Western Kentucky University
Applications of the Banach Fixed Point Theorem
Institution
Western Kentucky University
Faculty Advisor/ Mentor
Lan Nguyen
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.
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.