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A multi-step iterative method for approximating fixed points of Presic-Kannan operators

Author(s): M. Pacurar

Journal: Acta Mathematica Universitatis Comenianae
ISSN 0862-9544

Volume: LXXIX;
Issue: 1;
Start page: 77;
Date: 2010;
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Keywords: fixed point approximation | k-step iteration procedure | Presic type contraction condition | Kannan type operator | rate of convergence | data dependence | nonlinear difference equation

The convergence of a Presic type k-step iterative method for a new class of operators f : Xk ® X satisfying a general Presic type contraction condition is proved. Our result is completing an existing list of Presic type iteration methods, see [Rus I. A., An iterative method for the solution of the equation x = f(x, . . . ,x), Rev. Anal. Numer. Theor. Approx., 10(1) (1981), 95-100] and the recent [Ciric L. B., Presic S. B., On Presic type generalization of the Banach contraction mapping principle, Acta Math. Univ. Comenianae, 76(2) (2007), 143-147], having significant potential applications in the study of nonlinear differenceequations.
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