tailieunhanh - Báo cáo hoa học: "Research Article Bounds for Certain New Integral Inequalities on Time Scales"

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 Bounds for Certain New Integral Inequalities on Time Scales | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 484185 16 pages doi 2009 484185 Research Article Bounds for Certain New Integral Inequalities on Time Scales Wei Nian Li1 2 1 Department of Applied Mathematics Shanghai Normal University Shanghai 200234 China 2 Department of Mathematics Binzhou University Shandong 256603 China Correspondence should be addressed to Wei Nian Li wnli@ Received 31 March 2009 Accepted 10 June 2009 Recommended by Victoria Otero-Espinar Our aim in this paper is to investigate some new integral inequalities on time scales which provide explicit bounds on unknown functions. Our results unify and extend some integral inequalities and their corresponding discrete analogues. The inequalities given here can be used as handy tools to study the properties of certain dynamic equations on time scales. Copyright 2009 Wei Nian Li. 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 study of dynamic equations on time scales which goes back to its founder Hilger 1 is an area of mathematics that has recently received a lot of attention. For example we refer the reader to literatures 2-8 and the references cited therein. At the same time some fundamental integral inequalities used in analysis on time scales have been extended by many authors 9-14 . In this paper we investigate some new nonlinear integral inequalities on time scales which unify and extend some continuous inequalities and their corresponding discrete analogues. Our results can be used as handy tools to study the properties of certain dynamic equations on time scales. Throughout this paper a knowledge and understanding of time scales and time scale notation is assumed. For an excellent introduction to the calculus on time scales we refer the reader to monographes 2