Well-Posedness of Fixed Point Problem for Mappings Satisfying an Implicit Relation

Akkouchi, Mohamed; Popa, Valeríu

doi:10.1515/dema-2010-0418

Cited by 7 publications

(7 citation statements)

References 2 publications

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“…The notion of well-posedness was treated in many articles, for example the article of M. Akkouchi, V. Popa [1] and M. Boriceanu [4]. Now, we give this lemma which is a generalization of lemma 3.1 of [12].…”

Section: Definition 2 [14]mentioning

confidence: 96%

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Common fixed point theorems on spaces with vector-valued $b$-metrics

Safia¹,

Aliouche²,

Ellaggoune³

2017

MMN

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The purpose of this paper is to prove common fixed point theorems for two operators without the assumption of continuity on a set endowed with vector-valued b-metric and we also study the case of two vector-valued b-metrics. The well-posedness of the fixed point problem is also discussed and an application is presented for systems of operator equations in complete b-normed vector space. Our results improve and generalize theorems 2 and 5 of M. Boriceanu [5].

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Section: Definition 2 [14]mentioning

confidence: 96%

“…1, where x is a fixed point for f . (2) If, in addition, .I M 2P / is nonsingular and .I M 2P / 1 2 M n n .R C /, then x is unique.…”

Section: Common Fixed Point Theorems For Two Operators On Generalizedmentioning

confidence: 99%

Common fixed point theorems on spaces with vector-valued $b$-metrics

Safia¹,

Aliouche²,

Ellaggoune³

2017

MMN

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show abstract

“…In 1994, Mathews [20] introduced the concept of partial metric space as a part of study of denotional semantics of data flows and proved the Banach contraction principle in such spaces. Recently, in [2], [5], [9], [16], [17] and in other papers, some fixed point theorems under various contractive conditions in partial metric spaces are proved.…”

Section: Introductionmentioning

confidence: 99%

“…In [3], [4], [5], [6], [31], [32] the authors studied well posedness of fixed point problem for mappings satisfying implicit relations.…”

Section: Introductionmentioning

confidence: 99%