In this paper, we introduce an iterative scheme by viscosity approximation method
for obtaining a common element of the set of solutions of an equilibrium problem and the set of
fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for
an inverse-strongly monotone mapping in a Hilbert space. We obtain a strong convergence which
improves and extends S. Takahashi and W. Takahashi’s result [S. Takahashi, W. Takahashi, Viscosity
approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math.
Anal. Appl. 331 (2007) 506-515].
@article{1225813984,
author = {Wang, Shenghua and Zhou, Haiyun and Song, Jianmin},
title = {Viscosity approximation methods for equilibrium problems and fixed point problems of nonexpansive mappings and inverse-strongly monotone mappings},
journal = {Methods Appl. Anal.},
volume = {14},
number = {1},
year = {2007},
pages = { 405-420},
language = {en},
url = {http://dml.mathdoc.fr/item/1225813984}
}
Wang, Shenghua; Zhou, Haiyun; Song, Jianmin. Viscosity approximation methods for equilibrium problems and fixed point problems of nonexpansive mappings and inverse-strongly monotone mappings. Methods Appl. Anal., Tome 14 (2007) no. 1, pp. 405-420. http://gdmltest.u-ga.fr/item/1225813984/