L'Hôpital's Monotone Rule, Gromov'S Theorem, and Operations That Preserve the Monotonicity of Quotients


Ricardo Estrada, Miroslav Pavlović




We study several operators $T$ that when applied to both the numerator and denominator of an increasing, or decreasing, function $u/v$ produce another increasing, or decreasing, function $T(u)/T(v)$. We also give new proofs of the monotone form of L'Hôpital's rule and of Gromov's theorem.