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<p>In this work, the existence of fixed point results for the sum and the product of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44198_2025_297_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="65" /> </InlineMediaObject> <EquationSource Format="TEX">\((2m + 1)\)</EquationSource> </InlineEquation> operators <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44198_2025_297_Article_IEq2.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="131" /> </InlineMediaObject> <EquationSource Format="TEX">\(\sum _{j=1}^mA_j\cdot B_j+C,\)</EquationSource> </InlineEquation> acting on Banach algebras satisfying a sequential condition <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="44198_2025_297_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">\((\mathcal {P})\)</EquationSource> </InlineEquation> under weak topology is proved. This is achieved by means of the notion of countably condensing maps and the technique of the De Blasi measures of weak noncompactness. Moreover, we give an example of application to a functional nonlinear integral equation.</p>

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Fixed Points for Sum and Product of Countably Condensing Maps on Banach Algebra and Application

  • 期刊论文

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  • 发表日期：

    2025年9月3日

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  • Khaled Ben Amara,
  • Aref Jeribi,
  • Najib Kaddachi

摘要

In this work, the existence of fixed point results for the sum and the product of \((2m + 1)\) operators \(\sum _{j=1}^mA_j\cdot B_j+C,\) acting on Banach algebras satisfying a sequential condition \((\mathcal {P})\) under weak topology is proved. This is achieved by means of the notion of countably condensing maps and the technique of the De Blasi measures of weak noncompactness. Moreover, we give an example of application to a functional nonlinear integral equation.