H(?)lder Continuity Of General Mutivalues Vector Quasiequilibrium Problems And Well-posedness Of Nash-type Equilibrium Problems

In this thesis, we study two problems: H(o|¨)lder continuity of solutions to generalized vector quasiequilibrium problems and well-posedness of Nash-type equilibrium Problems. The detailed contents are listed as follows.In the metric spaces, we discuss the H(o|¨)lder continuities of solutions for two types of perturbed generalized vector quasiequilibrium problems. Generally speaking, the solution set of vector quasiequilibrium problems is set-valued. Until now there are few papers papers (see[1, 2]) to discuss the H(o|¨)lder continuities of solution maps for perturbed vector equilibrium problems when their solution maps are set-valued. Motivated by the work in [2], in this paper, we investigate sufficient conditions which guarantee the H(o|¨)lder continuities of the solution maps for the two classes of perturbed generalized vector quasiequilibrium problems (PGVQEP1) and (PGVQEP2), respectively. Finally, two examples are given to illustrate that our results are different from the corresponding ones in [3], [4].At the same time, we discuss the well-posedness of Nash-type equilibrium problems (NEP). We firstly define the approximating solution sequence of Nash-type equilibrium problems and give two kinds of definition of well-posedness for (NEP). Then in virtue of the measure of noncompactness, some sufficient conditions of well-posedness results for (NEP) are obtained. Our results are different from others.