The general tensor variational inequalities, recently introduced in Barbagallo et al. (J Nonconvex Anal 19:711–729, 2018), are very useful in order to analyze economic equilibrium models. For this reason, the study of existence and regularity results for such inequalities has an important rule to the light of applications. To this aim, we start to consider some existence and uniqueness theorems for tensor variational inequalities. Then, we investigate on the approximation of solutions to tensor variational inequalities by using suitable perturbed tensor variational inequalities. We establish the convergence of solutions to the regularized tensor variational inequalities to a solution of the original tensor variational inequality making use of the set convergence in Kuratowski’s sense. After that, we focus our attention on some stability results. At last, we apply the theoretical results to examine a general oligopolistic market equilibrium problem.

Barbagallo等人最近引入了一般张量变化不等式。（J Nonconvex Anal 19：711–729，2018），对于分析经济均衡模型非常有用。因此，针对这种不等式的存在性和正则性结果的研究对于应用具有重要的规则。为此，我们开始考虑一些关于张量变分不等式的存在性和唯一性定理。然后，我们通过使用适当的摄动张量变分不等式来研究张量变分不等式的近似解。我们利用Kuratowski的意义上的集合收敛性，建立了正则化张量变分不等式解的收敛性，从而解决了原始张量变分不等式的解。之后，我们将注意力集中在一些稳定性结果上。