Strong convergence results of two-steps modifying Halpern’s iteration for Bregman strongly nonexpansive multi-valued mappings in reflexive Banach spaces with application

Journal of inequalities and applications

Hongbo Liu¹ 

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

DOI  :  10.1186/1029-242X-2014-412

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, a two-steps modifying Halpern iteration for Bregman strongly nonexpansive multi-valued mappings in the framework of reflexive Banach spaces is established. Under suitable limit conditions, some strong convergence theorems for this iteration are proved. We apply our main results to solve classical 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), Li et al. (Fixed Point Theory Appl. 2013:197, 2013) and Chang and Wang (Appl. Math. Comput. 228:38-48, 2014).

【 授权许可】

CC BY