Banach contraction principles in fuzzy metric spaces

Abstract

[eng] In this paper we discuss the concept of Cauchy sequence due to Grabiec, that we call $G$-Cauchy, in the context of fuzzy metric spaces. It leads to introduce and study a concept of weak $G$-completeness in fuzzy and classical context. Then, we generalize the celebrated Grabiec's fuzzy Banach Contraction Principle. Also, we extend the Mihet's fixed point theorem given for weak $B$-contractive mappings.