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 ηη-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.