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.