By applying the technique of continuous partition of unity and Tychonoff’s fixed point theorem, some new collectively fixed point theorems for a family of set_valued mappings defined on the product space of noncompact G_convex spaces are proved. As applications, some nonempty intersetion theorems of Ky Fan type for a family of subsets of the product space of G_convex spaces are proved; An existence theorem of solutions for a system of nonlinear inequalities is given in G_convex spaces and some equilibrium existence theorems of abstract economies are also obtained in G_convex spaces. Our theorems improve, unify and generalized many important known results in recent literature.
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