Strong convergence theorems for a semigroup of asymptotically nonexpansive mappings

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