scholarly journals A modified viscosity implicit-type proximal point algorithm for monotone inclusions and asymptotically nonexpansive mappings in Hadamard spaces

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Shih-sen Chang ◽  
Jen-Chih Yao ◽  
Ching-Feng Wen ◽  
Lin Wang
Keyword(s):  
Proximal Point Algorithm ◽  
Nonexpansive Mappings ◽  
Proximal Point ◽  
Monotone Inclusions ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive

scholarly journals Proximal point algorithms involving Cesàro type mean of total asymptotically nonexpansive mappings in CAT(0) spaces

Filomat ◽  
2018 ◽  
Vol 32 (12) ◽  
pp. 4165-4176 ◽  
Author(s):  
Amna Kalsoom ◽  
Hafiz Fukhar-Ud-Din ◽  
Sara Najib
Keyword(s):  
Nonexpansive Mapping ◽  
Convex Function ◽  
Proximal Point Algorithm ◽  
Nonexpansive Mappings ◽  
Common Element ◽  
Proximal Point ◽  
Proximal Point Algorithms ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Total Asymptotically Nonexpansive Mappings

In this paper, we extend the proximal point algorithm proposed by Chang et al.[8] for total asymptotically nonexpansive mapping in CAT(0) spaces. We also demonstrate the ?-convergence and strong convergence to a common element of the set of minimizers of a convex function and the set of fixed points of the Ces?ro type mean of total asymptotically nonexpansive mappings in CAT(0) spaces.

scholarly journals Convergence Results for Proximal Point Algorithm in Complete Cat(0) Space for Multivalued Mappings

2021 ◽  
Vol 27 (1) ◽  
pp. 29-47
Author(s):  
Samir Dashputre ◽  
C. Padmavati ◽  
Kavita Sakure
Keyword(s):  
Proximal Point Algorithm ◽  
Nonexpansive Mappings ◽  
Multivalued Mappings ◽  
Proximal Point ◽  
Convergence Theorems ◽  
Numerical Example ◽  
Asymptotically Nonexpansive Mappings ◽  
Convergence Results ◽  
Asymptotically Nonexpansive

In this paper, we propose the modified proximal point algorithm with the process for three nearly Lipschitzian asymptotically nonexpansive mappings and multivalued mappings in CAT(0) space under certain conditions. We prove some convergence theorems for the algorithm which was introduced by Shamshad Hussain et al. [18]. A numerical example is given to illustrate the efficiency of proximal point algorithm for supporting our result.

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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