scholarly journals Strong Convergence Theorems of Viscosity Iterative Methods for a Countable Family of Strict Pseudo-contractions in Banach Spaces

2010 ◽  
Vol 2010 (1) ◽  
pp. 579725 ◽  
Author(s):  
Rabian Wangkeeree ◽  
Uthai Kamraksa
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Iterative Methods ◽  
Countable Family ◽  
Convergence Theorems

scholarly journals Strong Convergence Theorems for a Countable Family of Total Quasi-ϕ-Asymptotically Nonexpansive Nonself Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Liang-cai Zhao ◽  
Shih-sen Chang
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Equilibrium Problems ◽  
Approximation Problem ◽  
Countable Family ◽  
Convergence Theorems ◽  
Limit Condition ◽  
Asymptotically Nonexpansive ◽  
System Of Equilibrium Problems

The purpose of this paper is to introduce a class of total quasi-ϕ-asymptotically nonexpansive-nonself mappings and to study the strong convergence under a limit condition only in the framework of Banach spaces. As an application, we utilize our results to study the approximation problem of solution to a system of equilibrium problems. The results presented in the paper extend and improve the corresponding results announced by some authors recently.

scholarly journals Strong Convergence of a General Iterative Method for a Countable Family of Nonexpansive Mappings in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Chin-Tzong Pang ◽  
Eskandar Naraghirad
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Real Banach Space ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Accretive Operator ◽  
Common Fixed Points ◽  
Countable Family ◽  
Convergence Theorems ◽  
General Iterative Method

We introduce a general algorithm to approximate common fixed points for a countable family of nonexpansive mappings in a real Banach space. We prove strong convergence theorems for the sequences produced by the methods and approximate a common fixed point of a countable family of nonexpansive mappings which solves uniquely the corresponding variational inequality. Furthermore, we apply our results for finding a zero of an accretive operator. It is important to state clearly that the contribution of this paper in relation with the previous works (Marino and Xu, 2006) is a technical method to prove strong convergence theorems of a general iterative algorithm for an infinite family of nonexpansive mappings in Banach spaces. Our results improve and generalize many known results in the current literature.

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