Several iterative methods have been proposed in the literature for solving the variational inequalities in Hilbert or Banach spaces, where the underlying operator A is monotone and Lipschitz continuous. However, there are very few methods known for solving the variational inequalities, when the Lipschitz continuity of A is dispensed with. In this article, we introduce a projection-type algorithm for finding a common solution of the variational inequalities and fixed point problem in a reflexive Banach space, where A is pseudo-monotone and not necessarily Lipschitz continuous. Also, we present an application of our result to approximating solution of pseudo-monotone equilibrium problem in a reflexive Banach space. Finally, we present some numerical examples to illustrate the performance of our method as well as comparing it with related method in the literature.

中文翻译：

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使用投影方法求解伪单调变分不等式的强收敛定理

文献中已经提出了几种迭代方法来解决 Hilbert 或 Banach 空间中的变分不等式，其中底层算子 A 是单调的且 Lipschitz 连续的。然而，当省略 A 的 Lipschitz 连续性时，解决变分不等式的方法很少。在本文中，我们介绍了一种投影型算法，用于在自反 Banach 空间中寻找变分不等式和不动点问题的通用解，其中 A 是伪单调的，不一定是 Lipschitz 连续的。此外，我们将我们的结果应用于自反 Banach 空间中伪单调平衡问题的近似解。最后，