Weak and strong convergence of an iterative algorithm for Lipschitz pseudo-contractive maps in Hilbert spaces
Abstract
In this paper, let K be a closed convex subset of a real Hilbert space H and T: K → K a Lipschitz pseudo-contractive map such that F(T) 6= / 0. Let {αn}, {βn} and {γn} be real sequences in (0,1). For x1∈ K, let {xn} be generated iteratively by
xn+1= Pk[(1−αn−γn)xn+γnTyn],
yn= (1−βn)xn+βnTxn,n ≥ 1.
Under some mild conditions on parameters {αn}, {βn}, {γn}, we prove that our new iterative algorithm converges strongly to a fixed point of T. No compactness assumption is imposed on T and no further requirement is imposed on F(T).
Copyright © 2016 V.E. Ingbianfam, F.A. Tsav, I.S. Iornumbe. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
V. E. Ingbianfam, F. A. Tsav, I. S. Iornumbe, Weak and strong convergence of an iterative algorithm for Lipschitz pseudo-contractive maps in Hilbert spaces, Adv. Fixed Point Theory 6 (2016), 194–206.
BibTeX
@article{Ingbianfam2016,
author = {Ingbianfam, V.E. and Tsav, F.A. and Iornumbe, I.S.},
title = {Weak and strong convergence of an iterative algorithm for Lipschitz pseudo-contractive maps in Hilbert spaces},
journal = {Adv. Fixed Point Theory},
volume = {6},
year = {2016},
pages = {194--206},
doi = {}
}