General form of linear continuous functional and criterion of the best approximant in spaces with mixed integral metric

V.M. Traktyns'ka (Oles Honchar Dnipropetrovsk National University)
M.Ye. Tkachenko (Oles Honchar Dnipropetrovsk National University)

Abstract


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

Keywords


the bounded linear functional in spaces with mixed integral metric with weight; the criterion of best approximant in spaces with mixed integral metric with weight

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)

Lusternik L.A., Sobolev V.I. Elements of functional analysis, Moscow, 1965. (in Russian)

Nikolsky S.M. "Mean approximation of functions by trigonometrical polynomials", Izv. AN SSSR. Ser.: Matematika, 1946; 10(3): pp. 207-256. (in Russian)


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Copyright (c) 2014 V.M. Traktyns'ka, M.Ye. Tkachenko

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ISSN (Online): 2518-7996
ISSN (Print): 2312-9557