Fixed points of nonexpansive potential operators in Hilbert spaces

被引：5
|
作者：
Ricceri, Biagio [1 ]
机构：
[1] Univ Catania, Dept Math, I-95125 Catania, Italy
来源：
FIXED POINT THEORY AND APPLICATIONS | 2012年
关键词：
nonexpansive operator; potential operator; fixed point; well-posedness; NONLINEAR EIGENVALUE PROBLEMS; RICCERIS CONJECTURE;
D O I：
10.1186/1687-1812-2012-123
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we show the impact of certain general results by the author on the topic described in the title. Here is a sample: Let (X, <., .>) be a real Hilbert space and let T : X -> X be a nonexpansive potential operator. Then, the following alternative holds: either T has a fixed point, or, for each sphere S centered at 0, the restriction to S of the functional x -> integral(1)(0) < T(sx), x > ds has a unique global maximum towards which each maximizing sequence in S converges.
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页数：13
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