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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.

References [Enhancements On Off] (What's this?)

  • [1] F. Chan, D. Goldberg and S. Gonek, On extensions of an inequality among means, Proc. Amer. Math. Soc. 42 (1974), 202-207. MR 0338295 (49:3061)
  • [2] A. W. Marshall, I. Olkin and F. Proschan, Monotonicty of ratios of means and other applications of majorization, Inequalities (O. Shisha, Ed.), Academic Press, New York, 1967, pp. 177-190. MR 0237727 (38:6008)

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Keywords: Inequality among means, generalized means, majorization, Schur functions, monotonicity
Article copyright: © Copyright 1981 American Mathematical Society

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