On generalized vector equilibrium problems

摘要

An existence result for a generalized vector equilibrium problem is proved in a general topological vector space. As applications, existence results are derived for vector equilibrium problems and vector variational-like inequalities with set-valued mappings under Ψ-monotonicity condition and maximal Ψ-monotonicity condition. These results extend and unify a number of existence results for vector variational inequalities in the previous literature.