Near best approximation property of interpolation and Poisson polynomials in weighted variable exponent Smirnov classes

Abstract

Let $G$ be a bounded Jordan domain in the complex plane $\mathbb{C}$. In this work under some restrictions of ${G}$ the near best approximation property of complex interpolation and Poisson polynomials based on the Faber polynomials of $\overline{{G}}$ in the weighted variable exponent Smirnov classes ${E}_{\omega }^{p(\cdot )}{(G)}$ are proved.