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Volume 2, Issue 3, Article 33 |
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L'Hospital Type Rules for Oscillation, with Applications
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Authors: |
Iosif Pinelis, |
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Keywords:
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L'Hospital's Rule, Monotonicity, Oscillation, Convexity, Yao-Iyer Inequality, Bioequivalence Studies, Information Inequalities. |
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Date Received:
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29/01/01 |
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Date Accepted:
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03/05/01 |
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Subject Codes: |
26A48,26D10,26A51,26D15,60E15,62P10
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Editors: |
Alexandru Lupas (1942-2007), |
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Abstract: |
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 Topsře 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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