Convergence theorems of a new iteration for two nonexpansive mappings

The purpose of this paper is to introduce the following new general implicit iteration scheme for approximating the common fixed points of a pair of nonexpansive mappings in a uniformly convex Banach space: for any x(0) is an element of C, the iterative process {x(n)} defined by x(n) = a(n)x(n-1) + b(n)Ty(n) + c(n)Sx(n), y(n) = a'(n)x(n-1) + b'(n)x(n) + c'(n)Sx(n-1) + d'(n)Tx(n), where {a(n)}, {b(n)}, {c(n)}, {a'(n)}, {b'(n)}, {c'(n)}, {d'(n)} are seven sequences of real numbers satisfying a(n) + b(n) + c(n) = 1, a'(n) + b'(n) + c'(n) + d'(n) = 1, and T, S : C -> C are two nonexpansive mappings. We approximate the common fixed points of these two mappings by weak and strong convergence of the scheme.