Abstract <p>In this paper, we introduce and analyze several new classes of Weyl <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8276_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\rho\)</EquationSource> <!--LobJMat2560621Abbas-m1--> </InlineEquation>-almost periodic type functions <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8276_Article_IEq2.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="116" /> </InlineMediaObject> <EquationSource Format="TEX">\(F:\Lambda\times X\rightarrow Y\)</EquationSource> <!--LobJMat2560621Abbas-m2--> </InlineEquation>, where <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8276_Article_IEq3.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="86" /> </InlineMediaObject> <EquationSource Format="TEX">\(\emptyset\neq\Lambda\subseteq{\mathbb{R}}^{n}\)</EquationSource> <!--LobJMat2560621Abbas-m3--> </InlineEquation>, <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8276_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(X\)</EquationSource> <!--LobJMat2560621Abbas-m4--> </InlineEquation> is an arbitrary non-empty set, and <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8276_Article_IEq5.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(Y\)</EquationSource> <!--LobJMat2560621Abbas-m5--> </InlineEquation> is a locally convex space over the field of complex numbers. We furnish several structural results and present some applications to the abstract Volterra integro-differential equations in locally convex spaces.</p>

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Weyl Almost Periodic Functions in Locally Convex Spaces

  • S. Abbas,
  • V. E. Fedorov,
  • M. Kostić

摘要

Abstract

In this paper, we introduce and analyze several new classes of Weyl \(\rho\) -almost periodic type functions \(F:\Lambda\times X\rightarrow Y\) , where \(\emptyset\neq\Lambda\subseteq{\mathbb{R}}^{n}\) , \(X\) is an arbitrary non-empty set, and \(Y\) is a locally convex space over the field of complex numbers. We furnish several structural results and present some applications to the abstract Volterra integro-differential equations in locally convex spaces.