Common Fixed Point Theorems in a New Fuzzy Metric Space

Abstract

We generalize the Hausdorff fuzzy metric in the sense of Rodríguez-López and Romaguera, and we introduce a new $M_{\infty }$-fuzzy metric, where $M_{\infty }$-fuzzymetric can be thought of as the degree of nearness between two fuzzy sets with respect to any positive real number. Moreover, under $\varphi$-contraction condition, in the fuzzy metric space, we give some common fixed point theorems for fuzzy mappings.