# 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} }

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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