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<p>In this paper, the concepts of discrete pseudo <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathcal {S}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">S</mi> </math></EquationSource> </InlineEquation>-asymptotically affine periodic sequences and discrete weighted pseudo <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\mathcal {S}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">S</mi> </math></EquationSource> </InlineEquation>-asymptotically affine periodic sequences in Banach space are introduced and systematically investigated. This work naturally generalizes affine periodic sequences and their various extensions. As application, we establish sufficient criteria for the existence and uniqueness of discrete (weighted) pseudo <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\mathcal {S}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">S</mi> </math></EquationSource> </InlineEquation>-asymptotically affine periodic solution to fractional difference equations with Weyl (or Caputo) fractional difference, semilinear difference equations and Volterra difference equations. Finally, several illustrative examples are provided to demonstrate the main results.</p>

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Discrete (weighted) pseudo \(\mathcal {S}\)-asymptotic affine periodicity on Banach space and applications

  • 期刊论文

  • 发表日期：

    2025年12月2日

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  • Zhinan Xia,
  • Jinliang Chai

摘要

In this paper, the concepts of discrete pseudo \(\mathcal {S}\) S -asymptotically affine periodic sequences and discrete weighted pseudo \(\mathcal {S}\) S -asymptotically affine periodic sequences in Banach space are introduced and systematically investigated. This work naturally generalizes affine periodic sequences and their various extensions. As application, we establish sufficient criteria for the existence and uniqueness of discrete (weighted) pseudo \(\mathcal {S}\) S -asymptotically affine periodic solution to fractional difference equations with Weyl (or Caputo) fractional difference, semilinear difference equations and Volterra difference equations. Finally, several illustrative examples are provided to demonstrate the main results.