b-距离空间中有限个等式约束下的耦合不动点问题  

A COUPLED FIXED POINT PROBLEM UNDER A FINITENUMBER OF EQUALITY CONSTRAINTS IN b-METRIC SPACES

作　　者：贺丹妮 贺飞[1] HE Dan-ni;HE Fei(School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China)

机构地区：[1]内蒙古大学数学科学学院,内蒙古呼和浩特010021

出　　处：《数学杂志》2024年第2期169-181,共13页Journal of Mathematics

基　　金：国家自然科学基金资助(12061050);内蒙古自然科学基金资助(2020MS01004).

摘　　要：本文研究了b-距离空间中有限个等式约束下的耦合不动点问题.利用数学归纳法,获得了b-距离空间中一类有限个等式约束下的非线性压缩耦合不动点结果,将已有的Banach空间中的结果推广到b-距离空间中.特别地,我们结果中的压缩条件与空间系数无关.作为应用,得到了对称等式约束下的不动点定理,公共耦合不动点定理以及b-距离空间中非线性压缩不动点定理.这些结果可以推出许多已有结果,甚至将一些结果中的部分条件完全去掉.The coupled fixed point problem under a finite number of equality constraints in b-metric space is studied in this article.A class of nonlinear compressible coupled fixed point results under a finite number of equality constraints are obtained in b-metric space by the method of mathematical induction.Our results generalize the theorems from metric spaces to b-metric spaces.In particular,the contractive conditions in our results are independent of the contractive constant.As applications of our results,fixed point theorems under symmetric equality constraints,common coupled fixed point theorems and nonlinear contractive fixed point theorems in b-metric spaces are obtained.These results can deduce many existing results and even completely remove some conditions in some results.

关 键 词：b-距离空间 耦合不动点 等式约束 非线性压缩 

分 类 号：O177.91[理学—数学]