New Randers metrics defined by the other Randers metrics

In this short article, using a left-invariant Randers metric F, we define a new left-invariant Randers metric F̃. We show that F is of Berwald (Douglas) type if and only if F̃ is of Berwald (Douglas) type. In the case of Berwaldian metrics, we give the relation between their flag curvatures. Also, we have studied the relations between their base Riemannian metrics. Finally, as examples, the results are studied in the Heisenberg group and almost Abelian Lie groups.