y	y	PROPN
iajs-399	46	53	,	,	PUNCT
iajs-399	46	54	u|	u|	PROPN
iajs-399	46	55	�	�	PROPN
iajs-399	46	56	for	for	ADP
iajs-399	46	57	every	every	DET
iajs-399	46	58	x	x	SYM
iajs-399	46	59	≠	≠	PROPN
iajs-399	46	60	y	y	PROPN
iajs-399	46	61	&	&	CCONJ
iajs-399	46	62	𝑦	𝑦	PROPN
iajs-399	46	63	,	,	PUNCT
iajs-399	46	64	𝑢	𝑢	PROPN
iajs-399	46	65	𝜖	𝜖	PROPN
iajs-399	46	66	𝑋.	𝑋.	PROPN
iajs-399	46	67	definition	definition	NOUN
iajs-399	46	68	let	let	VERB
iajs-399	46	69	x	x	PRON
iajs-399	46	70	be	be	AUX
iajs-399	46	71	a	a	DET
iajs-399	46	72	2	2	NUM
iajs-399	46	73	-	-	PUNCT
iajs-399	46	74	normed	normed	ADJ
iajs-399	46	75	space	space	NOUN
iajs-399	46	76	.	.	PUNCT
iajs-399	47	1	with	with	ADP
iajs-399	47	2	the	the	DET
iajs-399	47	3	mapping	mapping	NOUN
iajs-399	47	4	t	t	NOUN
iajs-399	47	5	:	:	PUNCT
iajs-399	47	6	x	x	X
iajs-399	47	7	→	→	PUNCT
iajs-399	47	8	x	x	SYM
iajs-399	47	9	it	it	PRON
iajs-399	47	10	is	be	AUX
iajs-399	47	11	said	say	VERB
iajs-399	47	12	to	to	PART
iajs-399	47	13	be	be	AUX
iajs-399	47	14	lipschitzian	lipschitzian	ADJ
iajs-399	47	15	if	if	SCONJ
iajs-399	47	16	there	there	PRON
iajs-399	47	17	exists	exist	VERB
iajs-399	47	18	constant	constant	ADJ
iajs-399	47	19	α	α	PRON
iajs-399	47	20	≥	≥	NOUN
iajs-399	47	21	0	0	NUM
iajs-399	47	22	such	such	ADJ
iajs-399	47	23	that	that	DET
iajs-399	47	24	||t(x	||t(x	NOUN
iajs-399	47	25	)	)	PUNCT
iajs-399	47	26	t(y	t(y	NOUN
iajs-399	47	27	)	)	PUNCT
iajs-399	47	28	,	,	PUNCT
iajs-399	47	29	u||	u||	ADV
iajs-399	47	30	≤	≤	NUM
iajs-399	47	31	α	α	DET
iajs-399	47	32	||x	||x	NOUN
iajs-399	47	33	–	–	PUNCT
iajs-399	47	34	y	y	NOUN
iajs-399	47	35	,	,	PUNCT
iajs-399	47	36	u||	u||	ADV
iajs-399	47	37	for	for	ADP
iajs-399	47	38	all	all	DET
iajs-399	47	39	x	x	SYM
iajs-399	47	40	,	,	PUNCT
iajs-399	47	41	y	y	PROPN
iajs-399	47	42	,	,	PUNCT
iajs-399	47	43	u	u	NOUN
iajs-399	47	44	ϵ	ϵ	X
iajs-399	47	45	x	x	X
iajs-399	47	46	…	…	PUNCT
iajs-399	47	47	(	(	PUNCT
iajs-399	47	48	1.1	1.1	NUM
iajs-399	47	49	)	)	PUNCT
iajs-399	47	50	iiif	iiif	PROPN
iajs-399	48	1	α	α	NOUN
iajs-399	48	2	=	=	NOUN
iajs-399	48	3	1	1	NUM
iajs-399	48	4	then	then	ADV
iajs-399	48	5	t	t	PROPN
iajs-399	48	6	is	be	AUX
iajs-399	48	7	said	say	VERB
iajs-399	48	8	to	to	PART
iajs-399	48	9	be	be	AUX
iajs-399	48	10	non	non	ADJ
iajs-399	48	11	-	-	ADJ
iajs-399	48	12	expansive	expansive	ADJ
iajs-399	48	13	mapping	mapping	NOUN
iajs-399	48	14	such	such	ADJ
iajs-399	48	15	that	that	DET
iajs-399	48	16	||t𝓍𝓍	||t𝓍𝓍	NOUN
iajs-399	48	17	–	–	PUNCT
iajs-399	48	18	ty	ty	INTJ
iajs-399	48	19	,	,	PUNCT
iajs-399	48	20	u	u	NOUN
iajs-399	48	21	||	||	NOUN
iajs-399	48	22	≤	≤	NUM
iajs-399	48	23	||	||	PUNCT
iajs-399	49	1	𝓍𝓍	𝓍𝓍	PROPN
iajs-399	49	2	–	–	PUNCT
iajs-399	49	3	y	y	PROPN
iajs-399	49	4	,	,	PUNCT
iajs-399	49	5	u	u	PROPN
iajs-399	49	6	||	||	ADV
iajs-399	49	7	;	;	PUNCT
iajs-399	49	8	𝓍𝓍	𝓍𝓍	PRON
iajs-399	49	9	,	,	PUNCT
iajs-399	49	10	y	y	PROPN
iajs-399	49	11	,	,	PUNCT
iajs-399	49	12	u	u	NOUN
iajs-399	49	13	ϵ	ϵ	X
iajs-399	49	14	x	x	X
iajs-399	49	15	…	…	PUNCT
iajs-399	49	16	(	(	PUNCT
iajs-399	49	17	1.2	1.2	NUM
iajs-399	49	18	)	)	PUNCT
iajs-399	49	19	definition	definition	NOUN
iajs-399	49	20	let	let	VERB
iajs-399	49	21	x	x	PRON
iajs-399	49	22	be	be	AUX
iajs-399	49	23	a	a	DET
iajs-399	49	24	2	2	NUM
iajs-399	49	25	-	-	PUNCT
iajs-399	49	26	normed	normed	ADJ
iajs-399	49	27	space	space	NOUN
iajs-399	49	28	,	,	PUNCT
iajs-399	49	29	then	then	ADV
iajs-399	49	30	the	the	DET
iajs-399	49	31	mapping	mapping	NOUN
iajs-399	49	32	t	t	NOUN
iajs-399	49	33	:	:	PUNCT
iajs-399	49	34	x→x	x→x	NUM
iajs-399	49	35	is	be	AUX
iajs-399	49	36	said	say	VERB
iajs-399	49	37	to	to	PART
iajs-399	49	38	be	be	AUX
iajs-399	49	39	asymp	asymp	NOUN
iajs-399	49	40	-	-	PUNCT
iajs-399	49	41	totically	totically	ADV
iajs-399	49	42	nonexpansive	nonexpansive	ADJ
iajs-399	49	43	mapping	mapping	NOUN
iajs-399	49	44	if	if	SCONJ
iajs-399	49	45	there	there	PRON
iajs-399	49	46	exists	exist	VERB
iajs-399	49	47	a	a	DET
iajs-399	49	48	positive	positive	ADJ
iajs-399	49	49	sequence	sequence	NOUN
iajs-399	49	50	(	(	PUNCT
iajs-399	49	51	kn	kn	PROPN
iajs-399	49	52	)	)	PUNCT
iajs-399	49	53	ϵ	ϵ	PROPN
iajs-399	50	1	[	[	X
iajs-399	50	2	1,∞	1,∞	NUM
iajs-399	50	3	)	)	PUNCT
iajs-399	50	4	with	with	ADP
iajs-399	50	5	lim𝑛→∞(𝑘𝑛	lim𝑛→∞(𝑘𝑛	NOUN
iajs-399	50	6	)	)	PUNCT
iajs-399	50	7	=	=	SYM
iajs-399	50	8	1	1	NUM
iajs-399	50	9	,	,	PUNCT
iajs-399	50	10	such	such	ADJ
iajs-399	50	11	that	that	DET
iajs-399	50	12	||tn𝓍𝓍	||tn𝓍𝓍	PROPN
iajs-399	50	13	tny	tny	PROPN
iajs-399	50	14	,	,	PUNCT
iajs-399	50	15	u	u	PROPN
iajs-399	50	16	||	||	NOUN
iajs-399	50	17	≤	≤	NUM
iajs-399	51	1	kn	kn	PROPN
iajs-399	51	2	||	||	PROPN
iajs-399	52	1	𝓍𝓍	𝓍𝓍	PROPN
iajs-399	52	2	–	–	PUNCT
iajs-399	52	3	y	y	PROPN
iajs-399	52	4	,	,	PUNCT
iajs-399	52	5	u	u	NOUN
iajs-399	52	6	||	||	NOUN
iajs-399	52	7	…	…	PUNCT
iajs-399	52	8	(	(	PUNCT
iajs-399	52	9	1.3	1.3	NUM
iajs-399	52	10	)	)	PUNCT
iajs-399	52	11	for	for	ADP
iajs-399	52	12	all	all	DET
iajs-399	52	13	𝓍𝓍	𝓍𝓍	PROPN
iajs-399	52	14	,	,	PUNCT
iajs-399	52	15	y	y	PROPN
iajs-399	52	16	,	,	PUNCT
iajs-399	52	17	u	u	NOUN
iajs-399	52	18	ϵ	ϵ	X
iajs-399	52	19	x	x	X
iajs-399	52	20	and	and	CCONJ
iajs-399	52	21	n	n	PRON
iajs-399	52	22	≥1	≥1	NUM
iajs-399	52	23	.	.	PUNCT
iajs-399	52	24	.	.	PUNCT
iajs-399	53	1	definition	definition	NOUN
iajs-399	53	2	i.	i.	NOUN
iajs-399	53	3	if	if	SCONJ
iajs-399	53	4	s	s	VERB
iajs-399	53	5	a	a	DET
iajs-399	53	6	nonempty	nonempty	NOUN
iajs-399	53	7	subset	subset	NOUN
iajs-399	53	8	of	of	ADP
iajs-399	53	9	a	a	DET
iajs-399	53	10	2	2	NUM
iajs-399	53	11	-	-	PUNCT
iajs-399	53	12	normed	norme	VERB
iajs-399	53	13	space	space	NOUN
iajs-399	53	14	x	x	PUNCT
iajs-399	53	15	and	and	CCONJ
iajs-399	53	16	(	(	PUNCT
iajs-399	53	17	xn	xn	X
iajs-399	53	18	)	)	PUNCT
iajs-399	53	19	a	a	DET
iajs-399	53	20	bounded	bounded	ADJ
iajs-399	53	21	sequence	sequence	NOUN
iajs-399	53	22	in	in	ADP
iajs-399	53	23	x.	x.	NOUN
iajs-399	53	24	consider	consider	VERB
iajs-399	53	25	the	the	DET
iajs-399	53	26	functional	functional	ADJ
iajs-399	53	27	ra	ra	PROPN
iajs-399	53	28	(	(	PUNCT
iajs-399	53	29	·	·	PUNCT
iajs-399	53	30	,	,	PUNCT
iajs-399	53	31	(	(	PUNCT
iajs-399	53	32	xn	xn	NOUN
iajs-399	53	33	)	)	PUNCT
iajs-399	53	34	)	)	PUNCT
iajs-399	53	35	:	:	PUNCT
iajs-399	54	1	x	x	PUNCT
iajs-399	54	2	×	×	NOUN
iajs-399	54	3	x	x	PUNCT
iajs-399	54	4	→	→	X
iajs-399	54	5	r+	r+	PRON
iajs-399	54	6	defined	define	VERB
iajs-399	54	7	by	by	ADP
iajs-399	54	8	ra(x	ra(x	NOUN
iajs-399	54	9	,	,	PUNCT
iajs-399	54	10	(	(	PUNCT
iajs-399	54	11	xn	xn	NOUN
iajs-399	54	12	)	)	PUNCT
iajs-399	54	13	)	)	PUNCT
iajs-399	55	1	=	=	SYM
iajs-399	55	2	lim𝑛→∞	lim𝑛→∞	NOUN
iajs-399	55	3	𝑠𝑢𝑝||𝑥𝑛	𝑠𝑢𝑝||𝑥𝑛	ADJ
iajs-399	56	1	−	−	PROPN
iajs-399	57	1	𝑥,𝑢||	𝑥,𝑢||	INTJ
iajs-399	57	2	;	;	PUNCT
iajs-399	57	3	x	x	X
iajs-399	57	4	,	,	PUNCT
iajs-399	57	5	u	u	NOUN
iajs-399	57	6	ϵ	ϵ	X
iajs-399	57	7	x	x	PROPN
iajs-399	57	8	.	.	PUNCT
iajs-399	57	9	ii	ii	PROPN
iajs-399	57	10	.	.	PUNCT
iajs-399	58	1	the	the	DET
iajs-399	58	2	infimum	infimum	NOUN
iajs-399	58	3	of	of	ADP
iajs-399	58	4	ra	ra	PROPN
iajs-399	58	5	(	(	PUNCT
iajs-399	58	6	·	·	PUNCT
iajs-399	58	7	,	,	PUNCT
iajs-399	58	8	(	(	PUNCT
iajs-399	58	9	xn	xn	NOUN
iajs-399	58	10	)	)	PUNCT
iajs-399	58	11	)	)	PUNCT
iajs-399	58	12	over	over	ADP
iajs-399	58	13	s	s	NOUN
iajs-399	58	14	is	be	AUX
iajs-399	58	15	said	say	VERB
iajs-399	58	16	to	to	PART
iajs-399	58	17	be	be	AUX
iajs-399	58	18	the	the	DET
iajs-399	58	19	asymptotic	asymptotic	ADJ
iajs-399	58	20	radius	radius	NOUN
iajs-399	58	21	of	of	ADP
iajs-399	58	22	(	(	PUNCT
iajs-399	58	23	xn	xn	PROPN
iajs-399	58	24	)	)	PUNCT
iajs-399	58	25	with	with	ADP
iajs-399	58	26	respect	respect	NOUN
iajs-399	58	27	to	to	ADP
iajs-399	58	28	s	s	PRON
iajs-399	58	29	and	and	CCONJ
iajs-399	58	30	is	be	AUX
iajs-399	58	31	denoted	denote	VERB
iajs-399	58	32	by	by	ADP
iajs-399	58	33	ra(s	ra(	NOUN
iajs-399	58	34	,	,	PUNCT
iajs-399	58	35	(	(	PUNCT
iajs-399	58	36	xn	xn	NOUN
iajs-399	58	37	)	)	PUNCT
iajs-399	58	38	)	)	PUNCT
iajs-399	58	39	.	.	PUNCT
iajs-399	59	1	a	a	DET
iajs-399	59	2	point	point	NOUN
iajs-399	59	3	z	z	NOUN
iajs-399	59	4	∈	∈	NOUN
iajs-399	59	5	s	s	VERB
iajs-399	59	6	is	be	AUX
iajs-399	59	7	said	say	VERB
iajs-399	59	8	to	to	PART
iajs-399	59	9	be	be	AUX
iajs-399	59	10	an	an	DET
iajs-399	59	11	asymptotic	asymptotic	ADJ
iajs-399	59	12	center	center	NOUN
iajs-399	59	13	of	of	ADP
iajs-399	59	14	the	the	DET
iajs-399	59	15	sequence	sequence	NOUN
iajs-399	59	16	(	(	PUNCT
iajs-399	59	17	xn	xn	PROPN
iajs-399	59	18	)	)	PUNCT
iajs-399	59	19	with	with	ADP
iajs-399	59	20	respect	respect	NOUN
iajs-399	59	21	to	to	ADP
iajs-399	59	22	s	s	PRON
iajs-399	59	23	if	if	SCONJ
iajs-399	59	24	ra(z	ra(z	NOUN
iajs-399	59	25	,	,	PUNCT
iajs-399	59	26	(	(	PUNCT
iajs-399	59	27	xn	xn	NOUN
iajs-399	59	28	)	)	PUNCT
iajs-399	59	29	)	)	PUNCT
iajs-399	60	1	=	=	SYM
iajs-399	60	2	inf	inf	NOUN
iajs-399	60	3	{	{	PUNCT
iajs-399	60	4	ra(x	ra(x	NOUN
iajs-399	60	5	,	,	PUNCT
iajs-399	60	6	(	(	PUNCT
iajs-399	60	7	xn	xn	NOUN
iajs-399	60	8	)	)	PUNCT
iajs-399	60	9	)	)	PUNCT
iajs-399	60	10	:	:	PUNCT
iajs-399	61	1	x	x	X
iajs-399	61	2	∈	∈	PROPN
iajs-399	61	3	s	s	PART
iajs-399	61	4	}	}	PUNCT
iajs-399	61	5	the	the	DET
iajs-399	61	6	set	set	NOUN
iajs-399	61	7	of	of	ADP
iajs-399	61	8	all	all	DET
iajs-399	61	9	asymptotic	asymptotic	ADJ
iajs-399	61	10	centers	center	NOUN
iajs-399	61	11	of	of	ADP
iajs-399	61	12	(	(	PUNCT
iajs-399	61	13	xn	xn	PROPN
iajs-399	61	14	)	)	PUNCT
iajs-399	61	15	with	with	ADP
iajs-399	61	16	respect	respect	NOUN
iajs-399	61	17	to	to	ADP
iajs-399	61	18	s	s	PRON
iajs-399	61	19	is	be	AUX
iajs-399	61	20	denoted	denote	VERB
iajs-399	61	21	by	by	ADP
iajs-399	61	22	za(s,(xn)).if	za(s,(xn)).if	NOUN
iajs-399	61	23	(	(	PUNCT
iajs-399	61	24	xn	xn	X
iajs-399	61	25	)	)	PUNCT
iajs-399	61	26	converges	converge	VERB
iajs-399	61	27	strongly	strongly	ADV
iajs-399	61	28	to	to	ADP
iajs-399	61	29	x	x	SYM
iajs-399	61	30	∈	∈	PROPN
iajs-399	61	31	s	s	NOUN
iajs-399	61	32	,	,	PUNCT
iajs-399	61	33	then	then	ADV
iajs-399	61	34	za(s	za(s	NUM
iajs-399	61	35	,	,	PUNCT
iajs-399	61	36	(	(	PUNCT
iajs-399	61	37	xn	xn	NOUN
iajs-399	61	38	)	)	PUNCT
iajs-399	61	39	)	)	PUNCT
iajs-399	62	1	=	=	PRON
iajs-399	62	2	{	{	PUNCT
iajs-399	62	3	x	x	NOUN
iajs-399	62	4	}	}	PUNCT
iajs-399	62	5	.	.	PUNCT
iajs-399	63	1	results	result	NOUN
iajs-399	63	2	in	in	ADP
