Implicit iterative process for common fixed point of a finite family of asymptotically nonexpansive mappings

2008 ◽  
Vol 45 (2) ◽  
pp. 235-250
Author(s):  
Feng Gu
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Finite Family ◽  
Weak And Strong Convergence ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Implicit Iteration

The purpose of this paper is to study the weak and strong convergence of implicit iteration process to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of [1,2,4–9,11–15].

scholarly journals Convergence of an implicit iteration process with errors for two asymptotically nonexpansive mappings

2013 ◽  
Vol 46 (4) ◽  
Author(s):  
Seyit Temir
Keyword(s):  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Iterative Algorithms ◽  
Iteration Process ◽  
Weak And Strong Convergence ◽  
Implicit Iteration Process ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Implicit Iteration ◽  
Appl Math

AbstractThe purpose of this paper is to introduce an implicit iterative process with errors for approximating common fixed point of two finite families of asymptotically nonexpansive mappings in the framework of Banach space. The results presented in this paper extend and generalize the corresponding results of Qin et al. [Convergence analysis of implicit iterative algorithms for asymptotically nonexpansive mappings, Appl. Math. Comp. 210 (2009), 542–550], Thakur [Weak and strong convergence of composite implicit iteration process, Appl. Math. Comp. 190 (2007), 965–973] and some others.

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