Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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PROXIMAL TYPE CONVERGENCE RESULTS USING IMPLICIT RELATION AND APPLICATIONS

  • Om Prakash Chauhan (Department of Applied Mathematics, Jabalpur Engineering College) ;
  • Basant Chaudhary (Department of Applied Mathematics, Jabalpur Engineering College) ;
  • Harsha Atre (Department of Applied Sciences, National Institute of Technical Teachers Training and Research (NITTTR))
  • Received : 2023.07.24
  • Accepted : 2023.10.11
  • Published : 2024.03.15
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Abstract

The goal of this study is to instigate various new and novel optimum proximity point theorems using the notion of implicit relation type ℶ-proximal contraction for non-self mappings. An illustrated example is used to demonstrate the validity of the obtained results. Furthermore, some uniqueness results for proximal contractions are also furnished with partial order and graph. Various well-known discoveries in the present state-of-the-art are enhanced, extended, unified, and generalized by our findings. As an application, we generate some fixed point results fulfilling a modified contraction and a graph contraction, using the profundity of the established results.

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Acknowledgement

The authors are grateful to the learned referees for their careful reading of our manuscript especially for the comments and suggestions.

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