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$$\psi$$-weak contractions in fuzzy metric spaces. (English) Zbl 1260.54056
Summary: In this paper, the notion of $$\psi$$-weak contraction [B. E. Rhoades, Nonlinear Anal., Theory Methods Appl. 47, No. 4, 2683–2693 (2001; Zbl 1042.47521)] is extended to fuzzy metric spaces. The existence of common fixed points for two mappings is established where one mapping is $$\psi$$-weak contraction with respect to another mapping on a fuzzy metric space. Our result generalizes a result of V. Gregori and A. Sapena [Fuzzy Sets Syst. 125, No. 2, 245–252 (2002; Zbl 0995.54046)].

##### MSC:
 54H25 Fixed-point and coincidence theorems (topological aspects) 54E35 Metric spaces, metrizability