Advancing Common Fixed Point Theorems in Bipolar Fuzzy-2 Metric Space and Applications in Nonlinear Analysis

Authors

  • Rajesh Kumar Saini Department of Mathematical Sciences and Computer Applications Bundelkhand University, Jhansi, INDIA
  • Mukesh Kushwaha Department of Mathematical Sciences and Computer Applications Bundelkhand University, Jhansi, INDIA

Keywords:

Common Fixed Point Theorem, Bipolar Fuzzy-2 Metric Space, Fuzzy Metric Space

Abstract

This study advances common fixed point theorems (CFPT) in bipolar fuzzy-2 metric space 
(BF2MS) and explores their applications in nonlinear analysis. BF2MS generalizes traditional metric 
and fuzzy metric spaces (FMS) by incorporating dualistic relationships, allowing the representation of 
both attraction and repulsion effects. We extend classical fixed point theorems (FPTs) to BF2MS, 
establishing conditions for the existence of common fixed points (CFPs). The study's applications span 
nonlinear analysis, stability analysis, control theory, and multi-criteria decision-making under 
uncertainty. Our findings refine existing results and provide practical real-world applications, 
supported by numerical examples, enhancing fuzzy mathematics and nonlinear systems modeling. 

 

DOI 10.5281/zenodo.18262691

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Published

2026-04-25

Issue

Vol. 98 (2026): Neutrosophic Sets and Systems

Section

Article

License

Copyright (c) 2026 Neutrosophic Sets and Systems

Creative Commons License

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

 Creative Commons Attribution (CC BY) license.

How to Cite

Rajesh Kumar Saini, & Mukesh Kushwaha. (2026). Advancing Common Fixed Point Theorems in Bipolar Fuzzy-2 Metric Space and Applications in Nonlinear Analysis . Neutrosophic Sets and Systems, 98, 123-143. https://fs.unm.edu/nss8/index.php/111/article/view/7547