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<p>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 nonexpansive mappings in Banach spaces. The main novelty of our contribution lies in the so-called <i>optimal error bounds</i>, 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 <i>optimal error bounds</i> proposed in this paper can also be favorably applied to various types of iterative models to approximate common fixed points of nonexpansive mappings.</p>

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A new approach to convergence analysis of iterative models with optimal error bounds

  • 期刊论文

  • 发表日期：

    2025年3月13日

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  • Minh-Phuong Tran,
  • Thanh-Nhan Nguyen,
  • Thai-Hung Nguyen,
  • Tan-Phuc Nguyen,
  • Tien-Khai Nguyen,
  • Cong-Duy-Nguyen Nguyen,
  • Trung-Hieu Huynh

摘要

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 nonexpansive mappings in Banach spaces. The main novelty of our contribution lies in the so-called 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 optimal error bounds proposed in this paper can also be favorably applied to various types of iterative models to approximate common fixed points of nonexpansive mappings.