On Some Fundamental Integrodifferential Inequalities

Zareen A. Khan

Department of Mathematics, Princess Noura Bint Abdurehman University, Riyadh, KSA.

DOI: 10.4236/am.2014.519282                

Abstract

The aim of this present paper is to establish some new integrodifferential inequalities of Gronwall type involving functions of one independent variable which provide explicit bounds on unknown functions. The inequalities given here can be used in the analysis of a class of differential equations as handy tools.

Keywords

Integral Inequalities, Two Independent Variables, Nondecreasing, Nonincreasing

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Ragab, A.A. (2000) On Integral Inequalities and Their Applications. Kyungpook Mathematical Journal, 40, 357-370.
[2]	Pachpatte, B.G. (2001) On Some Fundamental Integral Inequalities and Their Discrete Analogues. Journal of Inequalities in Pure and Applied Mathematics, 2, 1-13.
[3]	Pachpatte, B.G. (1977) On Some Fundamental Integrodifferential and Integral Inequalities. Analele. Stiintifice ale. Universitati.Al.I.Cuza.din.Iasi, 33, 77-86.
[4]	Pachpatte, B.G. (1973) A Note on Gronwall-Bellman Inequalities. Journal of Mathematical Analysis and Applications, 44, 758-762.
[5]	Pachpatte, B.G. (1975) On Some Integral Inequalities Similar to Bellman-Bihari Inequality. Journal of Mathematical Analysis and Applications, 49, 794-802.
[6]	Pachpatte, B.G. (1974) An Integral Inequality Similar to Bellman-Bihari Inequality. Bulletin of the Greek Mathematical Society, 15, 7-12.
[7]	Pachpatte, B.G. (1977) A Note on Gronwall Type Integral and Integrodifferential Inequalities. Tamkang Journal of Mathematics, 8, 53-59.
[8]	Ullrich, D.F. (1969) Boundary Value Problems for a Class of Nonlinear Second Order Differential Equations. Journal of Mathematical Analysis and Applications, 28, 188-210.
[9]	Beckenbach, E.F. and Bellman, R. (1961) Inequalities. Springer-Verlag, Berlin Heidelberg. http://dx.doi.org/10.1007/978-3-642-64971-4
[10]	Meng, F.M. and Li, W.N. (2004) On Some Integral Inequalities and Their Applications. Applied Mathematics and Computation, 148, 381-392.
[11]	Hooker, J.W. (1969) Existence and Oscillations Theorems for a Class of Nonlinear Second Order Differential Equations. Journal of Differential Equations, 5, 283-306.
[12]	Ma, Q.H. and Debnath, L. (2003) A More Generalized Gronwall-Like Integral Inequality with Applications. International Journal of Mathematics and Mathematical Sciences, No. 15, 927-934.