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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Monotonicity, convexity and symmetric derivates


Author: Clifford E. Weil
Journal: Trans. Amer. Math. Soc. 221 (1976), 225-237
MSC: Primary 26A48; Secondary 26A51, 26A24
MathSciNet review: 0401994
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Abstract: If the first lower symmetric derivate of a continuous function is nonnegative, then it is nondecreasing. If the second lower symmetric derivate of a continuous function is nonnegative, then it is convex. In this paper it is shown that if continuity is replaced by Baire one, Darboux in each of these, then the resulting statements are true.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1976-0401994-1
PII: S 0002-9947(1976)0401994-1
Keywords: First lower symmetric derivate, second lower symmetric derivate, convex, monotone, Baire class one, Darboux functions
Article copyright: © Copyright 1976 American Mathematical Society