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

Abstract


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.

References


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)

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.


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

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

Korneichuk N.P., Babenko V.F., Ligun A.A. Extremum properties of polynomials and splines, Naukova dumka, 1992.

Krein M.G., Nudelman A.A. Problem of Markov moments and extremal problems, 1973.




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

  

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