A strong convergence theorem for solving the split feasibility and fixed point problems in Banach spaces

2018 ◽  
Vol 20 (4) ◽  
Author(s):  
Truong Minh Tuyen ◽  
Nguyen Song Ha
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Convergence Theorem ◽  
Fixed Point Problems ◽  
Strong Convergence Theorem ◽  
Split Feasibility

scholarly journals Convergence theorems for Bregman strongly nonexpansive mappings in reflexive Banach spaces

Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1525-1536 ◽  
Author(s):  
Habtu Zegeye
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Convergence Theorem ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Strong Convergence Theorem ◽  
Monotone Mappings ◽  
Convergence Theorems

In this paper, we study a strong convergence theorem for a common fixed point of a finite family of Bregman strongly nonexpansive mappings in the framework of reflexive real Banach spaces. As a consequence, we prove convergence theorem for a common fixed point of a finite family of Bergman relatively nonexpansive mappings. Furthermore, we apply our method to prove strong convergence theorems of iterative algorithms for finding a common zero of a finite family of Bregman inverse strongly monotone mappings and a solution of a finite family of variational inequality problems.

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