Existence and Uniqueness Analysis of Solutions in Integral Equations

Abstract

In this study, proofs of the existence and uniqueness of solutions in integral equations are presented. Based on the hypotheses given depending on the initial conditions and the properties of the equations, the existence of the solution has been demonstrated using Banach fixed point theorem and Lipschitz conditions. Again with the help of inequality techniques some qualitative behaviors of the solutions of the equation and limitation properties of the solutions were examined. With this evidence it has been observed that the contraction map in a complete space always has a fixed point.