Weakly monotone sets and continuous selection in asymmetric spaces

Author:

Tsar’kov I. G.

Abstract

Abstract Sets admitting a continuous selection from the set of near best approximations are studied. Applications of the geometric theory of approximation to the existence of continuous selections for the sets of -link piecewise linear functions, -link piecewise polynomial functions and generalizations thereof are also discussed. Bibliography: 23 titles.

Funder

Russian Foundation for Basic Research

Publisher

IOP Publishing

Subject

Algebra and Number Theory

Cited by 25 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Convexity of $$\delta$$-Suns and $$\gamma$$-Suns in Asymmetric Spaces;Russian Journal of Mathematical Physics;2024-06

2. Connectedness in asymmetric spaces;Journal of Mathematical Analysis and Applications;2023-11

3. Reflexivity for Spaces With Extended Norm;Russian Journal of Mathematical Physics;2023-09

4. Existence, uniqueness, and stability of best and near-best approximations;Russian Mathematical Surveys;2023

5. Continuous selections of set-valued mappings and approximation in asymmetric and semilinear spaces;Izvestiya: Mathematics;2023

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