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 and Asima Razzaque
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Moirangthem Pradeep Singh: Department of Mathematics, National Institute of Technology Manipur, Langol, Imphal 795004, India
Yumnam Rohen: Department of Mathematics, National Institute of Technology Manipur, Langol, Imphal 795004, India
Naeem Saleem: Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan
Khairul Habib Alam: Department of Mathematics, National Institute of Technology Manipur, Langol, Imphal 795004, India
Kumam Anthony Singh: Department of Mathematics, Manipur University, Canchipur, Imphal 795003, India
Asima Razzaque: Department of Basic Sciences, Deanship of Preparatory Year, King Faisal University Al Ahsa, Al Hofuf 31982, Saudi Arabia

Mathematics, 2023, vol. 11, issue 24, 1-18

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 S b -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 S b -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.

Keywords: S b -metric space; fixed point; Geraghty-type contraction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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