Support theorems for generalized monotone functions. (English) Zbl 1528.26010
S. Wąsowicz [J. Math. Anal. Appl. 332, No. 2, 1229–1241 (2007; Zbl 1122.26024); J. Math. Anal. Appl. 365, No. 1, 415–427 (2010; Zbl 1188.26009)] wrote two papers, where he investigated generalized support-type properties of convex functions wrt. Chebyshev systems. Since that Bessenyei wondered whether or not such proerties hold also for convexity (another name generalized monotonicity) wrt. so-called Beckenbach interpolation falimies. In the present paper the complete solution is given.
Reviewer: Szymon Wąsowicz (Bielsko-Biała)
MSC:
| 26A51 | Convexity of real functions in one variable, generalizations |
| 26A48 | Monotonic functions, generalizations |
| 26D15 | Inequalities for sums, series and integrals |
| 39B62 | Functional inequalities, including subadditivity, convexity, etc. |
| 41A17 | Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities) |
Keywords:
Beckenbach family; Chebyshev system; generalized monotonicity and convexity; quadrature formula; Hermite-Hadamard inequality; support theoremReferences:
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