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

摘要

In this paper, we find the least value α and the greatest value β such that the double inequality α L(a,b)+(1 . α )M(a,b) P(a, b) β L(a,b)+(1 . β )M(a, b) holds for all a, b 0 with a = b ,where L(a,b),M(a,b) and P(a,b) are the logarithmic, the Neuman-S′ andor, and the first Seiffert means of two positive numbers a and b, respectively.