Existence theorems for solutions of some nonlinear integral equations

In the fi rst chapter of this thesis consisting of five chapters, de finition, usage areas, classifi cation of integral equations and general information about studies carried out in this area are given. In the second chapter, some basic de nitions and theorems used in later chapters are given. In the third chapter, in space C[a,b], an existence theorem for solutions of a class of nonlinear integral equations is presented with its proof. In the fourth chapter, in space BC(R+), the class of integral equations considered in the third chapter is examined and the solvability of this equation is discussed under some suffi cient conditions. Also, some results about of properties of the solutions are given. Furthermore the some relations between this equation and some previous equations are explained with some examples. In the last chapter, in Banach algebras C[a,b] and BC(R+), a class of integral equations is handled and some su fficient conditions which guarantee that this class has at least one asymptotically stable solution are given.