STRONG AND Δ - CONVERGENCE THEOREMS USING MODIFIED PROXIMAL POINT ALGORITHM IN CAT(0) SPACES

2018 ◽  
Vol 7 (2) ◽  
pp. 8
Author(s):  
KUMAR DAS APURVA ◽  
DHAR DIWAN SHAILESH ◽  
DASHPUTRE SAMIR ◽  
◽  
◽  
...  
Keyword(s):  
Proximal Point Algorithm ◽  
Proximal Point ◽  
Convergence Theorems

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 Convergence Theorems of Modified Proximal Algorithms for Asymptotical Quasi-nonexpansive Mappings in CAT(0) Spaces

2018 ◽  
Vol 10 (2) ◽  
pp. 66
Author(s):  
Shengquan Weng ◽  
Dingping Wu
Keyword(s):  
Fixed Point ◽  
Convex Function ◽  
Finite Number ◽  
Iterative Process ◽  
Proximal Point Algorithm ◽  
Nonexpansive Mappings ◽  
Proximal Algorithms ◽  
Proximal Point ◽  
Convergence Theorems

In this paper, a new modified proximal point algorithm involving fixed point iterates of a finite number of asymptotically quasi-nonexpansive mappings in $CAT(0)$ spaces is proposed and been proved for the existence of a sequence generated by our iterative process converging to a minimizer of a convex function and a commen fixed point of a finite number of asymptotically quasi-nonexpansive mappings.

A two-phase-like proximal point algorithm in domains of positivity

2019 ◽  
Vol 343 ◽  
pp. 67-89
Author(s):  
R.M. Gregório ◽  
P.R. Oliveira ◽  
C.D.S. Alves
Keyword(s):  
Proximal Point Algorithm ◽  
Proximal Point ◽  
Two Phase
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