Applications Of Banach Fixed Point Theorem To Differential Equations

Banach fixed point theorem states sufficient conditions for the existence and uniqueness of a fixed point (point that is mapped onto itself). The applications of Banach fixed point theorem to differential equations arise in connection with certain class functions called contractions. The theorem also provides a constructive procedure (called iteration) by which we can obtain better and better approximation to the solution of a problem and error bounds. In this project we apply the existence, uniqueness and iterative properties of the theorem to Differential Equations.

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