A nonnegative sequence of \(\{a_n\}_{n\ge 0}\) satisfies the Briggs inequality if \(\begin{aligned} a_n^2(a_n^2-a_{n-1}a_{n+1})>a_{n-1}^2(a_{n+1}^2-a_na_{n+2}) \end{aligned}\) holds for any \(n\ge 1\) . In this paper we show that both the partition function \(\{p(n+N_0)\}_{n\ge 0}\) and the overpartition function \(\{\overline{p}(n+\overline{N}_0)\}_{n\ge 0}\) satisfy the Briggs inequality for some \(N_0\) and \(\overline{N}_{0}\) . Based on Chern’s formula for \(\eta \) -quotients, we further prove that the k-regular partition function \(\{p_k(n+N_{k})\}_{n\ge 0}\) and the k-regular overpartition function \(\{\overline{p}_k(n+\overline{N}_k)\}_{n\ge 0}\) also satisfy the Briggs inequality for \(2\le k\le 9\) and some \(N_k,\overline{N}_{k}\) .
