Menger概率度量空间压缩映象的公共不动点定理  

A Common Fixed Point Theorem of Contractive Mappingsin Menger Probabilistic Metric Spaces

作　　者：方楠楠 FANG Nan-nan(Ministry of General Education,Anhui Xinhua University,Hefei,Anhui,230088,China)

机构地区：[1]安徽新华学院通识教育部,安徽合肥230088

出　　处：《新疆师范大学学报（自然科学版）》2025年第2期67-76,共10页Journal of Xinjiang Normal University(Natural Sciences Edition)

基　　金：安徽新华学院校级科研一般项目(2021zr007)。

摘　　要：在Menger概率度量空间中,研究一种新的压缩条件,在这个条件下得到一个新的弱相容映象对的耦合重合点和公共耦合不动点定理。定理的证明通过以下三步展开:第一步:构造并证明gx_(n)和gy_(n)是柯西序列;第二步:证明(x^(*),y^(*))是弱相容映象对g和T的公共耦合重合点;第三步:证明此重合点的唯一性,进而得到了g和T的公共耦合不动点也是唯一的。该定理在一定程度上推广和发展了原有结果。In the framework of a Menger probabilistic metric spaces,we introduce a new class of contraction condition,and proves some new coupled coincidence point and common coupled fixed point theorems.This proof is completed through the following three steps.Step1:we show that gx_(n) and gy_(n) are Cauchy sequences;Step2:it will be proved that(x^(*),y^(*))is the common coupled point of coincidence of g and T;Step 3:the uniqueness of the common coupled point of coincidence of g and T is proved.This theorem improves the corresponding results in some references.

关 键 词：MENGER概率度量空间 耦合重合点 公共耦合不动点 

分 类 号：O177.91[理学—数学]