id	sid	tid	token	lemma	pos
ejde-76	1	1	electronic	electronic	ADJ
ejde-76	1	2	journal	journal	NOUN
ejde-76	1	3	of	of	ADP
ejde-76	1	4	differential	differential	ADJ
ejde-76	1	5	equations	equation	NOUN
ejde-76	1	6	,	,	PUNCT
ejde-76	1	7	vol	vol	NOUN
ejde-76	1	8	.	.	PUNCT
ejde-76	1	9	2022	2022	NUM
ejde-76	1	10	(	(	PUNCT
ejde-76	1	11	2022	2022	NUM
ejde-76	1	12	)	)	PUNCT
ejde-76	1	13	,	,	PUNCT
ejde-76	1	14	no	no	INTJ
ejde-76	1	15	.	.	NOUN
ejde-76	1	16	03	03	NUM
ejde-76	1	17	,	,	PUNCT
ejde-76	1	18	pp	pp	ADJ
ejde-76	1	19	.	.	PUNCT
ejde-76	2	1	1–10	1–10	PROPN
ejde-76	2	2	.	.	PUNCT
ejde-76	3	1	issn	issn	PROPN
ejde-76	3	2	:	:	PUNCT
ejde-76	3	3	1072	1072	NUM
ejde-76	3	4	-	-	SYM
ejde-76	3	5	6691	6691	NUM
ejde-76	3	6	.	.	PUNCT
ejde-76	4	1	url	url	PROPN
ejde-76	4	2	:	:	PUNCT
ejde-76	4	3	http://ejde.math.txstate.edu	http://ejde.math.txstate.edu	PROPN
ejde-76	4	4	or	or	CCONJ
ejde-76	4	5	http://ejde.math.unt.edu	http://ejde.math.unt.edu	VERB
ejde-76	4	6	duality	duality	NOUN
ejde-76	4	7	arguments	argument	NOUN
ejde-76	4	8	for	for	ADP
ejde-76	4	9	well	well	NOUN
ejde-76	4	10	-	-	PUNCT
ejde-76	4	11	posedness	posedness	NOUN
ejde-76	4	12	of	of	ADP
ejde-76	4	13	history	history	NOUN
ejde-76	4	14	-	-	PUNCT
ejde-76	4	15	dependent	dependent	ADJ
ejde-76	4	16	variational	variational	ADJ
ejde-76	4	17	inequalities	inequality	NOUN
ejde-76	4	18	rong	rong	PROPN
ejde-76	4	19	hu	hu	PROPN
ejde-76	4	20	,	,	PUNCT
ejde-76	4	21	mircea	mircea	PROPN
ejde-76	4	22	sofonea	sofonea	PROPN
ejde-76	4	23	abstract	abstract	PROPN
ejde-76	4	24	.	.	PUNCT
ejde-76	5	1	in	in	ADP
ejde-76	5	2	this	this	DET
ejde-76	5	3	article	article	NOUN
ejde-76	5	4	we	we	PRON
ejde-76	5	5	introduce	introduce	VERB
ejde-76	5	6	a	a	DET
ejde-76	5	7	concept	concept	NOUN
ejde-76	5	8	of	of	ADP
ejde-76	5	9	dual	dual	ADJ
ejde-76	5	10	problems	problem	NOUN
ejde-76	5	11	in	in	ADP
ejde-76	5	12	metric	metric	ADJ
ejde-76	5	13	spaces	space	NOUN
ejde-76	5	14	.	.	PUNCT
ejde-76	6	1	then	then	ADV
ejde-76	6	2	we	we	PRON
ejde-76	6	3	state	state	VERB
ejde-76	6	4	and	and	CCONJ
ejde-76	6	5	prove	prove	VERB
ejde-76	6	6	an	an	DET
ejde-76	6	7	equivalence	equivalence	NOUN
ejde-76	6	8	result	result	NOUN
ejde-76	6	9	concerning	concern	VERB
ejde-76	6	10	their	their	PRON
ejde-76	6	11	wellposedness	wellposedness	NOUN
ejde-76	6	12	with	with	ADP
ejde-76	6	13	respect	respect	NOUN
ejde-76	6	14	to	to	ADP
ejde-76	6	15	appropriate	appropriate	ADJ
ejde-76	6	16	tykhonov	tykhonov	ADJ
ejde-76	6	17	triples	triple	NOUN
ejde-76	6	18	.	.	PUNCT
ejde-76	7	1	we	we	PRON
ejde-76	7	2	exemplify	exemplify	VERB
ejde-76	7	3	this	this	DET
ejde-76	7	4	result	result	NOUN
ejde-76	7	5	in	in	ADP
ejde-76	7	6	the	the	DET
ejde-76	7	7	study	study	NOUN
ejde-76	7	8	of	of	ADP
ejde-76	7	9	a	a	DET
ejde-76	7	10	history	history	NOUN
ejde-76	7	11	-	-	PUNCT
ejde-76	7	12	dependent	dependent	ADJ
ejde-76	7	13	variational	variational	ADJ
ejde-76	7	14	inequality	inequality	NOUN
ejde-76	7	15	with	with	ADP
ejde-76	7	16	timedependent	timedependent	NOUN
ejde-76	7	17	constraints	constraint	NOUN
ejde-76	7	18	,	,	PUNCT
ejde-76	7	19	for	for	ADP
ejde-76	7	20	which	which	PRON
ejde-76	7	21	the	the	DET
ejde-76	7	22	dual	dual	ADJ
ejde-76	7	23	problem	problem	NOUN
ejde-76	7	24	is	be	AUX
ejde-76	7	25	in	in	ADP
ejde-76	7	26	a	a	DET
ejde-76	7	27	form	form	NOUN
ejde-76	7	28	of	of	ADP
ejde-76	7	29	a	a	DET
ejde-76	7	30	historydependent	historydependent	ADJ
ejde-76	7	31	inclusion	inclusion	NOUN
ejde-76	7	32	.	.	PUNCT
ejde-76	8	1	this	this	PRON
ejde-76	8	2	allows	allow	VERB
ejde-76	8	3	us	we	PRON
ejde-76	8	4	to	to	PART
ejde-76	8	5	deduce	deduce	VERB
ejde-76	8	6	a	a	DET
ejde-76	8	7	convergence	convergence	NOUN
ejde-76	8	8	result	result	NOUN
ejde-76	8	9	which	which	PRON
ejde-76	8	10	provides	provide	VERB
ejde-76	8	11	the	the	DET
ejde-76	8	12	continuous	continuous	ADJ
ejde-76	8	13	dependence	dependence	NOUN
ejde-76	8	14	of	of	ADP
ejde-76	8	15	the	the	DET
ejde-76	8	16	solution	solution	NOUN
ejde-76	8	17	with	with	ADP
ejde-76	8	18	respect	respect	NOUN
ejde-76	8	19	to	to	ADP
ejde-76	8	20	the	the	DET
ejde-76	8	21	data	datum	NOUN
ejde-76	8	22	.	.	PUNCT
ejde-76	9	1	we	we	PRON
ejde-76	9	2	end	end	VERB
ejde-76	9	3	this	this	DET
ejde-76	9	4	paper	paper	NOUN
ejde-76	9	5	with	with	ADP
ejde-76	9	6	an	an	DET
ejde-76	9	7	example	example	NOUN
ejde-76	9	8	which	which	PRON
ejde-76	9	9	represents	represent	VERB
ejde-76	9	10	an	an	DET
ejde-76	9	11	evidence	evidence	NOUN
ejde-76	9	12	of	of	ADP
ejde-76	9	13	our	our	PRON
ejde-76	9	14	abstract	abstract	ADJ
ejde-76	9	15	results	result	NOUN
ejde-76	9	16	.	.	PUNCT
ejde-76	10	1	1	1	X
ejde-76	10	2	.	.	X
ejde-76	10	3	introduction	introduction	NOUN
ejde-76	10	4	the	the	DET
ejde-76	10	5	concept	concept	NOUN
ejde-76	10	6	of	of	ADP
ejde-76	10	7	well	well	NOUN
ejde-76	10	8	-	-	PUNCT
ejde-76	10	9	posedness	posedness	NOUN
ejde-76	10	10	with	with	ADP
ejde-76	10	11	respect	respect	NOUN
ejde-76	10	12	to	to	ADP
ejde-76	10	13	a	a	DET
ejde-76	10	14	tykhonov	tykhonov	NOUN
ejde-76	10	15	triple	triple	NOUN
ejde-76	10	16	was	be	AUX
ejde-76	10	17	introduced	introduce	VERB
ejde-76	10	18	in	in	ADP
ejde-76	10	19	[	[	X
ejde-76	10	20	14	14	NUM
ejde-76	10	21	]	]	PUNCT
ejde-76	10	22	.	.	PUNCT
ejde-76	11	1	it	it	PRON
ejde-76	11	2	extends	extend	VERB
ejde-76	11	3	the	the	DET
ejde-76	11	4	concept	concept	NOUN
ejde-76	11	5	of	of	ADP
ejde-76	11	6	well	well	NOUN
ejde-76	11	7	-	-	PUNCT
ejde-76	11	8	posedness	posedness	NOUN
ejde-76	11	9	for	for	ADP
ejde-76	11	10	a	a	DET
ejde-76	11	11	minimization	minimization	NOUN
ejde-76	11	12	problem	problem	NOUN
ejde-76	11	13	,	,	PUNCT
ejde-76	11	14	introduced	introduce	VERB
ejde-76	11	15	in	in	ADP
ejde-76	11	16	the	the	DET
ejde-76	11	17	pioneering	pioneering	ADJ
ejde-76	11	18	work	work	NOUN
ejde-76	11	19	[	[	X
ejde-76	11	20	12	12	NUM
ejde-76	11	21	]	]	PUNCT
ejde-76	11	22	as	as	ADV
ejde-76	11	23	well	well	ADV
ejde-76	11	24	as	as	ADP
ejde-76	11	25	the	the	DET
ejde-76	11	26	concepts	concept	NOUN
ejde-76	11	27	of	of	ADP
ejde-76	11	28	well	well	ADV
ejde-76	11	29	-	-	PUNCT
ejde-76	11	30	posedness	posedness	NOUN
ejde-76	11	31	used	use	VERB
ejde-76	11	32	in	in	ADP
ejde-76	11	33	[	[	X
ejde-76	11	34	1	1	NUM
ejde-76	11	35	,	,	PUNCT
ejde-76	11	36	8	8	NUM
ejde-76	11	37	,	,	PUNCT
ejde-76	11	38	15	15	NUM
ejde-76	11	39	]	]	PUNCT
ejde-76	11	40	for	for	ADP
ejde-76	11	41	various	various	ADJ
ejde-76	11	42	optimization	optimization	NOUN
ejde-76	11	43	problems	problem	NOUN
ejde-76	11	44	and	and	CCONJ
ejde-76	11	45	[	[	X
ejde-76	11	46	2	2	NUM
ejde-76	11	47	,	,	PUNCT
ejde-76	11	48	3	3	NUM
ejde-76	11	49	,	,	PUNCT
ejde-76	11	50	4	4	NUM
ejde-76	11	51	,	,	PUNCT
ejde-76	11	52	5	5	NUM
ejde-76	11	53	,	,	PUNCT
ejde-76	11	54	6	6	NUM
ejde-76	11	55	,	,	PUNCT
ejde-76	11	56	7	7	NUM
ejde-76	11	57	,	,	PUNCT
ejde-76	11	58	13	13	NUM
ejde-76	11	59	]	]	PUNCT
ejde-76	11	60	for	for	ADP
ejde-76	11	61	various	various	ADJ
ejde-76	11	62	classes	class	NOUN
ejde-76	11	63	of	of	ADP
ejde-76	11	64	inequalities	inequality	NOUN
ejde-76	11	65	.	.	PUNCT
ejde-76	12	1	this	this	DET
ejde-76	12	2	abstract	abstract	ADJ
ejde-76	12	3	concept	concept	NOUN
ejde-76	12	4	was	be	AUX
ejde-76	12	5	applied	apply	VERB
ejde-76	12	6	in	in	ADP
ejde-76	12	7	[	[	X
ejde-76	12	8	10	10	NUM
ejde-76	12	9	]	]	PUNCT
ejde-76	12	10	in	in	ADP
ejde-76	12	11	the	the	DET
ejde-76	12	12	study	study	NOUN
ejde-76	12	13	of	of	ADP
ejde-76	12	14	variational	variational	ADJ
ejde-76	12	15	inequalities	inequality	NOUN
ejde-76	12	16	governed	govern	VERB
ejde-76	12	17	by	by	ADP
ejde-76	12	18	a	a	DET
ejde-76	12	19	history	history	NOUN
ejde-76	12	20	-	-	PUNCT
ejde-76	12	21	dependent	dependent	ADJ
ejde-76	12	22	operator	operator	NOUN
ejde-76	12	23	,	,	PUNCT
ejde-76	12	24	the	the	DET
ejde-76	12	25	so	so	ADV
ejde-76	12	26	-	-	PUNCT
ejde-76	12	27	called	call	VERB
ejde-76	12	28	history	history	NOUN
ejde-76	12	29	-	-	PUNCT
ejde-76	12	30	dependent	dependent	ADJ
ejde-76	12	31	variational	variational	ADJ
ejde-76	12	32	inequalities	inequality	NOUN
ejde-76	12	33	.	.	PUNCT
ejde-76	13	1	there	there	ADV
ejde-76	13	2	,	,	PUNCT
ejde-76	13	3	the	the	DET
ejde-76	13	4	well	well	NOUN
ejde-76	13	5	-	-	PUNCT
ejde-76	13	6	posedness	posedness	NOUN
ejde-76	13	7	with	with	ADP
ejde-76	13	8	respect	respect	NOUN
ejde-76	13	9	to	to	ADP
ejde-76	13	10	several	several	ADJ
ejde-76	13	11	tykhonov	tykhonov	NOUN
ejde-76	13	12	triples	triple	NOUN
ejde-76	13	13	was	be	AUX
ejde-76	13	14	studied	study	VERB
ejde-76	13	15	and	and	CCONJ
ejde-76	13	16	a	a	DET
ejde-76	13	17	strategy	strategy	NOUN
ejde-76	13	18	which	which	PRON
ejde-76	13	19	allows	allow	VERB
ejde-76	13	20	to	to	PART
ejde-76	13	21	deduce	deduce	VERB
ejde-76	13	22	convergence	convergence	NOUN
ejde-76	13	23	results	result	NOUN
ejde-76	13	24	was	be	AUX
ejde-76	13	25	discussed	discuss	VERB
ejde-76	13	26	.	.	PUNCT
ejde-76	14	1	an	an	DET
ejde-76	14	2	existence	existence	NOUN
ejde-76	14	3	and	and	CCONJ
ejde-76	14	4	uniqueness	uniqueness	NOUN
ejde-76	14	5	result	result	NOUN
ejde-76	14	6	for	for	SCONJ
ejde-76	14	7	a	a	DET
ejde-76	14	8	class	class	NOUN
ejde-76	14	9	of	of	ADP
ejde-76	14	10	history	history	NOUN
ejde-76	14	11	-	-	PUNCT
ejde-76	14	12	dependent	dependent	ADJ
ejde-76	14	13	inclusions	inclusion	NOUN
ejde-76	14	14	was	be	AUX
ejde-76	14	15	obtained	obtain	VERB
ejde-76	14	16	in	in	ADP
ejde-76	14	17	the	the	DET
ejde-76	14	18	recent	recent	ADJ
ejde-76	14	19	paper	paper	NOUN
ejde-76	15	1	[	[	X
ejde-76	15	2	9	9	NUM
ejde-76	15	3	]	]	PUNCT
ejde-76	15	4	.	.	PUNCT
ejde-76	16	1	this	this	DET
ejde-76	16	2	article	article	NOUN
ejde-76	16	3	represents	represent	VERB
ejde-76	16	4	a	a	DET
ejde-76	16	5	continuation	continuation	NOUN
ejde-76	16	6	of	of	ADP
ejde-76	16	7	[	[	X
ejde-76	16	8	9	9	NUM
ejde-76	16	9	,	,	PUNCT
ejde-76	16	10	10	10	NUM
ejde-76	16	11	,	,	PUNCT
ejde-76	16	12	14	14	NUM
ejde-76	16	13	]	]	PUNCT
ejde-76	16	14	.	.	PUNCT
ejde-76	17	1	here	here	ADV
ejde-76	17	2	,	,	PUNCT
ejde-76	17	3	we	we	PRON
ejde-76	17	4	complete	complete	VERB
ejde-76	17	5	the	the	DET
ejde-76	17	6	theoretical	theoretical	ADJ
ejde-76	17	7	study	study	NOUN
ejde-76	17	8	initiated	initiate	VERB
ejde-76	17	9	in	in	ADP
ejde-76	17	10	[	[	X
ejde-76	17	11	14	14	NUM
ejde-76	17	12	]	]	PUNCT
ejde-76	17	13	by	by	ADP
ejde-76	17	14	studying	study	VERB
ejde-76	17	15	the	the	DET
ejde-76	17	16	well	well	NOUN
ejde-76	17	17	-	-	PUNCT
ejde-76	17	18	posedness	posedness	NOUN
ejde-76	17	19	of	of	ADP
ejde-76	17	20	a	a	DET
ejde-76	17	21	couple	couple	NOUN
ejde-76	17	22	of	of	ADP
ejde-76	17	23	problems	problem	NOUN
ejde-76	17	24	in	in	ADP
ejde-76	17	25	duality	duality	NOUN
ejde-76	17	26	.	.	PUNCT
ejde-76	18	1	the	the	DET
ejde-76	18	2	idea	idea	NOUN
ejde-76	18	3	is	be	AUX
ejde-76	18	4	to	to	PART
ejde-76	18	5	deduce	deduce	VERB
ejde-76	18	6	the	the	DET
ejde-76	18	7	well	well	NOUN
ejde-76	18	8	-	-	PUNCT
ejde-76	18	9	posedness	posedness	NOUN
ejde-76	18	10	of	of	ADP
ejde-76	18	11	a	a	DET
ejde-76	18	12	problem	problem	NOUN
ejde-76	18	13	p	p	NOUN
ejde-76	18	14	by	by	ADP
ejde-76	18	15	using	use	VERB
ejde-76	18	16	the	the	DET
ejde-76	18	17	well	well	NOUN
ejde-76	18	18	-	-	PUNCT
ejde-76	18	19	posedness	posedness	NOUN
ejde-76	18	20	of	of	ADP
ejde-76	18	21	a	a	DET
ejde-76	18	22	different	different	ADJ
ejde-76	18	23	problem	problem	NOUN
ejde-76	18	24	q	q	NOUN
ejde-76	18	25	,	,	PUNCT
ejde-76	18	26	called	call	VERB
ejde-76	18	27	the	the	DET
ejde-76	18	28	dual	dual	ADJ
ejde-76	18	29	of	of	ADP
ejde-76	18	30	p.	p.	NOUN
ejde-76	18	31	the	the	DET
ejde-76	18	32	interest	interest	NOUN
ejde-76	18	33	in	in	ADP
ejde-76	18	34	this	this	DET
ejde-76	18	35	method	method	NOUN
ejde-76	18	36	arises	arise	VERB
ejde-76	18	37	in	in	ADP
ejde-76	18	38	the	the	DET
ejde-76	18	39	fact	fact	NOUN
ejde-76	18	40	that	that	SCONJ
ejde-76	18	41	in	in	ADP
ejde-76	18	42	several	several	ADJ
ejde-76	18	43	cases	case	NOUN
ejde-76	18	44	we	we	PRON
ejde-76	18	45	have	have	AUX
ejde-76	18	46	a	a	DET
ejde-76	18	47	number	number	NOUN
ejde-76	18	48	of	of	ADP
ejde-76	18	49	results	result	NOUN
ejde-76	18	50	in	in	ADP
ejde-76	18	51	the	the	DET
ejde-76	18	52	study	study	NOUN
ejde-76	18	53	of	of	ADP
ejde-76	18	54	problem	problem	NOUN
ejde-76	18	55	q	q	X
ejde-76	18	56	which	which	PRON
ejde-76	18	57	can	can	AUX
ejde-76	18	58	be	be	AUX
ejde-76	18	59	useful	useful	ADJ
ejde-76	18	60	in	in	ADP
ejde-76	18	61	the	the	DET
ejde-76	18	62	analysis	analysis	NOUN
ejde-76	18	63	of	of	ADP
ejde-76	18	64	problem	problem	NOUN
ejde-76	18	65	p.	p.	NOUN
ejde-76	18	66	this	this	PRON
ejde-76	18	67	represents	represent	VERB
ejde-76	18	68	the	the	DET
ejde-76	18	69	first	first	ADJ
ejde-76	18	70	trait	trait	NOUN
ejde-76	18	71	of	of	ADP
ejde-76	18	72	novelty	novelty	NOUN
ejde-76	18	73	of	of	ADP
ejde-76	18	74	the	the	DET
ejde-76	18	75	current	current	ADJ
ejde-76	18	76	paper	paper	NOUN
ejde-76	18	77	.	.	PUNCT
ejde-76	19	1	the	the	DET
ejde-76	19	2	second	second	ADJ
ejde-76	19	3	novelty	novelty	NOUN
ejde-76	19	4	is	be	AUX
ejde-76	19	5	that	that	SCONJ
ejde-76	19	6	we	we	PRON
ejde-76	19	7	use	use	VERB
ejde-76	19	8	these	these	DET
ejde-76	19	9	arguments	argument	NOUN
ejde-76	19	10	in	in	ADP
ejde-76	19	11	the	the	DET
ejde-76	19	12	study	study	NOUN
ejde-76	19	13	of	of	ADP
ejde-76	19	14	a	a	DET
ejde-76	19	15	history	history	NOUN
ejde-76	19	16	-	-	PUNCT
ejde-76	19	17	dependent	dependent	ADJ
ejde-76	19	18	variational	variational	ADJ
ejde-76	19	19	inequality	inequality	NOUN
ejde-76	19	20	which	which	PRON
ejde-76	19	21	is	be	AUX
ejde-76	19	22	more	more	ADV
ejde-76	19	23	general	general	ADJ
ejde-76	19	24	than	than	ADP
ejde-76	19	25	the	the	DET
ejde-76	19	26	inequality	inequality	NOUN
ejde-76	19	27	in	in	ADP
ejde-76	19	28	[	[	X
ejde-76	19	29	10	10	NUM
ejde-76	19	30	]	]	PUNCT
ejde-76	19	31	.	.	PUNCT
ejde-76	20	1	indeed	indeed	ADV
ejde-76	20	2	,	,	PUNCT
ejde-76	20	3	in	in	ADP
ejde-76	20	4	contrast	contrast	NOUN
ejde-76	20	5	with	with	ADP
ejde-76	20	6	[	[	X
ejde-76	20	7	10	10	NUM
ejde-76	20	8	]	]	PUNCT
ejde-76	20	9	,	,	PUNCT
ejde-76	20	10	the	the	DET
ejde-76	20	11	inequality	inequality	NOUN
ejde-76	20	12	we	we	PRON
ejde-76	20	13	consider	consider	VERB
ejde-76	20	14	in	in	ADP
ejde-76	20	15	this	this	DET
ejde-76	20	16	paper	paper	NOUN
ejde-76	20	17	involves	involve	VERB
ejde-76	20	18	a	a	DET
ejde-76	20	19	time	time	NOUN
ejde-76	20	20	-	-	PUNCT
ejde-76	20	21	dependent	dependent	ADJ
ejde-76	20	22	set	set	NOUN
ejde-76	20	23	of	of	ADP
ejde-76	20	24	constraints	constraint	NOUN
ejde-76	20	25	.	.	PUNCT
ejde-76	21	1	as	as	ADP
ejde-76	21	2	a	a	DET
ejde-76	21	3	consequence	consequence	NOUN
ejde-76	21	4	,	,	PUNCT
ejde-76	21	5	the	the	DET
ejde-76	21	6	dual	dual	ADJ
ejde-76	21	7	problem	problem	NOUN
ejde-76	21	8	of	of	ADP
ejde-76	21	9	this	this	DET
ejde-76	21	10	inequality	inequality	NOUN
ejde-76	21	11	is	be	AUX
ejde-76	21	12	given	give	VERB
ejde-76	21	13	by	by	ADP
ejde-76	21	14	a	a	DET
ejde-76	21	15	history	history	NOUN
ejde-76	21	16	-	-	PUNCT
ejde-76	21	17	dependent	dependent	ADJ
ejde-76	21	18	inclusion	inclusion	NOUN
ejde-76	21	19	,	,	PUNCT
ejde-76	21	20	already	already	ADV
ejde-76	21	21	studied	study	VERB
ejde-76	21	22	in	in	ADP
ejde-76	21	23	[	[	PUNCT
ejde-76	21	24	9	9	NUM
ejde-76	21	25	]	]	PUNCT
ejde-76	21	26	.	.	PUNCT
ejde-76	22	1	2010	2010	NUM
ejde-76	22	2	mathematics	mathematic	NOUN
ejde-76	22	3	subject	subject	NOUN
ejde-76	22	4	classification	classification	NOUN
ejde-76	22	5	.	.	PUNCT
ejde-76	23	1	35m86	35m86	NUM
ejde-76	23	2	,	,	PUNCT
ejde-76	23	3	49j40	49j40	NUM
ejde-76	23	4	,	,	PUNCT
ejde-76	23	5	47j20	47j20	NUM
ejde-76	23	6	.	.	PUNCT
ejde-76	24	1	key	key	ADJ
ejde-76	24	2	words	word	NOUN
ejde-76	24	3	and	and	CCONJ
ejde-76	24	4	phrases	phrase	NOUN
ejde-76	24	5	.	.	PUNCT
ejde-76	25	1	history	history	NOUN
ejde-76	25	2	-	-	PUNCT
ejde-76	25	3	dependent	dependent	ADJ
ejde-76	25	4	variational	variational	ADJ
ejde-76	25	5	inequality	inequality	NOUN
ejde-76	25	6	;	;	PUNCT
ejde-76	25	7	dual	dual	ADJ
ejde-76	25	8	problem	problem	NOUN
ejde-76	25	9	;	;	PUNCT
ejde-76	25	10	history	history	NOUN
ejde-76	25	11	-	-	PUNCT
ejde-76	25	12	dependent	dependent	ADJ
ejde-76	25	13	inclusion	inclusion	NOUN
ejde-76	25	14	;	;	PUNCT
ejde-76	25	15	tykhonov	tykhonov	ADJ
ejde-76	25	16	well	well	NOUN
ejde-76	25	17	-	-	PUNCT
ejde-76	25	18	posedness	posedness	NOUN
ejde-76	25	19	;	;	PUNCT
ejde-76	25	20	convergence	convergence	NOUN
ejde-76	25	21	results	result	NOUN
ejde-76	25	22	.	.	PUNCT
ejde-76	26	1	©	©	NOUN
ejde-76	26	2	2022	2022	NUM
ejde-76	26	3	.	.	PUNCT
ejde-76	27	1	this	this	DET
ejde-76	27	2	work	work	NOUN
ejde-76	27	3	is	be	AUX
ejde-76	27	4	licensed	license	VERB
ejde-76	27	5	under	under	ADP
ejde-76	27	6	a	a	DET
ejde-76	27	7	cc	cc	NOUN
ejde-76	27	8	by	by	ADP
ejde-76	27	9	4.0	4.0	NUM
ejde-76	27	10	license	license	NOUN
ejde-76	27	11	.	.	PUNCT
ejde-76	28	1	submitted	submit	VERB
ejde-76	28	2	august	august	PROPN
ejde-76	28	3	19	19	NUM
ejde-76	28	4	,	,	PUNCT
ejde-76	28	5	2021	2021	NUM
ejde-76	28	6	.	.	PUNCT
ejde-76	29	1	published	publish	VERB
ejde-76	29	2	january	january	PROPN
ejde-76	29	3	6	6	NUM
ejde-76	29	4	,	,	PUNCT
ejde-76	29	5	2022	2022	NUM
ejde-76	29	6	.	.	PUNCT
ejde-76	30	1	1	1	NUM
ejde-76	30	2	2	2	NUM
ejde-76	30	3	r.	r.	PROPN
ejde-76	30	4	hu	hu	PROPN
ejde-76	30	5	,	,	PUNCT
ejde-76	30	6	m.	m.	PROPN
ejde-76	30	7	sofonea	sofonea	PROPN
ejde-76	30	8	ejde-2022/03	ejde-2022/03	PROPN
ejde-76	30	9	the	the	DET
ejde-76	30	10	rest	rest	NOUN
ejde-76	30	11	of	of	ADP
ejde-76	30	12	this	this	DET
ejde-76	30	13	article	article	NOUN
ejde-76	30	14	is	be	AUX
ejde-76	30	15	structured	structure	VERB
ejde-76	30	16	as	as	SCONJ
ejde-76	30	17	follows	follow	VERB
ejde-76	30	18	.	.	PUNCT
ejde-76	31	1	in	in	ADP
ejde-76	31	2	section	section	NOUN
ejde-76	31	3	2	2	NUM
ejde-76	31	4	we	we	PRON
ejde-76	31	5	introduce	introduce	VERB
ejde-76	31	6	the	the	DET
ejde-76	31	7	concept	concept	NOUN
ejde-76	31	8	of	of	ADP
ejde-76	31	9	dual	dual	ADJ
ejde-76	31	10	problems	problem	NOUN
ejde-76	31	11	in	in	ADP
ejde-76	31	12	metric	metric	ADJ
ejde-76	31	13	spaces	space	NOUN
ejde-76	31	14	.	.	PUNCT
ejde-76	32	1	then	then	ADV
ejde-76	32	2	we	we	PRON
ejde-76	32	3	state	state	VERB
ejde-76	32	4	and	and	CCONJ
ejde-76	32	5	prove	prove	VERB
ejde-76	32	6	an	an	DET
ejde-76	32	7	equivalence	equivalence	NOUN
ejde-76	32	8	result	result	NOUN
ejde-76	32	9	,	,	PUNCT
ejde-76	32	10	theorem	theorem	VERB
ejde-76	32	11	2.2	2.2	NUM
ejde-76	32	12	.	.	PUNCT
ejde-76	33	1	in	in	ADP
ejde-76	33	2	section	section	NOUN
ejde-76	33	3	3	3	NUM
ejde-76	33	4	we	we	PRON
ejde-76	33	5	introduce	introduce	VERB
ejde-76	33	6	a	a	DET
ejde-76	33	7	history	history	NOUN
ejde-76	33	8	-	-	PUNCT
ejde-76	33	9	dependent	dependent	ADJ
ejde-76	33	10	variational	variational	ADJ
ejde-76	33	11	inequality	inequality	NOUN
ejde-76	33	12	p	p	NOUN
ejde-76	33	13	,	,	PUNCT
ejde-76	33	14	then	then	ADV
ejde-76	33	15	we	we	PRON
ejde-76	33	16	use	use	VERB
ejde-76	33	17	theorem	theorem	ADJ
ejde-76	33	18	2.2	2.2	NUM
ejde-76	33	19	to	to	PART
ejde-76	33	20	prove	prove	VERB
ejde-76	33	21	its	its	PRON
ejde-76	33	22	well	well	NOUN
ejde-76	33	23	-	-	PUNCT
ejde-76	33	24	posedness	posedness	NOUN
ejde-76	33	25	.	.	PUNCT
ejde-76	34	1	we	we	PRON
ejde-76	34	2	complete	complete	VERB
ejde-76	34	3	our	our	PRON
ejde-76	34	4	study	study	NOUN
ejde-76	34	5	in	in	ADP
ejde-76	34	6	section	section	NOUN
ejde-76	34	7	4	4	NUM
ejde-76	34	8	where	where	SCONJ
ejde-76	34	9	we	we	PRON
ejde-76	34	10	prove	prove	VERB
ejde-76	34	11	a	a	DET
ejde-76	34	12	convergence	convergence	NOUN
ejde-76	34	13	result	result	NOUN
ejde-76	34	14	which	which	PRON
ejde-76	34	15	states	state	VERB
ejde-76	34	16	the	the	DET
ejde-76	34	17	continuous	continuous	ADJ
ejde-76	34	18	dependence	dependence	NOUN
ejde-76	34	19	of	of	ADP
ejde-76	34	20	the	the	DET
ejde-76	34	21	solution	solution	NOUN
ejde-76	34	22	of	of	ADP
ejde-76	34	23	p	p	NOUN
ejde-76	34	24	with	with	ADP
ejde-76	34	25	respect	respect	NOUN
ejde-76	34	26	to	to	ADP
ejde-76	34	27	the	the	DET
ejde-76	34	28	data	datum	NOUN
ejde-76	34	29	.	.	PUNCT
ejde-76	35	1	we	we	PRON
ejde-76	35	2	end	end	VERB
ejde-76	35	3	this	this	DET
ejde-76	35	4	section	section	NOUN
ejde-76	35	5	by	by	ADP
ejde-76	35	6	recalling	recall	VERB
ejde-76	35	7	some	some	DET
ejde-76	35	8	basic	basic	ADJ
ejde-76	35	9	definitions	definition	NOUN
ejde-76	35	10	which	which	PRON
ejde-76	35	11	will	will	AUX
ejde-76	35	12	be	be	AUX
ejde-76	35	13	crucial	crucial	ADJ
ejde-76	35	14	in	in	ADP
ejde-76	35	15	the	the	DET
ejde-76	35	16	rest	rest	NOUN
ejde-76	35	17	of	of	ADP
ejde-76	35	18	the	the	DET
ejde-76	35	19	paper	paper	NOUN
ejde-76	35	20	.	.	PUNCT
ejde-76	36	1	consider	consider	VERB
ejde-76	36	2	an	an	DET
ejde-76	36	3	abstract	abstract	ADJ
ejde-76	36	4	mathematical	mathematical	ADJ
ejde-76	36	5	objectm	objectm	ADV
ejde-76	36	6	,	,	PUNCT
ejde-76	36	7	called	call	VERB
ejde-76	36	8	generic	generic	ADJ
ejde-76	36	9	“	"	PUNCT
ejde-76	36	10	problem	problem	NOUN
ejde-76	36	11	”	"	PUNCT
ejde-76	36	12	,	,	PUNCT
ejde-76	36	13	defined	define	VERB
ejde-76	36	14	in	in	ADP
ejde-76	36	15	a	a	DET
