Ioannis K. Argyros, Yeol Je Cho, Santhosh George Cameron University; University of Electronic Science and Technology of China; National Institute of Technology Karnataka
Abstract : In this paper, we present a local convergence analysis of a three point method with convergence order 1.839$\dots$ for approximating a locally unique solution of a nonlinear operator equation in setting of Banach spaces. Using weaker hypotheses than in earlier studies, we obtain: larger radius of convergence and more precise error estimates on the distances involved. Finally, numerical examples are used to show the advantages of the main results over earlier results.
Keywords : Banach space, three point method, divided difference of order one-two, radius of convergence, local convergence