id	sid	tid	token	lemma	pos
iajs-1816	1	1	microsoft	microsoft	PROPN
iajs-1816	1	2	word	word	PROPN
iajs-1816	1	3	426	426	NUM
iajs-1816	1	4	-	-	SYM
iajs-1816	1	5	435	435	NUM
iajs-1816	1	6	ihsciconf	ihsciconf	NOUN
iajs-1816	1	7	2017	2017	NUM
iajs-1816	1	8	special	special	ADJ
iajs-1816	1	9	issue	issue	NOUN
iajs-1816	1	10	ibn	ibn	PROPN
iajs-1816	1	11	al	al	PROPN
iajs-1816	1	12	-	-	PUNCT
iajs-1816	1	13	haitham	haitham	PROPN
iajs-1816	1	14	journal	journal	PROPN
iajs-1816	1	15	for	for	ADP
iajs-1816	1	16	pure	pure	ADJ
iajs-1816	1	17	and	and	CCONJ
iajs-1816	1	18	applied	apply	VERB
iajs-1816	1	19	science	science	NOUN
iajs-1816	1	20	https://doi.org/	https://doi.org/	NOUN
iajs-1816	1	21	10.30526/2017.ihsciconf.1816	10.30526/2017.ihsciconf.1816	NUM
iajs-1816	1	22	for	for	ADP
iajs-1816	1	23	more	more	ADJ
iajs-1816	1	24	information	information	NOUN
iajs-1816	1	25	about	about	ADP
iajs-1816	1	26	the	the	DET
iajs-1816	1	27	conference	conference	NOUN
iajs-1816	1	28	please	please	INTJ
iajs-1816	1	29	visit	visit	VERB
iajs-1816	1	30	the	the	DET
iajs-1816	1	31	websites	website	NOUN
iajs-1816	1	32	:	:	PUNCT
iajs-1816	1	33	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1816	1	34	   	   	SPACE
iajs-1816	1	35	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1816	1	36	   	   	SPACE
iajs-1816	1	37	mathematics|426	mathematics|426	PROPN
iajs-1816	1	38	    	    	SPACE
iajs-1816	1	39	fuzzy	fuzzy	ADJ
iajs-1816	1	40	fixed	fix	VERB
iajs-1816	1	41	point	point	NOUN
iajs-1816	1	42	theorem	theorem	NOUN
iajs-1816	1	43	for	for	ADP
iajs-1816	1	44	some	some	DET
iajs-1816	1	45	types	type	NOUN
iajs-1816	1	46	of	of	ADP
iajs-1816	1	47	fuzzy	fuzzy	ADJ
iajs-1816	1	48	jungck	jungck	NOUN
iajs-1816	1	49	contractive	contractive	ADJ
iajs-1816	1	50	mappings	mapping	NOUN
iajs-1816	1	51	in	in	ADP
iajs-1816	1	52	hilbert	hilbert	PROPN
iajs-1816	1	53	space	space	NOUN
iajs-1816	1	54	buthainah	buthainah	PROPN
iajs-1816	1	55	a.a.ahmed	a.a.ahme	VERB
iajs-1816	1	56	email	email	NOUN
iajs-1816	1	57	:	:	PUNCT
iajs-1816	1	58	buthainah_altai@scbaghdad.edu	buthainah_altai@scbaghdad.edu	PROPN
iajs-1816	1	59	manar	manar	PROPN
iajs-1816	1	60	falih	falih	PROPN
iajs-1816	1	61	dheyab	dheyab	PROPN
iajs-1816	1	62	email	email	NOUN
iajs-1816	1	63	:	:	PUNCT
iajs-1816	1	64	manarfalih@yahoo.com	manarfalih@yahoo.com	X
iajs-1816	1	65	dept	dept	PROPN
iajs-1816	1	66	.	.	PROPN
iajs-1816	1	67	of	of	ADP
iajs-1816	1	68	mathematics	mathematics	PROPN
iajs-1816	1	69	/	/	SYM
iajs-1816	1	70	college	college	NOUN
iajs-1816	1	71	of	of	ADP
iajs-1816	1	72	science	science	PROPN
iajs-1816	1	73	/	/	SYM
iajs-1816	1	74	university	university	PROPN
iajs-1816	1	75	of	of	ADP
iajs-1816	1	76	baghdad	baghdad	PROPN
iajs-1816	1	77	abstract	abstract	ADV
iajs-1816	1	78	in	in	ADP
iajs-1816	1	79	this	this	DET
iajs-1816	1	80	paper	paper	NOUN
iajs-1816	1	81	,	,	PUNCT
iajs-1816	1	82	developed	develop	VERB
iajs-1816	1	83	jungck	jungck	PROPN
iajs-1816	1	84	contractive	contractive	ADJ
iajs-1816	1	85	mappings	mapping	NOUN
iajs-1816	1	86	into	into	ADP
iajs-1816	1	87	fuzzy	fuzzy	ADJ
iajs-1816	1	88	jungck	jungck	NOUN
iajs-1816	1	89	contractive	contractive	ADJ
iajs-1816	1	90	and	and	CCONJ
iajs-1816	1	91	proved	prove	VERB
iajs-1816	1	92	fuzzy	fuzzy	ADJ
iajs-1816	1	93	fixed	fix	VERB
iajs-1816	1	94	point	point	NOUN
iajs-1816	1	95	for	for	ADP
iajs-1816	1	96	some	some	DET
iajs-1816	1	97	types	type	NOUN
iajs-1816	1	98	of	of	AUX
iajs-1816	1	99	generalize	generalize	VERB
iajs-1816	1	100	fuzzy	fuzzy	ADJ
iajs-1816	1	101	jungck	jungck	PROPN
iajs-1816	1	102	contractive	contractive	ADJ
iajs-1816	1	103	mappings	mapping	NOUN
iajs-1816	1	104	.	.	PUNCT
iajs-1816	2	1	keywords	keyword	NOUN
iajs-1816	2	2	:	:	PUNCT
iajs-1816	2	3	fuzzy	fuzzy	ADJ
iajs-1816	2	4	mapping	mapping	NOUN
iajs-1816	2	5	,	,	PUNCT
iajs-1816	2	6	fuzzy	fuzzy	ADJ
iajs-1816	2	7	fixed	fix	VERB
iajs-1816	2	8	point	point	NOUN
iajs-1816	2	9	and	and	CCONJ
iajs-1816	2	10	jungck	jungck	PROPN
iajs-1816	2	11	contractive	contractive	ADJ
iajs-1816	2	12	.	.	PUNCT
iajs-1816	3	1	ihsciconf	ihsciconf	PROPN
iajs-1816	3	2	2017	2017	NUM
iajs-1816	3	3	special	special	ADJ
iajs-1816	3	4	issue	issue	NOUN
iajs-1816	3	5	ibn	ibn	PROPN
iajs-1816	3	6	al	al	PROPN
iajs-1816	3	7	-	-	PUNCT
iajs-1816	3	8	haitham	haitham	PROPN
iajs-1816	3	9	journal	journal	PROPN
iajs-1816	3	10	for	for	ADP
iajs-1816	3	11	pure	pure	ADJ
iajs-1816	3	12	and	and	CCONJ
iajs-1816	3	13	applied	apply	VERB
iajs-1816	3	14	science	science	NOUN
iajs-1816	3	15	https://doi.org/	https://doi.org/	NOUN
iajs-1816	3	16	10.30526/2017.ihsciconf.1816	10.30526/2017.ihsciconf.1816	NUM
iajs-1816	3	17	for	for	ADP
iajs-1816	3	18	more	more	ADJ
iajs-1816	3	19	information	information	NOUN
iajs-1816	3	20	about	about	ADP
iajs-1816	3	21	the	the	DET
iajs-1816	3	22	conference	conference	NOUN
iajs-1816	3	23	please	please	INTJ
iajs-1816	3	24	visit	visit	VERB
iajs-1816	3	25	the	the	DET
iajs-1816	3	26	websites	website	NOUN
iajs-1816	3	27	:	:	PUNCT
iajs-1816	3	28	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1816	3	29	   	   	SPACE
iajs-1816	3	30	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1816	3	31	   	   	SPACE
iajs-1816	3	32	mathematics|427	mathematics|427	X
iajs-1816	3	33	    	    	SPACE
iajs-1816	3	34	1	1	NUM
iajs-1816	3	35	.	.	PUNCT
iajs-1816	4	1	introduction	introduction	NOUN
iajs-1816	4	2	the	the	DET
iajs-1816	4	3	concept	concept	NOUN
iajs-1816	4	4	of	of	ADP
iajs-1816	4	5	fuzzy	fuzzy	ADJ
iajs-1816	4	6	set	set	NOUN
iajs-1816	4	7	was	be	AUX
iajs-1816	4	8	introduced	introduce	VERB
iajs-1816	4	9	by	by	ADP
iajs-1816	4	10	l.zadeh	l.zadeh	NOUN
iajs-1816	4	11	[	[	X
iajs-1816	4	12	3]in	3]in	NUM
iajs-1816	4	13	(	(	PUNCT
iajs-1816	4	14	1965).after	1965).after	ADP
iajs-1816	4	15	that	that	PRON
iajs-1816	4	16	a	a	DET
iajs-1816	4	17	lot	lot	NOUN
iajs-1816	4	18	of	of	ADP
iajs-1816	4	19	work	work	NOUN
iajs-1816	4	20	has	have	AUX
iajs-1816	4	21	been	be	AUX
iajs-1816	4	22	done	do	VERB
iajs-1816	4	23	regarding	regard	VERB
iajs-1816	4	24	fuzzy	fuzzy	ADJ
iajs-1816	4	25	set	set	ADJ
iajs-1816	4	26	and	and	CCONJ
iajs-1816	4	27	fuzzy	fuzzy	ADJ
iajs-1816	4	28	mappings	mapping	NOUN
iajs-1816	4	29	.	.	PUNCT
iajs-1816	5	1	the	the	DET
iajs-1816	5	2	concept	concept	NOUN
iajs-1816	5	3	of	of	ADP
iajs-1816	5	4	fuzzy	fuzzy	ADJ
iajs-1816	5	5	mapping	mapping	NOUN
iajs-1816	5	6	was	be	AUX
iajs-1816	5	7	first	first	ADV
iajs-1816	5	8	introduced	introduce	VERB
iajs-1816	5	9	by	by	ADP
iajs-1816	5	10	heilpern	heilpern	NOUN
iajs-1816	5	11	[	[	X
iajs-1816	5	12	4].in	4].in	NUM
iajs-1816	5	13	(	(	PUNCT
iajs-1816	5	14	2001	2001	NUM
iajs-1816	5	15	)	)	PUNCT
iajs-1816	5	16	,	,	PUNCT
iajs-1816	5	17	estruch	estruch	ADJ
iajs-1816	5	18	and	and	CCONJ
iajs-1816	5	19	vidal	vidal	NOUN
iajs-1816	6	1	[	[	X
iajs-1816	6	2	1	1	NUM
iajs-1816	6	3	]	]	PUNCT
iajs-1816	6	4	proved	prove	VERB
iajs-1816	6	5	a	a	DET
iajs-1816	6	6	fuzzy	fuzzy	ADJ
iajs-1816	6	7	fixed	fix	VERB
iajs-1816	6	8	point	point	NOUN
iajs-1816	6	9	theorem	theorem	NOUN
iajs-1816	6	10	for	for	ADP
iajs-1816	6	11	fuzzy	fuzzy	ADJ
iajs-1816	6	12	contractive	contractive	ADJ
iajs-1816	6	13	mappings	mapping	NOUN
iajs-1816	6	14	.jungck	.jungck	PRON
iajs-1816	6	15	,	,	PUNCT
iajs-1816	6	16	g.[2][(1976	g.[2][(1976	NOUN
iajs-1816	6	17	)	)	PUNCT
iajs-1816	6	18	introduced	introduce	VERB
iajs-1816	6	19	jungck	jungck	NOUN
iajs-1816	6	20	contractive	contractive	ADJ
iajs-1816	6	21	mapping	mapping	NOUN
iajs-1816	6	22	and	and	CCONJ
iajs-1816	6	23	proved	prove	VERB
iajs-1816	6	24	fixed	fix	VERB
iajs-1816	6	25	point	point	NOUN
iajs-1816	6	26	theorems	theorem	NOUN
iajs-1816	6	27	.	.	PUNCT
iajs-1816	7	1	in	in	ADP
iajs-1816	7	2	this	this	DET
iajs-1816	7	3	paper	paper	NOUN
iajs-1816	7	4	,	,	PUNCT
iajs-1816	7	5	we	we	PRON
iajs-1816	7	6	introduced	introduce	VERB
iajs-1816	7	7	jungck	jungck	NOUN
iajs-1816	7	8	contractive	contractive	ADJ
iajs-1816	7	9	mapping	mapping	NOUN
iajs-1816	7	10	and	and	CCONJ
iajs-1816	7	11	studied	study	VERB
iajs-1816	7	12	some	some	DET
iajs-1816	7	13	results	result	NOUN
iajs-1816	7	14	of	of	ADP
iajs-1816	7	15	fuzzy	fuzzy	ADJ
iajs-1816	7	16	fixed	fix	VERB
iajs-1816	7	17	point	point	NOUN
iajs-1816	7	18	theorems	theorem	NOUN
iajs-1816	7	19	for	for	ADP
iajs-1816	7	20	some	some	DET
iajs-1816	7	21	types	type	NOUN
iajs-1816	7	22	of	of	ADP
iajs-1816	7	23	generalized	generalized	ADJ
iajs-1816	7	24	fuzzy	fuzzy	ADJ
iajs-1816	7	25	jungck	jungck	NOUN
iajs-1816	7	26	contractive	contractive	ADJ
iajs-1816	7	27	mapping	mapping	NOUN
iajs-1816	7	28	in	in	ADP
iajs-1816	7	29	hilbert	hilbert	PROPN
iajs-1816	7	30	space	space	NOUN
iajs-1816	7	31	.	.	PUNCT
iajs-1816	8	1	preliminaries	preliminary	NOUN
iajs-1816	8	2	in	in	ADP
iajs-1816	8	3	this	this	DET
iajs-1816	8	4	section	section	NOUN
iajs-1816	8	5	,	,	PUNCT
iajs-1816	8	6	we	we	PRON
iajs-1816	8	7	recall	recall	VERB
iajs-1816	8	8	some	some	DET
iajs-1816	8	9	basic	basic	ADJ
iajs-1816	8	10	definitions	definition	NOUN
iajs-1816	8	11	and	and	CCONJ
iajs-1816	8	12	preliminaries	preliminary	NOUN
iajs-1816	8	13	that	that	PRON
iajs-1816	8	14	will	will	AUX
iajs-1816	8	15	be	be	AUX
iajs-1816	8	16	needed	need	VERB
iajs-1816	8	17	in	in	ADP
iajs-1816	8	18	this	this	DET
iajs-1816	8	19	paper	paper	NOUN
iajs-1816	8	20	.	.	PUNCT
iajs-1816	9	1	definition	definition	NOUN
iajs-1816	9	2	2.1[3	2.1[3	NUM
iajs-1816	9	3	]	]	X
iajs-1816	9	4	:	:	PUNCT
iajs-1816	9	5	let	let	VERB
iajs-1816	9	6	h	h	NOUN
iajs-1816	9	7	be	be	AUX
iajs-1816	9	8	a	a	DET
iajs-1816	9	9	hilbert	hilbert	NOUN
iajs-1816	9	10	space	space	NOUN
iajs-1816	9	11	and	and	CCONJ
iajs-1816	9	12	f(h	f(h	PROPN
iajs-1816	9	13	)	)	PUNCT
iajs-1816	9	14	be	be	AUX
iajs-1816	9	15	a	a	DET
iajs-1816	9	16	collection	collection	NOUN
iajs-1816	9	17	of	of	ADP
iajs-1816	9	18	all	all	DET
iajs-1816	9	19	fuzzy	fuzzy	ADJ
iajs-1816	9	20	sets	set	NOUN
iajs-1816	9	21	in	in	ADP
iajs-1816	9	22	h	h	NOUN
iajs-1816	9	23	.	.	PUNCT
iajs-1816	10	1	let	let	VERB
iajs-1816	10	2	a	a	DET
iajs-1816	10	3	∈	∈	PROPN
iajs-1816	10	4	f	f	NOUN
iajs-1816	10	5	h	h	NOUN
iajs-1816	10	6	and	and	CCONJ
iajs-1816	10	7	α	α	NOUN
iajs-1816	10	8	∈	∈	PROPN
iajs-1816	11	1	[	[	X
iajs-1816	11	2	0	0	NUM
iajs-1816	11	3	,	,	PUNCT
iajs-1816	11	4	1	1	NUM
iajs-1816	11	5	]	]	PUNCT
iajs-1816	11	6	the	the	DET
iajs-1816	11	7	α	α	NOUN
iajs-1816	11	8	level	level	NOUN
iajs-1816	11	9	set	set	NOUN
iajs-1816	11	10	of	of	ADP
iajs-1816	11	11	a	a	PRON
iajs-1816	11	12	,	,	PUNCT
iajs-1816	11	13	denoted	denote	VERB
iajs-1816	11	14	by	by	ADP
iajs-1816	11	15	a	a	PRON
iajs-1816	11	16	is	be	AUX
iajs-1816	11	17	defined	define	VERB
iajs-1816	11	18	by	by	ADP
iajs-1816	11	19	a	a	DET
iajs-1816	11	20	=	=	SYM
iajs-1816	11	21	{	{	PUNCT
iajs-1816	11	22	u	u	NOUN
iajs-1816	11	23	:	:	PUNCT
iajs-1816	11	24	a(u	a(u	X
iajs-1816	11	25	)	)	PUNCT
iajs-1816	11	26	α	α	NOUN
iajs-1816	11	27	}	}	PUNCT
iajs-1816	11	28	if	if	SCONJ
iajs-1816	11	29	α	α	PRON
iajs-1816	11	30	∈	∈	NOUN
iajs-1816	11	31	0,1	0,1	NUM
iajs-1816	11	32	a	a	DET
iajs-1816	11	33	=	=	X
iajs-1816	11	34	u	u	NOUN
iajs-1816	11	35	:	:	PUNCT
iajs-1816	11	36	a	a	DET
iajs-1816	11	37	u	u	NOUN
iajs-1816	11	38	α	α	NOUN
iajs-1816	11	39	where	where	SCONJ
iajs-1816	11	40	b	b	NOUN
iajs-1816	11	41	denotes	denote	VERB
iajs-1816	11	42	the	the	DET
iajs-1816	11	43	closure	closure	NOUN
iajs-1816	11	44	of	of	ADP
iajs-1816	11	45	a	a	DET
iajs-1816	11	46	set	set	ADJ
iajs-1816	11	47	b.	b.	PROPN
iajs-1816	11	48	definition	definition	NOUN
iajs-1816	11	49	a	a	DET
iajs-1816	11	50	fuzzy	fuzzy	ADJ
iajs-1816	11	51	set	set	NOUN
iajs-1816	11	52	a	a	PRON
iajs-1816	11	53	is	be	AUX
iajs-1816	11	54	said	say	VERB
iajs-1816	11	55	to	to	PART
iajs-1816	11	56	be	be	AUX
iajs-1816	11	57	an	an	DET
iajs-1816	11	58	approximate	approximate	ADJ
iajs-1816	11	59	quantity	quantity	NOUN
iajs-1816	11	60	if	if	SCONJ
iajs-1816	11	61	and	and	CCONJ
iajs-1816	11	62	only	only	ADV
iajs-1816	11	63	if	if	SCONJ
iajs-1816	11	64	a	a	PRON
iajs-1816	11	65	is	be	AUX
iajs-1816	11	66	compact	compact	ADJ
iajs-1816	11	67	and	and	CCONJ
iajs-1816	11	68	convex	convex	VERB
iajs-1816	11	69	for	for	ADP
iajs-1816	11	70	each	each	DET
iajs-1816	11	71	α	α	NOUN
iajs-1816	11	72	∈	∈	NOUN
iajs-1816	11	73	0,1	0,1	NUM
iajs-1816	11	74	,	,	PUNCT
iajs-1816	11	75	and	and	CCONJ
iajs-1816	11	76	sup	sup	NOUN
iajs-1816	11	77	∈	∈	PROPN
iajs-1816	11	78	a(u	a(u	X
iajs-1816	11	79	)	)	PUNCT
iajs-1816	12	1	=	=	SYM
iajs-1816	12	2	1	1	NUM
iajs-1816	12	3	.when	.when	ADP
iajs-1816	12	4	a	a	PRON
iajs-1816	12	5	is	be	AUX
iajs-1816	12	6	an	an	DET
iajs-1816	12	7	approximate	approximate	ADJ
iajs-1816	12	8	quantity	quantity	NOUN
iajs-1816	12	9	and	and	CCONJ
iajs-1816	12	10	a(u	a(u	PROPN
iajs-1816	12	11	)	)	PUNCT
iajs-1816	13	1	=	=	SYM
iajs-1816	13	2	1	1	NUM
iajs-1816	13	3	for	for	ADP
iajs-1816	13	4	some	some	DET
iajs-1816	13	5	u	u	NOUN
iajs-1816	13	6	∈	∈	PROPN
iajs-1816	13	7	h	h	NOUN
iajs-1816	13	8	,	,	PUNCT
iajs-1816	13	9	a	a	PRON
iajs-1816	13	10	is	be	AUX
iajs-1816	13	11	identified	identify	VERB
iajs-1816	13	12	with	with	ADP
iajs-1816	13	13	an	an	DET
iajs-1816	13	14	approximate	approximate	NOUN
iajs-1816	13	15	of	of	ADP
iajs-1816	13	16	u	u	NOUN
iajs-1816	13	17	.	.	PUNCT
iajs-1816	14	1	the	the	DET
iajs-1816	14	2	collection	collection	NOUN
iajs-1816	14	3	of	of	ADP
