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

Let G be a bounded Jordan domain in the complex plane 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 G in the weighted variable exponent Smirnov classes Eωp(· )(G) are proved.