A fixed-point theorem of Krasnoselskii

被引：226
|
作者：
Burton, TA [1 ]
机构：
[1] So Illinois Univ, Dept Math, Carbondale, IL 62901 USA
来源：
APPLIED MATHEMATICS LETTERS | 1998年 / 11卷 / 01期
关键词：
fixed points; integral equation; periodic solutions;
D O I：
10.1016/S0893-9659(97)00138-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Krasnoselskii's fixed-point theorem asks for a convex set M and a mapping Pz = Bz + Az such that: (i) Bx + Ay is an element of M for each x, y is an element of M, (ii) A is continuous and compact, (iii) B is a contraction. Then P has a fixed point. A careful reading of the proof reveals that (i) need only ask that Bx + Ay is an element of M when x = Bx + Ay. The proof also yields a technique for showing that such x is in M.
引用
收藏
页码：85 / 88
页数：4
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