iajs-1816	14	4	all	all	DET
iajs-1816	14	5	fuzzy	fuzzy	ADJ
iajs-1816	14	6	sets	set	NOUN
iajs-1816	14	7	in	in	ADP
iajs-1816	14	8	h	h	NOUN
iajs-1816	14	9	is	be	AUX
iajs-1816	14	10	denoted	denote	VERB
iajs-1816	14	11	by	by	ADP
iajs-1816	14	12	f(h	f(h	PROPN
iajs-1816	14	13	)	)	PUNCT
iajs-1816	14	14	and	and	CCONJ
iajs-1816	14	15	w(h	w(h	PROPN
iajs-1816	14	16	)	)	PUNCT
iajs-1816	14	17	is	be	AUX
iajs-1816	14	18	the	the	DET
iajs-1816	14	19	sub	sub	NOUN
iajs-1816	14	20	collection	collection	NOUN
iajs-1816	14	21	of	of	ADP
iajs-1816	14	22	all	all	DET
iajs-1816	14	23	approximate	approximate	ADJ
iajs-1816	14	24	quantities	quantity	NOUN
iajs-1816	14	25	.	.	PUNCT
iajs-1816	15	1	definition	definition	NOUN
iajs-1816	15	2	let	let	VERB
iajs-1816	15	3	a	a	DET
iajs-1816	15	4	,	,	PUNCT
iajs-1816	15	5	b	b	PROPN
iajs-1816	15	6	∈	∈	PROPN
iajs-1816	15	7	w	w	PROPN
iajs-1816	15	8	h	h	NOUN
iajs-1816	15	9	and	and	CCONJ
iajs-1816	15	10	α	α	NOUN
iajs-1816	15	11	∈	∈	NOUN
iajs-1816	15	12	0,1	0,1	NUM
iajs-1816	15	13	.	.	PUNCT
iajs-1816	16	1	then	then	ADV
iajs-1816	16	2	i.	i.	PROPN
iajs-1816	16	3	δ	δ	PROPN
iajs-1816	16	4	(	(	PUNCT
iajs-1816	16	5	a	a	DET
iajs-1816	16	6	,	,	PUNCT
iajs-1816	16	7	b	b	NOUN
iajs-1816	16	8	)	)	PUNCT
iajs-1816	16	9	=	=	VERB
iajs-1816	16	10	inf	inf	PROPN
iajs-1816	16	11	∈	∈	PROPN
iajs-1816	16	12	,	,	PUNCT
iajs-1816	16	13	∈	∈	PROPN
iajs-1816	16	14	‖u	‖u	PROPN
iajs-1816	16	15	v‖	v‖	PROPN
iajs-1816	16	16	ii	ii	NOUN
iajs-1816	16	17	.	.	PUNCT
iajs-1816	17	1	d	d	X
iajs-1816	17	2	(	(	PUNCT
iajs-1816	17	3	a	a	DET
iajs-1816	17	4	,	,	PUNCT
iajs-1816	17	5	b	b	NOUN
iajs-1816	17	6	)	)	PUNCT
iajs-1816	17	7	=	=	SYM
iajs-1816	18	1	dis(a	dis(a	PROPN
iajs-1816	18	2	,	,	PUNCT
iajs-1816	18	3	b	b	PROPN
iajs-1816	18	4	)	)	PUNCT
iajs-1816	18	5	,	,	PUNCT
iajs-1816	18	6	where	where	SCONJ
iajs-1816	18	7	“	"	PUNCT
iajs-1816	18	8	dis	dis	PROPN
iajs-1816	18	9	”	"	PUNCT
iajs-1816	18	10	is	be	AUX
iajs-1816	18	11	the	the	DET
iajs-1816	18	12	hausdorff	hausdorff	PROPN
iajs-1816	18	13	distance	distance	PROPN
iajs-1816	18	14	iii	iii	NOUN
iajs-1816	18	15	.	.	PUNCT
iajs-1816	19	1	d(a	d(a	PROPN
iajs-1816	19	2	,	,	PUNCT
iajs-1816	19	3	b	b	X
iajs-1816	19	4	)	)	PUNCT
iajs-1816	19	5	=	=	SYM
iajs-1816	19	6	sup	sup	NOUN
iajs-1816	19	7	d	d	PROPN
iajs-1816	19	8	(	(	PUNCT
iajs-1816	19	9	a	a	PRON
iajs-1816	19	10	,	,	PUNCT
iajs-1816	19	11	b	b	NOUN
iajs-1816	19	12	)	)	PUNCT
iajs-1816	19	13	iv	iv	NOUN
iajs-1816	19	14	.	.	PUNCT
iajs-1816	20	1	δ	δ	PROPN
iajs-1816	20	2	(	(	PUNCT
iajs-1816	20	3	a	a	DET
iajs-1816	20	4	,	,	PUNCT
iajs-1816	20	5	b	b	NOUN
iajs-1816	20	6	)	)	PUNCT
iajs-1816	20	7	=	=	SYM
iajs-1816	20	8	sup	sup	PROPN
iajs-1816	20	9	δ	δ	PROPN
iajs-1816	20	10	(	(	PUNCT
iajs-1816	20	11	a	a	DET
iajs-1816	20	12	,	,	PUNCT
iajs-1816	20	13	b	b	NOUN
iajs-1816	20	14	)	)	PUNCT
iajs-1816	20	15	.	.	PUNCT
iajs-1816	21	1	it	it	PRON
iajs-1816	21	2	is	be	AUX
iajs-1816	21	3	to	to	PART
iajs-1816	21	4	be	be	AUX
iajs-1816	21	5	noted	note	VERB
iajs-1816	21	6	that	that	SCONJ
iajs-1816	21	7	for	for	ADP
iajs-1816	21	8	any	any	DET
iajs-1816	21	9	‘	'	PUNCT
iajs-1816	21	10	α	α	X
iajs-1816	21	11	’	'	PUNCT
iajs-1816	21	12	,	,	PUNCT
iajs-1816	21	13	δ	δ	PROPN
iajs-1816	21	14	is	be	AUX
iajs-1816	21	15	a	a	DET
iajs-1816	21	16	non	non	NOUN
iajs-1816	21	17	decreasing	decrease	VERB
iajs-1816	21	18	as	as	ADV
iajs-1816	21	19	well	well	ADV
iajs-1816	21	20	as	as	ADP
iajs-1816	21	21	continuous	continuous	ADJ
iajs-1816	21	22	function	function	NOUN
iajs-1816	21	23	.	.	PUNCT
iajs-1816	22	1	definition	definition	NOUN
iajs-1816	22	2	let	let	VERB
iajs-1816	22	3	a	a	DET
iajs-1816	22	4	,	,	PUNCT
iajs-1816	22	5	b	b	PROPN
iajs-1816	22	6	∈	∈	PROPN
iajs-1816	22	7	w	w	NOUN
iajs-1816	22	8	h	h	NOUN
iajs-1816	22	9	.	.	PUNCT
iajs-1816	23	1	an	an	DET
iajs-1816	23	2	approximate	approximate	ADJ
iajs-1816	23	3	quantity	quantity	NOUN
iajs-1816	23	4	a	a	PRON
iajs-1816	23	5	is	be	AUX
iajs-1816	23	6	said	say	VERB
iajs-1816	23	7	to	to	PART
iajs-1816	23	8	be	be	AUX
iajs-1816	23	9	more	more	ADV
iajs-1816	23	10	accurate	accurate	ADJ
iajs-1816	23	11	than	than	ADP
iajs-1816	23	12	b	b	NOUN
iajs-1816	23	13	(	(	PUNCT
iajs-1816	23	14	denoted	denote	VERB
iajs-1816	23	15	by	by	ADP
iajs-1816	23	16	a⊂	a⊂	NOUN
iajs-1816	23	17	b	b	NOUN
iajs-1816	23	18	if	if	SCONJ
iajs-1816	24	1	and	and	CCONJ
iajs-1816	24	2	only	only	ADV
iajs-1816	24	3	if	if	SCONJ
iajs-1816	24	4	a	a	DET
iajs-1816	24	5	u	u	PROPN
iajs-1816	24	6	b	b	PROPN
iajs-1816	24	7	u	u	PROPN
iajs-1816	24	8	,	,	PUNCT
iajs-1816	24	9	∀	∀	VERB
iajs-1816	24	10	u	u	NOUN
iajs-1816	24	11	∈	∈	PROPN
iajs-1816	24	12	h.	h.	NOUN
iajs-1816	24	13	definition	definition	NOUN
iajs-1816	24	14	a	a	DET
iajs-1816	24	15	mapping	mapping	NOUN
iajs-1816	24	16	m	m	NOUN
iajs-1816	24	17	from	from	ADP
iajs-1816	24	18	the	the	DET
iajs-1816	24	19	set	set	ADJ
iajs-1816	24	20	h	h	NOUN
iajs-1816	24	21	into	into	ADP
iajs-1816	24	22	w(h	w(h	NOUN
iajs-1816	24	23	)	)	PUNCT
iajs-1816	24	24	is	be	AUX
iajs-1816	24	25	said	say	VERB
iajs-1816	24	26	to	to	PART
iajs-1816	24	27	be	be	AUX
iajs-1816	24	28	fuzzy	fuzzy	ADJ
iajs-1816	24	29	mapping	mapping	NOUN
iajs-1816	24	30	.	.	PUNCT
iajs-1816	25	1	definition	definition	NOUN
iajs-1816	25	2	the	the	DET
iajs-1816	25	3	point	point	NOUN
iajs-1816	25	4	u	u	NOUN
iajs-1816	25	5	∈	∈	NOUN
iajs-1816	25	6	h	h	NOUN
iajs-1816	25	7	is	be	AUX
iajs-1816	25	8	called	call	VERB
iajs-1816	25	9	fixed	fix	VERB
iajs-1816	25	10	point	point	NOUN
iajs-1816	25	11	for	for	ADP
iajs-1816	25	12	the	the	DET
iajs-1816	25	13	fuzzy	fuzzy	ADJ
iajs-1816	25	14	mapping	mapping	NOUN
iajs-1816	25	15	m	m	VERB
iajs-1816	25	16	if	if	SCONJ
iajs-1816	25	17	{	{	PUNCT
iajs-1816	25	18	u}⊂tu	u}⊂tu	VERB
iajs-1816	25	19	.	.	PUNCT
iajs-1816	26	1	if	if	SCONJ
iajs-1816	26	2	u	u	PROPN
iajs-1816	26	3	⊂	⊂	PROPN
iajs-1816	26	4	tu	tu	PROPN
iajs-1816	26	5	is	be	AUX
iajs-1816	26	6	called	call	VERB
iajs-1816	26	7	fuzzy	fuzzy	ADJ
iajs-1816	26	8	fixed	fix	VERB
iajs-1816	26	9	point	point	NOUN
iajs-1816	26	10	of	of	ADP
iajs-1816	26	11	m	m	PROPN
iajs-1816	26	12	.	.	PUNCT
iajs-1816	27	1	we	we	PRON
iajs-1816	27	2	shall	shall	AUX
iajs-1816	27	3	use	use	VERB
iajs-1816	27	4	the	the	DET
iajs-1816	27	5	following	follow	VERB
iajs-1816	27	6	lemmas	lemmas	PROPN
iajs-1816	27	7	due	due	ADP
iajs-1816	27	8	to	to	ADP
iajs-1816	27	9	helipern	helipern	NOUN
iajs-1816	27	10	.	.	PUNCT
iajs-1816	28	1	lemma	lemma	PROPN
iajs-1816	28	2	δ	δ	PROPN
iajs-1816	28	3	(	(	PUNCT
iajs-1816	28	4	u	u	PROPN
iajs-1816	28	5	,	,	PUNCT
iajs-1816	28	6	b	b	NOUN
iajs-1816	28	7	)	)	PUNCT
iajs-1816	28	8	‖u	‖u	NOUN
iajs-1816	28	9	v‖	v‖	NOUN
iajs-1816	28	10	δ	δ	PROPN
iajs-1816	28	11	v	v	NOUN
iajs-1816	28	12	,	,	PUNCT
iajs-1816	28	13	b	b	NOUN
iajs-1816	28	14	,	,	PUNCT
iajs-1816	28	15	∀	∀	X
iajs-1816	28	16	u	u	NOUN
iajs-1816	28	17	,	,	PUNCT
iajs-1816	28	18	v	v	PROPN
iajs-1816	28	19	∈	∈	PROPN
iajs-1816	28	20	h.	h.	NOUN
iajs-1816	28	21	ihsciconf	ihsciconf	PROPN
iajs-1816	28	22	2017	2017	NUM
iajs-1816	28	23	special	special	ADJ
iajs-1816	28	24	issue	issue	NOUN
iajs-1816	28	25	ibn	ibn	PROPN
iajs-1816	28	26	al	al	PROPN
iajs-1816	28	27	-	-	PUNCT
iajs-1816	28	28	haitham	haitham	PROPN
iajs-1816	28	29	journal	journal	PROPN
iajs-1816	28	30	for	for	ADP
iajs-1816	28	31	pure	pure	ADJ
iajs-1816	28	32	and	and	CCONJ
iajs-1816	28	33	applied	apply	VERB
iajs-1816	28	34	science	science	NOUN
iajs-1816	28	35	https://doi.org/	https://doi.org/	NOUN
iajs-1816	28	36	10.30526/2017.ihsciconf.1816	10.30526/2017.ihsciconf.1816	NUM
iajs-1816	28	37	for	for	ADP
iajs-1816	28	38	more	more	ADJ
iajs-1816	28	39	information	information	NOUN
iajs-1816	28	40	about	about	ADP
iajs-1816	28	41	the	the	DET
iajs-1816	28	42	conference	conference	NOUN
iajs-1816	28	43	please	please	INTJ
iajs-1816	28	44	visit	visit	VERB
iajs-1816	28	45	the	the	DET
iajs-1816	28	46	websites	website	NOUN
iajs-1816	28	47	:	:	PUNCT
iajs-1816	28	48	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1816	28	49	   	   	SPACE
iajs-1816	28	50	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1816	28	51	   	   	SPACE
iajs-1816	28	52	mathematics|428	mathematics|428	PROPN
iajs-1816	28	53	    	    	SPACE
iajs-1816	28	54	lemma	lemma	PROPN
iajs-1816	28	55	if	if	SCONJ
iajs-1816	28	56	u	u	PROPN
iajs-1816	28	57	⊂	⊂	PROPN
iajs-1816	28	58	a	a	X
iajs-1816	28	59	,	,	PUNCT
iajs-1816	28	60	then	then	ADV
iajs-1816	28	61	δ	δ	PROPN
iajs-1816	28	62	(	(	PUNCT
iajs-1816	28	63	u	u	PROPN
iajs-1816	28	64	,	,	PUNCT
iajs-1816	28	65	b	b	PROPN
iajs-1816	28	66	)	)	PUNCT
iajs-1816	28	67	d	d	NOUN
iajs-1816	28	68	a	a	PRON
iajs-1816	28	69	,	,	PUNCT
iajs-1816	28	70	b	b	NOUN
iajs-1816	28	71	,	,	PUNCT
iajs-1816	28	72	∀	∀	PUNCT
iajs-1816	28	73	b	b	NOUN
iajs-1816	28	74	∈	∈	PROPN
iajs-1816	28	75	w	w	PROPN
iajs-1816	28	76	h	h	NOUN
iajs-1816	28	77	.	.	PUNCT
iajs-1816	29	1	lemma	lemma	PROPN
iajs-1816	29	2	let	let	VERB
iajs-1816	29	3	a	a	DET
iajs-1816	29	4	∈	∈	PROPN
iajs-1816	29	5	w	w	NOUN
iajs-1816	29	6	h	h	NOUN
iajs-1816	29	7	and	and	CCONJ
iajs-1816	29	8	u	u	PROPN
iajs-1816	29	9	∈	∈	PROPN
iajs-1816	29	10	h	h	NOUN
iajs-1816	29	11	,	,	PUNCT
iajs-1816	29	12	if	if	SCONJ
iajs-1816	29	13	u	u	PROPN
iajs-1816	29	14	⊂	⊂	PROPN
iajs-1816	29	15	a	a	X
iajs-1816	29	16	then	then	ADV
iajs-1816	29	17	δ	δ	PROPN
iajs-1816	29	18	(	(	PUNCT
iajs-1816	29	19	u	u	PROPN
iajs-1816	29	20	,	,	PUNCT
iajs-1816	29	21	a)=	a)=	PROPN
iajs-1816	29	22	0	0	NUM
iajs-1816	29	23	,	,	PUNCT
iajs-1816	29	24	for	for	ADP
iajs-1816	29	25	each	each	DET
iajs-1816	29	26	α	α	NOUN
iajs-1816	29	27	∈	∈	NOUN
iajs-1816	29	28	0,1	0,1	NUM
iajs-1816	29	29	.	.	PUNCT
iajs-1816	30	1	lemma	lemma	PROPN
iajs-1816	30	2	let	let	VERB
iajs-1816	30	3	h	h	PRON
iajs-1816	30	4	be	be	AUX
iajs-1816	30	5	a	a	DET
iajs-1816	30	6	hilbert	hilbert	NOUN
iajs-1816	30	7	space	space	NOUN
iajs-1816	30	8	and	and	CCONJ
iajs-1816	30	9	m	m	PRON
iajs-1816	30	10	fuzzy	fuzzy	ADJ
iajs-1816	30	11	mapping	mapping	NOUN
iajs-1816	30	12	from	from	ADP
iajs-1816	30	13	h	h	NOUN
iajs-1816	30	14	into	into	ADP
iajs-1816	30	15	w(h	w(h	NOUN
iajs-1816	30	16	)	)	PUNCT
iajs-1816	30	17	and	and	CCONJ
iajs-1816	30	18	u	u	PROPN
iajs-1816	30	19	∈	∈	PROPN
iajs-1816	30	20	h	h	NOUN
iajs-1816	30	21	,	,	PUNCT
iajs-1816	30	22	then	then	ADV
iajs-1816	30	23	there	there	PRON
iajs-1816	30	24	exists	exist	VERB
iajs-1816	30	25	u	u	PROPN
iajs-1816	30	26	∈	∈	PROPN
iajs-1816	30	27	h	h	NOUN
iajs-1816	30	28	such	such	ADJ
iajs-1816	30	29	that	that	SCONJ
iajs-1816	30	30	u	u	PROPN
iajs-1816	30	31	⊂	⊂	PROPN
iajs-1816	30	32	tu	tu	PROPN
iajs-1816	30	33	.	.	PUNCT
iajs-1816	31	1	fuzzy	fuzzy	ADJ
iajs-1816	31	2	fixed	fix	VERB
iajs-1816	31	3	point	point	NOUN
iajs-1816	31	4	theorem	theorem	NOUN
iajs-1816	31	5	for	for	ADP
iajs-1816	31	6	types	type	NOUN
iajs-1816	31	7	of	of	ADP
iajs-1816	31	8	fuzzy	fuzzy	ADJ
iajs-1816	31	9	jungck	jungck	NOUN
iajs-1816	31	10	the	the	DET
iajs-1816	31	11	scope	scope	NOUN
iajs-1816	31	12	of	of	ADP
iajs-1816	31	13	the	the	DET
iajs-1816	31	14	function	function	NOUN
iajs-1816	31	15	in	in	ADP
iajs-1816	31	16	this	this	DET
iajs-1816	31	17	section	section	NOUN
iajs-1816	31	18	,	,	PUNCT
iajs-1816	31	19	ω	ω	NUM
iajs-1816	31	20	the	the	DET
iajs-1816	31	21	class	class	NOUN
iajs-1816	31	22	of	of	ADP
iajs-1816	31	23	all	all	DET
iajs-1816	31	24	functins	functin	NOUN
iajs-1816	31	25	ψ	ψ	NOUN
iajs-1816	31	26	:	:	PUNCT
iajs-1816	31	27	0	0	NUM
iajs-1816	31	28	,	,	PUNCT
iajs-1816	31	29	∞	∞	PROPN
iajs-1816	31	30	→	→	SYM
iajs-1816	31	31	0	0	NUM
iajs-1816	31	32	,	,	PUNCT
iajs-1816	31	33	∞	∞	PROPN
iajs-1816	31	34	,	,	PUNCT
iajs-1816	31	35	where	where	SCONJ
iajs-1816	31	36	ψ	ψ	NOUN
iajs-1816	31	37	is	be	AUX
iajs-1816	31	38	non	non	ADJ
iajs-1816	31	39	-	-	ADJ
iajs-1816	31	40	decreasing	decrease	VERB
iajs-1816	31	41	and	and	CCONJ
iajs-1816	31	42	∑	∑	ADP
iajs-1816	31	43	ψ	ψ	ADP
iajs-1816	31	44	t	t	PROPN
iajs-1816	31	45	∞	∞	PROPN
iajs-1816	31	46	,	,	PUNCT
iajs-1816	31	47	for	for	ADP
iajs-1816	31	48	each	each	DET
iajs-1816	31	49	t	t	NOUN
iajs-1816	31	50	0	0	NUM
iajs-1816	31	51	and	and	CCONJ
iajs-1816	31	52	ψ	ψ	NOUN
iajs-1816	31	53	is	be	AUX
iajs-1816	31	54	n	n	PRON
iajs-1816	31	55	th	th	X
iajs-1816	31	56	iteration	iteration	NOUN
iajs-1816	31	57	of	of	ADP
iajs-1816	31	58	ψ	ψ	NOUN
iajs-1816	31	59	and	and	CCONJ
iajs-1816	31	60	ψ	ψ	X
iajs-1816	31	61	0	0	NUM
iajs-1816	31	62	0	0	NUM
iajs-1816	31	63	.	.	PUNCT
iajs-1816	32	1	first	first	ADV
iajs-1816	32	2	of	of	ADP
iajs-1816	32	3	all	all	PRON
iajs-1816	32	4	,	,	PUNCT
iajs-1816	32	5	we	we	PRON
iajs-1816	32	6	introduce	introduce	VERB
iajs-1816	32	7	the	the	DET
iajs-1816	32	8	following	follow	VERB
iajs-1816	32	9	definitions	definition	NOUN
iajs-1816	32	10	and	and	CCONJ
iajs-1816	32	11	examples	example	NOUN
iajs-1816	32	12	.	.	PUNCT
iajs-1816	33	1	definition	definition	NOUN
iajs-1816	33	2	let	let	VERB
iajs-1816	33	3	h	h	PRON
iajs-1816	33	4	be	be	AUX
iajs-1816	33	5	a	a	DET
iajs-1816	33	6	hilbert	hilbert	NOUN
iajs-1816	33	7	space	space	NOUN
iajs-1816	33	8	and	and	CCONJ
iajs-1816	33	9	m	m	PROPN
iajs-1816	33	10	,	,	PUNCT
iajs-1816	33	11	n	n	CCONJ
iajs-1816	33	12	:	:	PUNCT
iajs-1816	33	13	h→	h→	NOUN
iajs-1816	33	14	w	w	NOUN
iajs-1816	33	15	h	h	NOUN
iajs-1816	33	16	.	.	PUNCT
iajs-1816	34	1	a	a	DET
iajs-1816	34	2	fuzzy	fuzzy	ADJ
iajs-1816	34	3	mappings	mapping	NOUN
