Generalized KKM theorem with applications to generalized minimax inequalities and generalized equilibrium problems

In this paper, a generalized version of the famous KKM theorem is obtained by using the concept of generalized KKM mappings introduced by Chang and Zhang [5]. 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.