Convergence Criteria of Viscosity Common Fixed Point Iterative Process for Asymptotically Nonexpansive Nonself Mappings in Banach Spaces

Let X be a real arbitrary Banach space and let C be a nonempty closed convex nonexpansive retract of X with P as a nonexpansive retraction. For i=1,2, let T-i: C -> X be an asymptotically nonexpansive nonself mapping such that F (T-1) boolean AND F(T-2) not equal empty set in C -> Let f:C -> C be a contractive mapping and let {alpha(n)} and {beta(n)} be real sequences in [0,1]. Define {x(n)} and {y(n)} to be the iterative sequences y(n) = P(alpha(n)f(x(n)) + (1 - alpha(n)) (beta(n)x(n) + (1 - beta(n)) T-2 (PT2)(n-1)x(n)), x(n+n) = P(gamma(n)f(y(n)) + (1- gamma(n)) (delta(n)y(n) + (1-delta(n))T-1(PT1)(n-1)y(n))), n >= 1. Some strong convergence theorems of the sequence {x(n)} to a common fixed point of T-1 and T-2 are established under appropriate conditions.