Inequalities of Jackson type for ridge and polynomial approximation of harmonic functions

V.F. Babenko (Oles Honchar Dnipropetrovsk National University), http://orcid.org/0000-0001-6677-1914
D.A. Levchenko (Oles Honchar Dnipropetrovsk National University)

Abstract


New sharp Jackson type inequalities for ridge and polinomial approximation of some classes of functions harmonic inside unit disk are obtained.

Keywords


best approximation; modulus of continuity; Jackson type inequalities; harmonic function; ridge approximation

References


Babenko V.F., Levchenko D.A. "Uniformly distributed ridge approximation of certain classes of harmonic functions", Ukrainian Math. J., 2012; 64(10): pp. 1427-1432. (in Russian)

Zhuk V.V. "Some sharp inequalities between uniform approximations of periodic functions", Dokl. AN SSSR, 1967; 201: pp. 263-266. (in Russian)

Korneichuk N.P. "Exact constant in Jackson theorem of the best uniform appproximation of continuous periodic functions", Dokl. AN SSSR, 1962; 145: pp. 514-515. (in Russian)

Korneichuk N.P. "On exact constant in Jackson theorem for continuous periodic functions", Matem. zametki, 1982; 32(5): pp. 669-674. (in Russian)

Korneichuk N.P. Extremum problems in approximation theory, Moscow, 1976; 320 p. (in Russian)

Ligun A.A. "On exact constants of approximation of differentiable periodic functions", Matem. zametki, 1973; 14(1): pp. 21-30. (in Russian)

Chernykh N.I. "On Jackson inequality in $$$L_2$$$", Trudy MIAN SSSR, 1967; 88: pp. 71-74. (in Russian)


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Copyright (c) 2013 V.F. Babenko, D.A. Levchenko

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