The Product of Two Functions Using Positive Linear Operators

Abstract

In this paper we estimate the speed of convergence of the difference $L_n(fg)-(L_n f)\cdot (L_n g)$ towards 0, where $(L_n)$ are positive linear operators used in the approximation of continuous functions. We also study in what conditions the formula ${L'_n}(fg)-f {L'_n}g-g {L'_n}f \to 0$ holds true.