iajs-1816	34	4	m	m	VERB
iajs-1816	34	5	and	and	CCONJ
iajs-1816	34	6	n	n	PROPN
iajs-1816	34	7	are	be	AUX
iajs-1816	34	8	called	call	VERB
iajs-1816	34	9	fuzzy	fuzzy	ADJ
iajs-1816	34	10	jungck	jungck	NOUN
iajs-1816	34	11	contraction	contraction	NOUN
iajs-1816	34	12	mapping	mapping	NOUN
iajs-1816	34	13	if	if	SCONJ
iajs-1816	34	14	there	there	PRON
iajs-1816	34	15	exists	exist	VERB
iajs-1816	34	16	ξ	ξ	PROPN
iajs-1816	34	17	∈	∈	PROPN
iajs-1816	34	18	0	0	NUM
iajs-1816	34	19	,	,	PUNCT
iajs-1816	34	20	1	1	NUM
iajs-1816	34	21	,	,	PUNCT
iajs-1816	34	22	such	such	ADJ
iajs-1816	34	23	that	that	SCONJ
iajs-1816	34	24	d	d	PROPN
iajs-1816	34	25	t	t	PROPN
iajs-1816	34	26	u	u	PROPN
iajs-1816	34	27	,	,	PUNCT
iajs-1816	34	28	t	t	PROPN
iajs-1816	34	29	v	v	NUM
iajs-1816	35	1	ξd	ξd	PROPN
iajs-1816	35	2	s	s	PART
iajs-1816	35	3	u	u	NOUN
iajs-1816	35	4	,	,	PUNCT
iajs-1816	35	5	s	s	NOUN
iajs-1816	35	6	v	v	NOUN
iajs-1816	35	7	,	,	PUNCT
iajs-1816	35	8	for	for	ADP
iajs-1816	35	9	all	all	DET
iajs-1816	35	10	u	u	NOUN
iajs-1816	35	11	,	,	PUNCT
iajs-1816	35	12	v	v	PROPN
iajs-1816	35	13	∈	∈	PROPN
iajs-1816	35	14	h.	h.	PROPN
iajs-1816	35	15	example	example	NOUN
iajs-1816	35	16	let	let	VERB
iajs-1816	35	17	h	h	PROPN
iajs-1816	35	18	=[	=[	NOUN
iajs-1816	35	19	0	0	NUM
iajs-1816	35	20	,	,	PUNCT
iajs-1816	35	21	1	1	NUM
iajs-1816	35	22	]	]	PUNCT
iajs-1816	35	23	,	,	PUNCT
iajs-1816	35	24	let	let	VERB
iajs-1816	35	25	us	we	PRON
iajs-1816	35	26	define	define	VERB
iajs-1816	35	27	m	m	PROPN
iajs-1816	35	28	,	,	PUNCT
iajs-1816	35	29	n	n	CCONJ
iajs-1816	35	30	:	:	PUNCT
iajs-1816	35	31	h→	h→	NOUN
iajs-1816	35	32	w	w	NOUN
iajs-1816	35	33	h	h	NOUN
iajs-1816	35	34	by	by	ADP
iajs-1816	35	35	s	s	NOUN
iajs-1816	35	36	u	u	PROPN
iajs-1816	35	37	s	s	PROPN
iajs-1816	35	38	t	t	NOUN
iajs-1816	35	39	v	v	NOUN
iajs-1816	35	40	s	s	X
iajs-1816	35	41	⎩	⎩	NUM
iajs-1816	35	42	⎪	⎪	NOUN
iajs-1816	35	43	⎨	⎨	ADJ
iajs-1816	35	44	⎪	⎪	NOUN
iajs-1816	35	45	⎧0	⎧0	NOUN
iajs-1816	35	46	,	,	PUNCT
iajs-1816	35	47	0	0	NUM
iajs-1816	35	48	s	s	PART
iajs-1816	35	49	,	,	PUNCT
iajs-1816	35	50	s	s	PART
iajs-1816	35	51	,	,	PUNCT
iajs-1816	35	52	s	s	NOUN
iajs-1816	35	53	1	1	NUM
iajs-1816	35	54	and	and	CCONJ
iajs-1816	35	55	let	let	VERB
iajs-1816	35	56	ξ	ξ	SYM
iajs-1816	35	57	1	1	NUM
iajs-1816	35	58	.	.	PUNCT
iajs-1816	36	1	then	then	ADV
iajs-1816	36	2	,	,	PUNCT
iajs-1816	36	3	m	m	VERB
iajs-1816	36	4	and	and	CCONJ
iajs-1816	36	5	n	n	PRON
iajs-1816	36	6	are	be	AUX
iajs-1816	36	7	fuzzy	fuzzy	ADJ
iajs-1816	36	8	jungck	jungck	NOUN
iajs-1816	36	9	contraction	contraction	NOUN
iajs-1816	36	10	mapping	mapping	NOUN
iajs-1816	36	11	.	.	PUNCT
iajs-1816	37	1	definition	definition	NOUN
iajs-1816	37	2	let	let	VERB
iajs-1816	37	3	h	h	PRON
iajs-1816	37	4	be	be	AUX
iajs-1816	37	5	a	a	DET
iajs-1816	37	6	hilbert	hilbert	NOUN
iajs-1816	37	7	space	space	NOUN
iajs-1816	37	8	and	and	CCONJ
iajs-1816	37	9	m	m	PROPN
iajs-1816	37	10	,	,	PUNCT
iajs-1816	37	11	n	n	CCONJ
iajs-1816	37	12	:	:	PUNCT
iajs-1816	37	13	h→	h→	NOUN
iajs-1816	37	14	w	w	NOUN
iajs-1816	37	15	h	h	NOUN
iajs-1816	37	16	.	.	PUNCT
iajs-1816	38	1	a	a	DET
iajs-1816	38	2	fuzzy	fuzzy	ADJ
iajs-1816	38	3	mappings	mapping	NOUN
iajs-1816	38	4	{	{	PUNCT
iajs-1816	38	5	m	m	PROPN
iajs-1816	38	6	,	,	PUNCT
iajs-1816	38	7	n	n	CCONJ
iajs-1816	38	8	}	}	PUNCT
iajs-1816	38	9	are	be	AUX
iajs-1816	38	10	said	say	VERB
iajs-1816	38	11	to	to	PART
iajs-1816	38	12	be	be	AUX
iajs-1816	38	13	fuzzy	fuzzy	ADJ
iajs-1816	38	14	r∗	r∗	ADJ
iajs-1816	38	15	weakly	weakly	ADV
iajs-1816	38	16	commuting	commuting	NOUN
iajs-1816	38	17	if	if	SCONJ
iajs-1816	38	18	for	for	ADP
iajs-1816	38	19	each	each	DET
iajs-1816	38	20	x	x	NOUN
iajs-1816	38	21	,	,	PUNCT
iajs-1816	38	22	y	y	PROPN
iajs-1816	38	23	∈	∈	PROPN
iajs-1816	38	24	h	h	NOUN
iajs-1816	38	25	and	and	CCONJ
iajs-1816	38	26	r	r	NOUN
iajs-1816	38	27	0	0	NUM
iajs-1816	38	28	,	,	PUNCT
iajs-1816	38	29	such	such	ADJ
iajs-1816	38	30	that	that	SCONJ
iajs-1816	38	31	d	d	PROPN
iajs-1816	38	32	s	s	PROPN
iajs-1816	38	33	u	u	PROPN
iajs-1816	38	34	,	,	PUNCT
iajs-1816	38	35	t	t	PROPN
iajs-1816	38	36	v	v	NOUN
iajs-1816	38	37	r‖u	r‖u	NOUN
iajs-1816	38	38	v‖	v‖	NOUN
iajs-1816	38	39	.	.	PUNCT
iajs-1816	39	1	example	example	NOUN
iajs-1816	39	2	let	let	VERB
iajs-1816	39	3	h=[0,1	h=[0,1	PROPN
iajs-1816	39	4	]	]	PUNCT
iajs-1816	39	5	and	and	CCONJ
iajs-1816	39	6	define	define	VERB
iajs-1816	39	7	m	m	PROPN
iajs-1816	39	8	,	,	PUNCT
iajs-1816	39	9	n	n	CCONJ
iajs-1816	39	10	:	:	PUNCT
iajs-1816	39	11	h→	h→	NOUN
iajs-1816	39	12	w	w	NOUN
iajs-1816	39	13	h	h	NOUN
iajs-1816	39	14	be	be	AUX
iajs-1816	39	15	a	a	DET
iajs-1816	39	16	fuzzy	fuzzy	ADJ
iajs-1816	39	17	mapping	mapping	NOUN
iajs-1816	39	18	such	such	ADJ
iajs-1816	39	19	that	that	SCONJ
iajs-1816	39	20	m	m	NOUN
iajs-1816	39	21	=	=	NOUN
iajs-1816	39	22	n	n	PROPN
iajs-1816	39	23	for	for	ADP
iajs-1816	39	24	all	all	DET
iajs-1816	39	25	x	x	SYM
iajs-1816	39	26	∈	∈	PROPN
iajs-1816	39	27	[	[	X
iajs-1816	39	28	0,1	0,1	NUM
iajs-1816	39	29	]	]	PUNCT
iajs-1816	39	30	,	,	PUNCT
iajs-1816	39	31	t(u	t(u	NUM
iajs-1816	39	32	)	)	PUNCT
iajs-1816	39	33	is	be	AUX
iajs-1816	39	34	a	a	DET
iajs-1816	39	35	fuzzy	fuzzy	ADJ
iajs-1816	39	36	set	set	NOUN
iajs-1816	39	37	on	on	ADP
iajs-1816	39	38	h	h	NOUN
iajs-1816	39	39	given	give	VERB
iajs-1816	39	40	by	by	ADP
iajs-1816	39	41	,	,	PUNCT
iajs-1816	39	42	t(0)(s	t(0)(s	NOUN
iajs-1816	39	43	)	)	PUNCT
iajs-1816	40	1	=	=	SYM
iajs-1816	40	2	1	1	NUM
iajs-1816	40	3	,	,	PUNCT
iajs-1816	40	4	s	s	PART
iajs-1816	40	5	0	0	NUM
iajs-1816	40	6	α	α	NOUN
iajs-1816	40	7	,	,	PUNCT
iajs-1816	40	8	s	s	PART
iajs-1816	40	9	∈	∈	NOUN
iajs-1816	40	10	0	0	NUM
iajs-1816	40	11	,	,	PUNCT
iajs-1816	40	12	,	,	PUNCT
iajs-1816	40	13	s	s	PROPN
iajs-1816	40	14	∈	∈	PROPN
iajs-1816	40	15	,	,	PUNCT
iajs-1816	40	16	1	1	NUM
iajs-1816	40	17	ihsciconf	ihsciconf	NOUN
iajs-1816	40	18	2017	2017	NUM
iajs-1816	40	19	special	special	ADJ
iajs-1816	40	20	issue	issue	NOUN
iajs-1816	40	21	ibn	ibn	PROPN
iajs-1816	40	22	al	al	PROPN
iajs-1816	40	23	-	-	PUNCT
iajs-1816	40	24	haitham	haitham	PROPN
iajs-1816	40	25	journal	journal	PROPN
iajs-1816	40	26	for	for	ADP
iajs-1816	40	27	pure	pure	ADJ
iajs-1816	40	28	and	and	CCONJ
iajs-1816	40	29	applied	apply	VERB
iajs-1816	40	30	science	science	NOUN
iajs-1816	40	31	https://doi.org/	https://doi.org/	NOUN
iajs-1816	40	32	10.30526/2017.ihsciconf.1816	10.30526/2017.ihsciconf.1816	NUM
iajs-1816	40	33	for	for	ADP
iajs-1816	40	34	more	more	ADJ
iajs-1816	40	35	information	information	NOUN
iajs-1816	40	36	about	about	ADP
iajs-1816	40	37	the	the	DET
iajs-1816	40	38	conference	conference	NOUN
iajs-1816	40	39	please	please	INTJ
iajs-1816	40	40	visit	visit	VERB
iajs-1816	40	41	the	the	DET
iajs-1816	40	42	websites	website	NOUN
iajs-1816	40	43	:	:	PUNCT
iajs-1816	40	44	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1816	40	45	   	   	SPACE
iajs-1816	40	46	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1816	40	47	   	   	SPACE
iajs-1816	40	48	mathematics|429	mathematics|429	ADJ
iajs-1816	40	49	    	    	SPACE
iajs-1816	40	50	t(1)(s	t(1)(s	NOUN
iajs-1816	40	51	)	)	PUNCT
iajs-1816	40	52	=	=	SYM
iajs-1816	40	53	1	1	NUM
iajs-1816	40	54	,	,	PUNCT
iajs-1816	40	55	s	s	NOUN
iajs-1816	40	56	0	0	NUM
iajs-1816	40	57	3α	3α	NOUN
iajs-1816	40	58	,	,	PUNCT
iajs-1816	40	59	s	s	NOUN
iajs-1816	40	60	∈	∈	PROPN
iajs-1816	40	61	0	0	NUM
iajs-1816	40	62	,	,	PUNCT
iajs-1816	40	63	,	,	PUNCT
iajs-1816	40	64	s	s	PROPN
iajs-1816	40	65	∈	∈	PROPN
iajs-1816	40	66	,	,	PUNCT
iajs-1816	40	67	1	1	NUM
iajs-1816	40	68	for	for	ADP
iajs-1816	40	69	all	all	DET
iajs-1816	40	70	z	z	NOUN
iajs-1816	40	71	∈	∈	PROPN
iajs-1816	40	72	0	0	NUM
iajs-1816	40	73	,	,	PUNCT
iajs-1816	40	74	1	1	NUM
iajs-1816	40	75	t(z)(s	t(z)(s	NUM
iajs-1816	40	76	)	)	PUNCT
iajs-1816	40	77	=	=	SYM
iajs-1816	41	1	1	1	NUM
iajs-1816	41	2	,	,	PUNCT
iajs-1816	41	3	s	s	PART
iajs-1816	41	4	0	0	NUM
iajs-1816	41	5	α	α	NOUN
iajs-1816	41	6	,	,	PUNCT
iajs-1816	41	7	s	s	PART
iajs-1816	41	8	∈	∈	NOUN
iajs-1816	41	9	0	0	NUM
iajs-1816	41	10	,	,	PUNCT
iajs-1816	41	11	0	0	NUM
iajs-1816	41	12	,	,	PUNCT
iajs-1816	41	13	s	s	NOUN
iajs-1816	41	14	∈	∈	NOUN
iajs-1816	41	15	,	,	PUNCT
iajs-1816	41	16	1	1	NUM
iajs-1816	41	17	when	when	SCONJ
iajs-1816	41	18	0	0	NUM
iajs-1816	41	19	α	α	NOUN
iajs-1816	41	20	,	,	PUNCT
iajs-1816	41	21	then	then	ADV
iajs-1816	41	22	m	m	VERB
iajs-1816	41	23	0	0	NUM
iajs-1816	42	1	=	=	SYM
iajs-1816	42	2	m	m	VERB
iajs-1816	42	3	z	z	NOUN
iajs-1816	42	4	m	m	VERB
iajs-1816	42	5	1	1	NUM
iajs-1816	42	6	=	=	NOUN
iajs-1816	42	7	{	{	PUNCT
iajs-1816	42	8	0	0	NUM
iajs-1816	42	9	}	}	PUNCT
iajs-1816	42	10	m	m	VERB
iajs-1816	42	11	0	0	NUM
iajs-1816	42	12	m	m	VERB
iajs-1816	42	13	z	z	NOUN
iajs-1816	42	14	m	m	VERB
iajs-1816	42	15	1	1	NUM
iajs-1816	42	16	0	0	NUM
iajs-1816	42	17	,	,	PUNCT
iajs-1816	42	18	,	,	PUNCT
iajs-1816	42	19	m	m	VERB
iajs-1816	42	20	0	0	NUM
iajs-1816	42	21	m	m	VERB
iajs-1816	42	22	1	1	NUM
iajs-1816	42	23	0	0	NUM
iajs-1816	42	24	,	,	PUNCT
iajs-1816	42	25	1	1	NUM
iajs-1816	42	26	,	,	PUNCT
iajs-1816	42	27	m	m	VERB
iajs-1816	42	28	z	z	NOUN
iajs-1816	42	29	0	0	NUM
iajs-1816	42	30	,	,	PUNCT
iajs-1816	42	31	and	and	CCONJ
iajs-1816	42	32	n	n	PRON
iajs-1816	42	33	0	0	NUM
iajs-1816	42	34	=	=	SYM
iajs-1816	42	35	n	n	PART
iajs-1816	42	36	z	z	NOUN
iajs-1816	42	37	n	n	NOUN
iajs-1816	42	38	1	1	NUM
iajs-1816	42	39	=	=	NOUN
iajs-1816	42	40	{	{	PUNCT
iajs-1816	42	41	0	0	NUM
iajs-1816	42	42	}	}	PUNCT
iajs-1816	42	43	n	n	NOUN
iajs-1816	42	44	0	0	NUM
iajs-1816	42	45	n	n	CCONJ
iajs-1816	42	46	z	z	NOUN
iajs-1816	42	47	n	n	NOUN
iajs-1816	42	48	1	1	NUM
iajs-1816	42	49	0	0	NUM
iajs-1816	42	50	,	,	PUNCT
iajs-1816	42	51	,	,	PUNCT
iajs-1816	42	52	n	n	PROPN
iajs-1816	42	53	0	0	NUM
iajs-1816	42	54	n	n	CCONJ
iajs-1816	42	55	1	1	NUM
iajs-1816	42	56	0	0	NUM
iajs-1816	42	57	,	,	PUNCT
iajs-1816	42	58	1	1	NUM
iajs-1816	42	59	,	,	PUNCT
iajs-1816	42	60	n	n	NOUN
iajs-1816	42	61	z	z	NOUN
iajs-1816	42	62	0	0	NUM
iajs-1816	42	63	,	,	PUNCT
iajs-1816	42	64	.	.	PUNCT
iajs-1816	43	1	consequently	consequently	ADV
iajs-1816	43	2	d	d	X
iajs-1816	43	3	n	n	PRON
iajs-1816	43	4	u	u	NOUN
iajs-1816	43	5	,	,	PUNCT
iajs-1816	43	6	m	m	VERB
iajs-1816	43	7	v	v	NOUN
iajs-1816	43	8	h	h	NOUN
iajs-1816	43	9	n	n	ADP
iajs-1816	43	10	u	u	NOUN
iajs-1816	43	11	,	,	PUNCT
iajs-1816	43	12	m	m	VERB
iajs-1816	43	13	v	v	ADP
iajs-1816	43	14	0	0	NUM
iajs-1816	43	15	,	,	PUNCT
iajs-1816	43	16	∀	∀	X
iajs-1816	43	17	u	u	NOUN
iajs-1816	43	18	,	,	PUNCT
iajs-1816	43	19	v	v	PROPN
iajs-1816	43	20	∈	∈	PROPN
iajs-1816	43	21	h	h	NOUN
iajs-1816	43	22	,	,	PUNCT
iajs-1816	43	23	d	d	PROPN
iajs-1816	43	24	n	n	PRON
iajs-1816	43	25	u	u	NOUN
iajs-1816	43	26	,	,	PUNCT
iajs-1816	43	27	m	m	VERB
iajs-1816	43	28	v	v	NOUN
iajs-1816	43	29	h	h	NOUN
iajs-1816	43	30	n	n	ADP
iajs-1816	43	31	u	u	NOUN
iajs-1816	43	32	,	,	PUNCT
iajs-1816	43	33	m	m	VERB
iajs-1816	43	34	v	v	ADP
iajs-1816	43	35	0	0	NUM
iajs-1816	43	36	,	,	PUNCT
iajs-1816	43	37	∀	∀	X
iajs-1816	43	38	u	u	NOUN
iajs-1816	43	39	,	,	PUNCT
iajs-1816	43	40	v	v	PROPN
iajs-1816	43	41	∈	∈	PROPN
iajs-1816	43	42	h	h	NOUN
iajs-1816	43	43	,	,	PUNCT
iajs-1816	43	44	d	d	PROPN
iajs-1816	43	45	n	n	PRON
iajs-1816	43	46	u	u	NOUN
iajs-1816	43	47	,	,	PUNCT
iajs-1816	43	48	m	m	VERB
iajs-1816	43	49	v	v	NOUN
iajs-1816	43	50	h	h	NOUN
iajs-1816	43	51	n	n	ADP
iajs-1816	43	52	u	u	NOUN
iajs-1816	43	53	,	,	PUNCT
iajs-1816	43	54	m	m	VERB
iajs-1816	43	55	v	v	ADP
iajs-1816	43	56	0	0	NUM
iajs-1816	43	57	,	,	PUNCT
iajs-1816	43	58	∀	∀	X
iajs-1816	43	59	u	u	NOUN
iajs-1816	43	60	,	,	PUNCT
iajs-1816	43	61	v	v	NOUN
iajs-1816	43	62	∈	∈	NOUN
iajs-1816	43	63	0,1	0,1	NUM
iajs-1816	43	64	and	and	CCONJ
iajs-1816	43	65	u	u	NOUN
iajs-1816	43	66	,	,	PUNCT
iajs-1816	43	67	v	v	PROPN
iajs-1816	43	68	∈	∈	NOUN
iajs-1816	43	69	0,1	0,1	NUM
iajs-1816	43	70	,	,	PUNCT
iajs-1816	43	71	d	d	PROPN
iajs-1816	43	72	n	n	PRON
iajs-1816	43	73	u	u	NOUN
iajs-1816	43	74	,	,	PUNCT
iajs-1816	43	75	m	m	VERB
iajs-1816	43	76	v	v	NOUN
iajs-1816	43	77	h	h	NOUN
iajs-1816	43	78	n	n	ADP
iajs-1816	43	79	u	u	NOUN
iajs-1816	43	80	,	,	PUNCT
iajs-1816	43	81	m	m	VERB
iajs-1816	43	82	v	v	NOUN
iajs-1816	43	83	,	,	PUNCT
iajs-1816	43	84	∀	∀	NOUN
iajs-1816	43	85	v	v	ADP
iajs-1816	43	86	∈	∈	NOUN
iajs-1816	43	87	0,1	0,1	NUM
iajs-1816	43	88	and	and	CCONJ
iajs-1816	43	89	u	u	NOUN
iajs-1816	43	90	∈	∈	NOUN
iajs-1816	43	91	0,1	0,1	NUM
iajs-1816	43	92	.	.	PUNCT
iajs-1816	44	1	now	now	ADV
iajs-1816	44	2	,	,	PUNCT
iajs-1816	44	3	d	d	PROPN
iajs-1816	44	4	n	n	PRON
iajs-1816	44	5	u	u	NOUN
iajs-1816	44	6	,	,	PUNCT
iajs-1816	44	7	m	m	VERB
iajs-1816	44	8	v	v	NOUN
iajs-1816	44	9	=	=	SYM
iajs-1816	44	10	sup	sup	NOUN
iajs-1816	44	11	{	{	PUNCT
iajs-1816	44	12	d	d	NOUN
iajs-1816	44	13	n	n	NUM
iajs-1816	44	14	u	u	NOUN
iajs-1816	44	15	,	,	PUNCT
iajs-1816	44	16	m	m	VERB
iajs-1816	44	17	v	v	NOUN
iajs-1816	44	18	=	=	SYM
iajs-1816	44	19	d	d	PROPN
iajs-1816	44	20	n	n	CCONJ
iajs-1816	44	21	u	u	NOUN
iajs-1816	44	22	,	,	PUNCT
iajs-1816	44	23	m	m	VERB
iajs-1816	44	24	v	v	NOUN
iajs-1816	44	25	r‖u	r‖u	NOUN
iajs-1816	44	26	v‖	v‖	NOUN
iajs-1816	44	27	.	.	PUNCT
iajs-1816	45	1	then	then	ADV
iajs-1816	45	2	n	n	PROPN
iajs-1816	45	3	and	and	CCONJ
iajs-1816	45	4	m	m	PROPN
iajs-1816	45	5	is	be	AUX
