Error bounds for generalized mixed weak vector quasiequilibrium problems via regularized gap functions

This paper introduces regularized gap functions for a class of generalized mixed weak vector quasiequilibrium problems. Then, error boundsfor the concerning problems via regularized gap functions are established. Someexamples are provided to illustrate the results.

On the existence of solutions for vector quasiequilibrium problems

In this paper, we establish some existence theorems for vector quasiequilibrium problems in real locally convex Hausdorff topological vector spaces by using Kakutani-Fan-Glicksberg fixed-point theorem. Moreover, we also discuss the closedness of the solution sets for these problems. The results presented in the paper are new and improve some main results in the literature.

Painleve-Kuratowski convergences of the approximate solution sets for vector quasiequilibrium problems

In this paper, we study vector quasiequilibrium problems. After that, the Painlev´e-Kuratowski upper convergence, lower convergence and convergence of the approximate solution sets for these problems are investigated by using a sequence of mappings ΓC -converging. As applications, we also consider the Painlev´e-Kuratowski upper convergence of the approximate solution sets in the special cases of variational inequality problems of the Minty type and Stampacchia type. The results presented in this paper extend and improve some main results in the literature.

Upper Semicontinuity of Solution Mappings to Parametric Generalized Vector Quasiequilibrium Problems

We establish the upper semicontinuity of solution mappings for a class of parametric generalized vector quasiequilibrium problems. As applications, we obtain the upper semicontinuity of solution mappings to several problems, such as parametric optimization problem, parametric saddle point problem, parametric Nash equilibria problem, parametric variational inequality, and parametric equilibrium problem.