scholarly journals A counterexample to the approximation problem in Banach spaces

1973 ◽  
Vol 130 (0) ◽  
pp. 309-317 ◽  
Author(s):  
Per Enflo
Keyword(s):  
Banach Spaces ◽  
Approximation Problem

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.

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