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

Abstract

In this article, we introduce and study a class of generalized mixed vector equilibrium problems for multifunctions, which includes as special cases a 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 a new existence result of solutions for a class of generalized vector variational-like inequalities. ¶Dedicated to the memory of Prof. Dr Alexander Moiseevich Rubinov.