Geodesic
Cone-Monotone Functions: Differentiability and Continuity
Canadian journal of mathematics, Tome 57 (2005) no. 5, pp. 961-982

Voir la notice de l'article provenant de la source Cambridge University Press

We provide a porosity-based approach to the differentiability and continuity of real-valued functions on separable Banach spaces, when the function is monotone with respect to an ordering induced by a convex cone $K$ with non-empty interior. We also show that the set of nowhere $K$ -monotone functions has a $\sigma $ -porous complement in the space of continuous functions endowed with the uniform metric.
DOI : 10.4153/CJM-2005-037-5
Mots-clés : Primary: 26B05, secondary: 58C20, Cone-monotone functions, Aronszajn null set, directionally porous sets, Gâteaux differentiability, separable spaces 
Borwein, Jonathan M.; Wang, Xianfu. Cone-Monotone Functions: Differentiability and Continuity. Canadian journal of mathematics, Tome 57 (2005) no. 5, pp. 961-982. doi: 10.4153/CJM-2005-037-5
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