Sharp bounds by the power mean for the generalized Heronian mean
1 Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China
2 School of Mathematical Science, Anhui University, Hefei 230039, China
Journal of Inequalities and Applications 2012, 2012:129 doi:10.1186/1029-242X-2012-129Published: 7 June 2012
In this article, we answer the question: For p, ω ∈ ℝ with ω > 0 and p(ω - 2) ≠ 0, what are the greatest value r1 = r1(p, ω) and the least value r2 = r2(p, ω) such that the double inequality holds for all a, b > 0 with a ≠ b? Here Hp,ω(a, b) and Mr(a, b) denote the generalized Heronian mean and rth power mean of two positive numbers a and b, respectively.
2010 Mathematics Subject Classification: 26E60.