Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Topological vector space
  • smooth set
  • uniform differentiability
  • Gateaux differentiability

Mathematics Subject Classification

52A41, 49J50, 46A55

References

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Suggested citation

X. Y. Zheng, K. F. Ng. “Differentiability of Convex Functions on a Locally Convex Topological Vector Space.” Journal of Convex Analysis 26 (2019), No. 3, 761–772. https://doi.org/10.68381/jca26041

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Published by Heldermann Verlag, 2019. Rights now held by Banach Press LLC.