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

Muhammad Din, Umar Ishtiaq, Muzammil Mukhtar, Salvatore Sessa () and Hassan Ali Ghazwani ()
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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

Mathematics, 2024, vol. 12, issue 4, 1-18

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.

Keywords: fixed point; Hardy–Rogers-type contractions; uniqueness; ?-metric spaces; boundary value problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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