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<p>By using the Ishikawa iterative algorithm, we approximate fixed points and best proximity points of a relatively nonexpansive mapping. Furthermore, we use the von Neumann sequence to prove the convergence result in a Hilbert space setting. A comparison table is prepared using a numerical example which shows that the Ishikawa iterative algorithm is faster than some known iterative algorithms such as Picard and Mann iteration.</p>

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Convergence of Fixed Points for Relatively Nonexpansive Mappings via Ishikawa Iteration

  • 期刊论文

  • 发表日期：

    2025年6月18日

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  • Veerasamy Pragadeeswarar,
  • Raju Gopi,
  • Choonkil Park,
  • Jung Rye Lee

摘要

By using the Ishikawa iterative algorithm, we approximate fixed points and best proximity points of a relatively nonexpansive mapping. Furthermore, we use the von Neumann sequence to prove the convergence result in a Hilbert space setting. A comparison table is prepared using a numerical example which shows that the Ishikawa iterative algorithm is faster than some known iterative algorithms such as Picard and Mann iteration.