On approximation of functions by means of Fourier trigonometric series in weighted generalized grand Lebesgue spaces

Abstract

In the present work we investigate the approximation of the functions by the Zygmund means in the weighted generalized grand Lebesgue spaces. The estimates are obtained in terms of the best approximation and modulus of smoothness. Also, the approximation problems of Cesaro, Zygmund and Abel sums of Faber series in the generalized Smirnov classes defined on the bounded simply connected domains of complex plane are studied.