Halpern’s iteration for Bregman strongly nonexpansive multi-valued mappings in reflexive Banach spaces with application

Fixexd point theory and applications

Kelong Zheng¹  Hongbo Liu¹  Yi Li¹ 

[1] School of Science, Southwest University of Science and Technology, Mianyang Sichuan, China

关键词: Bregman strongly nonexpansive multi-valued mapping;    Legendre functions;    Bregman projection;    fixed point;    Halpern’s iteration sequence;   

DOI  :  10.1186/1687-1812-2013-197

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Bregman strongly nonexpansive multi-valued mapping in reflexive Banach spaces is established. Under suitable limit conditions, some strong convergence theorems for modifying Halpern’s iterations are proved. As an application, we utilize the main results to solve equilibrium problems in the framework of reflexive Banach spaces. The main results presented in the paper improve and extend the corresponding results in the work by Suthep et al. (Comput. Math. Appl. 64:489-499, 2012). MSC:47J05, 47H09, 49J25.

【 授权许可】

CC BY