On Logarithmic Convexity for Ky-Fan Inequality
© M. Anwar and J. Pečarić. 2008
Received: 19 November 2007
Accepted: 14 February 2008
Published: 5 March 2008
We give an improvement and a reversion of the well-known Ky-Fan inequality as well as some related results.
1. Introduction and Preliminaries
In , the second author proved the following result.
In this paper, we will give an improvement and reversion of Ky-Fan inequality as well as some related results.
2. Main Results
which completes the proof.
The proof is similar to the proof of Theorem 2.2.
Let us note that similar results for difference of power means were recently obtained by Simic in .
- Levinson N: Generalization of an inequality of Ky-Fan. Journal of Mathematical Analysis and Applications 1964,8(1):133–134. 10.1016/0022-247X(64)90089-7MATHMathSciNetView ArticleGoogle Scholar
- Pečarić J, Proschan F, Tong YL: Convex Functions, Partial Orderings, and Statistical Applications, Mathematics in Science and Engineering. Volume 187. Academic Press, Boston, Mass, USA; 1992:xiv+467.MATHGoogle Scholar
- Pečarić J: An inequality for 3-convex functions. Journal of Mathematical Analysis and Applications 1982,90(1):213–218. 10.1016/0022-247X(82)90055-5MATHMathSciNetView ArticleGoogle Scholar
- Simic S: On logarithmic convexity for differences of power means. Journal of Inequalities and Applications 2007, 2007:-8.Google Scholar
This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.