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2013 Strong Convergence Theorems for Semigroups of Asymptotically Nonexpansive Mappings in Banach Spaces
D. R. Sahu, Ngai-Ching Wong, Jen-Chih Yao
Abstr. Appl. Anal. 2013(SI60): 1-8 (2013). DOI: 10.1155/2013/202095

Abstract

Let X be a real reflexive Banach space with a weakly continuous duality mapping J φ . Let C be a nonempty weakly closed star-shaped (with respect to u ) subset of X . Let  =  { 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: y n = α n u + ( 1 α n ) T ( t n ) y n , for all n , converges strongly to a common fixed point of the semigroup for some suitably chosen parameters { α n } and { t n } . Our results extend and improve corresponding ones of Suzuki (2002), Xu (2005), and Zegeye and Shahzad (2009).

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D. R. Sahu. Ngai-Ching Wong. Jen-Chih Yao. "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

Information

Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 06209208
MathSciNet: MR3049365
Digital Object Identifier: 10.1155/2013/202095

Rights: Copyright © 2013 Hindawi

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Vol.2013 • No. SI60 • 2013
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