Three-step iterative algorithms for solving the system of generalized mixed quasi-variational-like inclusions

In this paper, we consider the system of generalized mixed quasi-variational-like inclusions in Hilbert spaces. We extend the auxiliary principle technique to develop a three-step iterative algorithm for solving the system of generalized mixed quasi-variational-like inclusions. Under the assumptions of the continuity and partially relaxed η-strong monotonicity of set-valued mappings, we establish the convergence for our algorithm. Our algorithm and its convergence results are new, and generalize Ding's predictor-corrector iterative algorithms. Moreover, our results unify some known results in the literature as well.