| Title:
|
Fixed point theorems for nonexpansive mappings in modular spaces (English) |
| Author:
|
Kumam, Poom |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
40 |
| Issue:
|
4 |
| Year:
|
2004 |
| Pages:
|
345-353 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we extend several concepts from geometry of Banach spaces to modular spaces. With a careful generalization, we can cover all corresponding results in the former setting. Main result we prove says that if $\rho $ is a convex, $\rho $-complete modular space satisfying the Fatou property and $\rho _r$-uniformly convex for all $r>0$, C a convex, $\rho $-closed, $\rho $-bounded subset of $X_\rho $, $T:C\rightarrow C$ a $\rho $-nonexpansive mapping, then $T$ has a fixed point. (English) |
| Keyword:
|
fixed point |
| Keyword:
|
modular spaces |
| Keyword:
|
$\rho $-nonexpansive mapping |
| Keyword:
|
$\rho $-normal structure |
| Keyword:
|
$\rho $-uniform normal structure |
| Keyword:
|
$\rho _r$-uniformly convex |
| MSC:
|
46A80 |
| MSC:
|
46B20 |
| MSC:
|
46E30 |
| MSC:
|
47H09 |
| MSC:
|
47H10 |
| idZBL:
|
Zbl 1117.47045 |
| idMR:
|
MR2129956 |
| . |
| Date available:
|
2008-06-06T22:44:17Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107918 |
| . |
| 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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| . |
