Predictor–corrector iterative algorithms for solving generalized mixed quasi-variational-like inclusion

By applying the concept of partially relaxed η -strong monotonicity of set-valued mappings due to author and the auxiliary variational inequality technique, some new predictor–corrector iterative algorithms for solving generalized mixed quasi-variational-like inclusions are suggested and analyzed. The convergence of the algorithms only need the continuity and the partially relaxed η -strongly monotonicity of set-valued mappings. The algorithm and convergence result are new, and generalize some recent known results in literatures.