Publications de l’Institut Mathématique, Nouvelle Série Vol. 101[115], pp. 11–24 (2017) 

L’HÔPITAL’S MONOTONE RULE, GROMOV’S THEOREM, AND OPERATIONS THAT PRESERVE THE MONOTONICITY OF QUOTIENTSRicardo Estrada, Miroslav PavlovićDepartment of Mathematics, Louisiana State University, Baton Rouge, LA 70803, U.S.A; University of Belgrade, Faculty of Mathematics, Belgrade, SerbiaAbstract: 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 $T\left(u\right)/T\left(v\right)$. We also give new proofs of the monotone form of L’Hôpital’s rule and of Gromov’s theorem. Keywords: Monotonicity; L’Hôpital’s monotone rule; Gromov’s theorem Classification (MSC2000): 26A48;26D10 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 24 Apr 2017. This page was last modified: 11 May 2017.
© 2017 Mathematical Institute of the Serbian Academy of Science and Arts
