In this paper, we prove a strong convergence theorem for finding a common element of the set of solutions of an equilibrium problem, the set of solutions of the variational inequality for a monotone mapping and the set of fixed points of a nonexpansive mapping in a Hilbert space by using a new hybrid method. Using this theorem, we obtain three new results for finding a solution of an equilibrium problem, a solution of the variational inequality for a monotone mapping and a fixed point of a nonexpansive mapping in a Hilbert space.
@article{1485,
title = {A Strong Convergence Theorem by a New Hybrid Method for an Equilibrium Problem with Nonlinear Mappings in a Hilbert Space},
journal = {CUBO, A Mathematical Journal},
volume = {10},
year = {2008},
language = {en},
url = {http://dml.mathdoc.fr/item/1485}
}
Shinzato, Rinko; Takahashi, Wataru. A Strong Convergence Theorem by a New Hybrid Method for an Equilibrium Problem with Nonlinear Mappings in a Hilbert Space. CUBO, A Mathematical Journal, Tome 10 (2008) . http://gdmltest.u-ga.fr/item/1485/