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

V.M. Traktyns'ka; M.Ye. Tkachenko

doi:10.15421/241411

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), https://orcid.org/0000-0002-9242-194X

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

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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

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)