The existence of the solutions of the nonlinear volterra integral equations

The present thesis consists of four chapter. In the first chapter of this thesis, the information was given about the integral equations and discussed types of nonlinear Volterra integral equations previously. In the second chapter, some basic definitions and theorems were given to understand other chapters easily. Basic concepts such as linear space, normed space, topological space, continuous operator and compact set were given. It was also given information about measure of noncompactness. In the third and fourth chapter, the existence of the solution of the nonlinear Volterra integral equations which are different type in the classical Banach space C[0;T] that is consist of all real functions defined and continuous on the interval [0;T] were investigated by using the fixed point theorem. In doing so, the hypotheses about the source term, integral multiplier and kernel term which are defined as known functions of nonlinear Volterra integral equation has been created and the existence of the solution has been proof. Moreover, in this chapter, some applications were given to understand the results more clearly.