Two strong convergence theorems for Bregman strongly nonexpansive operators in reflexive Banach spaces

2010 ◽  
Vol 73 (1) ◽  
pp. 122-135 ◽  
Author(s):  
Simeon Reich ◽  
Shoham Sabach
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Reflexive Banach Spaces ◽  
Convergence Theorems ◽  
Nonexpansive Operators

scholarly journals Strong Convergence Theorems for Quasi-Bregman Nonexpansive Mappings in Reflexive Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Mohammed Ali Alghamdi ◽  
Naseer Shahzad ◽  
Habtu Zegeye
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Maximal Monotone ◽  
Finite Family ◽  
Monotone Mappings ◽  
Reflexive Banach Spaces ◽  
Convergence Theorems

We study a strong convergence for a common fixed point of a finite family of quasi-Bregman nonexpansive mappings in the framework of real reflexive Banach spaces. As a consequence, convergence for a common fixed point of a finite family of Bergman relatively nonexpansive mappings is discussed. Furthermore, we apply our method to prove strong convergence theorems of iterative algorithms for finding a common solution of a finite family equilibrium problem and a common zero of a finite family of maximal monotone mappings. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

An iterative process for a hybrid pair of a Bregman strongly nonexpansive single-valued mapping and a finite family of Bregman relative nonexpansive multi-valued mappings in Banach spaces

2017 ◽  
Vol 33 (3) ◽  
pp. 287-300
Author(s):  
PREEYANUCH CHUASUK ◽  
◽  
ALI FARAJZADEH ◽  
ANCHALEE KAEWCHAROEN ◽  
RAVI P. AGARWAL ◽  
...  
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Iterative Process ◽  
Finite Family ◽  
Reflexive Banach Spaces ◽  
Convergence Theorems ◽  
Hybrid Pair

In this paper, we construct an iterative process involving a hybrid pair of a Bregman strongly nonexpansive single-valued mapping and a finite family of Bregman relative nonexpansive multi-valued mappings and prove strong convergence theorems of the proposed iterative process in reflexive Banach spaces under appropriate conditions. Our main results can be viewed as an improvement and extension of the several results in the literature.

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