# From the Hahn–Banach extension theorem to the isotonicity of convex functions and the majorization theory

@article{Niculescu2020FromTH,
title={From the Hahn–Banach extension theorem to the isotonicity of convex functions and the majorization theory},
author={Constantin P. Niculescu and Octav Olteanu},
journal={Revista de la Real Academia de Ciencias Exactas, F{\'i}sicas y Naturales. Serie A. Matem{\'a}ticas},
year={2020}
}
• Published 1 October 2020
• Mathematics
• Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
The property of isotonicity of a continuous convex function on the positive cone is characterized via subdifferentials. This is used to illustrate a new generalization of the Hardy–Littlewood–Polya inequality of majorization to the case of functions of a vector variable.
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