度量空间上B^(*)-隐式收缩条件和唯一公共不动点  

B^(*)-implicit contractive conditions and unique common fixed points on metric spaces

作　　者：朴勇杰[1] PIAO Yongjie(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：《中山大学学报（自然科学版）（中英文）》2022年第5期173-180,共8页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金(11361064,11761072)。

摘　　要：首先引进了一类新的3元实函数类B^(*)并给出映射的B^(*)-隐式收缩条件,然后得到具有两个不同度量的非空集合上两个映射在连续或非连续及空间的完备或非完备条件下的唯一公共不动点的存在性,还给出了无穷多个映射在非连续下的唯一公共不动点存在定理。最后,用两个具体例子验证了得到结果的正确性。所得结论推广和改进了一些已知结果,特别是Banach收缩原理,Chatterjea-型(公共)不动点定理及相应(公共)不动点定理。A new class B^(*)of 3-dimensional functions is introduced and a B^(*)-implicit contractive condition of mappings is given.Then the existence of unique common fixed points for two self-mappings on a nonempty set with two different metrics under the continuity or non-continuity of the given mappings and the completeness or non-completeness of the given metric spaces is obtained.The unique common fixed point theorems of an infinite family of non-continuous self-mappings is also given.Finally,two examples to verify the correctness of the obtained theorems are given.The obtained results generalize and improve some known results,for example,Banach contraction principle,Chatterjea-type(common)fixed point theorem and the corresponding(common)fixed point theorems.

关 键 词：B^(*)-隐式收缩 (公共)不动点 P-性质 

分 类 号：O177.91[理学—数学] O189.11[理学—基础数学]