平均非扩张映射的不动点性质  

The Fixed Point Property of Mean Non-expansive Mapping

作　　者：崔云安[1] 王晶辰 CUI Yun-an;WANG Jing-chen(Department of Mathematics,Harbin University of Science and Technology,Harbin 150080,China)

机构地区：[1]哈尔滨理工大学应用数学系,黑龙江哈尔滨150080

出　　处：《哈尔滨理工大学学报》2018年第4期122-126,共5页Journal of Harbin University of Science and Technology

基　　金：黑龙江省自然科学基金(A2015018)

摘　　要：主要探讨了有关平均非扩张映射的不动点性质,先验证了具有Opial性质的弱紧凸集在平均非扩张映射下具有不动点性质;接着探讨了平均非扩张映射下,具有渐近正规结构的自反Banach空间X中的弱紧凸集中存在不动点;最后证明了Garcia-Falset常数满足特定的不等式时,平均非扩张映射T具有不动点性质。In this paper,it mainly discussed the fixed point properties of the mean non-expansive mapping.First of all,it proved the weakly compact convex subset with Opial properties for mean non-expansive mapping that has weak fixed point property.Secondly,it discussed the weakly compact convex subset of reflexive Banach space X which has asymptotic normal structure that has a fixed point for mean non-expansive mapping Finally,it proved that when the Garcia-Falset constant satisfied specific inequality,the mean non-expansive mapping T has a fixed point.

关 键 词：平均非扩张映射 不动点 渐近正规结构 Garcia-Falset常数 

分 类 号：O177.2[理学—数学]