### Comparison theorems for derivatives and some of their applications

#### Abstract

#### Keywords

#### Full Text:

PDF (Русский)#### References

Kolmogorov A.N. "Une generalization de l’inegalite de M.J. Hadamard entre les bornes superieures des derivees successives d’une function", *C. r. Acad. sci. Paris*, 1938; 207: pp. 764-765. (in French)

Kolmogorov A.N. "On inequalities between upper bounds of consecutive derivatives of the function on infinite interval", *Uch. zap. MGU. Matematika*, 1939; 30(3): pp. 3-16. (in Russian)

Kolmogorov A.N. "On inequalities between upper bounds of consecutive derivatives of the function on infinite interval", *Izbr. tr. Matematika, mekhanika*, Nauka, Moscow, 1985; pp. 252-263. (in Russian)

Korneichuk N.P. *Extremal problems in approximation theory*, Moscow, 1976; 320 pp. (in Russian)

Korneichuk N.P. *Exact constants in approximation theory*, Moscow, 1987. 424 pp. (in Russian)

Korneichuk N.P., Babenko V.F., Ligun A.A. *Extremal properties of polynomials and splines*, Nauk. dumka, Kyiv, 1992. 304 pp. (in Russian)

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

Rodov A.M. "Relations between upper bounds of derivatives of functions of a real variable", *Izv. AN SSSR. Ser. matem.*, 1946; 10: pp. 257-270. (in Russian)

Ligun A.A. "Inequalities for upper bounds of functionals", *Analysis Math.*, 1976; 2(1): pp. 11-40.

Korneichuk N.P., Ligun A.A., Doronin V.G. *Approximation with constraints*, Kyiv, 1982; 250 pp. (in Russian)

Babenko V.F., Kofanov V.A., Pichugov S.A. "Comparison of rearrangement and Kolmogorov-Nagy type inequalities for periodic functions", *Approximation theory: A volume dedicated to Blagovest Sendov* (B. Bojanov, ed.), Darba, Sofia, 2002; pp. 24-53.

Babenko V.F., Kofanov V.A., Pichugov S.A. "Inequalities for norms of intermediate derivatives of periodic functions and their applications", *Ibid*; 3: pp. 251-376.

Sz.-Nagy B. "Über Integralungleichungen zwischen einer Funktion und ihrer Ableitung", *Acta. Sci. Math.*, 1941; 10: pp. 64-74. (in German)

DOI: https://dx.doi.org/10.15421/241204

### Refbacks

- There are currently no refbacks.

Copyright (c) 2012 V.F. Babenko, O.V. Kovalenko

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