Journal of Convex Analysis 30 (2023), No. 1, 359--369
Copyright Heldermann Verlag 2023
Support Theorems for Generalized Monotone Functions
Mihály Bessenyei
Institute of Mathematics, University of Debrecen, Hungary
besse@science.unideb.hu
Evelin Pénzes
Institute of Mathematics, University of Debrecen, Hungary
penzes.evelin@science.unideb.hu
This note presents a complete solution of the support problem for functions that are generalized monotone in the sense of Beckenbach. The key tool of the proof is Tornheim's uniform convergence theorem. As applications, we improve some known support results and give an abstract version of the Hermite-Hadamard inequality.
Keywords: Beckenbach family, Chebyshev system, generalized monotonicity and convexity, quadrature formula, Hermite-Hadamard inequality.
MSC: 26A51; 26D15, 39B62, 41A05, 41A55.
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