In this paper, we introduce a new inertial self-adaptive projection method for finding a common element in the set of solution of pseudomonotone variational inequality problem and set of fixed point of a pseudocontractive mapping in real Hilbert spaces. The self-adaptive technique ensures the convergence of the algorithm without any prior estimate of the Lipschitz constant. With the aid of Moudafi’s viscosity approximation method, we prove a strong convergence result for the sequence generated by our algorithm under some mild conditions. We also provide some numerical examples to illustrate the accuracy and efficiency of the algorithm by comparing with other recent methods in the literature.

中文翻译：

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伪单调变分不等式和不动点问题的具有自适应步长的强收敛惯性投影与收缩方法

在本文中，我们引入了一种新的惯性自适应投影方法，用于在伪希尔伯特空间中伪单调变分不等式问题的解集和伪压缩映射的不动点集中找到一个公共元素。自适应技术可确保算法的收敛性，而无需事先估计Lipschitz常数。借助Moudafi的粘度逼近方法，我们证明了在某些温和条件下，我们的算法生成的序列具有很强的收敛性。我们还提供了一些数值示例，通过与文献中的其他最新方法进行比较来说明该算法的准确性和效率。