Optimal Geometric Combination Bounds of Heronian Dual and Arithmetic Means for Seiffert Mean

摘要

We find the greatest value a and the least value β such that the double inequality A~a(a,b)H~(l-a)(a,b) < P(a,b) 0 with a ≠ b. Here A(a,b), H(a,b), and P(a,b) denote the arithmetic, Heronian dual, and Seiffert means of two positive numbers a and b, respectively.