Journal of Inequalities and Applications 
Volume 2008 (2008), Article ID 343024, 14 pages
doi:10.1155/2008/343024
Research Article

The Weighted Square Integral Inequalities for the First Derivative of the Function of a Real Variable

S. Hussain,1 J. Pečarić,1,2 and M. Shashiashvili1,3

 1Abdus-Salam School of Mathematical Sciences, GC University, 35-C-2 Gulberg-III, Lahore 54660, Pakistan
2Faculty of Textile Technology, University of Zagreb, 10000 Zagreb, Croatia
3Department of Probability Theory and Mathematical Statistics Chair, Tbilisi State University, 2 University Street, Tblisi 0143, Georgia
Received 20 May 2008; Accepted 30 July 2008

Recommended by Wing-Sum Cheung

Abstract

We generalize the square integral estimate for the derivative of the convex function by Shashiashvili (2005) to the case of the family of the weight functions, satisfying certain conditions. This kind of generalization is especially valuable in the problems of mathematical finance for construction of the discrete time hedging strategies.