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:209 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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