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.
We apply the Chebyshev coefficients λf and λb, recently introduced by the authors, to obtain some results related to certain geometric properties of Banach spaces. We prove that a real normed space E is an L1-predual if and only if λf(E) = 1/2, and that if a (real or complex) normed space E is a P1 space, then λb(E) equals λb(K), where K is the ground field of E.
The purpose of this paper is to obtain sufficient conditions, for a Banach space X to contain or exclude c0 or l1, in terms of the sets of best approximants in X for the elements in the bidual space.