scholarly journals Strong convergence of Krasnoselski-Mann iteration for a countable family of asymptotically nonexpansive mappings in CAT(0) spaces

2017 ◽  
Vol 10 (04) ◽  
pp. 1326-1333
Author(s):  
Shanguang Qian ◽  
Wei-Qi Deng
Keyword(s):  
Strong Convergence ◽  
Nonexpansive Mappings ◽  
Countable Family ◽  
Mann Iteration ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive

scholarly journals Strong Convergence Theorems for a Countable Family of Lipschitzian Mappings

2010 ◽  
Vol 2010 ◽  
pp. 1-17
Author(s):  
Weerayuth Nilsrakoo ◽  
Satit Saejung
Keyword(s):  
Iterative Method ◽  
Strong Convergence ◽  
Hybrid Method ◽  
Nonexpansive Mappings ◽  
Countable Family ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive Mappings ◽  
Lipschitzian Mappings ◽  
Asymptotically Nonexpansive ◽  
Special Cases

We modify the iterative method introduced by Kim and Xu (2006) for a countable family of Lipschitzian mappings by the hybrid method of Takahashi et al. (2008). Our results include recent ones concerning asymptotically nonexpansive mappings due to Plubtieng and Ungchittrakool (2007) and Zegeye and Shahzad (2008, 2010) as special cases.

scholarly journals Fibonacci–Mann Iteration for Monotone Asymptotically Nonexpansive Mappings in Modular Spaces

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 481 ◽  
Author(s):  
Buthinah Dehaish ◽  
Mohamed Khamsi
Keyword(s):  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Modular Function ◽  
Function Spaces ◽  
Mann Iteration ◽  
Modular Spaces ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Modular Function Spaces ◽  
Mann Iteration Process

In this work, we extend the fundamental results of Schu to the class of monotone asymptotically nonexpansive mappings in modular function spaces. In particular, we study the behavior of the Fibonacci–Mann iteration process, introduced recently by Alfuraidan and Khamsi, defined by

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