Landau–Kolmogorov problem for a class of functions absolutely monotone on a finite interval
- 39 Downloads
We solve the Landau–Kolmogorov problem for a class of functions absolutely monotone on a finite interval. For this class of functions, new exact additive inequalities of the Kolmogorov type are obtained.
KeywordsOrlicz Space Finite Interval Sign Alternation Successive Derivative Kolmogorov Type
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
- 6.A. Yu. Shadrin, “To the Landau–Kolmogorov problem on a finite interval,” in: B. Bojanov (editor), Open Problems in Approximation Theory, SCT, Singapore (1994), pp. 192–204.Google Scholar
- 9.Yu. V. Babenko, “Exact inequalities of Landau type for functions with second derivatives from the Orlicz space,” Vestn. Dnepropetr. Univ., Ser. Mat., 2, 18–22 (2000).Google Scholar
- 11.N. P. Korneichuk, V. F. Babenko, and A. A. Ligun, Extremal Properties of Polynomials and Splines [in Russian], Naukova Dumka, Kiev (1992).Google Scholar
- 12.V. F. Babenko, N. P. Korneichuk, V. A. Kofanov, and S. A. Pichugov, Inequalities for Derivatives and Their Applications [in Russian], Naukova Dumka, Kiev (2003).Google Scholar
- 15.D. V. Widder, The Laplace Transform, Princeton University, Princeton (1946).Google Scholar
- 16.D. S. Skorokhodov, “On the Landau–Kolmogorov problem for classes of functions absolutely monotone on a segment,” in: Abstracts of the Mathematical Congress (August 27–29, 2009, Kyiv) [in Ukrainian], Kyiv (2009).Google Scholar
- 17.M. G. Krein and A. A. Nudel’man, Markov Moment Problem and Extremal Problems [in Russian], Nauka, Moscow (1973).Google Scholar
- 18.A. N. Kolmogorov, “On inequalities between upper bounds of successive derivatives of an arbitrary function on an infinite interval,” Nauch. Zap. Mosk. Univ., 30, 3–16 (1939).Google Scholar
- 19.A. N. Kolmogorov, “On inequalities between upper bounds of successive derivatives of an arbitrary function on an infinite interval,” in: A. N. Kolmogorov, Selected Works. Mathematics and Mechanics [in Russian] (1985), pp. 252–263.Google Scholar
© Springer Science+Business Media, Inc. 2011