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)

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) doi:10.1007/BF01104884

Stechkin S.B. "The best approximation of linear operators", Matem. zametki, 1967; 1(2): pp. 137-148. (in Russian) doi:10.1007/BF01268056

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) doi:10.1007/BF01141940

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




  • There are currently no refbacks.

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

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Registered in


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