\(\psi\)-weak contractions in fuzzy metric spaces. (English) Zbl 1260.54056

Abbas, Mujahid; Imdad, Mohammad; Gopal, Dhananjay

Iran. J. Fuzzy Syst. 8, No. 5, 141-148 (2011).

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

Keywords:

weekly compatible mappings; fuzzy metric spaces; common fixed point; \(\psi\)-weak contractions