Halpern-Mann’s iterations for Bregman strongly nonexpansive mappings in reflexive Banach spaces with applications

Journal of inequalities and applications

Jin-hua Zhu¹ 

关键词: Bregman strongly nonexpansive mapping;    Bregman projection;    Legendre function;    totally convex function;    Halpern’s iteration;    Mann’s iteration;   

DOI  :  10.1186/1029-242X-2013-146

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We investigate strong convergence for Bregman strongly nonexpansive mappings by modifying Halpern and Mann’s iterations in the framework of a reflexive Banach space. As applications, we apply our main result to problems of finding zeros of maximal monotone operators and equilibrium problems in reflexive Banach spaces. MSC:47H05, 47H09, 47J25.

【 授权许可】

CC BY