A Generalized Integral Inequality on Discontinuous Functions in the Teaching of Mathematical Analysis

  • Bin Zheng
Keywords: Integral inequality, discontinuous function, Integral equation, Differential equation, Bounded

Abstract

In this paper, we research a generalized integral inequality with two independent variables for
discontinuous function in the teaching of the Mathematical Analysis course. The inequality provides
an explicit bound for solutions of certain integral equations. The obtained result extends some existing
results in the literature.

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References

[1] Z.L. Yuan, X.W. Yuan, F.W. Meng, Some new delay integral inequalities and their applications,
Appl. Math. Comput. 208 (2009) 231-237.[2] J. Wang, F. Meng, J. Gu, Estimates on some power nonlinear Volterra-Fredholm type dynamic
integral inequalities on time scales, Adv. Diff. Equ. 2017:257 (2017) 1-16.
[3] R. Xu, X. Ma, Some new retarded nonlinear Volterra-Fredholm type integral inequalities with maxima
in two variables and their applications. J. Ineq. Appl. 2017:187 (2017) 1-25.
[4] W.N. Li, M.A. Han, F.W. Meng, Some new delay integral inequalities and their applications, J.
Comput. Appl. Math. 180 (2005) 191-200.
[5] O. Lipovan, Integral inequalities for retarded Volterra equations, J. Math. Anal. Appl. 322 (2006)
349-358.
[6] B.G. Pachpatte, Explicit bounds on certain integral inequalities, J. Math. Anal. Appl. 267 (2002)
48-61.
[7] H. Liu, A class of retarded Volterra-Fredholm type integral inequalities on time scales and their
applications. J. Ineq. Appl. 2017:293 (2017) 1-15.
[8] B.G. Pachpatte, On some new nonlinear retarded integral inequalities, J. Inequal. Pure Appl. Math.
5 (2004) (Article 80).
[9] Y.G. Sun, On retarded integral inequalities and their applications, J. Math. Anal. Appl. 301 (2005)
265-275.
[10] R.A.C. Ferreira, D.F.M. Torres, Generalized retarded integral inequalities, Appl. Math. Letters 22
(2009) 876-881.
[11] R. Xu, Y.G. Sun, On retarded integral inequalities in two independent variables and their applications, Appl. Math. Comput. 182 (2006) 1260-1266.
[12] F.C. Jiang, F.W. Meng, Explicit bounds on some new nonlinear integral inequality with delay, J.
Comput. Appl. Math. 205 (2007) 479-486.
[13] L.Z Li, F.W. Meng, L.L. He, Some generalized integral inequalities and their applications, J. Math.
Anal. Appl. 372 (2010) 339-349.
[14] A. Gallo, A. M. Piccirillo, About some new generalizations of Bellman-Bihari results for integrofunctional inequalities with discontinuous functions and applications, Nonlinear Anal. 71 (2009)
e2276-e2287.
[15] G. Iovane, Some new integral inequalities of Bellman-Bihari type with delay for discontinuous functions, Nonlinear Anal. 66 (2007) 498-508.
[16] B.G. Pachpatte, Explicit bound on a retarded integral inequality, Math. Inequal. Appl. 7 (2004) 7-11.
[17] Q.H. Ma, J. Peˇcari´c, Estimates on solutions of some new nonlinear retarded Volterra-Fredholm type
integral inequalities, Nonlinear Anal. 69 (2008) 393-407.
Published
2018-11-30
How to Cite
Zheng, B. (2018). A Generalized Integral Inequality on Discontinuous Functions in the Teaching of Mathematical Analysis. IJRDO- Journal of Educational Research, 3(11), 55-65. https://doi.org/10.53555/er.v3i11.2536