| SHIH Mau-hsiang,TAM Ping-kwan.[J].数学年刊A辑,1999,20(2):159~168 |
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| ON TOPOLOGICAL LINEAR CONTRACTIONS ON NORMED SPACESAND APPLICATION |
| Received:April 03, 1998 Revised:September 14, 1998 |
| DOI： |
| 中文关键词: |
| 英文关键词:Contraction, Fixed point,
Stable solution |
| 基金项目: |
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| 中文摘要: |
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| 英文摘要: |
| Simultaneous contractifications, simultaneous proper contractifications and semigroup \linebreak (countable family or finite family) of commuting operators and of non-commuting operators are first given.Characterizations are given for a single bounded linear operator being a topological proper contraction.By using complexification of a real Banach space and by applying a fixed point theorem of Edelstein, it is shown that every compact topological strict contraction on a Banach space is a topological proper contraction.Finally, results on simultaneous proper contractification are applied to study the stability of a common fixed point of maps which are Fr\'echet
differentiable at that point. |
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