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The aim of this paper is to introduce the concepts of generalized \(\alpha _{\psi }^{\phi }-\) proximal contractive mappings and generalized \(\alpha _{\eta }^{\lambda }-\) proximal contractive mappings in fuzzy metric spaces. The existence and uniqueness of the best proximity point of such mappings are proved. The main results extend the comparable results in the existing literature in two ways: by generalizing the underlying spaces and by broadening the class of contractive mappings. Moreover, an illustrative example is provided to support the results presented herein. Finally, as an application, the approach of the best proximity point for solving Urysohn integral equations and boundary value problems for second-order differential equations is demonstrated.

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Best Proximity Points Theorems of Generalized \(\alpha ^{\phi }_{\psi }-\) Proximal Contractive Mappings with Applications

  • 章节

  • 发表日期：

    2026年

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  • Solomon Zerfu Degefa,
  • Mujahid Abbas,
  • Vizender Singh,
  • Yohannes Gebru Aemro

摘要

The aim of this paper is to introduce the concepts of generalized \(\alpha _{\psi }^{\phi }-\) proximal contractive mappings and generalized \(\alpha _{\eta }^{\lambda }-\) proximal contractive mappings in fuzzy metric spaces. The existence and uniqueness of the best proximity point of such mappings are proved. The main results extend the comparable results in the existing literature in two ways: by generalizing the underlying spaces and by broadening the class of contractive mappings. Moreover, an illustrative example is provided to support the results presented herein. Finally, as an application, the approach of the best proximity point for solving Urysohn integral equations and boundary value problems for second-order differential equations is demonstrated.