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: Generalized Gronwall-Bellman-type discrete inequalities and their applications | Feng et al. Journal of Inequalities and Applications 2011 2011 47 http content 2011 1 47 3 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access Generalized Gronwall-Bellman-type discrete inequalities and their applications Qinghua Feng1 2 Fanwei Meng2 and Yaoming Zhang 1 Correspondence fqhua@ 1School of Science Shandong University of Technology Zibo 255049 Shandong China Full list of author information is available at the end of the article Springer Abstract In this paper some new nonlinear Gronwall-Bellman-type discrete inequalities are established which can be used as a handy tool in the research of qualitative and quantitative properties of solutions of certain difference equations. The established results generalize some of the recent results obtained by Cheung and Ma respectively. Mathematics Subject Classification 2010 26D15 Keywords Discrete inequalities Difference equations Explicit bounds Qualitative analysis Quantitative analysis 1 Introduction In the past few years the research of Gronwall-Bellman-type finite difference inequalities has been payed much attention by many authors which play an important role in the study of qualitative as well as quantitative properties of solutions of difference equations such as boundedness stability existence uniqueness continuous dependence and so on. Many difference inequalities have been established see 1 - 11 and the references therein . But in the analysis of some certain difference equations the bounds provided by the earlier inequalities are inadequate and it is necessary to seek some new discrete inequalities in order to obtain a diversity of desired results. Our aim in this paper is to establish some new nonlinear Gronwall-Bellman-type discrete inequalities which provide new bounds for unknown functions lying in these inequalities. We will illustrate the usefulness of the established results by applying them to study the .
