Gronwall–Bellman Type Inequalities

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Published: 2021-11-13

Page: 122-129


Kemi Iyabo Apanpa

Department of Mathematics, University of Jos, Jos, Plateau State, Nigeria.

Kamilu Rauf

Department of Mathematics, University of Ilorin, Ilorin, Kwara State, Nigeria.

Oladipo Ebenezer Olaide

Department of Mathematics, University of Ilorin, Ilorin, Kwara State, Nigeria.

*Author to whom correspondence should be addressed.


Abstract

In mathematics, an integro-differential equation is an equation that covers various aspect of integrals and derivatives of an unknown function. Integral inequality act as an important role in the study of differential, integral and partial differential equations and have been of great use to Gronwall inequality.

In succession to our earlier work, we further provide a new generalized Gronwall inequality by giving two important lemmas to establish the important of our results. We further apply the inequality to a nonlinear integro-differential equation where we established that, the important of Gronwall-Bellman inequality to differential equations cannot be overlook.

Keywords: Gronwall-Bellman type inequality, non-negative continuous function, nonlinear integro-differential equations, inequalities, best possible constant


How to Cite

Apanpa, K. I., Rauf, K., & Olaide, O. E. (2021). Gronwall–Bellman Type Inequalities. Asian Journal of Pure and Applied Mathematics, 3(1), 122–129. Retrieved from https://globalpresshub.com/index.php/AJPAM/article/view/1337

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