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

V.F. Babenko (Oles Honchar Dnipropetrovsk National University),
D.A. Levchenko (Oles Honchar Dnipropetrovsk National University)


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.


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


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)

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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)

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