Monotonic solutions of nonlinear quadratic volterra integral equations

In the first chapter of this work which consists of four chapters, historical development of integral equations were given.In the second chapter, some definitions and theorems were given to understand following chapters more easily.In the third chapter, a measure of noncompactness which is used for solutions of integral equations was identified. In addition, two measures of noncompactness, Kuratowski and Hausdorff, were introduced. Differences and relations between these measures were also investigated.In the last chapter, nonlinear quadratic Volterra integral equations were studied. Moreover, the existence and monotony of solutions of nonlinear quadratic Volterra integral equations in the classical Banach space C[0,M] consisting of all real functions defined and continuous on the interval [0,M] were investigated by using of the fixed point theorem and measure of noncompactness. Furthermore, in this chapter, some applications were given to understand results more clearly.