Abstract : In this paper, we consider the existence of solutions to some generalized vector quasi-equilibrium-like problem under a $c$-diagonal qua-si-convexity assumptions, but not monotone concepts. For an example, in the proof of Theorem 1, the $c$-diagonally quasi-convex concepts of a set-valued mapping was used but monotone condition was not used. Our problem is a new kind of equilibrium problems, which can be compared with those of Hou et al. .
Keywords : vector quasi-equilibrium-like problem, $c$-diagonally quasi-convex, open lower sections, Browder fixed point theorem