A hybrid extragradient method extended to fixed point problems and equilibrium problems

Abstract

In this article, we present a new hybrid extragradient iteration method for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of equilibrium problems for a pseudomonotone and Lipschitz-type continuous bifunction. We obtain strongly convergent theorems for the sequences generated by these processes in a real Hilbert space.

Keywords:

• equilibrium problems
• pseudomonotone
• Lipschitz-type continuous
• strongly convergence
• extragradient method
• nonexpansive mapping

AMS Subject Classifications::

• 2010
• 65 K10
• 90 C25

Acknowledgements

The author thank the referee for his/her useful comments, remarks and important suggestions on this article. This work was supported by the Vietnam National Foundation for Science Technology Development (NAFOSTED).