Convergence analysis for solving equilibrium problems and split feasibility problems in Hilbert spaces

In this article, we propose four alternated inertial algorithms for finding a common solution of equilibrium problems and split feasibility problems in Hilbert spaces. We present a variable step size, which is not required to know the operator norm. Furthermore, these algorithms adopt the new convex subset form by a sequence of closed balls instead of half spaces, and it is easy to calculate the projections onto these sets. We establish strong and weak convergence theorems of these algorithms under some proper assumptions and also present a numerical experiment to illustrate the performance and the advantage of the proposed algorithms.