The Closeness Of Solution Sets And Second-order Optimality Conditions For Vector Equilibrium Problems

In the first part of this paper, it proves the closeness of solution sets for symmetric weak vector quasi-equilibrium problems, symmetric strong vector quasi-equilibrium problems and the generalized Ky Fan inequality problems with trifunctions satisfying certain conditions. It also proves the closeness of the set for strong saddle points for vector-valued functions; in the second part, by second-order epiderivatives,we present a few necessary and sufficient conditions for a weakly efficient solution, a Henig efficient solution, a globle efficient solution, an f-efficient solution, respectively, for the set-valued vector equilibrium problems without constraint(VEP). We also present a few necessary conditions for a weakly efficient solution, a Henig efficient solution, a global efficient solution, an f-efficient solution, respectively, for the vector set-valued vector equilibrium problems with constraints (VEPC).