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

0353273 - MÚ 2011 RIV US eng J - Journal Article
Cibulka, R. - Fabian, Marián
Attainment and (sub)differentiability of the infimal convolution of a function and the square of the norm.
Journal of Mathematical Analysis and Applications. Roč. 368, č. 2 (2010), s. 538-550. ISSN 0022-247X. E-ISSN 1096-0813
R&D Projects: GA ČR GA201/07/0394
Institutional research plan: CEZ:AV0Z10190503
Keywords : Infimal convolution * Strong attainment * Distance function * Fréchet smooth norm
Subject RIV: BA - General Mathematics
Impact factor: 1.174, year: 2010
http://www.sciencedirect.com/science/article/pii/S0022247X10002362

Let X be a Banach space whose norm is simultaneously LUR and Gateaux (Fréchet) smooth. Under some assumptions, it is shown that the infimal convolution of a fairly general function on X and the square of the norm is generically strongly attained and hence is Gateaux (Fréchet) differentiable. This contains a result of S. Dutta on distance functions.
Permanent Link: http://hdl.handle.net/11104/0192564