### On inequalities of Kolmogorov type for fractional derivatives of functions defined on the real domain

#### Abstract

#### Full Text:

PDF (Українська)#### References

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

Babenko V.F., Churilova M.S. "On inequalities of Kolmogorov type for derivatives of fractional order", *Res. Math.*, 2001; 6: pp. 16-20. (in Ukrainian)

Babenko V.F., Churilova M.S. "On inequalities of Kolmogorov type for derivatives of fractional order in multidimensional case", *Res. Math.*, 2003; 11: pp. 26-30. (in Russian)

Geisberg S.P. "Generalization of Hadamard inequality", *Researches on certain problems of constructive function theory: sb. nauch. tr. LOMI*, Leningrad, 1965; 50: pp. 42-54. (in Russian)

Geisberg S.P. "Fractional derivatives of functions bounded on the real domain", *Izv. vuzov. Matematika*, 1968; 11: pp. 51-69. (in Russian)

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

Samko S.G., Kilbas A.A., Marichev O.I. *Integrals and derivatives of fractional order and their applications*, Nauka i tekhnika, Minsk, 1987; 688 p. (in Russian)

Churilova M.S. "Inequalities of Landau-Kolmogorov type for fractional derivatives on the interval", *Res. Math.*, 2005; 13: pp. 47-56. (in Russian)

Arestov V.V. "Inequalities for fractional derivatives on the half-line", *Approximation theory: proc. conf.*, Warsaw, 1979; pp. 19-34.

Babenko V.F., Churilova M.S. "On the Kolmogorov type inequalities for fractional derivatives", *East J. Approx.*, 2002; 8(4): pp. 437-446.

Bojanov B., Naidenov N. "An extension of the Landau-Kolmogorov inequality. Solution of a problem of Erdös", *J. d'Analyse Mathematique*, 1999; 78: pp. 263-280. doi:10.1007/BF02791137

Magaril-Il'yaev G.G., Tikhomirov V.M. "On the Kolmogorov inequality for fractional derivatives on the half-line", *Anal. Math.*, 1981; 7(1): pp. 37-47. doi:10.1007/BF02102723

Stein E.M. "Functions of exponential type", *Ann. Math.*, 1957; 65(3): pp. 582-592. doi:10.2307/1970066

DOI: https://doi.org/10.15421/240804

### Refbacks

- There are currently no refbacks.

Copyright (c) 2008 V.F. Babenko, M.S. Churilova

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