| Title:
|
On zeros and fixed points of multifunctions with non-compact convex domains (English) |
| Author:
|
Park, Sehie |
| Author:
|
Bae, Jong Sook |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
34 |
| Issue:
|
2 |
| Year:
|
1993 |
| Pages:
|
257-264 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Using our own generalization [7] of J.C. Bellenger's theorem [1] on the existence of maximizable u.s.c\. quasiconcave functions on convex spaces, we obtain extended versions of the existence theorem of H. Ben-El-Mechaiekh [2] on zeros for multifunctions with non-compact domains, the coincidence theorem of S.H. Kum [5] for upper hemicontinuous multifunctions, and the Ky Fan type fixed point theorems due to E. Tarafdar [13]. (English) |
| Keyword:
|
convex space |
| Keyword:
|
$c$-compact set |
| Keyword:
|
real Hausdorff topological vector space (t.v.s.) |
| Keyword:
|
linear operator |
| Keyword:
|
locally convex |
| Keyword:
|
fixed point |
| Keyword:
|
coincidence |
| Keyword:
|
zero |
| Keyword:
|
upper hemicontinuous (u.h.c.) multifunction |
| MSC:
|
47H04 |
| MSC:
|
47H10 |
| idZBL:
|
Zbl 0834.47050 |
| idMR:
|
MR1241735 |
| . |
| Date available:
|
2009-01-08T18:03:14Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118579 |
| . |
| Reference:
|
[1] Bellenger J.C.: Existence of maximizable quasiconcave functions on paracompact convex spaces.J. Math. Anal. Appl. 123 (1987), 333-338. Zbl 0649.46006, MR 0883692 |
| Reference:
|
[2] Ben-El-Mechaiekh H.: Zeros for set-valued maps with non-compact domains.C. R. Math. Rep. Acad. Sci. Canada 12 (1990), 125-130. Zbl 0734.47028, MR 1070423 |
| Reference:
|
[3] Ky Fan: Some properties of convex sets related to fixed point theorems.Math. Ann. 266 (1984), 519-537. Zbl 0515.47029, MR 0735533 |
| Reference:
|
[4] Jiang J.: Fixed point theorems for paracompact convex sets.Acta Math. Sinica 4 (1988), 64-71. Zbl 0715.54032, MR 0953351 |
| Reference:
|
[5] Kum S.H.: Ph.D. Dissertation, Seoul National University, 1991.. |
| Reference:
|
[6] Lassonde M.: On the use of KKM multifunctions in fixed point theory and related topics.J. Math. Anal. Appl. 97 (1983), 151-201. Zbl 0527.47037, MR 0721236 |
| Reference:
|
[7] Park S., Bae J.S.: Existence of maximizable quasiconcave functions on convex spaces.J. Korean Math. Soc. 28 (1991), 285-292. Zbl 0756.47050, MR 1127833 |
| Reference:
|
[8] Park S.: Applications of maximizable linear functionals on convex sets.``Proc. in Honor of C. N. Lee'', 537-548, 1991. |
| Reference:
|
[9] Park S.: Fixed point theory of multifunctions in topological vector spaces.J. Korean Math. Soc. 29 (1992), 191-208. Zbl 0758.47048, MR 1157308 |
| Reference:
|
[10] Park S.: Generalized matching theorems for closed coverings of convex sets.Numer. Funct. Anal. and Optimiz. 11 (1990), 101-110. Zbl 0706.52001, MR 1058779 |
| Reference:
|
[11] Shih M.-H., Tan K.-K.: Covering theorems of convex sets related to fixed-point theorem.in ``Nonlinear and Convex Analysis (Proc. in Honor of Ky Fan)'' (B.-L. Lin and S. Simons, eds.), 235-244, Marcel Dekker, Inc., New York, 1987. MR 0892795 |
| Reference:
|
[12] Simons S.: On existence theorem for quasiconcave functions with applications.Nonlinear Anal. TMA 10 (1986), 1133-1152. MR 0857745 |
| Reference:
|
[13] Tarafdar E.: An extension of Fan's fixed point theorem and equilibrium point of an abstract economy.Comment. Math. Univ. Carolinae 31 (1990), 723-730. Zbl 0745.47046, MR 1091369 |
| . |
