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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.

On embeddings of function classes defined by constructive characteristics

Boris V. Simonov, Sergey Yu. Tikhonov (2006)

Banach Center Publications

In this paper we study embedding theorems for function classes which are subclasses of L p , 1 ≤ p ≤ ∞. To define these classes, we use the notion of best trigonometric approximation as well as that of a (λ,β)-derivative, which is the generalization of a fractional derivative. Estimates of best approximations of transformed Fourier series are obtained.

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