An implicitly defined iterative sequence for monotone operators in Banach spaces

Journal of inequalities and applications

Fumiaki Kohsaka¹ 

关键词: Banach space;    convex minimization;    mapping of firmly nonexpansive type;    fixed point;    monotone operator;    proximal point method;    variational inequality;   

DOI  :  10.1186/1029-242X-2014-181

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Given a monotone operator in a Banach space, we show that an iterative sequence, which is implicitly defined by a fixed point theorem for mappings of firmly nonexpansive type, converges strongly to a minimum norm zero point of the given operator. Applications to a convex minimization problem and a variational inequality problem are also included. MSC:47H05, 47J25, 47N10.

【 授权许可】

CC BY