Quasi-Equilibrium Problems and Fixed Point Theorems of the Sum of l.s.c. and u.s.c. Mappings
Keywords:
Generalized quasi-equilibrium problem, quasi-equilibrium problem of type I, type II, mixed quasi-equilibrium problem, upper semi-continuous mapping, lower semi-continuous mapping, fixed point theorem.Abstract
Wefirst formulate generalized quasi-equilibrium 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 well-known 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 quasi-equilibrium problems of types I, II and mixed quasi-equilibrium problems of these two types.
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