Abstract

It is shown that continuous approximately convex, semiconcave and strongly α(⋅)\alpha(\cdot)-paraconvex functions on Banach spaces have almost all (but not all) known first order differentiability properties of continuous convex functions. The main results easily follow from known (or essentially known) results on single-valuedness and continuity of submonotone operators.

Author information

Contact details are reproduced from the original publication and may be historical.

Luděk Zajíček

Charles University, Faculty of Mathematics and Physics, Sokolovská 83, 186 75 Praha 8, Czech Republic

zajicek@karlin.mff.cuni.cz

Keywords

  • Approximately convex function
  • semiconcave function
  • strongly α(⋅)-paraconvex function
  • submonotone operator
  • Fréchet differentiability
  • Gâteaux differentiability

Mathematics Subject Classification

46G05; 49J50

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Suggested citation

L. Zajíček. “Differentiability of Approximately Convex, Semiconcave and Strongly Paraconvex Functions.” Journal of Convex Analysis 15 (2008), No. 1, 1–15. https://doi.org/10.68381/jca15001

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Published by Heldermann Verlag, 2008. Rights now held by Banach Press LLC.