论文标题
在具有附加派生属性的附加功能上
On additive functions with additional derivation properties
论文作者
论文摘要
本文的目的是引入广义推导的概念，该概念衍生了几个变量的平滑矢量值函数的规定家族。建立了基本的微积分规则，然后得出的结果表明，如果函数$ f $满足添加定理，其确定操作相对于添加函数$ d $可导出，则功能$ f $本身对于$ d $衍生。作为这种方法的应用，获得了MAKSA最新结果的新证明。我们还扩展了Nishiyama和Horinouchi的结果，并提出了两个开放问题。
The purpose of this paper is to introduce the notion of a generalized derivation which derivates a prescribed family of smooth vector-valued functions of several variables. The basic calculus rules are established and then a result derived which shows that if a function $f$ satisfies an addition theorem whose determining operation is derivable with respect to an additive function $d$, then the function $f$ is itself derivable with respect to $d$. As an application of this approach, new proof of a generalization of a recent result of Maksa is obtained. We also extend the result of Nishiyama and Horinouchi and formulate two open problems.
