Common Interpolative Rational Type Contractions in Bipolar Metric Spaces

Abstract

The main objective of this study is to introduce an extended class of interpolative rational contractions in bipolar metric spaces and to establish common fixed point theorems for such mappings. Specifically, we consider mappings that satisfy a general contractive condition involving multiple distance terms and an associated control function, broadening the existing framework of fixed point theory. Our results not only unify but also significantly improve upon several well-known fixed point theorems in the current literature, including classical results for single mappings as well as those for pairs of mappings.

Moreover, the common fixed point results presented in this work are particularly noteworthy because they apply to pairs of mappings that share a common fixed point, even in the absence of strict monotonicity or continuity assumptions usually required in traditional fixed point theorems. This enhancement broadens the scope of applications to a wider range of problems in nonlinear analysis and optimization.

To demonstrate the practical relevance and sharpness of our theoretical findings, we also provide illustrative examples. These examples highlight how the newly established theorems can be applied in various mathematical settings, showcasing their robustness and versatility.