Iterative construction for common fixed points of finitely many nonexpansive mappings

Many problems encountered in applied mathematics can be recast as the problem of selecting a particular common fixed point of a family of nonexpansive mappings in a Banach space. In this paper, under the hypotheses that EE is a reflexive and strictly convex Banach spaces with a uniformly Gâeaux differentiable norm, the strong convergence of a iteration algorithm is proved for finding a common fixed point of a finite family of nonexpansive self-mappings defined on a closed convex subset KK of EE.