Explicit bounds on retarded Gronwall-Bellman inequality

Authors

  • Mohammad M.H Rashid Department ofMathematics & Statistics, Faculty of Science P.O.Box(7),Mu’tah university,Mu’tah-Jordan.

DOI:

https://doi.org/10.5556/j.tkjm.43.2012.476

Keywords:

explicit bounds, integral inequalities, Gronwall-Bellman inequality

Abstract

In this paper explicit bounds on retarded Gronwall-Bellman and Bihari-like integral inequalities are established.

Author Biography

Mohammad M.H Rashid, Department ofMathematics & Statistics, Faculty of Science P.O.Box(7),Mu’tah university,Mu’tah-Jordan.

References

R. P. Agarwal, E. Thandapani, Remarks on generalizations of Gronwall inequality, Chinese J. Math., 9:2 (1981), 1--22.

R. Bellman, The stability of solutions of linear differential equations, Duke Math. J, 10 (1943), 643--647.

R. Bellman, The boundedness of solutions of linear differential equations, Duke Math. J, 14 (1943), 83--97.

I. Bihari, A generalization of lemma of Bellman and its application to uniqueness problem of diAerential equations, Acta Math. Sci. Hungar., 7 (1965), 81--94.

I. Bihari, The asymptotic behaviour of a system of non-linear diAerential equations, Publ. Math. Inst. Hung. Acad. Sci., 8 (1964), 475--488.

B. G. Pachpatte, On some generalizations of Bellman's lemma, J. Math. Anal. Appl., 5 (1975), 141--150.

B. G. Pachpatte, Explicit bounds on certain integral inequalities, J. Math. Anal. Appl., 267 (2002), 48--61.

Downloads

Published

2012-03-31

How to Cite

Rashid, M. M. (2012). Explicit bounds on retarded Gronwall-Bellman inequality. Tamkang Journal of Mathematics, 43(1), 99-108. https://doi.org/10.5556/j.tkjm.43.2012.476

Issue

Section

Papers