Viscosity approximation of nonexpansive non-self mapping in hilbert spaces
Linfang Xing · Basic Sciences Journal of Textile Universities · 2005
.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 iterative sequences {x_t｝,{y_t} and the explicit iterative sequences {x_n},{y_n}.It is proved that T has fixed point if and only if the sequences {x_t},{y_t},{x_n},{y_n} are boundary.It is also proved,in satisfying appropriate conditions,the sequence {x_t},{y_t},{x_n} and {y_n} strongly converges to a fixed point of T.