Monotone path-connected sets in geometric approximation theory and their applications-Reference-Cited by-同舟云学术

Monotone path-connected sets in geometric approximation theory and their applications

Published:2024-07-28 Issue:2 Volume:2 Page:30-46
ISSN:2949-3919
Container-title:Mathematics and Theoretical Computer Science
language:
Short-container-title:jour

Author:

Alimov A. R.¹,Tsar’kov I. G.²

Affiliation:

1. Lomonosov Moscow State University

2. Lomonosov Moscow State University; Moscow Center for Fundamental and Applied Mathematics

Abstract

Monotone sets have been quite actively studied in recent years in geometric approximation theory. The concept of monotone path-connected sets has proved especially useful. The purpose of the present paper is to give a short but comprehensive survey on this topic; we also illustrate relations with key properties of approximating sets, of which we consider characterizations of best approximants, and properties of uniqueness and stability.

Publisher

Kazan Federal University

Reference19 articles.

1. A.R. Alimov, I.G. Tsar’kov, Geometric approximation theory, Springer Monographs in Mathematics, Springer, Cham, 2021. DOI: https://doi.org/10.1007/978-3-030-90951-2

2. D. Braess, Nonlinear approximation theory, Springer Ser. Comput. Math., vol. 7, Springer, Berlin, 1986. DOI: http://doi.org/10.1007/978-3-642-61609-9

3. A.R. Alimov, K.S. Ryutin, I.G. Tsar’kov, Existence, uniqueness, and stability of best and near-best approximations, Russ. Math. Surv. 78 (3), 399–442 (2023). DOI: https://doi.org/10.4213/rm10113e

4. L. P. Vlasov, Approximative properties of sets in normed linear spaces, Russ. Math. Surv. 28 (6), 1–66 (1973). DOI: https://doi.org/10.1070/rm1973v028n06abeh001624

5. A.L. Brown, Suns in normed linear spaces which are fi dimensional, Math. Ann. 279 (1), 87–101 (1987). DOI: https://doi.org/10.1007/BF01456192