Strong Convergence of Weighted Averaged Approximants of Asymptotically Nonexpansive Mappings in Banach Spaces without Uniform Convexity

Let C be a nonempty closed convex subset of a reflexive Banach space whose norm is uniformly Gâteaux differentiable, C C T → : an asymptotically nonexpansive mapping and P the sunny nonexpansive retraction from C onto . ) (T F In the paper, we introduce property (S) for mapping T as minimal condition for strong convergence to Px of the sequence } { n x defined by ( ) 0 1 , 1 N n x T x x n i n i ni n n n ≥ − + = ∑ = α α α , where } { n α and ) , 2 , 1 ( } { = i ni α are real sequences satisfying appropriate conditions and 0 N is sufficiently large natural number. 2000 Mathematics Subject Classification: 47H09, 47H10