Bulletin of the
Korean Mathematical Society BKMS

In this paper, we introduce an iterative sequence for finding solution of a system of mixed equilibrium problems and the set of fixed points of a nonexpansive mapping in Hilbert spaces. Then, the weak and strong convergence theorems are proved under some parameters controlling conditions. Moreover, we apply our result to fixed point problems, system of equilibrium problems, general system of variational inequalities, mixed equilibrium problem, equilibrium problem and variational inequality.

Keywords: nonexpansive mapping, system of mixed equilibrium problems, fixed point, weak convergence, strong convergence

MSC numbers: 49J30, 49J53, 47H09, 47H10