On the orbits of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>G</mml:mi></mml:math>-closure points of ultimately nonexpansive mappings

Kiang, Mo Tak

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Fixed Point Theory and Applications
Volume 2006 (2006), Article ID 96737, 4 pages
doi:10.1155/FPTA/2006/96737

On the orbits of G-closure points of ultimately nonexpansive mappings

Mo Tak Kiang

Department of Mathematics and Computing Science, Saint Mary's University, Halifax B3H 3C3, Nova Scotia, Canada

Received 24 March 2006; Accepted 12 April 2006

Copyright © 2006 Mo Tak Kiang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let X be a closed subset of a Banach space and G an ultimately nonexpansive commutative semigroup of continuous selfmappings. If the G-closure of X is nonempty, then the closure of the orbit of any G-closure point is a commutative topological group.