L’H?PITAL’S MONOTONE RULE, GROMOV’S THEOREM, AND OPERATIONS THAT PRESERVE THE MONOTONICITY OF QUOTIENTS

摘要

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’H?pital’s rule and of Gromov’s theorem.