Abstract In this article, we investigate the problem of approximating the fixed point for some function using a Mann iterative process with random errors. After establishing some exponential inequalities, we prove the complete convergence of Mann’s algorithm toward the fixed point and deduce a confidence interval for this one. In addition, we establish the convergence rate of Mann’s algorithm. Several numerical examples are sketched to illustrate the performance of the proposed algorithm.

中文翻译：

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Mann 随机算法的指数不等式

摘要 在本文中，我们研究了使用具有随机误差的曼恩迭代过程来逼近某个函数的不动点的问题。在建立了一些指数不等式之后，我们证明了 Mann 算法对不动点的完全收敛，并推导出了这个的置信区间。此外，我们建立了曼恩算法的收敛速度。绘制了几个数值例子来说明所提出算法的性能。