An extragradient method for relaxed cocoercive variational inequality and equilibrium problems
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.
Key wordsnonexpansive mapping relaxed cocoercive mapping variational inequality fixed point equilibrium problem extragradient method
AMS (2000) subject classification47H09 47J20
- Yao, J. C. and Chadli, O., Pseudomonotone Complementarity Problems and Variational Inequalities, in: J.P. Crouzeix, N. Haddjissas, S. Schaible (Eds.), Handbook of Generalized Convexity and Monotonicity, 2005, 501–558.Google Scholar
- Yao, Y., Liou, J.C. and Yao, J.C., An Extragradient Method for Fixed Point Problems and Variational Inequality Problems, Journal of Inequalities and Applications, (2007), Article ID 38752, 12 pages.Google Scholar