Convergence of Bregman Projection Methods for Solving Consistent Convex Feasibility Problems in Reflexive Banach Spaces

1997 ◽  
Vol 92 (1) ◽  
pp. 33-61 ◽  
Author(s):  
Y. Alber ◽  
D. Butnariu
Keyword(s):  
Banach Spaces ◽  
Projection Methods ◽  
Bregman Projection ◽  
Reflexive Banach Spaces ◽  
Convex Feasibility Problems ◽  
Convex Feasibility

Iterative approaches to convex feasibility problems in Banach spaces

2006 ◽  
Vol 64 (9) ◽  
pp. 2022-2042 ◽  
Author(s):  
John G. O’Hara ◽  
Paranjothi Pillay ◽  
Hong-Kun Xu
Keyword(s):  
Banach Spaces ◽  
Convex Feasibility Problems ◽  
Convex Feasibility

scholarly journals Convergence Theorems for Right Bregman Strongly Nonexpansive Mappings in Reflexive Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
H. Zegeye ◽  
N. Shahzad
Keyword(s):  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Maximal Monotone ◽  
Finite Family ◽  
Strong Convergence Theorem ◽  
Monotone Mappings ◽  
Important Class ◽  
Reflexive Banach Spaces ◽  
Convex Feasibility ◽  
Nonlinear Mappings

We prove a strong convergence theorem for a common fixed point of a finite family of right Bregman strongly nonexpansive mappings in the framework of real reflexive Banach spaces. Furthermore, we apply our method to approximate a common zero of a finite family of maximal monotone mappings and a solution of a finite family of convex feasibility problems in reflexive real Banach spaces. Our theorems complement some recent results that have been proved for this important class of nonlinear mappings.

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