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Vietnam Journal of Mathematics 39:2 (2011) 191-215

Generalized Quasi-Equilibrium Problems of

Type II and Their Applications

Nguyen Xuan Tan¹ and Nguyen Thi Quynh Anh²

¹Institute of Mathematics, 18 Hoang Quoc Viet, 10307 Hanoi, Vietnam

²Department of basic sciences, Thai Nguyen university of information and

communication Technology, Thai Nguyen, Vietnam

Abstract. The generalized quasi-equilibrium problem of type II is formulated and some sufficient conditions on the existence of its solutions are shown. As special cases, we obtain several results on the existence of solutions to ideal quasivariational inclusion problems, quasivariational relation problems of type II, generalized quasi-KKM theorems, etc. As corollaries, we shall show several results on the existence of solutions to other problems in the vector optimization theory concerning multivalued mappings.

2000 Mathematics Subject Classification: 49J27, 49J53, 91B50, 90C48.

Keywords: Generalized quasi-equilibrium problems of type II, upper and lower quasivariational inclusions, quasi-optimization problems, upper and lower C-quasiconvex multivalued mappings, upper and lower C- continuous multivalued mappings.

Email: nxtan@math.ac.vn [Corresponding Author]

Established by Vietnam Academy of Science and Technology & Vietnam Mathematical Society

Published by Springer since January 2013