Extended convergence of jarratt type methods

Abstract

The aim of this article is the extension of the convergence of Jarratt type methods for solving equations with Banach space valued operators. We develop w-continuity conditions and only hypotheses on the first derivative contrasting earlier work where hypotheses of order higher than one are used on the derivatives. We also provide error estimates and uniqueness results on the solution based on Lipschitz type conditions not available before. This is how we extend the applicability of these methods. Numerical experiments complete this study. © Available free at mirror sites of http://www.math.nthu.edu.tw/?amen/.