Fixed Point Theory and Applications 
Volume 2006 (2006), Article ID 10673, 20 pages
doi:10.1155/FPTA/2006/10673

Approximating fixed points of total asymptotically nonexpansive mappings

Ya. I. Alber,1 C. E. Chidume,2 and H. Zegeye2

 1Department of Mathematics, The Technion-Israel Institute of Technology, Haifa 32000, Israel
2The Abdus Salam International Centre for Theoretical Physics, Trieste 34014, Italy
Received 10 March 2005; Revised 7 August 2005; Accepted 28 August 2005

Abstract

We introduce a new class of asymptotically nonexpansive mappings and study approximating methods for finding their fixed points. We deal with the Krasnosel'skii-Mann-type iterative process. The strong and weak convergence results for self-mappings in normed spaces are presented. We also consider the asymptotically weakly contractive mappings.