L'Hospital-type rules for monotonicity

Pinelis Invents New Calculus Rules

Include these rules into standard calculus texts! (PDF)

A note in The American Mathematical Monthly (PDF)

7 papers in Journal of Inequalities in Pure and Applied Mathematics

Discrete versions of the rules (PDF)

Recent applications in:

Binomial upper bounds on generalized moments and tail probabilities of (super)martingales with differences bounded from above (click on this link, and then on the icon there) -- appeared in High Dimensional Probability. IMS Lecture Notes Monograph Series 2006, Vol. 51, 33-52. DOI: 10.1214/074921706000000743

Normal domination of (super)martingales (click on there)  -- appeared in Electron. J. Probab. 11 (2006), no. 39, 1049--1070 (electronic).

On inequalities for sums of bounded random variables (click on there)

Toward the best constant factor for the Rademacher-Gaussian tail comparison (click on there) -- to appear in European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics (16 pages)

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