Fixed point theorems for a class of nonlinear mappings related to maximal monotone operators in Banach spaces

被引：300
|
作者：
Kohsaka, Fumiaki [1 ]
Takahashi, Wataru [2 ]
机构：
[1] Tokyo Denki Univ, Dept Informat Environm, Chiba 2701382, Japan
[2] Tokyo Inst Technol, Dept Math & Comp Sci, Meguro Ku, Tokyo 1528552, Japan
来源：
ARCHIV DER MATHEMATIK | 2008年 / 91卷 / 02期
关键词：
firmly nonexpansive mapping; firmly nonexpansive type mapping; fixed point theorem; nonspreading mapping; resolvent of monotone operator;
D O I：
10.1007/s00013-008-2545-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, the class of nonspreading mappings in Banach spaces is introduced. This class contains the recently introduced class of firmly nonexpansive type mappings in Banach spaces and the class of firmly nonexpansive mappings in Hilbert spaces. Among other things, we obtain a fixed point theorem for a single nonspreading mapping in Banach spaces. Using this result, we also obtain a common fixed point theorem for a commutative family of nonspreading mappings in Banach spaces.
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页码：166 / 177
页数：12
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