Asymptotic stability of the solutions of the nonlinear volterra integral equations

In the first chapter of this work, consisting of four chapters, historical developments and usage areas of the integral equations are given.In the second chapter, some basic definitions and theorems are given to understand other chapters easily. Basic concepts such as linear space, metric space, normed space, topological space, continuous operator and compactness are given.In the third chapter, by defining the measure of noncompactness, Kuratowski measure of noncompactness and Hausdorff measure of noncompactness, which aredefined on any Banach space, are given. Moreover, the existence and the asymptotic stability of the solutions of the nonlinear Volterra integral equation is examined by using a fixed point theorem associated with the measure of noncompactness.In the fourth chapter, without using measure of noncompactness, suffcient conditions and some results about that the existence and asymptotic stability of the solution of the nonlinear Volterra integral equation, which are handled in thirdchapter, can also be obtained under weaker conditions than that of the third chapterare examined.