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Proceedings of the American Mathematical Society

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Unified treatment of some inequalities among ratios of means


Authors: Emad El-Neweihi and Frank Proschan
Journal: Proc. Amer. Math. Soc. 81 (1981), 388-390
MSC: Primary 26D20
MathSciNet review: 597647
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Abstract: Using majorization and Schur functions, Marshall, Olkin, and Proschan obtained a result concerning monotonicity of the ratio of means. This note shows that a slight extension of their result provides a unified method for obtaining and extending inequalities between means due to Chan, Goldberg, and Gonek, as well as deriving additional inequalities of the same type.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0597647-7
Keywords: Inequality among means, generalized means, majorization, Schur functions, monotonicity
Article copyright: © Copyright 1981 American Mathematical Society