| Best Simultaneous Approximation in $L^{\Phi}(I,X)$ |
| Received:July 21, 2008 Revised:January 05, 2009 |
| Key Words:
simultaneous approximation Orlicz spaces.
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| Fund Project:Supported by the Foundation of the Nationalities Committee of China (Grant No.05YN06) and the Educational Foundation of Yunnan Province (Grant No.07Z10533). |
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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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2010.05.013 |
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