In this paper, we are denoted to introducing the strict feasibility of a variational inclusion problem as a novel notion. After proving a new equivalent characterization for the nonemptiness and boundedness of the solution set for the variational inclusion problem under consideration, it is proved that the nonemptiness and boundedness of the solution set for the variational inclusion problem with a maximal monotone mapping is equivalent to its strict feasibility in reflexive Banach spaces.

中文翻译：

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自反Banach空间中变分包含问题的严格可行性

在本文中，我们将引入变分包含问题的严格可行性作为一种新颖的概念。在证明了所考虑的变分包含问题解集的非空性和有界性的一个新的等价刻画后，证明了具有最大单调映射的变分包含问题解集的非空性和有界性与其严格自反Banach空间的可行性。