Summary: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS: Vol. 104, No. 1, pp. 41­57, JANUARY 2000
General KKM Theorem with Applications to
Minimax and Variational Inequalities1
Q. H. ANSARI,2
Y. C. LIN,3
AND J. C. YAO
4
Communicated by F. Giannessi
Abstract. In this paper, a general version of the KKM theorem is
derived by using the concept of generalized KKM mappings introduced
by Chang and Zhang. By employing our general KKM theorem, we
obtain a general minimax inequality which contains several existing
ones as special cases. As applications of our general minimax inequality,
we derive an existence result for saddle-point problems under general
setting. We also establish several existence results for generalized vari-
ation inequalities and generalized quasi-variational inequalities.
Key Words. Generalized KKM mappings, transfer closed-valued map-
pings, -transfer lower semi-continuous functions, minimax inequalit-
ies, generalized variational inequalities, generalized quasi-variational
inequalities.

Source: Ansari, Qamrul Hasan - Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals

Collections: Mathematics