Fuzzy contractive mappings and fixed points in fuzzy metric spaces

Authors:
Dariusz Wardowski
Affiliations:
University of Łódź, Faculty of Mathematics and Computer Science, Department of Nonlinear Analysis, Banacha 22, 90-238 Łódź, Poland
Venue:
Fuzzy Sets and Systems
Year:
2013

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Abstract

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.