Existence Of Solutions Of Weak Set-valued Equilibrium Problems And Higher-order Error Bound For Difference Of Two Functions

In this paper,we mainly study the existence of solutions of weak set-valued equi-librium problems and the high-order error bounds of difference functions in real Banach spaces.Firstly,using the Fan-Glicksberg-Kakutani theorem,we obtain sufficient condi-tions for the existence of solution of weak set-valued equilibrium problems.Secondly,using the techniques of nonsmooth analysis,we obtain some necessary conditions and sufficient conditions for the existence of higher-order error bounds of difference functions with set constraints.