iajs-399	63	3	2	2	NUM
iajs-399	63	4	-	-	PUNCT
iajs-399	63	5	banach	banach	NOUN
iajs-399	63	6	spaces	space	NOUN
iajs-399	63	7	we	we	PRON
iajs-399	63	8	begin	begin	VERB
iajs-399	63	9	with	with	ADP
iajs-399	63	10	the	the	DET
iajs-399	63	11	following	following	NOUN
iajs-399	63	12	:	:	PUNCT
iajs-399	63	13	theorem	theorem	VERB
iajs-399	63	14	let	let	VERB
iajs-399	63	15	s	s	PRON
iajs-399	63	16	be	be	AUX
iajs-399	63	17	a	a	DET
iajs-399	63	18	nonempty	nonempty	ADV
iajs-399	63	19	closed	close	VERB
iajs-399	63	20	convex	convex	NOUN
iajs-399	63	21	subset	subset	NOUN
iajs-399	63	22	of	of	ADP
iajs-399	63	23	a	a	DET
iajs-399	63	24	uniformly	uniformly	ADV
iajs-399	63	25	convex	convex	ADJ
iajs-399	63	26	2	2	NUM
iajs-399	63	27	-	-	PUNCT
iajs-399	63	28	banach	banach	NOUN
iajs-399	63	29	space	space	NOUN
iajs-399	63	30	x	x	PUNCT
iajs-399	63	31	and	and	CCONJ
iajs-399	63	32	(	(	PUNCT
iajs-399	63	33	xn	xn	X
iajs-399	63	34	)	)	PUNCT
iajs-399	63	35	a	a	DET
iajs-399	63	36	bounded	bounded	ADJ
iajs-399	63	37	sequence	sequence	NOUN
iajs-399	63	38	in	in	ADP
iajs-399	63	39	s	s	PRON
iajs-399	63	40	such	such	ADJ
iajs-399	63	41	that	that	SCONJ
iajs-399	63	42	za(s	za(	NOUN
iajs-399	63	43	,	,	PUNCT
iajs-399	63	44	(	(	PUNCT
iajs-399	63	45	xn	xn	NOUN
iajs-399	63	46	)	)	PUNCT
iajs-399	63	47	)	)	PUNCT
iajs-399	64	1	=	=	PRON
iajs-399	64	2	{	{	PUNCT
iajs-399	64	3	z	z	NOUN
iajs-399	64	4	}	}	PUNCT
iajs-399	64	5	.	.	PUNCT
iajs-399	65	1	if	if	SCONJ
iajs-399	65	2	(	(	PUNCT
iajs-399	65	3	ym	ym	NOUN
iajs-399	65	4	)	)	PUNCT
iajs-399	65	5	is	be	AUX
iajs-399	65	6	a	a	DET
iajs-399	65	7	sequence	sequence	NOUN
iajs-399	65	8	in	in	ADP
iajs-399	65	9	s	s	PRON
iajs-399	65	10	such	such	ADJ
iajs-399	65	11	that	that	SCONJ
iajs-399	65	12	lim𝑚→∞	lim𝑚→∞	PROPN
iajs-399	65	13	𝑟𝑎	𝑟𝑎	PRON
iajs-399	65	14	(	(	PUNCT
iajs-399	65	15	ym	ym	PROPN
iajs-399	65	16	,	,	PUNCT
iajs-399	65	17	(	(	PUNCT
iajs-399	65	18	xn	xn	NOUN
iajs-399	65	19	)	)	PUNCT
iajs-399	65	20	)	)	PUNCT
iajs-399	66	1	=	=	SYM
iajs-399	66	2	ra(s	ra(	NOUN
iajs-399	66	3	,	,	PUNCT
iajs-399	66	4	(	(	PUNCT
iajs-399	66	5	xn	xn	NOUN
iajs-399	66	6	)	)	PUNCT
iajs-399	66	7	)	)	PUNCT
iajs-399	66	8	,	,	PUNCT
iajs-399	66	9	then	then	ADV
iajs-399	66	10	lim𝑚→∞	lim𝑚→∞	PROPN
iajs-399	66	11	𝑦𝑚=	𝑦𝑚=	PROPN
iajs-399	66	12	z	z	PROPN
iajs-399	66	13	.	.	PUNCT
iajs-399	67	1	345	345	NUM
iajs-399	67	2	|	|	ADV
iajs-399	67	3	mathematics	mathematics	PROPN
iajs-399	67	4	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	NUM
iajs-399	67	5	�	�	NOUN
iajs-399	67	6	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	NUM
iajs-399	67	7	:	:	PUNCT
iajs-399	67	8	a@âig@ú‹	a@âig@ú‹	PROPN
iajs-399	68	1	©	©	PROPN
iajs-399	68	2	@ü‹127@@öü»€a@i1@‚b«@h2014	@ü‹127@@öü»€a@i1@‚b«@h2014	PROPN
iajs-399	68	3	ibn	ibn	PROPN
iajs-399	68	4	al	al	PROPN
iajs-399	68	5	-	-	PUNCT
iajs-399	68	6	haitham	haitham	PROPN
iajs-399	68	7	jour	jour	X
iajs-399	68	8	.	.	PROPN
iajs-399	68	9	for	for	ADP
iajs-399	68	10	pure	pure	ADJ
iajs-399	68	11	&	&	CCONJ
iajs-399	68	12	appl	appl	PROPN
iajs-399	68	13	.	.	PUNCT
iajs-399	69	1	sci	sci	PROPN
iajs-399	69	2	.	.	PUNCT
iajs-399	69	3	vol	vol	NOUN
iajs-399	69	4	.	.	PROPN
iajs-399	70	1	27	27	NUM
iajs-399	70	2	(	(	PUNCT
iajs-399	70	3	1	1	NUM
iajs-399	70	4	)	)	PUNCT
iajs-399	70	5	2014	2014	NUM
iajs-399	70	6	proof	proof	NOUN
iajs-399	70	7	suppose	suppose	VERB
iajs-399	70	8	that	that	SCONJ
iajs-399	70	9	(	(	PUNCT
iajs-399	70	10	ym	ym	NOUN
iajs-399	70	11	)	)	PUNCT
iajs-399	70	12	does	do	AUX
iajs-399	70	13	not	not	PART
iajs-399	70	14	converge	converge	VERB
iajs-399	70	15	strongly	strongly	ADV
iajs-399	70	16	to	to	ADP
iajs-399	70	17	z.	z.	PROPN
iajs-399	70	18	then	then	ADV
iajs-399	70	19	there	there	PRON
iajs-399	70	20	exists	exist	VERB
iajs-399	70	21	a	a	DET
iajs-399	70	22	subsequence	subsequence	NOUN
iajs-399	70	23	(	(	PUNCT
iajs-399	70	24	ymi	ymi	NOUN
iajs-399	70	25	)	)	PUNCT
iajs-399	70	26	of	of	ADP
iajs-399	70	27	(	(	PUNCT
iajs-399	70	28	ym	ym	NOUN
iajs-399	70	29	)	)	PUNCT
iajs-399	70	30	such	such	ADJ
iajs-399	70	31	that	that	SCONJ
iajs-399	70	32	||ymi	||ymi	NOUN
iajs-399	70	33	z	z	NOUN
iajs-399	70	34	,	,	PUNCT
iajs-399	70	35	u||	u||	ADV
iajs-399	70	36	≥	≥	NOUN
iajs-399	70	37	d	d	X
iajs-399	70	38	>	>	X
iajs-399	70	39	0	0	PUNCT
iajs-399	71	1	for	for	ADP
iajs-399	71	2	all	all	DET
iajs-399	71	3	i	i	PRON
iajs-399	71	4	∈	∈	PROPN
iajs-399	71	5	n	n	CCONJ
iajs-399	71	6	,	,	PUNCT
iajs-399	71	7	u	u	PROPN
iajs-399	71	8	ϵ	ϵ	X
iajs-399	71	9	s.	s.	PROPN
iajs-399	71	10	by	by	ADP
iajs-399	71	11	the	the	DET
iajs-399	71	12	uniform	uniform	ADJ
iajs-399	71	13	convexity	convexity	NOUN
iajs-399	71	14	of	of	ADP
iajs-399	71	15	x	x	PRON
iajs-399	71	16	,	,	PUNCT
iajs-399	71	17	there	there	PRON
iajs-399	71	18	exists	exist	VERB
iajs-399	71	19	ε	ε	PROPN
iajs-399	71	20	>	>	X
iajs-399	71	21	0	0	NUM
iajs-399	71	22	such	such	ADJ
iajs-399	71	23	that	that	PRON
iajs-399	71	24	(	(	PUNCT
iajs-399	71	25	ra(s	ra(s	NUM
iajs-399	71	26	,	,	PUNCT
iajs-399	71	27	(	(	PUNCT
iajs-399	71	28	xn	xn	NOUN
iajs-399	71	29	)	)	PUNCT
iajs-399	71	30	)	)	PUNCT
iajs-399	72	1	+	+	CCONJ
iajs-399	72	2	ε)[1	ε)[1	PROPN
iajs-399	72	3	–	–	PUNCT
iajs-399	72	4	δx(d	δx(d	NOUN
iajs-399	72	5	/	/	SYM
iajs-399	72	6	ra(s,(xn	ra(s,(xn	NOUN
iajs-399	72	7	)	)	PUNCT
iajs-399	72	8	)	)	PUNCT
iajs-399	73	1	+	+	CCONJ
iajs-399	73	2	ε	ε	X
iajs-399	73	3	)	)	PUNCT
iajs-399	73	4	]	]	PUNCT
iajs-399	73	5	<	<	X
iajs-399	73	6	ra(s	ra(s	PROPN
iajs-399	73	7	,	,	PUNCT
iajs-399	73	8	(	(	PUNCT
iajs-399	73	9	xn	xn	NOUN
iajs-399	73	10	)	)	PUNCT
iajs-399	73	11	)	)	PUNCT
iajs-399	73	12	.	.	PUNCT
iajs-399	74	1	since	since	SCONJ
iajs-399	74	2	ra(z	ra(z	NOUN
iajs-399	74	3	,	,	PUNCT
iajs-399	74	4	(	(	PUNCT
iajs-399	74	5	xn	xn	NOUN
iajs-399	74	6	)	)	PUNCT
iajs-399	74	7	)	)	PUNCT
iajs-399	74	8	=	=	SYM
iajs-399	74	9	ra(s	ra(	NOUN
iajs-399	74	10	,	,	PUNCT
iajs-399	74	11	(	(	PUNCT
iajs-399	74	12	xn	xn	NOUN
iajs-399	74	13	)	)	PUNCT
iajs-399	74	14	)	)	PUNCT
iajs-399	74	15	,	,	PUNCT
iajs-399	74	16	there	there	PRON
iajs-399	74	17	exists	exist	VERB
iajs-399	74	18	no	no	DET
iajs-399	74	19	∈	∈	NOUN
iajs-399	74	20	n	n	PRON
iajs-399	74	21	such	such	ADJ
iajs-399	74	22	that	that	DET
iajs-399	74	23	||xn	||xn	NOUN
iajs-399	74	24	–	–	PUNCT
iajs-399	74	25	z	z	NOUN
iajs-399	74	26	,	,	PUNCT
iajs-399	74	27	u||	u||	ADV
iajs-399	74	28	≤	≤	NUM
iajs-399	74	29	ra(s	ra(	NOUN
iajs-399	74	30	,	,	PUNCT
iajs-399	74	31	(	(	PUNCT
iajs-399	74	32	xn	xn	NOUN
iajs-399	74	33	)	)	PUNCT
iajs-399	74	34	)	)	PUNCT
iajs-399	75	1	+	+	CCONJ
iajs-399	75	2	ε	ε	PROPN
iajs-399	75	3	for	for	ADP
iajs-399	75	4	all	all	DET
iajs-399	75	5	n	n	PRON
iajs-399	75	6	≥	≥	NOUN
iajs-399	75	7	no	no	INTJ
iajs-399	75	8	.	.	PUNCT
iajs-399	76	1	since	since	SCONJ
iajs-399	76	2	ra(ym	ra(ym	PROPN
iajs-399	76	3	,	,	PUNCT
iajs-399	76	4	(	(	PUNCT
iajs-399	76	5	xn	xn	NOUN
iajs-399	76	6	)	)	PUNCT
iajs-399	76	7	)	)	PUNCT
iajs-399	77	1	→	→	SYM
iajs-399	77	2	ra(s	ra(s	NUM
iajs-399	77	3	,	,	PUNCT
iajs-399	77	4	(	(	PUNCT
iajs-399	77	5	xn	xn	NOUN
iajs-399	77	6	)	)	PUNCT
iajs-399	77	7	)	)	PUNCT
iajs-399	77	8	as	as	ADP
iajs-399	77	9	m	m	PROPN
iajs-399	77	10	→	→	SYM
iajs-399	77	11	∞	∞	PROPN
iajs-399	77	12	and	and	CCONJ
iajs-399	77	13	hence	hence	ADV
iajs-399	77	14	ra(ymi	ra(ymi	VERB
iajs-399	77	15	,	,	PUNCT
iajs-399	77	16	(	(	PUNCT
iajs-399	77	17	xn	xn	NOUN
iajs-399	77	18	)	)	PUNCT
iajs-399	77	19	)	)	PUNCT
iajs-399	78	1	→	→	SYM
iajs-399	78	2	ra(s	ra(s	NUM
iajs-399	78	3	,	,	PUNCT
iajs-399	78	4	(	(	PUNCT
iajs-399	78	5	xn	xn	NOUN
iajs-399	78	6	)	)	PUNCT
iajs-399	78	7	)	)	PUNCT
iajs-399	78	8	as	as	ADP
iajs-399	78	9	i→∞	i→∞	NOUN
iajs-399	78	10	,	,	PUNCT
iajs-399	78	11	then	then	ADV
iajs-399	78	12	there	there	PRON
iajs-399	78	13	exists	exist	VERB
iajs-399	78	14	an	an	DET
iajs-399	78	15	integer	integer	NOUN
iajs-399	78	16	mo∈	mo∈	PROPN
iajs-399	78	17	n	n	CCONJ
iajs-399	78	18	such	such	ADJ
iajs-399	78	19	that	that	DET
iajs-399	78	20	||xn	||xn	NOUN
iajs-399	78	21	–	–	PUNCT
iajs-399	78	22	ymi	ymi	NOUN
iajs-399	78	23	,	,	PUNCT
iajs-399	78	24	u||	u||	ADV
iajs-399	78	25	≤	≤	NUM
iajs-399	78	26	ra(s	ra(	NOUN
iajs-399	78	27	,	,	PUNCT
iajs-399	78	28	(	(	PUNCT
iajs-399	78	29	xn	xn	NOUN
iajs-399	78	30	)	)	PUNCT
iajs-399	78	31	)	)	PUNCT
iajs-399	79	1	+	+	CCONJ
iajs-399	79	2	ε	ε	PROPN
iajs-399	79	3	for	for	ADP
iajs-399	79	4	all	all	DET
iajs-399	79	5	n	n	PRON
iajs-399	79	6	≥	≥	NOUN
iajs-399	79	7	mo	mo	PROPN
iajs-399	79	8	.	.	PUNCT
iajs-399	80	1	since	since	SCONJ
iajs-399	80	2	x	x	PRON
iajs-399	80	3	is	be	AUX
iajs-399	80	4	uniformly	uniformly	ADV
iajs-399	80	5	convex	convex	NOUN
iajs-399	80	6	,	,	PUNCT
iajs-399	80	7	||xn	||xn	NUM
iajs-399	80	8	–	–	PUNCT
iajs-399	80	9	(	(	PUNCT
iajs-399	80	10	z	z	NOUN
iajs-399	80	11	+	+	NOUN
iajs-399	80	12	ymi	ymi	NOUN
iajs-399	80	13	)	)	PUNCT
iajs-399	80	14	/	/	SYM
iajs-399	80	15	2	2	NUM
iajs-399	80	16	,	,	PUNCT
iajs-399	80	17	u||	u||	ADV
iajs-399	80	18	≤	≤	NOUN
iajs-399	81	1	[	[	PUNCT
iajs-399	81	2	1−δx	1−δx	NUM
iajs-399	81	3	(	(	PUNCT
iajs-399	81	4	d	d	NOUN
iajs-399	81	5	/	/	SYM
iajs-399	81	6	(	(	PUNCT
iajs-399	81	7	ra(s,(xn	ra(s,(xn	NOUN
iajs-399	81	8	)	)	PUNCT
iajs-399	81	9	)	)	PUNCT
iajs-399	81	10	)	)	PUNCT
iajs-399	81	11	]	]	PUNCT
iajs-399	81	12	(	(	PUNCT
iajs-399	81	13	ra(s,(xn	ra(s,(xn	NOUN
iajs-399	81	14	)	)	PUNCT
iajs-399	81	15	)	)	PUNCT
iajs-399	82	1	+	+	CCONJ
iajs-399	82	2	ɛ	ɛ	X
iajs-399	82	3	)	)	PUNCT
iajs-399	82	4	˂	˂	PROPN
iajs-399	82	5	ra(s,(xn	ra(s,(xn	NOUN
iajs-399	82	6	)	)	PUNCT
iajs-399	82	7	)	)	PUNCT
iajs-399	82	8	for	for	ADP
iajs-399	82	9	all	all	DET
iajs-399	82	10	n	n	PRON
iajs-399	82	11	≥	≥	NOUN
iajs-399	82	12	max	max	PROPN
iajs-399	82	13	{	{	PUNCT
iajs-399	82	14	no	no	INTJ
iajs-399	82	15	,	,	PUNCT
iajs-399	82	16	mo	mo	NOUN
iajs-399	82	17	}	}	PUNCT
iajs-399	82	18	this	this	PRON
iajs-399	82	19	implies	imply	VERB
iajs-399	82	20	that	that	SCONJ
iajs-399	82	21	ra	ra	PROPN
iajs-399	82	22	(	(	PUNCT
iajs-399	82	23	(	(	PUNCT
iajs-399	82	24	z	z	NOUN
iajs-399	82	25	+	+	X
iajs-399	82	26	ymi	ymi	PROPN
iajs-399	82	27	/	/	SYM
iajs-399	82	28	2	2	NUM
iajs-399	82	29	)	)	PUNCT
iajs-399	82	30	,	,	PUNCT
iajs-399	82	31	(	(	PUNCT
iajs-399	82	32	xn	xn	NOUN
iajs-399	82	33	)	)	PUNCT
iajs-399	82	34	)	)	PUNCT
iajs-399	82	35	<	<	X
iajs-399	82	36	ra(s	ra(s	PUNCT
iajs-399	82	37	,	,	PUNCT
iajs-399	82	38	(	(	PUNCT
iajs-399	82	39	xn	xn	NOUN
iajs-399	82	40	)	)	PUNCT
