Generalized Vector Implicit Quasi-Variational-like Inequality Problems

Generalized vector implicit quasi variational-like inequalities are a generalized form ofvariational-like inequalities, which cover elasticity, mechanics, physics, finance, control theoryand so on. They have become a significant foundation and tool for studying multiobjectiveprogram and equilibrium. The research on them involves functional analysis, convex analysis,set-valued analysis and fixed-point theory, which is of much academic value. This dissertation isdevoted to considering generalized vector implicit quasi variational-like inequality problems.The main results obtained can be summarized as follows:1. In chapter2, the existence of solutions to a class of generalized vector implicit quasivariational-like inequality problems(GVIQVLIP) is studied. The existence results ofGVIQVLIP is obtained by using KKM theorem under certain assumptions. And an exampleis given to illustrate the general results. Furthermore, the existence theorem of GVⅠQVⅠPis proved by using the result of [61].2. In chapter3, the existence of solutions to a class of generalized vector implicit quasivariational-like inequality problems(GVIQVLIP-Ⅰ) with set-valued mappings in Hausdorfftopological vector spaces is established. Under the assumptions of lower semi-continuity,affinity and monotonicity of mappings, the existence of solutions to equivalent problem withGVIQVLIP-) is proved by using KKM theorem.3. In chapter4, in views of gap functions, under certain assumptions, a class of generalizedvector implicit quasi variational-like inequality problem(GVIQVLIP-Ⅱ) is studied. First, thegap functions of SGVIQVLIP-Ⅱ) and the weakly generalized vector implicit quasiariational-like inquality problems(WGVIQVLIP-Ⅱ) are defined. Then the necessary andsufficient conditions for the strongly(weakly) generalized vector implicit quasivariational-like inequality problem are given by using of the gap functions.