EXISTENTIAL RESULTS FOR THE QUASIEQUILIBRIUM PROBLEM WITHOUT USING MONOTONICITY

In this paper, using the KKM method, we present existence theorems for the quasiequilibrium problem (QEP) in topological vector spaces without using the monotonicity condition and locally solvability. We also obtain the condition that the solution set is compact. As an application of the main result, we apply the existence theorem of a solution for QEP, to establish an existence theorem for quasioptimization problem without considering differentiability of the mappings. Finally, by providing an example , shows that the main result is a real improvement of the main theorem given in [1].