Electronic Journal: Southwest Journal of Pure and Applied Mathematics Internet: http://rattler.cameron.edu/swjpam.html ISSN 1083-0464 Vol. No. 02, 1996, pp. 42–47 Submitted: June 19, 1995. Published: September 25, 1996.

SUFFICIENT CONDITIONS FOR THE CONVERGENCE OF

ITERATIONS TO POINTS OF ATTRACTION IN BANACH SPACE

Ioannis K. Argyros

Abstract. In this study we provide weak sufficient conditions for the convergence of iterations to points of attraction in Banach space. Our results are used to show existence and uniqueness of solutions of nonlinear equations. We complete our study with an example that shows that our convergence results apply where earlier ones do not.

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

Key Words and Phrases. Banach space, points of attraction, nonlinear equation.

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Cameron University, Lawton, Oklahoma

E-mail Address: ioannisa@cameron.edu

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