Some Classical Problems of Geometric Approximation Theory in Asymmetric Spaces

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.