The main result offered by the authors is that \(\Gamma'(xy+t)\Gamma(x+t)\Gamma(y+t) \leq \Gamma(xy+t)\Gamma'(x+t)\Gamma'(y+t)\) for all nonnegative \(x\) and \(y\) iff \(t\geq a\) where \(\Gamma\) is Euler’s gamma function and \(a\) is the only positive number with \(\Gamma'(a)=\Gamma(a).\) They offer also a similar result with subadditivity in place of submultiplicity of \(\psi=\Gamma'/\Gamma\) and with \(\Gamma'(a)=0\) in place of \(\Gamma'(a)=\Gamma(a).\)