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Zbl 0847.26015
Sándor, J.
On refinements of certain inequalities for means. (English)
[J] Arch. Math., Brno 31, No.4, 279-282 (1995). ISSN 0044-8753; ISSN 1212-5059/e

The author offers results on how several published inequalities interrelate. Example: The author's inequality [Aequationes Math. 40, No. 2/3, 261-270 (1990; Zbl 0717.26014)] $(b\ln b- a\ln a)/(b- a)> 2+ \ln L- (G/L)$ implies {\it B. C. Carlson's} [Am. Math. Mon. 79, 615-618 (1972; Zbl 0241.33001)] $L< (2G+ A)/3$ ($A$ is the arithmetic mean, $G$ the geometric mean and $L= (b- a)/(\ln b- \ln a)$ is the logarithmic mean of two distinct positive numbers $a$ and $b$).
[J.Aczél (Waterloo / Ontario)]

MSC 2000:: *26D15 Inequalities for sums, series and integrals of real functions

Keywords: logarithmic mean; identric mean; arithmetic mean; inequalities between means; geometric mean

Citations: Zbl 0717.26014; Zbl 0241.33001

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Zentralblatt MATH Berlin [Germany]