In this paper, we introduce the concept of relative convex sequences and
establish their fundamental properties, highlighting their similarities to
those of convex sequences. Additionally, we prove new inequalities of the Lupas
and Hermite-Hadamard-Fej\'er type for relative convex sequences. In certain
cases, and as an application, we show how the concept of relative convexity can
facilitate the derivation of new inequalities for convex sequences.Comment: 12 page