In this paper, we study a set-valued extended generalized nonlinear mixed variational inequality problem and its generalized resolvent dynamical system. A three-step iterative algorithm is constructed for solving set-valued extended generalized nonlinear variational inequality problem. Convergence and stability analysis are also discussed. We have shown the globally exponential convergence of generalized resolvent dynamical system to a unique solution of set-valued extended generalized nonlinear mixed variational inequality problem. In support of our main result, we provide a numerical example with convergence graphs and computation tables. For illustration, a comparison of our three-step iterative algorithm with Ishikawa-type algorithm and Mann-type algorithm is shown.

中文翻译：

---

集值扩展广义非线性混合变分不等式问题和广义可解动力系统的稳定性和收敛性分析

在本文中，我们研究了一个集值扩展广义非线性混合变分不等式问题及其广义求解动力系统。构建了求解集值扩展广义非线性变分不等式问题的三步迭代算法。还讨论了收敛性和稳定性分析。我们已经展示了广义求解动力系统的全局指数收敛到集合值扩展广义非线性混合变分不等式问题的唯一解。为了支持我们的主要结果，我们提供了一个带有收敛图和计算表的数值示例。为了说明，显示了我们的三步迭代算法与 Ishikawa 型算法和 Mann 型算法的比较。