Let be a real reflexive Banach space with a weakly continuous duality mapping . Let be a nonempty weakly closed star-shaped (with respect to ) subset of . Let = be a uniformly continuous semigroup of asymptotically nonexpansive self-mappings of , which is uniformly continuous at zero. We will show that the implicit iteration scheme: , for all , converges strongly to a common fixed point of the semigroup for some suitably chosen parameters and . Our results extend and improve corresponding ones of Suzuki (2002), Xu (2005), and Zegeye and Shahzad (2009).
"Strong Convergence Theorems for Semigroups of Asymptotically Nonexpansive Mappings in Banach Spaces." Abstr. Appl. Anal. 2013 (SI60) 1 - 8, 2013. https://doi.org/10.1155/2013/202095