Semilocal convergence analysis of an efficient Steffensen-type fourth order method

In this study, the semilocal convergence of a Steffensen-type fourth order iterative method is analyzed to estimate the locally unique solutions of nonlinear systems in the Banach spaces. The sufficient conditions for the convergence of iterates are established under the assumptions of weaker Lipschitz continuity of the first order divided difference operators. The basic idea of the study is to develop the scalar majorizing sequences which are fundamental to provide the bounds on the proximity of successive iterates. Some numerical examples are provided to further validate the theoretical deductions.