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By using the volume form induced from the projective sphere bundle of the Finsler manifold, we study the Finsler minimal submanifolds. It is proved that such a volume form for the Randers metric F = α+β in a Randers space is just that for the Riemannian metric a, and therefore the Bernstein type theorem in the special Randers space of dimension ≤ 8 is true. Moreover, a Bernstein type theorem in the 3-dimensional Minkowski space is established by considering the volume form induced from the projective sphere bundle.

On Bernstein type theorems in Finsler spaces with the volume form induced from the projective sphere bundle