Sharp Remez-type inequalities of various metrics for the best approximations by a constant

A.Ye. Haidabura (Oles Honchar Dnipropetrovsk National University)
V.A. Kofanov (Oles Honchar Dnipropetrovsk National University),


We prove new sharp Remez-type inequalities of various metrics on the sets of functions with a given comparison function.


Remez-type inequalities of various metrics; the comparison function; classes of functions with a given comparison function


Bojanov B., Naidenov N. "An extension of the Landau-Kolmogorov inequality. Solution of a problem of Erdös", J. d'Analyse Mathematique, 1999; 78: pp. 263-280. doi:10.1007/BF02791137

Kofanov V.A. "Exact upper bounds of norms of functions and their derivatives on the classes of functions with given comparison function", Ukrainian Math. J., 2011; 63(7): pp. 969-984. (in Russian) doi:10.1007/s11253-011-0567-z

Remes E. "Sur une propriete еxtremale des polynomes de Tchebychef", Zapiski naukovo-doslid. in-tu matematyky i mekhaniky ta Kharkiv. mat. tov-va Kharkiv. derzh. un-tu. Seriya 4, 1936; 13(1): pp. 93-95. (in French)

Ganzburg M.I. "On a Remez-type inequality for trigonometric polynomials", J. of Approximation Theory, 2012; 164: pp. 1233-1237. doi:10.1016/j.jat.2012.05.006

Nursultanov E., Tikhonov S. "A sharp Remez inequality for trigonometric polynomials", Constructive Approximation, 2013; 38: pp. 101-132. doi:10.1007/s00365-012-9172-0

Borwein P., Erdelyi T. Polynomials and polynomial inequalities, New York, Springer, 1995.

Ganzburg M.I. "Polynomial inequalities on measurable sets and their applications", Constructive Approximation, 2001; 17: pp. 275-306. doi:10.1007/s003650010020

Kofanov V.A. "Sharp Remez-type inequalities for differentiable periodic functions, polynomials and splines", Ukrainian Math. J., 2016; 68(2): pp. 227-240. (in Russian) doi:10.1007/s11253-016-1222-5

Korneichuk N.P., Babenko V.F., Ligun A.A. Extremum properties of polynomials and splines, Naukova dumka, Kyiv, 1992; 304 p. (in Russian)




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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991