Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
843326 | Nonlinear Analysis: Theory, Methods & Applications | 2009 | 8 Pages |
Abstract
Let K be a nonempty closed convex subset of a real Banach space E. Let Tâ{T(t):tâR+} be a strongly continuous semi-group of asymptotically nonexpansive mappings from K into K with a sequence {Lt}â[1,â). Suppose F(T)â 0̸. Then, for a given u0âK and tn>0 there exists a sequence {un}âK such that un=(1âαn)T(tn)un+αnu0, for nâN such that {αn}â(0,1) and Ltnâ1<αn, where tnâR+. Suppose, in addition, that E is reflexive strictly convex with a uniformly Gâteaux differentiable norm and that limnââtn=â, limnââαn=limnââLtnâ1αn=0. Then the sequence {un} converges strongly to a point of F(T). Moreover, it is proved that an explicit sequence {xn} generated from x1âK by xn+1âαnu+(1âαn)T(tn)xn, nâ¥1, converges to a fixed point of T.
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Authors
Habtu Zegeye, Naseer Shahzad,