Proximal point algorithms based on S-iterative technique for nearly asymptotically quasi-nonexpansive mappings and applications

2020 ◽  
Author(s):  
D. R. Sahu ◽  
Ajeet Kumar ◽  
Shin Min Kang
Keyword(s):  
Nonexpansive Mappings ◽  
Iterative Technique ◽  
Proximal Point ◽  
Proximal Point Algorithms

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 Proximal point algorithms involving fixed point iteration for nonexpansive mappings in CAT(κ) spaces

2018 ◽  
Vol 34 (2) ◽  
pp. 229-237
Author(s):  
NUTTAPOL PAKKARANANG ◽  
◽  
POOM KUMAM ◽  
PRASIT CHOLAMJIAK ◽  
RAWEEROTE SUPARATULATORN ◽  
...  
Keyword(s):  
Fixed Point ◽  
Convex Optimization ◽  
Iterative Algorithm ◽  
Proximal Point Algorithm ◽  
Nonexpansive Mappings ◽  
Proximal Point ◽  
Fixed Point Iteration ◽  
Proximal Point Algorithms ◽  
Common Solution ◽  
Mild Conditions

In this paper, we propose a new modified proximal point algorithm involving fixed point iteration for nonexpansive mappings in CAT(1) spaces. Under some mild conditions, we prove that the sequence generated by our iterative algorithm ∆-converges to a common solution between certain convex optimization and fixed point problems.

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