TY - JOUR
A2 - Ansari, Qamrul Hasan
AU - Sahu, D. R.
AU - Wong, Ngai-Ching
AU - Yao, Jen-Chih
PY - 2013
DA - 2013/04/23
TI - Strong Convergence Theorems for Semigroups of Asymptotically Nonexpansive Mappings in Banach Spaces
SP - 202095
VL - 2013
AB - Let X be a real reflexive Banach space with a weakly continuous duality mapping Jφ. Let C be a nonempty weakly 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 show that 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).
SN - 1085-3375
UR - https://doi.org/10.1155/2013/202095
DO - 10.1155/2013/202095
JF - Abstract and Applied Analysis
PB - Hindawi Publishing Corporation
KW -
ER -