iajs-1816	45	6	fuzzy	fuzzy	ADJ
iajs-1816	45	7	r∗	r∗	ADJ
iajs-1816	45	8	weakly	weakly	ADJ
iajs-1816	45	9	commuting	commuting	NOUN
iajs-1816	45	10	.	.	PUNCT
iajs-1816	46	1	we	we	PRON
iajs-1816	46	2	prove	prove	VERB
iajs-1816	46	3	the	the	DET
iajs-1816	46	4	following	follow	VERB
iajs-1816	46	5	theorem	theorem	NOUN
iajs-1816	46	6	:	:	PUNCT
iajs-1816	46	7	theorem	theorem	NOUN
iajs-1816	46	8	let	let	VERB
iajs-1816	46	9	h	h	PRON
iajs-1816	46	10	be	be	AUX
iajs-1816	46	11	a	a	DET
iajs-1816	46	12	hilbert	hilbert	NOUN
iajs-1816	46	13	space	space	NOUN
iajs-1816	46	14	and	and	CCONJ
iajs-1816	46	15	m	m	PROPN
iajs-1816	46	16	,	,	PUNCT
iajs-1816	46	17	n	n	PRON
iajs-1816	46	18	be	be	VERB
iajs-1816	46	19	a	a	DET
iajs-1816	46	20	fuzzy	fuzzy	ADJ
iajs-1816	46	21	jungck	jungck	NOUN
iajs-1816	46	22	contractive	contractive	ADJ
iajs-1816	46	23	mappings	mapping	NOUN
iajs-1816	46	24	satisfy	satisfy	VERB
iajs-1816	46	25	the	the	DET
iajs-1816	46	26	following	follow	VERB
iajs-1816	46	27	conditions	condition	NOUN
iajs-1816	46	28	:	:	PUNCT
iajs-1816	46	29	1	1	X
iajs-1816	46	30	.	.	X
iajs-1816	46	31	n	n	PRON
iajs-1816	46	32	is	be	AUX
iajs-1816	46	33	continuous	continuous	ADJ
iajs-1816	46	34	fuzzy	fuzzy	ADJ
iajs-1816	46	35	mapping	mapping	NOUN
iajs-1816	46	36	.	.	PUNCT
iajs-1816	47	1	2	2	X
iajs-1816	47	2	.	.	X
iajs-1816	47	3	m(h)⊂	m(h)⊂	NOUN
iajs-1816	47	4	n	n	NUM
iajs-1816	47	5	h	h	NOUN
iajs-1816	47	6	.	.	PUNCT
iajs-1816	48	1	3	3	X
iajs-1816	48	2	.	.	X
iajs-1816	48	3	{	{	PUNCT
iajs-1816	48	4	n	n	X
iajs-1816	48	5	,	,	PUNCT
iajs-1816	48	6	m	m	AUX
iajs-1816	48	7	}	}	PUNCT
iajs-1816	48	8	are	be	AUX
iajs-1816	48	9	fuzzy	fuzzy	ADJ
iajs-1816	48	10	r∗	r∗	ADJ
iajs-1816	48	11	weakly	weakly	ADJ
iajs-1816	48	12	commuting	commuting	NOUN
iajs-1816	48	13	.	.	PUNCT
iajs-1816	49	1	then	then	ADV
iajs-1816	49	2	,	,	PUNCT
iajs-1816	49	3	there	there	PRON
iajs-1816	49	4	exists	exist	VERB
iajs-1816	49	5	u	u	PROPN
iajs-1816	49	6	∈	∈	PROPN
iajs-1816	49	7	h	h	NOUN
iajs-1816	49	8	such	such	ADJ
iajs-1816	49	9	that	that	SCONJ
iajs-1816	49	10	u	u	PROPN
iajs-1816	49	11	is	be	AUX
iajs-1816	49	12	a	a	DET
iajs-1816	49	13	common	common	ADJ
iajs-1816	49	14	fuzzy	fuzzy	ADJ
iajs-1816	49	15	fixed	fix	VERB
iajs-1816	49	16	point	point	NOUN
iajs-1816	49	17	of	of	ADP
iajs-1816	49	18	m	m	PROPN
iajs-1816	49	19	and	and	CCONJ
iajs-1816	49	20	n	n	PROPN
iajs-1816	49	21	.	.	PUNCT
iajs-1816	50	1	proof	proof	NOUN
iajs-1816	50	2	let	let	VERB
iajs-1816	50	3	u	u	PRON
iajs-1816	50	4	∈	∈	PROPN
iajs-1816	50	5	h	h	NOUN
iajs-1816	50	6	,	,	PUNCT
iajs-1816	50	7	there	there	PRON
iajs-1816	50	8	exists	exist	VERB
iajs-1816	50	9	u	u	PROPN
iajs-1816	50	10	∈	∈	PROPN
iajs-1816	50	11	nu	nu	PROPN
iajs-1816	50	12	⊂	⊂	PROPN
iajs-1816	50	13	mu	mu	PROPN
iajs-1816	50	14	.	.	PUNCT
iajs-1816	51	1	in	in	ADP
iajs-1816	51	2	general	general	ADJ
iajs-1816	51	3	,	,	PUNCT
iajs-1816	51	4	choose	choose	VERB
iajs-1816	51	5	u	u	PRON
iajs-1816	51	6	such	such	ADJ
iajs-1816	51	7	that	that	PRON
iajs-1816	51	8	for	for	ADP
iajs-1816	51	9	n	n	DET
iajs-1816	51	10	1	1	NUM
iajs-1816	51	11	,	,	PUNCT
iajs-1816	51	12	3,5	3,5	NUM
iajs-1816	51	13	,	,	PUNCT
iajs-1816	51	14	…	…	PUNCT
iajs-1816	51	15	…	…	PUNCT
iajs-1816	51	16	.	.	PUNCT
iajs-1816	52	1	u	u	PROPN
iajs-1816	52	2	∈	∈	PROPN
iajs-1816	52	3	n	n	CCONJ
iajs-1816	52	4	u	u	NOUN
iajs-1816	52	5	⊂	⊂	PROPN
iajs-1816	52	6	mu	mu	PROPN
iajs-1816	52	7	and	and	CCONJ
iajs-1816	52	8	‖	‖	PROPN
iajs-1816	52	9	u	u	PROPN
iajs-1816	52	10	u	u	PROPN
iajs-1816	52	11	‖	‖	PROPN
iajs-1816	52	12	=	=	PROPN
iajs-1816	52	13	δ	δ	ADJ
iajs-1816	52	14	u	u	NOUN
iajs-1816	52	15	,	,	PUNCT
iajs-1816	52	16	m	m	VERB
iajs-1816	52	17	u	u	NOUN
iajs-1816	52	18	d	d	X
iajs-1816	52	19	m	m	VERB
iajs-1816	52	20	u	u	NOUN
iajs-1816	52	21	,	,	PUNCT
iajs-1816	52	22	m	m	VERB
iajs-1816	52	23	u	u	NOUN
iajs-1816	52	24	so	so	ADV
iajs-1816	52	25	‖	‖	PROPN
iajs-1816	52	26	u	u	PROPN
iajs-1816	52	27	u	u	NOUN
iajs-1816	52	28	‖	‖	PROPN
iajs-1816	52	29	d	d	PROPN
iajs-1816	52	30	m	m	VERB
iajs-1816	52	31	u	u	NOUN
iajs-1816	52	32	,	,	PUNCT
iajs-1816	52	33	m	m	VERB
iajs-1816	52	34	u	u	NOUN
iajs-1816	52	35	since	since	SCONJ
iajs-1816	52	36	m	m	PROPN
iajs-1816	52	37	,	,	PUNCT
iajs-1816	52	38	n	n	PRON
iajs-1816	52	39	are	be	AUX
iajs-1816	52	40	a	a	DET
iajs-1816	52	41	fuzzy	fuzzy	ADJ
iajs-1816	52	42	jungck	jungck	NOUN
iajs-1816	52	43	contractive	contractive	ADJ
iajs-1816	52	44	mappings	mapping	NOUN
iajs-1816	52	45	,	,	PUNCT
iajs-1816	52	46	then	then	ADV
iajs-1816	52	47	‖	‖	PROPN
iajs-1816	52	48	u	u	PROPN
iajs-1816	52	49	u	u	NOUN
iajs-1816	52	50	‖	‖	PROPN
iajs-1816	52	51	d	d	PROPN
iajs-1816	52	52	m	m	VERB
iajs-1816	52	53	u	u	NOUN
iajs-1816	52	54	,	,	PUNCT
iajs-1816	52	55	m	m	VERB
iajs-1816	52	56	u	u	NOUN
iajs-1816	52	57	ξ	ξ	PROPN
iajs-1816	52	58	d	d	PROPN
iajs-1816	52	59	n	n	NUM
iajs-1816	52	60	u	u	NOUN
iajs-1816	52	61	,	,	PUNCT
iajs-1816	52	62	n	n	CCONJ
iajs-1816	52	63	u	u	NOUN
iajs-1816	52	64	ihsciconf	ihsciconf	NOUN
iajs-1816	52	65	2017	2017	NUM
iajs-1816	52	66	special	special	ADJ
iajs-1816	52	67	issue	issue	NOUN
iajs-1816	52	68	ibn	ibn	PROPN
iajs-1816	52	69	al	al	PROPN
iajs-1816	52	70	-	-	PUNCT
iajs-1816	52	71	haitham	haitham	PROPN
iajs-1816	52	72	journal	journal	PROPN
iajs-1816	52	73	for	for	ADP
iajs-1816	52	74	pure	pure	ADJ
iajs-1816	52	75	and	and	CCONJ
iajs-1816	52	76	applied	apply	VERB
iajs-1816	52	77	science	science	NOUN
iajs-1816	52	78	https://doi.org/	https://doi.org/	NOUN
iajs-1816	52	79	10.30526/2017.ihsciconf.1816	10.30526/2017.ihsciconf.1816	NUM
iajs-1816	52	80	for	for	ADP
iajs-1816	52	81	more	more	ADJ
iajs-1816	52	82	information	information	NOUN
iajs-1816	52	83	about	about	ADP
iajs-1816	52	84	the	the	DET
iajs-1816	52	85	conference	conference	NOUN
iajs-1816	52	86	please	please	INTJ
iajs-1816	52	87	visit	visit	VERB
iajs-1816	52	88	the	the	DET
iajs-1816	52	89	websites	website	NOUN
iajs-1816	52	90	:	:	PUNCT
iajs-1816	52	91	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1816	52	92	   	   	SPACE
iajs-1816	52	93	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1816	52	94	   	   	SPACE
iajs-1816	52	95	mathematics|430	mathematics|430	NOUN
iajs-1816	52	96	    	    	SPACE
iajs-1816	52	97	sine	sine	NOUN
iajs-1816	52	98	u	u	PROPN
iajs-1816	52	99	∈	∈	PROPN
iajs-1816	52	100	n	n	CCONJ
iajs-1816	52	101	u	u	NOUN
iajs-1816	52	102	and	and	CCONJ
iajs-1816	52	103	u	u	PROPN
iajs-1816	52	104	∈	∈	PROPN
iajs-1816	52	105	n	n	PRON
iajs-1816	52	106	u	u	NOUN
iajs-1816	52	107	.	.	PUNCT
iajs-1816	53	1	then	then	ADV
iajs-1816	53	2	,	,	PUNCT
iajs-1816	53	3	‖	‖	PROPN
iajs-1816	53	4	u	u	PROPN
iajs-1816	53	5	u	u	PROPN
iajs-1816	53	6	‖	‖	PROPN
iajs-1816	53	7	ξ	ξ	PROPN
iajs-1816	53	8	d	d	PROPN
iajs-1816	53	9	n	n	NUM
iajs-1816	53	10	u	u	NOUN
iajs-1816	53	11	,	,	PUNCT
iajs-1816	53	12	n	n	CCONJ
iajs-1816	53	13	u	u	NOUN
iajs-1816	53	14	=	=	NOUN
iajs-1816	53	15	ξ‖	ξ‖	ADJ
iajs-1816	53	16	u	u	X
iajs-1816	53	17	u	u	NOUN
iajs-1816	53	18	‖	‖	VERB
iajs-1816	53	19	whenever	whenever	SCONJ
iajs-1816	53	20	ξ	ξ	X
iajs-1816	53	21	∈	∈	PROPN
iajs-1816	53	22	(	(	PUNCT
iajs-1816	53	23	0	0	NUM
iajs-1816	53	24	,	,	PUNCT
iajs-1816	53	25	1	1	NUM
iajs-1816	53	26	)	)	PUNCT
iajs-1816	53	27	‖	‖	PROPN
iajs-1816	53	28	u	u	PROPN
iajs-1816	53	29	u	u	NOUN
iajs-1816	53	30	‖	‖	PROPN
iajs-1816	53	31	∑	∑	PROPN
iajs-1816	53	32	u	u	PROPN
iajs-1816	53	33	u	u	NOUN
iajs-1816	53	34	∑	∑	PROPN
iajs-1816	53	35	ξ	ξ	PROPN
iajs-1816	53	36	‖u	‖u	PROPN
iajs-1816	53	37	u	u	NOUN
iajs-1816	53	38	‖	‖	PROPN
iajs-1816	53	39	)	)	PUNCT
iajs-1816	53	40	‖u	‖u	NOUN
iajs-1816	54	1	u	u	X
iajs-1816	54	2	‖	‖	PROPN
iajs-1816	54	3	if	if	SCONJ
iajs-1816	54	4	n	n	PROPN
iajs-1816	54	5	→	→	SYM
iajs-1816	54	6	∞	∞	PROPN
iajs-1816	54	7	,	,	PUNCT
iajs-1816	54	8	then	then	ADV
iajs-1816	54	9	ξ	ξ	X
iajs-1816	54	10	converge	converge	NOUN
iajs-1816	54	11	to	to	ADP
iajs-1816	54	12	0	0	NUM
iajs-1816	54	13	.	.	PUNCT
iajs-1816	55	1	therefore	therefore	ADV
iajs-1816	55	2	the	the	DET
iajs-1816	55	3	sequence	sequence	NOUN
iajs-1816	55	4	{	{	PUNCT
iajs-1816	55	5	u	u	NOUN
iajs-1816	55	6	is	be	AUX
iajs-1816	55	7	a	a	DET
iajs-1816	55	8	cauchy	cauchy	ADJ
iajs-1816	55	9	sequence	sequence	NOUN
iajs-1816	55	10	in	in	ADP
iajs-1816	55	11	h	h	NOUN
iajs-1816	55	12	.	.	PUNCT
iajs-1816	56	1	so	so	ADV
iajs-1816	56	2	by	by	ADP
iajs-1816	56	3	completeness	completeness	NOUN
iajs-1816	56	4	of	of	ADP
iajs-1816	56	5	h	h	NOUN
iajs-1816	56	6	,	,	PUNCT
iajs-1816	56	7	{	{	PUNCT
iajs-1816	56	8	u	u	NOUN
iajs-1816	56	9	converge	converge	VERB
iajs-1816	56	10	to	to	ADP
iajs-1816	56	11	u	u	PROPN
iajs-1816	56	12	∈	∈	PROPN
iajs-1816	56	13	h	h	NOUN
iajs-1816	56	14	.	.	PUNCT
iajs-1816	57	1	now	now	ADV
iajs-1816	57	2	,	,	PUNCT
iajs-1816	57	3	since	since	SCONJ
iajs-1816	57	4	n	n	PRON
iajs-1816	57	5	is	be	AUX
iajs-1816	57	6	continuous	continuous	ADJ
iajs-1816	57	7	fuzzy	fuzzy	ADJ
iajs-1816	57	8	mapping	mapping	NOUN
iajs-1816	57	9	,	,	PUNCT
iajs-1816	57	10	then	then	ADV
iajs-1816	57	11	n	n	CCONJ
iajs-1816	57	12	u	u	NOUN
iajs-1816	57	13	also	also	ADV
iajs-1816	57	14	converges	converge	VERB
iajs-1816	57	15	on	on	ADP
iajs-1816	57	16	h.	h.	PROPN
iajs-1816	57	17	finally	finally	ADV
iajs-1816	57	18	,	,	PUNCT
iajs-1816	57	19	we	we	PRON
iajs-1816	57	20	show	show	VERB
iajs-1816	57	21	that	that	SCONJ
iajs-1816	57	22	δ	δ	PROPN
iajs-1816	57	23	u	u	PROPN
iajs-1816	57	24	,	,	PUNCT
iajs-1816	57	25	mu	mu	PROPN
iajs-1816	57	26	=	=	SYM
iajs-1816	57	27	0	0	NUM
iajs-1816	57	28	δ	δ	PROPN
iajs-1816	57	29	u	u	PROPN
iajs-1816	57	30	,	,	PUNCT
iajs-1816	57	31	m	m	VERB
iajs-1816	57	32	u	u	NOUN
iajs-1816	57	33	‖u	‖u	NOUN
iajs-1816	57	34	u‖	u‖	ADJ
iajs-1816	57	35	+	+	CCONJ
iajs-1816	57	36	d	d	PROPN
iajs-1816	57	37	n	n	PRON
iajs-1816	57	38	u	u	NOUN
iajs-1816	57	39	,	,	PUNCT
iajs-1816	57	40	mu	mu	PROPN
iajs-1816	57	41	since	since	ADV
iajs-1816	57	42	,	,	PUNCT
iajs-1816	57	43	{	{	PUNCT
iajs-1816	57	44	n	n	CCONJ
iajs-1816	57	45	,	,	PUNCT
iajs-1816	57	46	m	m	AUX
iajs-1816	57	47	}	}	PUNCT
iajs-1816	57	48	are	be	AUX
iajs-1816	57	49	fuzzy	fuzzy	ADJ
iajs-1816	57	50	r∗	r∗	ADJ
iajs-1816	57	51	weakly	weakly	ADJ
iajs-1816	57	52	commuting	commuting	NOUN
iajs-1816	57	53	.then	.then	PUNCT
iajs-1816	58	1	δ	δ	PROPN
iajs-1816	58	2	u	u	PROPN
iajs-1816	58	3	,	,	PUNCT
iajs-1816	58	4	n	n	CCONJ
iajs-1816	58	5	u	u	NOUN
iajs-1816	58	6	‖u	‖u	NOUN
iajs-1816	58	7	u‖	u‖	NOUN
iajs-1816	59	1	+	+	NOUN
iajs-1816	59	2	r‖	r‖	VERB
iajs-1816	59	3	u	u	PRON
iajs-1816	59	4	u‖	u‖	VERB
iajs-1816	59	5	.	.	PUNCT
iajs-1816	60	1	hence	hence	ADV
iajs-1816	60	2	,	,	PUNCT
iajs-1816	60	3	δ	δ	PROPN
iajs-1816	60	4	u	u	PROPN
iajs-1816	60	5	,	,	PUNCT
iajs-1816	60	6	n	n	CCONJ
iajs-1816	60	7	u	u	NOUN
iajs-1816	60	8	0	0	NUM
iajs-1816	60	9	and	and	CCONJ
iajs-1816	60	10	u	u	PROPN
iajs-1816	60	11	⊂	⊂	PROPN
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iajs-1816	61	2	u	u	PROPN
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iajs-1816	61	7	fixed	fix	VERB
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iajs-1816	61	28	point	point	NOUN
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iajs-1816	61	33	∎	∎	PROPN
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iajs-1816	61	35	let	let	VERB
iajs-1816	61	36	h	h	PRON
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iajs-1816	61	38	a	a	DET
iajs-1816	61	39	hilbert	hilbert	NOUN
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iajs-1816	61	41	and	and	CCONJ
iajs-1816	61	42	t	t	PROPN
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iajs-1816	61	49	satisfy	satisfy	VERB
iajs-1816	61	50	the	the	DET
iajs-1816	61	51	following	follow	VERB
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iajs-1816	61	53	:	:	PUNCT
iajs-1816	62	1	1	1	X
iajs-1816	62	2	.	.	X
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iajs-1816	62	18	,	,	PUNCT
iajs-1816	62	19	β	β	X
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iajs-1816	62	21	0,1	0,1	NUM
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iajs-1816	62	24	,	,	PUNCT
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iajs-1816	63	5	m	m	VERB
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iajs-1816	63	11	d	d	X
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iajs-1816	63	16	v	v	NOUN
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iajs-1816	63	21	n	n	CCONJ
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iajs-1816	63	24	2	2	NUM
iajs-1816	63	25	.	.	PUNCT
iajs-1816	64	1	m	m	PROPN
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iajs-1816	64	6	.	.	PUNCT
iajs-1816	65	1	3	3	X
iajs-1816	65	2	.	.	X
iajs-1816	65	3	n(h	n(h	PROPN
iajs-1816	65	4	)	)	PUNCT
iajs-1816	66	1	⊂	⊂	PROPN
iajs-1816	66	2	m	m	VERB
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iajs-1816	66	4	.	.	PUNCT
iajs-1816	67	1	4	4	X
iajs-1816	67	2	.	.	X
iajs-1816	67	3	{	{	PUNCT
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iajs-1816	67	8	are	be	AUX
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iajs-1816	67	10	r∗	r∗	ADJ
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iajs-1816	67	13	.	.	PUNCT
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iajs-1816	68	2	,	,	PUNCT
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iajs-1816	68	5	u	u	PROPN
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iajs-1816	68	10	u	u	PROPN
