| As an effective research tool,variational inequalities play an important role in the study of nonlinear problems,and are widely employed in Mechanics,Transportation,Economics,Engineering and other fields.Fuzzy hemivariational inequalities,involving not only the generalized(Clarke)subdifferential of non-convex and non-smooth function but also fuzzy mappings,are an important extension of variational inequalities and a crucial mathematical model on the research of frictional contact problems under uncertain environments.Therefore,the study of fuzzy variational-hemivariational inequalities has vital theoretical and practical significance.In this thesis,a class of fuzzy variational-hemivariational inequalities is considered in reflexive Banach spaces,and the solvability,uniqueness,well-posedness and metric characterizations of well-posedness are studied by applying fuzzy set theory,nonlinear analysis and convex analysis.The specific research content is as follows:Firstly,with the help of the membership function of fuzzy set,the fuzzy mapping involved in this thesis is converted into the corresponding set-valued operator,so that the studied fuzzy variational-hemivariational inequality is converted into a corresponding set-valued variational-hemivariational inequality.By virtue of the surjective lemma of setvalued mapping and under some suitable conditions,the existence and uniqueness of solution to the inequality are obtained under bounded and unbounded constraint sets,respectively.Then,by considering the perturbation problem of the inequality,the Levitin-Polyakα-well-posedness by perturbations of the inequality,including strong(weak)Levitin-Polyakα-well-posedness by perturbations and strong(weak)Levitin-Polyak α-well-posedness by perturbations in the generalized sense,are defined and the metric characterizations of different Levitin-Polyak α-well-posedness by perturbations are proved.Finally,this thesis proves the equivalence between the weak Levitin-Polyak α-well-posedness by perturbations of the inequality and its unique solvability under certain conditions,and gives a sufficient condition for the strong Levitin-Polyak α-well-posedness by perturbations in the generalized sense.The class of fuzzy variational-hemivariational inequalities studied in this thesis is the extension of hemivariational inequalities under uncertain environments in the existing literature.The obtained results of solvability and well-posedness extend the relevant research results of variational inequality and hemivariational inequality in the existing literature,which are of great significance. |
