Weak convergence theorems for asymptotically nonexpansive mappings in uniformly convex Banach spaces
Jarosław Górnicki · Czech digital mathematics library · 1989
In the present note, using specific uniformly convex Banach spaces techniques of asymptotic center we consider a necessary and sufficient condition for the weak convergence of trajectories of asymptotically nonexpansive mappings.The main result of this paper is contained in the following Theorem: Let E be a uniformly convex Banach space satisfying the Opial's condition, C a closed convex subset of E t T : C -• C an asymptotically nonexpansive mapping and x € C. Then {T n x} converges weakly to a fixed point of T iff T n + 1 x -T n x --0asn-+ +00