Implicit iteration process of nonexpansive non‐self‐mappings
Somyot Plubtieng, Rattanaporn Punpaeng · International Journal of Mathematics and Mathematical Sciences · 2005
Suppose C is a nonempty closed convex subset of real Hilbert space H. Let T : C → H be a nonexpansive non‐self‐mapping and P is the nearest point projection of H onto C. In this paper, we study the convergence of the sequences {xn}, {yn}, {zn} satisfying xn = (1 − αn)u + αnT[(1 − βn)xn + βnTxn], yn = (1 − αn)u + αnPT[(1 − βn)yn + βnPTyn], and zn = P[(1 − αn)u + αnTP[(1 − βn)zn + βnTzn]], where {αn}⊆(0, 1), 0 ≤ βn ≤ β < 1 and αn → 1 as n → ∞. Our results extend and improve the recent ones announced by Xu and Yin, and many others.