Firmly Nonexpansive Mappings and Maximally Monotone Operators: Correspondence and Duality

被引：40
作者：
Bauschke, Heinz H. [1 ]
Moffat, Sarah M. [1 ]
Wang, Xianfu [1 ]
机构：
[1] UBC Okanagan, Dept Math, Irving K Barber Sch, Kelowna, BC V1V 1V7, Canada
来源：
SET-VALUED AND VARIATIONAL ANALYSIS | 2012年 / 20卷 / 01期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Banach contraction; Convex function; Firmly nonexpansive mapping; Fixed point; Hilbert space; Legendre function; Maximally monotone operator; Nonexpansive mapping; Paramonotone; Proximal map; Rectangular; Resolvent; Subdifferential operator; FITZPATRICK FUNCTIONS; NONLINEAR OPERATORS; CONVERGENCE; EXTENSION;
D O I：
10.1007/s11228-011-0187-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The notion of a firmly nonexpansive mapping is central in fixed point theory because of attractive convergence properties for iterates and the correspondence with maximally monotone operators due to Minty. In this paper, we systematically analyze the relationship between properties of firmly nonexpansive mappings and associated maximally monotone operators. Dual and self-dual properties are also identified. The results are illustrated through several examples.
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页码：131 / 153
页数：23
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