实Hilbert空间中的非扩张非自映射的粘性迭代

Viscosity approximation of nonexpansive non-self mapping in hilbert spaces

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.