iajs-399	82	41	)	)	PUNCT
iajs-399	82	42	,	,	PUNCT
iajs-399	82	43	which	which	PRON
iajs-399	82	44	contradicts	contradict	VERB
iajs-399	82	45	the	the	DET
iajs-399	82	46	uniqueness	uniqueness	NOUN
iajs-399	82	47	of	of	ADP
iajs-399	82	48	the	the	DET
iajs-399	82	49	asymptotic	asymptotic	ADJ
iajs-399	82	50	center	center	NOUN
iajs-399	82	51	z.	z.	PROPN
iajs-399	82	52	■	■	PUNCT
iajs-399	82	53	theorem	theorem	VERB
iajs-399	82	54	let	let	VERB
iajs-399	82	55	s	s	PRON
iajs-399	82	56	be	be	AUX
iajs-399	82	57	a	a	DET
iajs-399	82	58	nonempty	nonempty	ADV
iajs-399	82	59	closed	close	VERB
iajs-399	82	60	convex	convex	NOUN
iajs-399	82	61	subset	subset	NOUN
iajs-399	82	62	of	of	ADP
iajs-399	82	63	a	a	DET
iajs-399	82	64	uniformly	uniformly	ADV
iajs-399	82	65	convex	convex	ADJ
iajs-399	82	66	2banach	2banach	NUM
iajs-399	82	67	space	space	NOUN
iajs-399	82	68	.	.	PUNCT
iajs-399	83	1	then	then	ADV
iajs-399	83	2	every	every	DET
iajs-399	83	3	bounded	bounded	ADJ
iajs-399	83	4	sequence	sequence	NOUN
iajs-399	83	5	(	(	PUNCT
iajs-399	83	6	xn	xn	X
iajs-399	83	7	)	)	PUNCT
iajs-399	83	8	in	in	ADP
iajs-399	83	9	x	x	PUNCT
iajs-399	83	10	has	have	VERB
iajs-399	83	11	a	a	DET
iajs-399	83	12	unique	unique	ADJ
iajs-399	83	13	asymptotic	asymptotic	ADJ
iajs-399	83	14	center	center	NOUN
iajs-399	83	15	with	with	ADP
iajs-399	83	16	respect	respect	NOUN
iajs-399	83	17	to	to	ADP
iajs-399	83	18	s	s	PRON
iajs-399	83	19	,	,	PUNCT
iajs-399	83	20	i.e.	i.e.	X
iajs-399	83	21	,	,	PUNCT
iajs-399	83	22	za(s	za(	NOUN
iajs-399	83	23	,	,	PUNCT
iajs-399	83	24	(	(	PUNCT
iajs-399	83	25	xn	xn	NOUN
iajs-399	83	26	)	)	PUNCT
iajs-399	83	27	)	)	PUNCT
iajs-399	84	1	=	=	PRON
iajs-399	84	2	{	{	PUNCT
iajs-399	84	3	z	z	NOUN
iajs-399	84	4	}	}	PUNCT
iajs-399	84	5	and	and	CCONJ
iajs-399	84	6	lim	lim	PROPN
iajs-399	84	7	𝑛→∞	𝑛→∞	NUM
iajs-399	84	8	sup‖𝑥𝑛	sup‖𝑥𝑛	PROPN
iajs-399	84	9	−	−	NOUN
iajs-399	84	10	𝑧,𝑢‖˂	𝑧,𝑢‖˂	PROPN
iajs-399	85	1	lim	lim	PROPN
iajs-399	85	2	𝑛→∞	𝑛→∞	NUM
iajs-399	85	3	sup‖𝑥𝑛	sup‖𝑥𝑛	PROPN
iajs-399	85	4	−	−	PROPN
iajs-399	85	5	𝑥	𝑥	NOUN
iajs-399	85	6	,	,	PUNCT
iajs-399	85	7	𝑢‖	𝑢‖	PROPN
iajs-399	85	8	𝑓𝑜𝑟	𝑓𝑜𝑟	ADV
iajs-399	85	9	𝑥	𝑥	PROPN
iajs-399	85	10	≠	≠	PROPN
iajs-399	85	11	𝑧	𝑧	X
iajs-399	85	12	,	,	PUNCT
iajs-399	85	13	𝑢	𝑢	X
iajs-399	85	14	𝜖	𝜖	PROPN
iajs-399	85	15	𝑆.	𝑆.	PROPN
iajs-399	85	16	theorem	theorem	NOUN
iajs-399	85	17	let	let	VERB
iajs-399	85	18	x	x	PRON
iajs-399	85	19	be	be	AUX
iajs-399	85	20	a	a	DET
iajs-399	85	21	uniformly	uniformly	ADV
iajs-399	85	22	convex	convex	ADJ
iajs-399	85	23	2	2	NUM
iajs-399	85	24	-	-	PUNCT
iajs-399	85	25	banach	banach	NOUN
iajs-399	85	26	space	space	NOUN
iajs-399	85	27	satisfying	satisfy	VERB
iajs-399	85	28	the	the	DET
iajs-399	85	29	opial	opial	ADJ
iajs-399	85	30	condition	condition	NOUN
iajs-399	85	31	and	and	CCONJ
iajs-399	85	32	s	s	VERB
iajs-399	85	33	a	a	DET
iajs-399	85	34	nonempty	nonempty	ADV
iajs-399	85	35	closed	close	VERB
iajs-399	85	36	convex	convex	NOUN
iajs-399	85	37	subset	subset	NOUN
iajs-399	85	38	of	of	ADP
iajs-399	85	39	x.	x.	NOUN
iajs-399	85	40	if	if	SCONJ
iajs-399	85	41	(	(	PUNCT
iajs-399	85	42	xn	xn	X
iajs-399	85	43	)	)	PUNCT
iajs-399	85	44	is	be	AUX
iajs-399	85	45	a	a	DET
iajs-399	85	46	sequence	sequence	NOUN
iajs-399	85	47	in	in	ADP
iajs-399	85	48	s	s	PRON
iajs-399	85	49	such	such	ADJ
iajs-399	85	50	that	that	PRON
iajs-399	85	51	xn	xn	PUNCT
iajs-399	86	1	→	→	SYM
iajs-399	86	2	z	z	X
iajs-399	86	3	,	,	PUNCT
iajs-399	86	4	then	then	ADV
iajs-399	86	5	z	z	PROPN
iajs-399	86	6	is	be	AUX
iajs-399	86	7	the	the	DET
iajs-399	86	8	asymptotic	asymptotic	ADJ
iajs-399	86	9	center	center	NOUN
iajs-399	86	10	of	of	ADP
iajs-399	86	11	(	(	PUNCT
iajs-399	86	12	xn	xn	PROPN
iajs-399	86	13	)	)	PUNCT
iajs-399	86	14	in	in	ADP
iajs-399	86	15	s.	s.	PROPN
iajs-399	86	16	proof	proof	NOUN
iajs-399	86	17	from	from	ADP
iajs-399	86	18	theorem	theorem	ADJ
iajs-399	86	19	2	2	NUM
iajs-399	86	20	-	-	SYM
iajs-399	86	21	2	2	NUM
iajs-399	86	22	,	,	PUNCT
iajs-399	86	23	za(s	za(	NOUN
iajs-399	86	24	,	,	PUNCT
iajs-399	86	25	(	(	PUNCT
iajs-399	86	26	xn	xn	NOUN
iajs-399	86	27	)	)	PUNCT
iajs-399	86	28	)	)	PUNCT
iajs-399	87	1	is	be	AUX
iajs-399	87	2	singleton	singleton	NOUN
iajs-399	87	3	.	.	PUNCT
iajs-399	88	1	let	let	VERB
iajs-399	88	2	za(s	za(	NOUN
iajs-399	88	3	,	,	PUNCT
iajs-399	88	4	(	(	PUNCT
iajs-399	88	5	xn	xn	NOUN
iajs-399	88	6	)	)	PUNCT
iajs-399	88	7	)	)	PUNCT
iajs-399	89	1	=	=	PRON
iajs-399	89	2	{	{	PUNCT
iajs-399	89	3	x	x	X
iajs-399	89	4	}	}	PUNCT
iajs-399	89	5	,	,	PUNCT
iajs-399	89	6	x	x	SYM
iajs-399	89	7	≠	≠	PROPN
iajs-399	89	8	z	z	NOUN
iajs-399	89	9	since	since	SCONJ
iajs-399	89	10	xn	xn	PROPN
iajs-399	89	11	→	→	SYM
iajs-399	89	12	z	z	X
iajs-399	89	13	,	,	PUNCT
iajs-399	89	14	by	by	ADP
iajs-399	89	15	the	the	DET
iajs-399	89	16	opial	opial	ADJ
iajs-399	89	17	condition	condition	NOUN
iajs-399	89	18	,	,	PUNCT
iajs-399	89	19	lim𝑛→∞	lim𝑛→∞	PROPN
iajs-399	89	20	𝑠𝑢𝑝‖𝑥𝑛	𝑠𝑢𝑝‖𝑥𝑛	PROPN
iajs-399	90	1	−	−	PROPN
iajs-399	90	2	𝑧	𝑧	ADJ
iajs-399	90	3	,	,	PUNCT
iajs-399	90	4	𝑢‖˂	𝑢‖˂	NOUN
iajs-399	90	5	lim𝑛→∞	lim𝑛→∞	NOUN
iajs-399	90	6	𝑠𝑢𝑝	𝑠𝑢𝑝	VERB
iajs-399	90	7	‖𝑥𝑛	‖𝑥𝑛	NUM
iajs-399	90	8	−	−	NOUN
iajs-399	90	9	𝑥,𝑢‖	𝑥,𝑢‖	NOUN
iajs-399	90	10	,	,	PUNCT
iajs-399	90	11	u	u	PROPN
iajs-399	90	12	ϵ	ϵ	X
iajs-399	90	13	s.	s.	PROPN
iajs-399	90	14	by	by	ADP
iajs-399	90	15	theorem	theorem	VERB
iajs-399	90	16	2	2	NUM
iajs-399	90	17	-	-	SYM
iajs-399	90	18	2	2	NUM
iajs-399	90	19	,	,	PUNCT
iajs-399	90	20	we	we	PRON
iajs-399	90	21	obtain	obtain	VERB
iajs-399	90	22	limn→∞	limn→∞	PRON
iajs-399	90	23	sup‖xn	sup‖xn	PROPN
iajs-399	90	24	−	−	NOUN
iajs-399	91	1	x	x	NOUN
iajs-399	91	2	,	,	PUNCT
iajs-399	91	3	u‖	u‖	ADP
iajs-399	91	4	<	<	X
iajs-399	91	5	lim𝑛→∞	lim𝑛→∞	PROPN
iajs-399	91	6	𝑠𝑢𝑝‖𝑥𝑛	𝑠𝑢𝑝‖𝑥𝑛	PROPN
iajs-399	91	7	−	−	PROPN
iajs-399	91	8	𝑧,𝑢‖.	𝑧,𝑢‖.	PROPN
iajs-399	91	9	therefore	therefore	ADV
iajs-399	91	10	,	,	PUNCT
iajs-399	91	11	z	z	NOUN
iajs-399	91	12	=	=	PUNCT
iajs-399	91	13	x.	x.	NOUN
iajs-399	91	14	■	■	PUNCT
iajs-399	91	15	theorem	theorem	VERB
iajs-399	91	16	let	let	VERB
iajs-399	91	17	x	x	PRON
iajs-399	91	18	be	be	AUX
iajs-399	91	19	a	a	DET
iajs-399	91	20	uniformly	uniformly	ADV
iajs-399	91	21	convex	convex	ADJ
iajs-399	91	22	2	2	NUM
iajs-399	91	23	-	-	PUNCT
iajs-399	91	24	banach	banach	NOUN
iajs-399	91	25	space	space	NOUN
iajs-399	91	26	,	,	PUNCT
iajs-399	91	27	let	let	VERB
iajs-399	91	28	s	s	PRON
iajs-399	91	29	be	be	AUX
iajs-399	91	30	a	a	DET
iajs-399	91	31	nonempty	nonempty	ADV
iajs-399	91	32	closed	close	VERB
iajs-399	91	33	convex	convex	NOUN
iajs-399	91	34	subset	subset	NOUN
iajs-399	91	35	of	of	ADP
iajs-399	91	36	x	x	PUNCT
iajs-399	91	37	and	and	CCONJ
iajs-399	91	38	t	t	PROPN
iajs-399	91	39	:	:	PUNCT
iajs-399	91	40	s→s	s→s	VERB
iajs-399	91	41	an	an	DET
iajs-399	91	42	asymptotically	asymptotically	ADV
iajs-399	91	43	non	non	ADJ
iajs-399	91	44	-	-	ADJ
iajs-399	91	45	expansive	expansive	ADJ
iajs-399	91	46	mapping	mapping	NOUN
iajs-399	91	47	.	.	PUNCT
iajs-399	92	1	if	if	SCONJ
iajs-399	92	2	(	(	PUNCT
iajs-399	92	3	𝓍𝓍n	𝓍𝓍n	NOUN
iajs-399	92	4	)	)	PUNCT
iajs-399	92	5	a	a	DET
iajs-399	92	6	bounded	bounded	ADJ
iajs-399	92	7	sequence	sequence	NOUN
iajs-399	92	8	in	in	ADP
iajs-399	92	9	s	s	PRON
iajs-399	92	10	such	such	ADJ
iajs-399	92	11	that	that	DET
iajs-399	92	12	lim𝑛→∞‖𝑥𝑛	lim𝑛→∞‖𝑥𝑛	PROPN
iajs-399	92	13	−	−	PROPN
iajs-399	92	14	𝑇𝑥𝑛	𝑇𝑥𝑛	PROPN
iajs-399	92	15	,	,	PUNCT
iajs-399	92	16	𝑢‖	𝑢‖	PROPN
iajs-399	92	17	=	=	SYM
iajs-399	92	18	0	0	NUM
iajs-399	92	19	;	;	PUNCT
iajs-399	92	20	𝑢	𝑢	PROPN
iajs-399	92	21	𝜖	𝜖	PROPN
iajs-399	92	22	𝑆	𝑆	PROPN
iajs-399	92	23	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
iajs-399	92	24	za	za	PROPN
iajs-399	92	25	(	(	PUNCT
iajs-399	92	26	s,(𝓍𝓍n	s,(𝓍𝓍n	NUM
iajs-399	92	27	)	)	PUNCT
iajs-399	92	28	)	)	PUNCT
iajs-399	93	1	=	=	PRON
iajs-399	93	2	{	{	PUNCT
iajs-399	93	3	v	v	NOUN
iajs-399	93	4	}	}	PUNCT
iajs-399	93	5	,	,	PUNCT
iajs-399	93	6	then	then	ADV
iajs-399	93	7	v	v	NOUN
iajs-399	93	8	is	be	AUX
iajs-399	93	9	the	the	DET
iajs-399	93	10	fixed	fix	VERB
iajs-399	93	11	point	point	NOUN
iajs-399	93	12	in	in	ADP
iajs-399	93	13	s.	s.	PROPN
iajs-399	93	14	proof	proof	NOUN
iajs-399	93	15	define	define	VERB
iajs-399	93	16	a	a	DET
iajs-399	93	17	sequence	sequence	NOUN
iajs-399	93	18	(	(	PUNCT
iajs-399	93	19	ym	ym	NOUN
iajs-399	93	20	)	)	PUNCT
iajs-399	93	21	in	in	ADP
iajs-399	93	22	s	s	PRON
iajs-399	93	23	by	by	ADP
iajs-399	93	24	ym	ym	PROPN
iajs-399	93	25	=	=	SYM
iajs-399	93	26	tmv	tmv	PROPN
iajs-399	93	27	,	,	PUNCT
iajs-399	93	28	m	m	VERB
iajs-399	93	29	ϵ	ϵ	X
iajs-399	93	30	n.	n.	NOUN
iajs-399	93	31	for	for	ADP
iajs-399	93	32	integers	integer	NOUN
iajs-399	93	33	n	n	CCONJ
iajs-399	93	34	,	,	PUNCT
iajs-399	93	35	m	m	VERB
iajs-399	93	36	ϵ	ϵ	NOUN
iajs-399	93	37	n	n	CCONJ
iajs-399	93	38	,	,	PUNCT
iajs-399	93	39	we	we	PRON
iajs-399	93	40	have	have	VERB
iajs-399	93	41	||	||	NOUN
iajs-399	94	1	ym	ym	INTJ
iajs-399	94	2	xn	xn	PROPN
iajs-399	94	3	,	,	PUNCT
iajs-399	94	4	u||	u||	ADV
iajs-399	94	5	≤	≤	NUM
iajs-399	94	6	||tmv	||tmv	NOUN
iajs-399	94	7	tmxn	tmxn	NOUN
iajs-399	94	8	,	,	PUNCT
iajs-399	94	9	u||	u||	ADV
iajs-399	94	10	+	+	CCONJ
iajs-399	94	11	||tmxn	||tmxn	ADV
iajs-399	94	12	–	–	PUNCT
iajs-399	94	13	tm-1xn	tm-1xn	NOUN
iajs-399	94	14	,	,	PUNCT
iajs-399	94	15	u||	u||	ADV
iajs-399	95	1	+	+	CCONJ
iajs-399	95	2	…	…	PUNCT
iajs-399	95	3	+	+	CCONJ
iajs-399	95	4	||txn	||txn	ADJ
iajs-399	95	5	–	–	PUNCT
iajs-399	95	6	xn	xn	NUM
iajs-399	95	7	,	,	PUNCT
iajs-399	95	8	u||	u||	ADV
iajs-399	95	9	≤	≤	NUM
iajs-399	95	10	km	km	NOUN
iajs-399	95	11	||v	||v	NOUN
iajs-399	95	12	–	–	PUNCT
iajs-399	95	13	xn	xn	NOUN
iajs-399	95	14	,	,	PUNCT
iajs-399	95	15	u||	u||	ADV
iajs-399	96	1	+	+	CCONJ
iajs-399	96	2	(	(	PUNCT
iajs-399	96	3	||txn	||txn	ADJ
iajs-399	96	4	–	–	PUNCT
iajs-399	96	5	xn	xn	NOUN
iajs-399	96	6	,	,	PUNCT
iajs-399	96	7	u||	u||	ADV
iajs-399	97	1	+	+	CCONJ
iajs-399	97	2	∑	∑	PUNCT
iajs-399	97	3	𝑘𝑖	𝑘𝑖	ADV
iajs-399	97	4	||	||	NOUN
iajs-399	98	1	𝑥𝑛	𝑥𝑛	PROPN
iajs-399	98	2	–	–	PUNCT
iajs-399	98	3	𝑇𝑥𝑛	𝑇𝑥𝑛	PROPN
iajs-399	98	4	,	,	PUNCT
iajs-399	98	5	𝑢||	𝑢||	PROPN
iajs-399	98	6	…	…	PUNCT
iajs-399	98	7	(	(	PUNCT
iajs-399	98	8	2.1)𝑚−1	2.1)𝑚−1	NUM
iajs-399	98	9	𝑖=1	𝑖=1	PROPN
iajs-399	98	10	then	then	ADV
iajs-399	98	11	by	by	ADP
iajs-399	98	12	condition	condition	NOUN
iajs-399	98	13	(	(	PUNCT
iajs-399	98	14	2.1	2.1	NUM
