Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 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
Proc. Amer. Math. Soc. 61 (1976), 255-261
DOI: https://doi.org/10.1090/S0002-9939-1976-0427564-2

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 $0 \leqslant k < n$.
References
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Bibliographic 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