M. Sh. Shabozov, A. A. Shabozova, “On simultaneous approximation of certain classes of functions in the Bergman space <nobr>$B_2$</nobr>”, Izv. Vyssh. Uchebn. Zaved. Mat., 2024, Number 6,Pages <nobr>80

This article is cited in 2 papers

On simultaneous approximation of certain classes of functions in the Bergman space $B_2$

M. Sh. Shabozov^ab, A. A. Shabozova^b

^a A. Dzhuraev Institute of Mathematics, National Academy of Sciences of Tajikistan, 299/1 Sadriddin Aini str., Dushanbe, 734063 Republic of Tajikistan
^b Tajik National University, 17 Rudaki Ave., Dushanbe, 734025 Republic of Tajikistan

Abstract: The problem of finding the supremums of the best simultaneous polynomial approximations of some classes of functions analytic in the unit disk and belonging to the Bergman space $B_2$ is considered. The indicated function classes are defined by the averaged values of the $m$th order moduli of continuity of the highest derivative bounded from above by some majorant $\Phi$.

Keywords: simultaneous approximation, upper bound, best approximation, Bergman space, modulus of continuity, majorant.

UDC: 517.5

Received: 03.05.2023
Revised: 23.06.2023
Accepted: 26.09.2023

DOI: 10.26907/0021-3446-2024-6-80-88