ON SOME GENERALIZED OPERATOR EQUILIBRIUM PROBLEMS

In this paper, we will introduce the generalized operator equlibrium problem and generalized operator quasi-equlibrium problem which generalize operator equlibrium problem due to Kazmi and Raouf into multi-valued and quasi-equlibrium problems. Using a Park's fixed point theorem, we will prove a new existence theorem on generalized operator equlibrium problem which serves as a basic existence theorem for various kinds of nonlinear problems.