On split equilibrium, variational inequality and fixed point problems for demicontractive multivalued mappings

In this paper, we study the problem of finding the common solutions of split equilibrium problem, variational inequality problem and common fixed point problem for demicontractive multivalued mappings in real Hilbert spaces. We propose a new inertial iterative algorithm with self-adaptive step size for approximating the solution of this problem. Under mild and standard conditions, we prove a strong convergence result for the sequence generated by our proposed algorithm without the knowledge of the operator norm. Moreover, we apply our result to study split minimization problem and provide some numerical experiments to demonstrate the applicability and performance of our algorithm in comparison with some of the related results in the literature.