A Note on the Stability of an Integral Equation

Let p: ℝ → ℂ be a continuous function. We give a sufficient condition in order that the integral equation \(f(t) = f(0) +{ \int \nolimits \nolimits }_{0}^{\,t}p(s)f(s)\,\mathrm{d}s\) have the Hyers–Ulam stability. We also prove that if p has no zeros, then the sufficient condition is a necessary condition.