Journal of Inequalities and Applications 
Volume 2006 (2006), Article ID 97860, 11 pages
doi:10.1155/JIA/2006/97860

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

Abstract

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.