Nash Game And Generalized Nonlinear Mixed Quasi-variational Inclusions

The theory of variational inequalities is an important branch of mathematics. It has many applications in theoritical and applied science. The problem of variational inclusions is an important extention in variational inequalities. Since it was proposed by A. Hassouni and A. Moudafi in 1994, there has been many achievements about it . In this paper, on the basis of papers by Khan M F and Ahmad R, we first discuss that the generalized Nash game model can be formulated into a quasi-variational inequality . Then we introduce and study a class of new generalized nonlinear mixed quasi-variational inclusions with relaxed monotone mappings and construct some iterative algorithms. We prove the existence of solutions for them and the convergence of the iterative sequences generated by the algorithms. Our results improve and extend the corresponding results in the recently literatures.