Sharp bounds for Seiffert mean in terms of root mean square

AbstractWe find the greatest value α and least value β in (1/ 2,1) such that the double inequality S(αa+(1-α)b,αb+(1-α)a)<T(a,b)<S(βa+(1-β)b,βb+(1-β)a) holds for all a,b > 0 with a ≠ b. Here, T(a, b) = (a-b)/[2 arctan((a-b)/(a + b))] and S(a, b) = [(a2 + b2)/2]1/ 2are the Seiffert mean and root mean square of a and b, respectively.2010 Mathematics Subject Classification: 26E60.