iajs-399	98	15	)	)	PUNCT
iajs-399	98	16	we	we	PRON
iajs-399	98	17	have	have	VERB
iajs-399	98	18	ra	ra	PROPN
iajs-399	98	19	(	(	PUNCT
iajs-399	98	20	ym	ym	INTJ
iajs-399	98	21	,	,	PUNCT
iajs-399	98	22	(	(	PUNCT
iajs-399	98	23	xn	xn	NOUN
iajs-399	98	24	)	)	PUNCT
iajs-399	98	25	)	)	PUNCT
iajs-399	99	1	=	=	SYM
iajs-399	99	2	lim𝑛→∞	lim𝑛→∞	NOUN
iajs-399	99	3	𝑠𝑢𝑝||𝑥𝑛	𝑠𝑢𝑝||𝑥𝑛	PROPN
iajs-399	99	4	–	–	PUNCT
iajs-399	99	5	𝑦𝑚	𝑦𝑚	NOUN
iajs-399	99	6	,	,	PUNCT
iajs-399	99	7	𝑢||	𝑢||	NUM
iajs-399	99	8	km	km	PROPN
iajs-399	99	9	ra(v	ra(v	PUNCT
iajs-399	99	10	,	,	PUNCT
iajs-399	99	11	(	(	PUNCT
iajs-399	99	12	xn	xn	NOUN
iajs-399	99	13	)	)	PUNCT
iajs-399	99	14	)	)	PUNCT
iajs-399	99	15	≤	≤	NUM
iajs-399	99	16	346	346	NUM
iajs-399	99	17	|	|	NOUN
iajs-399	99	18	mathematics	mathematic	NOUN
iajs-399	99	19	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	NUM
iajs-399	99	20	�	�	NOUN
iajs-399	99	21	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	NUM
iajs-399	99	22	:	:	PUNCT
iajs-399	99	23	a@âig@ú‹	a@âig@ú‹	PROPN
iajs-399	99	24	©	©	PROPN
iajs-399	99	25	@ü‹127@@öü»€a@i1@‚b«@h2014	@ü‹127@@öü»€a@i1@‚b«@h2014	PROPN
iajs-399	99	26	ibn	ibn	PROPN
iajs-399	99	27	al	al	PROPN
iajs-399	99	28	-	-	PUNCT
iajs-399	99	29	haitham	haitham	PROPN
iajs-399	99	30	jour	jour	X
iajs-399	99	31	.	.	PROPN
iajs-399	99	32	for	for	ADP
iajs-399	99	33	pure	pure	ADJ
iajs-399	99	34	&	&	CCONJ
iajs-399	99	35	appl	appl	PROPN
iajs-399	99	36	.	.	PUNCT
iajs-399	100	1	sci	sci	PROPN
iajs-399	100	2	.	.	PUNCT
iajs-399	100	3	vol	vol	NOUN
iajs-399	100	4	.	.	PROPN
iajs-399	101	1	27	27	NUM
iajs-399	101	2	(	(	PUNCT
iajs-399	101	3	1	1	NUM
iajs-399	101	4	)	)	PUNCT
iajs-399	101	5	2014	2014	NUM
iajs-399	101	6	km	km	NOUN
iajs-399	101	7	ra	ra	PROPN
iajs-399	101	8	(	(	PUNCT
iajs-399	101	9	s	s	PROPN
iajs-399	101	10	,	,	PUNCT
iajs-399	101	11	(	(	PUNCT
iajs-399	101	12	xn	xn	NOUN
iajs-399	101	13	)	)	PUNCT
iajs-399	101	14	)	)	PUNCT
iajs-399	101	15	.	.	PUNCT
iajs-399	102	1	=	=	PRON
iajs-399	103	1	hence	hence	ADV
iajs-399	103	2	ra	ra	PROPN
iajs-399	103	3	(	(	PUNCT
iajs-399	103	4	ym	ym	INTJ
iajs-399	103	5	,	,	PUNCT
iajs-399	103	6	(	(	PUNCT
iajs-399	103	7	xn	xn	NOUN
iajs-399	103	8	)	)	PUNCT
iajs-399	103	9	)	)	PUNCT
iajs-399	103	10	–	–	PUNCT
iajs-399	103	11	ra	ra	PROPN
iajs-399	103	12	(	(	PUNCT
iajs-399	103	13	s	s	PROPN
iajs-399	103	14	,	,	PUNCT
iajs-399	103	15	(	(	PUNCT
iajs-399	103	16	xn))|	xn))|	PROPN
iajs-399	103	17	≤	≤	NUM
iajs-399	103	18	km	km	PROPN
iajs-399	103	19	ra	ra	PROPN
iajs-399	103	20	(	(	PUNCT
iajs-399	103	21	s	s	PROPN
iajs-399	103	22	,	,	PUNCT
iajs-399	103	23	(	(	PUNCT
iajs-399	103	24	xn	xn	PROPN
iajs-399	103	25	)	)	PUNCT
iajs-399	103	26	)	)	PUNCT
iajs-399	103	27	ra	ra	PROPN
iajs-399	104	1	(	(	PUNCT
iajs-399	104	2	s	s	PROPN
iajs-399	104	3	,	,	PUNCT
iajs-399	104	4	(	(	PUNCT
iajs-399	104	5	xn	xn	NOUN
iajs-399	104	6	)	)	PUNCT
iajs-399	104	7	)	)	PUNCT
iajs-399	105	1	≤	≤	NOUN
iajs-399	105	2	(	(	PUNCT
iajs-399	105	3	km	km	NOUN
iajs-399	105	4	–	–	PUNCT
iajs-399	105	5	1	1	NUM
iajs-399	105	6	)	)	PUNCT
iajs-399	105	7	ra(s	ra(	NOUN
iajs-399	105	8	,	,	PUNCT
iajs-399	105	9	(	(	PUNCT
iajs-399	105	10	xn	xn	NOUN
iajs-399	105	11	)	)	PUNCT
iajs-399	105	12	)	)	PUNCT
iajs-399	106	1	→	→	SYM
iajs-399	106	2	0	0	NUM
iajs-399	106	3	as	as	ADP
iajs-399	106	4	m→∞.	m→∞.	PROPN
iajs-399	106	5	it	it	PRON
iajs-399	106	6	follows	follow	VERB
iajs-399	106	7	from	from	ADP
iajs-399	106	8	2	2	NUM
iajs-399	106	9	-	-	SYM
iajs-399	106	10	1	1	NUM
iajs-399	106	11	that	that	SCONJ
iajs-399	106	12	tmv	tmv	NOUN
iajs-399	106	13	→	→	SYM
iajs-399	106	14	v	v	NOUN
iajs-399	106	15	by	by	ADP
iajs-399	106	16	the	the	DET
iajs-399	106	17	continuity	continuity	NOUN
iajs-399	106	18	of	of	ADP
iajs-399	106	19	t	t	NOUN
iajs-399	106	20	we	we	PRON
iajs-399	106	21	have	have	VERB
iajs-399	106	22	ty	ty	NOUN
iajs-399	106	23	=	=	NOUN
iajs-399	106	24	t(lim𝑚→∞	t(lim𝑚→∞	NOUN
iajs-399	106	25	𝑇𝑚	𝑇𝑚	NOUN
iajs-399	106	26	𝑦	𝑦	NOUN
iajs-399	106	27	)	)	PUNCT
iajs-399	106	28	=	=	SYM
iajs-399	107	1	lim𝑚→∞	lim𝑚→∞	PROPN
iajs-399	107	2	𝑇𝑚+1	𝑇𝑚+1	VERB
iajs-399	107	3	𝑦	𝑦	NOUN
iajs-399	107	4	=	=	SYM
iajs-399	107	5	𝑦	𝑦	PROPN
iajs-399	107	6	.	.	PUNCT
iajs-399	108	1	theorem	theorem	NOUN
iajs-399	108	2	(	(	PUNCT
iajs-399	108	3	fixed	fix	VERB
iajs-399	108	4	point	point	NOUN
iajs-399	108	5	theorem	theorem	VERB
iajs-399	108	6	)	)	PUNCT
iajs-399	108	7	let	let	VERB
iajs-399	108	8	x	x	PRON
iajs-399	108	9	be	be	AUX
iajs-399	108	10	a	a	DET
iajs-399	108	11	uniformly	uniformly	ADV
iajs-399	108	12	convex	convex	ADJ
iajs-399	108	13	2	2	NUM
iajs-399	108	14	-	-	PUNCT
iajs-399	108	15	banach	banach	NOUN
iajs-399	108	16	space	space	NOUN
iajs-399	108	17	,	,	PUNCT
iajs-399	108	18	s	s	VERB
iajs-399	108	19	a	a	DET
iajs-399	108	20	nonempty	nonempty	ADV
iajs-399	108	21	closed	close	VERB
iajs-399	108	22	convex	convex	NOUN
iajs-399	108	23	bounded	bound	VERB
iajs-399	108	24	subset	subset	NOUN
iajs-399	108	25	of	of	ADP
iajs-399	108	26	x	x	PUNCT
iajs-399	108	27	and	and	CCONJ
iajs-399	108	28	t	t	PROPN
iajs-399	108	29	:	:	PUNCT
iajs-399	108	30	s	s	X
iajs-399	108	31	→	→	SYM
iajs-399	108	32	s	s	X
iajs-399	108	33	an	an	DET
iajs-399	108	34	asymptotically	asymptotically	ADV
iajs-399	108	35	non	non	ADJ
iajs-399	108	36	-	-	ADJ
iajs-399	108	37	expansive	expansive	ADJ
iajs-399	108	38	mapping	mapping	NOUN
iajs-399	108	39	,	,	PUNCT
iajs-399	108	40	then	then	ADV
iajs-399	108	41	t	t	PROPN
iajs-399	108	42	has	have	VERB
iajs-399	108	43	a	a	DET
iajs-399	108	44	fixed	fix	VERB
iajs-399	108	45	point	point	NOUN
iajs-399	108	46	in	in	ADP
iajs-399	108	47	s.	s.	PROPN
iajs-399	108	48	proof	proof	NOUN
iajs-399	108	49	for	for	ADP
iajs-399	108	50	fixed	fix	VERB
iajs-399	108	51	y	y	PROPN
iajs-399	108	52	ϵ	ϵ	X
iajs-399	108	53	s	s	X
iajs-399	108	54	and	and	CCONJ
iajs-399	108	55	r	r	NOUN
iajs-399	108	56	>	>	X
iajs-399	108	57	0	0	NUM
iajs-399	108	58	,	,	PUNCT
iajs-399	108	59	set	set	VERB
iajs-399	108	60	ry	ry	NOUN
iajs-399	108	61	=	=	SYM
iajs-399	108	62	{	{	PUNCT
iajs-399	108	63	r	r	NOUN
iajs-399	108	64	:	:	PUNCT
iajs-399	108	65	there	there	PRON
iajs-399	108	66	exists	exist	VERB
iajs-399	108	67	k	k	PROPN
iajs-399	108	68	ϵ	ϵ	PROPN
iajs-399	108	69	n	n	PROPN
iajs-399	108	70	with	with	ADP
iajs-399	108	71	s	s	NOUN
iajs-399	108	72	∩	∩	NOUN
iajs-399	108	73	(	(	PUNCT
iajs-399	108	74	⋂	⋂	PROPN
iajs-399	108	75	𝐵𝑟[𝑇𝑖	𝐵𝑟[𝑇𝑖	PROPN
iajs-399	108	76	𝑦	𝑦	NOUN
iajs-399	108	77	]	]	X
iajs-399	108	78	)	)	PUNCT
iajs-399	108	79	≠∞	≠∞	NOUN
iajs-399	108	80	𝑖=𝑘	𝑖=𝑘	PUNCT
iajs-399	108	81	ø	ø	NOUN
iajs-399	108	82	}	}	PUNCT
iajs-399	108	83	and	and	CCONJ
iajs-399	108	84	d	d	PROPN
iajs-399	108	85	=	=	SYM
iajs-399	108	86	diam	diam	PROPN
iajs-399	108	87	(	(	PUNCT
iajs-399	108	88	s	s	NOUN
iajs-399	108	89	)	)	PUNCT
iajs-399	108	90	.	.	PUNCT
iajs-399	109	1	then	then	ADV
iajs-399	109	2	d	d	X
iajs-399	109	3	ϵ	ϵ	X
iajs-399	109	4	ry	ry	NOUN
iajs-399	109	5	.	.	PUNCT
iajs-399	109	6	hence	hence	ADV
iajs-399	109	7	ry	ry	NOUN
iajs-399	109	8	≠	≠	PROPN
iajs-399	109	9	ø	ø	PROPN
iajs-399	109	10	.	.	PUNCT
iajs-399	110	1	let	let	VERB
iajs-399	110	2	ro	ro	PRON
iajs-399	110	3	=	=	VERB
iajs-399	110	4	inf	inf	PROPN
iajs-399	110	5	{	{	PUNCT
iajs-399	110	6	r	r	NOUN
iajs-399	110	7	:	:	PUNCT
iajs-399	110	8	r	r	NOUN
iajs-399	110	9	ϵ	ϵ	X
iajs-399	110	10	ry	ry	NOUN
iajs-399	110	11	}	}	PUNCT
iajs-399	110	12	,	,	PUNCT
iajs-399	110	13	fot	fot	VERB
iajs-399	110	14	each	each	DET
iajs-399	110	15	𝜀𝜀	𝜀𝜀	VERB
iajs-399	110	16	>	>	X
iajs-399	110	17	0	0	NUM
iajs-399	110	18	,	,	PUNCT
iajs-399	110	19	we	we	PRON
iajs-399	110	20	define	define	VERB
iajs-399	110	21	sɛ	sɛ	VERB
iajs-399	110	22	=	=	SYM
iajs-399	111	1	⋃	⋃	PROPN
iajs-399	111	2	(	(	PUNCT
iajs-399	111	3	⋂	⋂	PROPN
iajs-399	111	4	𝐵𝑟+ɛ∞	𝐵𝑟+ɛ∞	NUM
iajs-399	111	5	𝑖=𝑘	𝑖=𝑘	NUM
iajs-399	111	6	∞	∞	NUM
iajs-399	111	7	𝑘=1	𝑘=1	NOUN
iajs-399	112	1	[	[	X
iajs-399	112	2	ti	ti	X
iajs-399	112	3	y	y	PROPN
iajs-399	112	4	]	]	PUNCT
iajs-399	112	5	)	)	PUNCT
iajs-399	112	6	.	.	PUNCT
iajs-399	113	1	thus	thus	ADV
iajs-399	113	2	,	,	PUNCT
iajs-399	113	3	for	for	ADP
iajs-399	113	4	each	each	DET
iajs-399	113	5	ɛ	ɛ	PROPN
iajs-399	113	6	>	>	X
iajs-399	113	7	0	0	NUM
iajs-399	113	8	,	,	PUNCT
iajs-399	113	9	the	the	DET
iajs-399	113	10	set	set	NOUN
iajs-399	113	11	sɛ	sɛ	VERB
iajs-399	113	12	∩	∩	NOUN
iajs-399	113	13	s	s	PART
iajs-399	113	14	is	be	AUX
iajs-399	113	15	nonempty	nonempty	ADJ
iajs-399	113	16	and	and	CCONJ
iajs-399	113	17	convex	convex	ADJ
iajs-399	113	18	.	.	PUNCT
iajs-399	114	1	the	the	DET
iajs-399	114	2	reflexivity	reflexivity	NOUN
iajs-399	114	3	of	of	ADP
iajs-399	114	4	x	x	PRON
iajs-399	114	5	implies	imply	VERB
iajs-399	114	6	that	that	SCONJ
iajs-399	114	7	∩ɛ>0	∩ɛ>0	PROPN
iajs-399	114	8	(	(	PUNCT
iajs-399	114	9	𝑆𝜀	𝑆𝜀	NOUN
iajs-399	114	10	�	�	NOUN
iajs-399	114	11	∩	∩	NOUN
iajs-399	114	12	s	s	PART
iajs-399	114	13	)	)	PUNCT
iajs-399	114	14	≠	≠	PROPN
iajs-399	114	15	ø	ø	NOUN
iajs-399	114	16	let	let	VERB
iajs-399	114	17	𝓍𝓍	𝓍𝓍	PRON
iajs-399	114	18	ϵ	ϵ	X
iajs-399	114	19	∩ɛ>0	∩ɛ>0	X
iajs-399	114	20	(	(	PUNCT
iajs-399	114	21	𝑆𝜀	𝑆𝜀	PROPN
iajs-399	114	22	�	�	PROPN
iajs-399	114	23	∩	∩	NOUN
iajs-399	114	24	s	s	PART
iajs-399	114	25	)	)	PUNCT
iajs-399	114	26	and	and	CCONJ
iajs-399	114	27	ƞ	ƞ	X
iajs-399	114	28	>	>	X
iajs-399	114	29	0	0	NUM
iajs-399	114	30	,	,	PUNCT
iajs-399	114	31	there	there	PRON
iajs-399	114	32	exists	exist	VERB
iajs-399	114	33	an	an	DET
iajs-399	114	34	integer	integer	NOUN
iajs-399	114	35	no	no	PRON
iajs-399	114	36	such	such	ADJ
iajs-399	114	37	that	that	SCONJ
iajs-399	114	38	𝓍𝓍	𝓍𝓍	PROPN
iajs-399	114	39	–	–	PUNCT
iajs-399	114	40	tny	tny	NOUN
iajs-399	114	41	,	,	PUNCT
iajs-399	114	42	u||	u||	ADV
iajs-399	114	43	≤	≤	NUM
iajs-399	114	44	ro	ro	NOUN
iajs-399	115	1	+	+	NUM
iajs-399	115	2	ƞ	ƞ	NOUN
iajs-399	115	3	for	for	ADP
iajs-399	115	4	all	all	DET
iajs-399	115	5	n	n	PRON
iajs-399	115	6	≥	≥	NOUN
iajs-399	115	7	no	no	INTJ
iajs-399	115	8	,	,	PUNCT
iajs-399	115	9	u	u	NOUN
iajs-399	115	10	ϵ	ϵ	PROPN
iajs-399	115	11	s.	s.	PROPN
iajs-399	115	12	||	||	PROPN
iajs-399	116	1	now	now	ADV
iajs-399	116	2	let	let	VERB
iajs-399	116	3	𝓍𝓍	𝓍𝓍	PRON
iajs-399	116	4	ϵ	ϵ	X
iajs-399	116	5	∩ɛ>0	∩ɛ>0	X
iajs-399	116	6	(	(	PUNCT
iajs-399	116	7	𝑆𝜀	𝑆𝜀	NOUN
iajs-399	116	8	�	�	NOUN
iajs-399	116	9	∩	∩	NOUN
iajs-399	116	10	s	s	PART
iajs-399	116	11	)	)	PUNCT
iajs-399	116	12	and	and	CCONJ
iajs-399	116	13	suppose	suppose	VERB
