Hasan Parhodeh - Department of Mathematical, University of Qaemshahr Branch, Address, Iran,
Seyed Taghi Babazadeh - Department of Mathematical, University of Qaemshahr Branch, Address, Iran,

Discontinuous functions are important in many fields such as engineering, economic and game theory. In this study the fixed point theorem generalized for discontinuous functions. The existence of a fixed point is deter- mind when that any function from a non-empty polytope in the n-dimensional Euclidean space n into itself have locally gross direction preserving property. Then we use this quality to prove that there is a fixed point when the continuity condition is remove. Also, we ve been reviewed the application of fixed point theorem in game theories and especially the Nash equilibrium.

Fixed point, Discontinuites, Nash equilibrium, Game theory