Existence of a solution for a Linear Integral Equation via the Fixed point Theorem

Abstract

This study investigates the existence of a solution for a linear integral equation using Banach's fixed point theorem. We provide a clear analytical framework that establishes the necessary conditions for the existence and uniqueness of the solution. The work highlights the effectiveness of fixed point methods in the context of linear integral equations and offers a theoretical basis for their resolution. Illustrative examples are included to facilitate the understanding of the main results and the conditions under which the theorem can be applied.