Application of Integro-differential Equations on an Inequality of Opial and Gronwall

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Published: 2022-10-22

Page: 690-695


Kemi Iyabo Apanpa *

Department of Mathematics, University of Jos Jos, Plateau State, Nigeria Emmanuel Alayande College of Education, Oyo Oyo State, Nigeria.

Wahab Rafiu Adesola

Department of Mathematics, University of Jos Jos, Plateau State, Nigeria Emmanuel Alayande College of Education, Oyo Oyo State, Nigeria.

*Author to whom correspondence should be addressed.


Abstract

Inequalities remains an important aspect of analysis and its unique application to all areas of integro-differential equations cannot be underrated. Our aim is to derive a general equation showing relations between Opial and Gronwall inequalities, thereby using some integro-differential equation that solve into the obtained general equation to establish our result.

Keywords: Opial inequalities, gronwall-bellman type inequalities, differential equations, non-negative continuous functions, best possible constant


How to Cite

Apanpa, K. I., & Adesola, W. R. (2022). Application of Integro-differential Equations on an Inequality of Opial and Gronwall. Asian Journal of Pure and Applied Mathematics, 4(1), 690–695. Retrieved from https://globalpresshub.com/index.php/AJPAM/article/view/1682

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References

Bainvov D, Simeonov D. Integral inequalities and applications. Kluwer Academic Publishers, Dordrech. 1992;8-9.

Collin Mallows. An even simpler proof of Opial Inequality. In Proceedings of the American Mathematical Society. 1965;172-173.

DOI: 10.2307/2034023

Opial Z. Sur une inegalite. Ann.pol. Math. 1960;8:29-32.

Brauer F. A nonlinear variation of constants formula for Volterra equations, Mat. Systems Th. 1972;6:226-234.

Gronwall TH. Note on the derivatives with respect to a parameter of the solutions of a system of differential equations. Annan of Mathematics. 1919;20(2):292-296.

Pachpatte BG. A note on Gronwall-Bellman inequality. of Mathematical Analysis and Application. 1973;758-762.

Sun YG. On retarded integral inequalities and their applications. J. Math. Anal. Appl. 2005;301:265-275. [CrossRef]

Yasemin Basci, Dumitru Baleanu. New aspects of Opial-type integral inequalities. Basci and Baleanu Advances in Difference Equations; 2018.

Available: https://doi.org/10.1186/s13662-018-1912-4

Oguntuase JA. On an Inequality of Gronwall. Journal of Inequalities in Pure and Applied Mathematics. 2001;2(1):article 9.

Chidume C.E. Applicable Functional Analysis, Fundamental Theorems with Applications. International Centre for Theoretical Physics Trieste, Italy. 2003;76-77.

Apanpa et.al. A note on Gronwall-Bellman type integral inequalities. Nigeria Journal of Mathematics and Applications. 2018;27:116-131.

Apanpa et.al. Gronwall-Bellma type Inequalities. Asian Journal of Pure and Applied Mathematics. 2021;3(3):29-36.