Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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NEW BEST PROXIMITY POINT RESULTS FOR DIFFERENT TYPES OF NONSELF PROXIMAL CONTRACTIONS WITH AN APPLICATION

  • Khairul Habib Alam (Department of Mathematics, National Institute of Technology Manipur) ;
  • Yumnam Rohen (Department of Mathematics, Manipur University) ;
  • S. Surendra Singh (Department of Mathematics, National Institute of Technology Manipur) ;
  • Kshetrimayum Mangijaobi Devi (Department of Mathematics, Waikhom Mani Girls College) ;
  • L. Bishwakumar (Modern College)
  • Received : 2023.10.11
  • Accepted : 2024.02.17
  • Published : 2024.06.15
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Abstract

A new variety of non-self generalized proximal contraction, called Hardy-Rogers α+F-proximal contraction, is shown in this work. Also, with an example, we prove that such contractions satisfying some conditions must have a unique best proximity point. For some particular values of the constants, that we have used to generalize the proximal contraction, we conclude different α+F-proximal contraction results of the types Ćirić, Chatterjea, Reich, Kannan, and Banach with proof, that all such type of contractions must have unique best proximity point. We also apply our result to solve a functional equation.

Keywords

Acknowledgement

The referee's insightful comments on how to strengthen this paper were much appreciated by the writers. The UGC, New Delhi, is supporting Khairul Habib Alam, the first author.

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