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 $0 \leqslant k < n$.References
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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