In the present paper we are concerned with the problem of characterization of maps which can be expressed as an affine difference i.e. a map of the form

$$\begin{aligned} tf(x)+(1-t)f(y)-f(tx+(1-t)y), \end{aligned}$$

where \(t\in (0,1)\) is a given number. We give a general solution of the functional equation associated with this problem.

中文翻译：

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t-仿射差异和相关形式的表征

在本文中，我们关注地图的特征化问题，该问题可以表示为仿射差异，即形式为地图的地图

$$ \ begin {aligned} tf（x）+（1-t）f（y）-f（tx +（1-t）y），\ end {aligned} $$

其中\（t \ in（0,1）\）是给定的数字。我们给出了与此问题有关的泛函方程的一般解。