Semicontinuity and closedness of parametric generalized lexicographic quasiequilibrium problems

Abstract

Abstract This paper is mainly concerned with the upper semicontinuity, closedness, and the lower semicontinuity of the set-valued solution mapping for a parametric lexicographic equilibrium problem where both two constraint maps and the objective bifunction depend on both the decision variable and the parameters. The sufficient conditions for the upper semicontinuity, closedness, and the lower semicontinuity of the solution map are established. Many examples are provided to ensure the essentialness of the imposed assumptions.

Keywords

• parametric generalized lexicographic quasiequilibrium problem
• upper semicontinuity
• closedness and lower semicontinuity