General KKM theorem with applications to minimax and variational inequalities

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 empl oying our general KKM theorem, we obtain a general minimax inequality which contains several existing ones as special cases. As applications of our ge neral minimax inequality, we derive an existence result for saddle-point pr oblems under general setting. We also establish several existence results f or generalized variation inequalities and generalized quasi-variational ine qualities.