Strong convergence of nonexpansive nonself-mapping in Hilbert space
Rudong Chen, Zhichuan Zhu · International Mathematical Forum · 2007
Abstract. Let C be a closed convex subset of a Hilbert space X, T: C → H a non-expansive nonself-mapping such that F (T) = ∅. P: H → C is a projective operator, f: H → C is a fixed contractive. In this paper, we study the convergence of the following type sequence generated by xn+1 = P (αnf(xn) + (1 − αn)Txn) and prove the sequence {xn} converges strongly to a fixed point of F (T) under the weaker condition Txn+1 − Txn ⇀ 0, n → ∞. The result improves the result of Wittmann.