Abstract

We survey various boundedness, differentiability and extendibility properties of convex functions, and how they are related to sequential convergence with respect to various topologies in the dual space. It is also shown that if X/Y is separable then every continuous convex function on Y can be extended to a continuous convex function on X.

Author information

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

Jonathan Borwein

Faculty of Computer Science, Dalhousie University, Halifax, N.S., Canada B3H 1W5

jborwein@cs.dal.ca

Vicente Montesinos

Instituto de Matemática Pura y Aplicada, Universidad Politécnica, C/Vera s/n, 46022 Valencia, Spain

vmontesinos@mat.upv.es

Jon D. Vanderwerff

Dept. of Mathematics, La Sierra University, Riverside, CA 92515, U.S.A.

jvanderw@lasierra.edu

Keywords

  • Convex function
  • Schur property
  • Dunford-Pettis property
  • Grothendieck property
  • extensions

Mathematics Subject Classification

52A41; 46G05, 46N10, 49J50, 90C25

Suggested citation

J. Borwein, V. Montesinos, J. D. Vanderwerff. “Boundedness, Differentiability and Extensions of Convex Functions.” Journal of Convex Analysis 13 (2006), No. 3/4, 587–602.

Copyright Heldermann Verlag 2006