PENALTY METHOD FOR SET-VALUED QUASI-EQUILIBRIUM PROBLEMS.

The purpose of this paper is to investigate the existence of solutions of set-valued quasiequilibrium problems in real Banach spaces. We introduce a concept of Brezis pseudomonotonicity for set-valued mappings. By constructing appropriate constraint conditions for the weak coercive function and the objective mapping, we obtain a solution-existence result for usual set-valued equilibrium problems. By a sequence of penalized set-valued equilibrium problems, we obtain a solution-existence result for set-valued quasi-equilibrium problems. These results do not require the assumption of compactness of the constraint set, and improve the corresponding ones in the literature. [ABSTRACT FROM AUTHOR]