The existence of solutions for the system of vector quasi-equilibrium problems in topological order spaces

AbstractThis paper introduces two kinds of quasiconcave mappings which are different from the usual quasiconcave function. We establish a result for the existence of solutions for the system of vector quasi-equilibrium problems in the frame of topological order, by providing a maximal elements version of the well known Browder fixed points theorem

The Existence and Stability of Solutions for Vector Quasiequilibrium Problems in Topological Order Spaces

In a topological sup-semilattice, we established a new existence result for vector quasiequilibrium problems. By the analysis of essential stabilities of maximal elements in a topological sup-semilattice, we prove that for solutions of each vector quasi-equilibrium problem, there exists a connected minimal essential set which can resist the perturbation of the vector quasi-equilibrium problem

Multiobjective variational problems and generalized vector variational-type inequalities

The purpose of this paper is to generalize the vector variational-type inequalities, formulated by Kim [J. Appl. Math. Comput. 16 (2004) 279–287], by setting the norms into Minty and Stampacchia forms. We also demonstrate the relationships between these generalized inequalities and multiobjective variational problems, by using the notions of strongly convex functionals. The theoretical developments are illustrated through numerical examples