Abstract and Applied Analysis

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

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

Full-text: Open access

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).

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2012), Article ID 202095, 8 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393442740

Digital Object Identifier
doi:10.1155/2013/202095

Mathematical Reviews number (MathSciNet)
MR3049365

Zentralblatt MATH identifier
06209208

Citation

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


Export citation