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.
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