On unification of the strong convergence theorems for a finite family of total asymptotically nonexpansive mappings in banach spaces
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....
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Publishing Corporation
2012
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/24160/ http://irep.iium.edu.my/24160/ http://irep.iium.edu.my/24160/ http://irep.iium.edu.my/24160/1/mfms-JAM%282012%29.pdf |
| Summary: | 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. |
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