Existence Of Solutions For Generalized Strong Vector Equilibrium Problem

Equilibrium problems include optimization problems, Nash equilibrium problems,fixed points problems, saddle point problems and variational inequality problems asspecial cases. The model is abstracted from practical engineering technology andeconomic management problems, thus it has been widely applied. Human behaviorusually has the characteristics of multi-objective. So, the research is no longer limited tothe single objective problems, and is extended to the multi-objective problems. Theequilibrium problems also are expanded from scalar to vector equilibrium problem, arefarther extended to generalized vector equilibrium problems and generalized strongvector quasi-equilibrium problems with set-valued mappings.The existence of solutions for vector equilibrium problems is an important problemto research. If there is no solution, it will lose the actual application value. In view ofthis, this thesis is devoted to the existence of solutions for the generalized vectorequilibrium problems and the system of generalized strong vector quasi-equilibriumproblems. The existence results are generalized.In Chapter1, we introduced the background and the research situation of thegeneralized strong vector equilibrium problems. At the same time, the structure and themain results of this thesis were summarized.In Chapter2, a class of generalized strong vector equilibrium problems wasintroduced. With the mappings satisfying the conditions of upper semicontinuous,C (x)-continuity and convexity, we applied FKKM theorem to prove the existence ofsolutions for this class of generalized strong vector equilibrium problems. In addition,we extended the result to the existence of solutions for strong vector Q-implicitvariational inequality problems and strong vector Q-implicit complementarityproblems.In Chapter3, with the mappings satisfying the conditions of P-continuity, properlyP-quasiconvex and upper semicontinuous, we proved the existence of solutions for aclass of the system of generalized strong vector quasiequilibrium problems by K-F-G fixed-point theorem, the related properties of the balance neighborhood and convexcone.