Most Maximally Monotone Operators Have a Unique Zero and a Super-regular Resolvent

Xianfu Wang

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arXiv · 1301.6443

Most Maximally Monotone Operators Have a Unique Zero and a Super-regular Resolvent

Xianfu Wang

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Abstract

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.

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Xianfu Wang. 2013-01-28. Most Maximally Monotone Operators Have a Unique Zero and a Super-regular Resolvent. https://arxiv.org/abs/1301.6443

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