Convergence of the modified Halley's method for multiple zeros under H?lder continuous derivative

摘要

In this paper, the estimate of the radius of the convergence ball of the modified Halley's method for finding multiple zeros of nonlinear equations is provided under the hypotheses that the derivative f~((m + 1)) of function f is H?lder continuous, and f~((m + 1)) is bounded. The uniqueness ball of solution is also established. Finally, some examples are provided to show applications of our theorem.