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| 研究生： |
杜威仕 W. S. Duh |
|---|---|
| 論文名稱： |
堅固的非擴張映射在UCED巴納赫空間上的一些定點定理 Fixed Point Theorems for Firmly Nonexpansive Mappings in UCEDBanach Spaces |
| 指導教授： |
顏啟麟
Yan, Qi-Lin |
| 學位類別： |
碩士 Master |
| 系所名稱： |
數學系 Department of Mathematics |
| 論文出版年： | 1999 |
| 畢業學年度： | 87 |
| 語文別： | 英文 |
| 論文頁數： | 16 |
| 中文關鍵詞： | 堅固的 、非擴張的 、巴納赫空間 、定點 、定點定理 |
| 英文關鍵詞： | Fixed Point, Fixed Point Theorem, Firmly, Banach Space, UCEDBanach Space |
| 論文種類： | 學術論文 |
| 相關次數： | 點閱：181 下載：0 |
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本論文將推廣R. Smarzewski [9]的定理於任一方向均勻凸性( uniformly convex in every direction，簡寫成UCED )的巴納赫空間( Banach space )上，而得到以下主要結論:
令X 是一個在任一方向均勻凸性的巴納赫空間且C 是由X中有限n個非空弱緊緻(weakly compact)、凸子集 所成的聯集。若 是一個 堅固的非擴張( firmly nonexpansive)映射，其中 0≦λ≦1，則T在C中有定點(fixed point)。
This thesis will obtain a main result by extending the Theorem of R. Smarzewski [9] in a uniformly convex in every direction (UCED) Banach space:
Let X be a UCED Banach space, and C=∪Ck a union of nonempty weakly compact convex subsets of X. Suppose T is a firmly nonexpansive mapping for some 0≦λ≦1 . Then T has a fixed point in C.
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[9] R. Smarzewski, On firmly nonexpansive mappings, Proc. Amer. Math. Soc. 113 (1991), 723-725.
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