Approximation of Fixed Points of Asymptotically Nonexpansive Mappings

Let $T$ 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-$T$ is demiclosed and $T$ satisfies a strengthened regularity condition, the iteration process ${z_{n + 1}}: = {\mu _{n + 1}}{T^n}({z_n})$ converges strongly to some fixed point of $T$, provided $({\mu _n})$ has certain properties.