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 ...

Using a "summable" dichotomy and fixed-point theorems, we prove the existence of convergent and bounded solutions of nonlinear difference systems. © 1998 Elsevier Science Ltd. All rights reserved.

By using weighted summable dichotomies and Schauder's fixed point theorem, we prove the existence of convergent solutions of linear functional difference equations. We apply our result to Volterra difference equations with ...

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 ...

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 a superlinearly convergent method to solve a constrained system of nonlinear equations. The proposed procedure is an adaptation of the linear-programming-Newton method replacing the first-order information with ...

We show that under certain conditions there is a one-to-one correspondence between weighted bounded solutions of a linear nonautonomous Volterra difference system with infinite delay and its perturbed system. Under additional ...

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 ...