2018
Том 70
№ 7

All Issues

Akgün R.

Articles: 2
Article (English)

Polynomial approximation in Bergman spaces

Akgün R.

↓ Abstract

Ukr. Mat. Zh. - 2016. - 68, № 4. - pp. 435-448

The purpose of this work is to obtain Jackson and converse inequalities of the polynomial approximation in Bergman spaces. Some known results presented for the moduli of continuity are extended to the moduli of smoothness. We proved some simultaneous approximation theorems and obtained the Nikolskii – Stechkin inequality for polynomials in these spaces.

Article (English)

Trigonometric approximation of functions in generalized Lebesgue spaces with variable exponent

Akgün R.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 1. - pp. 3-23

We investigate the approximation properties of the trigonometric system in $L_{2\pi}^{p(\cdot)}$. We consider the fractional order moduli of smoothness and obtain direct, converse approximation theorems together with a constructive characterization of a Lipschitz-type class.