In this paper, a new class of set-valued inverse variational inequalities (SIVIs) are introduced and investigated in reflexive Banach spaces. Several equivalent characterizations are given for the set-valued inverse variational inequality to have a nonempty and bounded solution set. Based on the equivalent condition, we propose the stability result for the set-valued inverse variational inequality with both the mapping and the constraint set that are perturbed in a reflexive Banach space, provided that the mapping is monotone. Furthermore, some examples are shown to support the main results. The results in this paper generalize and extend some known results in this area.

在本文中，在自反 Banach 空间中引入并研究了一类新的集值逆变分不等式 (SIVI)。给出了具有非空和有界解集的集值逆变分不等式的几个等效特征。基于等价条件，我们提出了具有自反Banach空间中扰动的映射和约束集的集合值逆变分不等式的稳定性结果，前提是映射是单调的。此外，还显示了一些示例来支持主要结果。本文的结果概括和扩展了该领域的一些已知结果。