Strong Convergence to Common Fixed Points of a Finite Family of Nonexpansive Mappings

Let C be a closed convex subset of a Banach space E. A mapping T of C into itself is called nonexpansive if ‖Tx−Ty‖ ≤ ‖x− y‖ for all x, y ∈ C. We denote by F(T) the set of fixed points of T . Let T1,T2, . . . ,Tr be a finite family of nonexpansive mappings satisfying that the set F =⋂i=1F(Ti) of common fixed points of T1,T2, . . . ,Tr is nonempty. The problem of finding a common fixed point has been investigated by many researchers; see, for example, Atsushiba and Takahashi [1], Bauschke [2], Lions [3], Shimizu and Takahashi [4], Takahashi et al. [5], Zeng et al. [6]. To solve this problem, the iterative scheme x1 ∈ C and