TITLE:
Some Fixed Point Theorems for Fuzzy Iterated Contraction Maps in Fuzzy Metric Spaces
AUTHORS:
Lei Xia, Yuehan Tang
KEYWORDS:
Fixed Point, Iterated Contraction Map, Fuzzy Metric Space
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.1,
January
29,
2018
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.