Volume 11 Number 2 pp. 345-355 Quasi-equilibrium problems with lower and upper bounds in ordered topological spaces S. Al-Homidan and Q. H. Ansari Abstract In this paper, we consider quasi-equilibrium problem and implicit quasi-equilibrium problem with lower and upper bounds in the setting of ordered topological spaces. To prove the existence of their solutions, we establish a Fan-Browder type fixed point theorem and its equivalent maximal element theorem in the setting of ordered topological spaces. We introduce the concept of (α, β)-pseudodissipative maps. By using our maximal element theorem, we prove the existence of solutions of quasi-equilibrium problem with lower and upper bounds under (α, β)-pseudodissipative assumption. By using the selection of a multivalued map, we extend our results for implicit quasi-equilibrium problem for lower and upper bounds. Key words Mathematices Subject Classification Quasi-equilibrium problems, generalized implicit quasi-equilibrium problems, lower and upper bounds, ordered topological spaces, (α, β)-pseudodissipative maps, Fan-Browder type fixed point theorem, maximal element theoremm 49J40, 47J20, 47H06, 49J53 ONLINE SUBSCRIPTION (Institutional Subscription Only) Reference Copyright© 2010 Yokohama Publishers Back