Relaxed CQ algorithms involving the inertial technique for multiple-sets split feasibility problems

In this work, we introduce the inertial relaxed CQ algorithms for solving the multiple-sets split feasibility problems (MSFP) in the frameworks of Hilbert spaces. By mixing the inertial technique with the self-adaptive method, not only the computation on the matrix norm and the orthogonal projection is relaxed but also the convergence speed is improved. We then establish the strong convergence theorem by combining the relaxed CQ algorithm with Halpern's iteration process. Finally, we provide numerical experiments to illustrate the convergence behavior and the effectiveness of our proposed algorithm. The main result extends and improves the corresponding results.