论文标题:广义Baskakov算子的加权逼近及其它问题
The Weighted Approximation by the Generalized Baskakov Operators and Other Problems
论文作者
论文导师 薛银川,论文学位 硕士,论文专业 基础数学
论文单位 宁夏大学,点击次数 129,论文页数 51页File Size1230k
2005-03-01论文网 http://www.lw23.com/lunwen_44284322/
generalized Baskakov operators;estimation of remainder; weighted approximation;Ditizian-Totik modulus of smoothness; direct and converse theorems;Stancu-Kantorovic operators
本学位论文研究了广义Baskakov算子的加权逼近及余项估计,同时讨论了Stancu-kantorovic算子在B_a空间的逼近。主要内容分三个部分: 第一部分:在第二章中主要研究广义Baskakov算子逼近的余项估计,分别给出一元及二元广义Baskakov算子余项估计的几种形式。 第二部分:在第三章中利用2阶加Jacobi权Ditzian-Totik光滑模,讨论了广义Baskakov算子加Jacobi权的点态逼近,得到了点态逼近的正逆定理;利用r阶加Jacobi权Ditzian-Totik光滑模研究了广义Baskakov算子线性组合的加权逼近,给出了逼近定理。 第三部分:第四章讨论了Stancu-Kantorovic算子C_n(f,x)在B_a空间中的逼近,给出了逼近阶的估计。
In this paper, we discuss the weighted approximation by the generalized Baskakov operators and the estimation of their remainders, at the same time, we study the approximation by the Stancu-kantorovic operators on B_a space.The main contents are divided into three parts.Part I: in the second chapter, the estimation of the remainders of the generalized Baskakov operators are discussed, several forms about the estimation of the remainders of the generalized Baskakov operators of one variables and of two variables are obtained.Part II: in the third chapter, the pointwise approximation with Jacobi weight by the generalized Baskakov operators using two-order Ditizian-Totik modulus of smoothness and the direct and converse theorems for the pointwise approximation are given. In addition, the approximation with Jacobi weight by the linear combinations of the Baskakov operators using the r-order Ditizian-Totik modulus of smoothness is studied, the theorems of approximation are obtained.Part III: in the forth chapter, the approximation by the Stancu-Kantorovic operators on B_a space is discussed, the estimation of the approximation is given.
|
