  In this paper, we propose two parallel extragradient - viscosity methods for
finding a particular element in the common solution set of a system of
equilibrium problems and finitely many fixed point problems. This particular
point is the unique solution of a variational inequality problem on the common
solution set. The main idea of the paper is to combine three methods including
the extragradient method, the Mann iteration method, the hybrid
steepest-descent method with the parallel splitting-up technique to design the
algorithms which improve the performance over some existing methods. The
strongly convergent theorems are established under the widely used assumptions
for equilibrium bifunctions.