ejde-76	36	16	metric	metric	ADJ
ejde-76	36	17	space	space	NOUN
ejde-76	36	18	(	(	PUNCT
ejde-76	36	19	z	z	NOUN
ejde-76	36	20	,	,	PUNCT
ejde-76	36	21	d	d	NOUN
ejde-76	36	22	)	)	PUNCT
ejde-76	36	23	.	.	PUNCT
ejde-76	37	1	problem	problem	NOUN
ejde-76	37	2	m	m	PROPN
ejde-76	37	3	could	could	AUX
ejde-76	37	4	be	be	AUX
ejde-76	37	5	an	an	DET
ejde-76	37	6	equation	equation	NOUN
ejde-76	37	7	,	,	PUNCT
ejde-76	37	8	a	a	DET
ejde-76	37	9	minimization	minimization	NOUN
ejde-76	37	10	problem	problem	NOUN
ejde-76	37	11	,	,	PUNCT
ejde-76	37	12	a	a	DET
ejde-76	37	13	fixed	fix	VERB
ejde-76	37	14	point	point	NOUN
ejde-76	37	15	problem	problem	NOUN
ejde-76	37	16	,	,	PUNCT
ejde-76	37	17	an	an	DET
ejde-76	37	18	inclusion	inclusion	NOUN
ejde-76	37	19	or	or	CCONJ
ejde-76	37	20	an	an	DET
ejde-76	37	21	inequality	inequality	NOUN
ejde-76	37	22	problem	problem	NOUN
ejde-76	37	23	,	,	PUNCT
ejde-76	37	24	for	for	ADP
ejde-76	37	25	instance	instance	NOUN
ejde-76	37	26	.	.	PUNCT
ejde-76	38	1	we	we	PRON
ejde-76	38	2	associate	associate	VERB
ejde-76	38	3	to	to	ADP
ejde-76	38	4	problem	problem	NOUN
ejde-76	38	5	m	m	VERB
ejde-76	38	6	the	the	DET
ejde-76	38	7	concept	concept	NOUN
ejde-76	38	8	of	of	ADP
ejde-76	38	9	“	"	PUNCT
ejde-76	38	10	solution	solution	NOUN
ejde-76	38	11	”	"	PUNCT
ejde-76	38	12	which	which	PRON
ejde-76	38	13	follows	follow	VERB
ejde-76	38	14	from	from	ADP
ejde-76	38	15	the	the	DET
ejde-76	38	16	context	context	NOUN
ejde-76	38	17	.	.	PUNCT
ejde-76	39	1	the	the	DET
ejde-76	39	2	concept	concept	NOUN
ejde-76	39	3	of	of	ADP
ejde-76	39	4	well	well	NOUN
ejde-76	39	5	-	-	PUNCT
ejde-76	39	6	posedness	posedness	NOUN
ejde-76	39	7	for	for	ADP
ejde-76	39	8	problemm	problemm	NOUN
ejde-76	39	9	is	be	AUX
ejde-76	39	10	provided	provide	VERB
ejde-76	39	11	by	by	ADP
ejde-76	39	12	the	the	DET
ejde-76	39	13	following	follow	VERB
ejde-76	39	14	definition	definition	NOUN
ejde-76	39	15	.	.	PUNCT
ejde-76	40	1	definition	definition	NOUN
ejde-76	40	2	1.1	1.1	NUM
ejde-76	40	3	.	.	PUNCT
ejde-76	41	1	(	(	PUNCT
ejde-76	41	2	a	a	X
ejde-76	41	3	)	)	PUNCT
ejde-76	41	4	a	a	DET
ejde-76	41	5	tykhonov	tykhonov	NOUN
ejde-76	41	6	triple	triple	NOUN
ejde-76	41	7	is	be	AUX
ejde-76	41	8	a	a	DET
ejde-76	41	9	mathematical	mathematical	ADJ
ejde-76	41	10	object	object	NOUN
ejde-76	41	11	of	of	ADP
ejde-76	41	12	the	the	DET
ejde-76	41	13	form	form	NOUN
ejde-76	41	14	t	t	NOUN
ejde-76	41	15	=	=	SYM
ejde-76	41	16	(	(	PUNCT
ejde-76	41	17	i	i	PROPN
ejde-76	41	18	,	,	PUNCT
ejde-76	41	19	ω	ω	PROPN
ejde-76	41	20	,	,	PUNCT
ejde-76	41	21	c	c	NOUN
ejde-76	41	22	)	)	PUNCT
ejde-76	41	23	where	where	SCONJ
ejde-76	41	24	i	i	PRON
ejde-76	41	25	is	be	AUX
ejde-76	41	26	a	a	DET
ejde-76	41	27	given	give	VERB
ejde-76	41	28	nonempty	nonempty	NOUN
ejde-76	41	29	set	set	VERB
ejde-76	41	30	,	,	PUNCT
ejde-76	41	31	ω	ω	NUM
ejde-76	41	32	:	:	PUNCT
ejde-76	41	33	i	i	PRON
ejde-76	41	34	→	→	SYM
ejde-76	41	35	2z	2z	PRON
ejde-76	41	36	is	be	AUX
ejde-76	41	37	a	a	DET
ejde-76	41	38	nonempty	nonempty	ADJ
ejde-76	41	39	set	set	NOUN
ejde-76	41	40	-	-	PUNCT
ejde-76	41	41	valued	value	VERB
ejde-76	41	42	operator	operator	NOUN
ejde-76	41	43	and	and	CCONJ
ejde-76	41	44	c	c	NOUN
ejde-76	41	45	is	be	AUX
ejde-76	41	46	a	a	DET
ejde-76	41	47	nonempty	nonempty	ADJ
ejde-76	41	48	subset	subset	NOUN
ejde-76	41	49	of	of	ADP
ejde-76	41	50	sequences	sequence	NOUN
ejde-76	41	51	with	with	ADP
ejde-76	41	52	elements	element	NOUN
ejde-76	41	53	in	in	ADP
ejde-76	41	54	i.	i.	PROPN
ejde-76	41	55	(	(	PUNCT
ejde-76	41	56	b	b	NOUN
ejde-76	41	57	)	)	PUNCT
ejde-76	41	58	given	give	VERB
ejde-76	41	59	a	a	DET
ejde-76	41	60	tykhonov	tykhonov	NOUN
ejde-76	41	61	triple	triple	NOUN
ejde-76	41	62	t	t	NOUN
ejde-76	42	1	=	=	SYM
ejde-76	42	2	(	(	PUNCT
ejde-76	42	3	i	i	PROPN
ejde-76	42	4	,	,	PUNCT
ejde-76	42	5	ω	ω	PROPN
ejde-76	42	6	,	,	PUNCT
ejde-76	42	7	c	c	NOUN
ejde-76	42	8	)	)	PUNCT
ejde-76	42	9	,	,	PUNCT
ejde-76	42	10	a	a	DET
ejde-76	42	11	sequence	sequence	NOUN
ejde-76	42	12	{	{	PUNCT
ejde-76	42	13	zn	zn	NOUN
ejde-76	42	14	}	}	PUNCT
ejde-76	42	15	⊂	⊂	PROPN
ejde-76	42	16	z	z	PROPN
ejde-76	42	17	is	be	AUX
ejde-76	42	18	called	call	VERB
ejde-76	42	19	a	a	DET
ejde-76	42	20	t	t	NOUN
ejde-76	42	21	-approximating	-approximate	VERB
ejde-76	42	22	sequence	sequence	NOUN
ejde-76	42	23	if	if	SCONJ
ejde-76	42	24	there	there	PRON
ejde-76	42	25	exists	exist	VERB
ejde-76	42	26	a	a	DET
ejde-76	42	27	sequence	sequence	NOUN
ejde-76	42	28	{	{	PUNCT
ejde-76	42	29	θn	θn	NOUN
ejde-76	42	30	}	}	PUNCT
ejde-76	42	31	∈	∈	PROPN
ejde-76	42	32	c	c	NOUN
ejde-76	42	33	such	such	ADJ
ejde-76	42	34	that	that	SCONJ
ejde-76	42	35	zn	zn	PROPN
ejde-76	42	36	∈	∈	PROPN
ejde-76	42	37	ω(θn	ω(θn	NUM
ejde-76	42	38	)	)	PUNCT
ejde-76	42	39	for	for	ADP
ejde-76	42	40	each	each	DET
ejde-76	42	41	n	n	PRON
ejde-76	42	42	∈	∈	PROPN
ejde-76	42	43	n.	n.	NOUN
ejde-76	42	44	(	(	PUNCT
ejde-76	42	45	c	c	NOUN
ejde-76	42	46	)	)	PUNCT
ejde-76	42	47	given	give	VERB
ejde-76	42	48	a	a	DET
ejde-76	42	49	tykhonov	tykhonov	NOUN
ejde-76	42	50	triple	triple	NOUN
ejde-76	42	51	t	t	NOUN
ejde-76	42	52	=	=	SYM
ejde-76	42	53	(	(	PUNCT
ejde-76	42	54	i	i	PROPN
ejde-76	42	55	,	,	PUNCT
ejde-76	42	56	ω	ω	PROPN
ejde-76	42	57	,	,	PUNCT
ejde-76	42	58	c	c	NOUN
ejde-76	42	59	)	)	PUNCT
ejde-76	42	60	,	,	PUNCT
ejde-76	42	61	problem	problem	NOUN
ejde-76	42	62	m	m	NOUN
ejde-76	42	63	is	be	AUX
ejde-76	42	64	said	say	VERB
ejde-76	42	65	to	to	PART
ejde-76	42	66	be	be	AUX
ejde-76	42	67	t	t	NOUN
ejde-76	42	68	-wellposed	-wellpose	VERB
ejde-76	42	69	if	if	SCONJ
ejde-76	42	70	it	it	PRON
ejde-76	42	71	has	have	VERB
ejde-76	42	72	a	a	DET
ejde-76	42	73	unique	unique	ADJ
ejde-76	42	74	solution	solution	NOUN
ejde-76	42	75	and	and	CCONJ
ejde-76	42	76	every	every	DET
ejde-76	42	77	t	t	NOUN
ejde-76	42	78	-approximating	-approximate	VERB
ejde-76	42	79	sequence	sequence	NOUN
ejde-76	42	80	converges	converge	VERB
ejde-76	42	81	in	in	ADP
ejde-76	42	82	z	z	NOUN
ejde-76	42	83	to	to	ADP
ejde-76	42	84	its	its	PRON
ejde-76	42	85	solution	solution	NOUN
ejde-76	42	86	.	.	PUNCT
ejde-76	43	1	for	for	ADP
ejde-76	43	2	a	a	DET
ejde-76	43	3	tykhonov	tykhonov	ADJ
ejde-76	43	4	triple	triple	NOUN
ejde-76	43	5	t	t	NOUN
ejde-76	43	6	=	=	SYM
ejde-76	43	7	(	(	PUNCT
ejde-76	43	8	i	i	PROPN
ejde-76	43	9	,	,	PUNCT
ejde-76	43	10	ω	ω	PROPN
ejde-76	43	11	,	,	PUNCT
ejde-76	43	12	c	c	NOUN
ejde-76	43	13	)	)	PUNCT
ejde-76	43	14	we	we	PRON
ejde-76	43	15	refer	refer	VERB
ejde-76	43	16	to	to	ADP
ejde-76	43	17	i	i	PRON
ejde-76	43	18	as	as	ADP
ejde-76	43	19	the	the	DET
ejde-76	43	20	set	set	NOUN
ejde-76	43	21	of	of	ADP
ejde-76	43	22	parameters	parameter	NOUN
ejde-76	43	23	;	;	PUNCT
ejde-76	43	24	the	the	DET
ejde-76	43	25	family	family	NOUN
ejde-76	43	26	of	of	ADP
ejde-76	43	27	sets	set	NOUN
ejde-76	43	28	{	{	PUNCT
ejde-76	43	29	ω(θ)}θ∈i	ω(θ)}θ∈i	PRON
ejde-76	43	30	represents	represent	VERB
ejde-76	43	31	the	the	DET
ejde-76	43	32	family	family	NOUN
ejde-76	43	33	of	of	ADP
ejde-76	43	34	approximating	approximate	VERB
ejde-76	43	35	sets	set	NOUN
ejde-76	43	36	;	;	PUNCT
ejde-76	43	37	besides	besides	ADV
ejde-76	43	38	,	,	PUNCT
ejde-76	43	39	we	we	PRON
ejde-76	43	40	say	say	VERB
ejde-76	43	41	that	that	SCONJ
ejde-76	43	42	c	c	PROPN
ejde-76	43	43	defines	define	VERB
ejde-76	43	44	the	the	DET
ejde-76	43	45	criterion	criterion	NOUN
ejde-76	43	46	of	of	ADP
ejde-76	43	47	convergence	convergence	NOUN
ejde-76	43	48	.	.	PUNCT
ejde-76	44	1	we	we	PRON
ejde-76	44	2	remark	remark	VERB
ejde-76	44	3	that	that	SCONJ
ejde-76	44	4	approximating	approximate	VERB
ejde-76	44	5	sequences	sequence	NOUN
ejde-76	44	6	always	always	ADV
ejde-76	44	7	exist	exist	VERB
ejde-76	44	8	since	since	SCONJ
ejde-76	44	9	,	,	PUNCT
ejde-76	44	10	by	by	ADP
ejde-76	44	11	assumption	assumption	NOUN
ejde-76	44	12	,	,	PUNCT
ejde-76	44	13	c	c	NOUN
ejde-76	44	14	6=	6=	PROPN
ejde-76	44	15	∅	∅	NOUN
ejde-76	44	16	and	and	CCONJ
ejde-76	44	17	,	,	PUNCT
ejde-76	44	18	moreover	moreover	ADV
ejde-76	44	19	,	,	PUNCT
ejde-76	44	20	for	for	SCONJ
ejde-76	44	21	any	any	DET
ejde-76	44	22	sequence	sequence	NOUN
ejde-76	44	23	{	{	PUNCT
ejde-76	44	24	θn	θn	NOUN
ejde-76	44	25	}	}	PUNCT
ejde-76	44	26	∈	∈	PROPN
ejde-76	44	27	c	c	NOUN
ejde-76	44	28	and	and	CCONJ
ejde-76	44	29	any	any	DET
ejde-76	44	30	n	n	CCONJ
ejde-76	44	31	∈	∈	PROPN
ejde-76	44	32	n	n	CCONJ
ejde-76	44	33	,	,	PUNCT
ejde-76	44	34	the	the	DET
ejde-76	44	35	set	set	NOUN
ejde-76	44	36	ω(θn	ω(θn	NOUN
ejde-76	44	37	)	)	PUNCT
ejde-76	44	38	is	be	AUX
ejde-76	44	39	not	not	PART
ejde-76	44	40	empty	empty	ADJ
ejde-76	44	41	.	.	PUNCT
ejde-76	45	1	in	in	ADP
ejde-76	45	2	addition	addition	NOUN
ejde-76	45	3	,	,	PUNCT
ejde-76	45	4	we	we	PRON
ejde-76	45	5	recall	recall	VERB
ejde-76	45	6	that	that	SCONJ
ejde-76	45	7	the	the	DET
ejde-76	45	8	concept	concept	NOUN
ejde-76	45	9	of	of	ADP
ejde-76	45	10	approximating	approximate	VERB
ejde-76	45	11	sequence	sequence	NOUN
ejde-76	45	12	depends	depend	VERB
ejde-76	45	13	on	on	ADP
ejde-76	45	14	the	the	DET
ejde-76	45	15	tykhonov	tykhonov	NOUN
ejde-76	45	16	triple	triple	NOUN
ejde-76	45	17	t	t	PROPN
ejde-76	45	18	and	and	CCONJ
ejde-76	45	19	,	,	PUNCT
ejde-76	45	20	for	for	ADP
ejde-76	45	21	this	this	DET
ejde-76	45	22	reason	reason	NOUN
ejde-76	45	23	,	,	PUNCT
ejde-76	45	24	we	we	PRON
ejde-76	45	25	use	use	VERB
ejde-76	45	26	the	the	DET
ejde-76	45	27	terminology	terminology	NOUN
ejde-76	45	28	“	"	PUNCT
ejde-76	45	29	t	t	NOUN
ejde-76	45	30	-approximating	-approximate	VERB
ejde-76	45	31	sequence	sequence	NOUN
ejde-76	45	32	”	"	PUNCT
ejde-76	45	33	.	.	PUNCT
ejde-76	46	1	as	as	ADP
ejde-76	46	2	a	a	DET
ejde-76	46	3	consequence	consequence	NOUN
ejde-76	46	4	,	,	PUNCT
ejde-76	46	5	the	the	DET
ejde-76	46	6	concept	concept	NOUN
ejde-76	46	7	of	of	ADP
ejde-76	46	8	well	well	ADV
ejde-76	46	9	-	-	PUNCT
ejde-76	46	10	posedness	posedness	NOUN
ejde-76	46	11	depends	depend	VERB
ejde-76	46	12	on	on	ADP
ejde-76	46	13	t	t	PROPN
ejde-76	46	14	and	and	CCONJ
ejde-76	46	15	,	,	PUNCT
ejde-76	46	16	therefore	therefore	ADV
ejde-76	46	17	,	,	PUNCT
ejde-76	46	18	we	we	PRON
ejde-76	46	19	refer	refer	VERB
ejde-76	46	20	to	to	ADP
ejde-76	46	21	it	it	PRON
ejde-76	46	22	as	as	ADP
ejde-76	46	23	“	"	PUNCT
ejde-76	46	24	wellposedness	wellposedness	ADJ
ejde-76	46	25	with	with	ADP
ejde-76	46	26	respect	respect	NOUN
ejde-76	46	27	to	to	ADP
ejde-76	46	28	t	t	PROPN
ejde-76	46	29	”	"	PUNCT
ejde-76	46	30	or	or	CCONJ
ejde-76	46	31	“	"	PUNCT
ejde-76	46	32	t	t	NOUN
ejde-76	46	33	-well	-well	NOUN
ejde-76	46	34	-	-	PUNCT
ejde-76	46	35	posedness	posedness	NOUN
ejde-76	46	36	”	"	PUNCT
ejde-76	46	37	,	,	PUNCT
ejde-76	46	38	for	for	ADP
ejde-76	46	39	short	short	ADJ
ejde-76	46	40	.	.	PUNCT
ejde-76	47	1	2	2	X
ejde-76	47	2	.	.	X
ejde-76	47	3	an	an	DET
ejde-76	47	4	abstract	abstract	ADJ
ejde-76	47	5	equivalence	equivalence	NOUN
ejde-76	47	6	result	result	NOUN
ejde-76	47	7	consider	consider	VERB
ejde-76	47	8	two	two	NUM
ejde-76	47	9	abstract	abstract	ADJ
ejde-76	47	10	problems	problem	NOUN
ejde-76	47	11	p	p	NOUN
ejde-76	47	12	and	and	CCONJ
ejde-76	47	13	q	q	PROPN
ejde-76	47	14	formulated	formulate	VERB
ejde-76	47	15	in	in	ADP
ejde-76	47	16	the	the	DET
ejde-76	47	17	metric	metric	ADJ
ejde-76	47	18	spaces	space	NOUN
ejde-76	47	19	(	(	PUNCT
ejde-76	47	20	u	u	NOUN
ejde-76	47	21	,	,	PUNCT
ejde-76	47	22	du	du	PROPN
ejde-76	47	23	)	)	PUNCT
ejde-76	47	24	and	and	CCONJ
ejde-76	47	25	(	(	PUNCT
ejde-76	47	26	σ	σ	PROPN
ejde-76	47	27	,	,	PUNCT
ejde-76	47	28	dς	dς	PROPN
ejde-76	47	29	)	)	PUNCT
ejde-76	47	30	,	,	PUNCT
ejde-76	47	31	respectively	respectively	ADV
ejde-76	47	32	.	.	PUNCT
ejde-76	48	1	we	we	PRON
ejde-76	48	2	start	start	VERB
ejde-76	48	3	with	with	ADP
ejde-76	48	4	the	the	DET
ejde-76	48	5	following	follow	VERB
ejde-76	48	6	definition	definition	NOUN
ejde-76	48	7	.	.	PUNCT
ejde-76	49	1	definition	definition	NOUN
ejde-76	49	2	2.1	2.1	NUM
ejde-76	49	3	.	.	PUNCT
ejde-76	50	1	problems	problem	NOUN
ejde-76	50	2	p	p	PROPN
ejde-76	50	3	and	and	CCONJ
ejde-76	50	4	q	q	NOUN
ejde-76	50	5	are	be	AUX
ejde-76	50	6	said	say	VERB
ejde-76	50	7	to	to	PART
ejde-76	50	8	be	be	AUX
ejde-76	50	9	dual	dual	ADJ
ejde-76	50	10	of	of	ADP
ejde-76	50	11	each	each	DET
ejde-76	50	12	other	other	ADJ
ejde-76	50	13	if	if	SCONJ
ejde-76	50	14	there	there	PRON
ejde-76	50	15	exists	exist	VERB
ejde-76	50	16	a	a	DET
ejde-76	50	17	mapping	mapping	NOUN
ejde-76	50	18	d	d	NOUN
ejde-76	50	19	:	:	PUNCT
ejde-76	50	20	u	u	PROPN
ejde-76	50	21	→	→	PUNCT
ejde-76	50	22	σ	σ	NOUN
ejde-76	50	23	such	such	ADJ
ejde-76	50	24	that	that	PRON
ejde-76	50	25	:	:	PUNCT
ejde-76	50	26	(	(	PUNCT
ejde-76	50	27	a	a	X
ejde-76	50	28	)	)	PUNCT
ejde-76	50	29	d	d	NOUN
ejde-76	50	30	is	be	AUX
ejde-76	50	31	bijective	bijective	ADJ
ejde-76	50	32	;	;	PUNCT
ejde-76	50	33	(	(	PUNCT
ejde-76	50	34	b	b	X
ejde-76	50	35	)	)	PUNCT
ejde-76	50	36	both	both	PRON
ejde-76	51	1	d	d	NOUN
ejde-76	51	2	:	:	PUNCT
ejde-76	51	3	u	u	PROPN
ejde-76	51	4	→	→	SYM
ejde-76	51	5	σ	σ	PROPN
ejde-76	51	6	and	and	CCONJ
ejde-76	51	7	its	its	PRON
ejde-76	51	8	inverse	inverse	NOUN
ejde-76	51	9	d−1	d−1	PROPN
ejde-76	51	10	:	:	PUNCT
ejde-76	51	11	σ→	σ→	NOUN
ejde-76	51	12	u	u	NOUN
ejde-76	51	13	are	be	AUX
ejde-76	51	14	continuous	continuous	ADJ
ejde-76	51	15	;	;	PUNCT
ejde-76	51	16	(	(	PUNCT
ejde-76	51	17	c	c	X
ejde-76	51	18	)	)	PUNCT
ejde-76	51	19	u	u	NOUN
ejde-76	51	20	∈	∈	PROPN
ejde-76	51	21	u	u	NOUN
ejde-76	51	22	is	be	AUX
ejde-76	51	23	solution	solution	NOUN
ejde-76	51	24	of	of	ADP
ejde-76	51	25	problem	problem	NOUN
ejde-76	51	26	p	p	X
ejde-76	51	27	if	if	SCONJ
ejde-76	52	1	and	and	CCONJ
ejde-76	52	2	only	only	ADV
ejde-76	52	3	if	if	SCONJ
ejde-76	52	4	σ	σ	NOUN
ejde-76	52	5	=	=	SYM
ejde-76	52	6	du	du	NOUN
ejde-76	52	7	is	be	AUX
ejde-76	52	8	solution	solution	NOUN
ejde-76	52	9	of	of	ADP
ejde-76	52	10	problem	problem	NOUN
ejde-76	52	11	q.	q.	PROPN
ejde-76	52	12	if	if	SCONJ
ejde-76	52	13	(	(	PUNCT
ejde-76	52	14	a)–(c	a)–(c	NOUN
ejde-76	52	15	)	)	PUNCT
ejde-76	52	16	hold	hold	NOUN
ejde-76	52	17	we	we	PRON
ejde-76	52	18	say	say	VERB
ejde-76	52	19	that	that	DET
ejde-76	52	20	problem	problem	NOUN
ejde-76	53	1	q	q	NOUN
ejde-76	53	2	is	be	AUX
ejde-76	53	3	a	a	DET
ejde-76	53	4	dual	dual	ADJ
ejde-76	53	5	problem	problem	NOUN
ejde-76	53	6	of	of	ADP
ejde-76	53	7	problem	problem	NOUN
ejde-76	53	8	p	p	X
ejde-76	53	9	(	(	PUNCT
ejde-76	53	10	with	with	ADP
ejde-76	53	11	d	d	NOUN
ejde-76	53	12	)	)	PUNCT
ejde-76	53	13	and	and	CCONJ
ejde-76	53	14	,	,	PUNCT
ejde-76	53	15	conversely	conversely	ADV
ejde-76	53	16	,	,	PUNCT
ejde-76	53	17	problem	problem	NOUN
ejde-76	53	18	p	p	NOUN
ejde-76	53	19	is	be	AUX
ejde-76	53	20	a	a	DET
ejde-76	53	21	dual	dual	ADJ
ejde-76	53	22	problem	problem	NOUN
ejde-76	53	23	of	of	ADP
ejde-76	53	24	problem	problem	NOUN
ejde-76	53	25	q	q	X
ejde-76	53	26	(	(	PUNCT
ejde-76	53	27	with	with	ADP
ejde-76	53	28	d−1	d−1	PROPN
ejde-76	53	29	)	)	PUNCT
ejde-76	53	30	.	.	PUNCT
ejde-76	54	1	in	in	ADP
ejde-76	54	2	this	this	DET
ejde-76	54	3	framework	framework	NOUN
ejde-76	54	4	we	we	PRON
ejde-76	54	5	consider	consider	VERB
ejde-76	54	6	two	two	NUM
ejde-76	54	7	tykhonov	tykhonov	ADJ
ejde-76	54	8	triples	triple	NOUN
ejde-76	54	9	tp	tp	NOUN
ejde-76	54	10	=	=	PUNCT
ejde-76	54	11	(	(	PUNCT
ejde-76	54	12	i	i	PRON
ejde-76	54	13	,	,	PUNCT
ejde-76	54	14	ωp	ωp	PRON
ejde-76	54	15	,	,	PUNCT
ejde-76	54	16	c	c	X
ejde-76	54	17	)	)	PUNCT
ejde-76	54	18	and	and	CCONJ
ejde-76	54	19	tq	tq	ADP
ejde-76	54	20	=	=	SYM
ejde-76	54	21	(	(	PUNCT
ejde-76	54	22	i	i	NOUN
ejde-76	54	23	,	,	PUNCT
ejde-76	54	24	ωq	ωq	PROPN
ejde-76	54	25	,	,	PUNCT
ejde-76	54	26	c	c	NOUN
ejde-76	54	27	)	)	PUNCT
ejde-76	54	28	ejde-2022/03	ejde-2022/03	NOUN
ejde-76	54	29	duality	duality	NOUN
ejde-76	54	30	arguments	argument	NOUN
ejde-76	54	31	for	for	ADP
ejde-76	54	32	well	well	ADV
ejde-76	54	33	-	-	PUNCT
ejde-76	54	34	posedness	posedness	NOUN
ejde-76	54	35	3	3	NUM
ejde-76	54	36	in	in	ADP
ejde-76	54	37	which	which	PRON
ejde-76	54	38	the	the	DET
ejde-76	54	39	approximating	approximating	NOUN
ejde-76	54	40	sets	set	VERB
ejde-76	54	41	ωp	ωp	PRON
ejde-76	54	42	:	:	PUNCT
ejde-76	54	43	i	i	PROPN
ejde-76	54	44	→	→	SYM
ejde-76	54	45	2u	2u	PROPN
ejde-76	54	46	and	and	CCONJ
ejde-76	54	47	ωq	ωq	ADP
ejde-76	54	48	:	:	PUNCT
ejde-76	54	49	i	i	PRON
ejde-76	54	50	→	→	PUNCT
ejde-76	54	51	2σ	2σ	NUM
ejde-76	54	52	are	be	AUX
ejde-76	54	53	such	such	ADJ
ejde-76	54	54	that	that	SCONJ
ejde-76	54	55	ωp	ωp	PROPN
ejde-76	54	56	(	(	PUNCT
ejde-76	54	57	θ	θ	NOUN
ejde-76	54	58	)	)	PUNCT
ejde-76	54	59	=	=	PRON
ejde-76	54	60	{	{	PUNCT
ejde-76	54	61	u	u	NOUN
ejde-76	54	62	∈	∈	PROPN
ejde-76	54	63	u	u	NOUN
ejde-76	54	64	:	:	PUNCT
ejde-76	54	65	du	du	PROPN
ejde-76	54	66	∈	∈	PROPN
ejde-76	54	67	ωq(θ	ωq(θ	NOUN
ejde-76	54	68	)	)	PUNCT
ejde-76	54	69	}	}	PUNCT
ejde-76	54	70	,	,	PUNCT
ejde-76	54	71	ωq(θ	ωq(θ	NOUN
ejde-76	54	72	)	)	PUNCT
ejde-76	54	73	=	=	SYM
ejde-76	54	74	{	{	PUNCT
ejde-76	54	75	σ	σ	PROPN
ejde-76	54	76	∈	∈	PROPN
ejde-76	54	77	σ	σ	NOUN
ejde-76	54	78	:	:	PUNCT
ejde-76	54	79	d−1σ	d−1σ	NOUN
ejde-76	54	80	∈	∈	NOUN
ejde-76	54	81	ωp	ωp	X
ejde-76	54	82	(	(	PUNCT
ejde-76	54	83	θ	θ	NOUN
ejde-76	54	84	)	)	PUNCT
ejde-76	54	85	}	}	PUNCT
ejde-76	54	86	,	,	PUNCT
ejde-76	54	87	(	(	PUNCT
ejde-76	54	88	2.1	2.1	NUM
ejde-76	54	89	)	)	PUNCT
ejde-76	54	90	for	for	ADP
ejde-76	54	91	all	all	DET
ejde-76	54	92	θ	θ	PROPN
ejde-76	54	93	∈	∈	PROPN
ejde-76	54	94	i.	i.	NOUN
ejde-76	54	95	the	the	DET
ejde-76	54	96	interest	interest	NOUN
ejde-76	54	97	in	in	ADP
ejde-76	54	98	considering	consider	VERB
ejde-76	54	99	these	these	DET
ejde-76	54	100	tykhonov	tykhonov	NOUN
ejde-76	54	101	triples	triple	NOUN
ejde-76	54	102	follows	follow	VERB
ejde-76	54	103	from	from	ADP
ejde-76	54	104	the	the	DET
ejde-76	54	105	following	follow	VERB
ejde-76	54	106	equivalence	equivalence	NOUN
ejde-76	54	107	result	result	NOUN
ejde-76	54	108	.	.	PUNCT
ejde-76	55	1	theorem	theorem	VERB
ejde-76	55	2	2.2	2.2	NUM
ejde-76	55	3	.	.	PUNCT
ejde-76	56	1	let	let	VERB
ejde-76	56	2	p	p	NOUN
ejde-76	56	3	and	and	CCONJ
ejde-76	56	4	q	q	NOUN
ejde-76	56	5	be	be	AUX
ejde-76	56	6	dual	dual	ADJ
ejde-76	56	7	problems	problem	NOUN
ejde-76	56	8	(	(	PUNCT
ejde-76	56	9	with	with	ADP
ejde-76	56	10	d	d	PROPN
ejde-76	56	11	and	and	CCONJ
ejde-76	56	12	d−1	d−1	PROPN
ejde-76	56	13	,	,	PUNCT
ejde-76	56	14	respectively	respectively	ADV
ejde-76	56	15	)	)	PUNCT
ejde-76	56	16	.	.	PUNCT
ejde-76	57	1	then	then	ADV
ejde-76	57	2	problem	problem	NOUN
ejde-76	57	3	p	p	NOUN
ejde-76	57	4	is	be	AUX
ejde-76	57	5	tp	tp	AUX
ejde-76	57	6	-well	-well	NOUN
ejde-76	57	7	-	-	PUNCT
ejde-76	57	8	posed	pose	VERB
ejde-76	57	9	if	if	SCONJ
ejde-76	57	10	and	and	CCONJ
ejde-76	57	11	only	only	ADV
ejde-76	57	12	if	if	SCONJ
ejde-76	57	13	problem	problem	NOUN
ejde-76	57	14	q	q	NOUN
ejde-76	57	15	is	be	AUX
ejde-76	57	16	tq	tq	ADV
ejde-76	57	17	-	-	PUNCT
ejde-76	57	18	well	well	ADV
ejde-76	57	19	-	-	PUNCT
ejde-76	57	20	posed	pose	VERB
ejde-76	57	21	.	.	PUNCT
ejde-76	58	1	proof	proof	NOUN
ejde-76	58	2	.	.	PUNCT
ejde-76	59	1	assume	assume	VERB
ejde-76	59	2	that	that	SCONJ
ejde-76	59	3	problem	problem	NOUN
ejde-76	59	4	p	p	NOUN
ejde-76	59	5	is	be	AUX
ejde-76	59	6	tp	tp	AUX
ejde-76	59	7	-well	-well	NOUN
ejde-76	59	8	-	-	PUNCT
ejde-76	59	9	posed	pose	VERB
ejde-76	59	10	.	.	PUNCT
ejde-76	60	1	this	this	PRON
ejde-76	60	2	implies	imply	VERB
ejde-76	60	3	that	that	DET
ejde-76	60	4	problem	problem	NOUN
ejde-76	60	5	p	p	NOUN
ejde-76	60	6	has	have	VERB
ejde-76	60	7	a	a	DET
ejde-76	60	8	unique	unique	ADJ
ejde-76	60	9	solution	solution	NOUN
ejde-76	60	10	u	u	NOUN
ejde-76	60	11	∈	∈	PROPN
ejde-76	60	12	u	u	NOUN
ejde-76	60	13	.	.	PUNCT
ejde-76	61	1	moreover	moreover	ADV
ejde-76	61	2	,	,	PUNCT
ejde-76	61	3	it	it	PRON
ejde-76	61	4	follows	follow	VERB
ejde-76	61	5	from	from	ADP
ejde-76	61	6	properties	property	NOUN
ejde-76	61	7	(	(	PUNCT
ejde-76	61	8	a	a	X
ejde-76	61	9	)	)	PUNCT
ejde-76	61	10	and	and	CCONJ
ejde-76	61	11	(	(	PUNCT
ejde-76	61	12	c	c	X
ejde-76	61	13	)	)	PUNCT
ejde-76	61	14	in	in	ADP
ejde-76	61	15	definition	definition	NOUN
ejde-76	61	16	2.1	2.1	NUM
ejde-76	61	17	that	that	PRON
ejde-76	61	18	σ	σ	VERB
ejde-76	61	19	=	=	SYM
ejde-76	61	20	du	du	PROPN
ejde-76	61	21	is	be	AUX
ejde-76	61	22	the	the	DET
ejde-76	61	23	unique	unique	ADJ
ejde-76	61	24	solution	solution	NOUN
ejde-76	61	25	of	of	ADP
ejde-76	61	26	problem	problem	NOUN
ejde-76	61	27	q.	q.	PROPN
ejde-76	61	28	let	let	VERB
ejde-76	61	29	{	{	PUNCT
ejde-76	61	30	σn	σn	PROPN
ejde-76	61	31	}	}	PUNCT
ejde-76	61	32	⊂	⊂	PROPN
ejde-76	61	33	σ	σ	NOUN
ejde-76	61	34	be	be	AUX
ejde-76	61	35	a	a	DET
ejde-76	61	36	tq	tq	ADV
ejde-76	61	37	-	-	PUNCT
ejde-76	61	38	approximating	approximate	VERB
ejde-76	61	39	sequence	sequence	NOUN
ejde-76	61	40	for	for	ADP
ejde-76	61	41	problem	problem	NOUN
ejde-76	62	1	q.	q.	PROPN
ejde-76	63	1	then	then	ADV
ejde-76	63	2	there	there	PRON
ejde-76	63	3	exists	exist	VERB
ejde-76	63	4	a	a	DET
ejde-76	63	5	sequence	sequence	NOUN
