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The Approximation and Weighted Approximation for Some Positive Linear Operators

Author: GaoYi
Tutor: XueYinChuan
School: Ningxia University
Course: Basic mathematics
Keywords: Weighted Approximation Order of convergence Degree of approximation Weight function Inverse Theorems
CLC: O177.91
Type: Master's thesis
Year: 2005
Downloads: 68
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Abstract


This thesis focuses on three types of positive linear approximation operator and its weighted approximation . Chapter II study of a class of generalized Bernstein operators approximation . Discussion yuan Bernstein type operator approximation converse of the Jackson - type integral operator approximation estimated type and the the uniform approximation weak Steckin-Marchaud type inequality . And construct a binary simplex promotion Bernstein operators , given their uniform convergence is a necessary and sufficient condition to characterize the nature of their degree of approximation order continuous mode . Chapter III study of a class of binary generalized Baskakov operator approximation and its weighted approximation , focused on different weight functions such product binary operator and its derivative polynomial weighted space convergence and processing the the Jacobi weight of convergence order , $ result is extended to multiple situations . In the third quarter in the space of continuous functions on studies such non-product- type binary operator , and discuss some of the important properties of the operator , given a converse of local significance . Chapter IV is constructed for a class of recursive Kantorovich Operators C space and L_p space on the operator approach , using a different approach given its gradual progress type C space L_p (p gt; 1) the degree of approximation space is estimated that some meaningful results .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Functional Analysis > Nonlinear Functional Analysis
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