关于非扩张映像的修正粘滞迭代格式

Modified Viscosity Iterations for Nonexpansive Mapping

设H是Hilbert空间,X是Banach空间,C是H或X中的非空闭凸子集,T是C→C的非扩张映射,且f是C→C的压缩映射。受H.K.Xu对粘滞迭代算法讨论的启发,提出一种新的粘滞迭代算法,xn+1=T[(1-αn)xn+αn f(xn)],n≥0,其中x0∈C,C是Banach空间中的非空闭凸子集,分别在Hilbert空间和Banach空间框架下证明了序列{xn}是强收敛的。

Let H be a Hilbert space and X be a Banach space, C a nonempty closed convex subset of H or X,and T： C→ C a nonexpansive mapping. Movitated by H. K. Xu＇s studies of viscosity iterations for nonexpansive mapping, a new iterative method is generated as followed： where C is a closed convex subset of a Banach space and x0∈C,xn＋1=T[（1-αn）xn＋αnf（xn）],n≥0. We can get the strong convergence theorem both in Hilbert and Banaeh space