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)


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.


mixed integral metric; the best approximant


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)

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)

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


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