Approximation of Some Classes of Functions by Landau Type Operators

被引:0
作者
Octavian Agratini
Ali Aral
机构
[1] Babeş-Bolyai University,Faculty of Mathematics and Computer Science
[2] Romanian Academy,Tiberiu Popoviciu Institute of Numerical Analysis
[3] Kirikkale University,Department of Mathematics
来源
Results in Mathematics | 2021年 / 76卷
关键词
Landau operator; weighted space; Korovkin theorem; modulus of smoothness; 41A36; 41A25;
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摘要
This paper aims to highlight a class of integral linear and positive operators of Landau type which have affine functions as fixed points. We focus to reveal approximation properties both in 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} spaces and in 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} spaces (1≤p<∞)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(1\le p<\infty )$$\end{document}. Also, we give an extension of the operators to approximate real-valued vector functions. In this case, the study pursues the approximation of continuous functions on convex compacts. The evaluation of the rate of convergence in one and multidimensional cases is performed by using adequate moduli of smoothness.
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