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.

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.

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