On the Rall Contration Mapping Principle of the Fixed Point Theory with Application to Some Integral Equations
Eziokwu, C. Emmanuel *
Departments of Mathematics, College of Physical and Applied Science, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria.
Nnubia, Agatha
Departments of Mathematics, Facaulty of Physical Sciences, Nnamdi Azikiwe University, Awka, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
The contraction map as the basis of fixed point theory here was extensively studied as a map in a complete metric space that leads to successive approximations called iterations. Precisely, considered in this work, are the Banach and Rall contraction mapping principles. Convergence of the basic fixed point iteration based on these two theorems was as well explored. Finally, application of the said contraction mapping principle was made on the theory of Integral Equations and Non-linear Integral Equations of Radioactive Transfer.
Keywords: Contraction, fixed point convergence, integral equations, radioactive transfer