Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 140530, 8 pages
Research Article

Mann Type Implicit Iteration Approximation for Multivalued Mappings in Banach Spaces

1Department of Mathematics, Xidian University, Xi'an 710071, China
2Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China

Received 16 March 2010; Accepted 5 July 2010

Academic Editor: Mohamed Amine Khamsi

Copyright © 2010 Huimin He et al. 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.


Let K be a nonempty compact convex subset of a uniformly convex Banach space E and let T be a multivalued nonexpansive mapping. For the implicit iterates x0K, xn=αnxn-1+(1-αn)yn, ynTxn, n1. We proved that {xn} converges strongly to a fixed point of T under some suitable conditions. Our results extended corresponding ones and revised a gap in the work of Panyanak (2007).