Some Application of Fixed Point Theorem: A Case Study of Fuzzy Metric Space | Original Article

ABSTRACT:

Main aim of this paper is to prove some fixed point theorems in Fuzzy Metric spaces through rational inequality. Our results extends and generalizes the results of many other authors existing in the literature. In this paper, we manage iterative methods for approximation of fixed points and their applications. We initially talk about fixed point theorems for a non-expansive mapping or a group of non-expansive mappings. we study those fuzzy metrics M on X, in the George and Veeramani’s sense, such that At>0 M(x, Y, t) > 0. The continuous extension M0 of M to X2 ×[0,+∞[ is called extended fuzzy metric. We prove that M0 generates a metrizable topology on X, which can be described in a similar way to a classical metric. M0 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.