Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 987484, 9 pages
doi:10.1155/2010/987484
Research Article

Ostrowski Type Inequalities in the Grushin Plane

Heng-Xing Liu and Jing-Wen Luan

School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

Received 7 January 2010; Accepted 14 March 2010

Academic Editor: Kunquan Q. Lan

Copyright © 2010 Heng-Xing Liu and Jing-Wen Luan. 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

Motivated by the work of B.-S. Lian and Q.-H. Yang (2010) we proved an Ostrowski inequality associated with Carnot-Carathéodory distance in the Grushin plane. The procedure is based on a representation formula. Using the same representation formula, we prove some Hardy type inequalities associated with Carnot-Carathéodory distance in the Grushin plane.