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Some applications of geometric theory of approximations. (English. Russian original) Zbl 1477.41015

J. Math. Sci., New York 245, No. 1, 64-82 (2020); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 143, 63-80 (2017).
In the paper under review, the author studies approximation and structural geometric-topological properties of sets in a seminormed space and asymmetric spaces for which there exists a continuous selection for the best and near-best approximation operators. He discusses applications of the geometric theory of approximation to problems related to selections from multi-valued mappings, existence of fixed points, and smooth solutions of the eikonal equation.

MSC:

41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
54C65 Selections in general topology
78A05 Geometric optics
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