Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 491576, 5 pages
doi:10.1155/2009/491576
Research Article

On an Extension of Shapiro's Cyclic Inequality

Nguyen Minh Tuan1 and Le Quy Thuong2

1Department of Mathematical Analysis, University of Hanoi, 334 Nguyen Trai Street, Hanoi, Vietnam
2Department of Mathematics, University of Hanoi, 334 Nguyen Trai Street, Hanoi, Vietnam

Received 21 August 2009; Accepted 13 October 2009

Academic Editor: Kunquan Lan

Copyright © 2009 Nguyen Minh Tuan and Le Quy Thuong. 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

We prove an interesting extension of the Shapiro's cyclic inequality for four and five variables and formulate a generalization of the well-known Shapiro's cyclic inequality. The method used in the proofs of the theorems in the paper concerns the positive quadratic forms.