Error analysis of a new transformation for multiple zeros finding free from derivative evaluations

In this paper, we present the error analysis of a new transformation for multiple zeros finding without calculating derivatives, which is a kind of version proposed in a recent paper of this journal, see [1]. We prove that the new derivative-free transformation could succeed in the maximum accuracy that is attainable at fixed precision of computation and preserves the order of convergence of the iteration method in the case of multiple zeros and show the advantage of this new transformation, compared with the other ones.