On two classes of approximation processes of integral type

Abstract

The paper aims to study two classes of linear positive operators representing modifications of Picard and Gauss operators. The new operators reproduce both constants and a given exponential function. Approximation properties in polynomial weighted spaces are investigated and the speed of convergence is measured using a certain weighted modulus of smoothness. Also, the asymptotic behavior of the integral operators are established. Finally, aspects on generalized convexity are analyzed.