New fixed point theorems for set-valued contractions in b-metric spaces

Miculescu, Radu; Mihail, Alexandru

doi:10.1007/s11784-016-0400-2

Cited by 117 publications

(85 citation statements)

References 27 publications

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“…Now, by (Czerwik, 1993, pp.5-11, Theorem 1) that is, by (Miculescu, Mihail, 2017, Lemma 2.2. ), the majority of already known results can be improved.…”

Section: > M Nmentioning

confidence: 79%

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Contractive conditions in b-metric spaces

Došenović¹,

Pavlovic²,

Radenović³

2017

Vojnotehni?ki glasnik

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Abstract:The purpose of this paper is to consider various contractive conditions in b-metric spaces which have been recently published. Our results improve and complement many recent results from this field. Using the recently obtained result by R. Miculescu and A. Mihail (Miculescu & Mihail, 2017, pp.1-11) the authors of this article show that the proofs of the majority of known results in the context of b-metric spaces can be shortened.

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“…Now, by (Czerwik, 1993, pp.5-11, Theorem 1) that is, by (Miculescu, Mihail, 2017, Lemma 2.2. ), the majority of already known results can be improved.…”

Section: > M Nmentioning

confidence: 79%

“…Now, we can show that Lemma 2.2. from (Miculescu & Mihail, 2017) is an immediate consequence of the one part of Theorem 1 from (Czerwik, 1993, pp.5-11).…”

Section: > M Nmentioning

confidence: 82%

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Contractive conditions in b-metric spaces

Došenović¹,

Pavlovic²,

Radenović³

2017

Vojnotehni?ki glasnik

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“…Lemma 2.4 ( [14,21]). Let (X, d) be a complete b-metric space with the constant K 1 and {x n } be a sequence in X such that d(x n+1 , x n+2 ) αd(x n , x n+1 ) for all n = 0, 1, 2, .…”

Section: Resultsmentioning

confidence: 99%

Weakly (s,r)-contractive multi-valued operators on b-metric space

Ye¹,

Shen²

2018

J. Nonlinear Sci. Appl.

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“…However, we know from [28] that every sequence {µ n } in a bMS satisfying the property (5) is Cauchy.…”

Section: Mcrr-type Contractionmentioning

confidence: 99%

Fixed-Points of Interpolative Ćirić-Reich–Rus-Type Contractions in b-Metric Spaces

Debnath

Sen

2019

Symmetry

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The concept of symmetry is inherent in the study of metric spaces due to the presence of the symmetric property of the metric. Significant results, such as with the Borsuk-Ulam theorem, make use of fixed-point arguments in their proofs to deal with certain symmetry principles. As such, the study of fixed-point results in metric spaces is highly correlated with the symmetry concept. In the current paper, we first define a new and modifiedĆirić-Reich-Rus-type contraction in a b-metric space by incorporating the constant s in its definition and establish the corresponding fixed-point result. Next, we adopt an interpolative approach to establish some more fixed-point theorems. Existence of fixed points for ω-interpolativeĆirić-Reich-Rus-type contractions are investigated in this context. We also illustrate the validity of our results with some examples.

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New fixed point theorems for set-valued contractions in b-metric spaces

Cited by 117 publications

References 27 publications

Contractive conditions in b-metric spaces

Contractive conditions in b-metric spaces

Weakly (s,r)-contractive multi-valued operators on b-metric space

Fixed-Points of Interpolative Ćirić-Reich–Rus-Type Contractions in b-Metric Spaces

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