Comparison theorems for derivatives and some of their applications

V.F. Babenko (Oles Honchar Dnipropetrovsk National University), http://orcid.org/0000-0001-6677-1914
O.V. Kovalenko (Oles Honchar Dnipropetrovsk National University), http://orcid.org/0000-0002-0446-1125

Abstract


Analogues of Kolmogorov comparison theorems and some of their applicatons were established.

Keywords


comparison theorems; inequalities for derivatives

References


Kolmogorov A.N. "Une generalization de l’inegalite de M.J. Hadamard entre les bornes superieures des derivees successives d’une function", C. r. Acad. sci. Paris, 1938; 207: pp. 764-765. (in French)

Kolmogorov A.N. "On inequalities between upper bounds of consecutive derivatives of the function on infinite interval", Uch. zap. MGU. Matematika, 1939; 30(3): pp. 3-16. (in Russian)

Kolmogorov A.N. "On inequalities between upper bounds of consecutive derivatives of the function on infinite interval", Izbr. tr. Matematika, mekhanika, Nauka, Moscow, 1985; pp. 252-263. (in Russian)

Korneichuk N.P. Extremal problems in approximation theory, Moscow, 1976; 320 pp. (in Russian)

Korneichuk N.P. Exact constants in approximation theory, Moscow, 1987. 424 pp. (in Russian)

Korneichuk N.P., Babenko V.F., Ligun A.A. Extremal properties of polynomials and splines, Nauk. dumka, Kyiv, 1992. 304 pp. (in Russian)

Korneichuk N.P., Babenko V.F., Kofanov V.A., Pichugov S.A. Inequalities for derivatives and their applications, Nauk. dumka, Kyiv, 2003; 590 pp. (in Russian)

Rodov A.M. "Relations between upper bounds of derivatives of functions of a real variable", Izv. AN SSSR. Ser. matem., 1946; 10: pp. 257-270. (in Russian)

Ligun A.A. "Inequalities for upper bounds of functionals", Analysis Math., 1976; 2(1): pp. 11-40.

Korneichuk N.P., Ligun A.A., Doronin V.G. Approximation with constraints, Kyiv, 1982; 250 pp. (in Russian)

Babenko V.F., Kofanov V.A., Pichugov S.A. "Comparison of rearrangement and Kolmogorov-Nagy type inequalities for periodic functions", Approximation theory: A volume dedicated to Blagovest Sendov (B. Bojanov, ed.), Darba, Sofia, 2002; pp. 24-53.

Babenko V.F., Kofanov V.A., Pichugov S.A. "Inequalities for norms of intermediate derivatives of periodic functions and their applications", Ibid; 3: pp. 251-376.

Sz.-Nagy B. "Über Integralungleichungen zwischen einer Funktion und ihrer Ableitung", Acta. Sci. Math., 1941; 10: pp. 64-74. (in German)


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Copyright (c) 2012 V.F. Babenko, O.V. Kovalenko

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ISSN (Online): 2518-7996
ISSN (Print): 2312-9557