%0 Journal Article
%T Most Maximally Monotone Operators Have a Unique Zero and a Super-regular Resolvent
%A Xianfu Wang
%J Mathematics
%D 2013
%I arXiv
%X Maximally monotone operators play important roles in optimization, variational analysis and differential equations. Finding zeros of maximally monotone operators has been a central topic. In a Hilbert space, we show that most resolvents are super-regular, that most maximally monotone operators have a unique zero and that the set of strongly monotone mapping is of first category although each strongly monotone operator has a unique zero. The results are established by applying the Baire Category Theorem to the space of nonexpansive mappings.
%U http://arxiv.org/abs/1301.6443v1