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关于无界连续函数逼近
引用本文:郑成德,王仁宏. 关于无界连续函数逼近[J]. 数学季刊, 2003, 18(1): 44-48
作者姓名:郑成德  王仁宏
作者单位:1.Department of Basic Science,Dalian Railway Institute,Dalian 116028,China;2.Institute of Mathematics,Dalian University of Technology,Dalian 116024,China
摘    要:§ 1 . Introduction  Itisaveryimportantstudytoapproximatenonboundedcontinuousfunctionsdefinedonalargerange.Aneffectivemethodcalledthemethodofmultiplierenlargementhasbeenputfor wardandgreatlydevelopedbyHSULCandWANGReng Hong [1— 3].Thesecondauthorofthispaperinparticularhasprovedin [2 ]almostuniformlythatanynonboundedcontinuousfunctionsdefinedonawholerealaxiscanbeapproximatedbypolynomialoperators.We’llgen eralizeinthispaperthebasicprincipleofthismethod,andasanexample,Bernsteinpolynomial…

关 键 词:无界连续函数  乘子增大法  正线性算子  Bernstein多项式算子  函数逼近  Banach空间  泛函

On Approximation of Nonbounded Continuous Functions
ZHENG Cheng-de,WANG Ren-hong. On Approximation of Nonbounded Continuous Functions[J]. Chinese Quarterly Journal of Mathematics, 2003, 18(1): 44-48
Authors:ZHENG Cheng-de  WANG Ren-hong
Affiliation:[1]DepartmentofBasicScience,DalianRailwayInstitute,Dalian116028,China [2]InstituteofMathemat-ics,DalianUniversityofTechnology,Dalian116024,China
Abstract:This paper generalizes the basic principle of multiplier-enlargement approach to approximating any nonbounded continuous functions with positive linear operators,and as an example,Bernstein poly-nomial operators are analysed and studied.This paper gives a certain theorem as a general rule to ap-proximate any nonbounded continuous functions.
Keywords:positive linear operator  approximation of nonbounded continuous function  method of multiplier-enlargement  Bernstein polynomial operator
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