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

Ricardo Estrada | Zendy; Miroslav Pavlović | Zendy

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

Author(s) -

Ricardo Estrada,

Miroslav Pavlović

Publication year - 2017

Publication title -

publications de l institut mathematique

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.246

H-Index - 17

eISSN - 1820-7405

pISSN - 0350-1302

DOI - 10.2298/pim1715011e

Subject(s) - monotonic function , monotone polygon , mathematics , mathematical proof , function (biology) , quotient , discrete mathematics , lambda , combinatorics , pure mathematics , mathematical analysis , physics , geometry , evolutionary biology , optics , biology

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.

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