L’Hôpital’s monotone rule, Gromov’s theorem, and operations that preserve the monotonicity of quotients

Abstract

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?Hopital?s rule and of Gromov?s theorem.