An inertial-viscosity algorithm for solving split generalized equilibrium problem and a system of demimetric mappings in Hilbert spaces

In this paper, we introduce a new inertial-viscosity approximation method for solving a split generalized equilibrium problem and common fixed point problem in real Hilbert spaces. The algorithm is designed such that its convergence does not require the norm of the bounded linear operator underlying the split equilibrium problem. Moreover, a strong convergence result is proved under mild conditions in real Hilbert spaces. Furthermore, we give some numerical examples to show the efficiency and accuracy of the proposed method and we also compare the performance of our algorithm with other related methods in the literature.