The best approximation of certain unbounded operators on classes of multivariable functions

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

Abstract


We obtain the value of the best approximation of the linear combination, with non-negative coefficients, of the second partial derivatives and mixed derivatives of the second order on the class of multivariable functions with bounded third partial derivatives.

Keywords


best approximation of operator; module of continuity of operator; operator renewal; Kolmogorov type inequality

References


Korneichuk N.P., Babenko V.F., Kofanov V.A., Pichugov S.A. Inequalities for derivatives and their applications, Nauk. dumka, Kyiv, 2003; 590 p. (in Russian)

Konovalov V.N. "Sharp inequalities for norms of functions, third partial and second mixed derivatives", Matem. zametki, 1978; 23(1): pp. 67-78. (in Russian)

Stechkin S.B. "The best approximation of linear operators", Matem. zametki, 1967; 1(2): pp. 137-148. (in Russian)

Timoshin O.A. "The best approximation of second mixed derivative operator in L and C metrics on the plane", Matem. zametki, 1984; 36(3): pp. 369-375. (in Russian)

Shilov G.Ye. "On inequalities between derivatives", Sbor. rabot studench. nauchn. kruzhkov MGU, 1937; pp. 17-27. (in Russian)




DOI: https://dx.doi.org/10.15421/241205

  

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Copyright (c) 2012 V.F. Babenko, D.A. Levchenko

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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
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