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, issue 1

Abstract: Let X be a real reflexive Banach space with a weakly continuous duality mapping Jφ. Let C be a nonempty weakly closed star‐shaped (with respect to u) subset of X. Let ℱ = {T(t) : t ∈ [0, +∞)} be a uniformly continuous semigroup of asymptotically nonexpansive self‐mappings of C, which is uniformly continuous at zero. We will show that the implicit iteration scheme: yn = αnu + (1 − αn)T(tn)yn, for all n ∈ ℕ, converges strongly to a common fixed point of the semigroup ℱ for some suitably chosen parameters {αn} and {tn}. Our results extend and improve corresponding ones of Suzuki (2002), Xu (2005), and Zegeye and Shahzad (2009).

Date: 2013
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https://doi.org/10.1155/2013/202095

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:202095

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