The quasi-equilibrium inclusion problems of Blum–Oettli type are formulated and sufficient conditions on the existence of solutions are shown. As special cases, we obtain several results on the existence of solutions of general vector ideal (resp. proper, Pareto, weak) quasi-optimization problems, of quasivariational inequalities, and of quasivariational inclusion problems.
upper and lower quasivariational inclusions inclusions α-quasi-optimization problems vector optimization problem, quasi-equilibrium problems upper and lower C-quasiconvex multivalued mappings upper and lower C-continuous multivalued mappings
This is a preview of subscription content, log in to check access.
Blum, E., Oettli, W.: From optimization and student. 64, 1–23 (1993)Google Scholar
Fan, K.: A Minimax Inequality and Application. In: O. Shisha (Ed.) Inequalities III, Academic, New York, NY (pp. 33), (1972)Google Scholar
Gurraggio, A., Tan, N. X.: On general vector quasi-optimization problems. Math. Meth. Oper. Res. 55, 347–358 (2002)Google Scholar
Lin, L.J., Yu, Z. T., Kassay, G.: Existence of equilibria for monotone multivalued mappings and its applications to vectorial equilibria. J. Optim. Theory Appl. 114, 189–208 (2002)MathSciNetzbMATHGoogle Scholar
Luc, D.T.: Theory of vector optimization. Lect. Notes Eco. Math. Syst. 319, Springer-Verlag, (1989)Google Scholar
Luc, D.T., Tan, N.X.: Existence conditions in variational inclusions with constraints. Optimization 53 (5–6), 505–515 (2004)MathSciNetzbMATHGoogle Scholar
Minh, N.B., Tan, N.X.: Some sufficient conditions for the existence of equilibrium points concerning multivalued mappings. Vietnam. J. Math. 28, 295–310, (2000)zbMATHGoogle Scholar
Minh, N.B., Tan, N.X.: On the existence of solutions of quasivariational inclusion problems of Stampacchia type. Adv. Nonlinear Var. Inequal. 8, 1–16 (2005)MathSciNetzbMATHGoogle Scholar