Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2013, Special Issue (2012), Article ID 202095, 8 pages.
Strong Convergence Theorems for Semigroups of Asymptotically Nonexpansive Mappings in Banach Spaces
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).
Abstr. Appl. Anal., Volume 2013, Special Issue (2012), Article ID 202095, 8 pages.
First available in Project Euclid: 26 February 2014
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Sahu, D. R.; Wong, Ngai-Ching; Yao, Jen-Chih. Strong Convergence Theorems for Semigroups of Asymptotically Nonexpansive Mappings in Banach Spaces. Abstr. Appl. Anal. 2013, Special Issue (2012), Article ID 202095, 8 pages. doi:10.1155/2013/202095. https://projecteuclid.org/euclid.aaa/1393442740