On The Rate Of Convergence Of Bernstein-Bézier And Meyer-K(?)nig-Zeller-Bézier Operators

In this paper,we main discuss the rate of approximation of Two Bézier Type Operators.This paper is organized as following:In chapter 1 we give a brief review of approximation theory of op-erators(approximation by operators),then introduce the corresponding background:and the main contents of the paper.In chapter 2 we main investigate the rate of convergence of Bernstein-Bézier Operators for some absolutely:continuous functions.The approx-imation properties were studied in the case of 0＜α≤1 andα≥1 respectively.By using Bojanic-chengis method and analysis techniques, the rate of convergence of Bernstein-Bézier Operators was derived,in the first,we extended the result of Liu[10]and got the first central ab-solute moment B_n^(α)(|t-x|,x).Later,we estimated the other part B_n^(α)(integral from n=x to tφ_x(u)du,x).Lastly,an asymptotically estimate was obtained.In chapter 3 the rate of convergence of Meyer-K(o|¨)nig and Zeller-Bézier Operators for bounded functions was studied in the case of 0＜α≤1.Firstly,we give some definition and preliminary results.Then by means of the decomposition technique of Bojanic and Cheng,together with some results from probability theory and the exact bound of Meyer-K(o|¨)nig and Zeller Operators basis functions,the rate of convergence of Meyer-K(o|¨)nig and Zeller-Bézier Operators for bounded functions are ob-tained.We extend the work of[7].