Existence Of Solution And Error Bounds For Several Classes Of Variational Inequality Problems

Variational inequality is the equilibrium optimization problem has important applications in many fields of national economy.There are many special cases of vector equilibrium,such as vector variational inequalities and vector equilibrium problems.Existence of solutions of the variational inequality is a hot issue in the field of variational inequality,many scholars pay special attention to the existence of solutions of the variational inequality.The error bound is of variational inequalities reflect the premise of stability and sensitivity analysis.The gap function is an effective way to get the error bounds of variational inequalities.Howeve have the important theoretical significance and application value of existence and thus error bounds for solving inequality problem on the several classes.In this thesis,we discuss the generalized multivalued vector variational-like inequalities,and the existence of solutions for generalized strong vector quasi equilibrium problems.In addition,the gap function and global error bounds for generalized mixed quasi-variational inequalities we also discussed in this thesis.The main contents of this thesis are summarized as follows:In the second chapter,we consider two kinds of generalized multivalued vector variational-like inequalities in Banach spaces.By using the KKM theorem,under the condition of compactness and convexity.The existence of solutions for two classes of generalized multivalued vector variational like inequalities is obtained by using the lower semi continuity of multivalued mappings and the affine conditions of mappings.In the third chapter,under the conditions of naturally quasi C-convex,the definition of lower (-C)- contimuity and the Kakutani-Fan-Glicksberg fixed point theorem,an existence theorem of the solution to multivalued generalized strong vector quasi-equilibrium problems was established,without the assumption that the dual cone C*of the ordering cone C has a weak-star compact base.In the fourth chapter,In the space of Hilbert introduce a new class of generalized mixed quasi-variational inequality.By using the introduced regularized gap function and D-gap function,Under conditions of strongly mixed monotonicity and Lipschitz continuity,the global error bound of the generalized mixed quasi-variational inequality were obtained.