ASYMPTOTIC BEHAVIOR OF ALMOST-ORBITS OF ASYMPTOTICALLY NONEXPANSIVE FAMILIES IN THE INTERMEDIATE SENSE
Zeng Lu-chuan · Chinese Annals of Mathematics,series A · 2003
In this paper, let C be a nonempty subset of a uniformly convex Banach space E with a Frechet differentiable norm, let T = {T(t) : t ∈ S} be a family of self-mappings on C which is asymptotically nonexpansive in the intermediate sense, and let F be contained in F(T) which denotes the set of all common fixed points of T = (T(t) : t ∈ S}. It is shown that if u : S → C is an almost-orbit of T = {T(t) : t ∈ S} satisfying the conditions: (a) uw({u(t) : t ∈ 5}) F, and (b) co({u(t) : t ∈ 5} ∪ F) C, then, either (i) F = and lim ||u(t)|| = ∞ or (ii) F ≠ and u(t) converges weakly to an element of F.