Iterative Approximation of Common Fixed Points of Two Nonself Asymptotically Nonexpansive Mappings

Suppose that K is nonempty closed convex subset of a uniformly convex and smooth Banach space E with P as a sunny nonexpansive retraction and F := F(T(1)) boolean AND F(T(2)) = {x is an element of K : T(1)x = T(2)x = x} not equal empty set. Let T(1), T(2) : K -> E be two weakly inward nonself asymptotically nonexpansive mappings with respect to P with two sequences {k(n)((i))} subset of [1, infinity) satisfying Sigma(infinity)(n=1) (k(n)((i)) - 1) < infinity(i = 1,2), respectively. For any given x(1) is an element of K, suppose that {x(n)} is a sequence generated iteratively by x(n+1) = (1-alpha(n)) (PT(1))(yn)(n) + alpha(n)(PT(2))(yn)(n), y(n) = (1 - beta(n))x(n) + beta(n)(PT(1))(xn)(n), n is an element of N, where {alpha(n)} and {beta(n)} are sequences in [a, 1 - a] for some a is an element of (0, 1). Under some suitable conditions, the strong and weak convergence theorems of {x(n)} to a common fixed point of T(1) and T(2) are obtained.