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Dal'nevostochnyi Matematicheskii Zhurnal, 2024, Volume 24, Number 1, Pages 55–66
DOI: https://doi.org/10.47910/FEMJ202406 (Mi dvmg531) 		 
The best approximation of functions analytic in the unit circle in weighted Bergman space

M. R. Langarshoeva, A. G. Aydarmamadovab

a Academy Civil Protection the of Russian Ministry for Emergency Situations
b Tajik Technological University
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DOI: https://doi.org/10.47910/FEMJ202406
Abstract: In this paper, we obtained the exact inequalities between the best approximations of analytical in the unit circle functions and generalized modulus of continuity of the $m$-th order in the weighted Bergman space $B_{2,\gamma}.$ The exact values of $n$-widths of some classes of functions in a weighted Bergman space are calculated.
Key words: generalized modulus of continuity, best approximation, weighted Bergman space, complex algebraic polynomial, $n$-widths.
Received: 07.10.2022
Accepted: 14.11.2023
Document Type: Article
UDC: 517.5
MSC: Primary 42A10; Secondary 41A17, 41A44
Language: Russian
Citation: M. R. Langarshoev, A. G. Aydarmamadov, “The best approximation of functions analytic in the unit circle in weighted Bergman space”, Dal'nevost. Mat. Zh., 24:1 (2024), 55–66
Citation in format AMSBIB
\Bibitem{LanAyd24}
\by M.~R.~Langarshoev, A.~G.~Aydarmamadov
\paper The best approximation of functions analytic in the unit circle in weighted Bergman space
\jour Dal'nevost. Mat. Zh.
\yr 2024
\vol 24
\issue 1
\pages 55--66
\mathnet{http://mi.mathnet.ru/dvmg531}
\crossref{https://doi.org/10.47910/FEMJ202406}
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