Equivalence theorem for additive inequalities of Kolmogorov type

A.Ye. Haidabura (Oles Honchar Dnipropetrovsk National University)
V.A. Kofanov (Oles Honchar Dnipropetrovsk National University), http://orcid.org/0000-0003-0392-2257

Abstract


We prove the equivalence theorem for additive inequalities on a finite interval. Besides, we describe a pair of constants so that the additive inequalities with that constants are valid on the whole class of functions $$$L_s$$$.

Keywords


additive inequalities; equivalence theorem

References


Babenko V.F., Kofanov V.A., Pichugov S.A. "On additive inequalities between intermediate derivatives of functions, defined on a finite interval", Ukrainian Math. J., 1997; 49(5): pp. 619-678. (in Russian)

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)

Burenkov V.I. "On exact constants in inequalities for norms of intermediate derivatives on a finite interval", Trudy matem. in-ta im. V.A. Steklova AN SSSR, 1980; 156: pp. 22-29. (in Russian)

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

Shadrin Yu.A. "On exact constants in inequalities between norms of derivatives on a finite interval", Doklady RAN, 1992; 326(1): pp. 50-53. (in Russian)


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