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iajs-1816	68	20	n	n	PROPN
iajs-1816	68	21	.	.	PUNCT
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iajs-1816	69	2	let	let	VERB
iajs-1816	69	3	u	u	PRON
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iajs-1816	72	28	‖	‖	PROPN
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iajs-1816	72	43	‖	‖	PROPN
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iajs-1816	72	48	n	n	CCONJ
iajs-1816	72	49	u	u	X
iajs-1816	72	50	ψ	ψ	X
iajs-1816	72	51	β	β	X
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iajs-1816	72	54	u	u	PROPN
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iajs-1816	72	58	u	u	NOUN
iajs-1816	72	59	,	,	PUNCT
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iajs-1816	72	61	=	=	PROPN
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iajs-1816	72	63	m	m	VERB
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iajs-1816	72	65	,	,	PUNCT
iajs-1816	72	66	m	m	VERB
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iajs-1816	72	68	,	,	PUNCT
iajs-1816	72	69	,	,	PUNCT
iajs-1816	72	70	,	,	PUNCT
iajs-1816	72	71	,	,	PUNCT
iajs-1816	72	72	d	d	X
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iajs-1816	73	2	m	m	VERB
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iajs-1816	73	6	u	u	NOUN
iajs-1816	73	7	2	2	NUM
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iajs-1816	73	9	2017	2017	NUM
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iajs-1816	73	12	ibn	ibn	PROPN
iajs-1816	73	13	al	al	PROPN
iajs-1816	73	14	-	-	PUNCT
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iajs-1816	73	18	pure	pure	ADJ
iajs-1816	73	19	and	and	CCONJ
iajs-1816	73	20	applied	apply	VERB
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iajs-1816	73	22	https://doi.org/	https://doi.org/	NOUN
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iajs-1816	73	29	conference	conference	NOUN
iajs-1816	73	30	please	please	INTJ
iajs-1816	73	31	visit	visit	VERB
iajs-1816	73	32	the	the	DET
iajs-1816	73	33	websites	website	NOUN
iajs-1816	73	34	:	:	PUNCT
iajs-1816	73	35	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1816	73	36	   	   	SPACE
iajs-1816	73	37	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1816	73	38	   	   	SPACE
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iajs-1816	73	40	    	    	SPACE
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iajs-1816	73	44	u	u	NOUN
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iajs-1816	73	46	‖	‖	PROPN
iajs-1816	73	47	u	u	PROPN
iajs-1816	73	48	u	u	NOUN
iajs-1816	73	49	‖	‖	PROPN
iajs-1816	73	50	,	,	PUNCT
iajs-1816	73	51	‖	‖	PROPN
iajs-1816	73	52	‖	‖	PROPN
iajs-1816	73	53	‖	‖	PROPN
iajs-1816	73	54	‖	‖	PROPN
iajs-1816	73	55	,	,	PUNCT
iajs-1816	73	56	‖	‖	PROPN
iajs-1816	73	57	u	u	PROPN
iajs-1816	73	58	u	u	PROPN
iajs-1816	73	59	‖	‖	PROPN
iajs-1816	73	60	‖	‖	PROPN
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iajs-1816	73	62	u	u	PROPN
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iajs-1816	73	66	u	u	NOUN
iajs-1816	73	67	,	,	PUNCT
iajs-1816	73	68	u	u	NOUN
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iajs-1816	73	72	u	u	NOUN
iajs-1816	73	73	‖	‖	PROPN
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iajs-1816	73	75	‖	‖	PROPN
iajs-1816	73	76	‖	‖	PROPN
iajs-1816	73	77	,	,	PUNCT
iajs-1816	73	78	‖	‖	PROPN
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iajs-1816	73	81	‖	‖	PROPN
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iajs-1816	73	88	‖	‖	PROPN
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iajs-1816	73	95	‖	‖	PROPN
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iajs-1816	73	97	‖	‖	PROPN
iajs-1816	73	98	‖	‖	PROPN
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iajs-1816	73	100	‖	‖	PROPN
iajs-1816	73	101	‖	‖	PROPN
iajs-1816	73	102	‖	‖	PROPN
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iajs-1816	73	105	‖	‖	PROPN
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iajs-1816	73	110	‖	‖	PROPN
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iajs-1816	74	6	‖	‖	PROPN
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iajs-1816	74	9	u	u	X
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iajs-1816	74	11	‖	‖	PROPN
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iajs-1816	74	20	u	u	X
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iajs-1816	74	22	‖	‖	PROPN
iajs-1816	74	23	ψ	ψ	PROPN
iajs-1816	74	24	‖	‖	PROPN
iajs-1816	74	25	u	u	X
iajs-1816	74	26	u	u	NOUN
iajs-1816	74	27	‖	‖	PROPN
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iajs-1816	74	30	.	.	PUNCT
iajs-1816	75	1	‖	‖	PROPN
iajs-1816	75	2	u	u	X
iajs-1816	75	3	u	u	PROPN
iajs-1816	75	4	‖	‖	PROPN
iajs-1816	75	5	ψ	ψ	PROPN
iajs-1816	75	6	‖	‖	PROPN
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iajs-1816	75	8	u	u	PROPN
iajs-1816	75	9	‖	‖	PROPN
iajs-1816	75	10	‖	‖	PROPN
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iajs-1816	75	13	‖	‖	PROPN
iajs-1816	75	14	ψ	ψ	PROPN
iajs-1816	75	15	‖	‖	PROPN
iajs-1816	75	16	u	u	X
iajs-1816	75	17	u	u	NOUN
iajs-1816	75	18	‖	‖	PROPN
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iajs-1816	75	20	…	…	PUNCT
iajs-1816	75	21	…	…	PUNCT
iajs-1816	75	22	…	…	PUNCT
iajs-1816	75	23	ψ	ψ	X
iajs-1816	75	24	‖	‖	VERB
iajs-1816	75	25	u	u	PROPN
iajs-1816	75	26	u	u	PROPN
iajs-1816	75	27	‖	‖	PROPN
iajs-1816	75	28	‖	‖	PROPN
iajs-1816	75	29	u	u	PROPN
iajs-1816	75	30	u	u	NOUN
iajs-1816	75	31	‖	‖	PROPN
iajs-1816	75	32	∑	∑	PROPN
iajs-1816	75	33	ψ	ψ	ADP
iajs-1816	75	34	‖	‖	PROPN
iajs-1816	75	35	u	u	X
iajs-1816	75	36	u	u	NOUN
iajs-1816	75	37	‖	‖	PROPN
iajs-1816	75	38	.	.	PUNCT
iajs-1816	76	1	since	since	SCONJ
iajs-1816	76	2	,	,	PUNCT
iajs-1816	76	3	∑	∑	PUNCT
iajs-1816	76	4	ψ	ψ	X
iajs-1816	76	5	‖	‖	PROPN
iajs-1816	76	6	u	u	X
iajs-1816	76	7	u	u	NOUN
iajs-1816	76	8	‖	‖	PROPN
iajs-1816	76	9	∞	∞	PROPN
iajs-1816	76	10	therefore	therefore	ADV
iajs-1816	76	11	,	,	PUNCT
iajs-1816	76	12	the	the	DET
iajs-1816	76	13	sequence	sequence	NOUN
iajs-1816	76	14	{	{	PUNCT
iajs-1816	76	15	u	u	NOUN
iajs-1816	76	16	is	be	AUX
iajs-1816	76	17	a	a	DET
iajs-1816	76	18	cauchy	cauchy	ADJ
iajs-1816	76	19	sequence	sequence	NOUN
iajs-1816	76	20	in	in	ADP
iajs-1816	76	21	h.	h.	PROPN
iajs-1816	76	22	so	so	ADV
iajs-1816	76	23	by	by	ADP
iajs-1816	76	24	completeness	completeness	NOUN
iajs-1816	76	25	of	of	ADP
iajs-1816	76	26	h	h	NOUN
iajs-1816	76	27	,	,	PUNCT
iajs-1816	76	28	{	{	PUNCT
iajs-1816	76	29	u	u	NOUN
iajs-1816	76	30	converges	converge	VERB
iajs-1816	76	31	to	to	ADP
iajs-1816	76	32	x	x	PUNCT
iajs-1816	76	33	in	in	ADP
iajs-1816	76	34	h.	h.	PROPN
iajs-1816	76	35	now	now	ADV
iajs-1816	76	36	,	,	PUNCT
iajs-1816	76	37	since	since	SCONJ
iajs-1816	76	38	m	m	PROPN
iajs-1816	76	39	is	be	AUX
iajs-1816	76	40	continuous	continuous	ADJ
iajs-1816	76	41	fuzzy	fuzzy	ADJ
iajs-1816	76	42	mapping	mapping	NOUN
iajs-1816	76	43	,	,	PUNCT
iajs-1816	76	44	then	then	ADV
iajs-1816	76	45	m	m	VERB
iajs-1816	76	46	u	u	NOUN
iajs-1816	76	47	also	also	ADV
iajs-1816	76	48	converges	converge	VERB
iajs-1816	76	49	on	on	ADP
iajs-1816	76	50	h.	h.	PROPN
iajs-1816	76	51	finally	finally	ADV
iajs-1816	76	52	,	,	PUNCT
iajs-1816	76	53	we	we	PRON
iajs-1816	76	54	show	show	VERB
iajs-1816	76	55	that	that	SCONJ
iajs-1816	76	56	δ	δ	PROPN
iajs-1816	76	57	u	u	PROPN
iajs-1816	76	58	,	,	PUNCT
iajs-1816	76	59	nu	nu	PROPN
iajs-1816	76	60	=	=	SYM
iajs-1816	76	61	0	0	NUM
iajs-1816	76	62	δ	δ	PROPN
iajs-1816	76	63	u	u	PROPN
iajs-1816	76	64	,	,	PUNCT
iajs-1816	76	65	n	n	CCONJ
iajs-1816	76	66	u	u	NOUN
iajs-1816	76	67	‖u	‖u	NOUN
iajs-1816	76	68	u‖	u‖	ADJ
iajs-1816	77	1	+	+	CCONJ
iajs-1816	77	2	d	d	PROPN
iajs-1816	77	3	n	n	PRON
iajs-1816	77	4	u	u	NOUN
iajs-1816	77	5	,	,	PUNCT
iajs-1816	77	6	nu	nu	PROPN
iajs-1816	77	7	‖u	‖u	X
iajs-1816	77	8	u‖	u‖	X
iajs-1816	77	9	ψ	ψ	X
iajs-1816	77	10	β	β	X
iajs-1816	77	11	max	max	PROPN
iajs-1816	77	12	m	m	PROPN
iajs-1816	77	13	u	u	PROPN
iajs-1816	77	14	,	,	PUNCT
iajs-1816	77	15	u	u	PROPN
iajs-1816	77	16	m	m	NOUN
iajs-1816	77	17	u	u	NOUN
iajs-1816	77	18	,	,	PUNCT
iajs-1816	77	19	u	u	NOUN
iajs-1816	77	20	=	=	PROPN
iajs-1816	77	21	d	d	PROPN
iajs-1816	77	22	m	m	VERB
iajs-1816	77	23	u	u	NOUN
iajs-1816	77	24	,	,	PUNCT
iajs-1816	77	25	m	m	VERB
iajs-1816	77	26	u	u	NOUN
iajs-1816	77	27	,	,	PUNCT
iajs-1816	77	28	,	,	PUNCT
iajs-1816	77	29	,	,	PUNCT
iajs-1816	77	30	,	,	PUNCT
iajs-1816	77	31	d	d	X
iajs-1816	77	32	m	m	VERB
iajs-1816	77	33	u	u	NOUN
iajs-1816	77	34	,	,	PUNCT
iajs-1816	77	35	n	n	CCONJ
iajs-1816	77	36	u	u	NOUN
iajs-1816	78	1	d	d	NOUN
iajs-1816	78	2	m	m	VERB
iajs-1816	78	3	u	u	NOUN
iajs-1816	78	4	,	,	PUNCT
iajs-1816	78	5	n	n	CCONJ
iajs-1816	78	6	u	u	NOUN
iajs-1816	78	7	2	2	NUM
iajs-1816	78	8	since	since	ADV
iajs-1816	78	9	,	,	PUNCT
iajs-1816	78	10	{	{	PUNCT
iajs-1816	78	11	m	m	PROPN
iajs-1816	78	12	,	,	PUNCT
iajs-1816	78	13	n	n	CCONJ
iajs-1816	78	14	}	}	PUNCT
iajs-1816	78	15	are	be	AUX
iajs-1816	78	16	fuzzy	fuzzy	ADJ
iajs-1816	78	17	r∗	r∗	ADJ
iajs-1816	78	18	weakly	weakly	ADJ
iajs-1816	78	19	commuting	commuting	NOUN
iajs-1816	78	20	.then	.then	PUNCT
iajs-1816	79	1	δ	δ	PROPN
iajs-1816	79	2	u	u	PROPN
iajs-1816	79	3	,	,	PUNCT
iajs-1816	79	4	n	n	CCONJ
iajs-1816	79	5	u	u	NOUN
iajs-1816	79	6	‖u	‖u	NOUN
iajs-1816	79	7	u‖	u‖	VERB
iajs-1816	79	8	+	+	NOUN
iajs-1816	79	9	ψ	ψ	X
iajs-1816	79	10	‖	‖	ADJ
iajs-1816	79	11	u	u	NOUN
iajs-1816	79	12	u‖	u‖	NOUN
iajs-1816	79	13	.	.	PUNCT
iajs-1816	80	1	hence	hence	ADV
iajs-1816	80	2	,	,	PUNCT
iajs-1816	80	3	δ	δ	PROPN
iajs-1816	80	4	u	u	PROPN
iajs-1816	80	5	,	,	PUNCT
iajs-1816	80	6	n	n	CCONJ
iajs-1816	80	7	u	u	NOUN
iajs-1816	80	8	0	0	NUM
iajs-1816	80	9	and	and	CCONJ
iajs-1816	80	10	u	u	PROPN
iajs-1816	80	11	⊂	⊂	PROPN
iajs-1816	80	12	nu	nu	PROPN
iajs-1816	80	13	.	.	PROPN
iajs-1816	80	14	ihsciconf	ihsciconf	PROPN
iajs-1816	80	15	2017	2017	NUM
iajs-1816	80	16	special	special	ADJ
iajs-1816	80	17	issue	issue	NOUN
iajs-1816	80	18	ibn	ibn	PROPN
iajs-1816	80	19	al	al	PROPN
iajs-1816	80	20	-	-	PUNCT
iajs-1816	80	21	haitham	haitham	PROPN
iajs-1816	80	22	journal	journal	PROPN
iajs-1816	80	23	for	for	ADP
iajs-1816	80	24	pure	pure	ADJ
iajs-1816	80	25	and	and	CCONJ
iajs-1816	80	26	applied	apply	VERB
iajs-1816	80	27	science	science	NOUN
iajs-1816	80	28	https://doi.org/	https://doi.org/	NOUN
iajs-1816	80	29	10.30526/2017.ihsciconf.1816	10.30526/2017.ihsciconf.1816	NUM
iajs-1816	80	30	for	for	ADP
iajs-1816	80	31	more	more	ADJ
iajs-1816	80	32	information	information	NOUN
iajs-1816	80	33	about	about	ADP
iajs-1816	80	34	the	the	DET
iajs-1816	80	35	conference	conference	NOUN
iajs-1816	80	36	please	please	INTJ
iajs-1816	80	37	visit	visit	VERB
iajs-1816	80	38	the	the	DET
iajs-1816	80	39	websites	website	NOUN
iajs-1816	80	40	:	:	PUNCT
iajs-1816	80	41	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1816	80	42	   	   	SPACE
iajs-1816	80	43	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1816	80	44	   	   	SPACE
iajs-1816	80	45	mathematics|432	mathematics|432	NOUN
iajs-1816	80	46	    	    	SPACE
iajs-1816	80	47	clearly	clearly	ADV
iajs-1816	80	48	u	u	NOUN
iajs-1816	80	49	is	be	AUX
iajs-1816	80	50	a	a	DET
iajs-1816	80	51	common	common	ADJ
iajs-1816	80	52	fuzzy	fuzzy	ADJ
iajs-1816	80	53	fixed	fix	VERB
iajs-1816	80	54	point	point	NOUN
iajs-1816	80	55	of	of	ADP
iajs-1816	80	56	the	the	DET
iajs-1816	80	57	fuzzy	fuzzy	ADJ
iajs-1816	80	58	mappings	mapping	NOUN
iajs-1816	80	59	n	n	PRON
iajs-1816	80	60	and	and	CCONJ
iajs-1816	80	61	m	m	PROPN
iajs-1816	80	62	.in	.in	PUNCT
iajs-1816	80	63	particular	particular	ADJ
iajs-1816	80	64	if	if	SCONJ
iajs-1816	80	65	α	α	PROPN
iajs-1816	80	66	1	1	NUM
iajs-1816	80	67	,	,	PUNCT
iajs-1816	80	68	then	then	ADV
iajs-1816	80	69	u	u	NOUN
iajs-1816	80	70	is	be	AUX
iajs-1816	80	71	a	a	DET
iajs-1816	80	72	common	common	ADJ
iajs-1816	80	73	fixed	fix	VERB
iajs-1816	80	74	point	point	NOUN
iajs-1816	80	75	of	of	ADP
iajs-1816	80	76	t	t	PROPN
iajs-1816	80	77	and	and	CCONJ
iajs-1816	80	78	s.	s.	PROPN
iajs-1816	80	79	∎	∎	PROPN
iajs-1816	80	80	theorem	theorem	VERB
iajs-1816	80	81	let	let	VERB
iajs-1816	80	82	h	h	PRON
iajs-1816	80	83	be	be	AUX
iajs-1816	80	84	a	a	DET
iajs-1816	80	85	hilbert	hilbert	NOUN
iajs-1816	80	86	space	space	NOUN
iajs-1816	80	87	and	and	CCONJ
iajs-1816	80	88	n	n	NOUN
iajs-1816	80	89	,	,	PUNCT
iajs-1816	80	90	n	n	CCONJ
iajs-1816	80	91	,	,	PUNCT
iajs-1816	80	92	n	n	CCONJ
iajs-1816	80	93	be	be	AUX
iajs-1816	80	94	a	a	DET
iajs-1816	80	95	fuzzy	fuzzy	ADJ
iajs-1816	80	96	mappings	mapping	NOUN
iajs-1816	80	97	satisfies	satisfy	VERB
iajs-1816	80	98	the	the	DET
iajs-1816	80	99	following	follow	VERB
iajs-1816	80	100	conditions	condition	NOUN
iajs-1816	80	101	:	:	PUNCT
iajs-1816	80	102	1	1	X
iajs-1816	80	103	.	.	X
iajs-1816	80	104	d	d	NOUN
iajs-1816	80	105	n	n	X
iajs-1816	80	106	u	u	NOUN
iajs-1816	80	107	,	,	PUNCT
iajs-1816	80	108	n	n	PROPN
iajs-1816	80	109	v	v	X
iajs-1816	80	110	β	β	X
iajs-1816	80	111	d	d	X
iajs-1816	80	112	n	n	CCONJ
iajs-1816	80	113	u	u	NOUN
iajs-1816	80	114	,	,	PUNCT
iajs-1816	80	115	n	n	CCONJ
iajs-1816	80	116	u	u	X
iajs-1816	80	117	ξ	ξ	PROPN
iajs-1816	80	118	d	d	PROPN
iajs-1816	80	119	n	n	NUM
iajs-1816	80	120	v	v	NOUN
iajs-1816	80	121	,	,	PUNCT
