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 setvalued 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 quasivariational 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.

Keywords

• Mixed implicit quasi-variational inclusion
• Set-valued mapping
• Iterative algorithm
• Perturbed algorithm with errors
• Stability