On some new integral inequalities of Gronwall-Bellman-Bihari type with delay for discontinuous functions and their applications
type: Item
instance of: scholarly article
title: On some new integral inequalities of Gronwall-Bellman-Bihari type with delay for discontinuous functions and their applications
zbMATH Open document ID: 1334.26052
author: Lihong Zhang
author: Praveen Agarwal
author: Guotao Wang
author: Xiaohong Liu
published in: Indagationes Mathematicae. New Series
publication date: 2016-01-12T00:00:00Z
review text: During the past years, a number of efforts have been devoted to the integral inequalities. The results given by Gronwall, Bellman and Bihari and their linear and nonlinear generalizations in the case of continuous and discontinuous functions provide a fundamental role in the study of many qualitative properties of differential and integral equations (see [\textit{A. Gallo} and \textit{A. M. Piccirillo}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 67, No. 5, 1550--1559 (2007; Zbl 1124.26013)]). The authors give explicit bounds to some new nonlinear integral inequalities of Gronwall-Bellman-Bihari type with delay for discontinuous functions, which develop and improve certain results which were proved by \textit{F. Jiang} and \textit{F. Meng} [J. Comput. Appl. Math. 205, No. 1, 479--486 (2007; Zbl 1135.26015)]. An example is presented to show estimated solutions for an impulsive differential system. The article is systematically well-organized, and will be useful for beginners in the theory of integral inequalities.
reviewed by: Choonkil Park
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 45Gxx
Mathematics Subject Classification ID: 26D10
zbMATH DE Number: 6529292
zbMATH Keywords: integral inequality
zbMATH Keywords: discontinuous function
zbMATH Keywords: Gronwall-Bellman-Bihari type inequality
zbMATH Keywords: impulsive differential system
Wikidata QID: Q62617623
MaRDI profile type: Publication
full work available at URL: j.indag.2015.07.001
OpenAlex ID: W925966786
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DOI: 10.1016/J.INDAG.2015.07.001
description: scientific article; zbMATH DE number 6529292