Abstract
AbstractWe present a procedure to construct a compatible metric from a given fuzzy metric space. We use this approach to obtain a characterization of a large class of complete fuzzy metric spaces by means of a fuzzy version of Caristi’s fixed point theorem, obtaining, in this way, partial solutions to a recent question posed in the literature. Some illustrative examples are also given.
Highlights
1 Introduction and preliminaries Throughout this paper the symbols R, R+, and N will denote the set of all real numbers, the set of all non-negative real numbers and the set of all positive integers, respectively
Theorem was successfully applied to deduce several fixed point theorems for complete fuzzy metric spaces from the corresponding results for complete metric spaces
We prove that dα is a metric on X such that dα(x, y) ≤ for all x, y ∈ X
Summary
Introduction and preliminariesThroughout this paper the symbols R, R+, and N will denote the set of all real numbers, the set of all non-negative real numbers and the set of all positive integers, respectively. [ – ]) to deduce several fixed point theorems for complete fuzzy metric spaces from the corresponding results for complete metric spaces.
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