Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 97860, 11 pages

Inverses of new Hilbert-Pachpatte-type inequalities

Chang-Jian Zhao1 and Wing-Sum Cheung2

1Department of Information and Mathematics Sciences, College of Science, China Jiliang University, Hangzhou 310018, China
2Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong

Received 7 February 2006; Revised 3 June 2006; Accepted 5 June 2006

Copyright © 2006 Chang-Jian Zhao and Wing-Sum Cheung. 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 establish a new inequality of Hilbert type for a finite double number of nonnegative sequences of real numbers and some interrelated results, which are inverse and general forms of Pachpatte's and Handley's results. An integral version and some interrelated results are also obtained. These results provide some new estimates on such types of inequalities.