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 words

nonexpansive mapping relaxed cocoercive mapping variational inequality fixed point equilibrium problem extragradient method 

AMS (2000) subject classification

47H09 47J20 


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Copyright information

© Editorial Board of Analysis in Theory and Applications and Springer Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceKing Mongkut’s University of Technology Thonburi KMUTTBang-Mod, BangkokThailand

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