Abstract
There are very few papers that talk about the global convergence of iterative methods with the help of Banach spaces. The main purpose of this paper is to discuss the global convergence of third order iterative method. The convergence analysis of this method is proposed under the assumptions that Frechet derivative of first order satisfies continuity condition of the Holder. Finally, we consider some integral equation and boundary value problem (BVP) in order to illustrate the suitability of theoretical results.