Strong Convergence Theorems for Semigroups of Asymptotically Nonexpansive Mappings in Banach Spaces

D. R. Sahu, Ngai-Ching Wong and Jen-Chih Yao

Abstract and Applied Analysis, 2013, vol. 2013, 1-8

Abstract:

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).

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:202095

DOI: 10.1155/2013/202095

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