ejde-76	63	6	{	{	PUNCT
ejde-76	63	7	θn	θn	NOUN
ejde-76	63	8	}	}	PUNCT
ejde-76	63	9	∈	∈	PROPN
ejde-76	63	10	c	c	NOUN
ejde-76	63	11	such	such	ADJ
ejde-76	63	12	that	that	PRON
ejde-76	63	13	,	,	PUNCT
ejde-76	63	14	for	for	ADP
ejde-76	63	15	each	each	DET
ejde-76	63	16	n	n	PRON
ejde-76	63	17	∈	∈	PROPN
ejde-76	63	18	n	n	CCONJ
ejde-76	63	19	,	,	PUNCT
ejde-76	63	20	σn	σn	PROPN
ejde-76	63	21	∈	∈	PROPN
ejde-76	63	22	ωq(θn	ωq(θn	PROPN
ejde-76	63	23	)	)	PUNCT
ejde-76	63	24	,	,	PUNCT
ejde-76	63	25	i.e.	i.e.	X
ejde-76	63	26	,	,	PUNCT
ejde-76	63	27	d−1σn	d−1σn	PROPN
ejde-76	63	28	∈	∈	PROPN
ejde-76	63	29	ωp	ωp	X
ejde-76	63	30	(	(	PUNCT
ejde-76	63	31	θn	θn	NOUN
ejde-76	63	32	)	)	PUNCT
ejde-76	63	33	,	,	PUNCT
ejde-76	63	34	which	which	PRON
ejde-76	63	35	means	mean	VERB
ejde-76	63	36	that	that	SCONJ
ejde-76	63	37	{	{	PUNCT
ejde-76	63	38	d−1σn	d−1σn	NOUN
ejde-76	63	39	}	}	PUNCT
ejde-76	63	40	⊂	⊂	PROPN
ejde-76	63	41	u	u	PROPN
ejde-76	63	42	is	be	AUX
ejde-76	63	43	a	a	DET
ejde-76	63	44	tp	tp	NOUN
ejde-76	63	45	-approximating	-approximate	VERB
ejde-76	63	46	sequence	sequence	NOUN
ejde-76	63	47	for	for	ADP
ejde-76	63	48	problem	problem	NOUN
ejde-76	64	1	p.	p.	NOUN
ejde-76	64	2	therefore	therefore	ADV
ejde-76	64	3	,	,	PUNCT
ejde-76	64	4	using	use	VERB
ejde-76	64	5	the	the	DET
ejde-76	64	6	tp	tp	NOUN
ejde-76	64	7	-well	-well	NOUN
ejde-76	64	8	-	-	PUNCT
ejde-76	64	9	posedness	posedness	NOUN
ejde-76	64	10	of	of	ADP
ejde-76	64	11	problem	problem	NOUN
ejde-76	64	12	p	p	NOUN
ejde-76	64	13	and	and	CCONJ
ejde-76	64	14	the	the	DET
ejde-76	64	15	continuity	continuity	NOUN
ejde-76	64	16	of	of	ADP
ejde-76	64	17	operator	operator	NOUN
ejde-76	64	18	d	d	NOUN
ejde-76	64	19	to	to	PART
ejde-76	64	20	deduce	deduce	VERB
ejde-76	64	21	that	that	SCONJ
ejde-76	64	22	the	the	DET
ejde-76	64	23	sequence	sequence	NOUN
ejde-76	64	24	{	{	PUNCT
ejde-76	64	25	σn	σn	NOUN
ejde-76	64	26	}	}	PUNCT
ejde-76	64	27	converges	converge	NOUN
ejde-76	64	28	to	to	ADP
ejde-76	64	29	the	the	DET
ejde-76	64	30	unique	unique	ADJ
ejde-76	64	31	solution	solution	NOUN
ejde-76	64	32	σ	σ	PROPN
ejde-76	64	33	∈	∈	PROPN
ejde-76	64	34	σ	σ	NOUN
ejde-76	64	35	of	of	ADP
ejde-76	64	36	problem	problem	NOUN
ejde-76	64	37	q.	q.	PROPN
ejde-76	64	38	we	we	PRON
ejde-76	64	39	conclude	conclude	VERB
ejde-76	64	40	from	from	ADP
ejde-76	64	41	above	above	ADP
ejde-76	64	42	that	that	DET
ejde-76	64	43	problem	problem	NOUN
ejde-76	64	44	q	q	NOUN
ejde-76	64	45	is	be	AUX
ejde-76	64	46	tq	tq	ADV
ejde-76	64	47	-	-	PUNCT
ejde-76	64	48	well	well	ADV
ejde-76	64	49	-	-	PUNCT
ejde-76	64	50	posed	pose	VERB
ejde-76	64	51	.	.	PUNCT
ejde-76	65	1	similar	similar	ADJ
ejde-76	65	2	arguments	argument	NOUN
ejde-76	65	3	show	show	VERB
ejde-76	65	4	that	that	SCONJ
ejde-76	65	5	if	if	SCONJ
ejde-76	65	6	problem	problem	NOUN
ejde-76	65	7	q	q	NOUN
ejde-76	65	8	is	be	AUX
ejde-76	65	9	tq	tq	ADV
ejde-76	65	10	-	-	PUNCT
ejde-76	65	11	well	well	ADV
ejde-76	65	12	-	-	PUNCT
ejde-76	65	13	posed	pose	VERB
ejde-76	65	14	then	then	ADV
ejde-76	65	15	problem	problem	NOUN
ejde-76	65	16	p	p	NOUN
ejde-76	65	17	is	be	AUX
ejde-76	65	18	tp	tp	AUX
ejde-76	65	19	-well	-well	NOUN
ejde-76	65	20	-	-	PUNCT
ejde-76	65	21	posed	pose	VERB
ejde-76	65	22	,	,	PUNCT
ejde-76	65	23	which	which	PRON
ejde-76	65	24	completes	complete	VERB
ejde-76	65	25	the	the	DET
ejde-76	65	26	proof	proof	NOUN
ejde-76	65	27	.	.	PUNCT
ejde-76	66	1	�	�	PROPN
ejde-76	66	2	3	3	NUM
ejde-76	66	3	.	.	X
ejde-76	66	4	problem	problem	NOUN
ejde-76	66	5	statement	statement	NOUN
ejde-76	66	6	and	and	CCONJ
ejde-76	66	7	its	its	PRON
ejde-76	66	8	well	well	NOUN
ejde-76	66	9	-	-	PUNCT
ejde-76	66	10	posedness	posedness	NOUN
ejde-76	66	11	everywhere	everywhere	ADV
ejde-76	66	12	in	in	ADP
ejde-76	66	13	the	the	DET
ejde-76	66	14	rest	rest	NOUN
ejde-76	66	15	of	of	ADP
ejde-76	66	16	this	this	DET
ejde-76	66	17	article	article	NOUN
ejde-76	66	18	v	v	NOUN
ejde-76	66	19	will	will	AUX
ejde-76	66	20	be	be	AUX
ejde-76	66	21	a	a	DET
ejde-76	66	22	real	real	ADJ
ejde-76	66	23	hilbert	hilbert	NOUN
ejde-76	66	24	space	space	NOUN
ejde-76	66	25	.	.	PUNCT
ejde-76	67	1	we	we	PRON
ejde-76	67	2	use	use	VERB
ejde-76	67	3	(	(	PUNCT
ejde-76	67	4	·	·	PUNCT
ejde-76	67	5	,	,	PUNCT
ejde-76	67	6	·	·	PUNCT
ejde-76	67	7	)	)	PUNCT
ejde-76	67	8	v	v	NOUN
ejde-76	67	9	and	and	CCONJ
ejde-76	67	10	‖	‖	PROPN
ejde-76	67	11	·	·	PUNCT
ejde-76	67	12	‖v	‖v	NOUN
ejde-76	67	13	for	for	ADP
ejde-76	67	14	the	the	DET
ejde-76	67	15	inner	inner	ADJ
ejde-76	67	16	product	product	NOUN
ejde-76	67	17	and	and	CCONJ
ejde-76	67	18	the	the	DET
ejde-76	67	19	associated	associated	ADJ
ejde-76	67	20	norm	norm	NOUN
ejde-76	67	21	of	of	ADP
ejde-76	67	22	space	space	NOUN
ejde-76	67	23	v	v	NOUN
ejde-76	67	24	.	.	PUNCT
ejde-76	68	1	for	for	ADP
ejde-76	68	2	any	any	DET
ejde-76	68	3	nonempty	nonempty	ADV
ejde-76	68	4	closed	close	VERB
ejde-76	68	5	convex	convex	NOUN
ejde-76	68	6	set	set	VERB
ejde-76	68	7	k	k	PROPN
ejde-76	68	8	⊂	⊂	PROPN
ejde-76	68	9	x	x	X
ejde-76	68	10	we	we	PRON
ejde-76	68	11	denote	denote	VERB
ejde-76	68	12	by	by	ADP
ejde-76	68	13	pk	pk	NOUN
ejde-76	68	14	:	:	PUNCT
ejde-76	68	15	v	v	NOUN
ejde-76	68	16	→	→	SYM
ejde-76	68	17	k	k	PROPN
ejde-76	68	18	and	and	CCONJ
ejde-76	68	19	nk	nk	PROPN
ejde-76	68	20	:	:	PUNCT
ejde-76	68	21	v	v	X
ejde-76	68	22	→	→	SYM
ejde-76	68	23	2v	2v	PROPN
ejde-76	68	24	the	the	DET
ejde-76	68	25	projection	projection	NOUN
ejde-76	68	26	operator	operator	NOUN
ejde-76	68	27	on	on	ADP
ejde-76	68	28	k	k	PROPN
ejde-76	68	29	and	and	CCONJ
ejde-76	68	30	the	the	DET
ejde-76	68	31	outward	outward	ADJ
ejde-76	68	32	normal	normal	ADJ
ejde-76	68	33	cone	cone	NOUN
ejde-76	68	34	of	of	ADP
ejde-76	68	35	k	k	PROPN
ejde-76	68	36	,	,	PUNCT
ejde-76	68	37	respectively	respectively	ADV
ejde-76	68	38	.	.	PUNCT
ejde-76	69	1	moreover	moreover	ADV
ejde-76	69	2	,	,	PUNCT
ejde-76	69	3	we	we	PRON
ejde-76	69	4	use	use	VERB
ejde-76	69	5	notation	notation	NOUN
ejde-76	69	6	x	x	PUNCT
ejde-76	69	7	=	=	SYM
ejde-76	69	8	c([0	c([0	PROPN
ejde-76	69	9	,	,	PUNCT
ejde-76	69	10	t	t	X
ejde-76	69	11	]	]	PUNCT
ejde-76	69	12	;	;	PUNCT
ejde-76	69	13	v	v	X
ejde-76	69	14	)	)	PUNCT
ejde-76	69	15	for	for	ADP
ejde-76	69	16	the	the	DET
ejde-76	69	17	space	space	NOUN
ejde-76	69	18	of	of	ADP
ejde-76	69	19	continuous	continuous	ADJ
ejde-76	69	20	functions	function	NOUN
ejde-76	69	21	on	on	ADP
ejde-76	69	22	[	[	X
ejde-76	69	23	0	0	NUM
ejde-76	69	24	,	,	PUNCT
ejde-76	69	25	t	t	X
ejde-76	69	26	]	]	PUNCT
ejde-76	69	27	with	with	ADP
ejde-76	69	28	values	value	NOUN
ejde-76	69	29	in	in	ADP
ejde-76	69	30	v	v	NUM
ejde-76	69	31	,	,	PUNCT
ejde-76	69	32	equipped	equip	VERB
ejde-76	69	33	with	with	ADP
ejde-76	69	34	the	the	DET
ejde-76	69	35	norm	norm	NOUN
ejde-76	69	36	of	of	ADP
ejde-76	69	37	the	the	DET
ejde-76	69	38	uniform	uniform	ADJ
ejde-76	69	39	convergence	convergence	NOUN
ejde-76	69	40	.	.	PUNCT
ejde-76	70	1	finally	finally	ADV
ejde-76	70	2	,	,	PUNCT
ejde-76	70	3	we	we	PRON
ejde-76	70	4	mention	mention	VERB
ejde-76	70	5	that	that	PRON
ejde-76	70	6	,	,	PUNCT
ejde-76	70	7	unless	unless	SCONJ
ejde-76	70	8	stated	state	VERB
ejde-76	70	9	otherwise	otherwise	ADV
ejde-76	70	10	,	,	PUNCT
ejde-76	70	11	all	all	DET
ejde-76	70	12	the	the	DET
ejde-76	70	13	limits	limit	NOUN
ejde-76	70	14	below	below	ADV
ejde-76	70	15	are	be	AUX
ejde-76	70	16	considered	consider	VERB
ejde-76	70	17	as	as	ADP
ejde-76	70	18	n→∞	n→∞	NUM
ejde-76	70	19	,	,	PUNCT
ejde-76	70	20	even	even	ADV
ejde-76	70	21	if	if	SCONJ
ejde-76	70	22	we	we	PRON
ejde-76	70	23	do	do	AUX
ejde-76	70	24	not	not	PART
ejde-76	70	25	mention	mention	VERB
ejde-76	70	26	it	it	PRON
ejde-76	70	27	explicitly	explicitly	ADV
ejde-76	70	28	.	.	PUNCT
ejde-76	71	1	let	let	VERB
ejde-76	71	2	k	k	NOUN
ejde-76	71	3	:	:	PUNCT
ejde-76	72	1	[	[	X
ejde-76	72	2	0	0	NUM
ejde-76	72	3	,	,	PUNCT
ejde-76	72	4	t	t	X
ejde-76	72	5	]	]	PUNCT
ejde-76	72	6	→	→	SYM
ejde-76	72	7	2v	2v	PROPN
ejde-76	72	8	,	,	PUNCT
ejde-76	72	9	a	a	DET
ejde-76	72	10	:	:	PUNCT
ejde-76	72	11	v	v	NOUN
ejde-76	72	12	→	→	SYM
ejde-76	72	13	v	v	NOUN
ejde-76	72	14	,	,	PUNCT
ejde-76	72	15	s	s	PART
ejde-76	72	16	:	:	PUNCT
ejde-76	72	17	c([0	c([0	NOUN
ejde-76	72	18	,	,	PUNCT
ejde-76	72	19	t	t	X
ejde-76	72	20	]	]	PUNCT
ejde-76	72	21	;	;	PUNCT
ejde-76	72	22	v	v	X
ejde-76	72	23	)	)	PUNCT
ejde-76	72	24	→	→	SYM
ejde-76	72	25	c([0	c([0	PROPN
ejde-76	72	26	,	,	PUNCT
ejde-76	72	27	t	t	X
ejde-76	72	28	]	]	PUNCT
ejde-76	72	29	;	;	PUNCT
ejde-76	72	30	v	v	X
ejde-76	72	31	)	)	PUNCT
ejde-76	72	32	and	and	CCONJ
ejde-76	72	33	f	f	X
ejde-76	72	34	:	:	PUNCT
ejde-76	73	1	[	[	X
ejde-76	73	2	0	0	NUM
ejde-76	73	3	,	,	PUNCT
ejde-76	73	4	t	t	X
ejde-76	73	5	]	]	PUNCT
ejde-76	73	6	→	→	SYM
ejde-76	73	7	v	v	NOUN
ejde-76	73	8	.	.	PUNCT
ejde-76	74	1	with	with	ADP
ejde-76	74	2	these	these	DET
ejde-76	74	3	data	datum	NOUN
ejde-76	74	4	we	we	PRON
ejde-76	74	5	consider	consider	VERB
ejde-76	74	6	the	the	DET
ejde-76	74	7	following	follow	VERB
ejde-76	74	8	time	time	NOUN
ejde-76	74	9	-	-	PUNCT
ejde-76	74	10	dependent	dependent	ADJ
ejde-76	74	11	inequality	inequality	NOUN
ejde-76	74	12	.	.	PUNCT
ejde-76	75	1	problem	problem	NOUN
ejde-76	75	2	p.	p.	NOUN
ejde-76	75	3	find	find	VERB
ejde-76	75	4	a	a	DET
ejde-76	75	5	function	function	NOUN
ejde-76	75	6	u	u	PROPN
ejde-76	75	7	∈	∈	PROPN
ejde-76	75	8	c([0	c([0	NOUN
ejde-76	75	9	,	,	PUNCT
ejde-76	75	10	t	t	X
ejde-76	75	11	]	]	PUNCT
ejde-76	75	12	;	;	PUNCT
ejde-76	75	13	v	v	X
ejde-76	75	14	)	)	PUNCT
ejde-76	75	15	such	such	ADJ
ejde-76	75	16	that	that	SCONJ
ejde-76	75	17	the	the	DET
ejde-76	75	18	following	follow	VERB
ejde-76	75	19	inequality	inequality	NOUN
ejde-76	75	20	holds	hold	VERB
ejde-76	75	21	:	:	PUNCT
ejde-76	75	22	u(t	u(t	NOUN
ejde-76	75	23	)	)	PUNCT
ejde-76	75	24	∈	∈	PROPN
ejde-76	75	25	k(t	k(t	PROPN
ejde-76	75	26	)	)	PUNCT
ejde-76	75	27	and	and	CCONJ
ejde-76	75	28	(	(	PUNCT
ejde-76	75	29	au(t	au(t	NUM
ejde-76	75	30	)	)	PUNCT
ejde-76	75	31	,	,	PUNCT
ejde-76	75	32	v	v	ADP
ejde-76	75	33	−	−	PROPN
ejde-76	75	34	u(t))v	u(t))v	PROPN
ejde-76	75	35	+	+	CCONJ
ejde-76	75	36	(	(	PUNCT
ejde-76	75	37	su(t	su(t	NUM
ejde-76	75	38	)	)	PUNCT
ejde-76	75	39	,	,	PUNCT
ejde-76	75	40	v	v	ADP
ejde-76	75	41	−	−	PROPN
ejde-76	75	42	u(t))v	u(t))v	PROPN
ejde-76	75	43	≥	≥	X
ejde-76	75	44	(	(	PUNCT
ejde-76	75	45	f(t	f(t	PROPN
ejde-76	75	46	)	)	PUNCT
ejde-76	75	47	,	,	PUNCT
ejde-76	75	48	v	v	ADP
ejde-76	75	49	−	−	PROPN
ejde-76	75	50	u(t))v	u(t))v	PROPN
ejde-76	75	51	(	(	PUNCT
ejde-76	75	52	3.1	3.1	NUM
ejde-76	75	53	)	)	PUNCT
ejde-76	75	54	for	for	ADP
ejde-76	75	55	all	all	PRON
ejde-76	75	56	v	v	ADP
ejde-76	75	57	∈	∈	PRON
ejde-76	75	58	k(t	k(t	X
ejde-76	75	59	)	)	PUNCT
ejde-76	75	60	and	and	CCONJ
ejde-76	75	61	t	t	PROPN
ejde-76	75	62	∈	∈	PROPN
ejde-76	76	1	[	[	X
ejde-76	76	2	0	0	NUM
ejde-76	76	3	,	,	PUNCT
ejde-76	76	4	t	t	X
ejde-76	76	5	]	]	PUNCT
ejde-76	76	6	.	.	PUNCT
ejde-76	77	1	note	note	VERB
ejde-76	77	2	that	that	SCONJ
ejde-76	77	3	here	here	ADV
ejde-76	77	4	and	and	CCONJ
ejde-76	77	5	below	below	ADV
ejde-76	77	6	when	when	SCONJ
ejde-76	77	7	no	no	DET
ejde-76	77	8	confusion	confusion	NOUN
ejde-76	77	9	arises	arise	VERB
ejde-76	77	10	,	,	PUNCT
ejde-76	77	11	we	we	PRON
ejde-76	77	12	use	use	VERB
ejde-76	77	13	the	the	DET
ejde-76	77	14	shorthand	shorthand	NOUN
ejde-76	77	15	notation	notation	NOUN
ejde-76	77	16	su(t	su(t	NUM
ejde-76	77	17	)	)	PUNCT
ejde-76	77	18	to	to	PART
ejde-76	77	19	represent	represent	VERB
ejde-76	77	20	the	the	DET
ejde-76	77	21	value	value	NOUN
ejde-76	77	22	of	of	ADP
ejde-76	77	23	the	the	DET
ejde-76	77	24	function	function	NOUN
ejde-76	77	25	su	su	PROPN
ejde-76	77	26	at	at	ADP
ejde-76	77	27	the	the	DET
ejde-76	77	28	point	point	NOUN
ejde-76	77	29	t	t	PROPN
ejde-76	77	30	,	,	PUNCT
ejde-76	77	31	i.e.	i.e.	X
ejde-76	77	32	,	,	PUNCT
ejde-76	77	33	su(t	su(t	NUM
ejde-76	77	34	)	)	PUNCT
ejde-76	77	35	=	=	SYM
ejde-76	77	36	(	(	PUNCT
ejde-76	77	37	su)(t	su)(t	PROPN
ejde-76	77	38	)	)	PUNCT
ejde-76	77	39	.	.	PUNCT
ejde-76	78	1	moreover	moreover	ADV
ejde-76	78	2	,	,	PUNCT
ejde-76	78	3	for	for	ADP
ejde-76	78	4	an	an	DET
ejde-76	78	5	element	element	NOUN
ejde-76	78	6	v	v	ADP
ejde-76	78	7	∈	∈	NOUN
ejde-76	78	8	v	v	ADP
ejde-76	78	9	we	we	PRON
ejde-76	78	10	shall	shall	AUX
ejde-76	78	11	still	still	ADV
ejde-76	78	12	write	write	VERB
ejde-76	78	13	v	v	NOUN
ejde-76	78	14	for	for	ADP
ejde-76	78	15	the	the	DET
ejde-76	78	16	constant	constant	ADJ
ejde-76	78	17	function	function	NOUN
ejde-76	78	18	t	t	PROPN
ejde-76	78	19	7→	7→	NUM
ejde-76	78	20	v	v	NOUN
ejde-76	78	21	for	for	ADP
ejde-76	78	22	all	all	DET
ejde-76	78	23	t	t	NOUN
ejde-76	78	24	∈	∈	PROPN
ejde-76	79	1	[	[	X
ejde-76	79	2	0	0	NUM
ejde-76	79	3	,	,	PUNCT
ejde-76	79	4	t	t	NOUN
ejde-76	79	5	]	]	PUNCT
ejde-76	79	6	and	and	CCONJ
ejde-76	79	7	,	,	PUNCT
ejde-76	79	8	therefore	therefore	ADV
ejde-76	79	9	,	,	PUNCT
ejde-76	79	10	notation	notation	PROPN
ejde-76	79	11	sv	sv	PROPN
ejde-76	79	12	used	use	VERB
ejde-76	79	13	below	below	ADV
ejde-76	79	14	in	in	ADP
ejde-76	79	15	this	this	DET
ejde-76	79	16	section	section	NOUN
ejde-76	79	17	defines	define	VERB
ejde-76	79	18	an	an	DET
ejde-76	79	19	element	element	NOUN
ejde-76	79	20	of	of	ADP
ejde-76	79	21	x.	x.	NOUN
ejde-76	79	22	our	our	PRON
ejde-76	79	23	aim	aim	NOUN
ejde-76	79	24	in	in	ADP
ejde-76	79	25	what	what	PRON
ejde-76	79	26	follows	follow	VERB
ejde-76	79	27	is	be	AUX
ejde-76	79	28	to	to	PART
ejde-76	79	29	associate	associate	VERB
ejde-76	79	30	problem	problem	NOUN
ejde-76	79	31	p	p	NOUN
ejde-76	79	32	with	with	ADP
ejde-76	79	33	a	a	DET
ejde-76	79	34	dual	dual	ADJ
ejde-76	79	35	problem	problem	NOUN
ejde-76	79	36	q	q	NOUN
ejde-76	79	37	and	and	CCONJ
ejde-76	79	38	to	to	PART
ejde-76	79	39	deduce	deduce	VERB
ejde-76	79	40	its	its	PRON
ejde-76	79	41	well	well	NOUN
ejde-76	79	42	-	-	PUNCT
ejde-76	79	43	posedness	posedness	NOUN
ejde-76	79	44	with	with	ADP
ejde-76	79	45	respect	respect	NOUN
ejde-76	79	46	to	to	ADP
ejde-76	79	47	a	a	DET
ejde-76	79	48	specific	specific	ADJ
ejde-76	79	49	tykhonov	tykhonov	ADJ
ejde-76	79	50	triple	triple	NOUN
ejde-76	79	51	.	.	PUNCT
ejde-76	80	1	to	to	ADP
ejde-76	80	2	this	this	DET
ejde-76	80	3	end	end	NOUN
ejde-76	80	4	,	,	PUNCT
ejde-76	80	5	we	we	PRON
ejde-76	80	6	consider	consider	VERB
ejde-76	80	7	the	the	DET
ejde-76	80	8	following	follow	VERB
ejde-76	80	9	hypotheses	hypothesis	NOUN
ejde-76	80	10	.	.	PUNCT
ejde-76	81	1	(	(	PUNCT
ejde-76	81	2	h1	h1	PROPN
ejde-76	81	3	)	)	PUNCT
ejde-76	81	4	(	(	PUNCT
ejde-76	81	5	a	a	X
ejde-76	81	6	)	)	PUNCT
ejde-76	81	7	k	k	NOUN
ejde-76	81	8	:	:	PUNCT
ejde-76	82	1	[	[	X
ejde-76	82	2	0	0	NUM
ejde-76	82	3	,	,	PUNCT
ejde-76	82	4	t	t	X
ejde-76	82	5	]	]	PUNCT
ejde-76	82	6	→	→	SYM
ejde-76	82	7	2v	2v	PROPN
ejde-76	82	8	has	have	AUX
ejde-76	82	9	nonempty	nonempty	ADV
ejde-76	82	10	closed	close	VERB
ejde-76	82	11	and	and	CCONJ
ejde-76	82	12	convex	convex	ADJ
ejde-76	82	13	values	value	NOUN
ejde-76	82	14	.	.	PUNCT
ejde-76	83	1	(	(	PUNCT
ejde-76	83	2	b	b	X
ejde-76	83	3	)	)	PUNCT
ejde-76	83	4	for	for	ADP
ejde-76	83	5	each	each	DET
ejde-76	83	6	u	u	PROPN
ejde-76	83	7	∈	∈	PROPN
ejde-76	83	8	v	v	NOUN
ejde-76	83	9	,	,	PUNCT
ejde-76	83	10	t	t	PROPN
ejde-76	83	11	∈	∈	PROPN
ejde-76	84	1	[	[	X
ejde-76	84	2	0	0	NUM
ejde-76	84	3	,	,	PUNCT
ejde-76	84	4	t	t	NOUN
ejde-76	84	5	]	]	PUNCT
ejde-76	84	6	and	and	CCONJ
ejde-76	84	7	each	each	DET
ejde-76	84	8	sequence	sequence	NOUN
ejde-76	84	9	{	{	PUNCT
ejde-76	84	10	tn	tn	NOUN
ejde-76	84	11	}	}	PUNCT
ejde-76	84	12	⊂	⊂	PROPN
ejde-76	85	1	[	[	X
ejde-76	85	2	0	0	NUM
ejde-76	85	3	,	,	PUNCT
ejde-76	85	4	t	t	X
ejde-76	85	5	]	]	PUNCT
ejde-76	85	6	,	,	PUNCT
ejde-76	85	7	tn	tn	PROPN
ejde-76	85	8	→	→	SYM
ejde-76	85	9	t	t	PROPN
ejde-76	85	10	implies	imply	VERB
ejde-76	85	11	pk(tn)u→	pk(tn)u→	PROPN
ejde-76	85	12	pk(t)u	pk(t)u	PROPN
ejde-76	85	13	in	in	ADP
ejde-76	85	14	v	v	NUM
ejde-76	85	15	.	.	PUNCT
ejde-76	86	1	4	4	NUM
ejde-76	86	2	r.	r.	PROPN
ejde-76	86	3	hu	hu	PROPN
ejde-76	86	4	,	,	PUNCT
ejde-76	86	5	m.	m.	PROPN
ejde-76	86	6	sofonea	sofonea	PROPN
ejde-76	86	7	ejde-2022/03	ejde-2022/03	PROPN
ejde-76	86	8	(	(	PUNCT
ejde-76	86	9	h2	h2	PROPN
ejde-76	86	10	)	)	PUNCT
ejde-76	86	11	a	a	DET
ejde-76	86	12	:	:	PUNCT
ejde-76	86	13	v	v	NOUN
ejde-76	86	14	→	→	SYM
ejde-76	86	15	v	v	PROPN
ejde-76	86	16	is	be	AUX
ejde-76	86	17	a	a	DET
ejde-76	86	18	linear	linear	ADJ
ejde-76	86	19	continuous	continuous	ADJ
ejde-76	86	20	and	and	CCONJ
ejde-76	86	21	coercive	coercive	ADJ
ejde-76	86	22	operator	operator	NOUN
ejde-76	86	23	,	,	PUNCT
ejde-76	86	24	i.e.	i.e.	X
ejde-76	86	25	there	there	PRON
ejde-76	86	26	exist	exist	VERB
ejde-76	86	27	la	la	PROPN
ejde-76	86	28	,	,	PUNCT
ejde-76	86	29	ma	ma	PROPN
ejde-76	86	30	>	>	X
ejde-76	86	31	0	0	NUM
ejde-76	87	1	such	such	ADJ
ejde-76	87	2	that	that	SCONJ
ejde-76	87	3	‖au‖v	‖au‖v	PROPN
ejde-76	87	4	≤	≤	ADJ
ejde-76	87	5	la‖v‖v	la‖v‖v	NOUN
ejde-76	87	6	,	,	PUNCT
ejde-76	87	7	(	(	PUNCT
ejde-76	87	8	au	au	ADP
ejde-76	87	9	,	,	PUNCT
ejde-76	87	10	u)v	u)v	X
ejde-76	87	11	≥	≥	X
ejde-76	87	12	ma‖u‖2v	ma‖u‖2v	PROPN
ejde-76	87	13	∀u	∀u	PROPN
ejde-76	87	14	∈	∈	PROPN
ejde-76	87	15	v.	v.	CCONJ
ejde-76	87	16	(	(	PUNCT
ejde-76	87	17	h3	h3	NOUN
ejde-76	87	18	)	)	PUNCT
ejde-76	87	19	s	s	PART
ejde-76	87	20	:	:	PUNCT
ejde-76	87	21	c([0	c([0	NOUN
ejde-76	87	22	,	,	PUNCT
ejde-76	87	23	t	t	X
ejde-76	87	24	]	]	PUNCT
ejde-76	87	25	;	;	PUNCT
ejde-76	87	26	v	v	X
ejde-76	87	27	)	)	PUNCT
ejde-76	87	28	→	→	SYM
ejde-76	87	29	c([0	c([0	PROPN
ejde-76	87	30	,	,	PUNCT
ejde-76	87	31	t	t	X
ejde-76	87	32	]	]	PUNCT
ejde-76	87	33	;	;	PUNCT
ejde-76	87	34	v	v	X
ejde-76	87	35	)	)	PUNCT
ejde-76	87	36	is	be	AUX
ejde-76	87	37	a	a	DET
ejde-76	87	38	history	history	NOUN
ejde-76	87	39	-	-	PUNCT
ejde-76	87	40	dependent	dependent	ADJ
ejde-76	87	41	operator	operator	NOUN
ejde-76	87	42	,	,	PUNCT
ejde-76	87	43	i.e.	i.e.	X
ejde-76	87	44	,	,	PUNCT
ejde-76	87	45	there	there	PRON
ejde-76	87	46	exists	exist	VERB
ejde-76	87	47	ls	ls	PROPN
ejde-76	87	48	>	>	X
ejde-76	87	49	0	0	NUM
ejde-76	87	50	such	such	ADJ
ejde-76	87	51	that	that	SCONJ
ejde-76	87	52	‖su(t)−	‖su(t)−	PROPN
ejde-76	87	53	sv(t)‖v	sv(t)‖v	PROPN
ejde-76	87	54	≤	≤	X
ejde-76	88	1	ls	ls	ADJ
ejde-76	88	2	∫	∫	PROPN
ejde-76	88	3	t	t	PROPN
ejde-76	88	4	0	0	NUM
ejde-76	88	5	‖u(s)−	‖u(s)−	PROPN
ejde-76	88	6	v(s)‖v	v(s)‖v	NOUN
ejde-76	88	7	ds	ds	ADJ
ejde-76	88	8	∀u	∀u	NOUN
ejde-76	88	9	,	,	PUNCT
ejde-76	88	10	v	v	ADP
ejde-76	88	11	∈	∈	PROPN
ejde-76	88	12	c([0	c([0	NOUN
ejde-76	88	13	,	,	PUNCT
ejde-76	88	14	t	t	X
ejde-76	88	15	]	]	PUNCT
ejde-76	88	16	;	;	PUNCT
ejde-76	88	17	v	v	X
ejde-76	88	18	)	)	PUNCT
ejde-76	88	19	,	,	PUNCT
ejde-76	88	20	t	t	PROPN
ejde-76	88	21	∈	∈	PROPN
ejde-76	89	1	[	[	X
ejde-76	89	2	0	0	NUM
ejde-76	89	3	,	,	PUNCT
ejde-76	89	4	t	t	X
ejde-76	89	5	]	]	PUNCT
ejde-76	89	6	.	.	PUNCT
ejde-76	90	1	(	(	PUNCT
ejde-76	90	2	h4	h4	PROPN
ejde-76	90	3	)	)	PUNCT
ejde-76	90	4	f	f	PROPN
ejde-76	90	5	∈	∈	PROPN
ejde-76	90	6	c([0	c([0	PROPN
ejde-76	90	7	,	,	PUNCT
ejde-76	90	8	t	t	X
ejde-76	90	9	]	]	PUNCT
ejde-76	90	10	;	;	PUNCT
ejde-76	90	11	v	v	NOUN
ejde-76	90	12	)	)	PUNCT
ejde-76	90	13	.	.	PUNCT
ejde-76	91	1	note	note	VERB
ejde-76	91	2	that	that	SCONJ
ejde-76	91	3	assumption	assumption	NOUN
ejde-76	91	4	(	(	PUNCT
ejde-76	91	5	h2	h2	NOUN
ejde-76	91	6	)	)	PUNCT
ejde-76	91	7	implies	imply	VERB
ejde-76	91	8	that	that	SCONJ
ejde-76	91	9	the	the	DET
ejde-76	91	10	operator	operator	NOUN
ejde-76	91	11	a	a	PRON
ejde-76	91	12	is	be	AUX
ejde-76	91	13	invertible	invertible	ADJ
ejde-76	91	14	and	and	CCONJ
ejde-76	91	15	its	its	PRON
ejde-76	91	16	inverse	inverse	NOUN
ejde-76	91	17	a−1	a−1	PROPN
ejde-76	91	18	:	:	PUNCT
ejde-76	91	19	v	v	X
ejde-76	91	20	→	→	SYM
ejde-76	91	21	v	v	NUM
ejde-76	91	22	satisfies	satisfy	VERB
ejde-76	91	23	the	the	DET
ejde-76	91	24	inequalities	inequality	NOUN
ejde-76	91	25	‖a−1u‖v	‖a−1u‖v	X
ejde-76	91	26	≤	≤	NUM
ejde-76	91	27	1	1	NUM
ejde-76	91	28	ma	ma	PROPN
ejde-76	91	29	‖u‖v	‖u‖v	PROPN
ejde-76	91	30	,	,	PUNCT
ejde-76	91	31	(	(	PUNCT
ejde-76	91	32	a−1u	a−1u	ADV
ejde-76	91	33	,	,	PUNCT
ejde-76	91	34	u)v	u)v	X
ejde-76	91	35	≥	≥	NUM
ejde-76	91	36	ma	ma	PROPN
ejde-76	91	37	l2	l2	PROPN
ejde-76	91	38	a	a	DET
ejde-76	91	39	‖u‖2v	‖u‖2v	PROPN
ejde-76	91	40	∀u	∀u	PROPN
ejde-76	91	41	∈	∈	NOUN
ejde-76	91	42	v.	v.	CCONJ
ejde-76	91	43	(	(	PUNCT
ejde-76	91	44	3.2	3.2	NUM
ejde-76	91	45	)	)	PUNCT
ejde-76	91	46	next	next	ADV
ejde-76	91	47	,	,	PUNCT
ejde-76	91	48	we	we	PRON
ejde-76	91	49	consider	consider	VERB
ejde-76	91	50	the	the	DET
ejde-76	91	51	tykhonov	tykhonov	ADJ
ejde-76	91	52	triple	triple	NOUN
ejde-76	91	53	tp	tp	ADP
ejde-76	91	54	=	=	PUNCT
ejde-76	91	55	(	(	PUNCT
ejde-76	91	56	i	i	PRON
ejde-76	91	57	,	,	PUNCT
ejde-76	91	58	ωp	ωp	PRON
ejde-76	91	59	,	,	PUNCT
ejde-76	91	60	c	c	X
ejde-76	91	61	)	)	PUNCT
ejde-76	91	62	defined	define	VERB
ejde-76	91	63	as	as	SCONJ
ejde-76	91	64	follows	follow	VERB
ejde-76	91	65	:	:	PUNCT
ejde-76	91	66	i	i	PRON
ejde-76	91	67	=	=	PUNCT
ejde-76	91	68	r+	r+	ADV
ejde-76	91	69	,	,	PUNCT
