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.
Publication Source (Journal or Book title)
Publications de l'Institut Mathematique
Estrada, R., & Pavlović, M. (2017). L'hôpital's Monotone rule, Gromov's theorem, and operations that preserve the monotonicity of quotients. Publications de l'Institut Mathematique, 101 (115), 11-24. https://doi.org/10.2298/PIM1715011E