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On Generalized Sehgal–Guseman-Like Contractions and Their Fixed-Point Results with Applications to Nonlinear Fractional Differential Equations and Boundary Value Problems for Homogeneous Transverse Bars

Author

Listed:
  • Muhammad Din

    (Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan)

  • Umar Ishtiaq

    (Office of Research, Innovation and Commercialization, University of Management and Technology, Lahore 54770, Pakistan)

  • Muzammil Mukhtar

    (Department of Mathematics, The Islamia University of Bahawalpur, Bahawalnagar Campus, Bahawalnagar 62300, Pakistan)

  • Salvatore Sessa

    (Dipartimento di Architettura, Università Dinapoli Federico II, Via Toledo 403, 80121 Napoli, Italy)

  • Hassan Ali Ghazwani

    (Department of Mechanical Engineering, College of Engineering, Jazan University, Jazan P.O. Box 45124, Saudi Arabia)

Abstract

The goal of this study is to describe the class of modified Sehgal–Guseman-like contraction mappings and set up some fixed-point results in S -metric spaces. The class of generalized Sehgal–Guseman-like contraction mappings contains enhancements of Banach contractions, Kannan contractions, Chatterjee contractions, Chatterjee-type contractions, quasi-contractions, Ćirić–Reich–Rus-type contractions, Hardy–Rogers-type contractions, Reich-type contractions, interpolative Kannan contractions, interpolative Chatterjee contractions, among others, with their generalizations in S -metric spaces. We offer significant examples to substantiate the reliability of our results. This study also establishes consequential fixed-point results and applies them to nonlinear fractional differential equations and the boundary value problem for homogeneous transverse bars. At the end of the manuscript, we present an important open problem.

Suggested Citation

  • Muhammad Din & Umar Ishtiaq & Muzammil Mukhtar & Salvatore Sessa & Hassan Ali Ghazwani, 2024. "On Generalized Sehgal–Guseman-Like Contractions and Their Fixed-Point Results with Applications to Nonlinear Fractional Differential Equations and Boundary Value Problems for Homogeneous Transverse Ba," Mathematics, MDPI, vol. 12(4), pages 1-18, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:4:p:541-:d:1336272
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    References listed on IDEAS

    as
    1. Muhammad Nazam & Hüseyin Işik & Khalil Javed & Muhammad Naeem & Muhammad Arshad & Ching-Feng Wen, 2021. "The Existence of Fixed Points for a Different Type of Contractions on Partial b-Metric Spaces," Journal of Mathematics, Hindawi, vol. 2021, pages 1-11, August.
    2. Amjad Ali & Eskandar Ameer & Muhammad Arshad & Hüseyin Işık & Mustafa Mudhesh & Padmapriya Praveenkumar, 2022. "Fixed Point Results of Dynamic Process Dˇϒ,μ0 through FIC-Contractions with Applications," Complexity, Hindawi, vol. 2022, pages 1-8, February.
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