scholarly journals Weak and strong convergence theorems of modified Ishikawa iteration for an infinitely countable family of pointwise asymptotically nonexpansive mappings in Hilbert spaces

2011 ◽  
Vol 17 (2) ◽  
pp. 153-169
Author(s):  
Javad Balooee
Keyword(s):  
Strong Convergence ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Countable Family ◽  
Weak And Strong Convergence ◽  
Convergence Theorems ◽  
Ishikawa Iteration ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive

scholarly journals Strong Convergence of Hybrid Algorithm for Asymptotically Nonexpansive Mappings in Hilbert Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Juguo Su ◽  
Yuchao Tang ◽  
Liwei Liu
Keyword(s):  
Strong Convergence ◽  
Hilbert Spaces ◽  
Hybrid Algorithm ◽  
Nonexpansive Mappings ◽  
Iteration Scheme ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Iteration Methods ◽  
Mann’S Iteration

The hybrid algorithms for constructing fixed points of nonlinear mappings have been studied extensively in recent years. The advantage of this methods is that one can prove strong convergence theorems while the traditional iteration methods just have weak convergence. In this paper, we propose two types of hybrid algorithm to find a common fixed point of a finite family of asymptotically nonexpansive mappings in Hilbert spaces. One is cyclic Mann's iteration scheme, and the other is cyclic Halpern's iteration scheme. We prove the strong convergence theorems for both iteration schemes.

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