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On best approximation in fuzzy metric spaces

Naser Abbasi;  Hamid Mottaghi Golshan — 2015

Kybernetika

In this paper we introduce the notation of t-best approximatively compact sets, t-best approximation points, t-proximinal sets, t-boundedly compact sets and t-best proximity pair in fuzzy metric spaces. The results derived in this paper are more general than the corresponding results of metric spaces, fuzzy metric spaces, fuzzy normed spaces and probabilistic metric spaces.

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

Naser Abbasi;  Hamid Mottaghi Golshan — 2016

Kybernetika

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.

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