BANACH FIXED POINT THEOREM

Abstract

Banach fixed point theorem (contraction theorem) is a unique fixed point theorem on a mapping called the contraction of a complete metric space into it self. The space 𝑋 is said to be complete if every Cauchy sequence in 𝑋 converges. Banach fixed point theorem gives a sufficient condition for a function from a complete metric space to it self to have a unique fixed point. Application of banach fixed point theorem to guarantee the existence and uniqueness of the completion of first order linear differential equation. This completion can be solved easily and efficiently using the technique of iteration. Keywords : Fixed Point, Uniqueness, Contraction Mapping, Complete Metric Space.