Open Access Research

On Opial's type inequalities for an integral operator with homogeneous kernel

Chang-Jian Zhao1* and Wing-Sum Cheung2

Author Affiliations

1 Department of Mathematics, China Jiliang University, Hangzhou 310018, China

2 Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong

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Journal of Inequalities and Applications 2012, 2012:123 doi:10.1186/1029-242X-2012-123

Published: 30 May 2012

Abstract

In this article, we establish some new Opial's type integral inequalities for an integral operator with homogeneous kernel. The results in special cases yield some of the interrelated results and provide new estimates on inequalities of this type.

MS (2000) Subject Classification: 26D15.

Keywords:
Opial's inequality; Hölder's inequality; Jensen's inequality; integral operator; homogeneous kernel