Skip to Main Content

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

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A generalization of the arithmetic-geometric means inequality
HTML articles powered by AMS MathViewer

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
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 26A86
  • Retrieve articles in all journals with MSC: 26A86
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