The System of Vector Variational-like Inequalities with Weakly Relaxed $\{\eta_\gamma-\alpha_\gamma\}_{\gamma \in \Gamma}$ Pseudomonotone Mappings in Banach Spaces

In this paper, we introduce two concepts of weakly relaxed $\{\eta_\gamma-\alpha_\gamma\}_{\gamma \in \Gamma}$ pseudomonotone and demipseudomonotone mappings in Banach spaces. Then we obtain some results of the solutions existence for a system of vector variational-like inequalities with weakly relaxed $\{\eta_\gamma-\alpha_\gamma\}_{\gamma \in \Gamma}$ pseudomonotone and demipseudomonotone mappings in reflexive Banach spaces. Finally we show that our results improve and extend some corresponding results of Ref \cite{R5}.