摘要
设C为实H ilbert空间H的非空闭凸子集,P:H→C为最近点投影映射,T:C→H为非扩张映象,且T满足弱内向条件,f:C→C为压缩映象.t∈(0,1),定义了2种隐式粘性迭代序列{xt},{yt}和2种显式粘性迭代序列{xn},{yn},证明了T有不动点当且仅当序列{xt},{yt},{xn},{yn}有界.且在适当条件下,迭代序列(隐或显)强收敛于T的一个不动点.所得结果在实H ilbert空间上推广与发展了有关文献的相应结果.
Let C be a nonempty closed convex subset of a Hilbert space H,P：H→C be a nearest point projection, and T： C→H be a nonexpansive mapping satisfying the weakly inwardness condition, and f. C→ C be a fixed contractive mapping. Let the implicit iterafive sequences {xt}, {yt} and the explicit iterative sequences {xn}, {yn}. It is proved that Thas fixed point if and only if the sequences {xt}, {yt}, {xn}, {yn} are boundary. It is also proved, in satisfying appropriate conditions,the sequence {xt}, {yt}, {xn} and {yn} strongly converges to a fixed point of T.
出处
《纺织高校基础科学学报》
CAS
2005年第4期333-339,共7页
Basic Sciences Journal of Textile Universities
基金
国家自然科学基金资助项目(10471033
10271011)
关键词
非扩张映象
粘性迭代
不动点
弱内向条件
最近点投影
nonexpansive mappings
viscosity approximation methods
strong convergence theorems
fixed point
weak inwardness conditions
nearest point projection
