Some Classical Problems of Geometric Approximation Theory in Asymmetric Spaces

Abstract

We establish a number of theorems of geometric approximation theory in asymmetrically normed spaces. Sets with continuous selection of the near-best approximation operator are studied and properties of such sets are discussed in terms of $$\delta$$ -solar points and the distance function. A result on the coincidence of the classes of $$\delta$$ - and $$\gamma$$ -suns in asymmetric spaces is given. An asymmetric analogue of the Kolmogorov criterion for an element of best approximation for suns, strict suns, and $$\alpha$$ -suns is put forward.

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