Lyapunov-type inequalities for a second-order differential equation with a nonlocal source term

A second-order differential equation with a nonlocal source term, posed on an interval $ (a, b) $, is investigated. A general Lyapunov-type inequality for the considered differential equation is established. Our approach is completely different to those used in the literature. Namely, our method is based on the notion of the barycenter of a function and a Fejér-type inequality due to Pavić [Filomat. 32(16) (2018) 5793-5802]. Next, several Lyapunov-type inequalities are deduced for different types of boundary conditions.