Some Novel Coincidence and Fixed Point Results Based on Z Family of Functions in Fuzzy Metrics

This paper suggests some coincidence and fixed point theorems based on the Z family functions for set valued mappings. After that, we provide the concept of Z∗ family of functions, and prove some coincidence and fixed points results for strongly demicompact mappings in fuzzy metric space. We also suggest some examples to support our results. Eventually, we give the existence and uniqueness of a solution for a functional equation involved in a dynamic programming. Our results are novel and suggest a new direction to researchers who working in the theory of coincidence and fixed point.