| The research on well-posedness can be traced back to the 1960 s,involving optimization problems,variational inequality problems,equilibrium problems,fixed point problems and so on.As a generalization of variational and hemivariational inequalities,split hemivariational inequalities are composed of two hemivariational inequalities and a linear constraint equation,and have important applications in the fields of Mechanics,Engineering and Optimal Control.Therefore,in recent years,many scholars in related fields such as operations research have devoted themselves to the research of split hemivariational inequalities,including solvability,well-posedness and applications.This thesis mainly studies well-posedness in the sense of Tykhonov Triple for a class of split variational-hemivariational inequalities,that is,T-well-posedness,including the metric characterizations of T-well-posedness for the split variational-hemivariational inequality,the relationship between T-well-posedness of the split variational-hemivariational inequality and the existence and uniqueness of solutions,the continuous dependence of solutions for the split variational-hemivariational inequality.The specific research content is as follows:First of all,T-approximating sequence and T-well-posedness of the studied split variational-hemivariational inequality are defined by exploiting the concept of Tykhonov Triple and selecting the specific Tykhonov Triple.And the metric characterizations of different T-well-posedness are obtained under assumptions such as radially continuous monotonicity.Then,by proving the equivalence of three types of forms of the split variational-hemivariational inequality,this thesis presents the equivalence conditions between well-posedness and unique solvability of the split variational-hemivariational inequality and the sufficient condition of strong T-well-posedness in the generalized sense.Finally,with the help of T-well-posedness of the split variational-hemivariational inequality,the continuous dependence of the solution for the split variational-hemivariational inequality is obtained.Well-posedness of the split variational-hemivariational inequality in the sense of Tykhonov Triple studied in this thesis is an extension of the concepts of classical Tykhonov well-posedness,and the obtained conclusions in this thesis also generalized related research results on the well-posedness of split variational inequalities and split hemivariational inequalities in the existing literature. |
