Lower Semicontinuity Results in Parametric Multivalued Weak Vector Equilibrium Problems and Applications

This article gives new sufficient conditions for the lower semicontinuity of the solution mapping of a parametric multivalued weak vector equilibrium problem with moving cones. A scalarizing approach, based on the signed distance function of Hiriart Urruty is used to discuss this lower semicontinuity property. The main results of the article are obtained under some assumptions different from those introduced earlier by previous linear and nonlinear scalarizing approaches. Some applications to the study of connectedness of weak solution sets of multivalued vector equilibrium problems are given.