TY - JOUR
A2 - Xu, Hong Kun
AU - Yao, Yonghong
AU - Noor, Muhammad Aslam
AU - Mohyud-Din, Syed Tauseef
PY - 2009
DA - 2009/06/03
TI - Modified Iterative Algorithms for Nonexpansive Mappings
SP - 320820
VL - 2009
AB - 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 followingcontrol 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.
SN - 2090-3332
UR - https://doi.org/10.1155/2009/320820
DO - 10.1155/2009/320820
JF - Journal of Applied Mathematics and Stochastic Analysis
PB - Hindawi Publishing Corporation
KW -
ER -