Gronwall–Bellman Type Inequalities
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: Globin gene complex / Cotwin control study, Gronwall-Bellman type inequality, Bhopal gas tragedy, non-negative continuous function, Somatic mutation, nonlinear integro-differential equations, Haemoglobin gene Complex., inequalities, best possible constant