Optimal bounds for the Neuman-Sándor mean in terms of the convex combination of the first and second Seiffert means (Q1665805)

Summary: We find the least value \(\alpha\) and the greatest value \(\beta\) such that the double inequality \(\alpha P(a, b) +(1 - \alpha) T(a, b) < M(a, b) < \beta P(a, b) +(1 - \beta) T(a, b)\) holds for all \(a, b > 0\) with \(a \neq b\), where \(M(a, b), P(a, b)\), and \(T(a, b)\) are the Neuman-Sándor mean and the first and second Seiffert means of two positive numbers \(a\) and \(b\), respectively.