On Unification of the Strong Convergence Theorems for a Finite Family of Total Asymptotically Nonexpansive Mappings in Banach Spaces
Joint Authors
Saburov, Mansoor
Mukhamedov, Farrukh
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-21, 21 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-05-16
Country of Publication
Egypt
No. of Pages
21
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Mukhamedov, Farrukh& 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،Vol. 2012, no. 2012, pp.1-21.
https://search.emarefa.net/detail/BIM-993106
Modern Language Association (MLA)
Mukhamedov, Farrukh& Saburov, Mansoor. On Unification of the Strong Convergence Theorems for a Finite Family of Total Asymptotically Nonexpansive Mappings in Banach Spaces. Journal of Applied Mathematics No. 2012 (2012), pp.1-21.
https://search.emarefa.net/detail/BIM-993106
American Medical Association (AMA)
Mukhamedov, Farrukh& Saburov, Mansoor. On Unification of the Strong Convergence Theorems for a Finite Family of Total Asymptotically Nonexpansive Mappings in Banach Spaces. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-21.
https://search.emarefa.net/detail/BIM-993106
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-993106