In this paper, we present some new results on the existence of solutions of generalized variational inequalities for set-valued mappings in reflexive Banach spaces with Fréchet differentiable norms. Moreover, the structure of the solution sets is investigated. The result obtained in this paper improves and extends the ones announced by Fang and Peterson [S. C. Fang and E. L. Peterson, Generalized Variational Inequalities, J. Optim. Theory Appl., 38 (1982), 363-383] and others.

中文翻译：

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最大单调算子的广义变分不等式

在本文中，我们提出了一些关于在具有 Fréchet 可微范数的自反 Banach 空间中集合值映射的广义变分不等式的解的存在性的新结果。此外，研究了解集的结构。本文中获得的结果改进和扩展了方和彼得森 [SC 方和 EL 彼得森，广义变分不等式，J. Optim。理论应用 , 38 (1982), 363-383] 等。