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Strong Convergence Theorems for Semigroups of Asymptotically Nonexpansive Mappings in Banach Spaces.
- Source :
-
Abstract & Applied Analysis . 2013, p1-8. 8p. - Publication Year :
- 2013
-
Abstract
- Let X be a real reflexive Banach space with a weakly continuous duality mapping Jφ. Let C be a nonemptyweakly closed star-shaped (with respect to u) subset of X. Let F= {T(t) : t ∊ [0, + ∞)} be a uniformly continuous semigroup of asymptotically nonexpansive self-mappings of C, which is uniformly continuous at zero. We will showthat the implicit iteration scheme: yn = αnu+(1-αn)T(tn)yn, for all n ∊ N, converges strongly to a common fixed point of the semigroup F for some suitably chosen parameters {αn} and {tn}. Our results extend and improve corresponding ones of Suzuki (2002), Xu (2005), and Zegeye and Shahzad (2009). [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10853375
- Database :
- Academic Search Index
- Journal :
- Abstract & Applied Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 95426934
- Full Text :
- https://doi.org/10.1155/2013/202095