Ergodicity of the implicit midpoint rule for nonexpansive mappings

Journal of inequalities and applications

Hong-Kun Xu¹ 

关键词: ergodic;    implicit midpoint rule;    nonexpansive mapping;    projection;    Hilbert space;   

DOI  :  10.1186/1029-242X-2015-4

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We prove a mean ergodic theorem for the implicit midpoint rule for nonexpansivemappings in a Hilbert space. We obtain weak convergence for the general case andstrong convergence for certain special cases. MSC: 47J25, 47N20, 34G20, 65J15.

【 授权许可】

CC BY