Criterion of the best approximant for multivariable functions in spaces $$$L_{1,p_2,...,p_n}$$$ and $$$L_{p_1,...,p_{n-1},1}$$$
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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PDF (Українська)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)
DOI: https://doi.org/10.15421/241608
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Copyright (c) 2016 O.D. Kostyuk, V.M. Traktyns'ka, M.Ye. Tkachenko
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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
