Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



An example on the Mann iteration method for Lipschitz pseudocontractions

Authors: C. E. Chidume and S. A. Mutangadura
Journal: Proc. Amer. Math. Soc. 129 (2001), 2359-2363
MSC (2000): Primary 47H09, 47J25
Published electronically: January 18, 2001
MathSciNet review: 1823919
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An example of a Lipschitz pseudocontractive map with a unique fixed point is constructed for which the Mann iteration sequence fails to converge. This resolves a long standing open problem.

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Additional Information

C. E. Chidume
Affiliation: The Abdus Salam International Centre for Theoretical Physics, 34100 Trieste, Italy

S. A. Mutangadura
Affiliation: Department of Physics, University of Zimbabwe, Harare, Zimbabwe

Received by editor(s): December 14, 1999
Published electronically: January 18, 2001
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2001 American Mathematical Society