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

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.