Explicit bounds on certain integral inequalities

被引:76
作者
Pachpatte, BG
机构
[1] Aurangabad, 431 001, Maharashtra
关键词
explicit bounds; integral inequalities; two independent variable generalizations; differential and integral equations; partial derivatives; hyperbolic partial delay differential equations;
D O I
10.1006/jmaa.2001.7743
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper explicit bounds on retarded Gronwall-Bellman and Bihari-like integral inequalities and their two independent variable generalizations are established. Some applications are also given to illustrate the usefulness of one of our results. (C) 2002 Elsevier Science (USA).
引用
收藏
页码:48 / 61
页数:14
相关论文
共 10 条
[1]  
[Anonymous], 1919, ANN MATH
[2]  
[Anonymous], INTEGRAL INEQUALITIE
[3]  
Bainov D., 1992, Integral Inequalities and Applications. Mathematics and Its Applications
[4]  
Beckenbach E. F., 2012, Inequalities, V30
[5]  
Bellman R., 1943, DUKE MATH J, V10, P643, DOI [10.1215/S0012-7094-43-01059-2, 10.1215/s0012-7094-43-01059-2]
[6]  
Bihari I., 1956, ACTA MATH ACAD SCI H, V7, P81, DOI DOI 10.1007/BF02022967
[7]   A retarded Gronwall-like inequality and its applications [J].
Lipovan, O .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2000, 252 (01) :389-401
[8]   Nonlinear singular integral inequalities for functions in two and n independent variables [J].
Medved, M .
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2000, 5 (03) :287-308
[9]  
Pachpatte B., 1998, Mathematics in Science and Engineering, P197
[10]   On some new inequalities related to a certain inequality arising in the theory of differential equations [J].
Pachpatte, BG .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2000, 251 (02) :736-751