Monotonicity, convexity and symmetric derivates
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- by Clifford E. Weil PDF
- Trans. Amer. Math. Soc. 221 (1976), 225-237 Request permission
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.References
- A. M. Bruckner and J. G. Ceder, Darboux continuity, Jber. Deutsch. Math.-Verein. 67 (1964/65), no. Abt. 1, 93–117. MR 186761
- H. T. Croft, A note on a Darboux continuous function, J. London Math. Soc. 38 (1963), 9–10. MR 147588, DOI 10.1112/jlms/s1-38.1.9
- A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 221 (1976), 225-237
- MSC: Primary 26A48; Secondary 26A51, 26A24
- DOI: https://doi.org/10.1090/S0002-9947-1976-0401994-1
- MathSciNet review: 0401994