We first present a local convergence analysis for some families of fourth and six order methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Earlier studies have used ...

Under the hypotheses that a function and its Frechet derivative satisfy some generalized Newton-Mysovskii conditions, precise estimates on the radii of the convergence balls of Newton's method, and of the uniqueness ball ...

There is a need to extend the convergence domain of iterative methods for computing a locally unique solution of Banach space valued operator equations. This is because the domain is small in general, limiting the applicability ...

In this paper, we present the local results of the convergence of the two-step King-like method to approximate the solution of nonlinear equations. In this study, we only apply conditions to the first derivative, because ...

The aim of this paper is to present a new semi-local convergence analysis for Newton's method in a Banach space setting. The novelty of this paper is that by using more precise Lipschitz constants than in earlier studies ...

The study of the dynamics and the analysis of local convergence of an iterative method, when approximating a locally unique solution of a nonlinear equation, is presented in this article. We obtain convergence using a ...

In this work we are going to use the Kurchatov–Schmidt–Schwetlick-like solver (KSSLS) and the Kurchatov-like solver (KLS) to locate a zero, denoted by x∗ of operator F. We define F as F:D⊆B1⟶B2 where B1 and B2 stand for ...

We present the local convergence analysis and the study of the dynamics of a higher order iterative method in order to approximate a locally unique solution of multiplicity greater than one of a nonlinear equation. The ...

In this article, we propose a new research related to the convergence of the frozen Potra and Schmidt-Schwetlick schemes when we apply to equations. The purpose of this study is to introduce a comparison between two solutions ...

The convergence is developed for a large class of Chebyshev-two point-like methods for solving Banach space valued equations. Both the local as well as the semi-local convergence is provided for these methods under general ...