Connectedness and solarity in problems of best and near-best approximation

A. R. Alimov   ; I. G. Tsar'kov

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 71 (2016) no. 1, pp. 1-77

Résumé

This survey is concerned with structural characteristics of ‘suns’ in normed linear spaces, with special emphasis on connectedness and monotone path-connectedness. Consideration is given to both direct theorems in geometric approximation theory in which approximative properties of sets are derived from their structural characteristics, and converse theorems in which structural properties of sets are derived from their approximative characteristics. Geometric methods of approximation theory are employed in solving the eikonal equation. Bibliography: 231 titles.

Détail

Keywords: sun, strict sun, Chebyshev set, near-best approximation, connectedness, infinite connectedness, monotone path-connectedness
Mots-clés : eikonal equation.

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