一类新的F-型压缩映射的公共不动点定理  

Common fixed point theorems of a new class of F-type contractive mappings

作　　者：关洪岩[1] 王前程 GUAN Hongyan;WANG Qiancheng(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）》2023年第5期454-458,共5页Journal of Shenyang Normal University:Natural Science Edition

基　　金：辽宁省教育厅基本科研项目(JYTMS20231700)。

摘　　要：Banach压缩映射原理在非线性分析中起着重要作用,它是解决完备度量空间中不动点的存在性和唯一性问题的有效方法,在基础数学和应用数学中有着广泛的应用,近年来该定理在多个方面得到了推广。在b-度量空间的背景下,研究一类新的F-型压缩映射对的公共不动点定理。首先,在b-度量空间中引入一类新的平方型F-型压缩条件;其次,利用2个映射的包含关系,构造一个序列,并通过使用F-函数的性质、数学归纳法及压缩条件证明该序列相邻项距离的极限为零,进而得到该序列是一个柯西列;最后,结合空间的完备性和压缩条件,得出2个映射具有重合值,再利用映射的弱相容条件,进一步证明该映射对具有公共不动点,同时给出了一个具体例子来说明结果的有效性。The Banach contraction mapping principle plays an important role in nonlinear analysis.It is an effective method to solve the problem of the existence and uniqueness of fixed points in complete metric space.It has a wide range of applications in basic mathematics and applied mathematics,and has been promoted from various angles.In the setting of b-metric spaces,we study a new class of common fixed point theorems for F-type contraction mappings.Firstly,a new class of F-type contractive condition is introduced.After that,a new sequence is constructed by using the inclusion relation of two mappings.Using the properties of type F-functions,mathematical induction and contractive conditions,it is proved that the limit of the distance between adjacent terms is zero,then the sequence is Cauchy sequence.Secondly,combining the completeness of the space and contraction conditions,we prove that the two mappings possess a point of coincidence,and then they have a common fixed point by using of weak compatible conditions.At the same time,an example is provided to demonstrate the effectiveness of the results.

关 键 词：不动点 F-型压缩 b-度量空间 柯西列 

分 类 号：O174.1[理学—数学]