A generalization of Minty's lemma and its applications to generalized mixed vector equilibrium problems

In this article, we introduce and study a class of generalized mixed vector equilibrium problems for multifunctions, which includes as special cases it number of generalized vector variational inequalities, generalized vector variational-like inequalities and generalized vector equilibrium problems. We First establish a new vector version of Minty's lemma, and then prove an existence theorem Of solutions for the generalized mixed vector equilibrium problems by using thiS result. Furthermore, this existence theorem is applied to obtain it new existence result of solutions for a class of generalized vector variational-like inequalities.