On the rate of convergence of some discrete operators of two variables (Q1370580)

Consider the Boolean sum \(L_{m,n}\) of parametric extensions of two discrete univariate positive linear operators. The aim of this paper is to give an estimate of the degree of pointwise convergence of \(L_{m,n}f\) at these points \((x,y)\) at which the one-sided limits \(f(x,\pm y)\), \(f(\pm x, y)\), \(f(\pm x,\pm y)\) exist. A certain kind of bivariate analogue of the modulus of variation is used.