iajs-399	116	14	that	that	SCONJ
iajs-399	116	15	the	the	DET
iajs-399	116	16	sequence	sequence	NOUN
iajs-399	116	17	(	(	PUNCT
iajs-399	116	18	tn𝓍𝓍	tn𝓍𝓍	INTJ
iajs-399	116	19	)	)	PUNCT
iajs-399	116	20	does	do	AUX
iajs-399	116	21	not	not	PART
iajs-399	116	22	converge	converge	VERB
iajs-399	116	23	strongly	strongly	ADV
iajs-399	116	24	to	to	ADP
iajs-399	116	25	𝓍𝓍	𝓍𝓍	PRON
iajs-399	116	26	.	.	PUNCT
iajs-399	117	1	then	then	ADV
iajs-399	117	2	there	there	PRON
iajs-399	117	3	exists	exist	VERB
iajs-399	117	4	ɛ	ɛ	PROPN
iajs-399	117	5	>	>	X
iajs-399	117	6	0	0	PUNCT
iajs-399	117	7	and	and	CCONJ
iajs-399	117	8	a	a	DET
iajs-399	117	9	subsequence	subsequence	NOUN
iajs-399	117	10	(	(	PUNCT
iajs-399	117	11	tni𝓍𝓍	tni𝓍𝓍	NOUN
iajs-399	117	12	)	)	PUNCT
iajs-399	117	13	of	of	ADP
iajs-399	117	14	(	(	PUNCT
iajs-399	117	15	tnx	tnx	NOUN
iajs-399	117	16	)	)	PUNCT
iajs-399	117	17	.	.	PUNCT
iajs-399	118	1	such	such	ADJ
iajs-399	118	2	that	that	SCONJ
iajs-399	118	3	||tni	||tni	PROPN
iajs-399	118	4	𝓍𝓍	𝓍𝓍	PROPN
iajs-399	118	5	–	–	PUNCT
iajs-399	118	6	𝓍𝓍	𝓍𝓍	PROPN
iajs-399	118	7	,	,	PUNCT
iajs-399	118	8	u||	u||	ADV
iajs-399	118	9	≥	≥	X
iajs-399	118	10	ɛ	ɛ	X
iajs-399	118	11	,	,	PUNCT
iajs-399	118	12	for	for	ADP
iajs-399	118	13	all	all	DET
iajs-399	118	14	i=1,2	i=1,2	ADJ
iajs-399	118	15	,	,	PUNCT
iajs-399	118	16	…	…	PUNCT
iajs-399	118	17	.	.	PUNCT
iajs-399	119	1	suppose	suppose	VERB
iajs-399	119	2	kn	kn	PROPN
iajs-399	119	3	is	be	AUX
iajs-399	119	4	the	the	DET
iajs-399	119	5	lipschitz	lipschitz	NOUN
iajs-399	119	6	constant	constant	ADJ
iajs-399	119	7	of	of	ADP
iajs-399	119	8	tn	tn	PROPN
iajs-399	119	9	.	.	PUNCT
iajs-399	120	1	then	then	ADV
iajs-399	120	2	for	for	ADP
iajs-399	120	3	m	m	PROPN
iajs-399	120	4	>	>	X
iajs-399	120	5	n	n	CCONJ
iajs-399	120	6	,	,	PUNCT
iajs-399	120	7	we	we	PRON
iajs-399	120	8	have	have	VERB
iajs-399	120	9	||tn𝓍𝓍	||tn𝓍𝓍	PROPN
iajs-399	120	10	–	–	PUNCT
iajs-399	120	11	tm𝓍𝓍	tm𝓍𝓍	NOUN
iajs-399	120	12	,	,	PUNCT
iajs-399	120	13	u||	u||	ADV
iajs-399	120	14	≤	≤	NUM
iajs-399	120	15	kn	kn	PROPN
iajs-399	120	16	||𝓍𝓍	||𝓍𝓍	PROPN
iajs-399	120	17	–	–	PUNCT
iajs-399	120	18	tm	tm	NOUN
iajs-399	120	19	-	-	ADJ
iajs-399	120	20	n𝓍𝓍	n𝓍𝓍	NOUN
iajs-399	120	21	,	,	PUNCT
iajs-399	120	22	u||	u||	NOUN
iajs-399	120	23	.	.	PUNCT
iajs-399	121	1	suppose	suppose	VERB
iajs-399	121	2	that	that	SCONJ
iajs-399	121	3	ro	ro	PROPN
iajs-399	121	4	>	>	X
iajs-399	121	5	0	0	PUNCT
iajs-399	121	6	and	and	CCONJ
iajs-399	121	7	choose	choose	VERB
iajs-399	121	8	α	α	PROPN
iajs-399	121	9	>	>	X
iajs-399	121	10	0	0	NUM
iajs-399	121	11	such	such	ADJ
iajs-399	121	12	that	that	SCONJ
iajs-399	121	13	(	(	PUNCT
iajs-399	121	14	1	1	NUM
iajs-399	121	15	-θx	-θx	NOUN
iajs-399	121	16	(	(	PUNCT
iajs-399	121	17	(	(	PUNCT
iajs-399	121	18	ɛ	ɛ	PROPN
iajs-399	121	19	𝑟𝑜+𝛼	𝑟𝑜+𝛼	NUM
iajs-399	121	20	)	)	PUNCT
iajs-399	121	21	)	)	PUNCT
iajs-399	122	1	(	(	PUNCT
iajs-399	122	2	𝑟𝑜	𝑟𝑜	PROPN
iajs-399	122	3	+	+	SYM
iajs-399	122	4	𝛼	𝛼	X
iajs-399	122	5	)	)	PUNCT
iajs-399	122	6	˂	˂	NOUN
iajs-399	122	7	𝑟𝑜	𝑟𝑜	PRON
iajs-399	122	8	select	select	ADJ
iajs-399	122	9	n	n	PRON
iajs-399	122	10	such	such	ADJ
iajs-399	122	11	that	that	SCONJ
iajs-399	122	12	||	||	PROPN
iajs-399	123	1	𝓍𝓍	𝓍𝓍	PROPN
iajs-399	123	2	–	–	PUNCT
iajs-399	123	3	tn	tn	PROPN
iajs-399	123	4	𝓍𝓍,u||	𝓍𝓍,u||	NOUN
iajs-399	123	5	≥	≥	NOUN
iajs-399	123	6	ɛ	ɛ	PROPN
iajs-399	123	7	and	and	CCONJ
iajs-399	123	8	kn	kn	PROPN
iajs-399	123	9	=	=	PUNCT
iajs-399	123	10	(	(	PUNCT
iajs-399	123	11	ro	ro	X
iajs-399	123	12	+	+	NOUN
iajs-399	123	13	𝛼	𝛼	NUM
iajs-399	123	14	2	2	NUM
iajs-399	123	15	)	)	PUNCT
iajs-399	123	16	≤	≤	NOUN
iajs-399	124	1	ro	ro	NOUN
iajs-399	125	1	+	+	NUM
iajs-399	125	2	α	α	PRON
iajs-399	125	3	if	if	SCONJ
iajs-399	125	4	no	no	DET
iajs-399	125	5	≥	≥	NOUN
iajs-399	125	6	n	n	CCONJ
iajs-399	125	7	,	,	PUNCT
iajs-399	125	8	then	then	ADV
iajs-399	125	9	m	m	VERB
iajs-399	125	10	>	>	X
iajs-399	126	1	no	no	PRON
iajs-399	126	2	implies	imply	VERB
iajs-399	126	3	||𝓍𝓍	||𝓍𝓍	NOUN
iajs-399	126	4	–	–	PUNCT
iajs-399	126	5	tm	tm	PROPN
iajs-399	126	6	-	-	PROPN
iajs-399	126	7	ny	ny	PROPN
iajs-399	126	8	,	,	PUNCT
iajs-399	126	9	u||	u||	ADV
iajs-399	126	10	≤	≤	NUM
iajs-399	126	11	ro	ro	NOUN
iajs-399	127	1	+	+	NOUN
iajs-399	127	2	𝛼	𝛼	PROPN
iajs-399	127	3	2	2	NUM
iajs-399	127	4	.	.	PUNCT
iajs-399	128	1	since	since	SCONJ
iajs-399	128	2	||tn𝓍𝓍	||tn𝓍𝓍	PROPN
iajs-399	128	3	–	–	PUNCT
iajs-399	128	4	tmy	tmy	NOUN
iajs-399	128	5	,	,	PUNCT
iajs-399	128	6	u||	u||	ADV
iajs-399	128	7	≤	≤	NUM
iajs-399	128	8	kn	kn	PROPN
iajs-399	128	9	||𝓍𝓍	||𝓍𝓍	PROPN
iajs-399	128	10	–	–	PUNCT
iajs-399	128	11	tm	tm	PROPN
iajs-399	128	12	-	-	PROPN
iajs-399	128	13	ny	ny	PROPN
iajs-399	128	14	,	,	PUNCT
iajs-399	128	15	u||	u||	NOUN
iajs-399	128	16	kn	kn	PROPN
iajs-399	128	17	(	(	PUNCT
iajs-399	128	18	ro	ro	PROPN
iajs-399	128	19	+	+	NOUN
iajs-399	128	20	𝛼	𝛼	SYM
iajs-399	128	21	2	2	NUM
iajs-399	128	22	≤	≤	NUM
iajs-399	128	23	)	)	PUNCT
iajs-399	129	1	ro	ro	PROPN
iajs-399	130	1	+	+	CCONJ
iajs-399	130	2	α	α	NOUN
iajs-399	130	3	≤	≤	NOUN
iajs-399	130	4	and	and	CCONJ
iajs-399	130	5	||𝓍𝓍	||𝓍𝓍	NOUN
iajs-399	130	6	–	–	PUNCT
iajs-399	130	7	tmy	tmy	NOUN
iajs-399	130	8	,	,	PUNCT
iajs-399	130	9	u||	u||	ADV
iajs-399	130	10	≤	≤	NUM
iajs-399	131	1	ro	ro	NOUN
iajs-399	132	1	+	+	CCONJ
iajs-399	132	2	α	α	PRON
iajs-399	132	3	it	it	PRON
iajs-399	132	4	follows	follow	VERB
iajs-399	132	5	from	from	ADP
iajs-399	132	6	the	the	DET
iajs-399	132	7	uniform	uniform	ADJ
iajs-399	132	8	convexity	convexity	NOUN
iajs-399	132	9	of	of	ADP
iajs-399	132	10	x	x	DET
iajs-399	132	11	that	that	PRON
iajs-399	132	12	for	for	ADP
iajs-399	132	13	m	m	PROPN
iajs-399	132	14	>	>	NOUN
iajs-399	132	15	no	no	DET
iajs-399	132	16	||½	||½	NOUN
iajs-399	132	17	(	(	PUNCT
iajs-399	132	18	𝓍𝓍+	𝓍𝓍+	ADJ
iajs-399	132	19	tn𝓍𝓍	tn𝓍𝓍	NOUN
iajs-399	132	20	)	)	PUNCT
iajs-399	132	21	–	–	PUNCT
iajs-399	132	22	tmy	tmy	NOUN
iajs-399	132	23	,	,	PUNCT
iajs-399	132	24	u||	u||	ADV
iajs-399	132	25	≤	≤	NUM
iajs-399	132	26	(	(	PUNCT
iajs-399	132	27	1	1	NUM
iajs-399	132	28	–	–	PUNCT
iajs-399	132	29	θx	θx	PROPN
iajs-399	132	30	(	(	PUNCT
iajs-399	132	31	𝜀	𝜀	X
iajs-399	132	32	𝑟𝑜+𝛼	𝑟𝑜+𝛼	NUM
iajs-399	132	33	)	)	PUNCT
iajs-399	132	34	)	)	PUNCT
iajs-399	133	1	(	(	PUNCT
iajs-399	133	2	ro	ro	X
iajs-399	133	3	+	+	CCONJ
iajs-399	133	4	α	α	X
iajs-399	133	5	)	)	PUNCT
iajs-399	133	6	˂	˂	NOUN
iajs-399	133	7	ro	ro	NOUN
iajs-399	133	8	.	.	PUNCT
iajs-399	134	1	this	this	PRON
iajs-399	134	2	contradicts	contradict	VERB
iajs-399	134	3	the	the	DET
iajs-399	134	4	definition	definition	NOUN
iajs-399	134	5	of	of	ADP
iajs-399	134	6	ro	ro	INTJ
iajs-399	134	7	.	.	PUNCT
iajs-399	135	1	hence	hence	ADV
iajs-399	135	2	ro=	ro=	VERB
iajs-399	135	3	0	0	NUM
iajs-399	135	4	or	or	CCONJ
iajs-399	135	5	t𝓍𝓍	t𝓍𝓍	NOUN
iajs-399	135	6	=	=	SYM
iajs-399	135	7	𝓍𝓍.	𝓍𝓍.	NOUN
iajs-399	136	1	but	but	CCONJ
iajs-399	136	2	ro	ro	NOUN
iajs-399	136	3	=	=	NOUN
iajs-399	136	4	0	0	PROPN
iajs-399	136	5	implies	imply	VERB
iajs-399	136	6	that	that	SCONJ
iajs-399	136	7	(	(	PUNCT
iajs-399	136	8	tny	tny	NOUN
iajs-399	136	9	)	)	PUNCT
iajs-399	136	10	is	be	AUX
iajs-399	136	11	a	a	DET
iajs-399	136	12	cauchy	cauchy	ADJ
iajs-399	136	13	sequence	sequence	NOUN
iajs-399	136	14	and	and	CCONJ
iajs-399	136	15	hence	hence	ADV
iajs-399	136	16	lim𝑛→∞	lim𝑛→∞	PROPN
iajs-399	136	17	𝑇ny	𝑇ny	PROPN
iajs-399	136	18	=	=	NOUN
iajs-399	136	19	𝓍𝓍	𝓍𝓍	NOUN
iajs-399	136	20	=	=	PUNCT
iajs-399	136	21	t𝓍𝓍	t𝓍𝓍	NOUN
iajs-399	136	22	.	.	PUNCT
iajs-399	137	1	therefore	therefore	ADV
iajs-399	137	2	,	,	PUNCT
iajs-399	137	3	the	the	DET
iajs-399	137	4	set	set	VERB
iajs-399	137	5	∩ɛ>0(𝑆𝜀	∩ɛ>0(𝑆𝜀	NOUN
iajs-399	137	6	�	�	PROPN
iajs-399	137	7	∩	∩	NOUN
iajs-399	137	8	s	s	PART
iajs-399	137	9	)	)	PUNCT
iajs-399	137	10	is	be	AUX
iajs-399	137	11	a	a	DET
iajs-399	137	12	singleton	singleton	NOUN
iajs-399	137	13	that	that	PRON
iajs-399	137	14	is	be	AUX
iajs-399	137	15	a	a	DET
iajs-399	137	16	fixed	fixed	ADJ
iajs-399	137	17	point	point	NOUN
iajs-399	137	18	of	of	ADP
iajs-399	137	19	t.	t.	PROPN
iajs-399	137	20	■	■	PROPN
iajs-399	137	21	347	347	NUM
iajs-399	137	22	|	|	ADV
iajs-399	137	23	mathematics	mathematic	NOUN
iajs-399	137	24	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	NUM
iajs-399	137	25	�	�	NOUN
iajs-399	137	26	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	NUM
iajs-399	137	27	:	:	PUNCT
iajs-399	137	28	a@âig@ú‹	a@âig@ú‹	PROPN
iajs-399	137	29	©	©	PROPN
iajs-399	137	30	@ü‹127@@öü»€a@i1@‚b«@h2014	@ü‹127@@öü»€a@i1@‚b«@h2014	PROPN
iajs-399	137	31	ibn	ibn	PROPN
iajs-399	137	32	al	al	PROPN
iajs-399	137	33	-	-	PUNCT
iajs-399	137	34	haitham	haitham	PROPN
iajs-399	137	35	jour	jour	X
iajs-399	137	36	.	.	PROPN
iajs-399	138	1	for	for	ADP
iajs-399	138	2	pure	pure	ADJ
iajs-399	138	3	&	&	CCONJ
iajs-399	138	4	appl	appl	PROPN
iajs-399	138	5	.	.	PUNCT
iajs-399	139	1	sci	sci	PROPN
iajs-399	139	2	.	.	PUNCT
iajs-399	139	3	vol	vol	NOUN
iajs-399	139	4	.	.	PROPN
iajs-399	140	1	27	27	NUM
iajs-399	140	2	(	(	PUNCT
iajs-399	140	3	1	1	NUM
iajs-399	140	4	)	)	PUNCT
iajs-399	140	5	2014	2014	NUM
iajs-399	140	6	theorem	theorem	NOUN
iajs-399	140	7	let	let	VERB
iajs-399	140	8	x	x	PRON
iajs-399	140	9	be	be	AUX
iajs-399	140	10	a	a	DET
iajs-399	140	11	uniformly	uniformly	ADV
iajs-399	140	12	convex	convex	ADJ
iajs-399	140	13	2	2	NUM
iajs-399	140	14	-	-	PUNCT
iajs-399	140	15	banach	banach	NOUN
iajs-399	140	16	space	space	NOUN
iajs-399	140	17	,	,	PUNCT
iajs-399	140	18	s	s	VERB
iajs-399	140	19	a	a	DET
iajs-399	140	20	nonempty	nonempty	ADV
iajs-399	140	21	closed	close	VERB
iajs-399	140	22	convex	convex	NOUN
iajs-399	140	23	subset	subset	NOUN
iajs-399	140	24	of	of	ADP
iajs-399	140	25	x	x	PUNCT
iajs-399	140	26	and	and	CCONJ
iajs-399	140	27	t	t	PROPN
iajs-399	140	28	:	:	PUNCT
iajs-399	140	29	s	s	AUX
iajs-399	140	30	→	→	SYM
iajs-399	140	31	s	s	X
iajs-399	140	32	an	an	DET
iajs-399	140	33	asymptotically	asymptotically	ADV
iajs-399	140	34	non	non	ADJ
iajs-399	140	35	-	-	ADJ
iajs-399	140	36	expansive	expansive	ADJ
iajs-399	140	37	mapping	mapping	NOUN
iajs-399	140	38	,	,	PUNCT
iajs-399	140	39	u	u	PROPN
iajs-399	140	40	∈	∈	PROPN
iajs-399	140	41	s	s	NOUN
iajs-399	140	42	,	,	PUNCT
iajs-399	140	43	then	then	ADV
iajs-399	140	44	the	the	DET
iajs-399	140	45	follo	follo	ADJ
iajs-399	140	46	-	-	PUNCT
iajs-399	140	47	wing	wing	NOUN
iajs-399	140	48	statements	statement	NOUN
