Strong convergence theorems for nonexpansive semigroup in Banach spaces

Let K be a nonempty closed convex subset of a reflexive and strictly convex Banach space E   with a uniformly Gâteaux differentiable norm, and F={T(t):t>0} a nonexpansive self-mappings semigroup of K  , and f:K→K a fixed contractive mapping. The strongly convergent theorems of the following implicit and explicit viscosity iterative schemes {xn}{xn} are proved.xn=αnf(xn)+(1−αn)T(tn)xn,xn=αnf(xn)+(1−αn)T(tn)xn,xn+1=αnf(xn)+(1−αn)T(tn)xn.xn+1=αnf(xn)+(1−αn)T(tn)xn. And the cluster point of {xn}{xn} is the unique solution to some co-variational inequality.