Existence of solutions and Hadamard well-posedness for generalized strong vector quasi-equilibrium problems

In this paper, we establish an existence result for the (GSVQEP) without assuming that the dual of the ordering cone has a weak star compact base and give an example to show our existence theorem is different from the main result of Long et al. [X. J. Long, N. J. Huang, K. L. Teo, Math. Comput. Modelling, 47 (2008), 445451]. Furthermore, we introduce a concept of Hadamardtype wellposedness for the (GSVQEP) and establish sufficient conditions of Hadamard-type well-posedness for the (GSVQEP).