Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 845390, 8 pages
doi:10.1155/2010/845390
Research Article

Multiplicative Concavity of the Integral of Multiplicatively Concave Functions

Yu-Ming Chu1 and Xiao-Ming Zhang2

1Department of Mathematics, Huzhou Teachers College, Huzhou, Zhejiang 313000, China
2Haining College, Zhejiang TV University, Haining, Zhejiang 314400, China

Received 25 March 2010; Accepted 7 June 2010

Academic Editor: S. S. Dragomir

Copyright © 2010 Yu-Ming Chu and Xiao-Ming Zhang. 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

We prove that G(x,y)=|∫yxf(t)dt| is multiplicatively concave on [a,b]×[a,b] if f:[a,b]⊂(0,∞)→(0,∞) is continuous and multiplicatively concave.