Abstract
The purpose of this paper is to introduce the notion of fuzzy iterated contraction maps in fuzzy metric spaces and establish some new fixed point theorems for fuzzy iterated contraction maps in fuzzy metric spaces.
Highlights
We prove some new fixed point theorems for fuzzy iterated maps under different settings
Theorem 3.1 If T : C → C is a fuzzy iterated contraction and is continuous, where C is closed subset of a metric space X, T has a fixed point provided that T (C ) is compact
Proof: We show that the sequence {xn} has a convergent subsequence
Summary
In this paper we establish some new fixed point theorems for fuzzy iterated contraction maps in fuzzy metric spaces. We prove some new fixed point theorems for fuzzy iterated maps under different settings. Theorem 3.1 If T : C → C is a fuzzy iterated contraction and is continuous, where C is closed subset of a metric space X, T has a fixed point provided that T (C ) is compact.
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