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Another control condition in an iterative method for nonexpansive mappings

Published online by Cambridge University Press:  17 April 2009

Hong-Kun Xu
Hong-Kun Xu
Affiliation:
Department of Mathematics, University of Durban-Westville, Private Bag X54001, Durban 4000, South Africa, e-mail: hkxu@pixie.udw.ac.za
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Abstract

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We prove the convergence of an iterative method to a fixed point of a nonexpansive mapping in a uniformly smooth Banach space. We are able to relax one of the control conditions of P.L. Lions (1977).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 65 , Issue 1 , February 2002 , pp. 109 - 113
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Browder, F.E., ‘Convergence of approximants to fixed points of nonexpansive nonlinear mappings in Banach spaces’, Arch. Rational Mech. Anal. 24 (1967), 82–90.CrossRefGoogle Scholar
[2]Halpern, B., ‘Fixed points of nonexpanding maps’, Bull. Amer. Math. Soc. 73 (1967), 957–961.CrossRefGoogle Scholar
[3]Lions, P.L., ‘Approximation de points fixes de contractions’, C.R. Acad. Sci. Paris, Sér. A 284 (1977), 1357–1359.Google Scholar
[4]Reich, S., ‘Strong convergence theorems for resolvents of accretive operators in Banach spaces’, J. Math. Anal. Appl. 75 (1980), 287–292.CrossRefGoogle Scholar
[5]Reich, S., ‘Approximating fixed points of nonexpansive mappings’, Panamer. Math. J. 4 (1994), 23–28.Google Scholar
[6]Shioji, S. and Takahashi, W., ‘Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces’, Proc. Amer. Math. Soc. 125 (1997), 3641–3645.CrossRefGoogle Scholar
[7]Wittmann, R., ‘Approximation of fixed points of nonexpansive mappings’, Arch. Math. 58 (1992), 486–491.CrossRefGoogle Scholar