EXISTENCE OF SOLUTIONS FOR THE SYSTEM OF VECTOR QUASIEQUILIBRIUM PROBLEMS

Tóm tắt

In this paper, we study the systems of generalized multivalued strong vector quasiequilibrium problem (in short (SQVEP)) real locally convex Hausdorff topological vector spaces. This problem includes as special cases the generalized strong vector quasi-equilibrium problems, quasi-equilibrium problems, equilibrium problems and variational inequality problems. Then, we establish an existence theorem for its solutions by using fixed-point theorem. Moreover, we also discuss the closedness of the solution set for (SQVEP). The results presented in the paper improve and extend the main results of Long et al [Math. Comput. Model,47 445--451 (2008)] and Plubtieng - Sitthithakerngkietet [Fixed Point Theory Appl. doi:10.1155/2011/475121 (2011)].