A New Approach To the Solution of the Fredholm Integral Equation Via a Fixed Point on Extended <i>b</I>-metric Spaces

Abstract

It is very well known that real-life applications of fixed point theory are restricted with the transformation of the problem in the form of f(x) = x. (1) The Knaster-Tarski fixed point theorem underlies various approaches of checking the correctness of programs. (2) The Brouwer fixed point theorem is used to prove the existence of Nash equilibria in games. (3) Dlala et al. proposed a solution for magnetic field problems via the fixed point approach. In this paper, by obtaining the fixed point results in an extended b-metric space, we are able to consider real-life applications in a very general frame such as a simple and efficient solution for a Fredholm integral equation by using the technique of a fixed point in the consideration of a new abstract space: the extended b-metric space. Moreover, to address conceptual depth within this approach, we supply illustrative examples of usage where necessary.