| Title:
|
Multivalued pseudo-contractive mappings defined on unbounded sets in Banach spaces (English) |
| Author:
|
Morales, Claudio H. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
33 |
| Issue:
|
4 |
| Year:
|
1992 |
| Pages:
|
625-630 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $X$ be a real Banach space. A multivalued operator $T$ from $K$ into $2^X$ is said to be pseudo-contractive if for every $x,y$ in $K$, $u\in T(x)$, $v\in T(y)$ and all $r>0$, $\|x-y\|\leq \|(1+r)(x-y)-r(u-v)\|$. Denote by $G(z,w)$ the set $\{u\in K :\|u-w\|\leq \|u-z\|\}$. Suppose every bounded closed and convex subset of $X$ has the fixed point property with respect to nonexpansive selfmappings. Now if $T$ is a Lipschitzian and pseudo-contractive mapping from $K$ into the family of closed and bounded subsets of $K$ so that the set $G(z,w)$ is bounded for some $z\in K$ and some $w\in T(z)$, then $T$ has a fixed point in $K$. (English) |
| Keyword:
|
pseudo-contractive mappings |
| MSC:
|
47H04 |
| MSC:
|
47H09 |
| MSC:
|
47H10 |
| idZBL:
|
Zbl 0794.47038 |
| idMR:
|
MR1240184 |
| . |
| Date available:
|
2009-01-08T17:59:09Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118534 |
| . |
| 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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| . |
