Trigonometric approximation of functions f(x,y) of generalized Lipschitz class by double Hausdorff matrix summability method

Abstract

In this paper, we establish a new estimate for the degree of approximation of functions f(x,y) belonging to the generalized Lipschitz class Lip ((xi _{1}, xi _{2} );r ), r geq 1, by double Hausdorff matrix summability means of double Fourier series. We also deduce the degree of approximation of functions from Lip ((alpha ,beta );r ) and Lip(alpha ,beta ) in the form of corollary. We establish some auxiliary results on trigonometric approximation for almost Euler means and (C, gamma , delta ) means.