Abstract

In this paper, we prove that if a Banach space X admits a Lipschitz β-smooth bump function, then any continuous convex function on a convex open subset Ω of X is β-differentiable in a dense GδG_\delta subset of Ω.

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Yongxin Li

Nankai Institute of Mathematics, Tianjin, 300071, People’s Republic of China

Shuzhong Shi

Nankai Institute of Mathematics, Tianjin, 300071, People’s Republic of China

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Suggested citation

Y. Li, S. Shi. “Differentiability of Convex Functions on a Banach Space with Smooth Bump Function.” Journal of Convex Analysis 1 (1994), No. 1, 47–60. https://doi.org/10.68381/jca01003

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Published by Heldermann Verlag, 1994. Rights now held by Banach Press LLC.