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.
Citation Example:Akgün R. Polynomial approximation in Bergman spaces // Ukr. Mat. Zh. - 2016. - 68, № 4. - pp. 435-448.