In this paper, we deal with the study of convergence analysis of modified parameter based family of second derivative free continuation method for solving nonlinear equations. We obtain the order of convergence is at least ...

The principle aim of this manuscript is to propose a general scheme that can be applied to any optimal iteration function of order eight whose first substep employ Newton’s method to further develop new interesting optimal ...

We study the local convergence of a Newton-like method of convergence order six to approximate a locally unique solution of a nonlinear equation. Earlier studies show convergence under hypotheses on the seventh derivative ...

In this paper, we propose a center Lipschitz condition for the second Frechet derivative together with the use of restricted domains in order to improve the domain of starting points for Newton's method. In addition, we ...

We analyze the semilocal convergence of Newton's method under a center Lipschitz condition for the second derivative of the operator involved different from that used by other authors until now. In particular, we propose ...

A generic family of sixth-order modified Newton-like multiple-zero finders have been proposed in Geum et al. (2016). Among them we select a specific family of iterative methods with uniparametric bivariate polynomial weight ...