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Zbl 0976.26015
Sándor, J.
On certain inequalities for means. III.
(English)
[J] Arch. Math. 76, No.1, 34-40 (2001). ISSN 0003-889X; ISSN 1420-8938/e

A typical result offered is $$A^{2/3}G^{1/3}<P<\frac{2A+G}{3},$$ where $$P(x,y)=\frac{x-y} {4\arctan (x^{1/2}y^{-1/2})-\pi},$$ introduced by {\it H.-J. Seiffert} [e.g., Nieuw Arch. Wisk. (4) 13, No. 2, 195-198 (1995; Zbl 0830.26008)], and $A(x,y)$ and $G(x,y)$ are the arithmetic and geometric means, respectively, for positive reals $x\neq y$. \par [For Part I and II see {\it J. Sándor}, J. Math. Anal. Appl. 189, No. 2, 602-606 (1995; Zbl 0822.26014) and ibid. 199, No. 2, 629-635 (1996; Zbl 0854.26013), respectively].
[János Aczél (Waterloo/Ontario)]
MSC 2000:
*26D15 Inequalities for sums, series and integrals of real functions
26E60 Means

Keywords: inequalities; arithmetic mean; geometric mean

Citations: Zbl 0822.26014; Zbl 0830.26008; Zbl 0854.26013

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