Existence And Stability Of Solutions For Generalized Vector Equilibrium Problem

It is well known that, as an important branch of mathematics, equilibrium problems areapplied to the field of computer science, engineering technology, transportation, economics andmanagement et.al. Generalized vector equilibrium problems with set-valued mapping, involvingmultiobjective optimization problem, vector equilibrium problem, vector complementarityproblem, fixed point problem, saddle point problem, vector variational inequalities and so on.This dissertation is devoted to studying lexicographic vector equilibrium problems, generalizedvector equilibrium problems with set-valued mapping in Banach spaces and Hausdorfftopological vector spaces, respectively.The main results, obtained in this dissertation, may be summarized as follows:In chapter2, the concept of h C(x) pseudomonotonicity is introduced. By utilizing theexistence of solutions to the generalized vector equilibrium problems with a continuous selectiontheorem, the existence results for generalized vector equilibrium problems with set-valuedmappings are obtained.In chapter3, a generalized system in real Banach spaces is introduced. Using Brouwer’sfixed point theorem, some existence theorems of the generalized system without monotonicityare established. Further, the concept of C-strong pseudomonotonicity and Minty’s lemma forthe generalized system are extended. Then using the KKM-Fan lemma and Minty lemma, anexistence theorem for the generalized system with monotonicity in real reflexive Banach spacesis established.In chapter4, the lexicographic vector equilibrium problems is introduced. By using the ideaof sequential process, the upper semicontinuity and closedness of the solution set map areestablished for a parametric lexicographic generalized vector equilibrium problem.