An extragradient method for relaxed cocoercive variational inequality and equilibrium problems
Chaichana Jaiboon, Poom Kumam, Usa Wannasingha Humphries · Analysis in Theory and Applications · 2009
The purpose of this paper is to investigate the problem of finding the common element of the set of common fixed points of a countable family of nonexpansivemappings, the set of an equilibrium problem and the set of solutions of the variational inequality problem for a relaxed cocoercive and Lipschitz continuous mapping in Hilbert spaces. Then, we show that the sequence converges strongly to a common element of the above three sets under some parameter controlling conditions, which are connected with Yao, Liou, Yao, Takahashi and many others.