Ullah Kifayat, Arshad Muhammad
Department of Mathematics, International Islamic University, Sector H-10, Islamabad, 44000 Pakistan.
Springerplus. 2016 Sep 20;5(1):1616. doi: 10.1186/s40064-016-3056-x. eCollection 2016.
In this paper we propose a new iteration process, called AK iteration process, for approximation of fixed points for contraction mappings. We show that our iteration process is faster than the leading Vatan Two-step iteration process for contraction mappings. Numerical examples are given to support the analytic proofs. Stability of AK iteration process and data dependence result for contraction mappings by employing AK iteration process are also discussed.
在本文中，我们提出了一种新的迭代过程，称为AK迭代过程，用于逼近压缩映射的不动点。我们表明，我们的迭代过程比用于压缩映射的领先的瓦坦两步迭代过程更快。给出了数值例子以支持解析证明。还讨论了AK迭代过程的稳定性以及通过采用AK迭代过程得到的压缩映射的数据依赖性结果。
