Journal of Convex Analysis 13 (2006), No. 3, 587--602
Copyright Heldermann Verlag 2006
Boundedness, Differentiability and Extensions of Convex Functions
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
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.
Keywords: Convex function, Schur property, Dunford-Pettis property, Grothendieck property, extensions.
MSC: 52A41; 46G05, 46N10, 49J50, 90C25
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