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 Some Sublinear Dynamic Integral Inequalities on Time Scales | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 983052 10 pages doi 2010 983052 Research Article Some Sublinear Dynamic Integral Inequalities on Time Scales Yuangong Sun School of Science University of Jinan Jinan Shandong 250022 China Correspondence should be addressed to Yuangong Sun sunyuangong@ Received 7 July 2010 Revised 30 September 2010 Accepted 15 October 2010 Academic Editor Jewgeni Dshalalow Copyright 2010 Yuangong Sun. 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. We study some nonlinear dynamic integral inequalities on time scales by introducing two adjusting parameters which provide improved bounds on unknown functions. Our results include many existing ones in the literature as special cases and can be used as tools in the qualitative theory of certain classes of dynamic equations on time scales. 1. Introduction Following Hilger s landmark paper 1 there have been plenty of references focused on the theory of time scales in order to unify continuous and discrete analysis where a time scale is an arbitrary nonempty closed subset of the reals and the cases when this time scale is equal to the reals or to the integers represent the classical theories of differential and of difference equations. Many other interesting time scales exist for example T qN0 qt t e No for q 1 which has important applications in quantum theory T hN with h 0 T N2 and T H the space of the harmonic numbers. Recently many authors have extended some continuous and discrete integral inequalities to arbitrary time scales. For example see 2-14 and the references cited therein. The purpose of this paper is to further investigate some sublinear integral inequalities on time scales that have been studied in a recent paper 6 . By introducing two adjusting parameters
