两类修正的插值多项式在Orlicz空间内的逼近  

Approximation by Two Kinds of Modified Interpolation Polynomials in Orlicz Spaces

作　　者：牛彤彤[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010022

出　　处：《工程数学学报》2014年第1期103-111,共9页Chinese Journal of Engineering 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：插值逼近问题有着广泛的实际背景和应用前景.为了在较大范围内研究插值逼近问题,本文在连续函数空间和Lp空间内研究插值逼近方法的基础上,利用K-泛函、光滑模与极大函数等工具,借助不等式技巧,研究了两类修正的插值多项式在Orlicz空间内的逼近问题,得到了收敛速度估计的结果.所得结果对误差估计、精度分析等问题可以提供必要的理论分析依据和可参考的数据.由于Orlicz空间比连续函数空间和Lp空间涵盖更广泛,其拓扑结构也比Lp空间复杂得多,所以本文的结果具有一定的拓展意义.The interpolation approximation has a practical background and broad application prospects. In order to more comprehensively study the interpolation approximation, in this paper we investigate the approximation problem of two kinds of modified interpolation polyno-mials in Orlicz spaces based on the methods of the interpolation approximation in continuous functional space and Lp space. By using the tools of K-functional, modulus of smoothness, extreme maximum function, etc., and employing the inequality techniques, we obtain a theo-retical estimation for the convergence rate of the problem. The results of this paper provide a theoretical analysis basis and reference data for error estimation and precision analysis. Because the Orlicz space can be seen as an extensive concept of the traditional continuous functional space and Lp space, and its topological structure is more complicated than Lp space, the results of this paper have certain extension significance.

关 键 词：插值 多项式 ORLICZ空间 逼近 

分 类 号：O171.41[理学—数学]