| 关于无界连续函数逼近 |
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| 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 |
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| 作者姓名： | 郑成德 王仁宏 |
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| 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 |
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| 摘 要： | § 1 . Introduction Itisaveryimportantstudytoapproximatenonboundedcontinuousfunctionsdefinedonalargerange.Aneffectivemethodcalledthemethodofmultiplierenlargementhasbeenputfor wardandgreatlydevelopedbyHSULCandWANGReng Hong [1— 3].Thesecondauthorofthispaperinparticularhasprovedin [2 ]almostuniformlythatanynonboundedcontinuousfunctionsdefinedonawholerealaxiscanbeapproximatedbypolynomialoperators.We’llgen eralizeinthispaperthebasicprincipleofthismethod,andasanexample,Bernsteinpolynomial…
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| 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 |
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| ZHENG Cheng-de,WANG Ren-hong. On Approximation of Nonbounded Continuous Functions[J]. Chinese Quarterly Journal of Mathematics, 2003, 18(1): 44-48 |
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| Authors: | ZHENG Cheng-de WANG Ren-hong |
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| Affiliation: | [1]DepartmentofBasicScience,DalianRailwayInstitute,Dalian116028,China [2]InstituteofMathemat-ics,DalianUniversityofTechnology,Dalian116024,China |
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| 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. |
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| Keywords: | positive linear operator approximation of nonbounded continuous function method of multiplier-enlargement Bernstein polynomial operator |
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