New topological versions of the Fan-Browder fixed point theorem

We give several topological versions of the Fan-Browder fixed point theorem. In fact, we obtain a number of generalizations of the theorem for G-convex spaces and omega -connected spaces, and some variants for Phi -spaces and for complete LC-metric spaces. Several coincidence or fixed point theorems related to the theorem are given. One of our new theorems is applied to generalize the Fan intersection theorem and the Nash equilibrium theorem.