iajs-399	140	49	are	be	AUX
iajs-399	140	50	equivalent	equivalent	ADJ
iajs-399	140	51	:	:	PUNCT
iajs-399	140	52	1	1	X
iajs-399	140	53	)	)	PUNCT
iajs-399	140	54	t	t	PROPN
iajs-399	140	55	has	have	VERB
iajs-399	140	56	a	a	DET
iajs-399	140	57	fixed	fix	VERB
iajs-399	140	58	point	point	NOUN
iajs-399	140	59	.	.	PUNCT
iajs-399	141	1	2	2	X
iajs-399	141	2	)	)	PUNCT
iajs-399	141	3	there	there	PRON
iajs-399	141	4	exists	exist	VERB
iajs-399	141	5	a	a	DET
iajs-399	141	6	point	point	NOUN
iajs-399	141	7	xo	xo	PROPN
iajs-399	142	1	ϵ	ϵ	X
iajs-399	142	2	s	s	VERB
iajs-399	142	3	such	such	ADJ
iajs-399	142	4	that	that	SCONJ
iajs-399	142	5	the	the	DET
iajs-399	142	6	sequence	sequence	NOUN
iajs-399	142	7	(	(	PUNCT
iajs-399	142	8	tnxo	tnxo	PROPN
iajs-399	142	9	)	)	PUNCT
iajs-399	142	10	is	be	AUX
iajs-399	142	11	bounded	bound	VERB
iajs-399	142	12	.	.	PUNCT
iajs-399	143	1	3	3	X
iajs-399	143	2	)	)	PUNCT
iajs-399	143	3	there	there	PRON
iajs-399	143	4	exists	exist	VERB
iajs-399	143	5	a	a	DET
iajs-399	143	6	bounded	bounded	ADJ
iajs-399	143	7	sequence	sequence	NOUN
iajs-399	143	8	(	(	PUNCT
iajs-399	143	9	yn	yn	NOUN
iajs-399	143	10	)	)	PUNCT
iajs-399	143	11	in	in	ADP
iajs-399	143	12	s	s	PRON
iajs-399	143	13	such	such	ADJ
iajs-399	143	14	that	that	SCONJ
iajs-399	143	15	lim𝑛→∞‖𝑦𝑛	lim𝑛→∞‖𝑦𝑛	PROPN
iajs-399	144	1	−	−	PROPN
iajs-399	145	1	𝑇𝑦𝑛	𝑇𝑦𝑛	PROPN
iajs-399	145	2	,	,	PUNCT
iajs-399	145	3	𝑢‖	𝑢‖	PROPN
iajs-399	145	4	=	=	SYM
iajs-399	145	5	0	0	NUM
iajs-399	145	6	.	.	PUNCT
iajs-399	146	1	proof	proof	NOUN
iajs-399	146	2	(	(	PUNCT
iajs-399	146	3	1	1	NUM
iajs-399	146	4	)	)	PUNCT
iajs-399	146	5	⟹	⟹	NOUN
iajs-399	146	6	(	(	PUNCT
iajs-399	146	7	2	2	NUM
iajs-399	146	8	)	)	PUNCT
iajs-399	146	9	and	and	CCONJ
iajs-399	146	10	(	(	PUNCT
iajs-399	146	11	1	1	X
iajs-399	146	12	)	)	PUNCT
iajs-399	146	13	⟹	⟹	NOUN
iajs-399	146	14	(	(	PUNCT
iajs-399	146	15	3	3	X
iajs-399	146	16	)	)	PUNCT
iajs-399	146	17	follows	follow	VERB
iajs-399	146	18	easily	easily	ADV
iajs-399	146	19	.	.	PUNCT
iajs-399	147	1	(	(	PUNCT
iajs-399	147	2	3	3	X
iajs-399	147	3	)	)	PUNCT
iajs-399	147	4	⟹	⟹	NOUN
iajs-399	147	5	(	(	PUNCT
iajs-399	147	6	1	1	X
iajs-399	147	7	)	)	PUNCT
iajs-399	147	8	let	let	VERB
iajs-399	147	9	(	(	PUNCT
iajs-399	147	10	yn	yn	NOUN
iajs-399	147	11	)	)	PUNCT
iajs-399	147	12	be	be	VERB
iajs-399	147	13	a	a	DET
iajs-399	147	14	bounded	bounded	ADJ
iajs-399	147	15	sequence	sequence	NOUN
iajs-399	147	16	in	in	ADP
iajs-399	147	17	s	s	PRON
iajs-399	147	18	such	such	ADJ
iajs-399	147	19	that	that	DET
iajs-399	147	20	lim𝑛→∞	lim𝑛→∞	PROPN
iajs-399	147	21	�	�	PROPN
iajs-399	147	22	|𝑦𝑛	|𝑦𝑛	NUM
iajs-399	147	23	−	−	PROPN
iajs-399	147	24	𝑇𝑦𝑛	𝑇𝑦𝑛	PROPN
iajs-399	147	25	,	,	PUNCT
iajs-399	147	26	𝑢|	𝑢|	PROPN
iajs-399	147	27	�	�	PROPN
iajs-399	147	28	=	=	SYM
iajs-399	147	29	0	0	PUNCT
iajs-399	148	1	let	let	VERB
iajs-399	148	2	za	za	PROPN
iajs-399	148	3	(	(	PUNCT
iajs-399	148	4	s,(yn	s,(yn	ADJ
iajs-399	148	5	)	)	PUNCT
iajs-399	148	6	)	)	PUNCT
iajs-399	149	1	=	=	PRON
iajs-399	149	2	{	{	PUNCT
iajs-399	149	3	v	v	NOUN
iajs-399	149	4	}	}	PUNCT
iajs-399	149	5	,	,	PUNCT
iajs-399	149	6	therefore	therefore	ADV
iajs-399	149	7	,	,	PUNCT
iajs-399	149	8	by	by	ADP
iajs-399	149	9	theorem	theorem	ADJ
iajs-399	149	10	2	2	NUM
iajs-399	149	11	-	-	SYM
iajs-399	149	12	4	4	NUM
iajs-399	149	13	,	,	PUNCT
iajs-399	149	14	implies	imply	VERB
iajs-399	149	15	that	that	SCONJ
iajs-399	149	16	v	v	NOUN
iajs-399	149	17	is	be	AUX
iajs-399	149	18	a	a	DET
iajs-399	149	19	fixed	fix	VERB
iajs-399	149	20	point	point	NOUN
iajs-399	149	21	of	of	ADP
iajs-399	149	22	t.	t.	PROPN
iajs-399	149	23	■	■	PUNCT
iajs-399	149	24	corollary	corollary	ADJ
iajs-399	149	25	let	let	VERB
iajs-399	149	26	s	s	PRON
iajs-399	149	27	be	be	AUX
iajs-399	149	28	a	a	DET
iajs-399	149	29	nonempty	nonempty	ADV
iajs-399	149	30	closed	close	VERB
iajs-399	149	31	convex	convex	NOUN
iajs-399	149	32	subset	subset	NOUN
iajs-399	149	33	of	of	ADP
iajs-399	149	34	a	a	DET
iajs-399	149	35	strictly	strictly	ADV
iajs-399	149	36	convex	convex	ADJ
iajs-399	149	37	2	2	NUM
iajs-399	149	38	-	-	PUNCT
iajs-399	149	39	banach	banach	NOUN
iajs-399	149	40	space	space	NOUN
iajs-399	149	41	x	x	PUNCT
iajs-399	149	42	and	and	CCONJ
iajs-399	149	43	t	t	PROPN
iajs-399	149	44	:	:	PUNCT
iajs-399	149	45	s	s	X
iajs-399	149	46	→	→	SYM
iajs-399	149	47	x	x	X
iajs-399	149	48	a	a	DET
iajs-399	149	49	non	non	ADJ
iajs-399	149	50	-	-	ADJ
iajs-399	149	51	expansive	expansive	ADJ
iajs-399	149	52	mapping	mapping	NOUN
iajs-399	149	53	.	.	PUNCT
iajs-399	150	1	then	then	ADV
iajs-399	150	2	f(t	f(t	NOUN
iajs-399	150	3	)	)	PUNCT
iajs-399	150	4	is	be	AUX
iajs-399	150	5	closed	close	VERB
iajs-399	150	6	and	and	CCONJ
iajs-399	150	7	convex	convex	NOUN
iajs-399	150	8	.	.	PUNCT
iajs-399	151	1	we	we	PRON
iajs-399	151	2	have	have	AUX
iajs-399	151	3	seen	see	VERB
iajs-399	151	4	in	in	ADP
iajs-399	151	5	a	a	DET
iajs-399	151	6	corollary	corollary	ADJ
iajs-399	151	7	2	2	NUM
iajs-399	151	8	-	-	SYM
iajs-399	151	9	7	7	NUM
iajs-399	151	10	,	,	PUNCT
iajs-399	151	11	that	that	SCONJ
iajs-399	151	12	f(t	f(t	NOUN
iajs-399	151	13	)	)	PUNCT
iajs-399	151	14	is	be	AUX
iajs-399	151	15	closed	close	VERB
iajs-399	151	16	and	and	CCONJ
iajs-399	151	17	convex	convex	VERB
iajs-399	151	18	in	in	ADP
iajs-399	151	19	strictly	strictly	ADV
iajs-399	151	20	convex	convex	VERB
iajs-399	151	21	2banach	2banach	NUM
iajs-399	151	22	space	space	NOUN
iajs-399	151	23	for	for	ADP
iajs-399	151	24	non	non	ADJ
iajs-399	151	25	-	-	ADJ
iajs-399	151	26	expansive	expansive	ADJ
iajs-399	151	27	mappings	mapping	NOUN
iajs-399	151	28	.	.	PUNCT
iajs-399	152	1	however	however	ADV
iajs-399	152	2	,	,	PUNCT
iajs-399	152	3	we	we	PRON
iajs-399	152	4	think	think	VERB
iajs-399	152	5	that	that	SCONJ
iajs-399	152	6	corollary	corollary	ADJ
iajs-399	152	7	2	2	NUM
iajs-399	152	8	-	-	SYM
iajs-399	152	9	7	7	NUM
iajs-399	152	10	,	,	PUNCT
iajs-399	152	11	is	be	AUX
iajs-399	152	12	not	not	PART
iajs-399	152	13	true	true	ADJ
iajs-399	152	14	for	for	ADP
iajs-399	152	15	asymptotically	asymptotically	ADV
iajs-399	152	16	non	non	ADJ
iajs-399	152	17	-	-	ADJ
iajs-399	152	18	expansive	expansive	ADJ
iajs-399	152	19	mappings	mapping	NOUN
iajs-399	152	20	.	.	PUNCT
iajs-399	153	1	in	in	ADP
iajs-399	153	2	fact	fact	NOUN
iajs-399	153	3	,	,	PUNCT
iajs-399	153	4	we	we	PRON
iajs-399	153	5	have	have	AUX
iajs-399	153	6	:	:	PUNCT
iajs-399	153	7	theorem	theorem	VERB
iajs-399	153	8	let	let	VERB
iajs-399	153	9	x	x	PRON
iajs-399	153	10	be	be	AUX
iajs-399	153	11	a	a	DET
iajs-399	153	12	uniformly	uniformly	ADV
iajs-399	153	13	convex	convex	ADJ
iajs-399	153	14	2	2	NUM
iajs-399	153	15	-	-	PUNCT
iajs-399	153	16	banach	banach	NOUN
iajs-399	153	17	space	space	NOUN
iajs-399	153	18	,	,	PUNCT
iajs-399	153	19	s	s	VERB
iajs-399	153	20	a	a	DET
iajs-399	153	21	nonempty	nonempty	ADV
iajs-399	153	22	closed	close	VERB
iajs-399	153	23	convex	convex	NOUN
iajs-399	153	24	bounded	bound	VERB
iajs-399	153	25	subset	subset	NOUN
iajs-399	153	26	of	of	ADP
iajs-399	153	27	x	x	PUNCT
iajs-399	153	28	and	and	CCONJ
iajs-399	153	29	t	t	PROPN
iajs-399	153	30	:	:	PUNCT
iajs-399	153	31	s	s	X
iajs-399	153	32	→	→	SYM
iajs-399	153	33	s	s	X
iajs-399	153	34	an	an	DET
iajs-399	153	35	asymptotically	asymptotically	ADV
iajs-399	153	36	non	non	ADJ
iajs-399	153	37	-	-	ADJ
iajs-399	153	38	expansive	expansive	ADJ
iajs-399	153	39	mapping	mapping	NOUN
iajs-399	153	40	.	.	PUNCT
iajs-399	154	1	then	then	ADV
iajs-399	154	2	f(t	f(t	NOUN
iajs-399	154	3	)	)	PUNCT
iajs-399	154	4	is	be	AUX
iajs-399	154	5	closed	close	VERB
iajs-399	154	6	and	and	CCONJ
iajs-399	154	7	convex	convex	NOUN
iajs-399	154	8	.	.	PUNCT
iajs-399	155	1	proof	proof	NOUN
iajs-399	155	2	the	the	DET
iajs-399	155	3	closedness	closedness	NOUN
iajs-399	155	4	of	of	ADP
iajs-399	155	5	f(t	f(t	NOUN
iajs-399	155	6	)	)	PUNCT
iajs-399	155	7	is	be	AUX
iajs-399	155	8	obvious	obvious	ADJ
iajs-399	155	9	.	.	PUNCT
iajs-399	156	1	to	to	PART
iajs-399	156	2	show	show	VERB
iajs-399	156	3	convexity	convexity	NOUN
iajs-399	156	4	,	,	PUNCT
iajs-399	156	5	it	it	PRON
iajs-399	156	6	is	be	AUX
iajs-399	156	7	sufficient	sufficient	ADJ
iajs-399	156	8	to	to	PART
iajs-399	156	9	prove	prove	VERB
iajs-399	156	10	that	that	PRON
iajs-399	156	11	z	z	NOUN
iajs-399	156	12	=	=	PUNCT
iajs-399	156	13	(	(	PUNCT
iajs-399	156	14	𝓍𝓍	𝓍𝓍	PROPN
iajs-399	156	15	+	+	NUM
iajs-399	156	16	y	y	PROPN
iajs-399	156	17	)	)	PUNCT
iajs-399	156	18	/	/	SYM
iajs-399	156	19	2	2	NUM
iajs-399	156	20	ϵ	ϵ	ADP
iajs-399	156	21	f(t	f(t	NOUN
iajs-399	156	22	)	)	PUNCT
iajs-399	156	23	for	for	ADP
iajs-399	156	24	x	x	SYM
iajs-399	156	25	,	,	PUNCT
iajs-399	156	26	y	y	PROPN
iajs-399	156	27	and	and	CCONJ
iajs-399	156	28	u	u	X
iajs-399	157	1	ϵ	ϵ	PROPN
iajs-399	157	2	f(t),for	f(t),for	ADP
iajs-399	157	3	each	each	DET
iajs-399	157	4	n	n	NOUN
iajs-399	157	5	ϵ	ϵ	NOUN
iajs-399	157	6	n	n	CCONJ
iajs-399	157	7	,	,	PUNCT
iajs-399	157	8	we	we	PRON
iajs-399	157	9	have	have	VERB
iajs-399	157	10	||𝓍𝓍	||𝓍𝓍	PRON
iajs-399	157	11	–	–	PUNCT
iajs-399	157	12	tnz	tnz	NOUN
iajs-399	157	13	,	,	PUNCT
iajs-399	157	14	u||	u||	NOUN
iajs-399	157	15	=	=	X
iajs-399	157	16	||tn𝓍𝓍	||tn𝓍𝓍	PROPN
iajs-399	157	17	–	–	PUNCT
iajs-399	157	18	tnz	tnz	NOUN
iajs-399	157	19	,	,	PUNCT
iajs-399	157	20	u||	u||	ADV
iajs-399	157	21	≤	≤	NUM
iajs-399	157	22	kn	kn	PROPN
iajs-399	157	23	||𝓍𝓍	||𝓍𝓍	NOUN
iajs-399	157	24	–	–	PUNCT
iajs-399	157	25	z	z	NOUN
iajs-399	157	26	,	,	PUNCT
iajs-399	157	27	u||	u||	NOUN
iajs-399	157	28	=	=	SYM
iajs-399	157	29	½	½	NOUN
iajs-399	157	30	kn	kn	PROPN
iajs-399	157	31	||	||	PROPN
iajs-399	158	1	𝓍𝓍	𝓍𝓍	PROPN
iajs-399	158	2	–	–	PUNCT
iajs-399	158	3	y	y	NOUN
iajs-399	158	4	,	,	PUNCT
iajs-399	158	5	u||	u||	ADV
iajs-399	158	6	||y	||y	ADJ
iajs-399	158	7	–	–	PUNCT
iajs-399	158	8	tnz	tnz	NOUN
iajs-399	158	9	,	,	PUNCT
iajs-399	158	10	u||	u||	NOUN
iajs-399	158	11	=	=	NOUN
iajs-399	158	12	||tny	||tny	NOUN
iajs-399	158	13	–	–	PUNCT
iajs-399	158	14	tnz	tnz	NOUN
iajs-399	158	15	,	,	PUNCT
iajs-399	158	16	u||	u||	ADV
iajs-399	158	17	≤	≤	NUM
iajs-399	158	18	kn	kn	NOUN
iajs-399	158	19	||y	||y	PROPN
iajs-399	158	20	–	–	PUNCT
iajs-399	158	21	z	z	NOUN
iajs-399	158	22	,	,	PUNCT
iajs-399	158	23	u||	u||	NOUN
iajs-399	158	24	=	=	SYM
iajs-399	158	25	½	½	NOUN
iajs-399	158	26	kn	kn	PROPN
iajs-399	158	27	||𝓍𝓍	||𝓍𝓍	PROPN
iajs-399	158	28	–	–	PUNCT
iajs-399	158	29	y	y	NOUN
