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<p>In this paper, we utilize the AK-iteration procedure for hyperbolic metric spaces, ensuring the symmetry condition is met and establish the weak <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <msup> <mi>w</mi> <mn>2</mn> </msup> </math></EquationSource> <EquationSource Format="TEX">$w^{2}$</EquationSource> </InlineEquation>-stability and data dependence results for contraction mappings. Additionally, we establish several Δ-convergence and strong convergence theorems for the generalized <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math> <mo stretchy="false">(</mo> <mi>α</mi> <mo>,</mo> <mi>β</mi> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$(\alpha ,\beta )$</EquationSource> </InlineEquation>-nonexpansive (GABNE) mappings. To demonstrate it, we provide a numerical example of the GABNE-mappings, emphasizing the enhanced efficiency of the AK-iteration method relative to other iterative approaches. Additionally, the applications of the main results are demonstrated by solving 2<i>D</i> and 3<i>D</i> Volterra integral equations. These findings extend and improve numerous related results found in the current literature.</p>

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AK-iterative scheme for fixed point approximation in hyperbolic metric spaces and applications in Volterra integral equation

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月7日

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  • Fayyaz Ahmad,
  • Muhammad Samraiz,
  • Junaid Ahmad,
  • Sina Etemad,
  • Manuel De la Sen

摘要

In this paper, we utilize the AK-iteration procedure for hyperbolic metric spaces, ensuring the symmetry condition is met and establish the weak w 2 $w^{2}$ -stability and data dependence results for contraction mappings. Additionally, we establish several Δ-convergence and strong convergence theorems for the generalized ( α , β ) $(\alpha ,\beta )$ -nonexpansive (GABNE) mappings. To demonstrate it, we provide a numerical example of the GABNE-mappings, emphasizing the enhanced efficiency of the AK-iteration method relative to other iterative approaches. Additionally, the applications of the main results are demonstrated by solving 2D and 3D Volterra integral equations. These findings extend and improve numerous related results found in the current literature.