Extended fuzzy metrics and fixed point theorems

Abstract

In this paper, we study those fuzzy metrics M on X, in the George and Veeramani's sense, such that Λ t > 0 M(x, y, t) > 0. The continuous extension M 0 of M to X 2 × [0,+∞[ is called extended fuzzy metric. We prove that M 0 generates a metrizable topology on X, which can be described in a similar way to a classical metric. M 0 can be used for simplifying or improving questions concerning M; in particular, we expose the interest of this kind of fuzzy metrics to obtain generalizations of fixed point theorems given in fuzzy metric spaces.