On inequalities of Kolmogorov type for classes of functions that are multiply monotonic on a finite interval
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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. "Pointwise inequalities of Landau-Kolmogorov type for functions defined on a finite segment", Ukrainian Math. J., 2001; 52(2): pp. 270-275. doi:10.1023/A:1010469004645
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)
Krasnoselskii M.A., Rutitskii Ya.B. Convex functions and Orlich spaces, Moscow, 1958; (in Russian)
Krein S.G., Petunin Yu.I., Semyonov Ye.M. Interpolation of linear operators, Nauka, Moscow, 1978; 400 p. (in Russian)
Skorokhodov D.S. "On Landau-Kolmogorov problem on the segment for absolutely monotonic functions", Res. Math., 2009; 14: pp. 120-128. (in Russian)
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
Fink A.M. "Kolmogorov-Landau inequalities for monotone functions", J. Math. Appl., 1992; 90(1): pp. 251-258. doi:10.1016/0022-247X(82)90057-9
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
Naidenov N. "Landau-type extremal problem for the triple $$$\| f \|_{\infty}$$$, $$$\| f' \|_p$$$, $$$\| f'' \|_{\infty}$$$ on a finite interval", J. Approx. Theory, 2003; 123(2): pp. 147-161. doi:10.1016/S0021-9045(03)00081-9
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
Shadrin A.Yu. "To the Landau-Kolmogorov problem on a finite interval", Proc. Int. Conf. "Open Problems in Approximation Theory", Vonesta Voda, 1993; pp. 192-204.
DOI: https://doi.org/10.15421/241018
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