A fixed-point theorem of Krasnoselskii

被引：225

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

页码：85 / 88

页数：4