Geodesic
The cancellation law for inf-convolution of convex functions
Studia Mathematica, Tome 110 (1994) no. 3, pp. 271-282

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Conditions under which the inf-convolution of f and g $f □ g(x):= inf_{y+z=x}(f(y)+g(z))$ has the cancellation property (i.e. f □ h ≡ g □ h implies f ≡ g) are treated in a convex analysis framework. In particular, we show that the set of strictly convex lower semicontinuous functions $f: X → ℝ ∪ {+∞}$ on a reflexive Banach space such that $ lim_{∥x∥ → ∞} f(x)/∥x∥ = ∞$ constitutes a semigroup, with inf-convolution as multiplication, which can be embedded in the group of its quotients.
DOI : 10.4064/sm-110-3-271-282
Keywords: inf-convolution, convex functions, subdifferentials, the cancellation law, a characterization of reflexivity

Dariusz Zagrodny 1

1 
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Dariusz Zagrodny. The cancellation law for inf-convolution of convex functions. Studia Mathematica, Tome 110 (1994) no. 3, pp. 271-282. doi: 10.4064/sm-110-3-271-282

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