Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 824607, 9 pages
Generalized Mann Iterations for Approximating Fixed Points of a Family of Hemicontractions
1Department of Mathematics, University of Science and Technology of China, Hefei 230026, China
2School of Mathematical Sciences, Fudan University, Shanghai 200433, China
3Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China
Received 10 January 2008; Accepted 15 May 2008
Academic Editor: Hichem Ben-El-Mechaiekh
Copyright © 2008 Liang-Gen Hu 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.
This paper concerns common fixed points for a finite family of hemicontractions or a finite family of strict pseudocontractions on uniformly convex Banach spaces. By introducing a new iteration process with error term, we obtain sufficient and necessary conditions, as well as sufficient conditions, for the existence of a fixed
point. As one will see, we derive these strong convergence theorems in uniformly convex Banach spaces and without any requirement of the compactness on the domain of the mapping. The results given in this paper extend some previous theorems.