A New System Of Nonlinear Variational Inclusions Involving Maximal η-monotone Mapping

In this paper, A new system of generalized nonlinear variational inclusions involving maximal η-monotone mapping is introduced and studied in Hilbert spaces. We prove that the existence and uniqueness of solution of the system of generalized nonlinear variational inclusions by using the fixed point theorem.We also discuss the convergence of perturbed iterative algorithm for solving the system of nonlinear variational inclusions involving maximal η -monotone Mapping.First,we show the real background of the problems that we study, which comes from some optimization problems in network Economics, and we introduce the main works that have been studied by Anna Nagumey ,and we give example of changing spatial price equilibrium model to a classic variational inequality problem, so as to show that our works worthy of attention. Second, we introduce some basic conceptions, especially the definition of maximal η- monotone mapping, which is introduced by Huang and Fang, and we give one correlative important lemma. Section 3 is devoted to introduce the system of generalized nonlinear variational inclusions, and we prove that the existence and uniqueness of solution of the system of generalized nonlinear variational inclusions by using the fixed point theorem. Our main results are in the last two sections. In the last, we give some perturbed iterative algorithms, we prove the convergence ofiterative sequences generated by the iterative algorithms.Our results improve and generalize many known corresponding results.