A FIXED POINT THEOREM FOR A FAMILY OF MAPPINGS IN A FUZZYMETRIC SPACE 315 RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO Serie II, Tomo LII (2003), pp. 315-321 A FIXED POINT THEOREM FOR A FAMILY OF MAPPINGS IN A FUZZY METRIC SPACE CRISTINA DI BARI – CALOGERO VETRO In this paper we give a common fixed point theorem for a family of mappings of a G- complete fuzzy metric space ( X , M, ∗) into itself. From this result we deduce a common fixed point theorem for a family of mappings of a complete metric space ( X , d ) into itself. 1. Introduction. Many Authors have investigated the notion of fuzzy metric space [1, 2-4, 6, 9, 10] and the possibility of extending the Banach fixed point theorem to fuzzy contractive mappings on complete fuzzy metric space in several ways [5, 7, 11]. In this paper we give a common fixed point result for a class of mappings in the fuzzy metric spaces in the sense of Kramosil and Mich´ alek [9] which are complete in Grabiec’s sense [5]. The result was obtained by modifying the contractivity definition given by Gregori and Sapena [7]. Such result allows to get a common fixed point result for a family of mappings of a complete metric space ( X , d ) into itself. 2. Preliminaries on the fuzzy metric spaces. In this section we recall some notions and some results on the fuzzy metric spaces. DEFINITION 1. (Schweizer and Sklar [10]). A binary operation ∗ : Keywords: Fuzzy metric spaces, Common fixed points. Supported by University of Palermo.