度量空间上A*-隐式压缩映射族的唯一公共不动点  

UNIQUE COMMON FIXED POINTS FOR A*-IMPLICIT CONTRACTIVE MAPPINGS ON METRIC SPACES

作　　者：朴勇杰[1] PIAO Yong-jie(Department of Mathematics,College of Science,Yanbian University,Yanji 133002,China)

机构地区：[1]延边大学理学院数学系,吉林延吉133002

出　　处：《数学杂志》2022年第6期503-512,共10页Journal of Mathematics

基　　金：国家自然基金资助(11761072).

摘　　要：本文研究了度量空间上自映射族的唯一公共不动点存在性问题.通过引入一个新的三元函数类A*,类A*是已知类A和A^(*)的推广,并利用类A*建立映射族的隐式压缩条件,获得了度量空间上映射族具有唯一公共不动点的定理,所得结果很好地推广和改进了Banach型及Kannan型(公共)不动点定理及相应结果.最后,给出具体实例验证了所得结果的正确性.In this paper,we study the existence of unique fixed points of self-mapping families on metric spaces.By introducing a new ternary function class A*,which is a generalization of the known classes A and A*,and using class A* to establish the implicit contractive condition for the mapping family,we obtain the theorem that the mapping family has a unique common fixed point on metric space.Our results generalize and improve the(common)fixed point theorems and corresponding results of Banach type and Kannan type.Finally,some specific examples are given to verify the correctness of the results.

关 键 词：A-压缩 A^(*)-压缩 A*-压缩 公共不动点 

分 类 号：O177.3[理学—数学] O189.11[理学—基础数学]