In this work we study various gap functions for the generalized multivalued mixed variational-hemivariational inequality problems by using the \((\tau _{\mathscr {M}},\sigma _{\mathscr {M}})\)-relaxed cocoercive mapping and Hausdorff Lipschitz continuity. Moreover, we establish global error bounds for such inequalities using the characteristic of the Clarke generalized gradient method. As application, we present a stationary nonsmooth semipermeability problem.

中文翻译：

---

各种变型问题的误差边界和缺口函数

在这项工作中，我们使用\（（\ tau _ {\ mathscr {M}}，\ sigma _ {\ mathscr {M}}）\）松弛来研究广义多值混合变分半偏不等式问题的各种gap函数矫顽力映射和Hausdorff Lipschitz连续性。此外，我们使用Clarke广义梯度法的特征为此类不等式建立了全局误差界。作为应用，我们提出了一个平稳的非光滑半渗透性问题。