Geodesic
$\mathcal{K}$-functionals and exact values of $n$-widths in the Bergman space
Ural mathematical journal, Tome 3 (2017) no. 2, pp. 74-81

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In this paper, we consider the problem of mean-square approximation of complex variables functions which are regular in the unit disk of the complex plane. We obtain sharp estimates of the value of the best approximation by algebraic polynomials in terms of $\mathcal{K}$-functionals. Exact values of some widths of the specified class of functions are calculated.
Keywords: Bergman space, Best mean-square approximation, $\mathcal{K}$-functional, $n$-width. 
@article{UMJ_2017_3_2_a9,
     author = {Mukim S. Saidusajnov},
     title = {$\mathcal{K}$-functionals and exact values of $n$-widths in the {Bergman} space},
     journal = {Ural mathematical journal},
     pages = {74--81},
     publisher = {mathdoc},
     volume = {3},
     number = {2},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2017_3_2_a9/}
}
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Mukim S. Saidusajnov. $\mathcal{K}$-functionals and exact values of $n$-widths in the Bergman space. Ural mathematical journal, Tome 3 (2017) no. 2, pp. 74-81. http://geodesic.mathdoc.fr/item/UMJ_2017_3_2_a9/