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

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!
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Details