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  Volume 2, Issue 3, Article 33
L'Hospital Type Rules for Oscillation, with Applications

    Authors: Iosif Pinelis,  
    Keywords: L'Hospital's Rule, Monotonicity, Oscillation, Convexity, Yao-Iyer Inequality, Bioequivalence Studies, Information Inequalities.  
    Date Received: 29/01/01  
    Date Accepted: 03/05/01  
    Subject Codes:


    Editors: Alexandru Lupas (1942-2007),  

An algorithmic description of the dependence of the oscillation pattern of the ratio  f / g  of two functions f and g on the oscillation pattern of the ratio  f' / g'  of their derivatives is given. This tool is then used in order to refine and extend the Yao-Iyer inequality, arising in bioequivalence studies. The convexity conjecture by Topsøe concerning information inequalities is addressed in the context of a general convexity problem. This paper continues the series of results begun by the l'Hospital type rule for monotonicity. Other applications of this rule are given elsewhere: to certain information inequalities, to monotonicity of the relative error of a Padé approximation for the complementary error function, and to probability inequalities for sums of bounded random variables.

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