Common Fixed Point Theorems for Mappings Satisfying implicit Relation in Bipolar metric Space}

Authors

  • Murthy Penumarthy Parvateesam Department of Mathematics, Guru Ghasidas Vishwavidyalaya (A Central University), Bilaspur(CG), India, 495 009, India, India
  • Chandra Prakash Dhuri Department of Mathematics, Guru Ghasidas Vishwavidyalaya (A Central University), Bilaspur(CG), India, 495 009, India, India
  • Rajagopalan Ramaswamy Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj 11942 - Saudi Arabia https://orcid.org/0000-0001-9027-0810
  • Khizar Hyatt Khan Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj 11942 - Saudi Arabia
  • Ola Ashour Abdelnaby Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj 11942 - Saudi Arabia

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i2.5982

Keywords:

Fixed points, bipolar metric space, covariant map, contravariant map, compatible mapping of type (A), property (E.A.) Cauchy bisequence., Fixed points, bipolar metric space, contravariant map, compatible mapping of type (A), property (E.A.), Cauchy bisequence

Abstract

In this article, we introduce the concept of compatible mappings of type $(A)$ and weaken the same in the setting of Bipolar metric spaces and established fixed point results in the setting of Bipolar metric spaces, using implicit relation function. The derived results have been supplemented with suitable non-trivial examples. Our results have extended and generalized some results proven in the past and some open problems for future research has been given.

Author Biography

  • Rajagopalan Ramaswamy, Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj 11942 - Saudi Arabia

    Rajagopalan Ramaswamy is working as Associate Professor of Mathematics in Department of Mathematics, College of Science and Humnities, Prince Sattam Bin Abdulaziz University, Alkharj, Saudi Arabia. He got his Bachelor of Science in Mathematics in 1991. He got his Master of Computer Applications and Master of Science in Mathematics from Madurai Kamraj University Madurai and obtained his Ph D from Singhania University, Rajasthan, India. His research interest is focused but not limited to Fixed Point Theory and Applications, Game Theory, Non Linear Analysis, Mathematical Modelling

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Published

2025-05-01

Issue

Vol. 18 No. 2: (April 2025)

Section

Mathematical Analysis

License

Copyright (c) 2025 Murthy Penumarthy Parvateesam, Chandra Prakash Dhuri, Rajagopalan Ramaswamy, Khizar Hyatt Khan, Ola Ashour Abdelnaby

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How to Cite

Common Fixed Point Theorems for Mappings Satisfying implicit Relation in Bipolar metric Space}. (2025). European Journal of Pure and Applied Mathematics, 18(2), 5982. https://doi.org/10.29020/nybg.ejpam.v18i2.5982