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

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....

Full description

Bibliographic Details
Main Authors: Mukhamedov, Farrukh, Saburov, Mansoor
Format: Article
Language:English
Published: Hindawi Publishing Corporation 2012
Subjects:
QA Mathematics
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
id iium-24160
recordtype eprints
spelling iium-241602012-12-28T06:28:51Z http://irep.iium.edu.my/24160/ On unification of the strong convergence theorems for a finite family of total asymptotically nonexpansive mappings in banach spaces Mukhamedov, Farrukh Saburov, Mansoor QA Mathematics 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. Hindawi Publishing Corporation 2012 Article PeerReviewed application/pdf en http://irep.iium.edu.my/24160/1/mfms-JAM%282012%29.pdf 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 http://www.hindawi.com/journals/jam/2012/281383/ 10.1155/2012/281383
repository_type Digital Repository
institution_category Local University
institution International Islamic University Malaysia
building IIUM Repository
collection Online Access
language English
topic QA Mathematics
spellingShingle QA Mathematics
Mukhamedov, Farrukh
Saburov, Mansoor
On unification of the strong convergence theorems for a finite family of total asymptotically nonexpansive mappings in banach spaces
description 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.
format Article
author Mukhamedov, Farrukh
Saburov, Mansoor
author_facet Mukhamedov, Farrukh
Saburov, Mansoor
author_sort Mukhamedov, Farrukh
title On unification of the strong convergence theorems for a finite family of total asymptotically nonexpansive mappings in banach spaces
title_short On unification of the strong convergence theorems for a finite family of total asymptotically nonexpansive mappings in banach spaces
title_full On unification of the strong convergence theorems for a finite family of total asymptotically nonexpansive mappings in banach spaces
title_fullStr On unification of the strong convergence theorems for a finite family of total asymptotically nonexpansive mappings in banach spaces
title_full_unstemmed On unification of the strong convergence theorems for a finite family of total asymptotically nonexpansive mappings in banach spaces
title_sort on unification of the strong convergence theorems for a finite family of total asymptotically nonexpansive mappings in banach spaces
publisher Hindawi Publishing Corporation
publishDate 2012
url 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
first_indexed 2023-09-18T20:36:18Z
last_indexed 2023-09-18T20:36:18Z
_version_ 1777409068506284032

Similar Items