| Title:
|
An intersection theorem for set-valued mappings (English) |
| Author:
|
Agarwal, Ravi P. |
| Author:
|
Balaj, Mircea |
| Author:
|
O'Regan, Donal |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
58 |
| Issue:
|
3 |
| Year:
|
2013 |
| Pages:
|
269-278 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Given a nonempty convex set $X$ in a locally convex Hausdorff topological vector space, a nonempty set $Y$ and two set-valued mappings $T\colon X\rightrightarrows X$, $S\colon Y\rightrightarrows X$ we prove that under suitable conditions one can find an $x\in X$ which is simultaneously a fixed point for $T$ and a common point for the family of values of $S$. Applying our intersection theorem we establish a common fixed point theorem, a saddle point theorem, as well as existence results for the solutions of some equilibrium and complementarity problems. (English) |
| Keyword:
|
intersection theorem |
| Keyword:
|
fixed point |
| Keyword:
|
saddle point |
| Keyword:
|
equilibrium problem |
| Keyword:
|
complementarity problem |
| MSC:
|
47H04 |
| MSC:
|
47H10 |
| MSC:
|
49J53 |
| idZBL:
|
Zbl 1275.47105 |
| idMR:
|
MR3066821 |
| DOI:
|
10.1007/s10492-013-0013-7 |
| . |
| Date available:
|
2013-05-17T10:42:10Z |
| Last updated:
|
2023-08-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143278 |
| . |
| Reference:
|
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