The Baillon-Haddad Theorem Revisited

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

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.

An enhanced Baillon-Haddad theorem for convex functions on convex sets

The Baillon-Haddad theorem establishes that the gradient of a convex and continuously differentiable function defined in a Hilbert space is $β$-Lipschitz if and only if it is $1/β$-cocoercive. In this paper, we extend this theorem to Gâteaux differentiable convex functions defined on an open convex set of a Hilbert space. Finally, we give a characterization of $C^{1,+}$ convex functions in terms of local cocoercitivity.

Baillon-Bruck-Reich 重新审视：发散级数参数与线性情况下的强收敛性

Baillon-Bruck-Reich revisited: divergent-series parameters and strong convergence in the linear case

本文研究了非扩张映射在发散级数条件下的强收敛性，改进了Baillon、Bruck和Reich 1978年的经典结果。