Volume 2,  Issue 3, 2001

Article 33



E-Mail: ipinelis@mtu.edu

29 January, 2001; accepted 3 May, 2001.
Communicated by: A. Lupas

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.
Key words:
L'Hospital's Rule, Monotonicity, Oscillation, Convexity, Yao-Iyer Inequality, Bioequivalence Studies, Information Inequalities.

2000 Mathematics Subject Classification:
26A48, 26D10, 26A51, 26D15, 60E15, 62P10

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