BANACH'S FIXED POINT THEOREM ON THE EXISTENCE AND UNIQUENESS OF VOLTERRA INTEGRAL EQUATION SOLUTION
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Abstract
An integral equation is an inversion of a differential equation. Therefore, an integral equation can be seen as the solution of a differential equation with a given condition at an interval. So that through this integral equation, it can be ensured that the existence of a solution to the differential equation can be ascertained.
In this article, it is shown in a functional analysis how Banach's fixed-point theorem can show the existence and uniqueness of the solution of integral equations, so that it can guarantee the existence of the solution of a differential equation.
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