Weighted approximation by modified Picard operators

Herein, the aim is to further investigate the properties of the generalized Picard operators introduced in Agratini et al. (Positivity 3(21):1189–1199, 2017). The motivation is based on with the purpose of furnishing appropriate positive approximation processes in the setting of large classes of exponential weighted Lp spaces via different type theorems. For this propose, firstly we give the boundness of the operators, acting from an exponential weighted Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{p}$$\end{document} space into itself. Also, using an exponential weighted modulus of continuity a quantitative type theorem as well as the global smoothness property of the operators are presented. Then, we give pointwise approximation property of the operators at a generalized Lebesgue point. Finally under a certain condition, again the weighted Lp approximation is formulated without using Korovkin type theorem.