Nonlinear Ergodic Theorem for Positively Homogeneous Nonexpansive Mappings in Banach Spaces

2013 ◽  
Vol 35 (1) ◽  
pp. 85-98 ◽  
Author(s):  
Wataru Takahashi ◽  
Ngai-Ching Wong ◽  
Jen-Chih Yao
Keyword(s):  
Banach Spaces ◽  
Ergodic Theorem ◽  
Nonexpansive Mappings ◽  
Nonlinear Ergodic Theorem

scholarly journals The iterative solutions of split common fixed point problem for asymptotically nonexpansive mappings in Banach spaces

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yuanheng Wang ◽  
Xiuping Wu ◽  
Chanjuan Pan
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Optimization Problems ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Iteration Algorithm ◽  
Point Problem ◽  
Asymptotically Nonexpansive ◽  
Split Common Fixed Point

AbstractIn this paper, we propose an iteration algorithm for finding a split common fixed point of an asymptotically nonexpansive mapping in the frameworks of two real Banach spaces. Under some suitable conditions imposed on the sequences of parameters, some strong convergence theorems are proved, which also solve some variational inequalities that are closely related to optimization problems. The results here generalize and improve the main results of other authors.

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