F-Bipolar Metric Spaces: Fixed Point Results and Their Applications

The aim of this research article is to broaden the scope of fixed point theory in F-bipolar metric spaces by introducing the concept of rational (⋏,⋎,ψ)-contractions. These new contractions allow for the formulation of fixed point theorems specifically designed for contravariant mappings. The validity of our approach is substantiated by a meticulously crafted example. Moreover, we explore the practical implications of these theorems beyond the realm of fixed point theory. Notably, we demonstrate their effectiveness in establishing the existence and uniqueness of solutions to integral equations. Additionally, we investigate homotopy problems, focusing on the conditions for the existence of a unique solution within this framework.