The Study Of Berge And Hausdorff Continuity Of Solution Sets Mapping For Vector Equilibrium Problems

It is well known that the stability analysis of vector equilibrium problem is one of the hotspots in the theory and application of vector optimization(see[1-15,17-26,29-53]),and continuity is a crucial aspect of stability analysis.First and foremost,the lower semicontinuity of the solution set mapping to the generalized set-valued strongly vector equilibrium problem is investigated,by means of the properties of the set limit and the new assumption.Besides,the connectedness of approximate solutions and the Hausdorff upper(lower)semi-continuity of approximate solution mappings to parametric primal weak equilibrium problems are obtained.Under some weak assumptions,some sufficient conditions of the connectedness of approximate solutions and the Hausdorff continuity of approximate solution mappings to parametric dual weak vector equilibrium problems are obtained,by using the scalarization method.Last but not least,an application in the vector optimization problem is given.In chapter three,the lower semicontinuity of the solution mappings,to parametric generalized set-valued strong vector equilibrium problems,is proved,by using the prop-erties of the set limit and the hypothesis of weak/-property,and the method is different from the one used in[15].The obtained results generalize the corresponding ones in the literature([3,5-7,9,15]),examples are also provided for the illustration of the obtained results.In chapter four,we discuss the stability of parametric primal and dual weak vec-tor approximate equilibrium problems under the scalarization method.Firstly,the con-nectedness of approximate solutions and the Hausdorff upper(lower)semi-continuity of approximate solution mappings to parametric primal weak equilibrium problems,under the assumption of nearly C-subcovexlikeness,are obtained.Then,under some weak as-sumptions,some sufficient conditions of the connectedness of approximate solutions and the Hausdorff continuity of approximate solution mappings to parametric dual weak vec-tor equilibrium problems are obtained,by using the scalarization method.At last,an application in vector optimization problems is given.The obtained results improve and generalize the corresponding ones in the literature...