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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
##### Citations:
Zbl 0717.26014; Zbl 0241.33001
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