
Journal of Convex Analysis 30 (2023), No. 1, 359369 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 HermiteHadamard inequality. Keywords: Beckenbach family, Chebyshev system, generalized monotonicity and convexity, quadrature formula, HermiteHadamard inequality. MSC: 26A51; 26D15, 39B62, 41A05, 41A55. [ Fulltextpdf (122 KB)] for subscribers only. 