iajs-399	158	30	,	,	PUNCT
iajs-399	158	31	u||	u||	NOUN
iajs-399	158	32	by	by	ADP
iajs-399	158	33	the	the	DET
iajs-399	158	34	uniform	uniform	ADJ
iajs-399	158	35	convexity	convexity	NOUN
iajs-399	158	36	of	of	ADP
iajs-399	158	37	x	x	SYM
iajs-399	158	38	,	,	PUNCT
iajs-399	158	39	we	we	PRON
iajs-399	158	40	have	have	VERB
iajs-399	158	41	||z	||z	NOUN
iajs-399	158	42	–	–	PUNCT
iajs-399	158	43	tnz	tnz	NOUN
iajs-399	158	44	,	,	PUNCT
iajs-399	158	45	u||	u||	ADV
iajs-399	159	1	≤	≤	NUM
iajs-399	159	2	½	½	NOUN
iajs-399	160	1	[	[	X
iajs-399	160	2	1	1	NUM
iajs-399	160	3	λx(2	λx(2	PROPN
iajs-399	160	4	/	/	SYM
iajs-399	160	5	kn	kn	PROPN
iajs-399	160	6	)	)	PUNCT
iajs-399	160	7	]	]	PUNCT
iajs-399	161	1	kn	kn	PROPN
iajs-399	161	2	||𝓍𝓍	||𝓍𝓍	PROPN
iajs-399	161	3	–	–	PUNCT
iajs-399	161	4	y	y	NOUN
iajs-399	161	5	,	,	PUNCT
iajs-399	161	6	u||	u||	ADV
iajs-399	161	7	≤	≤	NUM
iajs-399	161	8	½	½	NOUN
iajs-399	162	1	[	[	X
iajs-399	162	2	1	1	NUM
iajs-399	162	3	–	–	PUNCT
iajs-399	162	4	λx	λx	NOUN
iajs-399	162	5	(	(	PUNCT
iajs-399	162	6	2	2	NUM
iajs-399	162	7	/	/	SYM
iajs-399	162	8	kn	kn	NOUN
iajs-399	162	9	)	)	PUNCT
iajs-399	162	10	]	]	PUNCT
iajs-399	163	1	kn	kn	PROPN
iajs-399	163	2	diam	diam	PROPN
iajs-399	163	3	(	(	PUNCT
iajs-399	163	4	s	s	NOUN
iajs-399	163	5	)	)	PUNCT
iajs-399	163	6	hence	hence	ADV
iajs-399	163	7	tnz	tnz	NOUN
iajs-399	163	8	→	→	SYM
iajs-399	163	9	z	z	NOUN
iajs-399	163	10	as	as	ADP
iajs-399	163	11	n	n	PROPN
iajs-399	163	12	→	→	SYM
iajs-399	163	13	∞	∞	PROPN
iajs-399	163	14	z	z	NOUN
iajs-399	163	15	is	be	AUX
iajs-399	163	16	a	a	DET
iajs-399	163	17	fixed	fix	VERB
iajs-399	163	18	point	point	NOUN
iajs-399	163	19	of	of	ADP
iajs-399	163	20	t	t	PROPN
iajs-399	163	21	,	,	PUNCT
iajs-399	163	22	by	by	ADP
iajs-399	163	23	the	the	DET
iajs-399	163	24	continuity	continuity	NOUN
iajs-399	163	25	of	of	ADP
iajs-399	163	26	t.	t.	PROPN
iajs-399	163	27	■	■	PROPN
iajs-399	163	28	348	348	NUM
iajs-399	163	29	|	|	ADV
iajs-399	163	30	mathematics	mathematics	PROPN
iajs-399	163	31	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	NUM
iajs-399	163	32	�	�	NOUN
iajs-399	163	33	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	NUM
iajs-399	163	34	:	:	PUNCT
iajs-399	163	35	a@âig@ú‹	a@âig@ú‹	PROPN
iajs-399	164	1	©	©	PROPN
iajs-399	164	2	@ü‹127@@öü»€a@i1@‚b«@h2014	@ü‹127@@öü»€a@i1@‚b«@h2014	PROPN
iajs-399	164	3	ibn	ibn	PROPN
iajs-399	164	4	al	al	PROPN
iajs-399	164	5	-	-	PUNCT
iajs-399	164	6	haitham	haitham	PROPN
iajs-399	164	7	jour	jour	X
iajs-399	164	8	.	.	PROPN
iajs-399	164	9	for	for	ADP
iajs-399	164	10	pure	pure	ADJ
iajs-399	164	11	&	&	CCONJ
iajs-399	164	12	appl	appl	PROPN
iajs-399	164	13	.	.	PUNCT
iajs-399	165	1	sci	sci	PROPN
iajs-399	165	2	.	.	PUNCT
iajs-399	165	3	vol	vol	NOUN
iajs-399	165	4	.	.	PROPN
iajs-399	166	1	27	27	NUM
iajs-399	166	2	(	(	PUNCT
iajs-399	166	3	1	1	NUM
iajs-399	166	4	)	)	PUNCT
iajs-399	166	5	2014	2014	NUM
iajs-399	166	6	references	reference	NOUN
iajs-399	166	7	1	1	NUM
iajs-399	166	8	.	.	PUNCT
iajs-399	166	9	gahler	gahler	PROPN
iajs-399	166	10	s.	s.	PROPN
iajs-399	166	11	,	,	PUNCT
iajs-399	166	12	(	(	PUNCT
iajs-399	166	13	1965	1965	NUM
iajs-399	166	14	)	)	PUNCT
iajs-399	166	15	,	,	PUNCT
iajs-399	166	16	linear	linear	ADJ
iajs-399	166	17	2	2	NUM
iajs-399	166	18	-	-	PUNCT
iajs-399	166	19	normietre	normietre	NOUN
iajs-399	166	20	raume	raume	NOUN
iajs-399	166	21	,	,	PUNCT
iajs-399	166	22	math	math	NOUN
iajs-399	166	23	.	.	PUNCT
iajs-399	167	1	nachr	nachr	PROPN
iajs-399	167	2	.	.	PROPN
iajs-399	167	3	,	,	PUNCT
iajs-399	167	4	28	28	NUM
iajs-399	167	5	,	,	PUNCT
iajs-399	167	6	pp	pp	ADJ
iajs-399	167	7	.	.	NOUN
iajs-399	167	8	1	1	NUM
iajs-399	167	9	–	–	SYM
iajs-399	167	10	43	43	NUM
iajs-399	167	11	.	.	NOUN
iajs-399	168	1	2	2	X
iajs-399	168	2	.	.	X
iajs-399	168	3	white	white	PROPN
iajs-399	168	4	a.	a.	PROPN
iajs-399	168	5	,	,	PUNCT
iajs-399	168	6	(	(	PUNCT
iajs-399	168	7	1969	1969	NUM
iajs-399	168	8	)	)	PUNCT
iajs-399	168	9	,	,	PUNCT
iajs-399	168	10	2	2	NUM
iajs-399	168	11	-	-	PUNCT
iajs-399	168	12	banach	banach	NOUN
iajs-399	168	13	spaces	space	NOUN
iajs-399	168	14	,	,	PUNCT
iajs-399	168	15	math	math	PROPN
iajs-399	168	16	nachr	nachr	PROPN
iajs-399	168	17	.	.	PUNCT
iajs-399	169	1	42	42	NUM
iajs-399	169	2	,	,	PUNCT
iajs-399	169	3	pp	pp	ADJ
iajs-399	169	4	.	.	PUNCT
iajs-399	170	1	43	43	NUM
iajs-399	170	2	–	–	PUNCT
iajs-399	170	3	60	60	NUM
iajs-399	170	4	.	.	X
iajs-399	171	1	3	3	X
iajs-399	171	2	.	.	NUM
iajs-399	171	3	rezapour	rezapour	PROPN
iajs-399	171	4	s.	s.	PROPN
iajs-399	171	5	,	,	PUNCT
iajs-399	171	6	(	(	PUNCT
iajs-399	171	7	2005	2005	NUM
iajs-399	171	8	)	)	PUNCT
iajs-399	171	9	,	,	PUNCT
iajs-399	171	10	quasi	quasi	ADJ
iajs-399	171	11	-	-	ADJ
iajs-399	171	12	chebyshew	chebyshew	ADJ
iajs-399	171	13	subspaces	subspace	NOUN
iajs-399	171	14	in	in	ADP
iajs-399	171	15	generalized	generalized	ADJ
iajs-399	171	16	normed	normed	ADJ
iajs-399	171	17	space	space	NOUN
iajs-399	171	18	,	,	PUNCT
iajs-399	171	19	international	international	ADJ
iajs-399	171	20	journal	journal	NOUN
iajs-399	171	21	of	of	ADP
iajs-399	171	22	pure	pure	ADJ
iajs-399	171	23	and	and	CCONJ
iajs-399	171	24	applied	apply	VERB
iajs-399	171	25	mathemetical	mathemetical	ADJ
iajs-399	171	26	scinces	scince	NOUN
iajs-399	171	27	,	,	PUNCT
iajs-399	171	28	vol	vol	NOUN
iajs-399	171	29	.	.	PROPN
iajs-399	171	30	2	2	NUM
iajs-399	171	31	,	,	PUNCT
iajs-399	171	32	no	no	INTJ
iajs-399	171	33	.	.	NOUN
iajs-399	171	34	1	1	NUM
iajs-399	171	35	,	,	PUNCT
iajs-399	171	36	pp	pp	ADJ
iajs-399	171	37	.	.	PUNCT
iajs-399	172	1	53	53	NUM
iajs-399	172	2	–	–	SYM
iajs-399	172	3	61	61	NUM
iajs-399	172	4	.	.	NOUN
iajs-399	173	1	4	4	NUM
iajs-399	173	2	.	.	NOUN
iajs-399	173	3	lawandowska	lawandowska	ADJ
iajs-399	173	4	z.	z.	PROPN
iajs-399	173	5	,	,	PUNCT
iajs-399	173	6	(	(	PUNCT
iajs-399	173	7	2003	2003	NUM
iajs-399	173	8	)	)	PUNCT
iajs-399	173	9	,	,	PUNCT
iajs-399	173	10	on	on	ADP
iajs-399	173	11	2	2	NUM
iajs-399	173	12	-	-	PUNCT
iajs-399	173	13	normed	norme	VERB
iajs-399	173	14	sets	set	NOUN
iajs-399	173	15	,	,	PUNCT
iajs-399	173	16	glasnik	glasnik	PROPN
iajs-399	173	17	math	math	PROPN
iajs-399	173	18	.	.	PUNCT
iajs-399	174	1	ser	ser	PROPN
iajs-399	174	2	.	.	PUNCT
iajs-399	174	3	iii	iii	PROPN
iajs-399	175	1	38(58	38(58	NUM
iajs-399	175	2	)	)	PUNCT
iajs-399	175	3	,	,	PUNCT
iajs-399	175	4	no	no	INTJ
iajs-399	175	5	.	.	NOUN
iajs-399	175	6	1	1	NUM
iajs-399	175	7	,	,	PUNCT
iajs-399	175	8	pp	pp	ADJ
iajs-399	175	9	.	.	PUNCT
iajs-399	176	1	99	99	NUM
iajs-399	176	2	–	–	PUNCT
iajs-399	176	3	110	110	NUM
iajs-399	176	4	.	.	X
iajs-399	177	1	5	5	NUM
iajs-399	177	2	.	.	PUNCT
iajs-399	177	3	.	.	PUNCT
iajs-399	178	1	khan	khan	PROPN
iajs-399	178	2	m.	m.	PROPN
iajs-399	178	3	s	s	PROPN
iajs-399	178	4	and	and	CCONJ
iajs-399	178	5	khan	khan	PROPN
iajs-399	178	6	m.	m.	PROPN
iajs-399	178	7	d.	d.	PROPN
iajs-399	178	8	,	,	PUNCT
iajs-399	178	9	(	(	PUNCT
iajs-399	178	10	1993	1993	NUM
iajs-399	178	11	)	)	PUNCT
iajs-399	178	12	,	,	PUNCT
iajs-399	178	13	involutions	involution	NOUN
iajs-399	178	14	with	with	ADP
iajs-399	178	15	fixed	fix	VERB
iajs-399	178	16	points	point	NOUN
iajs-399	178	17	in	in	ADP
iajs-399	178	18	2	2	NUM
iajs-399	178	19	-	-	PUNCT
iajs-399	178	20	banach	banach	NOUN
iajs-399	178	21	spaces	space	NOUN
iajs-399	178	22	,	,	PUNCT
iajs-399	178	23	internet	internet	NOUN
iajs-399	178	24	.	.	PUNCT
iajs-399	179	1	j.	j.	PROPN
iajs-399	179	2	math	math	PROPN
iajs-399	179	3	.	.	PUNCT
iajs-399	180	1	sci	sci	PROPN
iajs-399	180	2	,	,	PUNCT
iajs-399	180	3	16	16	NUM
iajs-399	180	4	,	,	PUNCT
iajs-399	180	5	429	429	NUM
iajs-399	180	6	–	–	SYM
iajs-399	180	7	434	434	NUM
iajs-399	180	8	.	.	NOUN
iajs-399	180	9	6	6	NUM
iajs-399	180	10	.	.	X
iajs-399	181	1	cho	cho	PROPN
iajs-399	181	2	y.	y.	PROPN
iajs-399	181	3	j.	j.	PROPN
iajs-399	181	4	,	,	PUNCT
iajs-399	181	5	huang	huang	PROPN
iajs-399	181	6	n.	n.	PROPN
iajs-399	181	7	and	and	CCONJ
iajs-399	181	8	long	long	ADJ
iajs-399	181	9	x.	x.	NOUN
iajs-399	181	10	,	,	PUNCT
iajs-399	181	11	(	(	PUNCT
iajs-399	181	12	1995	1995	NUM
iajs-399	181	13	)	)	PUNCT
iajs-399	181	14	,	,	PUNCT
iajs-399	181	15	some	some	DET
iajs-399	181	16	fixed	fix	VERB
iajs-399	181	17	point	point	NOUN
iajs-399	181	18	theorems	theorem	NOUN
iajs-399	181	19	for	for	ADP
iajs-399	181	20	non	non	ADJ
iajs-399	181	21	-	-	ADJ
iajs-399	181	22	linear	linear	ADJ
iajs-399	181	23	mappings	mapping	NOUN
iajs-399	181	24	in	in	ADP
iajs-399	181	25	2	2	NUM
iajs-399	181	26	-	-	PUNCT
iajs-399	181	27	banach	banach	NOUN
iajs-399	181	28	spaces	space	NOUN
iajs-399	181	29	,	,	PUNCT
iajs-399	181	30	far	far	PROPN
iajs-399	181	31	east	east	PROPN
iajs-399	181	32	j.	j.	PROPN
iajs-399	181	33	math	math	PROPN
iajs-399	181	34	.	.	PUNCT
iajs-399	182	1	sci	sci	PROPN
iajs-399	182	2	.	.	PROPN
iajs-399	182	3	,	,	PUNCT
iajs-399	182	4	3(2	3(2	NUM
iajs-399	182	5	)	)	PUNCT
iajs-399	182	6	,	,	PUNCT
iajs-399	183	1	pp	pp	ADP
iajs-399	183	2	.	.	PUNCT
iajs-399	184	1	125	125	NUM
iajs-399	184	2	–	–	SYM
iajs-399	184	3	133	133	NUM
iajs-399	184	4	.	.	PUNCT
iajs-399	185	1	7	7	X
iajs-399	185	2	.	.	PUNCT
iajs-399	185	3	mukti	mukti	PROPN
iajs-399	185	4	g.	g.	PROPN
iajs-399	185	5	,	,	PUNCT
iajs-399	185	6	mantu	mantu	PROPN
iajs-399	185	7	s.	s.	PROPN
iajs-399	185	8	and	and	CCONJ
iajs-399	185	9	baisanb	baisanb	PROPN
iajs-399	185	10	a.	a.	PROPN
iajs-399	185	11	p.	p.	PROPN
iajs-399	185	12	,	,	PUNCT
iajs-399	185	13	(	(	PUNCT
iajs-399	185	14	2009	2009	NUM
iajs-399	185	15	)	)	PUNCT
iajs-399	185	16	,	,	PUNCT
iajs-399	185	17	''	''	PUNCT
iajs-399	185	18	fixed	fix	VERB
iajs-399	185	19	point	point	NOUN
iajs-399	185	20	theorems	theorem	NOUN
iajs-399	185	21	for	for	ADP
iajs-399	185	22	a	a	DET
iajs-399	185	23	class	class	NOUN
iajs-399	185	24	of	of	ADP
iajs-399	185	25	mappings	mapping	NOUN
iajs-399	185	26	in	in	ADP
iajs-399	185	27	2	2	NUM
iajs-399	185	28	-	-	PUNCT
iajs-399	185	29	banach	banach	NOUN
iajs-399	185	30	space	space	NOUN
iajs-399	185	31	''	''	PUNCT
iajs-399	185	32	,	,	PUNCT
iajs-399	185	33	int	int	NOUN
iajs-399	185	34	.	.	PUNCT
iajs-399	186	1	journal	journal	PROPN
iajs-399	186	2	of	of	ADP
iajs-399	186	3	math	math	NOUN
iajs-399	186	4	.	.	PUNCT
iajs-399	187	1	analysis	analysis	NOUN
iajs-399	187	2	,	,	PUNCT
iajs-399	187	3	3	3	NUM
iajs-399	187	4	,	,	PUNCT
iajs-399	187	5	no	no	INTJ
iajs-399	187	6	.	.	NOUN
iajs-399	187	7	27	27	NUM
