In this paper we provide a complete description of projections in the convex hull of two surjective linear isometries (carrying a weighted composition operator form) on absolutely continuous function space AC(X, E), where X is a compact subset of \(\mathbb R\) with at least two points and E is a strictly convex normed space. Among the consequences of the main result, it is shown that generalized bi-circular projections are the only projections on AC(X) expressed as the convex combination of two surjective linear isometries, and an affirmative answer is given to the question in Botelho and Jamison (Canad Math Bull 53:398–403, 2010) for such spaces.

在本文中，我们提供了关于绝对连续函数空间AC（X，  E）上两个射影线性等式（带有加权合成算子形式）的凸包中投影的完整描述，其中X是\（\ mathbb的紧凑子集R'）至少有两个点，E是严格凸的范数空间。在主要结果的结果中，表明广义双圆投影是在AC（X）上唯一表示为两个射影线性等距线的凸组合的投影，并且在Botelho和Jamison中对该问题给出了肯定答案。 （Canad Math Bull 53：398–403，2010）。