scholarly journals New Iterative Approximation Methods for a Countable Family of Nonexpansive Mappings in Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-24
Author(s):  
Kamonrat Nammanee ◽  
Rabian Wangkeeree
Keyword(s):  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Countable Family ◽  
Approximation Methods ◽  
Iterative Approximation

scholarly journals The General Hybrid Approximation Methods for Nonexpansive Mappings in Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-19
Author(s):  
Rabian Wangkeeree
Keyword(s):  
Reflexive Banach Space ◽  
Nonexpansive Mappings ◽  
Linear Operators ◽  
Duality Mapping ◽  
Approximation Methods ◽  
Iterative Approximation ◽  
Bounded Linear ◽  
Weakly Continuous ◽  
Weakly Continuous Duality Mapping ◽  
Hybrid Approximation

We introduce two general hybrid iterative approximation methods (one implicit and one explicit) for finding a fixed point of a nonexpansive mapping which solving the variational inequality generated by two strongly positive bounded linear operators. Strong convergence theorems of the proposed iterative methods are obtained in a reflexive Banach space which admits a weakly continuous duality mapping. The results presented in this paper improve and extend the corresponding results announced by Marino and Xu (2006), Wangkeeree et al. (in press), and Ceng et al. (2009).

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