Bulletin of the Australian Mathematical Society

Research Article

A family of Chebyshev-Halley type methods in Banach spaces

J.M. Gutiérreza1 and M.A. Hernándeza1

a1 Dpt Matemáticas y Computación, Universidad de La Rioja, 26004 Logron¯o, Spain, e-mail: jmguti@siur.unirioja.es, mahernan@siur.unirioja.es

Abstract

A family of third-order iterative processes (that includes Chebyshev and Halley's methods) is studied in Banach spaces. Results on convergence and uniqueness of solution are given, as well as error estimates. This study allows us to compare the most famous third-order iterative processes.

(Received February 26 1996)