ejde-76	91	70	c	c	X
ejde-76	91	71	=	=	PRON
ejde-76	91	72	{	{	PUNCT
ejde-76	91	73	{	{	PUNCT
ejde-76	91	74	θn}n	θn}n	PROPN
ejde-76	91	75	:	:	PUNCT
ejde-76	91	76	θn	θn	ADP
ejde-76	91	77	∈	∈	PROPN
ejde-76	92	1	i	i	PRON
ejde-76	92	2	∀n	∀n	NUM
ejde-76	92	3	∈	∈	PROPN
ejde-76	92	4	n	n	CCONJ
ejde-76	92	5	,	,	PUNCT
ejde-76	92	6	θn	θn	ADJ
ejde-76	92	7	→	→	SYM
ejde-76	92	8	0	0	PROPN
ejde-76	92	9	as	as	ADP
ejde-76	92	10	n→∞	n→∞	NUM
ejde-76	92	11	}	}	PUNCT
ejde-76	92	12	(	(	PUNCT
ejde-76	92	13	3.3	3.3	NUM
ejde-76	92	14	)	)	PUNCT
ejde-76	92	15	and	and	CCONJ
ejde-76	92	16	,	,	PUNCT
ejde-76	92	17	for	for	ADP
ejde-76	92	18	each	each	DET
ejde-76	92	19	θ	θ	PROPN
ejde-76	92	20	≥	≥	NOUN
ejde-76	92	21	0	0	NUM
ejde-76	92	22	,	,	PUNCT
ejde-76	92	23	the	the	DET
ejde-76	92	24	set	set	NOUN
ejde-76	92	25	ωp	ωp	X
ejde-76	92	26	(	(	PUNCT
ejde-76	92	27	θ	θ	NOUN
ejde-76	92	28	)	)	PUNCT
ejde-76	92	29	is	be	AUX
ejde-76	92	30	defined	define	VERB
ejde-76	92	31	as	as	SCONJ
ejde-76	92	32	follows	follow	VERB
ejde-76	92	33	:	:	PUNCT
ejde-76	92	34	ωp	ωp	NOUN
ejde-76	92	35	(	(	PUNCT
ejde-76	92	36	θ	θ	NOUN
ejde-76	92	37	)	)	PUNCT
ejde-76	92	38	=	=	PRON
ejde-76	92	39	{	{	PUNCT
ejde-76	92	40	u	u	NOUN
ejde-76	92	41	∈	∈	PROPN
ejde-76	92	42	c([0	c([0	NOUN
ejde-76	92	43	,	,	PUNCT
ejde-76	92	44	t	t	X
ejde-76	92	45	]	]	PUNCT
ejde-76	92	46	;	;	PUNCT
ejde-76	92	47	v	v	X
ejde-76	92	48	)	)	PUNCT
ejde-76	92	49	:	:	PUNCT
ejde-76	92	50	u(t	u(t	NOUN
ejde-76	92	51	)	)	PUNCT
ejde-76	92	52	∈	∈	PROPN
ejde-76	92	53	k(t	k(t	PROPN
ejde-76	92	54	)	)	PUNCT
ejde-76	92	55	,	,	PUNCT
ejde-76	92	56	(	(	PUNCT
ejde-76	92	57	au(t	au(t	NUM
ejde-76	92	58	)	)	PUNCT
ejde-76	92	59	,	,	PUNCT
ejde-76	92	60	v	v	ADP
ejde-76	92	61	−	−	PROPN
ejde-76	92	62	u(t))v	u(t))v	PROPN
ejde-76	92	63	+	+	CCONJ
ejde-76	92	64	(	(	PUNCT
ejde-76	92	65	su(t	su(t	NUM
ejde-76	92	66	)	)	PUNCT
ejde-76	92	67	,	,	PUNCT
ejde-76	92	68	v	v	ADP
ejde-76	92	69	−	−	PROPN
ejde-76	92	70	u(t))v	u(t))v	PROPN
ejde-76	92	71	+	+	CCONJ
ejde-76	92	72	θ	θ	PROPN
ejde-76	92	73	≥	≥	NUM
ejde-76	92	74	(	(	PUNCT
ejde-76	92	75	f(t	f(t	PROPN
ejde-76	92	76	)	)	PUNCT
ejde-76	92	77	,	,	PUNCT
ejde-76	92	78	v	v	ADP
ejde-76	92	79	−	−	X
ejde-76	92	80	u(t))v	u(t))v	ADJ
ejde-76	92	81	∀	∀	NOUN
ejde-76	92	82	v	v	ADP
ejde-76	92	83	∈	∈	PROPN
ejde-76	92	84	k(t	k(t	PROPN
ejde-76	92	85	)	)	PUNCT
ejde-76	92	86	,	,	PUNCT
ejde-76	92	87	t	t	PROPN
ejde-76	92	88	∈	∈	PROPN
ejde-76	93	1	[	[	X
ejde-76	93	2	0	0	NUM
ejde-76	93	3	,	,	PUNCT
ejde-76	93	4	t	t	X
ejde-76	93	5	]	]	PUNCT
ejde-76	93	6	}	}	PUNCT
ejde-76	93	7	.	.	PUNCT
ejde-76	94	1	(	(	PUNCT
ejde-76	94	2	3.4	3.4	NUM
ejde-76	94	3	)	)	PUNCT
ejde-76	94	4	note	note	NOUN
ejde-76	94	5	that	that	SCONJ
ejde-76	94	6	ωp	ωp	PRON
ejde-76	94	7	(	(	PUNCT
ejde-76	94	8	θ	θ	PROPN
ejde-76	94	9	)	)	PUNCT
ejde-76	94	10	6=	6=	NOUN
ejde-76	94	11	∅	∅	NOUN
ejde-76	94	12	for	for	ADP
ejde-76	94	13	each	each	DET
ejde-76	94	14	θ	θ	PROPN
ejde-76	94	15	∈	∈	PROPN
ejde-76	94	16	r+	r+	NOUN
ejde-76	94	17	,	,	PUNCT
ejde-76	94	18	as	as	SCONJ
ejde-76	94	19	it	it	PRON
ejde-76	94	20	will	will	AUX
ejde-76	94	21	result	result	VERB
ejde-76	94	22	from	from	ADP
ejde-76	94	23	the	the	DET
ejde-76	94	24	proof	proof	NOUN
ejde-76	94	25	of	of	ADP
ejde-76	94	26	theorem	theorem	ADJ
ejde-76	94	27	3.2	3.2	NUM
ejde-76	94	28	below	below	ADV
ejde-76	94	29	.	.	PUNCT
ejde-76	95	1	to	to	PART
ejde-76	95	2	proceed	proceed	VERB
ejde-76	95	3	,	,	PUNCT
ejde-76	95	4	we	we	PRON
ejde-76	95	5	need	need	VERB
ejde-76	95	6	the	the	DET
ejde-76	95	7	following	follow	VERB
ejde-76	95	8	preliminary	preliminary	ADJ
ejde-76	95	9	result	result	NOUN
ejde-76	95	10	.	.	PUNCT
ejde-76	96	1	proposition	proposition	NOUN
ejde-76	96	2	3.1	3.1	NUM
ejde-76	96	3	.	.	PUNCT
ejde-76	97	1	under	under	ADP
ejde-76	97	2	assumptions	assumption	NOUN
ejde-76	97	3	(	(	PUNCT
ejde-76	97	4	h2)–(h4	h2)–(h4	NOUN
ejde-76	97	5	)	)	PUNCT
ejde-76	97	6	,	,	PUNCT
ejde-76	97	7	the	the	DET
ejde-76	97	8	operator	operator	NOUN
ejde-76	97	9	d	d	NOUN
ejde-76	97	10	:	:	PUNCT
ejde-76	97	11	c([0	c([0	PROPN
ejde-76	97	12	,	,	PUNCT
ejde-76	97	13	t	t	X
ejde-76	97	14	]	]	PUNCT
ejde-76	97	15	;	;	PUNCT
ejde-76	97	16	v	v	X
ejde-76	97	17	)	)	PUNCT
ejde-76	97	18	→	→	SYM
ejde-76	97	19	c([0	c([0	PROPN
ejde-76	97	20	,	,	PUNCT
ejde-76	97	21	t	t	X
ejde-76	97	22	]	]	PUNCT
ejde-76	97	23	;	;	PUNCT
ejde-76	97	24	v	v	X
ejde-76	97	25	)	)	PUNCT
ejde-76	97	26	defined	define	VERB
ejde-76	97	27	by	by	ADP
ejde-76	97	28	du(t	du(t	NOUN
ejde-76	97	29	)	)	PUNCT
ejde-76	97	30	=	=	SYM
ejde-76	97	31	au(t	au(t	PRON
ejde-76	97	32	)	)	PUNCT
ejde-76	98	1	+	+	CCONJ
ejde-76	98	2	su(t)−	su(t)−	PROPN
ejde-76	98	3	f(t	f(t	PROPN
ejde-76	98	4	)	)	PUNCT
ejde-76	98	5	∀u	∀u	NOUN
ejde-76	98	6	∈	∈	NOUN
ejde-76	98	7	c([0	c([0	NOUN
ejde-76	98	8	,	,	PUNCT
ejde-76	98	9	t	t	X
ejde-76	98	10	]	]	PUNCT
ejde-76	98	11	;	;	PUNCT
ejde-76	98	12	v	v	X
ejde-76	98	13	)	)	PUNCT
ejde-76	98	14	,	,	PUNCT
ejde-76	98	15	t	t	PROPN
ejde-76	98	16	∈	∈	PROPN
ejde-76	99	1	[	[	X
ejde-76	99	2	0	0	NUM
ejde-76	99	3	,	,	PUNCT
ejde-76	99	4	t	t	X
ejde-76	99	5	]	]	PUNCT
ejde-76	99	6	(	(	PUNCT
ejde-76	99	7	3.5	3.5	NUM
ejde-76	99	8	)	)	PUNCT
ejde-76	99	9	is	be	AUX
ejde-76	99	10	bijective	bijective	ADJ
ejde-76	99	11	and	and	CCONJ
ejde-76	99	12	has	have	VERB
ejde-76	99	13	inverse	inverse	NOUN
ejde-76	99	14	of	of	ADP
ejde-76	99	15	the	the	DET
ejde-76	99	16	form	form	NOUN
ejde-76	99	17	a−1+r	a−1+r	VERB
ejde-76	99	18	,	,	PUNCT
ejde-76	99	19	where	where	SCONJ
ejde-76	99	20	r	r	NOUN
ejde-76	99	21	:	:	PUNCT
ejde-76	99	22	c([0	c([0	NOUN
ejde-76	99	23	,	,	PUNCT
ejde-76	99	24	t	t	X
ejde-76	99	25	]	]	PUNCT
ejde-76	99	26	;	;	PUNCT
ejde-76	99	27	v	v	X
ejde-76	99	28	)	)	PUNCT
ejde-76	99	29	→	→	SYM
ejde-76	99	30	c([0	c([0	PROPN
ejde-76	99	31	,	,	PUNCT
ejde-76	99	32	t	t	X
ejde-76	99	33	]	]	PUNCT
ejde-76	99	34	;	;	PUNCT
ejde-76	99	35	v	v	X
ejde-76	99	36	)	)	PUNCT
ejde-76	99	37	is	be	AUX
ejde-76	99	38	a	a	DET
ejde-76	99	39	history	history	NOUN
ejde-76	99	40	-	-	PUNCT
ejde-76	99	41	dependent	dependent	ADJ
ejde-76	99	42	operator	operator	NOUN
ejde-76	99	43	with	with	ADP
ejde-76	99	44	constant	constant	ADJ
ejde-76	99	45	lr	lr	X
ejde-76	99	46	>	>	X
ejde-76	99	47	0	0	NUM
ejde-76	99	48	.	.	PUNCT
ejde-76	100	1	a	a	DET
ejde-76	100	2	proof	proof	NOUN
ejde-76	100	3	of	of	ADP
ejde-76	100	4	proposition	proposition	NOUN
ejde-76	100	5	3.1	3.1	NUM
ejde-76	100	6	can	can	AUX
ejde-76	100	7	be	be	AUX
ejde-76	100	8	found	find	VERB
ejde-76	100	9	in	in	ADP
ejde-76	100	10	[	[	X
ejde-76	100	11	11	11	NUM
ejde-76	100	12	,	,	PUNCT
ejde-76	100	13	p.55	p.55	NOUN
ejde-76	100	14	]	]	PUNCT
ejde-76	100	15	.	.	PUNCT
ejde-76	101	1	based	base	VERB
ejde-76	101	2	on	on	ADP
ejde-76	101	3	proposition	proposition	NOUN
ejde-76	101	4	3.1	3.1	NUM
ejde-76	101	5	we	we	PRON
ejde-76	101	6	consider	consider	VERB
ejde-76	101	7	the	the	DET
ejde-76	101	8	following	follow	VERB
ejde-76	101	9	problem	problem	NOUN
ejde-76	101	10	.	.	PUNCT
ejde-76	102	1	problem	problem	NOUN
ejde-76	102	2	q.	q.	PROPN
ejde-76	102	3	find	find	VERB
ejde-76	102	4	a	a	DET
ejde-76	102	5	function	function	NOUN
ejde-76	102	6	σ	σ	PROPN
ejde-76	102	7	∈	∈	PROPN
ejde-76	102	8	c([0	c([0	NOUN
ejde-76	102	9	,	,	PUNCT
ejde-76	102	10	t	t	X
ejde-76	102	11	]	]	PUNCT
ejde-76	102	12	;	;	PUNCT
ejde-76	102	13	v	v	X
ejde-76	102	14	)	)	PUNCT
ejde-76	102	15	such	such	ADJ
ejde-76	102	16	that	that	SCONJ
ejde-76	102	17	the	the	DET
ejde-76	102	18	following	follow	VERB
ejde-76	102	19	inclusion	inclusion	NOUN
ejde-76	102	20	holds	hold	VERB
ejde-76	102	21	:	:	PUNCT
ejde-76	102	22	−	−	ADP
ejde-76	102	23	σ(t	σ(t	PROPN
ejde-76	102	24	)	)	PUNCT
ejde-76	102	25	∈	∈	PROPN
ejde-76	102	26	nk(t)(a	nk(t)(a	NOUN
ejde-76	102	27	−1σ(t	−1σ(t	PROPN
ejde-76	102	28	)	)	PUNCT
ejde-76	103	1	+	+	NOUN
ejde-76	103	2	rσ(t	rσ(t	NOUN
ejde-76	103	3	)	)	PUNCT
ejde-76	103	4	)	)	PUNCT
ejde-76	103	5	∀	∀	PUNCT
ejde-76	104	1	t	t	X
ejde-76	104	2	∈	∈	PROPN
ejde-76	105	1	[	[	X
ejde-76	105	2	0	0	NUM
ejde-76	105	3	,	,	PUNCT
ejde-76	105	4	t	t	X
ejde-76	105	5	]	]	PUNCT
ejde-76	105	6	.	.	PUNCT
ejde-76	106	1	(	(	PUNCT
ejde-76	106	2	3.6	3.6	NUM
ejde-76	106	3	)	)	PUNCT
ejde-76	106	4	our	our	PRON
ejde-76	106	5	main	main	ADJ
ejde-76	106	6	result	result	NOUN
ejde-76	106	7	in	in	ADP
ejde-76	106	8	this	this	DET
ejde-76	106	9	section	section	NOUN
ejde-76	106	10	is	be	AUX
ejde-76	106	11	the	the	DET
ejde-76	106	12	following	following	NOUN
ejde-76	106	13	.	.	PUNCT
ejde-76	107	1	theorem	theorem	ADJ
ejde-76	107	2	3.2	3.2	NUM
ejde-76	107	3	.	.	PUNCT
ejde-76	108	1	assume	assume	VERB
ejde-76	108	2	(	(	PUNCT
ejde-76	108	3	h1)–(h4	h1)–(h4	ADJ
ejde-76	108	4	)	)	PUNCT
ejde-76	108	5	hold	hold	NOUN
ejde-76	108	6	.	.	PUNCT
ejde-76	109	1	then	then	ADV
ejde-76	109	2	problem	problem	NOUN
ejde-76	109	3	p	p	NOUN
ejde-76	109	4	is	be	AUX
ejde-76	109	5	tp	tp	AUX
ejde-76	109	6	-well	-well	NOUN
ejde-76	109	7	-	-	PUNCT
ejde-76	109	8	posed	pose	VERB
ejde-76	109	9	.	.	PUNCT
ejde-76	110	1	proof	proof	NOUN
ejde-76	110	2	.	.	PUNCT
ejde-76	111	1	the	the	DET
ejde-76	111	2	proof	proof	NOUN
ejde-76	111	3	will	will	AUX
ejde-76	111	4	be	be	AUX
ejde-76	111	5	carried	carry	VERB
ejde-76	111	6	out	out	ADP
ejde-76	111	7	in	in	ADP
ejde-76	111	8	several	several	ADJ
ejde-76	111	9	steps	step	NOUN
ejde-76	111	10	,	,	PUNCT
ejde-76	111	11	as	as	SCONJ
ejde-76	111	12	follows	follow	VERB
ejde-76	111	13	.	.	PUNCT
ejde-76	112	1	step	step	NOUN
ejde-76	112	2	1	1	NUM
ejde-76	112	3	.	.	PUNCT
ejde-76	113	1	we	we	PRON
ejde-76	113	2	prove	prove	VERB
ejde-76	113	3	that	that	SCONJ
ejde-76	113	4	problems	problem	NOUN
ejde-76	113	5	p	p	NOUN
ejde-76	113	6	and	and	CCONJ
ejde-76	113	7	q	q	NOUN
ejde-76	113	8	are	be	AUX
ejde-76	113	9	dual	dual	ADJ
ejde-76	113	10	problems	problem	NOUN
ejde-76	113	11	.	.	PUNCT
ejde-76	114	1	indeed	indeed	ADV
ejde-76	114	2	,	,	PUNCT
ejde-76	114	3	since	since	SCONJ
ejde-76	114	4	‖v‖x	‖v‖x	NOUN
ejde-76	114	5	=	=	PUNCT
ejde-76	114	6	max	max	PROPN
ejde-76	114	7	t∈[0,t	t∈[0,t	NOUN
ejde-76	114	8	]	]	X
ejde-76	114	9	‖v(t)‖v	‖v(t)‖v	ADJ
ejde-76	114	10	∀	∀	NOUN
ejde-76	114	11	v	v	ADP
ejde-76	114	12	∈	∈	PROPN
ejde-76	114	13	c([0	c([0	NOUN
ejde-76	114	14	,	,	PUNCT
ejde-76	114	15	t	t	X
ejde-76	114	16	]	]	PUNCT
ejde-76	114	17	;	;	PUNCT
ejde-76	114	18	v	v	X
ejde-76	114	19	)	)	PUNCT
ejde-76	114	20	,	,	PUNCT
ejde-76	114	21	it	it	PRON
ejde-76	114	22	is	be	AUX
ejde-76	114	23	easy	easy	ADJ
ejde-76	114	24	to	to	PART
ejde-76	114	25	see	see	VERB
ejde-76	114	26	that	that	SCONJ
ejde-76	114	27	any	any	DET
ejde-76	114	28	history	history	NOUN
ejde-76	114	29	-	-	PUNCT
ejde-76	114	30	dependent	dependent	ADJ
ejde-76	114	31	operator	operator	NOUN
ejde-76	114	32	h	h	NOUN
ejde-76	114	33	:	:	PUNCT
ejde-76	114	34	c([0	c([0	PROPN
ejde-76	114	35	,	,	PUNCT
ejde-76	114	36	t	t	X
ejde-76	114	37	]	]	PUNCT
ejde-76	114	38	;	;	PUNCT
ejde-76	114	39	v	v	X
ejde-76	114	40	)	)	PUNCT
ejde-76	114	41	→	→	SYM
ejde-76	114	42	c([0	c([0	PROPN
ejde-76	114	43	,	,	PUNCT
ejde-76	114	44	t	t	X
ejde-76	114	45	]	]	PUNCT
ejde-76	114	46	;	;	PUNCT
ejde-76	114	47	v	v	X
ejde-76	114	48	)	)	PUNCT
ejde-76	114	49	is	be	AUX
ejde-76	114	50	continuous	continuous	ADJ
ejde-76	114	51	.	.	PUNCT
ejde-76	115	1	therefore	therefore	ADV
ejde-76	115	2	,	,	PUNCT
ejde-76	115	3	proposition	proposition	NOUN
ejde-76	115	4	3.1	3.1	NUM
ejde-76	115	5	implies	imply	VERB
ejde-76	115	6	that	that	SCONJ
ejde-76	115	7	the	the	DET
ejde-76	115	8	operator	operator	NOUN
ejde-76	115	9	d	d	NOUN
ejde-76	115	10	defined	define	VERB
ejde-76	115	11	by	by	ADP
ejde-76	115	12	(	(	PUNCT
ejde-76	115	13	3.5	3.5	NUM
ejde-76	115	14	)	)	PUNCT
ejde-76	115	15	satisfies	satisfy	VERB
ejde-76	115	16	conditions	condition	NOUN
ejde-76	115	17	(	(	PUNCT
ejde-76	115	18	a	a	X
ejde-76	115	19	)	)	PUNCT
ejde-76	115	20	and	and	CCONJ
ejde-76	115	21	(	(	PUNCT
ejde-76	115	22	b	b	NOUN
ejde-76	115	23	)	)	PUNCT
ejde-76	115	24	in	in	ADP
ejde-76	115	25	definition	definition	NOUN
ejde-76	115	26	2.1	2.1	NUM
ejde-76	115	27	with	with	ADP
ejde-76	115	28	u	u	NOUN
ejde-76	115	29	=	=	PROPN
ejde-76	115	30	σ	σ	PROPN
ejde-76	115	31	=	=	SYM
ejde-76	115	32	c([0	c([0	PROPN
ejde-76	115	33	,	,	PUNCT
ejde-76	115	34	t	t	X
ejde-76	115	35	]	]	PUNCT
ejde-76	115	36	;	;	PUNCT
ejde-76	115	37	v	v	NOUN
ejde-76	115	38	)	)	PUNCT
ejde-76	115	39	.	.	PUNCT
ejde-76	116	1	ejde-2022/03	ejde-2022/03	NOUN
ejde-76	116	2	duality	duality	NOUN
ejde-76	116	3	arguments	argument	NOUN
ejde-76	116	4	for	for	ADP
ejde-76	116	5	well	well	ADV
ejde-76	116	6	-	-	PUNCT
ejde-76	116	7	posedness	posedness	NOUN
ejde-76	116	8	5	5	NUM
ejde-76	116	9	assume	assume	VERB
ejde-76	116	10	now	now	ADV
ejde-76	116	11	that	that	SCONJ
ejde-76	116	12	u	u	PROPN
ejde-76	116	13	∈	∈	PROPN
ejde-76	116	14	c([0	c([0	NOUN
ejde-76	116	15	,	,	PUNCT
ejde-76	116	16	t	t	X
ejde-76	116	17	]	]	PUNCT
ejde-76	116	18	;	;	PUNCT
ejde-76	116	19	v	v	X
ejde-76	116	20	)	)	PUNCT
ejde-76	116	21	is	be	AUX
ejde-76	116	22	a	a	DET
ejde-76	116	23	solution	solution	NOUN
ejde-76	116	24	of	of	ADP
ejde-76	116	25	problem	problem	NOUN
ejde-76	116	26	p	p	X
ejde-76	116	27	,	,	PUNCT
ejde-76	116	28	i.e.	i.e.	X
ejde-76	116	29	,	,	PUNCT
ejde-76	116	30	u(t	u(t	NOUN
ejde-76	116	31	)	)	PUNCT
ejde-76	116	32	∈	∈	PROPN
ejde-76	116	33	k(t	k(t	PROPN
ejde-76	116	34	)	)	PUNCT
ejde-76	116	35	and	and	CCONJ
ejde-76	116	36	(	(	PUNCT
ejde-76	116	37	f(t)−au(t)−	f(t)−au(t)−	PROPN
ejde-76	116	38	su(t	su(t	NUM
ejde-76	116	39	)	)	PUNCT
ejde-76	116	40	,	,	PUNCT
ejde-76	116	41	v	v	ADP
ejde-76	116	42	−	−	PROPN
ejde-76	116	43	u(t))v	u(t))v	ADJ
ejde-76	116	44	≤	≤	ADV
ejde-76	116	45	0	0	NUM
ejde-76	116	46	∀	∀	NOUN
ejde-76	116	47	v	v	ADP
ejde-76	116	48	∈	∈	PROPN
ejde-76	116	49	k(t	k(t	X
ejde-76	116	50	)	)	PUNCT
ejde-76	116	51	,	,	PUNCT
ejde-76	116	52	t	t	PROPN
ejde-76	116	53	∈	∈	PROPN
ejde-76	117	1	[	[	X
ejde-76	117	2	0	0	NUM
ejde-76	117	3	,	,	PUNCT
ejde-76	117	4	t	t	X
ejde-76	117	5	]	]	PUNCT
ejde-76	117	6	.	.	PUNCT
ejde-76	118	1	(	(	PUNCT
ejde-76	118	2	3.7	3.7	NUM
ejde-76	118	3	)	)	PUNCT
ejde-76	118	4	this	this	DET
ejde-76	118	5	inequality	inequality	NOUN
ejde-76	118	6	is	be	AUX
ejde-76	118	7	equivalent	equivalent	ADJ
ejde-76	118	8	to	to	ADP
ejde-76	118	9	the	the	DET
ejde-76	118	10	inclusion	inclusion	NOUN
ejde-76	118	11	f(t)−au(t)−	f(t)−au(t)−	PROPN
ejde-76	118	12	su(t	su(t	PROPN
ejde-76	118	13	)	)	PUNCT
ejde-76	118	14	∈	∈	PROPN
ejde-76	118	15	nk(t)(u(t	nk(t)(u(t	NOUN
ejde-76	118	16	)	)	PUNCT
ejde-76	118	17	)	)	PUNCT
ejde-76	118	18	∀	∀	PUNCT
ejde-76	119	1	t	t	X
ejde-76	119	2	∈	∈	PROPN
ejde-76	120	1	[	[	X
ejde-76	120	2	0	0	NUM
ejde-76	120	3	,	,	PUNCT
ejde-76	120	4	t	t	X
ejde-76	120	5	]	]	PUNCT
ejde-76	120	6	.	.	PUNCT
ejde-76	121	1	(	(	PUNCT
ejde-76	121	2	3.8	3.8	NUM
ejde-76	121	3	)	)	PUNCT
ejde-76	121	4	we	we	PRON
ejde-76	121	5	now	now	ADV
ejde-76	121	6	take	take	VERB
ejde-76	121	7	σ(t	σ(t	NOUN
ejde-76	121	8	)	)	PUNCT
ejde-76	121	9	=	=	PUNCT
ejde-76	121	10	du(t	du(t	X
ejde-76	121	11	)	)	PUNCT
ejde-76	121	12	for	for	ADP
ejde-76	121	13	all	all	DET
ejde-76	121	14	t	t	NOUN
ejde-76	121	15	∈	∈	PROPN
ejde-76	122	1	[	[	X
ejde-76	122	2	0	0	NUM
ejde-76	122	3	,	,	PUNCT
ejde-76	122	4	t	t	X
ejde-76	122	5	]	]	PUNCT
ejde-76	122	6	,	,	PUNCT
ejde-76	122	7	then	then	ADV
ejde-76	122	8	we	we	PRON
ejde-76	122	9	use	use	VERB
ejde-76	122	10	definition	definition	NOUN
ejde-76	122	11	(	(	PUNCT
ejde-76	122	12	3.5	3.5	NUM
ejde-76	122	13	)	)	PUNCT
ejde-76	122	14	and	and	CCONJ
ejde-76	122	15	proposition	proposition	NOUN
ejde-76	122	16	3.1	3.1	NUM
ejde-76	122	17	to	to	PART
ejde-76	122	18	see	see	VERB
ejde-76	122	19	that	that	SCONJ
ejde-76	122	20	σ(t	σ(t	NOUN
ejde-76	122	21	)	)	PUNCT
ejde-76	122	22	=	=	SYM
ejde-76	122	23	au(t	au(t	PRON
ejde-76	122	24	)	)	PUNCT
ejde-76	123	1	+	+	CCONJ
ejde-76	123	2	su(t)−	su(t)−	PROPN
ejde-76	123	3	f(t	f(t	PROPN
ejde-76	123	4	)	)	PUNCT
ejde-76	123	5	,	,	PUNCT
ejde-76	123	6	u(t	u(t	NOUN
ejde-76	123	7	)	)	PUNCT
ejde-76	123	8	=	=	PUNCT
ejde-76	123	9	a−1σ(t	a−1σ(t	X
ejde-76	123	10	)	)	PUNCT
ejde-76	124	1	+	+	NOUN
ejde-76	124	2	rσ(t	rσ(t	NOUN
ejde-76	124	3	)	)	PUNCT
ejde-76	124	4	∀	∀	PUNCT
ejde-76	125	1	t	t	X
ejde-76	125	2	∈	∈	PROPN
ejde-76	126	1	[	[	X
ejde-76	126	2	0	0	NUM
ejde-76	126	3	,	,	PUNCT
ejde-76	126	4	t	t	X
ejde-76	126	5	]	]	PUNCT
ejde-76	126	6	.	.	PUNCT
ejde-76	127	1	(	(	PUNCT
ejde-76	127	2	3.9	3.9	NUM
ejde-76	127	3	)	)	PUNCT
ejde-76	127	4	therefore	therefore	ADV
ejde-76	127	5	,	,	PUNCT
ejde-76	127	6	from	from	ADP
ejde-76	127	7	(	(	PUNCT
ejde-76	127	8	3.8	3.8	NUM
ejde-76	127	9	)	)	PUNCT
ejde-76	127	10	and	and	CCONJ
ejde-76	127	11	(	(	PUNCT
ejde-76	127	12	3.9	3.9	NUM
ejde-76	127	13	)	)	PUNCT
ejde-76	127	14	we	we	PRON
ejde-76	127	15	deduce	deduce	VERB
ejde-76	127	16	that	that	SCONJ
ejde-76	127	17	−	−	ADP
ejde-76	127	18	σ(t	σ(t	PROPN
ejde-76	127	19	)	)	PUNCT
ejde-76	127	20	∈	∈	PROPN
ejde-76	127	21	nk(t)(a	nk(t)(a	NOUN
ejde-76	127	22	−1σ(t	−1σ(t	PROPN
ejde-76	127	23	)	)	PUNCT
ejde-76	128	1	+	+	NOUN
ejde-76	128	2	rσ(t	rσ(t	NOUN
ejde-76	128	3	)	)	PUNCT
ejde-76	128	4	)	)	PUNCT
ejde-76	128	5	∀	∀	PUNCT
ejde-76	129	1	t	t	X
ejde-76	129	2	∈	∈	PROPN
ejde-76	130	1	[	[	X
ejde-76	130	2	0	0	NUM
ejde-76	130	3	,	,	PUNCT
ejde-76	130	4	t	t	X
ejde-76	130	5	]	]	PUNCT
ejde-76	130	6	,	,	PUNCT
ejde-76	130	7	(	(	PUNCT
ejde-76	130	8	3.10	3.10	NUM
ejde-76	130	9	)	)	PUNCT
ejde-76	130	10	which	which	PRON
ejde-76	130	11	shows	show	VERB
ejde-76	130	12	that	that	SCONJ
ejde-76	130	13	σ	σ	PROPN
ejde-76	130	14	is	be	AUX
ejde-76	130	15	a	a	DET
ejde-76	130	16	solution	solution	NOUN
ejde-76	130	17	of	of	ADP
ejde-76	130	18	problem	problem	NOUN
ejde-76	130	19	q.	q.	PROPN
ejde-76	130	20	conversely	conversely	ADV
ejde-76	130	21	,	,	PUNCT
ejde-76	130	22	if	if	SCONJ
ejde-76	130	23	σ	σ	PROPN
ejde-76	130	24	∈	∈	PROPN
ejde-76	130	25	c([0	c([0	NOUN
ejde-76	130	26	,	,	PUNCT
ejde-76	130	27	t	t	X
ejde-76	130	28	]	]	PUNCT
ejde-76	130	29	;	;	PUNCT
ejde-76	130	30	v	v	X
ejde-76	130	31	)	)	PUNCT
ejde-76	130	32	is	be	AUX
ejde-76	130	33	a	a	DET
ejde-76	130	34	solution	solution	NOUN
ejde-76	130	35	of	of	ADP
ejde-76	130	36	(	(	PUNCT
ejde-76	130	37	3.10	3.10	NUM
ejde-76	130	38	)	)	PUNCT
ejde-76	130	39	then	then	ADV
ejde-76	130	40	it	it	PRON
ejde-76	130	41	is	be	AUX
ejde-76	130	42	easy	easy	ADJ
ejde-76	130	43	to	to	PART
ejde-76	130	44	see	see	VERB
ejde-76	130	45	that	that	SCONJ
ejde-76	130	46	the	the	DET
ejde-76	130	47	function	function	NOUN
ejde-76	130	48	u(t	u(t	NOUN
ejde-76	130	49	)	)	PUNCT
ejde-76	130	50	=	=	SYM
ejde-76	130	51	d−1σ(t	d−1σ(t	PROPN
ejde-76	130	52	)	)	PUNCT
ejde-76	130	53	for	for	ADP
ejde-76	130	54	all	all	DET
ejde-76	130	55	t	t	NOUN
ejde-76	130	56	∈	∈	PROPN
ejde-76	131	1	[	[	X
ejde-76	131	2	0	0	NUM
ejde-76	131	3	,	,	PUNCT
ejde-76	131	4	t	t	PROPN
ejde-76	131	5	]	]	PUNCT
ejde-76	131	6	is	be	AUX
ejde-76	131	7	a	a	DET
ejde-76	131	8	solution	solution	NOUN
ejde-76	131	9	of	of	ADP
ejde-76	131	10	inequality	inequality	NOUN
ejde-76	131	11	(	(	PUNCT
ejde-76	131	12	3.7	3.7	NUM
ejde-76	131	13	)	)	PUNCT
ejde-76	131	14	.	.	PUNCT
ejde-76	132	1	we	we	PRON
ejde-76	132	2	deduce	deduce	VERB
ejde-76	132	3	from	from	ADP
ejde-76	132	4	here	here	ADV
ejde-76	132	5	that	that	DET
ejde-76	132	6	condition	condition	NOUN
ejde-76	132	7	(	(	PUNCT
ejde-76	132	8	c	c	NOUN
ejde-76	132	9	)	)	PUNCT
ejde-76	132	10	in	in	ADP
ejde-76	132	11	definition	definition	NOUN
ejde-76	132	12	2.1	2.1	NUM
ejde-76	132	13	is	be	AUX
ejde-76	132	14	also	also	ADV
ejde-76	132	15	satisfied	satisfied	ADJ
ejde-76	132	16	.	.	PUNCT
ejde-76	133	1	therefore	therefore	ADV
ejde-76	133	2	,	,	PUNCT
ejde-76	133	3	p	p	NOUN
ejde-76	133	4	and	and	CCONJ
ejde-76	133	5	q	q	NOUN
ejde-76	133	6	are	be	AUX
ejde-76	133	7	dual	dual	ADJ
ejde-76	133	8	problems	problem	NOUN
ejde-76	133	9	,	,	PUNCT
ejde-76	133	10	which	which	PRON
ejde-76	133	11	concludes	conclude	VERB
ejde-76	133	12	step	step	NOUN
ejde-76	133	13	1	1	NUM
ejde-76	133	14	.	.	PUNCT
ejde-76	134	1	step	step	NOUN
ejde-76	134	2	2	2	NUM
ejde-76	134	3	.	.	PUNCT
ejde-76	135	1	we	we	PRON
ejde-76	135	2	now	now	ADV
ejde-76	135	3	construct	construct	VERB
ejde-76	135	4	a	a	DET
ejde-76	135	5	tykhonov	tykhonov	NOUN
ejde-76	135	6	triple	triple	NOUN
ejde-76	135	7	tq	tq	ADV
ejde-76	135	8	and	and	CCONJ
ejde-76	135	9	prove	prove	VERB
ejde-76	135	10	the	the	DET
ejde-76	135	11	tq	tq	ADV
ejde-76	135	12	-	-	PUNCT
ejde-76	135	13	well	well	NOUN
ejde-76	135	14	-	-	PUNCT
ejde-76	135	15	posedness	posedness	NOUN
ejde-76	135	16	of	of	ADP
ejde-76	135	17	problem	problem	NOUN
ejde-76	135	18	q.	q.	PROPN
ejde-76	135	19	first	first	ADV
ejde-76	135	20	,	,	PUNCT
ejde-76	135	21	we	we	PRON
ejde-76	135	22	recall	recall	VERB
ejde-76	135	23	that	that	SCONJ
ejde-76	135	24	the	the	DET
ejde-76	135	25	existence	existence	NOUN
ejde-76	135	26	of	of	ADP
ejde-76	135	27	a	a	DET
ejde-76	135	28	unique	unique	ADJ
ejde-76	135	29	solution	solution	NOUN
ejde-76	135	30	to	to	ADP
ejde-76	135	31	problem	problem	NOUN
ejde-76	136	1	q	q	NOUN
ejde-76	136	2	follows	follow	VERB
ejde-76	136	3	from	from	ADP
ejde-76	136	4	a	a	DET
ejde-76	136	5	recent	recent	ADJ
ejde-76	136	6	result	result	NOUN
