Volume 2,  Issue 3, 2001

Article 33

L'HOSPITAL TYPE RULES FOR OSCILLATION, WITH APPLICATIONS

IOSIF PINELIS

DEPARTMENT OF MATHEMATICAL SCIENCES,
MICHIGAN TECHNOLOGICAL
UNIVERSITY, HOUGHTON, MI 49931, USA
 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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Generalized Auxiliary Problem Principle and Solvability of a Class of Nonlinear Variational Inequalities Involving Cocoercive and Co-Lipschitzian Mappings
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On Some Generalizations of Steffensen's Inequality and Related Results
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A Weighted Analytic Center for Linear Matrix Inequalities
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Good Lower and Upper Bounds on Binomial Coefficients
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Improvement of an Ostrowski Type Inequality for Monotonic Mappings and its Application for Some Special Means
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On the Utility of the Telyakovskii's Class S
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L'Hospital Type Rules for Oscillation, with Applications
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Matrix and Operator Inequalities
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Consequences of a Theorem of Erdös-Prachar
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On a Reverse of Jessen's Inequality for Isotonic Linear Functionals
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Lp-Improving Properties for Measures on R4 Supported on Homogeneous Surfaces in Some Non Elliptic Cases
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Some Properties of the Series of Composed Numbers
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