On Some Coincidence Best Proximity Point Results

Saleem, Naeem; Ahmad, Haroon; Aydi, Hassen; Gaba, Yaé Ulrich

doi:10.1155/2021/8005469

Cited by 6 publications

(2 citation statements)

References 21 publications

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“…In the literature of fixed point theory, the Banach contraction principle is very significant. Many authors have generalized this concept by utilizing various kinds of contraction mappings in several metric spaces (see, e.g., [1,3,5,12,13,21,25]). In 2016, Mutlu and Gürdal [14] introduced the notion of bipolar metric space, a sort of partial distance, as well as the relationship between metric spaces and bipolar metric spaces.…”

Section: Introductionmentioning

confidence: 99%

\'C}iri{\'c} Contraction with Graphical Structure of Bipolar Metric Spaces and Related Fixed Point Theorems

Younıs,

Mutlu,

Ahmad

2024

Hacettepe Journal of Mathematics and Statistics

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We present the novel concept of graphical bipolar metric-type space in this article, which combines the notions of graph theory with fixed point theory. We prove that Every bipolar metric space is a graphical bipolar metric space but the converse is not true in general. Various concepts like covariant mapping, contravariant mapping, and Cauchy bisequence are also discussed within the context of graphical bipolar metric-type spaces. Furthermore, in this study, we show that fixed point results exist in graphical structures of bipolar metric spaces and a series of examples are provided to support the main results within the realm of the graph structure.

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Section: Introductionmentioning

confidence: 99%

\'C}iri{\'c} Contraction with Graphical Structure of Bipolar Metric Spaces and Related Fixed Point Theorems

Younıs,

Mutlu,

Ahmad

2024

Hacettepe Journal of Mathematics and Statistics

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“…We refer to articles [14,18] in this direction. For more information about the existence of best proximity points for various classes of non-self mappings, one can see [17,20,21,22].…”

Section: Introductionmentioning

confidence: 99%

Best proximity point (pair) results via MNC in Busemann convex metric spaces

Gabeleh

Patle

2022

Appl. Gen. Topol.

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In this paper, we present a new class of cyclic (noncyclic) α-ψ and β-ψ condensing operators and survey the existence of best proximity points (pairs) as well as coupled best proximity points (pairs) in the setting of reflexive Busemann convex spaces. Then an application of the main existence result to study the existence of an optimal solution for a system of differential equations is demonstrated.

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Computation and convergence of fixed points in graphical spaces with an application to elastic beam deformations

Younis

Ahmad

Chen

et al. 2023

Journal of Geometry and Physics

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On Some Coincidence Best Proximity Point Results

Abstract: In this paper, we discuss some (coincidence) best proximity point results for generalized proximal contractions and λ − μ -proximal Geraghty contractions in controlled metric type spaces. To clarify our study, various examples are given and some conclusions are drawn.

Cited by 6 publications

References 21 publications

\'C}iri{\'c} Contraction with Graphical Structure of Bipolar Metric Spaces and Related Fixed Point Theorems

\'C}iri{\'c} Contraction with Graphical Structure of Bipolar Metric Spaces and Related Fixed Point Theorems

Best proximity point (pair) results via MNC in Busemann convex metric spaces

Computation and convergence of fixed points in graphical spaces with an application to elastic beam deformations

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