Modified Iterative Algorithms for Nonexpansive Mappings
Yonghong Yao, Muhammad Aslam Noor, Syed Tauseef Mohyud‐Din · International Journal of Stochastic Analysis · 2009
Let H be a real Hilbert space, let S, T be two nonexpansive mappings such that F(S)∩F(T) ≠ ∅, let f be a contractive mapping, and let A be a strongly positive linear bounded operator on H. In this paper, we suggest and consider the strong converegence analysis of a new two‐step iterative algorithms for finding the approximate solution of two nonexpansive mappings as xn+1 = βnxn + (1 − βn)Syn, yn = αnγf(xn) + (I − αnA)Txn, n ≥ 0 is a real number and {αn}, {βn} are two sequences in (0, 1) satisfying the following control conditions: (C1) lim n→∞ αn = 0, (C3) 0 < lim inf n→∞ βn≤lim sup n→∞ βn < 1, then ∥xn+1 − xn∥ → 0. We also discuss several special cases of this iterative algorithm.