| 孙芳美,吴嘎日迪.Kantorovich型分段Hermite插值在Orlicz空间内的逼近[J].井冈山大学自然版,2018,(1):1-4 |
| 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 |
| 投稿时间：2017-03-13 修订日期：2017-04-18 |
| DOI：10.3969/j.issn.1674-8085.2018.01.001 |
| 中文关键词: 分段Hermite插值 Orlicz空间 等距结点 逼近 |
| 英文关键词: piecewise Hermite interpolation Orlicz space equidistant notes approximation |
| 基金项目: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） |
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| 中文摘要: |
| 构造了一类积分型插值，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Lp空间，其拓扑结构也比连续函数空间和Lp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。 |
| 英文摘要: |
| 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. |
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