平均非扩张映射的不动点性质
作者 : 未知

  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�|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GarciaFalset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。
  关键词:平均非扩张映射;不动点;渐近正规结构;GarciaFalset常数
  DOI:10.15938/j.jhust.2018.04.023
  中图分类号: O177.2
  文献标志码: A
  文章编号: 1007-2683(2018)04-0122-05
  Abstract:In this paper, it mainly discussed the fixed point properties of the mean nonexpansive mapping. First of all, it proved the weakly compact convex subset with Opial properties for mean nonexpansive 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 nonexpansive mapping Finally, it proved that when the GarciaFalset constant satisfied specific inequality, the mean nonexpansive mapping T has a fixed point.
  Keywords:mean nonexpansive mapping; fixed point; asymptotic norml structure; GarciaFalset constant
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