Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 128258, 12 pages
Research Article

The Best Lower Bound Depended on Two Fixed Variables for Jensen's Inequality with Ordered Variables

Department of Automatic Control and Computers, University of Ploiesti, 100680 Ploiesti, Romania

Received 16 June 2010; Accepted 4 November 2010

Academic Editor: R. N. Mohapatra

Copyright © 2010 Vasile Cirtoaje. 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.


We give the best lower bound for the weighted Jensen's discrete inequality with ordered variables applied to a convex function 𝑓 , in the case when the lower bound depends on 𝑓 , weights, and two given variables. Furthermore, under the same conditions, we give some sharp lower bounds for the weighted AM-GM inequality and AM-HM inequality.