Geodesic
On /()X\)-convex functions
Commentationes Mathematicae, Tome 53 (2013) no. 2, p. 197−199.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

Let \(X\) be a Banach space. Let \(f(\cdot)\) be a real valued function defined on an open convex set \(\Omega \subset X^*\), where \(X^*\) as usual denote the conjugate space. We say that the function \(f(\cdot)\) is \(X$\)convex, if there is a set \(\Phi_f \subset X\) such that $$ f(x^*)= sup_{x \in \Phi_f, r \in \R} x^*(x)+r. \eqno{(1)}$$ In the paper it will be shown that if \(X\) is separable, then the function \(f(\cdot)\) is Frechet differentiable on a dense \(G_{\delta}\) set.
DOI : 10.14708/cm.v53i2.785
Mots-clés : \(X\)-convex functions, Frechet differentiability 
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Stefan Rolewicz. On /()X\)-convex functions. Commentationes Mathematicae, Tome 53 (2013) no. 2, p.  197−199. doi : 10.14708/cm.v53i2.785. http://geodesic.mathdoc.fr/articles/10.14708/cm.v53i2.785/

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