# Attainment and (sub)differentiability of the infimal/supremal convolution of a function and of the square of the norm

Speaker:

Fabian, Marian

Affiliation:

Mathematical Institute, Czech Academy of Science, Czech Republic ### Abstract

Let *TeX Embedding failed!* be a Banach space whose norm is LUR and Gateaux

(Fr\'echet) smooth. Under some mild assumptions, it is shown that the

infimal/supremal convolution of a fairly general function on *TeX Embedding failed!* and the

square of the norm is strongly attained, and hence

Gateaux (Fr\'echet) differentiable at points of a residual set. This

contains recent results

of P. Bandyopadhayay and S. Dutta on distance and farthest distance

functions.

References.

R. Cibulka, M. Fabian, *TeX Embedding failed!* *TeX Embedding failed!*,

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R. Cibulka, M. Fabian, *TeX Embedding failed!*

*TeX Embedding failed!*, *TeX Embedding failed!*

Video:

### Details

Date & Time:

Wednesday, May 18, 2011 - 10:45 - 11:15
Venue/Room:

ASB 10900 - ‹ previous
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