Bounds for the Arithmetic Mean in Terms of the Neuman-Sándor and Other Bivariate Means

Abstract

We present the largest values α1, α2, and α3 and the smallest values β1, β2, and β3 such that the double inequalities α1M(a,b)+(1-α1)H(a,b)0 with a≠b, where M(a,b), A(a,b), He(a,b), H(a,b) and H-(a,b) denote the Neuman-Sándor, arithmetic, Heronian, harmonic, and harmonic root-square means of a and b, respectively.