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Best Linear Approximation Methods for Some Classes of Analytic Functions on the Unit Disk

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Abstract

Considering Banach Hardy spaces and weighted Bergman spaces, we find the sharp values of the Bernstein, Kolmogorov, Gelfand, and linear n-widths for the classes of analytic functions on the unit disk whose moduli of continuity of the rth derivatives averaged with weight are majorized by a given function satisfying some constraints.

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Authors and Affiliations

  1. University of Central Asia, Tajik National University, Dushanbe, Tajikistan

    M. Sh. Shabozov

  2. Tajik National University, Dushanbe, Tajikistan

    M. R. Langarshoev

Authors
  1. M. Sh. Shabozov
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  2. M. R. Langarshoev
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Corresponding author

Correspondence to M. Sh. Shabozov.

Additional information

The authors are grateful to the referee for the valuable remarks.

Russian Text © The Author(s), 2019, published in Sibirskii Matematicheskii Zhurnal, 2019, Vol. 60, No. 6, pp. 1414–1423.

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Shabozov, M.S., Langarshoev, M.R. Best Linear Approximation Methods for Some Classes of Analytic Functions on the Unit Disk. Sib Math J 60, 1101–1108 (2019). https://doi.org/10.1134/S0037446619060181

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  • DOI: https://doi.org/10.1134/S0037446619060181

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