Best proximity points for (φ-ψ)-weak contractions and some applications

Fallahi, Kamal; Rad, Ghasem Soleimani; Fulga, Andreea

doi:10.2298/fil2306835f

Cited by 8 publications

(1 citation statement)

References 20 publications

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“…In 2021, Malih [13] explained the best approximation concept in metric space for contractions of an integral type via several methods. The investigation of integral-type contractions, along with the approach to best proximity points, was also generalized to encompass the study of metric spaces, as exemplified in the scholarly work presented in the studies of [14,15].…”

Section: Introductionmentioning

confidence: 99%

Best Approximation of Fixed-Point Results for Branciari Contraction of Integral Type on Generalized Modular Metric Space

Manav Tatar,

Agarwal

2023

Mathematics

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In the realm of generalized modular metric spaces, we substantiate the validity of fixed-point theorems with Branciari contractions. This paper expands and broadens the original theorems in this context. Subsequently, by building upon this foundation, we explore various integral contractions to identify and characterize fixed points within this context. To highlight the practical implications of our work, we introduce the concept of the best proximity pair, thereby culminating in the best approximation theorem. We apply this theoretical construct to a specific example—one that is guided by the best approximation method described in prior research.

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Section: Introductionmentioning

confidence: 99%

Best Approximation of Fixed-Point Results for Branciari Contraction of Integral Type on Generalized Modular Metric Space

Manav Tatar,

Agarwal

2023

Mathematics

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Fixed Point Theorems of Almost Generalized Contractive Mappings in b-Metric Spaces and an Application to Integral Equation

et al. 2023

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In this study, we have new fixed point results for weak contraction mappings in complete and partially ordered b-metric spaces. Our findings expand and generalize the results of Jachymski and Mituku et al and many more results in the literature as well. To illustrate our work, we present an application on the existence and uniqueness of a nonlinear quadratic integral problem solution. Moreover, an open problem is presented to enable the scope for future research in this area.

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Weak ψ-Contractions on Directed Graphs with Applications to Integral Equations

Filali,

Dilshad,

Akram

2024

Mathematics

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This article deals with a few outcomes ensuring the fixed points of a weak (G,ψ)-contraction map of metric spaces comprised with a reflexive and transitive digraph G. To validate our findings, we furnish several examples. The findings we obtain enable us to seek out the unique solution of a nonlinear integral equation. The outcomes presented herewith sharpen, subsume, unify, improve, enrich, and compile a number of existing theorems.

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Best proximity points for (φ-ψ)-weak contractions and some applications

Cited by 8 publications

References 20 publications

Best Approximation of Fixed-Point Results for Branciari Contraction of Integral Type on Generalized Modular Metric Space

Best Approximation of Fixed-Point Results for Branciari Contraction of Integral Type on Generalized Modular Metric Space

Fixed Point Theorems of Almost Generalized Contractive Mappings in b-Metric Spaces and an Application to Integral Equation

Weak ψ-Contractions on Directed Graphs with Applications to Integral Equations

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