Banach空间中α-β-非扩张映射的不动点定理  

On Fixed Points Theorem for α-β-Nonexpansive Mappings in Banach Spaces

作　　者：江雪梅[1] 邓璎函[2] 

机构地区：[1]西南大学数学与统计学院,重庆400715 [2]西南财经大学金融学院,成都611130

出　　处：《西南师范大学学报（自然科学版）》2012年第10期10-12,共3页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11071198);河南省科技发展计划(122300410256);河南省教育厅自然科学研究项目(2011B110025)

摘　　要：在Banach空间中引进一类非扩张映射,得到了它在一致凸Banach空间中存在不动点的充要条件.证明了在一定的条件下,这类非扩张映射的Ishikawa迭代序列收敛于它的不动点.最后给出了该序列强收敛到这类非扩张映射的不动点的一个充要条件.In this paper,a new nonexpansive mapping is introduced in Banach space.It obtains that a necessary and sufficient condition for the nonexpansive mapping exists fixed points in uniformly convex Banach space.It shows that the Ishikawa iteration sequence is convergent to a fixed point of the nonexpansive mapping.Finally,it obtains that a necessary and sufficient condition for the sequence is of strong convergence to a fixed point of the nonexpansive mapping.

关 键 词：α-β-非扩张映射 不动点定理 一致凸BANACH空间 ISHIKAWA迭代序列 

分 类 号：O177.91[理学—数学]