Upper semicontinuity in a parametric general variational problem and application

In this paper, we give sufficient conditions for the upper semicontinuity property of the solution mapping of a general model which includes many generalized vector quasi-equilibrium problems with set-valued maps as special cases. The main result generalizes and improves several recent results. An example is given to illustrate such generalization and improvement. The main result is also applied to a model which can be interpreted as a system of generalized vector quasi-equilibrium problems with moving cones. The main tools of the paper are some new notions of cone-semicontinuity properties and openness/closedness properties of families of set-valued maps.