In this paper, we first obtain a characterization of transfer weakly lower continuous functions. Then, by introducing the class of nearly quasi-closed set-valued mappings, we obtain some characterizations of set-valued mappings whose displacement functions are transfer weakly lower continuous. We also present some fixed point theorems for nearly quasi-closed set-valued mappings which are either nearly almost convex or almost affine. Finally, we construct an almost affine mapping $T:[0,1)\to \mathbb{R}$, which is not α-almost convex for any continuous and strictly increasing function $\alpha :[0,+\infty )\to [0,+\infty )$ with $\alpha (0)=0$. This example gives an affirmative response to the Question 3 of Jachymski (2015) [8].

在本文中，我们首先获得传递弱的连续函数的刻画。然后，通过介绍几乎准封闭的集值映射的类，我们获得了位移函数以弱弱连续传递的集值映射的一些特征。我们还为近似准闭集值映射提供了一些不动点定理，它们几乎是凸的或仿射的。最后，我们构建了一个近似仿射的映射$Ť：[0，\mathrm{1个}）\to \mathbb{[R}$，对于任何连续且严格增加的函数，它不是α-几乎凸的$\alpha ：[0，+\infty ）\to [0，+\infty ）$ 和 $\alpha （0）=0$。该示例对Jachymski（2015）的问题3给出了肯定的回答[8]。