Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


A generalization of the arithmetic-geometric means inequality

Authors: A. M. Fink and Max Jodeit
Journal: Proc. Amer. Math. Soc. 61 (1976), 255-261
MSC: Primary 26A86
MathSciNet review: 0427564
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 26A86

Retrieve articles in all journals with MSC: 26A86

Additional Information

PII: S 0002-9939(1976)0427564-2
Keywords: Inequalities, arithemetic-geometric mean inequality, convex functions
Article copyright: © Copyright 1976 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia