Convergence Radius of Osada’s Method for Multiple Roots under Hölder and Center—Hölder Continuous Conditions

Abstract

In recent years, some high—order iterative methods for finding multiple roots of nonlinear equations are presented. However, almost none of these methods give the information for the convergence radius. Recently, H. M. Ren and I. K. Argyros give an estimate of the convergence radius of the modified Newton’s method for multiple roots under Hölder and center—Hölder continuous conditions. In this paper, we estimate the convergence radius of Osada’s method for multiple roots under the same conditions. Also, some examples are provided to show applications of our theorems.