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Caristi’s fixed point theorem and its equivalences in fuzzy metric spaces. (English) Zbl 1389.54074

Summary: In this article, we extend Caristi’s fixed point theorem, Ekeland’s variational principle and Takahashi’s maximization theorem to fuzzy metric spaces in the sense of A. George and P. Veeramani [Fuzzy Sets Syst. 64, No. 3, 395–399 (1994; Zbl 0843.54014)]. Further, a direct simple proof of the equivalences among these theorems is provided.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54A40 Fuzzy topology
54E40 Special maps on metric spaces

Citations:

Zbl 0843.54014
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