Selections of the Best and Near-Best Approximation Operators and Solarity
- 5 Downloads
In a finite-dimensional Banach space, a closed set with lower semicontinuous metric projection is shown to have a continuous selection of the near-best approximation operator. Such a set is known to be a sun. In the converse question of the stability of best approximation by suns, it is proved that a strict sun in a finite-dimensional Banach space of dimension at most 3 is a P-sun, has a contractible set of nearest points, and admits a continuous ε-selection from the operator of near-best approximation for any ε > 0. A number of approximative and geometric properties of sets with lower semicontinuous metric projection are obtained.
Unable to display preview. Download preview PDF.
- 6.A. R. Alimov, “Continuity of the metric projection and local solar properties of sets,” Set-Valued Var. Anal., doi: 10.1007/s11228-017-0449-0 (2017).Google Scholar
- 21.I. G. Tsar’kov, “Some applications of geometric theory of approximations,” in Differential Equations. Mathematical Analysis (VINITI, Moscow, 2017), Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 143, pp. 63–80.Google Scholar