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Ball convergence theorems and the convergence planes of an iterative method for nonlinear equations
We study the local convergence of a method presented by Cordero et al. of convergence order at least five to approximate a locally unique solution of a nonlinear equation. These studies show the convergence under hypotheses ...
Ball comparison between frozen Potra and Schmidt-Schwetlick schemes with dynamical analysis
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 ...
Ball convergence for Steffensen-type fourth-order methods
We present a local convergence analysis for a family of Steffensen-type fourth-order methods in order to approximate a solution of a nonlinear equation. We use hypotheses up to the first derivative in contrast to earlier ...
Ball convergence of a sixth-order Newton-like method based on means under weak conditions
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 ...
Local convergence of fourth and fifth order parametric family of iterative methods in Banach spaces
This paper deal with the study of local convergence of fourth and fifth order iterative method for solving nonlinear equations in Banach spaces. Only the premise that the first order Frechet derivative fulfills the Lipschitz ...
Local convergence for multi-point-parametric Chebyshev–Halley-type methods of high
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 unified convergence analysis for secant-type methods
We present a unified local and semilocal convergence analysis for secant-type methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our analysis includes he computation ...
Study of a high order family: Local convergence and dynamics
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 ...
Local Convergence for an Improved Jarratt-type Method in Banach Space
We present a local convergence analysis for an improved Jarratt-type methods of order at least five to approximate a solution of a nonlinear equation in a Banach space setting. The convergence ball and error estimates are ...
Unified local convergence for newton's method and uniqueness of the solution of equations under generalized conditions in a Banach space
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 ...