Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 850215, 21 pages
doi:10.1155/2010/850215
Research Article

Jensen Type Inequalities Involving Homogeneous Polynomials

Jia-Jin Wen1 and Zhi-Hua Zhang2

1College of Mathematics and Information Science, Chengdu University, Sichuan 610106, China
2Department of Mathematics, Shili Senior High School in Zixing, Chenzhou, Hunan 423400, China

Received 4 November 2009; Revised 25 January 2010; Accepted 8 February 2010

Academic Editor: Soo Hak Sung

Copyright © 2010 Jia-Jin Wen and Zhi-Hua Zhang. 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.

Abstract

By means of algebraic, analytical and majorization theories, and under the proper hypotheses, we establish several Jensen type inequalities involving γth homogeneous polynomials as follows: ∑k=1mwkf(Xk)/f(In)≤[f(∑k=1mwkXkγ)/f(In)]1/γ, ∑k=1mwkf(Xk)/f(Nn)≤[f(∑k=1mwkXkγ)/f(Nn)]1/γ, and ∑k=1mwkf*(Xk)≤f*(∑k=1mwkXk), and display their applications.