On relaxations of contraction constants and Caristi’s theorem in b-metric spaces

Dung, Nguyen Van; Hang, Vo Thi Le

doi:10.1007/s11784-015-0273-9

Cited by 44 publications

(37 citation statements)

References 21 publications

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“…Otherwise, for all other definitions of the notions in b-metric spaces such as b-convergence, b-Cauchy sequence, b-completeness, see (Abbas et al, 2016(Abbas et al, , pp.1413(Abbas et al, -1429, (Ansari et al, 2017, pp.315-329), (Bakhtin, 1989, pp.26-37), (Huang et al, 2015), (Jovanović, 2016), , , (Zhang et al, 2017(Zhang et al, , pp.1334(Zhang et al, -1344 and the reference therein.…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

Contractive conditions in b-metric spaces

Došenović¹,

Pavlovic²,

Radenović³

2017

Vojnotehni?ki glasnik

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“…We say that (7) implies (5). We claim that F satisfies condition (5) with respect to α = ] ∈ A , but does not satisfy (7).…”

Section: Remark 7 If In the Previousmentioning

confidence: 99%

“…Recently, using the notion and properties of C * -algebra (see [15]), several authors ( [1], [2], [6], [10], [11], [12], [13], [14], [16], [18], [19]) have introduced and considered the concepts of C * -algebra-valued metric spaces as well as C * -algebra-valued b-metric spaces and have given some fixed point theorems for self-mappings satisfying contractive conditions on such spaces. It is possible to find some results concerning b-metric spaces in [3,5]. In this paper, some recent coupled fixed point results established for a complete C * -algebra valued b-metric space are generalized and improved, with much shorter proofs.…”

Section: Introductionmentioning

confidence: 99%

Coupled fixed point theorems in C*-algebra-valued b-metric spaces

Radenović¹,

Vetro²,

Nastasi³

et al. 2017

Sci Publ State Univ Novi Pazar Ser A

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In this paper, we give some coupled fixed point results in the framework of C * -algebra-valued b-metric spaces and in particular in the setting of C * algebra-valued metric spaces. These results, with shorter proofs, generalize and improve other theorems recently introduced. We have used a method of reducing coupled fixed point results to the respective ones for mappings with one variable in the framework of b-metric spaces. Finally, two examples are given to support our theoretical work.

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“…In essence, our results do not depend on the triangle inequality. Our ideas come from [4,6,11]. Furthermore, a system of integral equation which is the same as Theorem 4.1 in [2] is discussed.…”

Section: Theorem 12 ([2]mentioning

confidence: 99%

“…Let X be a set and let s 1 be a given real number. A functional d : X × X −→ R + is said to be a b-metric if the following conditions are satisfied: Since then, several authors have established the existence and uniqueness theorems of fixed points for single-valued operators in b-metric spaces [2,3,6,11,13,15].…”

Section: Introductionmentioning

confidence: 99%