Common Coupled Fixed Point Theorems without Compatibility in Partially Ordered Metric Spaces

  • K. R. Tijani Department of Mathematical Sciences, Osun State University, Osogbo, Nigeria
  • O. T. Wahab Department of Mathematics, Kwara State University, Malete, Nigeria
  • I. F. Usamot Department of Mathematics, University of Ilorin, Ilorin, Nigeria
  • S. M. Alata Department of Computer Science, Kwara -CAILS, Ilorin, Nigeria
DOI: https://doi.org/10.6084/m9.figshare.20716042
Keywords: Coupled fixed point of mappings,, Partially ordered metric spaces,, Common coupled fixed points, Identity mappings, Compatibility, Mixed monotone properties

Abstract

A perfect blend of requirements for the proof of common coupled fixed point theorems in partially ordered metric space without the assumptions of (weak) compatibility is accomplished. Previous attempts in this direction involving these assumptions mostly ensure existence of coupled coincidence points. In many existing works in this area, attempt have been made to prove the existence of common coupled fixed points. However, only identity mappings can satisfy the conditions of the theorems. The method of proof presented in this present work is powerful in view of the fact that it guarantees the existence of common coupled fixed points without the imposition of (weak) compatibility conditions and identity mappings. To illustrate the results, an example is provided. 

Published
2022-06-30
How to Cite
Tijani, K. R., Wahab, O. T., Usamot, I. F., & Alata, S. M. (2022). Common Coupled Fixed Point Theorems without Compatibility in Partially Ordered Metric Spaces. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 8(1), 88 - 100. https://doi.org/10.6084/m9.figshare.20716042
Issue
Vol 8 No 1 (2022)
Section
Articles

Copyright (c) 2022 K. R. Tijani, O. T. Wahab, I. F. Usamot, S. M. Alata

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

This is an Open Access article distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, adaptation, and reproduction in any medium, provided that the original work is properly cited.