半序概率度量空间中混合单调算子的耦合不动点定理  

Fixed point theorems of mixed monotone operators in partially ordered probabilistic metric spaces

作　　者：朱奋秀 ZHU Fen-xiu(School of Law and Business, Hubei University of Economics, Wuhan 430205 , P. R. C.)

机构地区：[1]湖北经济学院法商学院

出　　处：《西南民族大学学报（自然科学版）》2019年第3期314-317,共4页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：湖北经济学院法商学院科研资助项目(2018K12)

摘　　要：不动点理论是非线性泛函分析的重要组成部分.对非线性微分和积分方程的研究有重要意义.通过泛函在概率度量空间中引入半序关系,建立半序概率度量空间,在满足两点压缩和拉伸条件下,弱化混合单调算子的连续性,且通过构造集合,并证明集合存在极大元,利用Zron引理,从而证明满足条件的混合单调算子的耦合不动点定理.Fixed point theory is an indispensable part of nonlinear functional analysis and is of great significance in the research of differential and integral equations. A partial order is introduced by a function in probabilistic metric spaces. A class of mixed monotone operator is discussed under compression type and tension type in ordered metric spaces, and the continuity of operators is weakened. The Zron lemma is used to prove the coupled fixed point theorem of mixed monotone operators by constructing a set.

关 键 词：半序概率度量空间 不动点 混合单调算子 

分 类 号：O177.91[理学—数学]