Best Proximity Point Theorems on Rectangular Metric Spaces Endowed with a Graph

Souayah, Nizar; Aydi, Hassen; Abdeljawad, Thabet; Mlaiki, Nabil

doi:10.3390/axioms8010017

Cited by 15 publications

(8 citation statements)

References 24 publications

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“…An interesting generalization of Banach's result in the spaces endowed with graphs was given by Jachymski [5] which unifies the results of Ran and Reurings [2], Nieto and Lopez [24,25] and Edelstein [4]. Recently, Shukla and Shahzad [27] and Shahzad and Shukla [10] extended these results for single-valued and set-valued mappings in product spaces endowed with a graph-see also [28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 78%

On (G, G′)-Prešić–Ćirić Operators in Graphical Metric Spaces

Shukla¹,

Mlaiki

Aydi

2019

Mathematics

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Section: Introductionmentioning

confidence: 78%

On (G, G′)-Prešić–Ćirić Operators in Graphical Metric Spaces

Shukla¹,

Mlaiki

Aydi

2019

Mathematics

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“…The idea was inspired from the work of Jachymski [25] who provided strong results on combining fixed-point theory and graph theory. Afterwards, many researchers have developed this approach for different metric spaces with several contractions [26][27][28][29][30]. For the reader's convenience, we present some basic concepts and terminology of graph theory.…”

Section: Fixed-point Results For Graphic Contractions In Controlled Pmentioning

confidence: 99%

On Fixed-Point Results in Controlled Partial Metric Type Spaces with a Graph

Souayah

Mrad

2019

Mathematics

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Recently, Mlaiki et al. introduced the notion of a controlled metric type space which is a generalization of the b-metric space. In this work, we define the controlled partial metric type space and give some fixed-point theorems for extensions of Kannan contraction in this space with suitable conditions. Moreover, as an application, we derive a fixed-point theorem for graphic contraction on the considered metric space endowed with a graph.

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“…First, Jachymski [16] provided fixed point results when considering graphic contractions. For other details, see [12,[17][18][19][20][21][22][23].…”

Section: Some Results For Graphic Contractionsmentioning

confidence: 99%

New Fixed Point Results for Modified Contractions and Applications

et al. 2019

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In this study, we introduce a new type of contractive mapping to establish the existence and uniqueness of fixed points for this type of contraction. Some related examples are built demonstrating the superiority of our results compared to the existing onesin the literature. As applications of the results obtained, some new fixed point theorems are presented for graph-type contractions. Furthermore, sufficient conditions are discussed to ensure the existence underlying various approaches of a solution for a functional equation originating in dynamic programming.

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Best Proximity Point Theorems on Rectangular Metric Spaces Endowed with a Graph

Abstract: In this paper, we ensure the existence and uniqueness of a best proximity point in rectangular metric spaces endowed with a graph structure.

Cited by 15 publications

References 24 publications

On (G, G′)-Prešić–Ćirić Operators in Graphical Metric Spaces

On (G, G′)-Prešić–Ćirić Operators in Graphical Metric Spaces

On Fixed-Point Results in Controlled Partial Metric Type Spaces with a Graph

New Fixed Point Results for Modified Contractions and Applications

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