Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 24 (2017), No. 1, 333--347 Copyright Heldermann Verlag 2017 A Note on the Extension of Continuous Convex Functions from Subspaces Carlo Alberto De Bernardi Dip. di Matematica, Università di Milano, Via C. Saldini 50, 20133 Milano, Italy carloalberto.debernardi@gmail.com [Abstract-pdf] Let $Y$ be a subspace of a real normed space $X$. We say that the couple $(X,Y)$ has the {\em $\mathrm{CE}$-property} (convex extension property'') if each continuous convex function on $Y$ admits a continuous convex extension defined on $X$. By using techniques of Johnson and Zippin, we prove the following results about the $\mathrm{CE}$-property: if $X$ is the $c_0(\Gamma)$-sum or the $\ell_p(\Gamma)$-sum (\$1 Keywords: Convex function, extension, normed linear space. MSC: 52A41; 26B25, 46A99 [ Fulltext-pdf  (179  KB)] for subscribers only.