Generalized KKM theorem with applications to generalized minimax inequalities and generalized equilibrium problems. (English) Zbl 1121.49005

Summary: A generalized version of the famous KKM theorem is obtained by using the concept of generalized KKM mappings introduced by S. Chang and Y. Zhang [J. Math. Anal. Appl., No. 1, 208–223 (1991; Zbl 0739.47026)]. By employing our generalized KKM theorem, we obtain a generalized minimax inequality which includes several existing ones as special cases. Further, by applying our generalized minimax inequality we establish an existence result for the saddle-point problem under general setting. Finally, we also derive some existence results for generalized equilibrium problems and generalized variational inequalities.


49J30 Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
47H10 Fixed-point theorems
49J35 Existence of solutions for minimax problems


Zbl 0739.47026
Full Text: DOI