论文标题:Beta算子和Gamma算子的逼近性质研究
A Research of Approximate Properties of Beta and Gamma Type Operators
论文作者
论文导师 曾晓明,论文学位 硕士,论文专业 基础数学
论文单位 厦门大学,点击次数 123,论文页数 29页File Size1139K
2007-04-01论文网 http://www.lw23.com/lunwen_236912967/
Rate of approximation;; K—functional;; Global approximation
本文研究了Beta算子β_n(f,x)对绝对连续函数和一般有界函数的逼近以及Gamma算子G_n(f,x)在L_p空间中的逼近等价定理。本文由三章组成,其内容如下: 第一章首先对文中出现的定义和记号进行说明,然后介绍了一些相关的研究成果。 第二章引入了本文所要研究的Beta算子β_n(f,x),讨论了其对绝对连续函数及一般有界函数的逼近。利用经典的Bojanic-Cheng分解方法及分析技巧,分别对一阶绝对矩β_n(|t-x|,x)及符号函数β_n(sign(t-x),x)进行了估计,对两类函数类的逼近阶|β_n(f,x)-f(x)|的估计得到不错的结果及渐进展开公式。 第三章主要研究了Gamma算子在L_p空间中的逼近性质,利用了逆定理中常用的插补空间和K-泛函及光滑模的方法,建立了整体逼近的等价定理。
This paper is studied for the approximation of Beta operatorsβ_n(f, x) for absolutely continuous functions and bounded funtions, and the global approximation theorem for Gamma operators G_n(f, x) in L_p. This paper is organized as following: In chapter 1 we give an explanation of definitions and marks which were appeared in the paper and then introduce some researchful results. In chapter 2 we introduce a class of Beta operatorsβ_n(f,x), we study the rate of convergence of Beta type operators for some absolutely continuous functions and bounded functions, using classical decomposed method of Bojanic—Cheng and analytical ways, we estimate the first order absolute momentβ_n(|t-x|, x) and sigh functionsβ_n(sign(t-x), x) respectively, we get a better result of the rate of approximation for |β_n(f,x) - f(x)| and asymptotic formula. In chapter 3 The approximation properties of the Gamma operators in the spaces L_p(0,1) are discussed. We use the technique of interpolation spaces and characterization of K—functional and modulus of smoothness which has been used for inverse theorems. The equivalence theorem concerning the global aproximation by the Gamma operators is established.
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