Vol. LXXIX, 1 (2010)
p. 77 - 88

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

M. Pacurar

Received: December 15, 2008;   Revised: April 27, 2009;   Accepted: May 7, 2009

Abstract.   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 difference equations.

Keywords:  fixed point approximation; k-step iteration procedure; Presic type contraction condition; Kannan type operator; rate of convergence; data dependence; nonlinear difference equation.  

AMS Subject classification: Primary:  47H10, 54H25.  

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Acta Mathematica Universitatis Comenianae
ISSN 0862-9544   (Printed edition)

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Comenius University
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