zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On some equilibrium problems for multimaps. (English) Zbl 0990.49003
Summary: In this paper, we first establish the continuity property for multimaps and generalized Berge’s theorem for multimaps. Then we apply these results, and the Fan-Browder fixed point theorem, to establish the existence theorems of quasi-equilibrium problems and generalized quasi-equilibrium problems for multimaps.

49J35Minimax problems (existence)
90C47Minimax problems
49J40Variational methods including variational inequalities
49J53Set-valued and variational analysis
Full Text: DOI
[1] Aubin, J. P.; Cellina, A.: Differential inclusion. (1994)
[2] Blum, E.; Oettli, W.: From optimization and variational inequalities to equilibrium problems. Math. students 63, 123-145 (1994) · Zbl 0888.49007
[3] Browder, F. E.: The fixed point theory of multi-valued mapping in topological vector space. Math. ann. 177, 283-301 (1968) · Zbl 0176.45204
[4] Chang, S. S.; Lee, G. M.; Lee, B. S.: Vector quasi-inequalities for fuzzy mappings I. Fuzzy sets and systems 87, 307-315 (1997) · Zbl 0923.47037
[5] Chang, T. H.; Yen, C. L.: KKM properties and fixed point theorems. J. math. Anal. appl. 203, 224-235 (1996) · Zbl 0883.47067
[6] Hadžić, O.: Fixed point theory in topological vector spaces. (1984) · Zbl 0576.47030
[7] Horvath, C. D.: Contractibility and generalized convexity. J. math. Anal. appl. 156, 341-351 (1991) · Zbl 0733.54011
[8] Klee, V.: Leray-Schauder theory without local convexity. Math. ann. 141, 286-297 (1960) · Zbl 0096.08001
[9] J.E. Klein, A. Thompson, Theory of Correspondence, Wiley, 1984.
[10] B.S. Lee, G.M. Lee, S.S. Chang, Generalized vector variational inequalities for multifunctions, Proceedings of Workshop on Fixed Point Theory, June 1997, Poland. · Zbl 1012.47050
[11] Lin, L. J.; Yu, Z. T.: Fixed point theorems of KKM type maps. Nonlinear anal. TMA 38, 265-275 (1999) · Zbl 0947.47047
[12] Lin, L. J.: On generalized loose saddle point theorems for set valued maps, Proceedings of nonlinear analysis and convex analysis. (1999)
[13] Luc, D. T.: Theory of vector optimization, lecture notes in economics and mathematical, systems, vol. 319. (1989)
[14] S. Park, Fixed points and quasi-equilibrium problems, Math. Comput. Modelling, to appear. · Zbl 0983.47038
[15] Jan, K. K.; Yu, J.; Yuan, X. Z.: Existence theorems for saddle points of vector-valued maps. J. optim. Theory appl. 89, 731-747 (1996) · Zbl 0849.49009
[16] Tanaka, T.: Generalized quasiconvexities, cone saddle points and minimax theorems for vector valued functions. J. optim. Theory appl. 81, 355-377 (1994) · Zbl 0826.90102
[17] Weber, H.: Compact convex sets in non-locally convex linear spaces. Note math. 12, 271-289 (1992) · Zbl 0846.46004