
Journal of Convex Analysis 26 (2019), No. 3, 761772 Copyright Heldermann Verlag 2019 Differentiability of Convex Functions on a Locally Convex Topological Vector Space Xi Yin Zheng Dept. of Mathematics, Yunnan University, Kunming 650091, P. R. China xyzheng@ynu.edu.cn Kung Fu Ng Dept. of Mathematics, Chinese University of Hong Kong, Hong Kong, P. R. China kfng@math.cuhk.edu.hk We introduce the notion of a smooth set in a locally convex topological vector space and extend Asplund's result on the strong differentiability space. We also establish Gateaux differentiability of a continuous convex function in a locally convex topological vector space. In particular, we extend Mazur's classical theorem on Gateaux differentiability from a separable Banach space to a separable locally convex topological vector space. Keywords: Topological vector space, smooth set, uniform differentiability, Gateaux differentiability. MSC: 52A41, 49J50, 46A55 [ Fulltextpdf (108 KB)] for subscribers only. 