Weak and strong convergence of inertial-type iterative algorithms for solving split general system of generalized equilibrium problem

In this article, we generalize several equilibrium and variational inequality problems by introducing new general system of split generalized equilibrium problem. We introduce an inertial-type iterative algorithm and prove its weak convergence to the common solution of general system of split generalized equilibrium problem and fixed point problem of demicontractive mapping. We also prove strong convergence of the proposed algorithm by using shrinking projection method. Finally, we give numerical experiments to validate the performance of our algorithm and compare it with other existing method.