【作者】 连博勇；

【导师】 曾晓明；

【作者基本信息】 厦门大学 ， 基础数学， 2007， 硕士

【摘要】 本文主要研究了两类Bézier型算子列的逼近性质。本文由三节组成,其内容如下:第一节首先回顾了算子逼近论的发展及本文所做研究课题的发展情况,并简要介绍了本文的主要内容。第二节主要讨论了Bernstein-Bézier算子对一类绝对连续函数的逼近。在这节中主要利用经典的Bojanic-Cheng分解方法,结合分析技术,分别讨论了Bernstein-Bézier算子在0＜α≤1及α≥1时,对这类绝对连续函数的逼近。文中首先扩展了文献Liu[10]的结果,得到了Bernstein-Bézier算子的一阶中心绝对矩B_n^（α）（|t-x|,x）;接着估计了另外一项B_n^（α）（integral from n=x to t（φ_x（u）du）,x）,最后得到了比较精确的收敛阶。第三节主要讨论了Meyer-K（o|¨）nig and Zeller-Bézier算子在0＜α≤1时对一般有界函数的逼近。在这节我们首先给出了一些定义和记号,然后结合概率论的一些重要结果和Meyer-K（o|¨）nig and Zeller-Bézier算子基函数的界,研究了Meyer-K（o|¨）nig and Zeller-Bézier算子对这类一般有界函数的逼近。我们的研究结果拓展了文献[7]的研究工作,使之适用于更广泛的函数类。更多还原

【Abstract】 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].更多还原