河南师范大学学报(自然科学版)

2013, v.41;No.172(05) 9-12+18

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1种递推的Kantorovich型算子在L_P(P>1)空间上的逼近
Approximation on L_P (P>1)Space by a Kind of Recursive Kantorovich Type Operators

高义;
GAO Yi;School of Mathematics and Information Science,Beifang University of Nationalities;

摘要(Abstract):

构造出1种递推的Kantorovich型算子,研究了其在LP(P>1)空间上的收敛性和逼近特征,借助Hardy-Littlewood极大函数和Jensen不等式给出了该算子更加精细的逼近度估计,进而利用Lp空间中K-泛函和积分连续模的等价性获得了该算子的收敛阶为O(1/n(1/2)).
A kind of recursive Kantorovich type operators is constructed.The convergence for these operators and approximation characteristics on LP(P>1)space are studied.Then more sophisticated estimation of degree of approximation is obtained with using Hardy-Littlewood's maximal function and Jensen's inequality.At the same time,the order of convergence is characterized by 1/n(1/2) with the help of the equivalence of K-functional and odulus of integral continuity on LPspace.

关键词(KeyWords): Kantorovich算子;收敛;逼近度;LP空间
Kantorovich operators;convergence;degree of approximation;LP space

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金(61261043);; 北方民族大学科学研究项目(2012Y033)

作者(Authors): 高义;
GAO Yi;School of Mathematics and Information Science,Beifang University of Nationalities;

DOI: 10.16366/j.cnki.1000-2367.2013.05.036

参考文献(References):

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