Jackson–Stechkin type inequalities and widths of classes of functions in the weighted Bergman space
https://doi.org/10.22405/2226-8383-2021-22-2-135-144
Abstract
In extremal problems of the theory of approximation of functions an important role is played be exact inequalities of the value of the best polynomial approximation by means of averaged
values of the modules of continuity of higher orders of the derived functions. In this paper we present an inequality of type Ligun-two-sided estimate for the best weighted approximate
analytic functions in the unit disc from the Bergman space 𝐵_2,𝛾 . The resulting inequalities allow us to establish new connections between the constructive and structural properties of the
functions and for the corresponding classes of functions give an estimate from the top of the widths. The exact values of Bernstein, Kolmogorov, Gelfand, linear and projection n-widths of classes of analytic functions in unit discs defined by modules of continuity of higher orders of the derived functions in the space 𝐵_2,𝛾 averaged with positive weight are calculated
About the Author
Mukhtor Ramazonovich Langarshoev
College near Moscow «Energia»
Russian Federation
Russian Federation
candidate of physical and mathematical sciences
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Review
For citations:
Langarshoev M.R. Jackson–Stechkin type inequalities and widths of classes of functions in the weighted Bergman space. Chebyshevskii Sbornik. 2021;22(2):135-144. (In Russ.) https://doi.org/10.22405/2226-8383-2021-22-2-135-144
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