| SHI YINGGUANG.[J].数学年刊A辑,1980,1(2):235~244 |
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| BEST SIMULTANEOUS Lp APPROXIMATION |
| Received:November 20, 1978 |
| DOI： |
| 中文关键词: |
| 英文关键词: |
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| 英文摘要: |
| In this paper we discuss the exigtenoe of best simultaneous Lp approximation and
give the characterization theorems of best simultaneous Lp approximation using the
elements of an arbitrary quasioonvex set K in the space \[{L_p}(X,\sum ,\mu )\], A set \[K \subset {L_p}(X,\sum ,\mu )\]
is called quasiconvex if for arbitrary elements \[{h_1},{h_2} \in K\] there exists a sequenoe \[{t_n} > 0\] (n = l, 2, ...), \[{t_n} > 0\]->0 (n—>∞) such that \[{t_n}{h_1} + (1 - {t_n}){h_2} \in \bar K(n = 1,2,...)\]
where \[{\bar K}\] denotes a closure of K. |
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