Application of fixed point theorems to Cauchy problem and integral equations

vAPPLICATION OF FIXED POINT THEOREMS TO CAUCHY PROBLEMAND INTEGRAL EQUATIONS(M.Sc. Thesis)Ahmet AKBULUTGAZ UNIVERSITYINSTITUTE OF SCIENCE AND TECHNOLOGYJanuary 2007ABSTRACTIn the first part of this thesis, the information about fixed point theory has beengiven. In the second part, some fundamental concepts and theorems which aregoing to be used in the following parts have been given. In the third part, theapproximation methods for solving the Cauchy problem have been examined.In the fourth part, with the help of Banach fixed point theorem, conditionsrequired for the solutions of integral equations to exist and be unique have beenexamined. In the final part, the existence of continuous solutions over compactintervals of nonlinear Fredholm and Volterra integral equations have beenexamined. Furthermore, particularly the uniqueness of continuous solutions ofnonlinear Volterra integral equations has been examined.Science Code : 204.1.132Key Words : Fixed point, Cauchy problem, Integral equationPage Number : 99Adviser : Doç. Dr. A. Duran TÜRKOĞLU