Strong convergence theorems for a semigroup of asymptotically nonexpansive mappings

Let K be a nonempty closed convex subset of a real Banach space E. Let T:={T(t):t≥0} be a strongly continuous semigroup of asymptotically nonexpansive mappings from K into K with a sequence {Lt}∪[1,∞). Suppose F(T)≠Ø. Then, for a given uεK there exists a sequence {un}∪K such that un=(1-αn)1tn∫0tnT(s)unds+αnu, for nεN, where tnεR+, {αn}∪(0,1) and {Lt} satisfy certain conditions. Suppose, in addition, that E is reflexive strictly convex with a Gâteaux differentiable norm. Then, the sequence {un} converges strongly to a point of F(T). Furthermore, an explicit sequence {xn} which converges strongly to a fixed point of T is proved.