Fuzzy contractive mappings and fixed points in fuzzy metric spaces

In the paper we introduce a new concept of fuzzy contraction, which is a generalization of a fuzzy contractive mapping initiated in the article [V. Gregori, A. Sapena, On fixed-point theorems in fuzzy metric spaces, Fuzzy Sets and Systems 125 (2002) 245–252]. For this type of contraction the conditions guaranteeing the existence of fixed point in fuzzy M-complete metric spaces in the sense of George and Veeramani are established. The result is supported by examples.