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On the convergence of a higher order family of methods and its dynamics
In this paper, we present the study of the local convergence of a higher-order family of methods. Moreover, the dynamical behavior of this family of iterative methods applied to quadratic polynomials is studied. Some ...
Convergence of Newton's method under Vertgeim conditions: new extensions using restricted convergence domains
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 ...
Expanding the Applicability of a Third Order Newton-Type Method Free of Bilinear Operators
This paper is devoted to the semilocal convergence, using centered hypotheses, of a third order Newton-type method in a Banach space setting. The method is free of bilinear operators and then interesting for the solution ...
Extending the convergence domain of the Secant and Moser method in Banach Space
We present a new semilocal convergence analysis for the Secant and the Moser method in order to approximate a solution of an equation in a Banach space setting. Using the method of recurrent relations and weaker sufficient ...
Relaxed 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 the computation ...
The majorization method in the Kantorovich theory
The goal in this chapter is to present some improvements related to the convergence of Newton's and modified Newton's method by means of introducing and using the center Lipschitz condition. Using both conditions we obtain ...
Expanding the applicability of the Secant method under weaker conditions
We present a new semilocal convergence analysis for Secant method in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our analysis includes the computation of the bounds on ...
Comparing of the behaviour of iterative methods based on different means
Based on the modification of family of iterative processes of Chebyshev-Halley presented by M. Kansal et al. in [2], whose convergence is cubic, we will present in this talk a comparison between the behaviour of some members ...
Expanding the convergence domain for Chun-Stanica-Neta family of third order methods in banach spaces
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 ...
Enlarging the convergence domain of secant-like methods for equations
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 ...