Sharp Power Mean Bounds for the Combination of Seiffert and Geometric Means

الملخص EN

We answer the question: for α∈(0,1), what are the greatest value p and the least value q such that the double inequality Mp(a,b)0 with a≠b.

Here, Mp(a,b), P(a,b), and G(a,b) denote the power of order p, Seiffert, and geometric means of two positive numbers a and b, respectively.