A one-step implicit iterative method for two finite families of asymptotically nonexpansive mappings in a hyperbolic space

2018 ◽  
Vol 33 (3) ◽  
pp. 274-286
Author(s):  
Hafiz Fukhar-ud-din ◽  
Amna Kalsoom ◽  
Safeer H Khan
Keyword(s):  
Iterative Method ◽  
Hyperbolic Space ◽  
Nonexpansive Mappings ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Implicit Iterative Method ◽  
One Step

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.

Iterative algorithm for a split equilibrium problem and fixed problem for finite asymptotically nonexpansive mappings in Hlbert space

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1423-1434 ◽  
Author(s):  
Sheng Wang ◽  
Min Chen
Keyword(s):  
Equilibrium Problem ◽  
Iterative Algorithm ◽  
Nonexpansive Mappings ◽  
Common Element ◽  
Fixed Point Set ◽  
Split Equilibrium Problem ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Point Set ◽  
The Common

In this paper, we propose an iterative algorithm for finding the common element of solution set of a split equilibrium problem and common fixed point set of a finite family of asymptotically nonexpansive mappings in Hilbert space. The strong convergence of this algorithm is proved.

scholarly journals Strong Convergence Theorems for Common Fixed Points of an Infinite Family of Asymptotically Nonexpansive Mappings

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Yuanheng Wang
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Real Banach Space ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Common Fixed Points ◽  
Uniformly Gâteaux Differentiable Norm ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Differentiable Norm

In the framework of a real Banach space with uniformly Gateaux differentiable norm, some new viscosity iterative sequences{xn}are introduced for an infinite family of asymptotically nonexpansive mappingsTii=1∞in this paper. Under some appropriate conditions, we prove that the iterative sequences{xn}converge strongly to a common fixed point of the mappingsTii=1∞, which is also a solution of a variational inequality. Our results extend and improve some recent results of other authors.

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