ejde-76	136	7	proved	prove	VERB
ejde-76	136	8	in	in	ADP
ejde-76	136	9	[	[	X
ejde-76	136	10	9	9	NUM
ejde-76	136	11	]	]	PUNCT
ejde-76	136	12	.	.	PUNCT
ejde-76	137	1	next	next	ADV
ejde-76	137	2	,	,	PUNCT
ejde-76	137	3	we	we	PRON
ejde-76	137	4	use	use	VERB
ejde-76	137	5	notation	notation	NOUN
ejde-76	137	6	(	(	PUNCT
ejde-76	137	7	3.3	3.3	NUM
ejde-76	137	8	)	)	PUNCT
ejde-76	137	9	and	and	CCONJ
ejde-76	137	10	define	define	VERB
ejde-76	137	11	the	the	DET
ejde-76	137	12	tykhonov	tykhonov	NOUN
ejde-76	137	13	triple	triple	NOUN
ejde-76	137	14	tq	tq	ADP
ejde-76	137	15	=	=	SYM
ejde-76	137	16	(	(	PUNCT
ejde-76	137	17	i	i	NOUN
ejde-76	137	18	,	,	PUNCT
ejde-76	137	19	ωq	ωq	PRON
ejde-76	137	20	,	,	PUNCT
ejde-76	137	21	c	c	NOUN
ejde-76	137	22	)	)	PUNCT
ejde-76	137	23	as	as	SCONJ
ejde-76	137	24	follows	follow	VERB
ejde-76	137	25	:	:	PUNCT
ejde-76	137	26	ωq(θ	ωq(θ	X
ejde-76	137	27	)	)	PUNCT
ejde-76	137	28	=	=	SYM
ejde-76	137	29	{	{	PUNCT
ejde-76	137	30	σ	σ	PROPN
ejde-76	137	31	∈	∈	PROPN
ejde-76	137	32	c([0	c([0	NOUN
ejde-76	137	33	,	,	PUNCT
ejde-76	137	34	t	t	X
ejde-76	137	35	]	]	PUNCT
ejde-76	137	36	;	;	PUNCT
ejde-76	137	37	v	v	X
ejde-76	137	38	)	)	PUNCT
ejde-76	137	39	:	:	PUNCT
ejde-76	137	40	a−1σ(t	a−1σ(t	X
ejde-76	137	41	)	)	PUNCT
ejde-76	138	1	+	+	NOUN
ejde-76	138	2	rσ(t	rσ(t	NOUN
ejde-76	138	3	)	)	PUNCT
ejde-76	138	4	∈	∈	PROPN
ejde-76	138	5	k(t	k(t	PROPN
ejde-76	138	6	)	)	PUNCT
ejde-76	138	7	,	,	PUNCT
ejde-76	138	8	(	(	PUNCT
ejde-76	138	9	a−1σ(t	a−1σ(t	X
ejde-76	138	10	)	)	PUNCT
ejde-76	139	1	+	+	NOUN
ejde-76	139	2	rσ(t)−	rσ(t)−	PROPN
ejde-76	139	3	v	v	NOUN
ejde-76	139	4	,	,	PUNCT
ejde-76	139	5	σ(t))v	σ(t))v	ADJ
ejde-76	139	6	≤	≤	ADJ
ejde-76	139	7	θ	θ	PROPN
ejde-76	139	8	∀	∀	NOUN
ejde-76	139	9	v	v	ADP
ejde-76	139	10	∈	∈	PROPN
ejde-76	139	11	k(t	k(t	PROPN
ejde-76	139	12	)	)	PUNCT
ejde-76	139	13	,	,	PUNCT
ejde-76	139	14	t	t	PROPN
ejde-76	139	15	∈	∈	PROPN
ejde-76	140	1	[	[	X
ejde-76	140	2	0	0	NUM
ejde-76	140	3	,	,	PUNCT
ejde-76	140	4	t	t	X
ejde-76	140	5	]	]	PUNCT
ejde-76	140	6	}	}	PUNCT
ejde-76	140	7	(	(	PUNCT
ejde-76	140	8	3.11	3.11	NUM
ejde-76	140	9	)	)	PUNCT
ejde-76	140	10	for	for	ADP
ejde-76	140	11	each	each	DET
ejde-76	140	12	θ	θ	PROPN
ejde-76	140	13	≥	≥	NOUN
ejde-76	140	14	0	0	NUM
ejde-76	140	15	.	.	PUNCT
ejde-76	141	1	let	let	VERB
ejde-76	141	2	σ	σ	X
ejde-76	141	3	∈	∈	PROPN
ejde-76	141	4	c([0	c([0	NOUN
ejde-76	141	5	,	,	PUNCT
ejde-76	141	6	t	t	X
ejde-76	141	7	]	]	PUNCT
ejde-76	141	8	;	;	PUNCT
ejde-76	141	9	v	v	X
ejde-76	141	10	)	)	PUNCT
ejde-76	141	11	be	be	AUX
ejde-76	141	12	the	the	DET
ejde-76	141	13	solution	solution	NOUN
ejde-76	141	14	of	of	ADP
ejde-76	141	15	problem	problem	NOUN
ejde-76	141	16	q.	q.	PROPN
ejde-76	141	17	then	then	ADV
ejde-76	141	18	a−1σ(t	a−1σ(t	NUM
ejde-76	141	19	)	)	PUNCT
ejde-76	142	1	+	+	NOUN
ejde-76	142	2	rσ(t	rσ(t	NOUN
ejde-76	142	3	)	)	PUNCT
ejde-76	142	4	∈	∈	PROPN
ejde-76	142	5	k(t	k(t	PROPN
ejde-76	142	6	)	)	PUNCT
ejde-76	142	7	,	,	PUNCT
ejde-76	142	8	(	(	PUNCT
ejde-76	142	9	a−1σ(t	a−1σ(t	X
ejde-76	142	10	)	)	PUNCT
ejde-76	143	1	+	+	NOUN
ejde-76	143	2	rσ(t)−	rσ(t)−	PROPN
ejde-76	143	3	v	v	NOUN
ejde-76	143	4	,	,	PUNCT
ejde-76	143	5	σ(t))v	σ(t))v	ADJ
ejde-76	143	6	≤	≤	ADV
ejde-76	143	7	0	0	NUM
ejde-76	143	8	∀	∀	NOUN
ejde-76	143	9	v	v	ADP
ejde-76	143	10	∈	∈	PROPN
ejde-76	143	11	k(t	k(t	X
ejde-76	143	12	)	)	PUNCT
ejde-76	143	13	,	,	PUNCT
ejde-76	143	14	t	t	PROPN
ejde-76	143	15	∈	∈	PROPN
ejde-76	144	1	[	[	X
ejde-76	144	2	0	0	NUM
ejde-76	144	3	,	,	PUNCT
ejde-76	144	4	t	t	X
ejde-76	144	5	]	]	PUNCT
ejde-76	144	6	.	.	PUNCT
ejde-76	145	1	(	(	PUNCT
ejde-76	145	2	3.12	3.12	NUM
ejde-76	145	3	)	)	PUNCT
ejde-76	145	4	this	this	PRON
ejde-76	145	5	implies	imply	VERB
ejde-76	145	6	that	that	SCONJ
ejde-76	145	7	σ	σ	PROPN
ejde-76	145	8	∈	∈	PROPN
ejde-76	145	9	ωq(θ	ωq(θ	NOUN
ejde-76	145	10	)	)	PUNCT
ejde-76	145	11	for	for	ADP
ejde-76	145	12	each	each	DET
ejde-76	145	13	θ	θ	PROPN
ejde-76	145	14	∈	∈	PROPN
ejde-76	145	15	r+	r+	NOUN
ejde-76	145	16	and	and	CCONJ
ejde-76	145	17	,	,	PUNCT
ejde-76	145	18	therefore	therefore	ADV
ejde-76	145	19	,	,	PUNCT
ejde-76	145	20	tq	tq	ADV
ejde-76	145	21	is	be	AUX
ejde-76	145	22	a	a	DET
ejde-76	145	23	tykhonov	tykhonov	ADJ
ejde-76	145	24	triple	triple	NOUN
ejde-76	145	25	.	.	PUNCT
ejde-76	146	1	let	let	VERB
ejde-76	146	2	t	t	X
ejde-76	146	3	∈	∈	PROPN
ejde-76	147	1	[	[	X
ejde-76	147	2	0	0	NUM
ejde-76	147	3	,	,	PUNCT
ejde-76	147	4	t	t	NOUN
ejde-76	147	5	]	]	PUNCT
ejde-76	147	6	and	and	CCONJ
ejde-76	147	7	let	let	VERB
ejde-76	147	8	{	{	PUNCT
ejde-76	147	9	σn	σn	NOUN
ejde-76	147	10	}	}	PUNCT
ejde-76	147	11	⊂	⊂	PROPN
ejde-76	147	12	c([0	c([0	PROPN
ejde-76	147	13	,	,	PUNCT
ejde-76	147	14	t	t	X
ejde-76	147	15	]	]	PUNCT
ejde-76	147	16	;	;	PUNCT
ejde-76	147	17	v	v	X
ejde-76	147	18	)	)	PUNCT
ejde-76	147	19	be	be	AUX
ejde-76	147	20	a	a	DET
ejde-76	147	21	tq	tq	ADV
ejde-76	147	22	-	-	PUNCT
ejde-76	147	23	approximating	approximate	VERB
ejde-76	147	24	sequence	sequence	NOUN
ejde-76	147	25	for	for	ADP
ejde-76	147	26	problem	problem	NOUN
ejde-76	148	1	q.	q.	PROPN
ejde-76	149	1	then	then	ADV
ejde-76	149	2	there	there	PRON
ejde-76	149	3	exists	exist	VERB
ejde-76	149	4	a	a	DET
ejde-76	149	5	sequence	sequence	NOUN
ejde-76	149	6	{	{	PUNCT
ejde-76	149	7	θn	θn	NOUN
ejde-76	149	8	}	}	PUNCT
ejde-76	149	9	∈	∈	PROPN
ejde-76	149	10	c	c	NOUN
ejde-76	149	11	such	such	ADJ
ejde-76	149	12	that	that	PRON
ejde-76	149	13	,	,	PUNCT
ejde-76	149	14	for	for	ADP
ejde-76	149	15	each	each	DET
ejde-76	149	16	n	n	PRON
ejde-76	149	17	∈	∈	PROPN
ejde-76	149	18	n	n	CCONJ
ejde-76	149	19	,	,	PUNCT
ejde-76	149	20	σn	σn	PROPN
ejde-76	149	21	∈	∈	PROPN
ejde-76	149	22	ωq(θn	ωq(θn	PROPN
ejde-76	149	23	)	)	PUNCT
ejde-76	149	24	.	.	PUNCT
ejde-76	150	1	we	we	PRON
ejde-76	150	2	now	now	ADV
ejde-76	150	3	use	use	VERB
ejde-76	150	4	(	(	PUNCT
ejde-76	150	5	3.11	3.11	NUM
ejde-76	150	6	)	)	PUNCT
ejde-76	150	7	and	and	CCONJ
ejde-76	150	8	(	(	PUNCT
ejde-76	150	9	3.12	3.12	NUM
ejde-76	150	10	)	)	PUNCT
ejde-76	150	11	to	to	PART
ejde-76	150	12	deduce	deduce	VERB
ejde-76	150	13	that	that	PRON
ejde-76	150	14	(	(	PUNCT
ejde-76	150	15	a−1σ(t)−a−1σn(t	a−1σ(t)−a−1σn(t	PROPN
ejde-76	150	16	)	)	PUNCT
ejde-76	150	17	,	,	PUNCT
ejde-76	150	18	σ(t)−	σ(t)−	PROPN
ejde-76	150	19	σn(t))v	σn(t))v	PUNCT
ejde-76	150	20	≤	≤	PROPN
ejde-76	150	21	θn	θn	ADP
ejde-76	150	22	+	+	CCONJ
ejde-76	150	23	(	(	PUNCT
ejde-76	150	24	rσ(t)−rσn(t	rσ(t)−rσn(t	PROPN
ejde-76	150	25	)	)	PUNCT
ejde-76	150	26	,	,	PUNCT
ejde-76	150	27	σn(t)−	σn(t)−	PROPN
ejde-76	150	28	σ(t))v	σ(t))v	PROPN
ejde-76	150	29	.	.	PUNCT
ejde-76	151	1	using	use	VERB
ejde-76	151	2	(	(	PUNCT
ejde-76	151	3	3.2	3.2	NUM
ejde-76	151	4	)	)	PUNCT
ejde-76	151	5	and	and	CCONJ
ejde-76	151	6	the	the	DET
ejde-76	151	7	history	history	NOUN
ejde-76	151	8	-	-	PUNCT
ejde-76	151	9	dependence	dependence	NOUN
ejde-76	151	10	of	of	ADP
ejde-76	151	11	the	the	DET
ejde-76	151	12	operator	operator	NOUN
ejde-76	151	13	r	r	NOUN
ejde-76	151	14	we	we	PRON
ejde-76	151	15	find	find	VERB
ejde-76	151	16	that	that	SCONJ
ejde-76	151	17	ma−1‖σ(t)−	ma−1‖σ(t)−	PROPN
ejde-76	151	18	σn(t)‖2v	σn(t)‖2v	PROPN
ejde-76	151	19	≤	≤	PROPN
ejde-76	151	20	θn	θn	ADP
ejde-76	152	1	+	+	X
ejde-76	152	2	lr	lr	X
ejde-76	152	3	(	(	PUNCT
ejde-76	152	4	∫	∫	PROPN
ejde-76	152	5	t	t	PROPN
ejde-76	152	6	0	0	NUM
ejde-76	152	7	‖σ(s)−	‖σ(s)−	PUNCT
ejde-76	152	8	σn(s)‖v	σn(s)‖v	NOUN
ejde-76	152	9	ds	ds	X
ejde-76	152	10	)	)	PUNCT
ejde-76	152	11	‖σ(t)−	‖σ(t)−	PROPN
ejde-76	152	12	σn(t)‖v	σn(t)‖v	VERB
ejde-76	152	13	where	where	SCONJ
ejde-76	152	14	,	,	PUNCT
ejde-76	152	15	here	here	ADV
ejde-76	152	16	and	and	CCONJ
ejde-76	152	17	below	below	ADV
ejde-76	152	18	,	,	PUNCT
ejde-76	152	19	ma−1	ma−1	NOUN
ejde-76	152	20	=	=	SYM
ejde-76	152	21	ma	ma	PROPN
ejde-76	152	22	l2	l2	PROPN
ejde-76	152	23	a	a	PRON
ejde-76	152	24	.	.	PUNCT
ejde-76	153	1	therefore	therefore	ADV
ejde-76	153	2	,	,	PUNCT
ejde-76	153	3	the	the	DET
ejde-76	153	4	elementary	elementary	ADJ
ejde-76	153	5	inequality	inequality	PROPN
ejde-76	153	6	x2	x2	PROPN
ejde-76	153	7	≤	≤	PROPN
ejde-76	153	8	ax+	ax+	PROPN
ejde-76	153	9	b	b	NOUN
ejde-76	153	10	=	=	NOUN
ejde-76	153	11	⇒	⇒	NOUN
ejde-76	153	12	x	x	SYM
ejde-76	153	13	≤	≤	X
ejde-76	153	14	a+	a+	PUNCT
ejde-76	153	15	√	√	PROPN
ejde-76	153	16	b	b	X
ejde-76	153	17	∀x	∀x	NUM
ejde-76	153	18	,	,	PUNCT
ejde-76	153	19	a	a	PRON
ejde-76	153	20	,	,	PUNCT
ejde-76	153	21	b	b	X
ejde-76	153	22	>	>	X
ejde-76	153	23	0	0	NUM
ejde-76	153	24	implies	imply	VERB
ejde-76	153	25	that	that	SCONJ
ejde-76	153	26	‖σ(t)−	‖σ(t)−	PROPN
ejde-76	153	27	σn(t)‖v	σn(t)‖v	NOUN
ejde-76	153	28	≤	≤	NOUN
ejde-76	153	29	(	(	PUNCT
ejde-76	153	30	θn	θn	DET
ejde-76	153	31	ma−1	ma−1	PROPN
ejde-76	153	32	)	)	PUNCT
ejde-76	153	33	1/2	1/2	NUM
ejde-76	154	1	+	+	CCONJ
ejde-76	154	2	lr	lr	PROPN
ejde-76	154	3	ma−1	ma−1	PROPN
ejde-76	154	4	∫	∫	PROPN
ejde-76	154	5	t	t	PROPN
ejde-76	154	6	0	0	NUM
ejde-76	154	7	‖σ(s)−	‖σ(s)−	PROPN
ejde-76	154	8	σn(s)‖v	σn(s)‖v	NOUN
ejde-76	154	9	ds	ds	VERB
ejde-76	154	10	6	6	NUM
ejde-76	154	11	r.	r.	PROPN
ejde-76	154	12	hu	hu	PROPN
ejde-76	154	13	,	,	PUNCT
ejde-76	154	14	m.	m.	PROPN
ejde-76	154	15	sofonea	sofonea	PROPN
ejde-76	154	16	ejde-2022/03	ejde-2022/03	PROPN
ejde-76	155	1	and	and	CCONJ
ejde-76	155	2	,	,	PUNCT
ejde-76	155	3	using	use	VERB
ejde-76	155	4	gronwall	gronwall	PROPN
ejde-76	155	5	’s	’s	PART
ejde-76	155	6	argument	argument	NOUN
ejde-76	155	7	,	,	PUNCT
ejde-76	155	8	we	we	PRON
ejde-76	155	9	find	find	VERB
ejde-76	155	10	that	that	SCONJ
ejde-76	155	11	‖σ(t)−	‖σ(t)−	PROPN
ejde-76	155	12	σn(t)‖v	σn(t)‖v	NOUN
ejde-76	155	13	≤	≤	NOUN
ejde-76	155	14	(	(	PUNCT
ejde-76	155	15	θn	θn	DET
ejde-76	155	16	ma−1	ma−1	PROPN
ejde-76	155	17	)	)	PUNCT
ejde-76	155	18	1/2	1/2	NUM
ejde-76	155	19	e	e	NOUN
ejde-76	155	20	lr	lr	PROPN
ejde-76	155	21	m	m	PROPN
ejde-76	155	22	a−1	a−1	PROPN
ejde-76	155	23	t	t	PROPN
ejde-76	155	24	.	.	PUNCT
ejde-76	156	1	next	next	ADV
ejde-76	156	2	,	,	PUNCT
ejde-76	156	3	since	since	SCONJ
ejde-76	156	4	θn	θn	INTJ
ejde-76	156	5	→	→	SYM
ejde-76	156	6	0	0	NUM
ejde-76	156	7	we	we	PRON
ejde-76	156	8	deduce	deduce	VERB
ejde-76	156	9	that	that	SCONJ
ejde-76	156	10	σn	σn	PROPN
ejde-76	156	11	→	→	SYM
ejde-76	156	12	σ	σ	PROPN
ejde-76	156	13	in	in	ADP
ejde-76	156	14	c([0	c([0	PROPN
ejde-76	156	15	,	,	PUNCT
ejde-76	156	16	t	t	X
ejde-76	156	17	]	]	PUNCT
ejde-76	156	18	;	;	PUNCT
ejde-76	156	19	v	v	NOUN
ejde-76	156	20	)	)	PUNCT
ejde-76	156	21	.	.	PUNCT
ejde-76	157	1	we	we	PRON
ejde-76	157	2	conclude	conclude	VERB
ejde-76	157	3	from	from	ADP
ejde-76	157	4	here	here	ADV
ejde-76	157	5	that	that	DET
ejde-76	157	6	problem	problem	NOUN
ejde-76	157	7	q	q	NOUN
ejde-76	157	8	is	be	AUX
ejde-76	157	9	tq	tq	ADV
ejde-76	157	10	-	-	PUNCT
ejde-76	157	11	well	well	ADV
ejde-76	157	12	-	-	PUNCT
ejde-76	157	13	posed	pose	VERB
ejde-76	157	14	.	.	PUNCT
ejde-76	158	1	step	step	VERB
ejde-76	158	2	3	3	NUM
ejde-76	158	3	.	.	PUNCT
ejde-76	158	4	completion	completion	NOUN
ejde-76	158	5	of	of	ADP
ejde-76	158	6	the	the	DET
ejde-76	158	7	proof	proof	NOUN
ejde-76	158	8	.	.	PUNCT
ejde-76	159	1	let	let	VERB
ejde-76	159	2	θ	θ	PROPN
ejde-76	159	3	∈	∈	PROPN
ejde-76	159	4	r+	r+	X
ejde-76	159	5	,	,	PUNCT
ejde-76	159	6	u	u	PROPN
ejde-76	159	7	∈	∈	PROPN
ejde-76	159	8	c([0	c([0	NOUN
ejde-76	159	9	,	,	PUNCT
ejde-76	159	10	t	t	X
ejde-76	159	11	]	]	PUNCT
ejde-76	159	12	,	,	PUNCT
ejde-76	159	13	v	v	NOUN
ejde-76	159	14	)	)	PUNCT
ejde-76	159	15	and	and	CCONJ
ejde-76	159	16	let	let	VERB
ejde-76	159	17	σ	σ	X
ejde-76	159	18	=	=	SYM
ejde-76	159	19	du	du	PROPN
ejde-76	159	20	.	.	PUNCT
ejde-76	159	21	then	then	ADV
ejde-76	159	22	,	,	PUNCT
ejde-76	159	23	using	use	VERB
ejde-76	159	24	arguments	argument	NOUN
ejde-76	159	25	similar	similar	ADJ
ejde-76	159	26	to	to	ADP
ejde-76	159	27	those	those	PRON
ejde-76	159	28	used	use	VERB
ejde-76	159	29	to	to	PART
ejde-76	159	30	prove	prove	VERB
ejde-76	159	31	that	that	SCONJ
ejde-76	159	32	σ	σ	PROPN
ejde-76	159	33	satisfies	satisfie	NOUN
ejde-76	159	34	inequality	inequality	NOUN
ejde-76	159	35	(	(	PUNCT
ejde-76	159	36	3.10	3.10	NUM
ejde-76	159	37	)	)	PUNCT
ejde-76	159	38	if	if	SCONJ
ejde-76	159	39	and	and	CCONJ
ejde-76	159	40	only	only	ADV
ejde-76	159	41	if	if	SCONJ
ejde-76	159	42	u	u	NOUN
ejde-76	159	43	satisfies	satisfy	VERB
ejde-76	159	44	(	(	PUNCT
ejde-76	159	45	3.7	3.7	NUM
ejde-76	159	46	)	)	PUNCT
ejde-76	159	47	,	,	PUNCT
ejde-76	159	48	it	it	PRON
ejde-76	159	49	is	be	AUX
ejde-76	159	50	easy	easy	ADJ
ejde-76	159	51	to	to	PART
ejde-76	159	52	see	see	VERB
ejde-76	159	53	that	that	SCONJ
ejde-76	159	54	u	u	PROPN
ejde-76	159	55	∈	∈	NOUN
ejde-76	159	56	ωp	ωp	X
ejde-76	159	57	(	(	PUNCT
ejde-76	159	58	θ	θ	NOUN
ejde-76	159	59	)	)	PUNCT
ejde-76	159	60	⇐	⇐	ADJ
ejde-76	159	61	⇒	⇒	PROPN
ejde-76	159	62	σ	σ	PROPN
ejde-76	159	63	∈	∈	PROPN
ejde-76	159	64	ωq(θ	ωq(θ	NUM
ejde-76	159	65	)	)	PUNCT
ejde-76	159	66	.	.	PUNCT
ejde-76	160	1	we	we	PRON
ejde-76	160	2	conclude	conclude	VERB
ejde-76	160	3	from	from	ADP
ejde-76	160	4	here	here	ADV
ejde-76	160	5	that	that	PRON
ejde-76	160	6	ωp	ωp	X
ejde-76	160	7	(	(	PUNCT
ejde-76	160	8	θ	θ	PROPN
ejde-76	160	9	)	)	PUNCT
ejde-76	160	10	6=	6=	NOUN
ejde-76	160	11	∅	∅	NOUN
ejde-76	160	12	and	and	CCONJ
ejde-76	160	13	,	,	PUNCT
ejde-76	160	14	moreover	moreover	ADV
ejde-76	160	15	,	,	PUNCT
ejde-76	160	16	(	(	PUNCT
ejde-76	160	17	2.1	2.1	NUM
ejde-76	160	18	)	)	PUNCT
ejde-76	160	19	holds	hold	VERB
ejde-76	160	20	.	.	PUNCT
ejde-76	161	1	it	it	PRON
ejde-76	161	2	follows	follow	VERB
ejde-76	161	3	now	now	ADV
ejde-76	161	4	from	from	ADP
ejde-76	161	5	steps	step	NOUN
ejde-76	161	6	1	1	NUM
ejde-76	161	7	and	and	CCONJ
ejde-76	161	8	2	2	NUM
ejde-76	161	9	that	that	SCONJ
ejde-76	161	10	we	we	PRON
ejde-76	161	11	are	be	AUX
ejde-76	161	12	in	in	ADP
ejde-76	161	13	a	a	DET
ejde-76	161	14	position	position	NOUN
ejde-76	161	15	to	to	PART
ejde-76	161	16	use	use	VERB
ejde-76	161	17	theorem	theorem	ADJ
ejde-76	161	18	2.2	2.2	NUM
ejde-76	161	19	to	to	PART
ejde-76	161	20	conclude	conclude	VERB
ejde-76	161	21	the	the	DET
ejde-76	161	22	proof	proof	NOUN
ejde-76	161	23	of	of	ADP
ejde-76	161	24	theorem	theorem	ADJ
ejde-76	161	25	3.2	3.2	NUM
ejde-76	161	26	.	.	PUNCT
ejde-76	162	1	�	�	PROPN
ejde-76	162	2	4	4	NUM
ejde-76	162	3	.	.	PUNCT
ejde-76	163	1	a	a	DET
ejde-76	163	2	convergence	convergence	NOUN
ejde-76	163	3	result	result	NOUN
ejde-76	163	4	in	in	ADP
ejde-76	163	5	this	this	DET
ejde-76	163	6	section	section	NOUN
ejde-76	163	7	we	we	PRON
ejde-76	163	8	use	use	VERB
ejde-76	163	9	the	the	DET
ejde-76	163	10	well	well	NOUN
ejde-76	163	11	-	-	PUNCT
ejde-76	163	12	posedness	posedness	NOUN
ejde-76	163	13	of	of	ADP
ejde-76	163	14	problem	problem	NOUN
ejde-76	163	15	p	p	NOUN
ejde-76	163	16	with	with	ADP
ejde-76	163	17	respect	respect	NOUN
ejde-76	163	18	to	to	ADP
ejde-76	163	19	the	the	DET
ejde-76	163	20	tykhonov	tykhonov	ADJ
ejde-76	163	21	triple	triple	NOUN
ejde-76	163	22	tp	tp	NOUN
ejde-76	163	23	to	to	PART
ejde-76	163	24	deduce	deduce	VERB
ejde-76	163	25	a	a	DET
ejde-76	163	26	continuous	continuous	ADJ
ejde-76	163	27	dependence	dependence	NOUN
ejde-76	163	28	result	result	NOUN
ejde-76	163	29	of	of	ADP
ejde-76	163	30	the	the	DET
ejde-76	163	31	solution	solution	NOUN
ejde-76	163	32	with	with	ADP
ejde-76	163	33	respect	respect	NOUN
ejde-76	163	34	to	to	ADP
ejde-76	163	35	the	the	DET
ejde-76	163	36	data	datum	NOUN
ejde-76	163	37	.	.	PUNCT
ejde-76	164	1	to	to	ADP
ejde-76	164	2	this	this	DET
ejde-76	164	3	end	end	NOUN
ejde-76	164	4	we	we	PRON
ejde-76	164	5	assume	assume	VERB
ejde-76	164	6	that	that	SCONJ
ejde-76	164	7	(	(	PUNCT
ejde-76	164	8	h1	h1	PROPN
ejde-76	164	9	)	)	PUNCT
ejde-76	164	10	holds	hold	VERB
ejde-76	164	11	and	and	CCONJ
ejde-76	164	12	we	we	PRON
ejde-76	164	13	consider	consider	VERB
ejde-76	164	14	three	three	NUM
ejde-76	164	15	sequences	sequence	NOUN
ejde-76	164	16	{	{	PUNCT
ejde-76	164	17	an	an	X
ejde-76	164	18	}	}	PUNCT
ejde-76	164	19	,	,	PUNCT
ejde-76	164	20	{	{	PUNCT
ejde-76	164	21	sn	sn	X
ejde-76	164	22	}	}	PUNCT
ejde-76	164	23	and	and	CCONJ
ejde-76	164	24	{	{	PUNCT
ejde-76	164	25	fn	fn	NOUN
ejde-76	164	26	}	}	PUNCT
ejde-76	164	27	such	such	ADJ
ejde-76	164	28	that	that	SCONJ
ejde-76	164	29	,	,	PUNCT
ejde-76	164	30	for	for	ADP
ejde-76	164	31	each	each	DET
ejde-76	164	32	n	n	PRON
ejde-76	164	33	∈	∈	PROPN
ejde-76	164	34	n	n	CCONJ
ejde-76	164	35	,	,	PUNCT
ejde-76	164	36	the	the	DET
ejde-76	164	37	following	follow	VERB
ejde-76	164	38	conditions	condition	NOUN
ejde-76	164	39	hold	hold	VERB
ejde-76	164	40	.	.	PUNCT
ejde-76	165	1	(	(	PUNCT
ejde-76	165	2	h5	h5	PROPN
ejde-76	165	3	)	)	PUNCT
ejde-76	165	4	an	an	PRON
ejde-76	165	5	:	:	PUNCT
ejde-76	165	6	v	v	NOUN
ejde-76	165	7	→	→	SYM
ejde-76	165	8	v	v	NUM
ejde-76	165	9	satisfies	satisfie	NOUN
ejde-76	165	10	condition	condition	NOUN
ejde-76	165	11	(	(	PUNCT
ejde-76	165	12	h2	h2	NOUN
ejde-76	165	13	)	)	PUNCT
ejde-76	165	14	with	with	ADP
ejde-76	165	15	mn	mn	PROPN
ejde-76	165	16	>	>	X
ejde-76	165	17	0	0	PROPN
ejde-76	165	18	.	.	PUNCT
ejde-76	166	1	(	(	PUNCT
ejde-76	166	2	h6	h6	PROPN
ejde-76	166	3	)	)	PUNCT
ejde-76	166	4	sn	sn	PROPN
ejde-76	166	5	:	:	PUNCT
ejde-76	166	6	c([0	c([0	PROPN
ejde-76	166	7	,	,	PUNCT
ejde-76	166	8	t	t	X
ejde-76	166	9	]	]	PUNCT
ejde-76	166	10	;	;	PUNCT
ejde-76	166	11	v	v	X
ejde-76	166	12	)	)	PUNCT
ejde-76	166	13	→	→	SYM
ejde-76	166	14	c([0	c([0	PROPN
ejde-76	166	15	,	,	PUNCT
ejde-76	166	16	t	t	X
ejde-76	166	17	]	]	PUNCT
ejde-76	166	18	;	;	PUNCT
ejde-76	166	19	v	v	X
ejde-76	166	20	)	)	PUNCT
ejde-76	166	21	is	be	AUX
ejde-76	166	22	a	a	DET
ejde-76	166	23	history	history	NOUN
ejde-76	166	24	-	-	PUNCT
ejde-76	166	25	dependent	dependent	ADJ
ejde-76	166	26	operator	operator	NOUN
ejde-76	166	27	,	,	PUNCT
ejde-76	166	28	i.e.	i.e.	X
ejde-76	166	29	,	,	PUNCT
ejde-76	166	30	there	there	PRON
ejde-76	166	31	exists	exist	VERB
ejde-76	166	32	ln	ln	ADV
ejde-76	166	33	>	>	X
ejde-76	166	34	0	0	NUM
ejde-76	167	1	such	such	ADJ
ejde-76	167	2	that	that	SCONJ
ejde-76	167	3	‖snu(t)−	‖snu(t)−	PROPN
ejde-76	167	4	snv(t)‖v	snv(t)‖v	PROPN
ejde-76	167	5	≤	≤	PROPN
ejde-76	167	6	ln	ln	ADJ
ejde-76	167	7	∫	∫	PROPN
ejde-76	167	8	t	t	PROPN
ejde-76	167	9	0	0	NUM
ejde-76	168	1	‖u(s)−	‖u(s)−	PROPN
ejde-76	168	2	v(s)‖v	v(s)‖v	NOUN
ejde-76	168	3	ds	ds	VERB
ejde-76	168	4	for	for	ADP
ejde-76	168	5	all	all	DET
ejde-76	168	6	u	u	NOUN
ejde-76	168	7	,	,	PUNCT
ejde-76	168	8	v	v	NOUN
ejde-76	168	9	∈	∈	PROPN
ejde-76	168	10	c([0	c([0	NOUN
ejde-76	168	11	,	,	PUNCT
ejde-76	168	12	t	t	X
ejde-76	168	13	]	]	PUNCT
ejde-76	168	14	;	;	PUNCT
ejde-76	168	15	v	v	X
ejde-76	168	16	)	)	PUNCT
ejde-76	168	17	and	and	CCONJ
ejde-76	168	18	t	t	PROPN
ejde-76	168	19	∈	∈	PROPN
ejde-76	169	1	[	[	X
ejde-76	169	2	0	0	NUM
ejde-76	169	3	,	,	PUNCT
ejde-76	169	4	t	t	X
ejde-76	169	5	]	]	PUNCT
ejde-76	169	6	.	.	PUNCT
ejde-76	170	1	(	(	PUNCT
ejde-76	170	2	h7	h7	PROPN
ejde-76	170	3	)	)	PUNCT
ejde-76	170	4	fn	fn	PROPN
ejde-76	170	5	∈	∈	PROPN
ejde-76	170	6	c([0;t	c([0;t	PROPN
ejde-76	170	7	]	]	X
ejde-76	170	8	;	;	PUNCT
ejde-76	170	9	v	v	NOUN
ejde-76	170	10	)	)	PUNCT
ejde-76	170	11	.	.	PUNCT
ejde-76	171	1	then	then	ADV
ejde-76	171	2	we	we	PRON
ejde-76	171	3	consider	consider	VERB
ejde-76	171	4	the	the	DET
ejde-76	171	5	following	follow	VERB
ejde-76	171	6	variational	variational	ADJ
ejde-76	171	7	problem	problem	NOUN
ejde-76	171	8	.	.	PUNCT
ejde-76	172	1	problem	problem	NOUN
ejde-76	172	2	pn	pn	AUX
ejde-76	172	3	.	.	PROPN
ejde-76	172	4	find	find	VERB
ejde-76	172	5	a	a	DET
ejde-76	172	6	function	function	NOUN
ejde-76	172	7	un	un	PROPN
ejde-76	172	8	∈	∈	PROPN
ejde-76	172	9	c([0	c([0	PROPN
ejde-76	172	10	,	,	PUNCT
ejde-76	172	11	t	t	X
ejde-76	172	12	]	]	PUNCT
ejde-76	172	13	;	;	PUNCT
ejde-76	172	14	v	v	X
ejde-76	172	15	)	)	PUNCT
ejde-76	172	16	such	such	ADJ
ejde-76	172	17	that	that	SCONJ
ejde-76	172	18	the	the	DET
ejde-76	172	19	following	follow	VERB
ejde-76	172	20	inequality	inequality	NOUN
ejde-76	172	21	holds	hold	VERB
ejde-76	172	22	:	:	PUNCT
ejde-76	172	23	un(t	un(t	NUM
ejde-76	172	24	)	)	PUNCT
ejde-76	172	25	∈	∈	PROPN
ejde-76	172	26	k(t	k(t	PROPN
ejde-76	172	27	)	)	PUNCT
ejde-76	172	28	,	,	PUNCT
ejde-76	172	29	and	and	CCONJ
ejde-76	172	30	(	(	PUNCT
ejde-76	172	31	anun(t	anun(t	PROPN
ejde-76	172	32	)	)	PUNCT
ejde-76	172	33	,	,	PUNCT
ejde-76	172	34	v	v	ADP
ejde-76	172	35	−	−	PROPN
ejde-76	172	36	un(t))v	un(t))v	X
ejde-76	173	1	+	+	CCONJ
ejde-76	173	2	(	(	PUNCT
ejde-76	173	3	snun(t	snun(t	NOUN
ejde-76	173	4	)	)	PUNCT
ejde-76	173	5	,	,	PUNCT
ejde-76	173	6	v	v	ADP
ejde-76	173	7	−	−	PROPN
ejde-76	173	8	un(t))v	un(t))v	X
ejde-76	173	9	≥	≥	X
ejde-76	173	10	(	(	PUNCT
ejde-76	173	11	fn(t	fn(t	NUM
ejde-76	173	12	)	)	PUNCT
ejde-76	173	13	,	,	PUNCT
ejde-76	173	14	v	v	ADP
ejde-76	173	15	−	−	PROPN
ejde-76	173	16	un(t))v	un(t))v	PUNCT
ejde-76	173	17	(	(	PUNCT
ejde-76	173	18	4.1	4.1	NUM
ejde-76	173	19	)	)	PUNCT
ejde-76	173	20	for	for	ADP
ejde-76	173	21	all	all	PRON
ejde-76	173	22	v	v	ADP
