On Fixed-Point Equations Involving Geraghty-Type Contractions with Solution to Integral Equation

Moirangthem Pradeep Singh, Yumnam Rohen, Naeem Saleem*, Khairul Habib Alam, Kumam Anthony Singh, Asima Razzaque

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this study, the authors verify fixed-point results for Geraghty contractions with a restricted co-domain of the auxiliary function in the context of generalized metric structure, namely the (Formula presented.) -metric space. This new idea of defining Geraghty contraction for self-operators generalizes a large number of previously published, closely related works on the presence and uniqueness of a fixed point in (Formula presented.) -metric space. Also, the outcomes are achieved by removing the continuity constraint of self-operators. We also provide examples to elaborate on the obtained results and an application to the integral equation to illustrate the significance in the literature.

Original languageEnglish
Article number4882
JournalMathematics
Volume11
Issue number24
DOIs
Publication statusPublished - Dec 2023
Externally publishedYes

Keywords

  • Geraghty-type contraction
  • S-metric space
  • fixed point

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