On Approximation by Max-product Shepard Operators

In the present paper, we firstly give Jackson type estimates of approximation by max-product Shepard operators on [-1,1]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[-1,1]$$\end{document}, which combine pointwise and global estimates as a whole. Secondly, we investigate the weighted approximation by modified max-product Shepard operator for functions with singularities at the endpoints. Finally, we generalize max-product Shepard operators to the bounded convex set Ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf \Omega $$\end{document} on the scattered data, and obtain Jackson type estimates of approximation.