Criterion of the best approximant for multivariable functions in spaces $$$L_{1,p_2,...,p_n}$$$ and $$$L_{p_1,...,p_{n-1},1}$$$

O.D. Kostyuk; V.M. Traktyns'ka; M.Ye. Tkachenko

doi:10.15421/241608

Criterion of the best approximant for multivariable functions in spaces $L_{1,p_2,...,p_n}$ and $L_{p_1,...,p_{n-1},1}$

O.D. Kostyuk (Oles Honchar Dnipropetrovsk National University)
V.M. Traktyns'ka (Oles Honchar Dnipropetrovsk National University)
M.Ye. Tkachenko (Oles Honchar Dnipropetrovsk National University), https://orcid.org/0000-0002-9242-194X

Abstract

The questions of the characterization of the best approximant for the multivariable functions in spaces with mixed integral metric were considered in this article. The criterions of the best approximant in spaces

$L_{1,p_2,...,p_n}$ and

$L_{p_1,...,p_{n-1},1}$ is obtained.

Keywords

mixed integral metric; the best approximant

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References

Smirnov G.S. "General form of linear functional and criterion of polynomial of the best approximation in spaces with mixed integral metric", Ukrainian Math. J., 1973; 25(1): pp. 134-138. (in Russian) doi:10.1007/BF01085405

Smirnov G.S. "Criterion of polynomial of the best approximation in spaces $L_{p;1}$ , $L_{1;q}$ ", Ukrainian Math. J., 1973; 25(3): pp. 415-419. (in Russian) doi:10.1007/BF01091890

Traktyns'ka V.M. "Characterization of the best integral approximant of multivariable functions", Res. Math., 2007; 12: pp. 134-136. (in Russian)