Western Kentucky University

Poster Title

Applications of the Banach Fixed Point Theorem

Institution

Western Kentucky University

Abstract

We investigated the application of the Banach fixed-point theorem, especially as it applied to initial value problems in differential equations. Many partial differential equations (PDE’s) model biological growth and could be reduced to ordinary differential equations (ODE’s) with time delay on a real Banach space. Other PDE’s are abstract and non-homogeneous. For any contraction operator on a Banach space, the Banach fixed-point theorem could be used to prove the existence and uniqueness of a solution to these equations.

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Applications of the Banach Fixed Point Theorem

We investigated the application of the Banach fixed-point theorem, especially as it applied to initial value problems in differential equations. Many partial differential equations (PDE’s) model biological growth and could be reduced to ordinary differential equations (ODE’s) with time delay on a real Banach space. Other PDE’s are abstract and non-homogeneous. For any contraction operator on a Banach space, the Banach fixed-point theorem could be used to prove the existence and uniqueness of a solution to these equations.