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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A generalization of the arithmetic-geometric means inequality
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by A. M. Fink and Max Jodeit PDF
Proc. Amer. Math. Soc. 61 (1976), 255-261 Request permission

Abstract:

It is shown that the arithmetic mean of ${x_1}{w_1}, \ldots ,{x_n}{w_n}$ exceeds the geometric mean of ${x_1}, \ldots ,{x_n}$ unless all the $x$’s are equal, where ${w_1}, \ldots ,{w_n}$ depend on ${x_1}, \ldots ,{x_n}$ and satisfy $0 \leqslant {w_i} < 1$ unless ${x_i} = \min {x_k}$. This inequality is then applied to an integral inequality for functions $y$ defined on $[0,\;\infty )$ with ${y^{(k)}}$ convex and $0$ at $0$ for $0 \leqslant k < n$.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 61 (1976), 255-261
  • MSC: Primary 26A86
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0427564-2
  • MathSciNet review: 0427564