One of important topics in mathematics is investigation the extremum of a function , that has more important applications in many fields of science. From applicable overview , one of problems in this case is to get the answer for the extremum problem. Operation research , Control , Differential equation and analysis are fields that attention to this problem. Variational theory is these cases , that discussed with special conditions in analysis. We investigate one of these cases called "Borwein-Preiss variational principle" in this thesis , that has application in "Nash equilibrium point" that applicable in Game theory , and "Kuhn-Tucker Theorem" that applicable in Optimization.
