论文标题:Lupas-Baskakov型算子的逼近
The Approximation of Lupas-Baskakov-Type Operators
论文作者 刘国军
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 663,论文页数 68页File Size2034k
2003-04-05论文网 http://www.lw23.com/lunwen_274842/ Stechkin-Marchaud型不等式;Voronovskaja型渐近展开公式;同时逼近;Ditzian-Totik模;正逆定理;饱和定理
Lupas-Baskakov-type operators;approximation;modulus of smoothness;simultaneous approximation;linear combinations;direct and converse theorems
本学位论文讨论广义Baskakov算子及其修正算子的有关逼近性质，总共分为四章，主要包括以下几个方面的内容： 第一章讨论广义Baskakov算子的逼近性质。第一节吸收[3]的思想，在[2]的基础上得到了广义Baskakov算子r+s阶导数的点态和整体的逼近定理；第二节研究了广义Baskakov算子的Stechkin—Marchaud型不等式。 第二章研究修正的Baskakov—Beta算子的逼近定理。第一节给出该算子的Voronovskaja型渐近展开公式；第二节讨论该算子对有界变差函数的逼近。 第三章对一类Baskakov型积分算子进行研究。第一节研究这类算子的同时逼近；第二节讨论该算子线性组合在C_β[0，∞)上的逼近；第三节吸收[20]的思想，得到了该算子线性组合逼近的逆定理；第四节讨论该线性组合算子在C_β[0，∞)逼近的饱和定理。 第四章给出广义Baskakov算子用其部分和来代替进行逼近的一个充分必要条件。
This paper consists of four parts.In the first chapter, the approximation of Lupas-Baskakov-type operators in classicalspaces is studied. In section 1, the approximation of these operators in C[0, ∞) spaces isdiscussed, and both the pointwise and global equivalent theorems for approximation are obtained by using of the modulus of smoothness ω2λ (f,t); Furthermore, the relationsbetween the derivatives of these operators and the smoothness of the approximated functions are studied; By using of the modulus of smoothness w(f,t)p and the modifiedK-functional K (f, t) p, the equivalent theorems for approximation of these operators in Xp[0,∞) (1 ≤ p ≤∞) spaces are obtained in section 2; In section 3, the global approximation by these operators is further discussed in Lp[0,∞)(1≤ p≤∞) spaces and theconverse inequalities of the strong-type are obtained.In the second chapter, the approximation of the 2r-th linear combinations of Lupas-Baskakov-type operators is studied. In section 1, the equivalent theorems for the pointwise approximation are obtained by using of the modulus of smoothness of highorder w2r(f,t); In section 2, the pointwise estimates for the simultaneous approximationare further studied, and the equivalent theorems for approximation are obtained.In the third chapter, the approximation of the generalized Lupas-Baskakov integral operators is studied. In section 1, absorbing the ideas of paper [5], both the asymptotic representations and the theorems for the simultaneous approximation are obtained; Insection 2, the approximation for a class of functions Br(v) which is wider than thefunctions of bounded variation is discussed, and the estimates for the simultaneous approximation are obtained.In the fourth chapter, the approximation by others operators is studied. In section 1,the approximation by a new linear positive operators which were defined by P.N.Agrawal and K.J.Thamer in paper [4] is discussed in Lp[0,∞)(1 ≤ p ≤ ∞) spaces. With the ideals ofE.V.Wickeren in paper [6], the converse inequalities of the weak-type are obtained; In section 2, the converse inequalities of the strong-type are further discussed; In section 3, the simultaneous approximation by the modified Szasz operators with Jacobi weights is discussed, and the converse inequalities of weak-type are obtained; In section 4, the direct and converse theorems for the pointwise approximation by Baskakov operators are given, and the relations between the derivatives of the operators and the smoothness of the approximated functions are studied, which extend the results of paper [7].
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