On Review of the Fundamental Banach Fixed Point Theorem and It’s Basic Application
Eziokwu C. Emmanuel
Department of Mathematics, Okpara University of Agriculture, Umudike, Abia State, Nigeria.
Okereke N. Roseline *
Department of Mathematics, Okpara University of Agriculture, Umudike, Abia State, Nigeria.
Nwosu Chidinma
Department of Mathematics, Okpara University of Agriculture, Umudike, Abia State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This review presents detailed work on the contraction mapping principle; it also discusses various forms of the result, presenting their simple proofs. The results reviewed include the intermediate value theorem, fixed-point theorem, Brouwer fixed point theorem and mainly Banach fixed point theorem (contraction mapping principle). Finally, some of the fundamental applications in matrices, theory of integral equations, Real Analysis and differential equations were discussed.
Keywords: Root differentiation in Moghania cultures, Metric space, Tissue culture study on lac host, fixed point, contraction principle, fredholm integral equation, ordinary differential equations