Common fixed point Theorems for non compatible mappings in fuzzy metric spaces.

Abbas, Mujahid; Altun, Ishak; Gopal, Dhananjay

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Fixed point theorems of $G$ -fuzzy contractions in fuzzy metric spaces endowed with a graph

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Let $(X, M, *)$ be a fuzzy metric space endowed with a graph $G$ such that the set $V (G)$ of vertices of $G$ coincides with $X$ . Then we define a $G$ -fuzzy contraction on $X$ and prove some results concerning the existence and uniqueness of fixed point for such mappings. As a consequence of the main results we derive some extensions of known results from metric into fuzzy metric spaces. Some examples are given which illustrate the results.