非扩张映像不动点集与最佳逼近元

Set of fixed points of nonexpansive mapping and element of the best approximation in a Banach space

证明了严格凸Banach空间中非扩张映像T的不动点集F(T)是闭凸集,并证明了当F(T)是Hilbert空间闭线性子空间时,从空间中任一点x0出发的非扩张映像T的Ishikawa迭代序列若收敛于某不动点p,则p必是x0在F(T)中的最佳逼近元.

Let X be a strictly convex Banach space,T:D(T)→X be a nonexpansive mapping with F(T) nonempty,there F(T) is set of fixed points of T.Then F(T) is closed convex set.If F(T) is linear subspace in a Hilbert space and the Ishikawa iteration seguence from x_0∈D(T) of T converges a fixed point p∈F(T), then p is element of the best approimation of x_0 in F(T).