Approximation of fixed points of asymptotically nonexpansive mappings

Abstract

Let T T be an asymptotically nonexpansive self-mapping of a non-empty closed, bounded, and starshaped (with respect to zero) subset of a smooth reflexive Banach space possessing a duality mapping that is weakly sequentially continuous at zero. Then, if id- T T is demiclosed and T T satisfies a strengthened regularity condition, the iteration process z n + 1 := μ n + 1 T n ( z n ) {z_{n + 1}}: = {\mu _{n + 1}}{T^n}({z_n}) converges strongly to some fixed point of T T , provided ( μ n ) ({\mu _n}) has certain properties.