Convergence radius of Osada’s method under center-Hölder continuous condition

摘要

Recently, a new treatment based on Taylor’s expansion to give the estimate of the convergence radius of iterative method for multiple roots has been presented. It has been successfully applied to enlarge the estimate of the convergence radius of the modified Newton’s method for multiple roots. Using the similarly treatment, this paper investigates the convergence radius of the Osada’s method under the condition that the derivative f(m+1) of function f satisfies the center-Hölder continuous condition. By some examples, we show the treatment is simpler and efficient once again. The uniqueness ball of solution is also discussed.