On The Solution Set Of General Monotone Variational Inequalities

In this paper, we main study general variational inequalitiesand Equilibrium problem which can be divided into three aspects as fol-lowing: Firstly, we prove the equivalence between the characterization ofdual variational inequalities having nonempty bounded solution set and theexistence of strict feasible point; then, since the trivial solution of variationalinequalities maybe unbounded, we obtain that the existence of strict feasiblepoint is equivalent to the nonempty bounded solution set of general variationalinequalities provided the mapping G be stable quasimonotone; Secondly, weproved a kind of coercivity which is equivalent to the the nonempty solution setfor general vector variational inequalities; furthermore, we expound the minimalcondition for the nonempty bounded solution set for general vector variationalinequalities; Lastly, we define a kind of mapping be weak quasimonotonicitywhich is weaker than quasimonotonicity, and then we raise the conditionsfor Equilibrium problem to have solutions, and hence have extended someconclusions about variational inequalities.