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
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
Academic Editor: Wing-Sum Cheung
Copyright © 2008 S. Hussain et al. 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 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.