Expanding the Applicability of Some High Order Househölder-Like Methods

This paper is devoted to the semilocal convergence of a Househölder-like method for nonlinear equations. The method includes many of the studied third order iterative methods. In the present study, we use our new idea of restricted convergence domains leading to smaller γ-parameters, which in turn lead to the following advantages over earlier works (and under the same computational cost): larger convergence domain; tighter error bounds on the distances involved, and at least as precise information on the location of the solution.