Some Nonlinear Integral Inequalities for Integral Equations

Jump To References Section

Authors

  • Department of Mathematics, University of Pune, Pune-411007 ,IN
  • Department of Mathematics, Nowrosjee Wadia College of Arts and Science, Pune-411001, (M.S.) ,IN

Keywords:

Integral Equations, Integral Inequalities, Volterra Equations.

Abstract

In this paper, we establish some nonlinear integral inequalities and obtain an explicit bound for unknown function. These inequalities can be used as handy tools to study qualitative as well as quantitative properties of solutions of some nonlinear differential and integral equations.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Published

2016-12-01

How to Cite

Kendre, S. D., & Latpate, S. G. (2016). Some Nonlinear Integral Inequalities for Integral Equations. The Journal of the Indian Mathematical Society, 83(3-4), 313–321. Retrieved from https://informaticsjournals.co.in/index.php/jims/article/view/6611

 

References

A. Abdeldaim andM. Yakout, On some new inequalities of Gronwall-Bellman-Pachpatte type, Appl. Math. Comput., 217(2011), 7887–7899.

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

S. S. Dragomir, Inequalities for Stieltjes integrals with convex integrators and applications, Appl. Math. Lett., 20 (2007),123–130.

S. S. Dragomir, Inequalities for the Cebysev functional of two functions of selfadjoint operators in Hilbert spaces, Aust. J. Math. Anal. Appl., 6(1) (2009), Art. 7, 58 pp.

Fangcui Jiang and Fanwei Meng, Explicit bounds on some new nonlinear integral inequality with delay, J. Comput. Appl. Math., 205 (2007), 479–486.

Fan Wei Meng and Wei Nian Li, On some new integral inequalitise and their applications, Appl. Math. Comput. 148(2004),381–392.

Hongxia Zhang and Fanwei Meng, On certain integral inequalitis in two independent variables for retarded equations, Appl. Math. Comput., 203(2008),608–616.

B. G. Pachpatte, Inequalities for Differential and Integral Equations, Academic Press, New York and London, 1998.

B. G. Pachpatte, On some new inequality Suggested by the Study of Certain Epidemic Models, J. Math. Anal. Appl., 195 (1995), 638–644.

Olivia Lipovan, Integral inequalities for retarded Volterra equations, J. Math. Anal. Appl., 323 (2006), 349–358.

P. Waltman, Determinstic Threshold Models in the Theory of Epidemics, Lecture Notes in Biomathematics, Springer Verlag, New York, Vol.1, 1974.