Preprint A672/2010
Regularity results for semimonotone operators

Alfredo N. Iusem | Gárciga Otero, Rolando

**Keywords: **
hypomonotonicity | surjectivity | prox-regularity | semimonotonicity

We introduce the concept of $\rho$-semimonotone point-to-set operators
in Hilbert spaces. This notion is symmetrical with respect to the graph of $T$,
as is the case for monotonicity, but not for other related notions, like e.g.
hypomonotonicity, of which our new class is a relaxation. We give a necessary
condition for $\rho$-semimonotonicity of $T$ in terms of Lispchitz
continuity of $[T+\rho^{-1}I]^{-1}$ and a sufficient condition related to
expansivity of $T$. We also establish surjectivity results for maximal
$\rho$-semimonotone operators.