Approximation of certain bivariate functions by almost Euler means of double Fourier series

In this paper, we study the degree of approximation of 2π-periodic functions of two variables, defined on T2=[−π,π]×[−π,π]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$T^{2}=[-\pi,\pi]\times[-\pi,\pi]$\end{document} and belonging to certain Lipschitz classes, by means of almost Euler summability of their Fourier series. The degree of approximation obtained in this way depends on the modulus of continuity associated with the functions. We also derive some corollaries from our theorems.