On unification of the strong convergence theorems for a finite family of total asymptotically nonexpansive mappings in banach spaces

Mukhamedov, Farrukh and Saburov, Mansoor (2012) On unification of the strong convergence theorems for a finite family of total asymptotically nonexpansive mappings in banach spaces. Journal of Applied Mathematics, 2012. 281383 (1)-281383 (21). ISSN 1110-757X

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Abstract

We unify all known iterative methods by introducing a new explicit iterative scheme for approximation of common fixed points of finite families of total asymptotically I-nonexpansive mappings. Note that such a scheme contains a particular case of the method introduced by �C. E. Chidume and E. U. Ofoedu, 2009�. We construct examples of total asymptotically nonexpansive mappings which are not asymptotically nonexpansive. Note that no such kind of examples were known in the literature. We prove the strong convergence theorems for such iterative process to a common fixed point of the finite family of total asymptotically I-nonexpansive and total asymptotically nonexpansive mappings, defined on a nonempty closed-convex subset of uniformly convex Banach spaces. Moreover, our results extend and unify all known results.

Item Type:	Article (Journal)
Additional Information:	5537/24160
Uncontrolled Keywords:	asymptotically nonexpansive, banach spaces
Subjects:	Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User:	Dr. Farrukh Mukhamedov
Date Deposited:	11 Jun 2012 15:11
Last Modified:	28 Dec 2012 14:28
URI:	http://irep.iium.edu.my/id/eprint/24160

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