Collectively fixed point theorem and abstract economy in G-convex spaces

A new continuous selection theorem is first proved in noncompact G-convex spaces. By using the continuous selection theorem, a collectively fixed point theorem is obtained in noncompact G-convex spaces which truly generalizes Tarafdar's results to noncompact G-convex spaces. Finally, the collectively fixed point theorem is applied to generalize some known section theorem and to prove the existence of equilibrium points for abstract economies and qualiative games in which the commodity spaces are noncompact G-convex spaces and the set of agents may be infinite.