摘要
在半序拓扑空间内获得了非连续混合单调算子的耦合不动点定理:定理2设X是半序拓扑空间,M是X中的闭集,A:M×M→X是混合单调算子,又设(ⅰ)M的每一个全序子集都是相对紧的;(ⅱ)存在(x0,y0)∈M×M使得x0≤A(x0,y0),A(y0,x0)≤y0;则A在M×M中必有耦合不动点.还给出了它在Banach空间常微分方程中的应用.
The coupled fixed point theorems of discontinuous mixed monotone operators are obtained:Theorem 2 Let M be a closed subset of a partially ordered topological space X. Suppose that A:M ×M→X is a mixed monotone operator and the follwing conditions hold:(ⅰ) Each totally ordered subset of M is relatively compact;(ⅱ) There exists (x0, y0) ∈ M × M suchthat x0≤A(x0, y0), and A(y0, x0)≤y0 ;Then A has the coupled fixed point in M × M.The application to differential equation in a real Banach space is also given out.
出处
《西南师范大学学报(自然科学版)》
CAS
CSCD
1994年第2期128-133,共6页
Journal of Southwest China Normal University(Natural Science Edition)
关键词
拓扑空间
混合单调算子
耦合不动点
partially ordered topological space
mixed monotone operator
coupled fixed point