On Generalized Operator Mixed Vector Quasi-equilibrium Problem

In this paper, we study a new operator equilibrium problem which is a conjunction of two problems i.e., an operator vector quasi-equilibrium problem and an operator vector quasi-variational inequality problem. We call our problem as generalized operator mixed vector quasi-equilibrium problem. We prove some existence results for our problem in topological vector spaces by using 1-person game theorem and core of a set of operators. We do not use KKM-theory and generalized p-quasi convexity as used by other authors in related works. Some special cases of generalized operator mixed quasi-equilibrium problem are also discussed.