iajs-1816	80	122	n	n	PROPN
iajs-1816	80	123	v	v	X
iajs-1816	80	124	λ	λ	X
iajs-1816	80	125	d	d	PROPN
iajs-1816	80	126	n	n	PROPN
iajs-1816	80	127	u	u	NOUN
iajs-1816	80	128	,	,	PUNCT
iajs-1816	80	129	n	n	PROPN
iajs-1816	80	130	v	v	ADP
iajs-1816	80	131	γ	γ	X
iajs-1816	80	132	d	d	PROPN
iajs-1816	80	133	n	n	PROPN
iajs-1816	80	134	u	u	PROPN
iajs-1816	80	135	,	,	PUNCT
iajs-1816	80	136	n	n	PROPN
iajs-1816	80	137	v	v	ADP
iajs-1816	80	138	η	η	PROPN
iajs-1816	80	139	d	d	PROPN
iajs-1816	80	140	n	n	PROPN
iajs-1816	80	141	v	v	NOUN
iajs-1816	80	142	,	,	PUNCT
iajs-1816	80	143	n	n	PRON
iajs-1816	80	144	v	v	NOUN
iajs-1816	80	145	for	for	ADP
iajs-1816	80	146	all	all	DET
iajs-1816	80	147	u	u	NOUN
iajs-1816	80	148	,	,	PUNCT
iajs-1816	80	149	v	v	NOUN
iajs-1816	80	150	∈	∈	NOUN
iajs-1816	80	151	h	h	NOUN
iajs-1816	80	152	where	where	SCONJ
iajs-1816	80	153	γ	γ	PROPN
iajs-1816	80	154	,	,	PUNCT
iajs-1816	80	155	η	η	PROPN
iajs-1816	80	156	,	,	PUNCT
iajs-1816	80	157	β	β	X
iajs-1816	80	158	,	,	PUNCT
iajs-1816	80	159	λ	λ	PROPN
iajs-1816	80	160	,	,	PUNCT
iajs-1816	80	161	ξ	ξ	PROPN
iajs-1816	80	162	0	0	NUM
iajs-1816	80	163	with	with	ADP
iajs-1816	80	164	γ	γ	PROPN
iajs-1816	80	165	η	η	PROPN
iajs-1816	80	166	β	β	X
iajs-1816	80	167	λ	λ	X
iajs-1816	80	168	ξ	ξ	PROPN
iajs-1816	80	169	1	1	NUM
iajs-1816	80	170	.	.	PUNCT
iajs-1816	81	1	2	2	X
iajs-1816	81	2	.	.	X
iajs-1816	81	3	n	n	NOUN
iajs-1816	81	4	and	and	CCONJ
iajs-1816	81	5	n	n	PROPN
iajs-1816	81	6	are	be	AUX
iajs-1816	81	7	continuous	continuous	ADJ
iajs-1816	81	8	fuzzy	fuzzy	ADJ
iajs-1816	81	9	mapping	mapping	NOUN
iajs-1816	81	10	.	.	PUNCT
iajs-1816	82	1	3	3	X
iajs-1816	82	2	.	.	X
iajs-1816	82	3	n	n	PROPN
iajs-1816	82	4	(	(	PUNCT
iajs-1816	82	5	h	h	NOUN
iajs-1816	82	6	)	)	PUNCT
iajs-1816	82	7	⊂	⊂	PROPN
iajs-1816	82	8	n	n	NUM
iajs-1816	82	9	h	h	NOUN
iajs-1816	82	10	∩	∩	NOUN
iajs-1816	82	11	n	n	NOUN
iajs-1816	82	12	h	h	NOUN
iajs-1816	82	13	.	.	PUNCT
iajs-1816	83	1	4	4	X
iajs-1816	83	2	.	.	X
iajs-1816	83	3	{	{	PUNCT
iajs-1816	83	4	n	n	NOUN
iajs-1816	83	5	,	,	PUNCT
iajs-1816	83	6	n	n	CCONJ
iajs-1816	83	7	}	}	PUNCT
iajs-1816	83	8	and	and	CCONJ
iajs-1816	83	9	{	{	PUNCT
iajs-1816	83	10	n	n	NOUN
iajs-1816	83	11	,	,	PUNCT
iajs-1816	83	12	n	n	CCONJ
iajs-1816	83	13	}	}	PUNCT
iajs-1816	83	14	are	be	AUX
iajs-1816	83	15	fuzzy	fuzzy	ADJ
iajs-1816	83	16	r∗	r∗	ADJ
iajs-1816	83	17	weakly	weakly	ADJ
iajs-1816	83	18	commuting	commuting	NOUN
iajs-1816	83	19	.	.	PUNCT
iajs-1816	84	1	then	then	ADV
iajs-1816	84	2	,	,	PUNCT
iajs-1816	84	3	there	there	PRON
iajs-1816	84	4	exists	exist	VERB
iajs-1816	84	5	u	u	PROPN
iajs-1816	84	6	∈	∈	PROPN
iajs-1816	84	7	h	h	NOUN
iajs-1816	84	8	such	such	ADJ
iajs-1816	84	9	that	that	SCONJ
iajs-1816	84	10	u	u	PROPN
iajs-1816	84	11	is	be	AUX
iajs-1816	84	12	a	a	DET
iajs-1816	84	13	common	common	ADJ
iajs-1816	84	14	fuzzy	fuzzy	ADJ
iajs-1816	84	15	fixed	fix	VERB
iajs-1816	84	16	point	point	NOUN
iajs-1816	84	17	of	of	ADP
iajs-1816	84	18	n	n	PROPN
iajs-1816	84	19	,	,	PUNCT
iajs-1816	84	20	n	n	PROPN
iajs-1816	84	21	and	and	CCONJ
iajs-1816	84	22	n	n	NOUN
iajs-1816	84	23	.	.	PUNCT
iajs-1816	85	1	proof	proof	NOUN
iajs-1816	85	2	:	:	PUNCT
iajs-1816	85	3	let	let	VERB
iajs-1816	85	4	u	u	PRON
iajs-1816	85	5	∈	∈	PROPN
iajs-1816	85	6	h	h	NOUN
iajs-1816	85	7	,	,	PUNCT
iajs-1816	85	8	there	there	PRON
iajs-1816	85	9	exists	exist	VERB
iajs-1816	85	10	u	u	NOUN
iajs-1816	85	11	and	and	CCONJ
iajs-1816	85	12	u	u	PRON
iajs-1816	85	13	such	such	ADJ
iajs-1816	85	14	that	that	SCONJ
iajs-1816	85	15	u	u	PROPN
iajs-1816	85	16	∈	∈	PROPN
iajs-1816	85	17	n	n	CCONJ
iajs-1816	85	18	u	u	X
iajs-1816	85	19	⊂	⊂	X
iajs-1816	85	20	n	n	CCONJ
iajs-1816	85	21	u	u	NOUN
iajs-1816	85	22	and	and	CCONJ
iajs-1816	85	23	u	u	PROPN
iajs-1816	85	24	∈	∈	PROPN
iajs-1816	85	25	n	n	CCONJ
iajs-1816	85	26	u	u	X
iajs-1816	85	27	⊂	⊂	X
iajs-1816	85	28	n	n	PRON
iajs-1816	85	29	u	u	NOUN
iajs-1816	85	30	.	.	PUNCT
iajs-1816	86	1	by	by	ADP
iajs-1816	86	2	induction	induction	NOUN
iajs-1816	86	3	one	one	PRON
iajs-1816	86	4	can	can	AUX
iajs-1816	86	5	construct	construct	VERB
iajs-1816	86	6	a	a	DET
iajs-1816	86	7	sequence	sequence	NOUN
iajs-1816	86	8	{	{	PUNCT
iajs-1816	86	9	u	u	NOUN
iajs-1816	86	10	in	in	ADP
iajs-1816	86	11	h	h	NOUN
iajs-1816	86	12	,	,	PUNCT
iajs-1816	86	13	such	such	ADJ
iajs-1816	86	14	that	that	PRON
iajs-1816	86	15	for	for	ADP
iajs-1816	86	16	n=	n=	ADJ
iajs-1816	86	17	1	1	NUM
iajs-1816	86	18	,	,	PUNCT
iajs-1816	86	19	3	3	NUM
iajs-1816	86	20	,	,	PUNCT
iajs-1816	86	21	5	5	NUM
iajs-1816	86	22	,	,	PUNCT
iajs-1816	86	23	…	…	PUNCT
iajs-1816	86	24	..	..	PUNCT
iajs-1816	86	25	u	u	PROPN
iajs-1816	86	26	∈	∈	PROPN
iajs-1816	86	27	n	n	CCONJ
iajs-1816	86	28	u	u	X
iajs-1816	86	29	⊂	⊂	X
iajs-1816	86	30	n	n	CCONJ
iajs-1816	86	31	u	u	NOUN
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iajs-1816	86	33	u	u	PROPN
iajs-1816	86	34	∈	∈	PROPN
iajs-1816	86	35	n	n	CCONJ
iajs-1816	86	36	u	u	X
iajs-1816	86	37	⊂	⊂	X
iajs-1816	86	38	n	n	PRON
iajs-1816	86	39	u	u	NOUN
iajs-1816	86	40	.	.	PUNCT
iajs-1816	87	1	and	and	CCONJ
iajs-1816	87	2	‖	‖	PROPN
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iajs-1816	87	5	‖	‖	PROPN
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iajs-1816	87	10	n	n	CCONJ
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iajs-1816	87	13	n	n	PROPN
iajs-1816	87	14	u	u	NOUN
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iajs-1816	87	16	n	n	CCONJ
iajs-1816	87	17	u	u	NOUN
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iajs-1816	87	19	‖	‖	PROPN
iajs-1816	87	20	u	u	PROPN
iajs-1816	87	21	u	u	NOUN
iajs-1816	87	22	‖	‖	PROPN
iajs-1816	87	23	d	d	PROPN
iajs-1816	87	24	n	n	PRON
iajs-1816	87	25	u	u	NOUN
iajs-1816	87	26	,	,	PUNCT
iajs-1816	87	27	n	n	CCONJ
iajs-1816	87	28	u	u	NOUN
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iajs-1816	87	31	1	1	NUM
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iajs-1816	87	34	‖	‖	PROPN
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iajs-1816	87	36	u	u	NOUN
iajs-1816	87	37	‖	‖	PROPN
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iajs-1816	87	42	n	n	CCONJ
iajs-1816	87	43	u	u	NOUN
iajs-1816	87	44	β	β	PROPN
iajs-1816	87	45	d	d	PROPN
iajs-1816	87	46	n	n	CCONJ
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iajs-1816	87	49	n	n	CCONJ
iajs-1816	87	50	u	u	X
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iajs-1816	87	52	d	d	PROPN
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iajs-1816	87	54	u	u	NOUN
iajs-1816	87	55	,	,	PUNCT
iajs-1816	87	56	n	n	CCONJ
iajs-1816	87	57	u	u	NOUN
iajs-1816	87	58	λ	λ	X
iajs-1816	87	59	d	d	PROPN
iajs-1816	87	60	n	n	PROPN
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iajs-1816	87	62	,	,	PUNCT
iajs-1816	87	63	n	n	CCONJ
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iajs-1816	87	65	γ	γ	X
iajs-1816	87	66	d	d	PROPN
iajs-1816	87	67	n	n	PROPN
iajs-1816	87	68	u	u	PROPN
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iajs-1816	87	70	n	n	CCONJ
iajs-1816	87	71	u	u	PROPN
iajs-1816	87	72	η	η	PROPN
iajs-1816	87	73	d	d	PROPN
iajs-1816	87	74	n	n	PROPN
iajs-1816	87	75	u	u	NOUN
iajs-1816	87	76	,	,	PUNCT
iajs-1816	87	77	n	n	CCONJ
iajs-1816	87	78	u	u	PROPN
iajs-1816	87	79	‖	‖	PROPN
iajs-1816	87	80	u	u	X
iajs-1816	87	81	u	u	NOUN
iajs-1816	87	82	‖	‖	PROPN
iajs-1816	87	83	β	β	X
iajs-1816	87	84	‖	‖	PROPN
iajs-1816	87	85	u	u	PROPN
iajs-1816	87	86	u	u	PROPN
iajs-1816	87	87	‖	‖	PROPN
iajs-1816	87	88	ξ	ξ	PROPN
iajs-1816	87	89	‖	‖	PROPN
iajs-1816	87	90	u	u	PROPN
iajs-1816	87	91	u	u	NOUN
iajs-1816	87	92	‖	‖	PROPN
iajs-1816	87	93	λ	λ	PROPN
iajs-1816	87	94	‖	‖	PROPN
iajs-1816	87	95	u	u	X
iajs-1816	87	96	u	u	NOUN
iajs-1816	87	97	‖	‖	PROPN
iajs-1816	87	98	γ	γ	X
iajs-1816	87	99	‖	‖	PROPN
iajs-1816	87	100	u	u	PROPN
iajs-1816	87	101	u	u	PROPN
iajs-1816	87	102	‖	‖	PROPN
iajs-1816	87	103	η	η	PROPN
iajs-1816	87	104	‖	‖	PROPN
iajs-1816	87	105	u	u	PROPN
iajs-1816	87	106	u	u	NOUN
iajs-1816	87	107	‖	‖	ADJ
iajs-1816	87	108	hence	hence	ADV
iajs-1816	87	109	‖	‖	PROPN
iajs-1816	87	110	u	u	X
iajs-1816	87	111	u	u	NOUN
iajs-1816	87	112	‖	‖	PROPN
iajs-1816	87	113	ξ	ξ	PROPN
iajs-1816	87	114	‖	‖	PROPN
iajs-1816	87	115	u	u	PROPN
iajs-1816	87	116	u	u	PROPN
iajs-1816	87	117	‖	‖	PROPN
iajs-1816	87	118	η	η	PROPN
iajs-1816	87	119	‖	‖	PROPN
iajs-1816	87	120	u	u	PROPN
iajs-1816	87	121	u	u	NOUN
iajs-1816	87	122	‖	‖	PROPN
iajs-1816	87	123	β	β	X
iajs-1816	87	124	‖	‖	PROPN
iajs-1816	87	125	u	u	PROPN
iajs-1816	87	126	u	u	PROPN
iajs-1816	87	127	‖	‖	PROPN
iajs-1816	87	128	‖	‖	PROPN
iajs-1816	87	129	u	u	PROPN
iajs-1816	87	130	u	u	PROPN
iajs-1816	87	131	‖	‖	PROPN
iajs-1816	87	132	‖	‖	PROPN
iajs-1816	87	133	u	u	PROPN
iajs-1816	87	134	u	u	PROPN
iajs-1816	87	135	‖	‖	PROPN
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iajs-1816	88	1	putting	put	VERB
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iajs-1816	88	4	1	1	NUM
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iajs-1816	88	6	,	,	PUNCT
iajs-1816	88	7	we	we	PRON
iajs-1816	88	8	have	have	VERB
iajs-1816	88	9	‖u	‖u	NOUN
iajs-1816	88	10	u	u	PROPN
iajs-1816	88	11	‖	‖	ADJ
iajs-1816	88	12	q‖u	q‖u	ADJ
iajs-1816	88	13	u	u	NOUN
iajs-1816	88	14	‖	‖	ADJ
iajs-1816	88	15	now	now	ADV
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iajs-1816	88	18	any	any	DET
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iajs-1816	88	21	m	m	VERB
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iajs-1816	88	33	and	and	CCONJ
iajs-1816	88	34	applied	apply	VERB
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iajs-1816	88	36	https://doi.org/	https://doi.org/	NOUN
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iajs-1816	88	39	more	more	ADJ
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iajs-1816	88	42	the	the	DET
iajs-1816	88	43	conference	conference	NOUN
iajs-1816	88	44	please	please	INTJ
iajs-1816	88	45	visit	visit	VERB
iajs-1816	88	46	the	the	DET
iajs-1816	88	47	websites	website	NOUN
iajs-1816	88	48	:	:	PUNCT
iajs-1816	88	49	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1816	88	50	   	   	SPACE
iajs-1816	88	51	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1816	88	52	   	   	SPACE
iajs-1816	88	53	mathematics|433	mathematics|433	PROPN
iajs-1816	88	54	    	    	SPACE
iajs-1816	88	55	‖u	‖u	NOUN
iajs-1816	89	1	u	u	NOUN
iajs-1816	89	2	‖	‖	ADJ
iajs-1816	89	3	q‖u	q‖u	ADJ
iajs-1816	89	4	u	u	NOUN
iajs-1816	89	5	‖	‖	PROPN
iajs-1816	89	6	‖u	‖u	PROPN
iajs-1816	89	7	u	u	PROPN
iajs-1816	89	8	‖	‖	PROPN
iajs-1816	89	9	.	.	PUNCT
iajs-1816	89	10	‖u	‖u	NOUN
iajs-1816	89	11	u	u	PROPN
iajs-1816	89	12	‖	‖	PROPN
iajs-1816	89	13	q	q	PROPN
iajs-1816	89	14	q	q	X
iajs-1816	89	15	q	q	X
iajs-1816	89	16	⋯	⋯	PROPN
iajs-1816	89	17	q	q	PROPN
iajs-1816	89	18	‖u	‖u	NUM
iajs-1816	89	19	u	u	PROPN
iajs-1816	89	20	‖	‖	PROPN
iajs-1816	89	21	‖u	‖u	PROPN
iajs-1816	89	22	u	u	PROPN
iajs-1816	89	23	‖	‖	PROPN
iajs-1816	89	24	which	which	PRON
iajs-1816	89	25	implies	imply	VERB
iajs-1816	89	26	that	that	SCONJ
iajs-1816	89	27	‖u	‖u	NOUN
iajs-1816	89	28	u	u	PROPN
iajs-1816	89	29	‖	‖	PROPN
iajs-1816	89	30	→	→	SYM
iajs-1816	89	31	0	0	NUM
iajs-1816	89	32	as	as	ADP
iajs-1816	89	33	n	n	NOUN
iajs-1816	89	34	→	→	SYM
iajs-1816	89	35	∞	∞	NUM
iajs-1816	89	36	hence	hence	ADV
iajs-1816	89	37	{	{	PUNCT
iajs-1816	89	38	u	u	NOUN
iajs-1816	89	39	is	be	AUX
iajs-1816	89	40	cauchy	cauchy	ADJ
iajs-1816	89	41	sequance	sequance	NOUN
iajs-1816	89	42	in	in	ADP
iajs-1816	89	43	h	h	NOUN
iajs-1816	89	44	,	,	PUNCT
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iajs-1816	89	46	h	h	NOUN
iajs-1816	89	47	is	be	AUX
iajs-1816	89	48	a	a	DET
iajs-1816	89	49	hilbert	hilbert	NOUN
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iajs-1816	89	51	,	,	PUNCT
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iajs-1816	89	53	{	{	PUNCT
iajs-1816	89	54	u	u	NOUN
iajs-1816	89	55	is	be	AUX
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iajs-1816	89	60	,	,	PUNCT
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iajs-1816	89	71	n	n	CCONJ
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iajs-1816	89	81	,	,	PUNCT
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iajs-1816	89	83	show	show	VERB
iajs-1816	89	84	that	that	SCONJ
iajs-1816	89	85	δ	δ	PROPN
iajs-1816	89	86	u	u	PROPN
iajs-1816	89	87	,	,	PUNCT
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iajs-1816	89	89	u	u	NOUN
iajs-1816	89	90	=	=	NOUN
iajs-1816	89	91	0	0	NUM
iajs-1816	89	92	δ	δ	PROPN
iajs-1816	89	93	u	u	PROPN
iajs-1816	89	94	,	,	PUNCT
iajs-1816	89	95	n	n	CCONJ
iajs-1816	89	96	u	u	NOUN
iajs-1816	89	97	‖u	‖u	NOUN
iajs-1816	89	98	u‖	u‖	ADJ
iajs-1816	89	99	+	+	CCONJ
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iajs-1816	89	103	,	,	PUNCT
iajs-1816	89	104	n	n	CCONJ
iajs-1816	89	105	u	u	NOUN
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iajs-1816	89	107	u‖	u‖	X
iajs-1816	89	108	β	β	X
iajs-1816	89	109	d	d	PROPN
iajs-1816	89	110	n	n	CCONJ
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iajs-1816	89	112	,	,	PUNCT
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iajs-1816	89	114	u	u	X
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iajs-1816	89	128	u	u	NOUN
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iajs-1816	89	130	d	d	PROPN
