Abstract

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.

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Keywords

  • Beckenbach family
  • Chebyshev system
  • generalized monotonicity and convexity
  • quadrature formula
  • Hermite-Hadamard inequality

Mathematics Subject Classification

26A51; 26D15, 39B62, 41A05, 41A55

Suggested citation

M. Bessenyei, E. Pénzes. “Support Theorems for Generalized Monotone Functions.” Journal of Convex Analysis 30 (2023), No. 1, 359–369.

Copyright Heldermann Verlag 2023