关于Bernstein-Durrmeyer-Bzier算子在Orlicz空间内的逼近  

On approximation of Bernstein-Durrmeyer-Bzier operators in Orlicz spaces

作　　者：邓雪莉[1] 吴嘎日迪[1] 

机构地区：[1]内蒙古师范大学数学科学学院,呼和浩特内蒙古010022

出　　处：《纯粹数学与应用数学》2015年第3期307-317,共11页Pure and Applied Mathematics

基　　金：国家自然科学基金(11161033);内蒙古师范大学人才工程基金(RCPY-2-2012-K-036)

摘　　要：在连续函数空间和L_p空间内研究算子逼近方法的基础上,利用一阶DitzianTotik积分模与不等式技巧研究了Bernstein-Durrmeyer-Bzier算子在Orlicz空间内的逼近性质.得到了Bernstein-Durrmeyer-Bezier算子在Orlicz空间内的逼近正定理和逼近等价定理.由于Orlicz空间比连续函数空间和L_p空间都"大",其拓扑结构也比L_p空间复杂得多,所以本文的结果具有一定的拓展意义.In this paper we investigate the approximation problem of Bernstein-Durrmeyer-Bezier operators in Orlicz spaces based on the methods of studying the operator approximation in continuous function space and Lp space, and used the tools of Ditzian-Totik integral modulus, with the help of the inequality techniques, and obtain the results of direct theorem and equivalence theorem on approximation of Bernstein-Durrmeyer-Bezier operators in Orlicz spaces. Because the Orlicz space is ＂big＂ and its topological structure is more complicated than Lp space significance than continuous function space and Lp space, the results of this paper have certain expansion

关 键 词：Bezier型算子 逼近正定理 等价定理 K-泛函 光滑模 

分 类 号：O174.41[理学—数学]