Criterion of the best non-symmetric approximant for multivariable functions in spaces $$$L_{p_1,...,p_n}$$$

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 nonsymmetric approximant for the multivariable functions in spaces with mixed integral metric were considered in this article. The criterion of best nonsymmetric approximant in these spaces is obtained.

Keywords


mixed integral metric; the best non-symmetric approximant; non-symmetric norm

References


Kolmogorov A.N., Fomin S.V. Elements of function theory and functional analysis, Moscow, 1972. (in Russian)

Korneichuk N.P. Extremum problems in approximation theory, Moscow, 1976. (in Russian)

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)

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

Traktyns'ka V.M. "Criterion of the best non-symmetric approximant in spaces with mixed integral metric", Dnipr. Univ. Math. Bull., 1998; 3: pp. 119-122. (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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ISSN (Online): 2518-7996
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