Abstract
In 1975, Kramosil and Michalek [1] first introduced the concept of a fuzzy metric space. In 1994, George and Veeramani [2] slightly modified the concept of fuzzy metric space introduced by Kramosil and Michalek, defined a Hausdorff topology and proved some known results. In 1969, Rheinboldt [3] initiated the study of iterated contraction. The concept of iterated contraction proves to be very useful in the study of certain iterative process and has wide applicability in metric spaces. In this paper we introduce the notion of fuzzy iterated contraction maps in fuzzy metric spaces and establish some fixed point theorems for fuzzy iterated contraction maps in fuzzy metric spaces.
Highlights
Open Access fuzzy metric space introduced by Kramosil and Michalek, defined a Hausdorff topology and proved some known results
In this paper we introduce the notion of fuzzy iterated contraction maps in fuzzy metric spaces and establish some fixed point theorems for fuzzy iterated contraction maps in fuzzy metric spaces
We firstly give a notion of the fuzzy iterated contraction map in a fuzzy metric space, we prove some fixed point theorems for fuzzy iterated maps under different settings
Summary
We firstly give a notion of the fuzzy iterated contraction map in a fuzzy metric space, we prove some fixed point theorems for fuzzy iterated maps under different settings. Definition 3.1 If ( X , M ,*) is a fuzzy metric space such that Tx,T 2x,t x,Tx, t k for all x ∈ X ,t > 0, 0 < k < 1, T is said to be a fuzzy iterated contraction map. Remark 3.1 A fuzzy contraction map is continuous and is a fuzzy iterated contraction.
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