Set of fixed points of nonexpansive mapping and element of the best approximation in a Banach space
Yongfu Su · Basic Sciences Journal of Textile Universities · 2004
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).