"Non-strict" l'Hospital-Type Rules for Monotonicity: Intervals of Constancy

Abstract

Assuming that a "derivative" ratio rho:=f'/g' of the ratio r:=f/g of differentiable functions f and g is strictly monotonic (that is, rho is increasing or decreasing), it was shown in previous papers that then r can switch at most once, from decrease to increase or vice versa. In the present paper, it is shown that, if rho is non-strictly monotonic (that is, non-increasing or non-decreasing), then r can have at most one maximal interval of constancy (m.i.c.); on the other hand, any one m.i.c. of a given derivative ratio rho is the m.i.c. of an appropriately constructed original ratio r.

5 pages

References in corpus (5)

• Binomial upper bounds on generalized moments and tail probabilities of (super)martingales with differences bounded from above
• Topics in Special Functions
• Extremal Probabilistic Problems and Hotelling's T^2 Test Under Symmetry Condition
• L'Hospital-type rules for monotonicity and limits: Discrete case
• Toward the best constant factor for the Rademacher-Gaussian tail comparison

Cited by in corpus (5)

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• L'Hopital-Type Rules for Monotonicity with Application to Quantum Calculus
• Extension of Frame's type inequalities to Bessel and modified Bessel functions
• Generalized Huygens types inequalities for Bessel and modified Bessel functions