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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曼随机算法的指数不等式

在本文中，我们研究使用带有随机误差的Mann迭代过程逼近某些函数的不动点的问题。在建立了指数不等式之后，我们证明了Mann算法向固定点的完全收敛，并为此推导了一个置信区间。另外，我们建立了曼恩算法的收敛速度。绘制了几个数值示例，以说明所提出算法的性能。