G-度量空间上积分型压缩映射对的公共不动点定理  

Common fixed point theorem for a pair of contractive mappings with integral type on G-metric spaces

作　　者：关洪岩[1] 李超 GUAN Hongyan;LI Chao(College of Mathematics and Systems Science,Shenyang Normal University,Shenyang 110034,China)

机构地区：[1]沈阳师范大学数学与系统科学学院,沈阳110034

出　　处：《沈阳师范大学学报(自然科学版)》2025年第1期70-74,共5页Journal of Shenyang Normal University:Natural Science Edition

基　　金：辽宁省科技厅自然科学基金资助项目(2024-MS-108)。

摘　　要：在非线性分析中,Banach引入的Banach压缩映射原理是一个解决度量空间中的不动点的存在性和唯一性问题的经典而有力的工具,在基础数学和计算数学中有着广泛的应用,近年来在多个角度得到了推广。在G-度量空间的背景下,研究满足CLR性质的积分型压缩映射对具有公共不动点的条件。首先,在G-度量空间中引入可变距离函数Φ;其次,根据2个映射的包含关系构造一个序列,并通过Φ的性质、压缩条件等证明该序列是柯西列;再次,结合空间的完备性和压缩条件,得出这2个映射具有重合值,根据弱相容映射的性质,证明该映射对公共不动点的存在性,进而证明公共不动点的唯一性;最后,给出一个例子说明该定理的有效性。In nonlinear analysis,Banach introduces the Banach contraction mapping principle,which is a classic and powerful tool for solving the problem of the existence and uniqueness of fixed points in metric spaces.It has a wide range of applications in basic mathematics and computational mathematics.In recent years,this theorem has been promoted and applied from multiple perspectives.In the context of G-metric space,we study the conditions of common fixed points for contractive mappings with integral type satisfying the CLR property.Firstly,we introduce a variable distance functionΦin the G-metric space.Then,we construct a sequence based on the inclusion relationship between the two mappings,and prove that the sequence is a Cauchy sequence through the properties ofΦ,contractive conditions,etc.Afterwards,combining the completeness of spaces and contraction conditions,it is concluded that these two mappings have coincidence of points.Based on the properties of weakly compatible mappings,the existence of common fixed points for this pair of mappings is proved,and so the uniqueness of common fixed points.Finally,we provide an example to demonstrate the validity of the theorem.

关 键 词：不动点 Φ函数 G-度量空间 CLR性质 

分 类 号：O174.1[理学—数学]