We present a local convergence analysis of a derivative free fourth order method with one parameter based on rational interpolation in order to approximate a locally unique root of a function. The method is optimal in the ...

We present the local convergence analysis and the study of the dynamics of a two-step Newton-like method in order to approximate a locally unique solution of multiplicity one of a nonlinear equation.

We study the local convergence of Chebyshev–Halley methods with six and eight order of convergence to approximate a locally unique solution of a nonlinear equation. In Sharma (2015) (see Theorem 1, p. 121) the convergence ...

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 ...

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 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 are interested to justified two typical hypotheses that appear in the convergence analysis, |λ|≤2|λ|≤2 and z0z0 sufficient close to z∗z∗ . In order to proof these ideas, the dynamics of a damped ...

We present a semi-local convergence analysis of Newton's method in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Using center-Lipschitz condition on the first and the ...