Recently, the author, together with L. Leuştean and A. Nicolae, introduced the notion of jointly firmly nonexpansive families of mappings in order to investigate in an abstract manner the convergence of proximal methods. Here, we further the study of this concept, by giving a characterization in terms of the classical resolvent identity, by improving on the rate of convergence previously obtained for the uniform case, and by giving a treatment of the asymptotic behaviour at infinity of such families.

中文翻译：

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重新联合牢固地非扩展映射族

最近，作者与 L. Leuştean 和 A. Nicolae 一起引入了联合牢固非膨胀映射族的概念，以便以抽象的方式研究近端方法的收敛性。在这里，我们进一步研究了这个概念，通过根据经典解析恒等式给出特征，通过改进先前为统一情况获得的收敛速度，以及通过处理此类族在无穷大处的渐近行为.