Existence of fixed point and best proximity point of p-cyclic orbital phi-contraction map

Magadevan, Prabavathy; Karpagam, S.; Karapınar, Erdal

doi:10.15388/namc.2022.27.25188

Cited by 7 publications

(1 citation statement)

References 15 publications

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“…Remark 3.1. Note that in several papers (see for example [12]) the term p-cyclic is used to indicate an operator that is cyclic in terms of Definition 3.1, where p denotes the number of sets in the cyclic covering. This is still essentially different from what will be defined in the present paper as r-cyclic.…”

Section: Definition 31 ([21]mentioning

confidence: 99%

Synchronous r-cyclic contractions on metric spaces

Mădălina

2023

FPT-RO

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Motivated by the existence of cyclic phenomena in which some characteristics are mapped into corresponding ones over more than one phase, we introduce the r-cyclic operators with respect to a covering of a metric space and investigate their behavior. We study the convergence of the Picard iteration to a fixed point of such an operator under a Banach type generalized contraction condition. The obtained results may have interesting practical applications in various research areas.

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Section: Definition 31 ([21]mentioning

confidence: 99%

Synchronous r-cyclic contractions on metric spaces

Mădălina

2023

FPT-RO

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A New Approach to the Existence of Best Proximity Points With R‐Functions in the Framework of w‐Distances

Gabeleh,

Safari-Hafshejani,

Markin

2024

Journal of Function Spaces

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In this paper, we present a new approach to check the existence of best proximity points for R‐proximal contractions in the framework of metric spaces equipped with a w0‐distance and present elementary proofs of recent results by using the corresponding fixed point problems without the continuity assumption of the considered self‐mapping. We also discuss on cyclic Geraghty contractions and resolve the problem of the existence and convergence of the best proximity point for such a class of mappings.

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Best proximity points for alternative p-contractions

Zhou,

Secelean,

Saleem

et al. 2024

J Inequal Appl

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Cyclic mappings describe fixed paths for which each point is sequentially transmitted from one set to another. Cyclic mappings satisfying certain cyclic contraction conditions have been used to obtain the best proximity points, which constitute a suitable framework for the mirror reflection model. Alternative contraction mappings introduced by Chen (Symmetry 11:750, 2019) built a new model containing several mirrors in which the light reflected from a mirror does not go to the next mirror sequentially, and its path may diverge to any other mirror. The aim of this paper is to present a new variant of alternative contraction called alternative p-contraction and study its properties. The best proximity point result for such contractions under the alternative UC property is proved. An example to support the result proved herein is provided.

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Existence of fixed point and best proximity point of p-cyclic orbital phi-contraction map

Cited by 7 publications

References 15 publications

Synchronous r-cyclic contractions on metric spaces

Synchronous r-cyclic contractions on metric spaces

A New Approach to the Existence of Best Proximity Points With R‐Functions in the Framework of w‐Distances

Best proximity points for alternative p-contractions

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