Electronic Journal: Southwest Journal of Pure and Applied Mathematics Internet: http://rattler.cameron.edu/swjpam.html ISSN 1083-0464 Vol. No. 01, 1995, pp. 30-36. Submitted: May 12, 1995. Published: October 16, 1995.

RESULTS ON CONTROLLING THE RESIDUALS OF

PERTURBED NEWTON-LIKE METHODS ON BANACH

SPACES WITH A CONVERGENCE STRUCTURE

Ioannis K. Argyros

Abstract. In this study, we provide sufficient conditions for controlling the residuals of perturbed Newton-like methods, in such a way that the convergence of such methods is ensured. In order to achieve this, we apply a theorem due to Kantorovich on a setting of a regular space with a convergence structure.

(1991) A.M.S. (MOS) Subject Classification Codes. 65J15, 65B05, 47D15, 47H17, 49D15.

Key Words and Phrases. Newton-like methods, residuals.

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

E-mail Address: ioannisa@cua.cameron.edu

\begin{matrix}c \\ ◯ \end{matrix}1995 Cameron University