ejde-76	173	23	∈	∈	PRON
ejde-76	173	24	k(t	k(t	X
ejde-76	173	25	)	)	PUNCT
ejde-76	173	26	and	and	CCONJ
ejde-76	173	27	t	t	PROPN
ejde-76	173	28	∈	∈	PROPN
ejde-76	174	1	[	[	X
ejde-76	174	2	0	0	NUM
ejde-76	174	3	,	,	PUNCT
ejde-76	174	4	t	t	X
ejde-76	174	5	]	]	PUNCT
ejde-76	174	6	.	.	PUNCT
ejde-76	175	1	then	then	ADV
ejde-76	175	2	the	the	DET
ejde-76	175	3	arguments	argument	NOUN
ejde-76	175	4	in	in	ADP
ejde-76	175	5	section	section	NOUN
ejde-76	175	6	2	2	NUM
ejde-76	175	7	imply	imply	VERB
ejde-76	175	8	that	that	DET
ejde-76	175	9	problem	problem	NOUN
ejde-76	175	10	pn	pn	PROPN
ejde-76	175	11	has	have	VERB
ejde-76	175	12	a	a	DET
ejde-76	175	13	unique	unique	ADJ
ejde-76	175	14	solution	solution	NOUN
ejde-76	175	15	,	,	PUNCT
ejde-76	175	16	for	for	SCONJ
ejde-76	175	17	each	each	DET
ejde-76	175	18	n	n	PRON
ejde-76	175	19	∈	∈	PROPN
ejde-76	175	20	n.	n.	NOUN
ejde-76	175	21	assume	assume	VERB
ejde-76	175	22	now	now	ADV
ejde-76	175	23	that	that	SCONJ
ejde-76	175	24	(	(	PUNCT
ejde-76	175	25	h8	h8	PROPN
ejde-76	175	26	)	)	PUNCT
ejde-76	175	27	there	there	PRON
ejde-76	175	28	exists	exist	VERB
ejde-76	175	29	u0	u0	PROPN
ejde-76	175	30	∈	∈	PROPN
ejde-76	175	31	v	v	ADP
ejde-76	175	32	such	such	ADJ
ejde-76	175	33	that	that	DET
ejde-76	175	34	u0	u0	PROPN
ejde-76	175	35	∈	∈	PROPN
ejde-76	175	36	k(t	k(t	PROPN
ejde-76	175	37	)	)	PUNCT
ejde-76	175	38	for	for	ADP
ejde-76	175	39	all	all	DET
ejde-76	175	40	t	t	NOUN
ejde-76	175	41	∈	∈	PROPN
ejde-76	176	1	[	[	X
ejde-76	176	2	0	0	NUM
ejde-76	176	3	,	,	PUNCT
ejde-76	176	4	t	t	X
ejde-76	176	5	]	]	PUNCT
ejde-76	176	6	.	.	PUNCT
ejde-76	177	1	(	(	PUNCT
ejde-76	177	2	h9	h9	NOUN
ejde-76	177	3	)	)	PUNCT
ejde-76	177	4	(	(	PUNCT
ejde-76	177	5	a	a	X
ejde-76	177	6	)	)	PUNCT
ejde-76	177	7	for	for	ADP
ejde-76	177	8	each	each	DET
ejde-76	177	9	n	n	PRON
ejde-76	177	10	∈	∈	PROPN
ejde-76	177	11	n	n	CCONJ
ejde-76	177	12	there	there	PRON
ejde-76	177	13	exists	exist	VERB
ejde-76	177	14	αn	αn	NOUN
ejde-76	177	15	>	>	X
ejde-76	177	16	0	0	NUM
ejde-76	178	1	such	such	ADJ
ejde-76	178	2	that	that	SCONJ
ejde-76	178	3	‖anu−au‖v	‖anu−au‖v	PUNCT
ejde-76	178	4	≤	≤	PROPN
ejde-76	178	5	αn(‖u‖v	αn(‖u‖v	PROPN
ejde-76	179	1	+	+	CCONJ
ejde-76	179	2	1	1	X
ejde-76	179	3	)	)	PUNCT
ejde-76	179	4	∀u	∀u	NOUN
ejde-76	179	5	∈	∈	NOUN
ejde-76	179	6	v.	v.	CCONJ
ejde-76	179	7	(	(	PUNCT
ejde-76	179	8	b	b	NOUN
ejde-76	179	9	)	)	PUNCT
ejde-76	179	10	αn	αn	NOUN
ejde-76	179	11	→	→	SYM
ejde-76	179	12	0	0	NUM
ejde-76	180	1	as	as	ADP
ejde-76	180	2	n→∞.	n→∞.	PROPN
ejde-76	180	3	(	(	PUNCT
ejde-76	180	4	h10	h10	PROPN
ejde-76	180	5	)	)	PUNCT
ejde-76	180	6	(	(	PUNCT
ejde-76	180	7	a	a	X
ejde-76	180	8	)	)	PUNCT
ejde-76	180	9	for	for	ADP
ejde-76	180	10	each	each	DET
ejde-76	180	11	n	n	PRON
ejde-76	180	12	∈	∈	PROPN
ejde-76	180	13	n	n	CCONJ
ejde-76	180	14	there	there	PRON
ejde-76	180	15	exists	exist	VERB
ejde-76	180	16	βn	βn	VERB
ejde-76	180	17	>	>	X
ejde-76	180	18	0	0	NUM
ejde-76	180	19	such	such	ADJ
ejde-76	180	20	that	that	SCONJ
ejde-76	180	21	‖snu(t)−	‖snu(t)−	PROPN
ejde-76	180	22	su(t)‖v	su(t)‖v	NOUN
ejde-76	180	23	≤	≤	NUM
ejde-76	180	24	βn	βn	PUNCT
ejde-76	180	25	(	(	PUNCT
ejde-76	180	26	∫	∫	PROPN
ejde-76	180	27	t	t	PROPN
ejde-76	180	28	0	0	NUM
ejde-76	180	29	‖u(s)‖v	‖u(s)‖v	PROPN
ejde-76	180	30	ds+	ds+	NOUN
ejde-76	180	31	1	1	NUM
ejde-76	180	32	)	)	PUNCT
ejde-76	180	33	for	for	ADP
ejde-76	180	34	all	all	DET
ejde-76	180	35	u	u	PROPN
ejde-76	180	36	∈	∈	PROPN
ejde-76	180	37	c([0	c([0	NOUN
ejde-76	180	38	,	,	PUNCT
ejde-76	180	39	t	t	X
ejde-76	180	40	]	]	PUNCT
ejde-76	180	41	;	;	PUNCT
ejde-76	180	42	v	v	X
ejde-76	180	43	)	)	PUNCT
ejde-76	180	44	and	and	CCONJ
ejde-76	180	45	t	t	PROPN
ejde-76	180	46	∈	∈	PROPN
ejde-76	181	1	[	[	X
ejde-76	181	2	0	0	NUM
ejde-76	181	3	,	,	PUNCT
ejde-76	181	4	t	t	X
ejde-76	181	5	]	]	PUNCT
ejde-76	181	6	.	.	PUNCT
ejde-76	182	1	(	(	PUNCT
ejde-76	182	2	b	b	X
ejde-76	182	3	)	)	PUNCT
ejde-76	182	4	βn	βn	NOUN
ejde-76	182	5	→	→	SYM
ejde-76	182	6	0	0	NUM
ejde-76	182	7	as	as	ADP
ejde-76	182	8	n→∞.	n→∞.	PROPN
ejde-76	182	9	(	(	PUNCT
ejde-76	182	10	h11	h11	PROPN
ejde-76	182	11	)	)	PUNCT
ejde-76	182	12	fn	fn	PROPN
ejde-76	182	13	→	→	SYM
ejde-76	182	14	f	f	PROPN
ejde-76	182	15	in	in	ADP
ejde-76	182	16	c([0	c([0	PROPN
ejde-76	182	17	,	,	PUNCT
ejde-76	182	18	t	t	X
ejde-76	182	19	]	]	PUNCT
ejde-76	182	20	;	;	PUNCT
ejde-76	182	21	v	v	NOUN
ejde-76	182	22	)	)	PUNCT
ejde-76	182	23	.	.	PUNCT
ejde-76	183	1	ejde-2022/03	ejde-2022/03	NOUN
ejde-76	183	2	duality	duality	NOUN
ejde-76	183	3	arguments	argument	NOUN
ejde-76	183	4	for	for	ADP
ejde-76	183	5	well	well	ADV
ejde-76	183	6	-	-	PUNCT
ejde-76	183	7	posedness	posedness	NOUN
ejde-76	183	8	7	7	NUM
ejde-76	183	9	the	the	DET
ejde-76	183	10	main	main	ADJ
ejde-76	183	11	result	result	NOUN
ejde-76	183	12	of	of	ADP
ejde-76	183	13	this	this	DET
ejde-76	183	14	section	section	NOUN
ejde-76	183	15	is	be	AUX
ejde-76	183	16	the	the	DET
ejde-76	183	17	following	following	NOUN
ejde-76	183	18	.	.	PUNCT
ejde-76	184	1	theorem	theorem	VERB
ejde-76	184	2	4.1	4.1	NUM
ejde-76	184	3	.	.	PUNCT
ejde-76	185	1	assume	assume	VERB
ejde-76	185	2	(	(	PUNCT
ejde-76	185	3	h1)–(h11	h1)–(h11	NOUN
ejde-76	185	4	)	)	PUNCT
ejde-76	185	5	hold	hold	VERB
ejde-76	185	6	.	.	PUNCT
ejde-76	186	1	then	then	ADV
ejde-76	186	2	,	,	PUNCT
ejde-76	186	3	the	the	DET
ejde-76	186	4	solution	solution	NOUN
ejde-76	186	5	un	un	PROPN
ejde-76	186	6	of	of	ADP
ejde-76	186	7	problem	problem	NOUN
ejde-76	186	8	pn	pn	PROPN
ejde-76	186	9	converges	converge	VERB
ejde-76	186	10	to	to	ADP
ejde-76	186	11	the	the	DET
ejde-76	186	12	solution	solution	NOUN
ejde-76	186	13	u	u	NOUN
ejde-76	186	14	of	of	ADP
ejde-76	186	15	problem	problem	NOUN
ejde-76	186	16	p	p	X
ejde-76	186	17	,	,	PUNCT
ejde-76	186	18	i.e.	i.e.	X
ejde-76	186	19	,	,	PUNCT
ejde-76	186	20	un	un	PROPN
ejde-76	186	21	→	→	SYM
ejde-76	186	22	u	u	PROPN
ejde-76	186	23	in	in	ADP
ejde-76	186	24	c([0	c([0	PROPN
ejde-76	186	25	,	,	PUNCT
ejde-76	186	26	t	t	X
ejde-76	186	27	]	]	PUNCT
ejde-76	186	28	;	;	PUNCT
ejde-76	186	29	v	v	NOUN
ejde-76	186	30	)	)	PUNCT
ejde-76	186	31	.	.	PUNCT
ejde-76	187	1	(	(	PUNCT
ejde-76	187	2	4.2	4.2	NUM
ejde-76	187	3	)	)	PUNCT
ejde-76	187	4	proof	proof	NOUN
ejde-76	187	5	.	.	PUNCT
ejde-76	188	1	the	the	DET
ejde-76	188	2	proof	proof	NOUN
ejde-76	188	3	is	be	AUX
ejde-76	188	4	carried	carry	VERB
ejde-76	188	5	out	out	ADP
ejde-76	188	6	in	in	ADP
ejde-76	188	7	three	three	NUM
ejde-76	188	8	steps	step	NOUN
ejde-76	188	9	,	,	PUNCT
ejde-76	188	10	as	as	SCONJ
ejde-76	188	11	follows	follow	VERB
ejde-76	188	12	.	.	PUNCT
ejde-76	189	1	step	step	NOUN
ejde-76	189	2	1	1	NUM
ejde-76	189	3	.	.	PUNCT
ejde-76	190	1	we	we	PRON
ejde-76	190	2	prove	prove	VERB
ejde-76	190	3	that	that	SCONJ
ejde-76	190	4	there	there	PRON
ejde-76	190	5	exists	exist	VERB
ejde-76	190	6	m	m	VERB
ejde-76	190	7	>	>	X
ejde-76	190	8	0	0	NUM
ejde-76	190	9	such	such	ADJ
ejde-76	190	10	that	that	SCONJ
ejde-76	190	11	‖un(t)‖v	‖un(t)‖v	PROPN
ejde-76	190	12	≤m	≤m	PROPN
ejde-76	190	13	∀n	∀n	CCONJ
ejde-76	190	14	∈	∈	PROPN
ejde-76	190	15	n	n	CCONJ
ejde-76	190	16	,	,	PUNCT
ejde-76	190	17	t	t	PROPN
ejde-76	190	18	∈	∈	PROPN
ejde-76	191	1	[	[	X
ejde-76	191	2	0	0	NUM
ejde-76	191	3	,	,	PUNCT
ejde-76	191	4	t	t	X
ejde-76	191	5	]	]	PUNCT
ejde-76	191	6	.	.	PUNCT
ejde-76	192	1	(	(	PUNCT
ejde-76	192	2	4.3	4.3	NUM
ejde-76	192	3	)	)	PUNCT
ejde-76	192	4	let	let	VERB
ejde-76	192	5	n	n	PRON
ejde-76	192	6	∈	∈	PROPN
ejde-76	192	7	n	n	NOUN
ejde-76	192	8	and	and	CCONJ
ejde-76	192	9	t	t	PROPN
ejde-76	192	10	∈	∈	PROPN
ejde-76	193	1	[	[	X
ejde-76	193	2	0	0	NUM
ejde-76	193	3	,	,	PUNCT
ejde-76	193	4	t	t	X
ejde-76	193	5	]	]	PUNCT
ejde-76	193	6	.	.	PUNCT
ejde-76	194	1	then	then	ADV
ejde-76	194	2	,	,	PUNCT
ejde-76	194	3	using	use	VERB
ejde-76	194	4	(	(	PUNCT
ejde-76	194	5	4.1	4.1	NUM
ejde-76	194	6	)	)	PUNCT
ejde-76	194	7	with	with	ADP
ejde-76	194	8	v	v	NOUN
ejde-76	194	9	=	=	SYM
ejde-76	194	10	u0	u0	NOUN
ejde-76	194	11	∈	∈	PROPN
ejde-76	194	12	k(t	k(t	X
ejde-76	194	13	)	)	PUNCT
ejde-76	194	14	we	we	PRON
ejde-76	194	15	find	find	VERB
ejde-76	194	16	that	that	SCONJ
ejde-76	194	17	(	(	PUNCT
ejde-76	194	18	anun(t	anun(t	NOUN
ejde-76	194	19	)	)	PUNCT
ejde-76	194	20	,	,	PUNCT
ejde-76	194	21	un(t)−	un(t)−	PROPN
ejde-76	194	22	u0)v	u0)v	VERB
ejde-76	194	23	≤	≤	NOUN
ejde-76	194	24	(	(	PUNCT
ejde-76	194	25	snun(t	snun(t	NOUN
ejde-76	194	26	)	)	PUNCT
ejde-76	194	27	,	,	PUNCT
ejde-76	194	28	u0	u0	ADJ
ejde-76	194	29	−	−	PROPN
ejde-76	194	30	un(t))v	un(t))v	X
ejde-76	194	31	+	+	CCONJ
ejde-76	194	32	(	(	PUNCT
ejde-76	194	33	fn(t	fn(t	NUM
ejde-76	194	34	)	)	PUNCT
ejde-76	194	35	,	,	PUNCT
ejde-76	194	36	un(t)−	un(t)−	PROPN
ejde-76	194	37	u0)v	u0)v	ADJ
ejde-76	194	38	.	.	PUNCT
ejde-76	195	1	(	(	PUNCT
ejde-76	195	2	4.4	4.4	NUM
ejde-76	195	3	)	)	PUNCT
ejde-76	195	4	we	we	PRON
ejde-76	195	5	write	write	VERB
ejde-76	195	6	(	(	PUNCT
ejde-76	195	7	anun(t	anun(t	PROPN
ejde-76	195	8	)	)	PUNCT
ejde-76	195	9	,	,	PUNCT
ejde-76	195	10	un(t)−	un(t)−	PROPN
ejde-76	195	11	u0)v	u0)v	ADV
ejde-76	195	12	=	=	SYM
ejde-76	195	13	(	(	PUNCT
ejde-76	195	14	anun(t)−aun(t	anun(t)−aun(t	NOUN
ejde-76	195	15	)	)	PUNCT
ejde-76	195	16	,	,	PUNCT
ejde-76	195	17	un(t)−	un(t)−	PROPN
ejde-76	195	18	u0)v	u0)v	VERB
ejde-76	195	19	+	+	CCONJ
ejde-76	195	20	(	(	PUNCT
ejde-76	195	21	aun(t)−au0	aun(t)−au0	NOUN
ejde-76	195	22	,	,	PUNCT
ejde-76	195	23	un(t)−	un(t)−	PROPN
ejde-76	195	24	u0)v	u0)v	ADJ
ejde-76	196	1	+	+	CCONJ
ejde-76	196	2	(	(	PUNCT
ejde-76	196	3	au0	au0	PROPN
ejde-76	196	4	,	,	PUNCT
ejde-76	196	5	un(t)−	un(t)−	PROPN
ejde-76	196	6	u0)v	u0)v	VERB
ejde-76	196	7	,	,	PUNCT
ejde-76	196	8	then	then	ADV
ejde-76	196	9	we	we	PRON
ejde-76	196	10	use	use	VERB
ejde-76	196	11	cauchy	cauchy	NOUN
ejde-76	196	12	-	-	PUNCT
ejde-76	196	13	schwarz	schwarz	PROPN
ejde-76	196	14	inequality	inequality	NOUN
ejde-76	196	15	and	and	CCONJ
ejde-76	196	16	assumptions	assumption	NOUN
ejde-76	196	17	(	(	PUNCT
ejde-76	196	18	h2	h2	NOUN
ejde-76	196	19	)	)	PUNCT
ejde-76	196	20	,	,	PUNCT
ejde-76	196	21	(	(	PUNCT
ejde-76	196	22	h9)(a	h9)(a	NOUN
ejde-76	196	23	)	)	PUNCT
ejde-76	196	24	to	to	PART
ejde-76	196	25	see	see	VERB
ejde-76	196	26	that	that	DET
ejde-76	196	27	(	(	PUNCT
ejde-76	196	28	anun(t	anun(t	NOUN
ejde-76	196	29	)	)	PUNCT
ejde-76	196	30	,	,	PUNCT
ejde-76	196	31	un(t)−	un(t)−	PROPN
ejde-76	196	32	u0)v	u0)v	VERB
ejde-76	196	33	≥	≥	NOUN
ejde-76	196	34	−(αn(‖un(t)‖v	−(αn(‖un(t)‖v	NUM
ejde-76	196	35	+	+	CCONJ
ejde-76	196	36	1))‖un(t)−	1))‖un(t)−	NUM
ejde-76	196	37	u0‖v	u0‖v	PUNCT
ejde-76	197	1	+	+	CCONJ
ejde-76	197	2	ma‖un(t)−	ma‖un(t)−	PROPN
ejde-76	197	3	u0‖2v	u0‖2v	ADJ
ejde-76	197	4	−	−	PROPN
ejde-76	197	5	‖au0‖v	‖au0‖v	ADV
ejde-76	197	6	‖un(t)−	‖un(t)−	X
ejde-76	198	1	u0‖v	u0‖v	X
ejde-76	198	2	.	.	PUNCT
ejde-76	199	1	(	(	PUNCT
ejde-76	199	2	4.5	4.5	X
ejde-76	199	3	)	)	PUNCT
ejde-76	199	4	note	note	VERB
ejde-76	199	5	that	that	SCONJ
ejde-76	199	6	(	(	PUNCT
ejde-76	199	7	snun(t	snun(t	NOUN
ejde-76	199	8	)	)	PUNCT
ejde-76	199	9	,	,	PUNCT
ejde-76	199	10	u0	u0	ADJ
ejde-76	199	11	−	−	PUNCT
ejde-76	199	12	un(t))v	un(t))v	X
ejde-76	199	13	=	=	SYM
ejde-76	200	1	(	(	PUNCT
ejde-76	200	2	snun(t)−	snun(t)−	PROPN
ejde-76	200	3	sun(t	sun(t	PROPN
ejde-76	200	4	)	)	PUNCT
ejde-76	200	5	,	,	PUNCT
ejde-76	200	6	u0	u0	ADJ
ejde-76	200	7	−	−	PROPN
ejde-76	200	8	un(t))v	un(t))v	X
ejde-76	200	9	+	+	CCONJ
ejde-76	200	10	(	(	PUNCT
ejde-76	200	11	sun(t)−	sun(t)−	PROPN
ejde-76	200	12	su0(t	su0(t	PROPN
ejde-76	200	13	)	)	PUNCT
ejde-76	200	14	,	,	PUNCT
ejde-76	200	15	u0	u0	ADJ
ejde-76	200	16	−	−	PROPN
ejde-76	200	17	un(t))v	un(t))v	X
ejde-76	200	18	+	+	CCONJ
ejde-76	200	19	(	(	PUNCT
ejde-76	200	20	su0(t	su0(t	NOUN
ejde-76	200	21	)	)	PUNCT
ejde-76	200	22	,	,	PUNCT
ejde-76	200	23	u0	u0	ADJ
ejde-76	200	24	−	−	PROPN
ejde-76	200	25	un(t))v	un(t))v	X
ejde-76	200	26	.	.	PUNCT
ejde-76	201	1	then	then	ADV
ejde-76	201	2	,	,	PUNCT
ejde-76	201	3	it	it	PRON
ejde-76	201	4	follows	follow	VERB
ejde-76	201	5	from	from	ADP
ejde-76	201	6	assumptions	assumption	NOUN
ejde-76	201	7	(	(	PUNCT
ejde-76	201	8	h3	h3	NOUN
ejde-76	201	9	)	)	PUNCT
ejde-76	201	10	and	and	CCONJ
ejde-76	201	11	(	(	PUNCT
ejde-76	201	12	h10)(a	h10)(a	NUM
ejde-76	201	13	)	)	PUNCT
ejde-76	201	14	that	that	SCONJ
ejde-76	201	15	(	(	PUNCT
ejde-76	201	16	snun(t	snun(t	NOUN
ejde-76	201	17	)	)	PUNCT
ejde-76	201	18	,	,	PUNCT
ejde-76	201	19	u0	u0	ADJ
ejde-76	201	20	−	−	PROPN
ejde-76	201	21	un(t))v	un(t))v	NOUN
ejde-76	201	22	≤	≤	NUM
ejde-76	201	23	βn	βn	X
ejde-76	201	24	(	(	PUNCT
ejde-76	201	25	∫	∫	PROPN
ejde-76	201	26	t	t	PROPN
ejde-76	201	27	0	0	NUM
ejde-76	201	28	‖un(s)‖v	‖un(s)‖v	PROPN
ejde-76	201	29	ds+	ds+	NOUN
ejde-76	201	30	1	1	NUM
ejde-76	201	31	)	)	PUNCT
ejde-76	201	32	‖un(t)−	‖un(t)−	PUNCT
ejde-76	202	1	u0‖v	u0‖v	X
ejde-76	203	1	+	+	CCONJ
ejde-76	203	2	ls	ls	X
ejde-76	203	3	(	(	PUNCT
ejde-76	203	4	∫	∫	PROPN
ejde-76	203	5	t	t	PROPN
ejde-76	203	6	0	0	NUM
ejde-76	203	7	‖un(s)−	‖un(s)−	PROPN
ejde-76	203	8	u0‖v	u0‖v	ADV
ejde-76	203	9	ds	ds	PROPN
ejde-76	203	10	)	)	PUNCT
ejde-76	203	11	‖un(t)−	‖un(t)−	PUNCT
ejde-76	204	1	u0‖v	u0‖v	PRON
ejde-76	205	1	+	+	PUNCT
ejde-76	205	2	‖su0(t)‖v	‖su0(t)‖v	NUM
ejde-76	205	3	‖un(t)−	‖un(t)−	X
ejde-76	205	4	u0‖v	u0‖v	NOUN
ejde-76	205	5	.	.	PUNCT
ejde-76	206	1	(	(	PUNCT
ejde-76	206	2	4.6	4.6	NUM
ejde-76	206	3	)	)	PUNCT
ejde-76	206	4	moreover	moreover	ADV
ejde-76	206	5	,	,	PUNCT
ejde-76	206	6	we	we	PRON
ejde-76	206	7	have	have	VERB
ejde-76	206	8	(	(	PUNCT
ejde-76	206	9	fn(t	fn(t	NUM
ejde-76	206	10	)	)	PUNCT
ejde-76	206	11	,	,	PUNCT
ejde-76	206	12	un(t)−	un(t)−	PROPN
ejde-76	206	13	u0)v	u0)v	ADV
ejde-76	207	1	=	=	SYM
ejde-76	207	2	(	(	PUNCT
ejde-76	207	3	fn(t)−	fn(t)−	PROPN
ejde-76	207	4	f(t	f(t	PROPN
ejde-76	207	5	)	)	PUNCT
ejde-76	207	6	,	,	PUNCT
ejde-76	207	7	un(t)−	un(t)−	PROPN
ejde-76	207	8	u0)v	u0)v	VERB
ejde-76	207	9	+	+	CCONJ
ejde-76	207	10	(	(	PUNCT
ejde-76	207	11	f(t	f(t	PROPN
ejde-76	207	12	)	)	PUNCT
ejde-76	207	13	,	,	PUNCT
ejde-76	207	14	un(t)−	un(t)−	PROPN
ejde-76	207	15	u0)v	u0)v	VERB
ejde-76	207	16	≤	≤	NUM
ejde-76	207	17	‖fn(t)−	‖fn(t)−	PROPN
ejde-76	207	18	f(t)‖v	f(t)‖v	X
ejde-76	207	19	‖un(t)−	‖un(t)−	X
ejde-76	207	20	u0‖v	u0‖v	X
ejde-76	208	1	+	+	CCONJ
ejde-76	208	2	‖f(t)‖v	‖f(t)‖v	ADJ
ejde-76	208	3	‖un(t)−	‖un(t)−	ADJ
ejde-76	208	4	u0‖v	u0‖v	NOUN
ejde-76	208	5	.	.	PUNCT
ejde-76	209	1	(	(	PUNCT
ejde-76	209	2	4.7	4.7	NUM
ejde-76	209	3	)	)	PUNCT
ejde-76	209	4	we	we	PRON
ejde-76	209	5	now	now	ADV
ejde-76	209	6	combine	combine	VERB
ejde-76	209	7	inequalities	inequality	NOUN
ejde-76	209	8	(	(	PUNCT
ejde-76	209	9	4.4)–(4.7	4.4)–(4.7	NOUN
ejde-76	209	10	)	)	PUNCT
ejde-76	209	11	to	to	PART
ejde-76	209	12	see	see	VERB
ejde-76	209	13	that	that	DET
ejde-76	209	14	ma‖un(t)−	ma‖un(t)−	PROPN
ejde-76	209	15	u0‖v	u0‖v	PRON
ejde-76	209	16	≤	≤	NUM
ejde-76	209	17	βn	βn	PROPN
ejde-76	209	18	(	(	PUNCT
ejde-76	209	19	∫	∫	PROPN
ejde-76	209	20	t	t	PROPN
ejde-76	209	21	0	0	NUM
ejde-76	210	1	‖un(s)‖v	‖un(s)‖v	PROPN
ejde-76	210	2	ds+	ds+	NOUN
ejde-76	210	3	1	1	NUM
ejde-76	210	4	)	)	PUNCT
ejde-76	211	1	+	+	CCONJ
ejde-76	211	2	ls	ls	ADJ
ejde-76	211	3	∫	∫	PROPN
ejde-76	211	4	t	t	PROPN
ejde-76	211	5	0	0	NUM
ejde-76	211	6	‖un(s)−	‖un(s)−	PROPN
ejde-76	211	7	u0‖v	u0‖v	NOUN
ejde-76	211	8	ds	ds	ADJ
ejde-76	211	9	+	+	CCONJ
ejde-76	211	10	‖su0(t)‖v	‖su0(t)‖v	NUM
ejde-76	211	11	+	+	NUM
ejde-76	211	12	‖fn(t)−	‖fn(t)−	NOUN
ejde-76	211	13	f(t)‖v	f(t)‖v	NOUN
ejde-76	211	14	+	+	CCONJ
ejde-76	211	15	‖f(t)‖v	‖f(t)‖v	ADJ
ejde-76	211	16	+	+	NUM
ejde-76	211	17	αn(‖un(t)‖v	αn(‖un(t)‖v	NUM
ejde-76	211	18	+	+	CCONJ
ejde-76	211	19	1	1	NUM
ejde-76	211	20	)	)	PUNCT
ejde-76	211	21	+	+	CCONJ
ejde-76	211	22	‖au0‖v	‖au0‖v	NOUN
ejde-76	211	23	,	,	PUNCT
ejde-76	211	24	which	which	PRON
ejde-76	211	25	implies	imply	VERB
ejde-76	211	26	that	that	SCONJ
ejde-76	211	27	(	(	PUNCT
ejde-76	211	28	ma	ma	PROPN
ejde-76	211	29	−	−	PROPN
ejde-76	211	30	αn)‖un(t)‖v	αn)‖un(t)‖v	PROPN
ejde-76	211	31	8	8	NUM
ejde-76	211	32	r.	r.	PROPN
ejde-76	211	33	hu	hu	PROPN
ejde-76	211	34	,	,	PUNCT
ejde-76	211	35	m.	m.	PROPN
ejde-76	211	36	sofonea	sofonea	PROPN
ejde-76	211	37	ejde-2022/03	ejde-2022/03	PROPN
ejde-76	211	38	≤	≤	PROPN
ejde-76	211	39	βn	βn	PUNCT
ejde-76	211	40	(	(	PUNCT
ejde-76	211	41	∫	∫	PROPN
ejde-76	211	42	t	t	PROPN
ejde-76	211	43	0	0	NUM
ejde-76	211	44	‖un(s)‖v	‖un(s)‖v	PROPN
ejde-76	211	45	ds+	ds+	NOUN
ejde-76	211	46	1	1	NUM
ejde-76	211	47	)	)	PUNCT
ejde-76	212	1	+	+	CCONJ
ejde-76	213	1	ls	ls	ADJ
ejde-76	213	2	∫	∫	PROPN
ejde-76	213	3	t	t	PROPN
ejde-76	213	4	0	0	NUM
ejde-76	214	1	‖un(s)‖v	‖un(s)‖v	PROPN
ejde-76	214	2	ds+	ds+	NOUN
ejde-76	214	3	lst‖u0‖v	lst‖u0‖v	VERB
ejde-76	214	4	+	+	CCONJ
ejde-76	214	5	‖su0(t)‖v	‖su0(t)‖v	NUM
ejde-76	214	6	+	+	NUM
ejde-76	214	7	‖fn(t)−	‖fn(t)−	NOUN
ejde-76	214	8	f(t)‖v	f(t)‖v	NOUN
ejde-76	214	9	+	+	CCONJ
ejde-76	214	10	‖f(t)‖v	‖f(t)‖v	ADJ
ejde-76	214	11	+	+	NUM
ejde-76	214	12	αn	αn	NOUN
ejde-76	214	13	+	+	CCONJ
ejde-76	214	14	‖au0‖v	‖au0‖v	NOUN
ejde-76	215	1	+	+	ADJ
ejde-76	215	2	ma‖u0‖v	ma‖u0‖v	X
ejde-76	215	3	.	.	PUNCT
ejde-76	216	1	using	use	VERB
ejde-76	216	2	assumptions	assumption	NOUN
ejde-76	216	3	(	(	PUNCT
ejde-76	216	4	h9)(b	h9)(b	ADJ
ejde-76	216	5	)	)	PUNCT
ejde-76	216	6	,	,	PUNCT
ejde-76	216	7	(	(	PUNCT
ejde-76	216	8	h10)(b	h10)(b	NOUN
ejde-76	216	9	)	)	PUNCT
ejde-76	216	10	and	and	CCONJ
ejde-76	216	11	(	(	PUNCT
ejde-76	216	12	h11	h11	PROPN
ejde-76	216	13	)	)	PUNCT
ejde-76	216	14	,	,	PUNCT
ejde-76	216	15	there	there	PRON
ejde-76	216	16	exist	exist	VERB
ejde-76	216	17	n0	n0	X
ejde-76	216	18	∈	∈	PROPN
ejde-76	216	19	n	n	PRON
ejde-76	216	20	and	and	CCONJ
ejde-76	216	21	two	two	NUM
ejde-76	216	22	positive	positive	ADJ
ejde-76	216	23	constants	constant	NOUN
ejde-76	216	24	c0	c0	PROPN
ejde-76	216	25	and	and	CCONJ
ejde-76	216	26	c1	c1	PROPN
ejde-76	216	27	such	such	ADJ
ejde-76	216	28	that	that	SCONJ
ejde-76	216	29	‖un(t)‖v	‖un(t)‖v	VERB
ejde-76	216	30	≤	≤	NUM
ejde-76	216	31	c0	c0	NOUN
ejde-76	216	32	+	+	CCONJ
ejde-76	217	1	c1	c1	PROPN
ejde-76	217	2	∫	∫	PROPN
ejde-76	217	3	t	t	PROPN
ejde-76	217	4	0	0	NUM
ejde-76	218	1	‖un(s)‖v	‖un(s)‖v	X
ejde-76	218	2	ds	ds	PROPN
ejde-76	218	3	for	for	ADP
ejde-76	218	4	all	all	DET
ejde-76	218	5	n	n	PRON
ejde-76	218	6	≥	≥	NOUN
ejde-76	218	7	n0	n0	NUM
ejde-76	218	8	.	.	PUNCT
ejde-76	219	1	it	it	PRON
ejde-76	219	2	follows	follow	VERB
ejde-76	219	3	from	from	ADP
ejde-76	219	4	gronwall	gronwall	PROPN
ejde-76	219	5	’s	’s	PART
ejde-76	219	6	inequality	inequality	NOUN
ejde-76	219	7	that	that	PRON
ejde-76	219	8	‖un(t)‖v	‖un(t)‖v	VERB
ejde-76	219	9	≤	≤	PROPN
ejde-76	219	10	c0e	c0e	NOUN
ejde-76	219	11	c1	c1	NOUN
ejde-76	219	12	t.	t.	PROPN
ejde-76	219	13	this	this	DET
ejde-76	219	14	inequality	inequality	NOUN
ejde-76	219	15	completes	complete	VERB
ejde-76	219	16	the	the	DET
ejde-76	219	17	proof	proof	NOUN
ejde-76	219	18	of	of	ADP
ejde-76	219	19	(	(	PUNCT
ejde-76	219	20	4.3	4.3	NUM
ejde-76	219	21	)	)	PUNCT
ejde-76	219	22	.	.	PUNCT
ejde-76	220	1	step	step	NOUN
ejde-76	220	2	2	2	NUM
ejde-76	220	3	.	.	PUNCT
ejde-76	221	1	we	we	PRON
ejde-76	221	2	prove	prove	VERB
ejde-76	221	3	that	that	SCONJ
ejde-76	221	4	the	the	DET
ejde-76	221	5	sequence	sequence	NOUN
ejde-76	221	6	{	{	PUNCT
ejde-76	221	7	un	un	PROPN
ejde-76	221	8	}	}	PUNCT
ejde-76	221	9	⊂	⊂	NOUN
ejde-76	221	10	c([0	c([0	PROPN
ejde-76	221	11	,	,	PUNCT
ejde-76	221	12	t	t	X
ejde-76	221	13	]	]	PUNCT
ejde-76	221	14	;	;	PUNCT
ejde-76	221	15	v	v	X
ejde-76	221	16	)	)	PUNCT
ejde-76	221	17	is	be	AUX
ejde-76	221	18	a	a	DET
ejde-76	221	19	tp	tp	NOUN
ejde-76	221	20	-approximating	-approximate	VERB
ejde-76	221	21	sequence	sequence	NOUN
ejde-76	221	22	for	for	ADP
ejde-76	221	23	problem	problem	NOUN
ejde-76	221	24	p.	p.	NOUN
ejde-76	221	25	let	let	VERB
ejde-76	221	26	n	n	PRON
ejde-76	221	27	∈	∈	PROPN
ejde-76	221	28	n	n	CCONJ
ejde-76	221	29	,	,	PUNCT
ejde-76	221	30	t	t	PROPN
ejde-76	221	31	∈	∈	PROPN
ejde-76	222	1	[	[	X
ejde-76	222	2	0	0	NUM
ejde-76	222	3	,	,	PUNCT
ejde-76	222	4	t	t	NOUN
ejde-76	222	5	]	]	PUNCT
ejde-76	222	6	and	and	CCONJ
ejde-76	222	7	v	v	ADP
ejde-76	222	8	∈	∈	PROPN
ejde-76	222	9	k(t	k(t	PROPN
ejde-76	222	10	)	)	PUNCT
ejde-76	222	11	.	.	PUNCT
ejde-76	223	1	we	we	PRON
ejde-76	223	2	write	write	VERB
ejde-76	223	3	(	(	PUNCT
ejde-76	223	4	aun(t	aun(t	PROPN
ejde-76	223	5	)	)	PUNCT
ejde-76	223	6	,	,	PUNCT
ejde-76	223	7	v	v	ADP
ejde-76	223	8	−	−	PROPN
ejde-76	223	9	un(t))v	un(t))v	X
ejde-76	223	10	+	+	CCONJ
ejde-76	223	11	(	(	PUNCT
ejde-76	223	12	sun(t	sun(t	PROPN
ejde-76	223	13	)	)	PUNCT
ejde-76	223	14	,	,	PUNCT
ejde-76	223	15	v	v	ADP
ejde-76	223	16	−	−	PROPN
ejde-76	223	17	un(t))v	un(t))v	X
ejde-76	223	18	−	−	PROPN
ejde-76	223	19	(	(	PUNCT
ejde-76	223	20	f(t	f(t	PROPN
ejde-76	223	21	)	)	PUNCT
ejde-76	223	22	,	,	PUNCT
ejde-76	223	23	v	v	ADP
ejde-76	223	24	−	−	PROPN
ejde-76	223	25	un(t))v	un(t))v	X
ejde-76	223	26	=	=	SYM
ejde-76	223	27	(	(	PUNCT
ejde-76	223	28	anun(t	anun(t	PROPN
ejde-76	223	29	)	)	PUNCT
ejde-76	223	30	,	,	PUNCT
