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Convex functions and Schwarz derivatives


Author: Hajrudin Fejzić
Journal: Proc. Amer. Math. Soc. 123 (1995), 2473-2477
MSC: Primary 26A51
DOI: https://doi.org/10.1090/S0002-9939-1995-1254838-X
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.


References [Enhancements On Off] (What's this?)

  • [1] Z. Buczolich, Convexity and symmetric derivates of measurable functions, Real Anal. Exchange 16 (1990-91), 187-196. MR 1087484 (92a:26007)
  • [2] C. E. Weil, Monotonicity, convexity and symmetric derivates, Trans. Amer. Math. Soc. 221 (1976), 225-237. MR 0401994 (53:5817)
  • [3] A. Zygmund, Trigonometric series, Cambridge Univ. Press, Cambridge and New York, 1990.

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

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