## Abstract

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} ln^{m}(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.

Original language | English |
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Pages (from-to) | 94-104 |

Number of pages | 11 |

Journal | Azerbaijan Journal of Mathematics |

Volume | 2 |

Issue number | 2 |

State | Published - 2012 |

## Keywords

- Degree of approximation by polynomials
- Jackson type estimates
- Polynomial approximation in complex domains
- Shape preserving approximation