We present a new semilocal convergence analysis for Newton-like methods using restricted convergence domains in a Banach space setting. The main goal of this study is to expand the applicability of these methods in cases ...

We present new sufficient convergence conditions for the semilocal convergence of Newton’s method to a locally unique solution of a nonlinear equation in a Banach space. We use Hölder and center Hölder conditions, instead ...

We present a local convergence analysis for general multi-point-Chebyshev-Halley-type methods (MMCHTM) of high convergence order in order to approximate a solution of an equation in a Banach space setting. MMCHTM includes ...

A class of two-point quartic-order simple-zero finders and their dynamics are investigated in this paper by extending King’s fourth-order family of methods. With the introduction of an error corrector having a weight ...

A one-parametric family of fourth-order iterative methods for solving nonlinear systems is presented, proving the fourth-order of convergence of all members in this family, except one of them whose order is five. The methods ...

We present a new semilocal convergence analysis for Newton-like methods in order to approximate a locally unique solution of an equation in a Banach space setting. This way, we expand the applicability of these methods in ...

First, it is attempted to derive an optimal derivative-free Steffensen-King's type family without memory for computing a simple zero of a nonlinear function with efficiency index 4(1/3) approximate to 1.587. Next, since ...

In this paper, we study the stability of the rational function associated to a known family of eighth-order iterative schemes on quadratic polynomials. The asymptotic behavior of the fixed points corresponding to the ...

We present new semilocal and local convergence results for the Newton–Kantorovich method. These new results extend the applicability of the Newton–Kantorovich method on approximate zeros by improving the convergence domain ...

Traub’s method is a tough competitor of Newton’s scheme for solving nonlinear equations as well as nonlinear systems. Due to its third-order convergence and its low computational cost, it is a good procedure to be applied ...