In this paper, we introduce a new iterative process for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for an α-inverse-strongly-monotone, by combining an modified extragradient scheme with the viscosity approximation method. We prove a strong convergence theorem for the sequences generated by this new iterative process.
@article{bwmeta1.element.doi-10_2478_s11533-009-0003-x,
author = {Adrian Petru\c sel and Jen-Chih Yao},
title = {An extragradient iterative scheme by viscosity approximation methods for fixed point problems and variational inequality problems},
journal = {Open Mathematics},
volume = {7},
year = {2009},
pages = {335-347},
zbl = {1195.49017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0003-x}
}
Adrian Petruşel; Jen-Chih Yao. An extragradient iterative scheme by viscosity approximation methods for fixed point problems and variational inequality problems. Open Mathematics, Tome 7 (2009) pp. 335-347. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0003-x/
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