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

V.F. Babenko; D.A. Levchenko

doi:10.15421/241205

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

Full Text:

PDF (Русский)

References

Korneichuk N.P., Babenko V.F., Kofanov V.A., Pichugov S.A. Inequalities for derivatives and their applications, Naukova dumka, 2003.

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

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

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.

Shilov G.Ye. "On inequalities between derivatives", Sbor. rabot studench. nauchn. kruzhk. MGU, 1937; pp. 17-27.