Kybernetika 52 no. 6, 929-942, 2016

Caristi's fixed point theorem and its equivalences in fuzzy metric spaces

Naser Abbasi and Hamid Mottaghi GolshanDOI: 10.14736/kyb-2016-6-0929

Abstract:

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 George and Veeramani [A. George , P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems. 64 (1994) 395-399]. Further, a direct simple proof of the equivalences among these theorems is provided.

Keywords:

fuzzy metric space, Ekeland variational principle, Caristi's fixed point theorem, Takahashi's maximization theorem

Classification:

47H10, 58E30

paper.pdf

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