%0 Journal Article %A Ramandeep Behl and Prashanth Maroju and S. S. Motsa %D 2016 %J International Journal of Mathematical and Computational Sciences %B World Academy of Science, Engineering and Technology %I Open Science Index 119, 2016 %T Semilocal Convergence of a Three Step Fifth Order Iterative Method under Höolder Continuity Condition in Banach Spaces %U https://publications.waset.org/pdf/10005715 %V 119 %X In this paper, we study the semilocal convergence of a fifth order iterative method using recurrence relation under the assumption that first order Fréchet derivative satisfies the Hölder condition. Also, we calculate the R-order of convergence and provide some a priori error bounds. Based on this, we give existence and uniqueness region of the solution for a nonlinear Hammerstein integral equation of the second kind. %P 574 - 578