Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article The Weighted Square Integral Inequalities for the First Derivative of the Function of a Real Variable | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 343024 14 pages doi 2008 343024 Research Article The Weighted Square Integral Inequalities for the First Derivative of the Function of a Real Variable S. Hussain 1 J. Pecaric 1 2 and M. Shashiashvili1 3 1 Abdus-Salam School of Mathematical Sciences GC University 35-C-2 Gulberg-III Lahore 54660 Pakistan 2 Faculty of Textile Technology University of Zagreb 10000 Zagreb Croatia 3 Department of Probability Theory and Mathematical Statistics Chair Tbilisi State University 2 University Street Tblisi 0143 Georgia Correspondence should be addressed to S. Hussain tausef775650@ Received 20 May 2008 Accepted 30 July 2008 Recommended by Wing-Sum Cheung 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. 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. 1. Introduction The role of mathematical inequalities within the mathematical branches as well as in its enormous applications should not be underestimated. The appearance of the new mathematical inequality often puts on firm foundation for the heuristic algorithms and procedures used in applied sciences. The present paper considers new type of weighted square integral inequalities for the first derivative of the convex function the particular case which has been originally established by K. Shashiashvili and M. Shashiashvili 1 and subsequently applied to the hedging problems of mathematical finance by Hussain and Shashiashvili 2 . The convexity .
