On the degree of approximation of certain continuous bivariate functions by double matrix means of a double Fourier series

In this paper, we have studied the degree of approximation of certain bivariate functions by double factorable matrix means of a double Fourier series. Four theorems are proved using single rest bounded variation sequences, single head bounded variation sequences, double rest bounded variation sequences, and two non-negative mediate functions. These results expressed in terms of two functions of modulus type and two non-negative mediate functions, imply many particular results as shown at last section of this paper.

On the degree of approximation of certain continuous bivariate functions by double matrix means of a double Fourier series Keywords:

Double Fourier series , Lipschitz class , Factorable matrices , Ces`aro means , N orlund means , Riesz means