Generalized vector equilibrium problems on Hadamard manifolds

Abstract

In this paper, we study several types of Generalized Vector Equilibrium Problems (GVEP) on Hadamard manifolds. We prove sufficient conditions under which the solution set of (GVEP)'s is nonempty. As an application, we prove existence theorems for the system of generalized vector variational inequality problems and the system of generalized Pareto optimization problems.