| Title:
|
The characteristic of noncompact convexity and random fixed point theorem for set-valued operators (English) |
| Author:
|
Kumam, Poom |
| Author:
|
Plubtieng, Somyot |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
1 |
| Year:
|
2007 |
| Pages:
|
269-279 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $(\Omega ,\Sigma )$ be a measurable space, $X$ a Banach space whose characteristic of noncompact convexity is less than 1, $C$ a bounded closed convex subset of $X$, $KC(C)$ the family of all compact convex subsets of $C.$ We prove that a set-valued nonexpansive mapping $T\: C\rightarrow KC(C)$ has a fixed point. Furthermore, if $X$ is separable then we also prove that a set-valued nonexpansive operator $T\: \Omega \times C\rightarrow KC(C)$ has a random fixed point. (English) |
| Keyword:
|
random fixed point |
| Keyword:
|
set-valued random operator |
| Keyword:
|
measure of noncompactness |
| MSC:
|
47H09 |
| MSC:
|
47H10 |
| MSC:
|
47H40 |
| idZBL:
|
Zbl 1174.47042 |
| idMR:
|
MR2309965 |
| . |
| Date available:
|
2009-09-24T11:45:39Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128171 |
| . |
| Reference:
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