1 Erratum to: Positivity DOI 10.1007/s11117-015-0354-4

We acknowledge that some results of our original article have been proved earlier in [1, 2] by Elbour et al.

The first one is Theorem 2.8 of the original paper, which is exactly [1, Theorem 2.11]. But we provide a different way to prove “(iib) \(\Rightarrow \) (i)” of Theorem 2.8 of the original paper. The next one is Theorem 3.3 of the original paper, a few lines can prove it is exactly [1, Theorem 2.7]. Also, we introduce the theorem in a different way. At last, Theorem 2.1 and part of Theorem 2.6 of the original paper are contained in [2, Theorem 2.7] and [2, Corollary 2.11], respectively. We feel sorry about that we ignored [1, 2].