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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)

The purpose of this survey is to prove that the fixed point results for various multiplicative contractions are in fact equivalent to the corresponding fixed point results in (standard) metric spaces. For example, such are recent results established by He et al. (Fixed Point Theory Appl. 2014:48, 2014, Mongkolkeha and Sintunavarat (J. Nonlinear Sci. Appl. 8:1134Appl. 8: -1140Appl. 8: , 2015 and Abdou (J. Nonlinear Sci. Appl. 9:2347Appl. 9: -2363Appl. 9: , 2016) and all others from the list of references. Our results here generalize, complement, and improve recent ones from existing literature.MSC: Primary 47H10; secondary 54H25

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This paper attempts to prove fixed and coincidence point results in fuzzy metric space using multivalued mappings. Altering distance function and multivalued strong {bn}-fuzzy contraction are used in order to do that. Presented theorems are generalization of some well known single valued results. Two examples are given to support the theoretical results.