Dynamics of a higher-order family of iterative methods

New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence

Dynamics of a family of third-order iterative methods that do not require using second derivatives

The purpose of this article is to present results that amount to a description of the conjugacy classes of three third–order root–finding iterative methods that do not require the use of second derivatives for their formulation, for complex polynomials of degrees two, three and four. For degrees two and three, a full description of the conjugacy classes is accomplished, in each case, by a one–p...

A Family of Iterative Methods with Accelerated Eighth-Order Convergence

We propose a family of eighth-order iterative methods without memory for solving nonlinear equations. The new iterative methods are developed by using weight function method and using an approximation for the last derivative, which reduces the required number of functional evaluations per step. Their efficiency indices are all found to be 1.682. Several examples allow us to compare our algorith...

On the convergence of a higher order family of methods and its dynamics

where F is a differentiable function defined on a convex subset D of S with values in S, where S is R or C. using Mathematical Modelling. Except in special cases, the solutions of these equations can be found in closed form. This is the main reason why the most commonly used solution methods are usually iterative. In this work, we study the local convergence and the dynamics of the following op...

Iterative methods for finding nearest common fixed points of a countable family of quasi-Lipschitzian mappings

We prove a strong convergence result for a sequence generated by Halpern's type iteration for approximating a common fixed point of a countable family of quasi-Lipschitzian mappings in a real Hilbert space. Consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...