iajs-399	187	8	,	,	PUNCT
iajs-399	187	9	pp	pp	ADJ
iajs-399	187	10	.	.	PUNCT
iajs-399	187	11	1339	1339	NUM
iajs-399	187	12	–	–	PUNCT
iajs-399	187	13	1347	1347	NUM
iajs-399	187	14	.	.	PUNCT
iajs-399	188	1	8	8	NUM
iajs-399	188	2	.	.	X
iajs-399	188	3	kuldip	kuldip	PROPN
iajs-399	188	4	r.	r.	PROPN
iajs-399	188	5	and	and	CCONJ
iajs-399	188	6	sunil	sunil	PROPN
iajs-399	188	7	k.	k.	PROPN
iajs-399	188	8	s.	s.	PROPN
iajs-399	188	9	,	,	PUNCT
iajs-399	188	10	(	(	PUNCT
iajs-399	188	11	2011	2011	NUM
iajs-399	188	12	)	)	PUNCT
iajs-399	188	13	,	,	PUNCT
iajs-399	188	14	''	''	PUNCT
iajs-399	188	15	some	some	DET
iajs-399	188	16	sequence	sequence	NOUN
iajs-399	188	17	spaces	space	VERB
iajs-399	188	18	in	in	ADP
iajs-399	188	19	2	2	NUM
iajs-399	188	20	-	-	PUNCT
iajs-399	188	21	normed	norme	VERB
iajs-399	188	22	spaces	space	NOUN
iajs-399	188	23	defined	define	VERB
iajs-399	188	24	by	by	ADP
iajs-399	188	25	musielak	musielak	NOUN
iajs-399	188	26	-	-	PUNCT
iajs-399	188	27	orlisz	orlisz	ADJ
iajs-399	188	28	function	function	NOUN
iajs-399	188	29	''	''	PUNCT
iajs-399	188	30	,	,	PUNCT
iajs-399	188	31	acta	acta	PROPN
iajs-399	188	32	univ	univ	PROPN
iajs-399	188	33	.	.	PUNCT
iajs-399	189	1	sapientiae	sapientiae	PROPN
iajs-399	189	2	,	,	PUNCT
iajs-399	189	3	mathematical	mathematical	ADJ
iajs-399	189	4	,	,	PUNCT
iajs-399	189	5	3	3	NUM
iajs-399	189	6	,	,	PUNCT
iajs-399	189	7	1	1	NUM
iajs-399	189	8	,	,	PUNCT
iajs-399	189	9	pp	pp	ADJ
iajs-399	189	10	.	.	PUNCT
iajs-399	190	1	97	97	NUM
iajs-399	190	2	109	109	NUM
iajs-399	190	3	.	.	PUNCT
iajs-399	191	1	9	9	NUM
iajs-399	191	2	.	.	PUNCT
iajs-399	191	3	mukti	mukti	PROPN
iajs-399	191	4	g.	g.	PROPN
iajs-399	191	5	,	,	PUNCT
iajs-399	191	6	mantu	mantu	PROPN
iajs-399	191	7	s.	s.	PROPN
iajs-399	191	8	and	and	CCONJ
iajs-399	191	9	baisnab	baisnab	PROPN
iajs-399	191	10	a.	a.	PROPN
iajs-399	191	11	p.	p.	PROPN
iajs-399	191	12	,	,	PUNCT
iajs-399	191	13	(	(	PUNCT
iajs-399	191	14	2012	2012	NUM
iajs-399	191	15	)	)	PUNCT
iajs-399	191	16	,	,	PUNCT
iajs-399	191	17	''	''	PUNCT
iajs-399	191	18	caristi	caristi	ADJ
iajs-399	191	19	-	-	PUNCT
iajs-399	191	20	type	type	NOUN
iajs-399	191	21	fixed	fix	VERB
iajs-399	191	22	point	point	NOUN
iajs-399	191	23	theor	theor	PROPN
iajs-399	191	24	-	-	PUNCT
iajs-399	191	25	ems	ems	PROPN
iajs-399	191	26	in	in	ADP
iajs-399	191	27	2	2	NUM
iajs-399	191	28	-	-	PUNCT
iajs-399	191	29	banach	banach	NOUN
iajs-399	191	30	space	space	NOUN
iajs-399	191	31	''	''	PUNCT
iajs-399	191	32	,	,	PUNCT
iajs-399	191	33	gen	gen	PROPN
iajs-399	191	34	,	,	PUNCT
iajs-399	191	35	math	math	NOUN
iajs-399	191	36	.	.	PUNCT
iajs-399	192	1	notes	note	NOUN
iajs-399	192	2	,	,	PUNCT
iajs-399	192	3	8	8	NUM
iajs-399	192	4	,	,	PUNCT
iajs-399	192	5	no	no	INTJ
iajs-399	192	6	.	.	NOUN
iajs-399	192	7	1	1	NUM
iajs-399	192	8	,	,	PUNCT
iajs-399	192	9	pp	pp	ADJ
iajs-399	192	10	.	.	NOUN
iajs-399	192	11	1	1	NUM
iajs-399	192	12	–	–	PUNCT
iajs-399	192	13	5	5	NUM
iajs-399	192	14	.	.	SYM
iajs-399	192	15	10	10	NUM
iajs-399	192	16	.	.	PUNCT
iajs-399	193	1	george	george	PROPN
iajs-399	193	2	b.	b.	PROPN
iajs-399	193	3	and	and	CCONJ
iajs-399	193	4	lawrence	lawrence	PROPN
iajs-399	193	5	n.	n.	PROPN
iajs-399	193	6	,	,	PUNCT
iajs-399	193	7	(	(	PUNCT
iajs-399	193	8	2000	2000	NUM
iajs-399	193	9	)	)	PUNCT
iajs-399	193	10	,	,	PUNCT
iajs-399	193	11	functional	functional	ADJ
iajs-399	193	12	analysis	analysis	NOUN
iajs-399	193	13	,	,	PUNCT
iajs-399	193	14	canada	canada	PROPN
iajs-399	193	15	,	,	PUNCT
iajs-399	193	16	general	general	ADJ
iajs-399	193	17	pub	pub	NOUN
iajs-399	193	18	-	-	PUNCT
iajs-399	193	19	lishing	lishe	VERB
iajs-399	193	20	company	company	NOUN
iajs-399	193	21	.	.	PUNCT
iajs-399	194	1	11	11	NUM
iajs-399	194	2	.	.	PUNCT
iajs-399	195	1	dominic	dominic	PROPN
iajs-399	195	2	y.	y.	PROPN
iajs-399	195	3	and	and	CCONJ
iajs-399	195	4	marudai	marudai	PROPN
iajs-399	195	5	m.	m.	NOUN
iajs-399	195	6	,	,	PUNCT
iajs-399	195	7	(	(	PUNCT
iajs-399	195	8	2012	2012	NUM
iajs-399	195	9	)	)	PUNCT
iajs-399	195	10	,	,	PUNCT
iajs-399	195	11	''	''	PUNCT
iajs-399	195	12	best	good	ADJ
iajs-399	195	13	approximation	approximation	NOUN
iajs-399	195	14	in	in	ADP
iajs-399	195	15	uniformly	uniformly	ADV
iajs-399	195	16	convex	convex	VERB
iajs-399	195	17	2normed	2normed	NUM
iajs-399	195	18	space	space	NOUN
iajs-399	195	19	''	''	PUNCT
iajs-399	195	20	int	int	NOUN
iajs-399	195	21	.	.	PUNCT
iajs-399	196	1	journal	journal	PROPN
iajs-399	196	2	of	of	ADP
iajs-399	196	3	math	math	NOUN
iajs-399	196	4	.	.	PUNCT
iajs-399	197	1	analysis	analysis	NOUN
iajs-399	197	2	,	,	PUNCT
iajs-399	197	3	6	6	NUM
iajs-399	197	4	,	,	PUNCT
iajs-399	197	5	no	no	INTJ
iajs-399	197	6	.	.	NOUN
iajs-399	197	7	21	21	NUM
iajs-399	197	8	,	,	PUNCT
iajs-399	197	9	pp	pp	ADJ
iajs-399	197	10	.	.	PUNCT
iajs-399	197	11	1015	1015	NUM
iajs-399	197	12	–	–	PUNCT
iajs-399	197	13	1021	1021	NUM
iajs-399	197	14	.	.	PUNCT
iajs-399	198	1	349	349	NUM
iajs-399	199	1	|	|	ADV
iajs-399	199	2	mathematics	mathematics	PROPN
iajs-399	199	3	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	NUM
iajs-399	199	4	�	�	NOUN
iajs-399	199	5	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	NUM
iajs-399	199	6	:	:	PUNCT
iajs-399	199	7	a@âig@ú‹	a@âig@ú‹	PROPN
iajs-399	199	8	©	©	PROPN
iajs-399	199	9	@ü‹127@@öü»€a@i1@‚b«@h2014	@ü‹127@@öü»€a@i1@‚b«@h2014	PROPN
iajs-399	199	10	ibn	ibn	PROPN
iajs-399	199	11	al	al	PROPN
iajs-399	199	12	-	-	PUNCT
iajs-399	199	13	haitham	haitham	PROPN
iajs-399	199	14	jour	jour	X
iajs-399	199	15	.	.	PROPN
iajs-399	200	1	for	for	ADP
iajs-399	200	2	pure	pure	ADJ
iajs-399	200	3	&	&	CCONJ
iajs-399	200	4	appl	appl	PROPN
iajs-399	200	5	.	.	PUNCT
iajs-399	201	1	sci	sci	PROPN
iajs-399	201	2	.	.	PUNCT
iajs-399	201	3	vol	vol	NOUN
iajs-399	201	4	.	.	PROPN
iajs-399	202	1	27	27	NUM
iajs-399	202	2	(	(	PUNCT
iajs-399	202	3	1	1	NUM
iajs-399	202	4	)	)	PUNCT
iajs-399	202	5	2014	2014	NUM
iajs-399	202	6	بناخ	بناخ	NOUN
iajs-399	203	1	-2النقطة	-2النقطة	PROPN
iajs-399	203	2	الصامدة	الصامدة	PROPN
iajs-399	203	3	للتطبیقات	للتطبیقات	PROPN
iajs-399	203	4	شبة	شبة	NOUN
iajs-399	203	5	الالمتمددة	الالمتمددة	VERB
iajs-399	203	6	في	في	ADP
iajs-399	203	7	فضاء	فضاء	ADJ
iajs-399	203	8	سلمان	سلمان	NOUN
iajs-399	203	9	عبد	عبد	ADJ
iajs-399	203	10	سلوى	سلوى	NOUN
iajs-399	203	11	رفاه	رفاه	NOUN
iajs-399	203	12	ساجد	ساجد	PROPN
iajs-399	203	13	عبدعلي	عبدعلي	NOUN
iajs-399	203	14	جامعة	جامعة	PROPN
iajs-399	203	15	بغداد	بغداد	PROPN
iajs-399	203	16	/	/	SYM
iajs-399	203	17	كلیة	كلیة	PROPN
iajs-399	203	18	التربیة	التربیة	NOUN
iajs-399	203	19	للعلوم	للعلوم	NOUN
iajs-399	203	20	الصرفة	الصرفة	PROPN
iajs-399	203	21	أبن	أبن	NOUN
iajs-399	203	22	الھیثم	الھیثم	VERB
iajs-399	203	23	/قسم	/قسم	PUNCT
iajs-399	203	24	الریاضیات	الریاضیات	VERB
iajs-399	203	25	2013كانون	2013كانون	NUM
iajs-399	203	26	االول	االول	NOUN
iajs-399	203	27	4	4	NUM
iajs-399	203	28	:	:	PUNCT
iajs-399	203	29	في	في	X
iajs-399	203	30	،	،	PROPN
iajs-399	203	31	قبل	قبل	PROPN
iajs-399	203	32	البحث	البحث	PROPN
iajs-399	203	33	2013حزیران23	2013حزیران23	NUM
iajs-399	203	34	:	:	PUNCT
iajs-399	203	35	في	في	SCONJ
iajs-399	203	36	أستلم	أستلم	PROPN
iajs-399	203	37	البحث	البحث	PROPN
iajs-399	203	38	الخالصة	الخالصة	PROPN
iajs-399	203	39	الالمتمددة	الالمتمددة	PROPN
iajs-399	203	40	شبھ	شبھ	PROPN
iajs-399	203	41	تطبیقات	تطبیقات	NOUN
iajs-399	203	42	عرفناایضا	عرفناایضا	NOUN
iajs-399	203	43	،	،	X
iajs-399	203	44	.	.	PUNCT
iajs-399	204	1	بناخ-2فضاء	بناخ-2فضاء	VERB
iajs-399	204	2	في	في	ADP
iajs-399	204	3	الحقائق	الحقائق	NOUN
iajs-399	204	4	بعض	بعض	NOUN
iajs-399	204	5	قدمنا	قدمنا	PROPN
iajs-399	204	6	البحث	البحث	PROPN
iajs-399	204	7	خالل	خالل	PROPN
iajs-399	204	8	ھذا	ھذا	VERB
iajs-399	204	9	asymptotically	asymptotically	ADV
iajs-399	204	10	non	non	ADJ
iajs-399	204	11	-	-	ADJ
iajs-399	204	12	expansive	expansive	ADJ
iajs-399	204	13	mapping	mapping	NOUN
iajs-399	204	14	للتطبیقات	للتطبیقات	NOUN
iajs-399	204	15	غیر	غیر	PROPN
iajs-399	204	16	المتمددة	المتمددة	VERB
iajs-399	204	17	المعیاریة	المعیاریة	PROPN
iajs-399	204	18	بطریقة	بطریقة	ADJ
iajs-399	204	19	مشابھة-2لفضاءاتا	مشابھة-2لفضاءاتا	PROPN
iajs-399	204	20	في	في	ADP
iajs-399	204	21	بناخ.-2من	بناخ.-2من	PUNCT
iajs-399	204	22	التطبیقات	التطبیقات	PROPN
iajs-399	204	23	في	في	DET
iajs-399	204	24	فضاء	فضاء	NOUN
iajs-399	204	25	لھذا	لھذا	VERB
iajs-399	204	26	النمط	النمط	PROPN
iajs-399	204	27	نقاط	نقاط	PROPN
iajs-399	204	28	صامدة	صامدة	VERB
iajs-399	204	29	و	و	PRON
iajs-399	205	1	من	من	INTJ
iajs-399	205	2	ثم	ثم	ADV
iajs-399	205	3	البرھنة	البرھنة	PROPN
iajs-399	205	4	عن	عن	PROPN
iajs-399	205	5	وجود	وجود	NOUN
iajs-399	205	6	،	،	PROPN
iajs-399	205	7	في	في	ADP
iajs-399	205	8	الفضاءات	الفضاءات	PROPN
iajs-399	205	9	المعیاریة	المعیاریة	PROPN
iajs-399	205	10	العادیة	العادیة	PROPN
iajs-399	205	11	،	،	PROPN
iajs-399	205	12	نقطة	نقطة	PROPN
iajs-399	205	13	صامدة.تطبیق	صامدة.تطبیق	PROPN
iajs-399	205	14	ال	ال	ADP
iajs-399	205	15	متمدد	متمدد	X
iajs-399	205	16	،	،	X
iajs-399	205	17	تطبیق	تطبیق	PROPN
iajs-399	205	18	شبة	شبة	NOUN
iajs-399	205	19	ال	ال	ADP
iajs-399	205	20	متمددبناخ	متمددبناخ	ADJ
iajs-399	205	21	،	،	NOUN
iajs-399	205	22	-2	-2	NOUN
iajs-399	205	23	:	:	PUNCT
iajs-399	205	24	فضاء	فضاء	X
iajs-399	205	25	مفتاحیة	مفتاحیة	NOUN
iajs-399	205	26	الكلمات	الكلمات	VERB
iajs-399	205	27	ال	ال	ADP
iajs-399	205	28	350	350	NUM
iajs-399	205	29	|	|	NOUN
iajs-399	205	30	mathematics	mathematics	PROPN
iajs-399	205	31	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	@a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@úó‘ój	NUM
iajs-399	205	32	�	�	NOUN
iajs-399	205	33	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	n€a@î@úœäñ€a@‚ï‹»‹€@·ró	NUM
iajs-399	205	34	:	:	PUNCT
iajs-399	205	35	a@âig@ú‹	a@âig@ú‹	PROPN
iajs-399	206	1	©	©	PROPN
iajs-399	206	2	@ü‹127@@öü»€a@i1@‚b«@h2014	@ü‹127@@öü»€a@i1@‚b«@h2014	PROPN
iajs-399	206	3	ibn	ibn	PROPN
iajs-399	206	4	al	al	PROPN
iajs-399	206	5	-	-	PUNCT
iajs-399	206	6	haitham	haitham	PROPN
iajs-399	206	7	jour	jour	X
iajs-399	206	8	.	.	PROPN
iajs-399	206	9	for	for	ADP
iajs-399	206	10	pure	pure	ADJ
iajs-399	206	11	&	&	CCONJ
iajs-399	206	12	appl	appl	PROPN
iajs-399	206	13	.	.	PUNCT
iajs-399	207	1	sci	sci	PROPN
iajs-399	207	2	.	.	PUNCT
iajs-399	207	3	vol	vol	NOUN
iajs-399	207	4	.	.	PROPN
iajs-399	208	1	27	27	NUM
iajs-399	208	2	(	(	PUNCT
iajs-399	208	3	1	1	NUM
iajs-399	208	4	)	)	PUNCT
iajs-399	208	5	2014	2014	NUM