iajs-1816	89	131	n	n	PROPN
iajs-1816	89	132	u	u	PROPN
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iajs-1816	89	134	n	n	CCONJ
iajs-1816	89	135	u	u	PROPN
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iajs-1816	89	140	,	,	PUNCT
iajs-1816	89	141	n	n	CCONJ
iajs-1816	89	142	u	u	NOUN
iajs-1816	89	143	.	.	PUNCT
iajs-1816	90	1	since	since	ADV
iajs-1816	90	2	,	,	PUNCT
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iajs-1816	90	4	n	n	X
iajs-1816	90	5	,	,	PUNCT
iajs-1816	90	6	n	n	CCONJ
iajs-1816	90	7	}	}	PUNCT
iajs-1816	90	8	and	and	CCONJ
iajs-1816	90	9	{	{	PUNCT
iajs-1816	90	10	n	n	CCONJ
iajs-1816	90	11	,	,	PUNCT
iajs-1816	90	12	n	n	PRON
iajs-1816	90	13	are	be	AUX
iajs-1816	90	14	fuzzy	fuzzy	ADJ
iajs-1816	90	15	r∗	r∗	ADJ
iajs-1816	90	16	weakly	weakly	ADJ
iajs-1816	90	17	commuting	commuting	NOUN
iajs-1816	90	18	.then	.then	PUNCT
iajs-1816	91	1	δ	δ	PROPN
iajs-1816	91	2	u	u	PROPN
iajs-1816	91	3	,	,	PUNCT
iajs-1816	91	4	n	n	CCONJ
iajs-1816	91	5	u	u	NOUN
iajs-1816	91	6	λ	λ	PROPN
iajs-1816	91	7	γ	γ	X
iajs-1816	91	8	‖	‖	PROPN
iajs-1816	91	9	u	u	NOUN
iajs-1816	91	10	u‖	u‖	ADJ
iajs-1816	91	11	.	.	PUNCT
iajs-1816	92	1	consequently	consequently	ADV
iajs-1816	92	2	,	,	PUNCT
iajs-1816	92	3	δ	δ	PROPN
iajs-1816	92	4	u	u	PROPN
iajs-1816	92	5	,	,	PUNCT
iajs-1816	92	6	n	n	CCONJ
iajs-1816	92	7	u	u	NOUN
iajs-1816	92	8	0	0	NUM
iajs-1816	92	9	and	and	CCONJ
iajs-1816	92	10	u	u	PROPN
iajs-1816	92	11	⊂	⊂	PROPN
iajs-1816	92	12	nu	nu	PROPN
iajs-1816	92	13	.	.	PROPN
iajs-1816	93	1	clearly	clearly	ADV
iajs-1816	93	2	u	u	PROPN
iajs-1816	93	3	is	be	AUX
iajs-1816	93	4	a	a	DET
iajs-1816	93	5	common	common	ADJ
iajs-1816	93	6	fuzzy	fuzzy	ADJ
iajs-1816	93	7	fixed	fix	VERB
iajs-1816	93	8	point	point	NOUN
iajs-1816	93	9	of	of	ADP
iajs-1816	93	10	the	the	DET
iajs-1816	93	11	fuzzy	fuzzy	ADJ
iajs-1816	93	12	mappings	mapping	NOUN
iajs-1816	93	13	n	n	PRON
iajs-1816	93	14	,	,	PUNCT
iajs-1816	93	15	n	n	CCONJ
iajs-1816	93	16	,	,	PUNCT
iajs-1816	93	17	n	n	CCONJ
iajs-1816	93	18	,	,	PUNCT
iajs-1816	93	19	.in	.in	PUNCT
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iajs-1816	93	21	if	if	SCONJ
iajs-1816	93	22	α	α	PROPN
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iajs-1816	93	24	,	,	PUNCT
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iajs-1816	93	26	x	x	PUNCT
iajs-1816	93	27	is	be	AUX
iajs-1816	93	28	a	a	DET
iajs-1816	93	29	common	common	ADJ
iajs-1816	93	30	fixed	fix	VERB
iajs-1816	93	31	point	point	NOUN
iajs-1816	93	32	of	of	ADP
iajs-1816	93	33	n	n	PROPN
iajs-1816	93	34	,	,	PUNCT
iajs-1816	93	35	n	n	PROPN
iajs-1816	93	36	and	and	CCONJ
iajs-1816	93	37	n	n	NOUN
iajs-1816	93	38	.	.	PUNCT
iajs-1816	94	1	∎	∎	PROPN
iajs-1816	94	2	theorem	theorem	VERB
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iajs-1816	94	4	h	h	PRON
iajs-1816	94	5	be	be	AUX
iajs-1816	94	6	a	a	DET
iajs-1816	94	7	hilbert	hilbert	NOUN
iajs-1816	94	8	space	space	NOUN
iajs-1816	94	9	and	and	CCONJ
iajs-1816	94	10	n	n	NOUN
iajs-1816	94	11	,	,	PUNCT
iajs-1816	94	12	n	n	CCONJ
iajs-1816	94	13	,	,	PUNCT
iajs-1816	94	14	n	n	CCONJ
iajs-1816	94	15	be	be	AUX
iajs-1816	94	16	a	a	DET
iajs-1816	94	17	fuzzy	fuzzy	ADJ
iajs-1816	94	18	mappings	mapping	NOUN
iajs-1816	94	19	satisfy	satisfy	VERB
iajs-1816	94	20	the	the	DET
iajs-1816	94	21	following	follow	VERB
iajs-1816	94	22	conditions	condition	NOUN
iajs-1816	94	23	:	:	PUNCT
iajs-1816	94	24	1	1	X
iajs-1816	94	25	.	.	X
iajs-1816	94	26	d	d	NOUN
iajs-1816	94	27	n	n	X
iajs-1816	94	28	u	u	NOUN
iajs-1816	94	29	,	,	PUNCT
iajs-1816	94	30	n	n	PROPN
iajs-1816	94	31	v	v	X
iajs-1816	94	32	β	β	X
iajs-1816	94	33	d	d	X
iajs-1816	94	34	n	n	CCONJ
iajs-1816	94	35	u	u	NOUN
iajs-1816	94	36	,	,	PUNCT
iajs-1816	94	37	n	n	PRON
iajs-1816	94	38	v	v	NOUN
iajs-1816	94	39	.	.	PUNCT
iajs-1816	95	1	d	d	NOUN
iajs-1816	95	2	n	n	NUM
iajs-1816	95	3	v	v	NOUN
iajs-1816	95	4	,	,	PUNCT
iajs-1816	95	5	n	n	PROPN
iajs-1816	95	6	v	v	NOUN
iajs-1816	95	7	ξ	ξ	PROPN
iajs-1816	95	8	d	d	PROPN
iajs-1816	95	9	n	n	NUM
iajs-1816	95	10	v	v	NOUN
iajs-1816	95	11	,	,	PUNCT
iajs-1816	95	12	n	n	PRON
iajs-1816	95	13	v	v	NOUN
iajs-1816	95	14	.	.	PUNCT
iajs-1816	96	1	d	d	NOUN
iajs-1816	96	2	n	n	X
iajs-1816	96	3	u	u	NOUN
iajs-1816	96	4	,	,	PUNCT
iajs-1816	96	5	n	n	CCONJ
iajs-1816	96	6	u	u	NOUN
iajs-1816	96	7	λ	λ	X
iajs-1816	96	8	d	d	PROPN
iajs-1816	96	9	n	n	PROPN
iajs-1816	96	10	u	u	NOUN
iajs-1816	96	11	,	,	PUNCT
iajs-1816	96	12	n	n	PRON
iajs-1816	96	13	v	v	NOUN
iajs-1816	96	14	.	.	PUNCT
iajs-1816	97	1	d	d	NOUN
iajs-1816	97	2	n	n	NUM
iajs-1816	97	3	v	v	NOUN
iajs-1816	97	4	,	,	PUNCT
iajs-1816	97	5	n	n	CCONJ
iajs-1816	97	6	u	u	NOUN
iajs-1816	97	7	γ	γ	X
iajs-1816	97	8	‖v	‖v	ADJ
iajs-1816	97	9	u‖	u‖	NOUN
iajs-1816	97	10	for	for	ADP
iajs-1816	97	11	all	all	DET
iajs-1816	97	12	u	u	NOUN
iajs-1816	97	13	,	,	PUNCT
iajs-1816	97	14	v	v	NOUN
iajs-1816	97	15	∈	∈	NOUN
iajs-1816	97	16	h	h	NOUN
iajs-1816	97	17	where	where	SCONJ
iajs-1816	97	18	γ	γ	X
iajs-1816	97	19	,	,	PUNCT
iajs-1816	97	20	β	β	X
iajs-1816	97	21	,	,	PUNCT
iajs-1816	97	22	λ	λ	PROPN
iajs-1816	97	23	,	,	PUNCT
iajs-1816	97	24	ξ	ξ	PROPN
iajs-1816	97	25	0	0	NUM
iajs-1816	97	26	with	with	ADP
iajs-1816	97	27	2γ	2γ	NUM
iajs-1816	97	28	2β	2β	NUM
iajs-1816	97	29	λ	λ	NOUN
iajs-1816	97	30	2ξ	2ξ	NUM
iajs-1816	97	31	1	1	NUM
iajs-1816	97	32	.	.	PUNCT
iajs-1816	98	1	2	2	X
iajs-1816	98	2	.	.	X
iajs-1816	98	3	n	n	NOUN
iajs-1816	98	4	and	and	CCONJ
iajs-1816	98	5	n	n	PROPN
iajs-1816	98	6	are	be	AUX
iajs-1816	98	7	continuous	continuous	ADJ
iajs-1816	98	8	fuzzy	fuzzy	ADJ
iajs-1816	98	9	mapping	mapping	NOUN
iajs-1816	98	10	.	.	PUNCT
iajs-1816	99	1	3	3	X
iajs-1816	99	2	.	.	X
iajs-1816	99	3	n	n	PROPN
iajs-1816	99	4	(	(	PUNCT
iajs-1816	99	5	h	h	NOUN
iajs-1816	99	6	)	)	PUNCT
iajs-1816	99	7	⊂	⊂	PROPN
iajs-1816	99	8	n	n	NUM
iajs-1816	99	9	h	h	NOUN
iajs-1816	99	10	∩	∩	NOUN
iajs-1816	99	11	n	n	NOUN
iajs-1816	99	12	h	h	NOUN
iajs-1816	99	13	.	.	PUNCT
iajs-1816	100	1	ihsciconf	ihsciconf	PROPN
iajs-1816	100	2	2017	2017	NUM
iajs-1816	100	3	special	special	ADJ
iajs-1816	100	4	issue	issue	NOUN
iajs-1816	100	5	ibn	ibn	PROPN
iajs-1816	100	6	al	al	PROPN
iajs-1816	100	7	-	-	PUNCT
iajs-1816	100	8	haitham	haitham	PROPN
iajs-1816	100	9	journal	journal	PROPN
iajs-1816	100	10	for	for	ADP
iajs-1816	100	11	pure	pure	ADJ
iajs-1816	100	12	and	and	CCONJ
iajs-1816	100	13	applied	apply	VERB
iajs-1816	100	14	science	science	NOUN
iajs-1816	100	15	https://doi.org/	https://doi.org/	NOUN
iajs-1816	100	16	10.30526/2017.ihsciconf.1816	10.30526/2017.ihsciconf.1816	NUM
iajs-1816	100	17	for	for	ADP
iajs-1816	100	18	more	more	ADJ
iajs-1816	100	19	information	information	NOUN
iajs-1816	100	20	about	about	ADP
iajs-1816	100	21	the	the	DET
iajs-1816	100	22	conference	conference	NOUN
iajs-1816	100	23	please	please	INTJ
iajs-1816	100	24	visit	visit	VERB
iajs-1816	100	25	the	the	DET
iajs-1816	100	26	websites	website	NOUN
iajs-1816	100	27	:	:	PUNCT
iajs-1816	100	28	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1816	100	29	   	   	SPACE
iajs-1816	100	30	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1816	100	31	   	   	SPACE
iajs-1816	100	32	mathematics|434	mathematics|434	NOUN
iajs-1816	100	33	    	    	SPACE
iajs-1816	100	34	4	4	NUM
iajs-1816	100	35	.	.	PUNCT
iajs-1816	100	36	{	{	PUNCT
iajs-1816	101	1	n	n	NOUN
iajs-1816	101	2	,	,	PUNCT
iajs-1816	101	3	n	n	CCONJ
iajs-1816	101	4	}	}	PUNCT
iajs-1816	101	5	and	and	CCONJ
iajs-1816	101	6	{	{	PUNCT
iajs-1816	101	7	n	n	NOUN
iajs-1816	101	8	,	,	PUNCT
iajs-1816	101	9	n	n	CCONJ
iajs-1816	101	10	}	}	PUNCT
iajs-1816	101	11	are	be	AUX
iajs-1816	101	12	fuzzy	fuzzy	ADJ
iajs-1816	101	13	r∗	r∗	ADJ
iajs-1816	101	14	weakly	weakly	ADJ
iajs-1816	101	15	commuting	commuting	NOUN
iajs-1816	101	16	.	.	PUNCT
iajs-1816	102	1	then	then	ADV
iajs-1816	102	2	,	,	PUNCT
iajs-1816	102	3	there	there	PRON
iajs-1816	102	4	exists	exist	VERB
iajs-1816	102	5	u	u	PROPN
iajs-1816	102	6	∈	∈	PROPN
iajs-1816	102	7	h	h	NOUN
iajs-1816	102	8	such	such	ADJ
iajs-1816	102	9	that	that	SCONJ
iajs-1816	102	10	u	u	PROPN
iajs-1816	102	11	is	be	AUX
iajs-1816	102	12	a	a	DET
iajs-1816	102	13	common	common	ADJ
iajs-1816	102	14	fuzzy	fuzzy	ADJ
iajs-1816	102	15	fixed	fix	VERB
iajs-1816	102	16	point	point	NOUN
iajs-1816	102	17	of	of	ADP
iajs-1816	102	18	n	n	PROPN
iajs-1816	102	19	,	,	PUNCT
iajs-1816	102	20	n	n	PROPN
iajs-1816	102	21	and	and	CCONJ
iajs-1816	102	22	n	n	NOUN
iajs-1816	102	23	.	.	PUNCT
iajs-1816	103	1	proof	proof	NOUN
iajs-1816	103	2	similar	similar	ADJ
iajs-1816	103	3	to	to	PART
iajs-1816	103	4	prove	prove	VERB
iajs-1816	103	5	theorem	theorem	VERB
iajs-1816	103	6	3.7	3.7	NUM
iajs-1816	103	7	∎	∎	PROPN
iajs-1816	103	8	definition	definition	NOUN
iajs-1816	103	9	let	let	VERB
iajs-1816	103	10	h	h	PRON
iajs-1816	103	11	be	be	AUX
iajs-1816	103	12	a	a	DET
iajs-1816	103	13	hilbert	hilbert	NOUN
iajs-1816	103	14	space	space	NOUN
iajs-1816	103	15	and	and	CCONJ
iajs-1816	103	16	n	n	CCONJ
iajs-1816	103	17	,	,	PUNCT
iajs-1816	103	18	m	m	PROPN
iajs-1816	103	19	:	:	PUNCT
iajs-1816	103	20	h→	h→	NOUN
iajs-1816	103	21	w	w	NOUN
iajs-1816	103	22	h	h	NOUN
iajs-1816	103	23	.	.	PUNCT
iajs-1816	104	1	a	a	DET
iajs-1816	104	2	fuzzy	fuzzy	ADJ
iajs-1816	104	3	mappings	mapping	NOUN
iajs-1816	104	4	t	t	NOUN
iajs-1816	104	5	and	and	CCONJ
iajs-1816	104	6	s	s	PRON
iajs-1816	104	7	are	be	AUX
iajs-1816	104	8	called	call	VERB
iajs-1816	104	9	fuzzy	fuzzy	ADJ
iajs-1816	104	10	jungck	jungck	NOUN
iajs-1816	104	11	like	like	ADP
iajs-1816	104	12	contractive	contractive	ADJ
iajs-1816	104	13	mapping	mapping	NOUN
iajs-1816	104	14	,	,	PUNCT
iajs-1816	104	15	if	if	SCONJ
iajs-1816	104	16	there	there	PRON
iajs-1816	104	17	exists	exist	VERB
iajs-1816	104	18	ξ	ξ	PROPN
iajs-1816	104	19	∈	∈	PROPN
iajs-1816	104	20	0	0	NUM
iajs-1816	104	21	,	,	PUNCT
iajs-1816	104	22	1	1	NUM
iajs-1816	104	23	,	,	PUNCT
iajs-1816	104	24	such	such	ADJ
iajs-1816	104	25	that	that	SCONJ
iajs-1816	104	26	d	d	PROPN
iajs-1816	104	27	n	n	NUM
iajs-1816	104	28	u	u	NOUN
iajs-1816	104	29	,	,	PUNCT
iajs-1816	104	30	n	n	PROPN
iajs-1816	104	31	v	v	ADP
iajs-1816	104	32	ξ‖u	ξ‖u	NOUN
iajs-1816	104	33	v‖	v‖	NOUN
iajs-1816	104	34	ψ	ψ	X
iajs-1816	104	35	d	d	X
iajs-1816	104	36	m	m	VERB
iajs-1816	104	37	u	u	NOUN
iajs-1816	104	38	,	,	PUNCT
iajs-1816	104	39	m	m	VERB
iajs-1816	104	40	v	v	ADJ
iajs-1816	104	41	,	,	PUNCT
iajs-1816	104	42	for	for	ADP
iajs-1816	104	43	all	all	DET
iajs-1816	104	44	u	u	NOUN
iajs-1816	104	45	,	,	PUNCT
iajs-1816	104	46	v	v	PROPN
iajs-1816	104	47	∈	∈	PROPN
iajs-1816	104	48	h.	h.	NOUN
iajs-1816	104	49	theorem	theorem	NOUN
iajs-1816	104	50	let	let	VERB
iajs-1816	104	51	h	h	PRON
iajs-1816	104	52	be	be	AUX
iajs-1816	104	53	a	a	DET
iajs-1816	104	54	hilbert	hilbert	NOUN
iajs-1816	104	55	space	space	NOUN
iajs-1816	104	56	and	and	CCONJ
iajs-1816	104	57	n	n	CCONJ
iajs-1816	104	58	,	,	PUNCT
iajs-1816	104	59	m	m	AUX
iajs-1816	104	60	be	be	VERB
iajs-1816	104	61	a	a	DET
iajs-1816	104	62	fuzzy	fuzzy	ADJ
iajs-1816	104	63	jungck	jungck	NOUN
iajs-1816	104	64	like	like	ADP
iajs-1816	104	65	contractive	contractive	ADJ
iajs-1816	104	66	mappings	mapping	NOUN
iajs-1816	104	67	satisfies	satisfy	VERB
iajs-1816	104	68	the	the	DET
iajs-1816	104	69	following	follow	VERB
iajs-1816	104	70	conditions	condition	NOUN
iajs-1816	104	71	:	:	PUNCT
iajs-1816	105	1	1	1	X
iajs-1816	105	2	.	.	X
iajs-1816	105	3	m	m	PROPN
iajs-1816	105	4	is	be	AUX
iajs-1816	105	5	continuous	continuous	ADJ
iajs-1816	105	6	fuzzy	fuzzy	ADJ
iajs-1816	105	7	mapping	mapping	NOUN
iajs-1816	105	8	.	.	PUNCT
iajs-1816	106	1	2	2	X
iajs-1816	106	2	.	.	X
iajs-1816	107	1	n(h)⊂	n(h)⊂	PROPN
iajs-1816	107	2	m	m	PROPN
iajs-1816	107	3	h	h	NOUN
iajs-1816	107	4	.	.	PUNCT
iajs-1816	108	1	3	3	X
iajs-1816	108	2	.	.	X
iajs-1816	108	3	{	{	PUNCT
iajs-1816	108	4	m	m	PROPN
iajs-1816	108	5	,	,	PUNCT
iajs-1816	108	6	n	n	CCONJ
iajs-1816	108	7	}	}	PUNCT
iajs-1816	108	8	are	be	AUX
iajs-1816	108	9	fuzzy	fuzzy	ADJ
iajs-1816	108	10	r∗	r∗	ADJ
iajs-1816	108	11	weakly	weakly	ADJ
iajs-1816	108	12	commuting	commuting	NOUN
iajs-1816	108	13	.	.	PUNCT
iajs-1816	109	1	then	then	ADV
iajs-1816	109	2	,	,	PUNCT
iajs-1816	109	3	there	there	PRON
iajs-1816	109	4	exists	exist	VERB
iajs-1816	109	5	u	u	PROPN
iajs-1816	109	6	∈	∈	PROPN
iajs-1816	109	7	h	h	NOUN
iajs-1816	109	8	such	such	ADJ
iajs-1816	109	9	that	that	SCONJ
iajs-1816	109	10	u	u	PROPN
iajs-1816	109	11	is	be	AUX
iajs-1816	109	12	a	a	DET
iajs-1816	109	13	common	common	ADJ
iajs-1816	109	14	fuzzy	fuzzy	ADJ
iajs-1816	109	15	fixed	fix	VERB
iajs-1816	109	16	point	point	NOUN
iajs-1816	109	17	of	of	ADP
iajs-1816	109	18	n	n	PROPN
iajs-1816	109	19	and	and	CCONJ
iajs-1816	109	20	m	m	PROPN
iajs-1816	109	21	.	.	PUNCT
iajs-1816	110	1	proof	proof	NOUN
iajs-1816	110	2	trivial	trivial	ADJ
iajs-1816	110	3	∎	∎	PROPN
iajs-1816	110	4	definition	definition	NOUN
iajs-1816	110	5	let	let	VERB
iajs-1816	110	6	h	h	PRON
iajs-1816	110	7	be	be	AUX
iajs-1816	110	8	a	a	DET
iajs-1816	110	9	hilbert	hilbert	NOUN
iajs-1816	110	10	space	space	NOUN
iajs-1816	110	11	and	and	CCONJ
iajs-1816	110	12	n	n	CCONJ
iajs-1816	110	13	,	,	PUNCT
iajs-1816	110	14	m	m	PROPN
iajs-1816	110	15	:	:	PUNCT
iajs-1816	110	16	h→	h→	NOUN
iajs-1816	110	17	w	w	NOUN
iajs-1816	110	18	h	h	NOUN
