Abstract
Abstract In this paper, we introduce the concept of fuzzy mappings in Hausdorff fuzzymetric spaces (in the sense of George and Veeramani (Fuzzy Sets Syst.64:395-399, 1994)). We establish the existence of α-fuzzyfixed point theorems for fuzzy mappings in Hausdorff fuzzy metric spaces, whichcan be utilized to derive fixed point theorems for multivalued mappings. We alsogive an illustrative example to support our main result.
Highlights
In, Zadeh [ ] introduced and studied the concept of a fuzzy set in his seminal paper
The object of this paper is to study the role of some type of fuzzy mappings to ascertain the existence of fuzzy fixed point in Hausdorff fuzzy metric spaces
4 Conclusions In the present work we introduced a new concept of fuzzy mappings in the Hausdorff fuzzy metric space on compact sets, which is a partial generalization of fuzzy contractive mappings in the sense of George and Veeramani
Summary
In , Zadeh [ ] introduced and studied the concept of a fuzzy set in his seminal paper. Several researchers proved the fixed point theorems in fuzzy metric spaces such as in [ – ] and the references therein. Kiany and Amini-Harandi [ ] proved fixed point and endpoint theorems for multivalued contraction mappings in fuzzy metric spaces.
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