Banach Fixed Point Theorem in Fuzzy Metric Spaces

Abstract

In this paper, we study certain type of fuzzy metric spaces and then prove the completeness of this metric space, this metric space will be denoted by (F,ρ) where F is the family of all fuzzy subsets of the set of fuzzy numbers and ρ is the distance function. Then the statement and the proof of Banach fixed point theorem in the fuzzy metric space (F,ρ) is given as a main result.