iajs-1816	110	19	.	.	PUNCT
iajs-1816	111	1	a	a	DET
iajs-1816	111	2	fuzzy	fuzzy	ADJ
iajs-1816	111	3	mappings	mapping	NOUN
iajs-1816	111	4	t	t	NOUN
iajs-1816	111	5	and	and	CCONJ
iajs-1816	111	6	s	s	PRON
iajs-1816	111	7	are	be	AUX
iajs-1816	111	8	called	call	VERB
iajs-1816	111	9	fuzzy	fuzzy	ADJ
iajs-1816	111	10	jungck	jungck	NOUN
iajs-1816	111	11	generalized	generalize	VERB
iajs-1816	111	12	like	like	ADP
iajs-1816	111	13	contractive	contractive	ADJ
iajs-1816	111	14	mapping	mapping	NOUN
iajs-1816	111	15	,	,	PUNCT
iajs-1816	111	16	if	if	SCONJ
iajs-1816	111	17	there	there	PRON
iajs-1816	111	18	exists	exist	VERB
iajs-1816	111	19	ξ	ξ	PROPN
iajs-1816	111	20	∈	∈	PROPN
iajs-1816	111	21	0	0	NUM
iajs-1816	111	22	,	,	PUNCT
iajs-1816	111	23	1	1	NUM
iajs-1816	111	24	,	,	PUNCT
iajs-1816	111	25	such	such	ADJ
iajs-1816	111	26	that	that	SCONJ
iajs-1816	111	27	d	d	PROPN
iajs-1816	111	28	n	n	NUM
iajs-1816	111	29	u	u	NOUN
iajs-1816	111	30	,	,	PUNCT
iajs-1816	111	31	n	n	PROPN
iajs-1816	111	32	v	v	ADP
iajs-1816	111	33	ξ‖u	ξ‖u	NOUN
iajs-1816	111	34	v‖	v‖	NOUN
iajs-1816	111	35	ψ	ψ	X
iajs-1816	111	36	d	d	X
iajs-1816	111	37	m	m	VERB
iajs-1816	111	38	u	u	NOUN
iajs-1816	111	39	,	,	PUNCT
iajs-1816	111	40	n	n	CCONJ
iajs-1816	111	41	u	u	NOUN
iajs-1816	111	42	,	,	PUNCT
iajs-1816	111	43	d	d	PROPN
iajs-1816	111	44	n	n	CCONJ
iajs-1816	111	45	u	u	NOUN
iajs-1816	111	46	,	,	PUNCT
iajs-1816	111	47	m	m	VERB
iajs-1816	111	48	v	v	ADJ
iajs-1816	111	49	,	,	PUNCT
iajs-1816	111	50	for	for	ADP
iajs-1816	111	51	all	all	DET
iajs-1816	111	52	u	u	NOUN
iajs-1816	111	53	,	,	PUNCT
iajs-1816	111	54	v	v	PROPN
iajs-1816	111	55	∈	∈	PROPN
iajs-1816	111	56	h.	h.	NOUN
iajs-1816	111	57	theorem	theorem	NOUN
iajs-1816	111	58	let	let	VERB
iajs-1816	111	59	h	h	PRON
iajs-1816	111	60	be	be	AUX
iajs-1816	111	61	a	a	DET
iajs-1816	111	62	hilbert	hilbert	NOUN
iajs-1816	111	63	space	space	NOUN
iajs-1816	111	64	and	and	CCONJ
iajs-1816	111	65	n	n	CCONJ
iajs-1816	111	66	,	,	PUNCT
iajs-1816	111	67	m	m	AUX
iajs-1816	111	68	be	be	VERB
iajs-1816	111	69	a	a	DET
iajs-1816	111	70	fuzzy	fuzzy	ADJ
iajs-1816	111	71	jungck	jungck	NOUN
iajs-1816	111	72	generalized	generalize	VERB
iajs-1816	111	73	like	like	ADP
iajs-1816	111	74	contractive	contractive	ADJ
iajs-1816	111	75	mappings	mapping	NOUN
iajs-1816	111	76	satisfies	satisfy	VERB
iajs-1816	111	77	the	the	DET
iajs-1816	111	78	following	follow	VERB
iajs-1816	111	79	conditions	condition	NOUN
iajs-1816	111	80	:	:	PUNCT
iajs-1816	112	1	1	1	X
iajs-1816	112	2	.	.	X
iajs-1816	112	3	m	m	PROPN
iajs-1816	112	4	is	be	AUX
iajs-1816	112	5	continuous	continuous	ADJ
iajs-1816	112	6	fuzzy	fuzzy	ADJ
iajs-1816	112	7	mapping	mapping	NOUN
iajs-1816	112	8	.	.	PUNCT
iajs-1816	113	1	2	2	X
iajs-1816	113	2	.	.	X
iajs-1816	114	1	n(h)⊂	n(h)⊂	PROPN
iajs-1816	114	2	m	m	PROPN
iajs-1816	114	3	h	h	NOUN
iajs-1816	114	4	.	.	PUNCT
iajs-1816	115	1	3	3	X
iajs-1816	115	2	.	.	X
iajs-1816	115	3	{	{	PUNCT
iajs-1816	115	4	m	m	PROPN
iajs-1816	115	5	,	,	PUNCT
iajs-1816	115	6	n	n	CCONJ
iajs-1816	115	7	}	}	PUNCT
iajs-1816	115	8	are	be	AUX
iajs-1816	115	9	fuzzy	fuzzy	ADJ
iajs-1816	115	10	r∗	r∗	ADJ
iajs-1816	115	11	weakly	weakly	ADJ
iajs-1816	115	12	commuting	commuting	NOUN
iajs-1816	115	13	.	.	PUNCT
iajs-1816	116	1	then	then	ADV
iajs-1816	116	2	,	,	PUNCT
iajs-1816	116	3	there	there	PRON
iajs-1816	116	4	exists	exist	VERB
iajs-1816	116	5	u	u	PROPN
iajs-1816	116	6	∈	∈	PROPN
iajs-1816	116	7	h	h	NOUN
iajs-1816	116	8	such	such	ADJ
iajs-1816	116	9	that	that	SCONJ
iajs-1816	116	10	u	u	PROPN
iajs-1816	116	11	is	be	AUX
iajs-1816	116	12	a	a	DET
iajs-1816	116	13	common	common	ADJ
iajs-1816	116	14	fuzzy	fuzzy	ADJ
iajs-1816	116	15	fixed	fix	VERB
iajs-1816	116	16	point	point	NOUN
iajs-1816	116	17	of	of	ADP
iajs-1816	116	18	n	n	PROPN
iajs-1816	116	19	and	and	CCONJ
iajs-1816	116	20	m	m	PROPN
iajs-1816	116	21	.	.	PUNCT
iajs-1816	117	1	proof	proof	NOUN
iajs-1816	117	2	:	:	PUNCT
iajs-1816	117	3	trivial	trivial	ADJ
iajs-1816	117	4	∎	∎	PROPN
iajs-1816	117	5	definition	definition	NOUN
iajs-1816	117	6	let	let	VERB
iajs-1816	117	7	h	h	PRON
iajs-1816	117	8	be	be	AUX
iajs-1816	117	9	a	a	DET
iajs-1816	117	10	hilbert	hilbert	NOUN
iajs-1816	117	11	space	space	NOUN
iajs-1816	117	12	and	and	CCONJ
iajs-1816	117	13	n	n	CCONJ
iajs-1816	117	14	,	,	PUNCT
iajs-1816	117	15	m	m	PROPN
iajs-1816	117	16	:	:	PUNCT
iajs-1816	117	17	h→	h→	NOUN
iajs-1816	117	18	w	w	NOUN
iajs-1816	117	19	h	h	NOUN
iajs-1816	117	20	.	.	PUNCT
iajs-1816	118	1	a	a	DET
iajs-1816	118	2	fuzzy	fuzzy	ADJ
iajs-1816	118	3	mappings	mapping	NOUN
iajs-1816	118	4	t	t	NOUN
iajs-1816	118	5	and	and	CCONJ
iajs-1816	118	6	s	s	PRON
iajs-1816	118	7	are	be	AUX
iajs-1816	118	8	called	call	VERB
iajs-1816	118	9	fuzzy	fuzzy	ADJ
iajs-1816	118	10	jungck	jungck	NOUN
iajs-1816	118	11	slike	slike	PROPN
iajs-1816	118	12	contractive	contractive	ADJ
iajs-1816	118	13	mapping	mapping	NOUN
iajs-1816	118	14	,	,	PUNCT
iajs-1816	118	15	if	if	SCONJ
iajs-1816	118	16	there	there	PRON
iajs-1816	118	17	exists	exist	VERB
iajs-1816	118	18	ξ	ξ	PROPN
iajs-1816	118	19	∈	∈	PROPN
iajs-1816	118	20	0	0	NUM
iajs-1816	118	21	,	,	PUNCT
iajs-1816	118	22	1	1	NUM
iajs-1816	118	23	,	,	PUNCT
iajs-1816	118	24	such	such	ADJ
iajs-1816	118	25	that	that	SCONJ
iajs-1816	118	26	d	d	PROPN
iajs-1816	118	27	n	n	NUM
iajs-1816	118	28	u	u	NOUN
iajs-1816	118	29	,	,	PUNCT
iajs-1816	118	30	n	n	PROPN
iajs-1816	118	31	v	v	NOUN
iajs-1816	118	32	ξ	ξ	X
iajs-1816	118	33	m	m	VERB
iajs-1816	118	34	u	u	NOUN
iajs-1816	118	35	,	,	PUNCT
iajs-1816	118	36	v	v	NOUN
iajs-1816	118	37	ψ	ψ	NOUN
iajs-1816	118	38	m	m	VERB
iajs-1816	118	39	u	u	NOUN
iajs-1816	118	40	,	,	PUNCT
iajs-1816	118	41	v	v	INTJ
iajs-1816	118	42	,	,	PUNCT
iajs-1816	118	43	for	for	ADP
iajs-1816	118	44	all	all	DET
iajs-1816	118	45	u	u	NOUN
iajs-1816	118	46	,	,	PUNCT
iajs-1816	118	47	v	v	NOUN
iajs-1816	118	48	∈	∈	PROPN
iajs-1816	118	49	h	h	NOUN
iajs-1816	118	50	and	and	CCONJ
iajs-1816	118	51	m	m	PROPN
iajs-1816	118	52	u	u	NOUN
iajs-1816	118	53	,	,	PUNCT
iajs-1816	118	54	v	v	NOUN
iajs-1816	118	55	max	max	PROPN
iajs-1816	118	56	‖u	‖u	PROPN
iajs-1816	118	57	v‖	v‖	NOUN
iajs-1816	118	58	,	,	PUNCT
iajs-1816	119	1	d	d	PROPN
iajs-1816	119	2	n	n	X
iajs-1816	119	3	u	u	NOUN
iajs-1816	119	4	,	,	PUNCT
iajs-1816	119	5	m	m	VERB
iajs-1816	119	6	v	v	NOUN
iajs-1816	119	7	,	,	PUNCT
iajs-1816	119	8	d	d	PROPN
iajs-1816	119	9	m	m	VERB
iajs-1816	119	10	v	v	NOUN
iajs-1816	119	11	,	,	PUNCT
iajs-1816	119	12	n	n	PRON
iajs-1816	119	13	v	v	NOUN
iajs-1816	119	14	,	,	PUNCT
iajs-1816	119	15	d	d	PROPN
iajs-1816	119	16	m	m	VERB
iajs-1816	119	17	u	u	NOUN
iajs-1816	119	18	,	,	PUNCT
iajs-1816	119	19	n	n	PROPN
iajs-1816	119	20	v	v	NOUN
iajs-1816	120	1	d	d	NOUN
iajs-1816	120	2	m	m	NOUN
iajs-1816	120	3	v	v	NOUN
iajs-1816	120	4	,	,	PUNCT
iajs-1816	120	5	n	n	CCONJ
iajs-1816	120	6	u	u	NOUN
iajs-1816	120	7	2	2	NUM
iajs-1816	120	8	ihsciconf	ihsciconf	NOUN
iajs-1816	120	9	2017	2017	NUM
iajs-1816	120	10	special	special	ADJ
iajs-1816	120	11	issue	issue	NOUN
iajs-1816	120	12	ibn	ibn	PROPN
iajs-1816	120	13	al	al	PROPN
iajs-1816	120	14	-	-	PUNCT
iajs-1816	120	15	haitham	haitham	PROPN
iajs-1816	120	16	journal	journal	PROPN
iajs-1816	120	17	for	for	ADP
iajs-1816	120	18	pure	pure	ADJ
iajs-1816	120	19	and	and	CCONJ
iajs-1816	120	20	applied	apply	VERB
iajs-1816	120	21	science	science	NOUN
iajs-1816	120	22	https://doi.org/	https://doi.org/	NOUN
iajs-1816	120	23	10.30526/2017.ihsciconf.1816	10.30526/2017.ihsciconf.1816	NUM
iajs-1816	120	24	for	for	ADP
iajs-1816	120	25	more	more	ADJ
iajs-1816	120	26	information	information	NOUN
iajs-1816	120	27	about	about	ADP
iajs-1816	120	28	the	the	DET
iajs-1816	120	29	conference	conference	NOUN
iajs-1816	120	30	please	please	INTJ
iajs-1816	120	31	visit	visit	VERB
iajs-1816	120	32	the	the	DET
iajs-1816	120	33	websites	website	NOUN
iajs-1816	120	34	:	:	PUNCT
iajs-1816	120	35	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1816	120	36	   	   	SPACE
iajs-1816	120	37	www.ihsciconf.org	www.ihsciconf.org	ADV
iajs-1816	120	38	   	   	SPACE
iajs-1816	120	39	mathematics|435	mathematics|435	NOUN
iajs-1816	120	40	    	    	SPACE
iajs-1816	120	41	theorem	theorem	NOUN
iajs-1816	120	42	let	let	VERB
iajs-1816	120	43	h	h	PRON
iajs-1816	120	44	be	be	AUX
iajs-1816	120	45	a	a	DET
iajs-1816	120	46	hilbert	hilbert	NOUN
iajs-1816	120	47	space	space	NOUN
iajs-1816	120	48	and	and	CCONJ
iajs-1816	120	49	n	n	CCONJ
iajs-1816	120	50	,	,	PUNCT
iajs-1816	120	51	m	m	AUX
iajs-1816	120	52	be	be	VERB
iajs-1816	120	53	a	a	DET
iajs-1816	120	54	fuzzy	fuzzy	ADJ
iajs-1816	120	55	jungck	jungck	NOUN
iajs-1816	120	56	s	s	NOUN
iajs-1816	120	57	-	-	PUNCT
iajs-1816	120	58	like	like	ADJ
iajs-1816	120	59	contractive	contractive	ADJ
iajs-1816	120	60	mappings	mapping	NOUN
iajs-1816	120	61	satisfies	satisfy	VERB
iajs-1816	120	62	the	the	DET
iajs-1816	120	63	following	follow	VERB
iajs-1816	120	64	conditions	condition	NOUN
iajs-1816	120	65	:	:	PUNCT
iajs-1816	120	66	1	1	X
iajs-1816	120	67	.	.	X
iajs-1816	120	68	m	m	PROPN
iajs-1816	120	69	is	be	AUX
iajs-1816	120	70	continuous	continuous	ADJ
iajs-1816	120	71	fuzzy	fuzzy	ADJ
iajs-1816	120	72	mapping	mapping	NOUN
iajs-1816	120	73	.	.	PUNCT
iajs-1816	121	1	2	2	X
iajs-1816	121	2	.	.	X
iajs-1816	122	1	n(h)⊂	n(h)⊂	PROPN
iajs-1816	122	2	m	m	PROPN
iajs-1816	122	3	h	h	NOUN
iajs-1816	122	4	.	.	PUNCT
iajs-1816	123	1	3	3	X
iajs-1816	123	2	.	.	X
iajs-1816	123	3	{	{	PUNCT
iajs-1816	123	4	m	m	PROPN
iajs-1816	123	5	,	,	PUNCT
iajs-1816	123	6	n	n	CCONJ
iajs-1816	123	7	}	}	PUNCT
iajs-1816	123	8	are	be	AUX
iajs-1816	123	9	fuzzy	fuzzy	ADJ
iajs-1816	123	10	r∗	r∗	ADJ
iajs-1816	123	11	weakly	weakly	ADJ
iajs-1816	123	12	commuting	commuting	NOUN
iajs-1816	123	13	.	.	PUNCT
iajs-1816	124	1	then	then	ADV
iajs-1816	124	2	,	,	PUNCT
iajs-1816	124	3	there	there	PRON
iajs-1816	124	4	exists	exist	VERB
iajs-1816	124	5	u	u	PROPN
iajs-1816	124	6	∈	∈	PROPN
iajs-1816	124	7	h	h	NOUN
iajs-1816	124	8	such	such	ADJ
iajs-1816	124	9	that	that	SCONJ
iajs-1816	124	10	u	u	PROPN
iajs-1816	124	11	is	be	AUX
iajs-1816	124	12	a	a	DET
iajs-1816	124	13	common	common	ADJ
iajs-1816	124	14	fuzzy	fuzzy	ADJ
iajs-1816	124	15	fixed	fix	VERB
iajs-1816	124	16	point	point	NOUN
iajs-1816	124	17	of	of	ADP
iajs-1816	124	18	n	n	PROPN
iajs-1816	124	19	and	and	CCONJ
iajs-1816	124	20	m	m	PROPN
iajs-1816	124	21	.	.	PUNCT
iajs-1816	125	1	proof	proof	NOUN
iajs-1816	125	2	trivial	trivial	ADJ
iajs-1816	125	3	∎	∎	PROPN
iajs-1816	125	4	references	reference	NOUN
iajs-1816	125	5	[	[	X
iajs-1816	125	6	1	1	NUM
iajs-1816	125	7	]	]	SYM
iajs-1816	125	8	vd	vd	NOUN
iajs-1816	125	9	.	.	PUNCT
iajs-1816	126	1	estruch	estruch	ADJ
iajs-1816	126	2	and	and	CCONJ
iajs-1816	126	3	a.vidal	a.vidal	ADJ
iajs-1816	126	4	,	,	PUNCT
iajs-1816	126	5	“	"	PUNCT
iajs-1816	126	6	a	a	DET
iajs-1816	126	7	note	note	NOUN
iajs-1816	126	8	on	on	ADP
iajs-1816	126	9	fixed	fix	VERB
iajs-1816	126	10	fuzzy	fuzzy	ADJ
iajs-1816	126	11	points	point	NOUN
iajs-1816	126	12	for	for	ADP
iajs-1816	126	13	fuzzy	fuzzy	ADJ
iajs-1816	126	14	mappings”,rend	mappings”,rend	PROPN
iajs-1816	126	15	.	.	PUNCT
iajs-1816	126	16	ist	ist	PROPN
iajs-1816	126	17	.	.	PUNCT
iajs-1816	126	18	mat	mat	PROPN
iajs-1816	126	19	.	.	PUNCT
iajs-1816	126	20	univ	univ	PROPN
iajs-1816	126	21	.	.	PUNCT
iajs-1816	127	1	trieste.32,39	trieste.32,39	NOUN
iajs-1816	127	2	-	-	PUNCT
iajs-1816	127	3	45,2001	45,2001	VERB
iajs-1816	127	4	.	.	PUNCT
iajs-1816	128	1	[	[	X
iajs-1816	128	2	2	2	NUM
iajs-1816	128	3	]	]	X
iajs-1816	128	4	jungck	jungck	NOUN
iajs-1816	128	5	,	,	PUNCT
iajs-1816	128	6	g	g	NOUN
iajs-1816	128	7	commuting	commuting	NOUN
iajs-1816	128	8	mappings	mapping	NOUN
iajs-1816	128	9	and	and	CCONJ
iajs-1816	128	10	fixed	fix	VERB
iajs-1816	128	11	points	point	NOUN
iajs-1816	128	12	,	,	PUNCT
iajs-1816	128	13	the	the	DET
iajs-1816	128	14	american	american	PROPN
iajs-1816	128	15	mathematical	mathematical	PROPN
iajs-1816	128	16	monthly,.83	monthly,.83	PROPN
iajs-1816	128	17	.	.	PUNCT
iajs-1816	129	1	4,1976	4,1976	NOUN
iajs-1816	129	2	,	,	PUNCT
iajs-1816	129	3	261	261	NUM
iajs-1816	129	4	-	-	SYM
iajs-1816	129	5	263	263	NUM
iajs-1816	130	1	[	[	SYM
iajs-1816	130	2	3	3	NUM
iajs-1816	130	3	]	]	PUNCT
iajs-1816	130	4	l.a.zadeh	l.a.zadeh	NOUN
iajs-1816	130	5	,	,	PUNCT
iajs-1816	130	6	probability	probability	NOUN
iajs-1816	130	7	measures	measure	NOUN
iajs-1816	130	8	of	of	ADP
iajs-1816	130	9	fuzzy	fuzzy	ADJ
iajs-1816	130	10	events	event	NOUN
iajs-1816	130	11	,	,	PUNCT
iajs-1816	130	12	j.math.anal.appl.23,421427,.1968	j.math.anal.appl.23,421427,.1968	NOUN
iajs-1816	131	1	[	[	X
iajs-1816	131	2	4	4	NUM
iajs-1816	131	3	]	]	X
iajs-1816	131	4	s.heilpern	s.heilpern	ADJ
iajs-1816	131	5	,	,	PUNCT
iajs-1816	131	6	fuzzy	fuzzy	ADJ
iajs-1816	131	7	mappings	mapping	NOUN
iajs-1816	131	8	and	and	CCONJ
iajs-1816	131	9	fixed	fix	VERB
iajs-1816	131	10	point	point	NOUN
iajs-1816	131	11	theorem	theorem	VERB
iajs-1816	131	12	,	,	PUNCT
iajs-1816	131	13	j.math	j.math	NOUN
iajs-1816	131	14	.	.	PUNCT
iajs-1816	132	1	anal.83	anal.83	NOUN
iajs-1816	132	2	,	,	PUNCT
iajs-1816	132	3	566	566	NUM
iajs-1816	132	4	-	-	SYM
iajs-1816	132	5	569	569	NUM
iajs-1816	132	6	.	.	PUNCT
iajs-1816	132	7	1981	1981	NUM
iajs-1816	132	8	  	  	SPACE