【摘要】 Bernstein-Bézier算子是一种重要的逼近算子,在计算机辅助几何设计中也扮演了重要角色.为了进一步了解它的理论及其逼近性质,研究了它对一类绝对连续函数的逼近.本文主要利用经典的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.首先扩展了文献Liu的结果,得到了Bernstein-Bézier算子的一阶中心绝对矩B(nα)(t-x,x);接着估计了另外一项B(nα)(t∫xφx(u)du,x),最后得到了比较精确的收敛价.更多还原

【Abstract】 The purpose of this paper is to investigate the rate of convergence of Bernstein-Bézier Operator for some absolutely continuous functions.The approximation properties were studied in the case of 0<α≤1 and α≥1 respectively.By using Bojanic-Cheng’s method and analysis techniques,the rate of convergence of Bernstein-Bézier Operator was derived.In the first,the authors extended the result of Liu Z X and got the first central absolute moment B^（α）_n（t-x,x）.Later,the authors estimated the other part B^（α）_n（∫^t_xφ_x（u）du,x）.Lastly,an asymptotically optimal estimate was obtained.The result is helpful to understand the properties of Bézier Operator well,thus further research can be done.更多还原