Electronic Journal: Southwest Journal of Pure and Applied Mathematics Internet: http://rattler.cameron.edu/swjpam.html ISSN 1083-0464 Vol. No. 01, 1997, pp. 23–29. Submitted: March 15, 1997. Published: July 28, 1997.

A NEW CONVERGENCE THEOREM FOR STEFFENSEN’S

METHOD ON BANACH SPACES AND APPLICATIONS

Ioannis K. Argyros

Abstract. We provide sufficient conditions for the convergence of Steffensen’s method to a locally unique solution of a nonlinear operator equation on a Banach space. We use a fixed point theorem and a special choice of divided differences. Some applications of our results are also provided.

1991 A.M.S. (MOS) Subject Classification Codes. 65J15, 47H17, 49D15.

Key Words and Phrases. Steffensen’s method, fixed point theorem, Banach space, divided differences.

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Department of Mathematics, Cameron University, Lawton, OK 73505, U.S.A.

E-mail Address: ioannisa@cameron.edu

\begin{matrix}c \\ ◯ \end{matrix}1997 Cameron University