頁籤選單縮合
題 名 | Nonexpansive Retractions onto Closed Convex Cones in Banach Spaces |
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作 者 | 姚任之; | 書刊名 | Taiwanese Journal of Mathematics |
卷 期 | 14:3B 2010.06[民99.06] |
頁 次 | 頁1023-1046 |
分類號 | 314.751 |
關鍵詞 | Relatively nonexpansive mapping; Generalized nonexpansive mapping; Generalized projection; Sunny generalized nonexpansive retraction; Fixed point; Conditional expectation; |
語 文 | 英文(English) |
英文摘要 | Let E be a smooth, strictly convex and reflexive Banach space, let C∗ be a closed convex subset of the dual space E∗ of E and let ΠC∗ be the generalized projection of E∗ onto C∗. Then the mapping RC∗ defined by RC∗ =J−1ΠC∗ J is a sunny generalized nonexpansive retraction of E onto J−1C∗, where J is the normalized duality mapping on E. In this paper, we first prove that if K is a closed convex cone in E and P is the nonexpansive retaction of E onto K, then P a sunny generalized nonexpansive retraction of E onto K. Using this result, we obtain an equivalent condition for a closed half-space of E to be a nonexpansive retract of E. |
本系統中英文摘要資訊取自各篇刊載內容。