A hybrid extragradient method for Pseudomonotone equilibrium problems and fixed point problems

In this paper, we introduce 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 pseudomonotone and Lipschitz-type continuous bifunctions. The iterative process is based on two well-known methods: Hybrid and extragradient. We show that the iterative sequences generated by this algorithm converge strongly to the common element in a real Hilbert space.