Contravariant reich type F-contraction in F-bipolar metric spaces with application


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Authors

  • Muhammad Sarwar Department of Mathematics, University of Malakand, Chakdara Dir(L), 18000, Khyber Pakhtunkhwa, Pakistan
  • Nihar Ali Department of Mathematics, University of Malakand, Chakdara Dir(L), 18000, Khyber Pakhtunkhwa, Pakistan
  • Kamaleldin Abodayeh Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
  • Chanon Promsakon Department of Mathematics, Faculty of Applied Science, King Mongkutʼs University of Technology North Bangkok, Bangkok 10800, Thailand
  • Thanin Sitthiwirattham Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand

Keywords:

Fixed point, $F$-Bipolar Metric Spaces, Contravariant Reich Type $F$-Contraction;, Integral Equations

Abstract

In this work, we explore fixed point (FP) results using the concept of contravariant Reich-type F -contraction within the framework of F -bipolar metric spaces (F-BMS). Our findings extend certain results from the existing literature. Additionally, we provide an example and an application to demonstrate the existence and uniqueness of the integral equation (IE).

References

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Published

2025-09-03

How to Cite

Sarwar, M., Nihar Ali, Kamaleldin Abodayeh, Chanon Promsakon, & Thanin Sitthiwirattham. (2025). Contravariant reich type F-contraction in F-bipolar metric spaces with application. Results in Nonlinear Analysis, 8(2), 328–336. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/617

Issue

Vol. 8 No. 2 (2025): Online First

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Articles

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