Electronic Journal: Southwest Journal of Pure and Applied Mathematics Internet: http://rattler.cameron.edu/swjpam.html ISSN 1083-0464 Vol. No. 02, 1997, pp. 16–19. Submitted: September 12, 1997. Published: December 30, 1997.

RELAXING CONVERGENCE CONDITIONS FOR THE JARRATT METHOD

M.A. Hernández and M.A. Salanova

Abstract. We establish a convergence theorem for the Jarratt method by using recurrence relations. The purpose of this note is to relax convergence conditions and give an example where our convergence theorem can be applied but not other ones.

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

Key Words and Phrases. Jarrat method, nonlinear equations in Banach spaces fourth-order method, recurrence relations.

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University of La Rioja, Department of Mathematics and Computation C/ Luis de Ulloa s/n, 26004, Logroño, Spain.

E-mail address: mahernan@siur.unirioja.es

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