| Title:
|
Fixed points of asymptotically regular mappings in spaces with uniformly normal structure (English) |
| Author:
|
Górnicki, Jarosław |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
4 |
| Year:
|
1991 |
| Pages:
|
639-643 |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is proved that: for every Banach space $X$ which has uniformly normal structure there exists a $k>1$ with the property: if $A$ is a nonempty bounded closed convex subset of $X$ and $T:A\rightarrow A$ is an asymptotically regular mapping such that $$ \liminf _{n\rightarrow \infty } |\kern -0.8pt|\kern -0.8pt|T^n|\kern -0.8pt|\kern -0.8pt|< k, $$ where $|\kern -0.8pt|\kern -0.8pt|T|\kern -0.8pt|\kern -0.8pt|$ is the Lipschitz constant (norm) of $T$, then $T$ has a fixed point in $A$. (English) |
| Keyword:
|
asymptotically regular mappings |
| Keyword:
|
uniformly normal structure |
| Keyword:
|
fixed points |
| MSC:
|
46B20 |
| MSC:
|
47H10 |
| idZBL:
|
Zbl 0768.47027 |
| idMR:
|
MR1159810 |
| . |
| Date available:
|
2009-01-08T17:47:47Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118443 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| . |
