On some new integral inequalities of Gronwall-Bellman-Bihari type with delay for discontinuous functions and their applications

被引：35
|
作者：
Liu, Xiaohong [1 ]
Zhang, Lihong [2 ]
Agarwal, Praveen [3 ]
Wang, Guotao [2 ]
机构：
[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R China
[2] Shanxi Normal Univ, Sch Math & Comp Sci, Linfen 041004, Shanxi, Peoples R China
[3] Anand Int Coll Engn, Dept Math, Jaipur 303012, Rajasthan, India
来源：
INDAGATIONES MATHEMATICAE-NEW SERIES | 2016年 / 27卷 / 01期
关键词：
Integral inequalities; Discontinuous functions; Gronwall-Bellman-Bihari type inequalities; Impulsive differential systems; EXPLICIT BOUNDS; TIME SCALES; EQUATIONS;
D O I：
10.1016/j.indag.2015.07.001
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this article, some new explicit bounds on solutions to a class of new nonlinear integral inequalities of Gronwall-Bellman-Bihari type with delay for discontinuous functions are established. These inequalities generalize and improve some former famous results about inequalities, and which provide an excellent tool to discuss the qualitative and quantitative properties for solutions to some nonlinear differential and integral equations. To illustrate our results, we present an example to show estimated solutions for an impulsive differential system. (C) 2015 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：1 / 10
页数：10
相关论文
共 50 条
  • [11] On Some New Nonlinear Integral Inequalities of Gronwall-Bellman Type
    El-Owaidy, Hassan Mostafa
    Ragab, Abdelwahab Abbas
    Eldeeb, Ahmed Abdel-Moneim
    Abuelela, Waleed Mostafa Kamal
    KYUNGPOOK MATHEMATICAL JOURNAL, 2014, 54 (04): : 555 - 575
  • [12] On Some Generalizations Bellman-Bihari Result for Integro-Functional Inequalities for Discontinuous Functions and Their Applications
    Gallo, Angela
    Piccirillo, Anna Maria
    BOUNDARY VALUE PROBLEMS, 2009,
  • [13] Sharp Gronwall-Bellman type integral inequalities with delay
    Gyori, Istvan
    Horvath, Laszlo
    ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2016, (111) : 1 - 25
  • [14] SOME NEW NONLINEAR POWERED GRONWALL-BELLMAN TYPE RETARDED INTEGRAL INEQUALITIES AND THEIR APPLICATIONS
    Li, Zizun
    Wang, Wu-Sheng
    JOURNAL OF MATHEMATICAL INEQUALITIES, 2019, 13 (02): : 553 - 564
  • [15] Some New Gronwall-Bellman-Type Inequalities on Time Scales and Their Applications
    Zheng, Bin
    Feng, Qinghua
    Meng, Fanwei
    JOURNAL OF APPLIED MATHEMATICS, 2013,
  • [16] NEW EXPLICIT BOUNDS ON GRONWALL-BELLMAN-BIHARI-GAMIDOV INTEGRAL INEQUALITIES AND THEIR WEAKLY SINGULAR ANALOGUES WITH APPLICATIONS
    Mekki, M.
    Boukerrioua, K.
    Kilani, B.
    Sahari, M. L.
    KRAGUJEVAC JOURNAL OF MATHEMATICS, 2020, 44 (04): : 603 - 615
  • [17] Gronwall-Bellman type nonlinear delay integral inequalities on time scales
    Feng, Qinghua
    Meng, Fanwei
    Zheng, Bin
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 382 (02) : 772 - 784
  • [18] Nonlinear integral inequalities with delay for discontinuous functions and their applications
    Mi, Yuzhen
    Deng, Shengfu
    Li, Xiaopei
    JOURNAL OF INEQUALITIES AND APPLICATIONS, 2013,
  • [19] Some nonlinear Gronwall-Bellman type retarded integral inequalities with power and their applications
    Li, Zizun
    Wang, Wu-Sheng
    APPLIED MATHEMATICS AND COMPUTATION, 2019, 347 : 839 - 852
  • [20] Some new dynamic Gronwall–Bellman–Pachpatte type inequalities with delay on time scales and certain applications
    Ahmed A. El-Deeb
    Dumitru Baleanu
    Journal of Inequalities and Applications, 2022
12345