Existence Of Solutions And Well-posedness For Generalized Vector Quasi-equilibrium Problems

Generalized implicit vector quasi-equilibrium problems are generalized formequilibrium problems, constraint mappings are introduced in the generalized implicitvector quasi-equilibrium problems. So that the existence of solutions of such problemsbecome a difficult problems.In addition, most generalized vector quasi-equilibrium problems are difficult tosolve accurately. So that we can only design iteration sequence to approximate thesolution of the problems. It is another problem for us to research that what conditionscan ensure the iterative sequence converge to the solution of the original problem.Therefore, in this thesis existence of solutions and well-posedness for generalizedimplicit vector equilibrium problems are researched.Chapter2is is devoted to the existence of solutions of a class generalized implicitvector quasi-equilibrium problem including a set-valued mapping. First, under P-convex and P-continuous conditions, using the scalarization function and the theorem ofcontinuous partition of unity theorem, the existence of solutions of the generalizedimplicit vector quasi-equilibrium problems are established. Secondly, by the continuousselection theorems and fixed point theorems, without any monotonic assumption, theexistence theorem of the generalized strong implicit vector quasi-equilibrium problemare obtained, the results generalize the corresponding results in related literatures.In chapter3, the well-poaedness for parametric generalized strong vectorquasi-equilibrium problems are discussed. First, the well-poaedness for parametricgeneralized strong vector quasi-equilibrium problems are researched; Secondly, underthe well-posedness hypothesis, the continuity characterize of the solution set is given,and examples are given to illustrate the continuity of solution set.