Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

Some Nonlinear Integral Inequalities for Integral Equations


Affiliations
1 Department of Mathematics, University of Pune, Pune-411007, India
2 Department of Mathematics, Nowrosjee Wadia College of Arts and Science, Pune-411001, (M.S.), India
     

   Subscribe/Renew Journal


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.

Keywords

Integral Equations, Integral Inequalities, Volterra Equations.
Subscription Login to verify subscription
User
Notifications
Font Size


  • 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.

Abstract Views: 312

PDF Views: 1




  • Some Nonlinear Integral Inequalities for Integral Equations

Abstract Views: 312  |  PDF Views: 1

Authors

S. D. Kendre
Department of Mathematics, University of Pune, Pune-411007, India
S. G. Latpate
Department of Mathematics, Nowrosjee Wadia College of Arts and Science, Pune-411001, (M.S.), India

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.

Keywords


Integral Equations, Integral Inequalities, Volterra Equations.

References