Asymptotic Behaviour of Almost Orbits of Asymptotically Nonexpansive Mappings in Uniformly Convex Banach Spaces

Abstract:

      Let X be a uniformly convex Banach space with a Fréchet differentiable norm, C a bounded closed convex subset of X and T:C→C an asymptotically nonexpansive mapping. It is shown that if {x_ｎ:n≥1} is an almost orbit of T, then the sequence {x n} is weakly almost convergent to the unique point of the set ∩from∞to (n=1) co {x_i:i≥n}∩F(T), where F(T) is the fixed point set of T.