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 On Some Integral Inequalities on Time Scales and Their Applications | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 464976 13 pages doi 2010 464976 Research Article On Some Integral Inequalities on Time Scales and Their Applications Run Xu 1 Fanwei Meng 1 and Cuihua Song2 1 School of Mathematical Sciences Qufu Normal University Qufu 273165 Shandong China 2 School of Chemistry and Chemical Engineering Qufu Normal University Qufu 273165 Shandong China Correspondence should be addressed to Run Xu xurum2005@ Received 15 January 2010 Revised 3 March 2010 Accepted 18 March 2010 Academic Editor Martin Bohner Copyright 2010 Run Xu 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. The purpose of this paper is to investigate some new dynamic inequalities on time scales. We establish some new dynamic inequalities the results unify and extend some continuous inequalities and their corresponding discrete analogues. The inequalities given here can be used as tools in the qualitative theory of certain dynamic equations. Some examples are given in the end of this paper. 1. Introduction The theory of time scales was introduced by Hilger 1 in 1988 in order to contain both difference and differential calculus in a consistent way. Recently many authors have extended some fundamental integral inequalities used in the theory of differential and integral equations on time scales. For example we refer the reader to the papers 2-12 and the references cited there in. In this paper we investigate some nonlinear integral inequalities on time scales which extend some inequalities established by Li and Sheng 8 and Li 9 . The obtained inequalities can be used as important tools in the study of dynamic equations on time scales. Throughout this paper let us assume that we have already acquired the knowledge of time scales and time scales
