Kolmogorov-type inequalities on the whole line or half line and the Lagrange principle in the theory of extremum problems
Eurasian mathematical journal, Tome 2 (2011) no. 3, pp. 125-142.

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The paper is devoted to solving extremal problems related to Kolmogorov-type inequalities. All solutions are obtained with the help of the so-called Lagrange principle, which is a generalization of the Lagrange multiplier rule.
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V. Tikhomirov; A. Kochurov. Kolmogorov-type inequalities on the whole line or half line and the Lagrange principle in the theory of extremum problems. Eurasian mathematical journal, Tome 2 (2011) no. 3, pp. 125-142. http://geodesic.mathdoc.fr/item/EMJ_2011_2_3_a7/

[1] L. Lagrange, Théorie des fonctions analytiques, Impr. de la République, Paris, 1797

[2] V. M. Alexeev, V. M. Tikhomirov, S. V. Fomin, Optimal control, Consulting Bureau, New York, 1987 | MR

[3] E. Landau, “Einige ungleihungen für zweimal differentzierbar funktionen”, Proc. London Math. Soc. (2), 13 (1913), 43–49 | DOI | Zbl

[4] J. Hadamard, “Sur le nodule maximum d'une fonction et de ses dérivées”, C. R. Séances Soc. Math., 41 (1914), 68–72

[5] G. G. Hardy, J. E. Littlewood, G. Polya, Inequalities, Cambridge Univ. Press, Cambridge, 1934 | Zbl

[6] A. Kolmogorov, “Une generalisation de l'inégalité de M. J. Hadamard entre les bornes supérieures des dérivées d'une fonction”, C. R. Séances Soc. Math., 207 (1938), 764–765 | Zbl

[7] B. Sz.-Nagy, “Über integralungleichungen zwischen einer funktion und ihrer ableitung”, Acta Univ. Szeged Sect. Sci. Math., 10 (1941), 64–74 | MR

[8] E. M. Stein, “Functions of exponential type”, Ann. Math., 65:3 (1957), 582–592 | DOI | MR | Zbl

[9] A. T. Fuller, “Relay control systems optimized by various performance criteria”, Proc. First World Congress IFAC, Moscow, 1960, 510–519

[10] L. V. Taykov, “Inequalities of Kolmogorov type and best formula for numerical differentiation”, Mat. Zametki, 4:2 (1968), 233–238 (in Russian) | MR | Zbl

[11] V. V. Arestov, “On the best approximation of the differantiation operators”, Mat. Zametki, 5:3 (1969), 273–284 (in Russian) | MR | Zbl

[12] V. N. Gabushin, “On the best approximation of the differantiation operator on the half-line”, Mat. Zametki, 6:5 (1969), 573–582 (in Russian) | MR | Zbl

[13] G. G. Magaril-Il'yaev, “Inequalities for derivatives and duality”, Trudy Mat. Inst. Steklov, 161, 1983, 183–194 (in Russian) | MR | Zbl

[14] G. A. Kalyabin, “Sharp constants in inequalities for intermediate derivatives (the Gabushin case)”, Functional Analysis and its Applications, 38:3 (2004), 184–191 (in Russian) | DOI | MR | Zbl