非对称度量空间上的不动点定理  

The Fixed Point Theorem on Asymmetric Metric Space

作　　者：刘保庆[1] 姚雪春[1] 

机构地区：[1]南京财经大学应用数学学院,江苏南京210023

出　　处：《淮北师范大学学报（自然科学版）》2017年第1期17-23,共7页Journal of Huaibei Normal University：Natural Sciences

基　　金：国家自然科学基金青年基金项目(11401296);江苏省普通高校自然科学基金面上项目(14KJB110007);江苏省自然科学基金青年基金项目(BK20141008)

摘　　要：非对称度量是一种不一定满足对称性的度量,目前非对称度量空间的基本理论在多目标约束最优化、人工智能、非线性控制等领域已得到广泛应用.文章结合非对称伪度量区间的相关概念,研究非对称伪度量空间中的共线性问题与始点问题,给出并证明非对称度量空间上集值映射和有向压缩映射的不动点定理与弱一致映射的公共不动点定理.A quasi-metric is a distance function which is not necessarily satisfying symmetry. The fundamen-tal theory of quasi-metric spaces is widely used in the field of multi-objective constrained optimization,artifi-cial intelligence,nonlinear control,theoretical computer,etc. In this paper,we introduce relative notions ofpseudo-quasi-metric interval in pseudo-quasi-metric spaces. Based on that,collinear problems and startpoint problems are also considered on the pseudo-quasi-metric spaces. Moreover,a fixed point theorem ofthe set-valued situation,a fixed point theorem for directional contractions and a common fixed point theorem have been proved.

关 键 词：非对称度量空间 左(右)完备性 不动点定理 

分 类 号：O177.91[理学—数学]