Approximation of functions in the generalized Zygmund class using Hausdorff means

In this paper we investigate the degree of approximation of a function belonging to the generalized Zygmund class Zp(ω)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$Z_{p}^{(\omega)}$\end{document} (p≥1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$p \ge1$\end{document}) by Hausdorff means of its Fourier series. We also deduce a corollary and mention a few applications of our main results.