Numerical Approach to Fixed Point Theorems

Almost since L.E. Brouwer (1912) proved a remarkable result say- ing that any continuous function from the n-dimensional unit ball to itself has a fixed point, a point that is mapped by the function into itself. The Brouwer fixed point theorem was one of the early major achievements of algebraic topology. This celebrated theorem has been generalized in several ways. Nowadays, the Brouwer, Kakutani, and Tarski theorems have become the most often used tools in econom- ics, game theory and numerical analysis. In this paper, we give an elementary fixed point theorems and an algorithm to resolve the problem of fixed point theorems. Mathematics Subject Classification: Primary 47H10; Secondary 68W25