Predictor–corrector algorithms for solving generalized mixed implicit quasi-equilibrium problems

Abstract

In this paper, we introduce two new classes of operators–partially relaxed strongly pseudomonotonicity and partially relaxed strongly jointly pseudomonotonicity. We use the auxiliary principle technique to suggest a new class of iterative algorithms for solving generalized mixed implicit quasi-equilibrium problems. We also prove that the convergence of the suggested methods requires only the continuity and the partially relaxed strongly jointly pseudomonotonicity. Since generalized mixed implicit quasi-equilibrium problems include equilibrium, variational inequality and complementarity problems as specials, our results represent improvement and generalization of the previously known results.