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 JAMP  Vol.6 No.1 , January 2018
Some Fixed Point Theorems for Fuzzy Iterated Contraction Maps in Fuzzy Metric Spaces
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.
Cite this paper: Xia, L. and Tang, Y. (2018) Some Fixed Point Theorems for Fuzzy Iterated Contraction Maps in Fuzzy Metric Spaces. Journal of Applied Mathematics and Physics, 6, 224-227. doi: 10.4236/jamp.2018.61021.
References

[1]   Kramosil, I. and Michálek, J. (1975) Fuzzymetric and Statistical Mestric Spaces. Kybernetika, 11, 336-334.

[2]   George, A. and Veeramani, P. (1994) On Some Results in Fuzzy Metric Spaces. Fuzzy Sets and System, 64, 395-399.
https://doi.org/10.1016/0165-0114(94)90162-7

[3]   Rheinboldt, W.C. (1968) A Unified Convergence Theory for a Class of Iterative Process. SIAM Journal on Numerical Analysis, 5, 42-63.
https://doi.org/10.1137/0705003

 
 
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