Convex functions and Schwarz derivatives
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- by Hajrudin Fejzić
- Proc. Amer. Math. Soc. 123 (1995), 2473-2477
- DOI: https://doi.org/10.1090/S0002-9939-1995-1254838-X
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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
- Zoltán Buczolich, Convexity and symmetric derivates of measurable functions, Real Anal. Exchange 16 (1990/91), no. 1, 187–196. MR 1087484, DOI 10.2307/44153689
- Clifford E. Weil, Monotonicity, convexity and symmetric derivates, Trans. Amer. Math. Soc. 221 (1976), no. 1, 225–237. MR 401994, DOI 10.1090/S0002-9947-1976-0401994-1 A. Zygmund, Trigonometric series, Cambridge Univ. Press, Cambridge and New York, 1990.
Bibliographic Information
- © Copyright 1995 American Mathematical Society
- 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