Convergence analysis of Newton-type fixed point iteration methods

In this thesis, firstly a new iterative method called modified SP iterative method is introduced and it is compared that the convergence of this iteration with the other iterations in literature for contraction mappings in normed spaces. Then, this iteration and normal S-iteration is regenerated as form of Newton-like method and convergence theorems are demonstrated for nonlinear equations. Moreover, applications to initial value problems and boundary value problems of this methods are included and using iterative methods in this work, polynomiographies are obtained for different complex polynomial equations. Finally, it is proved that convergence theorems for continuous mappings on an arbitrary interval.