ejde-76	223	31	v	v	ADP
ejde-76	223	32	−	−	PROPN
ejde-76	223	33	un(t))v	un(t))v	X
ejde-76	223	34	+	+	CCONJ
ejde-76	223	35	(	(	PUNCT
ejde-76	223	36	snun(t	snun(t	NOUN
ejde-76	223	37	)	)	PUNCT
ejde-76	223	38	,	,	PUNCT
ejde-76	223	39	v	v	ADP
ejde-76	223	40	−	−	PROPN
ejde-76	223	41	un(t))v	un(t))v	X
ejde-76	223	42	−	−	PROPN
ejde-76	223	43	(	(	PUNCT
ejde-76	223	44	fn(t	fn(t	NUM
ejde-76	223	45	)	)	PUNCT
ejde-76	223	46	,	,	PUNCT
ejde-76	223	47	v	v	ADP
ejde-76	223	48	−	−	PROPN
ejde-76	223	49	un(t))v	un(t))v	X
ejde-76	223	50	+	+	CCONJ
ejde-76	223	51	(	(	PUNCT
ejde-76	223	52	aun(t)−anun(t	aun(t)−anun(t	PROPN
ejde-76	223	53	)	)	PUNCT
ejde-76	223	54	,	,	PUNCT
ejde-76	223	55	v	v	ADP
ejde-76	223	56	−	−	PROPN
ejde-76	223	57	un(t))v	un(t))v	X
ejde-76	223	58	+	+	CCONJ
ejde-76	223	59	(	(	PUNCT
ejde-76	223	60	sun(t)−	sun(t)−	PROPN
ejde-76	223	61	snun(t	snun(t	PROPN
ejde-76	223	62	)	)	PUNCT
ejde-76	223	63	,	,	PUNCT
ejde-76	223	64	v	v	ADP
ejde-76	223	65	−	−	PROPN
ejde-76	223	66	un(t))v	un(t))v	X
ejde-76	223	67	+	+	CCONJ
ejde-76	223	68	(	(	PUNCT
ejde-76	223	69	fn(t)−	fn(t)−	PROPN
ejde-76	223	70	f(t	f(t	PROPN
ejde-76	223	71	)	)	PUNCT
ejde-76	223	72	,	,	PUNCT
ejde-76	223	73	v	v	ADP
ejde-76	223	74	−	−	PROPN
ejde-76	223	75	un(t))v	un(t))v	PUNCT
ejde-76	223	76	,	,	PUNCT
ejde-76	223	77	then	then	ADV
ejde-76	223	78	we	we	PRON
ejde-76	223	79	use	use	VERB
ejde-76	223	80	inequality	inequality	NOUN
ejde-76	223	81	(	(	PUNCT
ejde-76	223	82	4.1	4.1	NUM
ejde-76	223	83	)	)	PUNCT
ejde-76	223	84	to	to	PART
ejde-76	223	85	find	find	VERB
ejde-76	223	86	that	that	SCONJ
ejde-76	223	87	(	(	PUNCT
ejde-76	223	88	aun(t	aun(t	X
ejde-76	223	89	)	)	PUNCT
ejde-76	223	90	,	,	PUNCT
ejde-76	223	91	v	v	ADP
ejde-76	223	92	−	−	PROPN
ejde-76	223	93	un(t))v	un(t))v	X
ejde-76	224	1	+	+	CCONJ
ejde-76	224	2	(	(	PUNCT
ejde-76	224	3	sun(t	sun(t	PROPN
ejde-76	224	4	)	)	PUNCT
ejde-76	224	5	,	,	PUNCT
ejde-76	224	6	v	v	ADP
ejde-76	224	7	−	−	PROPN
ejde-76	224	8	un(t))v	un(t))v	X
ejde-76	224	9	≥	≥	X
ejde-76	224	10	(	(	PUNCT
ejde-76	224	11	f(t	f(t	PROPN
ejde-76	224	12	)	)	PUNCT
ejde-76	224	13	,	,	PUNCT
ejde-76	224	14	v	v	ADP
ejde-76	224	15	−	−	PROPN
ejde-76	224	16	un(t))v	un(t))v	X
ejde-76	224	17	−	−	PROPN
ejde-76	225	1	‖aun(t)−anun(t)‖v	‖aun(t)−anun(t)‖v	PROPN
ejde-76	225	2	‖v	‖v	NOUN
ejde-76	225	3	−	−	PROPN
ejde-76	225	4	un(t)‖v	un(t)‖v	PROPN
ejde-76	225	5	−	−	PROPN
ejde-76	226	1	‖sun(t)−	‖sun(t)−	PROPN
ejde-76	226	2	snun(t)‖v	snun(t)‖v	PROPN
ejde-76	226	3	‖v	‖v	NOUN
ejde-76	226	4	−	−	PROPN
ejde-76	226	5	un(t)‖v	un(t)‖v	VERB
ejde-76	226	6	−	−	PROPN
ejde-76	226	7	‖fn(t)−	‖fn(t)−	PROPN
ejde-76	226	8	f(t)‖v	f(t)‖v	NUM
ejde-76	226	9	‖v	‖v	NOUN
ejde-76	226	10	−	−	PROPN
ejde-76	226	11	un(t)‖v	un(t)‖v	NOUN
ejde-76	226	12	.	.	PUNCT
ejde-76	227	1	therefore	therefore	ADV
ejde-76	227	2	,	,	PUNCT
ejde-76	227	3	(	(	PUNCT
ejde-76	227	4	h9)(a	h9)(a	PROPN
ejde-76	227	5	)	)	PUNCT
ejde-76	227	6	,	,	PUNCT
ejde-76	227	7	(	(	PUNCT
ejde-76	227	8	h10)(a	h10)(a	ADV
ejde-76	227	9	)	)	PUNCT
ejde-76	227	10	and	and	CCONJ
ejde-76	227	11	(	(	PUNCT
ejde-76	227	12	4.3	4.3	NUM
ejde-76	227	13	)	)	PUNCT
ejde-76	227	14	imply	imply	VERB
ejde-76	227	15	that	that	SCONJ
ejde-76	227	16	there	there	PRON
ejde-76	227	17	exists	exist	VERB
ejde-76	227	18	a	a	DET
ejde-76	227	19	constant	constant	ADJ
ejde-76	227	20	c	c	NOUN
ejde-76	227	21	>	>	X
ejde-76	227	22	0	0	NUM
ejde-76	227	23	such	such	ADJ
ejde-76	227	24	that	that	SCONJ
ejde-76	227	25	(	(	PUNCT
ejde-76	227	26	aun(t	aun(t	PROPN
ejde-76	227	27	)	)	PUNCT
ejde-76	227	28	,	,	PUNCT
ejde-76	227	29	v	v	ADP
ejde-76	227	30	−	−	PROPN
ejde-76	227	31	un(t))v	un(t))v	X
ejde-76	227	32	+	+	CCONJ
ejde-76	227	33	(	(	PUNCT
ejde-76	227	34	sun(t	sun(t	PROPN
ejde-76	227	35	)	)	PUNCT
ejde-76	227	36	,	,	PUNCT
ejde-76	227	37	v	v	ADP
ejde-76	227	38	−	−	PROPN
ejde-76	227	39	un(t))v	un(t))v	X
ejde-76	227	40	+	+	CCONJ
ejde-76	227	41	c(αn(m	c(αn(m	PROPN
ejde-76	227	42	+	+	NUM
ejde-76	227	43	1	1	NUM
ejde-76	227	44	)	)	PUNCT
ejde-76	227	45	+	+	CCONJ
ejde-76	227	46	βn(mt	βn(mt	X
ejde-76	228	1	+	+	CCONJ
ejde-76	228	2	1	1	X
ejde-76	228	3	)	)	PUNCT
ejde-76	228	4	+	+	NUM
ejde-76	228	5	‖fn(t)−	‖fn(t)−	PROPN
ejde-76	228	6	f(t)‖v	f(t)‖v	PROPN
ejde-76	228	7	)	)	PUNCT
ejde-76	228	8	≥	≥	X
ejde-76	228	9	(	(	PUNCT
ejde-76	228	10	f(t	f(t	PROPN
ejde-76	228	11	)	)	PUNCT
ejde-76	228	12	,	,	PUNCT
ejde-76	228	13	v	v	ADP
ejde-76	228	14	−	−	PROPN
ejde-76	228	15	un(t))v	un(t))v	X
ejde-76	228	16	.	.	PUNCT
ejde-76	229	1	(	(	PUNCT
ejde-76	229	2	4.8	4.8	NUM
ejde-76	229	3	)	)	PUNCT
ejde-76	229	4	we	we	PRON
ejde-76	229	5	define	define	VERB
ejde-76	229	6	θn	θn	INTJ
ejde-76	229	7	=	=	PUNCT
ejde-76	229	8	c(αn(m	c(αn(m	PROPN
ejde-76	230	1	+	+	PUNCT
ejde-76	231	1	1	1	X
ejde-76	231	2	)	)	PUNCT
ejde-76	231	3	+	+	CCONJ
ejde-76	231	4	βn(mt	βn(mt	X
ejde-76	232	1	+	+	CCONJ
ejde-76	232	2	1	1	X
ejde-76	232	3	)	)	PUNCT
ejde-76	232	4	+	+	NUM
ejde-76	232	5	‖fn(t)−	‖fn(t)−	PROPN
ejde-76	232	6	f(t)‖v	f(t)‖v	PROPN
ejde-76	232	7	)	)	PUNCT
ejde-76	232	8	,	,	PUNCT
ejde-76	232	9	(	(	PUNCT
ejde-76	232	10	4.9	4.9	NUM
ejde-76	232	11	)	)	PUNCT
ejde-76	232	12	and	and	CCONJ
ejde-76	232	13	combine	combine	VERB
ejde-76	232	14	(	(	PUNCT
ejde-76	232	15	4.8	4.8	NUM
ejde-76	232	16	)	)	PUNCT
ejde-76	232	17	,	,	PUNCT
ejde-76	232	18	(	(	PUNCT
ejde-76	232	19	4.9	4.9	NUM
ejde-76	232	20	)	)	PUNCT
ejde-76	232	21	,	,	PUNCT
ejde-76	232	22	(	(	PUNCT
ejde-76	232	23	3.4	3.4	NUM
ejde-76	232	24	)	)	PUNCT
ejde-76	232	25	to	to	PART
ejde-76	232	26	see	see	VERB
ejde-76	232	27	that	that	DET
ejde-76	232	28	un	un	PROPN
ejde-76	232	29	∈	∈	PROPN
ejde-76	232	30	ωp	ωp	X
ejde-76	232	31	(	(	PUNCT
ejde-76	232	32	θn	θn	NOUN
ejde-76	232	33	)	)	PUNCT
ejde-76	232	34	.	.	PUNCT
ejde-76	233	1	moreover	moreover	ADV
ejde-76	233	2	,	,	PUNCT
ejde-76	233	3	(	(	PUNCT
ejde-76	233	4	h9)(b	h9)(b	ADJ
ejde-76	233	5	)	)	PUNCT
ejde-76	233	6	,	,	PUNCT
ejde-76	233	7	(	(	PUNCT
ejde-76	233	8	h10)(b	h10)(b	NOUN
ejde-76	233	9	)	)	PUNCT
ejde-76	233	10	and	and	CCONJ
ejde-76	233	11	(	(	PUNCT
ejde-76	233	12	h11	h11	NOUN
ejde-76	233	13	)	)	PUNCT
ejde-76	233	14	imply	imply	VERB
ejde-76	233	15	that	that	SCONJ
ejde-76	233	16	θn	θn	X
ejde-76	233	17	→	→	SYM
ejde-76	233	18	0	0	PROPN
ejde-76	233	19	as	as	ADP
ejde-76	233	20	n	n	PROPN
ejde-76	233	21	→	→	SYM
ejde-76	233	22	∞.	∞.	PROPN
ejde-76	233	23	it	it	PRON
ejde-76	233	24	follows	follow	VERB
ejde-76	233	25	from	from	ADP
ejde-76	233	26	here	here	ADV
ejde-76	233	27	that	that	SCONJ
ejde-76	233	28	{	{	PUNCT
ejde-76	233	29	un	un	PROPN
ejde-76	233	30	}	}	PUNCT
ejde-76	233	31	is	be	AUX
ejde-76	233	32	a	a	DET
ejde-76	233	33	tp	tp	NOUN
ejde-76	233	34	-approximating	-approximate	VERB
ejde-76	233	35	sequence	sequence	NOUN
ejde-76	233	36	for	for	ADP
ejde-76	233	37	problem	problem	NOUN
ejde-76	233	38	p.	p.	NOUN
ejde-76	233	39	step	step	NOUN
ejde-76	233	40	3	3	NUM
ejde-76	233	41	.	.	PUNCT
ejde-76	233	42	completion	completion	NOUN
ejde-76	233	43	of	of	ADP
ejde-76	233	44	the	the	DET
ejde-76	233	45	proof	proof	NOUN
ejde-76	233	46	.	.	PUNCT
ejde-76	234	1	we	we	PRON
ejde-76	234	2	use	use	VERB
ejde-76	234	3	theorem	theorem	ADJ
ejde-76	234	4	3.2	3.2	NUM
ejde-76	234	5	and	and	CCONJ
ejde-76	234	6	definition	definition	NOUN
ejde-76	234	7	1.1(c	1.1(c	NUM
ejde-76	234	8	)	)	PUNCT
ejde-76	234	9	to	to	PART
ejde-76	234	10	deduce	deduce	VERB
ejde-76	234	11	the	the	DET
ejde-76	234	12	convergence	convergence	NOUN
ejde-76	234	13	(	(	PUNCT
ejde-76	234	14	4.2	4.2	NUM
ejde-76	234	15	)	)	PUNCT
ejde-76	234	16	,	,	PUNCT
ejde-76	234	17	which	which	PRON
ejde-76	234	18	concludes	conclude	VERB
ejde-76	234	19	the	the	DET
ejde-76	234	20	proof	proof	NOUN
ejde-76	234	21	.	.	PUNCT
ejde-76	235	1	�	�	PROPN
ejde-76	235	2	we	we	PRON
ejde-76	235	3	end	end	VERB
ejde-76	235	4	this	this	DET
ejde-76	235	5	section	section	NOUN
ejde-76	235	6	with	with	ADP
ejde-76	235	7	the	the	DET
ejde-76	235	8	following	follow	VERB
ejde-76	235	9	example	example	NOUN
ejde-76	235	10	in	in	ADP
ejde-76	235	11	which	which	PRON
ejde-76	235	12	v	v	NOUN
ejde-76	235	13	=	=	SYM
ejde-76	235	14	r.	r.	PROPN
ejde-76	235	15	example	example	NOUN
ejde-76	235	16	4.2	4.2	NUM
ejde-76	235	17	.	.	PUNCT
ejde-76	236	1	consider	consider	VERB
ejde-76	236	2	problem	problem	NOUN
ejde-76	236	3	p	p	NOUN
ejde-76	236	4	in	in	ADP
ejde-76	236	5	the	the	DET
ejde-76	236	6	particular	particular	ADJ
ejde-76	236	7	case	case	NOUN
ejde-76	236	8	when	when	SCONJ
ejde-76	236	9	k(t	k(t	VERB
ejde-76	236	10	)	)	PUNCT
ejde-76	236	11	=	=	PUNCT
ejde-76	237	1	[	[	X
ejde-76	237	2	0	0	NUM
ejde-76	237	3	,	,	PUNCT
ejde-76	237	4	2−	2−	NUM
ejde-76	237	5	e−t	e−t	NOUN
ejde-76	237	6	]	]	PUNCT
ejde-76	237	7	∀	∀	PUNCT
ejde-76	237	8	t	t	X
ejde-76	237	9	∈	∈	PROPN
ejde-76	238	1	[	[	X
ejde-76	238	2	0	0	NUM
ejde-76	238	3	,	,	PUNCT
ejde-76	238	4	t	t	X
ejde-76	238	5	]	]	PUNCT
ejde-76	238	6	,	,	PUNCT
ejde-76	238	7	au	au	ADP
ejde-76	238	8	=	=	SYM
ejde-76	238	9	u	u	NOUN
ejde-76	238	10	∀u	∀u	NOUN
ejde-76	238	11	∈	∈	PROPN
ejde-76	238	12	v	v	NOUN
ejde-76	238	13	,	,	PUNCT
ejde-76	238	14	su(t	su(t	NUM
ejde-76	238	15	)	)	PUNCT
ejde-76	238	16	=	=	SYM
ejde-76	239	1	∫	∫	PROPN
ejde-76	239	2	t	t	PROPN
ejde-76	239	3	0	0	NUM
ejde-76	239	4	u(s	u(s	X
ejde-76	239	5	)	)	PUNCT
ejde-76	239	6	ds	ds	ADJ
ejde-76	239	7	∀	∀	X
ejde-76	239	8	t	t	X
ejde-76	239	9	∈	∈	PROPN
ejde-76	240	1	[	[	X
ejde-76	240	2	0	0	NUM
ejde-76	240	3	,	,	PUNCT
ejde-76	240	4	t	t	X
ejde-76	240	5	]	]	PUNCT
ejde-76	240	6	,	,	PUNCT
ejde-76	240	7	u	u	PROPN
ejde-76	240	8	∈	∈	PROPN
ejde-76	240	9	c([0	c([0	NOUN
ejde-76	240	10	,	,	PUNCT
ejde-76	240	11	t	t	X
ejde-76	240	12	]	]	PUNCT
ejde-76	240	13	;	;	PUNCT
ejde-76	240	14	v	v	X
ejde-76	240	15	)	)	PUNCT
ejde-76	240	16	,	,	PUNCT
ejde-76	240	17	f(t	f(t	PROPN
ejde-76	240	18	)	)	PUNCT
ejde-76	241	1	=	=	SYM
ejde-76	241	2	t	t	NOUN
ejde-76	241	3	∀	∀	X
ejde-76	241	4	t	t	X
ejde-76	241	5	∈	∈	PROPN
ejde-76	242	1	[	[	X
ejde-76	242	2	0	0	NUM
ejde-76	242	3	,	,	PUNCT
ejde-76	242	4	t	t	X
ejde-76	242	5	]	]	PUNCT
ejde-76	242	6	.	.	PUNCT
ejde-76	243	1	ejde-2022/03	ejde-2022/03	NOUN
ejde-76	243	2	duality	duality	NOUN
ejde-76	243	3	arguments	argument	NOUN
ejde-76	243	4	for	for	ADP
ejde-76	243	5	well	well	ADV
ejde-76	243	6	-	-	PUNCT
ejde-76	243	7	posedness	posedness	NOUN
ejde-76	243	8	9	9	NUM
ejde-76	243	9	note	note	NOUN
ejde-76	243	10	that	that	SCONJ
ejde-76	243	11	in	in	ADP
ejde-76	243	12	this	this	DET
ejde-76	243	13	case	case	NOUN
ejde-76	243	14	inequality	inequality	NOUN
ejde-76	243	15	(	(	PUNCT
ejde-76	243	16	3.1	3.1	NUM
ejde-76	243	17	)	)	PUNCT
ejde-76	243	18	becomes	become	VERB
ejde-76	243	19	:	:	PUNCT
ejde-76	243	20	u(t	u(t	NOUN
ejde-76	243	21	)	)	PUNCT
ejde-76	243	22	∈	∈	PROPN
ejde-76	243	23	k(t	k(t	PROPN
ejde-76	243	24	)	)	PUNCT
ejde-76	243	25	and	and	CCONJ
ejde-76	243	26	(	(	PUNCT
ejde-76	243	27	u(t	u(t	PROPN
ejde-76	243	28	)	)	PUNCT
ejde-76	243	29	+	+	NUM
ejde-76	243	30	∫	∫	PROPN
ejde-76	243	31	t	t	PROPN
ejde-76	243	32	0	0	NUM
ejde-76	243	33	u(s	u(s	PROPN
ejde-76	243	34	)	)	PUNCT
ejde-76	243	35	ds−	ds−	PROPN
ejde-76	243	36	t	t	NOUN
ejde-76	243	37	)	)	PUNCT
ejde-76	243	38	(	(	PUNCT
ejde-76	243	39	v	v	NUM
ejde-76	243	40	−	−	PROPN
ejde-76	243	41	u(t	u(t	NOUN
ejde-76	243	42	)	)	PUNCT
ejde-76	243	43	)	)	PUNCT
ejde-76	243	44	≥	≥	NOUN
ejde-76	243	45	0	0	NUM
ejde-76	243	46	∀	∀	NOUN
ejde-76	243	47	v	v	ADP
ejde-76	243	48	∈	∈	PROPN
ejde-76	243	49	k(t	k(t	X
ejde-76	243	50	)	)	PUNCT
ejde-76	243	51	,	,	PUNCT
ejde-76	243	52	t	t	PROPN
ejde-76	243	53	∈	∈	PROPN
ejde-76	244	1	[	[	X
ejde-76	244	2	0	0	NUM
ejde-76	244	3	,	,	PUNCT
ejde-76	244	4	t	t	X
ejde-76	244	5	]	]	PUNCT
ejde-76	244	6	.	.	PUNCT
ejde-76	245	1	(	(	PUNCT
ejde-76	245	2	4.10	4.10	NUM
ejde-76	245	3	)	)	PUNCT
ejde-76	245	4	assume	assume	VERB
ejde-76	245	5	that	that	SCONJ
ejde-76	245	6	anu	anu	PROPN
ejde-76	245	7	=	=	PUNCT
ejde-76	245	8	n+	n+	ADP
ejde-76	245	9	1	1	NUM
ejde-76	245	10	n	n	NUM
ejde-76	245	11	u	u	NOUN
ejde-76	245	12	∀u	∀u	NOUN
ejde-76	245	13	∈	∈	PROPN
ejde-76	245	14	v	v	NOUN
ejde-76	245	15	,	,	PUNCT
ejde-76	245	16	snu(t	snu(t	NUM
ejde-76	245	17	)	)	PUNCT
ejde-76	245	18	=	=	SYM
ejde-76	245	19	n+	n+	PUNCT
ejde-76	245	20	1	1	NUM
ejde-76	245	21	n	n	NUM
ejde-76	245	22	∫	∫	PROPN
ejde-76	245	23	t	t	PROPN
ejde-76	245	24	0	0	NUM
ejde-76	245	25	u(s	u(s	X
ejde-76	245	26	)	)	PUNCT
ejde-76	245	27	ds	ds	ADJ
ejde-76	245	28	∀	∀	X
ejde-76	245	29	t	t	X
ejde-76	245	30	∈	∈	PROPN
ejde-76	246	1	[	[	X
ejde-76	246	2	0	0	NUM
ejde-76	246	3	,	,	PUNCT
ejde-76	246	4	t	t	X
ejde-76	246	5	]	]	PUNCT
ejde-76	246	6	,	,	PUNCT
ejde-76	246	7	u	u	PROPN
ejde-76	246	8	∈	∈	PROPN
ejde-76	246	9	c([0	c([0	NOUN
ejde-76	246	10	,	,	PUNCT
ejde-76	246	11	t	t	X
ejde-76	246	12	]	]	PUNCT
ejde-76	246	13	;	;	PUNCT
ejde-76	246	14	v	v	NOUN
ejde-76	246	15	)	)	PUNCT
ejde-76	246	16	,	,	PUNCT
ejde-76	246	17	fn(t	fn(t	PUNCT
ejde-76	246	18	)	)	PUNCT
ejde-76	247	1	=	=	PUNCT
ejde-76	247	2	t+	t+	PUNCT
ejde-76	247	3	1	1	NUM
ejde-76	247	4	n	n	NUM
ejde-76	247	5	∀	∀	NOUN
ejde-76	247	6	t	t	NOUN
ejde-76	247	7	∈	∈	PROPN
ejde-76	248	1	[	[	X
ejde-76	248	2	0	0	NUM
ejde-76	248	3	,	,	PUNCT
ejde-76	248	4	t	t	X
ejde-76	248	5	]	]	PUNCT
ejde-76	248	6	,	,	PUNCT
ejde-76	248	7	for	for	ADP
ejde-76	248	8	each	each	DET
ejde-76	248	9	n	n	PRON
ejde-76	248	10	∈	∈	PROPN
ejde-76	248	11	n.	n.	NOUN
ejde-76	248	12	then	then	ADV
ejde-76	248	13	,	,	PUNCT
ejde-76	248	14	inequality	inequality	NOUN
ejde-76	248	15	(	(	PUNCT
ejde-76	248	16	4.1	4.1	NUM
ejde-76	248	17	)	)	PUNCT
ejde-76	248	18	becomes	become	VERB
ejde-76	248	19	:	:	PUNCT
ejde-76	248	20	un(t	un(t	NUM
ejde-76	248	21	)	)	PUNCT
ejde-76	248	22	∈	∈	PROPN
ejde-76	248	23	k(t	k(t	PROPN
ejde-76	248	24	)	)	PUNCT
ejde-76	248	25	and(n+	and(n+	PROPN
ejde-76	248	26	1	1	NUM
ejde-76	248	27	n	n	DET
ejde-76	248	28	un(t	un(t	NUM
ejde-76	248	29	)	)	PUNCT
ejde-76	249	1	+	+	CCONJ
ejde-76	249	2	n+	n+	NUM
ejde-76	249	3	1	1	NUM
ejde-76	249	4	n	n	NUM
ejde-76	249	5	∫	∫	PROPN
ejde-76	249	6	t	t	PROPN
ejde-76	249	7	0	0	NUM
ejde-76	249	8	un(s	un(s	NUM
ejde-76	249	9	)	)	PUNCT
ejde-76	249	10	ds−	ds−	VERB
ejde-76	249	11	t−	t−	PROPN
ejde-76	249	12	1	1	NUM
ejde-76	249	13	n	n	NOUN
ejde-76	249	14	)	)	PUNCT
ejde-76	249	15	(	(	PUNCT
ejde-76	249	16	v	v	NUM
ejde-76	249	17	−	−	NOUN
ejde-76	249	18	un(t	un(t	NUM
ejde-76	249	19	)	)	PUNCT
ejde-76	249	20	)	)	PUNCT
ejde-76	249	21	≥	≥	X
ejde-76	249	22	0	0	NUM
ejde-76	249	23	(	(	PUNCT
ejde-76	249	24	4.11	4.11	NUM
ejde-76	249	25	)	)	PUNCT
ejde-76	249	26	for	for	ADP
ejde-76	249	27	all	all	PRON
ejde-76	249	28	v	v	ADP
ejde-76	249	29	∈	∈	PRON
ejde-76	249	30	k(t	k(t	X
ejde-76	249	31	)	)	PUNCT
ejde-76	249	32	and	and	CCONJ
ejde-76	249	33	t	t	PROPN
ejde-76	249	34	∈	∈	PROPN
ejde-76	250	1	[	[	X
ejde-76	250	2	0	0	NUM
ejde-76	250	3	,	,	PUNCT
ejde-76	250	4	t	t	X
ejde-76	250	5	]	]	PUNCT
ejde-76	250	6	.	.	PUNCT
ejde-76	251	1	it	it	PRON
ejde-76	251	2	is	be	AUX
ejde-76	251	3	easy	easy	ADJ
ejde-76	251	4	to	to	PART
ejde-76	251	5	see	see	VERB
ejde-76	251	6	that	that	SCONJ
ejde-76	251	7	in	in	ADP
ejde-76	251	8	this	this	DET
ejde-76	251	9	particular	particular	ADJ
ejde-76	251	10	case	case	NOUN
ejde-76	251	11	assumptions	assumption	NOUN
ejde-76	251	12	(	(	PUNCT
ejde-76	251	13	h1)–(h11	h1)–(h11	NOUN
ejde-76	251	14	)	)	PUNCT
ejde-76	251	15	are	be	AUX
ejde-76	251	16	satisfied	satisfied	ADJ
ejde-76	251	17	.	.	PUNCT
ejde-76	252	1	therefore	therefore	ADV
ejde-76	252	2	,	,	PUNCT
ejde-76	252	3	theorems	theorem	VERB
ejde-76	252	4	3.2	3.2	NUM
ejde-76	252	5	and	and	CCONJ
ejde-76	252	6	4.1	4.1	NUM
ejde-76	252	7	guarantee	guarantee	VERB
ejde-76	252	8	the	the	DET
ejde-76	252	9	unique	unique	ADJ
ejde-76	252	10	solvability	solvability	NOUN
ejde-76	252	11	of	of	ADP
ejde-76	252	12	inequalities	inequality	NOUN
ejde-76	252	13	(	(	PUNCT
ejde-76	252	14	4.10	4.10	NUM
ejde-76	252	15	)	)	PUNCT
ejde-76	252	16	and	and	CCONJ
ejde-76	252	17	(	(	PUNCT
ejde-76	252	18	4.11	4.11	NUM
ejde-76	252	19	)	)	PUNCT
ejde-76	252	20	as	as	ADV
ejde-76	252	21	well	well	ADV
ejde-76	252	22	as	as	ADP
ejde-76	252	23	the	the	DET
ejde-76	252	24	convergence	convergence	NOUN
ejde-76	252	25	(	(	PUNCT
ejde-76	252	26	4.2	4.2	NUM
ejde-76	252	27	)	)	PUNCT
ejde-76	252	28	.	.	PUNCT
ejde-76	253	1	this	this	DET
ejde-76	253	2	convergence	convergence	NOUN
ejde-76	253	3	can	can	AUX
ejde-76	253	4	be	be	AUX
ejde-76	253	5	proved	prove	VERB
ejde-76	253	6	directly	directly	ADV
ejde-76	253	7	.	.	PUNCT
ejde-76	254	1	indeed	indeed	ADV
ejde-76	254	2	,	,	PUNCT
ejde-76	254	3	consider	consider	VERB
ejde-76	254	4	the	the	DET
ejde-76	254	5	integral	integral	ADJ
ejde-76	254	6	equation	equation	NOUN
ejde-76	254	7	u(t	u(t	NOUN
ejde-76	254	8	)	)	PUNCT
ejde-76	255	1	+	+	NUM
ejde-76	255	2	∫	∫	PROPN
ejde-76	255	3	t	t	PROPN
ejde-76	255	4	0	0	NUM
ejde-76	255	5	u(s	u(s	X
ejde-76	255	6	)	)	PUNCT
ejde-76	255	7	ds	ds	PROPN
ejde-76	255	8	=	=	SYM
ejde-76	255	9	t	t	PROPN
ejde-76	255	10	∀	∀	X
ejde-76	255	11	t	t	X
ejde-76	255	12	∈	∈	PROPN
ejde-76	256	1	[	[	X
ejde-76	256	2	0	0	NUM
ejde-76	256	3	,	,	PUNCT
ejde-76	256	4	t	t	X
ejde-76	256	5	]	]	PUNCT
ejde-76	256	6	.	.	PUNCT
ejde-76	257	1	the	the	DET
ejde-76	257	2	solution	solution	NOUN
ejde-76	257	3	of	of	ADP
ejde-76	257	4	this	this	DET
ejde-76	257	5	equation	equation	NOUN
ejde-76	257	6	is	be	AUX
ejde-76	257	7	u(t	u(t	NOUN
ejde-76	257	8	)	)	PUNCT
ejde-76	257	9	=	=	SYM
ejde-76	257	10	1−	1−	NUM
ejde-76	257	11	e−t	e−t	NOUN
ejde-76	257	12	∀	∀	X
ejde-76	257	13	t	t	X
ejde-76	257	14	∈	∈	PROPN
ejde-76	258	1	[	[	X
ejde-76	258	2	0	0	NUM
ejde-76	258	3	,	,	PUNCT
ejde-76	258	4	t	t	X
ejde-76	258	5	]	]	PUNCT
ejde-76	258	6	.	.	PUNCT
ejde-76	259	1	(	(	PUNCT
ejde-76	259	2	4.12	4.12	NUM
ejde-76	259	3	)	)	PUNCT
ejde-76	259	4	and	and	CCONJ
ejde-76	259	5	,	,	PUNCT
ejde-76	259	6	since	since	SCONJ
ejde-76	259	7	0	0	NUM
ejde-76	259	8	≤	≤	NUM
ejde-76	259	9	1	1	NUM
ejde-76	259	10	−	−	NOUN
ejde-76	259	11	e−t	e−t	NOUN
ejde-76	259	12	≤	≤	NUM
ejde-76	259	13	2	2	NUM
ejde-76	259	14	−	−	NOUN
ejde-76	259	15	e−t	e−t	NOUN
ejde-76	259	16	for	for	ADP
ejde-76	259	17	all	all	DET
ejde-76	259	18	t	t	NOUN
ejde-76	259	19	∈	∈	PROPN
ejde-76	260	1	[	[	X
ejde-76	260	2	0	0	NUM
ejde-76	260	3	,	,	PUNCT
ejde-76	260	4	t	t	X
ejde-76	260	5	]	]	PUNCT
ejde-76	260	6	,	,	PUNCT
ejde-76	260	7	we	we	PRON
ejde-76	260	8	deduce	deduce	VERB
ejde-76	260	9	that	that	SCONJ
ejde-76	260	10	the	the	DET
ejde-76	260	11	function	function	NOUN
ejde-76	260	12	(	(	PUNCT
ejde-76	260	13	4.12	4.12	NUM
ejde-76	260	14	)	)	PUNCT
ejde-76	260	15	is	be	AUX
ejde-76	260	16	also	also	ADV
ejde-76	260	17	the	the	DET
ejde-76	260	18	solution	solution	NOUN
ejde-76	260	19	of	of	ADP
ejde-76	260	20	the	the	DET
ejde-76	260	21	history	history	NOUN
ejde-76	260	22	-	-	PUNCT
ejde-76	260	23	dependent	dependent	ADJ
ejde-76	260	24	inequality	inequality	NOUN
ejde-76	260	25	(	(	PUNCT
ejde-76	260	26	4.10	4.10	NUM
ejde-76	260	27	)	)	PUNCT
ejde-76	260	28	.	.	PUNCT
ejde-76	261	1	next	next	ADV
ejde-76	261	2	,	,	PUNCT
ejde-76	261	3	using	use	VERB
ejde-76	261	4	a	a	DET
ejde-76	261	5	similar	similar	ADJ
ejde-76	261	6	argument	argument	NOUN
ejde-76	261	7	based	base	VERB
ejde-76	261	8	on	on	ADP
ejde-76	261	9	the	the	DET
ejde-76	261	10	solvability	solvability	NOUN
ejde-76	261	11	of	of	ADP
ejde-76	261	12	the	the	DET
ejde-76	261	13	integral	integral	ADJ
ejde-76	261	14	equation	equation	NOUN
ejde-76	261	15	n+	n+	ADP
ejde-76	261	16	1	1	NUM
ejde-76	261	17	n	n	NUM
ejde-76	261	18	un(t	un(t	NUM
ejde-76	261	19	)	)	PUNCT
ejde-76	262	1	+	+	CCONJ
ejde-76	262	2	n+	n+	NUM
ejde-76	262	3	1	1	NUM
ejde-76	262	4	n	n	NUM
ejde-76	262	5	∫	∫	PROPN
ejde-76	262	6	t	t	PROPN
ejde-76	262	7	0	0	NUM
ejde-76	262	8	un(s	un(s	SYM
ejde-76	262	9	)	)	PUNCT
ejde-76	262	10	ds	ds	NOUN
ejde-76	262	11	=	=	PUNCT
ejde-76	262	12	t+	t+	PUNCT
ejde-76	262	13	1	1	NUM
ejde-76	262	14	n	n	NUM
ejde-76	262	15	∀	∀	NOUN
ejde-76	262	16	t	t	NOUN
ejde-76	262	17	∈	∈	PROPN
ejde-76	263	1	[	[	X
ejde-76	263	2	0	0	NUM
ejde-76	263	3	,	,	PUNCT
ejde-76	263	4	t	t	X
ejde-76	263	5	]	]	PUNCT
ejde-76	263	6	,	,	PUNCT
ejde-76	263	7	we	we	PRON
ejde-76	263	8	find	find	VERB
ejde-76	263	9	that	that	SCONJ
ejde-76	263	10	the	the	DET
ejde-76	263	11	solution	solution	NOUN
ejde-76	263	12	of	of	ADP
ejde-76	263	13	the	the	DET
ejde-76	263	14	history	history	NOUN
ejde-76	263	15	-	-	PUNCT
ejde-76	263	16	dependent	dependent	ADJ
ejde-76	263	17	variational	variational	ADJ
ejde-76	263	18	inequality	inequality	NOUN
ejde-76	263	19	(	(	PUNCT
ejde-76	263	20	4.11	4.11	NUM
ejde-76	263	21	)	)	PUNCT
ejde-76	263	22	is	be	AUX
ejde-76	263	23	un(t	un(t	NOUN
ejde-76	263	24	)	)	PUNCT
ejde-76	263	25	=	=	SYM
ejde-76	264	1	n	n	X
ejde-76	264	2	n+	n+	NUM
ejde-76	264	3	1	1	NUM
ejde-76	264	4	−	−	DET
ejde-76	264	5	n−	n−	NOUN
ejde-76	264	6	1	1	NUM
ejde-76	264	7	n+	n+	SYM
ejde-76	264	8	1	1	NUM
ejde-76	264	9	e−t	e−t	NOUN
ejde-76	264	10	∀	∀	NOUN
ejde-76	264	11	t	t	X
ejde-76	264	12	∈	∈	PROPN
ejde-76	265	1	[	[	X
ejde-76	265	2	0	0	NUM
ejde-76	265	3	,	,	PUNCT
ejde-76	265	4	t	t	X
ejde-76	265	5	]	]	PUNCT
ejde-76	265	6	.	.	PUNCT
ejde-76	266	1	(	(	PUNCT
ejde-76	266	2	4.13	4.13	NUM
