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<p>This study establishes the convergence equivalence of Picard, Mann, Ishikawa, and Picard-Mann hybrid schemes when addressing weak enriched <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {F}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">F</mi> </math></EquationSource> </InlineEquation>-contraction and weak enriched <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal {F^{\prime }}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="script">F</mi> <mo>′</mo> </msup> </math></EquationSource> </InlineEquation>-contraction, as defined by Zhou et al. (2024) [Journal of Inequalities and Applications (2024) 2024:23]. Our findings consolidate and expand upon existing contraction mapping methodologies within normed spaces. Numerical experiments validate our theoretical results. Moreover, we present stability analyses and dependence results for the iterative schemes. Finally, we apply general convergence principles for Krasnoselskii-type algorithms to variational inequality and split feasibility problems.</p>

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Equivalence and convergence analysis of fixed point iterative schemes using higher order averaged mappings

  • 期刊论文

  • 发表日期：

    2025年5月14日

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  • Mi Zhou,
  • Rizwan Anjum,
  • Liang Guo,
  • Muhammad Din,
  • Yeol Je Cho

摘要

This study establishes the convergence equivalence of Picard, Mann, Ishikawa, and Picard-Mann hybrid schemes when addressing weak enriched \(\mathcal {F}\) F -contraction and weak enriched \(\mathcal {F^{\prime }}\) F ′ -contraction, as defined by Zhou et al. (2024) [Journal of Inequalities and Applications (2024) 2024:23]. Our findings consolidate and expand upon existing contraction mapping methodologies within normed spaces. Numerical experiments validate our theoretical results. Moreover, we present stability analyses and dependence results for the iterative schemes. Finally, we apply general convergence principles for Krasnoselskii-type algorithms to variational inequality and split feasibility problems.