
Minimax Theory and its Applications 03 (2018), No. 1, 057072 Copyright Heldermann Verlag 2018 QuasiEquilibrium Problems and Fixed Point Theorems of the Sum of l.s.c. and u.s.c. Mappings Nguyen Xuan Tan Institute of Mathematics, 18 Hoang Quoc Viet, 10307 Hanoi, Vietnam nxtan@math.ac.vn Nguyen Quynh Hoa Thai Nguyen University of Economics and Business Administration, Tan Thinh Ward, Thai Nguyen City, Vietnam hoakhcb@gmail.com Nguyen Ba Minh University of Commerce, Hanoi, Vietnam baminhnguyen@tmu.edu.vn We first formulate generalized quasiequilibrium problems concerning multivalued mappings and give some sufficient conditions to the existence of their solutions. In particular, we establish several results on the existence of fixed points of the sum of l.s.c. and u.s.c. mappings. These generalize some wellknown fixed point theorems obtained by previous authors as Ky Fan, F. E. Browder and Ky Fan, X. Wu, L. J. Lin, and Z. T. Yu, etc. Lastly, we apply the obtained results to quasiequilibrium problems of types I, II and mixed quasiequilibrium problems of these two types. Keywords: Generalized quasiequilibrium problems, quasiequilibrium problems of type I, type II, mixed equasiequilibrium problems, upper semicontinuous mapping, lower semicontinuous mapping, fixed point theorem. MSC: 49J27, 49J53, 91B50, 90C48 [ Fulltextpdf (121 KB)] for subscribers only. 