| Title:
|
On a problem of Gulevich on nonexpansive maps in uniformly convex Banach spaces (English) |
| Author:
|
Park, Sehie |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
37 |
| Issue:
|
2 |
| Year:
|
1996 |
| Pages:
|
263-268 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $X$ be a uniformly convex Banach space, $D\subset X$, $f:D\to X$ a nonexpansive map, and $K$ a closed bounded subset such that $\overline{\text{co}}\,K\subset D$. If (1) $f|_K$ is weakly inward and $K$ is star-shaped or (2) $f|_K$ satisfies the Leray-Schauder boundary condition, then $f$ has a fixed point in $\overline{\text{co}}\,K$. This is closely related to a problem of Gulevich [Gu]. Some of our main results are generalizations of theorems due to Kirk and Ray [KR] and others. (English) |
| Keyword:
|
uniformly convex |
| Keyword:
|
Banach space |
| Keyword:
|
Hilbert space |
| Keyword:
|
contraction |
| Keyword:
|
nonexpansive map |
| Keyword:
|
weakly inward map |
| Keyword:
|
demi-closed |
| Keyword:
|
Rothe condition |
| Keyword:
|
Leray-Schauder condition |
| Keyword:
|
(KR)-bounded |
| Keyword:
|
Opial's condition |
| MSC:
|
47H10 |
| MSC:
|
54H25 |
| idZBL:
|
Zbl 0852.47029 |
| idMR:
|
MR1399001 |
| . |
| Date available:
|
2009-01-08T18:23:31Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118831 |
| . |
| 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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| . |
