On zeros and fixed points of multifunctions with non-compact convex domains

Sehie Park; Jong Sook Bae

Commentationes Mathematicae Universitatis Carolinae (1993)

  • Volume: 34, Issue: 2, page 257-264
  • ISSN: 0010-2628

Abstract

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Using our own generalization [7] of J.C. Bellenger’s theorem [1] on the existence of maximizable u.s.cq̇uasiconcave 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].

How to cite

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Park, Sehie, and Bae, Jong Sook. "On zeros and fixed points of multifunctions with non-compact convex domains." Commentationes Mathematicae Universitatis Carolinae 34.2 (1993): 257-264. <http://eudml.org/doc/247514>.

@article{Park1993,
abstract = {Using our own generalization [7] of J.C. Bellenger’s theorem [1] on the existence of maximizable u.s.cq̇uasiconcave 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].},
author = {Park, Sehie, Bae, Jong Sook},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {convex space; $c$-compact set; real Hausdorff topological vector space (t.v.s.); linear operator; locally convex; fixed point; coincidence; zero; upper hemicontinuous (u.h.c.) multifunction; coincidence; existence of maximizable u.s.c. quasiconcave functions on convex spaces; zeros for multifunctions with non-compact domains; upper hemicontinuous multifunctions; Ky Fan type fixed point theorems},
language = {eng},
number = {2},
pages = {257-264},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On zeros and fixed points of multifunctions with non-compact convex domains},
url = {http://eudml.org/doc/247514},
volume = {34},
year = {1993},
}

TY - JOUR
AU - Park, Sehie
AU - Bae, Jong Sook
TI - On zeros and fixed points of multifunctions with non-compact convex domains
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1993
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 34
IS - 2
SP - 257
EP - 264
AB - Using our own generalization [7] of J.C. Bellenger’s theorem [1] on the existence of maximizable u.s.cq̇uasiconcave 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].
LA - eng
KW - convex space; $c$-compact set; real Hausdorff topological vector space (t.v.s.); linear operator; locally convex; fixed point; coincidence; zero; upper hemicontinuous (u.h.c.) multifunction; coincidence; existence of maximizable u.s.c. quasiconcave functions on convex spaces; zeros for multifunctions with non-compact domains; upper hemicontinuous multifunctions; Ky Fan type fixed point theorems
UR - http://eudml.org/doc/247514
ER -

References

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  1. Bellenger J.C., Existence of maximizable quasiconcave functions on paracompact convex spaces, J. Math. Anal. Appl. 123 (1987), 333-338. (1987) Zbl0649.46006MR0883692
  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. (1990) Zbl0734.47028MR1070423
  3. Ky Fan, Some properties of convex sets related to fixed point theorems, Math. Ann. 266 (1984), 519-537. (1984) Zbl0515.47029MR0735533
  4. Jiang J., Fixed point theorems for paracompact convex sets, Acta Math. Sinica 4 (1988), 64-71. (1988) Zbl0715.54032MR0953351
  5. Kum S.H., Ph.D. Dissertation, Seoul National University, 1991, . 
  6. Lassonde M., On the use of KKM multifunctions in fixed point theory and related topics, J. Math. Anal. Appl. 97 (1983), 151-201. (1983) Zbl0527.47037MR0721236
  7. Park S., Bae J.S., Existence of maximizable quasiconcave functions on convex spaces, J. Korean Math. Soc. 28 (1991), 285-292. (1991) Zbl0756.47050MR1127833
  8. Park S., Applications of maximizable linear functionals on convex sets, ``Proc. in Honor of C. N. Lee'', 537-548, 1991. 
  9. Park S., Fixed point theory of multifunctions in topological vector spaces, J. Korean Math. Soc. 29 (1992), 191-208. (1992) Zbl0758.47048MR1157308
  10. Park S., Generalized matching theorems for closed coverings of convex sets, Numer. Funct. Anal. and Optimiz. 11 (1990), 101-110. (1990) Zbl0706.52001MR1058779
  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. MR0892795
  12. Simons S., On existence theorem for quasiconcave functions with applications, Nonlinear Anal. TMA 10 (1986), 1133-1152. (1986) MR0857745
  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. (1990) Zbl0745.47046MR1091369

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