In recent papers the convexity of quasiarithmetic means was characterized under twice differentiability assumptions. One of the main goals of this paper is to show that the convexity or concavity of a quasiarithmetic mean implies the the twice continuous differentiability of its generator. As a consequence of this result, we can characterize those quasiarithmetic means which admit a lower convex and upper concave quasiarithmetic envelop.

中文翻译：

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关于均值的 Jensen 凸包和 Jensen 凹包

在最近的论文中，拟算术平均值的凸性在两次可微性假设下被表征。本文的主要目标之一是证明拟算术均值的凸性或凹性意味着其生成器的两次连续可微性。作为这个结果的结果，我们可以表征那些允许下凸和上凹拟算术包络的拟算术均值。