论文标题
希尔伯特空间开放子集的Baillon-Haddad定理的简单证明
A simple proof of the Baillon-Haddad theorem on open subsets of Hilbert spaces
论文作者
论文摘要
我们提供了简单的证明，用于在希尔伯特空间的开放和凸子集上定义的凸函数的Baillon-Haddad定理。我们还陈述了一些概括和局限性。特别是，我们讨论了在Banach空间的开放式和凸子集上的Lipschitz连续性的等效表征。
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.
