In this study, we propose nonemptiness and boundedness of the solution set for a bifunction variational inequality problem with P-strict feasibility in reflexive Banach spaces. As a novel concept, P-strict feasibility for a bifunction variational inequality is introduced. Moreover, it is proved that a pseudomonotone bifunction variational inequality has a nonempty and bounded solution set if and only if it is P-strictly feasible in reflexive Banach spaces. Finally, some examples are given to illustrate the validity of the main results.

中文翻译：

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自反Banach空间中双功能变分不等式的P严格可行性

在这项研究中，我们提出自反Banach空间中具有P严格可行性的双功能变分不等式问题解集的非空性和有界性。作为一个新颖的概念，引入了双函数变分不等式的P-strict可行性。此外，证明了伪单调双函数变分不等式具有非空有界解集，当且仅当它在自反Banach空间中是P严格可行的。最后，通过一些例子说明了主要结果的有效性。