In this paper, we study a new approach related to the convergence analysis of Ishikawa-type iterative models to a common fixed point of two non-expansive mappings in Banach spaces. The main novelty of our contribution lies in the so-called \emph{optimal error bounds}, which established some necessary and sufficient conditions for convergence and derived both the error estimates and bounds on the convergence rates for iterative schemes. Although a special interest here is devoted to the Ishikawa and modified Ishikawa iterative sequences, the theory of \emph{optimal error bounds} proposed in this paper can also be favorably applied to various types of iterative models to approximate common fixed points of non-expansive mappings.

翻译：本文研究了一种新方法，用于分析Banach空间中Ishikawa型迭代模型收敛到两个非扩张映射公共不动点的性质。我们贡献的主要创新在于所谓的"最优误差界"，它建立了收敛的若干必要与充分条件，并推导出迭代格式的误差估计与收敛速率上界。尽管本文特别关注Ishikawa迭代序列及修正Ishikawa迭代序列，但所提出的"最优误差界"理论也可有效应用于各类逼近非扩张映射公共不动点的迭代模型。