Convergence Analysis of the Modified Chebyshev’s Method for Finding Multiple Roots

In this paper, an estimate of the radius of convergence ball of the modified Chebyshev’s method for finding multiple roots of nonlinear equations is provided under the hypotheses that the ( m + 1)st derivative f ( m + 1) of function f is Hölder continuous and bounded. The unique ball of a solution is also established. Finally, some examples are provided to show the effectiveness of our results.