TY - JOUR
A2 - Zhu, C.
A2 - Jung, J. S.
AU - Ali, Bashir
PY - 2011
DA - 2011/08/03
TI - Common Fixed Points Approximation for Asymptotically Nonexpansive Semigroup in Banach Spaces
SP - 684158
VL - 2011
AB - Let E be a real Banach space satisfying local uniform Opial's condition,whose duality map is weakly sequentially continuous. Let 𝒥:={T(t) t≥0} be a uniformly asymptotically regular family of asymptotically nonexpansivesemigroup of E with function k:[0,∞)→[0,∞). Let ℱ:=⋂t≥0F(T(t))≠∅ and f:E→E be weakly contractive map. Let G:E→E be δ-stronglyaccretive and λ-strictly pseudocontractive map with δ+λ>1. Let {tn} be an increasing sequence in [0,∞)and let{αn} and {βn} be sequences in [0,1] satisfying some conditions. For some positive real number γ appropriately chosen, let{xn} be a sequence defined by x0∈E, xn+1=βnxn+(1−βn)yn, yn=(I−αnG)T(tn)xn+αnγf(xn), n≥0. It is proved that {xn} converges strongly to a common fixed point q of thefamily 𝒥 which is also the unique solution of the variational inequality 〈(G−γf)q,j(q−x)〉≥0, for all x∈ℱ.
SN - null
UR - https://doi.org/10.5402/2011/684158
DO - 10.5402/2011/684158
JF - ISRN Mathematical Analysis
PB - International Scholarly Research Network
KW -
ER -