• Strong Convergence of Weighted Averaged Approximants of Asymptotically Nonexpansive Mappings in Banach Spaces without Uniform Convexity
D.R. Sahu, J.S. Jung and R.K. Verma
Abstract. Let C be a nonempty closed convex subset of a reflexive Banach space whose norm is uniformly Gâteaux differentiable, T:C ® C an asymptotically nonexpansive mapping and P the sunny nonexpansive retraction from C onto F(t). In the paper, we introduce property (S) for mapping T as minimal condition for strong convergence to Px of the sequence {x_n} defined by

where {a_n} and {a_ni} (i=1,2.) are real sequences satisfying appropriate conditions and N₀ is sufficiently large natural number.

2000 Mathematics Subject Classification: 47H09, 47H10