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<p>In this paper, we present an implicit and explicit viscosity iteration schemes tailored for non-expansive semigroups <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\{T(t):t \ge 0\}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">{</mo> <mi>T</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>:</mo> <mi>t</mi> <mo>≥</mo> <mn>0</mn> <mo stretchy="false">}</mo> </mrow> </math></EquationSource> </InlineEquation>. We rigorously establish that these iterative methods exhibit strong convergence to a unique common fixed point of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\{T(t):t \ge 0\}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">{</mo> <mi>T</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>:</mo> <mi>t</mi> <mo>≥</mo> <mn>0</mn> <mo stretchy="false">}</mo> </mrow> </math></EquationSource> </InlineEquation> within the rich structure of reflexive and strictly convex Banach spaces. Moreover, this fixed point is shown to be a solution to a specific variational inequality. The results not only enhance but also significantly extend several prominent findings available in the literature.</p>

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Iterative approximation to common fixed points of semigroups of nonexpansive mappings and variational inequalities in Banach spaces

  • 期刊论文

  • 发表日期：

    2025年10月6日

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  • Mahak Majeed,
  • Mohd Iqbal Bhat,
  • Khalid Fayaz,
  • Mudasir A Malik

摘要

In this paper, we present an implicit and explicit viscosity iteration schemes tailored for non-expansive semigroups \(\{T(t):t \ge 0\}\) { T ( t ) : t ≥ 0 } . We rigorously establish that these iterative methods exhibit strong convergence to a unique common fixed point of \(\{T(t):t \ge 0\}\) { T ( t ) : t ≥ 0 } within the rich structure of reflexive and strictly convex Banach spaces. Moreover, this fixed point is shown to be a solution to a specific variational inequality. The results not only enhance but also significantly extend several prominent findings available in the literature.