On Landau-Kolmogorov problem on the interval for absolutely monotonic functions

D.S. Skorokhodov (Oles Honchar Dnipropetrovsk National University), https://orcid.org/0000-0001-8494-5885


We solve the Landau-Kolmogorov problem and the Kolmogorov problem for three positive numbers on the class of functions which are absolutely monotonic on a finite interval.


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 Yu.V. "Exact inequalities of Landau type for functions with second derivatives from Orlich spaces", Res. Math., 2001; 5(2): pp. 238-243. (in Ukrainian)

Zvyagintsev A.I., Lepin A.Ya. "On exact Kolmogorov inequalities between upper bounds of function derivatives in the case $n = 3$", Latvian Matemat. Ezhegodnik, 1982; 26: pp. 176-181. (in Russian)

Korneichuk N.P., Babenko V.F., Ligun A.A. Extremum properties of polynomials and splines, Naukova dumka, 1992; 304 p. (in Russian)

Krein M.G., Nudelman A.A. Problem of Markov moments and extremal problems, 1973. (in Russian)

Bernstein S.N. "Sur les fonctions absolutement monotones", Acta Math., 1929; 52: pp. 1-66. (in French) doi:10.1007/BF02592679

Bojanov B., Naidenov N. "Examples of Landau-Kolmogorov inequality in integral norms on a finite interval", J. Approx. Theory, 2002; 117(1): pp. 55-73. doi:10.1006/jath.2002.3687

Chui C.K., Smith P.W. "A note on Landau's problem for bounded intervals", Amer. Math. Monthly, 1975; 82(9): pp. 927-929. doi:10.1080/00029890.1975.11993983

Landau E. "Einige Ungleichungen für zweimal differentiierbare Funktionen", Proc. London Math. Soc., 1913; 13(2): pp. 43-49. (in German) doi:10.1112/plms/s2-13.1.43

Sato M. "The Landau inequality for bounded intervals with $$$\| f^{(3)} \|$$$ finite", J. Approx. Theory, 1982; 34(2): pp. 159-166. doi:10.1016/0021-9045(82)90089-2

Widder D.V. The Laplace Transform, Princeton Math. Series, 1946.

DOI: https://doi.org/10.15421/240918



  • There are currently no refbacks.

Copyright (c) 2009 D.S. Skorokhodov

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