Approximation by Zygmund means in variable exponent Lebesque spaces

Abstract

In the present work we investigate the approximation of the functions by the Zygmund means in variable exponent Lebesgue spaces. Here the estimate which is obtained depends on sequence of the best approximation in Lebesgue spaces with variable exponent. Also, these results were applied to estimates of approximations of Zygmund sums in Smirnov classes with variable exponent defined on simply connected domains of the complex plane.