On zeros and fixed points of multifunctions with non-compact convex domains
Park, Sehie ; Bae, Jong Sook
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993), p. 257-264 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

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].

Publié le : 1993-01-01
Classification:  47H04,  47H10 
@article{118579,
     author = {Sehie Park and Jong Sook Bae},
     title = {On zeros and fixed points of multifunctions with non-compact convex domains},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {34},
     year = {1993},
     pages = {257-264},
     zbl = {0834.47050},
     mrnumber = {1241735},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118579}
}

Park, Sehie; Bae, Jong Sook. On zeros and fixed points of multifunctions with non-compact convex domains. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 257-264. http://gdmltest.u-ga.fr/item/118579/

Bellenger J.C. Existence of maximizable quasiconcave functions on paracompact convex spaces, J. Math. Anal. Appl. 123 (1987), 333-338. (1987) | MR 0883692 | Zbl 0649.46006

Ben-El-Mechaiekh H. Zeros for set-valued maps with non-compact domains, C. R. Math. Rep. Acad. Sci. Canada 12 (1990), 125-130. (1990) | MR 1070423 | Zbl 0734.47028

Ky Fan Some properties of convex sets related to fixed point theorems, Math. Ann. 266 (1984), 519-537. (1984) | MR 0735533 | Zbl 0515.47029

Jiang J. Fixed point theorems for paracompact convex sets, Acta Math. Sinica 4 (1988), 64-71. (1988) | MR 0953351 | Zbl 0715.54032

Kum S.H. Ph.D. Dissertation, Seoul National University, 1991, .

Lassonde M. On the use of KKM multifunctions in fixed point theory and related topics, J. Math. Anal. Appl. 97 (1983), 151-201. (1983) | MR 0721236 | Zbl 0527.47037

Park S.; Bae J.S. Existence of maximizable quasiconcave functions on convex spaces, J. Korean Math. Soc. 28 (1991), 285-292. (1991) | MR 1127833 | Zbl 0756.47050

Park S. Applications of maximizable linear functionals on convex sets, ``Proc. in Honor of C. N. Lee'', 537-548, 1991.

Park S. Fixed point theory of multifunctions in topological vector spaces, J. Korean Math. Soc. 29 (1992), 191-208. (1992) | MR 1157308 | Zbl 0758.47048

Park S. Generalized matching theorems for closed coverings of convex sets, Numer. Funct. Anal. and Optimiz. 11 (1990), 101-110. (1990) | MR 1058779 | Zbl 0706.52001

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

Simons S. On existence theorem for quasiconcave functions with applications, Nonlinear Anal. TMA 10 (1986), 1133-1152. (1986) | MR 0857745

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. (1990) | MR 1091369 | Zbl 0745.47046