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

  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},
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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ContentsIntroduction ??1. Sublinear operators ??2. Application of sublinear operators to the study of semigroups ??3. Superlinear point-set mappingsReferences

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