We present a semilocal convergence analysis of a third order method for approximating a locally unique solution of an equation in a Banach space setting. Recently, this method was studied by Chun, Stanica. and Neta. These ...

We present new sufficient convergence criteria for the convergence of the secant-method to a locally unique solution of a nonlinear equation in a Banach space. Our idea uses Lipschitz and center Lipschitz instead of just ...

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 ...

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 the computation ...

We present a new technique to improve the convergence domain for Newton’s method both in the semilocal and local case. It turns out that with the new technique the sufficient convergence conditions for Newton’s method are ...

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 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 ...

We present two new semilocal convergence analyses for secant-like methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. These methods include the secant, Newton's ...

We present a new convergence analysis, for the secant method in order to approximate a locally unique solution of a nonlinear equation in a Banach space. Our idea uses Lipschitz and center-Lipschitz instead of just Lipschitz ...

In this paper, we present the study of the semilocal and local convergence of an optimal fourth-order family of methods. Moreover, the dynamical behavior of this family of iterative methods applied to quadratic polynomials ...