We define a family of $C^1$ functions which we call "nowhere coexpanding functions" that is closed under composition and includes all $C^3$ functions with non-positive Schwarzian derivative. We establish results on the number and nature of the fixed points of these functions, including a generalisation of a classic result of Singer.

翻译：我们定义了一族$C^1$函数，称之为“无处可共扩张函数”，该族在复合运算下封闭，且包含所有具有非正Schwarz导数的$C^3$函数。我们建立了这些函数不动点的数量与性质方面的结果，包括对Singer经典结果的一个推广。