Several sharp inequalities about the first Seiffert mean.

In this paper, we deal with the problem of finding the best possible bounds for the first Seiffert mean in terms of the geometric combination of logarithmic and the Neuman-Sándor means, and in terms of the geometric combination of logarithmic and the second Seiffert means.

Optimal bounds for Neuman-Sándor mean in terms of the convex combination of the logarithmic and the second Seiffert means.

In the article, we prove that the double inequality [Formula: see text] holds for [Formula: see text] with [Formula: see text] if and only if [Formula: see text] and [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] denote the Neuman-Sándor, logarithmic and second Seiffert means of two positive numbers a and b, respectively.