Existence Results for Generalized Mixed Vector Variational-like Inequalities with a Variable Ordering Relation

The purpose of this paper is to study the solvability of the generalized mixed vector variational-like inequalities(for short, GMVVLI) with a variable ordering relation in reflexive Banach spaces, which is more general including many known vector (scalar) vector variational inequalities and vector (scalar) variational-like inequalities as special cases. According to completely continuous definition prove the existence results of strong solutions of GMVVL If or monotone vector multi-function by using the KKM-Fan theorem under mild assumptions. Our results presented here are extension and improvement of some earlier and recent results in the literature.