An iteration scheme for asymptotically nonexpansive mappings on uniformly convex metric spaces (Q2746988)

The paper studies the existence of fixed points for asymptotically nonexpansive mappings. It is shown that if \(T:A \to A\) is an asymptotically nonexpansive mapping of a nonempty convex closed bounded subset of a uniformly convex complete metric space, then \(T\) has a fixed point. Also, for asymptotically nonexpansive mappings defined on a 2-uniformly convex metric space, an iteration scheme, convergent to the fixed point, is constructed.