Continuous Convex $\mathrm{MS}$-Differentiable Function Need not Be $\mathrm{HL}$-Differentiable

V. I. Averbukh, T. Konderla

Mathematical Institute, Silesian University in Opava, Opava, Czech Republic

Abstract: We construct here an example of a continuous convex function on a locally convex space, which is $\mathrm{MS}$-differentiable at a point, but is not $\mathrm{HL}$-differentiable at this point.

Keywords: topological vector space, convex function, $\mathrm{MS}$-differentiability, $\mathrm{HL}$-differentiability, Fréchet differentiability, balanced absorbing subset, Minkowski function.

UDC: 517.2+517.98

Received: 16.12.2009
Revised: 08.02.2011

DOI: 10.4213/mzm8652

 English version: Mathematical Notes, 2012, 91:2, 153–160

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