Multi-step inertial algorithms for equilibrium, fixed point, general systems of variational inequalities and split feasibility problems

In this paper, we present two novel multi-step inertial iterative methods to approximate a common element that combines equilibrium problems with other problems in real Hilbert spaces. Firstly, by combining equilibrium problems, fixed point problems and a general system of variational inequalities, we adopt a conjugate gradient method to solve them. Secondly, by integrating equilibrium problems, fixed point problems and split feasibility problems, we employ a S-iteration process to address them. Under appropriate assumptions and mild conditions, we obtain strong convergence theorems of our proposed algorithms. Finally, some numerical experiments are provided to test and verify the efficiency of the proposed algorithms.