Connectedness And Well-Posedness Of Vector Equilibrium Problem

In this thesis,we study some problems in vector equilibrium and bilevel vector equilibrium,including the following works:1.We study the connectedness of approximate solutions set for parametric gen-eralized vector equilibrium problems.We firstly define some approximate solutions for the parametric generalized vector equilibrium which contains ?-weak approx-imate solution??-approximate solution??f-approximate solution and strong ef-fective solution set.A scalarization characterization of ?-approximate solutions for parametric generalized vector equilibrium problems is established by using the C-subconvelike property of the involved mappings.Further,the connectedness for two types approximate solutions sets are derived by using scalarization methods.Finally,the relationship among these approximate solution sets are obtained under some suitable conditions.2.We investigate the existence solutions and well-posedness of solutions for bilevel vector equilibrium problems.We firstly define a class of ?-approximate solu-tion for bilevel vector equilibrium problems.The existence solutions are established by using Fan-KKM theorem and other necessary conditions.We then explore on the relationship between the uniqueness of the solutions and the upper semicontinu-ity of approximating solution sets and the well-posedness for bilevel vector equilib-rium problems.We further prove that the generalized well-posedness can be equiv-alently characterized by the compactness of the solution sets and the upper semi-continuity of the approximating solution sets.Then the generalized well-posedness for bilevel vector equilibrium problems are derived.Finally,based on another k-ing of approximate solutions,we discuss well-posedness of necessary and sufficient conditions for bilevel vector equilibrium problems once again.