Authors: Le, Huynh My Van; Nguyen, Van Hung (2014)
In this paper, we study the systems of generalized quasiequilibrium problems which includes as special cases the generalized vector quasi-equilibrium problems, vector quasiequilibrium problems, and establish the existence results for its solutions by using fixed-point theorem. Moreover, we also discuss the closedness of the solution sets of systems of generalized quasiequilibrium problems. As special cases, we also derive the existence results for vector quasiequilibrium problems and vector quasivariational inequality problems. Our results are new and improve recent existing ones in the literature.
Authors: Nguyen, Van Hung; Phan, Thanh Kieu (2013)
In this paper we establish sufficient conditions for the solution mappings of parametric generalized vector quasiequilibrium problems to have the stability properties such as lower semicontinuity, upper semicontinuity, Hausdorff lower semicontinuity, continuity, Hausdorff continuity and closedness. The results presented in the paper improve and extend the main results of Kimura-Yao [J. Global Optim. 138, (2008) 429-- 443], Kimura-Yao [Taiwanese J. Math., 12, (2008) 649--669] and Anh-Khanh [J. Math. Anal. Appl., 294, (2004) 699--711]. Some examples are given to illustrate our results.