This paper presents an inertial Tseng extragradient method for approximating a solution of the variational inequality problem. The proposed method uses a single projection onto a half space which can be easily evaluated. The method considered in this paper does not require the knowledge of the Lipschitz constant as it uses variable stepsizes from step to step which are updated over each iteration by a simple calculation. We prove a strong convergence theorem of the sequence generated by this method to a solution of the variational inequality problem in the framework of a 2-uniformly convex Banach space which is also uniformly smooth. Furthermore, we report some numerical experiments to illustrate the performance of this method. Our result extends and unifies corresponding results in this direction in the literature.

本文提出了一种用于逼近变分不等式问题的解的惯性 Tseng 超梯度方法。所提出的方法使用单个投影到可以轻松评估的半空间上。本文中考虑的方法不需要 Lipschitz 常数的知识，因为它使用步到步的可变步长，通过简单的计算在每次迭代中更新。我们证明了由该方法生成的序列的强收敛定理，以解决同样光滑的 2-一致凸 Banach 空间框架中的变分不等式问题。此外，我们报告了一些数值实验来说明该方法的性能。我们的结果在文献中在这个方向上扩展并统一了相应的结果。