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

• 1:北方民族大学数学与信息科学学院

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)：

• [1]Müller M.Die Güte der Lp-approximation durch Kantorovic-polynome[J].Math Z,1976,151:243-247.
• [2]Grundmann A.Güteabschtzungen für den Kantorovic-operator in der L1-Norm[J].Math Z,1976,150:45-47.
• [3]Ditzian Z,May C P.Lp saturation and inverse theorems for modified Bernstein polynomials[J].J Indiana Math,1976,33:733-751.
• [4]Totik V.Problems and solutions concerning Kantorovich operators[J].J Approx Theory,1983,37:51-68.
• [5]Totik V.Approximation in L1 by kantorovich polynomials[J].Acta Sci Math,1983,46:211-222.
• [6]Heilmann M.Lp-saturation of some modified Bernstein operators[J].J Approx Theory,1988,54:260-273.
• [7]Ditzian Z,Zhou X.Kantorovich-Bernstein polynomials[J].Constr Approx,1990(3):421-435.
• [8]Zhou D X.Converse theorems for multidimensional Kantorovich operators[J].Analy Math,1993,19:85-100.
• [9]Agratini O.An approximation process of Kantorovich type[J].Mathematical Notes,2001,2(1):3-10.
• [10]Dogru O,zalp N.Approximation by Kantorovich type generalization of Meyer-Knig and Zeller operators[J].Glasn Math,2001,36:311-318.
• [11]Phillips G M.Bernstein polynomials based on q-integers[J].Ann Numer Math,1997,4:511-518.
• [12]Phillips G M.A survey of results on the q-Bernstein polynomials[J].IMA J Numerical analysis,2009,23:1-12.
• [13]Duman O,Ozarslan M,Biancamaria D.Modified Szsz-Mirakjan-Kantorovich operators preserving linear functions[J].Turk J Math,2009,33:151-158.
• [14]Dalmanoglua O,Dogru O.On statistical approximation properties of Kantorovich type q-Bernstein operators[J].Mathematical and Computer Modelling,2010,52:760-771.
• [15]Altomare F,Cappelletti M,Leonessa V.On a Generalization of Szsz-Mirakjan-Kantorovich Operators[J].Results Math,2013,63:837863.
• [16]高义,黄永东.一种递推的Kantorovich型算子的逼近[J].内蒙古大学学报:自然科学版,2011,42(6):610-617.
• [17]Campiti M,Metafune G.Approximation properties of recursively defined Bernstein-type operators[J].J Approx Theory,1996,87:243269.
• [18]Campiti M,Metafune G.Evolution equations associated with recursively defined Bernstein-type operators[J].J Approx Theory,1996,87:270-290.
• [19]周民强.调和分析讲义(实变方法)[M].北京:北京大学出版社,1999:43-58.