Exploring Proinov-type and Banach-type contractions in fuzzy bipolar metric spaces

Banach-type contractions have played an important role in fixed point theory. Recently, the newly introduced Proinov-type contractions have gained attention due to their wide applicability under various conditions. However, the study of these contractions in newly proposed generalized fuzzy metric spaces remains insufficiently explored. In this paper, we conduct an in-depth exploration of generalized Proinov-type and Banach-type contractions in the context of fuzzy bipolar metric spaces, a generalization of fuzzy metric spaces. We discuss several fixed-point findings for these contractions and provide illustrative examples. Importantly, our findings contribute to the resolution of previously open questions. Furthermore, we showcase the practical applicability of our results in solving integral equations.

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