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

Author

Listed:
  • 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
    Department of Mathematics, Manipur University, Canchipur, Imphal 795003, India)

  • Naeem Saleem

    (Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan
    Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa, Pretoria 0204, South Africa)

  • 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)

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.

Suggested Citation

  • Moirangthem Pradeep Singh & Yumnam Rohen & Naeem Saleem & Khairul Habib Alam & Kumam Anthony Singh & Asima Razzaque, 2023. "On Fixed-Point Equations Involving Geraghty-Type Contractions with Solution to Integral Equation," Mathematics, MDPI, vol. 11(24), pages 1-18, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:24:p:4882-:d:1294661
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