We give some new definitions of D *-metric spaces and we prove a common fixed point theorem for a class of mappings under the condition of weakly commuting mappings in complete D *-metric spaces. We get some improved versions of several fixed point theorems in complete D *-metric spaces.

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Abstract. In this paper, common fixed point theorems for fuzzy maps in fuzzy metric spaces are proved. These theorems are fuzzy version of some known results in ordinary metric spaces.

In this paper, we prove some common fixed point results for four mappings satisfying generalized contractive condition in S-metric space. Our results extend and improve several previous works. Keywords Common fixed point Á S-metric space Á Compatible mappings Mathematics Subject Classification 47H10 Á 54H25 1. Sðx; y; zÞ ¼ 0 if and only if x ¼ y ¼ z; 2. Sðx; y; zÞ Sðx; x; aÞ þ Sðy; y; aÞ þ Sðz; z; aÞ:The pair (X, S) is called an S-metric space. Example 1.2 [1]We can easily check that the following examples are S-metric spaces.1. Let X ¼ R n and jj Á jj be a norm on X. Then Sðx; y; zÞ ¼ jjy þ z À 2xjj þ jjy À zjj is an S-metric on X. In general, if X is a vector space over R and jj Á jj is a norm on X. Then it is easy to see that Sðx; y; zÞ ¼ jjay þ bz À kxjj þ jjy À zjj;where a þ b ¼ k for every a; b ! 1, is an S-metric on X. 2. Let X be a nonempty set and d 1 , d 2 be two ordinary metrics on X. Then Sðx; y; zÞ ¼ d 1 ðx; zÞ þ d 2 ðy; zÞ;is an S-metric on X.Mathematical Sciences (2018) 12:137-143 https://doi.org/10.1007/s40096-018-0252-6( 0123456789().,-volV) (0123456789().,-volV)