On refinements of certain inequalities for means. (English) Zbl 0847.26015

Sándor, J.

Arch. Math., Brno 31, No. 4, 279-282 (1995).

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 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 \(b\)).

Reviewer: J.Aczél (Waterloo / Ontario)

MSC:

26D15

Inequalities for sums, series and integrals

Keywords:

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

Citations:

Zbl 0717.26014; Zbl 0241.33001