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

MSC:
26D15 Inequalities for sums, series and integrals
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