Abstract
AbstractOur main purpose in this paper is to introduce the notion of φ -contractive mapping in fuzzy metric spaces and to present two new re-sults on the existence and the approximation of fixed point of nonlinearcontractions mappings and semigroups in fuzzy metric spaces. Theseresults are of interest in view of analogous results in metric spaces (seefor example [1], [7]) Mathematics Subject Classification: Primary 47H10, 54H25Keywords: Fixed point, fuzzy metric, left reversible semigroup, nonlinearcontractive conditions 1 Introduction Our terminology and notation for fuzzy metric spaces conform of that Georgeet al. [5, 6]. Recently Gregori et al. [4] have showed that the study of theintuitionistic fuzzy metric space (IFMS) ( X,M,N,∗,♦ ) can be reduced to thestudy of the fuzzy metric space (FMS) ( X,M,∗ ). More exactly, the topology τ ( MN ) of an IFMS ( X,M,N,∗,♦ ) coincides with the topology τ ( M ) generatedby the FMS ( X,M,∗ ), which has as a base the family of open sets. So, ourstudy is limited to FMSs.Definition 1.1
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