# 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.

## Authors

Octavian Agratini
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania

## Keywords

Linear positive operator · Picard operator · Gauss operator · Weighted space · Voronovskaja formula

## Paper coordinates

O. Agratini, A. Aral, E. Deniz, On two classes of approximation processes of integral type, Positivity, 21 (2017), pp. 1189-1199, https://doi.org/10.1007/s11117-016-0460-y

Positivity

Springer