A functional inequality related to Domar's uniform boundedness theorem

Thomas Ransford

We study the functional inequality \[ f(r+s)\le g(r)+αf(s) \quad(r,s>0). \] Here $g:(0,\infty )\to [0,\infty )$ is a given decreasing function, $\alpha$ is a constant such that $0<\alpha <1$, an…