Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Convex functions and Schwarz derivatives


Author: Hajrudin Fejzić
Journal: Proc. Amer. Math. Soc. 123 (1995), 2473-2477
MSC: Primary 26A51
MathSciNet review: 1254838
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Abstract: If the lower Schwarz derivate of a continuous function is nonnegative, then it is convex. The main result in this paper is that if the lower Schwarz derivate of a measurable function f is nonnegative, then there is a dense open set with f convex on each component.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1254838-X
Article copyright: © Copyright 1995 American Mathematical Society