A common fixed point result for multi-valued mappings in Hausdorff modular fuzzy b-metric spaces with application to integral inclusions

Abstract

The modular fuzzy b-metric space is defined in this study, and we are interested in proving a general common fixed point theorem for a pair of multi-valued mappings in Hausdorff modular fuzzy b-metric spaces. The work generalizes the findings in [H. Kerim, W. Shatanawi, A. Tallafha and T. A. M. Shatnawi, Fixed point theorems on modular fuzzy metric spaces, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 84 2022, 1, 47–58] and produce additional specific findings that are supported by examples. An application to prove the existence of an integral inclusion equation’s solution is shown to demonstrate the importance of our result.