TY - JOUR

T1 - 65 years since the paper "on the value of the best approximation of functions having a real singular point" by I. I. Ibragimov

AU - Leviatan, D.

AU - Shevchuk, I. A.

PY - 2012

Y1 - 2012

N2 - In his famous paper [15] Ibragim Ibishievich Ibragimov has given asymptotic values of the best uniform approximation of functions of the form (a - x)s lnm(a - x), (a ≥ 1). These results have led to the development of a series of new directions in approximation theory, including the following ones, to which we devote this paper. • Constructive characterization of approximation of functions on a closed interval. • Babenko spaces. • Ditzian-Totik moduli of smoothness. • Constructive characterization of approximation of functions on the sets of complex plane. • Shape preserving approximation. In particular, we will show how we have used the results by I. I. Ibragimov in our recent paper in Constructive Approximation.

AB - In his famous paper [15] Ibragim Ibishievich Ibragimov has given asymptotic values of the best uniform approximation of functions of the form (a - x)s lnm(a - x), (a ≥ 1). These results have led to the development of a series of new directions in approximation theory, including the following ones, to which we devote this paper. • Constructive characterization of approximation of functions on a closed interval. • Babenko spaces. • Ditzian-Totik moduli of smoothness. • Constructive characterization of approximation of functions on the sets of complex plane. • Shape preserving approximation. In particular, we will show how we have used the results by I. I. Ibragimov in our recent paper in Constructive Approximation.

KW - Degree of approximation by polynomials

KW - Jackson type estimates

KW - Polynomial approximation in complex domains

KW - Shape preserving approximation

UR - http://www.scopus.com/inward/record.url?scp=84893037200&partnerID=8YFLogxK

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AN - SCOPUS:84893037200

SN - 2218-6816

VL - 2

SP - 94

EP - 104

JO - Azerbaijan Journal of Mathematics

JF - Azerbaijan Journal of Mathematics

IS - 2

ER -