The criterion of the best approximant for the multivariable functions in the space $$$L_{p_1,...,p_{i-1},1,p_{i+1},...,p_n}$$$

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

doi:10.15421/241812

The criterion of the best approximant for the multivariable functions in the space $$$L_{p_1,...,p_{i-1},1,p_{i+1},...,p_n}$$$

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

Abstract

The questions of the characterization of the best approximant for the multivariable functions in the space with mixed integral metric were considered in this article. The criterion of the best approximant in space $$$L_{p_1,...,p_{i-1},1,p_{i+1},...,p_n}$$$ is obtained.

Keywords

mixed integral metric; the best approximant

MSC 2020

41A45; 46E30; 41A10

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References

Kostyuk O.D., Traktyns'ka V.M., Tkachenko M.Ye. "Criterion of the best approximant for multivariable functions in spaces $$$L_{1,p_2,...,p_n}$$$ and $$$L_{p_1,...,p_{n-1},1}$$$", Res. Math., 2016; 21: pp. 44-51. (in Ukrainian) doi:10.15421/241608

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.

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.

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