Solvability and iterative algorithms for a system of generalized nonlinear mixed quasivariational inclusions with "Equation missing" No EquationSource Format="TEX", only image and EquationSource Format="MATHML" -monotone operators

Abstract

Abstract In this paper, we introduce and discuss a new system of generalized nonlinear mixed quasivariational inclusions with ( H i , η i ) -monotone operators in Hilbert spaces, which includes several systems of variational inequalities and variational inclusions as special cases. By employing the resolvent operator technique associated with ( H i , η i ) -monotone operators, we suggest two iterative algorithms for computing the approximate solutions of the system of generalized nonlinear mixed quasivariational inclusions. Under certain conditions, we obtain the existence of solutions for the system of generalized nonlinear mixed quasivariational inclusions and prove the convergence of the iterative sequences generated by the iterative algorithms. The results presented in this paper extend, improve and unify many known results in recent literature. MSC:47J20, 49J40.