Banach空间中Reich-Takahashi迭代法的强收敛问题  

Strong convergence problem of the Reich-Takahashi iteration method in Banach spaces

作　　者：王绍荣[1] 陈瑛 

机构地区：[1]大理学院理学院,云南大理671000 [2]昆明师专,云南昆明650031

出　　处：《云南师范大学学报（自然科学版）》2006年第4期28-31,65,共5页Journal of Yunnan Normal University:Natural Sciences Edition

摘　　要：设E是一实的Banach空间,D是E的非空有界闭凸集,T:D→D是一渐近非扩张型映象。文章证明了,在一些适当的条件下,由修正的Reich-Takahashi迭代法(1.2)式所定义的序列{xn}强收敛到T的不动点,其中x0是D中任给一定点,{αn},{βn}是[0,1]中满足某些限制的数列。Let E be a real Banach Space, Let D be a nonempty bounded closed convex subset of E and T-D→D be an asymptotically nonexpansive mapping. It is shown that under some suitable conditions, the sequence {xn} defined by the modified Reich-Takahashi Iteration method （1.2） converges strongly to a fixed point of T, where x0 is any given point in D, and {αn}, {βn} are sequences in [0,1] with some restrictions.

关 键 词：渐近非扩张型映象 修正的Reich-Takahashi迭代法 不动点 

分 类 号：O177.91[理学—数学]