The characterization of the best approximant for the multivariable functions in the space $$$L_{p_1,..,p_n;\Omega }$$$

M.Ye. Tkachenko; V.M. Traktynska

doi:10.15421/241913

The characterization of the best approximant for the multivariable functions in the space $$$L_{p_1,..,p_n;\Omega }$$$

M.Ye. Tkachenko (Oles Honchar Dnipro National University), https://orcid.org/0000-0002-9242-194X
V.M. Traktynska (Oles Honchar Dnipro National University)

Abstract

The questions of the characterization of the best approximant in spaces of multivariable functions with mixed integral metric with weight were considered in this article. The general form of a bounded linear functional and the criterion of the best approximant in these spaces are obtained.

Keywords

multivariable functions; space with a mixed metric with weight; the linear continuous functional; the criterion of the best approximant

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References

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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

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

Traktynska V.M., Tkachenko M.Ye. "General form of linear continuous functional and criterion of the best approximant in spaces with mixed integral metric with weight", Res. Math., 2014; 19: pp. 91-97. (in Ukrainian) doi:10.15421/241411