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

   
Mobile Device Pairing
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 two inequalities involving means


Authors: Scott Lawrence and Daniel Segalman
Journal: Proc. Amer. Math. Soc. 35 (1972), 96-100
MSC: Primary 26A86
MathSciNet review: 0304586
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Fan has proven an inequality relating the arithmetic and geometric means of $ ({x_1}, \cdots ,{x_n})$ and $ (1 - {x_1}, \cdots ,1 - {x_n})$, where $ 0 < {x_i} \leqq \tfrac{1}{2},i = 1, \cdots ,n$. Levinson has generalized Fan's inequality; his result involves functions with positive third derivatives on (0, 1). In this paper, the above condition that requires $ 0 < {x_i} \leqq \tfrac{1}{2}$ has been replaced by a condition which only weights the $ {x_i}$ to the left side of (0, 1) in pairs, and Levinson's differentiability requirement has been replaced by the analogous condition on third differences.


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

DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0304586-X
PII: S 0002-9939(1972)0304586-X
Article copyright: © Copyright 1972 American Mathematical Society