| $L^{\Phi}(I,X)$中的最佳同时逼近 |
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| 引用本文： | 沈宗山,杨柱元.$L^{\Phi}(I,X)$中的最佳同时逼近[J].数学研究及应用,2010,30(5):863-868. |
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| 作者姓名： | 沈宗山 杨柱元 |
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| 作者单位： | 云南民族大学数学与计算机科学学院, 云南 昆明 650031; 云南中医学院中药学院, 云南 昆明 650500;云南民族大学数学与计算机科学学院, 云南 昆明 650031 |
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| 基金项目： | 国家民委科研基金项目(Grant No.05YN06),云南省教育厅科研基金项目(Grant No.07Z10533). |
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| 摘 要： | Let X be a Banach space and Ф be an Orlicz function. Denote by L^Ф（I,X） the space of X-valued （I）-integrable functions on the unit interval I equipped with the Luxemburg norm. For f1,f2,... ,fm ∈ L^Ф（I,X）, a distance formula distv（f1,f2,... ,fm,L^Ф（I,G）） is presented, where G is a close subspace of X. Moreover, some existence and characterization results concerning the best simultaneous approximation of L^Ф （I, G） in L^Ф （I, X） axe given.
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| 关 键 词： | simultaneous approximation Orlicz spaces. |
| 收稿时间： | 2008/7/21 0:00:00 |
| 修稿时间： | 1/5/2009 12:00:00 AM |
Best Simultaneous Approximation in $L^{\Phi}(I,X)$ |
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| Zong Shan SHEN and Zhu Yuan YANG.Best Simultaneous Approximation in $L^{\Phi}(I,X)$[J].Journal of Mathematical Research with Applications,2010,30(5):863-868. |
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| Authors: | Zong Shan SHEN and Zhu Yuan YANG |
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| Institution: | School of Mathematics and Computer Science, Yunnan Nationalities University, Yunnan 650031, P. R. China; School of Traditional Chinese Meteria Medica, Yunnan University of Traditional Chinese Medicine, Yunnan 650500, P. R. China;School of Mathematics and Computer Science, Yunnan Nationalities University, Yunnan 650031, P. R. China; |
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| Abstract: | Let $X$ be a Banach space and $\Phi$ be an Orlicz function. Denote by $L^{\Phi}(I,X)$ the space of $X$-valued $\Phi$-integrable functions on the unit interval $I$ equipped with the Luxemburg norm. For $f_{1},f_{2},\ldots,f_{m}\in L^{\Phi}(I,X)$, a distance formula $\dist_{\Phi}(f_{1},f_{2},\ldots,f_{m},L^{\Phi}(I, G))$ is presented, where $G$ is a close subspace of $X$. Moreover, some existence and characterization results concerning the best simultaneous approximation of $L^{\Phi}(I,G)$ in $L^{\Phi}(I,X)$ are given. |
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| Keywords: | simultaneous approximation Orlicz spaces |
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