正系数多项式倒数逼近的点态和整体估计(英文)  

Pointwise and Global Estimates for Reciprocal Approximation of Polynomials with Positive Coefficients

作　　者：曹飞龙[1] 

机构地区：[1]宁夏大学数学计算机学院,银川750021

出　　处：《应用数学》2003年第1期65-69,共5页Mathematica Applicata

基　　金：SupportedbyFoundationofScienceofNingxiaUniversity(No :O2 2 10 1) ;FoundationofscienceofHigherShoolofNingxia(No :JY2 0 0 2 10 7);FoundationofKeyItemofScienceandTechnologyofMinistryofEdca tionofChina

摘　　要：利用Ditzian Totik光滑模对于 [0 ,1 ]上定义的非负连续函数f(x) ,且f(x) 0 ,文中证明存在正系数多项式Pn(x)及常数C ,使得 f(x) - 1Pn(x) ≤Cwφλ f,n-1/ 2 φ(x) + 1n1-λ .当λ=1时 ,上述结果导出已有的整体估计 ,而当 0 ≤λ <1时 ,得到倒数逼近一个新的点态局部估计 .For nonegative function f(x) defined on ,and f0,using Ditzian-Totik's modulus of smoothness,it is proved in the present paper that there exist polynomials with positive coefficients,P n(x) and a constant C,such that f(x)-1P n(x)≤Cw φλf,n -1/2φ(x)+1n 1-λ.The case λ=1 in the above conclusion gives a global result obtained in whereas 0≤λ<1 gives a new pointwise local estimate for reciprocal approximation.

关 键 词：整体估计 正系数多项式 有理逼近 DITZIAN-TOTIK模 逼近阶 点态局部估计 

分 类 号：O174.41[理学—数学]