Iterative algorithms for solving generalized nonlinear mixed variational inequalities

A new concept of g-partially relaxed strong monotonicity of mappings is introduced. By applying the auxiliary variational inequality technique, some new predictor–corrector iterative algorithms for solving generalized nonlinear mixed variational inequalities are suggested and analyzed. The convergence of the algorithms only need the continuity and the g-partially relaxed strongly monotonicity of mappings. These algorithms and convergence result are new, and generalize some known results in literature.