On generalized vector implicit variational inequalities and complementarity problems

In this paper, two generalized vector implicit variational inequalities and three generalized vector implicit complementarity problems are introduced with a general order in ordered Banach spaces and the equivalence between them is studied under certain assumptions. Furthermore, some existence theorems for the generalized vector implicit variational inequalities are derived by using Lin's result (1986) and Nadler's result (1969). We affirmatively answer the open question proposed by Rapcsak (2000). Our results are the extension and improvement of the corresponding results in Huang and Li (2006).