论文标题
准孔循环功能的差异表征，没有两倍的可差度
Differential Characterization of Quasi-Concave Functions without Twice Differentiability
论文作者
论文摘要
本文为在Banach空间的开放式和凸子集上定义的实现功能提供了必要且充分的条件，该功能是准孔cove的，并且有足够的条件使该功能严格地是Quasi-concave。这些条件适用于连续可区分的函数，可满足温和的额外假设，并且不需要这些功能是两倍的可微分。因为对于连续可区分的函数，这两个额外的假设在两倍上是微不足道的，所以我们的结果是对经典结果的纯粹扩展。
This paper presents a necessary and sufficient condition for a real-valued function defined on an open and convex subset of a Banach space to be quasi-concave, and a sufficient condition for such a function to be strictly quasi-concave. These conditions are applicable to continuously differentiable functions that satisfy a mild additional assumption, and do not require the functions to be twice differentiable. Because this additional assumption is trivially satisfied for twice continuously differentiable functions, our results are pure extensions to classical results.
