In this paper, we establish a new iteration method, called an InerSP (an inertial S-iteration process), by combining a modified S-iteration process with the inertial extrapolation. This strategy is for speeding up the convergence of the algorithm. We then prove the convergence theorems of a sequence generated by our new method for finding a common fixed point of nonexpansive mappings in a Banach space. We also present numerical examples to illustrate that the acceleration of our algorithm is effective.

中文翻译：

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惯性S迭代过程

在本文中，我们将改进的S迭代过程与惯性外推相结合，建立了一种新的迭代方法，称为InerSP（惯性S迭代过程）。该策略是为了加快算法的收敛速度。然后，我们证明了通过我们的新方法生成的序列的收敛定理，该新方法用于查找Banach空间中非膨胀映射的公共固定点。我们还提供了数值示例来说明我们的算法的加速是有效的。