ejde-76	266	3	)	)	PUNCT
ejde-76	266	4	then	then	ADV
ejde-76	266	5	,	,	PUNCT
ejde-76	266	6	a	a	DET
ejde-76	266	7	simple	simple	ADJ
ejde-76	266	8	calculation	calculation	NOUN
ejde-76	266	9	shows	show	VERB
ejde-76	266	10	that	that	SCONJ
ejde-76	266	11	|un(t)−	|un(t)−	PROPN
ejde-76	266	12	u(t)|	u(t)|	PROPN
ejde-76	266	13	≤	≤	PROPN
ejde-76	266	14	3	3	NUM
ejde-76	266	15	n+	n+	SYM
ejde-76	266	16	1	1	NUM
ejde-76	266	17	∀	∀	NOUN
ejde-76	266	18	t	t	NOUN
ejde-76	266	19	∈	∈	PROPN
ejde-76	267	1	[	[	X
ejde-76	267	2	0	0	NUM
ejde-76	267	3	,	,	PUNCT
ejde-76	267	4	t	t	X
ejde-76	267	5	]	]	PUNCT
ejde-76	267	6	,	,	PUNCT
ejde-76	267	7	which	which	PRON
ejde-76	267	8	implies	imply	VERB
ejde-76	267	9	the	the	DET
ejde-76	267	10	convergence	convergence	NOUN
ejde-76	267	11	(	(	PUNCT
ejde-76	267	12	4.2	4.2	NUM
ejde-76	267	13	)	)	PUNCT
ejde-76	267	14	.	.	PUNCT
ejde-76	268	1	acknowledgments	acknowledgment	NOUN
ejde-76	268	2	.	.	PUNCT
ejde-76	269	1	this	this	DET
ejde-76	269	2	research	research	NOUN
ejde-76	269	3	was	be	AUX
ejde-76	269	4	supported	support	VERB
ejde-76	269	5	by	by	ADP
ejde-76	269	6	the	the	DET
ejde-76	269	7	european	european	PROPN
ejde-76	269	8	union	union	PROPN
ejde-76	269	9	’s	’s	PART
ejde-76	269	10	horizon	horizon	NOUN
ejde-76	269	11	2020	2020	NUM
ejde-76	269	12	research	research	NOUN
ejde-76	269	13	and	and	CCONJ
ejde-76	269	14	innovation	innovation	NOUN
ejde-76	269	15	programme	programme	NOUN
ejde-76	269	16	under	under	ADP
ejde-76	269	17	the	the	DET
ejde-76	269	18	marie	marie	PROPN
ejde-76	269	19	sklodowska	sklodowska	PROPN
ejde-76	269	20	-	-	PUNCT
ejde-76	269	21	curie	curie	PROPN
ejde-76	269	22	grant	grant	NOUN
ejde-76	269	23	agreement	agreement	NOUN
ejde-76	269	24	no	no	DET
ejde-76	269	25	823731	823731	NUM
ejde-76	269	26	conmech	conmech	NOUN
ejde-76	269	27	.	.	PUNCT
ejde-76	270	1	10	10	NUM
ejde-76	270	2	r.	r.	PROPN
ejde-76	270	3	hu	hu	PROPN
ejde-76	270	4	,	,	PUNCT
ejde-76	270	5	m.	m.	PROPN
ejde-76	270	6	sofonea	sofonea	PROPN
ejde-76	270	7	ejde-2022/03	ejde-2022/03	PROPN
ejde-76	270	8	references	reference	NOUN
ejde-76	270	9	[	[	X
ejde-76	270	10	1	1	NUM
ejde-76	270	11	]	]	PUNCT
ejde-76	270	12	dontchev	dontchev	NOUN
ejde-76	270	13	,	,	PUNCT
ejde-76	270	14	a.	a.	NOUN
ejde-76	270	15	l.	l.	PROPN
ejde-76	270	16	;	;	PUNCT
ejde-76	270	17	zolezzi	zolezzi	NOUN
ejde-76	270	18	,	,	PUNCT
ejde-76	270	19	t.	t.	PROPN
ejde-76	270	20	;	;	PUNCT
ejde-76	270	21	well	well	ADV
ejde-76	270	22	-	-	PUNCT
ejde-76	270	23	posed	pose	VERB
ejde-76	270	24	optimization	optimization	NOUN
ejde-76	270	25	problems	problem	NOUN
ejde-76	270	26	,	,	PUNCT
ejde-76	270	27	lecture	lecture	NOUN
ejde-76	270	28	notes	note	VERB
ejde-76	270	29	mathematics	mathematic	NOUN
ejde-76	270	30	1543	1543	NUM
ejde-76	270	31	,	,	PUNCT
ejde-76	270	32	springer	springer	NOUN
ejde-76	270	33	,	,	PUNCT
ejde-76	270	34	berlin	berlin	PROPN
ejde-76	270	35	,	,	PUNCT
ejde-76	270	36	1993	1993	NUM
ejde-76	270	37	.	.	PUNCT
ejde-76	271	1	[	[	X
ejde-76	271	2	2	2	NUM
ejde-76	271	3	]	]	X
ejde-76	271	4	fang	fang	X
ejde-76	271	5	,	,	PUNCT
ejde-76	271	6	y.	y.	PROPN
ejde-76	271	7	p.	p.	PROPN
ejde-76	271	8	;	;	PUNCT
ejde-76	271	9	huang	huang	PROPN
ejde-76	271	10	,	,	PUNCT
ejde-76	271	11	n.	n.	PROPN
ejde-76	271	12	j.	j.	PROPN
ejde-76	271	13	;	;	PUNCT
ejde-76	271	14	yao	yao	PROPN
ejde-76	271	15	,	,	PUNCT
ejde-76	271	16	j.	j.	PROPN
ejde-76	271	17	c.	c.	PROPN
ejde-76	271	18	;	;	PUNCT
ejde-76	271	19	well	well	ADJ
ejde-76	271	20	-	-	PUNCT
ejde-76	271	21	posedness	posedness	NOUN
ejde-76	271	22	by	by	ADP
ejde-76	271	23	perturbations	perturbation	NOUN
ejde-76	271	24	of	of	ADP
ejde-76	271	25	mixed	mixed	ADJ
ejde-76	271	26	variational	variational	ADJ
ejde-76	271	27	inequalities	inequality	NOUN
ejde-76	271	28	in	in	ADP
ejde-76	271	29	banach	banach	NOUN
ejde-76	271	30	spaces	space	NOUN
ejde-76	271	31	,	,	PUNCT
ejde-76	271	32	eur	eur	PROPN
ejde-76	271	33	.	.	PUNCT
ejde-76	272	1	j.	j.	PROPN
ejde-76	272	2	oper	oper	PROPN
ejde-76	272	3	.	.	PUNCT
ejde-76	273	1	res	res	PROPN
ejde-76	273	2	.	.	PROPN
ejde-76	273	3	,	,	PUNCT
ejde-76	273	4	201	201	NUM
ejde-76	273	5	(	(	PUNCT
ejde-76	273	6	2010	2010	NUM
ejde-76	273	7	)	)	PUNCT
ejde-76	273	8	,	,	PUNCT
ejde-76	273	9	682–692	682–692	NUM
ejde-76	273	10	.	.	PUNCT
ejde-76	274	1	[	[	X
ejde-76	274	2	3	3	NUM
ejde-76	274	3	]	]	PUNCT
ejde-76	274	4	goeleven	goeleven	VERB
ejde-76	274	5	,	,	PUNCT
ejde-76	274	6	d.	d.	PROPN
ejde-76	274	7	;	;	PUNCT
ejde-76	274	8	mentagui	mentagui	PROPN
ejde-76	274	9	,	,	PUNCT
ejde-76	274	10	d.	d.	PROPN
ejde-76	274	11	;	;	PUNCT
ejde-76	274	12	well	well	ADV
ejde-76	274	13	-	-	PUNCT
ejde-76	274	14	posed	pose	VERB
ejde-76	274	15	hemivariational	hemivariational	ADJ
ejde-76	274	16	inequalities	inequality	NOUN
ejde-76	274	17	,	,	PUNCT
ejde-76	274	18	numer	numer	PROPN
ejde-76	274	19	.	.	PUNCT
ejde-76	275	1	funct	funct	PROPN
ejde-76	275	2	.	.	PUNCT
ejde-76	276	1	anal	anal	PROPN
ejde-76	276	2	.	.	PUNCT
ejde-76	277	1	optim	optim	PROPN
ejde-76	277	2	.	.	PROPN
ejde-76	278	1	,	,	PUNCT
ejde-76	278	2	16	16	NUM
ejde-76	278	3	(	(	PUNCT
ejde-76	278	4	1995	1995	NUM
ejde-76	278	5	)	)	PUNCT
ejde-76	278	6	,	,	PUNCT
ejde-76	278	7	909–921	909–921	NUM
ejde-76	278	8	.	.	PUNCT
ejde-76	279	1	[	[	X
ejde-76	279	2	4	4	NUM
ejde-76	279	3	]	]	SYM
ejde-76	279	4	hu	hu	PROPN
ejde-76	279	5	,	,	PUNCT
ejde-76	279	6	r.	r.	PROPN
ejde-76	279	7	;	;	PUNCT
ejde-76	279	8	sofonea	sofonea	PROPN
ejde-76	279	9	,	,	PUNCT
ejde-76	279	10	m.	m.	NOUN
ejde-76	279	11	;	;	PUNCT
ejde-76	279	12	xiao	xiao	PROPN
ejde-76	279	13	,	,	PUNCT
ejde-76	279	14	y.	y.	PROPN
ejde-76	279	15	b.	b.	PROPN
ejde-76	279	16	;	;	PUNCT
ejde-76	279	17	tykhonov	tykhonov	NOUN
ejde-76	279	18	triples	triple	NOUN
ejde-76	279	19	and	and	CCONJ
ejde-76	279	20	convergence	convergence	NOUN
ejde-76	279	21	results	result	NOUN
ejde-76	279	22	for	for	ADP
ejde-76	279	23	hemivariational	hemivariational	ADJ
ejde-76	279	24	inequalities	inequality	NOUN
ejde-76	279	25	,	,	PUNCT
ejde-76	279	26	nonlinear	nonlinear	ADJ
ejde-76	279	27	anal	anal	PROPN
ejde-76	279	28	.	.	PUNCT
ejde-76	279	29	model	model	PROPN
ejde-76	279	30	.	.	PUNCT
ejde-76	280	1	control	control	PROPN
ejde-76	280	2	,	,	PUNCT
ejde-76	280	3	26	26	NUM
ejde-76	280	4	(	(	PUNCT
ejde-76	280	5	2021	2021	NUM
ejde-76	280	6	)	)	PUNCT
ejde-76	280	7	,	,	PUNCT
ejde-76	280	8	271	271	NUM
ejde-76	280	9	-	-	SYM
ejde-76	280	10	292	292	NUM
ejde-76	280	11	.	.	PUNCT
ejde-76	281	1	[	[	X
ejde-76	281	2	5	5	NUM
ejde-76	281	3	]	]	SYM
ejde-76	281	4	hu	hu	PROPN
ejde-76	281	5	,	,	PUNCT
ejde-76	281	6	r.	r.	PROPN
ejde-76	281	7	;	;	PUNCT
ejde-76	281	8	xiao	xiao	PROPN
ejde-76	281	9	,	,	PUNCT
ejde-76	281	10	y.	y.	PROPN
ejde-76	281	11	b.	b.	PROPN
ejde-76	281	12	;	;	PUNCT
ejde-76	281	13	huang	huang	PROPN
ejde-76	281	14	,	,	PUNCT
ejde-76	281	15	n.	n.	PROPN
ejde-76	281	16	j.	j.	PROPN
ejde-76	281	17	;	;	PUNCT
ejde-76	281	18	wang	wang	PROPN
ejde-76	281	19	,	,	PUNCT
ejde-76	281	20	x.	x.	NOUN
ejde-76	281	21	;	;	PUNCT
ejde-76	281	22	equivalence	equivalence	NOUN
ejde-76	281	23	results	result	NOUN
ejde-76	281	24	of	of	ADP
ejde-76	281	25	well	well	NOUN
ejde-76	281	26	-	-	PUNCT
ejde-76	281	27	posedness	posedness	NOUN
ejde-76	281	28	for	for	ADP
ejde-76	281	29	split	split	ADJ
ejde-76	281	30	variational	variational	ADJ
ejde-76	281	31	-	-	PUNCT
ejde-76	281	32	hemivariational	hemivariational	ADJ
ejde-76	281	33	inequalities	inequality	NOUN
ejde-76	281	34	,	,	PUNCT
ejde-76	281	35	j.	j.	PROPN
ejde-76	281	36	nonlinear	nonlinear	PROPN
ejde-76	281	37	convex	convex	PROPN
ejde-76	281	38	anal	anal	NOUN
ejde-76	281	39	.	.	PUNCT
ejde-76	282	1	20	20	NUM
ejde-76	282	2	(	(	PUNCT
ejde-76	282	3	2019	2019	NUM
ejde-76	282	4	)	)	PUNCT
ejde-76	282	5	,	,	PUNCT
ejde-76	282	6	447	447	NUM
ejde-76	282	7	-	-	SYM
ejde-76	282	8	459	459	NUM
ejde-76	282	9	.	.	PUNCT
ejde-76	283	1	[	[	X
ejde-76	283	2	6	6	NUM
ejde-76	283	3	]	]	X
ejde-76	283	4	lucchetti	lucchetti	PROPN
ejde-76	283	5	,	,	PUNCT
ejde-76	283	6	r.	r.	PROPN
ejde-76	283	7	;	;	PUNCT
ejde-76	283	8	patrone	patrone	PROPN
ejde-76	283	9	,	,	PUNCT
ejde-76	283	10	f.	f.	PROPN
ejde-76	283	11	;	;	PUNCT
ejde-76	283	12	a	a	DET
ejde-76	283	13	characterization	characterization	NOUN
ejde-76	283	14	of	of	ADP
ejde-76	283	15	tykhonov	tykhonov	ADJ
ejde-76	283	16	well	well	NOUN
ejde-76	283	17	-	-	PUNCT
ejde-76	283	18	posedness	posedness	NOUN
ejde-76	283	19	for	for	ADP
ejde-76	283	20	minimum	minimum	ADJ
ejde-76	283	21	problems	problem	NOUN
ejde-76	283	22	with	with	ADP
ejde-76	283	23	applications	application	NOUN
ejde-76	283	24	to	to	ADP
ejde-76	283	25	variational	variational	ADJ
ejde-76	283	26	inequalities	inequality	NOUN
ejde-76	283	27	,	,	PUNCT
ejde-76	283	28	numer	numer	PROPN
ejde-76	283	29	.	.	PUNCT
ejde-76	283	30	funct	funct	PROPN
ejde-76	283	31	.	.	PUNCT
ejde-76	284	1	anal	anal	PROPN
ejde-76	284	2	.	.	PUNCT
ejde-76	285	1	optim	optim	PROPN
ejde-76	285	2	.	.	PROPN
ejde-76	285	3	,	,	PUNCT
ejde-76	285	4	3	3	NUM
ejde-76	285	5	(	(	PUNCT
ejde-76	285	6	1981	1981	NUM
ejde-76	285	7	)	)	PUNCT
ejde-76	285	8	,	,	PUNCT
ejde-76	285	9	461–476	461–476	NUM
ejde-76	285	10	.	.	PUNCT
ejde-76	286	1	[	[	X
ejde-76	286	2	7	7	NUM
ejde-76	286	3	]	]	X
ejde-76	286	4	lucchetti	lucchetti	PROPN
ejde-76	286	5	,	,	PUNCT
ejde-76	286	6	r.	r.	PROPN
ejde-76	286	7	;	;	PUNCT
ejde-76	286	8	patrone	patrone	PROPN
ejde-76	286	9	,	,	PUNCT
ejde-76	286	10	f.	f.	PROPN
ejde-76	286	11	;	;	PUNCT
ejde-76	286	12	some	some	DET
ejde-76	286	13	prroperties	prropertie	NOUN
ejde-76	286	14	of	of	ADP
ejde-76	286	15	“	"	PUNCT
ejde-76	286	16	wellposed	wellposed	ADJ
ejde-76	286	17	”	"	PUNCT
ejde-76	286	18	variational	variational	ADJ
ejde-76	286	19	inequalities	inequality	NOUN
ejde-76	286	20	governed	govern	VERB
ejde-76	286	21	by	by	ADP
ejde-76	286	22	linear	linear	PROPN
ejde-76	286	23	operators	operator	NOUN
ejde-76	286	24	,	,	PUNCT
ejde-76	286	25	numer	numer	PROPN
ejde-76	286	26	.	.	PUNCT
ejde-76	287	1	funct	funct	PROPN
ejde-76	287	2	.	.	PUNCT
ejde-76	288	1	anal	anal	PROPN
ejde-76	288	2	.	.	PUNCT
ejde-76	289	1	optim	optim	PROPN
ejde-76	289	2	.	.	PROPN
ejde-76	289	3	,	,	PUNCT
ejde-76	289	4	5	5	NUM
ejde-76	289	5	(	(	PUNCT
ejde-76	289	6	1983	1983	NUM
ejde-76	289	7	)	)	PUNCT
ejde-76	289	8	,	,	PUNCT
ejde-76	290	1	349–361	349–361	NUM
ejde-76	290	2	.	.	PUNCT
ejde-76	291	1	[	[	X
ejde-76	291	2	8	8	NUM
ejde-76	291	3	]	]	X
ejde-76	291	4	lucchetti	lucchetti	PROPN
ejde-76	291	5	,	,	PUNCT
ejde-76	291	6	r.	r.	PROPN
ejde-76	291	7	;	;	PUNCT
ejde-76	291	8	convexity	convexity	NOUN
ejde-76	291	9	and	and	CCONJ
ejde-76	291	10	well	well	ADV
ejde-76	291	11	-	-	PUNCT
ejde-76	291	12	posed	pose	VERB
ejde-76	291	13	problems	problem	NOUN
ejde-76	291	14	,	,	PUNCT
ejde-76	291	15	cms	cms	NOUN
ejde-76	291	16	books	book	NOUN
ejde-76	291	17	in	in	ADP
ejde-76	291	18	mathematics	mathematic	NOUN
ejde-76	291	19	,	,	PUNCT
ejde-76	291	20	springerverlag	springerverlag	NOUN
ejde-76	291	21	,	,	PUNCT
ejde-76	291	22	new	new	PROPN
ejde-76	291	23	york	york	PROPN
ejde-76	291	24	,	,	PUNCT
ejde-76	291	25	2006	2006	NUM
ejde-76	291	26	.	.	PUNCT
ejde-76	292	1	[	[	X
ejde-76	292	2	9	9	NUM
ejde-76	292	3	]	]	SYM
ejde-76	292	4	nacry	nacry	NOUN
ejde-76	292	5	,	,	PUNCT
ejde-76	292	6	f.	f.	PROPN
ejde-76	292	7	;	;	PUNCT
ejde-76	292	8	sofonea	sofonea	PROPN
ejde-76	292	9	,	,	PUNCT
ejde-76	292	10	m.	m.	NOUN
ejde-76	292	11	;	;	PUNCT
ejde-76	292	12	a	a	DET
ejde-76	292	13	class	class	NOUN
ejde-76	292	14	of	of	ADP
ejde-76	292	15	nonlinear	nonlinear	ADJ
ejde-76	292	16	inclusions	inclusion	NOUN
ejde-76	292	17	and	and	CCONJ
ejde-76	292	18	sweeping	sweeping	ADJ
ejde-76	292	19	processes	process	NOUN
ejde-76	292	20	in	in	ADP
ejde-76	292	21	solid	solid	ADJ
ejde-76	292	22	mechanics	mechanic	NOUN
ejde-76	292	23	,	,	PUNCT
ejde-76	292	24	acta	acta	PROPN
ejde-76	292	25	appl	appl	PROPN
ejde-76	292	26	.	.	PROPN
ejde-76	293	1	math	math	PROPN
ejde-76	293	2	.	.	PUNCT
ejde-76	293	3	,	,	PUNCT
ejde-76	293	4	171	171	NUM
ejde-76	293	5	(	(	PUNCT
ejde-76	293	6	2021	2021	NUM
ejde-76	293	7	)	)	PUNCT
ejde-76	293	8	,	,	PUNCT
ejde-76	293	9	https://doi.org/10.1007/s10440-020-00380-4	https://doi.org/10.1007/s10440-020-00380-4	NUM
ejde-76	293	10	.	.	PUNCT
ejde-76	294	1	[	[	X
ejde-76	294	2	10	10	NUM
ejde-76	294	3	]	]	X
ejde-76	294	4	sofonea	sofonea	NOUN
ejde-76	294	5	,	,	PUNCT
ejde-76	294	6	m.	m.	NOUN
ejde-76	294	7	;	;	PUNCT
ejde-76	294	8	tykhonov	tykhonov	ADJ
ejde-76	294	9	triples	triple	NOUN
ejde-76	294	10	and	and	CCONJ
ejde-76	294	11	convergence	convergence	NOUN
ejde-76	294	12	results	result	NOUN
ejde-76	294	13	for	for	ADP
ejde-76	294	14	history	history	NOUN
ejde-76	294	15	-	-	PUNCT
ejde-76	294	16	dependent	dependent	ADJ
ejde-76	294	17	variational	variational	ADJ
ejde-76	294	18	inequalities	inequality	NOUN
ejde-76	294	19	,	,	PUNCT
ejde-76	294	20	itm	itm	PROPN
ejde-76	294	21	web	web	NOUN
ejde-76	294	22	of	of	ADP
ejde-76	294	23	conferences	conference	NOUN
ejde-76	294	24	,	,	PUNCT
ejde-76	294	25	34	34	NUM
ejde-76	294	26	,	,	PUNCT
ejde-76	294	27	01006	01006	NUM
ejde-76	294	28	(	(	PUNCT
ejde-76	294	29	2020	2020	NUM
ejde-76	294	30	)	)	PUNCT
ejde-76	294	31	third	third	ADJ
ejde-76	294	32	icamnm	icamnm	PROPN
ejde-76	294	33	2020	2020	NUM
ejde-76	294	34	,	,	PUNCT
ejde-76	294	35	https	https	NOUN
ejde-76	294	36	:	:	PUNCT
ejde-76	294	37	//doi.org/10.1051	//doi.org/10.1051	PROPN
ejde-76	294	38	/	/	SYM
ejde-76	294	39	itmconf/20203401006	itmconf/20203401006	NOUN
ejde-76	294	40	.	.	PUNCT
ejde-76	295	1	[	[	X
ejde-76	295	2	11	11	NUM
ejde-76	295	3	]	]	PUNCT
ejde-76	295	4	sofonea	sofonea	NOUN
ejde-76	295	5	,	,	PUNCT
ejde-76	295	6	m.	m.	NOUN
ejde-76	295	7	;	;	PUNCT
ejde-76	295	8	migórski	migórski	PROPN
ejde-76	295	9	,	,	PUNCT
ejde-76	295	10	s.	s.	PROPN
ejde-76	295	11	;	;	PUNCT
ejde-76	295	12	variational	variational	ADJ
ejde-76	295	13	-	-	PUNCT
ejde-76	295	14	hemivariational	hemivariational	ADJ
ejde-76	295	15	inequalities	inequality	NOUN
ejde-76	295	16	with	with	ADP
ejde-76	295	17	applications	application	NOUN
ejde-76	295	18	,	,	PUNCT
ejde-76	295	19	pure	pure	ADJ
ejde-76	295	20	and	and	CCONJ
ejde-76	295	21	applied	applied	ADJ
ejde-76	295	22	mathematics	mathematic	NOUN
ejde-76	295	23	,	,	PUNCT
ejde-76	295	24	chapman	chapman	PROPN
ejde-76	295	25	&	&	CCONJ
ejde-76	295	26	hall	hall	PROPN
ejde-76	295	27	/	/	SYM
ejde-76	295	28	crc	crc	PROPN
ejde-76	295	29	press	press	PROPN
ejde-76	295	30	,	,	PUNCT
ejde-76	295	31	boca	boca	PROPN
ejde-76	295	32	raton	raton	PROPN
ejde-76	295	33	-	-	PUNCT
ejde-76	295	34	london	london	PROPN
ejde-76	295	35	,	,	PUNCT
ejde-76	295	36	2018	2018	NUM
ejde-76	295	37	.	.	PUNCT
ejde-76	296	1	[	[	X
ejde-76	296	2	12	12	NUM
ejde-76	296	3	]	]	X
ejde-76	296	4	tykhonov	tykhonov	NOUN
ejde-76	296	5	,	,	PUNCT
ejde-76	296	6	a.	a.	NOUN
ejde-76	296	7	n.	n.	NOUN
ejde-76	296	8	;	;	PUNCT
ejde-76	296	9	on	on	ADP
ejde-76	296	10	the	the	DET
ejde-76	296	11	stability	stability	NOUN
ejde-76	296	12	of	of	ADP
ejde-76	296	13	functional	functional	ADJ
ejde-76	296	14	optimization	optimization	NOUN
ejde-76	296	15	problems	problem	NOUN
ejde-76	296	16	,	,	PUNCT
ejde-76	296	17	ussr	ussr	ADJ
ejde-76	296	18	comput	comput	NOUN
ejde-76	296	19	.	.	PUNCT
ejde-76	297	1	math	math	NOUN
ejde-76	297	2	.	.	PUNCT
ejde-76	298	1	math	math	NOUN
ejde-76	298	2	.	.	PUNCT
ejde-76	299	1	phys	phy	NOUN
ejde-76	299	2	.	.	PUNCT
ejde-76	300	1	6	6	NUM
ejde-76	300	2	(	(	PUNCT
ejde-76	300	3	1966	1966	NUM
ejde-76	300	4	)	)	PUNCT
ejde-76	300	5	,	,	PUNCT
ejde-76	301	1	631–634	631–634	NUM
ejde-76	301	2	.	.	PUNCT
ejde-76	302	1	[	[	X
ejde-76	302	2	13	13	NUM
ejde-76	302	3	]	]	X
ejde-76	302	4	xiao	xiao	PROPN
ejde-76	302	5	,	,	PUNCT
ejde-76	302	6	y.	y.	PROPN
ejde-76	302	7	b.	b.	PROPN
ejde-76	302	8	;	;	PUNCT
ejde-76	302	9	huang	huang	PROPN
ejde-76	302	10	,	,	PUNCT
ejde-76	302	11	n.	n.	PROPN
ejde-76	302	12	j.	j.	PROPN
ejde-76	302	13	;	;	PUNCT
ejde-76	302	14	wong	wong	PROPN
ejde-76	302	15	,	,	PUNCT
ejde-76	302	16	m.	m.	NOUN
ejde-76	302	17	m.	m.	NOUN
ejde-76	302	18	;	;	PUNCT
ejde-76	302	19	well	well	ADJ
ejde-76	302	20	-	-	PUNCT
ejde-76	302	21	posedness	posedness	NOUN
ejde-76	302	22	of	of	ADP
ejde-76	302	23	hemivariational	hemivariational	ADJ
ejde-76	302	24	inequalities	inequality	NOUN
ejde-76	302	25	and	and	CCONJ
ejde-76	302	26	inclusion	inclusion	NOUN
ejde-76	302	27	problems	problem	NOUN
ejde-76	302	28	,	,	PUNCT
ejde-76	302	29	taiwanese	taiwanese	PROPN
ejde-76	302	30	j.	j.	PROPN
ejde-76	302	31	math	math	PROPN
ejde-76	302	32	.	.	PUNCT
ejde-76	303	1	15	15	NUM
ejde-76	303	2	(	(	PUNCT
ejde-76	303	3	2011	2011	NUM
ejde-76	303	4	)	)	PUNCT
ejde-76	303	5	,	,	PUNCT
ejde-76	303	6	1261–1276	1261–1276	NUM
ejde-76	303	7	.	.	PUNCT
ejde-76	304	1	[	[	X
ejde-76	304	2	14	14	NUM
ejde-76	304	3	]	]	X
ejde-76	304	4	xiao	xiao	PROPN
ejde-76	304	5	,	,	PUNCT
ejde-76	304	6	y.	y.	PROPN
ejde-76	304	7	b.	b.	PROPN
ejde-76	304	8	;	;	PUNCT
ejde-76	304	9	sofonea	sofonea	PROPN
ejde-76	304	10	,	,	PUNCT
ejde-76	304	11	m.	m.	NOUN
ejde-76	304	12	;	;	PUNCT
ejde-76	304	13	tykhonov	tykhonov	NOUN
ejde-76	304	14	triples	triple	NOUN
ejde-76	304	15	,	,	PUNCT
ejde-76	304	16	well	well	ADV
ejde-76	304	17	-	-	PUNCT
ejde-76	304	18	posedness	posedness	NOUN
ejde-76	304	19	and	and	CCONJ
ejde-76	304	20	convergence	convergence	NOUN
ejde-76	304	21	results	result	NOUN
ejde-76	304	22	,	,	PUNCT
ejde-76	304	23	carphatian	carphatian	PROPN
ejde-76	304	24	j.	j.	PROPN
ejde-76	304	25	math	math	PROPN
ejde-76	304	26	.	.	PROPN
ejde-76	304	27	,	,	PUNCT
ejde-76	304	28	37	37	NUM
ejde-76	304	29	(	(	PUNCT
ejde-76	304	30	2021	2021	NUM
ejde-76	304	31	)	)	PUNCT
ejde-76	304	32	,	,	PUNCT
ejde-76	304	33	135–143	135–143	NUM
ejde-76	304	34	.	.	PUNCT
ejde-76	305	1	[	[	X
ejde-76	305	2	15	15	NUM
ejde-76	305	3	]	]	X
ejde-76	305	4	zolezzi	zolezzi	NOUN
ejde-76	305	5	,	,	PUNCT
ejde-76	305	6	t.	t.	PROPN
ejde-76	305	7	;	;	PUNCT
ejde-76	305	8	extended	extend	VERB
ejde-76	305	9	well	well	ADJ
ejde-76	305	10	-	-	PUNCT
ejde-76	305	11	posedness	posedness	NOUN
ejde-76	305	12	of	of	ADP
ejde-76	305	13	optimization	optimization	NOUN
ejde-76	305	14	problems	problem	NOUN
ejde-76	305	15	,	,	PUNCT
ejde-76	305	16	j.	j.	PROPN
ejde-76	305	17	optim	optim	PROPN
ejde-76	305	18	.	.	PUNCT
ejde-76	306	1	theory	theory	NOUN
ejde-76	306	2	appl	appl	PROPN
ejde-76	306	3	.	.	PROPN
ejde-76	307	1	,	,	PUNCT
ejde-76	307	2	91	91	NUM
ejde-76	307	3	(	(	PUNCT
ejde-76	307	4	1996	1996	NUM
ejde-76	307	5	)	)	PUNCT
ejde-76	307	6	,	,	PUNCT
ejde-76	307	7	257–266	257–266	NUM
ejde-76	307	8	.	.	PUNCT
ejde-76	308	1	rong	rong	PROPN
ejde-76	308	2	hu	hu	PROPN
ejde-76	309	1	school	school	PROPN
ejde-76	309	2	of	of	ADP
ejde-76	309	3	mathematical	mathematical	ADJ
ejde-76	309	4	sciences	sciences	PROPN
ejde-76	309	5	,	,	PUNCT
ejde-76	309	6	university	university	NOUN
ejde-76	309	7	of	of	ADP
ejde-76	309	8	electronic	electronic	ADJ
ejde-76	309	9	science	science	NOUN
ejde-76	309	10	and	and	CCONJ
ejde-76	309	11	technology	technology	NOUN
ejde-76	309	12	of	of	ADP
ejde-76	309	13	china	china	PROPN
ejde-76	309	14	,	,	PUNCT
ejde-76	309	15	chengdu	chengdu	PROPN
ejde-76	309	16	,	,	PUNCT
ejde-76	309	17	sichuan	sichuan	PROPN
ejde-76	309	18	611731	611731	NUM
ejde-76	309	19	,	,	PUNCT
ejde-76	309	20	china	china	PROPN
ejde-76	309	21	email	email	NOUN
ejde-76	309	22	address	address	NOUN
ejde-76	309	23	:	:	PUNCT
ejde-76	309	24	hrong1130@foxmail.com	hrong1130@foxmail.com	X
ejde-76	310	1	mircea	mircea	PROPN
ejde-76	310	2	sofonea	sofonea	PROPN
ejde-76	310	3	laboratoire	laboratoire	PROPN
ejde-76	310	4	de	de	X
ejde-76	310	5	mathématiques	mathématiques	PROPN
ejde-76	310	6	et	et	NOUN
ejde-76	310	7	physique	physique	NOUN
ejde-76	310	8	,	,	PUNCT
ejde-76	310	9	university	university	PROPN
ejde-76	310	10	of	of	ADP
ejde-76	310	11	perpignan	perpignan	PROPN
ejde-76	310	12	via	via	ADP
ejde-76	310	13	domitia	domitia	PROPN
ejde-76	310	14	,	,	PUNCT
ejde-76	310	15	52	52	NUM
ejde-76	310	16	avenue	avenue	NOUN
ejde-76	310	17	paul	paul	PROPN
ejde-76	310	18	alduy	alduy	PROPN
ejde-76	310	19	,	,	PUNCT
ejde-76	310	20	66860	66860	NUM
ejde-76	310	21	perpignan	perpignan	PROPN
ejde-76	310	22	,	,	PUNCT
ejde-76	310	23	france	france	PROPN
ejde-76	310	24	email	email	NOUN
ejde-76	310	25	address	address	NOUN
ejde-76	310	26	:	:	PUNCT
ejde-76	310	27	sofonea@univ-perp.fr	sofonea@univ-perp.fr	NOUN
ejde-76	311	1	1	1	NUM
ejde-76	311	2	.	.	PUNCT
ejde-76	311	3	introduction	introduction	NOUN
ejde-76	311	4	2	2	NUM
ejde-76	311	5	.	.	PUNCT
ejde-76	312	1	an	an	DET
ejde-76	312	2	abstract	abstract	ADJ
ejde-76	312	3	equivalence	equivalence	NOUN
ejde-76	312	4	result	result	VERB
ejde-76	312	5	3	3	NUM
ejde-76	312	6	.	.	X
ejde-76	312	7	problem	problem	NOUN
ejde-76	312	8	statement	statement	NOUN
ejde-76	312	9	and	and	CCONJ
ejde-76	312	10	its	its	PRON
ejde-76	312	11	well	well	ADV
ejde-76	312	12	-	-	PUNCT
ejde-76	312	13	posedness	posedness	NOUN
ejde-76	312	14	4	4	NUM
ejde-76	312	15	.	.	PUNCT
ejde-76	313	1	a	a	DET
ejde-76	313	2	convergence	convergence	NOUN
ejde-76	313	3	result	result	NOUN
ejde-76	313	4	acknowledgments	acknowledgment	NOUN
ejde-76	313	5	references	reference	NOUN