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The cancellation law for inf-convolution of convex functions

Dariusz Zagrodny — 1994

Studia Mathematica

Conditions under which the inf-convolution of f and g f g ( x ) : = i n f 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 + on a reflexive Banach space such that l i m x f ( x ) / x = constitutes a semigroup, with inf-convolution as multiplication, which can be embedded in the group of its quotients.

On maximal monotone operators with relatively compact range

Dariusz Zagrodny — 2010

Czechoslovak Mathematical Journal

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 T can be approximated by a sequence of maximal monotone operators of type NI, which converge to T in a reasonable sense (in the sense of Kuratowski-Painleve convergence).

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