In this paper, we consider a Banach generalized system of variational inequality problems by using the concept of Kangtunyakarn (Fixed Point Theory Appl 2014:123, 2014) and showed the equivalence between a Banach generalized system of variational inequality problems and fixed point problems. And also, using modified viscosity iterative method, we prove a strong convergence theorem for finding a common solution of a Banach generalized system of variational inequality problems and fixed point problems for a nonexpansive mapping. The main theorem presented in this paper extend the corresponding result of variational inequality problems introduced by Aoyama et al. (Fixed Point Theory Appl 2006:35390, https://doi.org/10.1155/FPTA/2006/35390, 2006). Moreover, we give some numerical examples for supporting our main theorem.

在本文中，我们使用Kangtunyakarn（Fixed Point Theory Appl 2014：123，2014）的概念来考虑变分不等式问题的Banach广义系统，并证明了变分不等式问题的Banach广义系统与不动点问题之间的等价性。而且，使用改进的粘度迭代法，我们证明了一个强的收敛定理，可用于为非膨胀映射找到变分不等式问题和不动点问题的Banach广义系统的通用解。本文提出的主要定理扩展了由Aoyama等人引入的变分不等式问题的相应结果。（固定点理论应用2006：35390，https://doi.org/10.1155/FPTA/2006/35390，2006）。此外，我们给出一些数值例子来支持我们的主要定理。