# The cancellation law for inf-convolution of convex functions

Studia Mathematica (1994)

- Volume: 110, Issue: 3, page 271-282
- ISSN: 0039-3223

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topZagrodny, Dariusz. "The cancellation law for inf-convolution of convex functions." Studia Mathematica 110.3 (1994): 271-282. <http://eudml.org/doc/216114>.

@article{Zagrodny1994,

abstract = {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.},

author = {Zagrodny, Dariusz},

journal = {Studia Mathematica},

keywords = {inf-convolution; convex functions; subdifferentials; the cancellation law; a characterization of reflexivity; cancellation property; Banach space; semi-continuous convex functions; subdifferential},

language = {eng},

number = {3},

pages = {271-282},

title = {The cancellation law for inf-convolution of convex functions},

url = {http://eudml.org/doc/216114},

volume = {110},

year = {1994},

}

TY - JOUR

AU - Zagrodny, Dariusz

TI - The cancellation law for inf-convolution of convex functions

JO - Studia Mathematica

PY - 1994

VL - 110

IS - 3

SP - 271

EP - 282

AB - 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.

LA - eng

KW - inf-convolution; convex functions; subdifferentials; the cancellation law; a characterization of reflexivity; cancellation property; Banach space; semi-continuous convex functions; subdifferential

UR - http://eudml.org/doc/216114

ER -

## References

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