Some Optimal Convex Combination Bounds Related To The Second Seiffert Mean

In this paper we derive some optimal convex combination bounds related to the second Seiffert mean. We find the greatest valuesα1 andа2 and the least valuesβ1 andβ2 such that the double inequalitiesα1T(a, b)+(1-α1)H(a, b)< A(a, b)<β1T(a, b)+(1-β1)H(a,b) and a2T(a,b)+(1-α2)G(a, b)< A(a, b)<β2T(a, b)+(1-β2)G(a, b) holds for all a, b> 0 with a≠b. Here A(a,b),H(a,b), G(a, b) and T(a,b) denote the arithmetic, harmonic, geometric, and the second Seiffert means of two positive numbers a and b, respectively.