Generalized nonlinear mixed implicit quasi-variational inclusions with set-valued mappings

Abstract

In this paper, we introduce and study a new class of implicit quasi-variational inclusions, which is called the generalized nonlinear mixed implicit quasi-variational inclusion with set-valued mappings. Using the resolvent operator technique for maximal monotone mapping, we construct some new iterative algorithms for solving this class of generalized nonlinear mixed implicit quasi-variational inclusions with non-compact set-valued mappings. We prove the existence of solution for this kind of generalized nonlinear mixed implicit quasi-variational inclusions with non-compact set-valued mappings and the convergence of iterative sequences generated by the algorithms. We also discuss the convergence and stability of perturbed iterative algorithm with errors for solving a class of generalized nonlinear mixed implicit quasi-variational inclusions with single-valued mappings.