A simple proof of the Baillon-Haddad theorem on open subsets of Hilbert spaces

Daniel Wachsmuth; Gerd Wachsmuth

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arXiv · 2204.00282

A simple proof of the Baillon-Haddad theorem on open subsets of Hilbert spaces

Daniel Wachsmuth·Gerd Wachsmuth

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Abstract

We give a simple proof of the Baillon-Haddad theorem for convex functions defined on open and convex subsets of Hilbert spaces. We also state some generalizations and limitations. In particular, we discuss equivalent characterizations of the Lipschitz continuity of the derivative of convex functions on open and convex subsets of Banach spaces.

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BibTeX RIS

Daniel Wachsmuth, Gerd Wachsmuth. 2022-04-01. A simple proof of the Baillon-Haddad theorem on open subsets of Hilbert spaces. https://arxiv.org/abs/2204.00282

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