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

Year 2024, Volume: 53 Issue: 1, 62 - 73, 29.02.2024

Ahmet Testici , Daniyal M. İsrafilzade

https://doi.org/10.15672/hujms.1176919

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.

Keywords

interpolating polynomials, Faber polynomials, weighted variable exponent Smirnov classes, Poisson polynomials, near the best approximation

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