Kantorovich型分段Hermite插值在Orlicz空间内的逼近  

ON APPROXIMATION BY KANTOROVICH TYPE OF PIECEWISE HERMITE INTERPOLATION IN ORLICZ SPACES

作　　者：孙芳美 吴嘎日迪[1] SUN Fang-mei, WU Ga-ridi(College of Mathematics Science, Inner Mongolia Normal University, Huhhot, Inner Mongolia 010022, Chin)

机构地区：[1]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022

出　　处：《井冈山大学学报（自然科学版）》2018年第1期1-4,共4页Journal of Jinggangshan University (Natural Science)

基　　金：国家自然科学基金项目(11161033);内蒙古自治区自然科学基金项目(2017MSO123);内蒙古自治区研究生科研创新基金项目(S20161013501)

摘　　要：构造了一类积分型插值,在连续函数空间和L_p空间内研究插值逼近方法的基础上,利用函数逼近论中的常用方法和技巧以及连续模、Holder不等式、Markov不等式等工具得到了该插值在Orlicz空间内的逼近定理。由于Orlicz空间包含连续函数空间和L_p空间,其拓扑结构也比连续函数空间和L_p空间复杂得多,且该类插值在基础研究和工程领域中有着非常重要的应用,所以论文的结果具有一定的拓展意义。We construct an integral type of interpolation based on the methods of studying the operator approximation in continuous function space and Lp space. We also used common measures and techniques in function approximation theory. Modulus of continuity, Holder inequality, Markov inequality are used as tools to obtain approximation theorem in Orlicz spaces. Because the Orlicz space includes continuous function space and Lp space, its topological structure is more complicated than Lp space. The results have certain expansion significance. Furthermore, this kind of interpolation is very important to basic research and engineering field.

关 键 词：分段Hermite插值 Orliez空间 等距结点 逼近 

分 类 号：O174.41[理学—数学]