Equilibrium of maximal monotone operator in a given set
Sufficient conditions for an equilibrium of maximal monotone operator to be in a given set are provided. This partially answers to a question posed in [10].
The cancellation law for inf-convolution of convex functions
Conditions under which the inf-convolution of f and g 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 on a reflexive Banach space such that constitutes a semigroup, with inf-convolution as multiplication, which can be embedded in the group of its quotients.
A weak* approximation of subgradient of convex function
On maximal monotone operators with relatively compact range
It is shown that every maximal monotone operator on a real Banach space with relatively compact range is of type NI. Moreover, if the space has a separable dual space then every maximally monotone operator can be approximated by a sequence of maximal monotone operators of type NI, which converge to in a reasonable sense (in the sense of Kuratowski-Painleve convergence).
Dedicatio
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