In this paper, we define a Halpern–Ishikawa type iterative method for approximating a fixed point of a Lipschitz pseudocontractive non-self mapping T in a real Hilbert space settings and prove strong convergence result of the iterative method to a fixed point of T under some mild conditions. We give a numerical example to support our results. Our results improve and generalize most of the results that have been proved for this important class of nonlinear mappings.

中文翻译：

---

Halpern–Ishikawa型迭代方法，用于逼近非自拟压缩映射的不动点

在本文中，我们定义了一种Halpern–Ishikawa型迭代方法，用于逼近真实希尔伯特空间设置中Lipschitz伪压缩非自映射T的不动点，并证明了该迭代方法在一定条件下对T的不动点的强收敛性温和的条件。我们给出一个数值示例来支持我们的结果。我们的结果改进并归纳了针对这一重要类别的非线性映射已证明的大多数结果。