Monotone path-connected sets in geometric approximation theory and their applications
https://doi.org/10.26907/2949-3919.2024.2.30-46
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.
Keywords
monotone path-connected set,
Chebyshev set,
sun,
best approximation,
stability of best approximation,
associated norm
Supporting agencies: The work was carried at M.V. Lomonosov Moscow State University at the expense of a grant by the Russian Science Foundation (project No. 22-11-00129).
About the Authors
A. R. Alimov
Lomonosov Moscow State University
Russian Federation
Alexey Rostislavovich Alimov
Russian Federation
Alexey Rostislavovich Alimov
1 Leninskie Gory, Moscow, 119991, Russia
I. G. Tsar’kov
Lomonosov Moscow State University;
Moscow Center for Fundamental and Applied Mathematics
Russian Federation
Russian Federation
Igor’ Germanovich Tsar’kov
1 Leninskie Gory, Moscow, 119991, Russia
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For citations:
Alimov A.R., Tsar’kov I.G. Monotone path-connected sets in geometric approximation theory and their applications. Mathematics and Theoretical Computer Science. 2024;2(2):30-46. (In Russ.) https://doi.org/10.26907/2949-3919.2024.2.30-46
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