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A Monotonicity Theorem and a Bernoulli-L’Hospital-Ostrowski Rule

Published online by Cambridge University Press:  20 November 2018

Chang-Ming Lee
Chang-Ming Lee*
Affiliation:
University of Wisconsin-MilwaukeeMilwaukee, Wisconsin53201
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Abstract

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It is proved that a function is nondecreasing if it is Baire one and Darboux and fulfills Lusin’s condition (N), and if its derivative is non-negative for almost every point at which the function is derivable. Using this result, a process to formulate various results on the existence and the valuation of indeterminate forms via various monotonicity theorems is illustrated. In particular, the ordinary Bernoulli-L’Hospital rule and some of its variations obtained recenty by A. M. Ostrowski are generalized.

Keywords

26A4826A0326A24monotonicity theoreml’Hospital ruleBaire one functionLusin’s condition (N)Banach condition (T2)
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 3 , 01 September 1984 , pp. 273 - 278
Copyright
Copyright © Canadian Mathematical Society 1984

References

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