Approximating fixed points of total asymptotically nonexpansive mappings

Alber, Ya. I.; Chidume, C. E.; Zegeye, H.

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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

Copyright © 2006 Ya. I. Alber 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.

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.