Fixed Point Theory and Applications
Volume 2006 (2006), Issue 1, Pages Article 10673, 20 p.
doi:10.1155/FPTA/2006/10673
Approximating fixed points of total asymptotically nonexpansive mappings
Ya.I. Alber1
, C.E. Chidume2
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
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.