Applications and Theoretical Foundations of Best Proximity Points in Generalized Interpolative Proximal Contractions

Authors

  • Khalil Javed International Islamic University Islamabad, Pakistan
  • Muhammad Nazam Department of Mathematics, Allama Iqbal Open University, H-8, Islamabad, Pakistan.
  • Muhammad Arshad Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad, Pakistan.
  • Manuel De la Sen Institute of Research and Development of Processes, Automatic Control Group ACG, Department of Electricity and Electronics; Faculty of Science and Technology, University of the Basque Country (UPV/EHU), Leioa 48940, Bizkaia, Spain.

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i4.6841

Keywords:

mathematical modeling, Cauchy sequence; Fixed points; O-metric space; Ultrametric space.

Abstract

This paper investigates optimal solutions for best proximity points through the framework of generalized interpolative proximal contractions. We introduce a new method that uses interpolation techniques to handle a wider class of mappings by expanding the concepts of classical proximal contraction. In the absence of a precise solution, best proximity point theorems investigate the existence of such best proximity points for approximate solutions to the fixed point problem. This article aims to develop the best proximity point theorems for contractive non-self mappings via interpolation to generate global optimal approximate solutions to particular fixed point equations. In addition to demonstrating the existence of the optimal proximity points, iterative techniques are also offered to locate such optimal approximative solutions. We illustrate the utility of our findings with a few instances. The value of our research is illustrated with a few examples and applications.

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Published

2025-11-05

Issue

Vol. 18 No. 4: (October 2025)

Section

Nonlinear Analysis

License

Copyright (c) 2025 Khalil Javed, Muhammad Nazam, Muhammad Arshad, Manuel De la Sen

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How to Cite

Applications and Theoretical Foundations of Best Proximity Points in Generalized Interpolative Proximal Contractions. (2025). European Journal of Pure and Applied Mathematics, 18(4), 6841. https://doi.org/10.29020/nybg.ejpam.v18i4.6841