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This paper aims to prove fixed-point theorems for \(F_{\mathcal {C}}\) -Geraghty-type contraction on S-metric space using the C-class function. In particular, our paper will extend the results by Qawaqweh et al. (Mathematics 7(2):132, 2019), Dutta and Choudhury (Fixed Point Theory Appl 2008:1–8, 2008), and Rashid et al. (Open Math 18(1):996–1005, 2020). Moreover, a vivid example is provided to illustrate the results. Finally, we demonstrate our results to prove the existence and uniqueness of the solution for the two-point boundary value problem of the second-order differential equation, investigate some unique solutions to the second-order differential equation, and give an application to the existence theorem for the solution of the first-order periodic problem.

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Fixed-Point Theorems for  \(F_{\mathcal {C}}\) Geraghty-Type Contraction on S-Metric Space with Some Applications

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  • 发表日期：

    2025年

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  • Lucas Wangwe,
  • Santosh Kumar

摘要

This paper aims to prove fixed-point theorems for \(F_{\mathcal {C}}\) -Geraghty-type contraction on S-metric space using the C-class function. In particular, our paper will extend the results by Qawaqweh et al. (Mathematics 7(2):132, 2019), Dutta and Choudhury (Fixed Point Theory Appl 2008:1–8, 2008), and Rashid et al. (Open Math 18(1):996–1005, 2020). Moreover, a vivid example is provided to illustrate the results. Finally, we demonstrate our results to prove the existence and uniqueness of the solution for the two-point boundary value problem of the second-order differential equation, investigate some unique solutions to the second-order differential equation, and give an application to the existence theorem for the solution of the first-order periodic problem.