Convergence analysis for solving the split equality equilibrium problem in Hilbert spaces

In this paper, we propose four alternated inertial algorithms with self-adaptive stepsize to address the split equality equilibrium problem (SEEP) in real Hilbert spaces, without the need for any prior knowledge of the operator norm. Moreover, these algorithms adopt the convex subset form by a sequence of closed balls rather than half-spaces, and it is simple to calculate the projections onto these sets. Under some proper assumptions, we demonstrate weak and strong convergence theorems of our algorithms, particularly strong convergence towards the minimum-norm solution of the SEEP. As application, we will utilize our results to study the split equality variational inequality problem. Finally, we provide a numerical example to illustrate the effectiveness of the proposed algorithms.