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Proceedings of the American Mathematical Society

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On extensions of an inequality among means


Authors: F. Chan, D. Goldberg and S. Gonek
Journal: Proc. Amer. Math. Soc. 42 (1974), 202-207
MSC: Primary 26A86
DOI: https://doi.org/10.1090/S0002-9939-1974-0338295-X
MathSciNet review: 0338295
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Abstract: An inequality of Fan relates the arithmetic and geometric means of x and $ 1 - x$. An extension to generalized means is conjectured. This conjecture is proven for several special cases. In addition, some counterexamples are given.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0338295-X
Keywords: Inequality among means, generalized means, arithmetic means, geometric means
Article copyright: © Copyright 1974 American Mathematical Society