关于平均非扩张映射的两个不动点性质  

On Two Fixed Point Properties of Mean Non-expansive Mappings

作　　者：左明霞 周夏 ZUO Ming-xia;ZHOU Xia(School of Sciences,Harbin University of Science and Technology,Harbin 150080,China)

机构地区：[1]哈尔滨理工大学理学院,哈尔滨150080

出　　处：《哈尔滨理工大学学报》2022年第3期157-162,共6页Journal of Harbin University of Science and Technology

基　　金：国家自然科学基金(11871181,71401047);黑龙江省自然科学基金(A2018006).

摘　　要：首先将文献[1]中的定理5.10的结果推广到一种更一般的映射形式,即映射T满足:supy∈E‖Tx-Ty‖≤supy∈E(a‖x-y‖+b‖x-Tx‖+c‖x-Ty‖),x∈K,a,b,c≥0,a+b+c≤1,证明了定义在自反的Banach空间中的具有正规结构的有界闭凸集K到其自身的该种映射存在不动点。然后在b-凸度量空间中,利用Mann迭代生成的序列,证明了平均非扩张映射在一定条件下存在唯一的不动点。Firstly,the result of theorem 5.10 in reference[1]is extended to a more general form of mapping,namely:supy∈E‖Tx-Ty‖≤supy∈E(a‖x-y‖+b‖x-Tx‖+c‖x-Ty‖),x∈K,a,b,c≥0,a+b+c≤1,and it is proved that there are fixed points for this kind of mapping which is from bounded closed convex subset K with normal structure of a reflexive Banach space into itself.Moreover,in convex b-metric space,it is proved that there is a unique fixed point for the mean non-expansive mapping under certain conditions by utilizing the sequence which is generated by Mann iteration.

关 键 词：平均非扩张映射 不动点 b-度量空间 MANN迭代 

分 类 号：O177.3[理学—数学]