Abstract
In this paper, we establish mixed integro-differential inequalities which can be used as handy tools to study properties of solutions of certain mixed integro-differential and differential equations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abdeldaim, A., Yakout, M.: On some new inequalities of Gronwall-Bellman-Pachpatte type. Appl. Math. Comput. 217, 7887–7899 (2011)
Bellman, R.: The stability of solutions of linear differential equations. Duke Math. J. 10, 643–647 (1943)
Dhakne, M.B., Lamb, G.B.: On globle existance of abstrct nonlinear integrodifferential equations. Indian J. Pure Appl. Math. 33(5), 665–676
El-Owaidy, H., Ragab, A., Abdeldaim, A.: On some new integral inequalities of Growall- Bellman type. Appl. Math. Comput. 106, 289–303 (1999)
Jiang, F., Meng, F.: Explicit bounds on some new nonlinear integral inequality with delay. J. Comput. Appl. Math. 205, 479–486 (2007)
Meng, F.W., Li, W.N.: On some new integral inequalitise and their applications. Appl. Math. Comput. 148, 381–392 (2004)
Gronwall, H.T.: Note on the derivatives with respect to a parameter of the solutions of a system of differential equations. Ann. Math. 2, 292–296 (1918–1919)
Li, L., Meng, F., He, L.: Some generalized integral inequalities and their applications. J. Math. Anal. Appl. 372, 339–349 (2010)
Pachpatte, B.G.: A note on Gronwall type integral and integro differential inequalities. Tamkang J. Math. 8, 53–59 (1977)
Pachpatte, B.G.: On some fundamental integro differential inequalities for differential equations. Chinese J. Math. 6(1), 17–23 (1978)
Pachpatte, B.G.: Inequalities for Differential and Integral Equations. Academic Press, New York and London (1998)
Pachpatte, B.G.: Integral and finite difference inequalities and applications. In: North-Holland Mathematics Studies, vol. 205. (2006)
Tidke, H.L., Dhakne, M.B.: Existance of solutions for nolinear mixed type integrodifferential equation of second order. Surv. Math. Appl. 5, 61–72 (2010)
Young-Ho, K.: Gronwall-Bellman and Pachpatte type integral inequalities with applications. Nonlinear Anal. 71, e2641–e2656 (2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer India
About this paper
Cite this paper
Kendre, S.D., Latpate, S.G. (2015). On Mixed Integro-Differential Inequalities and Applications. In: Agrawal, P., Mohapatra, R., Singh, U., Srivastava, H. (eds) Mathematical Analysis and its Applications. Springer Proceedings in Mathematics & Statistics, vol 143. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2485-3_44
Download citation
DOI: https://doi.org/10.1007/978-81-322-2485-3_44
Published:
Publisher Name: Springer, New Delhi
Print ISBN: 978-81-322-2484-6
Online ISBN: 978-81-322-2485-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)