On Sensitivity Analysis Of Solutions For A System Of Parametric Variational Inclusions

In this paper, we introduce a new system of variationalinclusions:We mainly discuss and study the parametric version of Problem (*).That is, for each fixedλ∈D, find (a,b) = (a(λ),b(λ))∈H×H suchthatwhich is called a system of parametric variational inclusions. With theproperties of the resolvent operator technique associated with (H,η)-monotone operators, where the resolvent operator Lip-schitz continuous, the equivalence between the system of paramet-ric variational inclusions and the fixed-point problems is proved andthe existence and uniqueness of solutions for this new system is es-tablished. A new iterative algorithm for computing the approximatesolutions is constructed and the convergence criteria of the iterativesequence generated by the iterative algorithm is given, too. At last,the sensitivity of solutions for the system of parametric variational in-clusions is analyzed. The results presented in this paper are new andimprove, extend the corresponding results due to Fang, Huang andThompson [Comput. Math. Appl.,49(2005),365–374] and Agar-wal, Cho and Huang [Appl. Math. Lett., 13(6)(2000), 19–24].