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| ON TOPOLOGICAL LINEAR CONTRACTIONS ON NORMED SPACESAND APPLICATION |
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Citation： |
SHIH Mau-hsiang,TAM Ping-kwan.ON TOPOLOGICAL LINEAR CONTRACTIONS ON NORMED SPACESAND APPLICATION[J].Chinese Annals of Mathematics B,1999,20(2):159~168 |
| Page view： 886
Net amount： 672 |
Authors： |
SHIH Mau-hsiang; TAM Ping-kwan |
Foundation： |
the Chinese University of
Hong Kong (No.2060144) and NSERC of Canada(A-8096) |
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| Abstract： |
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. |
Keywords： |
Contraction, Fixed point,
Stable solution |
Classification： |
46A32, 47A30, 39A11, 46N99, 47H10, 47H20 |
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